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## The “Greenhouse” Effect Explained in Simple Terms

Over the last few years I’ve written lots of articles relating to the inappropriately-named “greenhouse” effect and covered some topics in great depth. I’ve also seen lots of comments and questions which has helped me understand common confusion and misunderstandings.

This article, with huge apologies to regular long-suffering readers, covers familiar ground in simple terms. It’s a reference article. I’ve referenced other articles and series as places to go to understand a particular topic in more detail.

One of the challenges of writing a short simple explanation is it opens you up to the criticism of having omitted important technical details that you left out in order to keep it short. Remember this is the simple version..

### Preamble

First of all, the “greenhouse” effect is not AGW. In maths, physics, engineering and other hard sciences, one block is built upon another block. AGW is built upon the “greenhouse” effect. If AGW is wrong, it doesn’t invalidate the greenhouse effect. If the greenhouse effect is wrong, it does invalidate AGW.

The greenhouse effect is built on very basic physics, proven for 100 years or so, that is not in any dispute in scientific circles. Fantasy climate blogs of course do dispute it.

Second, common experience of linearity in everyday life cause many people to question how a tiny proportion of “radiatively-active” molecules can have such a profound effect. Common experience is not a useful guide. Non-linearity is the norm in real science. Since the enlightenment at least, scientists have measured things rather than just assumed consequences based on everyday experience.

### The Elements of the “Greenhouse” Effect

Atmospheric Absorption

1. The “radiatively-active” gases in the atmosphere:

• water vapor
• CO2
• CH4
• N2O
• O3
• and others

absorb radiation from the surface and transfer this energy via collision to the local atmosphere. Oxygen and nitrogen absorb such a tiny amount of terrestrial radiation that even though they constitute an overwhelming proportion of the atmosphere their radiative influence is insignificant (note 1).

How do we know all this? It’s basic spectroscopy, as detailed in exciting journals like the Journal of Quantitative Spectroscopy and Radiative Transfer over many decades. Shine radiation of a specific wavelength through a gas and measure the absorption. Simple stuff and irrefutable.

Atmospheric Emission

2. The “radiatively-active” gases in the atmosphere also emit radiation. Gases that absorb at a wavelength also emit at that wavelength. Gases that don’t absorb at that wavelength don’t emit at that wavelength. This is a consequence of Kirchhoff’s law.

The intensity of emission of radiation from a local portion of the atmosphere is set by the atmospheric emissivity and the temperature.

Convection

3. The transfer of heat within the troposphere is mostly by convection. The sun heats the surface of the earth through the (mostly) transparent atmosphere (note 2). The temperature profile, known as the “lapse rate”, is around 6K/km in the tropics. The lapse rate is principally determined by non-radiative factors – as a parcel of air ascends it expands into the lower pressure and cools during that expansion (note 3).

The important point is that the atmosphere is cooler the higher you go (within the troposphere).

Energy Balance

4. The overall energy in the climate system is determined by the absorbed solar radiation and the emitted radiation from the climate system. The absorbed solar radiation – globally annually averaged – is approximately 240 W/m² (note 4). Unsurprisingly, the emitted radiation from the climate system is also (globally annually averaged) approximately 240 W/m². Any change in this and the climate is cooling or warming.

Emission to Space

5. Most of the emission of radiation to space by the climate system is from the atmosphere, not from the surface of the earth. This is a key element of the “greenhouse” effect. The intensity of emission depends on the local atmosphere. So the temperature of the atmosphere from which the emission originates determines the amount of radiation.

If the place of emission of radiation – on average – moves upward for some reason then the intensity decreases. Why? Because it is cooler the higher up you go in the troposphere. Likewise, if the place of emission – on average – moves downward for some reason, then the intensity increases (note 5).

More GHGs

6. If we add more radiatively-active gases (like water vapor and CO2) then the atmosphere becomes more “opaque” to terrestrial radiation and the consequence is the emission to space from the atmosphere moves higher up (on average). Higher up is colder. See note 6.

So this reduces the intensity of emission of radiation, which reduces the outgoing radiation, which therefore adds energy into the climate system. And so the climate system warms (see note 7).

That’s it!

It’s as simple as that. The end.

### A Few Common Questions

There are almost 315,000 individual absorption lines for CO2 recorded in the HITRAN database. Some absorption lines are stronger than others. At the strongest point of absorption – 14.98 μm (667.5 cm-1), 95% of radiation is absorbed in only 1m of the atmosphere (at standard temperature and pressure at the surface). That’s pretty impressive.

By contrast, from 570 – 600 cm-1 (16.7 – 17.5 μm) and 730 – 770 cm-1 (13.0 – 13.7 μm) the CO2 absorption through the atmosphere is nowhere near “saturated”. It’s more like 30% absorbed through a 1km path.

You can see the complexity of these results in many graphs in Atmospheric Radiation and the “Greenhouse” Effect – Part Nine – calculations of CO2 transmittance vs wavelength in the atmosphere using the 300,000 absorption lines from the HITRAN database, and see also Part Eight – interesting actual absorption values of CO2 in the atmosphere from Grant Petty’s book

The complete result combining absorption and emission is calculated in Visualizing Atmospheric Radiation – Part Seven – CO2 increases – changes to TOA in flux and spectrum as CO2 concentration is increased

CO2 Can’t Absorb Anything of Note Because it is Only .04% of the Atmosphere

See the point above. Many spectroscopy professionals have measured the absorptivity of CO2. It has a huge variability in absorption, but the most impressive is that 95% of 14.98 μm radiation is absorbed in just 1m. How can that happen? Are spectroscopy professionals charlatans? You need evidence, not incredulity. Science involves measuring things and this has definitely been done. See the HITRAN database.

Water Vapor Overwhelms CO2

This is an interesting point, although not correct when we consider energy balance for the climate. See Visualizing Atmospheric Radiation – Part Four – Water Vapor – results of surface (downward) radiation and upward radiation at TOA as water vapor is changed.

The key point behind all the detail is that the top of atmosphere radiation change (as CO2 changes) is the important one. The surface change (forcing) from increasing CO2 is not important, is definitely much weaker and is often insignificant. Surface radiation changes from CO2 will, in many cases, be overwhelmed by water vapor.

Water vapor does not overwhelm CO2 high up in the atmosphere because there is very little water vapor there – and the radiative effect of water vapor is dramatically impacted by its concentration, due to the “water vapor continuum”.

The Calculation of the “Greenhouse” Effect is based on “Average Surface Temperature” and there is No Such Thing

Simplified calculations of the “greenhouse” effect use some averages to make some points. They help to create a conceptual model.

Real calculations, using the equations of radiative transfer, don’t use an “average” surface temperature and don’t rely on a 33K “greenhouse” effect. Would the temperature decrease 33K if all of the GHGs were removed from the atmosphere? Almost certainly not. Because of feedbacks. We don’t know the effect of all of the feedbacks. But would the climate be colder? Definitely.

See The Rotational Effect – why the rotation of the earth has absolutely no effect on climate, or so a parody article explains..

The Second Law of Thermodynamics Prohibits the Greenhouse Effect, or so some Physicists Demonstrated..

See The Three Body Problem – a simple example with three bodies to demonstrate how a “with atmosphere” earth vs a “without atmosphere earth” will generate different equilibrium temperatures. Please review the entropy calculations and explain (you will be the first) where they are wrong or perhaps, or perhaps explain why entropy doesn’t matter (and revolutionize the field).

See Gerlich & Tscheuschner for the switch and bait routine by this operatic duo.

And see Kramm & Dlugi On Dodging the “Greenhouse” Bullet – Kramm & Dlugi demonstrate that the “greenhouse” effect doesn’t exist by writing a few words in a conclusion but carefully dodging the actual main point throughout their entire paper. However, they do recover Kepler’s laws and point out a few errors in a few websites. And note that one of the authors kindly showed up to comment on this article but never answered the important question asked of him. Probably just too busy.. Kramm & Dlugi also helpfully (unintentionally) explain that G&T were wrong, see Kramm & Dlugi On Illuminating the Confusion of the Unclear – Kramm & Dlugi step up as skeptics of the “greenhouse” effect, fans of Gerlich & Tscheuschner and yet clarify that colder atmospheric radiation is absorbed by the warmer earth..

And for more on that exciting subject, see Confusion over the Basics under the sub-heading The Second Law of Thermodynamics.

Feedbacks overwhelm the Greenhouse Effect

This is a totally different question. The “greenhouse” effect is the “greenhouse” effect. If the effect of more CO2 is totally countered by some feedback then that will be wonderful. But that is actually nothing to do with the “greenhouse” effect. It would be a consequence of increasing temperature.

As noted in the preamble, it is important to separate out the different building blocks in understanding climate.

Miskolczi proved that the Greenhouse Effect has no Effect

Miskolczi claimed that the greenhouse effect was true. He also claimed that more CO2 was balanced out by a corresponding decrease in water vapor. See the Miskolczi series for a tedious refutation of his paper that was based on imaginary laws of thermodynamics and questionable experimental evidence.

Once again, it is important to be able to separate out two ideas. Is the greenhouse effect false? Or is the greenhouse effect true but wiped out by a feedback?

If you don’t care, so long as you get the right result you will be in ‘good’ company (well, you will join an extremely large company of people). But this blog is about science. Not wishful thinking. Don’t mix the two up..

Convection “Short-Circuits” the Greenhouse Effect

Let’s assume that regardless of the amount of energy arriving at the earth’s surface, that the lapse rate stays constant and so the more heat arriving, the more heat leaves. That is, the temperature profile stays constant. (It’s a questionable assumption that also impacts the AGW question).

It doesn’t change the fact that with more GHGs, the radiation to space will be from a higher altitude. A higher altitude will be colder. Less radiation to space and so the climate warms – even with this “short-circuit”.

In a climate without convection, the surface temperature will start off higher, and the GHG effect from doubling CO2 will be higher. See Radiative Atmospheres with no Convection.

In summary, this isn’t an argument against the greenhouse effect, this is possibly an argument about feedbacks. The issue about feedbacks is a critical question in AGW, not a critical question for the “greenhouse” effect. Who can say whether the lapse rate will be constant in a warmer world?

### Notes

Note 1 – An important exception is O2 absorbing solar radiation high up above the troposphere (lower atmosphere). But O2 does not absorb significant amounts of terrestrial radiation.

Note 2 – 99% of solar radiation has a wavelength <4μm. In these wavelengths, actually about 1/3 of solar radiation is absorbed in the atmosphere. By contrast, most of the terrestrial radiation, with a wavelength >4μm, is absorbed in the atmosphere.

Note 3 – see:

Density, Stability and Motion in Fluids – some basics about instability
Potential Temperature – explaining “potential temperature” and why the “potential temperature” increases with altitude
Temperature Profile in the Atmosphere – The Lapse Rate – lots more about the temperature profile in the atmosphere

Note 4 – see Earth’s Energy Budget – a series on the basics of the energy budget

Note 5 – the “place of emission” is a useful conceptual tool but in reality the emission of radiation takes place from everywhere between the surface and the stratosphere. See Visualizing Atmospheric Radiation – 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.

Also, take a look at the complete series: Visualizing Atmospheric Radiation.

Note 6 – the balance between emission and absorption are found in the equations of radiative transfer. These are derived from fundamental physics – see Atmospheric Radiation and the “Greenhouse” Effect – Part Six – The Equations – the equations of radiative transfer including the plane parallel assumption and it’s nothing to do with blackbodies. The fundamental physics is not just proven in the lab, spectral measurements at top of atmosphere and the surface match the calculated values using the radiative transfer equations – see Theory and Experiment – Atmospheric Radiation – real values of total flux and spectra compared with the theory.

Also, take a look at the complete series: Atmospheric Radiation and the “Greenhouse” Effect

Note 7 – this calculation is under the assumption of “all other things being equal”. Of course, in the real climate system, all other things are not equal. However, to understand an effect “pre-feedback” we need to separate it from the responses to the system.

### 245 Responses

1. I’ll play Devil’s Advocate. You’re too quick on step 5 (I know note 5 goes into more detail but that’s too much of a jump from a few words to lenghty posts).

Most of what you say has meaning only because of step 5. Please elaborate here, in a concise manner 8) – otherwise one could say that yes, the emission is from a higher altitude but there is more CO2 around so maybe the two effects balance each other somehow.

There is also the issue that even if the troposphere temperature decreases with height, the emission is determined by the temperature of the individual molecules.

Another point that need explanation – as CO2 is heavier than N2, H2O and O2 one might expect it to accumulate nearer to the ground. Has that got any contribution to give to atmospheric temperatures?

The trouble as usual is where to stop the simplification. One can easily understand the troposphere for example by assuming only convection is important. That’s too much of a simplification if the ground and the stratosphere are added. And so on and so forth.

• Omnologos,

From the point of view of a qualitative description little is missing from the step 5, but the unavoidability of the rise in the height of emission is perhaps best seen by an additional argument.

In another comment below I have discussed the role of the stratosphere. From such arguments we can conclude that it’s best to look at the fluxes near the tropopause. An altitude around 17 km might be most appropriate, when one value is used for all locations. (Alternatively a higher altitude could be chosen for tropics and a lower for higher latitudes.)

At such an altitude the up and down fluxes are nearly equal for the wavelengths of strongest absorption peaks of CO2 but at other wavelengths the downwards IR is much weaker than upwards.

When we look down from 17 km, the atmosphere looks very opaque at wavelengths of CO2 absorption peaks. All radiation that reaches the altitude comes from only little lower. At other IR wavelengths the opacity varies. In the atmospheric IR window even the surface is visible. Radiation that reaches the altitude comes from a distance that’s the smaller the more opaque the atmosphere is. Increasing opacity by adding CO2 is guaranteed to shorten the distance, i.e. to move the average height of emission up. That’s true even for the atmospheric IR window, because the share of radiation from the atmosphere goes up relative to that from the surface.

Mixing of gases is so strong throughout the whole atmosphere up to the turbopause at about 100 km altitude that the concentrations do not depend much on the altitude. Beyond that the share of lighter molecules starts to increase with altitude and that of the heavier ones like CO2 to decrease. It takes time for the increase in CO2 concentration to reach fully higher stratosphere, but within the troposphere and lower stratosphere only shorter term variability up to maximally a few years has a more local nature. Antarctic atmosphere follows Northern hemisphere with such a delay.

• omnologos,

There is no such thing as the temperature of individual molecules. Temperature is a statistical property. In simpler terms, a bulk property.

• omnologos,

Pekka is pointing out that all gases are at the same temperature in a “local part” of the atmosphere. See the section “Local Thermodynamic Equilibrium” in Planck, Stefan-Boltzmann, Kirchhoff and LTE.

This is true in the troposphere. As the air thins out well above the troposphere it eventually stops being true.

• More like 10 microseconds for vibrational equilibration, but it doesn’t really make a difference for this argument because the radiative lifetime of vibrationally excited molecules is of the order of 1 s.

Prekka is right for rotational equilibration

• Eli,

I based my estimate on the line width of the pressure broadened absorption and emission lines. My reasoning seems to be erroneous in not taking into account the influence of the more frequent changes in the rotational state and of the fact that those changes are sufficient for broadening the line that corresponds to a transition from a specific vibrational-rotational state to another specific vibrational-rotational state.

As you state it’s irrelevant for the main argument whether the time scale is 1ns or 10µs., but I’ll remember this point in the future.

I have presented similarly erroneous comments before, but again in connections where this doesn’t affect the main point made.

• You’re right of course. I should have perhaps spoken about the energy of the individual molecule. But I might be wrong again ;)

Anyway, the underlying question is that in your post you are assuming all molecules to be always in energy balance with the air surrounding them. This is of course just a simplification, and the issue is if the actual underlying mechanism need be added to understand the greenhouse effect to a large extent, in the free atmosphere.

• Omnologos,

The time scale for reaching the local thermal equilibrium within troposphere is nanoseconds, i.e. billionths of one second. Therefore it’s always safe to assume that the molecular energies are distributed according to the Boltzmann distribution and corresponding distributions for other forms of energy than translational motion.

2. Well done

However, think you missed the most important point with respect to saturation of CO2, that as the concentration increases, the level at which the atmosphere emits in the CO2 bending region rises to a colder level because the emission is trapped higher in the atmosphere Thus, until the level of emission to space hits the stratosphere where T increases with altitude, increasing CO2 will always slow down emission.

The pressure broadening and addition lines argument is actually irrelevant on a practical level.

• Even the case of stratosphere is more complex. The energy balance of the upper stratosphere is very weakly coupled to lower stratosphere and still less with the troposphere.

Additional CO2 will lead to a drop in the temperature of the upper stratosphere and that drop cancels almost totally the increase in radiation out of the stratosphere. That must be the case, because the stratosphere is stratified, i.e. has very little vertical mixing of air, and because the mean free path of the the dominant part of emitted IR is short even in the upper stratosphere. For these reasons the total energy transfer between upper stratosphere and lower parts of the atmosphere is so weak that local heating by solar radiation must be essentially equal to (net) emission of IR up through stratopause..

Thus Increasing CO2 increases emission out form the troposphere, but has only little influence in either direction for the emission from the stratosphere. A very small part of the increased upwards IR at a fixed altitude near tropopause is, however, compensated by increased downwards emission from the stratosphere. This leads also to a small change in net emission through the stratopause.

• Increasing CO2 DECREASES the emission from the troposphere. A simple way to think about this is that the concentration at the level at which the atmosphere emits is constant, because if concentration increased, then radiation would be trapped at the current emission level and would have to occur higher up, and if it decreased, emission would come from a lower level

• Eli,

Stupid of me to write as I wrote. You may notice that I have made the same argument you present elsewhere in this thread.

I was really thinking only about what happens for the radiation from stratosphere and how that extends a small effect down to tropopause.

3. I would also add to your Note 2 that most of the energy from the sun gets absorbed first into the top layers of the ocean – a lot of people seem to be surprised that surface heat anomaly has not raised much but the ocean one did.

4. on June 26, 2014 at 1:25 pm | Reply DeWitt Payne

SoD,

You might consider adding a sentence or two to the Energy Balance paragraph on changing ocean heat content as a measure of the TOA radiative energy balance.

5. Let’s assume that regardless of the amount of energy arriving at the earth’s surface, that the lapse rate stays constant and so the more heat arriving, the more heat leaves. That is, the temperature profile stays constant. (It’s a questionable assumption that also impacts the AGW question).

It doesn’t change the fact that with more GHGs, the radiation to space will be from a higher altitude. A higher altitude will be colder. Less radiation to space and so the climate warms – even with this “short-circuit”.

I don`t know how the lapse rate can stay constant with more GHGs. Must a higher altitude always be colder? And how much colder? Say: if it is 100 m higher? My question is about latent heat I think.

• Nobodyknows

I don`t know how the lapse rate can stay constant with more GHGs.

The lapse rate is the rate of change of temperature with height. The primary factor that determines this is called the “adiabatic lapse rate”, which is all due to the expansion of air (as it rises) into the lower pressure that you find at higher altitudes. When air expands it cools, a consequence of the first law of thermodynamics (work done = internal energy lost).

When we consider moist air the argument is the same but the calculation is more involved. Now we have to include the energy from latent heat as water vapor condenses out. This reduces the temperature drop with altitude.

See the links in note 3 for more detail.

• If the temperature gradient in the troposphere at more CO2 remains constant (correctly!), then the question remains as it comes to the increase in surface temperature.

The answer is simple: the altidude of the tropopause rises.

• Ebel,

The behavior of the altitude of the tropopause is related, but not exactly the same thing or quantitatively determining for the outcome as both the altitude and the temperature of tropopause may change. In the real atmosphere determining the height of the tropopause is also difficult, because the transition from the troposphere to the stratosphere is not sharp. Simple models are misleading when they produce a sharp well defined tropopause.

Most of the changes that result in radiative forcing and/or surface warming occur deep inside the troposphere, not at the tropopause.

• on June 26, 2014 at 2:46 pm | Reply DeWitt Payne

The temperature profile cannot remain constant. A radiative imbalance initially affects the atmosphere more than it does the surface. Even if you are talking about a new steady state after a step change increase in CO2, the atmosphere must still be warmer than it was before or there will still be a radiative imbalance. The lapse rate, that is the slope of the temperature profile may remain the same, but the temperature at every altitude in the troposphere will be higher.

Decreasing the lapse rate while holding the surface temperature constant to increase the temperature at the height of emission doesn’t work either. That would create a radiative imbalance at the surface. Downward emission to the surface is also higher with a lower lapse rate.

6. Sorry. I lost quotion marks in the two first paragraphs. [Moderator note – fixed that ]

7. Thanks for the replies. As I said I’m playing the Devil’s Advocare role. I think the looking-downward example by Pekka makes the situation quite clear. Also the mention of the turbopause.

8. Thank you for your replay De Witt.
“The lapse rate, that is the slope of the temperature profile may remain the same, but the temperature at every altitude in the troposphere will be higher.”

This puzzels me. If most of the TOA LR come from emission hight between 2 and 10 km, then the temperatures at that hights should cause most of the energy out. Then the stratospheric temperature should not contribute so much.

• on June 26, 2014 at 5:04 pm | Reply DeWitt Payne

You do understand that mathematically a straight line can be described by two independent parameters, the slope and the intercept. By independent, I mean that you can change one without affecting the other. Let’s say the slope of the temperature profile, lapse rate, is 6 K/km and the surface temp is 300K. That means that at an altitude of 10km, the temperature will be 240K. Lapse rate by convention is a positive number even though the slope is negative. If we then increase the surface temperature by 1K and keep the lapse rate constant, the temperature at 10km will be 241K.

The stratospheric temperature doesn’t contribute much. There’s not very much air above the tropopause and there’s hardly any water vapor. So the major radiative gases are ozone and carbon dioxide. Increasing ozone warms the stratosphere because it increases the absorption of incident solar radiation while increasing carbon dioxide cools it because it increases emission much more than it increases absorption.

9. Thank you very much !!
Re: “Water Vapor Overwhelms CO2”

Is it legit to suggest that since H2O vapour concentration is related to temp, and it never surpasses reasonable supersaturated levels because it freezes, rains out… that H2O is a pretty constant – inflexible – GHG? It seems that it is always destined to be more of a “feedback”, than a “driver”.

Is that fair? Too simplistic?

• manwichstick,

We definitely should think of water vapor as a feedback, even though it is the most important “greenhouse” gas.

A very readable and good summary of some basics is found in this free paper:
Water Vapor Feedback and Global Warming, I.M. Held & B.J. Soden, Annual Review of Energy and the Environment (2000).
They discuss the critical point that the large scale circulation determines the amount of water vapor above the boundary layer.

I noticed today that Isaac Held (lead author of that paper) has a new blog article on water vapor – 47. Relative humidity over the oceans which is very interesting. Isaac Held is always worth reading. He has made a big contribution to climate system dynamics over the last 35 years or so.

There is a series on water vapor on this blog – Clouds and Water Vapor. A comment from Part Seven – Upper Tropospheric Models & Measurement:

One of the key points is that the response of water vapor in the planetary boundary layer (the bottom layer of the atmosphere) is a lot easier to understand than the response in the “free troposphere”. But how water vapor changes in the free troposphere is the important question. And the water vapor concentration in the free troposphere is dependent on the global circulation, making it dependent on the massive complexity of atmospheric dynamics.

• Thanks for the extra references, and Frank, Eli, SoD.
Thanks for correcting me my absolute/relative humidity issue. I wasn’t choosing my words carefully – but you folks seemed to know what I was actually trying to ask.

• The ansatz is that relative humidity is constant. Since air temperature increases, the absolute humidity increases

• Manwichstick: Too simplistic. Water vapor concentration does not vary with temperature – the maximum amount of water air can hold AT EQUILIBRIUM varies with temperature. The only time water vapor varies with temperature is when the air is saturated – and that only occurs when liquid water and water vapor are both present. Such a true equilibrium only occurs in clouds (where moist air is rising) and very near the surface of liquid water. I believe that the air even a few meters above the surface of the ocean is typically is only 80-85% saturated (but would appreciate being corrected if the real figure is higher.) So mixing plays a big role in atmospheric water vapor concentration that many often ignore. Furthermore, the rate of evaporation can depend more on wind speed than temperature. (The air in contact with the ocean surface is saturated, so the evaporation rate depends on how fast saturated air is transported away from the surface.) It certainly appears likely that absolute humidity will increase with temperature, but whether this increase will be rapid enough to maintain constant relative humidity is another question.

Large seasonal changes in temperature are accompanied by large changes in absolute humidity. I’d be interested in any good information showing how RELATIVE humidity varies with seasonal changes in temperature.

10. SOD wrote: “At the strongest point of absorption – 14.98 μm (667.5 cm-1), 95% of radiation is absorbed in only 1m of the atmosphere (at standard temperature and pressure at the surface). That’s pretty impressive.”

However, at the tropopause (ca 100 mb), 5% of 14.98 um radiation passes through 10 m of atmosphere. In the stratosphere, (1-10 mb), 5% of 14.98 um radiation passes through 100-1000 m (0.1-1 km) of atmosphere. If you go high enough, even the strongest lines are not “saturated” and doubling CO2 will decrease the rate at which photons escape to space. So saturation by itself is actually irrelevant. (The temperature about one tau into the atmosphere from space is an issue and the temperature doesn’t fall at this altitude for the strongest lines.)

Furthermore, absorption is only part of the story: Twice as many CO2 molecules in the atmosphere emit twice as many photons towards space. The rate of radiative cooling to space is a complicated function of the number of emitting GHGs (primarily CO2 high in the atmosphere), the temperature of the GHGs (which effects the photon emission rate) and the probability of that an emitted photon escapes to space.

• Frank: Twice as many CO2 molecules in the atmosphere emit twice as many photons towards space.

Yeahbut – the rate of emission varies as the fourth power of temperature AND if you raise the effective altitude of emission, the pressure is lower, which means both fewer molecules AND as Pekka points out, squeezes the line shape effectively raising the absorption coefficient integrated over a line. Thus the total emission rate from the atmosphere decreases.

• Frank,

Here is the mental picture I have of doubling CO2 (from fig. 12 in Visualizing Atmospheric Radiation – Part Seven – CO2 increases:

That’s why I can’t do arithmetic on it. For the highly absorbing/highly emissive center of the band the effect is tiny. For the less absorbing side bands the effect is significant.

In my head I can’t average out a large set of numbers where the factor is exp(-something(v) x something doubling). As soon as people start explaining how to do it, my head starts hurting and I have to drink coffee or alcohol, depending on the time of day.

It’s why I like Matlab. I don’t have to manipulate complex stuff in my head. Instead I can run some numbers quickly, produce graphs, change a factor, produce more graphs. It’s a beautiful thing.

So if you can turn the real maths of this absorption & emission model into something conceptually simple that is wonderful. Lacking the mental maths skills I don’t see how it’s possible.

• SOD and DeWItt:

SOD wrote” “Frank, I’m probably not telling you anything you don’t know… The conceptual approach is always a good idea.. but there are significant non-linearities in absorption and emission – and these are integrated over wavenumber and height.”

I could have something wrong. I wrote the above comments because the primary effect of doubling CO2 is to produce twice as many photons from CO2 that travel half as far. This is my personal “big picture” to a first approximation. The lower temperature, lower density and narrower line width at a higher characteristic emission altitude cause a very modest reduction in this doubled emission – a reduction that would be almost negligible (assuming my calculations were correct) if increased absorption didn’t nearly offset increased emission. Another refinement would be to recognize that not all photons emitted by CO2 travel an average of half as far. Those reaching space or the earth (as DLR) don’t. IMO, there is too little emphasis on the big picture – twice as many photons traveling half as far – and too much emphasis on factors that reduce emission slightly. These factors are important to the GHE, but only because the primary factors mostly offset each other.

Perhaps some of my math or physic is wrong. I certainly haven’t properly dealt with the fact that each wavelength has a different characteristic emission altitude and that this altitude is not always in the troposphere where the lapse rate is constant. The effect of temperature on the flux at each individual wavelength does vary with 1/(exp(hv/kT)-1), but the difference between T and T+0.65 degK (100 meters higher) using this formula is 1.5% at 200 degK, 1.0% at 255 degK and 0.72% at 300 degK and 15 um. So T^4 appears to have been a reasonable approximation. I can’t find anything that suggests that my big picture – twice as many photons traveling half as far – is grossly wrong.

(I find the GHE much easily to understand using the Schwarzschild eqn. than any of the above.)

• on June 30, 2014 at 1:48 pm DeWitt Payne

Frank,

The total flux from a gray or black body increases with the fourth power of its temperature. That isn’t true for an individual emission line or for a non-gray spectrum. The rate of change of flux with temperature is dependent on the frequency. At very low frequencies, for example, the intensity is linear with temperature. For frequency, the dependence on temperature is 1/(exp(hν/kT)-1). Using T^4 is at best a crude approximation.

• Eli: The change in emission caused by a rising characteristic emission level appears to be minor compared with the doubling of emission associated with doubling CO2.

The density of the atmosphere drops by a factor of two about every 5.6 km, about 1.25% every 100 m. So, if the characteristic emission altitude rises 100 m, emission will be reduced 1.25% due to the decreased number of CO2 molecules at that higher altitude.

The temperature falls about 0.65 degK for every 100 m the characteristic emission level rises. At the blackbody equivalent temperature of 255 degK, an 0.65 degK decrease is an 0.25% decrease. Since emission varies with the fourth power of temperature, a 100 m increase in the characteristic emission altitude produces a 1% decrease in emission due to falling temperature.

Therefore, doubling CO2 doubles the number of photons emitted minus about 2.25% for every 100 m the characteristic emission altitude rises.

I couldn’t locate a reliable value for the rise in the of the characteristic emission level caused by doubling CO2. WIth a lapse rate of 6.5 degK/km, however, a no-feedbacks climate sensitivity of 1 degC for 2XCO2 is equivalent to less than 200 m change in altitude. In that case, the lower density and temperature of CO2 at a higher characteristic emission altitude would reduce emission from doubled CO2 by about 4%, reducing 200% emission from doubled CO2 to 192% emission. So, doubling CO2 does nearly double emission of photons by CO2 at the characteristic emission altitude.

The radiative forcing from 2XCO2 appears to be the result of two nearly offsetting factors: a) halving the mean free path of most photons absorbed by CO2 and b) doubling of emission from CO2. The 4% change in emission from lower density and temperature at a higher characteristic emission altitude becomes important only because these factors are nearly offsetting.

• The narrowing of the emission lines is probably also unimportant given a small rise in the characteristic emission altitude. As best I can tell, the total flux of photons emitted from each emission line depends only on the A21 emission coefficient and the fraction of GHG molecules in a particular vibrational (and rotational) excited state. When LTE exists, the fraction of molecules in an excited state depends on temperature. The fact that some GHGs are traveling away from or towards the direction of emission effects the width of the line, but not the number of photons emitted by a particular transition. The fact that some GHGs are in the process of colliding with another molecule when they are emitting a photon also effects the width of the line, but not the number of emitted photons.

The narrowing of lines does effect the distance an emitted photon travels before it is reabsorbed.

• Frank,

I’m probably not telling you anything you don’t know..

The conceptual approach is always a good idea.. but there are significant non-linearities in absorption and emission – and these are integrated over wavenumber and height..

The conceptual approach must be tested against the actual calculations from the equations of radiative transfer.

Doing a set of calculations might be a better idea – I can produce some numbers if that will help, x vs y.

• DeWitt,

If I’m understanding your question correctly.. the line strength is the total absorption under the curve. So when you integrate the absorption, a(w) vs wavenumber, w you get, S, the line strength (S is the parameter name in HITRAN).

So as the pressure decreases and the line width narrows, the peak of absorption is higher and the trough is lower.

I’m going from memory here, and it’s been a while. Did I understand the question? If so I can go and check my memory against a reference..

• DeWitt,

Narrower lines increase transmission of wavelengths far enough from the center of the line. Radiation that originates much lower in the atmosphere is therefore absorbed less, but radiation from above or not far below gets absorbed more strongly. As the same lineshape applies to both emission and absorption at nearby altitudes, the narrowing of the lines means that radiation originating high up in the stratosphere is very ofter absorbed not far from the point of emission.

• on June 29, 2014 at 8:00 pm DeWitt Payne

Pekka,

Yes, I understand that. But does the total flux integrated over the line decrease or increase? My thought was that it decreased because an emission line isn’t a δ function. Of course the line width doesn’t go to zero either.

• DeWitt,
It’s likely to increase in the upper stratosphere, because it’s so much warmer than the effective radiative temperature of the lower part of the atmosphere.

• on June 29, 2014 at 10:10 pm DeWitt Payne

Pekka,

I didn’t phrase that correctly. Does the integral of the absorption coefficient increase or decrease as line width decreases?

• Integral of the absorption coefficient does not change from line broadening. The integral of absorption of a layer of finite thickness decreases for radiation of smooth spectrum, but increases for radiation that’s has an intensity peak nearly as narrow as the absorption peak at the same wavelength.

• on June 29, 2014 at 2:13 pm DeWitt Payne

Eli,

squeezes the line shape effectively raising the absorption coefficient integrated over a line.

I may be misinterpreting what you wrote, but doesn’t narrowing the line decrease total absorption? A Dirac δ function line would absorb no radiation because there’s no radiation to absorb for a line with zero width even though the integral of the the absorption line is finite, specifically, equal to one.

• Frank,
The mean free path at the center of the line does not change that fast, because the line width depends on the pressure.

Based on some results that I have calculated the mean free path at the center of the peaks is only 1m at the altitude of 13 km. High in the stratosphere at 50 km the strongest peak leads a mean free path of only 10m at the center of that peak. What changes much more is the width of the peaks and the mean optical depth between the adjacent peaks whose energies are slightly different due to rotational states. When some peaks get lower by a factor of 10 only, the valleys between the peaks drop by a factor of around 10000.

These results are from an old calculation, and I don’t have proper documentation about those calculations, but I think that Voigt profile was used in obtaining those results.

These numbers come from this picture that I have presented before in another thread.

• What happens when a GHG molecule is high enough that an excited state is unlikely to be “relaxed” by a collision?

That is called the ionosphere and it is not in local thermodynamic equilibrium. Mostly what happens is that there is so much far UV that most of the molecules are dissociated. Go high enough and there is more O than O2 and lots of ions (N2 is the hardest to crack)

• Frank,

Where the change is line shape gets important is in understanding stratosphere. As lines are very narrow and strong at the center radiation from much lower altitudes passes mostly trough with little absorption, but radiation emitted in the upper stratosphere that’s much warmer than lower stratosphere and the tropopause cannot heat effectively lower altitudes. Radiation from those altitudes gets blocked effectively by layers just below, and has only very little influence further down.

The temperature profile of the stratosphere would be significantly different, if the line shape would not change with altitude.

• on June 27, 2014 at 12:33 am DeWitt Payne

Frank,

What happens when a GHG molecule is high enough that an excited state is unlikely to be “relaxed” by a collision? Does the probability of emission of a photon depend on the lifetime of the excited state (rather than B(lamba,T), since there is no T). Is there a simple formula for lifetime (which I probably have forgotten)?

The intensity of emission is determined by the number of molecules in the excited state, not the lifetime of an individual molecule in the excited state. The Einstein A21 coefficient, which has units of sec-1, multiplied by the number of molecules in the excited state in a unit volume is the emission intensity in that volume. The M-B equation tells you what fraction of molecules at a given temperature will have an energy greater than some level.

However, local thermodynamic equilibrium no longer holds when the probability that an excited molecule decays by radiation rather than collision gets too high. And too high isn’t very high. Without LTE, M-B statistics may no longer apply. Equipartition may not apply. The rate of emission may then depend on the rate of absorption of radiation because collisions are simply too rare to excite many molecules. An individual molecule could have a kinetic energy well above the energy level of an emitted photon, but without collisions, that energy can’t be translated into the vibrational state. I think. QM can be very strange.

• Peeka: Thanks for the correction. Averaged over a 0.1 um of so, I’m about right; but if you increase the resolution to 0.001 um, I’m wrong. I guess I should have rounded 14.98 um to 15.0 um instead of copying and pasting SOD’s number. Fortunately, that doesn’t change my main points – if you go high enough, doubling CO2 will make a difference in the probability of escaping to space – which is only part of the radiative cooling story.

What happens when a GHG molecule is high enough that an excited state is unlikely to be “relaxed” by a collision? Does the probability of emission of a photon depend on the lifetime of the excited state (rather than B(lamba,T), since there is no T). Is there a simple formula for lifetime (which I probably have forgotten)?

It seems to me that B(lamba,T) is telling us something (similar a Boltzmann distribution) about the equilibrium fraction of molecules with an energy E=hc/lamba above ground state at a temperature T. Actually, I’m not sure whether M-B or B-E statistics apply to this problem. The derivations I have seen don’t approach the situation from a “number of excited molecules times rate of emission per molecule” perspective.

11. There is really no dispute of there being a radiatively induced GHE by rational people. The argument is over how much net ‘enhancement’ to the GHE would or should result from additional GHGs.

• on June 27, 2014 at 1:33 am | Reply Climate Weenie

Right. Some of us like to point out the exaggerations of extent, effect, and impacts.

Perhaps it’s time for the science of joy.

12. My English is not so good to write the following text directly into English – so largely machine translation. For safety, I cling to the German text.

1) There is no saturation: Where is strongly absorbed, is also strongly emits – it’s just a high radiation transport resistance.
2) The oft-mentioned 33 K are only a lower limit of the greenhouse effect (Hölder’s inequality). On closer calculating higher values come out (Kramm about 115 K, 158 K Gerlich). The precise values for certain assumptions are misinterpreted as evidence to the contrary.
3) The decrease in intensity with higher = colder goes past the change in the temperature profile. With more CO2 the pressure of the tropopause decreases (the tropopause is higher) – Schwarzschild criterion. The longer troposphere at approximately constant temperature gradient leads to a larger temperature difference between surface and tropopause. This greater temperature difference is distributed to about 1/4 to the increase in surface temperature and 3/4 to the decrease in stratospheric temperature.
4) Due to the convection of the greenhouse gas, the mixing ratio to about 100 km altitude is constant. Without convection, the greenhouse gas would according to the molecular weight segregate something – but the time of separation is large compared to the circulation time.
5) If none of the isothermal conditions are present, also the distribution of the excited states are not in accordance with the local gas temperature – independent of the lifetime. Nevertheless, you can assign the distribution of the excited states by a Boltzmann temperature. With frequent collisions (LTE) but the difference is gas temperature and Boltzmann temperature well below 1 K.
7) The approximate constancy of relative humidity is due to the circulation and raining. To top rises to 100% saturated air and rains from on temperature decrease. In the ascended air therefore decreases the absolute humidity – while sinking so the relative humidity decreases. Due to the turbulence, the moist air rising and sinking dry air combine to create an average.
8) At the same width of the absorption lines the absorption length is proportional to the pressure. Wherein indication of the absorption length as the pressure difference, therefore, the pressure difference is independent of pressure. The mean pressure difference is approximately independent of the width of the lines.
9) At the tropopause is approximately the whole heat transport upward as radiation transport. In the layers below the tropopause of the total heat transport remains about the same – but because of the increasing radiation transport resistance (higher density) decreases proportion, which is transported beam, so that the convective transport increases.

1.) Es gibt keine Sättigung: Dort wo stark absorbiert wird, wird auch stark emittiert – es ist nur ein hoher Strahlungstransportwiderstand.
2.) Die oft genannten 33 K sind nur ein unterer Grenzwert des Treibhauseffektes (Höldersche Ungleichung). Bei genauerer Berechnung kommen höhere Werte heraus (Kramm ca. 115 K, Gerlich 158 K). Die genaueren Werte für bestimmte Annahmen werden fälschlich als Gegenbeweis interpretiert.
3.) Die Intensitätsabnahme mit höher = kälter geht an der Änderung des Temperaturprofils vorbei. Mit mehr CO2 sinkt der Tropopausendruck (die Tropopause wird höher) – Schwarzschild-Kriterium. Die längere Troposphäre führt bei annähernd konstanten Temperaturgradienten zu einer größeren Temperaturdifferenz zwischen Oberfläche und Tropopause. Diese größere Temperaturdifferenz verteilt sich zu ca. 1/4 auf die Zunahme der Oberflächentemperatur und zu 3/4 auf die Abnahme der Stratosphärentemperatur.
4.) Durch die Konvektion der Treibhausgase ist das Mischungsverhältnis bis etwa 100 km Höhe konstant. Ohne Konvektion würden sich die Treibhausgase entsprechend dem Molekulargewicht etwas entmischen – aber die Entmischungszeit ist groß gegenüber der Zirkulationszeit.
5.) Wenn keine isothermen Verhältnisse vorliegen, ist auch die Verteilung der angeregten Zustände nicht entsprechend der lokalen Gastemperatur – unabhängig von der Lebensdauer. Trotzdem kann man der Verteilung der angeregten Zustände nach Boltzmann eine Temperatur zuordnen. Bei häufigen Kollisionen (LTE) ist aber der Unterschied Gastemperatur und Boltzmanntemperatur weit unter 1 K.
6.) Die latente Wärme einschließlich Kondensationswärme führt nur zur Abnahme des trockenadiabatischen Gradienten (etwa 9,8 K/km) auf den feuchtadiabatischen Gradienten (etwa 6,5 K/km).
7.) Die näherungsweise Konstanz der relativen Luftfeuchtigkeit ist Folge der Zirkulation und Abregnen. Nach oben steigt 100% gesättigte Luft auf und regnet bei Temperaturabnahme ab. Bei der aufgestiegenen Luft nimmt deshalb die absolute Feuchtigkeit ab – beim Absinken sinkt also die relative Feuchtigkeit. Durch die Turbulenz vermischen sich die feuchte aufsteigende Luft und die absinkende trockenere Luft zu einem Mittelwert.
8.) Bei gleicher Breite der Absorptionslinien ist die Absorptionslänge proportional zum Druck. Bei Angabe der Absorptionslänge als Druckdifferenz ist deshalb die Druckdifferenz unabhängig vom Druck. Die mittlere Druckdifferenz ist näherungsweise unabhängig von der Breite der Linien.
9.) An der Tropopause ist näherungsweise der ganze Wärmetransport nach oben als Strahlungstransport. In den Schichten darunter bleibt der Gesamtwärmetransport etwa gleich – wegen des zunehmenden Strahlungstransportwiderstandes (höhere Dichte) sinkt aber Anteil, der strahlend transportiert wird, so daß der konvektive Transport zunimmt.

MfG

13. Just one point: While the CO2 is definitely a GHG and there is a “greenhouse” effect, there is considerable question as to how much CO2 has contributed to historic warming. The Mt. Pinatubo eruption showed, I believe, that CO2 is not as potent a GHG as was previously believe. ERBE readings done in the weeks and months after the eruption showed that a doubling of CO2 would see approximately a 1 C increase in global temperatures. That is below the IPCC’s business as usual scenario and of little concern.

• Alan: The Mt. Pinatubo eruption can be used to estimate ECS from fast feedbacks (clouds, water vapor) in the absence of slow feedbacks (ice-albedo). However, the answer one obtains depends on the model one uses to analyze the data and what data one uses. Should the temperature data be corrected for ENSO? The first post below reviews the literature (with links) and describes the results from a more comprehensive model (which appears credible, but which certainly isn’t peer-reviewed). The second updated post obtains a most likely ECS of 1.15 degC and can’t properly fit the data if ECS is outside the range 0.8-1.4 degC. The whole analysis is worth reading, especially if you want to understand why it is hard to get definitive results from climate data.

http://rankexploits.com/musings/2012/pinatubo-climate-sensitivity-and-two-dogs-that-didnt-bark-in-the-night/

http://rankexploits.com/musings/2012/pinatubo-climate-sensitivity-revisited/

Now that papers like Otto (2013) have made low values of ECS more likely, perhaps an analysis similar to this one can get through peer review.

• That is about what you get without any feedbacks.

14. Let’s assume that regardless of the amount of energy arriving at the earth’s surface, that the lapse rate stays constant and so the more heat arriving, the more heat leaves. That is, the temperature profile stays constant. (It’s a questionable assumption that also impacts the AGW question).

It doesn’t change the fact that with more GHGs, the radiation to space will be from a higher altitude. A higher altitude will be colder. Less radiation to space and so the climate warms – even with this “short-circuit”.

This seems to me to be a non-sequitur.

If convection dominates over radiative transfer as the primary heat transfer mechanism in the troposphere, an increase in radiative forcing from GHGs would still be overwhelmed by the dominant and stronger negative-feedback of increased convection.

Likewise, if an electrical circuit containing a resistor is “short-circuited,” increasing the resistance of the resistor will make no difference to the unimpeded flow of current via the “short-circuit.”

Who can say whether the lapse rate will be constant in a warmer world?

The lapse rate dT/dh = -g/Cp is dependent only upon gravity and atmospheric heat capacity at constant pressure. If anything, adding GHGs would increase Cp and thus decrease the lapse rate to cause cooling. A warmer world would increase evaporation and force lapse rates toward the steeper wet adiabatic to cause compensatory negative-feedback cooling.

with more GHGs, the radiation to space will be from a higher altitude. A higher altitude will be colder…

What altitude are you saying is the ERL? The tropopause is essentially isothermal, so an increase in average radiative altitude would make no difference in radiating temperature. The troposphere is dominated by the negative-feedback of increased convection, so an increase of radiative forcing from a higher ERL would be overwhelmed by negative-feedback from increased convection.

• Paul,

These are all good questions to ask.

If convection dominates over radiative transfer as the primary heat transfer mechanism in the troposphere, an increase in radiative forcing from GHGs would still be overwhelmed by the dominant and stronger negative-feedback of increased convection.

First of all, the “base case” is that of increases in a GHG like CO2 without any feedbacks. So let’s say – in hypothetical case A – that the lapse rate stays exactly the same. In case A, the radiation altitude has moved up.

We’ll come back to your early points later, so let’s pick up your final point, which impacts on this one:

What altitude are you saying is the ERL? The tropopause is essentially isothermal, so an increase in average radiative altitude would make no difference in radiating temperature. The troposphere is dominated by the negative-feedback of increased convection, so an increase of radiative forcing from a higher ERL would be overwhelmed by negative-feedback from increased convection.

Here’s what I said in note 5: ‘ the “place of emission” is a useful conceptual tool but in reality the emission of radiation takes place from everywhere between the surface and the stratosphere. See Visualizing Atmospheric Radiation – 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..’

Overall the atmosphere emits from a lot of different altitudes. These altitudes are highly wavelength dependent. Nearly all of the emission is well below the tropopause, in the troposphere. A tiny portion is from the most “saturated” part of the CO2 band in the stratosphere.

So basically almost all of the “greenhouse” effect is from the troposphere, and all of the effect of doubling CO2 is from the troposphere.

This is a “no feedback” case. Obviously the climate has feedbacks so this brings me to the point you have about convection, which I’ll pick up in the next comment.

• “A tiny portion is from the most “saturated” part of the CO2 band in the stratosphere.”

As already written – there is no saturation, not even for a tiny portion.

• Paul,

..If convection dominates over radiative transfer as the primary heat transfer mechanism in the troposphere, an increase in radiative forcing from GHGs would still be overwhelmed by the dominant and stronger negative-feedback of increased convection..
A warmer world would increase evaporation and force lapse rates toward the steeper wet adiabatic to cause compensatory negative-feedback cooling..

According to a random site, cp for air changes from 1.009 at -100’C to 1.005 at -50’C. So that’s about 0.01% per ‘C over that range.
Then from -50’C to +40’C it is constant.

I think we can work on the basis that cp is effectively constant over the temperature changes that might come from increases in CO2.

The dry adiabatic lapse rate will not be changing.
The moist adiabatic lapse rate will be changing if there is more moisture (or less moisture)

Here is a graphic of moist potential temperature (from Potential Temperature), annually averaged:

We can see that in the tropical troposphere the atmosphere is very effectively convecting to the moist adiabatic lapse rate (that’s what the vertical lines of moist potential temperature tell us).

So let’s consider an increase in CO2. On day one the temperature profile is still the same. The emission of radiation to space drops. Nothing happens to the temperature immediately but over the coming days, weeks and months the troposphere warms.

Why would it stop? Because the atmosphere and surface warm up until we reach a new equilibrium point. This has to happen via an increase in temperature. Without an increase in temperature there is no feedback to stop or reduce any climate warming.

So we are on the subject of feedbacks. Well, that’s a lot more complicated and not the subject of this article. But of course it is the interesting subject.

From what you argue we might expect three things:

1. Higher temperatures – which leads to more emission of radiation from the surface and the atmosphere. This is a negative feedback which reduces the impact of more CO2.

2. More water vapor – which leads to a “tropical hot spot” as the lapse rate is lower (ie less cooling per km of altitude) and so the temperature higher up in the atmosphere increases more than the temperature lower down. This is a negative feedback which reduces the impact of more CO2.

3. More water vapor – which is a “greenhouse” gas, aka “radiatively-active” gas, which moves the altitude of emission to space higher in the atmosphere which reduces radiation to space. This is a positive feedback which increases the impact of more CO2.

Is this what you were arguing for, or only 1&2? Surely you must also be arguing for 3 as well?

Of course, many people have used GCMs to try to calculate these different effects, and compared GCMs. Here’s an example from Quantifying Climate Feedbacks Using Radiative Kernels, by Brian Soden et al (2008). One of the coauthors is Isaac Held, both were referenced earlier in the comment thread:

I’m not saying this answer is correct. But it would be a difficult case to make that more water vapor would have an overall negative feedback.

• And just a further comment as the lapse rate always seems to lead to confused discussions.

Saying that the dry adiabatic lapse rate would remain the same is not the same thing as saying that the environmental lapse rate would remain the same in dry areas.

The adiabatic lapse rate only tells us how the temperature changes when convection happens relatively quickly. See the earlier cited articles in note 3 for more on this.

A reasonable case can be made for an “actual” (=environmental) lapse rate staying close to the moist adiabatic lapse rate in the tropics, because that is what we already observe in practice. There is lots of convection, and lots of very strong convection, in the tropics.

In the mid-latitudes and polar regions it is a different story.

Calculating how air expands and therefore loses heat is an easy calculation. Calculating how air moves around in the climate is a completely different story.

• Thank you for this answer SoD.
I think there has been too much confusion in discussions of climate change because the question of negative feedback of vater vapor has been avoided. And I don`t say that there is no positive feedback!

• on June 27, 2014 at 1:28 pm Climate Weenie

>>> 2. More water vapor – which leads to a “tropical hot spot”

So, by most examinations, warming has occurred, but the “tropical hot spot” has not. Evidently there are some shortcomings to this understanding.

• on June 27, 2014 at 3:04 pm | Reply DeWitt Payne

Paul,

If convection dominates over radiative transfer as the primary heat transfer mechanism in the troposphere, an increase in radiative forcing from GHGs would still be overwhelmed by the dominant and stronger negative-feedback of increased convection.

Dominates is a rather strong word. The net flows from the surface to the atmosphere and space are ~100W/m² by convection and ~~60 W/m² by radiation, with ~40 W/m² of the radiation going directly to space. Your shorted resistor analogy is incorrect. The question I would like you to answer is: How is convection going to increase if the temperature doesn’t increase?

• Pekka, a diode with significant leakage current would be even better. If you use an idealized diode you get trapped into the Gerlach argument about the second law not permitting any energy flow downwards in the atmosphere.

• A resistor is a bad analogy, because convection is more like a diode (or perhaps a zener diode). A diode lets current pass trough with little resistance as soon a threshold voltage is exceeded, but not when the voltage is in the wrong direction. Similarly convection grows with little resistance when temperature drops with altitude faster than the adiabatic lapse rate, but stops when that’s not the case.

15. Your base premise is wrong, SoD. After that, no appeal to ‘basic physics’ (or the ‘authority’ of Grant Petty, for that matter), no theoretically conjured up warming mechanisms and no calculations made will help you accomplish anything but a reinforcement of your original misconceptions about how the world works.

The earth system warms from the surface UP, not from some hypothesized atmospheric layer in radiative imbalance DOWN. The lapse rate is set from the surface and climbs up with convection bringing the surface heat into and up through the troposphere. The heat moves through the earth system in this way: sun >> surface >> troposphere >> out through the ToA. That’s why we always and only see this progression: surface temps up >> troposphere temps up (how? mostly from the transfer of latent heat through evaporation>condensation)* >> OLR at ToA up (why? from the increased temp and humidity/emissivity through the column below). Never the opposite.

*http://oceanworld.tamu.edu/resources/oceanography-book/Images/rain_ANN.png

The earth system, rather than ‘holding incoming energy back’, radiates whatever it needs to radiate to balance the incoming from the sun, from whatever level(s) convection brings the surface heat up to, from where the ‘radiatively active gases’ radiate it back out to space. (Without their presence, this would be a problem and the earth would be a much hotter and unstable place.) And that’s it. The surface temp is already set, by the incoming radiation from the sun in conjunction with the mass (heat capacity & weight) of the atmosphere on top of the solar-heated surface. Everything after that is just a result of temperature/temperature distribution and emissivity, always having to catch up with variations in solar input. The strange ‘effective (or average) emission height’ hypothesis is nothing but an attempt to turn everything we know about how the world works on its head. It is a result, not a cause of temperature (and emissivity) distribution.

This is what happens when good old meteorology and climatology become ‘high-jacked’ by radiative physicists insisting that their particular field of study in fact rules the roost.

I’m not disputing the radiative properties of the gases in question. Not even the temperature effect they might have in a closed glass box lab exeriment, by forcing reduced temp gradients away from the externally heated surface. What I’m saying is that, in the open surface/atmosphere system, they don’t matter. Well, they matter. The analogy simply fails. They do and can not determine the mean temp of the global surface. At all. Other (and equally ‘basic’) physical processes entirely do that.

The atmosphere does not owe its ability to warm to the presence of ‘radiatively active gases’. It owes its ability to cool adequately to the ‘radiatively active gases’. Because it warms by convection from the surface and cools by radiation to space. Increase its emissivity and you increase its abiity to cool. Basically, the only gas radiating to space from the troposphere is H2O, CO2 almost not at all:

And H2O in the atmosphere would, in purely radiative terms, cool the surface underneath, by absorbing and reflecting a massive portion (close to 80%) of the incoming solar radiation before it can ever be absorbed by the surface. Tropical rainforest areas are several degrees cooler in mean annual temps than tropical/subtropical desert areas. Even as they lie on average more directly under the sun, experience much smaller temp fluctuations than the deserts and would (according to ‘theory’) receive much, much more ‘back radiation’ from the moist atmosphere …

Now, this is how the atmosphere really makes the surface warmer than solar radiative equilibrium (because it sure does):

1) It has a mass and therefore a heat capacity. This means it is able to warm. It does so by being directly convectively coupled with the solar-heated surface below it. Regardless of whether that atmosphere contains radiatively active gases or not, it will warm – conductively>convectively. The atmosphere is able to warm. Space isn’t. Therefore the atmosphere sets up a temperature gradient away from the solar-heated surface that has a finite (sub-max) steepness. Space doesn’t. The atmosphere thus INSULATES the surface. Energy is not able to escape the surface as fast as it’s coming in before it has warmed to a higher mean temperature than before the atmosphere was put in place.

2) It has a mass and therefore a weight (it’s in a gravity field, after all). It therefore exerts a pressure on the solar-heated surface above 0. Unlike space. This pressure makes it harder for energy to escape the surface than without such pressure AT EQUAL TEMPERATURE in two ways: i) it suppresses the evaporation rate, and ii) it suppresses (upward) buoyant acceleration of heated surface air. (The second point here is more subtle and complex than the first one, because it also needs to take into account an atmospheric density distribution factor to work, but that’s for another day. It is still the main reason why the surface of Venus is so hot.)

This is why Mars’s atmosphere is not capable of warming the surface to a mean global temp above pure radiative equilibrium with the sun (S-B) (rather the opposite), even with 95% CO2 in it. It is far from massive enough …

• Not much point me having a discussion with Kristian.

Readers interested in Kristian’s point of view, please review our discussion in Visualizing Atmospheric Radiation – Part Three – Average Height of Emission.

When someone replies to this question:

But just to help me, why not tell me what you think. Same surface temperature, same atmospheric temperature profile, more GHGs: what happens to OLR?

– in the way that Kristian did you realize there is no point.
When Kristian comes forward with a textbook (never), or says “oh, I got that wrong”, then we can pick up the discussion. Until then..

• I’m not trying to have a ‘discussion’ with you, SoD. There’s no point in that, I agree …

When someone like SoD simply doesn’t understand that the question asked is completely confined within the framework of his interpretation of how the world works and then doesn’t like the answer, then any sane person would see there is no point trying to have a normal ‘on-the-ball’ discussion about how the surface of the earth is warmed beyond pure solar radiative equilibrium.

I will have no revelations here, that’s for sure. Only reiterations of purely theoretical concepts never even remotely verified by real-world observations.

• Edim,

A totally wrong answer. Without GHGs the surface would radiate directly to the space and would be much colder (like 30C colder) than it is,

You wrote about the radiation from the atmosphere, but no radiation from the atmosphere would be needed to make the surface cold in absence of down-welling IR radiation from the atmosphere to the surface.

• on July 1, 2014 at 2:11 pm DeWitt Payne

Edim,

The question was rhetorical, as I didn’t expect an answer from Kristian, and I answered it myself in the comment. Apparently you only read the first sentence.

• DeWitt Payne,

“What’s the physical mechanism that causes an atmosphere to INSULATE a planetary surface when radiation is the only means for energy to flow to space?”

The mechanism is the radiation being the only means for energy to flow to space. Only the radiatively active gases, the so-called greenhouse gases, can (effectively) cool the atmosphere, by radiating to space. The surface is easily cooled non-radiatively by the atmosphere (low thermal resistance at the surface/atmosphere interface), but only the atmospheric ‘greenhouse gases’ can effectively transfer the gained atmospheric energy to space (high thermal resistance at the TOA). The bulk of the atmosphere (N2, O2) insulates the surface by having a very high thermal resistance to space.

• on June 28, 2014 at 9:35 pm DeWitt Payne

Kristian,

Replace SoD by Kristian in the second paragraph and you have the real situation. Once again proving that irony always increases. I believe there’s even a relevant biblical quote:

…first cast out the beam out of thine own eye; and then shalt thou see clearly to cast out the mote out of thy brother’s eye.

Matthew 7:5 KJV.

While I’m on the subject: What’s the physical mechanism that causes an atmosphere to INSULATE a planetary surface when radiation is the only means for energy to flow to space? Oh, wait, I know the answer: An atmosphere that can absorb and emit radiation in the wavelength range emitted by the surface, is more transparent to incoming solar radiation than radiation emitted from the surface and where the temperature decreases with altitude. That’s the greenhouse effect in a nutshell.

• on June 27, 2014 at 3:09 pm | Reply DeWitt Payne

Sorry, can’t resist.

The atmosphere thus INSULATES the surface. Energy is not able to escape the surface as fast as it’s coming in before it has warmed to a higher mean temperature than before the atmosphere was put in place.

You do understand that that statement is complete nonsense. No, I guess you don’t. Loschmidt was right about the lapse rate, but for the wrong reason.

• You’re a funny guy, DeWitt. No ‘Mr Know-It-All’ arrogance at all.

You don’t ‘get’ common insulation, is that it, Payne …?

• on June 28, 2014 at 7:30 pm | Reply Climate Weenie

Kristian,

I tend to agree that Meteorology is run roughshod by some ( not necessarily anyone here ) who exaggerate the effects of radiative forcing.

But I would challenge you reflect upon two truths.

1. Convection tends to cool the surface and warm aloft, but only radiance ( by definition ) can remove the surplus energy received from the sun to restore balance to earth. The only way that convection can help restore balance is if it also invokes some process which changes radiance ( increase albdeo, lower average cloud height, change in water vapor profile, etc. ) as SoD has laid out.

2. ‘Radiation Fog’ occurs when one GHG ( water vapor ) is reduced, allowing more intense surface cooling. What is the corollary of this?

16. Sorry, the first link got deactivated by the asterisk. Here it is:

17. Kristian wrote: [Energy flows] sun >> surface >> troposphere >> out through the ToA.

When temperature is stable, the power flux through each step (>>) needs to be equal. What happens if we slow down the “troposphere >> out through the ToA” step with additional GHGs while all of the others remain the same? Won’t the troposphere warm? Won’t this eventually slow down convection (which depends on the lapse rate) and increase DLR? NET radiation does flow through the system in the direction you indicate, but the fluxes are two-way in all cases. (The flux from the earth to the sun and space to the earth are both negligible, of course.)

• No, I’m talking what IN THE DATA FROM THE REAL WORLD, Frank.

It’s nice to have theoretical armchair hypotheses, ideas about how the world should work. If what they’re claiming is happening can’t be observed in the real-world data, then it’s not science. It’s pseudo-science. An unsubstantiated claim.

What works in the lab doesn’t necessarily work in the large-scale Earth system. The two are not analogous.

You have to check it empirically first. +CO2 >> +T. Tropospheric warming >> surface warming. Where’s the signal?

• Kristian: In the real world, I can heat a pot of water from the bottom with or without a lid to reduce convective loss of heat from the top of the water. Will the presence of a lid change the amount of time it takes for the pot to boil? Or better still, see if a lid effects the equilibrium temperature of the water in the pot when when the heat source adjusted so that the temperature is near boiling.

If you know the answer for a pot of water, you know the answer for the atmosphere. So don’t duck the question I asked: “When temperature is stable, the power flux through each step (>>) needs to be equal. What happens if we slow down the “troposphere >> out through the ToA” step with additional GHGs while all of the others remain the same?”

Fundamental principles of science that can be tested or accurately measured in the laboratory apply to the atmosphere. The molecules and photons involved don’t know whether they are in a laboratory or the atmosphere, they will behave the same in either location under the same conditions. Therefore there is no doubt that a sudden doubling of CO2 will reduce the flux of OLR at the TOA. Like pot of water at equilibrium, slowing heat loss from the top will result in warming below.

Weather forecasts demonstrate that we can make models that do a reasonable job of representing the physics of heat transfer in the atmosphere. The radiative transfer calculations performed by forecasting models tell us how much the temperature will fall each night in the absence of SWR and how much that drop will be moderated by DLR from low clouds. Those forecasts tell us where convection will carry water vapor aloft producing clouds and rain. We also understand that those forecasts start failing about a week into the future because we don’t know the current state of the atmosphere accurately enough. If we make slight changes in the initialization conditions of the model (within the error of our knowledge of those conditions), those small changes will alter next week’s weather forecast.

There are numerous problems with converting weather forecasting models into AOGCMs capable of predicting future climate. Weather forecasting models have been tested against observations, but the important predictions of AOGCMs can’t be confirmed by observations. There are numerous parameters in AOGCMs that can’t be accurately calculated laboratory physics or unambiguously determined from observations. Those parameters dramatically influence feedbacks and climate sensitivity. There is no way for us to know which set of parameters (if any) will produce the best representation of our climate after CO2 has doubled or tripled. Given that we are effectively halfway to 2XCO2, it sure looks like the parameter sets used by the models used by the IPCC are over-estimating feedbacks or under-estimating natural variability. Climate models also fail to accurately reproduce phenomena like the MJO or ENSO. You could, if you want, characterize belief in the predictions of such models as pseudo-science. It makes far more sense to challenge religious belief in projections of CAGW than SOD’s scientific explanation of the greenhouse effect.

“…At the strongest point of absorption – 14.98 μm (667.5 cm-1), 95% of radiation is absorbed in only 1m of the atmosphere….”

A skeptic I debate says in response:
“..Modtran shows that only 4% of the 14.98 micron radiation is lost in 1 meter.. Modtran models 70 km as the TOA. At that point Modtran shows that the 14.98-micron radiation has lost 70% or its radiation.”

Can you comment on the his 4% vs your 95%? Did you maybe mean 10 meters?
Also, for practical purposes, the radiative TOA is somewhere near the tropopause, isn’t it?

• on June 28, 2014 at 3:04 pm | Reply DeWitt Payne

bobmaginnis,

There’s another tool on the web for looking at absorption spectra: http://www.spectralcalc.com. There’s lots more you can do there, but you have to subscribe to do that. Lets look at the transmittance spectrum for a 1 m path length at 400 ppmv CO2 at a total pressure of 1013.25mbar and 296K. It looks to me like the transmittance at the peak is about 1%, not 96%.

Now lets look at MODTRAN under similar conditions, observation looking down, US 1976 Standard Atmosphere, 400 ppmv CO2 and a surface temperature of 296K and 668 cm-1. But instead of just looking at radiance, lets go to the raw data and look at transmittance as well. The units are height in km, radiance in W/(m² cm-1). Transmittance is a dimensionless number with a range of 0 to 1.

0.000 0.449 0.31468
0.002 0.449 0.16111
0.040 0.449 0.00000
70.00 0.221 0.00000

0.002km, 2m, is the smallest increment in altitude that produces a change in the data. We can see two things, a viewing height in MODTRAN of 0m isn’t actually 0m. The second is that the transmittance at 2 m is about half what it was at a nominal 0m. If we convert to absorbance by taking the log of the ratio of the transmittances we get a value of -0.2907. Dividing by 2 to get absorbance/m it’s -0.14535, or a transmittance of 0.716, which is a fair bit smaller than 0.96. Transmittance is 0 to five decimal places at an altitude of 40m. Using the calculated absorbance/m, the actual viewing height at a nominal 0.000km is actually more like 0.0034km.

70km is not the TOA for MODTRAN. It goes to 100km. 70km is just the default observation height. So the skeptic you debate is, shall we say, somewhat unskilled in the use of MODTRAN and spectrophotometry in general.

• MODTRAN parameterizes the absorption of bands, rather than doing a complete line-by-line calculation. The MOD part refers to moderate spectral resolution, just as the HI in HITRAN refers to high resolution. It is averaging over all of the sharp features in the real spectrum. It does a good job overall in a really short time. You can read several SoD articles in the time it takes to complete one line-by-line run.

• bobmaginnis,

The absorption value at a specific wavelength depends on the pressure and temperature (primarily pressure because this varies so much more than temperature as we go up through the atmosphere).

The calculation I gave is at surface pressure (1000 mbar) and temperature.

At 100mbar the story is quite different, here is a comparison from Grant Petty’s book, reproduced in Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part Eight:

Onto Modtran. If your debating friend is using the online Modtran calculator, it’s important to understand that Modtran calculates absorption and emission.

Likewise, if you take a look at the calculations I have produced using a line by line model, say in Visualizing Atmospheric Radiation – Part Two you can see that the 15 μm (667 cm-1) radiance is still “alive and kicking” no matter how far you go up through the atmosphere.

E.g., figure 3:

– where the bottom curve is at 23km, the top curve is the surface.

The atmosphere emits strongly if it absorbs strongly. But it emits at the local temperature of the atmosphere.

To calculate absorption you need to know the line strength, the concentration of the absorbing gas and the path length. Then the calculation is quite straightforward, from the Beer-Lambert law.

Perhaps you can ask your debating partner for what they think is the line strength and their source. Or what Modtran tool they are using and are they sure they are calculating absorption only.

Radiative TOA. Well this is just a reference point for a calculation. If you want to know what the spectrum or the flux is at a given height in the atmosphere you need to state the height (and also you will need to know some other conditions like surface temperature etc).

• Ebel,

Very nice graph, thanks.

19. Basically, run a way warming hasn’t happened. I still think that the heat is released, rather than retained. If the models that were run were correct, I don’t think there would be any doubt on my part at all. However, the models have failed. Now, that would mean that the feedback is wrong in the way you envision it. …. Lately, however, and the fact that SoD does present the ideas with evidence, rather than just shouting me down, What if that is correct and there is something else that is as large or larger than the feedback from co2. Going back to 1997/98 ‘all things being equal’ it should be much warmer under that scenario, but it isn’t. CO2 levels have certainty exceed all estimates. So the question becomes why, if your analysis is correct why hasn’t the temperature increased ? Would we be facing much colder temperatures?
I also found Pekka’s comment about the resistor interesting because in electrical systems you have a capacitor as well. Combing the two gives a different graph than just a straight line.

• on June 29, 2014 at 12:59 pm | Reply Climate Weenie

It depends on which aspect of ‘the models’ you are referring to.

The problem doesn’t appear to lie with radiative forcing.
The warming we observe in the satellite era is roughly consistent with the RF we calculate.

The problem is that the GHG growth rate ( with which the RF and warming rates corresponds ) is less than the low end scenario of previous IPCC reports.

This low rate can then be exceeded by natural variability more frequently and for longer periods than the high rates.

Global warming is real, but exaggerated.

• As Fermi said about extraterrestrials, where are they? That, of course is the problem with invoking mysterious stuff.

20. Kristian,

We have a few rules on this blog. One is civility. Another one is not just repeating the same points.

Repetition – it’s frustrating when no one answers your question the way you want it answered. Maybe people have just missed your point or ignored you or haven’t understood what you are really getting at. However, at the discretion of the moderator, continual repetition may be snipped or just deleted to avoid a discussion being hijacked or just made less interesting to other readers.

If you find your future comments are not appearing then you will know why (the amazing insight of your science?)

It’s clear what you think.

I haven’t got much patience for people who have no interest in science, no interest in learning, make ridiculous claims as a substitute for learning and start insulting people when they keep pointing out the basic flaws in your claims.

Proven experimental science is not armchair science because you don’t like it, or don’t like the conclusions it leads to.

Probably time to claim victory and move on to other locations that need your real world science insights.

21. Thanks very much for such a clear and simple run through of the greenhouse effect, very helpful for non-experts to read and to link to.

22. @ Eli Rabett:

“”However, think you missed the most important point with respect to saturation of CO2, that as the concentration increases, the level at which the atmosphere emits in the CO2 bending region rises to a colder level because the emission is trapped higher in the atmosphere…””

Ok, we heard about that. But if there is more emission (and absorbtion!) of IR radiation at this “higher level”, so this level could reach the temperature of the level bevore, level at, lets say 300ppm CO2?

• on June 29, 2014 at 2:16 pm | Reply DeWitt Payne

Yes.

But since we assume that the lapse rate doesn’t change much, the atmosphere below that level extending all the way to the surface must warm as well.

23. […] reading comprehension skills than others. In the end, we each believe what we choose to believe. The “Greenhouse” Effect Explained in Simple Terms | The Science of Doom __________________ 98 Boxster 2.5L BSX #129 PCA National DE Instructor PCA Zone 8 DE/Time Trial […]

24. According to the observations (RATPAC) the trend is positive in the troposphere and almost the same (constant temperature gradient), negative in the stratosphere.

• According to that picture all models predict a significant lapse rate change in the troposphere. The observations shown are not conclusive. They seem to be consistent with the models, but also with no change in the lapse rate. The central values of the observation indicate a smaller change than predicted by the models and also a change that does not extend as high up before being affected by the stronger opposite trend of the stratosphere.

• The lapse rate in the troposphere almost does not depend on the concentration of greenhouse gases. At best, the water vapor content change something – but then that’s not the effect as a greenhouse gas, but the heat of condensation.

In the stratosphere ozone affects, otherwise the observation would be almost vertical.

There is therefore a discrepancy between observation and models, ie the model assumptions are not sufficient or excessive.

• Ebel,

According to the present understanding the negative lapse rate feedback is an essential part of the feedbacks as shown the the picture of this comment

http://scienceofdoom.com/2014/06/26/the-greenhouse-effect-explained-in-simple-terms/#comment-66524

Lapse rate feedback means that the lapse rate is reduced, when surface temperature rises. The effect looks small on the scale of your picture, but that’s an artifact of the scale more suitable for understanding the stratosphere.

25. Thanks guys, but I do not really understand.

The height of the tropopause is already and almost determined by the heat content below. The differences between high and low latitudes are well known.
If the temperature at the tropopause changes by 1K, so the hight varies by about 150m and the temperature at the surface also changes by 1K. The lapsrate remains constant. Or is there a quicker T change at 200 hPa?

• The dry lapse rate is very close to a constant, but the moist lapse rate decreases when temperature rises and the absolute humidity increases. The actual average lapse rate is between these cases. According to the climate models the average lapse rate does also decrease, which is a natural result as it’s affected by both the dry and moist lapse rates.

Decreasing lapse rate means that upper troposphere warms at a fixed altitude faster than the surface. As the moist lapse rate applies mainly to tropics, the extra warming of the upper troposphere is expected to lead to the the “tropical hot spot”. If that prediction is not correct as some observations suggest, that would mean that models fail in calculating those details of circulation that determine the tropical average lapse rate.

• on June 30, 2014 at 6:22 pm | Reply DeWitt Payne

As the moist lapse rate applies mainly to tropics, the extra warming of the upper troposphere is expected to lead to the the “tropical hot spot”. If that prediction is not correct as some observations suggest, that would mean that models fail in calculating those details of circulation that determine the tropical average lapse rate.

That’s not entirely surprising if you think about it. Moisture saturated updrafts are very localized. The updraft area is much, much smaller than the size of the grid blocks used in climate models. Most of the mass of air that goes up comes back down in the same area. The moisture in the updraft condenses and rains out, so the downward moving air is drier. The turbulence associated with air movement causes mixing that lowers the average humidity to less than saturated. Less than saturated means that you can’t use the moist lapse rate, which is 100% RH at all altitudes, or the dry lapse rate. It’s somewhere in between.

Climate models cannot calculate this because they don’t have fine enough resolution. So it’s calculated using simplified approximations, or parameterized in the parlance. As I remember, the parameterizations are based on short term behavior, which is fairly well characterized by observations with weather balloons and other measurements. Basically it’s a radiative/convective calculation where the temperature profile is forced to remain within certain bounds. But it’s not at all clear that long term behavior, years to decades, is accurately modeled.

Some would even argue that you couldn’t calculate it even if you had orders of magnitude faster computers because at very high resolution, the problem ceases to be constrained by boundary conditions and becomes an initial value constrained problem, or a weather model, and chaos, literally, ensues.

• DeWItt: Do cloud resolving models what the environmental lapse rate should be in tropical regions?

• on June 30, 2014 at 10:22 pm DeWitt Payne

Frank,

There are no cloud resolving climate models. Anything with a resolution that fine is a weather model, so it’s not clear that producing the correct environmental lapse rate in a weather model means much for predicting the evolution of the tropical hot spot.

26. on June 30, 2014 at 7:09 pm | Reply Peter O'Donnell Offenhartz

I have a question about SOD’s “note 5” posted back on June 26th. Satellite observations and MODTRAN agree that the effective emission temperature of the main CO2 band is approximately -50C. This is also the temperature of the tropopause at temperate and equatorial latitudes. I assume this means that most emission in this band occurs at or near the tropopause at 10km, i.e., this is the altitude where the optical density of the atmosphere in this band (looking downward from space) is about unity. However, while it is true that

“If the place of emission of radiation – on average – moves upward for some reason then the intensity decreases. Why? Because it is cooler the higher up you go in the troposphere. Likewise, if the place of emission – on average – moves downward for some reason, then the intensity increases (note 5).”

It simply isn’t true that it’s “coooler the higher up you go” when you’re in or above the tropopause, which is apparently where the emission in the main CO2 band occurs.

• Peter

Here is a graph of calculated values from a typical tropical cloud free atmosphere, originally posted here:

The graph shows the cumulative flux reaching TOA from each altitude. We can see that about 250 out of the 273 W/m2 reaching TOA in this case comes from a height below 13 km. In this case the tropopause will be about 17km.

The reason why the simple calculation (calculating the temperature from the total emission and looking up the height of that temperature) doesn’t work is a significant proportion of radiation comes from the surface and the highly emissive water vapor in the boundary layer within the first km above the surface.

The other way to get a conceptual grasp of the problem – the atmospheric emissivity & absorptivity at the tropopause is relatively low, mainly because there’s (almost) no water vapor there. (I could calculate it if I fired up the old calculations). So there’s no way that the tropopause could be “the place of emission for the climate system”.

• on June 30, 2014 at 10:25 pm Peter O'Donnell Offenhartz

I didn’t say “that the tropopause could be ‘the place of emission for the climate system'”. I did imply that the tropopause could be the place of emission for the CO2 band (not the peak, which arises in the stratosphere). I assume that’s why the effective emission temperature in this band is circa -50C.

• Peter,

Sorry I didn’t read your question properly. In the center of the CO2 band, the emission to space is from the stratosphere. In another part of the band, the emission to space is from the tropopause, and in other parts of the band, the emission to space is from the troposphere.

The CO2 band is very wide.

• on June 30, 2014 at 11:12 pm Peter O'Donnell Offenhartz

Agreed.

• The changes to the edges of the CO2 peak are of minor importance. The main effect is where it is already the absorption length is important.

The logarithm function is only an approximation – not a law.

• on July 1, 2014 at 5:41 am DeWitt Payne

I’ve modified the graph to include markers on the lines rather than just color.

It makes a great difference whether this altitude is above or below the tropical tropopause.

Not really. Band wing emission will always originate below the tropopause, as can be seen by the brightness temperature. Emission from the center of the band will always be from the stratosphere if the observation height is high enough.

The reason that radiative forcing is defined at the tropopause is because emission from the stratosphere doesn’t count. It won’t change after the stratosphere is allowed to cool to the new steady state. It looks different in MODTRAN because you can’t change the temperature profile in the stratosphere in MODTRAN. Well, you can, but not in the web implementation that everyone uses because it’s free.

• on July 5, 2014 at 1:12 am Peter O'Donnell Offenhartz

Thanks for putting marking labels on your graph for colorblind people like me.

I don’t think the “effective emission temperature” at lower altitudes is particularly meaningful. After all, we are saying is that at relatively low altitudes the atmosphere is optically thick in the CO2 band, thus reducing the magnitude of the emission. However, at 70 km, the translation between emission intensity and effective emission temperature is real: The emission intensity really does tell us about the temperature of the source emission. According to Pierrehumbert’s book, emission occurs (for any given band) at the altitude where the optical density (looking downward) is of order unity; or, in other words, the altitude where the photonic mean free path approaches infinity.

Insofar as I can tell, in the broad CO2 band, much or most of this emission has a source temperature close to that of the equitorial tropopause. It is otherwise difficult to explain why the measured (and calculated) emission temperature is so low, ca -50C.

• Peter,

First a technical comment. The optical depth of one from TOA to a particular altitude does not tell about an mean free path approaching infinity. It tells directly that the fraction 1/e or about 37% of radiation that enters this layer from below exits the atmosphere. In case of uniform density the mean free path is equal to the thickness of the layer that has the mean free path of one.

It’s true that the effective radiative temperature of radiation well inside the CO2 absorption peak does not change much with concentration, but it does change at the edge of the peak. What happens at the edges of the CO2 peak is, what leads to the radiative forcing. That the effect comes from the edges explains also the approximately logarithmic dependence of the forcing on the concentration.

• on July 1, 2014 at 1:56 am DeWitt Payne

Peter,

I assume that’s why the effective emission temperature in this band is circa -50C.

Well, no. The temperature is ~220K because from the TOA, nearly all the emission at the bottom of the well comes from the stratosphere, not the tropopause. Here’s a plot of brightness temperature from 600-800cm-1 from two altitudes looking down, 70km and 17km and 400 and 800 ppmv CO2. The temperature at 17 km is 194.8K. The minimum temperature for 17km looking down is 195.20K at 400ppmv CO2 and 195.04K at 800ppmv CO2. Obviously the temperature at the peak of the CO2 band, the minimum temperature changes very little because the radiation orginates very close to the observation height.

For 70km looking down, the brightness temperature at 668cm-1 is 246.99K (36.78km, linear interpolation) at 400ppmv CO2 and 250.15K (38.23km) at 800ppmv CO2.

• on July 1, 2014 at 4:23 am Peter O'Donnell Offenhartz

Alas, I am color blind, and cannot make sense of your plots. In addition I am in the process of moving to summer quarters. I will have a closer look at your data when I am settled.

It is indeed the entire 600-800 cm-1 band that is of interest. My question has to do with the altitude at which the optical density of the atmosphere (looking down) at any wavelength is of order unity, per theory. [This is where the mean free photonic path becomes infinite.] It makes a great difference whether this altitude is above or below the tropical tropopause.

• on June 30, 2014 at 7:52 pm | Reply DeWitt Payne

If you look at the effective emission temperature for the bottom of the CO2 well for each atmosphere and compare it to the temperature profile for each atmosphere (Show Raw Data), you will find that the temperature corresponds to an altitude below the tropopause in every case. So the temperature is still decreasing with altitude. The emission in the center of the band does come from the stratosphere. But the stratosphere equlibrates rapidly so that very soon after a step change in CO2, the stratosphere will cool enough that the emission from the stratosphere will be equal to the emission before the step change.

• on July 1, 2014 at 9:08 pm | Reply Climate Weenie

And the Western view:

http://cimss.ssec.wisc.edu/goes/rt/viewdata.php?product=gw_all

demonstrates the hot, and relatively dry signal, allowing the surface to appear through many of the bands obscured by cloud and water vapor in the east.

• on July 1, 2014 at 9:06 pm | Reply Climate Weenie

Here’s a great image to visualize various bands and emissions:

http://cimss.ssec.wisc.edu/goes/rt/viewdata.php?product=gcall

the 14.3 um band ( sorry, don’t do wavenumbers ) is toward the middle of the CO2 and notice no clouds are discernable – because the emissions are from the stratosphere.

Stepping away from the center and more and more lower features are apparent.

Sorry, dunno what this appears like to the color blind ( the red-to-yellow-to-blue-to-grey may appear as a mess, but the distinctness of the clouds is the feature ).

• on July 1, 2014 at 11:26 pm DeWitt Payne

Wavenumbers are easy. That’s why they’re often used instead of frequency in Hz or radians/sec. Just convert the wavelength to cm and divide into 1. For example, 15μm is 0.0015 cm. 1/0.0015 = 666.67cm-1.

27. The brightness temperature of the radiation into space is the result of the average temperature in the absorption length. In the middle of the 15 micron band of the absorption length is very short and only goes up into the warm ozone layer – which leads to the summit. In the diagram, the absorption length is specified as the pressure difference across a vertical layer with the absorption length:

The height of the tropopause depends from the intensity of the heat flux and the concentration of greenhouse gases in the stratosphere (Schwarzschild criterion). That is why at the equator to the higher tropopause.

An increase in the surface temperature by 3 K, an increase of the old temperature levels by about 500 m. In this area, the humidity is higher and the lapse rate is lower. On the other side, above the atmosphere colder and thus the humidity lower, bringing the lapse rate further approaches the trockenadiabatischen value. The mean temperature is almost the same everywhere, whether on water or dry land because of pressure equalization via winds. Even in the height of the local temperature gradient approaches the average value.

Die Helligkeitstemperatur der Strahlung ins All ist die Folge der mittleren Temperatur in der Absorptionslänge. In der Mitte der 15 µm-Bande ist die Absorptionslänge besonders kurz und reicht nur bis in die warme Ozonschicht – was zur Spitze führt. Im Diagramm ist die Absorptionslänge als Druckdifferenz über einer vertikalen Schicht mit der Absorptionslänge angegeben:

Die Höhe der Tropopause hängt von der Intensität des Wärmestroms und der Konzentration der Treibhausgase in der Stratosphäre ab (Schwarzschild-Kriterium). Deswegen ist am Äquator die Tropopause höher.

Eine Steigerung der Oberflächentemperatur um 3 K bedeutet einen Anstieg des alten Temperaturniveaus um ca. 500 m. In diesem Bereich ist die Luftfeuchtigkeit höher und damit der Temperaturgradient niedriger. Auf der anderen Seite ist oben die Atmosphäre kälter und damit die Luftfeuchtigkeit geringerer, womit sich der Temperaturgradient weiter dem trockenadiabatischen Wert nähert. Der mittlere Temperaturgradient ist wegen des Druckausgleichs über Winde fast überall gleich, ob über Wasser oder trockenem Land. Auch in der Höhe nähert sich der örtliche Temperaturgradient dem durchschnittlichem Wert.

MfG

28. on July 7, 2014 at 10:00 pm | Reply DeWitt Payne

SoD,

the inappropriately-named “greenhouse” effect

And again I beg to differ. The planet is just a greenhouse with perfect insulation. A glass covered greenhouse will have a higher temperature during the day than a greenhouse with LWIR transparent windows. How much higher depends on how well insulated it is and the type of glass used. Triple glazed low-e glass will make a very large difference.

• DeWitt: A greenhouse prevent some losses by convection, but the atmosphere does not. Maybe you can say that the stratosphere behaves like a greenhouse, but putting more CO2 into the stratosphere causes cooling. IMO, the name is “inappropriate” because it causes more confusion than enlightenment. A reliable list of useful and misleading parallels between greenhouses and GHGs might be useful.

• on July 8, 2014 at 1:19 am DeWitt Payne

Frank,

A greenhouse prevent some losses by convection, but the atmosphere does not.

Umm, the atmosphere cannot lose energy by convection or conduction to space. The vacuum of space is perfect insulation for conduction and convection.

The efficiency of a greenhouse is highly dependent on the quality of its insulation, but the radiative emission characteristics of the glazing is still significant. For economic reasons, though, most people build greenhouses with the cheapest possible glazing, single layer polyethylene film. It’s only if you’re trying to grow tropical plants in Minnesota, say, (or putting windows on your house) that more expensive solutions are needed.

• on July 8, 2014 at 7:55 pm DeWitt Payne

Frank,

You cannot ignore the spectral properties of the stratosphere to make a point about lack of convection. It’s not lack of convection that makes the temperature increase with altitude. The increase of temperature with altitude causes the lack of convection.

Unless it’s coated, the emissivity of glass in the LW IR is nearly one. Kirchhoff’s Law requires it. A low-e coating increases reflectivity in the LW IR. Since the sum of reflectivity and absorptivity/emissivity must be one, emissivity is reduced in the coating. If the outer surface of the glass is cooler than the interior surface of the greenhouse, then the temperature of the surface inside the greenhouse exposed to the sun must increase compared to a greenhouse with an IR transparent cover, much like the surface of the Earth when CO2 in the atmosphere is increased. This is easily proven experimentally, Wood 1909 notwithstanding.

Because even a single glass layer has a non-zero R value, the exterior surface of the glass will be cooler than than the interior when the sun is shining. A low emissivity coating on the glass will increase the effect.

Obviously, the increase in temperature will not be as much as it would be if the walls of the greenhouse were unable to conduct heat away by conduction/convection to the outside. But it will be increased compared to a greenhouse with an IR transparent cover. Better insulation increases the temperature further.

• DeWitt: To analyze the situation properly, I need to account for the SWR flux reaching the ground under the greenhouse, the LWR flux from the ground to the inside of the glass, the LWR flux from the glass to the ground, thermal flux though the glass, and the LWR radiative loss from the outside of the glass. Unless I’m on the moon, I also need to include the DLR flux from the atmosphere to the outside of the greenhouse. Then I need to solve for three unknown temperatures: ground, inside of the glass, and outside of the glass. To do so, I have energy balance at the ground, the inside of the glass, the outside of the glass, and the law for thermal diffusion through the glass which relies on the temperature gradient through the glass.

How analogous is this situation to the atmospheric GHE? It does remind me of a slab atmosphere models for the greenhouse effect (which are good physics exercises, but too different from reality to avoid misconceptions). WIth the simplest slab atmospheres, you assume both surfaces of the slab have the same temperature and you don’t worry about the flux through the slab. Since you mention R values for glass, I assume that you are concerned about the flux through the glass in a greenhouse.

• on July 7, 2014 at 11:39 pm DeWitt Payne

Frank,

Any enclosed space decreases energy loss from the inside of the space by convection. But unless the walls are transparent to incident solar radiation it can’t be a greenhouse. See Pekka’s comment below.

The stratosphere is a reverse greenhouse because it’s more transparent to LW radiation than to SW radiation. That makes the temperature increase with altitude. The single layer non-reflective atmosphere model works the same way. If the atmosphere layer is more transparent to SW than to LW radiation, the surface is warmer than the atmosphere. In the opposite case, the atmosphere is warmer than the surface.

• DeWItt: I picked the stratosphere because convection is unimportant there, not because it is warmed by ozone. I’ve always thought Pekka’s definition of a GHG was the right one – a gas that interferes more with outgoing than with incoming radiation.

Does a greenhouse interfere more with outgoing than incoming radiation? The glass does block LWR, but an additional critical factor is that the emissivity of the glass is less than the ground. Comparing the emissivity of a solid and a gas gets fairly tricky. I think we learn a lot from throughly understanding the principles behind greenhouses and GHGs. Unfortunately, it is human nature to sometimes take what we have learned about one situation and confidently apply it to another situation without the careful analysis one might use with a totally new situation. Or worse, confidently apply faulty understanding from one situation to another. I appreciate that our host and many commenters take the time to attempt to minimize the dissemination of faulty information and I hope many lurkers can tell the difference.

• DeWitt,

I understand your point. But I’m running with Frank’s point of view (July 7, 2014 at 10:19 pm).

• on July 8, 2014 at 1:45 am DeWitt Payne

They coat the surfaces exposed to vacuum of a glass dewar flask with silver for a reason. The low emissivity of the silver coating plays an important part in reducing the rate of heat transfer to or from the contents of the flask.

Yet more proof, if any was needed, that Wood’s 1909 experiment, regardless of his credentials as an experimental physicist, was badly flawed. Absent all the recent hoopla about Wood’s experiment, I seriously doubt you would refer to the greenhouse appellation as inappropriate. His note, which was promptly rebutted without dispute by no less an authority than Charles Greeley Abbot, never should have been resurrected as being definitive.

• When we discuss the GHE of the Earth system, it’s of little or no value to go into the details of an actual greenhouse.

How glazing reduces heat losses is important in designing energy efficient windows, but that’s a very different issue. (It’s, however, significant that my IR thermometer gives a reading of about +18C when I direct it to my windows of triple glazing in winter with -15C outdoor temperature. The heat losses from my house would be very much higher if the windows were transparent to IR.)

• As in ‘..the name is “inappropriate” because it causes more confusion than enlightenment..

Whether or not it should is another question that isn’t very interesting to me. Better to explain how radiatively-active gases absorb and emit radiation than get into discussions about parallels. Just my opinion, not trying to convert anyone.

29. The fundamental point shared by a greenhouse and the atmosphere is that they let solar radiation to enter more freely than they let energy to escape. That justifies the expression for me, further details are of lesser significance.

• Pekka, this is the nearest definition to a ‘greenhouse effect’ that I’ve read here, but you’ve wrongly included radiative gasses in your dialogue.

This dialogue causes confusion because to “let energy to escape.” doesn’t describe the ‘form’ of energy that is permitted “to escape” when any ‘radiative gas’ that is active in the LW emission frequency eventually loses energy as it escapes Earth’s atmosphere. This is ‘energy transmission’ (whatever the rate).

No. Any ‘greenhouse effect’ effectively ‘confines energy’ within a ‘given boundary’. ‘Radiative gasses’ that are active within the LW spectra are ‘unbounded’ and not ‘confined’. Thus, don’t equate to the criteria for a ‘greenhouse’ label.

However, the ‘change of state’ that H2O undergoes does fall into this ‘greenhouse’ category. I would draw your attention to the atmospheric hydrological cycle, with an emphasis on ‘latency’.

Best regards, Ray Dart.

• “I don’t understand why you think that latent heat is in some way deserving of special consideration.”

Because ‘latent heat’ is bounded by a ‘greenhouse’, where ‘radiation’ (a less efficient ‘energy transport’ mode) isn’t bounded. Thus, where ‘latent heat’ is active, a greater ‘bulk’ of energy transport is possible.

“The average water vapor content in a column of the atmosphere is equivalent to a layer of liquid water 2.5 cm deep. Annual rainfall averages 100 cm.”

I don’t know where your data comes from, but Trenberth et al offer a best average ‘global’ anual precipitation rate of ~1m (that’s about 1 ton of water per year for every square metre of Earth’s surface). However, this only relates to ‘~residency time’ indication and not a ‘latent heat activity’ indicator as the group suggest. The ‘ice : water : vapour’ total atmospheric content may well indicate the latent heat property of Earth’s atmosphere (this changes diurnally), but precipitation doesn’t indicate this (only the sustainability of H2O in Earth’s atmosphere).

“The atmosphere cannot lose any energy to space except by radiation. But it does this constantly, so the energy is only contained in the sense that the lake on a river behind a dam is contained. It’s constantly flowing in and out.”

Exactly. The ‘greenhouse’ loses heat by ‘radiation’, which is less efficient than convective transport of latent heat. Thus, heat builds its flux density ‘within’ the greenhouse.

The ‘lake, river, dam’ scenario only teaches ‘some’ smoothing of a ‘dynamic’ system. It’s not really a good scenario to show this.

“The walls of a greenhouse can lose energy by conduction and convection as well as radiation. If the loss is great enough, the temperature in the greenhouse will drop enough to cause condensation of some of the water vapor. That energy is not ‘contained’ by the greenhouse.”

No, but the ‘latent heat’ is ‘absent’ outside the greenhouse!!!

When we observe Earth’s atmosphere, the altitude of the greenhouse is high enough to radiate thermal energy from the phase change of latent heat from the lower ‘atmosphere/ocean surface’ directly to space.

Best regards, Ray.

• on July 9, 2014 at 4:00 pm DeWitt Payne

Ray,

I don’t understand why you think that latent heat is in some way deserving of special consideration. The average water vapor content in a column of the atmosphere is equivalent to a layer of liquid water 2.5 cm deep. Annual rainfall averages 100 cm. The atmosphere cannot lose any energy to space except by radiation. But it does this constantly, so the energy is only contained in the sense that the lake on a river behind a dam is contained. It’s constantly flowing in and out.

The walls of a greenhouse can lose energy by conduction and convection as well as radiation. If the loss is great enough, the temperature in the greenhouse will drop enough to cause condensation of some of the water vapor. That energy is not ‘contained’ by the greenhouse.

• “No, it doesn’t. Energy isn’t confined by either a greenhouse or the Earth’s atmosphere.”

The ‘hydrological cycle’ does/is, and this is where ‘latent heat’ is stored. If you’d read my post in its full context this should be aparent.

“A greenhouse has energy flowing in and out constantly.”

Yes, but not in a ‘latent’ form.

“The flow in goes to zero when the sun goes down, but the energy flow out never stops as long as the temperature inside is higher than the temperature outside.”

Please expand on this! You seem to be discussing ‘radiation’, not ‘latent heat’ bounded by a ‘greenhouse’.

Best regards, Ray.

• on July 8, 2014 at 3:08 am DeWitt Payne

Ray,

Any ‘greenhouse effect’ effectively ‘confines energy’ within a ‘given boundary’.

No, it doesn’t. Energy isn’t confined by either a greenhouse or the Earth’s atmosphere. A greenhouse has energy flowing in and out constantly. The flow in goes to zero when the sun goes down, but the energy flow out never stops as long as the temperature inside is higher than the temperature outside.

30. SOD, this thread doesn’t make sense. What happened to ‘latent transport’???

Best regards, Ray.

• on July 8, 2014 at 3:12 am | Reply DeWitt Payne

Latent heat transport is still convection. Water vapor must be transported by physical movement of moist air to where it condenses. Correct me if I’m wrong, but I believe that there was a paragraph in the post above titled Convection.

31. “Emission to Space

5. Most of the emission of radiation to space by the climate system is from the atmosphere, not from the surface of the earth. This is a key element of the “greenhouse” effect”

Can you explain this image

http://www.nasa.gov/mission_pages/GOES-P/news/infrared-image.html

• Determining the precise share of OLR emission that originates from the surface is quite difficult. The 2009 paper of Trenberth, Fasullo, and Kiehl: Earth’s Global Energy Budget gave the estimate of 40 W/m^2 or 17% while a later estimate of Costa and Shine is only half of that with an uncertainty of 20%. The upper limit is thus 10% of OLR. 90-93% of OLR originates in the atmosphere according to this estimate.

• I am a big fan of evolution and just love how things change with time.

In an eyeblink, just 7 years, the Earth energy budget has evolved

Love how Wild et al., just give up on the atmospheric window;

http://www.iac.ethz.ch/people/wild/Wildetal_IRS2012_GlobalEnergyBalance.pdf

A mature field with all the fundamentals known to 3 standard deviations and physics all solved.

• DocMartyn,

I’m not sure what point you are trying to make.

Hopefully you are now clear why the 10.6 μm image of the earth shows most features of the surface whereas the 6.5 μm image shows the atmosphere?

On the atmospheric window, it is a curiosity value, that is, the value itself is not used in any important calculations. The subject is covered in Kiehl & Trenberth and the Atmospheric Windowhow much radiation escapes to space through the “atmospheric window”, why its value isn’t that important but the complete story anyway.

It’s also covered by a paper which is cited in the above article: Outgoing Longwave Radiation due to Directly Transmitted Surface Emission, Costa & Shine (2012). They note that previous estimates have been ad hoc and make an attempt to calculate this curiosity value.

I looked at your graphic of energy balance progression.

Here’s what Kiehl and Trenberth said in their 1997 paper:

We know everything accurately to 3 standard deviations

Oh no, they didn’t. They said things like:

..The values from our study are listed in Table 1 and are discussed in more detail in the following sections. There is considerable variation for any given flux of energy. For example, values for the net surface shortwave flux range from 154 to 174 W m−2..

..Mean values of the total solar irradiance have varied in different satellite missions from about 1365 to 1373 W m−2 (see National Academy of Sciences 1994 for a review; also Ardanuy et al. 1992)..

..We do not explicitly include the effects of aerosols in the shortwave budget calculations because aerosol optical properties vary greatly due to chemical composition. Thus it is problematic to include them in a global budget..

..Our surface shortwave absorbed flux of 168 W m−2 agrees quite well with the majority of values near 170 W m−2 in Table 1. Recently, results from three observational studies (Cess et al. 1995; Ramanathan et al. 1995; Pilewskie and Valero 1995) suggest that clouds may absorb significantly more shortwave radiation than is accounted for in model calculations (such as the models employed in the present study). These results suggest that the cloudy sky absorption may be approximately 20– 25 W m−2 greater than models predict..

..Gleckler and Weare (1995) estimate zonal mean errors in bulk latent heat fluxes of at least ±25 W m−2, and a large portion of this is likely to be systematic (arising from the exchange coefficient, and biases in surface wind speed, moisture gradients, and sea surface and air temperatures..

• I’m with you Pekka. Latent heat doesn’t have any prefference for temperature, only its environment. It just ‘adds/subtracts to it’ (dependant on the environmental scenario).

Best regards, Ray.

• DocMartyn,

Here are three images taken at three different wavelengths:

You can see the 6.7 μm image looks completely different from the 10.7 μm image. The 6.7 μm is “seeing” water vapor in the atmosphere.

• DocMartyn,

In Note 5 I said this:

the “place of emission” is a useful conceptual tool but in reality the emission of radiation takes place from everywhere between the surface and the stratosphere. See Visualizing Atmospheric Radiation – Part Three – Average Height of Emissionthe complex subject of where the TOA radiation originated from, what is the “Average Height of Emission” and other questions.

Note that some of the radiation reaching TOA comes from the surface. The reason is that the absorption in the atmosphere depends very strongly on wavelength. 8-12 μm is commonly called the atmospheric window – for the reason that in this wavelength band the surface emission mostly gets through.

The image you provided is at 10.6 μm – where the atmospheric absorption is very low. That’s why it is a heavily used band – you can “see” the surface quite well.

Here is a spectrum shown in Theory and Experiment – Atmospheric Radiation – originally from the textbook Atmospheric Radiation: Theoretical Basis, Goody & Yung (1989)

– Note the measured and theoretical curves are offset for easier comparison.

Zooming in a section and adding the blackbody emission curves for different temperatures for reference:

It should be clear that surface radiation is mostly getting through in 8-12 μm, but elsewhere the radiation is a lower intensity and therefore is coming from the atmosphere.

In the link cited in note 5 of the article I provided a calculation which broke down the TOA radiation by wavenumber (for one particular temperature and humidity profile):

– Note that the right axis is wavenumber – 10 μm is 1000 cm-1 in “wavenumber” – and the left axis is height in km.

We see that in the “atmospheric window” between 800 cm-1 to 1200 cm-1 the surface transmits almost “straight through” (62% of surface flux makes it straight through to the top of atmosphere in this wavenumber range). A small component comes from around the center of the CO2 band (667 cm-1) from the top layer. The rest mostly comes from the “wings” of the CO2 band and where the water vapor absorption is not so strong, around 400 cm-1.

• So can I take it that when you stated:-
“Most of the emission of radiation to space by the climate system is from the atmosphere,”

What you really meant was that

“Approximately XX%of the emission of radiation to space by the climate system is from the atmosphere, and 100-XX% of the emission of radiation to space come from the land/ocean surface via the atmospheric window”

Calculating 100-XX% is non-trivial for a cloudy, rotating planet with a tilted axis but from the 8-13 um window it is at least 50% and probably up to 70%.

• DocMartyn ,

And the page you linked to provides this information, e.g.:

Pop quiz: why, when CO2’s peak absorption is at 15.0 μm is this satellite channel to measure CO2 at 13.3 μm?

• “Pop quiz: why, when CO2′s peak absorption is at 15.0 μm is this satellite channel to measure CO2 at 13.3 μm?”

There is essentially no absorbance of H2O after 12.5 μm, but the CO2 peak at 14.5 μm is saturated. So you need to be somewhere between 12.5 and 14.5μm.

32. , SoD

Just for the record I will ask you one last time.

Where did you get the idea that Gerlich & Tscheuschner said that the warmer Earth cannot absorb radiation from a colder atmosphere?

“see Kramm & Dlugi On Illuminating the Confusion of the Unclear – Kramm & Dlugi step up as skeptics of the “greenhouse” effect, fans of Gerlich & Tscheuschner and yet clarify that colder atmospheric radiation is absorbed by the warmer earth.”

Perhaps it is because you don’t know the difference between energy and heat!

The G&T paper is freely available on the web.

You were not the only one to misread their paper.

Eli Rabett made the same mistake and went on in his silly paper to say that HEAT travels from the colder atmosphere to the warmer Earth.
To make this error it is about as gross as it gets. .

In their reply to Rabett et al G&T make it quite clear that the radiation is absorbed.
Whats so difficult to understand about energy transfer between a hot and a colder object……

energy can be transferred in both directions
Heat can only be transferred in one direction always from hotter to colder object.
If you find that difficult to grasp then this simple reminder will keep you right.
Heat has the ability to do work in the given situation.

.
.

• Bryan,

The differentiation that you make is wrong. When atmosphere emits radiation, the energy is taken from the heat of the atmosphere. When that radiation is absorbed by the surface it adds to the heat of the surface.

When we have a process that takes heat from one place and adds it to another, it makes sense to say that heat is transferred.

Classical thermodynamics is a formal theory that considers heat only on the level of net heat transfer. When discussion is restricted in that way, heat is always transferred from warmer to colder, but today’s physics knows more and allows for discussing further details. Classical thermodynamics is a very restricted theory, it does not make sense to exclude all the additional knowledge. It’s a very unfortunate habit of many skeptics to claim that what was known more than 100 yeas ago should be taken as more reliable than the present knowledge forgetting all the theoretical development and all the evidence collected since those pioneers of science.

The paper of G&T has been discussed sufficiently before and found totally worthless. Most of that material is still openly available. Is that not enough?

• on July 15, 2014 at 2:18 pm DeWitt Payne

Bryan,

SoD,Pekka and De Witt promote alarmist end of world scenarios.
There’s nothing new in that.

Weak attempt at deflection by creating a straw man. Please cite an example. Simply stating that there is a greenhouse effect and that, all other things being equal, increased CO2 will cause an increase in temperature doesn’t qualify as either alarmist or an end of the world scenario.

As for the rest, please show in detail how any of what we’ve written results in an actual violation of the Second Law by causing the entropy of the system to decrease using equations and numbers not hand waving, incorrectly, about heat.

Speaking of which:

You keep using that word. I do not think it means what you think it means.

Inigo Montoya, The Princess Bride

• Welcome back, Bryan! No discussion of the inappropriately-named “greenhouse” effect would be complete without your much loved self-parodying style.

In concise summary I say that the surface of the earth absorbs energy from the atmosphere and this must change its temperature compared with if it did not absorb it. Bryan says this cannot happen but will never say which bit is wrong:
1. absorption of energy from a colder atmosphere by a warmer earth
2. energy not lost or destroyed (1st law of thermodynamics)
3. energy increasing internal energy (“”)
4. increase in internal energy changing temperature

Bryan has maybe forgotten that I scanned the pages of 6 heat transfer textbooks demonstrating that radiation from colder bodies was absorbed by warmer bodies.

Here is the article: Amazing Things we Find in Textbooks – The Real Second Law of Thermodynamicssimple but necessary – pages from six heat transfer textbooks to confirm the stuff that so many people dispute.

Here is a quote from Bryan in that long fascinating exchange:

SoD

I think its you who’s having a laugh.

You must have searched through hundreds of textbooks to find the few above who have been a bit careless with their thermodynamic definitions.

I think the authors would be appalled at your use of their lack of clarity namely to prove that heat flows from a colder object to an object at a higher temperature.

What happened to the 99.999% of textbooks which give correct definitions that you must have discarded to pick your chosen sample.

We notice that there are no Physics Textbooks in your sample.

Why do you think that is?

I don’t know what you hope to gain by misleading people who might not know enough to see through a bogus scam..

Interested readers should follow the whole thread through, including the book put forward by Bryan.. well, it brought a smile to my face..

Of course, if the radiation from the colder body was absorbed by the hotter body (as Bryan now “clearly states”) then people who believe in the first law of thermodynamics would expect it to change the temperature of that body compared with if that energy was not absorbed.

And thus, interested readers should follow what Bryan says about that energy. And his enthusiasm for “answering” the question of what happens to that energy when absorbed. Specifically, what is the equation for temperature change? Why so difficult to get an answer for a simple equation.

I only know one relevant equation for temperature change of a body with a specific heat capacity,cp and a mass, m. It says if a body emits 5J and gains 3J then we can calculate the temperature change, ΔT = (5-3)/m.cp

In the case where the 3J comes from a colder body where does that leave Bryan? And so, we painfully come to realize, this is why the question never gets answered by Bryan. No equation for temperature change is ever provided.

I assume that Bryan does not know the equation for temperature change of a body. I have pressed Bryan at length many times on this subject, e.g., in this question and this question.

No answer on the equation for temperature change.

Instead, lots of implication that our ideas somehow violate the second law of thermodynamics without actually explaining how.

Then we look back a little further in history on this blog we find something else. Despite his apparent current viewpoint, Bryan seemed convinced that the warmer body could not absorb energy from the hotter body, or that the amount was wrong, or “it depends” but never sure exactly why..

Scienceofdoom and others think that the hot surface has no option but to absorb a photon from the cold surface.
I think a lot of this radiation is in fact scattered from the hot surface and is not absorbed.

Proving the “backradiation” if it exists is very smal and certainly nothing remotely like 300W/m2.

In this comment I tried to pin Bryan down on a very specific point:

When 10um radiation from a -10′C body reaches a 0′C surface how much of this 10um radiation is absorbed compared with the scenario of 10um radiation from a +10′C body.

As usual he was confused:

..Well again it depends on the surface..

So no wonder we are all confused about Bryan.

The second law of thermodynamics is neatly confronted via the equation for entropy.

The Three Body Problema simple example with three bodies to demonstrate how a “with atmosphere” earth vs a “without atmosphere earth” will generate different equilibrium temperatures.

Here is an extract:

So if we take bucket A full of water at 80°C and bucket B full of water at 10°C, Science of Doom is saying that bucket A will heat up because of bucket B? Right! That’s ridiculous and climate science is absurd!

Yes, if anyone was saying that it would be ridiculous. I agree. To take one example from many, in The Real Second Law of Thermodynamics I said:

Put a hold and cold body together and they tend to come to the same temperature, not move apart in temperature.

Of course, it could be that I am inconsistent in my application of this principle..

– so instead I pose a problem of calculating entropy in the case where the atmosphere does change the temperature of the earth compared with a no atmosphere case.

And I ask for readers who – like Bryan – think it is wrong. Just do the entropy calculation and demonstrate that my example has violated the second law of thermodynamics.

Bryan has not yet provided his proof, despite his many comments on that article.

I assume that he doesn’t know what entropy is.

I assume that all the people who are convinced the “greenhouse” effect is a violation of the second law of thermodynamics don’t know what entropy is either.

Otherwise they could just show up and point out where I made a mistake in my entropy calculation and the whole thing would be sorted out.

• Why is the nature of heat transfer discussed mainly in textbooks of heat transfer rather than in textbooks of physics? The basic answer is simple

– It’s a central question for heat transfer, not for general physics.

Another essential point is that

– Discussing heat transfer in both directions separately rather than the net effect only is of interest almost solely for radiative heat transfer.

What physics textbooks write about radiative heat transfer is in full agreement with what textbooks of heat transfer write, but few of the physics textbooks go even as far as calculating the radiative heat transfer between two bodies. Physics textbooks discuss, how a surface or gas absorbs, transmits, reflects, or scatters radiation. They tell also what’s the source or sink of the energy of the photons. How to use that knowledge in calculation of heat transfer is left to the textbooks of heat transfer.

• Pekka says that heat is…….

“always transferred from warmer to colder,”
In classical physics

” but today’s physics knows more and allows for discussing further details.”

Perhaps you could point the readers to some ‘new’ physics textbook that claims that heat can be spontaneously transferred from colder to warmer objects.

I have not come across any and I doubt you have either.

It looks a bit suspicious that the ‘greenhouse theory’ advocates seem to depend on ‘new unpublished physics’ to support their conjecture.

You have yet to show that anything in the G&T paper is incorrect and to dismiss it as worthless is merely empty rhetoric.
Now as the pause in global temperatures rise is almost 20 years, despite increasing atmospheric CO2 , perhaps a little more skepticism would be helpful .

• Bryan,

All (or at least almost all) textbooks of heat transfer tell about the present way of considering physics. SoD has presented numerous copies of such textbook pages on this site.

That G&T is incorrect has been shown so many times that doing it once more is totally pointless. SoD has done it here. I wrote a couple of comments about that at Climate Etc, similar evidence has been presented on really many other web sites as well.

• Pekka says

“All (or at least almost all) textbooks of heat transfer tell about the present way of considering physics.”

That should be easy then, to supply the readers with the name of ONE physics textbook to answer my question above

“Perhaps you could point the readers to some ‘new’ physics textbook that claims that heat can be spontaneously transferred from colder to warmer objects.”

I don’t think you can!

• Bryan,

I’m sure that you know, what I’m talking about as you were the first commenter on this thread

http://scienceofdoom.com/2010/10/07/amazing-things-we-find-in-textbooks-the-real-second-law-of-thermodynamics/

If you cannot see, how the examples prove you wrong, it’s your problem.

• Readers will note that Pekka cannot name one physics textbook that states
that heat can be spontaneously transferred from colder to warmer objects.
No amount of equivocation on his part can hide the dead end that he has arrived at.

How can anyone take seriously a conjecture that relies on the the impossible spontaneous transfer of heat from a colder to a hotter object?

Now just in case any reader thinks that Pekka’s viewpoint is seriously considered let me assure you that;

Every physics textbook and physics department on this planet unanimously agree with Clausius that heat cannot be spontaneously transferred from colder to warmer objects.

• SoD,Pekka and De Witt promote alarmist end of world scenarios.
There’s nothing new in that.

http://abhota.info/end2.htm

The trouble is by mutual self support they have created for themselves (here on this site) an alternative universe where heat (they claim) is spontaneously transferred from colder to warmer objects.

Any careful reader will note that SoD has not answered my question about the basis of his mistaken interpretation of the G&T paper.
I cannot see much point in SoDs comments since they are based on a mistaken interpretation….. they are as GG pointed out in his reply ….’vacuous’.

I had a chemistry teacher who thought that mass and weight were the same thing.
Indeed chemists still use the term atomic weight.

Now if it was important for the greenhouse theory that mass and weight were identical then SoD could no doubt find several chemistry textbooks where a sloppy writing style might give this impression.

If you want to know the correct definition of words like heat,energy,mass and weight you must look up a physics textbook.

Surely we can all agree on that!

Thats why SoD and Pekka are now ‘hung up’ and ‘out to dry’

Because they cannot name even one physics textbook that supports their interpretation that photons from a colder object absorbed by a warmer object can be called heat.

The more intense and wider frequency photon stream from the hot object cannot be separated from the energy stream from the colder.
Heat transferred is the difference between the two streams and is always from hotter to colder.
Zemansky summed it up rather well in his classic textbook ‘heat and thermodynamics’ when writing about radiative transfer.

‘The difference between the energy absorbed by a body and that emitted is called heat and is always from a higher to a lower temperature.’

• Photons are not heat, photons get their energy from heat and their energy becomes heat when they are absorbed. That’s, how they transfer heat.

Classical Thermodynamics is an axiomatic mathematical theory that describes well a limited set of phenomena. It was originally not derived from anything; it’s an ad hoc theory that gets its justification as physical theory from the agreement with observations in its limited range of applicability. It’s even presently a very useful theory, but it’s not the most fundamental theory of physics as it can be derived from more fundamental theories through statistical mechanics with some help from quantum mechanics. The deeper nature of heat is also described by the more fundamental theories.

Arguing against the more fundamental theories based on the very limited Classical Thermodynamics and its axiomatic definition of heat is ridiculous.

The semantic question of what we should refer to by the word heat would be irrelevant in absence of the further violation of logic based on picking one definition to state that heat can flow only from hot to cold, and then switching to another definition to “prove” explicit falsehoods about real physics.

33. on July 14, 2014 at 6:20 pm | Reply DeWitt Payne

SoD and Frank,

To continue flogging the deceased equine: If ‘greenhouse effect’ is an inappropriate name because you think it might be confusing somehow, please suggest some other name that would make sense to the general public. I can’t think of anything.

DeSaussure called his glass covered insulated box a hotbox. Somehow, the hotbox effect, doesn’t have the same ring. Not to mention that it’s unlikely that anyone but a student of the history of science would get the reference.

• DeWitt

Please note that Pekka in effect now concedes that no physics textbook can be found where the definition of heat will allow heat to be transferred spontaneously from a colder to a warmer object.

If you wish to check the second law and entropy statements there are several freely available on the web.

Here is a convenient one

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/seclaw2.html#c2

• All Bryan is doing with his very poor job on sophistry is pointing out that textbooks say E1-E2 > 0 – which everyone else states over and over, no one is confused, we all agree (note 1).

Byran tries to pretend we are saying E1-E2 can be any value, including < 0.

We are not, but you have to sympathize with Bryan, misrepresentation is his only way out.

Unfortunately, apart from the people unable to add up, Bryan’s problem is clearly obvious.

If E1 = 5, E2 = 3, what is the loss in energy by the hotter body?

I say 5 – 3 = 2

Bryan says 5 – 3 = 5

Note 1: E1 = energy emitted by the hotter body; E2 = energy absorbed from the colder body by the hotter body

According to Bryan, the first law of thermodynamics is wrong.

Energy disappears after being absorbed.

If Bryan was interested in physics he would explain this point. If G&T were interested in physics they would explain this point.

Expect more bluster.

• Bryan,

Do you now tell that you agree fully with textbook physics, and that you have no objection to the standard description except that you wish to use the word heat only as it’s defined in Classical Thermodynamics?

If that’s the case, we can all end this discussion noting that the only disagreement is on the semantics.

• Pekka

I always try to keep within the framework of standard physics.
My use the word heat is in line with any physics textbook that I know of.

Of course anyone can redefine a word and with a full explanation of what they mean by the word they can be understood.
However using words like heat mass energy force and so on in an unconventional way (without explanation) can only lead to confusion.

I cant see any point in that approach .

“If that’s the case, we can all end this discussion noting that the only disagreement is on the semantics.”

• Bryan,

You should finally understand that there’s nothing unusual (let alone wrong) in discussing heat transfer in the way textbooks of heat transfer do. You may prefer the definition of Classical Thermodynamics, but you have no justification for expecting that others would do the same. You are not the highest authority on the meaning of words. There’s nothing “comic” in the discussion of Halpern et al. There’s nothing contrary the the standard use of the words. They do also explain in detail and correctly, what the issue is.

The different energy fluxes of the Earth system can be grouped in many different correct ways. In some of these ways the downwelling radiation forms it’s own component, and is then the largest energy flux that heats the surface. That’s a correct description. Another correct description combines first the downwelling and upwelling IR fluxes as a single net flux that’s upwards.

Both of the above alternatives are correct, and neither can be used as an argument against the correctness of the other.

You may have read correct texts of atmospheric physics, but it’s clear that you have not understood them.

You make the assertion

The Halpern et al paper in effect proposed that the atmosphere was like an electric blanket with its own heat source – the greenhouse gasses.

It seems obvious that you haven’t understood at all, what they write. Please tell, where their argument is based on an own heat source for the atmosphere. (It’s clear that there’s nothing like that in their argument, that’s just a strawman presented by you.)

Debunking a paper that lacks internal logic as the G&T paper does, is somewhat problematic. To me the most serious fault of the G&T paper is that it does not even try to justify it’s conclusions. It just declares them implying that they follow in some miraculous way from the matter covered by the paper, while no such connection is presented or is possible to present. (It’s not possible, because the conclusions are wrong.) It’s difficult to make specific arguments against something that does exist, it’s only possible to observe that the conclusions lack all justification. If someone disagrees, he must be able to tell step by step, how the logic works, when the paper doesn’t even try. Halpern et al find some specific erroneous details, but those are not the worst problem of the paper, only the beginning.

• DeWitt

Only some of the proponents of the greenhouse theory make the mistake of violating the second law.

For instance in the comic paper by Halpern et al one section is devoted to saying the greenhouse theory does not violate the second law.
To illustrate they show HEAT moving from colder atmosphere to warmer Earth surface.
They did not say that their use of the word is in any way unusual not realising that they proved the the very point that G&T were making.

Now to make your points without making the gross mistake of getting your definitions mixed up is not too hard if you have been educated properly.

I recommended that SoD read ……

Thermal Radiation heat Transfer, by Siegel & Howell (freely downloadable set of files on the NASA , 3 volumes 1968-1971, NASA Ref SP-164. Check http://ntrs.nasa.gov/search.jsp

Or the lecture notes by Rodrigo Cabellero often recommended by yourself, again freely available.

These authors can make their points without getting their definitions confused.

The Halpern paper in effect proposed that the atmosphere was like an electric blanket with its own heat source – the greenhouse gasses.

Cabellero on the other hand was describing something more like a blanket or the insulating effect of the atmosphere.

The Cabellero approach is much more plausible .
But plausible does not mean it is how the actual atmosphere works but that is a whole new topic.

SoD obviously does not intend to give evidence to support his mistaken interpretation of G&T in that they believe that radiation from a colder body cannot be absorbed by a warmer one.

Instead he seems much more comfortable attacking the bogus proposal that he thinks they should have said.
He has dug a massive hole for himself and yet keeps digging!

• on July 15, 2014 at 9:07 pm DeWitt Payne

Bryan,

Of course he does. No one ever said it did. You stand the logic on its head to claim that we do. There is nothing in the physics of the greenhouse effect that violates the Second Law. Heat flows from the hotter Sun to the colder Earth. Heat then flows from the Earth’s surface to the colder atmosphere by radiation and convection and to space from the atmosphere and from the atmosphere to space by radiation.

But, the temperature of the surface of the Earth is dependent on the temperature of the atmosphere. If the temperature of the atmosphere increases, so must the temperature of the surface of the Earth to maintain the flow of heat out to match the flow in from the Sun. But heat continues to flow from warmer to colder, never the other way around.

The simplest example is two infinite parallel planes separated by a vacuum at temperature T1 and T2. If T1 = T2, then no heat flows, by the classical definition of heat. If a flow of heat is imposed between the two planes, then the temperatures are not independent. I can’t find the character Q with a dot over it to represent heat flux so I’ll use F and ignore emissivity.

F = σ(T1^4-T2^4)

If F = 0, then T1 = T2

If F ≠ 0 then T1 = (F/σ + T2^4)^¼

If F is positive then T1 > T2

Increasing T2 therefore must increase T1, but heat never flows from the plane at T2 to the plane at T1. And nobody ever said it did. The heat flowing into the plane at T1 causing the flux F between the planes is the source of the temperature increase of T1.

• DeWitt,

I like the name: Inappropriately-named “greenhouse” effect
It’s snappy, concise, and straight away tells everyone what you stand for.

Alternatives: The phenomenon previously known as the greenhouse effect
Slightly more uptempo pop reference.

The effect of radiatively-active gases in moving the emission of radiation to space to a higher colder altitude
Losing its snappiness slightly.

If you had discovered it we would have called it: The DeWitt effect

Most physics phenomena doesn’t have a description, instead they are named after the person who got their publication out slightly ahead of (or after but with more fanfare and panache) the person who really discovered it.

34. on July 14, 2014 at 11:56 pm | Reply DeWitt Payne

Most physics phenomena doesn’t have a description, instead they are named after the person who got their publication out slightly ahead of (or after but with more fanfare and panache) the person who really discovered it.

In that case, we should call it the Arrhenius Effect, as he was the first one to propose that ΔF = αln(C/Co). Or perhaps the Fourier Effect as he was the first to publish that the Earth’s surface was warmer than it should be, given its distance from the sun and likened the process to de Saussure’s hotbox.

• on July 15, 2014 at 12:02 am | Reply DeWitt Payne

According to Wikipedia, Alexander Graham Bell was the first to use a greenhouse as an analogy.

• John Nielsen-Gammon wrote a series of posts arguing for the name Tyndall Gas Effect.

Needless to say, greenhouse effect remains the name in use.

• Checking the claims of the original paper of G&T as stated in the abstract we find:

By showing that (a) there are no common physical laws between the warming phenomenon in glass houses and the fictitious atmospheric greenhouse effects,

no common physical laws is too strong, but otherwise I might agree on that

(b) there are no calculations to determine an average surface temperature of a planet,

That’s clearly against the indisputable facts, as it’s easy to find very many such calculations, how accurate they are is another question discussed recently on this site as well.

(c) the frequently mentioned difference of 33 C is a meaningless number calculated wrongly,

Again too strong. The number is based in part on arbitrary assumptions concerning the albedo, but their claim is highly exaggerated and misleading.

(d) the formulas of cavity radiation are used inappropriately,

I don’t think that formulas of cavity radiation are used at all. Thus it’s difficult to see, how they are used inapproriately.

(e) the assumption of a radiative balance is unphysical,

The assumption of radiative balance of the Earth system as whole is highly physical within some limits, otherwise balance of radiation is important for some subsystems like the stratosphere, but less for others

(f) thermal conductivity and friction must not be set to zero, the atmospheric greenhouse conjecture is falsified.

Thermal conductivity is insignificant in most cases, but important in some, most importantly the skin of the ocean.

The final comment lacks justification in the paper. The same error applies to the chapter of conclusions.

In this final comment they present the main conclusion picked from the paper. That’s, however, the particular conclusion that’s presented without even attempt to justify it, as the paper does not study the actual existing theory of atmospheric physics, it finds errors in the strawmen built by the authors.

• on July 16, 2014 at 1:33 pm DeWitt Payne

Bryan,

Are you denying that the atmosphere emits radiation?

If not, then are you denying that the surface of the Earth absorbs about 98% of that radiation?

If so, what then happens to the radiation that is reflected by the surface and why isn’t it measured by spectrophotometers, IR thermometers and pyrgeometers?

Pekka,

G&T’s argument about glass greenhouses is based almost solely on Wood, 1909. That note flew in the face of all previous experimental work starting with de Saussure. You can tell G&T are theoretical physicists because anyone with a strong experimental background would see all the flaws in the experimental design and the inadequate description of the experiment itself. The main flaw being that the covers were not switched between boxes to see if the boxes were identical with regard to insulation and thermometer placement.

The paper was rebutted shortly thereafter and Wood did not defend his results or conclusions. Therefore, G&T’s statement that there are no physical laws in common between the atmospheric greenhouse and a glass greenhouse was not proven.

In fact, de Saussure’s multi-layer hot box works much the same as the atmospheric greenhouse effect, or at least the gray atmosphere simplification, complete with a temperature difference between the glass layers.

G&T’s reference to the cavity radiation formula means the Planck equation for the emission of a black body. A Hohlraum, or cavity radiator, is the best way to approximate a black body. By incorrect, I’m pretty sure they mean using the Stefan-Boltzmann equation. That equation assumes constant emissivity at all wavelengths, which isn’t true of the atmosphere and is only a good approximation of the surface. But, as usual, this is a straw man as the S-B equation is only used to calculate an effective temperature from the integral of the actual emission spectrum. The effective temperature is then just another way of stating the total flux.

• Pekka

“Please tell, where their argument is based on an own heat source for the atmosphere”

Because it claims it emits heat to the warmer Earth surface.

Its a bit tiresome going over the same points again
We have already agreed that the second law forbids this.
This is not within the framework of physics.

You have failed to provide a physics textbook to support your claims.

You seem to accept sloppy descriptions from Halpern because ‘you have guessed what they really meant to say’

The Halpern comment was about the second law, so sloppy argumentation is not permissible.

Now in certain contexts convenient labels may be given.
For instance the use of the term centrifugal force is often used.
Its quite all right in a certain context.

However if the discussion is about real forces on a satellite (say) then to say that centrifugal force is a real force rather than pseudo force would be mistaken.

You say
“To me the most serious fault of the G&T paper is that it does not even try to justify it’s conclusions. It just declares them ”

Yet you do not give any examples, you just make a declaration!

• That atmosphere emits radiation requires only that it’s heated by some mechanism. All climate scientists agree that the main source of energy is solar radiation, which heats mainly the surface (or ocean below the surface). The atmosphere is heated mainly by the surface by all forms of heat transfer (mainly radiation, convection and latent heat transfer). There’s nothing that contradicts that in the paper of Halpern et al or in any of the posts or comments of SoD, DeWitt or myself.

Your claim on the above is totally false and lacks all justification.

The role of various textbooks has been explained to you tens of times.

Actually I just read the reply of G&T to the Halpern et al paper. In that reply they tell that their original paper was not supposed to be anything more that a debuttal of false simplifications. I.e., they write in that reply that they haven’t even tried to claim that there’s something wrong in the standard theory itself, only in some simplifications selected by themselves. It’s funny that they say in their reply that they have never claimed that the standard theory is false.

Every simplification is false in some obvious way – otherwise they were not simplifications. They cannot be judged on that basis alone. They should be judged on their educational value. I would agree that some of the commonly presented simplifications have not been particularly good on that basis as they may lead to false ideas about the GHE.

The way the paper of G&T is commonly understood is, however, not in agreement with their reply.

35. DeWitt Payne says
Bryan,

“Are you denying that the atmosphere emits radiation?”

No

“If not, then are you denying that the surface of the Earth absorbs about 98% of that radiation?”

Not sure about that particular detail.

“If so, what then happens to the radiation that is reflected by the surface and why isn’t it measured by spectrophotometers, IR thermometers and pyrgeometers?”

DeWitt this is about the best summary of what pyrgeometers measure.

• on July 22, 2014 at 3:08 am | Reply DeWitt Payne

Bryan,

That article isn’t very good. It’s clearly written to confirm your incorrect opinion that pyrgeometers do not in fact measure integrated radiant flux over the wavelength range allowed to reach the detector. They do. But they measure it by difference rather than as an absolute because it isn’t possible to have a reference temperature of 0K. If the reference mass could be maintained at absolute zero, a pyrgeometer would, in fact, measure absolute total radiant flux.

A pyrgeometer or an IR thermometer measures heat flow, in the classical thermodynamic sense of heat, from or to a high thermal conductivity mass of known temperature through an insulating layer using the voltage from a thermopile with junctions on both sides of the insulating layer as the measure of the temperature difference across the layer. Any heat flow through the layer will cause a temperature difference across the layer and thus the voltage to be different from zero. It will be positive or negative depending on whether heat is flowing in or out. The greater the difference in effective temperature, the greater the heat flow. If the voltage is zero, then there is no heat flow and the radiant flux of the field of view impinging on the detector is the same as the flux leaving the detector. The device is calibrated using a cavity radiator or hohlraum, which is an extremely good approximation of a black body.

You like to focus on the negatives of pyrgeometers, which, like any other instrument, are not perfect. But IR spectrophotometers give results that are in agreement with results from pyrgeometers and with theoretically calculated spectra within experimental error. IR thermometers work on exactly the same principle as a pyrgeometer. IR thermometers can correctly measure temperature when the emissivity of the object being measured is known, so there is no good reason to doubt the validity of pyrgeometric measurements.

So yes, Virginia, the atmosphere does radiate in the thermal IR. Pyrgeometers, IR thermometers and IR spectrophotometers all measure this radiation, as they would measure the radiation from a solid object, and the results agree with theory. The difference is that IR thermometers and pyrgeometers integrate over a large spectral range while IR spectrophotometers resolve the distribution of the radiation by frequency or wavelength.

Since atmospheric radiation does vary strongly with wavelengths, if it were reflected by the surface to any significant extent, it would be obvious from the spectrum of radiation observed from the surface. But it isn’t observed because, for most of the Earth’s surface, reflection is insignificant.

• DeWitt,

Emissivity suddenly comes into sharp focus when members of the illuminati come to realize that the emission of radiation from the climate system can’t possibly be the same as the emission of radiation from the earth’s surface. After all that talk about averaging temperatures not working, it turns out that you don’t need to average anything, only sum the energy. There is no flawed assumption.

And if the emitted radiation by the climate system is much greater than emitted radiation from the surface, that’s actually the “greenhouse” effect. It can’t be, it’s forbidden by theory..

Damn, what to do?

Unless.. the emissivity was much lower than anyone said.. that must be it.

Ah, I bet no one has measured it, they just assumed it. Oh, measurements. Lots of measurements.

Ah, they must be based on a flawed instrument.

Ah ha, the instrument relies on physics theory (unlike say “thermometers”, “magflow meters” and all instruments in use in process plants which magically convert the measured parameter into an output without relying on “physics theory”).

You can’t make this stuff up.

I questioned a few things – like here:

..Of course, many people do tedious experiments and write them up in dull papers. But why bother reading them? Remember just a few weeks of writing blog articles can save minutes of research time.

What is the source of the first graph? The one with the footnote that doesn’t match the title?

For anyone with a passing interest in actual science the fact that contributor ‘Max’ has found a graph with a totally different value from decades of study by hundreds of experienced researchers would be worth checking..

And then:

..A person with a spreadsheet can write any value they want for thermal emission of radiation from the surface and then balance it with a downward component from the atmosphere.

What has Wayne Jackson demonstrated? That if you type an invented value of upward emission in and then divide it by the Stefan-Boltzmann equation it gives you an invented value of emissivity.

Well, as the blog owner has explained “some people” doubt the measured values of radiation. That’s pretty convincing evidence..

And a bit later:

Here is a list of MODIS products. MYD11C3 says “Land Surface Temperature & Emissivity”

This is a “land” product. The data sets for this product are all related to land – MODIS/Aqua Land Surface Temperature/Emissivity Monthly L3 Global 0.05Deg CMG.

It seem that your commenter Max added the footer that stated it was ocean emissivity. Well, up to him or the blog owner to provide his source..

Then someone told me a few home truths:

S.o.D’s sarcasm looks like an attempt to cover for the MODIS team’s poor data representation, and to distract attention from the glaring errors in the Trenberth-Keihl energy budget.

And it just keeps getting better from there. I couldn’t make up stuff this good.

36. SOD, Pekka, DeWitt, or Bryan:

There appears to be a dilemma that none of you want to specify in your stale debate. An electric field is a vector quantity. When the electric field from two charges overlap, we usually perform the vector addition and refer to a single resulting field.

Radiative flux is a vector quantity. When a downward and an upward radiative flux “pass through” each other, we argue about whether they cancel. When we discuss the heat transferred by the radiation, we cancel (ie. perform the vector addition). However, we know that the photons passing past each other do not cancel – they certainly aren’t vectors. Those photons can be counted when the reach a detector (facing up or down) through the energy they carry, so the energy fluxes don’t cancel as they pass through each other. Is there a consistent way to know when one should and shouldn’t add these vector quantities?

• on August 4, 2014 at 4:43 pm | Reply DeWitt Payne

Frank,

Radiative flux is a vector quantity.

No, it isn’t. That’s the mistake that G&T make when they criticize energy balance diagrams. The surface defining the flux has an orientation, but the flux through that surface is not a vector. It’s a scalar.

• DeWitt: FWIW, Wikipedia identifies eight fluxes (including radiation and energy) vector quantities.

http://en.wikipedia.org/wiki/Flux

Forces and fields follow the rules of vector addition (and cancel). Opposing fluxes of photons and matter do not cancel, so it makes some sense to treat them as scalars. However, flux in more than one dimension is described with vector notation.

• Frank,

Flux density can be a vector or scalar. But it can only be a vector if you are describing the flux density at a specific point and time specified by the investigator and calculated by integrating the intensity over the entire sphere surrounding the point. When you integrate over a hemisphere defined by a plane selected by the investigator, the result is a scalar not a vector.

Wikipedia Spectral flux density:

Scalar definition of flux density – ‘hemispheric flux density’

The scalar approach defines flux density as a scalar-valued function of a direction and sense in space prescribed by the investigator at a point prescribed by the investigator. [emphasis added]

Vector definition of flux density – ‘full spherical flux density’

The vector approach defines flux density as a vector at a point of space and time prescribed by the investigator.[emphasis added]

What we refer to as DLR and OLR, for example, are scalar quantities, not vectors. The same goes for convection. The actual angular sense is lost, not preserved, during the integration. The scalar value could, in principle, be caused by a high intensity narrow beam or a high intensity from a narrow angle like incident sunlight or from a diffuse source like a cloud covered sky.

• Frank,

The photons are effectively independent, because they are incoherent, meaning that the phases of the oscillating electric and magnetic fields are independent. Considering photons emitted at different locations independent is an extremely good approximation for the IR radiation in the atmosphere.

A well known example of the situation, where the radiation is coherent is a laser, where the ‘s’ refers to stimulated. Stimulated radiation is coherent, i.e. locked to the phase of the radiation that is stimulating further emission.

Coefficients found from the HITRAN database contain also the coefficient for stimulated emission. Applying that coefficient in the appropriate formula confirms that stimulated emission is negligible in comparison with spontaneous emission for IR in the atmosphere.

The same facts can be concluded from the theory of Quantum Electrodynamics, which is built on the Feynman diagrams. All simple Feynman diagrams correspond to incoherent photons, but more complex ones represent processes that involve two or more photons. These more complex diagrams tell about phenomena were considering photons independent is insufficient. Quantitatively these corrections are negligible in situations relevant for IR radiation in the atmosphere.

In addition to lasers, much that we know about radiowaves is strongly influenced by coherence. Considering radiowaves in terms of incoherent photons can not explain anything we are accustomed to attach to them.

• Frank

Waves (EM or otherwise) pass through each other unchanged.
Only at a specific point will opposing waves interfere and cause a resultant value.

37. For most scientific subjects of wide importance, it’s not hard to find review articles explaining the principles involved and summarizing current knowledge.

Maybe I have not looked in the right places but I have not found such a review article dealing with the greenhouse effect. Do they exist? Where should I look?

• Martin A,

I’ve tried in the past to find ones on Planck’s law, Stefan Boltzmann relationship and other fundamental heat transfer, but the best I was able to do was get The Theory of Heat Radiation by Max Planck published in 1914.

It seems that the review papers for stuff well-proven 100 years ago will be in some archives of an august library and not on Google scholar.

For the “greenhouse” effect, the best I can offer are the papers which explained the “radiative-convective” effect – that is, the thermal structure of the atmosphere:

Thermal equilibrium of the atmosphere with a convective adjustment, Manabe & Strickler (1964)

Thermal equilibrium of the atmosphere with a given distribution of relative humidity, Manabe & Wetherald (1967)

Climate Modeling through Radiative Convective Methods, Ramanathan & Coakley (1978)

– the above papers are all free

There is an excellent review article which was made by Ramanathan on invitation:
Trace Gas Greenhouse Effect and Global Warming, V. Ramanathan, Royal Swedish Academy of Sciences (1998)

– sadly this is behind a paywall, but I’ll happily email it to anyone who wants to read it.

38. Sod,

I would love to receive that article

Thanks!

I would be grateful for the Ramanathan review article. I’m assuming that you have my email address.

40. on August 8, 2014 at 4:41 am | Reply Chic Bowdrie

I’m troubled by definitions of the greenhouse effect based on the presence of IR absorbing gases. Clearly the planet would be warmer simply due to the presence of N2 alone compared to no atmosphere. IMO, one should consider alternative possible outcomes resulting from the addition of IR absorbing gases. The most obvious would be the current atmosphere. CO2 doubling or an equivalent projected increase in IR active gases describes another outcome sometimes called an enhanced greenhouse effect. You include this latter outcome as part 6 of the general greenhouse effect where you state “If we add more radiatively-active gases (like water vapor and CO2) then the atmosphere becomes more ‘opaque’ to terrestrial radiation and the consequence is the emission to space from the atmosphere moves higher up (on average). Higher up is colder.”

In note 6 you add “It [a constant lapse rate] doesn’t change the fact that with more GHGs, the radiation to space will be from a higher altitude.”

Where has that fact been established? More IR absorbing gases seems as likely to radiate more to space than less. Your explanation given in The Earth’s Energy Budget – Part Three does not reference any supporting data.

• Chic,

Clearly the planet would be warmer simply due to the presence of N2 alone compared to no atmosphere.

With an N2 atmosphere the surface would be radiating directly to space. The atmosphere would not be interacting with this radiation, it would not be absorbing or emitting.

Therefore, the outgoing longwave radiation of approximately 240 W/m2 would be from the surface.

Or if we want to avoid averages, the OLR of 240 x 5.1×1014 x 86,400 x 365 J/year would be from the surface.

Correct or not?

In note 6 you add “It [a constant lapse rate] doesn’t change the fact that with more GHGs, the radiation to space will be from a higher altitude.”

Where has that fact been established? More IR absorbing gases seems as likely to radiate more to space than less. Your explanation given in The Earth’s Energy Budget – Part Three does not reference any supporting data.

Using the equations of radiative transfer. If we take the case “pre-feedback” then for any given surface temperature and lapse rate we can calculate the changes.

I did the calculation in Visualizing Atmospheric Radiation – Part Seven – CO2 increases.

The code for this is shown in Part Five – The Code – this is just a numerical integration of the equations of radiative transfer.

Obviously I wasn’t the first. I did these calculations so that we could probe into the details and understand at what wavelengths the largest effects were found. And also so the code could be inspected and questioned.

The first paper that really nailed the problem was Thermal equilibrium of the atmosphere with a given distribution of relative humidity, Manabe & Wetherald (1967).
A later more comprehensive paper is Climate Modeling through Radiative Convective Methods, Ramanathan & Coakley (1978).

Note that my calculations are not a GCM, they just calculate how a change in CO2 causes a reduction in OLR for a given temperature profile.

• Chic,

A N2 atmosphere would still warm due to conduction and convection.

Interesting. Let’s go back to the key point and confirm your thinking:

Where is the emission to space from (with an N2 atmosphere)?
What is the globally averaged OLR?

• on August 8, 2014 at 5:52 pm Chic Bowdrie

sod,

Emission to space from the surface, of course. However, the surface must warm unless it reflects 100% of incoming solar. I assumed the other extreme, 100% absorption or an average of 340 W/m2. OLR would also be 340 W/m2 by definition of in equaling out.

The key point here is that some conduction will occur and the only way that energy can escape is reverse conduction. Convection will oppose that process. So a quasi-equilibrium will develop at altitude with an average global surface temperature that can only be speculated by estimating the daily and latitudinal extremes.

• on August 8, 2014 at 4:09 pm Chic Bowdrie

SOD,

“Therefore, the outgoing longwave radiation of approximately 240 W/m2 would be from the surface. Or if we want to avoid averages . . . .”

A N2 atmosphere would still warm due to conduction and convection. There would be more solar insolation without clouds, possibly 340 W/m2 depending on albedo. Because there is no cooling at altitude, the surface would be much warmer than 255 K depending the magnitude of temperature swings between day and night. So on average an inert atmosphere would be warmer than no atmosphere, but not as warm as our current atmosphere.

“Note that my calculations are not a GCM, they just calculate how a change in CO2 causes a reduction in OLR for a given temperature profile.”

Your calculations are impressive, but I’m still left wanting for evidence that the calculations reflect reality. This from your Ramanathan and Coakley (R&C) reference page 482:

“In judging the importance of [radiative-convective model] results it should be remembered that they represent only the sensitivity of the model climate to perturbations in the atmospheric constituents and that the sensitivity of the model may not reflect the climate sensitivity of the actual earth-atmosphere system. For the CO2-climate problem, however, the increase in Ts due to an increase in CO2 computed by the radiative-convective model is within 20% of the increase in Ts computed by a three-dimensional GCM.”

With GCMs missing the mark by so much, how can they be used to validate R&C’s model?

Also in the literature references, I found no evidence indicating more IR absorbing gases raise an effective emission height. I’m going through Visualizing Atmospheric Radiation – Part Seven – CO2 increases to see if I can find it there.

• on August 8, 2014 at 8:53 pm DeWitt Payne

Chic,

If we started out at, say, the temperature of the cosmic microwave background, 2.75K, and turned the sun on, the presence of an atmosphere would cause the surface to have a lower temperature than for no atmosphere until the atmosphere reached steady state. The atmosphere can’t be warmer than the warmest spot on the surface. The warmest spot on the surface could also not be warmer than if there were no atmosphere. So once steady state is achieved, no further energy will be transferred from the surface to the atmosphere and vice versa, assuming no convection. If you allow convection, the equator wouldn’t be as hot and the poles wouldn’t be as cold, but the average would be only slightly higher.

Nitrogen isn’t perfectly transparent to IR because of collision induced absorption. But the absorptivity is so low and at such long wavelength that it wouldn’t make much difference.

• on August 9, 2014 at 6:18 am Chic Bowdrie

DeWitt,

If you want to start with a 3K planet and turn the sun on, then let’s do that for both cases—no atmosphere and a N2 atmosphere devoid of any IR activity. Assume both planets have the same albedo = 1. The sun will continue to warm the surfaces of both planets until they become hot enough to radiate on average the same energy as they receive. I call this a quasi-steady state because the planet’s surfaces are constantly heated and cooled as they rotate and revolve around the sun. Because some of the energy absorbed by the surface of the N2 planet is conducted into the atmosphere and convected upwards, this atmosphere will continue to warm until reaching an average temperature profile similar to Earth’s dry lapse rate. Because this N2 atmosphere provides some insulation not possible with a no atmosphere planet, the average global temperature of the N2 planet will be greater than the no atmosphere planet. You cannot assume no convection when a planet has an atmosphere.

“The atmosphere can’t be warmer than the warmest spot on the surface.”

On average, of course. But every night, the atmosphere will be warming the cooler surface by conduction.

“The warmest spot on the surface could also not be warmer than if there were no atmosphere.”

I can’t agree with that. The no-atmosphere surface does not have the “back” conduction provided by the atmosphere.

• on August 9, 2014 at 7:07 pm Chic Bowdrie

Assume both planets have no albedo or at least anything other than 1. Sorry.

• Chick,

The N2 atmosphere cannot affect the surface temperature in any other way than by transferring a little heat from one spot of the surface to another and by storing a little heat, when the surface is hot, and later release the same amount to the surface, when the surface is cooler. It cannot influence the effective radiative temperature of the surface as virtually all radiation is absorbed by the surface and emitted by the surface.

Thus the surface emits as much at it absorbs. This requirement of energy balance determines the surface temperature. N2 atmosphere cannot changed that much, as the only effect comes from the lesser temporal and spatial variability of the surface temperature. With the T^4 behavior of the Stefan-Boltzmann law the same average T^4 leads to slightly warmer average T, when the variability is less.

Lesser variability means that the maximum temperature is reduced and the minimum temperature increased.

• on August 9, 2014 at 8:30 pm Chic Bowdrie

Pekka,

“With the T^4 behavior of the Stefan-Boltzmann law the same average T^4 leads to slightly warmer average T, when the variability is less. Lesser variability means that the maximum temperature is reduced and the minimum temperature increased.”

This much I understand and agree with totally. Which is why I don’t understand why you think an atmosphere, albeit inert, “cannot influence the effective radiative temperature of the surface ….” If any radiation absorbed by the surface is conducted, then the atmosphere will convect it upwards. Once that energy is elevated it won’t readily be returned to the surface. Conduction is too slow and convection isn’t driven in that direction. Assuming realistic thermal conductivities, it may take some time, but eventually the atmosphere will establish a lapse rate with a warmer average temperature than a similar planet with no atmosphere.

Another way to look at it is both planets will eventually radiate the same amount as received. But the atmosphere planet has that extra heat capacity due to the atmosphere. It has to be saturated before the final pseudo- or quasi- equilibrium is reached.

• Chic,
The atmosphere cannot convect or conduct heat upwards for long, because the heat cannot go anywhere from a non-emitting atmosphere and the heat capacity of the atmosphere itself is small. All the heat that goes up must soon come back down. There’s no net transfer of energy either up or down over a full year.

The surface is heated only by the sun, and cooled with the total power of emission that corresponds to the surface temperature. A N2 atmosphere changes that very little. Therefore the surface is would have nearly the same temperature as without any atmosphere. The only significant additional energy flow to the Earth surface is the downwelling radiation from the atmosphere, but N2 does emit such radiation to a significant degree leading to a cold surface (near 0C with zero albedo).

• on August 9, 2014 at 9:19 pm Chic Bowdrie

Pekka,

“The atmosphere cannot convect or conduct heat upwards for long, because the heat cannot go anywhere from a non-emitting atmosphere and the heat capacity of the atmosphere itself is small.”

The atmosphere only needs a non-zero heat capacity to gain heat. Once heated, the N2 near the surface must rise. It isn’t coming back as fast as it goes up because of the dynamics of convection.

I don’t understand the context of “no net transfer of energy either up or down over a full year.

We may have to start putting some numbers up or we’ll end up at an impasse.

First let’s try a thought experiment. If I irradiate ice in a vacuum with IR, will it melt?

• on August 9, 2014 at 9:21 pm Chic Bowdrie

More appropriately, will it sublime?

41. […] that there have been more than 50 posts on this topic (post your comments on those instead). See The “Greenhouse” Effect Explained in Simple Terms and On Uses of A 4 x 2: Arrhenius, The Last 15 years of Temperature History and […]

42. […] wrote The “Greenhouse” Effect Explained in Simple Terms to make it simple, yet not too simple. But that article relies on (and references) many basics […]

43. […] wrote The “Greenhouse” Effect Explained in Simple Terms to make it simple, yet not too simple. But that article relies on (and references) many basics […]

44. “If we add more radiatively-active gases (like water vapor and CO2) then the atmosphere becomes more “opaque” to terrestrial radiation and the consequence is the emission to space from the atmosphere moves higher up (on average). Higher up is colder”

OK, I’ll stick my neck out.
I have the same problem that Peter O’Donnell Offenhartz alluded to earlier.
I have used MODTRAN to view the spectra for Tropical and Arctic Summer atmospheres (didn’t look at the others).
http://climatemodels.uchicago.edu/modtran/modtran.html

This does seem to indicate that the Effective Radiating Level of radiation coming from the bottom of the ‘CO2 well’, around wavenumber 666 is in the stratosphere, a region where temperature increases with altitude.
For example, look down from 70km and observe the bottom of the ‘CO2 well’, around wavenumber 666. This, presumably, radiation from the Effective Radiating Level(ERL).
Estimate its temperature by reference to nearby the plank curves.
Now look down from progressively lower and lower altitudes. What happens? When we get to 40km, we see that the bottom of the CO2 well appears to be emanating from somewhere ‘cooler’ than it was when viewed from 70km.
If the temperature at ERL was decreasing with altitude, it should appear to radiate from somewhere warmer as we descend.
The argument based on ERL is very easy to understand and I have used this argument myself, after reading your blog. But it does rely on the ERL being in the troposphere, and it doesn’t appear to be.

Or, have I done something wrong?

• MikeB,

If CO2 only absorbed across wavenumbers 666 – 668 cm-1 with such a huge absorption then more CO2 would cause less warming – for exactly the reasons you describe.

But CO2 absorbs across a much much wider range, with most of that absorption being many orders of magnitude lower. Consequently, the emission to space from most of the CO2 band is from the troposphere.

Take a look at Visualizing Atmospheric Radiation – Part Seven – CO2 increases. Hopefully the bigger picture as explained makes sense. But feel free to ask further questions.

• MikeB: You are exactly correct. If temperature didn’t drop with altitude, the GHE wouldn’t exist. As radiation (I_0) of a given wavelength passes an incremental distance (ds) through the atmosphere, the change (dI) is caused by both emission (first term) and absorption (second term) of the Schwarzschild eqn:

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

where n is the density of GHG and o is its absorption cross-section. Outward radiation (I_0) comes from below – produced by a B(lamba,T) term usually with a higher T. So the term in brackets is usually negative and increasing n decreases the outward flux. Above the tropopause, however, temperature increases with altitude and the ERL for the strongest CO2 emission bands is in the stratosphere.

MODTRAN is numerical integrating the Schwarzschild eqn upward and downward through the atmosphere over all wavelengths. If you look down from the tropopause (which varies with latitude) and then the TOA (70 km), you will see that OLR increases a few W/m2 above the tropopause. (Globally OLR decreases from about 390 W/m2 to 240 W/m2 with increasing altitude, so the increase due to emission from the stratosphere is pretty small.)

• on May 15, 2015 at 2:02 pm | Reply DeWitt Payne

By convention, forcing is measured at the tropopause. In fact, you are also supposed to allow the stratosphere to equilibrate. Adding CO2 will cool the stratosphere. But the contribution from the stratosphere is small enough that if you measure the change in upward radiation (looking down) at the tropopause it’s pretty close. Looking down from the top of the atmosphere, emission from the center of the CO2 band will increase if you increase CO2. But if the stratosphere were allowed to cool, it wouldn’t change very much.

When you change the temperature in MODTRAN, you only change the temperature in the first ten kilometers above the surface. If you measure the difference in upward radiation starting at the surface and moving upward, the difference increases, reaches a maximum and then decreases. If the stratosphere were allowed to equilibrate, it would reach a maximum and then not change much with altitude.

45. SoD
Thank you for the reply. If you repeat the experiment you will see that whole base of ‘CO2 well’, from wavenumber 640 to 680 (as far as I can tell) is already in a region where temperatures increase with increasing altitude.
I was ignoring the central ‘blip’ at wavenumber 666 although I think an upward blip like this is also an indication of temperature inversion.

This is not to say that increasing CO2 levels will not widen the CO2 absorption band in the ‘wings’. Modtran also shows a reduction in upward IR heat flux with increasing CO2. That is accepted. The only point I am making is that the argument for the greenhouse effect based on the ERL raising to a level which is cooler doesn’t seem to be supported. But, it is not supported by evidence and I have never seen any statement or reference saying that the ERL is in the troposphere.
So, I think the argument from this perspective is, for the want of a better word, wrong. I think we are back to ‘back radiation’ providing an additional heating flux on the ground.

• MikeB,

Another point – as I stated in Note 5:

The “place of emission” is a useful conceptual tool but in reality the emission of radiation takes place from everywhere between the surface and the stratosphere. See Visualizing Atmospheric Radiation – 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.

Conceptual tools have their uses. They have their limitations as well.

If this conceptual tool has lost its usefulness, instead just think about OLR reducing due to more GHGs.

Visualizing Atmospheric Radiation – Part Seven – CO2 increases shows how the “no feedback” result of doubling CO2 is calculated and which wavenumbers make the largest contribution.

The maths is the result. Graphs and explanations are ways to help us grasp it.

I found the subject difficult to grasp until I was able to carry out the calculations myself. I realize this is out of reach for most people – you need a lot of time and a tool like Matlab to be able to carry out the intensive numerical calculations required by the equations of radiative transfer.

But I am more than happy to produce the results in different ways for interested commenters..

• on May 20, 2015 at 8:43 pm Chic Bowdrie

Scienceofdoom,

“Conceptual tools have their uses. They have their limitations as well.”

Very true. The problem I see with concepts like ERL and a MODRAN tool is the emphasis on a static atmosphere, where a snapshot of the atmosphere in one century can be compared one in another; where you have time to calculate the effect of a change in CO2 and speculate on the amount of energy that might be represented by those calculations. In reality, energy fluxes through the atmosphere are constantly changing. During the day, CO2 and H2O molecules absorb radiation at the Earth’s surface and transfer that energy to the bulk air where it rises higher up in the atmosphere to eventually be transferred back again as radiation to space. What is needed is a conceptual tool that reflects what is happening in real time, not calculated differences between snapshots in time.

• on May 18, 2015 at 1:26 pm | Reply DeWitt Payne

The effective level of radiation emission is a mathematical construct. You take the average global emission, 239W/m², convert it to temperature and use a standard atmospheric temperature profile to convert temperature to altitude. That’s 254.8K. Using the 1976 U.S. Standard Atmosphere profile with a surface temperature of 288.2K, that’s 5.14km. An increase in surface temperature of 1K would raise that level to 5.29km.

The other thing you have to remember is that most atmospheric emission comes from water vapor, and that comes from the lower troposphere. The scale height for water vapor is ~2km. That means that 86.5% of all the water vapor in the atmosphere is below an altitude of 4km. Adding CO2 has no immediate effect on water vapor emission and, if you allow the stratosphere to equilibrate, no effect on emission at the CO2 band peak. But it does increase the effective emission level in the band wings.

• MikeB:

..The only point I am making is that the argument for the greenhouse effect based on the ERL raising to a level which is cooler doesn’t seem to be supported. But, it is not supported by evidence and I have never seen any statement or reference saying that the ERL is in the troposphere.
So, I think the argument from this perspective is, for the want of a better word, wrong. I think we are back to ‘back radiation’ providing an additional heating flux on the ground..

If you arbitrarily define the CO2 band to be 650-690 cm-1 then you are correct. If you define the CO2 band to be the whole band then you are not correct.

In this calculated graphic (from Visualizing Atmospheric Radiation – Part Seven – CO2 increases) you can see that for a given surface temperature the TOA flux is reduced due to doubling CO2, and you can see which wavenumbers provide the effect:

In this graphic, from Visualizing Atmospheric Radiation – Part Three – Average Height of Emission you can see where the TOA radiation is emitted from as a function of both wavenumber and altitude:

[The 0-1500 is wavenumbers in cm-1 and the 0-20 is altitude in km]

• SOD and MikeB: The difference between the 280 and 560 ppm of CO2 lines might be clearer.

By defining the TOA as 50 hPa (19 km) in the above graphs, SOD is missing the changes to TOA caused by some of the stratosphere. Using the MODTRAN calculator (US standard atmosphere, no clouds, 400 ppm CO2 and NO other GHGs), I find that the altitude with the minimum value for OLR is 20 km. OLR rises 0.5 W/m2 by 30 km and 1.6 W/m2 by 70 W/m2. The biggest visible change is associated with the narrow 666 cm-1 line in the middle of the band, but the effective radiation temperature of the whole band rises from just below 220 degK at 20 km to just above 220 degK. Doubling CO2 to 800 ppm decreases OLR by 3.0 W/m2 at 70 km and 3.6 W/m2 at 20 km. (I suspect that MODTRAN, like SOD, calculates equilibrium temperatures for the stratosphere.)

Most of the action is in the troposphere. 400 ppm of CO2 alone can reduce OLR by about 100 W/m2 between the surface and 12 km, reduces another 1.6 W/m2 between 12 and 20 km, and adds back 1.6 W/m2 from 20 to 70 km (from the relatively warm stratosphere). Doubling CO2 reduces OLR whether the TOA is at 50 hPa (19 km) or 70 km.

Caveat: When I added the default amount of other GHGs (including stratospheric O3, the change in OLR between 20 km and 70 km was only 0.1 W/m2, not 1.6 W/m2. In a US standard atmosphere with no GHGs except stratospheric O3, OLR decreases steadily with altitude beginning above 12 km – because the surface of the earth is warmer than the stratosphere. The colder atmosphere between doesn’t absorb or emit significantly at these wavelengths (even when the default tropospheric ozone is included). So, stratospheric CO2 and O3 have opposite effects on OLR that nearly cancel.

• on May 19, 2015 at 7:38 pm DeWitt Payne

Frank,

MODTRAN keeps the temperature above 13km constant. In reality, an increase in CO2 will cause the stratosphere to cool rapidly, in weeks to a few months, and there will be little or no increase in emission with altitude above the tropopause. That’s why the official protocol for calculating radiative forcing from ghg’s requires that the stratosphere be allowed to equilibrate while the troposphere is held constant.

46. on May 18, 2015 at 8:51 pm | Reply Peter O'Donnell Offenhartz

@DeWitt Payne

I’m not sure you have answered MikeB’s question. You provide a “scale height” for water vapor and another height for ALL infrared-absorbing gases taken together. How about a scale height for carbon dioxide by itself.

47. on May 18, 2015 at 11:12 pm | Reply DeWitt Payne

CO2 is a well mixed gas, unlike water vapor. The scale height is the same as for the other well mixed gases, ~8km. Therefore at 4km for the 1976 U.S. Standard atmosphere, the pressure is 701mbar, meaning 70% of the atmosphere and by extension the CO2 in the atmosphere is above that altitude, compared to 13.5% of the water vapor. And again, most of the atmospheric emission to space comes from water vapor, so all the emission to space from water vapor is from below 4km, That also doesn’t include the emission through the atmospheric window directly from the surface.

• DeWitt: You didn’t account for the fact that there is much less CO2 (.04% or 400 ppm) in the atmosphere than water vapor (about 1% or 10,000 ppm) near the surface. Atmospheric pressure is 10,000 kg/m2. At 4 km, you are still beneath about 4.2 kg of the 6 kg (70%) of CO2 above every m2 of the surface. At 4 km, you are still beneath 8 kg of the 62 kg (13.5%) of water vapor over every m2 of surface. (This is after converting ppmv to ppmw. There are about 4-fold times as many water vapor molecules as CO2 molecules above 4 km.) You also have to factor in the difference in cross-section.

If you remove all of the other GHGs from the MODTRAN calculator for the US standard atmosphere, water vapor emission for 100-400 cm-1 has an effective radiation temperature of 230-240 degK (8 km) and above 1300 cm-1 of 240-260 degK (6 km). The lowest effect radiation temperature for CO2 is 220 degK (10 km)

• on May 19, 2015 at 2:29 am DeWitt Payne

My numbers say 25kg water vapor/m², i.e. 25mm of liquid water, not 62kg or 62mm. But you have a point. Water vapor absorbs strongly below 400cm-1 which is still well within the thermal IR range. Still, if we set CO2, methane and tropospheric ozone to zero, atmospheric transmittance increases rapidly with altitude. Tropical atmosphere (for maximum water vapor content), looking up

0km 0.163
2km 0.348
4km 0.490
8km 0.711

The troposphere in the tropics stops at about 17km altitude.

48. Chic Bowdrie wrote: “The problem I see with concepts like ERL and a MODRAN tool is the emphasis on a static atmosphere, where a snapshot of the atmosphere in one century can be compared one in another; where you have time to calculate the effect of a change in CO2 and speculate on the amount of energy that might be represented by those calculations. In reality, energy fluxes through the atmosphere are constantly changing. During the day, CO2 and H2O molecules absorb radiation at the Earth’s surface and transfer that energy to the bulk air where it rises higher up in the atmosphere to eventually be transferred back again as radiation to space. What is needed is a conceptual tool that reflects what is happening in real time, not calculated differences between snapshots in time.”

That is what climate models, cloud-resolving models and re-analysis of weather data to do for us – but then you are buried in data from which it is difficult to abstract important concepts. Satellites are continuously monitoring the changes in OLR and reflected SWR. Their data says that climate models do a good job of representing OLR from clear skies (the GHE and water-vapor plus lapse rate feedback) and a poor job with clouds and ice-albedo feedback.

http://www.pnas.org/content/110/19/7568.full.pdf

• on May 23, 2015 at 6:40 pm | Reply Chic Bowdrie

Frank,

Thank you for the response and the paper which AFAICT says, “the gain factors of longwave CRF obtained from most of the CMIP models have positive values, in contrast to the small negative values obtained from satellite observations.” Hopefully someone in the climate model community got the word.

Meanwhile a novice like me continues frustrated over the use of spectrograms showing that IR absorbing gases absorb some of the radiation at some point after it leaves the surface and emit it somewhere higher up. This technique is used to quantify the amount of extra energy that is “trapped” due to increasing CO2. All that is left is to associate the trapped energy with some amount of temperature increase. Most of the climate debate is over the magnitude of the temperature change. Scientists who look into all the actual energy transfer scenarios involved, ie conduction, evaporation, radiation, and convection, surmise that temperature gradients and energy fluxes are not all determined by radiation physics. IOW, it is not enough for models to accurately predict OLR from atmospheric composition and temperature at altitude. There has to be some consideration for how the energy got there in the first place. I know that’s what the GCMs are supposed to include, but there’s more wrong with them than just cloud radiative forcing.

This is not meant to be a criticism of SoD’s work exhaustive work here. I’m just not able to understand how doubling CO2 can lead to lower “spectral emitted power” at 50 hPa as indicated in the response to MikeB above. At that elevation if CO2 isn’t radiating at least as much, what else is?

• Chic wrote: “Scientists who look into all the actual energy transfer scenarios involved, ie conduction, evaporation, radiation, and convection, surmise that temperature gradients and energy fluxes are not all determined by radiation physics. IOW, it is not enough for models to accurately predict OLR from atmospheric composition and temperature at altitude.”

When I first came to SOD, I used to hate all of the emphasis on radiation and the lack of discussion about convection. Surface temperature is controlled by both. My biases made it hard to always remember that the only way for energy to enter or leave the planet is by radiation. Convection merely redistributes the energy that is present. We can calculate the amount of heat transported by radiation, but not by convection. Physics only tells us when an unstable lapse rate will permit buoyancy-driven vertical convection, not how much energy will be carried upwards by it. It doesn’t tell us why the earth’s average lapse rate is 6.5 K/km, instead of some other value. So SOD can (and does) tell us far more about radiation than convection.

I used to dream that winds over the ocean could blow faster, causing more evaporation and transporting more heat away from the surface. Unfortunately, the more heat that is carried aloft from the surface, the smaller the likelihood of an unstable lapse rate. The heat un the upper troposphere has to escape to space before more can arrive.

Chic wrote: “Hopefully someone in the climate model community got the word.”

One of the co-authors of the above PNAS paper is Manabe, one of the original developers of the GFDL climate model (and co-author of the first paper on “radiative-convective equilibrium”). He may be the driving force behind the Coupled Model Intercomparison Project (CMIP) including experiments on seasonal change. It is hard to believe they don’t recognize these problems, whether they discuss them fully or not. Policymakers desperately need useful projections and have invested billions(?) in climate models. Complete public candor has its drawbacks.

49. on May 24, 2015 at 10:03 pm | Reply Chic Bowdrie

Frank, your comment reminded me of my first foray into the “deep” science of climate change. That was right here at ScienceofDoom. Now I dream about being reincarnated as a climate scientist. So many questions, so little time.

You said, “We can calculate the amount of heat transported by radiation, but not by convection.”

Is that strictly true or is it just a lot more difficult to set up and solve the differential equations involved? I haven’t delved into that yet, but my understanding is that an unstable lapse rate is caused by the heat produced at the surface when the sun comes up. That heat does not wait for a signal from the TOA to see if there’s room for more heat up there. Are we on the same page with that? Also, I’m pretty sure the lapse rate is calculable from thermodynamic principles.

• Chic,

You said, “We can calculate the amount of heat transported by radiation, but not by convection.”

Is that strictly true or is it just a lot more difficult to set up and solve the differential equations involved? I haven’t delved into that yet, but my understanding is that an unstable lapse rate is caused by the heat produced at the surface when the sun comes up. That heat does not wait for a signal from the TOA to see if there’s room for more heat up there. Are we on the same page with that?

We can write an equation for heat transported by radiation. We have some data required – the temperature profile, the concentration of GHGs and their absorption properties.

The equation can be solved (a numerical solution can be obtained given the data noted above).

We can write an equation for heat transported by convection.

But we can’t solve it. Take a look at Turbulence, Closure and Parameterization.

..Also, I’m pretty sure the lapse rate is calculable from thermodynamic principles.

This is partly correct.

The lapse rate under convection can be calculated. See Potential Temperature. In the tropics, due to the large amount of convection (even though a larger area has subsiding air than has ascending air), the temperature profile roughly matches this calculated lapse rate.

Outside the tropics there is much less convection and the lapse rate often doesn’t match the calculated lapse rate under convection.

• on May 26, 2015 at 4:40 am Chic Bowdrie

SoD,

Sorry I didn’t catch your response until now. You write,

“We can write an equation for heat transported by convection. But we can’t solve it.”

Does that include numerical methods? If you can write an equation, a numerical method solution should be possible. Or is it similar to the turbulence problem that is too massive even for today’s computers?

• Chic Bowdrie,

Does that include numerical methods? If you can write an equation, a numerical method solution should be possible. Or is it similar to the turbulence problem that is too massive even for today’s computers?

If you take a look at the article I linked, Turbulence, Closure and Parameterization, you will see the answer to your questions:

1. Does that include numerical methods? – Yes
2. If you can write an equation, a numerical method solution should be possible – Not necessarily
3. Or is it similar to the turbulence problem that is too massive even for today’s computers? – It is exactly “the turbulence problem that is too massive for today’s computers”. And tomorrow’s. And probably the computers in 2035.

• Chic commented: “That heat does not wait for a signal from the TOA to see if there’s room for more heat up there.”

Upward buoyancy-driven convection only occurs when the rising air is warmer – and therefore less dense – than the air it displaces – even after it has expanded (under the reduced pressure) and cooled. The “signal to continue rising” is the temperature of the air immediately above a rising parcel of air.

Dry and moist adiabatic lapse rates can be calculated from first principles: http://scienceofdoom.com/2011/06/12/paradigm-shifts-in-convection-and-water-vapor/. However, these simply tell you when or where the lapse rate is unstable – it doesn’t tell you how much latent heat (and simple heat?) will move upwards through an unstable region before it stops being unstable.

Lapse rates in the real world are highly irregular: perturbed by the diurnal cycle (ground, with higher emissivity, cools at night faster than the air immediately above) and perturbed in temperate zones by colliding masses of warmer and colder air. Radiosondes are launched twice a day from several hundred(?) sites around the globe and the altitude vs temperature profiles or “soundings” (posted on the web somewhere) are used to initialize weather prediction programs. The are often displayed on Skew-T diagrams.

FWIW, I have asked and searched for an explanation for why the earth’s average environmental lapse rate in the troposphere is 6.5 K/km and never gotten one. We can calculate how much an increase in absolute humidity will change the lapse rate in a world with 2XCO2 (to my knowledge, the only recognized form of lapse rate feedback), but I can’t see an unambiguous reason why that humidity-induced change must be a change from today’s value, 6.5 K/km. If the Hadley circulation were to speed up in a 2XCO2 world, stronger trade winds would produce more evaporation and the ITCZ would carry more heat to the top of the troposphere, reducing the overall lapse rate. However, only radiation can carry that heat from the upper troposphere to space and 2XCO2 slows this process. Furthermore, the amount of air ascending and descending must be equal, and descent requires increasing density by radiative cooling. If a faster Hadley circulation carried heat HIGHER, heat could escape more easily. Convection in tropical regions does reach far higher than in temperate ones, and I’ve tried reading (without comprehension) papers explaining why the top of the convective region is located where it is.

50. on May 25, 2015 at 12:22 pm | Reply Chic Bowdrie

Frank,

That is why a simple quantitative dynamic model of the processes we are discussing would be helpful. Saying what would happen is really just giving our opinion of what should happen. You seem convinced that 2xCO2 slows radiation to space. Other than something generated from a computer model. where is the data showing that is true?

Your interpretation is based on an assumption that more GHGs will make emission to space occur higher up in the atmosphere. SoD makes the same assumption in this post. I would like to see that data as well.

My understanding is that 6.5 K/km is a result of surface evaporation and cloud formation. The latent heat is removed from the surface and released at altitude forcing a reduction in the dry lapse rate.

• Chic wrote: “My understanding is that 6.5 K/km is a result of surface evaporation and cloud formation. The latent heat is removed from the surface and released at altitude forcing a reduction in the dry lapse rate.”

If relative humidity over the oceans ever reached 100%, there would be no more surface evaporation. So evaporation itself is limited by the rate at which convection carries moist air away from the surface.

In fact, there is a very thin adhering layer of air above the ocean where the relative humidity is 100% (equilibrium), and the rate of evaporation is limited by transport out of this thin layer. For this reason, winds are at least as important as SST for evaporation rate. Turbulent convection associated with surface winds mixes a boundary layer (1-2 km thick?) of the atmosphere with some air from above, producing a fairly homogeneous layer with about 80% relative humidity and sometimes boundary layer clouds at the top. Convection raises parcels of air from the boundary layer into the “free troposphere” until clouds form and rain falls. However, during this process some drier descending air is turbulently mixed into the rising air (“entrainment”). 6.5 K/km is the end result of a very complicated process involving dry and moist lapse rates that are not perfectly adiabatic. The large grid cells in climate models can’t reproduce these processes from first principles, so they must be parameterized.

I bought Grant Petty’s book on Atmospheric Radiation and his other book on Atmospheric Thermodynamics. Purely physics and chemistry of the atmosphere. Neither climate change nor the IPCC are mentioned in the index. Equivalent texts can easily run \$100+ and not be as good.

• on May 25, 2015 at 8:09 pm DeWitt Payne

Chic,

I don’t think you have a grasp of the complexity of what you’re asking. Frank mentioned atmospheric boundary layer above. That’s only a small part of the atmosphere. Here’s an article about the structure of the ABL and its diurnal variation. You can also look at SURFRAD data to see how EM radiation levels and meteorological data vary daily at nine different US sites. We have data, we don’t, and aren’t likely to ever get, a simple conceptual model.

• on May 25, 2015 at 7:12 pm | Reply Chic Bowdrie

DeWitt,

Thanks for the info on microwave emission and suggestion to get my own copy of Petty’s book.

However, I’m not challenging the results from radiative transfer based models which accurately predict OLR. But AFAIK these are point-in-time measurements. Do these models account for the net input and output over a 24 hour period or longer? This may be the objective of GCMs, but 1) they aren’t accurate and 2) they are too complicated for any conceptual learning. At least, I would have to retire and make it a full-time project learning how they work.

Also, I wouldn’t call a model a radiative-convective one if it can’t calculate the contribution of convection in real time. Isn’t that contribution most crucial when the static or stable atmosphere is perturbed? Which happens essentially around the clock and causes a lot more than a few degrees of perturbation.

• Chic wrote: “Also, I wouldn’t call a model a radiative-convective one if it can’t calculate the contribution of convection in real time.”

By specifying the composition, temperature and pressure, one can calculate (from first principles and measured absorption cross-sections) the OLR and DLR flux into and out of any layer of atmosphere thin enough that these inputs can be treated as constants. An average of 240 W/m2 of post albedo SWR passes through the atmosphere with about 162 W/m2 reaching the surface.

If average temperature is assume to be constant with time (steady-state), we know that OLR – DLR + convected heat (latent plus simple) must equal the inward flux of SWR at that altitude (a value between 162 and 240 W/m2 which increases with altitude). We can calculate OLR-DLR for any input temperature profile (say one from observations). Convection must be providing the rest of the needed outward flux of heat. That is radiative-convective equilibrium (at least as I understand it).

If the temperature at a particular location is not assumed to be in a steady state, then the temperature will rise or fall when convection doesn’t deliver the appropriate upward flux. Falling local temperature tends to: 1) promote convection from below (via a less stable lapse rate from below), 2) suppress upward convection from the location, and 3) suppress radiative cooling. Rising local temperature does the opposite. These tendencies gradually restore local radiative-convective equilibrium. So the concept can be applied to steady state and non-steady state situations.

At altitudes where the atmosphere is too optically thick for the necessary outward flux to be maintained by solely by net outward LWR, the lapse rate with be determined by convection. When the atmosphere becomes optically thin enough that convection is no longer needed, we say that atmosphere is in a radiative equilibrium and has lapse rate that can be calculated from first principles. The tropopause marks the altitude where convection is no longer needed.

• on May 25, 2015 at 1:45 pm | Reply DeWitt Payne

Chic,

Radiative transfer is about as bullet proof as anything in climate science can get. The properties of the absorption/emission lines of H2O, CO2 and the other radiatively active ghg’s have been measured in the lab and in the field. They have also been calculated using quantum mechanics from first principles, ab initio. The database containing this information, HITRAN, was originally started by the Air Force as a research tool for imaging and heat seeking missiles. The radiative transfer equation is about as solid as F=ma. Calculated atmospheric emission spectra have been compared many times to measured spectra with agreement on the order of 1%. The same theory is used to calculate atmospheric temperature profiles from satellite measurements of microwave emission from oxygen near 60 GHz.

If you’re really serious, you should buy Grant Petty’s A First Course in Atmospheric Radiation. It’s only \$36 direct from the publisher.

There are simple one dimensional radiative convective models, but they don’t actually calculate convection, you set a limit for convective stability. You can start out with about any surface temperature and air temperature and they will converge to a temperature profile that looks very much like the standard average profile based on measurements. Beyond that, you must have a full bore Air Ocean General Circulation Computer Model. There is no in between conceptual model.

The general assumption is that the current atmospheric profiles for different regions happen for a good reason even if we can’t say why with high confidence and that a perturbation of a few degrees won’t change them much.

51. on May 26, 2015 at 12:34 am | Reply Chic Bowdrie

Frank,

Evaporation above a body of water would produce less dense air capable of generating its own convection even with an otherwise stable temperature profile (no wind or excess solar insolation etc.). Cooler denser and less humid air will displace the saturated air. Otherwise your brief description of a “very complicated process” seems straight forward. I’m curious why you noted that climate change and IPCC are not mentioned in Petty’s books.

In your later comment you write, “Convection must be providing the rest of the needed outward flux of heat. That is radiative-convective equilibrium (at least as I understand it).” This is the reason a dynamic model would be helpful, so we can understand the radiative-convective dance. There is no static equilibrium in the real world. A dynamic model can eliminate the wind, etc. and just focus on a column of air subjected to a daily dose of sun. The initial conditions will eventually transition into final values that repeat every day. This should allow greater insight into when, where, and how much convection contributes to the heat transfer process.

DeWitt,

I don’t know what I don’t know, but I do know atmospheric physics is complex. I’m just not satisfied with hand-waving conceptual explanations such as Frank and I discussed. Thanks again for the references, in case I start working on my own dynamic model.

• Chic wrote: “I’m just not satisfied with hand-waving conceptual explanations such as Frank and I discussed.

“Hand-waving” hurts, but perhaps it is accurate given the limitations of fluid mechanics. I’d love to read a better explanation, if you ever find one. I struggled with the incompatibility of radiation (W/m2) and convection (degK/km). FWIW, you can track convection of latent heat in the real world by the amount of precipitation that falls. The global average is roughly 1 m/year (1 m3/m2/yr) and that can be converting into W/m2 (with some uncertainty since some comes down as ice, rather than liquid water.) IIRC, the KT energy balance diagram gets its value for latent heat from such a calculation. Simply heat is a fudge factor (“consistent with other data) that makes the radiative imbalance agree with estimates from ARGO)

• on May 27, 2015 at 10:11 am Chic Bowdrie

I hope you aren’t taking the hand-waving remark as a criticism. Everybody does it and it is one of the ways we learn from each other. Not everyone has the time or expertise to do the elaborate maths that SoD provides.

I should probably just leave it at that, but then you suggest convection has units of degK/km. That is a temperature distribution. Convection moves energy through the atmosphere and therefore has to have units of W. Precipitation would account for some convection, but wouldn’t there still be much convection occurring even during periods of clear skies?

• Chic wrote: “I’m curious why you noted that climate change and IPCC are not mentioned in Petty’s books.”

Climate change and the IPCC are politicized. Get your atmospheric physics and chemistry from someone like Petty who doesn’t over-simplify or distort so that we can all understand/fear the potential looming danger.

SOD once recommend a book called “Elementary Climate Physics”. It has a worked example with a rising characteristic emission level predicting 18 degC warming from 2XCO2! I still haven’t figured out what assumptions permitted this travesty. I also have an aversion to presenting models of the earth with isothermal optically thick layers, which magically emit blackbody radiation from both sides, but don’t have any mechanism (i.e. a temperature gradient) that allows energy to pass through the layer. I have enough trouble figuring out what to believe without having to doubt my reference books.

When you move from atmospheric physics and chemistry to the more complex subject of climate change, you can’t avoid the possibility of bias.

Unfortunately, material from the skeptics is even less reliable.

Grant Petty has nothing to sell – except his passion for clearly explaining atmospheric physics and chemistry and a great price.

• Chic,

Saturated air at 30C contains 4.2% water vapor. That reduces the density 1.6% from that of dry air. The same reduction is obtained by raising the temperature by about 5C. The heat used to evaporate water from 0% to 4.2%, would raise the air temperature by nearly 100C. Thus evaporation is not a important factor on driving convection, rather the contrary. In practice the differences in humidity are much smaller, but the ratio remains the same.

From the point of view of modeling it’s important to notice that radiative heat transfer can be calculated reliably and reasonably accurately, when the state of the atmosphere is known. The relationship between the temperature profile and the strength of convection goes in the way that small changes in the temperature profile lead to large changes in the strength of convection when the adiabatic lapse rate is locally exceeded. Combining these two observations we can conclude that we can calculate most directly
– the temperature profile and

Furthermore we can estimate the total energy transfer from the power of heating of the surface.

The strength of convection can then be deduced by subtracting radiative energy transfer from the total energy transfer. Trying to do it in other ways is bound to be much less accurate than this approach.

As has already been discussed, the lapse rate is well determined by known physics, wherever vertical convection takes place. Diurnal and other temporal variation as well as spatial variability at all scales from tens of meters to thousands of kilometers are another major complication as is also horizontal mixing and all other weather related phenomena. This kind of complexity seems to lead to the typical value of 6.5 C/km for the environmental lapse rate, but deriving the value by a model calculation is surely very difficult, perhaps impossible based on present knowledge.

• on May 26, 2015 at 9:13 pm Chic Bowdrie

Pekka,

It’s not a matter of whether humidity or temperature is more important. Any perturbation of an equilibrium temperature profile may result in convection. I think I follow what you’re saying about energy flux constraining convection, but it’s no consolation if my ultimate goal is understanding the process rather than having an ax to grind. I look forward to reading the comments of Isaac Held. Thanks.

• on May 26, 2015 at 6:33 pm Chic Bowdrie

Hi Pekka.

Are you sure the air temperature has to change during evaporation? If so it wouldn’t be called latent heat. Evaporation takes heat out of the surface. The energy is transferred, but there’s no change in T. It’s like a phase change. I don’t do climate science, but if there was any doubt about a principle as basic as this, I would be headed to the lab to experiment right now.

You are in agreement with SoD on the impossibility of modelling convection dynamically if that is what you are getting at. I’m not interested in calculating lapse rates or OLR as a function of atmosphere composition. I’m proposing to use the parameters we know, DSR, OLR, atmosphere composition, heat capacities, etc. with the equations we know to produce a dynamic model that illustrates how energy is transferred through the atmosphere. Static models are used all the time to explain how radiation works. It’s time to demonstrate, not just explain, how convection, evaporation, and conduction work in conjunction with radiation. Ignorance is not bliss.

• Chic,

The temperature need not change in evaporation, but the point I tried to make is that temperature gradients are much much more important in driving convection than the smaller mass of H2O as compared with N2 and O2.

The other point I tried to make is that one order of looking at the main variables is likely to be more productive than another. Specifically it’s very difficult to calculate convection from the equations of fluid dynamics like the Navier-Stokes equation, while constraining the strength of convection is possible based on estimated energy fluxes.

I propose that you read the latest blog post of Isaac Held and in particular his paper on the importance of understanding the basics in climate modeling. (Held gave the link to this paper in his answer to SoD.)

Held has written many posts where he discussed, what can be learned from general principles and simple models. That’s an important approach, but many essential issues remain poorly understood. The Earth system is inherently complex, and many of its features may be impossible to understand in any other way than using large complex models. That’s unfortunate, but that may be true.

52. on May 27, 2015 at 12:00 am | Reply Chic Bowdrie

From Isaac Held’s “The Gap Between Simulation and Understanding in Climate Modelling:”

“Conceptual research versus hierarchy development. A theoretically inclined researcher might design and build a model for a particular purpose and then discard the model. The model is not intended, in many cases, to have life of its own, but is, rather, a temporary expedient. In the limiting case, the model is not fully described and the result not fully reproducible. Or, an existing model might be used in the same way, but with the focus on the concept, not on the model itself. I refer to this as conceptual research. Much of the best work with comprehensive models can be classified as conceptual, as can, for example, much of the paleoclimatic research with computationally efficient climate models of intermediate complexity. In this context the model is a useful tool that helps one think about the system and search for ways in which to interpret observations.”

“The health of climate theory/modeling in the coming decades is threatened by a growing gap between high-end simulations and idealized theoretical work. In order to fill this gap, research with a hierarchy of models is needed. But, to be successful, this work must progress toward two goals simultaneously. It must, on the one hand, make contact with the high-end simulations and improve the comprehensive model development process; otherwise, it is irrelevant to that process, and, therefore, to all of the important applications that are built on our ability to simulate. On the other hand, it must proceed more systematically toward the creation of a hierarchy of lasting value, providing a solid framework within which our understanding of the climate system, and that of future generations, is embedded.”

My desire for a conceptual dynamic model illustrating the synergism between convection and radiation is probably at the bottom end of Helm’s hierarchy of models. Somewhere somebody must have been there, done that. However, it would certainly be an improvement over the static radiation models front and center in most presentations of the greenhouse effect.

• Chic,

My desire for a conceptual dynamic model illustrating the synergism between convection and radiation is probably at the bottom end of Helm’s hierarchy of models. Somewhere somebody must have been there, done that. However, it would certainly be an improvement over the static radiation models front and center in most presentations of the greenhouse effect.

[Isaac Held is the author, not Helm].

The challenge is modeling convection – movement of the atmosphere. Lack of success in modeling this turbulent atmosphere isn’t because it isn’t seen critically important or because somehow climate science thinks “radiation is it”.

Convection has way more focus in climate science than calculations of radiation. Interested people reading basic explanations of the greenhouse effect will obviously see a lot about radiation because it – along with the lapse rate – are the key determinants of the basic greenhouse effect.

Actual climate science research efforts have a completely different focus from presentations of the building blocks of basic science to the public and enthusiastic climate science amateurs.

Radiative-convective models – such as Thermal equilibrium of the atmosphere with a given distribution of relative humidity, Manabe & Wetherald (1967) and Climate Modeling through Radiative-Convective Models Ramanathan & Coakley (1978) – are perhaps the simplest step forward. These rely on the observation that when the temperature profile reaches a certain point, convection is initiated. In the tropics the calculated adiabatic lapse rate is quite close to the actual measured lapse rate.

All models of atmospheric circulation require parameterizations. There are many thousands of papers on the subject of atmospheric circulation. Held himself has made some great contributions. You can see the kind of work in a paper like Nonlinear axially symmetric circulations in a nearly inviscid atmosphere, Held & Hou (1980), or from another well-known author in Baroclinic Instability, Pierrehumbert & Swanson (1995). These papers -and pretty much every paper on atmospheric circulation – unfortunately jump straight into intensive maths.

If you are interested in gaining understanding of the topic I recommend An Introduction to Dynamic Meteorology, James R. Holton. First I recommend reading a more introductory book on fluid dynamics that derives and explains the Navier-Stokes equations. I think Holton’s book is excellent although it is a little too difficult for me. I was never able to really get an understanding of conservation of potential vorticity although I am determined to give it another go.

• on May 27, 2015 at 10:17 am Chic Bowdrie

Good stuff. Of course I’m interested in gaining understanding. I just don’t have the time right now. If you have, please give it another go. Your blog is a great classroom.

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