On a couple of occasions, I’ve noted that near infrared water vapor parameterizations in HITRAN-1996 were incorrect and wondered about what the impact of these changes would have been on a non-retuned GCM. It looks like Collins et al JGR 2006 have done something like that – implementing HITRAN changes up to 2003. Unfortunately, they did not attempt to implement the most up-to-date changes as of 2006 (or even implement 2004 changes). Collins et al 2006 excuse this on the following basis:
In general, the radiative parameterizations in GCMs are updated infrequently and are not consistent with the latest LBL calculations of H2O shortwave absorption.
While this may be standard practice in GCM circles, given the amount of weight being placed on GCM prognostications, this seems like a pretty casual way of doing business, especially given that Collins et al are aware of other changes:
There are independent indications that the near-infrared absorption calculated using the latest HITRAN may be underestimated.
However, that’s not the topic of today’s post. It turns out that the difference between old and new parameterizations is about 3.4 wm-2 and that this amount is absorbed in the atmosphere. Collins et al:
The updates to the parameterization of water vapor extinction increase the shortwave convergence in the atmosphere by approximately 3.4 W m-2.
The amount (3.4 wm-2) is obviously very similar to the forcing from doubled CO2 (3.7-4 wm-2). So in a sense, Collins et al, by testing the impact of the 3.4 wm-2 change in atmospheric “convergence”, may provide interesting information on sensitivity where there are no built-in expectations for the answer. I say this because it’s hard not to think that tests on the impact of doubled CO2 within climate models – from a statistical point of view – have become so stylized that they amount to little more than a type of Kabuki theatre. Here there are no built-in expectations. Before you read on, write down your guess as to the impact on average temperature obtained by Collins et al and compare it to their result which I’ll give below.
I do not claim any particular authority on these models and am posting up some notes on my reading, which I’ve tried to do carefully but I could easily have misunderstood something. So bear that in mind. Collins et al describe the difference in parameterizations as follows:
In this paper, we demonstrate the effects of recent changes in water vapor spectroscopy on the climate simulated with the Community Atmosphere Model (CAM). In the original shortwave parameterization for CAM [Briegleb, 1992], the absorption by water vapor is derived from the LBL calculations by Ramaswamy and Freidenreich [1991]. In turn, these LBL calculations are based upon the 1982 AFGL line data [Rothman et al., 1983]. The original parameterization did not include the effects of the water vapor continuum in the visible and near-infrared. In the new version of CAM, the parameterization is based upon HITRAN-2K [Rothman et al., 2003], and it incorporates the CKD 2.4.1 prescription for the continuum. For the broadband shortwave absorption of interest here, the differences between using CKD 2.4.1 and MT_CKD are negligible.
They report the following direct effects of the changes:
The updates to the parameterization of water vapor extinction increase the shortwave convergence in the atmosphere by approximately 3.4 W m-2. … This increase is accompanied by a increase in total solar energy absorbed at the top of the climate by 0.6 Wm-2 and a reduction in surface insolation by 2.8 Wm-2.
They go on to say that the impact of these changes is primarily on the hydrological cycle:
The change in surface insolation is balanced primarily by a reduction in latent heat flux, although the sensible and net upward longwave fluxes also decrease… The global precipitation rate falls by -0.05 mm d-1 to balance the reduction in surface evaporation. The net effect of the greater near-infrared absorption is to weaken the hydrological cycle by approximately 2% while increasing the amount of precipitable water by the same percentage.
Their Table 8 shown below shows the following impacts of these changes on a coupled model – the slab ocean seems more relevant here than the prescribed ocean. As I understand it, the impact of increased atmospheric absorption in the amount of 3.4 wm-2 on a coupled model with slab ocean is 0.122 K. I’ve written to Collins asking him to confirm that my understanding of this is correct (and, if not, to provide what their estimated impact is).
collin1.gif
Now I understand that there are differences between an “increase in shortwave convergence” of 3.4 wm-2 and an increase in “radiative forcing” of 3.7 wm-2 due to doubled CO2. I realize that one is inbound radiation and one is outbound radiation; I realize that one is shortwave and one is longwave. I just don’t understand why there is a difference of 1.5 orders of magnitude in temperature impact, by which one leads to a change in temperature of 0.122 K and the other leads to projected changes of 1.5 to 4.5 K, with some models yielding even higher results. I’m not saying that any of the calculations are wrong – merely that I’m puzzled by the seeming disproportion in results. I firmly believe that this sort of effect should be explicable in relatively simple terms without needing to rely on GCMs and would welcome any explanations.
Collins, W. D., J. M. Lee-Taylor, D. P. Edwards, and G. L. Francis (2006), Effects of increased near-infrared absorption by water vapor on the climate system, J. Geophys. Res., 111, D18109, doi:10.1029/2005JD006796.
Climate Audit 
47 Comments
The 1.5 to 4.5K increase includes all the feedbacks, especially the positive ones. Maybe the 0.122K doesn’t include all the feedbacks?
While I havn’t followed Jonathan Tennyson’s (University College London) water vapour calculations recently, I’m surprised that Collins et al havn’t done so. Tennyson has a tremendous publication record for such calculations for various molecules. Steve, you might want to ask him if he has compared his results to those of Collins.
Roger Bell
Maybe the models are programed to ignore “feedbacks,” from this type of impact, since humans didn’t cause it.
I think I can put it in simple terms. You basically had it right that the crucial difference is inbound versus outbound.
In one case you are intercepting a photon that would otherwise hit the ground, while in the other you are intercepting one that would have been lost to space. The former therefore has a smaller effect on the earth-atmosphere system’s energy budget because that photon would have been absorbed later anyway.
#4. You’re just asserting something, not providing an argument. Obviously I’m aware that in bound and outbound are different – I pointed it out. I’ve tried to develop a rationale for WHY it would make an order-of-magnitude difference and I can’t find one; my rough calculations indicate that the difference maybe would be a double – that’s all. It doesn’t help to merely say that one is inbound and one is outbound. I know that. If you can show some calculations justifying the difference, then please do so. Otherwise, if you’ll permit me to say so, you don’t have any idea how the calculations work, it’s just that you’re prepared to accept them without worrying about it.
There’s some interesting stuff here, and some things I don’t understand.
First off, they say:
Now, this is incoming solar radiation. Any solar radiation that reaches the surface gets the benefit of the “greenhouse effect”. Any solar radiation that is absorbed by the atmosphere does not. Thus, the net effect of this change, other things being equal, will be to reduce the net greenhouse efficiency. And this, of course, will make for a cooler surface temperature, not a warmer one. As a simple thought experiment to verify which way increased atmospheric absorption changes temperature, imagine if the atmosphere was perfectly clear to sunlight – we’d live on a warmer planet.
Next, they say:
Now, if 3.4 more W/m2 are absorbed in the atmosphere, how come the surface insolation only goes down 2.8 W/m2? Where did the other 0.6 W/m2 that ended up in the atmosphere come from?
More questions than answers, but I can’t see how increased atmospheric absorption leads to a warmer surface.
w.
OK, another try in response to #5.
By absorbing solar radiation in the atmosphere instead of the surface you only change the vertical distribution of heating, not the net amount. Why the surface effect is 0.122 K warming rather than zero, I don’t know, and maybe would need a full model. I was just trying to explain why it is closer to a zero effect than to the CO2 effect, which was the original question.
#7. With respect, your argument here is just arm-waving.
The greenhouse effect from additional CO2 comes from the impact of absorbing outbound energy at rather high altitudes, which causes 50% of it to be back-radiated to earth and only 50% of it continuing to space. If the same molecules also intercept inbound solar radiation, they would radiate 50% back to space and only 50% down. It’s a type of reverse greenhouse effect.
For outbound radiation, you have the additional situation where you the back-radiated energy has to be re-emitted and so it gets intercepted. But this is a geometric sum and under plausible proportions the geometric sum of say 1+1/2 + 1/2^2 +.. would be 2. So I could see how the inbound-outbound argument could gross up the impact to say 2 times 0.122 deg C, but not an order-of-magnitude.
These issues should not require a full GCM to explain. Quite the opposite – the GCMs have so many other things involved that they don’t explain the matter at all. The seeming paradox should be explicable with no more than a few paragraphs of argument. However, there’s no point saying that it merely changes the vertical distribution – someone could say that about additional CO2 and we’re no further ahead in our understanding.
Since this thread seems, in large part, to be a reasonable attempt to understand the Collins et al result, let me try to help.
The surface and the troposphere are very tightly coupled in the model, not primarily by radiation but rather by evaporation from the surface and condensation in the troposphere. Therefore depositing more solar energy in the troposphere rather than the surface has no effect on the temperature of either the surface or the troposphere, to first approximation (as stated in #7). The hydrological cycle will be weakened, because there will be less energy for surface evaporation.
However, by absorbing more solar flux in the troposphere, one will reduce, by a small amount, the reflection to space of the solar flux by the surface and by low level clouds, providing a net gain for the troposphere-earth system, which will warm a bit. It is this net gain — the radiative forcing — that controls temperatures. In addition, since the surface-troposphere coupling is not infinitely stiff, given that the exchange of energy has been reduced the surface will cool a bit with respect to the troposphere, so it will warm less than the troposphere in response to this reduction in reflection.
Isaac, good to hear from you. A question about the “coupling” of the surface and troposphere, which you say are “tightly coupled” by latent heat transfer. However, the Kiehl/Trenberth global energy budget puts the radiation from the surface to the troposphere at about 340 W/m2, and the latent heat transfer at 78 W/m2. These are overall figures, so the incremental numbers for a change in forcing sounds like they are much more heavily weighted to the latent heat side. Which is reasonable.
However, while this explains the small change from a large forcing change in water vapor absorption, what it doesn’t explain is the claimed large surface temperature increase from a slightly larger CO2 forcing. If the troposphere and the surface are tightly coupled as you say, the CO2 forcing should be largely expressed as a change in latent heat, with only a small surface temperature change. But according to the model, it’s not.
That’s the puzzle in the results, that neither you nor anyone else has explained.
w.
Isaac, I don’t understand the following comment:
Let’s suppose that NIR absorption is increased by 3 wm-2. Re-emission will presumably go half up and half down, reducing downward NIR by 1.5 wm-2. If NIR albedo is 0.3 (and I understand that NIR albedo tends to be less than overall albedo), then NIR reflection is reduced by 0.3*1.5. On an overall basis, inbound NIR reaching the surface would increase by 1.5 -0.45 = 1.05 wm-2. So I don’t understand why you say that there is a net gain in the troposphere-earth system. As you’ve expressed it, it doesn’t make sense to me at all. Could I trouble you to clarify this further. Alternatively, perhaps you give me a reference to an article or text where someone calculates the impact of inbound absorption and outbound absorption side by side to show the difference? I’d be happy to work through it as some readers here would be interested. (If side-by-side calculations don’t exist anywhere, that seems too bad, as they would be instructive to me at least and perhaps others.)
Steve,
Once the shortwave has been absorbed it has contributed to the earth-atmosphere
heat budget. You don’t need to go another step and try to follow the IR.
Given this, Isaac’s explanation is that by absorbing the shortwave, you
are pre-empting the possibility it will be reflected and lost by albedo effects,
making it a more effective process.
re #11:
I am not sure where you are getting the half up and half down part. At the relevant wavelenths the thermal emission is presumably negligible and the radiation is just being absorbed.
#12. My understanding of the quantum mechanics is that if a molecule is excited at a NIR frequency, it re-emits at a NIR frequency, rather than an IR frequency. Although I guess it could de-excite in steps, but my guess is that whatever the excitation was is also most likely to be the major re-emission. So I don’t see that it’s entering the IR balance just yet – it’s still in the shortwave NIR. (Maybe I’m wrong; I don’t claim any expertise here.) So you’ve got a molecule that’s re-emitting in the NIR range, 50% up and 50% down. And so I think that my analysis follows.
Again, it would be nice to see a citation to a text or other reference that discusses this situation. It’s hard to believe that there isn’t a detailed discussion somewhere in the vast corpus of climate science, but no one seems to have volunteered one.
#14 The emission is proportional to the Planck function at the relevant wavelength and at the temperature of the atmosphere. The absorption is proportional to the incident intensity at this wavelength, which is independent of this Planck function (one can think of it as more or less determined by the Planck function of the solar photosphere). So the absorption is far larger than the emission. Dennis Hartmann’s Intro to Physical Climatology might be a place to start.
You’re right of course, Dr. Held, but an important point is just where in the atmosphere the absorption occurs. If it occurs high in the atmosphere, then the odds that the next emission of the energy in the NIR (which will doubtless be in the long wavelength IR), will escape, will approach 50% as Steve suggests. At lower altitudes, it will gradually approach the situation of being emitted directly from the ground.
So just what is the average altitude of absorption of NIR? And more importantly, how is it changed by a putative increase in water vapor concentrations as a positive feedback from increased CO2? Is there a readily available paper or monograph which gives this information?
thanks. I’ll take a look at it. Obviously I mostly work at statistical issues on proxies so please pardon the physics. However, I may be able to explain this to some readers here who come from a similar perspective.
If the absorption is greater than the emission, I would have thought that this would increase the proportion of molecules in an excited state and that this would be impossible. But I’ll see what Hartmann has to say and why this doesn’t happen. So if you don’t mind stopping in again in a couple of days after I look at this text, I’d appreciate it and will make my best efforts to make any necessary explanations to readers here.
re: #17 Steve,
The main point is that when it comes emitting IR, it tends to be a slower process than the mean time between collisions of molecules. So the energy is thermalized before it can be re-emitted. This means that only a small number of IR emitting molecules will have a sufficient energy at any given time to emit. This is why there are so many more absorptions of NIR than emissions. For long-wave IR there’s not quite as much difference since we’re near the black-body peak for the atmosphere. So there’s a very rough equality between emission and absorption.
One of the amazing gaps in the various IPCC reports is a clear intermediate-level exposition of the physics of how additional CO2 causes a temperature increase. There’s a passing discussion in IPCC SAR, but that’s all that I could locate. I’ll do a post on this. When they were scoping IPCC AR4, I suggested to Mike MacCracken that this would be very useful. I think that he passed the suggestion to Susan Solomon. IPCC 4AR didn’t do that, but found space for an extraordinarily self-indulgent history of climate science that is irrelevant to policy-makers.
An interesting comparison of the albedo of the surface and clouds.
I agree with the essence of Dave Dardinger’s qualitative explanation of the absorbtion, heating effects and re-emission for IR radiation and I also agree that putting some actual numbers (even approximations) with details of the energy transfers could impart even a better feel for the process.
Isaac, you say:
Once it is absorbed as you describe, the absorbed radiative energy doesn’t stay in the atmosphere. It is turned into heat, and will leave the atmosphere by one of a few routes. The majority will leave the atmosphere by radiation, at a variety of temperatures and wavelengths depending on instantaneous conditions around the globe. This is the radiation Steve is referring to as the half up and half down.
The effect of inbound absorption of solar radiation on atmospheric temperature is actually quite curious. As a thought experiment, consider a planet, no atmosphere, flat black, surrounded by a thin shell, 100% clear to incoming solar, 100% opaque to outgoing IR. Obviously, this represents a theoretically perfect atmospheric “greenhouse” shell.
Now suppose we change it so that more incoming radiation is absorbed in the shell, say 25% absorption. Will the temperature of the shell rise or fall?
…
…
…
…
The curious answer is that the temperature of the shell doesn’t change one iota. To understand this counterintuitive result, first consider how much of the incoming solar radiation heats the atmosphere in the perfect case.
The answer is, all of the incoming solar radiation heats the atmosphere. Of course it passes through the earth first, but after that, every bit of the incoming energy is absorbed on the outbound leg. The atmosphere receives one sun’s worth of energy.
Next, consider the situation where a quarter of the incoming radiation is absorbed by the atmosphere. Now how much of the incoming solar radiation heats the atmosphere? Once again, all of it heats the atmosphere, every bit, some directly on the inbound leg and the rest indirectly on the outbound leg of the trip.
Thus, either way, the total heating of the atmospheric shell is exactly the same. It gets all of the solar energy, 100% of it, either way. So its temperature doesn’t change at all.
For the surface, however, the situation is quite different. In the perfect case, all of the sun’s radiation heats the surface. But increased atmospheric absorption decreases the amount passing through the earth watt for watt – an incoming watt absorbed by the atmosphere is a watt lost from the surface. But unlike the atmospheric shell, the total surface heating is reduced, and thus the surface cools down.
Unless I misunderstand the table above, it seems to say that as less insolation hits the surface, the surface air temperature goes up. Now, I know some folks are into warming and all, but claiming that reducing the amount of sunlight hitting the surface is going to increase the SAT is simply not believable.
w.
#14,15. Let me go back to my question in #11 (which I’ll re-state here.) I acknowledge your point that the at the temperature of the troposphere, absorbed NIR will not be re-emitted in NIR wave lengths (due to Planck function), but my original points was unrelated to the wave length of the re-emission and, it seems to me, the issue applies to IR re-emission. Let me state the problem for me – the seeming asymmetry between effects of inbound and outbound absorption – in a different way though.
The example in Collins et al pertains to increased atmospheric absorption of NIR in the amount of (say) 3 wm-2. If CO2 absorption also increases by 3 wm-2 (a bit less than doubling), then the situation seems to me to be as follows:
– 3 additional wm-2 of inbound NIR is absorbed, of which 50% is re-emitted up and 50% down (as IR agreeing with your observation).
– 3 additional wm-2 of outbound IR is absorbed, of which 50% is re-emitted up and 50% down (AGW).
The net result of the two effects is that the inbound radiation is unchanged (although all 6 wm-2 are IR rather than 3 wm-1 NIR, 3 wm-2 IR); and the outbound radiation is unchanged. So I would have thought that, in a first calculation, the surface temperature would remain unchanged regardless of whether the troposphere was tightly linked to surface or not.
The quandary comes from the seeming asymmetry of the two components. Considered individually, the additional inbound absorption is held to have an impact of 0.12 K; while the additional outbound absorption is held to have a direct impact of 1.2K and total impact of 2-4.5K. I realize that there is an albedo issue, but not enough to account for the difference (which could be accounted for by modifying the proportions of inbound and outbound absorption.
#23:
The absorbed radiation is not re-radiated in the infrared. The temperature would have to increase in order to increase the IR cooling, but there is no reason for the temperature to increase (in steady state). The troposphere and surface are strongly coupled by non-radiative fluxes, and increase or decrease in temperature in response to the net heating of the troposphere+surface, and this net heating has not changed, to first approximation. The increase in solar heating of the atmosphere is primarily balanced within the atmosphere by a reduction in latent heat release, consistent with a reduction in evaporation, not by an increase in radiative cooling. Increasing CO2 decreases the IR cooling to space of the coupled surface+troposphere system; nothing comparable is happening here.
#22:
I don’t think you can understand what the model is doing until you accept the fact that its surface and troposphere are strongly coupled and that you cannot warm or cool one without warming or cooling the other.
I’m going to keep this thread fairly clear so that only a couple of issues are raised here. I’ve deleted some posts, which ordinarily would not be remotely an issue. Re-submit on Unthreaded if you feel it important.
re 19:
A straightforward summary on climate sensitivity is given by Nir Shaviv
http://www.sciencebits.com/OnClimateSensitivity
Here is an applet where you can play with albedo, emissivity and solar constant
http://home.casema.nl/errenwijlens/co2/sb.htm
re: #26
The Nir Shaviv link is quite good and understandable. Has it been countered by anyone? In particular has it been attacked by anyone who has the training and ability to be believed?
I get the feeling that Steve M is looking for stepwise detail of what energy transformations and transfers occur with the extra NIR absorption. Shaviv’s explanation, while clear and understandable, looks at the “macro” physics of climate sensitivity, but this case calls for a “micro” explanation.
Held’s explanation I think derives from his climate models and how they would handle the extra NIR absorption. What trips me up is the use of the term “to the first approximation”. What I understand from his explanation is that the extra NIR is absorbed in the troposphere and is not re-radiated but is stored as heat that does not change the temperature (to the first approximation) of the troposphere. The strong non-radiative coupling of troposphere and surface in equilibrium transfers the energy through changes in evaporation.
Even if one qualitatively accepts the transfers of energy by the prescribed non-radiative mechanism, I seem to be missing the justification for the statement that this effect does compare quantitatively with the CO2 effects.
You have to separate the instantaneous view from the equilibrium view.
The equilibrium view is what I believe Isaac Held is presenting, and is the
one needed to explain climate change. In instantaneous
terms, the extra absorption goes into a temperature increase in the atmosphere where it
is absorbed, and a reduction below that in the atmosphere and at the ground,
where that energy is no longer reaching. This temperature effect is a small
part of the total temperature change due to physics and dynamics,
and even only represents a small percentage
of absorbed solar energy. Beyond that it can only be traced meaningfully
through its effect on the temperature and solar flux.
To me, the clearest link to warming is though the albedo effect. By
absorbing more solar energy, you also prevent some part of it from being
reflected back to space, so it contributes positively to the heat budget.
It is analogous to putting soot in the atmosphere.
#29. Jim, my problem is with the verbal explanations. IT should be possible to provide simple energy budgets for these verbal explanations and I’d certainly appreciate one. Without some budgets and accounting, one person’s explanation is another person’s arm-waving. I’m really not trying to be obstreperous about this. I have no position on the matter. My starting-point in any analysis is that people know what they’re doing, not the opposite. (I presumed that about Mann and the Hockey Team and reached opposite conclusions only after very patient analysis.) My assumption here is that people probably know what they’re doing, but aren’t very good at explaining it. I’m not assuming that anyone’s wrong about anything, I’m just saying that I don’t understand the explanations, which have now been repeated multiple times and I still don’t understand them.
Now the fact that I don’t understand the explanations is probably not of great concern to anyone, but you should at least contemplate the possibility that, if I can’t understand the explanation, it’s probably not explained very well. Budgets and numbers are always good and if you (or Isaac Held) can provide ballpark numbers for the various fluxes here, I think that it would be instructive not just for me, but for others. The flip side is that if such numbers aren’t easily provided (and they seem like pretty obvious budgets), then maybe people have arm-waved through some problems and there’s something worth working through in more detail. I’d be surprised, but obviously I’ve encountered the odd surprise in this field.
Re: #29 Jim,
I’m wondering about that albedo thing. Most of the reflection of Earth is from the clouds anyway, so it’s going to be a fairly small % difference.
Re: #30 Steve,
That’s my problem too. I read Isaac’s message several times and just couldn’t figure it out. I resisted responding because I figured it probably does mean something and if it were questionable someone else would do a better job of asking a question than I would.
I just can’t figure out what he meant by,
It’s true NIV absorbed isn’t re-radiated in the NIV, but it will be re-radiated as Long-wave IR. And there will be a delay in the re-radiation. And it may connected with convection and so forth, but ultimately the only way heat gets out of the atmosphere is via radiation.
Jonathan Tennyson is a co-author of a paper “Water on the Sun” (Contemporary Physics 1998, vol39,number 4, pages 283-294.) He says that “The most interesting result is the insight given to understanding how our own
atmosphere absorbs sunlight and the possible consequences that this may have for modelling the greenhouse effect.” He is a very powerful physicist and a very nice person. If you Google him you can print out the
paper. Doing so may lead to a more significant discussion here.
Roger Bell
I think even more hand-waving is needed to produce numerical evidence, but here goes.
Let’s say we have 3.4 W/m^2 absorbed by this water vapor process.
Let’s use the current estimates of albedo of 0.30.
Let’s say half this albedo has already acted by the time the water vapor absorbs it,
e.g. high clouds. (This is the hand-waving factor)
This means that 0.5*0.30*3.4 = 0.51 W/m^2 is absorbed that would otherwise have been reflected.
0.51 W/m^2 more energy absorbed by the earth-atmosphere system actually corresponds
to a change in equilibrium temperature of 0.144 K (delta T = delta E / 4*sigma*T^3),
where delta E is 0.51, sigma = 5.67e-8, and I take T to be 250 K (the radiative temperature
of the earth). This says nothing about how that radiative temperature change is distributed,
but it gives a correct order of magnitude.
One question I have is Collins et al wording here that Willis also quoted in #6:
This is confusing. Do they mean 3.4 W/m2 increase in total incoming NIR absorbed by water vapor, or simply a resolution change (convergence?) of 0.6 + 2.8 = 3.4?
I presume that they meant an increase since the underlying problem was the under-estimation of NIR absorption parameters in the GCMs and they need to estimate the impact of an under-estimation in the same order of magnitude as the increase from doubled CO2 – which is what prompted the post (the supposed explanations still being incomprehensible to me.)
Could part of the (qualitative) explanation have to do with the facts that CO2 is evenly distributed in the troposphere while water vapor is concentrated near the surface?
My mental model is that the impact of CO2 occurs primarily at the higher altitudes. On the other hand, increased absorbtion by water vapor would mainly occur near the earth’s surface, in the bottom couple of kilometers of the atmosphere, beneath the CO2 “greenhouse roof”.
I am not sure what kind of equation you are looking for. The key point is simply that non-radiative fluxes dominate the exchange of energy between surface and troposphere and that these provide a much stronger coupling than the radiative fluxes. Let me try to be more explicit, although the following is just a transposition into equations of what I have already said.
Lump the sensible heat exchange between surface and atmosphere together with the latent energy exchange, and assume that all of the infrared that is emitted by the surface is absorbed in the atmosphere (just to simplify a little). I assume a steady state in the following.
Atmospheric balance: solar heating of atmosphere (QA) + upward infrared from surface (IS) + latent heat of condensation (L) = downward infrared to surface (ID) + upward infrared to space (IU)
QA + IS + L = ID + IU
Surface balance: solar heating of surface (QS) + downward infrared from atmosphere (ID) = latent heat of evaporation (L) + upward infrared flux to atmosphere (IS)
QS +ID = IS + L
The sum of these is the top-of-atmosphere balance:
QA +QS = IU
Let TA = atmospheric temperature and TS = surface temperature, and suppose
IS is a function of TS; ID is a function of TA; IU is a function of TA; L is a function of TS -TA
Perturb the system by perturbing QA and QS, and setting
d(IU)/d(TA) = b; d(IS)/d(TS) = c; d(ID)/d(TA) = e; dL/d(TS) = g = -dL/d(TA)
(g is positive and much bigger than b, c, or e, perhaps 20 W/m2)
Define
d(L + IS ‘€” ID)/d(TS) = g +c = gS; d(L + IS – ID)/d(TA) = – g ‘€” e = – gA
Now perturb QA and QS by dQA and dQS respectively, resulting in the temperature perturbations dTS and dTA
dQA = b dTA ‘€”gS dTS +gA dTA; dQS = gS dTS ‘€” gA dTA; d(QA+QS) = b dTA.
So
dTA = (dQA + dQS)/b;
dTS = (gA/gS) dTA + (1/gS) dQS = (gA/gS)(1/b) dQA + ((1/gS) +(gA/gS)(1/b)) dQS
dQA and dQS in these expressions need not be due to changes in solar absorption; they can also be the direct result of changes in infrared fluxes due to CO2.
case 1: dQS = – dQA (atmospheric heating has increased, but the surface heating has decreased by the same amount ‘€” rough approximation to what happens when one increases solar absorption in the atmosphere)
dTA = 0 ; dTS = -dQA/gS (the atmospheric temperature does not change, while the surface cools a little bit)
case 2: case 1 modified by assuming that the solar flux incident on the surface is decreased by dQA, but the surface has an albedo a, so dQS = -(1-a) dQA. (Assuming that the reflected flux just escapes to space.)
dTA = (a/b) dQA
dTS = [(a/b)(gA/gS) – (1/gS)(1-a)] dQA
(the atmosphere warms a bit due to decreased reflection by the surface+atmosphere; the surface could warm or cool depending on the magnitudes of a,b, gS, gA. For g sufficiently large, the surface warms, following the atmosphere.
case 3: CO2 doubling; dIU =-3.7 w/m2; ID increases by a comparable amount.
dQS = dID;
dQA = – dIU – dID;
F = dQS + dQA =-dIU = radiative forcing.
The value of dID, or, equivalently, the decomposition of F into dQA and dQS, doesn’t matter to first approximation ‘€” suppose, for example, that IU decreases and ID increases by the same amount, so that dQA = 0. Then
dTA = F/b;
dTS =[ (gA/gS) (1/b) + (1/gS)}] F ‘€” about the same as dTA
Common mistakes in thinking about the response to CO2:
Thinking about the surface budget rather than the surface+atmosphere budget, and then computing the response of TS to changes in ID by fixing TA. This mistake sometimes underlies estimates of very small sensitivities.
Computing the response of TS to changes in ID by fixing L. This does not result in very small sensitivities, but it is still wrong, making it look like the temperature response depends of dID rather than dIU.
#34. I agree it is horribly worded, but I guess the 0.6 is the reduced reflected component
coming out the top. This is the part that contributes to net warming.
It is convergence because there is less coming out the top, and less coming out the bottom,
so there is more being absorbed in the atmosphere.
As far as CO2 goes, the full 3.7-4 W/m^2 (from post #1) is available for warming. So the
effect would be six times greater. This still only gives 1 C, so other effects such as
positive IR feedback due to water vapor and additional anthropogenic gases make up the rest
of the double-CO2 warming scenario.
The Royal Astronomical Society publishes A&G – news and reviews in Astronomy and Geophysics. The current issue – February 2007, Vol48, Issue 1, contains the article Cosmoclimatology: a new theory emerges. This new theory, by Henrik Svensmark of Copenhagen draws attention to an overlooked mechanism of climate change: clouds seeded by cosmic rays.
Abstract
Changes in the intensity of galactic cosmic rays alter the Earth’s cloudiness. A recent experiment has shown how electrons liberated by cosmic rays assist in making aerosols, the building blocks of cloud condensation nuclei, while anomalous climate trends in Antarctica confirm the role of clouds in helping drive climate change. Variations in the cosmic ray influx due to solar magnetic activity account well for climactic fluctuations on decadal, centennial and millennial timescales. Over longer intervals, the changing galactic environment of the solar system has had dramatic consequences, including Snowball Earth episodes. A new contribution to the faint young Sun paradox is also on offer.
Roger Bell
37: isaac: OK, I got through most of your math, and I think I understand your reasoning (although you sure left a lot of steps out). A couple of questions, regarding Case 3 (doubling CO2):
1. You don’t present a sensitivity value. How is b calculated, and what value is used?
2. Are you sure that dIU and dID both have a value of 3.7 wm-2? It seems to me that the changes should each be 1/2 that value.
3. Maybe another common mistake in thinking about the response to CO2 is ignoring any negative feedback due to increased cloudiness?
RE: #36 – Except for the industrial areas that have higher local CO2 and of course, in any valley affected by an inversion ….. There may be localality even in terms of CO2 effects.
I have gone through Isaac Held’s equilibrium explanation of what can happen to the 3.4 W/m^2 of NIR radiation absorbed by water vapor in the troposphere and, while I understand this is how the problem is handled in climate modeling, it is not as clear as following the radiation absorbed to the point of heating the earth’s surface. I can make a comparison using something similar to what Nir Shaviv does at http://www.sciencebits.com/OnClimateSensitivity ,but get bogged down still when looking at a single process like the absorption of the extra NIR in the troposphere.
I need a check of my thinking here on the attempts to quantify the surface temperature changes from 3.4 W/m^2 of NIR radiation being completely absorbed by water vapor in the troposphere versus allowing this amount radiation to pass through the troposphere without absorption. The effect of the foregoing is to be compared to that of a CO2 doubling radiative forcing of 3.8 W/m^2.
Can we, at least to a first approximation, compare directly the surface temperature effects of the 3.8 W/m^2 and the 3.4 W/m^2 passing unabsorbed through the troposphere? (I think that the answer to this depends on where in the troposphere most of the extra NIR radiation is absorbed and to that I could not find a direct answer) If we can, than would the simple calculation of surface temperature change be made by assuming a climate sensitivity with net positive feedback of approximately 0.75 degrees K per W/m^2 yield, for the doubling of CO2, a temperature change of 2.85 degrees K and for the unabsorbed NIR radiation a temperature change of 2.45 degrees K. If these calculations are approximately correct, we can then compare them to the case where the 3.4 W/m^2 of NIR is absorbed in the troposphere by water vapor.
Firstly, since the net calculated effect from climate models is that the difference in the 3.4 W/m^2 of NIR radiation being absorbed and being unabsorbed is a surface temperature change of approximately 0.12 degree K, we would have to conclude that the portion of the energy from that absorption that passes through to the surface must be approximately 95% of that of the portion that makes in through from the unabsorbed case.
Secondly, if my thinking is correct to this point, then all the convincing I would need for the accounting of this small difference in temperature change between the absorbed and unabsorbed cases would be to show me how this energy absorbed in the troposphere gets to the surface — in at least semi-quantitative terms.
Isaac Held implies that the transport process is entirely non-radiative (as it would have to be to account for almost all the energy being directed towards the surface), which would imply that the absorbed NIR energy must first heat the troposphere and then be transported away to the surface by convection, conduction or I assume by the hydrological cycle. Held’s equilibrium explanation of this process is not intuitively clear to me and I would be the first to admit that that may be from my lack of correctly understanding it.
Well, in order to determine whether Isaac Held’s ideas are valid, I decided to build a simple radiation balance model. It’s in Excel, quite straightforward. I learned a lot from the building of the model.
Now, the first thing that you have to understand is that you cannot successfully model the earth with a single atmospheric greenhouse “shell”. This is because a single greenhouse shell would not warm the earth enough to match the known conditions. A single perfect, 100% effective greenhouse shell can do no more than double the incoming radiation. Let us call the incoming radiation from the sun “S” (in watts/m2). At equilibrium, a perfect greenhouse shell must radiate S watts outward, and S watts inward. At equilibrium, then, the planet receives S watts/m2 from the sun, and S watts/m2 from the shell, for a total planetary surface radiation temperature of 2 * S.
The energy from the sun (after albedo) is about 235 W/m2 (all numbers here are somewhat uncertain, I’ll give them as exact figures but please understand that they are approximations). With a single perfect shell, this would mean the equilibrium temperature of the earth would be 470 W/m2. The problem is that the radiation temperature of the earth is 390 W/m2, which means that there are losses amounting to 80 W/m2.
But we know that the losses from sensible heat (24 W/m2) and latent heat (78 W/m2) total 102 W/m2, more than would be available if there were only a single shell. Therefore, the single shell model is energetically impossible. Accordingly, I built a two shell model, as it is the simplest model which provides enough energy to accommodate the known losses. This means that the stratosphere and the troposphere must function as independent absorber/emitters of IR energy.
I have included in the model the very reasonable assumption by Dr. Held that much of the change in energy is taken up by changes in sensible and latent heat losses, rather than in temperature change.
There are some interesting outcomes from the fact that a single-shell model won’t work for the earth. One is that equations such as those given by Dr. Held are not applicable, because they are for a single shell model.
Another is that with two shells, there are some curious interactions and outcomes. One is that it makes a large difference exactly where the energy is absorbed. If the additional 3.2 W/m2 is split between the troposphere and the TOA (as in Collins), I get numbers which are close to those reported by Collins et al. However, there is an important difference. As I had speculated above, the surface does not warm when more energy is absorbed in the troposphere, it cools. However, the changes in temperature are quite small. According to radiative balance, given the absorption of an additional 0.6 W/m2 at the top of the atmosphere and an additional absorption of 2.8 W/m2 in the troposphere, my figures and Collins figures look like this:
SHORTWAVE________Collins___MineTOA__________________0.6____0.6
Troposphere__________2.8____2.8
TOTAL________________3.4____3.4
Surface_____________-2.8___-2.8
So far, so good. The surface change is lower than the atmospheric change because of albedo. However, the problem arises because they have increased the sensible and latent heat by too much. The increased absorption in the atmosphere yields increased downwelling long wave, about +0.7 W/m2. This partially offsets the loss of solar radiation. This means that the total change in incoming radiation at the surface (shortwave plus longwave) is about -2.1 W/m2.
But in their results, the change in sensible + latent heat losses is said to be -2.2 W/m2, which is more than the change in total downwelling radiation. This is why they claim that the surface is warming … but it makes no sense physically. Why would the change in losses be greater than ‘ˆ†W, the change in incoming radiation?
Using a physically plausible coupling between the drop in downwelling radiation at the surface and the drop in latent + sensible heat loss, the surface must cool rather than warm. They claim a warming of 0.2°C results from the increased IR absorption in the atmosphere. My radiation balance model shows a cooling of 0.2°C, rather than a warming.
Next, there’s another oddity about a two-shell model. A change of IR absorption in the troposphere alone does not alter the TOA downwelling radiation one bit. TOA radiation only changes when the absorption of the stratospheric layer changes. Thus, the relative change in stratospheric and tropospheric absorption is a major factor in the “climate sensitivity”, which is defined as the ratio of a change in TOA forcing versus a change in surface temperature. This brings up the question of how the effect of a doubling of CO2 (which the IPCC says causes a 3.7 W/m2 change in TOA forcing) is calculated. I have not been able to find accurate information on this question, and would appreciate any pointers.
Finally, according to the model, the climate sensitivity is about 0.2°C per W/m2, in good agreement with the figures from Idso’s “natural experiments” and Lindzen’s estimates, but far lower than the IPCC figures.
I have posted the model for download here, and I invite people to experiment with it and report their findings.
w.
Thank you, Willis. With regard to :
The easiest approach is to have a single Boolean somewhere, called “BreakCircular”, for example, which is normally set to FALSE.
Ensure that every looped calculation includes, somewhere within the loop, a condition of the form ” if( BreakCircular , 0 , …) “, where the “…” represents whatever you want to calculate in that cell.
In this worksheet, you need them in cells G32, H24, and I16.
Then, when the spreadsheet blows up on you, you just need to set BreakCircular to TRUE, and the spreadsheet will clear. You can then track down the original source of the problem, fix it, and reset BreakCircular to FALSE.
re: #43 Willis,
Excellent. I’d noticed also that Dr. Held’s equations were essentially the one-shell case and that sort of is what I was getting at in #16. But I hadn’t thought about trying to do the calculations you did. Still, I need to go look at your spreadsheet as one thing bothers me. Sensible and Latent heat don’t remain total losses to the system. Latent heat is released in the atmosphere and then this is kinetic energy of the gasses in the atmosphere and will result in long-wave IR part of which will escape and part return to the surface.
Admittedly a lot of this additional IR is present prior to a perturbation, but it will itself be perturbed by the surface changes.
Willis: Oddly (coincidently?) your sensitivity factor agrees almost exactly with mine in post # 44, Unthreaded. LOL.
fFreddy, lovely solution to the “off-the-rails” problem.
Dave, the sensible and latent heat, as you point out, are not lost to the system. They are merely transferred from the surface to the troposphere and stratosphere.
jae, it’s coincidence … isn’t life grand?\
w.