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## Visualizing Atmospheric Radiation – Part Two

We reviewed some simple concepts in Part One.

I’ve created a MATLAB model which can do a reasonable job of calculating radiative transfer through the atmosphere. More details about the model to follow, but first let’s look at an actual result and the implications.

There are a whole set of starting conditions, some of which are:

• 10 layers (of roughly equal pressure change)
• surface temperature = 288K (15ºC)
• boundary layer humidity (BLH) = 80%, and boundary layer top of 920hPa
• free tropospheric humidity (FTH) = 40%
• lapse rate (the temperature profile in the atmosphere) = 6.5 K/km
• tropopause at 11.7km, isothermal atmosphere above at 212K and TOA at 50hPa

Figure 1

There’s a little too much information when we see all layers, so here are just four (see note 1):

Figure 2 – Selected layers

What do we see?

Start at the top – the blue line – this is the emission of radiation upwards from the surface. In this case, for simplicity, the surface emissivity = 1.0 (see note 2) so this is the Planck function at 288K. The next curve down is at 2800m up where the temperature has dropped to 270K. The red curve is at 6740m & 244K, and the bottom curve is at 23km & 212K, well into the stratosphere.

Let’s zoom in on one region of wavenumbers/wavelengths:

Figure 3 – Expanded view

First, the region 640-700 cm-1 (14.3-15.6μm). The upward radiation at each higher altitude (which corresponds to each lower curve in the figure) is at the Planck blackbody function for the temperature of that layer.

The reason is that the incident radiation gets completely absorbed. Nothing gets out the other side. Transmissivity = 0, absorptivity = 1. It is “saturated”.

But we don’t see zero radiation. Why not?

The atmosphere is a strong absorber at these wavelengths, and therefore a strong emitter at these wavelengths. So each layer emits as a blackbody (in this region of wavelengths). We can easily see the temperature of the atmosphere from the Planck function if we are able to measure the radiation from these highly absorbing/emitting wavelengths.

Second, the region near 850 cm-1 (below 12μm). See that the upward radiation at each altitude is almost at the surface radiation value. This is in the “atmospheric window” where the absorption is very low. The atmosphere is almost transparent at these wavelengths. So the absorption is low and the emission is low. But the starting point, if we can use that term, is the emission at the surface temperature of 288K. And so, in this wavelength region, at any point in the atmosphere the upwards radiation is close to the Planck curve of 288K. Basically, the intensity of radiation stays the same as it travels upward through the atmosphere because there is little absorption.

### Transmitted Radiation Only

Just to make the subject of emission even clearer, here is a calculation where the atmosphere magically does not emit any radiation – compare this with figure 2:

Figure 4 – No emission by the atmosphere

Even if we just look at the first 3 layers of the model (1.8km) we get pretty much the same view – i.e., most of the surface radiation is absorbed before we get very far through the atmosphere, but of course it is very wavelength dependent:

Figure 5 – No emission by the atmosphere

My calculation says that of 376 W/m² of surface emitted radiation between 200 cm-1 and 2500 cm-1, 75 W/m² (20%) gets transmitted to the top of atmosphere (note 4).

This is not all through the “atmospheric window” – you can see the wavelength dependence in figure 4. I calculate 61 W/m² through the atmospheric window (8-12μm), which means in that wavelength range 62% of surface radiation is being transmitted.

### Up and Down Flux

Let’s look at the total (longwave) flux up and down through the atmosphere (note 3):

Figure 6

Notice that the downward flux is zero at the top of atmosphere. This is a boundary condition – there is no (significant) source of longwave radiation coming from outside the atmosphere. As we go down through the atmosphere it gets warmer and so the atmosphere emits more and more. Also as we go down the atmosphere there is much more water vapor, meaning the emissivity of the atmosphere increases significantly. So the atmosphere emits ever more radiation the closer we get to the surface.

We have already considered the upward transmission of radiation. Here the blue line on the graph is simply the sum (the “integral”) of the spectral components we saw in earlier graphs.

Why does the flux reduce with height? Because the absorption of upward radiation is greater than the emission of radiation upwards at each height.

If this point is not clear, please reread this article and Part One – if you are confused over this fundamental point it will be impossible to make good progress in understanding atmospheric radiation.

The absorptivity (the ability of the atmosphere to absorb radiation) is equal to the emissivity (the ability of the atmosphere to emit radiation) at any given wavelength. So why isn’t emission = absorption?

Because the incident upward radiation on a given layer comes from a higher temperature source:

• Absorption =incident radiation x absorptivity
• Emission = Planck function (blackbody radiation value) at the temperature of the gas x emissivity

Please ask if this is not crystal clear.

### Net Flux & Heating or Cooling

If we want to do any heat transfer calculations we need to look at how the flux changes through the atmosphere. How much radiation enters and how much leaves (see note 5). Anything different from zero for a given layer means there must be heating or cooling by radiation. (This could be balanced by convection – and by absorbed solar radiation).

Let’s see the flux changes for each layer:

Figure 7

What this is showing is the calculation of (radiation in – radiation out) for each layer. As should be obvious from the previous figure, the upward path of longwave radiation is heating the atmosphere (more is absorbed than is emitted), whereas the downward path of longwave radiation is cooling the atmosphere (more is emitted than is absorbed).

When we sum both up we find that the atmosphere is cooling via radiation. “Greenhouse” gases are cooling the atmosphere! If only climate science considered the basics!

Each of the layers in the model contains a similar number of molecules – this is because I divided the atmosphere up into approximately equal pressure sections. This means that 10 W/m² cooling in any layer should equate to similar temperature changes in each layer, but let’s do that calculation anyway (heating rate per unit area/[specific heat capacity x density x depth of layer]):

Figure 8 – Heating (cooling) from longwave radiation

The atmosphere is not actually transparent to solar radiation and you can find similar graphs of Net Shortwave Heating per Day in many climate science textbooks and papers.  The humid lower atmosphere gets a strong solar heating via water vapor. See Atmospheric Radiation and the “Greenhouse” Effect – Part Eleven – Heating Rates.

My graph doesn’t actually reproduce the magnitude of the cooling rates seen for standard atmospheres – typically around 2°C/day in the lower atmosphere but I’m pleased with getting the profile quite similar – remember that the “divergence” is the difference between two values. In this case, the up and down fluxes are in the 200-400 W/m² range, while the net is around 10-20 W/m².

To see what actual difference there is from a more complete model we would need to plug in one of the “standard atmospheres” and compare. The exact profile of water vapor concentration and atmospheric temperature have a big effect – something we will be looking at in detail anyway in later articles.

### Convection

The calculation of radiative transfer in the atmosphere can be done for a given profile without knowing anything about convection. That is, if we know where we are right now – without knowing how we got here – we can still do an accurate calculation of how energy moves through the atmosphere by radiation.

If we want to predict the result of how the radiative heating/cooling changes the surface and atmospheric temperature then of course we need a model of convection – and atmospheric circulation.

### Conclusion

What the model has done so far is taken:

• a given temperature profile
• a given concentration of GHGs including water vapor
• the large spectroscopic database of absorption lines complied by professionals over decades

– and used basic theory well-known and proven for many decades to calculate the upward and downward path of radiation through the atmosphere.

There’s lots to consider further. But the points and subjects in this article are all fundamental to understanding atmospheric radiation. So if anything is not clear, please ask questions.

Related Articles

Part One – some background and basics

Part Two – some early results from a model with absorption and emission from basic physics and the HITRAN database

Part Three – Average Height of Emission – the complex subject of where the TOA radiation originated from, what is the “Average Height of Emission” and other questions

Part Four – Water Vapor – results of surface (downward) radiation and upward radiation at TOA as water vapor is changed

Part Five – The Code – code can be downloaded, includes some notes on each release

Part Six – Technical on Line Shapes – absorption lines get thineer as we move up through the atmosphere..

Part Seven – CO2 increases – changes to TOA in flux and spectrum as CO2 concentration is increased

Part Eight – CO2 Under Pressure – how the line width reduces (as we go up through the atmosphere) and what impact that has on CO2 increases

Part Nine – Reaching Equilibrium – when we start from some arbitrary point, how the climate model brings us back to equilibrium (for that case), and how the energy moves through the system

Part Ten – “Back Radiation” – calculations and expectations for surface radiation as CO2 is increased

Part Eleven – Stratospheric Cooling – why the stratosphere is expected to cool as CO2 increases

Part Twelve – Heating Rates – heating rate (‘C/day) for various levels in the atmosphere – especially useful for comparisons with other models.

### References

The data used to create these graphs comes from the HITRAN database.

The HITRAN 2008 molecular spectroscopic database, by L.S. Rothman et al, Journal of Quantitative Spectroscopy & Radiative Transfer (2009)

The HITRAN 2004 molecular spectroscopic database, by L.S. Rothman et al., Journal of Quantitative Spectroscopy & Radiative Transfer (2005)

### Notes

Note 1: There is a slight inconsistency in the data presentation. There are 11 boundaries and therefore 10 layers. The spectra are calculated at the boundaries. The water vapor mixing ratio is calculated in the middle of the layer.

The calculation of emission of radiation is based on the temperature and the concentration of each GHG, including water vapor, in the mid-layer (the mid-pressure point in each layer) .

Note 2: The surface emissivity for the ocean, for example, is about 0.96 – see Emissivity of the Ocean. In some parts of the blogworld assuming an emissivity of 1.0 is a heresy that demonstrates what these inappropriately-named “skeptics” have known all along, climate science assumes an “unphysical blackbody model of the world”! And therefore cannot be taken seriously. More exclamation marks and so on.

I could have set an emissivity of 0.96 for the surface and this would have reduced the emitted upward radiation from the surface by 4%. But then for a radiative transfer calculation I would need to reflect 4% of the downward atmospheric radiation upwards (what is not absorbed or transmitted must be reflected). So in fact the upward radiation difference for the two cases (emissivity of 1.0 and 0.96) is quite small, less than 1% and not particularly useful for this calculation.

Note 3: Climate science uses the conventions of shortwave and longwave radiation. Shortwave is wavelengths less than 4μm (wavenumbers greater than 2500cm-1), while longwave is greater than 4μm.

99% of solar radiation is shortwave, while 99% of all terrestrial radiation is longwave. This makes it easy to separate the two. See The Sun and Max Planck Agree – Part Two.

Note 4: The emission of thermal radiation by a surface at 288K with an emissivity of 1.0 is 390 W/m². This is across all wavelengths. The model looks at the range of wavenumbers that equates to 4-50μm to ease up the calculation effort required. Almost all of the “missing spectrum” is in the far infra-red (longer wavelengths/lower wavenumbers), and is subject to relatively high absorption from water vapor.

Note 5: If you hear the technical term flux divergence it is essentially the same thing. Flux divergence is per unit volume so it isn’t such a useful value. Instead the most common term is heating rate which divides the gain (loss) in radiation energy by the heat capacity to calculate the radiative heating (cooling) rate per unit of time (typically per day).

### 530 Responses

• Hockey Schtick,

It’s difficult to have a meaningful discussion with someone who believes in a different framework of physics.

Check out the Etiquette:

Basic Science is Accepted – This blog accepts the standard field of physics as proven. Arguments which depend on overturning standard physics, e.g. disproving quantum mechanics, are not interesting until such time as a significant part of the physics world has accepted that there is some merit to them.

Claes Johnson is warmly embraced by so many people who have no idea about physics. He is a smart guy no doubt. Readers with a passing knowledge of physics realize he is in disagreement with many tens of thousands of physicists (nothing to do with climate science here) who have come before him, who are also very smart people.

Claes Johnson doesn’t accept modern statistical thermodynamics.

In his delightfully crystal clear way, he says:

You claim in the post following this one (comments are closed) that I consider quantum mechanics to be a mistake. This is not a correct description of my position. I consider the statistical Copenhagen Interpretation to be non-physical as did Einstein and Schrodinger, but there may be a version of quant mech which is free of statistics and which is not a mistake.

As and when the physics world starts seriously questioning the last 100 years of physics fundamentals then this blog will open up discussion on whether or not quantum mechanics and statistical thermodynamics are just plain wrong.

Until that time we will stay with standard textbook physics.

I happily accept that IF standard textbook physics is wrong then climate science will need to be reviewed.

• Hockey Schtick,

If by some miracle, Claes Johnson could come up with a comprehensive theory of quantum mechanics that did not involve statistics, it wouldn’t result in falsification of the greenhouse effect. Much of the HITRAN database consists of measured line strengths and shape factors. Now using the consensus version of QM, the lines can also be calculated ab initio. The observed lines and the calculated lines are in close agreement. If CJ’s theory did not reproduce those results, it would be, as he says about consensus QM, unphysical because it would not agree with observation.

What science does is create mathematical models of physical behavior. So in some sense it’s always wrong because the map is not the territory. Consensus QM works. In particular, Quantum Electrodynamics works spectacularly well. You only replace something that works with something that works better. CJ claims he can explain certain features of the photoelectric effect without requiring photons. That’s nice. But it’s barely scratching the surface. And there’s no evidence at all that it will produce a self-consistent theory that works better than consensus QM.

1. A few quick notes on the model.

1.a) HITRAN database used for five “greenhouse” gases:
– water vapor
– CO2
– O3
– CH4
– N2O

2. The line shape is Lorenzian (collisional broadening), and I have not yet worked out how to implement the Voigt profile for the upper troposphere (the line shape changes at much lower pressures).
The total absorption is calculated for each layer using the line shape for each line within 200 cm-1 – 2500 cm-1 based on the pressure and temperature of the midpoint of that layer and the values in the HITRAN database.

3. The Δv (wavelength interval) for each layer and each gas is currently 1cm-1. This can be varied. I changed it to .2cm-1 and .1cm-1 and the results of OLR and DLR were only very slightly different.

4. Concentrations of GHGs:
-water vapor – using the saturation vapor pressure for the temperature of the midpoint of the layer and the prescribed RH (different for boundary layer and free troposphere).
CO2- 360ppm, O3- 50ppbv, N2O- 319ppbv, CH4- 1775ppbv
– Did not consider any isotopologues of these gases, for reasons of speed, but the code already includes this capability if required.

5. The water vapor continuum absorption is implemented and can be turned off to see what happens. More in some later results. The continuum is implemented following Pierrehumbert 2010. I’m not certain about my implementation despite reading a number of papers (including Clough 1989 and Vigasin 2000) but it’s a starting point.

6. The model can be run to see how temperature adjusts – via a radiative convective method where the atmospheric temperature always adjusts back to the prescribed lapse rate if the environmental lapse rate is too high (i.e., the atmosphere is unstable).

7. No solar heating of the atmosphere – this is a weak point – especially for the effects of more water vapor in the lower troposphere, and for sorting out the stratospheric temperature profile.

8. Poor ozone distribution – just well-mixed at the moment.

9. The stratosphere is just fixed at isothermal – i.e., as if solar heating balances any radiative cooling. This is clearly incorrect and the stratospheric temperature does have a significant effect on the troposphere.

• The number of absorption lines used from the HITRAN database:

Water vapor – 6,007
CO2 – 53,757
O3 – 153,248
N2O – 16,725
CH4 – 57,580

Total 287,317 lines.

I could make the code much more efficient. Drop the weakest 50% of the lines, stop using O3.. but the code runs ok.

A run with Δv =1 cm-1, 10 layers takes about 10 minutes.

2. Maybe I missed something obvious, but I don’t see a link to the database. Is the Matlab program reading a data file for absorption values at individual wavelengths? If so, can you link the file? Is it using an interface to the Spectralcalc site? Will you share the Matlab program at some point? Thanks.

• Ron,

Whether SoD used Spectralcalc site or not, it’s very easy to get the data for the same number of lines from their site. The numbers of lines agree, when only the most common isotopes are taken into account.

• Ron,

The Matlab program is reading every absorption line (for water vapor, CO2, O3, N2O, CH4) out of the HITRAN database.

You can find information on the HITRAN database – here, including a request form to get access to it. A good start is to read the 2004 paper, reference above.

Yes, I will be providing the MATLAB program shortly.

• Thanks. Looks like there might be a background check involved. ITAR? Don’t answer that. :D

3. So basically the reason why the atmosphere directly radiates more power to the surface than it does out the TOA is due to the lapse rate (i.e. temperature decreases with altitude), correct?

• RW,

That is correct.

• And the primary reason for the lapse rate is due to gravity, right?

• No.

Gravity alone does not explain the lapse rate, not even the existence of a decreasing temperature with altitude. To explain that we need thermodynamics of expanding moist gas and quantitative understanding of radiative heat transfer. Only with all of these we can understand why there’s a troposphere with a lapse rate controlled by convection as well as a stratosphere that doesn’t follow that.

There fore gravity is not “the primary reason”, it’s just one of many equally important factors.

• Stating the basics in another way:

– the role of gravity is to prevent atmosphere from escaping and in maintaining the pressure gradient

– the primary reason for the lapse rate is the GHE (or the properties of radiative heat transfer). That leads to a decreasing temperature with altitude

– GHE alone would make the lapse rate of the troposphere steeper than is stable against convection. Therefore convection will reduce the lapse rate to a stable value. Here both thermodynamics of gases and gravity have their roles.

• Not disagreeing with anyone, but the lapse rate by itself does not tell you anything about the temperature at any point in the atmosphere, for that you also need the surface temperature, and that is substantially determined by the greenhouse effect.

• Yes, we must also fix the level of temperatures.

More fundamentally that’s done by requiring that the energy flows up and down balance at TOA, exactly for a stationary Earth system, and with an appropriate net flux down for an Earth that’s still warming.

• RW,

An isothermal atmosphere would not have a greenhouse effect. However, a one dimensional isothermal atmosphere that isn’t perfectly transparent isn’t stable because the top radiates more energy than it absorbs. When he gets his radiative/convective model running, SoD could demonstrate that an isothermal atmosphere, whether initially warmer or colder than the steady state, will converge over time to the same environmental lapse rate and temperature.

4. SoD,

This work is much appreciated, and helpful!

I am am just missing (or confused) about one thing from your calculations. As the upper atmosphere thins so surely more LTE radiation must be transmitted from one particular level through colder layers above to space. Each level emissions is not just determined by its local temperature but must also include the net flux transmitted from warmer lower levels minus the downward flux from all colder upper levels.

So If direct transmission is say 0.001% at the surface then eventually an increasing proportion of photons with altitude will transfer upwards to colder less dense layers so that net transmission increases with height. There cannot just be one TOA where radiation is assumed to escape to space but rather a whole spectrum of heights each contributing to the “effective emission height”.

Seen from satellite it indeed appears to result in one effective temperature say 220K for the 15 micron band – but that is just the net integral of all radiation from the whole atmosphere. It cannot all originate from just one lapse rate height where T=220K !

P.S. My favorite software is IDL -but I just can’t justify the price !

• In a stationary atmosphere the net energy flux must be zero at every level. At the top of atmosphere outgoing longwave IR must balance net downwards SW, and that remains true trough the stratosphere. As some SW is absorbed the net IR must also decrease slowly coming down from TOA. When the troposphere is reached convection is also present and is the stronger the closer to the surface we get (latent heat transfer adds also to the convection).

From the above we know that net upwards LW is weakest at the surface and grows slowly with altitude all the way to TOA.

IR of 15 um transfers very little energy at all altitudes up to middle stratosphere, because at that wavelength the downwards flux is nearly as strong as the upwards one. All the radiation to the space is emitted very high up in the atmosphere at the wavelength of peak emissivity. That’s visible as a narrow peak in the spectrum of radiation to space because the upper stratosphere is warmer than the lower stratosphere. This effect is missing in models based on thick layers.

• Clive,

..As the upper atmosphere thins so surely more LTE radiation must be transmitted from one particular level through colder layers above to space. Each level emissions is not just determined by its local temperature but must also include the net flux transmitted from warmer lower levels minus the downward flux from all colder upper levels..

I’m not sure whether there is just some lack of clarity in your description or a fundamental misunderstanding, so I’ll take it as you’ve written it just so we can confirm we have the same understanding.

The radiation measured up from each layer is the “locally emitted” plus the proportion of upward radiation transmitted through from below. The downward flux has no bearing on this at all. We don’t subtract it from the upward flux.

If I’ve missed your point, have another go at explaining it.

There cannot just be one TOA where radiation is assumed to escape to space but rather a whole spectrum of heights each contributing to the “effective emission height”.

This is correct and I hope to produce some plots shortly showing proportion of TOA “locally emitted” from each layer below. (Just need to recode some parts to collate this extra information).

• SoD,

The radiation measured up from each layer is the “locally emitted” plus the proportion of upward radiation transmitted through from below. The downward flux has no bearing on this at all. We don’t subtract it from the upward flux.

I was really meaning the net radiative transfer. Lets call it R.

R = “locally emitted” + “up radiation transmitted from warmer levels below” – “down radiation transmitted from colder levels above”.

R increases with height . R decreases with more GHGs (CO2).

For T=288K and zero CO2 content the radiated energy to space for the 13-17 micron band would be about 72 watts/m2.

For T=288K and CO2 = 300ppm then this is reduced to about 37 watts/m2.

The difference around 35 watts/m2 is absorbed by CO2 molecules in the atmosphere. More is absorbed near the surface forming part of radiative heat transfer. Pekka argues acts to steepen the lapse rate which induces convection to restore it.

There are two effects working against each other which determine how much each height contributes. The lower levels are warmer, contain more net CO2 molecules and therefore emit (and absorb) higher fluxes of 13-15 micron photons. The higher levels are thiner and more photons from below are transmitted through it. However they are cooler and emit less photons even though there is a higher probability they reach space. By calculating the flux of radiation to space from each level we can visualize the “effective height of emission” for different CO2 concentrations in the atmosphere. The result is shown in Figure 2 at http://clivebest.com/blog/?p=4475 . This radiation doesn’t all come from some mythical “effective emission height”. It actually spans a wide range of different levels, but currently peaks around 4000 m.

We can then integrate the total radiation loss to space for different CO2 levels in the atmosphere. If you now vary CO2 concentrations to study radiation losses in the atmosphere, you discover something for me amazing. For conditions on Earth today with T=288K, lapse=6.5C/km, the maximum radiation loss through the atmosphere by CO2 corresponds to ~300 ppm. For lower concentrations direct radiation to space from the surface increases rapidly see figure 3. Can it really be a coincidence that natural CO2 levels just happen to coincide with maximum radiative transfer ?

Disclaimer: All the above assumes I am using the right Beers Lambert absorption data for 15 micron CO2 ( I am not using HITRAN)….. The absorption coefficient k for the 13-17 micron band has been measured to be 1.48 m-1 atm-1 (Essenhigh 2001).

• Clive,

..I was really meaning the net radiative transfer. Lets call it R.

R = “locally emitted” + “up radiation transmitted from warmer levels below” – “down radiation transmitted from colder levels above”..

Ok, the first part is fine. “Net radiation transfer = R”.

The second part is not fine. We have to separate the two fluxes – up and down. This is because they travel independently – but both contribute to heat transfer when they change with height.

It’s correct to work out heat transfer by summing how both change in a given layer in the atmosphere.

So we have R(up) and R(down).

R(up) = “locally emitted up” + “up radiation transmitted from warmer levels below”
R(down) = “locally emitted down” + “down radiation transmitted from colder levels above [correctly shortly after original comment posted]”

Of course a small note that the words ‘warmer’ & ‘colder’ in the above descriptions don’t apply to the stratosphere, but eliminating them has, of course, no effect on the physics.

Then if we want to work out heat transfer we need to know energy change in a layer ΔE = [ΔR(up) + ΔR(down) Convective heat transfer rate]*Δt, where t is time.

We also have to be careful with the signs of ΔR(up) and ΔR(down) to ensure that both are +ve for net energy absorbed.

• Clivebest,

When we consider only the wavelengths of highest emissivity near 15 µm, we notice that practically all radiation is absorbed very close to the point of emission. That makes the atmosphere a very good insulator for energy transfer by such radiation. What’s seen from space originates totally somewhere in the upper stratosphere or even above the stratosphere.

The linewidth of CO2 emission and absorption is small in upper stratosphere where pressure broadening is almost nonexistent and only Doppler broadening important on top of the narrow natural width of the emission/absorption lines. Therefore moving off from the center of the line we start to see the broader peak from lower stratosphere. The center peak tells about the higher temperature of the upper stratosphere, the broader peak about the low temperatures of lower stratosphere. We must look at wavelengths further off from the peak to see anything coming from troposphere.

For all wavelengths of strong absorption what we see from the space tells only about the temperatures and concentrations of upper atmosphere. For radiative heat transfer within the atmosphere those wavelengths are most significant which have rather high mean free paths like kilometers or at least hundreds of meters.

The total level of IR radiation is at all altitudes of troposphere rather close to the value that corresponds to the local temperature. It’s only little dependent on the emissivity of the air mixture at that altitude. Smaller emissivity leads, however, to a larger difference between upwards and downwards radiation and thus to more net radiative energy transfer upwards.

For the wavelengths of very little absorption the clear sky radiation is almost all upwards and close to the emission from the surface. Thus in this special case the local temperature does not tell well the approximate total intensity of IR radiation, but for most wavelengths it does much better.

• Pekka,

When we consider only the wavelengths of highest emissivity near 15 µm, we notice that practically all radiation is absorbed very close to the point of emission. That makes the atmosphere a very good insulator for energy transfer by such radiation. What’s seen from space originates totally somewhere in the upper stratosphere or even above the stratosphere.

You are looking at just the central line in the 13-17 micron band. I have been searching out data to get a grip on this – which is not behind a pay-wall. Please look at http://clivebest.com/?attachment_id=4498. The units are a bit strange but the experimental data indeed show that the transmission covers hundreds of meters even at surface atmospheric pressure for CO2 levels of 0.0003 ppm. Log10(u) is cm of (pure) CO2 at 1.5 atmosphere.

Therefore (I claim) radiative heat transfer in the mid troposphere is important. The atmosphere is not a good insulator for wavelengths across the 15 micron band. The situation you describe of thermalized up going radiation is rue on Venus. The 2 micron bands are indeed opaque on Earth.

SoD,

The second part is not fine. We have to separate the two fluxes – up and down. This is because they travel independently – but both contribute to heat transfer when they change with height.

Yes I understand that and believe I have handled all that correctly. They do travel independently. However each level can be treated just like the surface. So exact analogy to Trenberth et al. we find R = 356 watts/m2 (upgoing IR non-window) – 333 watts/m2(downgoing GHGs) = 23 watts/m2 net radiative transfer.

So you can continue this calculation up in altitude, but must carefully keep the book-keeping to derive the net up-going heat flux.

• Clive,

I did comment on purpose on what happens at wavelengths of strongest absorption as it’s not really possible to give any simple description that’s applicable for all wavelengths.

One nice presentation is given in the Physics Today article of Pierrehumbert. Figure 2 of that article shows the absorption coefficients of CO2 and H2O at half atmospheric pressure. There we can see that the main peak tops at 10000 m^2/kg. That corresponds to a mean free of about 0.3 m. The strongest side-peaks peak at one tenth of that and the absorption minima between those side peaks at about 10 m^2/kg corresponding to a mean free path of 300 m. Near the surface the mean free path of the minima is well less than that due to more broadening on top of the higher density.

The above applies best to the range 14.4 – 15.6 µm. Further out from the center absorption gets gradually weaker. In the middle of troposphere the valleys between peaks lead to significant heat transfer from this range of wavelengths, near the surface only more distant tails are really significant. In the lower troposphere water vapor shortens the mean free path as well in particular on the long wavelength side of the 15 µm peak as the much higher concentration compensates for the smaller absorption coefficient.

• Clive

..Yes I understand that and believe I have handled all that correctly..

I expected that you had. Just the description was off so I thought I would check.

5. Pekka Pirila,

Why is GHE a necessary determinant of the atmospheric temperature profile? Aren’t the pressure gradient and moisture profile sufficient?

• The moist adiabatic lapse rate is not a necessary consequence of pressure gradient and moisture profile, because it’s an upper limit that can be maintained only by pushing continuously towards that limit. In other words the adiabatic lapse rate can be maintained only when some mechanisms tries to create a steeper lapse rate.

The mechanism that tries to maintain the steeper lapse rate within the troposphere is radiative heat transfer. In radiative heat transfer both SW from sun and LW from Earth surface and atmosphere must be included. How important the role of LW emission and absorption is can be understood when it’s realized that the altitude of the tropopause is determined by the properties of LW emission and absorption in the atmosphere in combination with the value of the adiabatic lapse rate.

At altitudes below the tropopause (i.e. in troposphere) radiation alone would lead to steeper lapse rate and it does the pushing against the limit.

In stratosphere radiation alone leads to a less steep lapse rate than adiabatic. Therefore there’s no vertical convection and the stratosphere is stratified as its name implies.

What I have written in this comment about the influence of radiation describes exactly the theory that is behind the kind of GHE we have on Earth.

• Pekka Pirila,

“How important the role of LW emission and absorption is can be understood when it’s realized that the altitude of the tropopause is determined by the properties of LW emission and absorption in the atmosphere in combination with the value of the adiabatic lapse rate”.

However, given that: (a) the properties of LW emission and absorption are independent of latitude whereas (b) moisture content and lapse rate are latitude-dependent and (c) tropopause altitude and moisture content are maxima in the tropics, doesn’t this indicate that GHE plays a bit role in the determination of the temperature profile?

Expressed differently: The height of the tropopause is determined by the intersection between a fixed radiation equilibrium profile and a lapse rate that varies directly with moisture content. It’s the variable lapse rate that makes for latitudinally different tropopause altitudes. And it’s moisture content that determines the lapse rate and hence the temperature profile.

• John Millet,

The height of the tropopause is determined by the intersection between a fixed radiation equilibrium profile and a lapse rate that varies directly with moisture content. It’s the variable lapse rate that makes for latitudinally different tropopause altitudes.

The height of the tropopause is determined by the scale height of the atmosphere. The scale height is determined by the gas constant (R), the acceleration of gravity (g), and the average temperature (harmonic mean) from the surface to altitude z, which, in spite of what you might think, doesn’t vary all that much for different lapse rates. Which means the average surface temperature is the most important factor with the lapse rate as a second order effect.

See Chapter 2: The Thermodynamics of Dry Air in R. Caballero’s Lecture Notes. If you haven’t read it, and from your questions I would guess that to be true, you should. You really can’t ask intelligent questions until you have a good idea of the fundamentals. Meteorologists have been working on this for quite some time. You’ll likely notice that atmospheric radiation isn’t even mentioned in Chapter 2. The lapse rate is something to be measured, not calculated. The scale height is only mentioned in Chapter 3, The Thermodynamics of Moist Air as it relates to the scale height of water vapor, which is about 1/4 that of dry air because saturation vapor pressure of water is strongly dependent on temperature.

• Which, btw, means that lapse rate feedback isn’t exactly what you might think it to be. When the surface heats up, so does the atmosphere, which then expands. That raises the effective emission height, which is a function of pressure, reducing the amount of radiation that would have gone to space from the increase in temperature alone. Note that this feature is NOT captured by MODTRAN or any other radiative transfer program that I know of.

• DeWitt Payne,

I didn’t make it up.

From Pierrehumbert “Principles of Planetary Climate”:

“The main factor governing the tropopause height is the lapse rate. If the lapse rate is weaker,
then one has to go to higher altitudes in order to intersect the radiative equilibrium profile. In the
warm tropics, the moist adiabat has significantly weaker gradient than the dry adiabat. In fact,
a radiative-convective calculation based on the radiative effects of a dry CO2/air atmosphere, but
employing the moist adiabat in the temperature profile, yields a tropopause height of 130mb when
the surface temperature is 300K. This is quite consistent with the observed tropopical tropopause
height. This suggests that the effects of moisture on lapse rate are more important than the
radiative effects of tropospheric moisture in elevating the tropical tropopause. In other words,
the main reason the Earth’s present tropical tropopause is higher in altitude than the midlatitude
tropopause is that the tropical lapse rate is weaker, owing to the greater influence of moisture for
Earthlike tropical temperatures”.

• John,

You are certainly right in stating that there are latitudinal differences and that the tropopause altitude is higher in the tropics than at middle latitudes. In polar winter the situation is also different as the dry cold troposphere has little convection and a smaller lapse rate due to colder surface and low troposphere.

The simple descriptions of origins of lapse rate are incomplete as they don’t discuss all the variability that affects the average profile. If the case would not be this we would see cleaner cases of dry and moist adiabatic lapse rates rather than something intermediate. The simple descriptions are, however, useful and provide a reasonable understanding of the structure of the atmosphere.

The crossing that Pierrehumbert refers to applies always to the local lapse rate at that particular altitude comparing that to the lapse rate that radiation alone would produce at that altitude. Even in tropics the absolute moisture level is small at high altitudes and for low absolute moisture the difference between dry and moist lapse rates is small.

In a rising convective flow the moist lapse rate is in force even when the absolute moisture is low and in a subsiding flow the dry adiabat applies even when the absolute moisture is high because the relative humidity is less than 100% in subsiding flow. The moist lapse rate depends, however, on the absolute moisture (or equivalently on the local temperature) and gets close to the dry lapse rate at low temperatures.

The lapse rate that would result from radiation alone depends on the GHG concentration but not very strongly. Even in the limit of optically thin atmosphere the tropopause would be not drop close to the surface. In that limit the temperature of the tropopause would be about 45 C less than the surface temperature. (In that limit GHE is absent, the surface is very cold and the tropopause even colder.)

6. There appears to be general agreement that GHE is a necessary determinant of surface temperature which effect is to raise it. Why? The surface lies between two heat sources, internal and external. Its temperature will reflect their combined effects. Assuming the former’s effect to be constant, changes in surface temperature result only from changes in the latter (the sun) which varies with its power generation and the earth’s distance from it. The atmosphere, with its traces of radiatively-active particles, weakens the sun’s effect on surface temperature by directly absorbing some of its power and (theoretically) emitting it to the surface at reduced strength. The atmosphere also absorbs radiation returned from the surface to space and emits it at lower strength. That is, the atmosphere retains some of the return radiation and consequently warms. But what physics says that the surface, the source of the retained energy, must also warm? Why wouldn’t the warming in the atmosphere reduce the lapse rate, leaving surface temperature unchanged?

• John Millet,

Why wouldn’t the warming in the atmosphere reduce the lapse rate, leaving surface temperature unchanged?

Because reducing the lapse rate means the troposphere as a whole warms and you get increased radiation to space from higher up. But the incoming energy is still the same, so the upper troposphere must cool and restore the original environmental lapse rate. The evidence is that the environmental lapse rate is pretty stable.

• DeWitt Payne,

“Because reducing the lapse rate means the troposphere as a whole warms..”

That’s not quite right. Depicting the lapse rate as a backward sloping line on a graph, reducing the lapse rate (numerically) implies a clockwise rotation about the surface anchor in which the troposphere warms differentially with altitude. Equal warming of the troposphere as a whole implies a rightward shift in the line, its slope remaining constant.

The global average lapse rate might be stable but it does vary latitudinally.

• John Millet,

Think about it a little more. If the lapse rate is reduced at the same surface temperature, every altitude in the troposphere warms some. Obviously, the higher altitudes warm more, but the total energy content of the troposphere increases and therefore, the average temperature increases. That also means more radiation down as well as up.

This has consequences. More total emission requires more energy coming into the atmosphere. Increased CO2 will absorb a little more of the surface emitted radiation, but not enough to make up the difference. Convective transfer from the surface is unlikely to increase because a lower lapse rate means a more stable atmosphere.

• Reduction of the lapse rate trough warming of the upper troposphere would mean that convection cannot proceed. Thus the lower troposphere could cool only by radiation up, but that’s not as strong as the heating by solar SW. Thus the lower troposphere would warm again and restore the original lapse rate.

The lapse rate may vary a little due to changes in moisture levels and in circulation, but the lapse cannot change independently as long as convection is needed to transfer all the heat that solar SW brings to the surface and that’s not used to warm the oceans, surface soil and lowermost troposphere.

If the lapse rate would go down more than thought by main stream climate science that would make the GHE even stronger than presently estimated.

• Sounds a bit extreme.

As you say, the surface loses most of the heat it gains from the sun through convection. Most of this starts with evaporation from ocean surfaces. This is a function of the surface temperature and the temperature difference between the surface and the top of the atmospheric surface layer. It’s not clear to me how a rise of temperature in the upper troposphere would affect this – the atmospheric temperature profile is not a linear constant; the lapse rate is an average slope of that profile over the height of the troposhere. Moreover, is it not the case that the latent heat extracted from the surface is convected upwards according to the pressure profile rather than the temperature profile?

• John,

The averages are not decisive but the local conditions. This is a rather severe complication because all the weather variability, both spatial and temporal tells about large deviations from the average.

Based on the local conditions rising vertical convection stops unless it’s maintained by a temperature profile that’s steeper than the moist adiabatic lapse rate or is forced by pressure deviations from the stable values (such pressure deviations must be ultimately due to thermally driven convection somewhere else). On the other hand a temperature profile that’s much steeper than the moist adiabatic lapse rate leads to stronger convection until the profile is again close to the moist adiabatic one.

When the surface is heated strongly by solar radiation at low latitudes it will warm up until heat gets removed with a rate equal to the heating. The radiative heat transfer cannot increase much due to phenomena described in the postings of this series. Thus convection (including latent heat transfer) is the form of heat transfer that reacts most strongly to restore the balance. The right strength of rising convection is possible only when the temperature profile is slightly steeper than the moist adiabatic lapse rate as far up as the convection is strong. This determines rather accurately the lapse rate at that location. In subsiding regions the lapse rate is similarly close to dry adiabatic lapse rate.

What happens to the average lapse rate depends on the relative weight the rising and subsiding regions have in averaging as well as on many more complex phenomena that occur at the boundaries between rising and subsiding regions. As the rising and subsiding regions are often interspersed the boundary regions may cover a major part of the total. That again makes it more difficult to determine the average lapse rate. Even so the lapse rate cannot be set freely but is forced to some value by the need of right overall rate for convective heat transfer from the surface to upper troposphere.

7. I have a really basic question. How is the energy exchange between the trace GHGs and the rest of the atmosphere handled in this model?

• David Wojick,

In brief, the absorbed energy by a GHG is thermalized by the local atmosphere. That is, the energy is redistributed by collisons with other molecules and contributes to the heat (internal energy) of the local atmosphere.

In the case of the sample spectra and flux graphs above they are produced from the instantaneous state of the atmosphere (prescribed).

In the case where I run through time steps to find out how the atmospheric radiation change the state of the atmosphere:

Change in Energy per unit area, ΔE = Energy Absorbed less Energy Emitted.
Change in Temperature, ΔT = ΔE / [cp.ρ.d]
where cp = specific heat capacity of the atmosphere, ρ = density, d = thickness of layer of atmosphere.

• Thanks SoD. How do you determine how much absorbed energy is thermalized as opposed to being emitted by the GHG molecules?

• David Wojick,

The time between collisions is so short in the lower atmosphere that 100% can be considered to be thermalized.

The emission of radiation by GHG’s is then a spontaneous process defined by Planck’s law (and the emissivity of each GHG at a given wavelength).

• To state this more quantitatively. (I hope I didn’t make errors in the following. They are possible on the details, not on the basic message.)

The natural lifetime of the vibrational excitation that corresponds to the 15 µm radiation is 0.65 s. (The Einstein coefficient that’s the inverse of lifetime is 1.54 1/s.) That tells how long it would take on the average for the excited molecule to emit the photon in free space.

The time between collisions of an CO2 molecule with some other molecule is about 0.1 ns under conditions of near surface atmosphere. Thus each CO2 molecule has billions of collisions during one natural lifetime of the state. The likelihood that an vibrationally excited molecule loses it’s excitation in a single collision is high making the lifetime a fraction of nanosecond. Thus only something like 0.00000001% of excitations lead to emission of a photon. The line width (half-width at half maximum) due to pressure broadening is 0.074 1/cm which corresponds trough unit conversions and Heisenberg uncertainty formula to 0.07 ns indicating that essentially every collision leads to de-excitation of an excited state.

Every CO2-molecule spends about 7% of time in an excited state that could emit a 15 µm photon (3.5% in each of the two transverse modes). During every second each molecule gets excited to such a state more than hundred million times and de-excited equally often. Almost all this is due to molecular collisions while less than one case in billion is due to absorption or emission of radiation.

Higher up in the atmosphere these numbers change as the time between collisions is inversely proportional to pressure and to the square root of the absolute temperature.

• Thanks all for these useful answers. So emission is not a direct function of absorption, as the absorbed energy diffuses via collisions. I then have two more basic questions. First, are the collision energy transfers all quantized? Second, given these numbers why (or how) does emission occur at all? (I am working on a simple “packet switching network” model of the GHE.)

• David,

In every case of emission or absorption the energy of the emitting/absorbing material must change by the amount that maintains energy conservation. A individual molecule not in contact with other molecules may have four types of energy, kinetic energy, rotational energy, vibrational energy, and energy of electron orbits. The kinetic energy is not quantized, all other forms are.

The energy levels related to electron orbits are so high that they are significant in the atmosphere only in the absorption of high energy UV photons from sun.

Almost all emission and absorption of radiation in the atmosphere involves only one molecule and the photon. In that case the change in kinetic energy is dictated by the conservation of linear momentum to have an unique small value that depends on the energy of the photon emitted or absorbed.

As both rotational and vibrational energy is quantized an individual molecule can emit and absorb only at energies that correspond to these excited states. In case of CO2 only one specific vibrational state is important for IR. Rotational transitions by themselves have very low energies outside the range of IR, but combined rotational and vibrational transitions are important and lead to the side peaks on both sides of the main 15 µm peak.

In exceptional cases emission or absorption occurs at a time two molecules are so close that they both get involved in the transitions. In that case the energy is not quantized. These cases lead to the continuum emission and absorption, which is, however, very weak for CO2. It’s a little more common for H2O, because water molecules have a weak tendency to stick together trough the hydrogen bond.

In solids and liquids molecules are always so close to each other that continuum emission and absorption is very important and no narrow lines are present at IR energies.

The emission occurs at all because the collisions don’t prevent it even when they are hugely more common. The likelihood of the order of one in billion is enough when there are billions of billions of molecules present even in very small volumes and several percent of them in the excited state that makes the emission possible.

The lifetimes are always average ones. A lifetime of one billion units tells that the emission occurs with the probability of one in billion within one unit of time.

8. […] « Visualizing Atmospheric Radiation – Part Two […]

9. Well done Pekka and SOD. One caveat

The rules of thumb, which are pretty good here are that collisional vibrational energy transfer (VET) usually requires ~100 to 1000 collisions. Rotational energy transfer takes 1 to 10 depending on the spacing between the rotational levels. 1 us or a bit longer would be a good guess for the lifetime of a vibrationally excited CO2 molecule.

VET only gets much more efficient if the accepting molecule has a vibrational level that exactly matches that of the excited partner, thus CO2(v=1)) + CO2(v=0) is efficient, but has no effect on the question at hand.

Best

10. SoD,

How is it known or derived that the probability of ‘stimulated’ emission occurring is generally low in the atmosphere? I’m not sure I quite understand that claim in general.

• RW,

For stimulated emission to dominate requires a very high EM flux density like you find in lasers. And you don’t get that sort of intensity unless you’ve managed to create a population inversion with way more molecules in the excited state than you could get thermally. The intensity of atmospheric emission is orders of magnitude less than that and by definition there is no population inversion because as we well know, the atmosphere is in Local Thermodynamic Equilibrium. You might get an inversion in the vicinity of a lightning bolt, but you wouldn’t get coherent radiation because you wouldn’t have conveniently placed mirrors. Lasers use flash lamps, electrical discharges or chemistry to produce population inversions.

The other reason it’s known is that measured emission line intensity is proportion to the A21 Einstein coefficient for spontaneous emission to such a high degree that there can be no significant stimulated emission.

11. […] We’ve looked, via the model, at how radiation travels through, and interacts with, the atmosphere. But this has been for one set of atmospheric conditions which are listed in Part Two. […]

12. Pekka,

I found where I saw the comment about modeling perfectly transparent atmospheres. It was Raymond Pierrehumbert commenting at Rabett Run.

We’ve done some simulations of IR-transparent atmospheres for tide-locked planets, but they’re not published yet. You do establish an adiabat due to surface-driven convection (remember turbulent heat exchange) but the whole atmosphere fills up with the potential temperature determined by the hottest spot on the planet. Earlier, we published some simulations in a similar spirit for the Hadley cell in the transparent limit, in QJRMS.[my emphasis]

The QJRMS paper is here: http://onlinelibrary.wiley.com/doi/10.1002/qj.271/pdf
and the section of interest is 6.1 on page 13 of the paper or page 1281 of the journal.

The title of the post with the comment is: “The indelible dumbness of physicists”

• This makes perfect sense after thinking about the processes behind atmospheric circulation, especially subsidence, as discussed in Clouds & Water Vapor – Part Five – Back of the envelope calcs from Pierrehumbert.

• DeWitt,

The comment of Raypierre is at the other end of the set of possible outcomes as I see them. The other end is that where only a thin layer deviates from isothermal.

The chapter 6.1 of the paper argues along closely the same line I have argued stating:

This situation arises in the optically thin limit, optical depth -> 0. In this limit, the atmosphere cannot lose entropy radiatively in the subsiding branch. Entropy is then homogenised in the interior, though conduction from the surface maintains an entropy gradient in a shallow boundary layer.

Then they mention simulations with very small emissivity telling that

the atmosphere slowly fills with air of potential temperature equal to the warmest surface temperature until all gradients in the interior are wiped out and motion ceases, aside from a very shallow circulation driven by the small amount of thermal diffusion from the ground (analogously, in the oceanic context where Sandström’s work originated, the basin fills with the coldest, densest water).

This is again exactly what I did expect, because even extremely small optical depth wins over conduction.

For me it’s still an open question what would happen with exactly zero optical depth. It’s likely that no model has been constructed to be valid in that case. Therefore also the simulations of the paper have been done for a very small rather than zero optical depth.

13. DeWitt Payne,

“Think a little more about it”

All altitudes warm some whether (a) the surface temperature is fixed and the lapse rate changes or (b) the lapse rate is fixed and the surface temperature changes. In consequence of the resultant increased emission from the atmosphere, a balancing increment of energy into it is required. I think you are saying that the surface temperature must increase to meet that requirement, that is, (b) must apply.

Question: Where does the necessary temperature-raising increment of energy into the surface come from? The sun’s input hasn’t changed. Input from the atmosphere would merely be giving back to the surface what the surface had already given up to the atmosphere and there would be no surface temperature increase, that is, (a) applies.

See also my (somewhat ambitious) response to Pekka.

• John,

When less energy is lost than is absorbed, energy accumulates. Solar absorption hasn’t changed, but emission has decreased. So the energy to warm is, as always, coming from the sun. As Pekka points out below, the analogy of increased insulation, i.e. increased thermal resistance is apt in this case. If you increase the resistance in a circuit at constant current, the voltage drop across the resistor increases even though the current hasn’t changed.

• DeWitt,

All of this I know. The point at issue is whether the accumulated energy in the atmosphere results in a change in the lapse rate or a change in surface temperature. Or, in a graphical depiction, whether the temperature profile rotates clockwise or shifts to the right.

Hartmann, citing Matanabe, shows the dry and moist temperature profiles intersecting, not at the surface, but a bit above it in the surface layer. This dictates a common temperature just above the surface but different ones at the surface under the different moisture conditions – the moist surface being the cooler. Conversely, aloft, the moist profile is the warmer. These profiles are maxima, actual profiles lying variably between the extremes depending on locality, latitudinally and vertically.

Energy transport by radiative transfer from the surface to the atmosphere results in cooling at the surface and warming aloft. This can be depicted graphically as a clockwise rotation of the temperature profile, about a point in the surface layer, similar to that described above for changing moisture conditions.

The energy content of the system hasn’t increased as a result of the radiation transfer, it has been re-distributed. Only an increase in solar input can increase the system’s energy content and that is externally ordained. There being no change in the system’s energy content there is no change in the system’s average temperature. What has changed is the temperature profile – cooler at the surface, warmer aloft. GHGs and moisture steepen the temperature profile (increase the angle to the horizontal).

• John Millet,

Only an increase in solar input can increase the system’s energy content and that is externally ordained.

Oh, really. If you actually believe that, you’re beyond help.

Energy content in a steady state system can be increased either by increasing rate of the energy coming in or by lowering the rate of energy going out.

If I have a tank with water coming in at the top and out through a valve at the bottom, the level in the tank will reach a steady state. If I reduce the flow through the valve on the bottom or increase the flow into the tank, the level will increase until a new steady state is reached (or the tank overflows).

14. Pekka Pirila,

“Based on the local conditions rising vertical convection stops unless it’s maintained by a temperature profile that’s steeper than the moist adiabatic lapse rate”

Shouldn’t “steeper” read “less steep” – a temperature profile steeper than the moist adiabatic lapse rate is tending towards isothermal and certain death to convection?

If that be so, do I read you correctly (paraphrasing): Rising convection strength varies inversely with deviation of the slope of the temperature profile from the moist adiabatic lapse rate; and it ceases if the slope rises above that rate. Convection waxes and wanes in order to maintain the slope of the temperature profile slightly below the moist adiabatic for rising air mass and slightly above the dry adiabatic for subsiding mass?

If so, the question immediately arises: What causes convection to wax and wane? In models, modelers are the cause (as I understand to be the case). This could reasonably be seen, I think it fair to say, as the radiative tail wagging the convective dog. Could it be that in the real atmosphere, instead, the lapse rate fluctuates between the dry and moist adiabatic lapse rates as an effect of convection? I attempt to make that case below:

I visualise convection proceeding in two stages, each initiated by a horizontal temperature gradient and maintained by a vertical pressure gradient. The lapse rate, a vertical temperature gradient, doesn’t feature explicitly in the process.

In the first stage, while convection begins as the result of a horizontal temperature difference between adjoining regions (of the ocean surface, say, reflecting clear sky or cloudy conditions) it proceeds as a result of a vertical pressure gradient. The initial horizontal temperature gradient gives rise to a horizontal pressure gradient which moves air mass towards the region of lower pressure (as the warming air there expands). The lateral pressures on the parcel forces it upwards. The moist air mass movement continues upward until the water vapour turns liquid and precipitates, transforming latent heat to sensible heat which warms and expands the now drier air mass.

In the second stage, beginning roughly mid-troposphere, and as at the surface, horizontal temperature and pressure gradients result from the differential heating and the drier air mass is forced upwards by pressure differential. How high in the troposphere the air mass reaches is determined by the strength of the mid-troposphere temperature/pressure gradient between the rising, warm, dry air mass and the surrounding, subsiding, cool (having lost energy to space by radiation) dry mass. In turn, the higher the convection reaches the less is the temperature-dependent radiative cooling. Consequently, convective strength and the height reached are reduced. This inter-dependence between the horizontal temperature gradient at the mid-troposphere and radiation at the tropopause constitutes an automatic stabiliser of upper troposphere temperature, each waxing and waning in opposite phase. The waxing and waning of the mid-troposphere horizontal temperature gradient is reflected in fluctuation of the lapse rate between the dry and moist adiabatic limits. The lapse rate is an effect of the convective-radiative process, not its cause.

• John,

What’s steeper and what’s less steep depends on the way we look at it (or draw the graph). My way of thinking is that it’s steeper when temperature changes more for the same change in altitude.

All the energy to drive the convection comes from the sun. When it heats warm spots like equatorial surface and while the balancing loss of heat originates from colder places like the atmosphere near tropopause we have the conditions that maintain convection. As the heating from the sun does not change much and as the radiative heat transfer is also largely given by the constitution of the atmosphere convection is the component of energy balance that changes most easily and adapts to the other components.

As I tried to explain the certain presence of convection determines the lapse rate. I continued to tell that this doesn’t happen quite as simply as is often presented, but that’s even so the basic determinant of the lapse rate.

It’s true as DeWitt wrote that the lapse rate is nearly constant (not exactly, but nearly) and that everything from the surface to the tropopause warms approximately by the same amount.

You asked in your reply to him, “Where does the necessary temperature-raising increment of energy into the surface come from?”.

Where does the warming increment come when you go out in a cold winter day wearing a thick parka rather than a light jacket? Or where does it com from when you add a layer of insulation to the walls of a house?

• Pekka Pirila,

I take that as basic agreement between us that the cause-effect arrow is from convection to lapse rate.

“everything from the surface to the tropopause warms approximately by the same amount”

I deal with this point in my response to DeWitt.

“Where does the necessary temperature-raising increment of energy into the surface come from?”.

My question was in response to DeWitt’s suggestion that energy input to the atmosphere was necessary to balance the increased emission resulting from the accumulated energy and temperature increase. Implicit in the question was its answer: only from the sun – and that is not going to happen.

As to your questions, would the temperature of either my body or the house furnace be increased by the insulation? I think not. I will of course feel more comfortable in the warmer surroundings which mitigate the rate of energy loss. But my temperature won’t increase.

• John Millett on January 11, 2013 at 4:02 am,

You’ve made my day!

1. What is energy?
2. What is power?
3. What is temperature?
4. a) If the system is in balance, we keep power in constant but reduce power out, what are the implications for energy stored as a result of the first law of thermodynamics?
b) what are the implications for temperature?

A few important questions that everyone studying the subject of climate should understand how to answer (correctly).

• John,

Your body temperature would increase wearing a parka in comparison with going out during a cold winter day (say -25 C / -13 F) in a thin jacket and staying there for a few hours. You would even stay alive and not die of hypothermia.

In the case of the house you may either reduce the power of heating or let the temperature rise.

Accepting that sun heats as before, an atmosphere that doesn’t allow the heat to get out from the surface to the space as easily, will lead to warmer surface and to a warmer troposphere. The top of troposphere moves a little higher and above that altitude other factors determine whether the temperature goes up or down.

15. General note – I found that WordPress now offers the ability to customize themes (on a hosted WordPress blog).

ITEM 1

I changed the hyperlink font because it’s annoying that links in comments look almost like the non-linked text. Sorry to everyone it has annoyed from the start.

If I change it a lot (using the “dummy easy to use change something mode”) it upsets some other things, like heading styles and backgrounds.

So I tried red but other stuff got screwed up.

I can change the CSS but that means remembering how to do CSS (last used some years ago), learning what the CSS is for this style, etc. In the mean time, Voigt profiles to work out and articles about water vapor to write.

QUESTION – Is the new link font (please refresh your browser) easy to see or do I need to change it further?

ITEM 2

Any other style issues on the blog that people would like to see changed?

(“Style” = fonts, colors, graphics.
“Style ≠ caustic reflections on other commenters’ use of laws of thermodynamics, subject matter posting, etc)

16. Underline would, of course, be better, but this is a definite improvement on my screen.

17. Thank you, gentlemen all, for this and related conversations. Something for me to think about over the next month or so in Antarctica. I’ve packed Pekka’s parka – no chance of hypothermia! But, Pekka, can a temperature that is higher than it would have been under different conditions be said to have increased?

DeWitt, relax! I don’t believe what I said – except in the context in which it was said, namely, whether warming of the atmosphere by radiative transfer of energy from the surface reflects an increase in the system’s energy content or a re-distribution of it. In that context, before any consideration of radiation to space from the atmosphere, only solar input could increase the system’s energy content. Of course, when the discussion gets to that further consideration, reducing output to space will raise the system’s energy content, as well.

Relating this context to the tank analogy, the outlet valve setting is fixed; and the tank has two compartments and a pump transferring water from the bottom one to the top one. Water flows into the bottom compartment, is pumped up to the top compartment where the (fixed) outlet valve is located. The inter-compartmental transfer of water doesn’t increase the total water content – the rise in the level in the top compartment is offset by the fall in the bottom one.

SOD, I could probably earn a pass mark on such an examination, but let’s leave it till later. My response to DeWitt is relevant.

I wish you well and good speed in developing the new material.

18. […] of different CO2 concentrations using the atmospheric radiation model described (briefly) in Part Two and in detail in Visualizing Atmospheric Radiation – Part Five – […]

19. […] atmospheric model is described in brief in Part Two and in a comment, then in detail in Part Five – […]

20. […] 10 atmospheric layers in the model with a top of atmosphere at 50 hPa. More about the model in Part Two and Part Five – […]

21. […] and emission of radiation in the atmosphere we can do some “experiments”. See Part Two and Part Five – […]

22. […] Part Two we covered quite a bit of ground. At the end we looked at the first calculation of heating rates. […]

23. […] Visualizing Atmospheric Radiation – Part Two I describe the basics of a MATLAB line by line calculation of radiative transfer in the atmosphere. […]

24. Hockey Schtick posted this comment onto another thread. I’m reposting it here for now to avoid derailing another article. In time I will create a post on this amazing topic and gather all related comments into said thread.
———

SoD

Do you disagree with this statement from Claes Johnson?

“Planck’s Law, which is the basis of Stefan-Boltzmann’s Law, describes one-way heat transfer from a warm body to a colder surrounding. Planck and Stefan-Boltzmann did not speak about two-way heat transfer, only about one-way heat transfer from warm to cold.”

Why do you disagree with the following [see link below for context]:

sigma (T_a^4 – T_s^4) = True Stefan-Boltzmann Law

of the form

Net-Input = sigma T_a^4 – sigma T_s^4 = False Stefan Boltzmann Law,

sigma T_a^4 = Net-Input + sigma T_s^4 = False Stefan Boltzmann Law,

obtained by algebraic reformulation of the True Stefan-Boltzmann Law. But the seemingly innocent algebraic reformulation leads to a False Stefan-Boltzmann Law, because the algebra has no physical meaning:

To rewrite Net-Input as the difference of the gross quantities sigma T_a^4 and sigma T_s^4 has no physical meaning, since sigma T_a^4 is the radiance from the atmosphere into a surrounding at 0 K and sigma T_s^4 is the radiance from the DLR-meter into a surrounding at 0 K, and this is not the physics of the interaction between atmosphere and DLR-meter described by sigma (T_a^4 – T_s^4) according to the True Stefan-Boltzmann Law.

http://claesjohnson.blogspot.com/2013/01/the-big-ipcc-bluff-of-co2-alarmism-dlr.html

• And my other optional question, do you think that, if Claes Johnson is correct, all heat transfer textbooks (which include radiative heat transfer) need to be rewritten – or they are fine as they are ?

(I know the answer to this one, but do you?)

• Hockey Schtick,

Did you read my earlier comment in response to your last recommendation for Claes “no photons” Johnson?

Did you understand it?

Let me ask you a question, which you need to answer in order to proceed, (i.e., not have me delete your future comments which in any case breach the blog etiquette) –

Do you think that photons exist?

25. […] Part Two – some early results from a model with absorption and emission from basic physics and the HITRAN database […]

26. […] Part Two – some early results from a model with absorption and emission from basic physics and the HITRAN database […]

27. […] Clouds & Water Vapor – Part Six – Nonlinearity and Dry Atmospheres Visualizing Atmospheric Radiation – Part Two […]

28. […] Part Two – some early results from a model with absorption and emission from basic physics and the HITRAN database […]

29. […] do this I used the Matlab model already created and explained – in brief in Part Two and with the code in Part Five – The Code (note 2). The change in surface emissivity is […]

30. I don’t recall which thread we were discussing this in, but I’ve deduced that he ‘average net transmittance’ or net ‘T’ must simply be an integral of the emission that’s transmitted into space from the multiple layers which is weighted by the Planck Function of the surface temperature. This makes perfect sense since the radiating plane from which the radiant opacity though the whole mass of the atmosphere is being measured is that of the surface.

Geez. If this is really true, then how come no one knew or could confirm this? The calculated TOA flux changes — even though much of the emission originates from the atmosphere — would then be based on the radiating plane of the surface, i.e. the power radiated from the surface. This also means there is a total amount of power considered to be absorbed and transmitted, and the difference between the net ‘T’ and the amount absorbed, i.e. 1-‘T’, is equal to the power radiated from the surface (which in the steady-state is also equal to the net power gained at the surface).

• on May 20, 2014 at 3:59 am | Reply DeWitt Payne

RW,

If you would write equations that describe your thinking it would be much easier to understand. As it is, I’m not really sure what you’re describing.

• Maybe you can help me formulate the equations, as I’m not sure what they would be. As I understand it, the net transmittance or net ‘T’ is an integral function composed of the multiple atmospheric layers of the spectral transmittance evaluated at the temperature of the surface, i.e. the Planck spectrum of radiant energy emitted by the surface as consequence of the temperature of the surface.

As a simple example, if the surface were at a temperature where 400 W/m^2 were radiated as a consequence of its temperature, and the net ‘T’ emerged to be about 0.25, it means 100 W/m^2 of the Planck spectrum of energy is considered to be transmitted to space and the difference of 300 W/m^2 (i.e. 1-‘T’) is the amount of the spectrum’s energy that is considered to be absorbed by the atmosphere (i.e. ‘blocked’ or attenuated from leaving at the TOA). To further apply this simple example to 2xCO2 — assuming a net increase in absorption of 4 W/m^2 — it would mean the spectral transmittance would decrease by 4 W/m^2 (from 100 W/m^2 to 96 W/m^2) and amount of the spectrum absorbed would increase by 4 W/m^2 (from 300 W/m^2 to 304 W/m^2).

• I understand the basics is for increased opacity, each layer absorbs a little more and emits a little more.

• RW: When you are considering radiation emitted by a filament at several thousand degC in the lamp of a laboratory spectrophotometer and then passing through a homogeneous sample near room temperature, all you need to worry about is absorption and the path length of the sample. When you are considering radiation passing through our non-homogenous atmosphere, you need to consider both absorption and emission in a layer thin enough that density and temperature are effectively constant. The Schwartzschild equation covers this situation:

dI = emission – absorption
dI = n*o*B(lamba,T)*ds – n*o*I_0*ds = n*o*[B(lamba,T) – I_0]*ds

dI is the incremental change in wavelength at a particular wavelength as it passes an incremental distance, ds, through the atmosphere, I_0 is the intensity of light at that wavelength entering the increment ds, n is the number of GHG molecules, o is their absorption/emission cross-section at that wavelength, and B(lamba,T) is that Planck function at the temperature T of the gas in the increment and wavelength. The equation is numerically integrated (by MODTRAN or HITRAN, for example) over all wavelengths over the path of interest: usually from the surface to space (TOA flux) and space to the surface (DLR). In those cases, one only worries about the component of the emitted flux in the vertical directions. Additional terms can be added to account for scattering by particles. You must specify the atmospheric temperature profile and GHG concentration(s) profile before calculating anything.

In the laboratory spectrophotometer, I_0>>B(lamba,T). Integration of the remaining absorption term for a homogeneous sample gives Beer’s Law: I/I_0 = exp(-nos)

When light has passed through a homogeneous gas long enough for emission and absorption to come into equilibrium at a particular wavelength, “Blackbody intensity” is present at that wavelength. This happens at strongly absorbed wavelengths in the troposphere, but not at all wavelengths.

• on May 23, 2014 at 2:35 pm DeWitt Payne

This is why you see a deep valley in the emission spectrum of the Earth near 15 μm. The effective emission temperature at the bottom of the valley is ~200K while the surface temperature is close to 300 K. Increasing atmospheric CO2 makes the valley wider and lowers emission to space.

• on May 23, 2014 at 2:31 pm DeWitt Payne

Suppose you are observing a black body emitter through a column of gas where at some wavelengths the optical density is > 7 so less than 0.1% of the radiation at that wavelength from the black body passes through the column without being absorbed. If the column of gas is maintained at 300 K, how does the observed spectrum change as the temperature of the black body is increased from near absolute zero?

The answer is that near absolute zero, you will observe only the emission spectrum of the gas and essentially no radiation at wavelengths where the optical density of the gas is zero. As the temperature of the black body increases, the valleys in the spectrum will start to be filled. When the black body is at 300 K, the spectrum will be the same whether a gas is present in the column or not, the spectrum of a black body at 300 K. As the temperature increases, radiation intensity will increase at wavelengths where the gas absorbs less. Radiation will also increase at the wavelengths of maximum absorption, but only by a tiny fraction. At very high temperature for the black body, the spectrum will be an absorption spectrum where the emission from the gas and the residual transmission is small.

So yes, the total emission at the top of the column does increase as the emitting surface temperature increases. The converse is the greenhouse effect: When the gas temperature is less than the black body temperature, if you increase the integrated optical density of the gas column, the black body temperature will have to increase to maintain the same integrated emission intensity at the top of the column.

31. What is the physical meaning of ‘net transmittance’ for a multilayer atmosphere? What does this number quantify?

• RT simulations fundamentally quantify changes in net absorption and net transmittance through the entire mass of an atmosphere. If ‘A’ is defined as net absorption and ‘T’ is defined as net transmittance, ‘T’ is then just 1-A. An RT simulation for a global atmosphere calculates an average net transmittance or an average net ‘T’. I’m simply asking what the physical meaning of this quantity is.

Is it not the fraction of the surface radiated Planck spectrum that is transmitted to space?

• As mentioned before, for increased opacity, each layer becomes a slightly better absorber and emitter, and after up/down emission and absorption changes are considered, there is a TOA flux decrease. This and what I’ve outlined above is the most fundamental thing and RT simulation is doing.

• The transmission of surface IR photons through the atmosphere within 13-17 microns is ~0.05. The balance between atmospheric emission and surface emission for the same wavelength range varies with CO2 concentration and is approximately shown here.

• It also means for a TOA flux decrease (increased atmospheric opacity), A increases by the same amount T decreases. Or if the TOA flux decreased by 4 W/m^2 (like for 2xCO2), A would increase to 304 W/m^2 and T would decrease to 96 W/m^2.

• Net absorption and net transmittance of the Planck spectrum of energy radiated from the surface. I understand it includes transmission that originates from the atmosphere, but that transmission isn’t arbitrary or all of it — it’s the specifically and only the incremental amount of the surface radiated Planck spectrum of energy that is transmitted. It also means there is a total amount of power absorbed and transmitted (something disputed here before) and the sum of the two is specifically equal to the power radiated from the surface (which in the steady-state is also equal to the net power gained at the surface). This is incredibly basic and essential as far as I’m concerned.

If the net ‘T’ is 0.25, and ‘A’ is defined as net absorption, A = 1-T and T = 1-A; and T + A = 1, where 1 is equal to the power radiated from the surface. If 400 W/m^2 is radiated from the surface and T = 0.25, it means 100 W/m^2 is transmitted to space (400 x 0.25 = 100) and 300 W/m^2 is absorbed by the atmosphere (400 x 0.75 = 300).

• on May 24, 2014 at 1:37 pm DeWitt Payne

Net absorption or transmittance of what, radiation from the surface? That’s the only definition that has a convenient physical meaning. As Pekka points out, it’s not very useful. If you look at individual layers of the atmosphere, you have to include radiation from the atmosphere above as well as radiation from the surface and atmosphere below. Because energy transfer from convection is significant in the lower atmosphere, emission will exceed absorption in the lower layers. And for energy balance, you also have to include absorption of incident solar radiation.

Your focus on only absorption and transmission has been leading you astray pretty much from the beginning.

• It’s probably best to forget totally the concept, because it’s highly misleading. Only a small fraction of radiation to the space is transmitted trough the whole atmosphere, and all the ratios vary for a multitude of reasons.

It’s better to look separately at the intensities at each altitude, and to use transmittance only for layers thin enough to transmit most of the radiation considered. That’s what the simulation do, and for very good reasons.

• RW,

Transmittance is a well understood and very fundamental concept. The transmittance of the atmosphere is the proportion of radiation that is transmitted through the atmosphere.

You have ‘defined’ something called ‘net transmittance’ and now you are asking everyone what it is.

A radiative transfer calculation does not calculate ‘an average net transmittance’.

A radiative transfer calculation calculates emission and absorption through the atmosphere and lets the person doing the calculations summarize the results in a variety of ways – as in the article above. For example, I could calculate total flux at TOA compared with flux emitted from the surface. I could calculate total downward flux at the surface. I could plot a graph of upward and downward flux as a function of height for given concentrations of various GHGs. Like in figure 6.

That’s why De Witt suggested that you write equations. No one really understands what your question is.

The value of flux at TOA depends upon all of the factors in the RT equations – temperature profile of the atmosphere, GHG concentration, absorption properties of each GHG. [TOA flux] / [Surface flux] does not equal [average net transmittance] unless you define that ratio to be this new parameter. But even if you do I still don’t know what your question is trying to elicit.

• Mind you, I’m not referring to the direct surface transmittance, but rather the spectral transmittance through a multi-layer atmosphere RT simulation, which I believe is evaluated or weighted by the spectrum radiated from the surface as a consequence of the surface temperature.

• To use the same numbers I used above, for there to be +4 W/m^2 of net absorption and -4 W/m^2 of net transmittance (like for 2xCO2), ‘T’ would decrease from 0.25 to 0.24 (96/400 = 0.24) and ‘A’ would increase from 0.75 to 0.76 (304/400 = 0.76); and 0.24 + 0.76 = 1 just as 0.25 + 0.75 = 1. Now, you and everyone seem to be saying this is not correct? This is essentially all I’m trying to establish and/or verify.

(*In this example — just to absolutely clear, ‘T’ is defined as net transmittance and ‘A’ is defined as net absorption).

• “The value of flux at TOA depends upon all of the factors in the RT equations – temperature profile of the atmosphere, GHG concentration, absorption properties of each GHG.”

I understand this. That is, I understand these things ultimately determine the amounts of absorption and transmittance.

• “The change in opacity through the whole atmosphere is ‘vanilla’ transmittance. This is completely different from the radiative forcing of 3.7 W/m2 which is the change in flux absorbed by the atmosphere/ocean as a result of doubling CO2.

In a basic physics or engineering course, units are a subject. It’s dull but essential. Transmittance is in dimensionless units (flux/flux) and radiative forcing is in W/m2.

Chalk and cheese.

“3.7 W/m^2 of net absorption increase for 2xCO2” is clearly not in units of transmittance.

Yes, but ultimately the 3.7 W/m^2 is due to a decrease in net transmittance and an increase in net absorption, is it not? Moreover, it is the incremental increase in the surface Planck spectrum of energy that’s absorbed by the atmosphere, where as before 2xCO2 it was transmitted through the atmosphere to space (i.e. not captured). Right?

I understand that transmittance and absorption are dimensionless fractions, as I believe I outlined this in an above post. Are you saying that net absorption and net transmittance for such simulations are not fractions of the power radiated from the surface?

• RW,

I don’t believe I ever said it did (or would). How are you interpreting what I’ve said as saying this?

I’m just trying to understand what you are thinking.

The alternative is saying nothing because I can’t understand what you are thinking.

• RW,

The context I’m referring to are changes in opacity through the whole atmosphere, i.e. from the surface all the way through to the TOA. For example, like the RT simulation that arrives at about 3.7 W/m^2 of net absorption increase for 2xCO2..

The change in opacity through the whole atmosphere is ‘vanilla’ transmittance. This is completely different from the radiative forcing of 3.7 W/m2 which is the change in flux absorbed by the atmosphere/ocean as a result of doubling CO2.

In a basic physics or engineering course, units are a subject. It’s dull but essential. Transmittance is in dimensionless units (flux/flux) and radiative forcing is in W/m2.

Chalk and cheese.

3.7 W/m^2 of net absorption increase for 2xCO2” is clearly not in units of transmittance.

• “[TOA flux] / [Surface flux] does not equal [average net transmittance] unless you define that ratio to be this new parameter.”

I don’t believe I ever said it did (or would). How are you interpreting what I’ve said as saying this?

• “A radiative transfer calculation does not calculate ‘an average net transmittance’.”

No, not necessarily, but a global average or average of a whole atmosphere does calculate an average net transmittance, which is really just the spectral transmittance — or just the fraction of the surface emitted Planck spectrum of energy that is transmitted to space. Increase or decreases in opacity through the whole atmosphere are quantified via changes in absorption and transmittance of this spectrum’s energy.

“A radiative transfer calculation calculates emission and absorption through the atmosphere and lets the person doing the calculations summarize the results in a variety of ways – as in the article above. For example, I could calculate total flux at TOA compared with flux emitted from the surface. I could calculate total downward flux at the surface. I could plot a graph of upward and downward flux as a function of height for given concentrations of various GHGs. Like in figure 6.”

The context I’m referring to are changes in opacity through the whole atmosphere, i.e. from the surface all the way through to the TOA. For example, like the RT simulation that arrives at about 3.7 W/m^2 of net absorption increase for 2xCO2.

• I don’t think it best to forget the concept before I can confirm what it actually means. I understand that the primary focus are the TOA flux changes for GHG concentration changes.

It’s a simple question. What is the physical meaning of ‘net transmittance’ through a multi-layer RT simulation? Either it’s the fraction of the Planck flux radiated from the surface that is transmitted to space or it’s not.

• I don’t see how you can think that. This is the most basic thing and RT simulation of the atmosphere is doing.

• RW,

You can never confirm, what it really means, because it has no well defined meaning. That’s exactly the reason for forgetting it.

• on May 24, 2014 at 1:39 pm DeWitt Payne

Either it’s the fraction of the Planck flux radiated from the surface that is transmitted to space or it’s not.

Of course it is. So what? By itself, it’s not very meaningful.

• It is relevant because the TOA flux changes would then be weighted by increase or decrease in the amount of the Planck Flux radiated from the surface that is transmitted and absorbed.

32. on May 24, 2014 at 11:39 pm | Reply John Millett

DeWitt Payne May 23 2.30PM

“Increasing atmospheric CO2 makes the valley wider and lowers emission to space.”

Why doesn’t increasing the width of the emitting valley of the spectrum also increase its emission?

• John:

di = n*o*[B(lamba,T) – I_0]*ds

You have just asked what happens when n becomes larger. The absolute value of the answer depends on the sign of the term in brackets. For the upward flux passing through the troposphere from warmer to colder, the term in brackets is negative. At low altitudes, upward I_0 comes mostly from the warmer ground, which has a larger B(lamba,T) than the air above.

At strongly absorbed wavelengths (the center of the 15 um CO2 band) or when large amounts of GHG are present (tropical humidity, Venuvian CO2) and the term in brackets is very close to zero. Some say absorption is saturated, but this is misleading. Absorption and emission are in equilibrium.

• John: The intensity of radiation traveling through a medium always changes towards “blackbody intensity”, but the rate of change depends on n and o. Since the temperature, density and composition of the atmosphere change with altitude, it is difficult for emission and absorption to fully come into equilibrium (I_0 = B(lamba,T). However, for the 15 um band of CO2 (and for water vapor) in the lower troposphere, n*o is big enough that emission and absorption are effectively in equilibrium. In this case, some people mistakenly ignore emission and say that the CO2 “absorption is saturated”. This misrepresent the real situation. When I_0 = B(lamba,T), changing n [GHG density] can’t change the radiative flux; when I_0 is very close to B(lamba,T), that change will be negligible. Only when n*o has the correct magnitude can n change the flux. When considering the whole atmosphere, n*o causes the biggest change in upward flux (radiative forcing) on the edges of the strongest absorptions (as Pekka notes).

However, even this is an over-simplification, because n*o changes with altitude. Consider how doubling CO2 changes radiation as it passes through the stratosphere. At altitudes where absorption of UV by ozone and oxygen increase temperature, I_0 is less than B(lamba,T). Under these circumstances, increasing CO2 increases the flux thereby cooling the stratosphere. On Venus, absorption and emission are not in equilibrium above about 70 km above the surface, and the temperature is still dropping with altitude. Changes in the amount of CO2 in the upper Venusian atmosphere will produce a radiative forcing, even though the CO2 absorption is saturated. This situation is easier to analyze in terms of the “critical emission level” (the altitude the average photon escaping to space is emitted from).

• John,

The formula Frank presented applies to every wavelength separately. Thus outgoing radiation gets reduced at every wavelength. The change is largest at the edges of the 15µm band, but the sign is the same everywhere as long as we are considering the troposphere, where the temperature drops with altitude. (The stratosphere is different, but has only little influence on the troposphere or the surface.)

• on May 26, 2014 at 5:01 am John Millett

Frank,

If I understand you correctly: making n larger has negligible effect at the centre of the 15um CO2 band because the term in brackets is practically zero. But it has effects off-centre. It introduces wings – or widens the valley (copying DeWitt’s terminology). It also deepens the valley, by increasing the altitude of final unimpeded emission. It seems to me that the wings would increase emission at all altitudes while deepening would reduce it only at the increased altitude.

• on May 25, 2014 at 1:35 pm | Reply DeWitt Payne

If the atmosphere were optically thin near 15 μm, that question would make sense. It’s not and it doesn’t.

• I believe because of the lapse rate, i.e. temperature decreases with height.

• As opposed to the other way around.

33. RW,

I understand that transmittance and absorption are dimensionless fractions, as I believe I outlined this in an above post. Are you saying that net absorption and net transmittance for such simulations are not fractions of the power radiated from the surface?

Transmittance is a dimensionless parameter, a ratio of powers.
Absorptance is likewise.
Absorption is a flux in units of W/m2.
This isn’t trying to be picky. It’s easy to misunderstand a question.

Yes, but ultimately the 3.7 W/m^2 is due to a decrease in net transmittance and an increase in net absorption, is it not? Moreover, it is the incremental increase in the surface Planck spectrum of energy that’s absorbed by the atmosphere, where as before 2xCO2 it was transmitted through the atmosphere to space (i.e. not captured). Right?

Wrong.

With 2xCO2 transmittance through the atmosphere will reduce, (and absorptance will increase).

But it’s possible for the change to be very small, even insignificant. It might be that all of the effects are due to the mid to upper troposphere being more opaque (lower transmittance) at wavelengths that had zero transmittance through the whole atmosphere.

Or a combination of the lower transmittance countered by a higher atmospheric temperature.

One thing is for sure – you cannot deduce that the atmospheric transmittance has changed from 0.25 to 0.24 because 396 x ΔTransmittance = radiative forcing.

Atmospheric transmittance might have changed from 0.250 to 0.249.

34. on May 25, 2014 at 1:32 pm | Reply DeWitt Payne

RW,

If you want to look at how atmospheric transmittance varies under changing conditions, try the online MODTRAN program. Set the conditions, click on ‘Show Raw Model Output’ and scroll down to the bottom. For the default settings, Tropical atmosphere, etc. the transmittance from 100-1500 cm-1 is 0.1473. For CO2 260 ppmv, changing nothing else, it’s 0.1485. At 560 ppmv CO2, it’s 0.1460.

The surface emission at 299.7K is 417.306 W/m². That makes the reduction in transmission of surface radiation from 280 ppmv ( 61.97 W/m²) to 560 ppmv CO2 ( 60.93 W/m² ) equal 1.04 W/m². Meanwhile the reduction in emission at the tropopause (MODTRAN doesn’t change the stratosphere) is 292.428 – 287.907 = 4.521 W/m². So the reduction in direct transmission is only 23% of the overall reduction. Which makes sense, at least to me.

And that’s for clear sky. With clouds, the transmittance from the ground is zero, nada, zip. Clouds cover ~60% of the surface. You could look at clouds as forming a new, higher, colder surface, but that gets really tricky.

• I also said that the net transmittance, i.e. the spectral transmittance, is not the direct surface transmittance. I also said I know much of the reduced emission at the TOA originates from the atmosphere.

• Either ‘net transmittance’ is the spectral transmittance of the spectrum emitted by the surface or it’s not. Net absorption ‘A’ of the spectrum emitted by the surface is then just 1-T. The point is the TOA flux changes calculated are specificallychanges in net absorption and net transmittance of the surface emitted spectrum of energy, which is a radiated power flux density. Because of this, the incremental TOA power flux changes are incremental increases or decreases that are weighted specifically by the surface emitted power flux density.

In the example above, for there to be +4 W/m^2 of net absorption there needs to be -4 W/m^2 of net transmittance (like for the example of 2xCO2), where net transmittance ‘T’ would decrease from 0.25 to 0.24 (96/400 = 0.24) and net absorption ‘A’ would increase from 0.75 to 0.76 (304/400 = 0.76); and 0.24 + 0.76 = 1 just as 0.25 + 0.75 = 1. That is, if the surface emitted power flux is 400 W/m^2 as a consequence of the surface temperature.

The main point is changes in opacity are specifically changes in the fraction of the surface emitted spectrum of energy that is transmitted or absorbed, and that this the most basic thing and RT simulation is calculating, i.e. changes in net absorption and net transmittance.

• on May 25, 2014 at 4:18 pm DeWitt Payne

What you call net transmittance T, more specifically the net absorptivity (1-T) is identical to the effective emissivity. That’s the emissivity you get if you plug the surface temperature and TOA emission into the Stefan-Boltzmann equation and solve for the emissivity. It has no more physical meaning than the effective emission temperature you get if you set emissivity to one and solve for temperature. It’s just a number you can calculate. It’s similar in principle to Miskolczi’s τ (tau in case the font in your browser is as bad as mine for Greek letters) and is just as irrelevant in the real world.

• on May 27, 2014 at 1:03 pm DeWitt Payne

A quick and dirty estimate from MODTRAN: Tropical atmosphere default settings looking down.
altitude power transmittance
0.0 km 417.306 0.823 (obviously 0 km isn’t actually zero.)
0.5 km 414.794 0.295

Ignoring the surface layer, that means that 123.1053 of the 414.794 at 0.5 km comes from below and the layer emission must then be 291.7 W/m², or 70% of the total. And that’s just one layer that’s too thick. As I said above, total emission from within the atmosphere is much, much larger than the emission from the surface.

• RW,

Also, if this is correct — using the numbers in my example, it means if the net ‘T’ is 0.25, it means 100 W/m^2 of the spectrum of energy emitted by the surface is transmitted to space and the difference of 300 W/m^2, i.e. (1-0.25)*400, is the amount of the surface emitted spectrum that is absorbed by the atmosphere.

Again, either this is correct or it’s not. Everyone seems to be saying that it’s not.

You keep using a term called ‘net T’.

I don’t know what ‘net T’ is.

Can you write an equation for it?

A different parameter which I will call T is transmittance.
T= Iout/Iin

T is a term which only considers the fraction of incident radiation which is transmitted, it does not consider any radiation emitted.

Using your numbers above and considering T, not ‘net T’, if T=0.25 and Iin = 400 W/m2, then 100 W/m2 is transmitted and 300 W/m2 ” is the amount of the surface emitted spectrum that is absorbed by the atmosphere.”

So your words are correct with the parameter called transmittance and I don’t know if your words are correct with the parameter you call ‘net transmittance’.

If it is different from transmittance then it will only be an unlikely coincidence that your words are correct.

• on May 27, 2014 at 4:30 am DeWitt Payne

Thinking more about the problem, it’s actually not going to be simple. The layer thickness must be such that it’s optically thin at all wavelengths. Or, one would have to separately integrate in fairly small wavelength increments. For strongly absorbing wavelengths, like the peak of CO2 absorption, the thickness would have to be on the order of a few cm near the surface. That calculation might take some time.

• on May 27, 2014 at 4:18 am DeWitt Payne

RW,

The other problem is that although you give lip service to atmospheric emission, you obviously don’t really believe in it. The evidence for this is that you keep referring to the 400 W/m² emitted by the surface as if it were the total emission of the surface and the atmosphere. It’s not. I don’t know what the total would be if you integrated all emission upward over the altitude range from the surface to the TOA, but it’s obvious that it would be much larger than emission by the surface alone, perhaps orders of magnitude larger. But almost all of it is also absorbed by the atmosphere. That’s because atmospheric emission, unlike surface emission, is all at wavelengths that are strongly absorbed by the radiatively active components of the atmosphere, i.e. greenhouse gases.

Perhaps SoD or Pekka could calculate this number as they have radiative transfer model programs. I don’t think you can back calculate it from MODTRAN data.

• on May 27, 2014 at 3:16 am DeWitt Payne

RW,

In the example above, for there to be +4 W/m^2 of net absorption there needs to be -4 W/m^2 of net transmittance (like for the example of 2xCO2), where net transmittance ‘T’ would decrease from 0.25 to 0.24 (96/400 = 0.24) and net absorption ‘A’ would increase from 0.75 to 0.76 (304/400 = 0.76); and 0.24 + 0.76 = 1 just as 0.25 + 0.75 = 1. That is, if the surface emitted power flux is 400 W/m^2 as a consequence of the surface temperature.

This statement is not correct. This is exactly the same mistake you’ve been making all along. It’s the reason you question the Trenberth, et.al. energy balance diagrams. Absorption of surface radiation does not have to balance the reduction in emission. And, as I pointed out above with the MODTRAN example, it doesn’t. That’s because most of the radiation emitted to space originates in the atmosphere, not the surface. When the optical density is high, it is nearly 100% absorbed. Peak emission intensity to space happens at the altitude where the optical density at a given wavelength, which decreases with increasing altitude, is 1.0. Increasing atmospheric absorption raises this altitude. Since emission is controlled by temperature, not concentration and temperature in the troposphere, where most emission originates, decreases with altitude, increased absorptivity means less emission.

We’ve told you this again and again. Also, your ‘net transmission’ term seems to mean different things at different times, none of which are clear.

I, for one, am no longer interested in getting you to see the light, as it were. Read a book. Grant Petty is a good one and is only \$36 direct from the publisher, Sundog, last I checked. That’s written at the advanced undergraduate level. Obviously, this means a familiarity with calculus at least, which seems based on the evidence of your posts, is beyond you. If that book makes no sense to you, or you disagree with it, you can’t be helped.

Cabellero’s Lecture Notes are no longer available for free. It will be published as an ebook by IOP sometime this year.

• on May 27, 2014 at 3:18 am DeWitt Payne

That’s increased absorptivity, not absorption. Absorption at lower altitudes is, as I noted above, effectively 100%. So it can’t be increased.

• Also, if this is correct — using the numbers in my example, it means if the net ‘T’ is 0.25, it means 100 W/m^2 of the spectrum of energy emitted by the surface is transmitted to space and the difference of 300 W/m^2, i.e. (1-0.25)*400, is the amount of the surface emitted spectrum that is absorbed by the atmosphere.

Again, either this is correct or it’s not. Everyone seems to be saying that it’s not.

• I said I was not talking about the direct surface transmittance.

• on May 25, 2014 at 2:57 pm | Reply DeWitt Payne

To put it another way: The absorption of surface radiation is 23% of the forcing, the other 77% is from reduced emission.

We keep telling you that your focus solely on absorption is why you don’t understand the overall process. It’s annoying that you keep coming back with little more than a rephrasing of your flawed concept.

• RW,

You seem to mean by net transmittance the ratio of outgoing radiation to the radiation from the surface. If that’s the case you must accept that the concept has no other meaning than that. It cannot be determined in any other way, no properties can be assumed for it, etc. It’s just a name for the result of a specific calculation (and might in principle be also measured).

Why do you consider that concept to be of any significance. I’m suspicious that you wish that some assumptions can be done on its constancy or something like that, but such assumptions cannot be done. The concept leads to no additional understanding.

A concept defined like that is problematic in other cases. We might look at downwelling radiation from a high cloud. For such radiation the net transmittance would be more than one. Does that make sense?

35. RW,

You would save yourself a lot of time, and make the world a happier place if you bought a couple of textbooks on radiation, like the one by Grant Petty, and studied them. Spending countless hours trying to get everyone to see the world in the same mysterious way you see it, and to answer the 100s of questions that mostly we can’t quite understand, is not very productive.

There is a reason why the many people answering questions on this blog think the same way, despite never having met, and never having studied in the same place.

I applaud your attempt to understand radiative transfer but your results to questions ratio seems extremely low.

If understanding and formulating equations are the difficulty get a second hand textbook on engineering maths, won’t cost you much, and will enable you to phrase your questions in a way that both question and answer will be illuminating. I expect that the “results to questions ratio” will go up by a factor of 10 to 100.

• In short, what I refer to as the net ‘T’ or ‘net transmittance’ is just the spectral transmittance, or the fraction of the surface emitted spectrum that is transmitted to space. If ‘A’ is defined as net absorption, then ‘A’ is just the fraction of the surface emitted spectrum that is absorbed by the atmosphere. ‘T’ is then just equal to 1-A and ‘A’ is equal to 1-T, where 1 is equal the power radiated from the surface. (*I fully understand that both ‘T’ and ‘A’ include emission that originates from the atmosphere and not just the surface — and in fact most of the emission, transmitted and absorbed, originates from the atmosphere and not the surface).

Ultimately, either RT simulations are fundamentally quantifying changes in net absorption and net transmittance for changes in GHG concentrations or they are not, and these changes — the ones considering opacity changes through the whole atmosphere — are weighted by the power density emitted from the surface and emitted Planck spectrum of the surface or they are not.

For the example of 4 W/m^2 for 2xCO2, the 4 W/m^2 is the additional amount or fraction of the surface emitted spectrum that is absorbed or captured by the atmosphere or it’s not.

• on May 28, 2014 at 2:18 pm DeWitt Payne

For the example of 4 W/m^2 for 2xCO2, the 4 W/m^2 is the additional amount or fraction of the surface emitted spectrum that is absorbed or captured by the atmosphere or it’s not.

It’s not. This is not the first time that you have been told this.

36. Looking at this another way, the 4 W/m^2 (really 3.6-3.7 W/m^2) from 2xCO2 is referred to as the net absorption increase, right. In your own words (or using equations), how would you articulate the physical meaning of ‘net absorption increase’ in this context. Net absorption increase of what specifically?

• on May 28, 2014 at 2:21 pm | Reply DeWitt Payne

the 4 W/m^2 (really 3.6-3.7 W/m^2) from 2xCO2 is referred to as the net absorption increase, right.

No, it’s not. It’s called a forcing.

how would you articulate the physical meaning of ‘net absorption increase’ in this context. Net absorption increase of what specifically?

You wouldn’t because your premise is wrong.

• Gunnar Myhre, who is the standard reference for the 3.7 W/m^2 in the literature, specifically said it is the net absorption increase.

• BTW, I have Grant Petty’s book and even asked him a few questions about some of this. Curiously, when I said the 3.7 W/m^2 is the ‘net absorption increase’ he knew and understood immediately what the 3.7 W/m^2 was.

• So something is amiss here.

• I note also above that you keep saying you don’t know what ‘net transmittance’ is. I’ll turn it back to you and ask you to define net absorption. Does it not follow that net absorption and net transmittance are directly related to one another?

• on May 28, 2014 at 2:07 pm DeWitt Payne

Why? Seriously. As pointed out over and over again, there is no more need for a definition of ‘net absorption’ than there is for ‘net transmittance’. In atmospheric radiative transfer, those concepts have no physical meaning. You can’t even easily define total emission as I pointed out above, to which you haven’t replied, btw. You can only define emission at a given altitude for a given layer thickness. If you don’t have total emission, you can’t define net emission. And you can’t define net transmittance or absorption either.

• on May 28, 2014 at 2:12 pm DeWitt Payne

You clearly have a physical concept in mind that is different from the standard view. You apparently need concepts like net transmittance and net absorption to support your preconception. Give it up. The standard physics works very well. There is every reason to believe that your concept is wrong.

• Hopefully, you can see where I’m going with this. If net absorption increases, it thus follows that net transmittance — of something at least — decreases, right? Do we at least agree that in order to have a net absorption increase, there needs to be net transmittance decrease? In more general sense, do you at least agree that for there to be an absorption increase there needs to be a transmittance decrease?

• RW wrote: “We don’t say net transmittance or the spectral transmittance is 10%, but we say the direct surface transmittance is 0.10.”

According to Google, the term “direct surface transmittance” has been used in five sources – four of them written by you (RW) at three different climate websites. This is a term you have invented.

I (and apparently others) object to your use of the term “transmittance” when describing the radiation traveling from a source to a destination or a detector is significantly INCREASED by emission from the intervening medium. Transmittance is defined as “the fraction of incident electromagnetic radiation at a specified wavelength that passes through a sample”, a definition that doesn’t consider the possibility that the sample emits some of the light that emerges from it. When emission is important, don’t use the term “transmittance”. Therefore I said above that 10% of the photons emitted by the surface “directly escape to space” – trying to avoid any implication that the outward flux at the TOA is only 10% of surface emission.

RW wrote: “The point is the TOA flux calculations are weighted by the spectrum of energy emitted from the surface and not the spectrums (of lower temperature) emitted in the atmosphere. Right?”

Wrong. SInce the TOA LWR flux averages 239 W/m2 (close to incoming post-albedo SWR) and since 10% of surface emission is only 40 W/m2, many more of the photons escaping to space are emitted from [GHG] molecules in the atmosphere than molecules on the surface. However, I wouldn’t say TOA emission is “weighted” by either source. The intensity of radiation (at all wavelengths) is CHANGED when it passes through a medium. Considering the fate of individual photons in the flux is unnecessary:

dI = emission – absorption
dI = n*o*B(lamba,T)*ds – n*o*I_0*ds = n*o*[B(lamba,T) – I_0]*ds

The only time the rate of change is zero is when the incoming light (I_0) has blackbody intensity (B(lamba,T)). In other words, blackbody radiation arises when radiation passes far enough through a homogeneous medium that absorption and emission have come into equilibrium. Unfortunately, the troposphere is not homogeneous in temperature, density or composition; and the radiation passing through it is always changing! The rate of change with distance traveled is proportional to the density of molecules in the path (n) and their cross-section for both emission and absorption (o).

When docking spacecraft, you can’t rely on familiar physics such as g = 9.8 m/s2, d = at2/2, and centripetal force = mv2/r. For example, accelerating a spacecraft takes it to a higher orbit where its orbital velocity is lower! You need to go back to fundamental physics: F = Gm1m2/r2 and F_x = m*(dx2/dt2) and numerically integrate acceleration over all three dimensions. Likewise, when dealing with atmospheric radiation, you need to numerically integrate the above Schwarzschild eqn (using MODTRAN for example) or trust the results of those who have. Concepts and intuition from laboratory spectrophotometers are inadequate.

• “RW asked: In more general sense, do you at least agree that for there to be an absorption increase there needs to be a transmittance decrease?

Absolutely NOT.”

Geez, I guess I should have added “of some sort” to the end of that question.
Can we agree?

• “In the KT energy balance diagram, about 10% of the photons emitted by the surface (about 400 W/m2) escape directly to space, but we don’t say that transmittance is 10% – because the actual average flux to space is 239 W/m2 (the amount needed to balance incoming post-albedo SWR).”

We don’t say net transmittance or the spectral transmittance is 10%, but we say the direct surface transmittance is 0.10.

I thought I clarified that I’m not referring to the direct surface transmittance. The point is the TOA flux calculations are weighted by the spectrum of energy emitted from the surface and not the spectrums (of lower temperature) emitted in the atmosphere. Right?

• The 10% of surface photons that escape to space indeed cool the surface. The 90% which are absorbed by the atmosphere are thermalised and then re-emitted multiple times by molecules throughout the troposphere. It is only because temperature falls with altitude that the “greenhouse effect” reduces radiation losses above a vacuum. The environmental lapse rate is fundamental to calculating the earth’s energy balance. This depends on CO2 levels and knock on effects on related H20 levels and clouds which remain the largest uncertainty. One analogy is that clouds modify the topology of the radiating surface – rather similar to the effect of mountain ranges such as the Himallayas. How all these secondary effects play out in the future is far from certain. I am sure some surprises are awaiting.

• RW asked: In more general sense, do you at least agree that for there to be an absorption increase there needs to be a transmittance decrease?

Absolutely NOT. Your thoughts are appropriate for experiments done with a laboratory spectrophotometer, but not the atmosphere. A spectrophotometer has a radiation source (lamp filament) with a temperature of several thousand degC. Its emission is intense enough to overpower emission from both the sample and everything else in the lab, which are near room temperature. Under these circumstances, radiation that is not absorbed IS transmitted. However, there is no law demanding conservation of radiation: absorption + transmission is not a constant. Conservation of energy does not USUALLY require conservation (or balance) of radiation or radiative flux.

In the atmosphere, both absorption and emission are important. Radiation traveling in any direction is reduced by absorption AND increased by emission. In the KT energy balance diagram, about 10% of the photons emitted by the surface (about 400 W/m2) escape directly to space, but we don’t say that transmittance is 10% – because the actual average flux to space is 239 W/m2 (the amount needed to balance incoming post-albedo SWR). More radiation leaves an average layer of the troposphere than is absorbed by that layer, because the troposphere is heated by latent heat from condensation of water vapor. More radiation can leave any object than is absorbed by that object, but conservation of energy demands that the object’s internal energy (temperature) decrease. Based on the rate of ocean warming measured with ARGO, we believe that 0.6 W/m2 more radiant energy is absorbed by the planet than is emitted to space.

37. Also, if there is a ‘net absorption increase’ there must be a prior total amount of net absorption, right? That is, unless net absorption is zero prior to the increase.

• on May 28, 2014 at 2:33 pm | Reply DeWitt Payne

We know the transmittance of surface emitted radiation from RT calculations. This was pointed out to you above, and you said:

I said I was not talking about the direct surface transmittance.

But then you say:

In short, what I refer to as the net ‘T’ or ‘net transmittance’ is just the spectral transmittance, or the fraction of the surface emitted spectrum that is transmitted to space.

And then:

(*I fully understand that both ‘T’ and ‘A’ include emission that originates from the atmosphere and not just the surface — and in fact most of the emission, transmitted and absorbed, originates from the atmosphere and not the surface).

Then why do you insist that the value of the emission is 400 W/m²? That is just the emission from the surface and does not include any of the emission from the atmosphere, which, as I pointed out above, is much, much greater than 400 W/m².

• “The forcing is calculated solely from the reduction in the integrated emission spectrum at the TOA”

But not the integrated emission spectrum of the surface?

• “The surface emission spectrum plays zero role in calculating the forcing.”

Huh? Zero role?

“In fact, it’s forced to be constant before and after the step change in ghg concentration.”

This seems like a contradiction to what you say above. I fully understand the surface spectrum is fixed before and after the step change in ghg concentration. That would not change of course until the surface temperature changed.

• on May 28, 2014 at 8:55 pm DeWitt Payne

Because the changes being calculated at the TOA are weighted or measured by the spectrum emitted from the surface.

No, they’re not. The forcing is calculated solely from the reduction in the integrated emission spectrum at the TOA after the stratosphere is allowed to equilibrate, or at the tropopause, there’s not much difference. The surface emission spectrum plays zero role in calculating the forcing. In fact, it’s forced to be constant before and after the step change in ghg concentration.

The temperature change required to reestablish radiative balance does affect the surface emission, but there is no change in surface emission until its temperature changes.

So something is amiss here.

Just because someone thinks they understand what you’re asking does not establish it as a scientific principle. It’s distinctly possible they were humoring you so you would go away.

Chapter 3 of Gerlich and Tscheuschner is full of quotes from scientists ‘explaining’ the greenhouse effect that lack scientific rigor.

• “Then why do you insist that the value of the emission is 400 W/m²?

Because the changes being calculated at the TOA are weighted or measured by the spectrum emitted from the surface.

• Which prior to 2xCO2, we know net absorption is not zero because we have a radiatively induced GHE already.

38. RW,

For me it has been rather obvious, what you mean with those words, but why did you start by asking

What is the physical meaning of ‘net transmittance’ for a multilayer atmosphere? What does this number quantify?

You have decided to use a concept that contains the word transmittance, but which is not a transmittance, but a new and somewhat misleading name for the ratio of OLR and surface emission. It’s nothing else. Please, stop bothering us by your pointless semantics. Forget the concept of net transmittance, when it is as useless and confusing as the above discussion shows.

39. Just to be absolutely clear, the context is a multi-layer atmospheric radiative transfer simulation.

• on May 28, 2014 at 9:35 pm | Reply DeWitt Payne

About which, you seem to understand little. What about the nearly 80 W/m² of incident solar radiation that is absorbed by clouds, water vapor, oxygen and ozone? That contributes to emission at the TOA too. All the energy emitted does not come solely from the surface.

By the way, the surface transfers energy to the atmosphere by convection as well as radiative emission. In fact, the net energy transfer by convection (~100 W/m² ) is greater than the net transfer by radiation ( ~66 W/m²). This energy transfer is important to the overall energy balance, as is the atmospheric absorption of incident solar radiation, which determines the total emission to space. You continue to ignore that and focus solely on the surface radiative emission. So your 400 W/m² number isn’t correct either. But that’s been pointed out to you over and over again too.

Ghg forcing is caused by a net reduction in transmission, not transmittance, of radiative energy to space. Transmittance has a specific meaning:

In optics and spectroscopy, transmittance is the fraction of incident light at a specified wavelength that passes through a sample.

Of course you can integrate over a transmittance spectrum and calculate an average transmittance, but that’s not how you’re using the term you call transmittance. T = (1-A) only when T is actually transmittance, not transmission.

Radiation is the only means that energy can be emitted by the planet to space. It’s not, however, the only means that energy can be transmitted from the surface to the atmosphere as well as within the atmosphere. You have to include conduction and convection in the atmosphere and at the surface, a concept that seems foreign to you despite the lip service you sometimes give it.

If the energy input remains constant, then the energy not emitted is absorbed by the system. However, attempting to do calculations based on an arbitrary ratio of the change in absorbed energy with the surface energy emission, particularly just the radiative emission, is nugatory (look it up).

• That is, the 4 W/m^2 is a decrease in transmission from what prior amount of transmission?

• “By the way, the surface transfers energy to the atmosphere by convection as well as radiative emission. In fact, the net energy transfer by convection (~100 W/m² ) is greater than the net transfer by radiation ( ~66 W/m²). This energy transfer is important to the overall energy balance, as is the atmospheric absorption of incident solar radiation, which determines the total emission to space. You continue to ignore that and focus solely on the surface radiative emission.”

What you are describing is relevant for determining the path the system takes from one equilibrium state to another, such as doubled CO2 — but doesn’t seem relevant to the issues surrounding radiative transfer simulation (i.e. what we are primarily discussing).

• “Ghg forcing is caused by a net reduction in transmission, not transmittance, of radiative energy to space. Transmittance has a specific meaning:

In optics and spectroscopy, transmittance is the fraction of incident light at a specified wavelength that passes through a sample.

Of course you can integrate over a transmittance spectrum and calculate an average transmittance, but that’s not how you’re using the term you call transmittance. T = (1-A) only when T is actually transmittance, not transmission.”

Now you seem to be parsing words. ‘Transmission’ quantifies a power flux density, where as ‘transmittance’ is a dimensionless fraction of a power flux density.

• Let me turn this around and ask you, if transmission decreases by 4 W/m^2 for 2xCO2, what was the total transmission in W/m^2 prior to the decrease?

• on May 29, 2014 at 12:32 am DeWitt Payne

I’m getting bored. I’ll just answer one of your points.

Now you seem to be parsing words. ‘Transmission’ quantifies a power flux density, where as ‘transmittance’ is a dimensionless fraction of a power flux density.

Of course I am. That’s what science is all about. Terms of art have to mean the same thing to everyone or communication fails, as it is clearly doing here. Transmittance, the term of art, is defined as a dimensionless fraction of the initial intensity (I/Io), not just any power flux density and is only measurable if sample emission is insignificant. That’s not true in the atmosphere thermal IR wavelengths.

We can calculate fairly accurately the transmittance of the surface radiation for a wide range of wavelengths for well mixed atmospheric gases knowing only the volumetric mixing ratio and the pressure vs altitude. Less accurately, we can add water vapor to the mix, but that requires that we know at least the humidity vs altitude profile as well. But we can’t measure transmittance for a full vertical column of the atmosphere for most of the thermal IR wavelength range because the atmosphere may also be emitting strongly at the same wavelength and the optical density can be so high that transmittance is nearly zero to many decimal places.

In the lab, it’s difficult to measure transmttance less than 0.001 for a variety of reasons. Atmospheric transmittance is much less than that at many wavelengths. Measuring the spectral flux density at the top and bottom of the atmosphere is in no way a measure of transmittance (T) or absorptance (A) (defined as 1-T), net or gross. Absorption is not the same thing as absorptance either.

If you want to make up your own physics, start your own blog and do it there.

• I don’t think I’m making up any physics. I’m certainly not trying to. SoD and many others outright acknowledge that radiative transfer is one of the most difficult things to understand and fully grasp. I think I’m asking more than fair questions, yet I don’t seem to be getting clear answers. Curiously some of the answers are confirming and some are denying, yet the claims seem to largely overlap and contradict each other. It may be that you and others are not fully understanding my questions (or why I’m asking), and perhaps that is somewhat my fault for not articulating them sufficiently. But I’m staunchly not trying to make up any physics — I’m genuinely trying to understand the accepted/established physics.

• I should further add that I don’t see the relevance of this agreed to point.

• “All the energy emitted does not come solely from the surface.”

Again, I’m well aware of this. There is no requirement that the calculated TOA fluxes must be all from energy that originated from the surface (either that radiated from the surface or that which leaves surface non-radiantly). Indeed some of it can be post albedo solar power absorbed by the atmosphere and re-radiated back up.

40. “It’s the reason you question the Trenberth, et.al. energy balance diagrams.”

Actually, I really don’t anymore, though I take many of the numbers with a grain of salt, including the 40 W/m^2 of direct surface transmittance (as recent papers show it more likely only about 20 W/m^2). My biggest gripe is the non-radiant flux from the surface of 102 W/m^2, which is not the net transfer from the surface to the atmosphere, i.e. up minus down, but is the total amount of non-radiant flux from the surface to the atmosphere. This effectively makes Trenberth’s model and equivalent model. I certainly agree with the basic depiction of more radiant energy/power entering the surface than leaving and it showing a decent amount of the post albedo solar flux being absorbed by the atmosphere. Other than the post albedo solar flux, the surface radiation flux and the non-radiant energy flux leaving the surface, I take the rest of the numbers with a grain of salt.

• on May 28, 2014 at 9:39 pm | Reply DeWitt Payne

My biggest gripe is the non-radiant flux from the surface of 102 W/m^2, which is not the net transfer from the surface to the atmosphere, i.e. up minus down, but is the total amount of non-radiant flux from the surface to the atmosphere.

Yes, it is the net transfer, not the total. No one bothers to try to calculate the total. I guess you could, but it seems pointless. Why you continue to think it isn’t the net transfer is beyond my comprehension.

• I should point out that I do agree that the net transfer is from the surface to the atmosphere. And as I said, I agree with the basic depiction of more radiant power entering the surface than leaving the surface.

• “I would point out to you that for there to be energy transfer to the surface, the atmosphere would have to be warmer than the surface.”

I don’t see why it would have to be given there is significant post albedo solar energy passing through the atmosphere to the surface. That and on average the temperature of the atmosphere is colder than the surface.

Maybe you mean net energy transfer, rather than additional net energy gained. I agree net energy transfer or flow must be from the surface to the atmosphere and not the other way around, because it’s required to satisfy the 2nd Law.

• “Yes, it is the net transfer, not the total. No one bothers to try to calculate the total. I guess you could, but it seems pointless. Why you continue to think it isn’t the net transfer is beyond my comprehension.”

Read the paper again — it’s the total amount not the net transfer. I too though it was the net transfer until someone pointed out it wasn’t. Then I read the paper again and found it is indeed the total amount.

• on May 28, 2014 at 9:52 pm DeWitt Payne

I would point out to you that for there to be energy transfer to the surface, the atmosphere would have to be warmer than the surface. That results in a temperature inversion, which, in the absence of wind, prevents convection. This is why you get dew and frost on surfaces on clear, calm, cold nights. The energy transfer from the atmosphere to the surface is tiny compared to the loss by radiation to a clear night sky.

Even with a wind blowing to minimize the thickness of the stagnant surface layer, conduction through that layer requires a large difference in temperature. That happens so little for transfer from the air to the surface that it can be ignored. In fact, energy transfer from the surface by convection, called sensible transfer, is small compared to latent transfer by evaporation and condensation of water, less than 20% of the total.
Evaporation and precipitation resulting in energy transfer from the surface to the atmosphere far outweighs the latent energy transfer in the other direction caused by the formation of dew or frost.

• on May 29, 2014 at 12:41 am DeWitt Payne

It is the total amount of the transfer from the surface to the atmosphere. The energy balance fails otherwise, and it doesn’t fail.

Total likely refers to the sum of sensible and latent transfer. I don’t need to read it again. You are the one that needs to read it again and provide the quote you think proves that you are correct and I’m wrong.

• I didn’t say Trenberth’s depiction fails to balance. It does balance, but the point is it’s an equivalent balance. That is the rates of joules gained at lost at the surface and the TOA are the same as the actual, measured/derived balance. The point is the 102 W/m^2 of non-radiant flux is the total amount of non-radiant energy leaving the surface, which is then then offset solely by direct radiant power from the atmosphere (or Sun). There is no offsetting component of non-radiant energy entering the surface from the atmosphere. If it were, the amount would not be 102 W/m^2, but an amount less and there would less direct radiant power emitted from the atmosphere to the surface.

The 324 W/m^2 of ‘back radiation’ (really just downward LW) is to be taken with a grain of salt as there is no way to get a global average of downward LW unless you have instruments ‘looking up’ all over the globe, which we don’t have.

• Page 7 (Trenberth 2009):

“GPCP values
are considered most reliable (Trenberth et al. 2007b),
and for 2000–04 the global mean is 2.63 mm day−1,
which is equivalent to 76.2 W m−2 latent heat flux. For the same period, global CMAP values are similar
at 2.66 mm day−1, but values are smaller than GPCP
from 30° to 90° latitude and larger from 30°S to
30°N. If the CMAP extratropical values are mixed
with GPCP tropical values, and vice versa, the global
result ranges from 2.5 to 2.8 mm day−1. In addition,
new results from CloudSat (e.g., Stephens and Haynes
2007) may help improve measurements, with prospects
mainly for increases in precipitation owing to
undersampling low, warm clouds. Consequently,
the GPCP values are considered to likely be low. In view of the energy imbalance at the surface and the
above discussion, we somewhat arbitrarily increase
the GPCP values by 5%, in order to accommodate
likely revisions from CloudSat studies and to bring
them closer to CMAP in the tropics and subtropics.
Hence, the global value assigned is 80.0 W m−2
(2.76 mm day−1).”

It’s just based on the global average rate of evaporation. There is nothing that indicates the 80 W/m^2 of latent heat flux represents the net transfer from the surface to the atmosphere. What makes you think that is what the 80 W/m^2 is a measure of?

• ” I don’t need to read it again. You are the one that needs to read it again and provide the quote you think proves that you are correct and I’m wrong.”

OK, let me find it again.

41. As I said, I too thought the 102 W/m^2 was non-radiant flux up minus non-radiant flux down at the surface/atmosphere boundary, but there is apparently nothing that indicates this in the paper. I assume you agree there is non-radiant energy flux from the atmosphere to the surface in the form of precipitation, wind, lightning, weather, etc. — all of which move energy non-radiantly from the atmosphere to the surface. There is no quantification of this component in Trenberth’s depiction.

• RW,

You are right in that the number 102 W/m^2 is the net non-radiant flux. There hasn’t been any attempt to determine the up and down non-radiant fluxes separately, but the flux from the atmosphere to the surface is much smaller, and actually very difficult to define separately.

There’s some non-radiant flux also from the atmosphere to the surface. Two forms of that come to mind:
– conduction, when air is warmer than the surface
– condensation on cold surfaces

Both of these are very much smaller than corresponding components in the opposing direction. Both occur typically during nights and are usually far less than day-time heat transfer at the same location in the opposite direction.

Measuring directly any of the nob-convective fluxes is extremely difficult on global scale. Therefore the numbers are estimates based on indirect arguments. Those arguments give the net, not up and down separately.

• “You are right in that the number 102 W/m^2 is the net non-radiant flux.”

The point is it’s not the net non-radiant flux, i.e. up minus down, but rather the total amount of non-radiant flux leaving the surface.

• Maybe that’s what you meant to say?

42. “I’m getting bored.

Either that or I’m asking logical questions you don’t know how to answer properly. Or perhaps never thought much about given the TOA flux changes for GHG concentration changes are the main focus.

I’ll repeat the critical questions:

If transmission (your term) decreases by 4 W/m^2 for 2xCO2, what was the total transmission in W/m^2 prior to 2xCO2 — from which the 4 W/m^2 is the incremental decrease in?

If absorption increases by 4 for 2xCO2, what was the total amount of absorption prior to 2xCO2 — from which the 4 W/m^2 is the incremental increase in.

There has to be an answer to this, because the +4 W/m^2 is not an arbitrary incremental increase and decrease of nothing or some unknown or unquantifiable thing.

• RW,

Net emission and net absorption of upwards radiation in the atmosphere are meaningful concepts and opposite of each other. Both are expressed in units of W/m^2 (or in W for the global total). Net transmission in the same units makes also sense.

The problem arises, when you switch to the relative value of net transmittivity, because the emission from the surface is only a fraction of all upwards gross emission. That’s the step that I see as totally unnecessary, potentially misleading, and so confusing that the outcome is the above exchange of comments.

43. RW asked: “If transmission (your term) decreases by 4 W/m^2 for 2xCO2, what was the total transmission in W/m^2 prior to 2xCO2 — from which the 4 W/m^2 is the incremental decrease in?”

Radiative transfer calculations are only possible when you define the temperature, composition and density at all altitudes. 4 W/m2 would be the instantaneous decrease in outward TOA flux from an instantaneous doubling in CO2. This 4 W/m2 is subtracted from the 239 W/m2 of LWR leaving the earth for space that balances the incoming post-albedo SWR absorbed by the surface and atmosphere. This imbalance will slowly cause the earth and atmosphere to warm until they again radiate a total of 239 W/m2. Note that I said the decrease in “outward TOA flux” not the decrease in transmission.

RW also asks: “If absorption increases by 4 [W/m2] for 2xCO2, what was the total amount of absorption prior to 2xCO2 — from which the 4 W/m^2 is the incremental increase in.”

As I discussed above, transmittance and absorptance (or transmission and absorption) are terms that are not useful in the atmosphere where EMISSION is important. When these terms are used, transmittance plus absorptance = 1; radiation that isn’t absorbed is transmitted. These principles are followed for a sample in a laboratory spectrophotometer which emits much less radiation than the lamp in the spectrophotometer. The situation in the atmosphere is complicated by emission. It is confusing, if not meaningless, to apply these terms to the atmosphere.

• “Radiative transfer calculations are only possible when you define the temperature, composition and density at all altitudes. 4 W/m2 would be the instantaneous decrease in outward TOA flux from an instantaneous doubling in CO2. This 4 W/m2 is subtracted from the 239 W/m2 of LWR leaving the earth for space that balances the incoming post-albedo SWR absorbed by the surface and atmosphere. This imbalance will slowly cause the earth and atmosphere to warm until they again radiate a total of 239 W/m2. Note that I said the decrease in “outward TOA flux” not the decrease in transmission.

This is not an answer to my question. I already know that the 4 W/m^2 is the decrease in TOA flux of 239 W/m^2. 239 W/m^2 at the TOA is not transmitted instantaneously prior to 2xCO2. The GHE exists prior to 2xCO2, which means there is radiative forcing prior to 2xCO2, though everyone responds as if otherwise. 2xCO2 is an increase in radiative forcing or an enhancement of the GHE.

• Perhaps a better way to ask this question is what is radiative forcing of the atmosphere prior to 2xCO2. How much upwelling IR in W/m^2 is absorbed by the atmosphere?

• on May 30, 2014 at 6:09 pm DeWitt Payne

If you do an RT simulation of GHG concentrations prior to 2xCO2, what is the net absorption?

You have never defined the term ‘net absorption’ adequately. Therefore it’s not possible to calculate it. You have been offered several definitions and either rejected them outright or failed to respond. I can think of only two definitions:

Anet = (1-Tnet) , 0≤Anet≤1 where Tnet is the calculated transmissivity for surface radiation only. That one you have rejected.

Anet = ∫ Inet(z)dz – I(∞) where z is altitude measured from the surface and Inet(z) is the net flux density upwards at altitude z, Inet(z) = (I(z)-T(z,z-dz)*I(z-dz) where T(z,z-dz) is the transmittance from z-dz to z and I(z) is the total flux density. The integration range is 0 to ∞. The units of An are then W/m². As both Pekka and I have pointed out, this is a number quite a bit larger than the value of I(0) ≅ 400 W/m² and is difficult to calculate or even estimate accurately. You continue to fail to accept or deny that this is a correct definition of ‘net absorption’.

If you don’t know the value of ∫ Inet(z)dz [z = 0 → ∞], then trying to look at the ratio of I(∞) to ∫ Inet(z)dz [z = 0 → ∞] and how it changes with CO2 concentration is rather pointless, like most of this discussion.

• The 4 W/m^2 of net absorption increase4 for 2xCO2 — what is net absorption in W/m^2 prior to 2xCO2? It’s not zero, right? What is it?

If you do an RT simulation of GHG concentrations prior to 2xCO2, what is the net absorption? When I say 239 W/m^2 is not transmitted instantaneously — I just mean there is an amount instaneously captured by the atmosphere (as opposed to being transmitted to space). The 4 W/m^2 is the incremental increase in that which is instantaneously captured.

• I looked at the numbers from one radiative transfer calculation based on the US standard atmosphere. The numbers are not right for the full real atmosphere, but they have a message.

In that calculation
– the emission from the surface is 391 W/m^2
– the outgoing flux to space is 261 W/m^2
– the upwards emission within the atmosphere is 1472 W/m^2
– the absorption of upwards radiation in the atmosphere is 1602 W/m^2

Thus the total emission and absorption in the atmosphere are several times larger than the emission from the surface. This general observation is true also for the real atmosphere although the numbers are significantly different from this single clear sky case.

When the absorption and emission within the atmosphere are so dominating, it does not make sense to use that kind of concept of “net transmissivity” RW has been proposing.

• RW asked: a) “What is radiative forcing of the atmosphere prior to 2xCO2?” b) How much upwelling IR in W/m^2 is absorbed by the atmosphere?

a) Radiative forcing is the instantaneous radiative imbalance created by a CHANGE from typical “pre-industrial conditions”: doubling CO2, a drop in solar output, increased reflection by aerosols in the stratosphere after a volcanic eruption, etc. By definition, the radiative forcing for 1XCO2 is zero. The greenhouse effect existed before anthropogenic GHG’s, but radiative forcing “did not exist” in some senses because it was zero.

b) The KT energy balance diagram says that 356 W/m2 of surface emission is absorbed by the atmosphere (including clouds).

RW says: “239 W/m^2 at the TOA is not transmitted instantaneously prior to 2xCO2”

This statement appears to be wrong. Before anthropogenic forcing became significant, 239 W/m2 WAS both the downward flux of post-albedo SWR and the TOA outward flux of LWR. Outward flux is the amount of power passing through a plane per unit area. Your use of the term transmitted is confusing since it implies “transmission” through some distance with possible losses due to absorption and possibly gain due to emission.

Based on the rate of heat accumulation in the ocean measured by ARGO, the best estimate is that 0.6 W/m2 more power is being delivered by SWR than is currently escaping as LWR. The total forcing (reduction in TOA flux) is about 2 W/m2, but the earth has warmed enough to increase LWR by about 1.4 W/m2.

44. on May 30, 2014 at 5:01 am | Reply John Millett

Frank, May 29, 9.26PM

Your reference to a cooling stratosphere, because increasing CO2 would cause emission, [B(Lamda,T)], to exceed absorption, I_0, puzzles me. Let me propose a slightly different view.

The stratosphere is warming, not cooling, as altitude increases. Increasing CO2 would affect emission and absorption equally at all altitudes. Stratospheric temperatures would continue to rise with altitude. Temperature reduction and cooling would occur in the next zone up. Solar radiation, at constant intensity, is the dominant agent in the warming zones. Its absorption, by reducing densities of absorbers as altitudes increase, causes higher temperature at the lower densities. In the stratosphere I_0 would include the solar effect and would exceed [B(Lamda, T)]. In the next zone up, the solar effect reduces to zero and the equation reverts to emission exceeds absorption and temperatures fall.

• John,
The energy balance at some specific point of the upper stratosphere has three main components:

1) warming from absorption of solar radiation, mostly UV
2) warming from absorption of IR coming from the other parts of the atmosphere. This occurs mostly at the strongest peaks around 15 µm.
3) cooling from emission of IR. This occurs again mostly at the strongest peaks around 15 µm.

These three components must sum to zero to have balance. Thus the difference between emission and absorption of IR must equal absorption of solar radiation. That balance is reached at a rather high temperature. Therefore upper stratosphere is warmer than lower stratosphere.

Increasing CO2 has very little influence on absorption of solar radiation, but it increases both the emission and absorption of IR. When both grow the larger (i.e. emission) grows faster. Therefore the upper stratosphere cools from the earlier value. That continues until a balance is reached again at a lower temperature (but still at a warmer temperature than that of the lower stratosphere).

• on June 1, 2014 at 1:46 am DeWitt Payne

John,

The key to whether temperature increases or decreases with altitude is the ratio of the absorptivity of incident solar radiation to the absorptivity of LW IR radiation. If the ratio is greater than one as it is in the stratosphere, temperature increases with altitude. If it’s lower than one, as it is in the troposphere, in part because all the short wavelength UV has already been absorbed, temperature decreases with altitude. The tropopause is the crossover point. Well, it’s more complicated than that, but it’s one way to look at it.

• Clive,

You got all right as far as can see.

• on June 1, 2014 at 1:22 am John Millett

Thank you Pekka,

This is how I visualise the atmosphere:

The tropopause delimits the minimum density and temperature of the troposphere. It is reached by a continuous process of IR absorption and emission in which emission exceeds absorption, as you say, until they come into equilibrium which continues for a short distance into the stratosphere.

Thereafter in the stratosphere’s continuous process absorption exceeds emission and the stratosphere warms, implying that absorption of solar radiation exceeds the (negligible) difference between IR emission and absorption and practically alone drives the warming. It does so by acting upon increasingly less density of absorbers through the height of the stratosphere.

Your last paragraph says to me that the upper stratosphere is always warmer than the lower but cooler than it would be with lower densities of CO2, the whole being IR-driven. The question posed for me is: What induces the stratospheric reversion to the tropospheric emission-absorption relationship after that relationship reaches equilibrium at the tropopause and continues briefly into the stratosphere?

• John,

One way of stating the difference is:

– In the stratosphere there’s very little vertical transport of energy in any other way than by radiation. Therefore the temperature is determined by local radiative energy balance at every altitude. Total emission of radiation is equal to to total absorption. Emission of IR is larger than absorption of IR the difference being absorption of solar SW.

– In the troposphere radiative energy transfer is only part of the total, and the temperature profile is controlled by convective energy transfer. Radiation alone would make the lapse rate larger. That leads to instability and so much convection that stability is reached. Total emission of radiation is smaller than total absorption of radiation, the difference is covered by convective energy transfer. Absorption of solar SW is not very important. Therefore emission of IR is also smaller than absorption of IR except near the tropopause, where solar SW has some more influence.

This is the fundamental difference. Within the troposphere radiative energy transfer affects the temperature essentially only

1) by making it troposphere, i.e. by trying to induce a lapse rate larger than the stability limit.

2) by determining the overall temperature level.

Thus radiative energy transfer determines both the altitude of tropopause and its temperature. Combining that with the lapse rate determined by convective processes temperatures are determined at all altitudes of the troposphere and the surface.

• Pekka,

This is indeed an excellent explanation of net energy transfer through the atmosphere. Let me see if I understand all this properly?

If hypothetically there was no convection then the lapse rate would just be determined by pure radiative equilibrium leading to a far steeper lapse rate with a high surface temperature. The upward radiative energy flux induces adiabatic convection and evaporation which reduces the lapse rate towards the (moist) adiabatic lapse rate. This also drives the earth’s weather systems and Hadley cells

The tropopause is the height where the net IR radiative transfer becomes zero and convection stops. This happens when transmission becomes > absorption . Above this height the air is stratified and temperature is mainly determined by the balance between absorbed UV and emitted IR. A doubling of CO2 in the stratosphere would actually increase IR losses in the central 15 micron band.

• John: I prefer to consult the Schwarzschild eqn. For the strongly absorbed 15 um CO2 band, both absorption and emission are in equilibrium through the troposphere with the intensity of radiation entering any layer (I_0) roughly equal to B(lamba,T). At the tropopause, the intensity of the 15 um radiation entering the stratosphere is B(15 um, 215 degK). This radiation enters the warmer stratosphere, which has been heated by solar UV to as high as 270 degK. Using these values in the Schwarzschild eqn:

dI/ds = n*o*{B(lamba,T) – I_0}
= n*o*{B(15 um, 270 degK) – B(15 um, 215 degK)}

The term in brackets is obviously greater than zero, so doubling n will increase dI/ds – removing more energy from the stratosphere and transporting it to space (and the troposphere).

Increased CO2 wouldn’t cool the stratosphere is it wasn’t warmed by absorption of solar UV.

• on June 1, 2014 at 3:35 am John Millett

Frank,

A quibble about how much, not whether, dI/ds changes – it seems to me that taking n*o* outside the brackets carries some risk – n is not constant within the troposphere and is unlikely to be so in the 2-3 times larger extent of the stratosphere. How much change is all due to the intensity difference between entering IR and solar radiation.

At the tropopause and for a brief distance into the stratosphere, n has become constant along with equilibrium between emission and absorption of 15 um. Would doubling n affect this condition? I don’t think it would. What, then, would cause a change of IR behaviour in the rest of the stratosphere?

45. DeWitt, Pekka, RW, SOD: Do the terms absorption/absorptance and transmission/transmittance have a clear meaning or utility in describing radiation traveling from Location1 to Location2 through the atmosphere, if emission contributes to the intensity arriving at Location2?

If one considers only photons of one particular wavelength, some photons may make the trip without ever being absorbed. In other cases, one might envision part of the distance being covered by photon1, a second leg being covered by photon2 and the remaining segment by photon3. Three hv of energy is absorbed and three hv of energy was emitted, producing 1 hv of flux. Was 1 hv of energy “transmitted” from Location1 to Location2? What do we say about the photons that were emitted in the opposite direction (Location2 to Location1)? Do they cancel some of the transmission?

I’ve avoided these questions by relying on the Schwarzschild eqn to calculate changing flux without describing the mechanistic details.

On May 30, 2014 at 8:28 am, Pekka calculated the total energy absorbed and emitted along such paths. To do so, he integrated the Schwarzschild eqn using atmospheric layers thin enough that their composition and temperature could be treated as constants and I_0 is also a constant. However, for the 15 um CO2 absorption, I_0 is a constant because absorption and emission are in equilibrium, not because the layer is thin enough that their is negligible chance of a photon being absorbed before it escapes a layer. Could Pekka’s calculation have missed a number of absorptions and emissions because they took place within a layer?

• on May 30, 2014 at 8:11 pm | Reply DeWitt Payne

Frank,

You can calculate transmittance and absorptance for a path through the atmosphere ignoring emission, you just can’t measure it. One would have to define mathematically what one meant by transmission or absorption for those terms to have physical meaning.

Photons traveling in the opposite direction can be ignored.

Could Pekka’s calculation have missed a number of absorptions and emissions because they took place within a layer?

Probably. One would have to make several calculations with thinner and thinner layers to see when layer thickness stopped making a significant difference. Going from a viewing height in MODTRAN from 0 km to 0.01 km changes the average transmittance from 0.8230 to 0.6467 from 100-1500 cm-1 and there are frequency ranges where the transmittance is already zero to four decimal places. At 0.10 km, it’s 0.4370. As you moved higher in the atmosphere, the layer thickness could increase. I would try for approximately constant mass/layer. Since water vapor is the major player at low altitude, probably constant mass of water vapor initially.

• “The fraction of the surface spectrum that is being transmitted/absorbed already.”

Or the transmittance/absorption overlap of the surface spectrum.

• One could define transmittance and absorbance as the fraction of PHOTONS that do and don’t pass through a “sample”. The atmosphere could be a sample. When emission is significant (as in the atmosphere), one can’t directly measure these quantities – the flux leaving the “sample” includes both transmitted and emitted photons.

I suspect that little climate science depends on the transmittance of the atmosphere as defined above. If only 5% of the photons emitted by the surface escaped directly to space (5% transmittance), the atmospheric emission to space in the KT energy balance diagram would be adjusted upward by 20 W/m2. The detectors in space measure the total LWR flux.

• on May 31, 2014 at 8:09 pm DeWitt Payne

Frank,

I suspect that little climate science depends on the transmittance of the atmosphere as defined above.

Which is precisely the point we have been trying to make to RW. It’s not the details of the absorption and emission within the atmosphere that are important, it’s the energy balance at the top and bottom.

• From RW’s recent comments it appears clear that he has now a rather good understanding of the situation. That leaves me, however, even more puzzled over his insistence to discuss concepts that are not appropriate for describing radiative energy transfer through the atmosphere.

• “Which is precisely the point we have been trying to make to RW. It’s not the details of the absorption and emission within the atmosphere that are important, it’s the energy balance at the top and bottom.”

I’ve essentially said this myself. The terms ‘net absorption’ and ‘net transmittance’ as I’ve been using them are specifically those affecting the TOA flux in relation to the energy balance at the surface; hence their importance. Geez.

• RW: When you use the word “net” in “net transmittance” or “net absorption”, you are implying that something is being excluded or subtracted from the transmittance. Transmittance is already incident radiation minus absorption. What else is being subtracted? In practice something is being added – emission.

DefinitionNET

1) free from all charges or deductions: as
a) remaining after the deduction of all charges, outlay, or loss — compare gross
b) excluding all tare
2) excluding all nonessential considerations : basic, final

Perhaps you are trying to define “net absorption” as absorption minus emission. Then “net transmission” would be the incident flux minus “net absorption”. In this case, the normalized values, “net transmittance” and “net absorptance”, could be greater than 1.

• I also understand that the term ‘transmittance’ is more typically defined and thought of as simply the amount of incident radiation that passes through a single layer, but it’s also defined as that which passes through a ‘sample’. In this case, the sample is the whole mass of the atmosphere from the surface to the TOA. That is, I believe ‘net transmittance’ specifically quantifies something about the path of radiation from the surface to the TOA. Or more specifically it quantifies the fraction of the surface spectrum that is instantaneously transmitted to space, where as ‘net absorption’ quantifies the fraction of the surface spectrum that is instantaneously captured by the atmosphere.

• RW,

Remember that my corrected calculation told that less than 0.1% of all upwards emitted radiation exits the atmosphere or originates from the surface. More than 99.9% is both emitted and absorbed within the atmosphere. Transmission of radiation is thus a very weak process and describing the outgoing radiation as transmitted in any sense does not sound a good description. Therefore the concept of net transmission of radiation is highly questionable.

• “RW: When you use the word “net” in “net transmittance” or “net absorption”, you are implying that something is being excluded or subtracted from the transmittance.”

Yes.

“Transmittance is already incident radiation minus absorption. What else is being subtracted?”

The fraction of the surface spectrum that is being transmitted/absorbed already.

• Frank,
My calculation is certainly not accurate. It’s based on SoD’s radiative transfer model, which does perhaps not handle the optically thick layers as correctly as possible. It does not have any special provision for handling situations, where the mean free path is not larger than layer thickness. It seems, however, to be the case that this has relatively little influence on the final outcome. (Comparing calculations with a different number of layers tells, how serious the related error is, and my recollection is that the error is found to be rather small.)

Based on rapid check of the code, I think that the model calculates the total emission more correctly than some other details. (I didn’t study this point carefully.)

• on May 30, 2014 at 10:44 pm DeWitt Payne

I don’t think that layer thickness has much effect on total flux once you get to 30 layers or so. It might depend somewhat on whether you use the average layer temperature for all wavelengths or use the layer top temperature for strongly absorbing wavelengths. Layer thickness may have a stronger effect on net flux, though.

In fact, another quick and dirty. MODTRAN from 0 to 0.5 km at 100 m intervals calculates as 1030 W/m² absorbed while as a single step, it’s 293 W/m². And at 100m thickness, many frequency bands have zero transmittance so smaller steps would still significantly increase absorption. I may do 0 to 0.1 km in 20 m step just out of curiosity.

• on May 30, 2014 at 11:36 pm DeWitt Payne

Twenty meter steps looks like somewhat more than a factor of two increase in absorption compared to 100 meter steps. A two meter step is another significant increase, but at that point the layer absorption isn’t zero for any wavelength and the number of highly absorbing bands is fairly small, so probably not a whole lot more to gain by going to smaller steps. So in round numbers, the total absorption for the first 100 meters is going to be on the order of 5,000 W/m².

• DeWitt,

As I wrote (having some uncertainty at the time), SoD’s model calculates the full emission essentially correctly even with thick layers as it doesn’t take into account absorption within the emitting layer. This should probably be changed for other calculations, but in this case the result is more correct.

The upward flux at the top of the atmosphere does not change very much due to this crude approximation of the model, because the absorption in the next layer is very high in all cases, where the absorption in the emitting layer is important, and because the optical depth decreases gradually moving up to the topmost layers.

• My previous message is not correct. When i looked more carefully at the code I realized that I had misinterpreted one variable. Thus the total emission is significantly larger than the number I gave, and the model works on this point similarly with MODTRAN.

• It was also easy to add one more variable to simply add up total emission. The resulting value is still very much higher (by factor of about 300) than the one I got based on false interpretation of the variables. Thus less than 0.1% of all emission exits the atmosphere.

46. “Remember that my corrected calculation told that less than 0.1% of all upwards emitted radiation exits the atmosphere or originates from the surface. More than 99.9% is both emitted and absorbed within the atmosphere.”

I don’t know where you’re getting these numbers, but the direct surface transmittance is agreed to be about 5-10% — at least on global average for Earth. Moreover, the amount of the direct surface transmittance is not germane to the concept of ‘net transmittance’ as it applies to a multi-layer RT simulation, as only a small fraction of the direct surface transmittance contributes to the ‘net transmittance’.

• “You appear to be the only one who thinks this. You’ve also never explained why you think it’s fundamental.”

Because it specifically quantifies the total radiative forcing of the GHE as it applies to the surface energy balance prior to the incremental increase for 2xCO2.

• It’s one way of expressing the final result of the radiative transfer calculation. You seem to be the only one to think that it’s in somehow a good way, while others who have commented here think that it’s a poor and useless way.

Knowing this number for one case does not help in any way in estimating, what happens in other cases, they must be calculated exactly as without knowing this number for the first case.

• That is, prior to the imposed imbalance from 2xCO2, the power radiated from the surface is equal to the net power gained at the surface, which is the net result of all of the effects, radiant and non-radiant, known and unknown — that occur in between the boundary of the surface and the TOA (and really also that occur from the surface to other parts of the surface, like oceanic circulation currents).

‘Net absorption’ is the amount of this surface power density that is instantaneously captured by the atmosphere and is what is driving the GHE or the +33C (+150 W/m^2 of net gain) measured/derived at the surface.

• “Knowing this number for one case does not help in any way in estimating, what happens in other cases, they must be calculated exactly as without knowing this number for the first case.”

Yes, I do understand that the incremental changes calculated at the TOA are the primary focus; however, if the +3.7 W/m^2 is the net absorption increase, it’s important to understand what the quantification of net absorption is and why it’s the specific measure for quantifying so-called ‘radiative forcing’ of climate.

• Also, this was a concept disputed here in a discussion some time back, though I don’t specifically remember what thread. That is, it was disputed that there was a total power flux in W/m^2 considered to be absorbed (and transmitted) by the atmosphere and that it was a fraction of the power density emitted by the surface.

• Also, I don’t understand how you could think it’s not important to know if the +3.7 W/m^2 is specifically an increase in net absorption and a decrease in net transmittance. This seems to be about a basic as it gets so far as understanding what ‘radiative forcing’ actually is a measure of.

• on June 2, 2014 at 2:37 pm | Reply DeWitt Payne

I don’t know where you’re getting these numbers

Pekka and I explained in great detail how that number was obtained. Either you didn’t bother to read the series of comments above here and continuing here, or you’re incapable of understanding. I lean towards the latter interpretation, which is why I’m largely ignoring you.

‘Net transmittance’ is a term that has meaning only to you. You have never written an equation that defines it. In spectroscopy, transmittance has a specific meaning. It’s a measure of attenuation solely, T = I(z)/I(0) where I(z) is always less than I(0). There is no ‘net’ transmittance, only transmittance.

If you mean the ratio of the flux density at the top of the atmosphere to the flux density at the surface, we’ve also explained in great detail why that number has little meaning. And the change in that ratio after instantaneous doubling of CO2 has, if anything, less meaning.

• That should say:

“as the direct surface transmittance only contributes a small fraction of the ‘net transmittance”.

• RW,

You are the only one, who can tell anything about net transmittance, because you are the only one, who thinks that the concept exists for the atmosphere. All the others have just explained, why they dislike the idea of using that expression.

• Yes, I believe it is a key concept because it quantifies the specific amount of power in W/m^2 that is instantaneously transmitted and absorbed by the atmosphere, and that the +4 W/m^2 for 2xCO2 is the incremental decrease/increase of each. I also think it is the most fundamental thing to understand so far as what is ultimately being calculated by a multi-layer atmospheric RT simulation.

• on June 2, 2014 at 2:39 pm DeWitt Payne

I also think it is the most fundamental thing to understand so far as what is ultimately being calculated by a multi-layer atmospheric RT simulation.

You appear to be the only one who thinks this. You’ve also never explained why you think it’s fundamental.

47. Above, Frank asked RW: When you use the word “net” in “net transmittance” or “net absorption”, you are implying that something is being excluded or subtracted from the transmittance. Transmittance is already incident radiation minus absorption. What else is being subtracted? In practice something is being added – emission.

RW replied on June 2, 2014 at 1:21 am: “What else is being subtracted? The fraction of the surface spectrum that is being transmitted/absorbed ALREADY.” (my emphasis) “Or the transmittance/absorption overlap of the surface spectrum.”

The word “already” suggests that RW is concerned with what happens both before and after CO2 doubles. About 10% of the photons emitted by the surface escape directly to space through 1XCO2 and this won’t change appreciably when CO2 doubles. The few photons that escape directly to space have wavelengths that aren’t absorbed significantly by GHGs. To a first approximation, those photons aren’t important to radiative forcing or the GHE.

90% of the photons that escape to space are emitted by GHGs in the atmosphere. Photons emitted by GHGs are also absorbed by GHGs. That is why other commentators are trying to direct your attention away from transmittance and absorption – terms aren’t defined or useful when EMISSION is important. The GHE and radiative forcing take place at the wavelengths GHGs emit – and absorb – not the wavelengths that let a few photons escape directly to space!

When you attempt to understand radiative forcing in terms of transmittance , you will always be left confused about radiative forcing. Something important IS missing.

Forget transmittance and consider some general principles applicable to the atmosphere (where radiative forcing arises), not the surface: With 2XCO2, there are twice as many CO2 molecules in the atmosphere emitting photons, but less chance that any photon emitted by a CO2 molecule will escape to space. If f is the chance that an upward emitted photon escapes directly to space from a certain altitude through 1XCO2, then f^2 is the chance of escape through 2XCO2 (assuming other GHGs don’t interfere). The characteristic emission level is the altitude from which the average photon escapes to space. With 2XCO2, the characteristic emission level will be higher – and therefore colder – than with 1XCO2. Fewer photons are emitted from CO2 molecules at higher altitudes of the troposphere. Unfortunately, these general principles conflict with each other and therefore don’t tell anyone whether doubling CO2 will increase or decrease the radiative flux to space! Only calculations using the correct physics equations can provide an answer:

dI = emission – absorption (along a path)
dI = n*o*B(lamba,T)*ds – n*o*I_0*ds = n*o*[B(lamba,T) – I_0]*ds

For OLR passing through the troposphere, I_0 comes from the warmer surface or warmer lower altitudes, so the [B(lamba,T) – I_0] term is negative. (I_0 arises from B(lamba,higher T)). In that case, doubling CO2 (doubling n) reduces the outward flux. The size of the change requires detailed calculations (which take into account overlapping absorption bands). One also needs to consider the change in DLR.

• Which requires the atmosphere and ultimately the surface to warm by some amount in order to re-establish equilibrium with space (or least this is the basic theory of CO2 induced global warming).

Note I’m not disputing any of this kind of basic stuff. Actually, I’m not really trying to dispute much of anything here — rather I’m trying to understand the fundamentals and the actual physical meaning of what a multi-layer atmospheric RT simulation calculates in the case of 2xCO2 and increased ‘radiative forcing’ from increased GHGs.

• RW: When one moves from the radiation imbalance at the TOA to the radiation imbalance at the tropopause, one needs to consider the enhanced DLR from 2XCO2 coming from the stratosphere into the troposphere. There is about 19.6 (1XCO2) or 21.2 W/m2 (2X) of DLR coming down through 12 km according to Modtran in the US Standard atmosphere without clouds. This 1.6 W/m2 difference isn’t miniscule. The difference is similar at 17 km.

At the tropopause, “net” refers to the change in the OLR FLUX minus change in DLR FLUX (and SWR, if any). When one is discussing the radiative imbalance at the TOA, there is no need for the term “net”. I brought up the difference between the tropopause and the TOA simply because it provided one possible rational for your use of the term “net” and it explains what is being subtracted (DLR).

Above, I wrote (with emphasis now added): “You would be using the correct terminology if you said 240 W/m2 of 390 W/m2 of surface flux is transmitted through the atmosphere, and this transmission drops to 236 W/m2 with 2XCO2. Unfortunately, this statement is GROSSLY MISLEADING because it IGNORES EMISSION and the fact that 90% of the photons comprising the 390 W/m2 of surface flux fail to escape to space.” It is possible to describe forcing as a 3.7 W/m change in FLUX rather than a change in TRANSMISSION. Why continue to use the term that other commenters find misleading??? Is there something wrong with “flux”? Adding “net” to make “net transmission” doesn’t help, because no one knows what is subtracted. You appear to be implying subtraction by absorption and addition by emission, but the term transmission already accounts for subtraction by absorption. When emission isn’t important, “transmission” means “after absorption” and “net transmission” leaves readers wondering what else is subtracted besides absorption.

Much of this is mere terminology, but life it much less complicated when terms mean the same thing to everyone. Equations are even better for the same reason. Most readers won’t assume emission is included when you use the term transmission (or transmittance).

Yes, there was a GHE before CO2 rose, but – by definition – radiative imbalance or forcing was 0 W/m2 before CO2 began to increase enough to change the mean global temperature (1850-1930). Net flux at the TOA is SWR-OLR. Net flux at the tropopause is SWR+DLR-OLR. That DLR is emitted from the stratosphere.

• I note also that you are referring to the 3.7 W/m^2 a the ‘net change in flux’ rather than a change in net absorption and net transmission, as I’m referring to it. My question is how are you defining and quantifying ‘net flux’ in W/m^2 prior to 2xCO2?

You do agree there is a radiatively induced GHE prior to 2xCO2, right?

• RW: 3.7 W/m2 is NOT the “net absorption” increase or the “net transmission” decrease; it is the net change in the FLUX of radiation leaving the troposphere. The OLR flux in much of the troposphere is mostly due to atmospheric emission and the DLR flux (333 W/m2 at the surface according to KT) is ALL due to atmospheric emission.

Technically, 3.7 W/m2 is the change in the net flux across the tropopause after the stratosphere has adjusted to 2XCO2 (not the reduction in the net flux at the TOA). In this case, “net” means OLR – DLR (including changes, if any, in SWR caused by doubling CO2).

Flux is a flow across a plane: ONE plane. Absorption is the difference in flux at TWO different locations (planes), when emission is NOT important. Transmittance is the RATIO of fluxes at TWO different locations (when emission isn’t important) and is a dimensionless number less than 1 (not something reported in W/m2). Transmission and absorption are measured in W/m2, but they both involve two locations and the assumption that no emission occurs between them. If you understand the basics, it helps if you use the correct terminology. 3.7 W/m2 is a change in the flux across the tropopause.

You would be using the correct terminology if you said 240 W/m2 of 390 W/m2 of surface flux is transmitted through the atmosphere, and this transmission drops to 236 W/m2 with 2XCO2. Unfortunately, this statement is grossly misleading because it ignores emission and the fact that 90% of the photons comprising the 390 W/m2 of surface flux fail to escape to space.

• Frank,

The so-called stratospheric adjustment is miniscule, so why even bother to include it or mention it? It’s really not relevant to what we are discussing. Besides, after the ‘adjustment’, the net change at the TOA is still about 3.6-3.7 W/m^2, which is about the amount instantaneously calculated at the TOA anyway.

You seem to be arguing semantics, so it’s hard to know how to respond (or what to respond to). Yes, technically when referring to the 3.7 W/m^2, it would be the net transmission decrease and not the net transmittance decrease. It would also be the net absorption increase, but the ‘net’ — as I’m using it — is referring to the absorption of upwelling LW radiation, independent of how much post albedo solar power is entering the system. You seem to be conflating the IPCC’s definition of RF with what is being calculated via the RT simulation.

• “90% of the photons that escape to space are emitted by GHGs in the atmosphere. Photons emitted by GHGs are also absorbed by GHGs. That is why other commentators are trying to direct your attention away from transmittance and absorption – terms aren’t defined or useful when EMISSION is important. The GHE and radiative forcing take place at the wavelengths GHGs emit – and absorb – not the wavelengths that let a few photons escape directly to space!”

I have already said I know and/or agree with all of this. Have you read all my posts? For the 2xCO2 case, each layer absorbs a little more from above and below and subsequently emits a little more both upwards and downwards. The calculated -3.7 W/m^2 at the TOA is net effect after all of these things have occurred ‘instantaneously’.

This doesn’t change that ultimately the 3.7 W/m^2 is still the net absorption increase and the net transmittance decrease of the surface emitted spectrum of energy (and not some other spectrum or combination of spectrums). That is, it’s the reduction in the amount of the surface spectrum that is instantaneously transmitted to space, or the 15u centered ‘valley’ widening from 2xCO2 slightly reduces the amount of the surface spectrum that is instantaneously transmitted directly into space.

• I note also that you are referring to the 3.7 W/m^2 a the ‘net change in flux’ rather than a change in net absorption and net transmission, as I’m referring to it. My question is how are you defining and quantifying ‘net flux’ in W/m^2 prior to 2xCO2?

You do agree there is a radiatively induced GHE prior to 2xCO2, right?

48. Frank,

“RW: When one moves from the radiation imbalance at the TOA to the radiation imbalance at the tropopause, one needs to consider the enhanced DLR from 2XCO2 coming from the stratosphere into the troposphere. There is about 19.6 (1XCO2) or 21.2 W/m2 (2X) of DLR coming down through 12 km according to Modtran in the US Standard atmosphere without clouds. This 1.6 W/m2 difference isn’t miniscule.”

I’m going by what’s in Myhre’s paper. The ‘stratospheric adjustment’ is less than 0.1 W/m^2 (I recall about 0.06 W/m^2).

“It is possible to describe forcing as a 3.7 W/m change in FLUX rather than a change in TRANSMISSION. Why continue to use the term that other commenters find misleading??? Is there something wrong with “flux”? Adding “net” to make “net transmission” doesn’t help, because no one knows what is subtracted. You appear to be implying subtraction by absorption and addition by emission, but the term transmission already accounts for subtraction by absorption. When emission isn’t important, “transmission” means “after absorption” and “net transmission” leaves readers wondering what else is subtracted besides absorption.”

I thought I explained this clearly. My use of the word ‘net’ in the context of net transmission and net absorption is the amount of surface spectrum in W/m^2 that is being absorbed and transmitted already. By ‘transmitted’ I mean that amount which passes into space and by ‘absorbed’ I mean that amount blocked or attenuated from passing into space.

“Yes, there was a GHE before CO2 rose, but – by definition – radiative imbalance or forcing was 0 W/m2 before CO2 began to increase enough to change the mean global temperature (1850-1930).”

In a kind of proprietary IPCC definition sense, yes, but not in a raw physics sense. In reality, the 3.7 W/m^2 is the incremental increase in radiative forcing or an enhancement of the already existing radiatively induced, i.e. ‘forced’, GHE. This is a key question for you and everyone — and one I note that you don’t seem to be able to answer. That is, what is the total radiative forcing in W/m^2 driving the GHE prior to 2xCO2? I contend it is the total net absorption of the surface spectrum of energy, and the 3.7 W/m^2 is the incremental increase in this total.

Using the numbers from above, if net absorption ‘A’ were equal to 0.75 and net transmittance ‘T’ were equal to 0.25, and the surface were at a temperature where it radiated 400 W/m^2 as a consequence of its temperature — net absorption is equal to 300 W/m^2; and radiative forcing of the GHE is 300 W/m^2 (or is the amount that is instantaneously ‘captured’ by the atmosphere). Upon a doubling of CO2 (assuming 4 W/m^2), an additional 4 W/m^2 is captured, increasing radiative forcing from 300 W/m^2 to 304 W/m^2.

As I’m understanding you and everyone, you are saying this is not correct, right?

• That should have said:

“My use of the word ‘net’ in the context of what’s being subtracted for net transmission and net absorption is the amount of surface spectrum in W/m^2 that is being absorbed and transmitted already.

49. RW wrote: “Using the numbers from above, if net absorption ‘A’ were equal to 0.75 and net transmittance ‘T’ were equal to 0.25, and the surface were at a temperature where it radiated 400 W/m^2 as a consequence of its temperature — net absorption is equal to 300 W/m^2; and radiative forcing of the GHE is 300 W/m^2 (or is the amount that is instantaneously ‘captured’ by the atmosphere). Upon a doubling of CO2 (assuming 4 W/m^2), an additional 4 W/m^2 is captured, increasing radiative forcing from 300 W/m^2 to 304 W/m^2.

As I’m understanding you and everyone, you are saying this is not correct, right?”

I think the phrase “not even wrong” summarizes it best. Absorption and transmission (with or without “net”) are not suitable terms when emission is significant. Absorption is different from absorptance and transmission is different from transmittance. Absorptance + transmittance don’t equal 1 when emission is involved. The GHE isn’t easily quantified: Some say 33 degK (not W/m2) using over-simplified arguments. Some say the GHE is the difference between surface OLR and TOA OLR, but that is not 300 W/m2 either. Radiative forcing and the GHE are different concepts. Further discussion along these lines appears pointless.

A simple answer we can discuss: The surface OLR (a flux) is about 390 W/m2. That upward flux (I_0) is modified according to the Schwarzschild eqn:

dI = emission – absorption
dI = n*o*B(lamba,T)*ds – n*o*I_0*ds

This eqn is numerically integrated over layers (ds) thin enough that n, T and I_0 can be treated as constants within a layer. These values are chosen to match the current atmosphere. The result is a TOA flux of about 239 W/m2 for the current atmosphere and 235 W/m2 for the current atmosphere with 2XCO2 (and no other changes). Using this eqn, the upward flux leaving each layer for the layer above is correctly calculated. This isn’t “transmission” or “net transmission” because emission is important. dI is positive in the stratosphere – making transmittance greater than 100%! Some photons are emitted and absorbed within a single layer, so we aren’t accounting for all of the photons absorbed.

The same equation takes the negligible downward flux from space (I_0 = 0 W/m2) and increments the downward LWR flux from each layer to produce a DLR flux at the surface of about 333 W/m2. Since the initial flux is zero, the terms absorption and transmission are totally worthless in describing this essential phenomena.

You can use such radiative transfer calculations to ask questions about what would happen if you removed all of the CO2 or GHG from the atmosphere, but I find the answers meaningless. We can calculate the changed radiative flux, but CAN’T accurately predict what will happen afterwards under radically different conditions. We don’t even have a satisfactory answer for doubling carbon dioxide: A 70% likelihood that ECS is 1.5-4.5 degC certainly is inadequate! The narrower projections from climate models can’t be trusted because they contain dozens of adjustable parameters. The overall uncertainty arising from the uncertainty in these parameters has never been properly characterized.

• BTW, I should clarify that I’m not specifically saying net absorption is 300 W/m^2 for Earth (it may be more or less). I’m just using it as a simplified example assuming a calculated net transmittance of 0.25 and a surface emitted power of 400 W/m^2.

• “The GHE isn’t easily quantified: Some say 33 degK (not W/m2) using over-simplified arguments. Some say the GHE is the difference between surface OLR and TOA OLR,”

I’m not talking about the net effect at the surface which is due to the ‘forcing’, but rather the ‘forcing’ itself that ultimately is responsible for the net effect at the surface.

• Frank,

Climate science doesn’t quantify ‘forcing’ as having anything to do with the amount of downward LW passing from the atmosphere to the surface — or even having anything to do with downward LW in general, so I don’t even know why you would invoke that.

In an atmosphere with no GHGs and clouds, there would be no upwelling IR captured and thus no GHE. All upwelling IR would pass straight into space.

• RW: Forcing is the term we use for small changes in the current radiation balance of the planet. Not for the whole greenhouse effect.

In an atmosphere with no GHGs, there would be no DLR. You could – if you wished – consider the greenhouse effect to be “forced” TO A FIRST APPROXIMATION by the 333 W/m2 of DLR that reaches the surface. However, the balance between incoming (SWR and DLR) and outgoing (OLR and convection) is critical to energy balance at any altitude. At the TOA, there is no DLR or convection, but the OLR flux depends on what happens below. So it isn’t correct to say that the GHE is forced by any one phenomena like DLR – is a an emergent property of the whole system, not of any one flux.

• You seem to be using semantics to dodge my question, which I think is more than a fair one.

Let me try asking it this way: If you do an RT simulation of the atmosphere prior to 2xCO2, what is be calculated by the simulation? And what is the quantification of the calculation in W/m^2?

• on June 4, 2014 at 8:11 pm DeWitt Payne

Is your reading comprehension that bad? The result of the calculation is the radiant flux passing through a unit area on a plane at the chosen observation altitude in the direction opposite the direction of observation. That is if the observer is looking down, the radiant flux is upward and vice versa. More specifically, it’s the integral over the wavelength range of interest of the hemispherical spectral flux density. The net flux at that altitude is the difference between the upward and downward flux at that altitude. For example, the net flux over the full wavelength range at the Earth’s surface according to TFK09 is 102 W/m² if you subtract upward from downward. The net flux at the TOA is < 1 W/m².

Semantics, that’s rich coming from you. You’re the one playing Humpty Dumpty with the language by using terms that only you understand. And I’m not sure about you.

• “being calculated”

• Properly formatted table for June 5, 2014 at 4:48 pm

Height OLR OLR OLR DLR DLR DLR (all W/m2)
(km) 1XCO2 2XCO2 Change 1XCO2 2XCO2 Change
0 360.5 360.5 0.0 256.5 259.8 3.3
1 352.3 352.0 -0.3 219.1 222.8 3.7
2 337.9 337.2 -0.7 186.9 190.9 4.0
3 324.7 323.7 -1.0 158.4 162.5 4.1
5 302.9 301.2 -1.7 109.6 113.2 3.6
8 280.7 278.0 -2.7 54.8 57.2 2.4
12 266.9 263.4 -3.5 19.6 21.2 1.6
17 263.3 259.8 -3.5 11.9 13.6 1.7
25 260.8 257.5 -3.3 5.8 7.1 1.3
40 261.2 257.5 -3.7 1.8 2.2 0.4
70 261.7 258.7 -3.0 0.0 0.1 0.0

• on June 5, 2014 at 5:15 pm DeWitt Payne

The correct term is transfer, not transmission, transmittance, absorption, absorptance or even emission. Solving the Swarzchild equation for a given atmospheric path produces a transfer function for EM radiation at any given wavelength.

• on June 5, 2014 at 5:13 pm DeWitt Payne

Frank,

MODTRAN only integrates the spectrum from 100-1500cm-1. It also uses a surface emissivity of 0.98, but doesn’t include reflection of DLR from the surface in the OLR calculation. The result is that OLR at 0 km for the US standard atmosphere is about 23 W/m@#178; less than the S-B equation result, 383.341 vs 360.474 from MODTRAN. The atmosphere is effectively opaque for frequencies <100 cm-1 and >1500cm-1.

The other thing that’s mildly annoying is that 0 km isn’t actually at the surface. If you look at the raw results, the integrated transmissivity at nominal 0 km is 0.8919 for the US Standard Atmosphere. That works out to about 2 m above the surface.

The reason why clouds have a significant effect is that the transmissivity of clouds is zero. Effectively you establish a new surface a couple of km above the ground which is colder than the ground.

• RW: If you go to http://forecast.uchicago.edu/modtran.html and use the online calculator to numerically integrate the Schwarzschild eqn, you will get the following fluxes at various heights. I chose the 1976 US Standard Atmosphere with no clouds or rain – which for reasons I don’t understand begins with a surface upward flux of 360 W/m2 (blackbody equivalent temperature of 282 degK). 1XCO2 = 280 ppm. 2XCO2 = 560 ppm. Default choices for the other GHGs and water vapor. I don’t understand the differences between the US standard atmosphere and the best possible model for the real atmosphere, but the absence of clouds is a big deal. The flux through the TOA is greater without clouds. The website offers a variety of atmospheres: tropical, midlatitude summer and winter, and polar summer and winter. Perhaps the planet as a whole is best represented by a properly weighted mixture of all five of these. I don’t know enough about the details of these atmospheres, so I’m offering them representative output for an arbitrary atmosphere, not the planet as a whole.

Height OLR OLR OLR DLR DLR DLR (W/m2) (km) 1XCO2 2XCO2 Change 1XCO2 2XCO2 Change
0 360.5 360.5 0.0 256.5 259.8 3.3
1 352.3 352.0 -0.3 219.1 222.8 3.7
2 337.9 337.2 -0.7 186.9 190.9 4.0
3 324.7 323.7 -1.0 158.4 162.5 4.1
5 302.9 301.2 -1.7 109.6 113.2 3.6
8 280.7 278.0 -2.7 54.8 57.2 2.4
12 266.9 263.4 -3.5 19.6 21.2 1.6
17 263.3 259.8 -3.5 11.9 13.6 1.7
25 260.8 257.5 -3.3 5.8 7.1 1.3
40 261.2 257.5 -3.7 1.8 2.2 0.4
70 261.7 258.7 -3.0 0.0 0.1 0.0

The changed flux means that power will be used to warm (or cool) various locations in the atmosphere and surface (from DLR), but all we are doing here is the instantaneous change in flux. These numbers have nothing to do with temperature change because they don’t consider heat capacity or changes in convection (which carries about half of the outward flux of power, mostly as the latent heat in rising water vapor).

Note the importance of the change in DLR for this particular atmosphere. The initial DLR flux is zero at the TOA. I hope you see why transmission and absorption aren’t useful terms to describe what happens as radiation passes through the atmosphere. Emission is equally important for OLR, but its role is obscured by the initial flux from the surface.

• on June 4, 2014 at 7:47 pm | Reply DeWitt Payne

Frank,
My only quibble:

Some photons are emitted and absorbed within a single layer, so we aren’t accounting for all of the photons absorbed. [emphasis added]

I would replace Some with Nearly all, or perhaps ‘Nearly all photons emitted within a single layer are also absorbed within that layer’ and replace all with most or some other word that implies that 99.9+% of all photons emitted within the atmosphere are absorbed within the atmosphere.

50. “Semantics, that’s rich coming from you. You’re the one playing Humpty Dumpty with the language by using terms that only you understand. And I’m not sure about you.”

I don’t understand why you don’t understand my fundamental question? It seems more than fair and very straightforward. The 3.7 W/m^2 is the additional amount instantaneously captured by the atmosphere, i.e. attenuated from leaving at the TOA — for 2xCO2, right? What is the total amount in W/m^2 which instantaneously captured prior to 2xCO2? And what is it referred to as?

Is the 3.7 W/m^2 the incremental increase in power captured by the atmosphere or not? The amount captured by the atmosphere prior to 2xCO2 is not zero, right? What is it?

51. Rephrased for maximum clarification:

The amount of powercaptured by the atmosphere prior to 2xCO2 is not zero, right? How much is it?

52. Frank concluded:

I think the phrase “not even wrong” summarizes it best..

Sadly, this is true.

The riddles posed by RW make no coherent sense. This would be clear if they were all written down as equations. None of us can work out what those equations are because the questions are sometimes “equationable” and sometimes not. “Equationable” questions are usually contradicted by later “equationable” questions, without RW realizing. And in the middle, stuff we can’t even understand.

Not even wrong.

• The question I posed is ridiculously straightforward. Either the 3.7 W/m^2 is the additional amount of power captured by the atmosphere or it’s not. If it is, the most elementary logic says there must be an amount of power prior to 2xCO2 that is captured, from which the 3.7 W/m^2 is the incremental increase in.

This is the quantity, i.e. the amount of power, that I’m referring to as ‘net absorption’. Geez.

• on June 5, 2014 at 7:13 pm DeWitt Payne

The full wavelength range includes SW as well as LW radiation, so it’s 0→∞, the same range as is used to convert the Planck equation to the Stefan-Boltzmann equation.

100% of what? Emission from the surface? Puhleeze. That would make LW DLR at the surface effectively ∞%. Both percentages have little meaning.

Geez indeed.

• on June 5, 2014 at 7:18 pm DeWitt Payne

Frank,

The increase in absorption of radiation emitted from the surface by the atmosphere after doubling CO2 can be calculated. I did it above for the tropical atmosphere. It’s on the order of 1 W/m². The rest is already 100% absorbed.

• RW: I’m going to take a chance and partially contradict DeWitt here. Immediately after a theoretical doubling of CO2, 3.7 W/m2 of power is going into warming the surface and troposphere. This is not necessarily an increase in absorption, it could be a decrease in emission. When we integrate the Schwarzschild, we aren’t keeping separate track of the absorption and emission change for each layer – both contribute to changes in the I_0 entering the layer above. As unusual, “net absorption” is a confusing term to use with a phenomena that involves both absorption and emission. The word “net absorption” is even more misleading when we recognize that most of the “retained power” is used to heat the ocean, not the atmosphere. This illustrates the importance of DLR to the GHE, not merely absorption of outgoing radiation. We need to analyze the system as a whole, not focus on one aspect – absorption.

As the planet warms, it will radiate more to space and the 3.7 W/m2 radiative imbalance will decrease, as will the rate of warming. Eventually a new equilibrium will be reached where there is no “retention of power”. So before doubling, it makes even less sense to ask about the “net absorption” associated with the GHE. When temperature is stable, the inward and outward fluxes are always equal: SWR = OLR (at the TOA), SWR + DLR = OLR + convection (everywhere)

Since SOD likes equations, does anyone see a problem with this one?

SWR + DLR = OLR + convection + power retained as internal energy

RW can pretend that “power retained as internal energy” is “net absorption by CO2”, but that won’t explain why most of it ends up in the ocean.

• Franck,

I agree with you when you say “it could be a decrease in emission”. As CO2 levels rise so does the effective emission height in the atmosphere defined as when more than 50% of 15 micron photons escape unimpeded to space. Each layer in the atmosphere below this height is in local thermodynamic equilibrium following the environmental lapse rate. CO2 molecules at any height radiate proportional to the local T^4. Each line in the CO2 emission spectrum have different intensities corresponding to different emission heights. The central lines are already saturated well above the tropopause so any increased CO2 levels have no net warning effect and cause even a cooling effect as the central line way up in the stratosphere moves to a warmer level.

So net CO2 greenhouse warming is really due to the side bands of the 15 micron whose effective emission height increases thereby reducing IR emission because of the lower temperatures at these new heights. This reduces the net heat loss from the surface thereby forcing surface temperatures to rise until a new energy balance is reached for this CO2 level whereby incoming equals outgoing radiation. This equilibrium temperature increase can be shown to depend on the logarithm of CO2 levels.

• “….wavelength range specifically?”

• “A more correct statement would be that the net radiative flux over the full wavelength range at the TOA becomes negative.”

OK, can you define for me what you mean by ‘the full wavelength range at the TOA’? This would be helpful. If what you are describing is not the wavelength rage of the surface spectrum, then what wavelength specifically?

• That should say:

“That is, the added CO2 further reduces the instantaneous emission to space,”

• The last time I checked emission to space is a power flux density, and a reduction in emission to space would also be a reduction in a power flux density. Geez.

And of course I’m referring to upwelling IR instantaneously captured. I know the change in the amount of SW from the Sun captured is miniscule, hence why I’m ignoring it.

‘Emission to space’ — as you’re referring to it — is not 100% prior to 2xCO2. If it were, we would not have a radiatively induced GHE prior to 2xCO2, but we clearly do. In fact, it is the basis for the whole CO2 induced warming effect in the first place. That is, the added CO2 reduces the instantaneous emission to space, which in turn requires the atmosphere and ultimately the surface to warm by some amount in order to re-establish equilibrium with space.

You guys are unbelievable.

• on June 5, 2014 at 3:46 pm DeWitt Payne

RW,

It’s not.

What you continually fail to comprehend is that there is no additional power captured. The only power to capture is incident solar radiation and changing CO2 has only a miniscule effect on that, on the order of 0.1 W/m². What changes is the emission to space, and that decreases because the height of emission increases and temperature decreases with altitude. The First Law then requires that energy to go somewhere, but referring to it is as ‘net absorption’ is misleading, so no one but you uses that terminology.

A more correct statement would be that the net radiative flux over the full wavelength range at the TOA becomes negative.

• “Sadly, this is true.”

On the contrary, I would argue. That no one here can understand what I’m asking seems exponentially sadder than my inability to describe it in specific equation form. I believe it would be some sort of integral function composed of the multiple layers evaluated using the Planck Spectrum emitted from the surface as a consequence of the surface temperature. It may also be referred to as the ‘spectral transmittance’ or ‘spectral absorption’ evaluated at the temperature of the surface. I’m not entirely sure. I’m only sure it is the quantity in W/m^2 from which changes occur (from changes in GHGs) that climate science considers to be ‘forcing’.

I’m most certainly interested in learning the equations that describe this, but first comes understanding and internally conceptualizing the basics so far as what ultimately being calculated in regards to this quantity. If ‘net absorption’ is not the correct term, then what is and what is the amount in W/m^2 prior to changes?

53. RW is excessively focused on the “net absorption” of OLR by CO2. The enhanced greenhouse effect is produced by absorption and EMISSION of LWR in all directions. (OLR and DLR.) 3.7 W/m2 is not the change produced by “net absorption” – it is the instantaneous radiative imbalance created at the tropopause by absorption and EMISSION by doubled CO2 throughout the atmosphere.

An imbalance is created throughout the atmosphere and surface. At an near the surface, the increase in DLR is more important than the decrease in OLR.

• ” The enhanced greenhouse effect is produced by absorption and EMISSION of LWR in all directions.

I’ve said this myself, BTW. Each layer becomes a slightly better absorber and emitter, but the net effect of this is an instantaneous power flux change at the TOA. For the 2xCO2 case, the power flux instantaneously transmitted to space decreases by 3.7 W/m^2 as a result of each layer becoming a slightly better absorber and emitter in the LW IR.

• Also, I believe why the instantaneous flux transmitted to space decreases instead of increases is because of the lapse rate, i.e. temperature decrease with height. If it were the other way around, i.e. temperature were to increase with height, added GHGs would actually increase the instantaneous flux transmitted to space, which would enhance the radiative cooling of the system or act to further cool it rather than warm it.

• So yes, I’m fully aware that the calculated TOA flux change of 3.7 W/m^2 for 2xCO2 is the result of both emission and absorption changes through the atmosphere. That still doesn’t change that ultimately what is being calculated is fundamentally a change in absorption and transmission relative to power passing into space or power attenuated from passing into space.

• “RW is excessively focused on the “net absorption” of OLR by CO2.”

Yes, because this is the amount — from which the calculated changes at the TOA (from changes in GHG concentrations) — that climate science quantifies as ‘forcing’. What other reason would there be to focus on it? It is the fundamental starting point from which the entire CO2 induced AGW theory is based, hence why understanding it’s precise physical meaning is of paramount importance.

54. Frank,

You’re talking about what happens to the energy after absorption. I’m not. I’m talking about what is calculated via the RT simulation and that is specifically an ‘instantaneous’ TOA power flux change and no way account for or makes any assumptions as to what happens the attenuated power after absorption.

• RW: I do’t believe I am talking about “what happens to the energy after absorption when I refer to power that has been retained as internal energy. Power is energy per unit time, a rising temperature (a rate) is also energy per unit time, calculated with the aid of the heat capacity of the substance retaining the energy. To reach the future, one multiplies a rate (the present) by a period of time.

• RW,

In reply to my question you referenced the surprisingly accurate WUWT figure as backup for your earlier statement.

The ratio of heat capacity of the ocean to the atmosphere = 1000x.

My calculation and WUWT both agree.

This means 0.1% of the energy is stored in the atmosphere and 99.9% is stored in the ocean.

This 100x different from your value of 99.999%.

On the challenge to your bogus idea about all atmospheric energy being stored in liquid water:

Why? Clouds are the main repository of energy, i.e. joules, in the atmosphere. The gaseous components of the atmosphere barely contain any energy relative to the clouds. The volumetric heat capacity of air is infinitesimal — something like 1 3000th of that of water.

“How much mass do you think there is in liquid water in the atmosphere?”

I don’t know, but I bet the total is way less than than the total contained in the clouds.

Let’s do the calculation (all in SI units):

Water: density =1000, cp = 4200, therefore heat cap per m3 = 4.2×106

Air (at STP): density = 1.3, cp = 1000, therefore heat cap per m3 = 1.3×103

So the ratio is 1/3200 – you can call this infinitesimal if you like but then you fall into the trap which I will label “sloppy” or “completely bogus” by then neglecting to do any kind of calculation.

Let’s see what I mean by taking the approach of labelling values “infinitesimal”:

The mass of air in the atmosphere is infinitesimally large compared with the mass of condensed water.
The heat capacity of air is infinitesimally small compared with that of water.

The overall ratio = infinitesimal large / infinitesimal small = about 1. Or in fact might be anything from ∞ to 1/∞ when we use “infinitesimal” in this kind of “rigorous” way.

Let’s do the calculation using real values:

Heat capacity of the atmosphere = Mass of the atmosphere x heat capacity of air = 5.3 x 1018 x 1005 = 5.3 x 1021 J/K

Let’s assume that all water vapor is condensed into clouds to get an extreme case.
This is the “total precipitable water vapor” (TPW) also known as “column integrated water vapor (IWV)” – this would be a 2.5 cm (0.025m) column averaged across the surface of the earth.

Heat capacity of all water & water vapor in the atmosphere = Mass of the liquid x heat capacity of the liquid = Surface area of earth x 0.025 x density x heat capacity =
5.1 x 1014 x 0.025 x 1000 x 4200 = 1.3 x 1016 x 4200 = 5.4 x 19 J/K

So, taking the extreme case the heat capacity of the air is 100x the heat capacity of all the condensed water and water vapor.

Instead of “way less” my calculation says it is at least 100x more.

Of course, when we consider only condensed water in clouds the value will be greater still.

• That should have said:

“No solar energy is trapped, but of course solar energy can and does accumulate.”

The reason why I consider it not accurate to say solar energy is trapped is because if the Sun were to hypothetically stop shining, the Earth would immediately begin to cool — i.e. it wouldn’t retain its accumulated energy.

Forgive me, but also think many misunderstand the physics driving the GHE because they think energy is being ‘trapped’ by added GHGs. I guess it’s kind of pet peeve of mine.

• SoD,

““Energy, i.e., power” ? These are two different things.”

Well, yes. Power is just energy divided by time.

“Energy does persist for a very long time in the atmosphere. The reason the atmosphere cools down and heats up is the boundary conditions keep changing (on a daily and seasonal basis as well as on other time periods). The rate of energy change, ie net power, is determined by the boundary conditions.”

I think you misunderstood me. My point is the atmosphere is not a bottomless sink of energy — the atmosphere is continuously pumped ‘new’ joules from the surface and Sun . In an approximate steady-state condition, there has to be an equal amount of power coming out of the atmosphere as is going in, otherwise joules would be accumulating (or decreasing) in the atmosphere.

“Have you done the maths here?
Mass of the atmosphere = 5.3 x 1018 kg
Mass of the ocean = 1.3 x 1021 kg
Specific heat capacity of dry air at STP = 1005 J/kg.K
Specific heat capacity of water = 4180 J/kg.K

Would you like to revise your first number?”

I’m going by this calculation here:

“I haven’t done the maths but I think your claim about “almost all” of atmospheric energy in clouds is completely bogus.”

Why? Clouds are the main repository of energy, i.e. joules, in the atmosphere. The gaseous components of the atmosphere barely contain any energy relative to the clouds. The volumetric heat capacity of air is infinitesimal — something like 1 3000th of that of water.

“How much mass do you think there is in liquid water in the atmosphere?”

I don’t know, but I bet the total is way less than than the total contained in the clouds.

“You keep using this term – post-albedo solar power. It has some significance to you.

The climate system contains energy, not power. The system loses energy to cool down and gains energy to heat up.”

Yes, of course.

“The GHGs don’t “delay the release” they change the amount of energy being absorbed by the climate system.”

Yes, they do — GHGs delay the release of post albedo solar power back into space. This delay ultimately increases the net rate joules are gained at the surface, thus elevating the surface temperature above what it would otherwise.

“And your last sentence seems equally strange. Solar energy is trapped. But there is no marker on a joule. Solar energy is trapped in the soil in the midday sun. Soil emits thermal radiation based on its temperature. No one in heat transfer is attempting to line up the delays between these events to account for the time lag of joules because they have no significance and all joules are indistinguishable from all other joules. We don’t care.”

In my view, the word ‘trap’ is misnomer, because it implies to stop and hold in place. No solar energy is trapped, but of course solar can and does accumulates. If solar energy were truly being ‘trapped’ it would be forever accumulating, rather than accumulating until the rate of energy input equals the rate of energy output.

“But you have some idea about accounting for “power” in a way that no one who writes textbooks ever discusses.

Well, I don’t think so. I’m a bit puzzled why you think I do.

• RW,

Power — in the case of power absorbed by GHGs in the atmosphere — is not really ‘retained’ in the atmosphere, but rather its exit from the system at the TOA is just delayed. It’s important to note that energy, i.e. power, in the atmosphere ‘blocked’ from exiting at the TOA in the immediate present doesn’t persist for very long, otherwise it wouldn’t cool down at night. .

“Energy, i.e., power” ? These are two different things. You will say you know this and why am I splitting hairs but I’m trying to help. There’s some conceptual issue you seem to have.

Energy does persist for a very long time in the atmosphere. The reason the atmosphere cools down and heats up is the boundary conditions keep changing (on a daily and seasonal basis as well as on other time periods). The rate of energy change, ie net power, is determined by the boundary conditions.

The heat capacity is air is infinitesimally ‘thin’ thermally and over 99.999% of the thermal energy in the system is contained below the surface (primarily in the oceans), and of the tiny fraction contained within the atmosphere almost all of it is contained within the clouds and not within the gaseous components of the atmosphere.

Have you done the maths here?
Mass of the atmosphere = 5.3 x 1018 kg
Mass of the ocean = 1.3 x 1021 kg
Specific heat capacity of dry air at STP = 1005 J/kg.K
Specific heat capacity of water = 4180 J/kg.K

Would you like to revise your first number?
I haven’t done the maths but I think your claim about “almost all” of atmospheric energy in clouds is completely bogus. How much mass do you think there is in liquid water in the atmosphere?

The way increased GHGs elevate the surface temperature above what it would otherwise be is to further delay the release of post albedo solar power back into space. No incoming solar energy is really trapped or hidden anywhere, though of course more joules can accumulate below the surface/atmosphere boundary as a result of increased GHG absorption.

You keep using this term – post-albedo solar power. It has some significance to you.

The climate system contains energy, not power. The system loses energy to cool down and gains energy to heat up.

The GHGs don’t “delay the release” they change the amount of energy being absorbed by the climate system.

And your last sentence seems equally strange. Solar energy is trapped. But there is no marker on a joule. Solar energy is trapped in the soil in the midday sun. Soil emits thermal radiation based on its temperature. No one in heat transfer is attempting to line up the delays between these events to account for the time lag of joules because they have no significance and all joules are indistinguishable from all other joules. We don’t care.

But you have some idea about accounting for “power” in a way that no one who writes textbooks ever discusses.

• Power — in the case of power absorbed by GHGs in the atmosphere — is not really ‘retained’ in the atmosphere, but rather its exit from the system at the TOA is just delayed. It’s important to note that energy, i.e. power, in the atmosphere ‘blocked’ from exiting at the TOA in the immediate present doesn’t persist for very long, otherwise it wouldn’t cool down at night. The heat capacity is air is infinitesimally ‘thin’ thermally and over 99.999% of the thermal energy in the system is contained below the surface (primarily in the oceans), and of the tiny fraction contained within the atmosphere almost all of it is contained within the clouds and not within the gaseous components of the atmosphere.

The way increased GHGs elevate the surface temperature above what it would otherwise be is to further delay the release of post albedo solar power back into space. No incoming solar energy is really trapped or hidden anywhere, though of course more joules can accumulate below the surface/atmosphere boundary as a result of increased GHG absorption.

• “Yes (water & water vapor).
99% of the energy absorbed by the atmosphere goes into increasing the temperature of the (dry) air, and 1% into the water vapor and water.

Conversely, if the atmosphere cools by 1K then the heat released by the air will be 100x the heat released by the water vapor & condensed water.”

Good. See, we can come to agreement and I can readily admit when I’m shown to be in significant error.

Now maybe we can get back to the main subject, which is atmospheric radiative transfer and the exchanges Frank and I are having (and to some extent Dewitt). Perhaps you can help us reconcile our inability to come to agreement on the concept of ‘radiative forcing’ as it relates to what I’m referring to as ‘net absorption’.

I fully understand that ‘climate science’ defines what is refers to as ‘Radiative Forcing’ as a calculated TOA flux change from the current or prior existing global average atmosphere, and that by its technical definition — ‘Radiative Forcing’ is zero prior to any changes from this initial global average atmosphere. However, in a more raw physics sense, there is certainly radiative forcing prior to 2xCO2, because we already have a radiatively induced, i.e. radiatively forced, GHE. Doubling CO2 really just further enhances the GHE, or the 3.7 W/m^2 is really just an incremental increase in the total amount radiative forcing that already exists.

Can you agree with this in basic principle? Do you understand the logic I’m using and why I’m using this as a starting point?

• RW

I think I now understand what you’re saying, and that is to raise all the air in the atmosphere 1K, it takes 100x the joules as it takes to raise the all the water in the atmosphere 1K. Do I understand you correctly now?

Yes (water & water vapor).
99% of the energy absorbed by the atmosphere goes into increasing the temperature of the (dry) air, and 1% into the water vapor and water.

Conversely, if the atmosphere cools by 1K then the heat released by the air will be 100x the heat released by the water vapor & condensed water.

You should verify the calculation for yourself.

• SoD,

“In reply to my question you referenced the surprisingly accurate WUWT figure as backup for your earlier statement.

The ratio of heat capacity of the ocean to the atmosphere = 1000x.

My calculation and WUWT both agree.

This means 0.1% of the energy is stored in the atmosphere and 99.9% is stored in the ocean.

This 100x different from your value of 99.999%.”

How do you figure? I get less than 0.001 or 0.000892 and change.

To arrive at this, I’m simply dividing (5 x 10 to the 21st power) by (5.6 x 10 to 24th power) — from the figures reference here:

I’m referring to total joules contained within — not heat capacity (volumetric or otherwise).

• “On the challenge to your bogus idea about all atmospheric energy being stored in liquid water:

Let’s do the calculation (all in SI units):

Water: density =1000, cp = 4200, therefore heat cap per m3 = 4.2×106

Air (at STP): density = 1.3, cp = 1000, therefore heat cap per m3 = 1.3×103

So the ratio is 1/3200 – you can call this infinitesimal if you like but then you fall into the trap which I will label “sloppy” or “completely bogus” by then neglecting to do any kind of calculation.”

Well, please forgive me — I just know it’s about 1 3000th of that of water from previous discussions elsewhere. As far as I’m concerned 1 3000th is infinitesimal.

BTW, I’m mainly referring to the kinetic energy of the O2 and N2 molecules since they are by far most numerous molecules in the atmosphere and make up the bulk of the gaseous components of the atmosphere. The point is the total energy, i.e. joules, contained in those gases is an infinitesimal fraction of the total kinetic energy contained within the clouds.

“Let’s see what I mean by taking the approach of labelling values “infinitesimal”:

The mass of air in the atmosphere is infinitesimally large compared with the mass of condensed water.
The heat capacity of air is infinitesimally small compared with that of water.

The overall ratio = infinitesimal large / infinitesimal small = about 1. Or in fact might be anything from ∞ to 1/∞ when we use “infinitesimal” in this kind of “rigorous” way.

Let’s do the calculation using real values:

Heat capacity of the atmosphere = Mass of the atmosphere x heat capacity of air = 5.3 x 1018 x 1005 = 5.3 x 1021 J/K

Let’s assume that all water vapor is condensed into clouds to get an extreme case.
This is the “total precipitable water vapor” (TPW) also known as “column integrated water vapor (IWV)” – this would be a 2.5 cm (0.025m) column averaged across the surface of the earth.

Heat capacity of all water & water vapor in the atmosphere = Mass of the liquid x heat capacity of the liquid = Surface area of earth x 0.025 x density x heat capacity =
5.1 x 1014 x 0.025 x 1000 x 4200 = 1.3 x 1016 x 4200 = 5.4 x 19 J/K

So, taking the extreme case the heat capacity of the air is 100x the heat capacity of all the condensed water and water vapor.

Instead of “way less” my calculation says it is at least 100x more.

Of course, when we consider only condensed water in clouds the value will be greater still.”

I’m afraid I’m not quite following this and don’t see where you are going with it. I’m referring to total joules contained within, where as you seem to be referring to total heat capacity contained within. Forgive me if I’m not understanding you on this.

• RW,

..This means 0.1% of the energy is stored in the atmosphere and 99.9% is stored in the ocean.

This 100x different from your value of 99.999%.”

How do you figure? I get less than 0.001 or 0.000892 and change.

To arrive at this, I’m simply dividing (5 x 10 to the 21st power) by (5.6 x 10 to 24th power) — from the figures reference here:

http://wattsupwiththat.files.wordpress.com/2011/04/atmosphere-vs-ocean-heat-capacity.jpg

Now I see why we are all having these Alice in Wonderland experiences..

Once you get up to speed with the extreme maths involved I hope you can reflect and see that we are only able to “get on the same page” on even this simplest of subjects by writing down an equation. Now finally we can see where the differences lie.

If you were able to write down equations for most of your statements on radiative forcing you would find that sometimes one side of your equation was in different units from the other side. And other times that a given equation was different from an earlier version of your equation.

I’m referring to total joules contained within — not heat capacity (volumetric or otherwise).

No you’re not. Well, you should be. Heat capacity tells you how much energy in Joules is required to lift the temperature by 1K.

Given that in any given locale the atmosphere, water vapor, ocean are all at roughly the same temperature you want to know how the energy gets divided up.

Total energy – would you like to pick away at that one? I don’t think you do.

First law of thermodynamics equations (conservation of energy) take as a given that we are talking about energy change because working out “total internal energy” is a challenge and not necessary to calculate conservation.

• RW,

Well, please forgive me — I just know it’s about 1 3000th of that of water from previous discussions elsewhere. As far as I’m concerned 1 3000th is infinitesimal.

And if you read the rest of my explanation, and taken the time to understand it, then you would understand why your approach of labeling a number “infinitesimal” causes problems.

When you read and understand my comment let me know then we can move forward.

I can’t explain it any clearer.

To critique French you have to be able to speak French. I think everyone understands that concept.

To critique thermodynamics you have to be able to understand thermodynamics. In climate blogs this is seen as just being picky.

Entertaining.

I wait for the light to dawn on percentages, heat capacity, total energy and one large number divided by another large number.

I think that means I can go back to my work for a long time..

• “Now I see why we are all having these Alice in Wonderland experiences.”

Well I’m not having any such experiences, except maybe with Frank, as I can’t figure out why he doesn’t understand what I mean by ‘net absorption’, especially since it’s specifically the incremental changes from it that climate science quantifies as ‘forcing’.

“Once you get up to speed with the extreme maths involved I hope you can reflect and see that we are only able to “get on the same page” on even this simplest of subjects by writing down an equation. Now finally we can see where the differences lie.

If you were able to write down equations for most of your statements on radiative forcing you would find that sometimes one side of your equation was in different units from the other side. And other times that a given equation was different from an earlier version of your equation.”

Well, I’ve had to keep changing the wording used because it was apparently confusing everyone, so I have probably done that to some degree.

I understand that ‘transmittance’ is a dimensionless fraction of incident radiant power transmitted through a medium, where as ‘transmission’ is referring to a specific power flux density transmitted through a medium.

“No you’re not.”

Yes, I was/am.

“Well, you should be. Heat capacity tells you how much energy in Joules is required to lift the temperature by 1K.

Given that in any given locale the atmosphere, water vapor, ocean are all at roughly the same temperature you want to know how the energy gets divided up.

Total energy – would you like to pick away at that one? I don’t think you do.

First law of thermodynamics equations (conservation of energy) take as a given that we are talking about energy change because working out “total internal energy” is a challenge and not necessary to calculate conservation.”

I understand; however, this was not the context of my initial remarks above.

• “And if you read the rest of my explanation, and taken the time to understand it, then you would understand why your approach of labeling a number “infinitesimal” causes problems.

When you read and understand my comment let me know then we can move forward.

I can’t explain it any clearer.”

Well yes, I certainly understand that just because the heat capacity of one thing is much lower than the heat capacity of another thing — it doesn’t mean the number of joules contained within the thing with a lower heat capacity must be lower than the thing with a higher heat capacity. You have to consider the mass and volume of the things you’re comparing.

As an example, if two things occupy the same volume of space and have different masses, the thing with more mass will have more joules contained within it (assuming each thing is at the same temperature).

“To critique French you have to be able to speak French. I think everyone understands that concept.

To critique thermodynamics you have to be able to understand thermodynamics. In climate blogs this is seen as just being picky.

Entertaining.

I wait for the light to dawn on percentages, heat capacity, total energy and one large number divided by another large number.”

I’m glad you’re finding this entertaining. So you’re saying the total joules contained within the atmospheric water are 100x times less than the total joules contained within the gases of the atmosphere (i.e. mainly O2 and N2)?

If so, maybe I am indeed in error about that. I recall it from a previous discussion somewhere, though perhaps I misunderstood what was being said and claimed. I admit you are correct that I did not calculated it from scratch myself.

“I think that means I can go back to my work for a long time..”

Gee, thanks for the insult.

• OK, I see it — you’ve made your point. I think my error was I misunderstood what I heard from a previous discussion. I think it was that almost all of the joules contained within the H2O in the atmosphere — both the kinetic and latent — are contained within the clouds and not within the vapor. And that the clouds are the primary repository of the latent heat of evaporated water from the surface.

• “As an example, if two things occupy the same volume of space and have different masses, the thing with more mass will have more joules contained within it (assuming each thing is at the same temperature).”

Furthermore, raising the temperature of the thing with more mass will require more joules, where as the thing will less mass will require fewer joules to raise its temperature (assuming an equal temperature increase for each thing).

• I also now see that the figures referenced are ‘per kelvin’, and thus not quantifications of total joules stored within as I had thought.

• “So you’re saying the total joules contained within the atmospheric water are 100x times less than the total joules contained within the gases of the atmosphere (i.e. mainly O2 and N2)?”

I think I now understand what you’re saying, and that is to raise all the air in the atmosphere 1K, it takes 100x the joules as it takes to raise the all the water in the atmosphere 1K. Do I understand you correctly now?

• By ‘attenuated power’ I simply mean the power instantaneously ‘blocked’ from passing into space. I would use the word absorbed power, but that seems to confuse everyone for some reason that eludes me.

55. I should further clarify that what I mean by ‘net absorption’ and ‘net transmission’ is relative to power instantaneously attenuated from passing into space to power instantaneously passing into space, and that in the case of 2xCO2, this is after the emission and absorption increases from the multiple layers increases due to the added CO2.

• Should have said:

“….this is after the emission and absorption from the multiple layers has increased due to the added CO2.

56. RW wrote: “I’ve said this myself, BTW. Each layer becomes a slightly better absorber and emitter, but the net effect of this is an instantaneous power flux change at the TOA. For the 2xCO2 case, the power flux instantaneously transmitted to space decreases by 3.7 W/m^2 as a result of each layer becoming a slightly better absorber and emitter in the LW IR.”

Seems perfect. No mention of transmission or absorption that creates confusion about emission.

RW added: “That still doesn’t change that ultimately what is being calculated is fundamentally a change in absorption and transmission relative to power passing into space or power attenuated from passing into space.”

I can’t agree here. Doubling CO2 doubles emission. Suppose we could double CO2 by adding special CO2 molecules that absorb but not emit. The resulting radiative forcing would be massively greater that 3.7 W/m2. 3.7 W/m2 is the net result of both absorption and emission.

Since doubling CO2 has negligible effect on the 10% of photons that escape directly from the surface to space, they aren’t involved in 3.7 W/m2 of radiative forcing. So radiative forcing has nothing to do with “transmission” from surface to space. In any case, transmission isn’t a useful term when emission is important.

Thousands of LWR photons are emitted by the atmosphere for every one that escapes to space or is absorbed by the surface. The fate of about one percent of those photons escaping to space or being absorbed by the surface is changed by doubling CO2. This change in fate is important, but it is only a tiny part of what is going on.

• “I can’t agree here. Doubling CO2 doubles emission. Suppose we could double CO2 by adding special CO2 molecules that absorb but not emit. The resulting radiative forcing would be massively greater that 3.7 W/m2. 3.7 W/m2 is the net result of both absorption and emission.”

Once again we agree, so I don’t know what the problem is.

“Since doubling CO2 has negligible effect on the 10% of photons that escape directly from the surface to space, they aren’t involved in 3.7 W/m2 of radiative forcing. So radiative forcing has nothing to do with “transmission” from surface to space.

As stated by me prior, only a small fraction of the 3.7 W/m^2 is from a reduction in the direct surface transmittance. Indeed most of is a reduction in emission that originates from the atmosphere. So again, I fail to see the problem.

• “Please cite a published, peer reviewed literature or standard text book reference for this remarkable assertion. Personal communications are not sufficient.”

The surface emitted spectrum of energy is the Planck emitted spectrum as a consequence of the surface temperature, right? This spectrum is also associated with a power flux density dictated by Stefan-Boltzmann, is it not?

• on June 6, 2014 at 8:29 pm DeWitt Payne

And that power is specifically quantified as fraction of the power radiated from the surface, because the TOA flux changes are weighted by the surface emitted spectrum of energy.

Please cite a published, peer reviewed literature or standard text book reference for this remarkable assertion. Personal communications are not sufficient.

• And that power is specifically quantified as fraction of the power radiated from the surface, because the TOA flux changes are weighted by the surface emitted spectrum of energy.

• The disagreement is with this statement: “That still doesn’t change that ultimately what is being calculated is fundamentally a change in absorption and transmission relative to power passing into space or power attenuated from passing into space.”

When 2XCO2 mean that twice as many photons are being emitted by CO2 molecules and the mean free path of those photons before absorption has been reduced by 50%, we are not dealing with a phenomena that can be described only in terms of absorption or transmission.

• “When 2XCO2 mean that twice as many photons are being emitted by CO2 molecules and the mean free path of those photons before absorption has been reduced by 50%, we are not dealing with a phenomena that can be described only in terms of absorption or transmission.”

Yes, but so far as what ultimately is being calculated — we are dealing with a phenomena that fundamentally involves changes in absorption and transmission, relative to power passing into space to power attenuated from passing into space.

• Dewitt,

No answer to this?

57. RW writes: “Yes, but so far as what ultimately is being calculated — we are dealing with a phenomena that fundamentally involves changes in absorption and transmission, relative to power passing into space to power attenuated from passing into space.”

What is calculated by the Schwarzschild equation is a change in FLUX, not a change in absorption or transmission. No methods that calculate absorption and transmission (such as Beer’s Law) apply to situations like the atmosphere where emission is important.

390 W/m2 are emitted by the surface and 239 W/m2 (1XCO2) or 235 W/m2 (2XCO2) reach space. “Reaching space” is not equivalent to transmission, only 10% of the photons emitted by the surface (39 W/m2) escape directly to space. You also know that at least 390-39 = 351 W/m2 is absorbed, yet the difference between surface and TOA flux is 151 or 155 W/m2. The output from Schwarzschild equation can’t be sensibly interpreted in terms of “absorption” and “transmission”.

• on June 6, 2014 at 8:25 pm | Reply DeWitt Payne

Frank,

As you pointed out above, RW’s conception of net absorption, what I understand of it anyway, fails when going downward from space to the surface. The fact that this doesn’t seem to bother him is telling. If you add incident solar flux to the downward LW flux you get negative net absorption because the total flux increases as altitude decreases. Negative absorption would seem to be an oxymoron. But at least then the percentage increase isn’t infinite.

• on June 6, 2014 at 10:15 pm DeWitt Payne

I’ve only done it over a very limited range of altitude, 0-0.5km, just to see what layer thickness seemed reasonable. As I decreased the layer thickness, the altitude range also decreased. As I remember, the point of diminishing returns was around 2m. At that point I was only calculating the total absorption for a change in altitude of 10m. It’s up there somewhere in this thread.

Pekka did it, to get his 99.9+% number, but I don’t know the details like layer thickness.

• DeWitt: Even worse, upward transmission through the stratosphere is also greater than 100%. In my dreams, RW will eventually realize that radiative forcing comes from the Schwarzschild eqn and that this output isn’t consistent with the conventional understanding of transmission and absorption. A long time ago, I wrote a lot of ignorant comments trying to understand radiative forcing in terms of absorption – all while knowing that I was missing terms for emission. One look at the Schwarzschild eqn (thanks to SOD) fixed most of my problems. I can’t tell if RW ever looks at the eqn, doesn’t really understand what the terms mean, or just interprets it differently.

This thought prompted another look, which I hadn’t considered before:

Integral [dI] from I_surf to I_TOA =
Integral [n*o*B(T)*ds] from s=0 to s=TOA (total emission?)
– Integral [n*o*I*ds] from s=0 to s=TOA (total absorption?)
= -151 W/m2 for 1X CO2. (“net absorption”?)

I believe that RW has rejected this definition for “net absorption” somewhere above. Have you ever calculated “total emission” and “total absorption” by this method?

• My value for the total emission in the atmosphere is based on calculating directly the total emission without any requirement that the photons reach the surface of the layer. Thus the result is essentially independent on the layer thickness. Doing such a calculation was easy, because I could modify the code.

The layer thickness affects the results only as much as it affects the temperature profile and density profile of the atmosphere.

58. RW

I fully understand that ‘climate science’ defines what is refers to as ‘Radiative Forcing’ as a calculated TOA flux change from the current or prior existing global average atmosphere, and that by its technical definition — ‘Radiative Forcing’ is zero prior to any changes from this initial global average atmosphere. However, in a more raw physics sense, there is certainly radiative forcing prior to 2xCO2, because we already have a radiatively induced, i.e. radiatively forced, GHE. Doubling CO2 really just further enhances the GHE, or the 3.7 W/m^2 is really just an incremental increase in the total amount radiative forcing that already exists.

RF(t=0) = 0, by definition
at time t=0 a step change in GHGs (2xCO2) is magically induced into the atmosphere.
RF(t=1s) = 3.7 W/m2, ignoring (for the sake of simplicity) the complete definition of radiative forcing which includes stratospheric adjustment

ΔRF = RF(t=1) – RF(t=0)

ΔRF = ΔS – ΔOLR

where ΔS = change in solar radiation absorbed from the tropopause down, in W/m2
ΔOLR = change in outgoing longwave radiation from the climate system at the tropopause, in W/m2

The sign convention is important, if OLR reduces then -ΔOLR > 0, i.e., there is positive radiative forcing, i.e. heating.

I gave up reading your confusing words a while ago, so if you have a question be sure to phrase it very precisely.

• “I gave up reading your confusing words a while ago, so if you have a question be sure to phrase it very precisely.”

First, I’m assuming this is a conversation and exchange which is being conducted in good faith and that you and others are not being deliberately defiant to me so as to prove and demonstrate some kind of point to yourselves.

I am trying to phrase my question precisely, but you have to meet me half way. I don’t know any other way to proceed other than to take it one step at a time using the best language I can think of.

The RT calculated 3.7 W/m^2 from 2xCO2 — it is the instantaneous flux change, i.e. flux decrease, at the TOA, right?

It can also be correctly said that for 2xCO2, the atmosphere instantaneously captures an additional 3.7 W/m^2, right?

Can we agree on the these two thing as well as the language that describes them?

• RW,

The RT calculated 3.7 W/m^2 from 2xCO2 — it is the instantaneous flux change, i.e. flux decrease, at the TOA, right?

Not precisely, but mostly. There are two terms on the right hand side of the equation. I haven’t looked up recently how much of the change is due to more solar radiation being absorbed by the atmosphere.

I’m sure that change in OLR is most of the ΔRF, and it might be that ΔS is negligible.

It can also be correctly said that for 2xCO2, the atmosphere instantaneously captures an additional 3.7 W/m^2, right?

It’s not a very precise way of writing but it’s a reasonable description.

• “I don’t like the word delay here, as it refers to a time difference. All radiative effects are so fast that any delays related to them are totally irrelevant (one second is a very long time for radiative transfer within the troposphere, but instantaneous from other points of view).”

I would say the delay is caused by the GHGs re-radiating the upwelling IR captured by the atmosphere back downwards toward the surface, where some of it passes to the surface and/or some of it passes back down to lower parts of the atmosphere; where it again (likely) gets re-radiated. This occurs over and over again until the captured IR energy either passes into space or is gained back by the surface somehow in some way; where it again it can either be re-radiated by the surface or leave the surface in non-radiant form — to eventually (and likely) be radiated again in the atmosphere….and so on and so forth.

The net result of these processes of absorption and re-radiation ultimately delays the ultimate release of incoming post albedo solar power back into space, elevating the surface temperature above what it would otherwise be. From a continuous balanced point of view, the difference between the post albedo solar flux and the net flux gained at the surface (about 150 W/m^2) is energy, i.e. power, that is really never actually leaving the surface since it’s continuously needed in addition to the 240 W/m^2 entering from the Sun to replace the 390 W/m^2 radiated away as consequence of the surface temperature.

• I don’t like the word delay here, as it refers to a time difference. All radiative effects are so fast that any delays related to them are totally irrelevant (one second is a very long time for radiative transfer within the troposphere, but instantaneous from other points of view). Furthermore the real world changes are slow. On that scale nothing that occurs in the atmosphere causes observable delays.

• Or at least this is my own personal conceptual understanding of the fundamental physics driving the GHE.

Think about it — if there were no delay of absorbed solar energy’s release back into space, how could the surface temperature be above 255K? I agree the delay is fairly short lived — like on time scales of minutes to hours; clearly demonstrated by the diurnal temperature swings.

• “What does “captured by the atmosphere” mean?”

Instantaneously ‘blocked’ from exiting at the TOA, or instantaneously attenuated from passing into space.

“A sudden increase in CO2 concentration decreases the IR flux up from the atmosphere and increases the IR flux from the atmosphere to the surface. Both changes are equally instantaneous.”

No disagreement with this.

“Thus atmosphere captures the difference of these two changes.”

I don’t understand. I would say the surface captures the increased IR passing from the atmosphere to the surface and the atmosphere captures the reduced IR passing from the atmosphere to space.

“The role of GHGs is not to capture any energy, the role is to make it more difficult for the energy to pass from the surface to the space. The more difficult it’s for the energy to pass through the atmosphere, the hotter must the surface be to result in the energy balance of the Earth.”

Well yes, I certainly agree. However, I would describe the role GHGs play is to delay the passage of surface energy back into space, thus elevating the surface temperature above what it would otherwise be in the process. The delay is accomplished the GHGs preventing a portion of the upwelling IR emitted by the surface and atmosphere — acting to cool — from passing into space. The requires the atmosphere and ultimately the surface to be at higher temperature in order to achieve equilibrium with space. In effect, it takes more energy, i.e. upwelling IR power, to ‘push through’ the 240 W/m^2 entering from the Sun back out to space.

In simple systems lingo, for Earth you could say that it takes about 390 W/m^2 of net gain at the surface to allow about 240 W/m^2 to leave the system at the TOA, offsetting the 240 W/m^2 entering the system from the Sun.

• RW,

What does “captured by the atmosphere” mean? To me it means something that stays at least momentarily in the atmosphere. A sudden increase in CO2 concentration decreases the IR flux up from the atmosphere and increases the IR flux from the atmosphere to the surface. Both changes are equally instantaneous. Thus atmosphere captures the difference of these two changes.

In many ways the amount of IR emitted by the surface is not an essential factor, what’s more essential is the total energy flux from the surface to the atmosphere. The heat capacity of the atmosphere is rather small. Therefore this net flux is always close to the flux through any fixed level of the atmosphere like the tropopause. The role of GHGs is not to capture any energy, the role is to make it more difficult for the energy to pass from the surface to the space. The more difficult it’s for the energy to pass through the atmosphere, the hotter must the surface be to result in the energy balance of the Earth.

The difficulty cannot be measured by the transmittance of energy – that’s always essentially 100%, it’s measured by the difference between the surface temperature and the effective radiative temperature of the Earth as seen from space.

• on June 8, 2014 at 7:35 pm David Wojick

Pekka, “captured by the atmosphere” may be the right term. As you explained to me some time ago, when a GHG molecule absorbs an LWR photon that energy is immediately lost to the surrounding air via kinetic transfer. Hence captured by the atmosphere. It then wanders around until it is finally emitted by another GHG molecule. It is this wandering about that is GH warming. Adding GHG molecules increases the average random walk duration, hence it increases the warming (ignoring all else that may be going on).

Kinetic transfer is essential to this concept, which may explain why trying to explain enhanced warming simply in terms of radiative transfer seems to lead to confusion.

David

• I should better say:

“I understand that the 3.7 W/m^2 includes a reduction in the surface IR –> TOA component as well as a reductionin the atmosphere IR –> TOA component, but all of the 3.7 W/m^2 is that which is additionally captured by the atmosphere — not that which is additionally captured by the surface.

• “Actually 3.7 W/m^2 is not the amount captured by the atmosphere but by the combination of the atmosphere and the surface. Part of that goes immediately to the surface.”

What?

I understand that the 3.7 W/m^2 includes a surface IR –> TOA component as well as an atmosphere IR –> TOA component, but all of the 3.7 W/m^2 is that which is additionally captured by the atmosphere — not that which is additionally captured by the surface.

• Actually 3.7 W/m^2 is not the amount captured by the atmosphere but by the combination of the atmosphere and the surface. Part of that goes immediately to the surface.

• Not precisely, but mostly. There are two terms on the right hand side of the equation. I haven’t looked up recently how much of the change is due to more solar radiation being absorbed by the atmosphere.

I’m sure that change in OLR is most of the ΔRF, and it might be that ΔS is negligible.

Well yes, I know there are two terms on the ‘right side of the equation’ as you say, but the total SW component — I thought at least — doesn’t change. What changes a tiny bit is how much SW is absorbed by the atmosphere, but the total SW absorbed into the system remains fixed.

“It’s not a very precise way of writing but it’s a reasonable description.”

OK. Is it reasonable also then that if the 3.7 W/m^2 is the additional amount of power instantaneously captured by the atmosphere, there would be a prior total amount of power in W/m^2 that is instantaneously captured — from which the 3.7 W/m^2 is the incremental increase in?

• RW said on June 8, 2014 at 8:01 pm:

From a continuous balanced point of view, the difference between the post albedo solar flux and the power radiated by the surface (about 150 W/m^2) is additional energy, i.e. additional power, that is really never actually leaving the surface since it’s continuously needed in addition to the 240 W/m^2 entering from the Sun to replace the 390 W/m^2 radiated away as consequence of the surface temperature.

I’m going to have a stab at rewriting so it means something in physics. Or nothing in physics, but at least it will be clear. We will work in per unit area globally annually average.

A = “the difference between the post albedo solar flux and the power radiated by the surface”

x = “the post albedo solar flux” = 240 W/m2
y = “power radiated by the surface” = E = 390 W/m2

B = “is additional energy” in units of Joules/m2

C = “i.e. additional power” in units of W/m2

D = “the 240 W/m^2 entering from the Sun” = x

E = “the 390 W/m^2 radiated away as consequence of the surface temperature.” = y

z = “surface temperature” = 288K

A = x – y = -150 W/m2

“is additional energy, i.e. additional power, that is really never actually leaving the surface since it’s continuously needed” – non physics

Energy/power a) doesn’t appear b) doesn’t “never leave” – because it is “continuously needed”.

The value A tells us nothing about surface energy balance because x is not solar radiation absorbed at the surface.

The value y tells us an incomplete story about one component of the surface energy balance (power out) because y is only one component of energy lost from the surface.

I don’t know what B and C are meant to be.

Do you want to comment on how we are doing so far?

• RW,
The typical life time of an vibrational excitation of CO2 in the troposphere is around 1 nanosecond. Every CO2 molecule gets excited and de-excited hundreds of millions times every second. In very few cases (about 1 in billion) is absorption or emission involved, but the rates of absorption and emission adjust to a new CO2 concentration in microseconds. The local thermodynamic equilibrium is reached equally rapidly.

All that happens simultaneously throughout the atmosphere and all adjustments that do not require movement of the gas are essentially complete in a fraction of one second. For the tropospheric effects forcing is defined for that case. The stratospheric adjustment includes temperature changes, which take longer to be completed, but the stratospheric adjustment is not large, when the calculation is done for the energy balance near the tropopause (slightly on the stratospheric side).

• Pekka commented June 8, 2014 at 3:16 pm:

Actually 3.7 W/m^2 is not the amount captured by the atmosphere but by the combination of the atmosphere and the surface. Part of that goes immediately to the surface.

This is correct. The values are shown in the results just cited from Collins et al 2006.

RW doesn’t understand this.

Prior to the CO2 doubling, 240 W/m2 was pouring into the climate system, and 240 W/m2 was pouring out of the climate system.

With more GHGs, and immediately after the change the climate system is at exactly the same temperature.
240 W/m2 now pours into the climate system, and 235 W/m2 now pours out of the climate system.

[Taking the numbers cited from Collins et al, given we are talking about 200hPa, the actual values are:

239.2 W/m2 into the climate system
234.5 W/m2 out of the climate system]

Of course, with everything at the same temperature but more GHGs there must be more radiation from the atmosphere to the surface. This is true regardless of whatever is happening at the tropopause.

We can think of it as some proportion of the 200hPa radiative forcing is going into the atmosphere and the balance is going into the surface.

[In the case of (just) cloudy skies I expect the change at the surface to be zero because the emission of radiation from clouds downwards makes the change from more CO2 insignificant. Unfortunately, in climate science terminology, “all skies” which is the relative proportion of whatever we are measuring over both clear and cloudy skies is usually called “cloudy skies”]

• RW said on June 8, 2014 at 2:26 pm:

Well yes, I know there are two terms on the ‘right side of the equation’ as you say, but the total SW component — I thought at least — doesn’t change. What changes a tiny bit is how much SW is absorbed by the atmosphere, but the total SW absorbed into the system remains fixed.

Given that a certain percentage of solar radiation is reflected by the surface, absorbing more solar radiation in the atmosphere may well change the total absorbed solar radiation. There is no a priori reason to assume it will be fixed. In the case of our definition of radiative forcing at 200hPa (see my extract from Collins et al 2006), with significant increase in solar absorption above 200hPa there is actually a significant decrease in solar absorption below 200hPa.

None of this is particularly important for your question though. Whatever that question is..

..OK. Is it reasonable also then that if the 3.7 W/m^2 is the additional amount of power instantaneously captured by the atmosphere, there would be a prior total amount of power in W/m^2 that is instantaneously captured — from which the 3.7 W/m^2 is the incremental increase in?

No, you are starting to confuse wording about radiative forcing with your own confused ideas about heat transfer.

When we talk about radiative forcing we are introducing an arbitrary ridiculous idea. The idea is “instantaneous doubling of CO2”.

In physics this would be a “step function”. When we say instantaneous, we mean 0.0000000001 second right after this change. I wrote it as 1 second in my comment of June 7, 2014 at 6:58 am. Actually, the earlier sentence needs correcting, I meant 0.0000000000000000000001 second after the change.

Hopefully you understand the meaning of instantaneous in that context.

Now we come to your wording: “..there would be a prior total amount of power in W/m^2 that is instantaneously captured..

Every second (globally annually averaged) the climate system emits about 240 W/m2 to space. Every second the climate system absorbs about 240 W/m2 from space.

So what on earth are you trying to get at?

Restating the obvious with strange terminology? Or some deeper meaning?

Yes the climate system absorbs energy in any given instant. Therefore, “instantaneously” the climate system absorbs energy. Therefore, “instantaneously” the climate system emits energy.

If you want to know how much W/m2 (power) you need to define which instant. If you want to know how much J/m2 (energy) you need to define how long the instant is as well as which instant.

What is this question??

• Sorry, there is no preview or editing feature here. SoD, you can delete the above post [- deleted].

That should have said:

““From a continuous balanced point of view, the difference between the post albedo solar flux and the power radiated by the surface (about 150 W/m^2) is additional energy, i.e. additional power, that is really never actually leaving the surface since it’s continuously needed in addition to the 240 W/m^2 entering from the Sun to replace the 390 W/m^2 radiated away as consequence of the surface temperature.”

• Pekka,

If you have come to understand it a somewhat different way, I don’t necessarily object. Like I say, this is just kind of my own conceptual understanding.

• For the sake of completeness I looked up results from an inter-comparison paper.

Whatever these values are is a totally different issue from whatever it is that RW is confused about.

But for completeness.. these are from Radiative forcing by well-mixed greenhouse gases: Estimates from climate models in the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4),
W. D. Collins et al, JGR (2006).

In this paper, various GCMs were compared with each other and with line by line calculations. So for the sake of the inter-comparison project they neglected stratospheric adjustment and cloudy skies.

However, it is at least a useful set of values for our discussion. I use values from the line by line models rather than the GCMs.

For the case 2b-1a: CO2 changes from 287-574 with no other GHG change. I.e., a doubling of CO2 from pre-industrial values.

At 200 hPa (proxy for the tropopause), longwave forcing = 5.5 W/m2
This is -ΔOLR in my equation (comment of June 7, 2014 at 6:58 am) – this is a reduction in OLR at 200 hPa as a result of an immediate doubling of CO2.

Shortwave forcing = -0.8 W/m2. This means a reduction in solar radiation absorbed in the troposphere due to increased CO2. This might be surprising (it was to me initially), but the shortwave forcing at top of model is positive, which it must be.

At the surface, longwave forcing = 1.6 W/m2
Shortwave forcing = -1.0 W/m2

At 200 hPa, total forcing, ΔRF = 4.7 W/m2
At the surface, total forcing = 0.6 W/m2

(Differences from standard expected is due to only considering clear skies with perhaps some small differences from no stratospheric adjustment).

59. It’s possible to imagine an alternative Earth system that differs from the real one by having a very small surface emissivity of IR, but the same emissivity of the atmospheric gases. The SW absorptivity of the surface is assumed to be the same as for the real world.

In that case the surface would be heated by SW only and cooled by conduction/convection and latent heat transfer. The balance at the top of the atmosphere would be the same, but all emission would originate in the atmosphere. That would result to a surface temperature not very different from the real one, but an infinite net transmissivity using the definition of RW, as the radiation at OLR would be equal to the present but emission by the surface zero. (The surface would, however, reflect or scatter IR emitted by the atmosphere.)

One related concept used quite often is emissivity of the Earth defined by the ratio of actual OLR to that a black body of the temperature of the Earth surface would emit. In that consideration the atmosphere has the role of selective coating that allows the Earth absorb a larger fraction of solar SW than the emissivity defined in this paragraph.

60. Sorry to dive in at this late stage, but I think there is a simpler way to derive CO2 radiative forcing which avoids most of the complexity of a full blown radiative transfer from the surface through the atmosphere. This is based on the temperature of the effective emission height for IR photons of a given wavelength.

Imagine a downward flux of IR photons originating from space. We assume a US standard atmosphere. Then for each wavelength using HITRAN we can calculate the height at which more than half of the incident photons are absorbed by CO2 molecules in the atmosphere. This is the same as the effective emission height for upwelling photons from lower atmospheric levels in local thermodynamic equilibrium.

Then for each wavelength we can calculate the emitted radiance and the result agrees almost perfectly with Nimbus spectra. see The CO2 GHE demystified

It also allows “derive” the formula RF = 5.3 ln(C/C0) which had previously been a mystery to me (actually I got 6.6!). You can also calculate the net temperature effects of different CO2 concentrations on earth -ignoring all other feedbacks. see Radiative Forcing of CO2

• on June 7, 2014 at 1:51 pm | Reply DeWitt Payne

clivebest,

Strictly speaking, the effective height of emission for a given wavelength is considered to be the altitude where the optical density reaches a value of 1.0 starting from infinite altitude and going downward. So the fraction absorbed at that altitude is then (1 – 1/e) = 0.632.

• That’s really quite interesting because I just used an absorption fraction of 0.5 so my effective emission heights are probably a bit too high. As a result I end up with slightly higher values for ECS = 1.5C and CO2 forcing DS = 6.6ln(C/C0). I really should repeat the calculation to see if using your definition then results in the canonical values of 1.1C and 5.3ln(C/C0) – thanks !

• DeWitt,

I don’t agree on that. My view is that the effective radiative height is determined as follows:

1) Determine the profile of the atmosphere
2) Calculate OLR radiation.
3) Calculate the temperature that corresponds to the total OLR radiation according to Stefan-Boltzmann law for black body.
4) Check the altitude which has that temperature.

I cannot see any other possibility for getting the result.

• The density of air with altitude is determined by barometric pressure. For a well-mixed gas the density of CO2 with height is determined by the overall concentration in ppm. Therefore at any altitude we know the number of CO2 molecules/m^3. The cross section for the absorption of IR photons of wavelength λ is given by the HITRAN database. Therefore we can calculate at which altitude a fraction = 0.632 of incident photons arriving from the TOA have been absorbed. Since absorption + transmission = 1 this height is exactly the same as the effective emission height for radiative transfer photons upwards of wavelength λ transmitted from all lower levels in the atmosphere and surface.

The only criteria that determines the emission of IR photons of wavelength λ by CO2 molecules in all the optically thick layers below is the local thermalized temperature (Kirchoff’s law). This emission intensity is given by Boltzman’s distribution.

So really the only missing information by not doing the full radiative transfer calculation is the net radiative flux passing from level n to level n+1. However because this does not change the temperature of level n+1 away from the lapse rate due to convection, it makes no difference to the OLR from the TOA for that wavelength. Therefore by varying the concentration of CO2 you can calculate the change in OLR at the TOA for each wavelength. Integrating over wavelength gives you the net CO2 forcing as a function of CO2.

• Clive,

As every altitude contributes a little to the outgoing radiation, the emission at every altitude must be included and the share of that exiting at TOA determined. When that’s done all essential parts of the full radiative transfer calculation are included. Some collection of results may be skipped, but nothing essential of the full calculation.

• Pekka,

Yes of course that is true in a precise way, but all you are really saying is that there is no exact “emission height” but instead a diffuse range of heights which contribute to OLR. Despite this the average of all those emissions will still result in an effective SB temperature corresponding to a particular height in the atmosphere.

• I understand the raising of the emission height for 2xCO2 is not direct, but more an effective raising of the emission height. This is because much of the emission that is further absorbed originates from the layers within the atmosphere — all of which are located at different heights.

• much of the emission that is further absorbed originates from the layers within the atmosphere

Indeed, more than 99.9% originates in the atmosphere.

• on June 7, 2014 at 6:49 pm DeWitt Payne

Pekka,

An RT calculation isn’t perfectly accurate either because a finite number of layers are used. The question is still, is there a significant difference between using the altitude for a given wavelength where the optical depth equals 1.0 or calculating the altitude from the temperature profile using the brightness temperature at that wavelength?

• DeWitt and Clive,

Estimating the change in effective emission height in some way without the full radiative calculation tells semiquantitatively, how increased CO2 leads to forcing, but such an approach is not precise even for a single clear sky case, and does not allow for estimating, how large the error is.

A full calculation by a model like MODTRAN or SoD’s model gives quantitative results for given atmospheric profiles like the standard atmospheres.

To get a real global value further modeling is needed to combine several radiative transfer calculations done for a number of different atmospheric profiles, many of them with clouds. The calculation of Myhre is probably the best known example of that.

The effective emission height is a quantity that can be used to describe the final result, but it’s not part of any of the quantitative calculations.

• on June 7, 2014 at 5:38 pm DeWitt Payne

Pekka,

The weighting function for emission W(z) = dI/dz (or transmissivity dt/dz) peaks at an optical depth of 1.0. For a wavelength where the atmosphere is optically thin, this is at the surface. This is according to R. Caballero in section 5.15 Effective Emission Level of his lecture notes (unfortunately no longer available for free). See also Grant Petty, A First Course in Atmospheric Radiation, second edition page 193. The altitude of peak absorption is also the altitude of peak emission.

That’s the justification for my position.

• on June 7, 2014 at 5:43 pm DeWitt Payne

Pekka,

Since you have easy access to a line by line program, you could calculate your way and my way and see if the difference is significant. I’m betting not.

• Clive,

I didn’t say “assume” but “consider”. Assume would refer to having the same effective emission height for every wavelength which is exactly what I said to be totally wrong. For single wavelengths the value varies from close to the surface to very close to the level selected for determining OLR. Almost every height within the atmosphere is the effective radiation height for some wavelength.

By “consider” I mean actually to define the concept as a single effective number according to the approach described in my comment of June 7, 2014 at 2:58 pm a little lower in this thread. That’s what I have understood to be the normal practice.

• It’s normal to consider one single effective emission height for all IR. As different wavelengths have very different absorption lengths or optical depths, the practical question is finding the correctly weighted effective value. That’s the one that really requires a full model calculation, and is very difficult or impossible to estimate otherwise.

• No it is not “normal” to accept there is one single effective emission height for all IR, although some text books might imply that. Once you accept that each wavelength has a different effective emission height then there really is almost no difference.

• Clive,
What you describe is a partial version of the full radiative transfer calculation. The partial version gives a result that’s not very far from that of a full calculation. There’s, however, some difference, and the only way of figuring that out is the full calculation.

The effective emission height cannot be determined in any other way than by calculating the OLR flux and checking, what’s the height that has the corresponding black body temperature. It’s one way of describing the final result, not a quantity that could be used to determine the OLR flux or imbalance.

• Basically right, but the only way to determine, how much the effective emission height goes up, is to do the full calculation that includes all layers from the surface up. Part of the result comes from the reduction in radiation from the surface to the space. All heights contribute to the result.

• Even the full radiative transfer calculation has to assume a temperature profile in the atmosphere. Of course you are right photons escape from different heights for a given wavelength to space. However as we agreed last time radiative energy balance does not determine the temperature gradient in the troposphere. That is determined by the (moist) adiabatic lapse rate. Radiative transfer drives convection to maintain the lapse rate and maximize cooling.

The effect of doubling CO2 is to raise the altitude where photons in each 15 micron line escape to space. This is at a lower temperature for those lines within the troposphere. The net effect is to reduce OLR by 3.5 watts/m2.

61. on June 6, 2014 at 6:24 pm, RW wrote:

“Yes, but so far as what ultimately is being calculated — we are dealing with a phenomena that fundamentally involves changes in absorption and transmission, relative to power passing into space to power attenuated from passing into space. And that power is specifically quantified as fraction of the power radiated from the surface, because the TOA flux changes are weighted by the surface emitted spectrum of energy.

Later he added: “The surface emitted spectrum of energy is the Planck emitted spectrum as a consequence of the surface temperature, right? This spectrum is also associated with a power flux density dictated by Stefan-Boltzmann, is it not?”

In reality, the “power passing into space” is not “quantified as a fraction of the power radiated from the surface”. TOA flux changes are NOT “weighted by the surface emitted spectrum of energy”. DeWitt asked you to document these statements, not explain that the surface emits according to Planck and S-B.

The power passing into space is quantified by numerical integration of the Schwarzschild eqn. Numerical integration produces a flux, not an absorptance or transmittance. The flux can not be used to calculate transmission or absorption, these terms don’t apply when emission contributes to the final flux.

Suppose one could magically raise the surface temperature to 342 degK and leave the temperature of the atmosphere unchanged. That rise is enough double surface OLR, but only 10% of those photons escape to space. So the direct to space flux would double, from 39 W/m2 to 78 W/m2. The rest of the TOA flux is emitted by GHGs in the atmosphere, and atmospheric emission is proportional to the Planck function (B(lamba,T)). SInce the temperature of the atmosphere hasn’t changed, the remaining 200 W/m2 reaching space won’t have changed. The power radiated to space depends mostly on the temperature of the atmosphere – it is certainly not a fixed fraction of the surface emission.

• Frank,

I appreciate your willingness to keep exchanging on this, but we don’t seem to be getting anywhere or making any progress.

Once again, I’m not referring to the direct surface transmittance, and I have stated multiple times that I know most of the TOA flux is from emission that originates from the atmosphere. And of course emission contributes to the final TOA flux, as it would have to since you can’t have a flux transmission (anywhere) without first have emission somewhere else prior.

• RW: As best I can tell, we aren’t getting anywhere because – after you correctly describe the atmosphere in terms of emission and absorption by various layers of the atmosphere – you immediately revert to a incorrect description based on transmittance. I’ll make one last try at explaining when the concept of transmittance is and is NOT useful. SOD will appreciate the clarity added by equations.

Accord to the KT energy balance diagram, 161 W/m2 of 239 W/m2 of post-albedo solar SWR is transmitted through the atmosphere to the surface and 78 W/m2 is absorbed by the atmosphere. The transmittance of the atmosphere for SWR is 67% and the absorptance is 33%. Transmittance + absorptance = 1. This approach works because the amount of SWR emitted by the atmosphere is negligible compared with the intensity of SWR. (By including the phrase “post-albedo”, I have avoided complications due to reflection from cloud tops and the surface.)

Transmittance + absorptance = 1 for experiments performed with a spectrophotometer. A spectrophotometer has a light source nearly as hot as the surface of the sun that makes thermal emission negligible. The additive inverse of the log (chemistry) or ln (physics) of the transmittance affords the absorbance – which is linearly proportional to the concentration of the absorbing species and path length for HOMOGENEOUS samples (Beer’s Law). Beer’s Law is extremely useful, but not for a non-homogenous atmosphere where emission is important.

UNLIKE the situation with SWR and spectrophotometers, the atmosphere does EMIT a significant amount of LWR. Equations and concepts useful for the former are misleading or wrong when applied to atmospheric LWR. The surface emits 396 W/m2, but only 10% of those photons escape directly to space (40 W/m2) – 10% “transmittance”. However the flux at the top of the atmosphere is 239 W/m2 – 60% “transmittance” of surface flux. Is transmittance 10% or 60%? Is absorptance 90% or 40%? Confusion reigns unless every uses the same number.

The 50% difference is caused by emission, BUT emission is not equal to 50% of the surface flux! On its way down from space, the emitted photons that build up as DLR eventually total 333 W/m2 (84% of surface OLR). Many more DLR photons are absorbed on their way to the surface. “Total emission” in either direction is certainly greater than 100% of surface OLR, perhaps hundreds of percent greater.

The equation that correctly describes this situation is:

Surface OLR – “total absorption” + “total emission” = TOA flux

where “total absorption” and “total emission” account for the energy in all of the photons absorbed and emitted along the upward path to space. It is an integrated version of the Schwarzschild equation. Unfortunately “total absorption” and “total emission” are NOT found in standard textbooks like Petty’s. If we divide both sides of this equation by Surface OLR and rearrange some terms, we get:

(TOA flux/Surface OLR) + (total absorption/Surface OLR)
– (total emission/Surface OLR) = 1

What do these terms mean?

TOA flux/Surface OLR: This is ONE way to define tRansmittance in the presence of emission, 60% in this case. I’ve capitalize the second letter to indicate this is not classical transmittance. When defined this way, tRansmittance differs from the fraction of photons that escape directly to space.

Total absorption/Surface OLR: This is ONE way to define aBsorptance in the presence of emission. When defined this way, aBsorptance can be greater than 1.

Total emission/Surface OLR: The above two ratios make intuitive sense, but the ratio of emission by atmospheric GHGs to emission by surface molecules doesn’t have any intuitive meaning to me. Substituting:

tRansmittance + aBsorptance – ??? = 1

This is why the use of transmittance and absorptance is confusing and unworkable for LWR in the atmosphere. We don’t even a standard name for the critical emission term and we never discuss total absorption and total emission.

Notice that when emission is negligible, this equation reduces to the conventional description of transmittance and absorbance:

Transmittance + absorptance = 1

62. SoD,

“Given that a certain percentage of solar radiation is reflected by the surface, absorbing more solar radiation in the atmosphere may well change the total absorbed solar radiation. There is no a priori reason to assume it will be fixed.”

Oh right, I hadn’t considered that.

“Pekka commented June 8, 2014 at 3:16 pm:

Actually 3.7 W/m^2 is not the amount captured by the atmosphere but by the combination of the atmosphere and the surface. Part of that goes immediately to the surface.

This is correct. The values are shown in the results just cited from Collins et al 2006.

RW doesn’t understand this.”

Actually, you are correct I did not know this, but now that I think about it — it makes perfect sense, because the difference between the two would be the net imbalance imposed on the system.

“No, you are starting to confuse wording about radiative forcing with your own confused ideas about heat transfer.”

I don’t understand how I am (or what makes you think so).

When we talk about radiative forcing we are introducing an arbitrary ridiculous idea. The idea is “instantaneous doubling of CO2″.

In physics this would be a “step function”. When we say instantaneous, we mean 0.0000000001 second right after this change. I wrote it as 1 second in my comment of June 7, 2014 at 6:58 am. Actually, the earlier sentence needs correcting, I meant 0.0000000000000000000001 second after the change.

Hopefully you understand the meaning of instantaneous in that context.”

Yes, of course — this is essentially always how I’ve understood it.

“Now we come to your wording: “..there would be a prior total amount of power in W/m^2 that is instantaneously captured..”

Every second (globally annually averaged) the climate system emits about 240 W/m2 to space. Every second the climate system absorbs about 240 W/m2 from space.”

Yes, of course. How is this related to what a multi-layer atmospheric RT simulation is ultimately calculating in the context of ‘instantaneous’ flux at the TOA? It would not be — at least directly.

“So what on earth are you trying to get at?

Restating the obvious with strange terminology? Or some deeper meaning?

Yes the climate system absorbs energy in any given instant. Therefore, “instantaneously” the climate system absorbs energy. Therefore, “instantaneously” the climate system emits energy.

If you want to know how much W/m2 (power) you need to define which instant. If you want to know how much J/m2 (energy) you need to define how long the instant is as well as which instant.”

No, no. I think I now see the disconnect here.

“What is this question??”

What I’m asking is in the context of what the RT simulation ultimately calculates. We don’t need an RT simulation to tell us that in any one instant — if the system is in balance — that 240 W/m^2 enters from the Sun and 240 W/m^2 exits at the TOA, right? So why would you invoke that?

We need and use an RT simulation to ultimately calculate an ‘instantaneous’ flux attenuated from exiting at the TOA, right? Because the change in ‘instantaneous’ flux attenuation is what climate science quantifies a ‘forcing’, right?

• RW

What I’m asking is in the context of what the RT simulation ultimately calculates. We don’t need an RT simulation to tell us that in any one instant — if the system is in balance — that 240 W/m^2 enters from the Sun and 240 W/m^2 exits at the TOA, right? So why would you invoke that?

Exactly. Why would I invoke it? Because you asked on June 8, 2014 at 2:26 pm “Is it reasonable also then that if the 3.7 W/m^2 is the additional amount of power instantaneously captured by the atmosphere, there would be a prior total amount of power in W/m^2 that is instantaneously captured” – and I’m grasping at why anyone would ask if we can all agree that the atmosphere emits and absorb energy both before and after the (hypothetical) radiative forcing event
Let’s all agree that we agree. No need to even bring it up.

We need and use an RT simulation to ultimately calculate an ‘instantaneous’ flux attenuated from exiting at the TOA, right? Because the change in ‘instantaneous’ flux attenuation is what climate science quantifies a ‘forcing’, right?

Yes.

Back to the question at the top: “What I’m asking is in the context of what the RT simulation ultimately calculates.

For the same temperature of atmosphere and surface, what is the change in absorbed solar radiation + outgoing longwave radiation:

ΔRF = ΔS – ΔOLR for the same temperature conditions before and after the step change in GHGs.

• RW

If an RT simulation were done prior to any GHG changes (like from 2xCO2) — with the system in balance — what would the simulation ultimately be calculating for an ‘instantaneous’ flux attenuation at the TOA? The calculated ‘instantaneous’ flux attenuation at the TOA is not zero prior to 2xCO2, right?

Can you please review my statement of June 7, 2014 at 6:58 am.

The usual meaning of Δ is “change in”, “after – before”. Just in case I wrote out exactly what it meant.

ΔRF = RF(t=1) – RF(t=0)

What is the sound of one hand clapping?

What is the difference between RF(t=0)?

• And just for clarity:
RF(t=0) – RF(t=0) = 0, or in mathematical language:
RF(t=0) – RF(t=0) ≡ 0

• “Exactly. Why would I invoke it? Because you asked on June 8, 2014 at 2:26 pm “Is it reasonable also then that if the 3.7 W/m^2 is the additional amount of power instantaneously captured by the atmosphere, there would be a prior total amount of power in W/m^2 that is instantaneously captured” – and I’m grasping at why anyone would ask if we can all agree that the atmosphere emits and absorb energy both before and after the (hypothetical) radiative forcing event. Let’s all agree that we agree. No need to even bring it up.”

OK.

“Yes.

Back to the question at the top: “What I’m asking is in the context of what the RT simulation ultimately calculates.”

For the same temperature of atmosphere and surface, what is the change in absorbed solar radiation + outgoing longwave radiation:

ΔRF = ΔS – ΔOLR for the same temperature conditions before and after the step change in GHGs.”

Understood; however, let me trying asking the question this way:

If an RT simulation were done prior to any GHG changes (like from 2xCO2) — with the system in balance — what would the simulation ultimately be calculating for an ‘instantaneous’ flux attenuation at the TOA? The calculated ‘instantaneous’ flux attenuation at the TOA is not zero prior to 2xCO2, right?

• Should have said:

“Because the change in ‘instantaneous’ flux attenuation is what climate science quantifies as ‘forcing’, right?”

63. SoD,

“The value A tells us nothing about surface energy balance because x is not solar radiation absorbed at the surface.”

I never said or implied that it was; however, it is the only significant source of power entering the system. The atmosphere creates no energy of its own.

It’s important to note that my statement says absolutely nothing about why the surface energy balance is what it is — only that it is a net of about 390 W/m^2 (i.e. a net of about 390 W/m^2 is gained at the surface/atmosphere boundary); easily deduced because we have a measured surface temperature of about 288K which S-B dictates radiates about 390 W/m^2, and which in turn — for a state of energy balance — must be replaced, otherwise the surface cools and radiates less or warms and radiates more.

That the surface gains a net of about 390 W/m^2 while about 240 W/m^2 enter and leave from the Sun is the net result of all of the effects, radiant and non-radiant, known and unknown, that occur in the system — both between the atmosphere and space and that occur at and/or below the surface.

“The value y tells us an incomplete story about one component of the surface energy balance (power out) because y is only one component of energy lost from the surface.”

Yes, y is incorrect — it shouldn’t be a negative number in the context I was using it. The phrasing is wrong — it should be the reverse, or 150 W/m^2 is the difference between the power radiated from the surface and the post albedo solar power entering the system.

I don’t know what B and C are meant to be.”

C is the additional amount of net power entering the surface that is not directly supplied into the system by the Sun. Power is just energy divided by time. A watt is one joule per second. A watt per meter squared is one joule per second incident on or leaving a square meter area.

“Do you want to comment on how we are doing so far?”

OK, I think.

• RW:

..That the surface gains a net of about 390 W/m^2

No.

C is the additional amount of net power entering the surface that is not directly supplied into the system by the Sun.

I don’t even know what you are trying to state. Various people on this article have already explained that net means something minus something else. You need to specifically define it. (Tautology for emphasis).

Generally – don’t write net without defining it unless you means something obvious like “net energy absorbed” which is energy in – energy out. And in this discussion, given your vague definitions so far, don’t ever use it without defining it.

Power entering the surface = DLR + f1.f2.S + K2

where DLR = downward longwave radiation from the atmosphere

S = solar radiation not reflected by the atmosphere (which is not 240 W/m2 because this is the value after considering both atmospheric/cloud reflection and surface reflection)

f1 = fraction not absorbed by the atmosphere (from memory about 2/3)
f2 = fraction absorbed by the surface (about 0.8)

K2 = sensible and latent heat entering the surface. The surface is almost always warmer than the atmosphere above it, so this value is almost always zero. I included it for completeness. Sensible and latent heat leaving the surface is estimated using a variety of measures and necessitates being a net value. Where “net” = energy transferred from the surface by sensible and latent heat minus energy transferred to the surface by sensible and latent heat = K1 – K2

DLR ≅ 320 W/m2
f1.f2.S ≅ 170 W/m2
K2 = zero for sake of this argument

So the surface does not gain a net of about 390 W/m2.

The surface gains a gross of about 490 W/m2
And the surface loses a gross of about 490 W/m2

The surface gains a net of about zero.

In the earlier rewrite of your statements I asked “Do you want to comment on how we are doing so far?

The answer is not “OK”. The answer is “we” have written down the surface temperature, the emitted flux from the surface and total energy absorbed from the sun and that’s it – basically nothing of value.

• “So the surface does not gain a net of about 390 W/m2.

The surface gains a gross of about 490 W/m2
And the surface loses a gross of about 490 W/m2

The surface gains a net of about zero.”

I disagree that for a state of balance the surface gains a net of about zero, for if it were — it would be at 0K and not 288K. It would be correct to say that net energy flow at the surface is zero.

I understand and would say that the ‘net power gained’ or ‘net energy gained’ (or lost) is the power gained that results in a specific temperature — or is the sensible heat that results in change in temperature. The amount of power in each case is dictated by S-B.

The gross flux gained involves how the net flux is physically manifested at the surface/atmosphere boundary. For a temperature of 288K, the only requirement for balance is that all power in excess of 390 W/m^2 entering the surface must be exactly offset by power in excess of 390 W/m^2 leaving the surface. The point being the gross flux gained says nothing about a particular temperature, as there are an infinite number of potential surface temperatures that could have same amount of gross power entering and leaving.

The bottom line is for the surface to be at 288K, any power in excess of 390 W/m^2 entering and leaving the surface must be net zero across the surface/atmosphere boundary. Or that such excess joules entering and leaving are perpetually ‘in limbo’, i.e they are neither adding or taking away joules from the surface (nor are they adding or taking away joules from the atmosphere). They are joules that are circulating within the system.

“I don’t even know what you are trying to state. Various people on this article have already explained that net means something minus something else. You need to specifically define it. (Tautology for emphasis).

“C is the additional amount of net power entering the surface that is not directly supplied into the system by the Sun.

I don’t even know what you are trying to state. Various people on this article have already explained that net means something minus something else. You need to specifically define it. (Tautology for emphasis).”

That atmosphere creates no energy and/or power of its own, right? In a state of balance, excluding diurnal fluctuations, simultaneously and continuously the surface gains a net of 390 W/m^2 while 240 W/m^2 both enters and leaves. The difference is 150 W/m^2 of power input to the surface which is occurring at the same time the only power source entering the system — 240 W/m^2 — is also leaving at the TOA. The key point is if the difference of 150 W/m^2 were not being additionally gained at the surface, the surface would be either cooling or warming, and thus not be in steady-state.

Because of this, it is valid to consider the 150 W/m^2 to be the additional amount of net power entering the surface that is not directly supplied into the system by the Sun. Note that in a system that has both radiant and non-radiant energy as sources (and that can enter and leave) — it would not be valid consider the 150 W/m^2 as such.

• I give some examples of formula that I know and the other regular commenters will also recognize:

Rout = εσT4… the Stefan-Boltzmann law, where Rout = emission of thermal radiation, ε=emissivity, σ=5.67×10-8

Rin = Rincident x &alpha(λ)… radiation absorbed = incident radiation x absorptivity at wavelength λ

ΔT = ΔQ/(mc)…. change in temperature = change in energy/(mass x specific heat capacity)

then you get formulas for convective heat transfer which are parameterized equations relating to wind speed, surface roughness, etc

Hopefully this will help you create your formula for NPG.

• Of course, the numbers I cite are assuming the surface emissivity is 1. Obviously if it were not 1, then that would have to be accounted for.

• Or the surface — at 288K — is really only gaining 390 W/m^2 while 240 W/m^2 enters and leaves the system.

• Of course, I understand that the GPI and GPO are made up of specific combinations of radiant and non-radiant power — each of which have complex interdependencies with the other. In the case of the Earth, more radiant power enters the surface than leaves the surface, and more non-radiant power leaves the surface than enters the surface.

Generally, both radiant and non-radiant energy flow out from the surface is temperature dependent and radiant and non-radiant energy flow in to the surface is not temperature dependent. But these things involve the path that the system takes from one equilibrium state to another. Once a state of balance has been physically manifested — however its actually been physically manifested — certain basic deductions about energy flow can be easily deduced as I have done.

• I guess my ultimate point is the actual rate joules are being added to the surface is at a rate of 390 W/m^2 — not 490 W/m^2, and is the same amount of power a black body surface in vacuum would be gaining if it were at a temperature of 288K. The NPG is just the amount of power — for a state of energy balance — that’s needed to replace the power radiated away as a consequence of the surface temperature.

• Or more precisely:

Version 1 would simply be NPG = S-B power out for 288K.

Version 2 is more complicated, as it would be the difference between gross power entering and leaving (which the two — for a state of balance — must be equal regardless) plus the S-B power out for 288K. If the gross power in and out were 490 W/m^2 and the gross power in increased to 500 W/m^2, the NPG would be 400 W/m^2 (or +10 W/m^2). If the gross power in decreased from 490 W/m^2 to 480 W/m^2, the NPG would be 380 W/m^2 (or -10 W/m^2)

In short, NPG = (GPI – GPO) + S-B power out, where:

NPG = Net power gained
GPI = Gross power in
GPO = Gross power out
S-B power out = Stefan-Bolzmann power out.

Plugging in the above numbers in the first example, we get NPG = (500 W/m^2 – 490 W/m^2) + 390 W/m^2 = 400 W/m^2.

Is this good enough?

• Assuming an initial starting temperature of 288K and a surface emissivity of 1?

• SoD,

“It should be clear that I was “putting words into RW’s mouth” to try and nail down his position.”

OK, fair enough.

“RW has a term called NPG, defined so:

NPG = (GPI – GPO) + S-B power out

OK, it’s time to add it all up:

NPG = (absorbed thermal radiation + conduction in + convection in) – (thermal emission of radiation + conduction out + convection out) + thermal emission of radiation

We can neglect conduction because it is usually insignificant in the climate system. We will take “convection” as a net emitted term, i.e. “convection” = convection out – convection in = positive from the surface to the atmosphere, for reasons already explained.

So, NPG = absorbed thermal radiation – thermal emission of radiation + thermal emission of radiation – convection

NPG = absorbed thermal radiation – convection

As a value, globally annually averaged, NPG ≅ 320 + 170 – 100 = 390

Oh – magic – it’s the emission of thermal radiation from the surface!!!”

Joy, joy.

Oh, wait a minute, hold on..

GPI – GPO = 0.

Yes, it’s true. Now we know what they are. This is the first law of thermodynamics, energy in – energy out = energy retained. Seeing as we are in approximate energy balance, energy in – energy out = 0.

So RW has created a very useful equation.

It is called NPG = a parameter I picked that I want to explain somehow

More formally, NPG = (x – x) + a parameter I picked that I want to explain somehow

Writing down “my invented parameter” = “the parameter I want to appear in my result” is not thermodynamics, not physics.

My question, probably a few days after other commenters, why have I spent so long on this experience?

RW, I don’t doubt you are trying. But after all this effort, now we have written down an equation and therefore proven that if we say x = y, then we know x = y; this is not progress.

We have just defined that x = y. Just because we wanted x to equal y isn’t justification for creating x.

In my defense, you were the one who pushed this particular point — not me. My formula, though arguably overly abbreviated, is still correct, but more importantly it demonstrates that my basic conceptual understanding of NPG as I had been referring to it was/is correct. Something you — at least apparently — felt I didn’t understand and/or wasn’t using properly. Perhaps justifiably so — given my history here — I’ll admit. OK?

Once again, my statements above regarding the +150 W/m^2 of non-system entering solar power ‘simultaneously’ gained at the surface are not stating anything about the thermodynamic path the system takes to manifest and/or maintain the +150 W/m^2, but just that it is the net result of the (average) thermodynamic path taken. Or it’s the net result of all the physical processes, radiant and non-radiant, known and unknown, that occur in between the boundaries of surface and the TOA (as well as at and below the surface).

That is — excluding diurnal fluctuations, simultaneously, a net of (about) 390 W/m^2 is gained by the surface while 240 W/m enters the system from the Sun and 240 W/m^2 leaves the system at the TOA. This the net flow of energy, i.e. the actual rates of joules gained and lost, that occurs in and out of the whole system on a continuum basis — for a state of balance (or at least an approximate state of balance).

Can we agree on this?

• Or perhaps a bit better phrased:

“Excluding diurnal fluctuations, simultaneously, a net of (about) 390 W/m^2 is added to the surface while 240 W/m enters the system from the Sun and 240 W/m^2 leaves the system at the TOA.”

• RW,

Writing down your equation is very valuable because it makes your strange ideas much clearer. I need to rewrite that – it makes the strangeness of your ideas more obvious.

Hopefully we can use these equations to demonstrate that they are random inventions.

First of all, the idea of an equation isn’t just to to work backwards from the number you want to get out by inventing various ideas along the way.

The idea is to use physics principles to (in this case) understand the climate better, or to prove or disprove an idea.

Right now, the equations are “not even wrong”.

Let’s take it one step at a time..

Your definition of a previously unknown physics quantity, net power gained or NPG, which is not “net energy flow” has now been defined mathematically:

In short, NPG = (GPI – GPO) + S-B power out, where:

NPG = Net power gained
GPI = Gross power in
GPO = Gross power out
S-B power out = Stefan-Bolzmann power out.

Unfortunately the terms involved in the definition of this “as yet to achieve popular thermodynamics use” term are themselves mysteries.

Gross power out, GPO, is not a thermodynamics definition yet. Causal readers might think it is:

GPO = thermal emission of radiation + conducted heat + sensible/latent heat
or in words, GPO = radiated emission + conduction + convection

But it’s clear from the equation that it can’t be, so what is it?

GPI = ? – Perhaps GPI = absorbed thermal radiation + conduction + convection?

Of course, if my suggestions are correct then your equation is wrong.

There’s a reason why this equation, or anything like this equation, never appears in a textbook. And it’s not because everyone in heat transfer has missed something..

Let me paraphrase, based on my current understanding:

NPG = (GPI – GPO) + S-B power out

Can be translated as:

a random term = another random term – yet another random term + emission of thermal radiation

RW, what is wrong with the first law of thermodynamics? Why not use that as a constraint and add up terms that everyone can understand?

• RW,

You make this hotch-potch statement (like 100s of earlier statements):

That atmosphere creates no energy and/or power of its own, right? In a state of balance, excluding diurnal fluctuations, simultaneously and continuously the surface gains a net of 390 W/m^2 while 240 W/m^2 both enters and leaves. The difference is 150 W/m^2 of power input to the surface which is occurring at the same time the only power source entering the system — 240 W/m^2 — is also leaving at the TOA. The key point is if the difference of 150 W/m^2 were not being additionally gained at the surface, the surface would be either cooling or warming, and thus not be in steady-state.

This is probably the reason why your equation (see my last comment) is a bunch of random terms that make no thermodynamics sense.

The system called the climate system is in overall (approximate) energy balance.

The system called the surface is in overall (approximate) energy balance.

Your statement makes no thermodynamic sense and is not based on any thermodynamics principles.

The first law of thermodynamics says that energy is conserved.

You are trying to apply this law to explain why at one boundary – the edge of the climate system – the gross energy rates are different from the gross energy rates at a completely different boundary.

The reason is simple. Energy, not power, has been retained in the climate system. Power is not conserved. Energy is conserved.

If you lag the outside of a pipe (with a constant flow of constant temperature liquid), the outside of the pipe gets hotter than without lagging it. You don’t need to invent a whole bunch of new terminology to explain it.

There is a simple reason. Do you know what it is????

• on June 9, 2014 at 12:07 pm DeWitt Payne

RW,

In a state of balance, excluding diurnal fluctuations, simultaneously and continuously the surface gains a net of 390 W/m^2 while 240 W/m^2 both enters and leaves. The difference is 150 W/m^2 of power input to the surface

You have been saying this for a long time. It’s still wrong. Energy input to the surface (TFK09) is 161 + 333 = 494 W/m². That’s the total or the gross, not 390 W/m². Energy leaving the surface is 396 + 97 = 493 W/m². The net energy rate of gain, in – out, is ~1 W/m². That makes the difference between the energy flux in at the TOA less reflected power and energy flux in at the surface = 494-239 = 255 W/m², not 150 W/m².

Your energy flows don’t balance. They’re wrong. Your idea that convection from the surface to the atmosphere doesn’t count was, is and will always be wrong.

Note that I’m quoting this from a comment by SoD, not you. I don’t read your comments. You also might want to reread think a little more before hitting the Post Comment button.

• “First of all, the idea of an equation isn’t just to to work backwards from the number you want to get out by inventing various ideas along the way.

The idea is to use physics principles to (in this case) understand the climate better, or to prove or disprove an idea.”

Agreed.

• “Gross power out, GPO, is not a thermodynamics definition yet. Causal readers might think it is:

GPO = thermal emission of radiation + conducted heat + sensible/latent heat
or in words, GPO = radiated emission + conduction + convection

Yes, of course. My formula was just in terms of basic in and out energy flow, independent of the combination of energy types that make up the total in and out flows. It was also in the context of an already measured steady-state surface temperature, independent of how it has been physically manifested.

“The reason is simple. Energy, not power, has been retained in the climate system. Power is not conserved. Energy is conserved.”

Yes, of course. Joules are conserved. The point is in order to retain an accumulated amount of joules that has manifested a particular temperature, the same amount of joules per second must arrive as leave, otherwise cooling or warming occurs.

• On my attempts to clarify the formula from RW, he stated:

Once again just to absolutely clear, I agree your equations are correct. Why would I disagree with them? Why would anyone?

This was the formula where I was still unsure, as I had previously asked on June 9, 2014 at 8:14 am:

..Let me paraphrase, based on my current understanding:

NPG = (GPI – GPO) + S-B power out

Can be translated as:

a random term = another random term – yet another random term + emission of thermal radiation

It should be clear that I was “putting words into RW’s mouth” to try and nail down his position.

Ok, so “my equation is correct”. Let’s take that as evidence. Citing from my earlier comment, and taking out the question marks:

GPO = thermal emission of radiation + conducted heat + sensible/latent heat

GPI = absorbed thermal radiation + conduction + convection

RW has a term called NPG, defined so:

NPG = (GPI – GPO) + S-B power out

OK, it’s time to add it all up:

NPG = (absorbed thermal radiation + conduction in + convection in) – (thermal emission of radiation + conduction out + convection out) + thermal emission of radiation

We can neglect conduction because it is usually insignificant in the climate system. We will take “convection” as a net emitted term, i.e. “convection” = convection out – convection in = positive from the surface to the atmosphere, for reasons already explained.

So, NPG = absorbed thermal radiation – thermal emission of radiation + thermal emission of radiation – convection

NPG = absorbed thermal radiation – convection

As a value, globally annually averaged, NPG ≅ 320 + 170 – 100 = 390

Oh – magic – it’s the emission of thermal radiation from the surface!!!

Joy, joy.

Oh, wait a minute, hold on..

GPI – GPO = 0.

Yes, it’s true. Now we know what they are. This is the first law of thermodynamics, energy in – energy out = energy retained. Seeing as we are in approximate energy balance, energy in – energy out = 0.

So RW has created a very useful equation.

It is called NPG = a parameter I picked that I want to explain somehow

More formally, NPG = (x – x) + a parameter I picked that I want to explain somehow

Writing down “my invented parameter” = “the parameter I want to appear in my result” is not thermodynamics, not physics.

My question, probably a few days after other commenters, why have I spent so long on this experience?

RW, I don’t doubt you are trying. But after all this effort, now we have written down an equation and therefore proven that if we say x = y, then we know x = y; this is not progress.

We have just defined that x = y. Just because we wanted x to equal y isn’t justification for creating x.

• BTW, I have only persisted with this point because I think it may come into play regarding what is specifically quantified (and why) in an RT simulation, and how the flux changes at the TOA are weighted, but the truth is I don’t know yet.

As acknowledged by me prior, I didn’t know the 3.7 W/m^2 is the difference between the instantaneous IR TOA flux decrease and the instantaneous IR surface increase, but this makes sense to me and is easy to internally conceptualize — both why the TOA decreases and the surface increases (i.e. because of the lapse rate), and why the difference between the two is the net ‘instantaneous’ imbalance imposed on the system.

I have heard the 3.7 W/m^2 referred to as the ‘net absorption change’, which may just mean the incremental difference between the TOA and surface IR flux changes. Maybe someone knows?

• “If you lag the outside of a pipe (with a constant flow of constant temperature liquid), the outside of the pipe gets hotter than without lagging it. You don’t need to invent a whole bunch of new terminology to explain it.

There is a simple reason. Do you know what it is????”

Because the rate at which heat escapes the outside of the pipe decreases? That is, the lag acts as thermal insulation for the pipe?

I don’t understand where you’re going with this question.

• “Gross power out, GPO, is not a thermodynamics definition yet. Causal readers might think it is:

GPO = thermal emission of radiation + conducted heat + sensible/latent heat
or in words, GPO = radiated emission + conduction + convection

But it’s clear from the equation that it can’t be, so what is it?

GPI = ? – Perhaps GPI = absorbed thermal radiation + conduction + convection?”

Of course, if my suggestions are correct then your equation is wrong.

Once again just to absolutely clear, I agree your equations are correct. Why would I disagree with them? Why would anyone? I’m certainly not denying that in addition to thermal radiation leaving the surface there is also conduction and convection leaving the surface, and I’m certainly not denying that in addition to radiation entering the surface there is also conduction and convection entering the surface (though I note not according to Trenberth on the latter two). Is this what you think I think?

GPO is by definition all of the components that contribute to the total power leaving the surface. That’s what makes it ‘gross’. GPI is by definition all of the components that contribute to the total power entering the surface. Again, this is what makes it ‘gross’ and not ‘net’.

Forgive me, but I don’t understand where you’re going with this.

• SoD,

“There’s a reason why this equation, or anything like this equation, never appears in a textbook. And it’s not because everyone in heat transfer has missed something..”

In short, I think disconnect lies here. My statements are not in the context of ‘heat transfer’, which generally involves the process of heat transfer from one equilibrium state to another.

The context of my comments are that of stripping the system down to the flow of energy, i.e. power, in and out of the whole system once an equilibrium state has been already been physically manifested.

In thermodynamics, the former, i.e. ‘heat transfer’, is said to be a ‘Process function’ (or ‘path function’):

http://en.wikipedia.org/wiki/Process_function

where as the latter is said to be a ‘State function’:

http://en.wikipedia.org/wiki/Functions_of_state

BTW, I’m persisting with this because I think it may eventually be relevant to radiative transfer and what I’m referring to as ‘net absorption’ and ‘net transmittance’, where each is a fraction of the surface power (i.e. the net of 390 W/m^2 gained at the surface and the 390 W/m^2 radiated from the surface as a consequence). But I don’t know yet.

• RW

I said:

Unfortunately the terms involved in the definition of this “as yet to achieve popular thermodynamics use” term are themselves mysteries.

But you haven’t defined them. I attempted to clarify by suggesting a particular formula (comment of June 9, 2014 at 8:14 am) for GPO and GPI. You responded:

Yes, of course. My formula was just in terms of basic in and out energy flow, independent of the combination of energy types that make up the total in and out flows. It was also in the context of an already measured steady-state surface temperature, independent of how it has been physically manifested.

This is some kind of goobledy-gook to me.

Look at my particular formula. See that it is specific – a reader will know exactly what it is from the formula.

Whereas your description is waffle. Go through my attempt to define your thoughts and confirm or deny each component of GPO and GPI.

We can’t move forward until you do. When you have clarified your terms, \$10 says we will be able to show that your equation violates the first law of thermodynamics.

In a separate comment I also asked:

If you lag the outside of a pipe (with a constant flow of constant temperature liquid), the outside of the pipe gets hotter than without lagging it. You don’t need to invent a whole bunch of new terminology to explain it.

There is a simple reason. Do you know what it is????

• “Go through my attempt to define your thoughts and confirm or deny each component of GPO and GPI.”

Yes, I have no issue with how you’re breaking down GPO and GPI. Why would I?

• “Power gained that results in a specific temperature? version 1
Sensible heat that results in change in temperature? version 2

Version 1:
NPG is a function of rate of total energy in, and is in units of W/m2?

Version 2:
NPG is a function of sensible heat in or out or both? and is in units of J/m2?

NPG is energy in? Energy out? Whatever you want it to be?”

In both cases the units are W/m^2. In both cases, NPG is energy in.

“Please write down a formula. You have the word “net” in there.

I already said, please be specific about “net”. Some value minus some other value.

If you can’t write down a formula or a precise definition it is because you just invented something. And none of us know what it is.”

Version 1 would simply be NPG = S-B power out.

Version 2 is more complicated, as it would be the difference between gross power entering and leaving (which for a state of balance must equal regardless) plus the S-B power out for 288K. If the gross power in increased from say 490 W/m^2 to 500 W/m^2, the NPG would be 400 W/m^2 (or +10 W/m^2). If the gross power in decreased from 490 W/m^2 to 480 W/m^2, the NPG would be 380 W/m^2 (or -10 W/m^2)

In short, NPG = (GPI – GPO) + S-B power out, where:

NPG = Net power gained
GPI = Gross power in
GPO = Gross power out
S-B power out = Stefan-Bolzmann power out.

• RW

I disagree that for a state of balance the surface gains a net of about zero, for if it were — it would be at 0K and not 288K. It would be correct to say that net energy flow at the surface is zero.

Let’s say net energy flow at the surface = 0.

Let’s define net energy flow = rate of energy in – rate of energy out

If you want to try a physics definition of “net energy gain” we can review it… and here it is:

I understand and would say that the ‘net power gained’ or ‘net energy gained’ (or lost) is the power gained that results in a specific temperature — or is the sensible heat that results in change in temperature. The amount of power in each case is dictated by S-B.

This is not a physics definition. It’s two different vague statements (for apparently the same “idea”) that have different units.

Net power gain = NPG = ? what’s the formula

Power gained that results in a specific temperature? version 1
Sensible heat that results in change in temperature? version 2

Version 1:
NPG is a function of rate of total energy in, and is in units of W/m2?

Version 2:
NPG is a function of sensible heat in or out or both? and is in units of J/m2?

NPG is energy in? Energy out? Whatever you want it to be?

Please write down a formula. You have the word “net” in there.

I already said, please be specific about “net”. Some value minus some other value.

If you can’t write down a formula or a precise definition it is because you just invented something. And none of us know what it is.

64. SoD,

BTW, do you see that I am progressing? That is, I’m learning things I didn’t know or that I was in error about. This is the learning process and — I assume at least — is the main purpose of this site.

I recall you’ve said yourself that understanding atmospheric radiative transfer is extremely difficult — even for someone such as yourself that has formal training the necessary science and math. I think this exchange we are having will likely not only help me to better and more properly understand RT, but has the potential to help everyone — at least to some degree.

65. Dewitt,

“Energy input to the surface (TFK09) is 161 + 333 = 494 W/m². That’s the total or the gross, not 390 W/m². Energy leaving the surface is 396 + 97 = 493 W/m². The net energy rate of gain, in – out, is ~1 W/m².

Yes, and I have said this myself — i.e. that the total power incident on and leaving the surface is about 490 W/m^2, but the point is it does not establish a particular temperature — let alone a temperature of 288K.

“Your energy flows don’t balance. They’re wrong. Your idea that convection from the surface to the atmosphere doesn’t count was, is and will always be wrong.

When it ‘counts’ depends on the context. Of course, relative to raw thermodynamics as SoD points out, it certainly counts. It certainly counts and must be accounted for when trying to determine the path the system takes from one equilibrium state to another. My context was that of a measured temperature already in a state of balance. In that context, the power incident on and leaving the surface in excess of the power radiated from surface as a consequence of the surface temperature can never count, i.e. such excess joules per second are neither adding or taking away joules from the surface.

• The primary point being the net rate of gain at the surface is actual rate of power input to the surface or the actual rate which at which the surface is gaining joules. This is the case not just at the surface, but really any layer within the atmosphere as well.

Ultimately, the surface temperature is slaved to the black body baseline if the surface emissivity is 1. On the input side — for a state of balance, the net power gained must always be equal to the S-B radiant power out, regardless how much total power is incident on and leaving the surface.

• Or you might say temperature is slaved to power in this respect by the S-B law.

66. RW: What counts doesn’t depend on context. Energy (Joules) is always conserved, so everything ALWAYS counts with regard to energy. When the energy flowing into an object – from all sources and by all mechanisms – is not equal to the energy flowing out, the difference (incoming – outgoing) appears as the “internal energy” (kinetic, vibrational, rotational, electronic) of the object – its temperature. When an object is at equilibrium with its surroundings, its temperature isn’t changing and incoming = outgoing. (However, equilibrium does not exist immediately after an instantaneous doubling of CO2.) Equilibrium temperature depends on ALL mechanisms by which energy can be transported, ie convection and conduction in addition to radiation.

Power is energy per unit time (Watts). For any period of time short enough for the energy flow to be effectively constant, we can express the law of conservation of energy in terms of power. The rate of energy flow into internal energy becomes a rate of temperature change. (This gets a little tricky, because a temperature change also produces a change in emitted radiation. This problem can be mathematically addressed for infinitesimal periods of time using derivatives, dE/dt.)

Climate science deals most often with power flux, power per unit area (W/m2). The law of conservation of energy can also be expressed in terms of power flux. Flux is a vector quantity, meaning that it has both a magnitude and a direction. Vector addition (also done with forces) involves more than just adding magnitudes, but climate science often avoids these complications by considering only the components of flux perpendicular to the surface: DLR and OLR. Mathematically, energy fluxes that are vectors can cancel (net OLR = OLR-DLR). However, since the photons that carry energy in both directions are real and don’t cancel (or annihilate each other), we usually do NOT talk about one net radiative flux (“net OLR”). Instead, we refer to two opposing fluxes (OLR and DLR).

Since photons are only one of many forms of energy, they are not conserved. They are absorbed, increasing internal energy of the absorbing molecule, and emitted, decreasing it. Absorbed energy is immediately shared by collisions. Instead of conserving photons, we merely “account” for them using all possible sources and fates: The number of photons traveling in a given direction is the number already going in that direction – the number absorbed (from those going that direction) + the number emitted (into that direction) +/- the number scattered +/- the number reflected +/- the number refracted. Fortunately, only the first three or two possibilities are significant in many cases.

• Frank,

“RW: What counts doesn’t depend on context.”

I really depends on what one means by the word ‘counts’, right?

I fully understand that — universally — the only requirement for balance is that total power in = total power out. This is trivial in relation to any particular temperature, because there are an infinite number of possible temperatures that can be manifested with the same amount of equal total power in and out.

You see, with a total of 490 W/m^2 entering and leaving the surface, there are still an infinite number of possible surface temperatures that can be manifested, even with radiation, conduction, convection, etc. — as modes of heat transfer — all occurring.

Can you explain to me using only units of power, i.e. W/m^2, and not components of heat transfer — why the surface temperature is 288K and not some other temperature? This is the critical question that Dewitt — at least — doesn’t seem to be able to ever answer.

“(However, equilibrium does not exist immediately after an instantaneous doubling of CO2.) Equilibrium temperature depends on ALL mechanisms by which energy can be transported, ie convection and conduction in addition to radiation.”

Yes agreed, of course.

I see nothing to really disagree with in the rest of your post.

67. On lagging pipes..

If you lag the outside of a pipe (with a constant flow of constant temperature liquid), the outside of the pipe gets hotter than without lagging it. You don’t need to invent a whole bunch of new terminology to explain it.

There is a simple reason. Do you know what it is????

In response, RW said:

Because the rate at which heat escapes the outside of the pipe decreases? That is, the lag acts as thermal insulation for the pipe?

I don’t understand where you’re going with this question.

In response to a question from Frank, RW said:

Can you explain to me using only units of power, i.e. W/m^2, and not components of heat transfer — why the surface temperature is 288K and not some other temperature? This is the critical question that Dewitt — at least — doesn’t seem to be able to ever answer.

The two questions are the same phenomenon.

The calculation of external pipe temperature upon adding lagging is a calculation which depends upon the heat transfer coefficient of the lagging, its thickness, the pipe thickness, the energy rate input into the pipe (from the hot water) and the external room temperature.

The question posed of DeWitt by RW is exactly the same problem but with radiative heat transfer instead of conductive heat transfer.

But in the case of the radiative heat transfer RW is trying to magic up a (nonsense) formula which “explains” why the surface is hotter than the outside. In the case of the lagged pipe “everyone knows” why it is hotter and no one is trying to magic up a formula which “explains” why the surface is hotter than the outside.

68. on June 10, 2014 at 1:38 pm | Reply DeWitt Payne

RW,

The surface temperature isn’t 288K in the TFK09 energy balance. LW emission from the surface is 396 W/m². If we assume a surface emissivity of 0.98 then the surface temperature is 290.55K. The surface temperature is whatever is required to (nearly) balance the energy flows. If, for example, global precipitation were higher, the surface temperature would be lower and conversely.

The rate of convective heat transfer determines how much the surface temperature is reduced compared to a purely radiative energy balance. We estimate convective heat transfer by subtracting radiative flux upward from radiative flux downward because radiative flux is easier to measure. More of the solar energy absorbed by the surface is lost by convection (97 W/m²) than by radiation (63 W/m²).

• I’m going by the ’97 diagram, which has the surface at 288K. And of course, I agree with your comments, but I don’t feel they are an answer to my question.

There are infinite number of thermodynamic paths that can manifest a surface temperature of 288K, right? There are also an infinite number of temperatures that can manifested with the same amount of equal total power in and out, right. Can you — using only units of power in W/m^2 — explain what is universally required for a surface to be at 288K and not some other temperature?

• “Like I am somehow clear about what you think? Like I have any idea? I’m obviously playing some kind of game here? Is that what you think?”

I don’t know.

“Really, I have absolutely no idea what is in your head.”

I guess not.

<When I pinned you down to an equation it turns out to be “Parameter I have invented” = x – x + “the thing I want it to mean”.

It’s not an ‘invented parameter’ — it’s a basic fact of physics (i.e. a universal physical law). The ‘net power gained’ (or lost) is generally considered to be the sensible heat that results in a change in temperature, where as in the steady-state, the sensible heat is considered to be equal to zero.

Still, the bottom line is for a surface to remain at some specific temperature T, the power the surface radiates away as a consequence of its temperature — dictated by S-B — must be replaced, otherwise the surface cools and radiates less (i.e. negative sensible heat) or warms and radiates more (i.e. positive sensible heat).

So even though in the steady-state, the sensible heat is equal to zero, it doesn’t mean the ‘net power gained’ (or ‘net energy gained’) is also equal to zero, for it must always be a positive number for any temperature above 0K, and is dictated by the S-B equation.

“At least that’s how it appeared to me. Your conclusion upon my above distillation of your physics was:

..My formula, though arguably overly abbreviated, is still correct, but more importantly it demonstrates that my basic conceptual understanding of NPG as I had been referring to it was/is correct. Something you — at least apparently — felt I didn’t understand and/or wasn’t using properly..

So that’s all good then.

Like I said, my work is done. Expect no more from me.”

Alright. Can we move on now to RT simulation — the subject of this thread?

• I should add:

“So even though in the steady-state, the sensible heat is equal to zero, it doesn’t mean the ‘net power gained’ (or ‘net energy gained’) is also equal to zero, for it must always be a positive number for any temperature above 0K, and is dictated by the S-B equation, independent of physical manifestation.

• The above reply of mine is to Dewitt.

• ..Of course, radiative transfer in a raw sense involves heat transfer. Geez.

Like I am somehow clear about what you think? Like I have any idea? I’m obviously playing some kind of game here? Is that what you think?

Really, I have absolutely no idea what is in your head.

When I pinned you down to an equation it turns out to be “Parameter I have invented” = x – x + “the thing I want it to mean”.

At least that’s how it appeared to me. Your conclusion upon my above distillation of your physics was:

..My formula, though arguably overly abbreviated, is still correct, but more importantly it demonstrates that my basic conceptual understanding of NPG as I had been referring to it was/is correct. Something you — at least apparently — felt I didn’t understand and/or wasn’t using properly..

So that’s all good then.

Like I said, my work is done. Expect no more from me.

• “RW,

So no heat is transferred?

Radiative transfer does not require a “heat transfer calculation”?

We have made such progress. My work is done.”

No. Come on. I mean so far as the radiative transfer simulation that quantifies climate GHG ‘forcing’, or what is referred to as the ‘instantaneous’ change or flux imbalance imposed for increased GHGs.

Of course, radiative transfer in a raw sense involves heat transfer. Geez.

• RW,

So no heat is transferred?

Radiative transfer does not require a “heat transfer calculation”?

We have made such progress. My work is done.

• RW,

They are called boundary conditions in heat transfer problems.
You apply the equations of heat transfer via conduction, convection and radiation to the imposed boundary conditions and out pops your answer.

If you read a book on heat transfer instead of trying to convert everyone to y=x-x+y solutions it might be beneficial.

Have a read of Heat Transfer Basics – Part Zero – a few examples of heat transfer, simple stuff but often misunderstood.

• I said before that my context is not that of heat transfer. Radiative Transfer — in the context we are discussing it, i.e. climate ‘forcing’, does not involve a heat transfer calculation.

• ” I mean so far as the radiative transfer simulation that quantifies climate GHG ‘forcing’, or what is referred to as the ‘instantaneous’ change or flux imbalance imposed for increased GHGs.”

What mean — if it’s not clear — is the RT simulation that calculates instantaneous ‘net absorption’ changes for GHG concentration changes, comes before any heat transfer calculation, since a heat transfer calculation inherently follows — no precedes — an imposed imbalance.

• So if there was no convection (impenetrable horizontal strata) so that the atmosphere could only lose heat through pure radiative balance presumably the surface temperature would be 16C warmer or 306C ?

• Clive,

Given that I have the Matlab line by line radiative transfer program, it’s something I’ve been thinking about doing in the last few weeks – working out the surface temperature with no convection, and looking at a few other elements of that world..

• Clive: I believe your value is too low. A source cited by a textbook I have says surface temperature without convection would rise to about 330 degK. (J Atmos Sci (1964) 21, 370. I remember seeing 343 degK somewhere else.

• on June 10, 2014 at 3:19 pm DeWitt Payne

I assume you mean 306K, not 306°C. It would be hotter, exactly how much is not a trivial calculation. The atmosphere would be hotter as well, at least close to the surface. The lapse rate would be a lot higher close to the surface too. The calculation has probably been done somewhere.

• DeWitt: I think we estimate convective transfer of latent heat (water vapor) from the precipitation, an average of 1 m per year or 1 m^3/m^2. The exact amount of heat released depends on the proportion of liquid and solid precipitation.

Trenberth assigns a value to convection of simple heat so that all other fluxes add up properly, including the very small flux (0.6 W/m2) to internal energy that is causing global warming.

• DeWitt: I believe they cross-check the convection of simple heat with models.

• on June 10, 2014 at 5:32 pm DeWitt Payne

I should go back to the paper, but as I remember, the precipitation calculation is more of a cross check than an estimate. As you say, sensible heat transfer is whatever’s left over that’s needed to achieve balance.

69. RW asked: “Can you explain to me using only units of power, i.e. W/m^2, and not components of heat transfer — why the surface temperature is 288K and not some other temperature?”

To my knowledge, no simple calculation produces a surface temperature of 288 degK. Radiative transfer calculations without any convection produce surface temperatures near 350 degK. Convection is responsible for lowering it to 288 degK. We can use physics to predict what lapse rate (decrease in temperature with increasing altitude) should be unstable to buoyancy-driven convection, but not how much energy does flow upward (in W/m2) via convection. (From the amount of precipitation that falls, we can calculate how much heat that was originally in the surface and is release in the upper atmosphere when water condenses.)

Crudely, surface temperature is controlled by the temperature at the lowest altitude where radiation prevails (about 10-17 km above the surface, about 220 deg) and the lapse rate from there to the surface (6.5 degC/km).

• “To my knowledge, no simple calculation produces a surface temperature of 288 degK.”

Well yes, of course — there is no simple calculation that specifically produces a temperature of 288K (as there are an infinite number of possible physical manifestations), but that’s not what I mean and not what I’m asking. Sorry if my question wasn’t clear.

There is just one universal physical property that all surfaces at a steady-state temperature of 288K (with an emissivity of 1) must have, and that is all power in excess of 390 W/m^2 entering the surface must be exactly equal to power in excess of 390 W/m^2 leaving the surface.

• “Don’t jump to conclusions. Carefully analyze ALL of the fluxes. Confirm your analysis (a hypothesis) with experimental data.”

Well, I think you may be jumping to conclusions about my conclusions.

• RW: Technically, you are correct, but you appear to be switching cause and effect. Steady state temperature is not a property of a surface! Conservation of energy is a universal law that applies to all surfaces. When incoming energy equals outgoing energy (including the 390 W/m2 of blackbody radiation the surface emits), the surface temperature will not change. Otherwise the surface temperature will rise or fall until incoming energy equals outgoing energy. A stable surface temperature is created by the surface and its surrounding environment, it is not a property of a surface!

This illustrates why you have trouble: You know what the answer should be – a steady state temperature of 288 degK – and you twist the situation until it agrees with your preconceptions. For you, the difference between incoming and outgoing energy (not counting OLR) is a UNIVERSAL PROPERTY of a 288 degK surface – come hell or high water! Scientists evaluate all of the energy entering and leaving a surface and decide if they are in balance. If not, they calculate a new temperature where they will be in equilibrium (and how quickly they will approach equilibrium). If the temperature is not behaving as they expected, they re-evaluate all facets of the problem.

Here’s example of how to and how not to analyze surface temperature: a) The wrong way. Many skeptics believe that the surface of the ocean can’t be absorbing DLR (333 W/m2) because all DLR is absorbed in the top 10 um of water. If that much energy were deposited in a thin layer, the water would boil away, so DLR (if it really exists) can’t be warming the oceans!!! b) The right way to approach such problems. What are the energy inputs and outputs for this very thin layer of water? Evaporation takes place from the top layer of molecules on the surface, so about 80 W/m2 is lost that by that route. LWR photons emitted by water molecules well below the surface are absorbed before the can reach the surface, so the 390 W/m2 that leaves the surface is emitted from the top 10 um of the surface. So far, the surface has a DEFICIT of about 135 W/m2 despite receiving 333 W/m2 of DLR. So far, we have a surface that is going to freeze, not boil! If the sun is shining, some or all of the deficit can be made up by the top 10 um absorbing solar SWR. Otherwise the deficit must come from the water below the top 10 um – by convection and/or conduction. (The water below is warmed during the day by sunlight that penetrates below the top 10 um.) Both conduction and convection require that the top 10 um be colder (and denser for convection) than the water below. At night, it is clear that the top 10 um of the ocean should be colder than the water below despite the DLR. During the day, the situation depends on how much solar SWR reaches the surface (sunny? at noon?) and how much is absorbed a various depths. c) Now that we think we have properly analyzed all of the energy fluxes, do experiments in the real ocean confirm or contradict your analysis?

Don’t jump to conclusions. Carefully analyze ALL of the fluxes. Confirm your analysis (a hypothesis) with experimental data.

70. “Steady state temperature is not a property of a surface!”

Agreed, of course.

“This illustrates why you have trouble: You know what the answer should be – a steady state temperature of 288 degK – and you twist the situation until it agrees with your preconceptions.”

The 288K temperature has already been physically manifested and is measured — not derived or surmised from the manifesting thermodynamic components (i.e. radiation, conduction, convection, etc.)

“Many skeptics believe that the surface of the ocean can’t be absorbing DLR (333 W/m2) because all DLR is absorbed in the top 10 um of water.”

While I admit am a so-called ‘skeptic’ of large global warming effects from anthropogenic CO2 emissions, this notion — to me at least — seems completely nonsensical.

“If that much energy were deposited in a thin layer, the water would boil away, so DLR (if it really exists) can’t be warming the oceans!!! b) The right way to approach such problems. What are the energy inputs and outputs for this very thin layer of water? Evaporation takes place from the top layer of molecules on the surface, so about 80 W/m2 is lost that by that route. LWR photons emitted by water molecules well below the surface are absorbed before the can reach the surface, so the 390 W/m2 that leaves the surface is emitted from the top 10 um of the surface. So far, the surface has a DEFICIT of about 135 W/m2 despite receiving 333 W/m2 of DLR. So far, we have a surface that is going to freeze, not boil! If the sun is shining, some or all of the deficit can be made up by the top 10 um absorbing solar SWR. Otherwise the deficit must come from the water below the top 10 um – by convection and/or conduction.”

What you seem to be describing here is the superposition principle:

http://en.wikipedia.org/wiki/Superposition_principle

…as it applies to the surface energy balance. Indeed, the balance at the surface is the sum of the fluxes in and out, where the additive superposition principle must apply to the effects of energy (and power) on the temperature of a system boundary. That is, to the extent that more direct radiant energy (from the atmosphere and Sun) is entering the surface than leaving, it must be largely replacing the non-radiant energy leaving the surface, but not returned (as non-radiant).

If you want to use Trenberth’s numbers (i.e. the ’97 numbers) — to the extent that 492 W/m^2 of radiant power enters the surface from the atmosphere and Sun (324 W/m^2 + 168 W/m^2 = 492 W/m^2), 102 W/m^2 of it must be exactly replacing the 102 W/m^2 of non-radiant flux (evapotranspiration and thermals) leaving the surface, but not coming back as non-radiant.

The key distinction that makes all steady-state surface temperatures of 288K unique, relative to total power incident on and leaving, is that all non-radiant power leaving the surface must be in excess of the 390 W/m^2 directly radiated from the surface as a consequence of its temperature (dictated by S-B), but there is no such requirement for the proportions of radiant and non-radiant power entering the surface from the atmosphere.

The whole point is the actual rate that joules are being added to the surface, for a steady-state temperature of 288K, is 390 W/m^2 — not 490 W/m^2, and which is the same rate that a 288K black body surface in vacuum — receiving only radiant power — would be gaining.

This is ultimately really all I’ve been trying to say.

• RW: If you read the first sentence of the wikipedia article you linked, you see that the superimposition principle applies to linear systems. The amount of radiation emitted with temperature (W = oT^4) is not linear. Convection, which begins when the lapse rate exceeds a critical threshold, is certainly not linear. The relevant principle is conservation of energy, in my example expressed in terms of energy per unit time.

Given the surface temperature of the earth and its emissivity, we know that OLR = 390 W/m2. Conservation of energy demands that:

Incoming = Outgoing + Retained heat causing warming

SWR + DLR = OLR + convection latent and simple heat + z

where z is the amount of energy that is slowing raising the temperature of the earth. z is about 0.6 W/m2 according to the latest rate of ocean warming from ARGO. This is small enough to ignore, making Incoming = Outgoing.

What do we know about these fluxes? Given our knowledge of surface temperature and emissivity, we are reasonably sure that OLR is about 390 W/m2. Given that average precipitation is about 1 m (m^3/m^2) per year, which means that the water vapor took about 80 W/m2 from the surface and released it (latent heat) in the atmosphere as it condensed to make liquid water or ice. We don’t have reliable observations for convection of simple heat, but the outgoing side of the equation needs to total at least 470 W/m2. So we know that the incoming flux needs to be at least 470 W/m2 or the law of conservation of energy will be violated.

KT get their values for SWR and DLR from radiation transfer calculation using an atmosphere with clouds, composition and temperature chosen for this publication. There is some observational evidence to support their modeling work and it confirms that SWR + DLR must be about 450 W/m2 or greater.

It doesn’t make sense to argue with measurements of SWR+DLR reaching the surface, radiation transfer calculations of SWR+DLR reaching the earth and the law of conservation of energy (given our knowledge of OLR and latent heat).

• “The amount of radiation emitted with temperature (W = oT^4) is not linear.

It effectively is though for a state of balance, and thus the superposition principle applies. Of course, it doesn’t apply to the path the system takes from one equilibrium state to another, which is highly non-linear — but it must apply to the ultimate end point, i.e. the new emergent equilibrium, independent of the non-linear path it takes to get there.

• And yes, I know that the amount of radiant power emitted as a consequence of temperature — increases with temperature (dictated by S-B). That is, each incremental degree K of warming requires more and more W/m^2 of net gain in order to effect and sustain it.

• Frank,

I should say that I agree the path the system takes to maintain equilibrium is non-linear as well. Maybe this is what you’re getting at? Still though, relative to the required manifested boundary fluxes needed to maintain balance, it is effectively linear, because the aggregate dynamics of all the thermodynamic components must net out to be the same (i.e. a net of 390 W/m^2 gained at the surface while 240 W/m^2 enters and leaves the system).

• Perhaps more precisely phrased as:

“The whole point is the actual rate that joules are being added to the surface, for a steady-state temperature of 288K, is 390 W/m^2 — not 490 W/m^2, and which is the same rate that a 288K black body surface in a vacuum — receiving and emitting only radiant power — would be gaining.”

71. “This is ultimately really all I’ve been trying to say.”

And that these (390 W/m^2 at the surface and 240 W/m^2 at the TOA) are the actual rates of joules gained and lost in and out of the whole Earth-atmosphere system on a continuum basis — for a state of balance.

• on June 13, 2014 at 1:34 am | Reply DeWitt Payne

Why can’t you see that you’re wrong about convection somehow cancelling. It can’t. If net convection were zero, then there’s 100 W/m² missing from the energy balance. The flow into the surface is ~490 W/m², therefore the flow out of the surface must be nearly equal. That’s only true if the convective flow is 100 W/m² from the surface to the atmosphere with no cancellation. It’s blindingly obvious to someone who isn’t blinding himself as you are.

• How are you interpreting my me as claiming convection is zero? I’ve never said or implied such, as of course there is significant convection from the surface to the atmosphere. Why don’t you see that 100 W/m^2 of radiant power from the atmopshere and Sun is replacing the 100 W/m^2 of convective flux leaving the surface but not coming back?

• convection is not net zero across the surface/atmosphere boundary.

• That is 100 W/m^2 of the 490 W/m^2 of radiant power from the atmosphere and Sun.

• on June 12, 2014 at 7:05 pm | Reply DeWitt Payne

Only the TOA number is correct. The surface absorbs ( a better word than gains) ~490 W/m² (~160 W/m² incident solar, ~330 W/m² DLR from the atmosphere and an insignificant amount by convection), not 390 W/m². The surface then emits slightly less than 490 W/m², ~390 W/m² in the form of LW IR and ~100 W/m² as sensible and latent heat (convection).

The atmosphere then emits 200 W/m² of OLR (40 W/m² of LW IR from the surface is transmitted directly from the surface to space) and 330 W/m² of DLR to the surface for a total of 530 W/m². The atmosphere absorbs 80 W/m² of incident solar radiation, 350 W/m² of the 390 W/m² surface upward LW radiation and 100 W/m² of energy by convection from the surface or 530 W/m², which, not surprisingly, equals the amount absorbed.

These numbers balance. Yours don’t and never have. You can go on about your surface ‘net’ energy gained of 390 W/m² all day, but it isn’t net by any normal definition of the word.

• “and thus are a net zero gain/loss across the surface/atmosphere boundary.

• “The surface absorbs ( a better word than gains) ~490 W/m² (~160 W/m² incident solar, ~330 W/m² DLR from the atmosphere and an insignificant amount by convection), not 390 W/m². The surface then emits slightly less than 490 W/m², ~390 W/m² in the form of LW IR and ~100 W/m² as sensible and latent heat (convection).

The atmosphere then emits 200 W/m² of OLR (40 W/m² of LW IR from the surface is transmitted directly from the surface to space) and 330 W/m² of DLR to the surface for a total of 530 W/m². The atmosphere absorbs 80 W/m² of incident solar radiation, 350 W/m² of the 390 W/m² surface upward LW radiation and 100 W/m² of energy by convection from the surface or 530 W/m², which, not surprisingly, equals the amount absorbed.”

I don’t disagree, but why don’t you see that the 100 W/m^2 of power in excess of 390 W/m^2 entering and leaving the surface are perpetually cancelling one another out? That is, those joules entering an leaving the surface are neither adding or taking away joules from the surface, and thus are a net zero gain across the surface/atmosphere boundary.

I’m perplexed by everyone’s staunch resistance to this notion.

72. RW wrote: “Convection is not net zero across the surface/atmosphere boundary.”

Great. Here is how you calculate how much power is convected as latent heat: Average precipitation is about 1 m per year or 1 m^3/m^2 per year. A m^3 of water weighs 10^3 kg. Every kg of water removes 2.44*10^6 J of energy from the ocean when it evaporates (at 25 degC) and releases the same amount of energy to the atmosphere when it condenses to make liquid water. Another 0.33*10^6 J is released if the water freezes in the atmosphere and falls as snow or ice. That gives us about 2.5*10^9 joules per year per m^2. Dividing by 31,556,736 s/yr gives 79 J/s/m2 = 79 W/m2 of latent heat lost by the surface and being gained by the atmosphere.

When added to the 390 W/m2 of OLR leaving the surface, this gives at least 470 W/m2 of energy leaving the surface (before adding convection of simple heat).

• I should say that I certainly agree that convection makes the surface cooler than it would otherwise be (at least as a first order effect). Maybe my comments are being interpreted as if convection has no influence on the surface temperature? I’m certainly not claiming that.

• Yeah, no disagreement. Convection is net positive from the surface to the atmosphere, i.e. more convective power leaves the surface than enters the surface.

The point you and Dewitt seem to be missing is that — for a state of balance — all convective power leaving the surface must be in excess of the power radiated from the surface and that the surface emits 390 W/m^2 of radiant power solely due to its temperature (and emissivity), but there is no such requirement for the amounts of radiant and convective power entering the surface from the atmosphere.

The bottom line is a watt is a watt, a joule is a joule, independent of whether it’s radiant or non-radiant. The surface itself doesn’t distinguish or assign some special attribute to convective power and radiant power entering and leaving it. All it needs to be in balance is for the total power entering it to be equal to the total power leaving it, and all it needs to be at a temperature of 288K (with an emissivity of 1) is for all power in excess of 390 W/m^2 entering it to be equal to all power in excess of 390 W/m^2 leaving it.

Maybe the issue is ‘net power gained’ is more formally expressed as ‘net energy gained’ — I don’t know, but there should not be this kind of stark resistance to the notion of there being a net power gain at the surface or there being fluxes across the surface/atmosphere boundary that are net zero (i.e. neither adding or taking away joules).

• Now, all of this being understood, I still don’t understand why ‘net absorption’ is claimed here to be equal to zero prior to 2xCO2? Or have I misunderstood everyone?

Comment of June 8, 2014 at 11:43 pm

• “It’s a shame, because it’s such an amazing discovery..”

No, it’s a shame because it’s so incredibly elementary, yet no one is willing to acknowledge it.

• “Statements this melodramatic should really be accompanied by appropriate mood music. Screechy violins, deep organ sounds.

No one can understand what on earth you are on about.

When we reduced it down to an equation it was “parameter I created” = “parameter I want it to mean”.

You are right. The parameter you created is equal to the parameter you want it to mean.

It’s your parameter. You are entitled to it. No one else is interested in it. No one cares. It’s a shame, because it’s such an amazing discovery..”

I said I agreed with your more detailed equations which included all the separate thermodynamic components. Moreover, what on Earth is so hard to understand here? There are an infinite number of thermodynamic paths that can manifest a surface temperature of 288K, right? I’m simply stating the universal properties of all surface temperatures of 288K, independent of manifesting thermodynamic path. Of course, to a large degree these properties are trivial, but they none the less properly quantify the rates of joules gained and lost in and out of the whole system.

I only initially made this point because I think it may come into play for radiative transfer simulations and why the surface temperature, surface radiant power, and the surface radiated spectrum is what’s used as the measure for quantifying opacity through the whole mass of the atmosphere, but I truly don’t know yet and may very well be wrong.

The revelation to me that the 3.7 W/m^2 is really the difference between the ‘instantaneous’ flux decrease at the TOA and the ‘instantaneous’ IR flux increase at the surface — is making a lot of sense and is easy to internally conceptualize. Why it’s referred to as the ‘net absorption’ increase (i.e. it’s the net imbalance imposed on the system) also makes sense. Moreover, I understand the reason why the IR flux decreases at the TOA and increases at the surface is because of the lapse rate, i.e. temperature decreases with height. If it were the other way around, i.e. temperature increased with height, the IR flux at the TOA would increase and the IR flux at the surface would decrease (and GHGs would actually enhance the radiative cooling of the system, rather than enhance the radiative warming).

Now, all of this being understood, I still don’t understand why ‘net absorption’ is claimed here to be equal to zero prior to 2xCO2? Or have I misunderstood everyone?

• Why you or anyone would feel the need to dispute that is strange. Or maybe you think I’m implying something beyond just that?

• RW

I don’t understand your stark defiance to this fundamental point of mine.

Statements this melodramatic should really be accompanied by appropriate mood music. Screechy violins, deep organ sounds.

No one can understand what on earth you are on about.

When we reduced it down to an equation it was “parameter I created” = “parameter I want it to mean”.

You are right. The parameter you created is equal to the parameter you want it to mean.

It’s your parameter. You are entitled to it. No one else is interested in it. No one cares. It’s a shame, because it’s such an amazing discovery..

• “The emission of thermal radiation from a surface depends on its emissivity, which in turn is NOT independent of its material, in fact, completely dependent on its material.”

OK, yes — emissivity of a surface is not independent of its material, but if the material is different and the emissivity is the same, the radiant power emitted from the surface is independent of the material, where as the convected flux from the surface is still highly dependent on the material. This is the fundamental difference between what I’m saying and your comment above I quoted.

Most of the Earth’s surface has an emissivity fairly close to 1, though I know desserts are the biggest deviation. None the less, my comments stipulate an emissivity of 1, and are in the context of global averaged emissivity of near 1.

I don’t understand your stark defiance to this fundamental point of mine. Surely you must agree that if the surface emissivity is 1, any power in excess of 390 W/m^2 entering and leaving the surface must be net zero across the surface/atmosphere boundary, otherwise the surface temperature could not be 288K.

• “We could just as easily rewrite the mishmash statement from RW above:

“All radiative power leaving the surface must be in excess of the convective/latent heat radiated from the surface, and the surface transfers 100 W/m2 solely due to the temperature and moisture imbalance between the surface and the atmosphere immediately above..“”

The difference is the convective flux from the surface depends largely on what matter the surface consists of — in addition to its temperature, where as the radiant flux from the surface is solely due to its temperature and emissivity, independent of the matter it’s made up of.

• Also, the 288K surface temperature is measured — not derived, and thus has already been thermodynamically manifested. I’m only deducing what I’m deducing about energy flow, energy gain, net energy gain etc., because we have a measured surface temperature. I think you may be reading a bit too much into what I’m saying, or you think I’m stating something about the thermodynamic path the system is taking to manifest 288K at the surface. I’m not.

• The difference is the convective flux from the surface depends largely on what matter the surface consists of — in addition to its temperature, where as the radiant flux from the surface is solely due to its temperature and emissivity, independent of the matter it’s made up of.

The emission of thermal radiation from a surface depends on its emissivity, which in turn is NOT independent of its material, in fact, completely dependent on its material.

Emission of thermal radiation from desert sand at 288K will be around 280 W/m2 whereas emission of thermal radiation from the ocean at 288K will be around 370 W/m2.

• “There is no requirement for any temperature to be any temperature, there is no requirement for any one power minus another power to be any value. The only requirement is for the conservation of energy.”

Completely agree.

• RW says,

..all convective power leaving the surface must be in excess of the power radiated from the surface and that the surface emits 390 W/m^2 of radiant power solely due to its temperature (and emissivity), but there is no such requirement for the amounts of radiant and convective power entering the surface from the atmosphere..

There is no requirement for any temperature to be any temperature, there is no requirement for any one power minus another power to be any value. The only requirement is for the conservation of energy.

The surface absorbs radiation according to its absorptivity, which is close to 1 for most surfaces, the surface emits thermal radiation according to its temperature and emissivity. The transfer of sensible heat is due to the difference between surface and atmospheric temperature, wind speed and surface type. The transfer of latent heat is due to the moisture available in the surface, the moisture level in the atmosphere just above and the wind speed.

All of these combine to determine a surface temperature.

We could just as easily rewrite the mishmash statement from RW above:

All radiative power leaving the surface must be in excess of the convective/latent heat radiated from the surface, and the surface transfers 100 W/m2 solely due to the temperature and moisture imbalance between the surface and the atmosphere immediately above..

• SoD,

“Can you please review my statement of June 7, 2014 at 6:58 am.

The usual meaning of Δ is “change in”, “after – before”. Just in case I wrote out exactly what it meant.

ΔRF = RF(t=1) – RF(t=0)

What is the sound of one hand clapping?

What is the difference between RF(t=0)?”

I understand the 3.7 W/m^2 for 2xCO2 is the ‘net absorption’ change, and that by the IPCC’s definition of RF, RF is zero prior to 2xCO2.

So what am I missing here? If you run an RT simulation of a global average atmosphere prior to doubling CO2, what does the simulation calculate? You’re saying there is not a total amount in W/m^2 that is calculated as net absorbed?

• “What is the definition of transmissivity?

Proportion of incident radiation that is transmitted. It is a fraction, well a number between 0.0 and 1.0.

The atmospheric absorptivity is isotropic as far as longwave radiation is concerned.

If 90% of 10 μm radiation is transmitted between 1km to 2km, then 90% of 10 μm radiation is transmitted between 2km to 1km.”

I didn’t know you meant specific to wavelength; however, transmissivity is not required to be equal for total incident power coming from both directions, right?

I’m thinking this because the proportions of wavelengths to power vary by temperature of emission, which decreases with height.

• “I have absolutely no idea what this means.

Transmittance or transmissivity can be reduced or increased by more or less GHGs. What is “attenuation of transmittance by the atmosphere”?”

Reduced transmission (to space) from increased absorption by GHGs.

• OK, I guess you could use them for that, but that’s not their primary purpose, which as I understand is for quantifying IR opacity of the atmosphere. Besides, I would at least intuitively think the satellite measurments have a lower margin of error than an RT simulation. Maybe like only 1-2%, but I really don’t know.

• so maybe the question is relative to atmospheric IR opacity, if you run an RT simulation prior to 2xCO2 or any GHG changes, what is being quantified in this regard? If increased opacity is quantified as a net absorption increase, how is net absorption itself in the aggregate quantified?

• If transmission can’t decrease, how can the flux at the TOA decrease for the increased opacity case? Doesn’t the TOA flux decrease have to be the result of an absorption increase somewhere else? Doesn’t an absorption increase require a transmission decrease?

It’s my understanding that there are essentially only three possible fates to radiant power incident on an object. It can either be absorbed, transmitted, reflected, or some combination of all three.

• We don’t need or use an RT simulation to determine OLR or absorbed solar radiation, as we have satellites measurements that tell us those things.

What was the OLR when CO2 was 280ppm? And when CH4 was 800ppb? How does OLR change when we go from 280ppm to 380ppm.

The absolute error on a satellite measurement of OLR is how many W/m2? Let’s say 5 W/m2.

So why compare a calculation of “the future” with a measurement of the present, when you can get a better understanding of the change by comparing two calculations. Otherwise you might be mistaking a change for an absolute measurement error. Or you might think the change is double what it would actually be.

Of course, many comparisons have been done of OLR calculations vs OLR measurements, e.g.:

• on June 17, 2014 at 1:15 am DeWitt Payne

RW,

Consider this thought experiment. Suppose you were at the top of a tall building with a detector tuned to the CO2 line at 667.494 cm-1. I have a laser that emits at 667.494cm-1 on the ground aimed at you. Can you detect the emission from that laser?

The answer is no, you can’t. For any laser power short of heating the air in the beam to a plasma, all the radiation from the laser will be absorbed and thermalized before it gets to you. Doubling the CO2 would have no effect because you can’t transmit less than zero.

You would detect emission with your detector, but it would be the same in any direction that you pointed it. That’s because the emission temperature of CO2 at that frequency would be the same. If you doubled the CO2 concentration, the emission wouldn’t change. You can’t emit more than a black body at that temperature and the emission is already at that level.

Now get in a plane and fly at 5 km altitude. Your detector will see a lower emission. Is this because surface radiation has been attenuated further? No. If you couldn’t see a laser on the surface from a tall building, you certainly can’t see the surface at a higher altitude. You see less emission because the air is colder at 5 km than it is near the surface. Since the absorptivity is 1, the emission will be the same as from a black body at the local temperature.

It has nothing to do with the EM radiation emitted from the surface at the CO2 frequency. The only connection with the surface is through the surface temperature controlling, on average, the temperature of the air at 5 km via the environmental lapse rate.

And that’s why the total emission measured at the tropopause after doubling the CO2 concentration and allowing the stratosphere to equilibrate is lower than before doubling. The emission from the wings of the CO2 band where the extinction coefficient is lower is coming from a higher altitude where it’s colder.

• “You are creating definitions and then asking us to explain these definitions.”

I’m not creating definitions, but trying to describe fundamental concepts as best I can. Everyone’s process of learning is different. For me, I first need to understand and/or have a basic conceptual picture before I’m likely to understand any equation or series of equations.

“I have explained what ΔRF is. I have explained what an RT simulation calculates. It calculates the terms in ΔRF.”

Yes, I fully understand this component.

“You have decided that an RT simulation calculates some unclear definition and now you want me to explain this unclear definition to you.”

I haven’t decided anything. The concept I’m attempting to describe is that of atmospheric opacity — mainly in the LW IR. More specifically how atmospheric opacity is quantified by these RT simulations.

It’s my understanding that atmospheric opacity increases when CO2 is double or when GHGs are added — not that atmospheric opacity goes from zero to 3.7 W/m^2 or from zero to some other positive number.

“When atmospheric opacity to longwave radiation goes up, immediately after, OLR goes down.

It’s pretty simple.”

Yes, this part is easy to understand but it doesn’t quantify or say anything about opacity in the aggregate. It rather just quantifies an incremental change in opacity from some non-specified or non-defined quantity.

“If the climate was in balance before, after OLR goes down as a result of increased atmospheric opacity, there will now be an imbalance in energy.

That’s pretty simple too.”

Yes of course, as again this is very easy to understand.

“Transmission from the surface to TOA is a different value from transmission from 5km to TOA.”

Understood.

“You can see the equation for OLR in eqn 16 in Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part Six – The Equations. And its explanation is given as:

The intensity at the top of atmosphere equals..

The surface radiation attenuated by the transmittance of the atmosphere, plus..

The sum of all the contributions of atmospheric radiation – each contribution attenuated by the transmittance from that location to the top of atmosphere”

This seems to be describing some sort of integral of all the layers (including the surface) to the TOA, where for an opacity increase each layer transmits a little less through to the TOA.

“You just have no idea what you are inquiring about. And I have no idea either.”

I think I have an idea but may not be articulating it properly. Let me ask you, what does atmospheric opacity in the LW IR mean to you? How would you describe or define it in a general sense?

To me, it’s the absorption of upwelling IR from the surface and atmosphere acting to cool that is absorbed by GHGs in the atmosphere (i.e. ‘blocked’ from passing into space). It is the fundamental reason why we have a radiative induced GHE in the first place. Moreover, the theory behind additional GHGs causing global warming is that atmospheric opacity to the IR increases due to more GHGs in the atmosphere (and to a small extent a negligible amount of additional SW is absorbed by the atmosphere).

• I think I have an idea but may not be articulating it properly. Let me ask you, what does atmospheric opacity in the LW IR mean to you? How would you describe or define it in a general sense?

Opacity is the opposite of transmissivity, effectively it is the technical term, absorptivity.

Transmissivity, t = 1-a, where a = absorptivity
And for interest, t=exp(-τ), where τ = optical thickness

However, there is no general term t or a in the atmosphere. We have define either the specific values vs wavelength and height, or we have to define its “aggregate” for a specific situation.

Transmissivity, t(λ,z1, z2) means t is a function of λ and z1, z2 (wavelength and the heights between which we are measuring transmissivity).

You could define transmissivity that you are interested in as the value from the surface to TOA for a blackbody surface emission at a particular temperature. That would be a different value at another temperature. And a different value at a different height.

With a given GHG change you might have zero change in transmissivity from the surface to TOA and yet a significant change in transmissivity from 5km to TOA.

Calculating OLR tells you the practical outcome of all of the changes in transmissivity. You can’t “average” transmissivity and hope to get a useful value. You can’t weight it by the Planck emission curve from the surface and hope to get a useful value.

• Would it be accurate to say — for the increased opacity case — that transmissivity to the TOA decreases and transmissivity to the surface increases?

• And which is the amount which increases by 3.7 W/m^2 when CO2 is doubled?

• If you run an RT simulation of a global average atmosphere prior to doubling CO2, what does the simulation calculate?

Outgoing longwave radiation (OLR), absorbed solar radiation, other parameters of interest.

• Would it be accurate to say — for the increased opacity case — that transmissivity to the TOA decreases and transmissivity to the surface increases?

No, it would be inaccurate.

t(λ, z1, z2) = t(λ, z2, z1).

Transmissivity is the same in both directions.

If you increase the amount of GHGs somewhere in the atmosphere then t(λ, z1, z2) will be either the same or greater.

t(λ, z1, z2) can be the same because:
– the GHGs didn’t increase between z1 and z2
– the GHG has no absorption at λ (i.e. t=1)
– the change was insignificant
– t(λ, z1, z2) = 0 due to an already very high absorption

• Isn’t what your describing for emission and not transmission?

• “The intensity at the top of atmosphere equals..

The surface radiation attenuated by the transmittance of the atmosphere, plus..

The sum of all the contributions of atmospheric radiation – each contribution attenuated by the transmittance from that location to the top of atmosphere”

I think this is what I don’t understand. How can surface radiation be attenuated by transmittance of the atmosphere? Isn’t surface emitted radiation attenuated by absorption of the surface radiation by the atmosphere?

If transmittance is defined as the fraction of radiation that passes through a layer or object, how can radiant power into the atmosphere be attenuated by transmittance of the atmopshere?

• Sorry I wrote rubbish in my last statement.

Here is the rewrite with bold for the change

——————————-
t(λ, z1, z2) = t(λ, z2, z1).

Transmissivity is the same in both directions.

If you increase the amount of GHGs somewhere in the atmosphere then t(λ, z1, z2) will be either the same or lower.

t(λ, z1, z2) can be the same because:
– the GHGs didn’t increase between z1 and z2
– the GHG has no absorption at λ (i.e. t=1)
– the change was insignificant
– t(λ, z1, z2) = 0 due to an already very high absorption

• “Here is the rewrite with bold for the change”

OK, but what do you mean about transmissivity being the same in both directions? I assume by both directions you mean incident radiant power from both above and below?

• I wrote:

“I think this is what I don’t understand. How can surface radiation be attenuated by transmittance of the atmosphere? Isn’t surface emitted radiation attenuated by absorption of the surface radiation by the atmosphere?”

Maybe you mean attenuation of transmittance by the atmosphere from each layer to the TOA? Now that would make sense to me.

• OK, but what do you mean about transmissivity being the same in both directions? I assume by both directions you mean incident radiant power from both above and below?

What is the definition of transmissivity?

Proportion of incident radiation that is transmitted. It is a fraction, well a number between 0.0 and 1.0.

The atmospheric absorptivity is isotropic as far as longwave radiation is concerned.

If 90% of 10 μm radiation is transmitted between 1km to 2km, then 90% of 10 μm radiation is transmitted between 2km to 1km.

• I wrote:

“I think this is what I don’t understand. How can surface radiation be attenuated by transmittance of the atmosphere? Isn’t surface emitted radiation attenuated by absorption of the surface radiation by the atmosphere?”

Maybe you mean attenuation of transmittance by the atmosphere from each layer to the TOA? Now that would make sense to me.

I have absolutely no idea what this means.

Transmittance or transmissivity can be reduced or increased by more or less GHGs. What is “attenuation of transmittance by the atmosphere”?

• OK, but why is it not accurate to say that — for the increased opacity case — transmission in the aggregate through the TOA decreases and transmission in the aggregate through to the surface increases?

For the IR flux passing into space to decrease, doesn’t transmission through the TOA have to decrease (from increased absorption)? And for the IR flux passing from the atmosphere to the surface, doesn’t transmission to the surface have to increase (from increased emission)?

• That should have said:

“And for the IR flux passing from the atmosphere to the surface to increase, doesn’t transmission to the surface have to increase (from increased emission)?

• on June 18, 2014 at 9:54 pm DeWitt Payne

RW,

Transmissivity is not the same as flux. Transmissivity is the fraction of incident flux for a given narrow wavelength range at one end of the path that reaches the other end. If you have emission as well as absorption and worse, the path isn’t isotropic and isothermal, the flux you measure at one end of the path will be different than if you reverse the direction of measurement.

In spectrophotometry, one correction for this sort of thing is to modulate the incident radiation and then detect only the modulated signal by using a filter on the detector tuned to the modulating frequency. In that case, the direction of measurement will not make a difference as long as the transmissivity isn’t too small. For path lengths through the atmosphere longer than 1 km, most wavelengths in the thermal IR will have a transmissivity to low to detect a modulated signal.

• I didn’t know you meant specific to wavelength; however, transmissivity is not required to be equal for total incident power coming from both directions, right?

I’m thinking this because the proportions of wavelengths to power vary by temperature of emission, which decreases with height.

Transmissivity for a given spectrum will be the same in both directions. Obviously if you put 1W up through a layer of the atmosphere with a different spectrum from 1W down through the same layer of the atmosphere then you can’t expect transmissivity to be the same for both.

Likewise if you put 1W up through a layer of the atmosphere with spectrum A and 1W up through the same layer with spectrum B the transmissivity will not be the same (except by some surprising coincidence).

• How can atmospheric opacity in the aggregate be quantified as total OLR (or about 240 W/m^2)? For opacity to increase, net transmission to space has to decrease, and net absorption has to increase. If the full 240 W/m^2 of OLR is already being fully net absorbed, how can net absorption increase and net transmission decrease? Or how can net transmission decrease if it’s already zero?

You are creating definitions and then asking us to explain these definitions.

I have explained what ΔRF is. I have explained what an RT simulation calculates. It calculates the terms in ΔRF.

You have decided that an RT simulation calculates some unclear definition and now you want me to explain this unclear definition to you.

If the full 240 W/m^2 of OLR is already being fully net absorbed, how can net absorption increase and net transmission decrease?

There is no “240 W/m^2 of OLR is already being fully net absorbed“. It’s just a meaningless hodgepodge of words.

When atmospheric opacity to longwave radiation goes up, immediately after, OLR goes down.

It’s pretty simple.

If the climate was in balance before, after OLR goes down as a result of increased atmospheric opacity, there will now be an imbalance in energy.

That’s pretty simple too.

Or how can net transmission decrease if it’s already zero?” I have no idea what net transmission is. Transmission, on the other hand, is not zero from anywhere. Transmission from the surface to TOA is a different value from transmission from 5km to TOA.

You can see the equation for OLR in eqn 16 in Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part Six – The Equations. And its explanation is given as:

The intensity at the top of atmosphere equals..

The surface radiation attenuated by the transmittance of the atmosphere, plus..

The sum of all the contributions of atmospheric radiation – each contribution attenuated by the transmittance from that location to the top of atmosphere

..I’m not inquiring about the IPCC’s definition of RF, which I know already.

You just have no idea what you are inquiring about. And I have no idea either.

• “Same answer as before. OLR.”

I don’t understand this. How can atmospheric opacity in the aggregate be quantified as total OLR (or about 240 W/m^2)? For opacity to increase, net transmission to space has to decrease, and net absorption has to increase. If the full 240 W/m^2 of OLR is already being fully net absorbed, how can net absorption increase and net transmission decrease? Or how can net transmission decrease if it’s already zero?

As original explained on June 7, 2014 at 6:58 am:

ΔRF = ΔS – ΔOLR”

I’m not inquiring about the IPCC’s definition of RF, which I know already.

• “You can have poor absolute accuracy but excellent repeatability. So you know if the value is changing and by how much. But you didn’t know exactly what it was at the start.”

Understood.

• ..so maybe the question is relative to atmospheric IR opacity, if you run an RT simulation prior to 2xCO2 or any GHG changes, what is being quantified in this regard? If increased opacity is quantified as a net absorption increase, how is net absorption itself in the aggregate quantified?

Same answer as before. OLR.

As original explained on June 7, 2014 at 6:58 am:

ΔRF = ΔS – ΔOLR

• You need to understand error analysis.
You have different error sources. One common error source in measurement is absolute error.

For example, measuring incoming solar radiation. You have absolute error, long term drift, repeatability and resolution. Each one is different.

You can have poor absolute accuracy but excellent repeatability. So you know if the value is changing and by how much. But you didn’t know exactly what it was at the start.

For example:

• We don’t need or use an RT simulation to determine OLR or absorbed solar radiation, as we have satellites measurements that tell us those things.

So what are ‘the other parameters of interest’? What am I missing here? If someone ran and RT simulation of a global average atmosphere prior to 2xCO2 or any other GHG changes, what parameters does the simulation output? How are they quantified? What are the quantifications relative to the 3.7 W/m^2 change introduced when CO2 is doubled?

Are these not fair and logical questions?

• I appreciate your sticking with me on this, as I do want to learn it correctly.

• SoD,

I know you can’t average transmissivity and derive anything useful, but I’m wondering if ‘net transmittance’ may simply the difference between the IR power emitted from the surface and the IR power emitted to the surface? If a ‘net absorption’ increase is quantified as the difference between the decreased IR power emitted to space to the increased IR power emitted to the surface, that would seem to make sense.

I’m glad you agree that opacity is essentially the same thing as absorptivity. The question then I guess how do we define and quantify net opacity through the whole mass of the atmosphere?

73. RW wrote (with my emphasis): “I don’t understand your stark defiance to this FUNDAMENTAL point of mine. Surely you must agree that if the surface emissivity is 1, any power in excess of 390 W/m^2 entering and leaving the surface must be net zero across the surface/atmosphere boundary, otherwise the surface temperature could not be 288K.”

There is nothing “fundamental” in your statement, which confuses cause and effect. Conservation of energy is fundamental. All of the power fluxes entering and leaving a surface determine how fast that surface’s temperature is CHANGING – NOT the surface temperature! The temperature of a surface depends on the internal energy of the surface, which is the net result of all PAST power fluxes into and out of the surface. The CURRENT fluxes tell you how FAST the temperature is currently changing. Pay attention to the units: Energy, joules; power joules.

Your remarks continuously confuse cause and effect. The temperature and emissivity of a surface determine ONLY the outward flux and spectrum of emission from a surface – which we call OLR for the surface of the earth. The other fluxes determine the surface energy IMBALANCE – which is rarely exactly zero. The other fluxes to and from the surface are real – they don’t “cancel” leaving a net inward flux of 390 W/m2 to automatically balance OLR. The photons of SWR and DLR reaching the surface are just as real – and totally independent of surface temperature – as the photons of OLR (which depend on temperature). The photons of SWR and DLR don’t sense the earth’s temperature and decide whether or not to be absorbed when they arrive at the surface. The composition of the surface determines whether photons are absorbed or reflected (absorptivity) when they arrive at the surface – not some mathematical requirement for producing a stable temperature.

The kinetic energy of the water molecules evaporating from the ocean is real: An average 2.7 kg of water (2.7 mm) evaporates from every m^2 of surface every day of the earth and returns as rainfall, leaving 6,800,000 joules of energy behind in the atmosphere that was previously in the ocean. That is the source of the 79 W/m2 flux in the KT diagram for convection of latent heat. That energy isn’t “cancelled” on cloudy days when SWR is too weak to produce a surface energy balance. The rate at which water evaporates depends weakly on surface temperature, but dramatically on wind speed. It takes a whole winter of weak SWR for the ocean to cool a few degC. and that small change in temperature produces very little change in the rate of evaporation.

• “There is nothing “fundamental” in your statement, which confuses cause and effect.”

My statement doesn’t imply anything about cause.

“All of the power fluxes entering and leaving a surface determine how fast that surface’s temperature is CHANGING – NOT the surface temperature!”

I would say all of the power fluxes entering and leaving determine whether and by how much the surface temperature is changing, but yes of course I agree the surface temperature itself doesn’t determine all the fluxes.

” The other fluxes determine the surface energy IMBALANCE – which is rarely exactly zero. The other fluxes to and from the surface are real – they don’t “cancel” leaving a net inward flux of 390 W/m2 to automatically balance OLR.”

Of course, if there is an imbalance they are not cancelling one another, but if there is balance they most certainly are cancelling one another.

“The photons of SWR and DLR reaching the surface are just as real – and totally independent of surface temperature – as the photons of OLR (which depend on temperature).”

Yes, of course. Generally energy flow into the surface is not temperature dependent, where as generally energy flow out of the surface is (both radiant and non-radiant).

“The photons of SWR and DLR don’t sense the earth’s temperature and decide whether or not to be absorbed when they arrive at the surface. The composition of the surface determines whether photons are absorbed or reflected (absorptivity) when they arrive at the surface – not some mathematical requirement for producing a stable temperature.”

Again, yes of course. My statement is not claiming otherwise.

74. SOD, Pekka or DeWItt: Reviewing fundaments has made me realize that I don’t fully understand “convection of simple heat” on the KT energy balance diagram. This is a flux from the surface to the atmosphere. Photons and water vapor cross the interface between the surface and the atmosphere, resulting a flux of energy. What is crossing this interface in the case of simple heat?

When water crosses the interface between the surface and the atmosphere, we call it evaporation, not convection. Convection takes the latent heat in the water vapor high enough for the water to condense, converting latent heat into simple heat. So the evaporation/convection/condensation cycle might be called “convection of latent heat”, even though the physical fluxes across the interface are really evaporation and precipitation.

What is happening at the interface that physically produces a flux of simple energy from the surface to the atmosphere? The only hypothesis I can come up with involves molecular collisions between molecules in the air and surface. As far as I know, the correct technical name for heat transfer by collisions is conduction.

• Frank,

Take the sun warming the earth’s surface by radiation. How does heat transfer from the surface to the atmosphere apart from radiation? Of course at the boundary it’s only by conduction. Convection is (the transfer of heat via) the bulk movement of fluids and the surface isn’t moving. Also, right at the surface the air is not actually moving either.

But if conduction, not convection was the dominant (or even significant) form of heat transfer then we would rely on the heat diffusion through the entire atmosphere. How long from the surface to the tropopause? If we looked up the thermal conductivity of air: 0.024 W/mK and applied that to let’s say a 100K difference over 10km.. Hc = 0.024 x 100 / 10000 = 0.00024 W/m2 or 240 μW/m2. It’s nothing effectively in comparison to radiation and so there would be only heat transfer by radiation in the atmosphere.

So some heat transfer by diffusion is necessary across the boundary, and then convection sweeps it away.

This is true in most “classic” convection problems where you have something like a heated metal surface and a fluid flowing over the surface. Conduction is necessary across the boundary or no heat would flow, and then convection actually does “all” of the work.

And when we look across a boundary layer we are considering a very short distance. Let’s say 1 μm (I haven’t looked up any typical values).

So with air, let’s say a 1K difference across a 1 μm boundary, now the heat transfer, Hc = 0.024 x 1/ 1×10-6 = 24 kW/m2.

So across these tiny distances conduction does something quite impressive. Of course, with no convection the heat transfer would quickly stop as the heat transfer would wipe out the small temperature difference we just described over that first 1 μm..

• on June 14, 2014 at 8:27 pm | Reply DeWitt Payne

Sensible heat is due to conduction across the surface /atmosphere interface. It’s rate depends on the temperature gradient at the surface in degrees/unit length. Now if conduction by diffusion was the only means of sensible heat transfer in the atmosphere than the rate of sensible energy transfer would be slow because the gradient would reduce over time and conduction by diffusion in the atmosphere is slow. But the atmosphere is in motion. This results in a thinning of the boundary layer and a relatively constant temperature gradient that increases with wind velocity. But even with no wind, turbulent eddy conduction is much faster than diffusion.

It’s called sensible heat because the temperature change can be measured with a thermometer or some other device. See for example this paper, which describes the measurement of sensible heat flux by measuring the air density fluctuations caused by turbulent eddies.

• DeWItt and SOD: Thanks for the replies. I figured conduction must be involved. So the process of transfer of simple heat and latent heat (water vapor) is similar. Water vapor or air molecules warmed by the surface diffuse a short distance (perhaps 1 um for the reason SOD suggests). Then “advection” or “bulk motion” moves those molecules much further than they can travel by diffusion. (“Convection” apparently cover both bulk motion and molecular diffusion.)

I’m not sure I understand the mechanism of convection once conduction has carried simple heat several um above the surface. When I refer to convection, I often use the phrase “buoyancy-driven convection” – meaning the type of convection that develops when an unstable lapse rate is present. I’m not sure that term lapse rate is the appropriate term for distances of a few meters or if convection over those first few meters (but not the first few um where conduction is important) is driven by differences in density. There is also the possibility of turbulent flow. DeWItt mentioned something called “turbulent eddy conduction”, but he may be referring to “eddy diffusion”.

• So the process of transfer of simple heat and latent heat (water vapor) is similar.

It’s not only similar, it’s essentially identical, so the same equations can be used to describe both, and knowing a heat transfer coefficient you can derive the mass transfer coefficient for the same conditions

Only the units differ – mass transfer is driven by the difference between liquid saturated vaour pressure and bulk vapour pressure, heat transfer by the difference between surface temperature and bulk temperature

• on June 16, 2014 at 10:11 pm DeWitt Payne

Frank,

Convection is the term used when there is bulk motion of the medium. As I remember, convection is used by meteorologists for buoyancy driven vertical bulk movement. Advection is used for horizontal bulk movement. Advection is driven by the pressure gradient force. Air wants to flow from regions of high pressure to regions of low pressure.

The pressure gradient force is a main driver of the major atmospheric circulations like the Hadley, Ferrel and Polar cells. That’s because the altitude at constant pressure decreases with increasing latitude because average temperature decreases with increasing latitude leading to increased atmospheric density. So air at high altitude wants to flow towards the poles from the equator, causing a return flow at the surface. High solar heating at the equator is another driver.

Eddy diffusion is a commonly used term, but it isn’t really diffusion. Turbulent eddies at all scales are dissipative, which means there must be a source of energy to sustain the turbulence.

75. .. and “boundary layer” is the wrong term. The boundary layer is the layer of fluid from the stationary fluid at the boundary through to the free flowing fluid.

There’s another term but I can’t recall off the top of my head what it is.

• on June 14, 2014 at 10:28 pm | Reply DeWitt Payne

Diffusion layer? I think that’s the term we used in electrochemistry for things like rotating disk electrodes.

76. Alright,

Getting back to this, I understand the 3.7 W/m^2 for 2xCO2 is the calculated difference between the reduced IR flux passing out the TOA and the increased IR flux passing to the surface. I don’t know what the actual numbers are, but let’s say if it were -6 W/m^2 at the TOA and +2.3 W/m^2 at the surface, this would make the net absorption increase 3.7 W/m^2 (-6 + 2.3 = -3.7) or a net of -3.7 W/m^2 at the TOA.

Correct?

Furthermore, I understand the way RT the differential equation integrates the emission and absorption of each layer into the calculation that arrives at the 3.7 W/m^2 is as follows (assuming a 4 layer RT simulation):

‘After’ each layer subsequently absorbs a little more from above and below and emits a little more upwards and downwards due to added GHGs:

For the portion of the amount that constitutes the IR flux decrease at the TOA, there is a surface IR to the TOA absorption increase, a layer 1 IR to the TOA absorption increase, a layer 2 to the TOA absorption increase, a layer 3 to the TOA absorption increase, and a layer 4 to the TOA absorption increase (or at least the sum of the changes from all the layers — for absorption — is positive, resulting in an IR flux decrease at the TOA).

For the portion of the amount that constitutes the IR flux increase at the surface, there is a layer 1 IR to surface transmission increase, a layer 2 IR to the surface transmission increase, a layer 3 IR to the surface transmission increase, and a layer 4 IR to the surface transmission increase (or at least the sum of the changes from all the layers — for transmission to the surface — is positive, resulting in an IR flux increase at the surface).

Right?

• “Your statement is correct. So long as when you say “ultimately” you change it to “immediately”.

Thank you. Yes, I understand it would essentially be immediately or ‘instantaneously’.

As each layer subsequently absorbs a little more from above and below and emits a little more upwards and downwards due to added GHGs:

For the portion of the amount that constitutes the IR flux decrease at the TOA, there is a surface IR to the TOA absorption increase, a layer 1 IR to the TOA absorption increase, a layer 2 to the TOA absorption increase, a layer 3 to the TOA absorption increase, and a layer 4 to the TOA absorption increase (or at least the sum of the changes from all the layers — for absorption — is positive, resulting in an IR flux decrease at the TOA).

For the portion of the amount that constitutes the IR flux increase at the surface, there is a layer 1 IR to surface transmission increase, a layer 2 IR to the surface transmission increase, a layer 3 IR to the surface transmission increase, and a layer 4 IR to the surface transmission increase (or at least the sum of the changes from all the layers — for transmission to the surface — is positive, resulting in an IR flux increase at the surface).

• OK.

• RW,

You can download an excell spreadsheet which is a rough approximation to exactly what you are describing. The 15 micron absorption band is approximated with a simple Beer-Lambert transmission. The atmosphere is divided into 100m layers with standard pressure and temperature dependence and varying CO2 levels. A doubling of CO2 from 300ppm to 600ppm decreases radiative flux by about 8W/m2. This exaggerates the greenhouse effect because it doesn’t handle properly individual line strengths and it oversimplifies the atmosphere. However it is does illustrative of what you describe.

• SoD,

Does the word ‘spectral transmittance’ have any meaning to you in regards to a multi-layer atmospheric radiative transfer simulation?

• The next question I have is how is opacity (and transparency) in the aggregate quantified by these RT simulations? I don’t see that covered in this tutorial.

• on June 28, 2014 at 5:25 pm | Reply DeWitt Payne

RW,

Correct?

No.

Radiative forcing is defined as the difference between the total flux (SW plus LW) downward at the tropopause and the total flux upward at the same altitude after the stratosphere is allowed to radiatively equilibrate from the step change but no change is allowed in the troposphere. Flux at the surface has nothing to do with this calculation.

Because the total SW flux and the downward LW flux from the stratosphere doesn’t change much, it’s fairly safe to just calculate the difference between the upward LW flux at the tropopause before and after the step change.

• RW,

Your statement is correct. So long as when you say “ultimately” you change it to “immediately”.

“Immediately” there is no temperature change so the description is correct.
“Ultimately” there will be a temperature change so the description will change. It might still be correct but that depends on the temperature changes that result.

• I’m only trying to get and verify a basic conceptual picture of what an RT simulation is doing. More specific details will only make sense to me if the basic conceptual picture is correct.

I understand that each layer has an amount of radiant power absorbed (from above and below), transmitted through (from above and below), and emitted (both up and down). I understand that for the increased opacity case (due to added GHGs), each layer absorbs a little more radiation from above and below and subsequently emits a little more upwards and downwards, which ultimately results in a decreased IR flux passing out the TOA and an increased IR flux passing to the surface.

Is this correct?

• on June 29, 2014 at 7:08 pm DeWitt Payne

RW,

Stop using the terms ‘transmission’ and ‘absorption’ We’ve told you this over and over. It’s leading you astray, or leading you to a preconceived and incorrect conclusion. The important number is the upward and downward flux at the top and bottom of each layer, which, as you’ve been told over and over, is the sum of the radiation transmitted and the radiation emitted. But transmission is strongly dependent on the chosen layer thickness and wavelength.

For wavelengths where the transmittance through the layer is zero, increasing CO2 has no effect on the flux. Absorptivity and emissivity are equal by Kirchhoff’s Law and you can’t have an absorptivity or emissivity greater than one. So the total flux downward to the surface and upward to the layer above only increases over a narrow wavelength range on the short wavelength side of the CO2 band. That amount is only a fraction of the total forcing at the tropopause.

If you don’t use enough layers, then the assumption that the temperature at the top and bottom of each layer is the same fails and the calculation is no longer accurate. The temperature of each layer decreases with altitude, until you reach the tropopause, anyway. But at that point, the absorptivity at most wavelengths is small, except for the peak of the CO2 band centered at ~668 cm-1, the ozone band at ~1050 cm-1 and some water vapor emission from 100-400 cm-1.

Through most of the atmosphere at constant ghg concentration and temperature profile, each layer sees more flux from below and less flux from above because the layer below is warmer and the layer above is colder. The layers in the troposphere are not in radiative balance. Each layer emits more than it absorbs. The deficit is made up by convective energy transfer. That’s why the temperature profile in an RT calculation must be specified. Otherwise you need to do a radiative/convective calculation, which requires additional assumptions. The stratosphere is in radiative balance because convection is negligible.

Note that none of the flux emitted downward at high altitude reaches the surface. About 90% of the total LW flux to the surface originates within ~100m of the surface.

• Ultimately, you have to divide the atmosphere into a finite number of layers and specify each layer being at a particular temperature, no?

“The important number is the upward and downward flux at the top and bottom of each layer, which, as you’ve been told over and over, is the sum of the radiation transmitted and the radiation emitted.”

How are you interpreting what I’ve said as conflicting with this? Ultimately, after each layer absorbs a little more from above and below and subsequently emits a little more upwards and downwards, it’s the sum of the changes from each layer to the TOA and from each layer to the surface that determines the final result, is it not?

I’m only saying — for the increased opacity case — the sum of the changes from all the layers to the TOA for absorption has to be positive and greater than the sum of the changes for transmission to the surface.

How else would it possible for the difference between the TOA and surface IR fluxes to be positive for absorption?

• Ultimately, these RT simulations are quantifying the change in IR flux passing out the TOA and the change in IR flux passing out to the surface, right? And the some of these two changes is the final net change calculated, right?

• I should rephrase this more precisely:

“How else would it possible for the difference between the atmosphere –>TOA and atmosphere –> surface IR fluxes to be positive for absorption?

• on June 29, 2014 at 10:12 pm DeWitt Payne

RW,

I detect the distinct odor of the Socratic Method here. I won’t play that game. Bye.

• One step at a time here. For now, I’m only focused on what the RT simulation itself is doing.

77. It might be more correct to say — for the increased opacity case — that for each layer’s emitted IR to the TOA there is an absorption/transmission change, and for that to the TOA, the sum of the changes from all the layers is positive for absorption, and for that to the surface, the sum of the changes from all the layers for transmission is positive. The result of which is a reduced IR flux passing out the TOA and an increased IR flux passing to the surface.

• Or simply there is no requirement that the absorption change from each individual layer to the TOA is positive.

78. I found where we were discussing this last year, as I’ve been doing some more research. I understood everyone here to be saying that the aggregated sum (from the multiple layers) of the total power transmitted to space and the total power captured by the atmosphere was not equal to the power radiated from the surface (in an initial steady-state condition)?

That is, the calculation of transmittance ‘T’ through a multilayer simulation, does not quantify the total amount of power captured and transmitted, where if as a simple example ‘T’ were 0.25 and the surface was at a temperature where it radiated 400 W/m^2, it means 300 W/m^2 of upwelling IR is captured by the atmosphere and 100 W/m^2 is transmitted through into space.

Is this correct?

• RW

The ‘not’ in the sentence leaves me a little confused. But it has been a long day.

Transmittance, T, is always a ratio.
By definition, T = Radiation transmitted/radiation incident.
(It makes no comment on radiation emitted from that layer)

And now all problems are your own, stemming from imprecise definitions and lack of clarity around the problem.

If the surface radiates 400 W/m2 and T=0.25 then the radiation from the surface leaving through the top of atmosphere = 100 W/m2.

There isn’t a debate. It is a definition.
[Just like 10 divided by 2 equals the number of times 2 can be ‘fitted into’ 10.. The answer is 5. No debate, it is a definition].

It says nothing about emission because transmittance is about transmittance.

The top of atmosphere upwards radiation equals (in this case) 100 + X.

Where X= the atmospheric emitted radiation that makes it to the top (ie is not reabsorbed)

• “Transmittance, T, is always a ratio”

I understand that. That is, the quantification of ‘T’ itself is not a power density, but instead a fraction of some total emitted IR power density. Sorry if I wasn’t clear on that.

I’m trying to form a basic conceptual understanding of opacity and transparency in the aggregate, i.e for the whole mass of the atmosphere (from the surface all the way through to the TOA). I understand there is a calculated ‘T’ that quantifies transparency in the aggregate, even though most of the transmitted emission passing through the TOA originates from the atmosphere and not the surface. In other words, the ‘T’ I’m thinking of is not the direct surface transmittance. I believe it quantifies something regarding the transparent regions of the absorption spectrum as well as the total amount of power transmitted through all of the layers into space, where the total quantification of power transmitted ends up being a fraction of the amount equal to the power radiated from the surface. And absorption ‘A’ is the difference and quantifies the total amount of power captured by the atmosphere (from all the contributing layers), where T = 1-A and A = 1-T (where 1 is equal to the power density radiated from the surface).

I suspect part of the problem is most people are focused on the incremental changes that put the system out of radiative balance with the Sun, rather than prior to any incremental changes with the system and surface in a steady-state.

• And if this was somehow missed by me back when and actually is correct, what specifically forces the aggregation of the total power absorbed and the total power transmitted to be equal the power radiated from the surface?

• RW

And if this was somehow missed by me back when and actually is correct, what specifically forces the aggregation of the total power absorbed and the total power transmitted to be equal the power radiated from the surface?

I recognize and applaud your efforts to understand the subject. I’m not sure I can help.

I can’t understand what you are even asking. Total power absorbed where? Total power transmitted from where through what?

What is ‘aggregation of the total power absorbed’. Aggregation implies a sum (or integral). A sum of what? Something over time? Over area? Over height? If it is crystal clear to you it is like mud to me.

My suggestion, which I am sure I have made before.. Once you can write the question down with more specific definitions, you will probably answer your own question. Or realize you are asking a question that doesn’t have an answer.. Or is the wrong question.

• “I can’t understand what you are even asking. Total power absorbed where? Total power transmitted from where through what?

What is ‘aggregation of the total power absorbed’. Aggregation implies a sum (or integral). A sum of what?”

For a multi-layer simulation is there not a quantification of a total amount of power that passes through into space which includes emission that originates from the atmosphere as well as the surface? The ‘T’ I’m referring to quantifies this amount of power. It is not the direct surface transmittance, which is solely the surface IR => TOA component, but ‘T’ that quantifies transmittance through the whole mass of the atmosphere. Yes, I believe it would be some sort of integral of emission from the layers that passes into space.

• And also, I assume that for a simulation done at equilibrium with the surface in balance, the amount of power transmitted to the surface from the multiple layers is not considered, though of course it is considered for a net induced imbalance case, like from 2xCO2, that effects transmission through to the TOA and to the surface.

• It seems the quantification of ‘T’ as it applies to the whole mass of the atmosphere must quantify something regarding the transparent regions of the absorption spectrum. SoD, I don’t see the concept and quantification of transmittance ‘T’ through the whole mass of the atmosphere covered in your series here. Or am I missing it?

Of course, I understand what ‘T’ means relative one layer’s emission incident on another layer, i.e. generally some fraction of the emitted IR is transmitted through a layer and some fraction is absorbed by a layer; however, how is transmittance quantified in the aggregate through the whole mass of the atmosphere? I would very much like to finally fully understand this.

79. SoD,

As I’ve understood you (please correct me if I’m wrong), is you have no knowledge of or no concept of a ‘T’ (transmittance) and ‘A’ (absorption) calculation that quantifies transparency and opacity in the aggregate for a multi-layer atmospheric RT simulation.

• Where for such a simulation absorption ‘A’ is equal to 1-‘T’ and 1 is equal to the power radiated from the surface even though most of the absorbed or attenuated emission last originates from the atmosphere.

• RW: Traditional concepts of absorption and transmission only apply when the material in question doesn’t emit a significant amount of radiation. A laboratory spectrophotometer uses a filament in a light bulb heated to several thousand degC as its light source. The radiation from that light sources swamps out the emission from the air and the spectrophotometer itself at room temperature. Absorptance plus transmittance = 1 only when emission is negligible.

In the atmosphere, both emission and absorption are both relevant. Just because the surface emits 400 W/m2 and only 240 W/m2 escape to space doesn’t mean that 60% of the photons are transmitted through the atmosphere. Only about 10% escape directly to space. The remaining escaping photons are emit by the atmosphere, not the surface.

Both absorption and emission from incremental layers are integrated along a path from the surface to space (OLR) or space to the surface (DLR). Read about the Schwarzschild eqn.

• Frank,

“Both absorption and emission from incremental layers are integrated along a path from the surface to space (OLR) or space to the surface (DLR). Read about the Schwarzschild eqn.”

Yes, I understand that, but I also understand it’s ultimately based on optical depth, which I don’t think is directly related to OLR or DLR. The direct surface transmittance might only be 0.1 (or less), but the spectral transmittance of the surface is more like 0.25 or nearly 100 W/m^2. The spectral transmittance evaluated at the surface temperature is what gives a true measure of IR transparency and opacity through the whole mass of the atmosphere, and it is specifically quantified as a fraction of the surface radiative power even though much of the attenuated emission originates from the atmospheric layers and not just the surface.

This is the point I was trying to get at for so long. Yes, each layer emits and ‘sees’ a little more of the spectrum than the surface alone does. I understand for the imposed imbalance state of increased GHGs, each layer absorbs a little more from above and below and emits a little more upwards and downwards, from which the changes in optical depth through to the TOA and through to the surface from all the layers are re-calculated to arrive at the net change in absorption.

• Frank,

Though since the incremental increases and/or decreases in optical depth would effectively cause incremental changes in OLR and DLR, I see your point.

My point was and is the spectral transmittance (not the direct surface transmittance) is what gives a true measure of IR transparency through the whole mass of the atmosphere, i.e. from the surface all the way through the TOA. If the spectral ‘T’ is 0.25 and the surface is at a temperature where it is emitting 400 W/m^2, it means that 100 W/m^2 of the 400 W/m^2 radiated from the surface is effectively transmitted into space instantaneously and 300 W/m^2 is captured by the atmosphere or attenuated from passing into space. Using these numbers, the 300 W/m^2 captured, i.e. ‘blocked’ from passing into space, is what is driving the GHE prior to an imposed imbalance.

So-called radiative forcing is the incremental increase in the prior 300 W/m^2 already being captured, or about +3.6 W/m^2; but the 3.6 W/m^2 is the difference between the reduced IR passing out the TOA and the increased IR passing to the surface, i.e. the net imbalance imposed. It’s none the less still effectively an increase from 300 W/m^2 to 303.6 W/m^2, because the 3.6 W/m^2 is specifically that of upward emitted IR additionally captured.

I don’t know, to me this is the most basic thing to first understand and is ultimately the most basic thing IR radiative transfer is actually doing, but I guess everyone learns differently.

• RW,
The way you describe the situation is perhaps acceptable as a way of describing the final outcome, but it’s terrible, when you try to understand the actual mechanisms of the Earth atmosphere.

Your approach works for normal thermal insulation. It works partially for purely radiative heat transfer, but it becomes a major obstacle for understanding, when we consider the atmosphere, because it fails, when convection is important as well.

Your approach is incompatible with the important role of the lapse rate determined by properties of convection.

• Frank,

Sorry I’m late on this.

“In the atmosphere, both emission and absorption are both relevant. Just because the surface emits 400 W/m2 and only 240 W/m2 escape to space doesn’t mean that 60% of the photons are transmitted through the atmosphere.”

Yes, I fully understand that, but the IPCC quantifies incremental GHG absorption as ‘radiative forcing’, but in a raw physics sense ‘radiative forcing’ is really not zero prior to a GHG imposed imbalance, because we already have a radiatively induced GHE due to the presence of GHGs. What added GHGs do is enhance the already existing GHE.

The spectral transmittance ‘T’ and the spectral absorptivity ‘A’ are based on optical depth, i.e. from the surface through the TOA. ‘A’ effectively quantifies ‘radiative forcing’ in the aggregate prior to an imposed imbalance (and is what is driving the GHE prior to an imposed imbalance). Both ‘T’ and ‘A’ are instantaneous and do not account for subsequent re-emission of absorption by the separate layers. The sum of ‘T’ and ‘A’ always equals 1, where 1 in this case is equal to the power radiated from the surface; however, the spectral ‘T’ is not quantifying the direct surface transmittance, which may only be about 20-40 W/m^2 instead of about 100 W/m^2 (for the spectral ‘T’).

I should note that I understand only for the imposed imbalance state is increased absorption (from above and below) and subsequent re-emission being done, from which then the changes in optical depth through to the TOA and through to the surface are then calculated to arrive at the net change in absorption. For the prior steady-state, the calculation of the spectral ‘T’ and ‘A’ is instantaneous from the surface and all the layers and does not factor in any absorption (from either above or below) and subsequent re-emission from any of the layers. It’s just based on simultaneous emission of upwelling IR from the surface and layers and how much of the optical depth is ‘seen’ and not ‘seen’ all the way through to the TOA.

I’m also aware that most of the transmitted emission to space (about 240 W/m^2), last originates from the atmosphere and not the surface.

• Dewitt,

“RW has, in the past, completely ignored convection. At one point he insisted that there was no net transfer of energy from the surface to the atmosphere by convection.”

I certainly agree that convection, i.e. net non-radiative flux, is from the surface to the atmosphere. Or that more radiant flux is incident on the surface from the atmosphere and Sun than is emitted from the surface.

• Pekka,

“Even in the case that defines forcing, the results are modified by the fact that the atmospheric temperature profile is different from what radiative heat transfer alone would produce. The full profile must be taken into account in the calculation of the forcing. The result is different from the case determined by radiative energy transfer alone.”

I certainly agree that convection contributes to the temperature profile and ultimately to why increased GHG enhance the radiative warming of the system. If that’s what you mean.

“It differs in such a way that concepts like transmittance in the form you use it become impediment for understanding, not an useful step in that.”

I don’t agree. Basic concepts involving the aggregate transparency and absorptivity of radiation passing through the whole of a medium provide a useful foundation and make the added details easier to see and understand.

• on June 8, 2015 at 4:31 pm DeWitt Payne

Pekka,

RW has, in the past, completely ignored convection. At one point he insisted that there was no net transfer of energy from the surface to the atmosphere by convection. I don’t know if he still does, but it seems likely. I’m not interested in finding out.

• Dewitt,

“No, it isn’t. It’s effectively the difference between emission at the tropopause at the two levels of CO2.”

Well yeah, but the calculated 3.6 W/m^2 includes a so-called stratospheric adjustment, so it can be considered through the TOA. At least this is what Gunnar Myhre told me at one point. The stratospheric adjustment is like less than 0.1 W/m^2, so why even bother to include it? The bottom line is the RT simulation itself calculates about 3.6 or 3.7 watts being additionally captured by the atmosphere for 2xCO2.

• Pekka,

“The way you describe the situation is perhaps acceptable as a way of describing the final outcome, but it’s terrible, when you try to understand the actual mechanisms of the Earth atmosphere.

Your approach works for normal thermal insulation. It works partially for purely radiative heat transfer, but it becomes a major obstacle for understanding, when we consider the atmosphere, because it fails, when convection is important as well.

Your approach is incompatible with the important role of the lapse rate determined by properties of convection.”

I’m not following you here. As I understand it, convection is not involved in the calculation of so-called ‘radiative forcing’, i.e incremental increases in atmospheric opacity from added GHGs. These calculated changes are ‘instantaneous’ in that they don’t involve how the other components like convection respond to the imbalance.

• RW,

Convection is essential, because it determines largely the temperature profile.

For comparison we may consider normal thermal insulation. In that case the heat flux depends linearly on the heat conductivity. That linear dependence makes arguments of the type you present valid.

In the atmosphere the relationship between the “radiative conductivity” and heat flux is different, because changes in radiative energy transfer are combined with changes in convection. The changes in convection effectively cancel some changes in radiative energy transfer leaving a modified overall outcome.

Even in the case that defines forcing, the results are modified by the fact that the atmospheric temperature profile is different from what radiative heat transfer alone would produce. The full profile must be taken into account in the calculation of the forcing. The result is different from the case determined by radiative energy transfer alone. It differs in such a way that concepts like transmittance in the form you use it become impediment for understanding, not an useful step in that.

• on June 8, 2015 at 2:35 am DeWitt Payne

RW,

So-called radiative forcing is the incremental increase in the prior 300 W/m^2 already being captured, or about +3.6 W/m^2; but the 3.6 W/m^2 is the difference between the reduced IR passing out the TOA and the increased IR passing to the surface, i.e. the net imbalance imposed.

No, it isn’t. It’s effectively the difference between emission at the tropopause at the two levels of CO2.

MODTRAN 1976 US Standard Atmosphere, clear sky, default settings for everything but CO2:

12 km(beginning of the tropopause) looking down:

280 ppmv CO2 266.931 W/m²
560 ppmv CO2 263.446 W/m²
difference : 3.485 W/m²

280 ppmv CO2 transmittance 0.2604
560 ppmv CO2 transmittance 0.2544
surface emission 100-1500cm-1 360.472 W/m²
transmitted from the surface to space:
280 ppmv CO2 0.2604 * 360.472 = 93.867 W/m²
560 ppmv CO2 0.2544 * 360.472 = 91.704 W/m²
difference 2.163 W/m²

0 km looking up:

280 ppmv CO2: 256.507 W/m²
560 ppmv CO2: 259.772 W/m²
difference: 3.265 W/m²

sum of reduced transmittance plus increased downward emission:

5.428 W/m²

As usual, you’ve invented your own definitions which have only a vague relation to reality.

The only reason I’ve even bothered to reply to this particular post is that I’m somewhat bored. I won’t make that mistake again.

• on March 31, 2015 at 2:06 pm DeWitt Payne

Frank,

An IR spectrophotometer normally uses an electrically heated rod or cylinder (globar or Nernst glower) rather than a light bulb and the temperature is 1,500-2,200K. But that’s still far higher intensity at any give wavenumber than from a gas at 300K.

Tungsten filament light bulbs are used for UV/VIS spectrophotometry where gas emission at room temperature would always be negligible.

• SoD,

I should also add that I think the aggregate T and A I’m thinking of are based on probability density functions of GHG absorption and GHG transmission (into space) as a function of wavelength. I believe it’s some sort of spectral integration from the multiple layers based on optical depth and is ‘instantaneous’ in that it does not include re-emission by the atmosphere.

What I’m trying to understand is how this integration or aggregation of the emission per layer, per wavelength is used to arrive at the calculation of T and A for the whole mass of the atmosphere.

In the simple example I mentioned above, if the surface were at a temperature where it emitted 400 W/m^2 per the S-B law in the steady-state, and the calculated ‘T’ I’m referring to came to 0.25, it would mean 300 W/m^2, i.e. (1-0.25)*400, is instantaneously captured by the atmosphere and 100 W/m^2, i.e. 0.25*400, is instantaneously transmitted into space. Even though this T (and subsequent A) is ultimately quantified as a fraction of the surface radiant power, it is not the direct surface transmittance (i.e. the power directly radiated from the surface that passes straight through entire atmosphere into space).

The 300 W/m^2 is what would constitute ‘radiative forcing’ in the aggregate and is what is driving the GHE prior to an imposed imbalance. Now, I understand that the IPCC and/or climate science considers ‘forcing’ to be zero prior to an imposed imbalance; however, this is not really correct in raw physics sense since we already have a radiatively induced GHE. What I mean is prior to an imposed imbalance, the atmosphere is already opaque to a large degree in the LWIR, and this opacity is why we have a radiatively induced GHE elevating the surface temperature above what it would otherwise be. What added GHGs do is increase or enhance the opacity of the atmosphere to LWIR, thus pushing the system to a warmer equilibrium surface temperature in order to maintain pure radiative balance with the Sun at the TOA.

For doubled CO2, it is widely agreed that net absorption of LWIR increases by about 3.6 W/m^2, so using the examples from above, total or aggregate ‘radiative forcing’ would effectively increase from 300 W/m^2 to 303.6 W/m^2, thus putting the system out of balance with the income radiation from the Sun by 3.6 W/m^2 (or creating a -3.6 W/m^2 deficit at the TOA).

• I should add here that the ‘T’ I’m referring to would be considered to be the spectral transmittance evaluated at the temperature of the surface. I understand it’s what gives a true measure of IR transparency and opacity through the whole mass of the atmosphere, i.e. from the surface all the way through to the TOA, and is ‘instantaneous’ in that it does not include subsequent re-emission of absorption.

What I understand the emission from the layers do per wavelength is further increase the optical depth that was not prior absorbed by the layer beneath it. i.e. the absorbed emission from the surface increases the optical depth some, the absorbed emission from the first layer increases the optical depth some more, the absorbed emission from the second layer a little more and so on and so forth through all the layers. I understand that once a particular wavelength is totally opaque, i.e. its transmittance is zero, then the optical depth at this wavelength is no longer increased by absorbed emission at that wavelength from a layer above. This would be the point where a particular wavelength is considered to be ‘saturated’.

I think this is kind of analogous to light passing through a semi-opaque medium in the steady-state in that simultaneously more light can’t be absorbed by the medium and transmitted through the medium than is supplied into the medium in the first place, as that would violate COE (assuming the medium has no alternate energy source). The difference is the atmosphere is effectively both supplied light externally and internally re-emits absorbed light at the same time, but it none the less can’t have more light, i.e. energy, absorbed and transmitted out its opposite side (the TOA) than is being supplied in from the one side (the surface) at the same time, i.e. ‘instantaneously’ or in any one instant.

The other analogous difference is the atmosphere can only lose ‘light’, i.e. EM energy, out its opposite boundary as ‘light’, where as in the first example, some of the absorbed light can be thermalized and lost from the medium by conduction and/or convection (assuming the medium is surrounded by matter). Since the emitted EM energy from the surface, i.e. the sole source of the ‘light’ entering the medium (the atmosphere), and is a direct consequence of the net amount of energy input to the surface, at any one instant, there can’t be more EM light transmitted through the whole of the atmosphere and absorbed by the atmosphere than is initially radiated in from the surface, as that would violate COE (in the steady-state).

I believe this is why the spectral transmittance ‘T’ and subsequently the spectral opacity ‘A’ are quantified as fractions of the power directly radiated from the surface even though most of the absorbed and transmitted emission originates from the atmosphere.

Is this perhaps making any sense now?

• I should add that in the example above using ‘light’ instead of LWIR is that the only real difference of course is the frequency of the emitted photons. I believe it’s analogous because either way it’s still a measure of transparency of EM radiation passing through a medium.

• Another way of illustrating this might be when the transmittance of a particular wavelength is zero, the wavelengths of those photons emitted from the surface must be 100% absorbed (i.e. attenuated from passing into space). Since an amount equal to all the photons emitted from the surface must either be transmitted to space or absorbed ( i.e. added to energy stored by the atmosphere) the sum of transmittance and absorption of the power radiated from the surface must be 1. That is, the atmosphere does not have an infinite capacity to store energy, so in the steady-state, it contains as much energy as it can hold and there must be an equal amount of energy continuously coming out as is going in. Thus the total amount of IR power transmitted through the atmosphere and absorbed by the atmosphere must be equal to the power radiated from the surface.

• I understand that the emitted power densities from each separate layer, including the surface, have probability density functions of absorption and transmittance per wavelength from their location to the TOA. I think the spectral integration of these probability density functions of IR emission from each layer are what are used to arrive at the aggregate ‘T’ and ‘A’ I’m referring to. If so, I would like to see and understand specifically how this is all integrated or aggregated to arrive at the calculation of ‘T’ and ‘A’ that quantifies LWIR transparency and opacity in the aggregate for the whole mass of the atmosphere, i.e. from the surface all the way through to the TOA.