### Learning from a simple model

Filed under: — gavin @ 10 April 2007

A lot of what gets discussed here in relation to the greenhouse effect is relatively simple, and yet can be confusing to the lay reader. A useful way of demonstrating that simplicity is to use a stripped down mathematical model that is complex enough to include some interesting physics, but simple enough so that you can just write down the answer. This is the staple of most textbooks on the subject, but there are questions that arise in discussions here that don’t ever get addressed in most textbooks. Yet simple models can be useful there too.

I’ll try and cover a few ‘greenhouse’ issues that come up in multiple contexts in the climate debate. Why does ‘radiative forcing’ work as method for comparing different physical impacts on the climate, and why you can’t calculate climate sensitivity just by looking at the surface energy budget. There will be mathematics, but hopefully it won’t be too painful.

So how simple can you make a model that contains the basic greenhouse physics? Pretty simple actually. You need to account for the solar radiation coming in (including the impact of albedo), the longwave radiation coming from the surface (which depends on the temperature) and some absorption/radiation (the ’emissivity’) of longwave radiation in the atmosphere (the basic greenhouse effect). Optionally, you can increase the realism by adding feedbacks (allowing the absorption or albedo to depend on temperature), and other processes – like convection – that link the surface and atmosphere more closely than radiation does. You can skip directly to the bottom-line points if you don’t want to see the gory details.

#### The Greenhouse Effect

The basic case is set up like so: Solar radiation coming in is , where is the albedo, TSI the solar ‘constant’ and the factor 4 deals with the geometry (the ratio of the area of the disk to the area of the sphere). The surface emission is where is the Stefan-Boltzmann constant, and is the surface temperature and the atmospheric radiative flux is written , where is the emissivity – effectively the strength of the greenhouse effect. Note that this is just going to be a qualitative description and can’t be used to quantitatively estimate the real world values.

There are three equations that define this system – the energy balance at the surface, in the atmosphere and for the planet as a whole (only two of which are independent). We can write the equations in terms of the energy fluxes (instead of the temperatures) since it makes the algebra a little clearer.

Surface:
Atmosphere:
Planet:

The factor of two for A (the radiation emitted from the atmosphere) comes in because the atmosphere radiates both up and down. From those equations you can derive the surface temperature as a function of the incoming solar and the atmospheric emissivity as:

If you want to put some vaguely realistic numbers to it, then with S=240 W/m2 and =0.769, you get a ground temperature of 288 K – roughly corresponding to Earth. So far, so good.

Point 1: It’s easy to see that the G (and hence ) increases from S to 2S as the emissivity goes from 0 (no greenhouse effect) to 1 (maximum greenhouse effect) i.e. increasing the greenhouse effect warms the surface.

This is an extremely robust result, and indeed has been known for over a century. One little subtlety, note that the atmospheric temperature is cooler than the surface – this is fundamental to there being a greenhouse effect at all. In this example it’s cooler because of the radiative balance, while in the real world it’s cooler because of adiabatic expansion (air cools as it expands under lower pressure) modified by convection.

Now what happens if something changes – say the solar input increases, or the emissivity changes? It’s easy enough to put in the new values and see what happens – and this will define the sensitivity of system. We can also calculate the instantaneous change in the energy balance at the top of the atmosphere as or changes while keeping the temperatures the same. This is the famed ‘radiative forcing’ you’ve heard so much about. That change (+ve going down) is:

where are the small changes in solar and change in emissivity respectively. The subscripts indicate the previous equilibrium values We can calculate the resulting change in G as:

so there is a direct linear connection between the radiative forcing and the resulting temperature change. In more complex systems the radiative forcing is a more tightly defined concept (the stratosphere or presence of convection make it a little more complex), but the principle remains the same:

Point 2: Radiative forcing – whether from the sun or from greenhouse gases – has pretty much the same effect regardless of how it comes about.

#### Climate Sensitivity

The ratio of is the sensitivity of to the forcing for this (simplified) system. To get the sensitivity of the temperature (which is the more usual definition of climate sensitivity, ), you need to multiply by i.e. . For the numbers given above, it would be about 0.3 C/(W/m2). Again, I should stress that this is not an estimate for the real Earth!

As an aside, there have been a few claims (notably from Steve Milloy or Sherwood Idso) that you can estimate climate sensitivity by dividing the change in temperature due to the greenhouse effect by the downwelling longwave radiation. This is not even close, as you can see by working it through here. The effect on due to the greenhouse effect (i.e. the difference between having and its actual value) is , and the downward longwave radiation is just , and dividing one by the other simply gives – which is not the same as the correct expression above – in this case implying around 0.2 C/(W/m2) – and indeed is always smaller. That might explain it’s appeal of course (and we haven’t even thought about feedbacks yet…).

Point 3: Climate sensitivity is a precisely defined quantity – you can’t get it just by dividing an energy flux by any old temperature.

#### Feedbacks

Now we can make the model a little more realistic by adding in ‘feedbacks’ or amplifying factors. In this simple system, there are two possible mechanism – a feedback on the emissivity or on the albedo. For instance, making the emissivity a function of temperature is analogous to the water vapour feedback in the real world and making the albedo a function of temperature could be analogous to the ice-albedo or cloud-cover feedbacks. We can incorporate the first kind of physics by making dependent on the temperature (or for arithmetical convenience). Indeed, if we take a special linear form for the temperature dependence and write:

then the result we had before is still a solution (i.e. ). However, the sensitivity to changes (whether in the greenhouse effect or solar input) will be different and will depend on . The new sensitivity will be given by

So if is positive, there will be an amplification of any particular change, if it’s negative, a dampening i.e. if water vapour increases with temperature that that will increase the greenhouse effect and cause additional warming. For instance, , then the sensitivity increases to 0.33 C/(W/m2). We could do a similar analysis with a feedback on albedo and get larger sensitivities if we wanted. However, regardless of the value of the feedbacks, the fluxes before any change will be the same and that leads to another important point:

Point 4: Climate sensitivity can only be determined from changes to the system, not from the climatological fluxes.

#### Summary

While this is just a simple model that is not really very Earth-like (no convection, no clouds, only a single layer etc.), it does illustrate some relevant points which are just as qualitatively true for GCMs and the real world. You should think of these kinds of exercises as simple flim-flam detectors – if someone tries to convince you that they can do a simple calculation and prove everyone else wrong, think about what the same calculation would be in this more straightforward system and see whether the idea holds up. If it does, it might work in the real world (no guarantee though) – but if it doesn’t, then it’s most probably garbage.

N.B. This is a more pedagogical and math-heavy article than most of the ones we post, and we aren’t likely to switch over exclusively to this sort of thing. But let us know if you like it (or not) and we’ll think about doing similar pieces on other key topics.

### 296 Responses to “Learning from a simple model”

1. 151
Steve Milesworthy says:

#109 I’m getting to grips with feedbacks, but in the Soden and Held paper it talks about “Planck” feedback of about 3.2W/m^2/K calculated from models. Where exactly is this measured, given that it is different (and lower) from the expected increase in G of about 5.5W/m^2/K.

[Response: That the longwave increase as temperature increases – i.e. what you would get just from the Stefan-Boltzmann . It’s slightly different in each model because the temperature distribution is slightly different, but those differences are not very significant. -gavin]

2. 152
J.C.H says:

{I would like to recommend that Buffalo Bill be posthumously recognized as a top-notch environmentalist. … Whales are big, do they flatulate alot? Everyone get your guns. It’s time to wipe out more species and save the planet from extinction! } – Comment by Harry Robertson

Partner, this town ain’t big enough for both of us.

The problem with your theory is very similar to the problem with the veggie lover theory of eating less beef – incompletely thought out.

On the whole, countries that don’t eat much meat tend to have more cattle, not less. To control a cattle population you need to kill them on a fairly regular basis.

The Buffalo Bills were dead enders. They worked their way to the unemployment line. My ancestors, along with other stockmen like them, brought in fine purebred bulls from England – Herefords and Shorthorns, etc. – and before long our bulls had knocked up enough cows to refill the vast prairies, from Texas to the Dakota territories, with tens of millions of tasty methane belching bovines. We quickly nullified your ancestors’ work.

I doubt elephants and whales produce much methane. It’s not the animal’s size that does it. I would bet a little goat produces a whole bunch more methane than an elephant or a whale.

If you think cow methane is a joke, you would be belching a mistake.

3. 153
Figen Mekik says:

Sorry for the naive question, but wouldn’t a salt greenhouse dissolve when it rains?

4. 154
The Wonderer says:

I would like to thank the commentator above (currently 138) who has shared with us proof that the greenhouse effect does not exist, thus saving many of us from unneeded worry and misdirected study. And I doubt anyone here is in a position to question the authority of someone who has the depth of knowledge to combine the shorthand notation of a chemist with that of a mathematician in a single post. Dennis, I would like to alert you to another important proof from 1934 ( here ), highlighting the impossibility of bee flight (reportedly originating from an engineer, no less). I desperately need someone who is willing to invest the time to alert everyone on the beekeeping blogs to this result, and I think you are just the right person for the job.

5. 155
The Wonderer says:

Marion (#149)

I am not making an argument as to whether engineers have more cranks in the ranks, but that when we have those crank engineers, it is not a result of insufficient math in school. Therefore, it is not any more dangerous for Gavin to put math in his posts. I now apologize to everyone for stoking this thread, and second Tamino’s request above to judge on the issues alone.

6. 156
Chuck Booth says:

Sorry that this is a bit off topic:

Re #132 Dr. Jorgensen-Petersen
As it turns out, the comments from Laurie David and Sheryl Crow about lake effect snow are supported by research from Colgate University:
http://www.sciencedaily.com/releases/2003/11/031106052121.htm

…at least in the short term. With further warming, lake effect snowfall may diminish:

7. 157
Jim says:

Re 149.

I will stoke it some. I am one of those pesky MS EE guys. So I guess calculus, multivariable cacl, ODE,PDE, Linear algrebra, complex variables, probability theory, numerical analysis, discrete mathematics thermodynamics, electromag field dynamics, static/fluid dynamics are not a broad spectrum of math eh? Don’t forget that CE/ME/EEs have to take organic chem, at least one quantum physics course, computer programming languages.(In my case ADA95, C, Fortan77/90, and micro assembly) We have to take all of this stuff before we can even take classes that deal with the major such as core EE and electives.

What you said is perposterous, and it is not like phsyics majors have to take any more math.

In any case every scientfic field has it share of cranks. To assume that one has more than any other is simply snobbery and is not true.

8. 158
steve says:

Question. I am somewhat confused by the Venus comparison. I thought that the CO2 warming was rather small, but amplified by a large water vapor feedback. If Venus had water to cause this enhanced greenhouse effect, but now does not have water, why didn’t the planet cool at least a little after all of the water was gone?

9. 159

[[In this model, only the CO2 is actually being heated, not the molecules around it]]

CO2 is part of the atmosphere. If it increases its energy, and heats up, it will radiate. Some of the radiation will go back to the ground. Some of it will be absorbed at other levels. But it’s silly to say only the CO2 will heat. Try heating just one color in a boiling pot full of oil paints.

Another way the CO2 can lose the new energy is by bumping into another nearby molecule — “collisional de-excitation.” That then speeds up the neighboring molecule. Since temperature is a function of molecular motion, this happening on a large scale means the whole local atmosphere heats up.

James, your model violates conservation of energy.

10. 160

[[Question: Why isn’t the equation for surface flux: S + 1/2*lambda*A = G, since half the atmospheric flux goes up and half goes down? ]]

Because the total energy radiated by the atmosphere (in this model) is 2 lambda A, not lambda A.

11. 161

[[#121 …why is the radiation condidered spread out evenly when in reality it does not? The very reason for Climate/Weather is a differential in temperature , pressure driven by diurnal effects and the strength of solar radiation at every given location. A philosophical question so to speak, just exploring the meaning of this ‘spread the energy evenly about idea.’.. I would rather enjoy equations dealing with the dark side of the Earth and one with only the bright side. Applying 1/2 a sphere with T^4=S/(SBconstant *(1-0.5*lambda))gives interesting results,applying it to the dark side does not give any result. I really like simple models /equations as concepts explaining things, if well written they have great impact on spreading out knowledge of climate science. …..This is another great post! ]]

The model is averaged over time. You can consider a lit day side and a dark night side, but it doesn’t apply entirely because there’s a little bit of thermal inertia. Long-term averaging seems to work better.

12. 162

[[Interesting gas vs. solid discussion. When does a gas become dense enough to act like a liquid/solid? What is the surface of the Sun, e.g? ]]

Gas starts acting like liquid when, either due to low temperature or high pressure, or both, the non-zero size of the atoms or molecules affects their motion. The ideal gas law assumes atoms/molecules which are mathematical points.

Liquids become solids when the individual particles can’t easily move around or through one another any more.

I think the surface of the sun is a gas. (Jumpin’ Jack Flash, it’s a gas gas gas!)

13. 163
John Mashey says:

re: engineers
“But frankly, engineers have given the world more than their share of cranks”

This is a mathematical statement: of the population of cranks, a higher percentage are engineers than the percentage of engineers in the overall population. The cited evidence seems insufficient to support this … assuming that one can define a crank.

From a 2001 poll, 28 percent of respondents believed in astrology, 52 percent didn’t, and 18 percent weren’t sure…
http://www.nsf.gov/statistics/seind02/c7/c7s5.htm
I’m not sure where the line is crossed from “Read the horoscopes” into astrology crankhood, but it would nor surprise me if there were more of the latter than there are engineers in the US :-).

While anecdotes are not good statistics, I’d observe that few disciplines are immune from crankhood, including physicists & chemists:

– William Shockley, physicist (Nobel for transistor) … then race, eugenics

– Linus Pauling, quantum chemist (Nobel for chemical bond research, plus Nobel Peace prize) … then off into Vitamin C (I have no strong opinion about potential efficacies of Vitamin C, but it is clear that Pauling’s strength of belief in it got way ahead of any evidence).

– John Mack (Harvard MD/psychiatrist) – UFO abductions

– Frederick Seitz, Fred Singer, William Nierenberg, Robert Jastrow [all physicists] … then George C. Marshall Institute, SEPP, etc…

In any case, at least based on the sampling from various blogs, it’s not clear to me that either scientists or engineers have more than their share of cranks compared to people with minimal technical background, but when they are, they tend to be more visible and get quoted as authorities. If you read CSICOP’s “The Skeptical Inquirer”, many of the crank ideas come from people neither engineers nor scientists.

re: James Hogan (whose SF stories I’ve often enjoyed): I once took him over to Silicon Graphics to see the current state of immersive visualization, and then went out to dinner. He of course has not worked as an engineer for a long time, but has a positive fascination with offbeat theories … which of course, can be a good source for story ideas.

14. 164
Steve Bloom says:

Re #s 134/7: Just to clarify, Real Clear Politics is a wingnut site and the author has long-time associations with the Ayn Rand “Objectivist” school of libertarianism, which latter seems to have decided that Lysenko knew something when it comes to the science (in that any science that has implications conflicting with their ideology must perforce be wrong). Snark aside, I don’t think these right-wing echo machine pieces by non-scientists are worth responding to.

15. 165
James says:

Barton,

That is the point. In the model where CO2 radiates the same energy as it receives, only the CO2 heats up. This is because CO2 will absorb and radiate in precisely the frequencies that it can absorb and radiate, and no others.

I didn’t actually propose a model. I said that the Boltzmann distribution needs to be used for a gas. The Boltzman distribution is based on a collisional distribution of states. If the gas radiates all of the energy it receives, thermodynamics is violated.

This assumption was built into Gavin’s model, which, as he stated, is only a very rough model, so I’ll give him no further grief about it.

If, as I said, a considerable amount of the energy is distributed into gas motion, which is unavailable to the solid, then the gas will radiate less energy than it receives. Try out the absorption and radiation model, but scale the reemited energy by a factor on the order of 10^-7. This provides a more realistic idea of the background radiaiton contribution of CO2.

This does not consider additional absorption by the rotational wings of the bands, nor absorption by the numerous CO2 combination bands which are not saturated.

The energy remaining in the spectrum that can be absorbed by CO2 dwarfs any warming effect of reradiation.

And yes, only if CO2 discards the vibrational energy it receives by collisional deactivation can it heat its surroundings. It does indeed do this quite effectively. The surroundings are warmed, and the radiaiton from CO2 is reduced dramatically. Remember that energy from the excited bending mode can either be reemitted, or it can be collisionally distributed to warm the atmosphere. Doing both is a violation of conservation of energy.

[Response: But what is your point? More complicated models (i.e. GCMs) conserve energy – the radiation absorption by GHGs adds to the layer temperature, just as the radiation from the layer is a cooling term. The net radiation budget is not closed (since temperature changes can occur due to multiple effects – latent heat release, advection, convection etc.) but the net effect of atmospheric absorption has impacts very similar to that shown above. Your point would only be a fundamental flaw if the resulting behaviour once you include these effects was completely different. It’s not. – gavin]

16. 166

#145 Robin, Thanks again, I did see much longer string equations from a GCM model or two, the standard simplifcation given by Gavin helps describe the entire climate system relatively well, but It is solar centric, much rather see an equation recognizing the atmosphere itself as a heat source, independent of solar input, the atmosphere is warming the dark polar regions, there is a great misunderstanding of it, I give you one example: 2005 , At about the time when NASA, Hansen and NOAA declared 2005 as going to be the warmest year in history, NOAA seasonal forecast came out with a very cold winter 05-06 projection, prompting amongst other things a spike in fuel costs, history showed the winter of 05-06 quite warm except for Central Russia (and some parts of Europe), on what basis does the warmest year in history cools down faster in darkness? Heat radiation in darkness needs simplifications. Even in near isolation, somehow Isolated from weather systems which were warmer, as with March 2007 for North American Arctic, with little or no advection from the South, the atmosphere maintained a warm surface temperature at about -46 C (High Arctic) at the coldest peak of the coldest North American Arctic air mass in years. I somehow doubt that the High Arctic got a great piece of that heat transfer process from locations having direct solar radiation, at least not on the surface.

17. 167
James says:

The point is that we can put a limit on the total warming by CO2.

Once radiant energy is absorbed by CO2, fractionally a very small part is reemited. That reemited portion will be slowed in its escape to space if CO2 concentrations increase, similar to putting more rungs in a ladder. If the reemitted portion is large enough, than it will be a controlling factor in temperature, and will continue to increase temperature regardless of band saturation. My point is that the reradiated portion is very small relative to the absorbed and not reradiated energy. This provides a limit for total CO2 warming.

The larger portion of the absorbed energy will not be emitted to space by CO2. It’s residence time in the atmosphere will be roughly determined by the speed with which it can travel through the atmosphere mechanically, something on the order of the speed of sound in a particular layer of atmosphere. Increases in this component lead to much larger T effects, but fortunately can be bounded by the absorption spectrum.

Basically, looking at the current absorption spectrum, and subtracting it from a fully saturated absorption spectrum, should provide an amount of energy roughly equal to what is left for CO2 to absorb and dissipate as heat.

[Response: This doesn’t follow at all. There are multiple emitters/absorbers in the atmosphere and radiative cooling (by clouds, water vapour and CO2) occurs whatever the temperature the air is. This cooling is a very large part of the emission to space and that is certainly not a minor effect. The only limit you could conceivably get would be if all of the CO2 absorption bands and their fringes were saturated. But they aren’t, and Venus demonstrates quite adequately that any effective limit on CO2 forcing is significantly warmer than anything we’d really like to deal with (not that that is likely on Earth). -gavin]

18. 168
Pat says:

Re 123 – (echoing 159) – I attempted to calculate a likely ratio of collision frequency to photon absorption/emission frequency, and found it quite high, at least below 100 km (where almost all of the atmosphere is). This suggests that molecular collisions are frequent enough that CO2 will be at essentially the same temperature as the air containing it.

(If 300 ppm CO2 in air were able to absorb or emit 0.05 W/m2 along a path length of 1 kg air/m2 (that would be 1 meter path through air at a density of 1 kg/m3, or a 10 meter path through air at a density of 0.1 kg/m3, etc.) (in the band centered at 15 microns), this would mean that for every absorption or every emission of a photon by CO2, there would be around 16 trillion collisions with another molecule at the surface (around 100 million collisions per second), or around 1.6 million at 100 km height (around 1000 collisions per second).

Even if at 300 ppm CO2 the entire blackbody radiation at 300 K (just under 460 W/m2) in a path of 1 kg air/m3 (I’m pretty sure that’s far more opaque than CO2 actually is), the ratio of molecular collisions to photon absorptions by a CO2 molecule would be 1.6 billion at the surface and 160 at 100 km.

19. 169
James says:

Basic difference between the absorption and dissipation vs. absorption and reemission.

Increasing absorption and dissipation provides primarily a decrease in the escape of radiation from the planet’s surface to space. This effect is acting on the lambda G component of the model.

Increasing absorption and reemission increases the residence time of the radiation absorbed. The excited state lifetime of the CO2 molecule is rather long compared to how long the photon remains unabsorbed once emitted. Multiple absorptions and reemissions lead to increased residence time of the energy in the atmosphere. Emitting in all directions also slows escape to space. This is acting on the Lambda A component of the model.

If the lambda A component of the model is on the same order of magnitude as the lamda G, it can quickly dominate. The excited state population for a particular gaseous state can be described as a percentage of the total gas molecules in the sample. Doubling the sample (or the CO2 concentration in this case) will double the number of excited molecules. The excited molecules are candidates for emission or collisional deactivation. Based on the state of the sample, the number of excited molecules that survive to emission is also a percentage of the total number of excited molecules. What happens here is that because both the number of excited molecules and the number of emitting molecules are based on a percentage of the whole, if you double the number of molecules, you will double the emission.

Obviously, both effects happen simultaneously, but considered separately, a doubling of the CO2 concentration doubles the emission, the lambda A effect, while doubling the CO2 concentration does not double the lambda G effect, which follows a log relation.

If the lambda A effect is on the order of the lambda G effect, then it becomes very large and is controlling. If the lambda A effect is orders of magnitude smaller than the lambda G effect, then it will not be significant.

20. 170
Pat says:

Re 165,167

You seem to be focusing on the immediate aftermath of a photon absorption. True, most of the radiant energy absorbed by greenhouse gasses will be redistributed by collision before it can be reradiated – after one time step wherein a population of photons are absorbed by a population of molecules.

But that just heats the air. By collision, the temperature of CO2 will tend to be the same as that of the air, and it will emit photons thermally. The lack of heat resulting from this emission is again redistributed by collision, cooling the nongreenhouse gas molecules.

The same goes for greenhouse agents in general – clouds, etc. – and also for SW radiation (solar radiation) absorption in the air. The transparent component of the air just adds heat capacity – you could think of it as attaching a pool to a lake. water can be flow into the pool and out of the pool by hoses (absorption and emission); flow between the pool and the lake causes the water level to move more slowly in response to an imbalance in inflow and outflow in the hoses than it otherwise would (heat capacity).

Yes a gas will have different radiative properties than a solid or liquid, but this just changes the emissivity and absorptivity – you can still multiply emissivity by the blackbody radiation to find the emitted radiation (do this as a function of wavelength to reduce emissivity’s dependence on temperature), assuming local thermodynamic equilibrium, which is accurate in the vast majority of the atmosphere for the vast majority of the energy involved.

(visualization – each molecule in a population of like molecules can be assigned a (wavelength-dependent) cross section – an absorption cross section (equal to the emission cross section if the population of molecules is in LTE), and if necessary a scattering cross section. What this means is that, averaged over time, each molecule acts as a sphere with a cross sectional area (through the great circle of the sphere) which can absorb radiation from any direction proportional to the intensity of the radiation * the (absorption) cross sectional area, emit as a blackbody from the surface of this sphere (emission cross section), and scatter light intercepted by the sphere defined by the scattering cross section. (PS scattering cross section + absorption cross section = extinction cross section.)

Over a short enough distance that the path is nearly transparent, cross sections of each kind add linearly, but when emission and extinction become significant, there will be significant overlap as molecules block each other (from the viewer); over longer and longer distances the cross sections fill in the holes and emissivity approaches 1; absorptivity + scattering (as in a kind of diffuse reflection) approaches 1, transmission (from the other end) approaches 0.)

21. 171
James says:

I’ll try this again.

CO2
~300K
1 atm
15 micron bending mode
Boltzmann distribution, roughly 4% excited

400 ppm CO2
16 ppm excited bend of CO2

Only excited CO2 can emit.
1 atm pressure
about 10^5 collisions of CO2 in the spontaneous emission excited state lifetime

Of the excited CO2 molecules, roughly 1 in 10^5 actually emit a photon, the rest collisionally deactivate.

400 ppm CO2
16 ppm excited bending mode
16 x 10^-5 ppm emitting

In the field of a blackbody at 300K and 1 atm pressure of air, the emission from CO2 is several orders of magnitude smaller than the absorption. The difference is made up collisionally. CO2 will not emit radiation at the same rate as the solid, because it has many more modes of kinetic energy available to it then the solid has.

In the above example, 800 ppm CO2 will have twice as many photons generated, but the absorption of planetary radiation will not double because it is governed by a log dependence.

[Response: This is irrelevant. Any additional absorption will increase the mean temperature of the layer, which will cause an increase in emission from all radiating components (clouds, water vapour, and yes, CO2). -gavin]

22. 172
Pat says:

Re 168 (last paragraph)- I rounded the blackbody radiation at 300 K up to 500 W/m2 to get a factor of 10,000, I forgot to note that.

(For the following – did I already post this – I had left my computer for a while after typing something similar and then it was gone and I don’t remember what I did with it – sorry if this is redundant:)

Re 166,167:

You seem to only be looking at the immediate effect of a population of photons being absorbed by a population of molecules. Yes, molecular collisions redistribute energy from absorbed photons from the absorbing molecules to the entire local population of gas molecules. But as the emitting molecules as a population have the same temperature as the other molecules because of those collisions, they can thermally emit radiation as they would at that temperature. And the loss of energy by emission is also redistributed among the other molecules.

The transparent component just adds its heat capacity to the process; the radiation emitters and absorbers allow energy to be gained or lost until the temperature approaches equilibrium, while the redistribution of energy among the other components means that the process happens with the heat capacity (energy per unit change in temperature) of all components present (generally including even nongaseous components, some of which may be absorbers, emitters, and/or scatterers).

PS for those of you with a few hours of free time on your hands – with the essentially accurate assumption of LTE (local thermodynamic equilibrium), I attemped an in depth description of the greenhouse effect and atmospheric radiation (among some other things) here:
http://blog.sciam.com/index.php?title=liveblog_james_hansen_can_we_still_avoid&more=1&c=1&tb=1&pb=1&cat=19
(starting at November 25; you can stop when you get to “January 19, 2007 @ 22:59” – or you can stop earlier, of course)

23. 173
William Astley says:

I do not see how the simple model disproof’s, Warwick Hughes’ methodology to estimate the earth’s sensitivity to a change incoming radiation & back radiation. (See link attached below for Hughes’ data and thoughts. Also note that Hughes does not differentiate whether the back radiation is from GHG, or other molecules in the atmosphere. Also note Hughes includes incoming solar radiation.) Can the planet be treated as a black box where the variable is X (solar incoming radiation plus back radiation) vs Y planetary temperature? (See next comment and paper for details concerning the Global Mean Energy Budget.)

Comment:
There is a significant amount of energy that is transferred from the earth’s surface to higher regions of the atmosphere by thermals and latent heat. See my next question.

http://www.warwickhughes.com/papers/idso98.htm

Also, I do not understand why the simple model does not include the estimated 24 W/m2 for thermals and 78 W/m2 for the latent heat of water that is evaporated at the earth’s surface and then is condensated higher in the atmosphere (See the link to Kiehl’s paper “Earth’s Annual Global Mean Energy Budget”, below, page 206 of his paper.) As oceans cover roughly 70% of the earth’s surface would there be an expected increase in evaporation that would partially offset an increase in back radiation due to a GHG increase or an increase incoming radiation due to a decrease in cloud cover?

[Response: Idso’s experiments all involve random temperatures divided by random fluxes – all at the surface and none related to global long term feedbacks – they have absolutely no relevance to climate sensitivity as normally defined. There were whole journal issues devoted to pointing out the flaws in Idso’s arguments (Climatic Change for instance). -gavin]

24. 174
Geoff Russell says:

Regarding #152 which doesn’t belong in this thread, but I
suppose two wrong postings cancel out ;) J.C.H states — “On the whole, countries that don’t eat much meat tend to have more cattle, not less. To control a cattle population you need to kill them on a fairly regular basis.”

If by “on the whole” you mean India, then this is probably true, but the
top 5 countries with the biggest cattle populations are (in order):

Brazil, India, China, US, and Argentina.

The top 5 cattle meat producers are (in order):

US, Brazil, China, Argentina, Australia.

India is the 10th biggest producer of cattle meat.
Partly this is because its animals are small — average carcase weight
103kg. The average US carcase weight is 347kg. All
this data is from the FAO database.

When the wool price crashed in the 90’s Australia reduced its sheep flock from
160 million to about 110 million — this lead to a large regrowth of what
we call ‘scrub’. Australia will meet it Kyoto targets, and the only sector which
has made significant emissions saving is “land use change” and all that
regrown scrub is a big part of that — I’m currently trying to work out
exactly how big. The bottom line here is that livestock reduction can
be an effective source of emission reductions. It involves no new technology,
and has an immediate impact on forcings. Livestock reduction works on
many levels, reduced methane, increased (re)afforestation, and reduced fossil
fuel emissions.

25. 175
Fred Mann says:

Hello,
I know this is slightly off topic, but I was wondering if someone could point me to some articles (this site or others) which you feel best describe the consequences of global warming. Obviously, the most important thing to consider with regards this issue is the EFFECT of global warming on mankind, and not the warming per se.
Ideally, I would like to see verifiable/verified predictions of how GW will impact our lives — i.e. what crops will be harmed and when/where, how high will sea levels rise, which species of plants/animals may be threatened and which species may be HELPED (I’m assuming it can’t be bad for everyone/everything), etc.
Thanks,
Fred Mann

26. 176
Tavita says:

Re: 118 “Plus, I know I’m being a heretic here, but what exactly did you find wrong with Lindzen’s statement? Certainly not all of it…”

How about most of it? The main premise is that things won’t be so bad due to global warming, but this is in the face of overwelming evidence to the contrary in the most recent IPCC report

http://www.ipcc.ch/SPM13apr07.pdf

and in a report by a group of generals and admirals who cite serious national security concerns.

http://news.yahoo.com/s/ap/20070415/ap_on_sc/warming_security

http://securityandclimate.cna.org/

For instance,

* Projected climate change poses a serious threat to America’s national security.

* Climate change acts as a threat multiplier for instability in some of the most volatile regions of the world.

* Projected climate change will add to tensions even in stable regions of the world.

* Climate change, national security and energy dependence are a related set of global challenges.

In particular, with regard to the potential negative effect on the economy that Lindzen basicly cites as a reason to do nothing,

Gen. Anthony “Tony” Zinni, Bush’s former Middle East envoy, one of the authors of the report, said,

“We will pay for this one way or another,” wrote Zinni, former commander of U.S. Central Command. “We will pay to reduce greenhouse gas emissions today, and we’ll have to take an economic hit of some kind. Or we will pay the price later in military terms. And that will involve human lives. There will be a human toll.”

Finally, this may be nit picking, but for Lindzen to cite the late Roger Revelle as saying that,

“the evidence for global warming thus far doesn’t warrant any action unless it is justifiable on grounds that have nothing to do with climate.”

seems rather disingenous to me since the good professor passed away in 1991. I would submit that the evidence “thus far” has changed just a bit since then.

27. 177

[[In any case every scientfic field has it share of cranks. To assume that one has more than any other is simply snobbery and is not true. ]]

Engineering is a professional field, but it’s not a “scientific field.”

28. 178
Lynn Vincentnathan says:

Re #138, well, it’s been over 40 years since I took college intro to physics & my memory is quite fuzzy, but if I recall (I think in the optics chapter), that when light goes through glass (or water) at an angle it sorta breaks up into different bands (like a rainbow), and something about the infrared section of light not being able to reflect back out through the glass (or water) as well, due to its wavelength being longer. And that’s the band of light that causes the (most) warming.

So what I understand, the GHGs sorta act like that glass & don’t let the infrared bands out as much, but reflect or deflect them back down to earth.

I’m probably totally totally off on this. My memory is extremely fuzzy.

29. 179
Phillip Shaw says:

Re #177,

BPL, you’re correct when you say that engineering is a professional field, not a scientific one. All I would add is that it is important to understand the dependency/synergy between engineering and science.

Engineering needs to be grounded in sound science to produce the amazing developments, such as PCs and air travel, that we take for granted. Poor engineering can usually be traced back to flawed understanding of the underlying science.

Science needs engineering to create the tools, such as satellites and particle accelerators, they use to advance our knowledge.

Without good engineers, scientists would not have journals to publish their papers in (no printing technology), or the internet we’re using for this dialog. Any scientists who feel engineers aren’t their peers are welcome to try to carry out their studies using only pencil and paper. Oops, both pencils and paper are products of engineering. They should try carrying out their studies by writing on animal hides with a burnt stick.

As you may have discerned, I’m an engineer.

Regards,

30. 180
Carol says:

RE #178: The light that comes from the sun has many wavelengths. Most of those wavelengths come through our atmosphere and bounce off of the surface of the plant. Green house gases don’t absorb all wavelengths, they only absorb very specific wavelengths, most of those being in what is called the infrared band. Carbon dioxide responds to a few bands, which are very narrow. Water vapor responds to quite a few bands. You can pretty much tell how much of the infrared gets absorbed in the atmosphere, by how much infrared leaks back out into space. Currently, our satellites pick up almost no infrared going out, so the carbon dioxide and water vapor is already absorbing all of the infrared that is hitting the earth. According to the FTIR spectroscopists, all of the infrared is being absorbed within about 100 feet of the surface of the planet.

31. 181

[[Without good engineers, scientists would not have journals to publish their papers in (no printing technology), or the internet we’re using for this dialog. Any scientists who feel engineers aren’t their peers are welcome to try to carry out their studies using only pencil and paper. Oops, both pencils and paper are products of engineering. They should try carrying out their studies by writing on animal hides with a burnt stick.]]

And let engineers try to get along for a month without the food raised by farmers.

The point stands — engineers are not scientists, and scientists are rightly pissed off when engineers call themselves scientists, especially when they go on to babble about how the scientists are all wrong about some well-established theory (evolution, global warming, relativity, quantum mechanics, etc.).

32. 182
Carol says:

Re #64: Warning here, I am an engineer, so I may not see things the same way as some of the pure scientists do . . .

Just out of curiousity: I hear that doubling the carbon dioxide will increase the temperature by a certain amount. If the carbon dioxide in the atmosphere is already saturated, then where will the extra infrared come from that will cause the temperature to increase? That is, if you compare carbon dioxide to being a very large sponge, and you are sopping up a tablespoon of water that was spilled, then what does it matter if you have a larger sponge? The amount of infrared that is coming into the atmosphere is a constant. Carbon dioxide already absorbs everything that it can from the wavelengths that it can absorb from. Why would the temperature increase?

[Response: Because it is not saturated. -gavin]

33. 183
Carol says:

RE #181 [engineers are not scientists, and scientists are rightly pissed off when engineers call themselves scientists]

You have it slightly wrong. Engineers are rightly pissed off when anyone calls them a scientist. And if the scientists are not doing their job (scientific method) of questioning everything, especially those well-established theories that everyone knows are right, then it falls to the engineers to enter into heated debate about these issues.

Arguing with an engineer is like wrestling in the mud with a pig. After a few hours, you realize the pig likes it.

34. 184
Hank Roberts says:

Wait!
Carol, re 180/178, you wrote:
“… Currently, our satellites pick up almost no infrared going out, so the carbon dioxide and water vapor is already absorbing all of the infrared that is hitting the earth. According to the FTIR spectroscopists, all of the infrared is being absorbed within about 100 feet of the surface of the planet.”

What’s this then? Infrared photographs from satellites are routine.
http://goes.gsfc.nasa.gov/pub/goes/first_g9ir.gif
http://weather.msfc.nasa.gov/irgrp/

Where did you read that “our satellites pick up almost no infrared going out, so the carbon dioxide and water vapor is already absorbing all of the infrared” and who are the “FTIR spectroscopists” you rely on?

http://www.realclimate.org/index.php/archives/2006/01/calculating-the-greenhouse-effect/#comment-7793

35. 185
Phillip Shaw says:

Re #181,

I am not disagreeing with you. Anybody, no matter how accomplished they may be in their area of specialization, is essentially a layman in matters outside their specialty. Perhaps a well-informed layman, but still a layman, and the professionals in any field are justified when they get irritated by pushy laymen. As Clint Eastwood said “A man’s got to know his limitations.”. Words to live by.

I have never called myself a scientist, nor am I aware of any of the hundreds of engineers I’ve worked with during my career calling themselves scientists. So I feel that’s a bit of a strawman.

My only point is that scientists and engineers are, in reality, a team. It is counterproductive for one element of a team to deride another. The reason I get irritated with comments such as #1 and #149 above are the explicit put-downs of engineers and the implicit elitism that scientists are superior and somehow removed from petty human foibles. There are as many cranks and egotists among scientists as there are in any cross-section of our population.

Engineeringly Yours,

36. 186
Hank Roberts says:

Note — trying to be thorough in replying, for the subsequent readers who may come along and need more help sorting out who claims what to be true.

“Carbon dioxide” +infrared +saturated +bands

The first is to the American Institute of Physics page, Spencer Weart’s comprehensive history (also linked in the sidebar).

The second is to the PR/advocacy site JunkScience.

AIP first — documented, you can read the footnotes and check this yourself:
The Carbon Dioxide Greenhouse Effect
http://www.aip.org/history/climate/co2.htm

“… The early studies … were measuring bands of the spectrum at sea-level pressure and temperature. Fundamental physics theory, and a few measurements made at low pressure in the 1930s, showed that in the frigid and rarified upper atmosphere, the nature of the absorption would change. The bands seen at sea level were actually made up of overlapping spectral lines, all smeared together. Improved physics theory, developed by Walter Elsasser during the Second World War, and laboratory studies during the war and after confirmed the point. At low pressure each band resolved into a cluster of sharply defined lines, like a picket fence, with gaps between the lines where radiation would get through.(24)
… theoretical physicist Lewis D. Kaplan …. In 1952, he showed that in the upper atmosphere the saturation of CO2 lines should be weak. [Bands are not saturated–hr] Thus adding more of the gas would make a difference in the high layers, changing the overall balance of the atmosphere. Meanwhile, precise laboratory measurements found that the most important CO2 absorption lines did not lie exactly on top of water vapor lines. Instead of two overlapping bands, there were two sets of narrow lines with spaces for radiation to slip through.(25)
(snipped from the AIP History page, link above).

Second Google hit with that search is to the PR/advocacy site, JunkScience.com.

I don’t provide links to junk PR sites myself, I don’t see any reason to increase their Google page rank when I’m pointing them out only to note that they’re bogus, not good info. Google doesn’t make that distinction when ranking number of links counted.

I’d imagine you know how to find them; I wonder if they’re your source for what you believe? If so, be skeptical of people who claim they’re on your side in politics.

Compare what they say there to the AIP history page. JunkScience is telling you — if it were the current truth —what the physicists knew a century ago.

Who ya gonna believe, the people who pretend they’re on your side, and feed you lies and spin? “Just because you’re on their side doesn’t mean they’re on your side.” — Teresa Nielsen Hayden.

37. 187
James says:

Gavin,

In fact it is quite relevant.

The starting point of some climatological models appears to be the “local thermodynamic equilibrium” argument, as understood by climate scientists.

This provides the postulate that to maintain thermal equilibrium, radiation absorption and emission between substances must be the same, the radiation cancels, and the substances remain in thermal equilibrium.

This model is incorrect, and not just by a little bit.

In fact, substances emit radiation characteristic of the state of the system.

The concept of requiring equal radiation for equal temperatures is based on Kirchoff’s laws from 1887. There is also Arrhenius’ writing in 1896.

Boltzman published his theory of the distribution of states in 1896, and committed suicide in 1906 because his theories were widely rejected by his peers.

S=klogW is written on his tombstone.

Max Planck published quantum theory in 1900.

Kirchoff’s laws work quite well for substances that are similar to each other, solids fall into this category due to the restriction of particle movement within them. Kirchoff, however, did not have the benefit of knowing the Boltzman distribution, neither did Arrhenius. Both brilliant men, but science progresses past the best of us eventually. Many folks thought physics was finished with Newton.

Two substances in thermal equilibrium will have the same average kinetic energy of the particles that compose them. If these samples are composed of the same substance, in the same state, then the radiation fields will also be the same. Otherwise, the radiation fields will not be the same.

It would be difficult perhaps to have two substances more different than solid and gas, particularly with respect to the distribution of energy within the phases.

Because gasses have orders of magnitude more mechanical motion available to them than do solids, the radiation field of a gas at the same temperature as a solid (thermal equilibrium) will in fact be orders of magnitude less than the radiation field of the solid.

It doesn’t really matter whether the gas receives its energy by radiation, or by collision. The Boltzmann distribution will prevail.

Moving up out of the atmosphere, the next layer of gas adjacent to the first one will be in largely the same state, and will therefore emit radiation just as its predecessor.

The big conceptual error occurs with the starting point of the model.

When the gas is in thermal equilibrium with the planet, it most emphatically does not have a radiation field anything like that of the planet. Hence my rough guess of decreasing lambda A by about seven orders of magnitude.

In fact, the emission from a gas is not dependent on same scaled function of T^4.

To calculate the emission from a gas requires knowledge of the state parameters of the gas. Any statement that a gas must emit what it has absorbed from the planet blackbody like radiation field is simply incorrect. Scaling the T^4 dependence is similarly incorrect. Such a model probably requires dynamic correction of the T^4 coefficient as the model falls outside of measured temperature values while tracking the radiation upward to higher altitudes.

Remember, you can model any data set an infinite number of ways, but most of these ways will be incorrect and will not lead to useful predictions. We can use an epicycle on epicycle model of planetary orbit, or we can declare the solar system center of mass to be somewhere in the sun instead of at the earth.

As several folks have pointed out, the CO2 excited by earth’s radiation field very effectively dumps its energy into the atmosphere, causing a warming effect.

For CO2 to then emit this same energy requires a reaccumulation of the energy in the CO2 excited mode. Clearly CO2 cannot emit from the ground state. The reaccumulation of any fraction of that original energy on the same order as that absorbed from the planet’s radiation field is entropically unlikely.

The gas will obtain the Boltzmann distribution at its T, which can be measured, and will emit based on that value and the collisional frequency.

You can try this at home. Go to your local gym. Drop a basketball on the floor. The ball will bounce successively lower, and then stop bouncing. Wait for the ball to spontaneously begin bouncing by gathering energy dissipated into the floor as heat. WHen the ball begins to bounce on its own by gathering heat from the floor, come back to your computer and post that absorption = emission because the ball and the floor are in thermal equilibrium.

[Response: With all due respect, LTE does not imply that “radiation absorption and emission between substances must be the same”, only that the energy of the all the molecules in the air mass is distributed evenly – something which is easily true up until the mesosphere and is related precisely to the much faster collisional losses vs. radiative losses. Looking at any GCM you would see clearly that net LW radiation is not zero in the atmosphere. The emission by GHGs in any layer is governed by the temperature of that layer, not by what the absorbed radiation is. You continue to confuse a pedagogical tool (which in any case could be easily adapted to include this effect), and GCMs which do this as correctly as possible. -gavin]

38. 188
Lynn Vincentnathan says:

#180 (re #178 & 138), you’ve said it better than I did, but the question raised in #138 was about whether GHGs are like real greenhouses, with similar principles involved. I sort of thought this might be the case, based on what I learned 40 years ago, but I may be wrong.

At any rate, the effect of GHGs is at least like a real greenhouse in that the world warms, as do greenhouses. But I’m unclear whether the actual mechanism of absorption and reflection of light is similar between the 2 (GHGs & glass).

Even if not, I still think “greenhouse effect” is a good metaphor, since it is easy to understand. We’ve all had the experience of a car with closed windows sitting in the sun being hotter than the outside temp.

And I also think “Venus effect” & “runaway warming” are okay metaphors for a hysteresis or limited runaway situation of positive feedbacks becoming predominant over negative feedbacks for some time (as happened on earth 55 & 251 mya & could happen again), even if earth cannot go into a permanent runaway condition (until the sun becomes much hotter billions of years from now). And I understand that even in the worst-of-the-worst-case scenarios, our current warming period would not extend beyond 100,000 years, maybe 200,000 years max, before cooling back down, and that this is very unlikely, though possible.

Metaphors are not perfect or exact, only suggestive, and are used as a short-hand for something that is difficult or complicated to explain.

39. 189

In a greenhouse, the gas keeps hot air from rising (i.e. it “inhibits convection”). That’s the main thing that keeps a greenhouse hot. In the atmosphere “greenhouse effect,” certain gases trap infrared radiation, heat up, and radiate their own increased heat back to the ground (as well as in all other directions). So it’s a misnomer. But at this point, the usage is too well-established to correct. I think some astronomers tried to get everybody to call it “the atmosphere effect” for a while, but they didn’t get anywhere.

[Response: If you keep the metaphor at the level of ‘the greenhouse/greenhouse gas reduces heat losses and keeps the surface warmer than it would otherwise be’, it works fine. As does the ‘blanket’ metaphor. All metaphors break down at some point and this one is as useful as can be expected. Nit-picking on whether the relevant heat loss is radiative or convective is really beside the point. – gavin]

40. 190
Jeremy says:

Is there a good place to read about quantitative questions on absorption
of infrared by CO2 and water vapour?

The kind of questions I have in mind are:

How close are we to saturation for the frequencies absorbed by CO2
(respectively, water vapour)?

What is the overlap?

As I understand it (correct me if I’m wrong!) it’s believed that on Venus
there was a runaway greenhouse effect involving temperatures rising to
the boiling point of water and all the water evaporating. But now the
atmosphere of Venus is almost all CO2 (??), so currently the Venusian
greenhouse effect is all due to CO2, and the temperature is something
like 735 K. I’m a bit confused about how that’s consistent with us
(Earth) being anywhere close to saturation of CO2 absorption and only
being around 300 K. I think Venus is less than 10% closer to the Sun
than we are: does that make such a big difference, or is there another
reason?

[Response: See here for a discussion about the overlaps on Earth: http://www.realclimate.org/index.php?p=142 – gavin]

41. 191
David B. Benson says:

Re #175: Fred Mann — See the IPCC report linked on the side-bar…

42. 192
43. 193
Dennis Brown says:

Hello, from the Nit-picker:
First, this site has an outstanding degree of solid facts and very knowledgeable people writing in and I enjoy reading the posts as well as the articles.
Global Warming is a misnomer – pure and simple. Like all such misnomers, it is irritating – like the term Big Bang for the “start” of the universe – it was neither big nor a bang (as quoted from others) so I guess we can or have to live with another one.
The article I read the original discussion on salt and glass green houses and the explanation about how these structures really stay warm was in the Science weekly magazine (published some time in the late 1980’s??? Sorry for the lack of a date.)

P.S. a calculation of the thrust/lift issue of a bee’s flight dynamic by using standard (non-critical) aerodynamic theory fails to capture the correct method that these amazing creatures exploit to achieve flight; yet I fail to see the relevancy of that keen observation has with my discussion of a valid point on the relevancy of “Green House” term but I guess, using the writer’s logic, I must conclude that they just don’t like bee’s.

44. 194
greg says:

I found this posting of great help in figuring out the whole climate change and the short lesson that Gavin gave is great and there should be more like it and allow people to work through and think about the debate and know for themselves what is total bull and not. I believe that people should discover things and idea. If more people would try to do just that the debate would be easier. thanks also the EDGCM people and staff it is a great program and look forward to using it with the youung adults I work with and mentor on science.

45. 195
Ken Coffman says:

I would appreciate comments about how effective Nitrogen is as a greenhouse gas. Thanks.

[Response: N2 is not a greenhouse gas at all. N2O (laughing gas) is, and human related increases mean it has a ‘radiative forcing’ of about 0.15 W/m2 (compared to about 1.6 and 0.6 W/m2 for CO2 and CH4 respectively). -gavin]

46. 196
Jim says:

Actually Barton, I think you are a little wrong with your line of reasoning, and it sounds alot like snobbery.

Someone here posted (I think it was you as a matter of fact.) that the difference between scientists and engineers was that scientists developed new ideas and engineers made products. That is a fallacy. I have known “scientists” that did engineering and engineers that did what you call “science”. I have worked with lots of each at LANL NHMFL so I have a good data sample to use. Also I worked with an engineer that worked on the Apollo spacecrafts at LANL. To say he did not do that for the love of science because he is an “engineer” is totally insane!

The educations of both are very very similar. You are implying that scientists by education are more savy than engineers. Sorry that does not compute as again the education and math/science backgrounds are almost the same.
In any case scientists are also “professionals” as they get paid for their work, just like engineers. I have never heard of physicists getting food stamps!

You don’t hear of biologists being good at physics and physcists being good at geology. Same as engineers. To say that a “scientists” can grasp concepts that are outside of their competency than engineers is wishful thinking considering the similarity of say physics and engineering.

This pig doesn’t like it when the cows say that he doesn’t know the color of corn!

47. 197
Ron Taylor says:

Oh boy! I have been catching up on this thread and I am astounded to find the engineer versus scientist posts. Just cool it folks. I was trained as an engineer in the 50s (whoa, yeah, that long ago) and remember those silly debates at that time. For basic science, I depend on the scientists who are specialists in the field under consideration. If they have an engineering problem, I assume they will check with an engineer. Gee, we got more important problems just now…

[Response: Well said. No more of these comments, ok folks. – mike]

48. 198
Blair Dowden says:

Re: Discussion of the greenhouse effect – I have written up my understanding of how it works (mainly learned here, though any errors are my own) on this page.

I hope this is helpful. Any comments or corrections would be appreciated.

49. 199
Chris C says:

James,

I think you may have missed the point of this post. It is a simple model that is used to explain the basics of the greenhouse effect to the lay-person.

It is not a skelatal structure for a Atmosphere-Ocean Global Circulation Model. It is not even a structure for an advanced energy balence model. The Quantum mechanical effects are included in theses models, as well as full radiative transfer models, dynamic effects from atmopsheric/oceanic motion, pressure and doppler line broadening etc…
Checkout

They do not assume LTE. They do not assume Kirchoff’s law is valid and they most certainly do not assume that the atmosphere is solid.

The model presented in this article is to illustrate the concepts. Too attempt to explain a GCM with the effects you have mentioned would be well and truley beyond the grasp of a layman, ad they’d get lost in the detail.

50. 200
Jim says:

Fine with me. I just don’t like being patronized.