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).
http://claesjohnson.blogspot.com/2013/01/the-fallacy-of-ghe.html
Hockey Schtick,
It’s difficult to have a meaningful discussion with someone who believes in a different framework of physics.
Check out the Etiquette:
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:
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.
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.
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.
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.
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,
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.
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,
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,
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).
Using your terminology:
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,
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,
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
I expected that you had. Just the description was off so I thought I would check.
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 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.)
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,
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.
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.
[...] « Visualizing Atmospheric Radiation – Part Two [...]
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
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.
[...] 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. [...]
Pekka,
I found where I saw the comment about modeling perfectly transparent atmospheres. It was Raymond Pierrehumbert commenting at Rabett Run.
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:
Then they mention simulations with very small emissivity telling that
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.
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,
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).
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.
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)
Here is an example of a link.
Underline would, of course, be better, but this is a definite improvement on my screen.
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.
[...] of different CO2 concentrations using the atmospheric radiation model described (briefly) in Part Two and in detail in Visualizing Atmospheric Radiation – Part Five – [...]
[...] atmospheric model is described in brief in Part Two and in a comment, then in detail in Part Five – [...]
[...] 10 atmospheric layers in the model with a top of atmosphere at 50 hPa. More about the model in Part Two and Part Five – [...]
[...] and emission of radiation in the atmosphere we can do some “experiments”. See Part Two and Part Five – [...]
[...] Part Two we covered quite a bit of ground. At the end we looked at the first calculation of heating rates. [...]
[...] Visualizing Atmospheric Radiation – Part Two I describe the basics of a MATLAB line by line calculation of radiative transfer in the atmosphere. [...]
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
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?
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?)
[...] Part Two - some early results from a model with absorption and emission from basic physics and the HITRAN database [...]
[...] Part Two - some early results from a model with absorption and emission from basic physics and the HITRAN database [...]
[...] Clouds & Water Vapor – Part Six – Nonlinearity and Dry Atmospheres Visualizing Atmospheric Radiation – Part Two [...]
[...] Part Two - some early results from a model with absorption and emission from basic physics and the HITRAN database [...]
[...] 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 [...]