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Clouds and Water Vapor – Part One – Responses

After posting Part Two on water vapor, some people were unhappy that questions from Part One were not addressed.

I have re-read through the many comments and questions and attempt to answer them here. I ignore the questions unrelated to the feedbacks of water vapor and clouds – like the many questions about the moon, answered in Lunar Madness and Physics Basics. I also ignore the personal attacks from a commenter that my article(s) was/were deceptive.

The Definition

The major point from the perspective of a few commenters (including critics of Part Two) was about the radiometric definition of the “greenhouse” effect.

Ramanathan analyzed the following equation:

F = σT4 – G

where F is outgoing longwave radiation (OLR) at top of atmosphere (TOA), T is surface temperature, and G is the “greenhouse” effect.

For newcomers, F averages around 240 W/m² (and higher in clear sky conditions).

The first term on the right, σT4, is the Stefan-Boltzmann equation which calculates radiation from a surface from its temperature, e.g., for a 288K surface (15°C) the surface radiation = 390 W/m².

If the atmosphere had no radiative absorbers (no “greenhouse” effect) then F= σT4, which means G=0. See The Hoover Incident.

The approach Ramanathan took was to find out the actual climate response over 1988-89 from ERBE scanner data. What happens to the parameters F and G when temperature increases?

Why is it important?

If increasing CO2 warms the planet, will there be positive, negative or no feedback from water vapor? Apparently, Ramanathan thought that analyzing the terms in the equation under changing conditions could shed some light on the subject.

However, the equation itself was brought into question, mainly by Colin Davidson, in a number of comments including:

..In the section “Greenhouse Effect and Water Vapour”, he introduces an equation:

F = σTs^4 – G

I didn’t understand what this equation was trying to say. How are the Surface Radiation and the Outgoing Long Range Radiation linked, noting that there are other fluxes from the Surface into the Atmosphere? And one of these (evaporation) is stronger than the NET Surface radiation, while direct Conduction is also a significant flux?
The sentence “So the radiation from the earth’s surface less the “greenhouse” effect is the amount of radiation that escapes to space.” is not accurate.

Missing from this sentence are the following:
Incoming Solar Radiation Absorbed by the Atmosphere(A);
Evaporated Water from the Surface(E);
Direct Conduction from Surface to Atmosphere(C)
Back-Radiation from Atmosphere to Surface (B)

Writing down the fluxes for the atmosphere as a black box:
F= A+(S-B)+E+C (where S=Stephan-Boltzmann Surface Radiation),
Making G = S-F = B-A-E-C

So G doesn’t appear to me to make much PHYSICAL sense, and is certainly NOT the “Greenhouse Effect”, as the evaporative and conductive species are not greenhouse animals, but B and A certainly belong in the zoo..

And:

..I have shown that both those claims are incorrect. G does not represent the “Greenhouse” effect of an IR active atmosphere, as it contains terms (Evaporation and Conduction) which are plainly IR insensitive, nor does it represent the upward surface flux less the amount of longwave radiation leaving the planet.

What G represents is anyone’s guess, but it is not an easily identifiable physical quantity.

Hence my problem with the equation F=S-G as a starting point for any analysis – it doesn’t seem to represent anything coherent. Why not start with the TOA balance, the Surface balance, or the Atmospheric balance?

I am concerned about this. Is the whole theorem of climate sensitivity based on the incorrect notion that the factor G represents the Greenhouse Effect?

In this post I summarise some of my concerns.

1. F= Sunlight – Reflected sunlight. Unless the earth’s short-wave albedo changes, the Outgoing Long-Wave Radiation(F) is constant, whatever the state of the Greenhouse. So dF/dTs does not represent the Greenhouse Effect, but is a representation of the change of surface temperature with cloudiness.

2. F= S(urface Radiation) + G, but G= E(vaporation) +C(onduction) + A(bsorbed Solar Radiation) – B(ack Radiation). Of these terms, only A and B are Greenhouse dependent. C and E are Greenhouse independent. dG/dTs is therefore not a measure of the Greenhouse Effect.

3. It is unclear if the amount of radiation from the surface escaping “through the window” direct to space is constant. If CO2 concentration increases we expect some tightening of the window, but not much. On the other hand any increase in surface temperature will increase the amount of radiation, so the two processes may balance. Kiehl and Trenberth keep this constant at 40W/m^2 despite raising the surface temperature over time by 1DegC, suggesting that it may be close to constant.

Assuming that is so, the fluxes warming the atmosphere from the Surface are constant, the (B)ack radiation increasing by roughly the same as the sum of the increases in Radiation from the Surface(S) and (E)vaporation. Basically when the surface temperature increases, the increase in Evaporation is balanced by a
decrease in Net Surface Radiation Absorbed by the Atmosphere.
As the heat entering the lower atmosphere is unchanged (though the amounts entering at each height will change), the overall Lapse Rate to the tropopause will be unchanged. So the temperature at the Tropopause will always be the Surface Temperature minus a Constant. The sensitivity of the Tropopause temperature is therefore the same as (and driven by) the sensitivity of the Surface temperature to changes in “forcing” (either solar or back-radiation).

This sensitivity is between 0.095 and 0.15 DegC/W/m^2.

And a search in that post will highlight all the other comments.

My attempts at explaining the concept did not appear successful. I don’t think I will have any more success this time, but clearly others think it is important.

I find Colin’s comments confused, but I’ll start with the main point of Ramanathan (paraphrased by me):

What happens if the climate warms from CO2 (or solar or any other cause) – will water vapor in the climate increase, causing a larger “greenhouse” effect?

That’s the question that many people have asked. These people include well-known figures like Richard Lindzen and Roy Spencer, who believe that negative feedbacks dominate.

Scenarios to Demonstrate the Usefulness of the Definition

If the surface temperature in one location goes from 288K (15°C) to 289K (16°C) the surface radiation will increase by 5.4 W/m². (The Stefan-Boltzmann law). How can we determine whether positive or negative feedbacks exist?

Condition 1. Suppose under clear skies when the temperature was 288K we measured OLR = 265 W/m² and when the temperature increased to 289K we measured OLR = 275 W/m². That means OLR has increased by 10 W/m² for a surface radiation increase of 5.4 W/m². Let’s call this condition Good.

Condition 2. Suppose instead that when the temperature increased to 289K we measured OLR = 265W/m². That means OLR has not changed when surface radiation increased by 5.4 W/m². Let’s call this condition Bad.

• In condition Good we have negative feedback, where the atmospheric “greenhouse” response to higher temperatures is to reduce its absorption of longwave radiation
• In condition Bad we have positive feedback – the situation where more heat has been trapped by the atmosphere – the atmosphere has increased its absorption of longwave radiation

Whether or not more heat also leaves the surface by evaporation or conduction doesn’t really matter for this analysis. It doesn’t tell us what we need to know.

In fact, it’s quite likely that if evaporation increases we might find that positive feedback exists. However, that depends on exactly where the water vapor ends up in the atmosphere (as the absorption of longwave radiation by water vapor is non-linear with height) and how this also changes the lapse rate (as the moist lapse rate is less than the dry lapse rate).

It’s possible that if convective heat fluxes from the surface increase we might find that negative feedback exists – this is because heat moved from the surface to higher levels in the atmosphere increases the ability of the atmosphere to radiate out heat. This is also part of the lapse rate feedback.

But all of these different effects are wrapped up in the ultimate question of how much heat leaves the top of atmosphere as a function of changes in the surface temperature. This is what feedback is about.

So for feedback we really want to know – does the absorptance of the atmosphere increase as surface temperature increases? (see note 3).

That’s as much as I can explain as to why this measure is the useful one for understanding feedback. This is why everyone that deals with the subject reviews the same fundamental equation. This includes those who believe that negative feedbacks dominate.

See Note 2 and Note 3.

Colin Davidson’s points

Colin often makes very sensible statements and points but many of the statements and claims cited earlier suffer from irrelevance, inaccuracy or a lack of any proof.

Missing the point – as I described above – was the main problem. In the interests of completeness we will consider some of his statements.

The third comment cited above indicates one of the main problems with his approach:

..Unless the earth’s short-wave albedo changes, the Outgoing Long-Wave Radiation(F) is constant, whatever the state of the Greenhouse. So dF/dTs does not represent the Greenhouse Effect..

This is not the case. Suppose that absorbed solar radiation is constant. This does not mean that OLR (=”F” in Colin’s description) will be constant. From the First Law of Thermodynamics:

Energy in = Energy out + energy added to the system

In long term equilibrium energy in = energy out. However, we want to know what happens if something disturbs the system. For example, if increased CO2 reduces OLR then heat will be added to the climate system until eventually OLR rises to match the old value – but with a higher temperature in the climate. The same is the case with any other forcing. (See The Earth’s Energy Budget – Part Two).

In fact we expect that for a particular location and time OLR won’t equal solar radiation absorbed. We also have the problem that any “out of equilibrium” signal we might try to measure at TOA is very small, and within the error bars of our measuring equipment.

I didn’t understand what this equation was trying to say. How are the Surface Radiation and the Outgoing Long Range Radiation linked, noting that there are other fluxes from the Surface into the Atmosphere? And one of these (evaporation) is stronger than the NET Surface radiation, while direct Conduction is also a significant flux?

This is a very basic point. The surface radiation and outgoing longwave radiation (OLR) are linked by the equations of atmospheric absorption and emission (see note 4). With no absorption, OLR = surface radiation. The more the concentration of absorbers in the atmosphere the greater the difference between surface radiation and OLR. If we want to find out the feedback effect of water vapor this is exactly the relationship we need to study. Surface radiation and OLR are linked by the very effect we want to study.

A similar problem is suggested in the second comment cited:

..Hence my problem with the equation F=S-G as a starting point for any analysis – it doesn’t seem to represent anything coherent. Why not start with the TOA balance, the Surface balance, or the Atmospheric balance?

How is it possible to extract positive or negative feedback from these?

We expect that at TOA and at the surface the long term global annual average will balance to zero. But we can’t easily measure evaporation or sensible heat. Without carefully placed pyrgeometers we can’t measure DLR (downward longwave radiation) and without pyranometers we can’t measure the incident solar radiation at the surface. In any case even if we had all of these terms it doesn’t help us extract the sign or magnitude of the water vapor feedback.

If we had lots of measurement capability at a particular location it might help us to estimate the evaporation. But then we have the problem of where does this water vapor end up? This is a problem that Richard Lindzen has frequently made – and is also made by Held & Soden in their review article (cited in Part Two). Approaching the problem (from the surface energy balance) without knowing the answer to where water vapor ends up we can’t attempt to calculate the sign of water vapor feedback.

Colin also makes a number of other comments of dubious relevance in the last section of text I extracted.

He states that evaporation and conduction are “greenhouse independent” – but I question this. More “greenhouse” gases mean more surface irradiation from the atmosphere, and therefore more evaporation and conduction (and convection).

The amount of radiation escaping through the so-called “atmospheric window” is not constant (perhaps a subject for a later article). The rest of the statement covers the belief in some kind of simplified atmospheric model where everything is in balance – and therefore a positive feedback is defined out of existence:

Basically when the surface temperature increases, the increase in Evaporation is balanced by a decrease in Net Surface Radiation Absorbed by the Atmosphere.
As the heat entering the lower atmosphere is unchanged (though the amounts entering at each height will change), the overall Lapse Rate to the tropopause will be unchanged. So the temperature at the Tropopause will always be the Surface Temperature minus a Constant. The sensitivity of the Tropopause temperature is therefore the same as (and driven by) the sensitivity of the Surface temperature to changes in “forcing” (either solar or back-radiation).

When surface temperature increases, evaporation is not balanced by a decrease in net surface radiation absorbed by the atmosphere. In fact, when surface temperature increases, surface radiation increases and possible atmospheric absorption of this radiation increases (due to humidity increases from more evaporation). Exactly what change this brings in DLR (atmospheric radiation received by the surface) is a question to be answered. By saying everything is in balance means that the solution about positive feedback is already known. If so, this needs to be demonstrated – not claimed.

The rest of the statement above suffers from the same problem. None of it has been demonstrated. If I understand it at all, it’s kind of a claim of climate equilibrium which therefore “proves” (?) that there isn’t water vapor feedback. However, I don’t really understand what it might demonstrate.

Other Comments Needing Response from the Original Article

From Leonard Weinstein:

Since the issue is not resolved that the temperature in the upper troposphere has increased, and the relative humidity has not stayed nearly constant (it has clearly decreased) over the period of greatest lower troposphere temperature increase, the argument seems less than resolved. The lack of increased water vapor in the stratosphere pushes that point even further.

The argument isn’t resolved by this piece of work. This is one attempt to measure the effect over a period of good quality data.

Finely, the data and analysis of Roy Spencer seems to lead to different conclusions even on the data interpretation. Can you point out his errors and respond to those issues?

Roy Spencer’s analysis doesn’t address this period of measurement. His paper is about the period from 2000-2008.

From NicL:

However, I take issue with your statement “It should be clear from these graphics that observed variations in the normalized “greenhouse” effect are largely due to changes in water vapor.” The spatial maps referred to merely indicate a correlation between these two things. It is unscientific to infer causation from correlation. Ramathan himself goes no further than to say the graphics suggest that variations in water vapour rather than lapse rates contribute to regional variations in the greenhouse effect.

It’s unscientific to infer causation from correlation in the absence of a theory that links them together. It’s solidly established that water vapor absorbs longwave radiation from the surface, and it’s solidly established that CO2 and other “greenhouse” gases are well-mixed through the atmosphere, while water vapor is not. Therefore, there is a strong theoretical link.

I think, in common with various other repondants, that changes in lapse rates and in the height of the tropopause are key issues in modelling the greenhouse effect, yet they seem rarely discussed. Ramanathan’s chapter does not really cover them.

What makes you say they are rarely discussed? There are many papers discussing the different processes involved in modeling water vapor feedback. However, Ramanathan’s chapter is primarily about measurements. Of course he refers to the different aspects of feedback in the chapter.

Conclusion

One commenter in part two said:

I want to give him a chance to reflect on whether he wants to defend the Ramanathan analysis in Part 1 or separate himself with dignity, which he can still do..

The primary question seemed to be the approach, and not the results, of Ramanathan.

Ramanathan tested the changes in atmospheric absorptance of longwave radiation with temperature changes. To claim this is inherently wrong is a bold claim and one I can’t understand. Neither can Richard Lindzen or Roy Spencer, at least, not from anything I have read of their work.

There are other possible approaches to Ramanathan’s results. Other researchers may have replicated his work and found different results. Other researchers may have analyzed different periods and found different changes.

There are also theoretical considerations – whether changes in the equilibrium temperature as a result of increased CO2 can be considered as the same conditions under which seasonal changes indicated positive water vapor feedback.

The question for readers to ask is: Did Ramanathan find something important that needs to be considered?

Ramanathan himself said:

However, our results do not necessarily confirm the positive feedback resulting from the fixed relative humidity models for global warming, for the present results are based on annual cycle.
If I someone can point out the theoretical flaw in Ramanathan’s work then I might “separate myself with dignity” otherwise I will be happy to stand by the idea that he has demonstrated something that needs to be considered.

Articles in this Series

Part One – introducing some ideas from Ramanathan from ERBE 1985 – 1989 results

Part Two – some introductory ideas about water vapor including measurements

Part Three – effects of water vapor at different heights (non-linearity issues), problems of the 3d motion of air in the water vapor problem and some calculations over a few decades

Part Four – discussion and results of a paper by Dessler et al using the latest AIRS and CERES data to calculate current atmospheric and water vapor feedback vs height and surface temperature

Part Five – Back of the envelope calcs from Pierrehumbert – focusing on a 1995 paper by Pierrehumbert to show some basics about circulation within the tropics and how the drier subsiding regions of the circulation contribute to cooling the tropics

Part Six – Nonlinearity and Dry Atmospheres – demonstrating that different distributions of water vapor yet with the same mean can result in different radiation to space, and how this is important for drier regions like the sub-tropics

Part Seven – Upper Tropospheric Models & Measurement – recent measurements from AIRS showing upper tropospheric water vapor increases with surface temperature

Note 1.

The actual change in emission of radiation for a 1°C rise in temperature depends on the temperature itself, one of the many non-linearities in science. The example in the article was for the specific temperature of 288K, along with the desire to avoid confusing readers with too many caveats.

Here is the graph of radiation change for a 1°C rise vs temperature:

For the mathematicians it is an easy exercise. For non-mathematicians, the change in radiation = 4σT³ W/m².K (obtained by differentiating the Stefan-Boltzmann equation with respect to T).

Note 2.

This article is about a specific point in Ramanathan’s work queried by some of my readers. His explanation of how to determine feedbacks is much more lengthy and includes some important points, especially the demonstration of the relationships in time between the various changes. These are important for the determination of cause and effect. See the original article and especially the online chapter for more a detailed explanation.

Note 3.

The rate of change of surface radiation with temperature, σdT4/dT = 4σT³ W/m².K (see note 1) is 5.4W/m² per K at 288K. However, the rate of change of OLR, dF/dT, for the no feedback condition is slightly more challenging to determine and not intuitively obvious.

Ramanathan, based on his earlier work from 1981, determined the “no feedback” condition (i.e., without lapse-rate feedback or water vapor feedback) was dF/dT=3.3 W/m².K. And for positive feedback this parameter, dF/dT would be less than 3.3.

Roy Spencer and William Braswell in their just-published work in JGR, On the diagnosis of radiative feedback in the presence of unknown radiative forcing has exactly the same value as the determination of the no feedback condition.

Note 4.

There are many different formulations of the solutions to the radiative transfer equations. This version is from Ramanathan’s chapter in Frontiers of Climate Modeling:

This is just to demonstrate that there is a strong mathematical link between surface radiation and OLR, and one that is very relevant for determining whether positive or negative feedbacks exist.

105 Responses

1. Thanks SoD, great post. I’m going to respond soon.
Now just an early, here yet unfounded note on your last sentence: Miskolczi has pointed out that this strong mathematical link between surface radiation and OLR is actually a constant. [It is a function of tau of course, but the solution of the equation determining it is a constant.]

Miklos

2. Re: “Ramanathan tested the changes in atmospheric absorptance of longwave radiation with temperature changes.”

Miskolczi did the same. The result:

Miklos

3. Dear scienceofdoom,

Ramanthan’s clear sky empirical result to his radiative transfer equation (5.4) is G=131 Wm-2 or, normalized to surface radiation, g=0.33 (1/3) .

Miskolczi’s theoretical derivation for the flux relations in the clear-sky case (using the well known old surface and atmospheric balance equations, and his new flux relationship Aa=Ed, found in analyzing the TIGR2 database in 2004; Aa being the absorbed part of the LW surface upward radiation in the atmosphere, Ed being the “back radiation”, LW emitted downward by the atmoshere, and Su is the surface upward LW radiation, sigma*Ts^4):

OLR/Su=2/3 => G=Su/3 => g=1/3 .

Miskolczi’s general theoretical solution of the radiative transfer equation is

OLR/Su=f(tau)

where f is the transfer function, f(tau)=2/(1+tau+exp(-tau)), coming from the solution of the finite Schwarzschild-equation.

Hence we have

OLR/Su=(3+2Ta)/5 ,

with Ta=exp(-tau), “flux transmittance” in Ramanathan’s Eq. 5.4.

The numerical solution of this equation is a constant,

tau=1.867561…

The global average empirical tau is
— on the TIGR2 radiosonde database: 1.8693
— on the NOAA/NCEP 61 years average: 1.8688
— on Trenberth’s 2009 enrgy budget: 1.8779.

Hence, there must be a dynamic conpensation effect (a zero or not-significantly positive water vapor-temperature feedback PLUS a negative temperature-LW absorption feedback) that keeps the global LW average absorption property (“the greenhouse effect”) of our atmposphere stable.

–>This all, altogether, shows that the amount of radiation escaping through the so-called “atmospheric window” … IS constant.

–> If CO2 concentration increases we expect some tightening of the window… yes, but the overall effect of water vapor amount/distribution and temperature distribution changes as a reaction counterbalance this tightening, KEEPING the window constant.

For details, esp. for his 2004, 2007 and the most recent, August 2010 articles, see http://miskolczi.webs.com .

Sorry for being so long; if something is not clear, just ask!
And many thanks for your attention….

Miklos

4. And finally,

On Miskolczi’s new, above-mentioned Aa=Ed relationship, a detailed discussion can be find at Roy Spencer’s blog:

Thanks,
Miklos

• Miklos,
Your first post on this topic sites Miskolczi’s contention that the “…this strong mathematical link between surface radiation and OLR is actually a constant.”

(I’m a little unclear, but I think you mean that the relationship is linearly related by a constant, but regardless…)

And your last link to Roy Spencer’s blog leads to a refutation that Miskolczi has demonstrated any such thing.

“Now, it might well be that nature has such a greenhouse effect-stabilizing mechanism in place, and that the total greenhouse effect stays at a relatively constant value for a given amount of absorbed solar energy. I have sometimes advanced the same possibility myself.

But I do not believe that Miskolczi has demonstrated either that it is the case, or why it should be the case. ”

I’m confused as to what your point is.

• Chris G:

Yes I mean that “the strong mathematical link between the (clear sky) Su and OLR” is actually a constant, Su/OLR=3/2, or, in a function of the greenhouse effect, Su/OLR=(1+tau+exp(-tau))/2, where tau has a constant (stable, time-independent, stationary) value under the specific conditions prevailing in the Earth-atmosphere system.

If you follow the discussion on Roy Spencer’s blog, you can’t see any refutation of Miskolczi’s statement. You can see several argumentations FOR his statement, and some misunderstandings about what that statement really means.

It can be useful to read the comments there, if one wants to understand the content of the disputed equation, and the operation of the greenhouse effect itself.

Regards,
Miklos

5. OLR through the ‘window’ is greatly affected by cloud cover, something Miskolczi apparently ignores when calculating his average tau. Clouds completely block all OLR from the surface. The new surface is then the cloud tops, which are at a lower temperature than the ground. They are also at higher altitude, so the window is wider and there’s less absorption by the intervening atmosphere overall.

Model climate sensitivity is a function of the change in evaporation/precipitation rate with temperature for the model. Models that have a high rate of change have lower climate sensitivity. So while I don’t question R&C’s determination of the rate of change of OLR with surface temperature, there is still the question of how much the surface temperature will change for CO2 doubling. The calculated forcing depends a lot on the assumption that all other things won’t change or won’t change very much.

6. DeWitt Payne:

You writes Miskolczi ignores the cloud effect on OLR window. Not at all: see this quote from his 2007 paper:

and his comments in the Kiehl-Trenberth 1997 energy budget:

7. As this thread is basically on Ramanathan’s greenhouse factor definition, let me continue on it:

I think yes, it is reasonable to define the “surplus”, or “extra”, or “greenhouse” temperature as the difference of the surface temperature if GHGs are present in the air (Ts) and the surface temperature in lack of these gases (Te, effective temperature): Tg=Ts-Te, or, in LW fluxes,

G = Su – OLR.

But also, as this is the difference of IR heating at the ground (coming from the presence of IR-active gases in the air) and IR cooling at TOA from the same source, we can write:

G = Ed – Eu

(where Ed is atmospheric emitted downward LW [“back radiation”] at the ground and Eu is atmospheric emitted upward LW at TOA).

So, in the clear sky case we will have

G = Su – OLR = Ed – Eu .

This is a very important relationship. From this it follows directly (see http://miskolczi.webs.com/Figure1.jpg) that

G = Su – OLR = Aa – Eu = Ed – Eu .

Hence

Aa=Ed ,

or, with other words, Ed=SuA, where A is the normalized atmospheric LW absorptance, A=Aa/Su (=1–exp(–tau) in Ramanthan’s greenhouse equation 5.4).

This is the first of Miskolczi’s basic relationships. If one accepts this (Roy Spencer seems to be just on the way to do so—see the link above to his blog), one makes the first big step to accept the theoretical constancy of Earth’s greenhouse effect.

For a detailed calculation of G (or, better, of tau), see http://miskolczi.webs.com/tau.jpg .

8. Miklos Zagoni on August 29, 2010 at 12:24 pm:

–>This all, altogether, shows that the amount of radiation escaping through the so-called “atmospheric window” … IS constant.

When you say “constant” what exactly do you mean? With respect to which parameter(s)?

9. scienceofdoom:

The energy (St) escaping through the “window” (or, more precisely, in the transmitted part of the surface upward radiation) is constant with respect to OLR (!), independently of changes in CO2 (or other atmospheric trace GHG), on climatic time-scales (~ some decades), in global averge.

10. The precise statement is this:

The tau (global average IR GHG optical thickness) has a theoretically predictable stable (constant) value, tau=1.867561… under the conditions prevailing in Earth’s atmosphere. Tau is defined as tau=-ln(St/Su) , where Su depends on OLR as OLR/Su= f(tau)=2/(1+tau+exp(-tau)) with the value given above. Therefore OLR/Su has an equilibrium value at 0.6618 for clear-sky. Having OLR constant, St remains constant, independently of the GHG constituents (as far as there is a practically infinite reservoir of GHG’s — water vapor — in the oceans, for dynamic compensation). The play is going on through evaporation and precipitation, under the rigorous constraint of energy conservation (limit of available incoming energy).

11. Miklos Zagoni:

I might have misunderstood what you mean by the “atmospheric window”. Can you define it?

12. SoD,

“I also ignore the personal attacks from a commenter that my article(s) was/were deceptive.”

When I read this, I thought “What moron would suggest that?” So I went back to the comments to find the moron. And, unless you have moderated out some other d***head, I found that… the moron was me.

I believe that your comment is a response to my use of the word “disingenuous”. I guess I could try to explain, justify, defend, delimit or distinguish the use of the word, but at the end of the day it does not matter. You clearly felt insulted by it, and that it was a “personal attack”. And I really really never intended that.

So, you have my most sincere and profound apology. “Deceptive” is not a word I associate with your site.

• Paul_K, no it wasn’t about you.

I was referring to comments from the original post, Part One.

13. scienceofdoom:

To ease the progress, may I turn the question back and ask for your definition of “atmospheric window”? I don’t want to escape from answering, only to shorten the process. But if you still ask me to start, I will.

DeWitt Payne:

May I ask you please what is your accepted value for OLR through the “window”?

• I’m not going to get into a discussion of the nuts and bolts of Miskolczi. I’ve stated my opinion elsewhere that what he is doing is applying what amounts to a single layer gray atmosphere toy model to a complex system. Toy models have their uses, but they also have their limits.

• About his single layer gray atmosphere toy model, see his

14. scienceofdoom:

You can find

(a) Ramanathan’s definition in his Eq. 5.4;

(b) Kiehl and Trenberth’s definition in their KT97: http://www.geo.utexas.edu/courses/387h/PAPERS/kiehl.pdf;

(c) NASA CERES science team definition in http://ceres.larc.nasa.gov/documents/STM/2005-11/miskolczi_airs.pdf ;

(d) Miskolczi’s definition in
http://miskolczi.webs.com/tau.jpg ; and

(e) his comments on KT97 definition in

15. SoD,
A nice post. You wrote:

“Ramanathan tested the changes in atmospheric absorptance of longwave radiation with temperature changes. To claim this is inherently wrong is a bold claim and one I can’t understand.”

To be clear, I would not argue with this statement. It was the ATTRIBUTION of such change solely to water vapour which caused me, and continues to cause me, grave doubts about the validity of the analysis.

It is worth reminding ourselves of what caused the changes (in G) and what was actually measured. The latitide-averaged changes in temperature were due in this analysis to the annual seasonal cycle. This is brought about by a tiny change in TSI, a much larger relative change in SH and NH absorbed TSI, and a large-scale redistribution of atmospheric heat and oceanic heat, including the reversal of some major streams and currents. Now consider any latitude which has achieved its MAXIMUM averaged temperature for that year. What controls the OLR emitted from that latitude at its maximum temperature? The local surface temperature and atmospheric GHG content are certainly controls, but the other major controlling factor is the local vertical temperature profile, which is a function of not just the water vapour profile, but also the local controls on atmospheric sensible heat content for that time of year.

So, I (still) have four areas of concern about the analysis:

1) A necessary but not sufficient requirement for validating the analysis is that the sensible heat content of the atmosphere stays constant through the entire annual cycle – otherwise dG/dT must reflect the change.
2) Even if the total sensible heat content of the atmosphere stays constant overall, the systematic abstraction and addition of sensible heat during local winter and local summer respectively gives rise to false latitude measures of dG/dT.
3)Since the temperature change is largely a SW effect, atmospheric heating will be bottom-up. Thus, as our selected latitude approaches its maximum surface temperature, mid to upper tropospheric temperatures are still trying to catch up, giving rise to a low OLR measurement (relative to a quasi equilibrium for that surface temperature). The same is true in reverse as our latitude approaches its lowest temperature. Hence there is a systematic bias in dG/dT.
4) There is a significant and measurable change in atmospheric CO2 during the annual cycle, which will also contribute to the dG/dT term.

Thanks.

16. SOD and Colin: In the equation F = oT^4 – G, the term G is confusing because it could stand for many things. Many readers may feel that G stands for a purely radiative greenhouse effect and Gclear for the greenhouse effect where clouds aren’t present. In Part 1 and Ramanathan’ paper, dGclear/dT seems to be equated with water vapor feedback or, more correctly, with the combined water vapor/lapse rate feedback. If we focus what is and is not included in G, it may be possible to reconcile both Colin’s and SOD’s points of view.

In SOD’s section “Scenarios to Demonstrate the Usefulness of the Definition”, it is NOW clear that G includes everything that effects energy transport from the surface to space. This pragmatic “black-box” definition includes radiation, convection, clouds, latent heat and conduction. When we plot this G vs temperature, we are looking how ALL these factors change with temperature – in other words, all feedbacks (that operate on the timescale of the temperature change). Gclear is an attempt to include all feedbacks that operate in the absence of clouds. In the troposphere, convection and latent heat (and conduction?) control the lapse rate, so the term “combined water vapor/lapse rate feedback” actually includes many of the important phenomena that Colin feels are absent from Ramanathan’s F = oT^4 – G.

DLR (downward long wavelength radiation from the atmosphere to the surface of the earth) is one of Colin’s phenomena that is clearly NOT included in G. As GHG’s change climate, DLR will certainly change. However, DLR has no direct effect energy transport from the surface to space. Instead, changes in DLR appear in the equation F = oT^4 – G via DLR’s effect on surface temperature, T. So my hypothesis is that when we plot G vs T, we are properly taking into account all of Colin’s factors. On the other hand, when we consider just G alone, we run into difficulties. (In Part 1, these difficulties were taken into consideration by calculating gclear = Gclear/oT^4.)

If this is correct, it shouldn’t make any difference if 95% of the energy were removed from the surface of the earth by radiation or 95% were removed by convection and evaporation. The observed dG/dT is the observed dG/dT – it is independent whatever mechanisms link changes in surface temperature to changes in OLR. However, we do need to be careful what we CALL dG/dT, because the name frequently implies a mechanism. Those with a radiation-centric view will tend to call it water vapor feedback (in clear skies) and those with a convection-centric view may forget that the “combined water vapor/lapse rate feedback” includes the phenomena they feel are neglected.

Spencer, Lindzen and others seem to focus on dG/dT instead of dGclear/dT, possible because it may be difficult to distinguish a thin cloud layer from clear skies. Also, when one analyzes only clear skies, dG/dT is biased for regions where air is subsiding, relative humidity is lower, and the logarithm of the water vapor change (and therefore the absorption change) may be larger. From a practical point of view, the total feedback is the only important factor – not how much feedback is due to water vapor, clouds, and lapse rate/convection. (The combined approach does spoil the fun of alarmists who want to focus on the worst case scenario for each feedback.)

17. Miklos,

So he uses a line-by-line model to calculate the average LW optical depth. Yawn. Because then he still plugs it into a 1 dimensional, single layer gray atmosphere radiative/convective model. Look at the model in chapter 6.4.3 of A First Course in Atmospheric Radiation, 2nd Edition, Grant W. Petty. One only needs to add convective fluxes to and from the atmosphere to the surface and then claim all sorts of fixed relationships between the fluxes.

If the above link doesn’t work, find the book in Amazon, look inside and search on ‘6.4.3’. Pick the link for page 139.

• DeWitt Payne:

Thanks,
Miklos

18. ScienceOfDoom – one comment on this post – you seem to suggest that the “water vapor feedback” could be negative.

I think it’s important to precisely define the feedback terms, because with a proper definition of the “water vapor feedback” I don’t see how a negative value is possible.

Soden and Held’s 2006 paper “An Assessment of Climate Feedbacks in Coupled Ocean–Atmosphere Models”, J. Climate, Vol. 19, p. 3354 – describes the linearized feedback parameters (lambda’s) and separately defines “water vapor”, “lapse rate” and “cloud” feedback parameters that distinguish the different effects associated with changes in water content of the atmosphere.

In the case of water vapor, in this context, the only thing that changes when water vapor levels change, with “lapse rate” and “cloud” conditions held constant, is the infrared absorption and emission in the atmosphere. So increasing water vapor will force a stronger greenhouse effect, i.e. positive feedback, with those other things held the same.

Unless you propose some mechanism by which increased temperatures result in *decreased* levels of water vapor in the atmosphere, it seems there is no question the water vapor feedback (defined to exclude those other changes) has to be positive. Soden and Held find it quite tightly constrained at about 1.8 W/m^2 K.

• There are several mechanisms by which warmer temperature could result in a negative water vapor feedback. 1) Warming puts in more water vapor into the lower troposphere and less water vapor in the upper atmosphere. Temperature in the upper atmosphere is controlled by radiative cooling and less water vapor there will increase radiative cooling – a negative feedback. Temperature in the lower troposphere is controlled by the lapse rate and lapse rate feedback provides a second negative feedback. 2) The rate of evaporation may depend on more than (water) temperature. When the air over water is saturated with water vapor, the rate at which the saturated air is replaced with unsaturated air becomes the limiting factor in transporting water vapor into the atmosphere. If a warmer earth results in less mixing of air above the ocean, water vapor feedback could be negative. 3) The amount of water vapor in the atmosphere is controlled by both the rate of evaporation and the rate of precipitation. If the increase in precipitation is greater than the increase in evaporation on a warmer planet, water vapor feedback could be negative.

Are these mechanisms likely? Are other mechanisms possible? Who knows? However, just because the Clausius–Clapeyron equation says a warmer atmosphere CAN hold more water vapor doesn’t mean more water vapor WILL be present at altitudes that will produce a strongly positive feedback. The atmosphere is not in equilibrium or even close to equilibrium. If it were, we wouldn’t have some locations with nearly 100% relative humidity and others with <10% humidity.

We need reliable observational evidence to confirm the hypothesis that water vapor feedback is strongly positive. SOD has offered some observational evidence and generously and patiently allowed us to discuss its meaning.

Soden and Held (2006) "observe" only computer models, not the real atmosphere. Unfortunately, the grid cells used by these models are far larger than the size of the physical inhomogeneity in the distribution and transport of water vapor. Furthermore, Stainforth et al (Nature, 2006, 433, 403-406) have reported that a Hadley model produces climate sensitivities from 11 when cloud parameters are varied within physically sensible ranges. The idea that “observations” of poor computer models “tightly constrains” water vapor feedback in the real atmosphere is an illusion.

• For very limited observational evidence suggesting that mechanism 1 could be real, see: Gilbert, E&E (2010) 21, 263-275.

19. I would like to thank Science_Of_Doom on two counts:
Firstly, he has provided an ad-hominem free site on which discussion can take place, and he polices this very effectively. This means that all “sides” of an issue can state a case and ENGAGE with the opposing views. Well Done!
Secondly, he has graciously spent time on my objections to the basic Greenhouse equation, and I would like to thank him for that, as I realise that he is very busy just policing, and developing new posts, and getting on with his day job!

I would also like to preface my remarks with the caveat that everything below is predicated on STABLE EQUILIBRIUM states of the climate system – the sort of system depicted in Kiehl & Trenberth 1997, and reproduced in IPCC AR4 WG1 Chapter 1. I realise that this is not the real world, which is dynamic, chaotic and inhomogenous – and I hope to come back to that in future posts.

If we look at the 3 entities in the KT world – planetary boundary, surface and atmosphere, we get the following equations – noting that there are no transients in the KT empire:

(1). Incoming Sunlight = OLR (F) + Reflected Sunlight

(2). Sunlight Absorbed at the Surface (S) = Surface Radiation to Space “through the window” + Net Surface Radiation absorbed by the atmosphere + Evaporated water(E) + Conduction (C)

(3). OLR(F) = Net Surface Radiation absorbed by the atmosphere + Condensed water(E) + Conduction (C) +
Surface Radiation to Space “through the window” + Sunlight absorbed by the Atmosphere.

If we look at two limiting cases, I think these will be instructive:

CASE 1: A PERFECT GREENHOUSE KT PLANET
Here the atmosphere is IR opaque. All surface radiation is absorbed in the first 1mm, All Back Radiation comes from the first 1mm of atmosphere, Conduction is zero as the lowest air is as hot as the Surface. Note that the NET Surface Radiation absorbed by the atmosphere in this case is ZERO, as Back radiation = Surface Radiation.

(2). becomes: Sunlight Absorbed at the Surface (S) = Evaporated water(E)

(3). becomes: OLR(F) = Condensed water(E) + Sunlight absorbed by the Atmosphere.

In a perfect Greenhouse, the only mechanism for removal of energy from the surface to the atmosphere and then out to space is by evaporated water, which releases its Latent Heat to the atmosphere, which reaches the Radiative Top of the atmosphere by convection/conduction.

CASE 2: AN IR TRANSPARENT ATMOSPHERE KT PLANET
There is no back radiation, and all surface radiation shoots straight out into space.

(2) becomes: Sunlight Absorbed at the Surface (S) = Surface Radiation to Space “through the window” Evaporated water(E) + Conduction (C)

(3). becomes:
OLR(F) = Condensed water(E) + Conduction (C) +
Surface Radiation to Space “through the window” , the implication being that Conduction is negative, ie that the atmosphere is hotter than the surface, this being maintained by the evaporation of water.

Now let’s look at two more KT worlds.

THE 1997 15DegC KT PLANET
(1). Incoming Sunlight = OLR (F) + Reflected Sunlight

(2). Sunlight Absorbed at the Surface (S) = Surface Radiation to Space “through the window” + Net Surface Radiation absorbed by the atmosphere + Evaporated water(E) + Conduction (C)
The Net radiation absorbed by the atmosphere is very small, only 26W/m^2. Evaporated Water at 78W/m^2 is 3 times this and Conduction at 24W/m^2 is about the same.

(3). OLR(F) = Net Surface Radiation absorbed by the atmosphere + Condensed water(E) + Conduction (C) +
Surface Radiation to Space “through the window” + Sunlight absorbed by the Atmosphere.

THE 18DegC KT PLANET
IPCC AR4 predicts (semantically equivalent to postulates, prognosticates, projects, guesses, estimates, soothsays) a 3DegC surface temperature rise for a doubling of CO2. What does this world look like?
1). If albedo does not change then F, the OLR, does not change (see equation 1).
2). The temperature differential between the surface and the atmosphere is likely to be about the same as in the 15DegC case. This implies that Conduction remains the same. The CO2 Greenhouse Window will tighten a very little (it’s already almost perfect) and this tightening is offset by an increased intensity, so the Surface Radiation through the window is likely to be about the same as in the 15DegC case. Surface Radiation and Back Radiation and Evaporation all increase, but the Net Radiation from the Surface into the atmosphere must fall by the same amount that Evaporation increased. IE, the Back Radiation must increase by MORE than the Surface Radiation. This situation is exacerbated if the albedo changes, or if there is significant additional atmospheric absorption of sunlight.

SUMMARY
In a KT planet which transitions from one STABLE EQUILIBRIUM state to a second STABLE EQUILIBRIUM state, where the temperature difference is small:
1. Any change in OLR is due to a change in Albedo.
2. The energy transport from the surface to the atmosphere is about the same (unless sunlight absorbed by the surface is reduced by increased albedo, or by increased atmospheric absorption of sunlight). The transportation mechanism changes, however, with lesser transport by radiation, and greater transport by evaporation.
3. This change will mean a different temperature profile through the atmosphere, but the total energy into the atmosphere is the same, so the temperature at the Tropopause will be the same. This temperature is tied to the Surface Temperature,
4. The surface sensitivity to changes in forcing is between 0.1 and 0.2 DegC/W/m^2 (max to zero increase in evaporation). The Tropospheric temperature change rate is the same, as its temperature is tied to the surface.
5. The implication is that to get a 3DegC change to the planetary temperature you need to have a Back Radiation change of 15-30W/m^2.
6. Mind you, that’s only for KT planets!

• When discussing a 288 degK planet, Colin says (9/1 12:36 am): “2) The temperature differential between the surface and the atmosphere is likely to be about the same as in the 15DegC case”.

This statement may be incorrect. Increasing GHGs require the “average” photon escaping from the atmosphere to space to be emitted from higher in the atmosphere, where it is colder. To return OLR to equilibrium with incoming sunlight, the temperature of the atmosphere where the “average” escaping photon is emitted should rise until it returns to the previous value. Assuming that the lapse rate is fixed from the surface to the altitude the “average” escaping photon is emitted, a higher average altitude of emission will translate to a warmer surface. The 1 degK rise in temperature predicted for 2X CO2 without feedbacks requires the altitude of “average photon emission” to rise about 0.15 km (150 m). See Lindzen’s “Taking Greenhouse Warming Seriously” (Energy & Environment, 18, 935-948, 2007; www-eaps.mit.edu/faculty/lindzen/PublicationsRSL)

The KT energy budget has limited usefulness. To maintain equilibrium, 235 w/m^2 of energy needs to be transported through all altitudes of the atmosphere. The proportion of this energy transported by radiation, convection and latent heat CHANGES with altitude and GHG concentration. Possible climate change can’t be understood assuming KT’s energy budget is static.

Any comments on my long post trying to reconcile your view with SOD’s?

20. There is an error in para 3. above. It should read:
“3. This change will mean a different temperature profile through the atmosphere, but the total energy into the atmosphere is the same, so the temperature difference between the surface and the Tropopause will be the same. The Tropopause temperature is tied to the Surface Temperature, it moves up and down with the surface temperature.”

21. Arthur Smith:

ScienceOfDoom – one comment on this post – you seem to suggest that the “water vapor feedback” could be negative.

I think it’s important to precisely define the feedback terms, because with a proper definition of the “water vapor feedback” I don’t see how a negative value is possible..

I’m not sure where I have suggested that in the post.

However, many things are possible. And it’s important before we’ve considered all the evidence to open up to what might be possible.

Unless you propose some mechanism by which increased temperatures result in *decreased* levels of water vapor in the atmosphere, it seems there is no question the water vapor feedback (defined to exclude those other changes) has to be positive.

There are many challenges with understanding water vapor feedback. One of them is the non-linear feedback with height in the atmosphere and location. It’s easy to consider the scenario of total water vapor being constant and yet the overall feedback effect being negative – this is from the location of the water vapor.

Move water vapor downwards and from drier to wetter locations and the same total water vapor will produce less absorptance.

Well, I don’t think that was in my post, but it is all for further exploration.

• But non-linear feedback is a second-order effect; that’s why I asked about definitions. Strictly the water-vapor feedback (at least the Soden and Held version) is defined as a linearization, a partial derivative, changing water vapor levels alone, while keeping lapse rate, clouds, etc. fixed and under the condition of uniformly increased troposphere temperature (the Planck response that other feedbacks are measured against). So there should be no nonlinearity to worry about.

Yes, if you redistribute water vapor within the atmosphere the greenhouse impact will change. But under the theoretical constraint of changing only temperature uniformly and holding all else fixed while allowing water vapor levels to change, it seems to me this has to result in either the same or increased water vapor levels everywhere, no? So a positive feedback is forced?

The negative feedback Lindzen talks about relates to cloud effects, not water vapor alone, though he misleadlingly conflates the two in articles written for the general public. Unless I’m really missing something there…

22. Colin Davidson:

I think there are a few interesting points to take up in further posts.

There are many assumptions that I’m not sure about, including the “atmospheric window”.

The question I wanted to take up here was about the usefulness of the Kiehl & Trenberth “energy budget” for analyzing changes.

Many people over many decades have been intrigued by the question of the relative proportion of each factor at the surface and the TOA.

This latest, and often-cited, diagram/paper is just in the same vein.

Its purpose is not for dynamic considerations, and it’s not a claim that the world is static. It’s simply an interesting analysis of the relative proportion of effects.

Let’s suppose we can’t decide whether this is a useful or useless endeavor.

In any case, the purpose of the paper wasn’t to illuminate the response of the climate system to dynamic changes. Using it to analyze the climate response to dynamic changes probably won’t be a useful exercise. Other resources will be needed for that exercise.

23. Miklos Zagoni:

In response to my question asking for a definition of “the window”, which is claimed to be constant, said:

You can find

(a) Ramanathan’s definition in his Eq. 5.4;

Cryptic, and no you can’t. You can see his definition of the “atmospheric window” in other papers, e.g., Satellite observations of the water vapor greenhouse effect and column longwave cooling rates, JGR (2004) – where he defines “the window” as 8-12um.

(b) Kiehl and Trenberth’s definition in their KT97: http://www.geo.utexas.edu/courses/387h/PAPERS/kiehl.pdf

They define it the same way as Ramanathan, “..The largest
emission occurs between 8 and 12 um (the so-called atmospheric window)..”

(d) Miskolczi’s definition in http://miskolczi.webs.com/tau.jpg

No definition of it here.

(e) his comments on KT97 definition in

That’s why I wanted a precise definition. It looks like from this last link that Miskolczi “defines” others to be wrong by using a different definition:

This is wrong; the transmitted flux density can not be localized to the 8–12 μm spectral range. There is significant transmitted flux density in the far infrared (FIR) and medium
infrared (MIR) spectral regions
.”

So back to my original question:

Citing your comment from August 29, 2010 at 12:24 pm:

–>This all, altogether, shows that the amount of radiation escaping through the so-called “atmospheric window” … IS constant.

When you say “constant” what exactly do you mean? With respect to which parameter(s)?

So, as Miskolczi uses a different definition of “the window” to the rest of the world, and as you claim this to be constant, please define exactly what it is that remains constant.

24. scienceofdoom:

(a) Ramanathan says: “expression in square parentheses thus represents the absorptance”. Therefore, (1-absorptance) represents the transmittance. This is the real (physical) window: what leaves the atmosphere without absorbed and re-emitted, i.e., unimpeded.

(b) KT definition: 8-12 um is only a “cut” from OLR. They say, “the largest emission occurs” here. But this region is not completely transparent, and there are also non-zero transmission outside this region.

(c) NASA CERES measures window between 8.1-11.8 um.

(d) The correct – physical – definition of it is “transmittance”: surface upward LW radiation minus atmospheric LW absorptance (defined on the WHOLE spectrum): St=Su-Aa. This is computed by Ramanathan, and that is computed LBL by Miskolczi.

(e) In his comments M. points out this problem with the KT definition: it is not a physical, but only a technical definition; and contradicts what is shown graphically on their chart KT97 Fig7, as the graphics there shows correctly def (d).

The greenhouse effect in the world does not depend on your technical definition whether the window is defined between 8-12 or 8.1-11.8 or else. It depends on the physical quantity of the absorbed LW in the air. And the

absorbed (Aa) = Su – transmitted (St).

“Transmitted” (St) is the physical meaning of “window”.

When you are talking about Ramanathan’s G=Su-OLR (Su=sigma*Ts^4), or the same G=Ed-Eu (Ed: “Back Radiation”, Eu: atmospheric upward LW rad.), you have to define them correctly: Su=Aa+St, OLR=St+Eu.

Miklos

25. There is no transmission directly to space from the surface in the far IR. Absorption in the FIR is dominated by the strong water vapor continuum spectrum in that region. The water vapor continuum is not included in the HITRAN database. It’s currently calculated using a semi-empirical fit to the measured data known as the CKD model. There is considerable controversy as to the theoretical origin of the continuum spectrum.

See brief review here:

• To put some numbers out: The far IR is defined as 10 – 400 cm-1. MODTRAN average transmittance for 100-400 cm-1 is 0.0000. For the range of 5 to 100 cm-1 and a surface temperature of 288.2 K, total emission is only 2.09 W/m2 out of 391.2 W/m2 total (emissivity = 1). So even if there were some slight transparency in this range, it wouldn’t be significant. There might be some transparency in the near IR, but again, there’s not all that much power (21.4 W/m2 1500-3000 cm-1)

wavenumber transmittance net flux(w/m2)

100-400 0 0
400-700 0.022 2.75
700-1300 0.576 89.8
1300-1500 0.0079 0.15

That means 97% of the transmitted flux is in the range from 700-1300 cm-1. Looks like a window to me.

• DeWitt Payne:

I confirm your 21 Wm-2 against WIN for a Ts=310K warm mid-lat profile (h2o ~ 2 prcm). (But I can’t see how it would be 97%, related to 390 Wm-2.)

Although, for example in a cold dry Antarctic profile (Ts ~ 232K, h2o ~ 0.11 prcm), the ratio WINDOW/TOTAL is less than 1/2 .

Miklos

26. Science_Of_Doom commented:
“The question I wanted to take up here was about the usefulness of the Kiehl & Trenberth “energy budget” for analyzing changes.

Many people over many decades have been intrigued by the question of the relative proportion of each factor at the surface and the TOA.

This latest, and often-cited, diagram/paper is just in the same vein.

Its purpose is not for dynamic considerations, and it’s not a claim that the world is static. It’s simply an interesting analysis of the relative proportion of effects.

Let’s suppose we can’t decide whether this is a useful or useless endeavor.

In any case, the purpose of the paper wasn’t to illuminate the response of the climate system to dynamic changes. Using it to analyze the climate response to dynamic changes probably won’t be a useful exercise. Other resources will be needed for that exercise.”

Frank also commented:
“The KT energy budget has limited usefulness. To maintain equilibrium, 235 w/m^2 of energy needs to be transported through all altitudes of the atmosphere. The proportion of this energy transported by radiation, convection and latent heat CHANGES with altitude and GHG concentration. Possible climate change can’t be understood assuming KT’s energy budget is static. ”

I agree that the KT world is a very innaccurate version of the real thing. Everything is average, and nothing is dynamic.
I think, however it is a useful model in trying to understand what a peturbed system will tend to do, and in sorting out the roles of the various pieces. For me it throws up these queries:
1. How much is sunlight reaching the surface further attenuated if CO2 is doubled?
2. Where does that additional energy absorbed by the atmosphere enter the atmnosphere?
3. The role of evaporation in determining surface temperature change is critical. No-one knows what happens to this when temperature rises – it could change anywhere between 0 and 10% per DegC. This means a factor of 2 to 3 in the temperature response of the surface to forcing changes. How do we measure this critical value?
4. What is the relationship of cloud cover to evaporation? If cloud cover changes, so does albedo, directly affecting the climate by changing the attenuation of sunlight reaching the surface.
5. With a doubling of CO2 and a probable increase in evaporation, what happens to relative humidity, which affects the height at which clouds form? This is important as low clouds may affect back-radiation, but high clouds won’t because atmospheric radiative interaction with the surface is at low altitudes.
6. The KT model suggests that temperature at high altitudes is related to surface temperature – as the surface temperature increases, so does the atmospheric temperature at altitude, by the same amount. Does it?

The real world situation is highly chaotic, with many linked and interacting variables, the primary ones being the Earth’s rotation, and the weather. This makes it extremely difficult to understand who is doing what to whom. In this regard I think Dr Spencer’s work, in which he plots the change in Surface temperature against change in OLR is fascinating. His simple model seems to emulate the climate system more accurately than the IPCC models – he may be onto something. It is of some interest that he deduces a climate sensitivity of 0.6DegC, a number close to the KT surface sensitivity calculated for a mid-high rate of change of evaporation with temperature.

27. Frank (1Sep, 1309) kindly responded to my post, saying:
“When discussing a 288 degK planet, Colin says (9/1 12:36 am): “2) The temperature differential between the surface and the atmosphere is likely to be about the same as in the 15DegC case”.

This statement may be incorrect. Increasing GHGs require the “average” photon escaping from the atmosphere to space to be emitted from higher in the atmosphere, where it is colder. To return OLR to equilibrium with incoming sunlight, the temperature of the atmosphere where the “average” escaping photon is emitted should rise until it returns to the previous value. Assuming that the lapse rate is fixed from the surface to the altitude the “average” escaping photon is emitted, a higher average altitude of emission will translate to a warmer surface. The 1 degK rise in temperature predicted for 2X CO2 without feedbacks requires the altitude of “average photon emission” to rise about 0.15 km (150 m). See Lindzen’s “Taking Greenhouse Warming Seriously” (Energy & Environment, 18, 935-948, 2007; www-eaps.mit.edu/faculty/lindzen/PublicationsRSL)”

I don’t see any problem between the two statements:
1. Colin : The high altitude temperature is in a fixed relationship with the Surface.
2. Frank: The height of emission will increase, translating to a warmer surface.

That is, the mechanism is:
Imbalance in the high troposphere, causing that portion to heat up. That heating translates to an imbalance at the surface, causing the surface to heat up. That causes to low troposphere to heat up, causing increased emission from the water vapour layer, causing less energy to be radiated from the CO2 layer, causing cooling etc, until everything settles into a new balance (only in a KT world. The real world is never in balance!). The end point is a balanced system where the amount of change in surface temperature is governed by the surface sensitivity.

28. on September 2, 2010 at 1:29 am | Reply Colin Davidson

Frank wrote (30Aug, 21, 2122):
“DLR (downward long wavelength radiation from the atmosphere to the surface of the earth) is one of Colin’s phenomena that is clearly NOT included in G. ”

Firstly, l would like to thank Frank for his comments. However I do not agree with the quoted statement above.

The Greenhouse Equation cited by Science_Of_Doom is:

But, neglecting transients,

Net_Energy_Input_into_Atmosphere = Sunlight_Absorbed_by_Atmosphere +(Surface_Radiation – Surface_Radiation_direct_to_Space_through_the_Window – Back_Radiation) + Evaporation + Conduction,

Resulting in:

F= Sunlight_Absorbed_by_Atmosphere +Surface_Radiation – Back_Radiation + Evaporation + Conduction,

So,
G=Sunlight_Absorbed_by_Atmosphere – Back_Radiation + Evaporation + Conduction

G, the Greenhouse Factor, clearly includes Back Radiation.

• Collin,

You have made a sign error in your equation:

Correctly:

That makes a change of sign also in your last equation:

“G=Sunlight_Absorbed_by_Atmosphere – Back_Radiation + Evaporation + Conduction”,

correctly:

– G=Sunlight_Absorbed_by_Atmosphere – Back_Radiation + Evaporation + Conduction,

or, putting it more clearly,

G = Back_Radiation – (Sunlight_Absorbed_by_Atmosphere + Evaporation + Conduction)

Miklos

• Colin:
Sorry for my typo in your name.
Miklos

• Colin:

… or, to put it even more clearly, your equation reads:

* * *

Colin calls it Back_Radiation, Frank notes it as DLR (“downward long wavelength radiation from the atmosphere to the surface of the earth”).

Scienceofdoom, may I suggest to you to introduce some common notations for these quantities on your blog?

In my – not necessarily acceptable – notation, Back Radiation is Emitted_Downward_by_the_atmosphere, Ed,

while Colin’s Energy _radiated_to_Space-by_Atmosphere is Eu, Emitted_Upward_by_the_atmosphere.

OLR is given – I wouldn’t call it F ; let it be OLR.

Surface_Upward_radiation is also given, Su.

So in my notation, Ramanathn’s and Colin’s equations are as follows:

G = Su – OLR ; G = Ed – Eu .

But clearly notations do not matter too much. Anyone may suggest better ones if he/she likes; I surely will accept them.

Miklos

29. on September 2, 2010 at 1:34 am | Reply Colin Davidson

Frank wrote (30Aug, 21, 2122):
“If this is correct, it shouldn’t make any difference if 95% of the energy were removed from the surface of the earth by radiation or 95% were removed by convection and evaporation. The observed dG/dT is the observed dG/dT – it is independent whatever mechanisms link changes in surface temperature to changes in OLR. However, we do need to be careful what we CALL dG/dT, because the name frequently implies a mechanism. Those with a radiation-centric view will tend to call it water vapor feedback (in clear skies) and those with a convection-centric view may forget that the “combined water vapor/lapse rate feedback” includes the phenomena they feel are neglected.

Spencer, Lindzen and others seem to focus on dG/dT instead of dGclear/dT, possible because it may be difficult to distinguish a thin cloud layer from clear skies. Also, when one analyzes only clear skies, dG/dT is biased for regions where air is subsiding, relative humidity is lower, and the logarithm of the water vapor change (and therefore the absorption change) may be larger. From a practical point of view, the total feedback is the only important factor – not how much feedback is due to water vapor, clouds, and lapse rate/convection. ”

I agree with all of this comment.

30. Miklos,

The 97% refers to the total transmitted flux of 92.7 W/m2. The transmitted flux is 100*92.7/391.2 = 23.7% of the total flux. The transmitted flux in the window from 700-1300cm-1 is then 100*89.8/391.2 = 22.96%

• DeWitt Payne:

Your atmosphere with a total transmitted flux St=92.7 Wm-2 does not seem to represent the real global average. It seems to be the U.S. Standard Atmosphere 1976, with appendix B of Liou for humidity profile. But that profile contains only about 1.43 prcm, almost only half of the real one. KT97 dimineshed further that quantity by about 12%. Calculating LBL that atmosphere, we have really St~90 Wm-2, with only about 70 Wm-2 in the WIN region (833-1250 cm-1), and 20 Wm-2 outside of it. Concerning the real greenhouse effect (global average IR tau), only the ratio St/Su counts, and those ratios for USST76 (where St=90), KT97 (St=40), and the real one, are very different.

Miklos

• Yes, it’s the 1976 atmosphere. Your definition of the window is way too narrow. Almost all of the 20 W/m2 outside your 833-1250 window is in the 700-833 range. For the 1976 atmosphere, 20.6 W/m2 is transmitted from 700-832 cm-1. At 1252 cm-1 the transmittance is 0.4. 1300 or even 1350 is better.

• Re: DeWitt Payne on September 3, 2010 at 2:31 pm

You wrote:
“Your definition of the window is way too narrow. Almost all of the 20 W/m2 outside your 833-1250 window is in the 700-833 range. For the 1976 atmosphere, 20.6 W/m2 is transmitted from 700-832 cm-1.”

Dear DeWitt, you know as well as me that 8 – 12 um (=833 – 1250 cm-1) is not MY definition of window; this is the “official” IPCC-Kiehl-Trenberth definition of window. This casts some light on the credibility of their numbers…

Miklos

31. on September 3, 2010 at 1:50 am | Reply Colin Davidson

In his main post, Science_Of_Doom says:
“Colin also makes a number of other comments of dubious relevance in the last section of text I extracted.

He states that evaporation and conduction are “greenhouse independent” – but I question this. More “greenhouse” gases mean more surface irradiation from the atmosphere, and therefore more evaporation and conduction (and convection).

The amount of radiation escaping through the so-called “atmospheric window” is not constant (perhaps a subject for a later article). The rest of the statement covers the belief in some kind of simplified atmospheric model where everything is in balance – and therefore a positive feedback is defined out of existence…”

I don’t agree with the last phrase. Suppose CO2 is doubled. It must be possible to construct a KT diagram for the new situation. That KT diagram will contain all the steady state “feedbacks”, positive or negative. These help to maintain the elevated surface temperature – indeed using the KT diagram it is possible to deduce the magnitude and sign of the “feedback” “forcing” required to maintain the system with an elevated surface temperature.
The numbers for a temperature elevated by 3 DegC are 15 to 30W/m^2, depending on whether evaporation increases by 0%/DegC through to 6%/DegC. (This assumes no change in conduction – ie that the temperature differential between the surface and the atmosphere is the same for all steady state surface temperatures. This may or may not be the case.)

One of the many problems for everyone trying to establish what is causing what and where the system will go to next (if we can ever do that for this classic chaotic system) is that we are in some respects too close – it is hard to get global averages. Perhaps we should be looking at distant monitors which cannot resolve latitudinal/land/sea/cloud differences. Something like the monitoring of earthlight, and the monitoring of IR, but from a distant orbit (pluto?).

• “He states that evaporation and conduction are “greenhouse independent” – but I question this. More “greenhouse” gases mean more surface irradiation from the atmosphere, and therefore more evaporation and conduction (and convection).”

I gotta ask what may be a dumb Q… how much of a factor is wind in evaporation… and how much of a factor is a differential in air pressure(or T) in wind… and if the differential is changed is it possible that this may have an effect on total evaporation… or has SST been firmly established as the predominant driver of evaporation? It just seems to me that this would vary vrs latitude, ambient air T etc. Cold winds straight off the pole here across the southern ocean, carry a bit o water(and a lot o sodium to boot)

• Mike: The amount of vapor present at equilibrium immediately above liquid water depends on the temperature of the water. However, diffusion is a very slow way of transferring water vapor from near the surface of liquid water into the bulk of the atmosphere. Convection (wind) can move water vapor away from liquid water much faster and therefore dramatically increase the rate of evaporation. I vaguely remember reading that GCMs use empirical parameters to model how wind influences evaporation.

• Thank you Frank.

• Mike Ewing,
Try this empirical equation. It works for my swimming pool!:-
http://www.engineeringtoolbox.com/evaporation-water-surface-d_690.html

32. Colin Davidson wrote (9/2 12:54 am):

“I don’t see any problem between the two statements:
1. Colin : The high altitude temperature is in a fixed relationship with the Surface.
2. Frank: The height of emission will increase, translating to a warmer surface.”

I’m not sure how much we disagree. You often focus on the surface of the earth, but there are advantages to starting higher in the atmosphere. When SOD analyzed the hollow PVC sphere, he started with the outer surface and relied on the fact that it had to emit X W/m^2 at equilibrium to determine the temperature of the outer surface. Then SOD calculated how big the temperature gradient to the inside surface had to be to deliver enough energy to the outside surface by conduction. If we apply the same strategy to the earth, we know that 235 W/m^2 must be emitted from the earth’s “outside surface” to balance the 235 W/m^2 absorbed by the ground, ocean and lower atmosphere. Although there is no tangible “outside surface” that is the source of all of the photons that leave the earth (these photons come from the surface and all altitudes), we can consider the average altitude from which photons escape as the “emitting outer surface”. When GHG’s increase, the average photon needs to be emitted from a higher altitude (so it escapes past the same number of absorbing GHGs). The average temperature of photon emission, however, needs to remain the same, so that oT^4 still totals 235 W/m^2. This defines an average temperature for the “outer emitting surface” of the earth. The altitude of this “outer surface” changes with the amount of GHG in the atmosphere in a manner analogous to increasing the thickness of the PVC shell.

Continuing the hollow PVC shell analogy, we determine the temperature gradient between the surface of the earth and the “outer surface of the atmosphere” (or altitude from which the average escaping photon is emitted). Since the temperature of the “outer surface” is fixed, the steepness of that temperature gradient and the distance spanned by the temperature gradient determine the temperature of the surface of the earth. (In the same manner, the equation for conduction and the thickness of the PVC shell determine the temperature of the inside surface of the PVC shell).

The span of the temperature gradient increases when GHG’s raise the height of the average emitting altitude. This increases surface temperature. This might be considered to be the surface manifestation of the radiative forcing defined at the tropopause

The span of the temperature gradient increases when water vapor increases near the tropopause and blocks outgoing radiation (just like other GHG’s). This is the classic positive water vapor feedback and is also felt at the surface of the earth. However, this positive water vapor feedback shouldn’t operate below the tropopause, where the temperature is controlled by the lapse rate. Where water vapor impedes radiative cooling, the temperature gradient steepens and convection (and latent heat) increase until a stable lapse rate is restored.

The steepness of the temperature gradient between the surface and the average emission altitude is determined by the lapse rate. Increasing humidity in the lower atmosphere reduces the lapse rate, lowering the temperature rise produced by GHGs. Technically, this is a (negative) lapse rate feedback opposing the warming produced by increased GHGs.

From this perspective, it seems confusing to say: “the high altitude temperature is in a fixed relationship with the Surface.” Another confusing statement is: “The end point is a balanced system where the amount of change in surface temperature is governed by the surface sensitivity.” Temperature at the surface and at all altitudes is controlled by the need to maintain a constant upward flux of energy through the atmosphere equal to flux the deposited by sunlight. Nothing is fixed except lapse rate and even lapse rate changes with water vapor. (An 0.1 degK/km change in lapse rate is very significant when it spans about 10 km.) Most confusing of all is a focus on the KT energy transfer diagram. However small (or large) the percentage of energy transferred vertically by radiation at the surface, that percentage grows to 100% at the tropopause. When GHGs interfere with radiative cooling low in the atmosphere or DLR increases surface temperature, convection and latent heat automatically compensate. Aside from clouds, the two key factors controlling surface temperature appear to be the altitude from which the average escaping photon is emitted and the lapse rate from there to the surface.

33. I moderated out my own last comment for breaching blog guidelines.

Miklos Zagoni:

Re: DeWitt Payne on September 3, 2010 at 2:31 pm

You wrote:
“Your definition of the window is way too narrow. Almost all of the 20 W/m2 outside your 833-1250 window is in the 700-833 range. For the 1976 atmosphere, 20.6 W/m2 is transmitted from 700-832 cm-1.”

Dear DeWitt, you know as well as me that 8 – 12 um (=833 – 1250 cm-1) is not MY definition of window; this is the “official” IPCC-Kiehl-Trenberth definition of window. This casts some light on the credibility of their numbers…

Is your central point that the conventional definition of the “atmospheric window” = “8-12um” is wrong?

If so, and we decided for one crazy minute to allow the world to use that old “flawed” definition – is there any problem with the “credibility” of the K&T numbers?

• I would like to thank Frank for his long response.
I think we are quite close in understanding, but:
1. The “Outer Surface” from which radiation to Space occurs is actually 3 surfaces –
A. The planetary surface, for frequencies which are not absorbed by the GHGs.
B. The top of the Water Vapour. This top will be different for different frequencies, but roughly it is where the water vapour is mostly purged from the atmosphere – around the cloud tops. Above this there is insufficient water vapour to absorb all the water emitted photons.
C. The top of the CO2. This top is reckoned to be near the Tropopause, but will vary for different frequencies. In the centre of the wavenumber 670 lines, the Top is high in the stratrosphere.

If CO2 is doubled in concentration, the CO2 top moves towards outer space, until the overlying CO2 is insufficient to block all CO2 emitted photons. For most CO2 frequencies, the Top is now at a lower temperature (but not for the centres of the 670 lines, where it is higher), so less energy is radiated. This defecit (presumably taking into account the Stratospheric cooling as well….) is reckoned to be 3.7W/m^2. This will cause atmospheric heating until the defecit is eliminated.

That heating may cause several things to happen:
1. The Top of the water layer, from which the great majority of the energy radiated to space comes, will heat up, and therefore relatively more energy will now radiate from this part of the atmosphere.
2. The surface will heat up. This will:
A. Increase the amount of energy radiating direct to Space.
B. Probably increase the evaporation rate.
C. Thus possibly increasing the water vapour content of the air.
D. Thus possibly raising the water vapour top. Which is then cooler, reducing the emission to space…

All the changes cease when the system is in balance. At that time:
1. The amount of energy leaving the surface exactly equals the sunlight absorbed by the surface. If (due to increased cloud) that is less than the previous state, the temperature differential between the surface and 11km will increase. If there is less cloud, then the temperature differential will decrease.
2. The relative importance of the 3 different mechanisms for getting surface energy into the atmosphere will change. But the changes in relativity between the different transport mechanisms does not affect the temperature at the 11km point. This is only affected but the amount of energy entering the atmosphere.
3. The surface must be in balance. This constrains the temperature increase to that which can be maintained. In the case of a doubling of CO2 a 3DegC temperature increase is claimed. This requires a very large increase in Back Radiation (even larger if cloud cover increases). I’m not sure that this can be achieved with water vapour feedback/cloud reflections.

• SoD:

DeWitt Payne has pointed out above that the definition of Atmospheric Window in IPCC 2007 AR4 WG1 Chapter 1 Figure 1 (= Kiehl-Trenberth 1997 Figure 7), 8-12 micrometer, contains huge numerical error, making their global energy balance distribution and the consequences drawn from it unacceptable.

Paul_K:

– Conservation of energy in the Mi2007 paper was applied not to “the atmosphere”, but to the sum of given radiative fluxes in the atmsophere;
– Virial theorem is an explantion of a well-founded empirical relationship there;
– The correctness of his reference to the Kirchhoff Law was shown in Roy Spencer’s blog referred above;
– The stability of tau is proven again in Mi’s August 2010 paper.

If not here, we may go into the details of the operation of greenhouse effect anywehere else if it is better convenient.

Miklos

• SoD:

“If so, and we decided for one crazy minute to allow the world to use that old “flawed” definition – is there any problem with the “credibility” of the K&T numbers?”

Nothing else than that their quantity for the “Atmospheric Window” (40 W/m2) is way too small (as their window is too narrow); the correct number (calculated in the correct window – i.e, on the full range, 4 – 500 um, what e.g. Ramanathan also uses in his Eq. 5.4 above), is higher by about 50 %.

Needless to say, the greenhouse effect (all of its definitions, from Schwarzschild to Eddington to Chandrasekhar to Goody to Ramanathan) depends on the “surface transmitted/surface upward” ratio. So answer your question yourself: is there any problem with the “credibility” of the K&T numbers?

Miklos

34. Miklos Zagoni,
I have a great respect for you (and for Dr Miskolzci). I know that you are intellectually honest. However, you are hijacking this thread!
I loved the original Miskolzci paper; however, the empirical evidence for constant optical depth, while tantalising, is unprovable within the error bars on the data. The theoretical foundation is shaky, particularly the (method for) application of conservation of energy to the atmosphere, although I see some retreat from the Virius theorem? And some concerns over mis-statement of Kirchoff?
My main point is this:- we were talking about Ramanathan’s use of annual cycle data to prove a positive (short-term) water vapour feedback, and Miskolzci, in my view, requires a separate discussion.

35. SoD,

“I moderated out my own last comment for breaching blog guidelines.”

Quis custodiet ipsos custodes?

However, I wish you could moderate yourself to get back to the main theme of THIS article, which was to address the (pathetic though they may be) questions posed from Part 1.

Smiley face witheld by server.

Paul

36. Paul_K:

There are a lot of questions from the three articles on this subject.

I think the best way to explore many of them is further articles. Otherwise we will never leave this article – as the subject is so complex. If simple answers could nail the problem then there wouldn’t be 100s of further papers on the subject.

291 further papers cite Observational determination of the greenhouse effect by Raval and Ramanathan (1989) – which was the main paper drawn on for the chapter in Frontiers of Climate Modeling.

However, I see you have specific questions from earlier (August 30, 2010 at 3:27 pm). I will try and understand them and comment.

• SoD,

I’m sorry about my sense of humour, but I cannot resist pointing out that the infamous Mann, Bradley Hughes 1998 has well over 1000 citations!!

I look forward to your considered responses.

Paul

37. Arthur Smith:

..Unless you propose some mechanism by which increased temperatures result in *decreased* levels of water vapor in the atmosphere, it seems there is no question the water vapor feedback (defined to exclude those other changes) has to be positive.

and I responded:

There are many challenges with understanding water vapor feedback. One of them is the non-linear feedback with height in the atmosphere and location. It’s easy to consider the scenario of total water vapor being constant and yet the overall feedback effect being negative – this is from the location of the water vapor.

Said, September 3, 2010 at 4:37 pm:

But non-linear feedback is a second-order effect; that’s why I asked about definitions. Strictly the water-vapor feedback (at least the Soden and Held version) is defined as a linearization, a partial derivative, changing water vapor levels alone, while keeping lapse rate, clouds, etc. fixed and under the condition of uniformly increased troposphere temperature (the Planck response that other feedbacks are measured against). So there should be no nonlinearity to worry about.

Yes, if you redistribute water vapor within the atmosphere the greenhouse impact will change. But under the theoretical constraint of changing only temperature uniformly and holding all else fixed while allowing water vapor levels to change, it seems to me this has to result in either the same or increased water vapor levels everywhere, no? So a positive feedback is forced?

Perhaps in GCM’s, which is what the Soden and Held 2006 paper were evaluating.

But I don’t agree that even this theoretical constraint has to result in “the same or increased water vapor levels everywhere” – the reason being that relative humidity can easily be thought of as constant in the boundary layer, but above the boundary layer it is very much dependent on the coldest point from which that parcel of air has come.

That is, above the ocean there is an “infinite” supply of water vapor. But in the “free troposphere” there is a very finite supply and depends on where that air has traveled from.

The negative feedback Lindzen talks about relates to cloud effects, not water vapor alone, though he misleadlingly conflates the two in articles written for the general public. Unless I’m really missing something there…

I don’t know about the “articles for the general public”, but in his many papers there is much which relates specifically to water vapor.

For example, The importance and nature of the water vapor budget in nature and models from 1996;
Distribution of tropical tropospheric water vapor, Sun and Lindzen, from 1993.

• I guess I ought to actually read some of Lindzen’s papers then.

But I think the issue is what else is being held constant. Yes, water vapor “depends on where that air has traveled from.” But the concept of a linearized feedback is under the assumption that “all else held constant” which I take to include the pathways in which air moves about within the atmosphere. Under a uniform warming condition (the Planck response), under the condition that all air is moving around exactly as it was before, the only change should be an increase in water vapor, to some degree, everywhere in the troposphere.

Other effects are nonlinear and therefore should be absent from a linearized response analysis focused on just the water vapor issue. If there are other linear terms that need to be handled as well, for example regarding the temperature profile itself (lapse rate), cloud formation, etc. then let them vary separately…

Or is the idea that things are somehow inherently so nonlinear that you cannot linearize and separate in this fashion? I still feel there’s something fundamental in this that I’m not getting about what you or Lindzen are claiming… so I’ll do some reading at least…

• Ok, those two Lindzen papers are interesting, certainly – I’m fascinated by some of the detailed convection issues relating to the Hadley cells, ITCZ, etc. However, they’re addressed primarily to understanding the distribution of water vapor as a whole, and become exceedingly qualitative when it comes to the question of how that distribution changes under warming conditions.

For example, the claim that “If the updraft can persist longer, there will be more water substance transported to the upper troposphere … In a warmer climate, the surface air will likely contain more water vapor and the warm rain process will be more efficient… the onset of rain can be 15% faster when surface temperature is increased by 2 K […]” which the authors seem to be using to imply that the updraft will persist for less time and so there will be *less* water transported up, though they don’t actually quite say that. It seems very backwards logic…

38. Regarding SOD 9/4 11:28. I would certainly like to hear more on the question 1-3 raised by Paul_K and his overall comment that changes in G include more than just water vapor feedback.

Paul_K comments that “A necessary but not sufficient requirement for validating the analysis is that the sensible heat content of the atmosphere stays constant through the entire annual cycle – otherwise dG/dT must reflect the change.” If the 1988 data contain an overall trend in sensible heat content, that trend could vary from year to year. I skimmed a significant number of papers without success trying to see if other authors have been able to replicate the tight linear relationship between Gclear and T using other years and other sources of data. With 25 years of satellite data available, our understanding of the combined water vapor / lapse rate feedback shouldn’t depend on a single year that might contain an unusual trend.

I’d also like to hear you defend or reject analyzing dGclear/dT for specific bands of latitudes when large amounts of energy are transported poleward.

39. Frank,
Thanks for some thoughtful input on this issue.

I was struck by some things you wrote on 30th August:
“As GHG’s change climate, DLR will certainly change. However, DLR has no direct effect energy transport from the surface to space. Instead, changes in DLR appear in the equation F = oT^4 – G via DLR’s effect on surface temperature, T.” AND “The observed dG/dT is the observed dG/dT – it is independent whatever mechanisms link changes in surface temperature to changes in OLR.”

I don’t disagree with anything you wrote, but at the same time, I believe that it is worthwhile emphasising that the mechanism that causes the temperature change has a fundamental effect on how G behaves.

Consider a very simple non-seasonal earth model in radiative balance. If we turn up TSI a bit to yield a 1degreeK rise in surface temperature (at equilibrium), we expect to see a monotonic increase in OLR, and a small positive or negative change in G, depending on whether feedbacks are positive or negative, until it asymptotes to a new value.
We can compare this to the case where, instead of adjusting TSI, we now increase CO2 to yield the same 1 degreeK rise in temperature (again at equilibrium). The behaviour of OLR and G are markedly different from the previous case. We now expect to observe a DECREASE in OLR followed by a rise in OLR until radiative balance is again achieved. In this case, G increases initially to a level compatible with the increased CO2, which level is then modified positively or negatively depending on temperature feedbacks, and a new asymptotic value is achieved.

The main point I want to make from this is that, self-evidently, it is not possible to assert a unique relationship between G and T. The relationship will always be determined by the actual mechanism for changing the surface temperature.

40. Frank:

Regarding SOD 9/4 11:28. I would certainly like to hear more on the question 1-3 raised by Paul_K and his overall comment that changes in G include more than just water vapor feedback.

Paul_K comments that “A necessary but not sufficient requirement for validating the analysis is that the sensible heat content of the atmosphere stays constant through the entire annual cycle – otherwise dG/dT must reflect the change.”

It’s definitely an interesting question. I’m not sure I fully understand the point yet, so need to find a bit of time to think.

If the 1988 data contain an overall trend in sensible heat content, that trend could vary from year to year. I skimmed a significant number of papers without success trying to see if other authors have been able to replicate the tight linear relationship between Gclear and T using other years and other sources of data. With 25 years of satellite data available, our understanding of the combined water vapor / lapse rate feedback shouldn’t depend on a single year that might contain an unusual trend.

Until the start of the CERES data, the ERBE 1985-1989 was the best quality data. The ERBE data following (which lasts up to 1999 with a gap around 1993 from memory) was not such good quality.

Ramanathan makes kind of the same point you do.

And he did explain the reasons for choosing 1988-1989. This doesn’t mean people have to accept it, but his chapter explained the basis for understanding causality through a clear seasonal signal (lost during the ENSO period).

People have also since written about the dangers of using ENSO based responses to reach any conclusions about the climate response to global warming – for example, Water vapor and cloud feedback over the tropical oceans: Can we use ENSO as a surrogate for climate change?, Lau et al, GRL (1996).

Their answer was “no” – stretched out over 4 pages. Interestingly though it was in part inspired/provoked by Thermodynamic regulation of ocean warming by cirrus clouds deduced from observations of the 1987 El Nino, Ramanathan and Collins, Nature 1991.

I’d also like to hear you defend or reject analyzing dGclear/dT for specific bands of latitudes when large amounts of energy are transported poleward.

Another interesting question where I think maybe I’m missing something important.

Certainly to only cover the tropics generates a problem because much energy, as you correctly say, is transported to the poles. However, the analysis extended to the whole globe:

Which seems to demonstrate that the tropics have the highest “greenhouse” effect and this is partly, but not completely, counter-acted by the extratropics. (At least in the period examined).

The reasons behind this kind of analysis are based in the theoretical understanding that the tropics are where the strongest water vapor feedback is expected to occur. See Ramanathan 1981, and about 100 other papers.

I’m also somewhat confused by Richard Lindzen taking a body blow at Ravel and Ramanathan 1989 (the basis of the chapter from the book):

..Certain primitive attempts in this direction assumed that local temperature or regional seasonal variability might serve in this regard (Raval and Ramanathan 1989)..

-from Seasonal surrogate for climate, Lindzen et al, Journal of Climate, 1995 – and then producing an analysis for just the tropics for an extended ERBE period (Lindzen and Choi 2009).. but I haven’t had the chance to really think about this one either. Perhaps his point is that he finds the opposite for the tropics. Anyway I digress.. All for another article.

I am not sure why there are not yet many papers appearing which analyze the same question with the CERES data set. Maybe I just haven’t found them yet.

41. SOD: Thank you for your reply. Modifying Ramanathan’s equation to include a term for the net energy exported (E) to other latitudes not included in the analysis, one could write:

F + E = σT4 – G

Ignoring E, clearly makes G and dG/dT bigger than they would be otherwise. (I have no idea if E is or is not a significant fraction of G.) In Figure 5.14, dG/dT would be too high for the tropics, correct for the planet as a whole, and too low (but not shown) if restricted to polarward of 30 or 60 deg.

In Part 1, dG/dT is defined extremely well in Figure 5.12b and even in Figure 5.12a, where the change in T and G is much smaller. The “only” way the conclusion about strongly positive feedback could be wrong would be if the error in the data were much larger than would normally be expected from the tightness of the fit. I’d like to see data from a dozen or more months spread over a decade or more when the average global temperature was 290.00+/-0.25 degK to see how tightly Ga clusters about 132 W/m^2. And the same thing for the other end of the line. Then I’d give up all hope that water vapor / lapse rate feedback isn’t strongly positive. Unfortunately, Ramanathan chose to show only one of four years of data. Whatever happened during the other three years appears to be relevant to me. If dGa/dT is different during El Nino years, that is relevant. If there is no clearly defined relationship between Ga and T during some periods and a well defined relationship during others, then that is relevant too. I’m not naive enough to accept the existence of a strongly positive feedback on the basis of one year’s data out of several decades.

42. Paul_K: Thanks for your reply of 9/6 1:10 am. I was pleased that I had reconciled Colin’s and SOD’s perspectives and worried that it might have been regarded as lengthy nonsense when it initially didn’t receive comment.

I agree with you that the relationship between G and T will depend on the mechanism (forcing) causing T to change when the change in T is faster than the system can restore equilibrium. For slower changes, mechanism may not make a difference.

43. SoD, Frank,

So that you don’t go too far with my “interesting question”, I would like to correct a mis-statement (or rather an overstatement) on my part.

I wrote:
“A necessary but not sufficient requirement for validating the analysis is that the sensible heat content of the atmosphere stays constant through the entire annual cycle – otherwise dG/dT must reflect the change.”

What I should have written is:

“A necessary but not sufficient requirement for validating the analysis is that the sensible heat content of the atmosphere is a constant (i.e. unique) function of surface temperature, so that a change in average temperature during the annual seasonal cycle can be considered equivalent to a change in average temperature brought about by any other type of forcing.”

While still an unrealistic requirement, I suspect that this is in fact much closer to Ramanathan’s actual assumption. My apologies for the misdirection.

44. SoD,
I was giving some thought (again) to the problem of trying to measure any type of feedback during a short term transient.
Ramanathan’s conclusions are, amongst other things, dependent on his derivation of “dFc/dT = 3.3 without lapse rate and water vapour feedback” plus his assumption that one can attribute the variation in dG/dT to (just) lapse rate and water vapour changes.
So I decided to see if I could test both assumptions using a simple heat balance model which does some accounting for time dependence. The result is so surprising that I suspect it may be wrong! If so, I would be delighted if you could identify where the error is.

The basic model I used is a single heat capacity model:
dH/dt = Q-E = flux in – flux out = CdTs/dt
;where: H = heat (energy), t = time, Ts = surface temp, C = heat capacity (joules/degree K), Q = TSI*co-albedo, and
E = OLR = sigma*Ts^4 – G.

Define equilibrium climate sensitivity, (1/lamda), as the equilibrium temperature response to a forcing of F watts/m^2. (lamda has units of watts/m^2/deg K).

Where a single impulse forcing produces an exponential temperature response towards equilibrium, the solution for a series of constant stacked forcings for this system – equilvalent to a linear increase in forcing with time – is well-documented:
DeltaTs = b( (t-tau) + tau* exp(-t/tau))/lamda (Eq. 1)
;where the forcing F = bt and tau is the time equilibration constant equal to C/lamda. (This is the same equation cited by Schwartz.)

Differentiating Eq 1 w.r.t. time, we obtain:
d(DeltaTs)/dt= b(1 – exp(-t/tau))/lamda = A, say (Eq 2)

Now given a linear increase in forcing, which I am using to approximate the increase in TSI over the annual cycle, we can write:-
C*dTs/dt = C*d(deltaTs)/dt = C*A = flux in – flux out
= Q(t=0) + F(t) – (sigma * Ts^4 – G)
Rearranging and differentiating w.r.t. DeltaTs, we then obtain:
dG/d(DeltaTs) = C *(dA/dt)*(dt/dDeltaTs) – dF/dt*(dt/dDeltaTs) + 4*sigma*(Ts^3)
= C*(dA/dt – dF/dt)/A + 4*sigma*(Ts^3) (Eq 3).

From Eq 2, we have dA/dt = b*exp(-t/tau)/(lamda*tau).
Since F = bt, we can also write dF/dt = b. Making these substitutions into the first term above (and recalling that C/lamda = tau), we find that the first expression is equal to -lamda (!!!!)

Thus we obtain:

dG/dDeltaTs (= dG/dTs) = 4* sigma*Ts^3 – lamda.

Two big conclusions from this:-

1) The only feedback elements which I have assumed constant in this analysis are those associated with change in co-albedo, and change in surface transmissivity. ALL OTHER FEEDBACKS ARE INCLUDED IN THE dG/DTs term.
2) Given Ramanathan’s data, we can substitute:-
4* sigma*Ts^3 = 5.5 and dG/dTs = 3.5. This yields an approximation of climate sensitivity of around 2 watts/m^2/deg K (without accounting for co-albedo and surface transmissivity changes) or about 0.5 degrees K per watt/m^2.

I should emphasis that none of the above helps remove the doubts I have about using the annual data as a “proxy” for longer term temperature change brought about by a different heating mechanism.

45. CO2 forcing for a given change in ppmv is greatest in the tropics because the atmosphere in the tropics is warmer and thus thicker. The temperature difference between the surface and the tropopause is greater so when the CO2 band expands you get a bigger effect than at the poles. For example, MODTRAN calculates that for sub-Arctic winter, the change in the outgoing radiation at 70 km looking down for a change from 280 to 560 ppmv CO2 is 1.664 W/m2. The same change in CO2 for the tropical atmosphere is 3.171 W/m2. But if water vapor feedback is strongest in the tropics, then why is it that the models predict, correctly IMO, that the greatest temperature increase will be at the poles?

Just because KT97 refers to 8-12 micrometers as being ‘the’ window does not mean that their estimate of 99 W/m2 clear sky transmitted LW radiation is only in 8-12 micrometer range. Most of it is, but not all. In TFK2009 they don’t refer to a ‘window’ at all. Is 99 W/m2 for S_t clear sky a reasonable estimate? I haven’t seen anything that would imply that there’s a gross error.

• DeWitt Payne,
Can you clarify what you meant when you wrote:
“But if water vapor feedback is strongest in the tropics, then why is it that the models predict, correctly IMO, that the greatest temperature increase will be at the poles?”

Are you suggesting that this is indirect evidence that the Ramanathan analysis is flawed? Or are you asking for clarification on what other mechanisms “explain” why the models predict what they do?
Thanks
Paul

46. on September 10, 2010 at 11:37 am | Reply Harold Pierce Jr

Below is a comment that I recently posted on Roy Spencer’s blog.

RE: The Positive Water Feedback Hypothesis

At 14 deg C and 1 atm .pressure, 1 cu. meter of air has 12.1 g of water vapor for 100% humidity. If the temperature of the air is increased to 15 deg C, 1 cu. meter will now have 12.8 g of water vapor for 100% humidity , a small increase of only 0.7 g or 6.7% of water vapor. However, 100% humidity only occurs if it is raining or snowing or if there is dense fog. So how does the enormous amounts of surface water enter the atmosphere?

The wind is the force that transports surface water into the atmosphere and is far more important than simple evaporation of water in still air. When wind blows over a body of water, the surface will cool but water will still be transported into the air. Due to their momentum the much heavier nitrogen and oxygen molecules and argon atoms just blast the lighter water molecules out the surface water into the air. The lake effect is due to strong winds blowing water vapor from warm surface water onto the usually colder land.

Changes in air pressure are also more important than a slight increase in air temperature as is shown on an aneriod barometer. An air pressure drop of a few inches (ca 60 mm) of mercury will often cause rain or snow. If pressure increases, the air becomes dry. The heat of vaporization of liquid is depends mostly on external pressure. The low air pressure in tropical a cyclone cause enormous quantities of water to “flash evaporate” into the air as it moves into warm coastal waters.

Clouds are liquid water in the air and depending on local temperature, pressure and humidity, they can readily release water vapor into the air or drop excess moisture as rain, snow or ice pellets. On average cloud cover in the atmosphere is about 65%.

Clouds also contain atmospheric gases and can transport these, in particular CO2, from one local to an other local where these gases can be released into the air or be deposited on the surface in rain drops.

Over land transpiration from plants contributes to the local humidity as does respiration from all plants and animals which includes soil organisms such as worms and insects.

I don’t recall reading that climate models take the above into account.

47. on September 10, 2010 at 11:57 am | Reply Harold Pierce Jr

The earth has thick atmosphere that retards the escape of energy from the surface. The equations used for climate calculatons don’t take in account the R factor. The tropopause is like a pane of glass that prevents the movment of mass from the troposphere to the stratosphere.

Anyone know of calculations which incorporate the R factor?

48. Harold Pierce Jr:

The earth has thick atmosphere that retards the escape of energy from the surface. The equations used for climate calculatons don’t take in account the R factor. The tropopause is like a pane of glass that prevents the movment of mass from the troposphere to the stratosphere.

Anyone know of calculations which incorporate the R factor?

I don’t know what you’ve been reading, but stick around and try reading some of the articles here. You might be surprised.

The “R factor”?

The atmosphere slows the escape of energy by absorption of longwave radiation.

The equations that govern this process are known as the radiative transfer equations and are actually used in all climate models. Amazing but true.

You can read the basics in the seven part series on CO2.

The atmosphere also has huge effects on climate via absorption of solar radiation, movement of latent heat from the surface, precipitation, clouds, winds – and yes, climate scientists have heard of all these and attempt, however imperfectly, to put them into their climate models.

49. Paul_K:

I did promise a response, which I now regret, not because you don’t pose interesting questions but because I’m still struggling to “get the point” – and later, the maths, and it’s been a challenging couple of weeks with First Life..

From August 30, 2010 at 3:27 pm:

It is worth reminding ourselves of what caused the changes (in G) and what was actually measured. The latitide-averaged changes in temperature were due in this analysis to the annual seasonal cycle. This is brought about by a tiny change in TSI, a much larger relative change in SH and NH absorbed TSI, and a large-scale redistribution of atmospheric heat and oceanic heat, including the reversal of some major streams and currents. Now consider any latitude which has achieved its MAXIMUM averaged temperature for that year. What controls the OLR emitted from that latitude at its maximum temperature? The local surface temperature and atmospheric GHG content are certainly controls, but the other major controlling factor is the local vertical temperature profile, which is a function of not just the water vapour profile, but also the local controls on atmospheric sensible heat content for that time of year.

Yes.
No one disputes that lapse rate changes (the vertical temperature profile) and water vapor changes both contribute to the feedback.

1) A necessary but not sufficient requirement for validating the analysis is that the sensible heat content of the atmosphere stays constant through the entire annual cycle – otherwise dG/dT must reflect the change.

This is the bit I don’t understand.

For example, the sensible heat content might go up because of positive feedback acting on a small surface temperature increase. Or the reverse (amplified cooling from a small surface temperature decrease).

But if we can’t allow this data because the sensible heat content has changed it seems like we won’t find what we are looking for even if it is there.

2) Even if the total sensible heat content of the atmosphere stays constant overall, the systematic abstraction and addition of sensible heat during local winter and local summer respectively gives rise to false latitude measures of dG/dT.

Here I think you touch on something important. Can we measure the “local” changes up through the atmosphere and relate them to the surface?

If there are significant heat fluxes laterally (there are) and the OLR response to water vapor and temperature profile is non-linear (it is) then simply equating the “local” (vertically correlated) data is risky.

If the OLR response to temperature profile and water vapor was linear then we could be confident in the results obtained – because an addition of heat in one location would be the result of a subtraction of heat in another location. Non-linear climate response means that we can’t be certain, without further demonstration, that we have measured a real positive feedback.

Likewise if a negative feedback was measured.

In the words of Richard Lindzen, The Importance and Nature of the Water Vapor Budget in Nature and Models, 1996:

Thus Raval and Ramanathan (1989) attempted to relate water vapor to surface temperature on a point by point basis. Unfortunately, most of the tropics consists in subsiding air whose moisture is not associated with the surface below..

.. the effect of OLR of a given change in humidity in a dry region is twice that of a moist region..

He has some good points.

3)Since the temperature change is largely a SW effect, atmospheric heating will be bottom-up. Thus, as our selected latitude approaches its maximum surface temperature, mid to upper tropospheric temperatures are still trying to catch up, giving rise to a low OLR measurement (relative to a quasi equilibrium for that surface temperature). The same is true in reverse as our latitude approaches its lowest temperature. Hence there is a systematic bias in dG/dT.

This would cancel out with a linear response. It might cancel out with a non-linear response but that needs to be demonstrated. Over a decadal time response we might be able to ascertain more.

50. Paul_K from September 7, 2010 at 1:41 pm:

It seems like there is some assumed knowledge in the steps you have taken – can you explain them in some detail or point towards the source?

I’m not clear about the “forcing” concept in this model – as to whether some kind of bulk heat capacity with an external slowly changing forcing relates to what we are trying to solve.

And I can’t follow your maths. That doesn’t mean it’s wrong.

51. SoD,

Thank you for the response and your patience!

I agree largely with your response to my original statement regarding the need for a constant sensible heat content in Ramanathn’s analysis. My original statement was just wrong.
If you check my post of Sept 7th, 12:15, you will see that I withdrew the statement, and replaced it with what I should have said in the first instance. My apologies again for the misdirection.

In terms of your “getting my point”, I believe that you have done so when you wrote:-

“If there are significant heat fluxes laterally (there are) and the OLR response to water vapor and temperature profile is non-linear (it is) then simply equating the “local” (vertically correlated) data is risky.”

However, I am still not completely comfortable with your follow-up comment:-

“If the OLR response to temperature profile and water vapor was linear then we could be confident in the results obtained – because an addition of heat in one location would be the result of a subtraction of heat in another location. Non-linear climate response means that we can’t be certain, without further demonstration, that we have measured a real positive feedback.”

At 65 degrees latitude, the variation in TSI during the annual cycle amounts to greater than 25% – almost two orders of magnitude larger than the variation expected from a change in GHGs. This gives rise to huge temperature swings at that latitude, but the average surface temperature of the planet changes by only a few degrees. Additionally, there are radical changes in subtropical deep convection currents and the divergence flux, as we go through the annual cycle, giving rise to huge movements of sensible heat around the globe. Given that (we agree that) the OLR response at any given location is non-linear with respect to local water vapour and temperature profile, then it is a huge leap of faith to assume that the OLR response to the annual cycle change in AVERAGE surface temperature represents a good proxy response for the expected change in AVERAGE temperature arising from a very different mechanism – like, for example, a change in atmospheric CO2. I think we are fairly closely agreed on this?

So the only reason for my discomfort in what you wrote was that you suggest that the non-linearity of response is the ONLY problem:-“If the OLR response to temperature profile and water vapor was linear then WE COULD BE CONFIDENT IN THE RESULTS OBTAINED…” (My emphasis.)

Here, we still disagree, because it seems clear to me that the response function dG/dT includes terms other than water vapour and lapse rate, but to explain why I will have to return to the messy mathematics I started in my post of Sept 7th, 1:41 pm, to clarify and to add a couple of things. I will save this for a separate post, since I clearly need to give you a better reference for my earlier post.

Thanks again for your detailed response.

52. Paul_K,

SoD made the statement above that water vapor feedback was expected to be the strongest in the tropics. But the effect on surface temperature will be the weakest in the tropics and the strongest at high latitude. That requires that at the new steady state, high latitudes must radiate a higher flux of LW. But the total flux must remain the same at steady state so the tropics will have to radiate less than they do now. The only way that can happen is if the surface temperature in the tropics increases less than the instantaneous forcing change from doubling CO2 would imply with no meridional heat transfer. Since the usual definition of feedback applies to the effect of forcing on surface temperature, I don’t see how you can say that water vapor feedback will be strongest in the tropics unless you consider water vapor feedback as net negative.

• De Witt,

“But the effect on surface temperature will be the weakest in the tropics and the strongest at high latitude. That requires that at the new steady state, high latitudes must radiate a higher flux of LW. But the total flux must remain the same at steady state so the tropics will have to radiate less than they do now.”

You mean this the other way round?
Paul

• No. Polar amplification means that high latitudes warm faster than low latitudes. The most likely way that can happen is if there is increased heat transfer from low to high latitude. The change in albedo from reduced sea ice doesn’t fit with the observation that temperature in the Arctic is increasing faster in the winter than the summer. The LW emission vs latitude already shows excess absorption compared to emission in the tropics and excess emission compared to absorption at latitudes more than 40 degrees from the equator. An increase in ghg’s will then make the LW curve even flatter.

MODTRAN says that a 1 degree surface temperature increase in the tropics combined with doubling CO2 (280-560 ppmv) results in a 0.41 W/m2 increase in OLR. For sub-Arctic atmosphere the same change results in an increase in OLR of 0.97 W/m2. Absent a significant decrease in albedo, the requirement for constant total emission means the temperature in the tropics will increase less than the higher forcing in the tropics, resulting in lower OLR, and the poles will increase faster than the lower forcing resulting in higher OLR.

53. SoD,

I promised to clarify my post of Sept 7th, 1:41 pm, and to explain why I am still strongly in disagreement with the suggestion that the ONLY problem with the Ramanathan analysis is the averaging problem, i.e. the problem that arises from the large movements of sensible heat around the globe during the annual cycle combined with (the fact of) the non-linearity of OLR response.

My post of Sept 7th, 1:41 is largely based on the basic energy balance equation. It is referenced by Schwartz 2007 “HEAT CAPACITY, TIME CONSTANT, AND SENSITIVITY OF EARTH’S
CLIMATE SYSTEM”, although he certainly did not invent it. My only addition was to substitute a term: OLR = surface radiation –G in place of a S-B expression based on surface temperature for outgoing radiation.

However, there is a simpler derivation of what I showed in my previous post, if one starts with the more common form of the simple feedback equation (NOTE THAT THE SYMBOL “” is supposed to be a greek Delta, but I can’t sort out the postscript problem!) :
C*dT/dt = F-lamda*T ( Eq 1.)
but C dT/dt = Power in – Power out = Q – E = gamma * TSI – (epsilon*sigma* Ts^4 – G) (Eq 2.)
where gamma = co-albido, epsilon= surface transmissivity, Ts = surface temperature.
After a forcing, F, C dT/dt = gamma *Tsi(t=0) + F – (epsilon*sigma*Ts^4 – G) (Eq 3.)
Equating Eq 1 and Eq 3, we obtain:
F – lamda*T = gamma *Tsi(t=0) + F – (epsilon*sigma*Ts^4 – G) (Eq 4.)
Re-arranging Eq 4, we obtain :
G = – lamda*T – gamma*Tsi(t=0) + epsilon*sigma*Ts^4 (Eq 5.)
Differentiating Eq 5 w.r.t T, we see that:
dG/dT = 4* epsilon *sigma*Ts^3 – lamda – Tsi(t=0)* d(gamma)/dT +sigma*Ts^4*d(epsilon)/dT (Eq 6.)
If we assume (and it’s a mighty big assumption) that the co-albido and surface transmissivity remain constant, then we obtain :-
dG/dT = 4* epsilon *sigma*Ts^3 – lamda (Eq 7.)
This was the result I showed in my post of Sept 7th, 01:41p.m.

We should note three things at this point:
1) Lamda includes ALL feedbacks
2) We have already explicitly assumed that co-albido and surface transmissivity are invariant with temperature
3) The form of this equation relates to the behaviour of G in direct response to the forcing F, which in this case is the increase in insolation due to the annual cycle, but this behaviour is SUPERPOSED on top of any other forcing or feedback effects which are still in the works; i.e. have not yet worked through to equilibrium.

Lastly, having recently read Roy Spencer’s paper: “On the diagnosis of radiative feedback in the presence of unknown radiative forcing” JGR 2010, I note that he would replace the F term on the response side of the equations above as follows:-

F(t) = f(t) + N(t) + S(t)
where f is any external source of radiative forcing such as
anthropogenic greenhouse gas emissions; N is any internally
generated nonfeedback source of radiative forcing such as
circulation‐induced changes in cloud cover; and S is any
nonradiative forcing of temperature change such as tropical
intraseasonal oscillations in the rate of heat transfer from
the ocean to the atmosphere.

If Dr Spencer’s findings are valid, then the additional N and S terms add further confounding factors to the interpretation of dG/dT.

All-in-all, I do not believe that it was valid for Dr Ramanathan to interpret his results SOLELY in terms of lapse rate and water vapour feedback – even with his stated qualification about multi-decadal response times.

54. SoD,
I think I should have added to my above post that the derivation of the expression in Eq 7 shown therein
(dG/dT = 4* epsilon *sigma*Ts^3 – lamda) can strictly only be shown to apply to an assumed constant impulse forcing F.

My earlier post, (Sept 7th, 1:41), is more general, but unfortunately more complicated, in that it shows that the same expression is obtained for the assumption of any linear change of F with time.

Paul

55. […] Part One Responses attempted a fuller answer to various questions and objections about Part One […]

56. SoD,
I notice a deafening silence since my last post. That is presumably because I am embarrassingly wrong, or everyone is bored with the subject or no-one can be bothered to check my high-school math.

My assertion is that the expression dG/dT is picking up signals from ALL feedbacks, as indicated by the maths, and that it is a conceptual error to assume that one can deduce anything about water vapour and lapse rate feedback from the Ramanathan analysis.

Maybe it will help if I offer a very simple illustration that dG/dT is picking up SW feedbacks – without leaping into abstract maths.

Suppose (for example) in the first case that the change in TSI during the annual cycle gives rise to a mean temperature change of 5 degrees without any feedbacks at all, AND that all feedbacks are zero-valued.

Now consider the same system where there is a 1 degree positive feedback from water vapour and lapse rate, and a compensatory 1 degree negative feedback from an increase in albedo. Assuming similar equilibration timing for all forcings and feedbacks, the temperature change in the two systems is the same 5 degrees over the same timeframe. Moreover, the OLR in the second system must asymptote to the same OLR as in the first system.

So the change in G – for the same 5 degree temperature change – is very similar between the two systems (and actually identical if equilibration timing is identical). Hence dG/dT is similar for the two systems. But one has a large positive water vapour/lapse rate feedback and the other has zero. This clearly raises some massive questions about the validity of the Ramanathan analysis.

This simple example importantly serves to illustrate that dG/dT DOES NOT JUST REFLECT A CHANGE IN ATMOSPHERIC ABSORPTANCE, but must account for other feedbacks as well.
Paul

57. SoD,
I have a bad case of foot-in-mouth disease. The simple example in my previous post does not work because the two systems asymptote to a different OLR. PLEASE IGNORE.

Try these two cases instead:-
First case – an increase in TSI gives rise to an increase in average temperature of 5 degrees with no feedbacks and all feedbacks are zero-valued.
Second case – same as first case but with a positive water vapour/lapse rate feedback of 1 degree and a negative feedback from transmissivity of 1 degree (i.e. an increase in transmissivity due to increasing temperatures).

Both cases see a 5 degree change in temperature. Both case asymptote to the same OLR. Hence dG/DT is the same for the two cases, but one has a strong positive water vapour and the other has zero.
Same conclusions as in my previous post, but this could be described as a LW feedback effect.

So, a further modification of the (wrong) example from my previous post:-

First case – an increase in TSI gives rise to an increase in average temperature of 7 degrees with no feedbacks and has a 2 degree negative feedback due to an increase in albedo. Water vapour feedback (and other feedbacks) are zero.
Second case for comparison – an increase in TSI gives rise to an increase in average temperature of 3 degrees with no feedbacks and has a positive water vapour feedback of 2 degrees (and no other feedbacks).
Both cases see a 5 degree change in temperature. Both cases asymptote to the same OLR, so dG/dT is the same for both. But water vapour feedback is different between the two cases. This now demonstrates a SW impact on interpretation of dG/dT.

Same conclusions.
Paul

Paul

58. Paul:

I think I understand your point. In essence there are other climate signals and changes in OLR can just as easily be correlated to these other forcings.

This is the challenge of understanding climate. “If all other things are equal..” and of course they never are.

The question might be asked about the practical size of the other forcings. So for example, with your TSI forcing causing a change of 5’C – well, in that scenario of course we will get confused. We could ask whether that scenario is realistic..

And then we could say, well, climate is complex we can’t extract one signal from that complexity, let’s have a few Belgian beers instead. But undaunted, intrepid researchers try and find signals that match a theory.

Then other researchers try and find alternatives.

So.. if there was a longer term signal that kept showing a positive feedback, with an appropriate lag from surface temperature increases and matched the measurement of changes in water vapor we might say – ok, prove me wrong find the other forcings that are producing this repeatable signal.

In Part Three we look at some long term results from Sun & Oort. They have a different approach and find a water vapor response in the tropics alone that lies between constant specific humidity (no feedback) and constant relative humidity (where the GCMs are apparently grouping).

They can equally be criticized for not taking into account everything.

And that last comment is not having a go at your ideas, by the way. It’s what we should be doing, trying to shoot down every theory that comes along.

59. Hi SOD,
Many thanks for the response, but I am feeling frustrated. You wrote:-“I think I understand your point.” Unfortunately, it is clear from your comments that you do not. I don’t hold you responsible for this. My frustration comes from my inability to articulate the argument in such a way that it is immediately clear.

I am not nitpicking at the assumptions in Ramanathan’s analysis. Nor am I calling on any unspecifiied “longer term signal that kept showing a positive feedback, with an appropriate lag from surface temperature increases and matched the measurement of changes in water vapor…”.

I am saying that the Ramanathan analysis is fundamentally flawed, and gives rise to an invalid conclusion NB not just a poor approximation, but an invalid conclusion. I may be wrong in this, of course, but I want you to understand exactly what I am trying to say. I think I can now see the full chain of logic which leads to the flaw, and I will try to highlight this.

Ramanathan’s definition of G is a measure of atmospheric absorptance, as you pointed out. This is TRUE. Hence dG/dT is a measure of the rate of change in atmospheric absorptance with temperature. This is also TRUE by definition. The fallacy comes from his belief that this rate of change is controlled only by (those) atmospheric elements which control LW absorption, of which water vapour and lapse rate, are by far the biggest. This seemingly intuitively obvious step is FALSE, and leads to a dramatically false conclusion. I believe that it stems from what I would call a “LW-centric” view that is apparent in Ramanathan’s derivation.

I refer to Eq 6 in my post of Sept 14th, 11:01:-
dG/dT = 4* epsilon *sigma*Ts^3 – lamda – Tsi(t=0)* d(gamma)/dT +sigma*Ts^4*d(epsilon)/dT (Eq 6.)

Although the derivation of this in that post stems from a single constant impulse forcing, my post of Sept 7th suggests that a similar result is obtained for the assumption of a forcing which is linearly increasing with time – probably a much better approximation of the seasonal cycle we are testing.

Recall that lamda was defined as the total climate sensitivity, expressed in units of Watts/m^2/deg C. This equation shows that dG/dT is not just responding to water vapour. It is responding to ALL FEEDBACKS, of which water vapour is just one. It is also responding to any change in albido or transmissivity which occurs over the period, whether these are feedback effects or spontaneous random changes. I will come back to albedo because it is critically important here and is one of the main things which I believe renders Ramanathan’s conclusions invalid.

My illustrative examples in my Sept 20th were not intended to be “realistic”. They were intended solely to illlustrate in simple terms what the maths already reveals. They showed that the “secant gradient”, dG/dT can give the same result over a wide range of water vapour assumptions, and, secondly, that (contrary to Ramanathan’s assertion) SW effects impact the gradient. (Having said this, I am still surprised at your comment:-“So for example, with your TSI forcing causing a change of 5′C – well, in that scenario of course we will get confused.” Recall that what Ramanathan is actually examining here is a change of about 4.1 deg C induced by the TSI forcing [about 0.3%, IIRC] brought about by the seasonal/orbital cycle!)

Now let’s see if we can reconstruct Ramanathan’s error.
I start with Eq 6 above and now wish to consider the “no feedbacks” case. I assume that the emissivity, gamma, and the co-albedo, epsilon, are both zero, and I obtain:-
dG/dT = 4* epsilon *sigma*Ts^3 – lamda (Eq 7.)

In the case of no feedbacks, we can calculate lamda directly from S-B. For an albedo of 0.3, and emissivity of 1, we obtain a grey-earth climate sensitivity of 0.3 deg C/(watts/m^2) which gives a value of lamda of (1/0.3) = 0.33.

So we obtain for the no feedback case:-
dG/dT = 4* epsilon *sigma*Ts^3 – 0.33

Ah, but wait, isn’t this exactly what Ramanathan said? Well, yes, but he obtained the value of 0.33 not by calculating lamda, but by directly calculating dFc/DT for a no feedbacks case (where Ramanathans definition of Fc is the clear air OLR). Is this just a co-incidence? The answer is that it is not a coincidence – dFc/dT is obtained from the same S-B equation with the same parameters, and (for no feedbacks) is mathematically identical to lamda.

So Ramanathan and I agree on the no-feedbacks case, but when I add back in feedbacks, I get Eq 6. When Ramanathan adds back feedbacks, he assumes that the only feedbacks which will affect atmospheric absorptance must be direct LW controls, hence his conclusion that the shift away from the no-feedbacks case is caused predominantly by water vapour (and lapse rate). This is what I am describing as “LW-centric”. The more valid reality is that, as one moves away from the no feedbacks case ALL feedbacks affect the dG/dT term, as observable in Eq 6.

So, is this difference important? Is it perhaps possible that the predominant feedback is, in any case, water vapour and that his conclusion is safe?

For the answer to this latter question, I want to return to albido. It should be re-emphasised that the albedo term occurs twice in Eq 6. It occurs explicitly in the term (sigma*Ts^4*d(epsilon)/dT ) and it also occurs implicitly as one of the feedbacks in lamda, since this represents total equilibrium climate sensitivity.

I have been unable to find any papers dealing with estimated change in average planetary albido during the annual cycle, but it is substantial, as this NASA site demonstrates.
http://earthobservatory.nasa.gov/IOTD/view.php?id=5471
So I don’t have to look to far to find a signal that renders Ramanathan’s conclusions fundamentally unsafe. There is at least one substantial feedback which affects dG/DT and which was not accounted for by Ramanathan – because, in my view, he took a LW-centric view of G.

60. Paul_K:

For the changes in planetary albedo, take a look at The Earth’s Energy Budget – Part Four – Albedo.

• Thanks SoD. Yes, the Hatzianastassiou data gives us a good indication. That shows an annual variation in albedo of about 4% albedo fraction in each hemisphere, which because of asynchronicity yields a global average change of a little over 2% albedo fraction. Since this is on monthly averaged data, we can assert that the true annual change is actually a little higher than this. Allowing for the fact that the low co-albedo applies to the low TSI (winter) and the high co-albedo applies to the high TSI (summer), we can reasonably infer that the globally averaged albedo feedback over the seasonal cycle should amount to something larger than 6 W/m^2 – more than enough to explain most if not all of the movement of dG/dT from the “no feedback” case. Certainly large enough to confound Ramanathan’s assumption that he was observing (only) a water vapour effect.

61. Hi SoD,
I have just re-read my post of Sept 22, 11:14, and realised that I made a silly transcription error. I wrote “0.33” several times, when I should have written “3.3”. The error should have been obvious, and I hope did not cause any confusion.
The relevant extract (corrected) should read:-

“In the case of no feedbacks, we can calculate lamda directly from S-B. For an albedo of 0.3, and emissivity of 1, we obtain a grey-earth climate sensitivity of 0.3 deg C/(watts/m^2) which gives a value of lamda of (1/0.3) = 3.3.

So we obtain for the no feedback case:-
dG/dT = 4* epsilon *sigma*Ts^3 – 3.3

Ah, but wait, isn’t this exactly what Ramanathan said? Well, yes, but he obtained the value of 3.3 not by calculating lamda, but by directly calculating dFc/DT for a no feedbacks case (where Ramanathans definition of Fc is the clear air OLR). Is this just a co-incidence?”

Apologies yet again.

62. It looks like we did some re-invention of the wheel.

Extract from WG1 of AR4:-

“Attempts to directly confirm the water vapour feedback by correlating spatial surface fluctuations with spatial OLR fluctuations were carried out by Raval and Ramanathan (1989). Their results are difficult to interpret, as they involve the effects of circulation changes as well as direct thermodynamic control (Bony et al., 1995). Inamdar and Ramanathan (1998) showed that a positive correlation between water vapour, greenhouse effect and SST holds for the entire tropics at seasonal time-scales. This is consistent with a positive water vapour feedback, but it still cannot be taken as a direct test of the feedback as the circulation fluctuates in a different way over the seasonal cycle than it does in response to doubling of CO2.”

63. That should be WG1 of TAR, and not AR4.

64. Paul_K from September 14, 2010 at 11:01 pm:

I wish I had looked up Schwarz 2007 at the start..
Anyway, just a note that I am reading it and will respond in due course to your train of thought.

Earlier you said:

I notice a deafening silence since my last post. That is presumably because I am embarrassingly wrong, or everyone is bored with the subject or no-one can be bothered to check my high-school math.

Easy questions get answered quickly and it feels like progress for me. Hard questions get long pauses. That’s a good thing.

Also you said:

You wrote:-”I think I understand your point.” Unfortunately, it is clear from your comments that you do not. I don’t hold you responsible for this. My frustration comes from my inability to articulate the argument in such a way that it is immediately clear.

I will endeavor to succeed in understanding your point second (or is it third?) time around.

65. Paul_K

Rereading your post of September 7, 2010 at 1:41 pm I still can’t get to the bottom of the maths, although it was helpful to read the paper by Schwarz.

I do follow the maths in your post of September 14, 2010 at 11:01 pm and perhaps we should consider that as the “base case” even though it is the response to an impulse forcing.

By the way, the approach I take to getting greek letters in the comment section is to copy and paste from a page like this in Wikipedia.
And I found the only way to really read the equations was to write them out on paper..

I think I do now understand your point. And if I do understand it, I think you might have tricked yourself.

Let’s review the equation from note 4:

This is the equation for G.

Note that it contains a term for optical depth and one for temperature gradient (lapse rate).

And nothing else.

This is the result of applying fundamental physics to determine the relationship between surface radiation and TOA longwave radiation.

So how is it that your apparently correct derivation of September 14, 2010 at 11:01 pm includes terms for the albedo and for the TSI?

I reproduce the equation using T’ for change in temperature and some greek letters, apologies if I have anything slightly out:

dG/dT’ = 4εσT^3 – λ – J.dγ/dT + σT^4.dε/dT

-where:
λ = total climate feedback parameter
J = TSI incident but averaged over the surface of the earth, ie TSI/4;
γ = “coalbedo” = 1-albedo
and in the last term, dε/dT is the partial derivative term

One obvious way to reconcile the fundamental physics with your derivation is that because λ is the total feedback term and includes changes in albedo and changes in TSI then the last three terms remove albedo and TSI changes from the greenhouse effect (absorptance), G.

After all, now I believe I see your point that “Ramanathan is fundamentally wrong because..” I can’t see how the fundamental physics of the radiative transfer equations can be wrong and need to include albedo.

If you see what I’m getting at?

66. The last part of my comment above might not be clear to people.

What I’m suggesting is that the total climate feedback, λ, does include changes in solar irradiance and earth albedo – but:

λ – J.dγ/dT + σT^4.dε/dT (the last three terms in the equation above)

is the climate feedback less these two changes.

67. SoD,
A very sincere thank you. You have completely grasped my argument (right or wrong), despite my various attempts to mislead you with mis-statements, transcription errors, primitive nomenclature and other slipshod errors.

You are both right and wrong, I believe, in your comments on albedo. You are sufficiently right that I wish that I hadn’t leapt onto albedo as a simple way of illustrating the problem with Ramanathan’s interpretation of the dG/dT observations.

You are right in suggesting that the term, – J.dγ/dT, acts as a COMPENSATION to the inclusion of the co-albedo feedback term included in λ, but I don’t believe that that it can eliminate all of the effect. The co-albedo feedback embedded in λ is a constant – representing the final EQUILIBRIUM effect of the feedback. The term, – J.dγ/dT, is a function of T, and can only be constant (given the assumption of a single constant impulse forcing) if dγ/dT is constant. Hence there is still an impact on dG/dT. However, I will give some more thought to this. I especially wish to re-derive the expression for dG/dT when the forcing is allowed to vary with time AND one assumes a changing co-albido.

For now, however, I would like to return to the case where co-albedo and emissivity are assumed to be invariant. The expression for dG/dT reduces to:-
dG/dT = 4εσT^3 – λ (Equation 7)

I refer to Ramanathan’s Equation 5.4 for the definition of Ga. Ga is dependent on, inter alia, the vertical temperature profile. This is controlled not just by the presence or absence of LW absorbers in the atmosphere. It is controlled by the amount of, and distribution of, sensible heat at the point of calculation. As Equation 7 above suggests, any feedbacks which affect the amount of, and distribution of, sensible heat will therefore be reflected in dG/dT.

68. SoD

You wrote, in discussing Ramanathan’s Equation 5.4 for the definition of Ga:

“Note that it contains a term for optical depth and one for temperature gradient (lapse rate). And nothing else.” I think you were emphasising this to underline your resistance to considering the possibility that changing albedo might have an effect on dGa/dT.

I doubt very much that you are getting confused about the relationship, but just to be clear…

For a small interval dz’, Ga could be said to be dependent on the “lapse rate” across the interval. The integration over dz’ means that Ga is dependent on the (entire) vertical temperature profile.

However, the Ga calculation (Eq 5.4) is good for a specific location (area) on the planet with a known vertical temperature profile. The aggregate calculation is the integral over all such areal elements of the surface emission minus the OLR. Anything which moves sensible heat around (vertically or horizontally) will therefore have an impact on (the aggregate) Ga, and on dGa/dT.

Because we are looking at a transient effect, I don’t think that it is outside the bounds of possibility that dG/dT is responsive to a changing albedo – via the changed temperature profiles “seen” by the Ga calculation. Inspection of the equation derived from energy balance:-

dG/dT’ = 4εσT^3 – λ – J.dγ/dT + σT^4.dε/dT

suggests that this would be mathematically equivalent to having a non-linear change of average planetary albedo with change in average surface temperature.

But I will do some more checking.

69. Paul_K from September 27, 2010 at 8:02 am:

You are right in suggesting that the term, – J.dγ/dT, acts as a COMPENSATION to the inclusion of the co-albedo feedback term included in λ, but I don’t believe that that it can eliminate all of the effect. The co-albedo feedback embedded in λ is a constant – representing the final EQUILIBRIUM effect of the feedback. The term, – J.dγ/dT, is a function of T, and can only be constant (given the assumption of a single constant impulse forcing) if dγ/dT is constant. Hence there is still an impact on dG/dT.

λ is a constant because we’ve called it a constant..
dγ/dT is one of terms in λ, therefore:

1. λ is not a “constant” – just a value we calculated on the day to encompass one scenario over one arbitrary time period OR
2. dγ/dT is a “constant” for this scenario over this arbitrary time period OR
3. The fundamental equation of radiative transfer of longwave radiation through the atmosphere needs to include shortwave albedo

I’m not choosing 3. I think the issue is in the original mathematical manipulation.

I refer to Ramanathan’s Equation 5.4 for the definition of Ga. Ga is dependent on, inter alia, the vertical temperature profile. This is controlled not just by the presence or absence of LW absorbers in the atmosphere. It is controlled by the amount of, and distribution of, sensible heat at the point of calculation. As Equation 7 above suggests, any feedbacks which affect the amount of, and distribution of, sensible heat will therefore be reflected in dG/dT.

I agree.

70. Paul_K on September 27, 2010 at 11:54 am:

.. I think you were emphasising this to underline your resistance to considering the possibility that changing albedo might have an effect on dGa/dT
..Anything which moves sensible heat around (vertically or horizontally) will therefore have an impact on (the aggregate) Ga, and on dGa/dT.

I agree.

Although as a further point note that with the massive movement of sensible heat from equator to poles the environmental lapse rate is still quite close to the adiabatic lapse rate (with the appropriate amount of moisture). It either heats the surface or gets radiated out the "top" and the environmental lapse rate re-establishes – roughly speaking.

71. A question, and a couple of thoughts on various posts:
Does anyone know of any GCM run with no CO2 in the atmosphere? It would seem to me that this would be an elementary baseline to start from.

“Strictly the water-vapor feedback (at least the Soden and Held version) is defined as a linearization, a partial derivative, changing water vapor levels alone, while keeping lapse rate, clouds, etc. fixed and under the condition of uniformly increased troposphere temperature ”

All the discussion of waterl vapor in the atmosphere and trying to study the effects of changing water vapor independently while holding other variales constant seems ludicrous. It only takes a little bit of observation to see that the atmosphere reacts with a multitude of changes as a result of solar radiation. Just watch the weather on any summer day. All the various energy transfer mechanisms start to work shortly after sunrise- evaporation of dew, dramatic changes in humidity and temperature, formation of thermals, cloud development, thunder storms(under the right conditions), ending up with a reverse sequence later in the day as the temperature drops, the humidity goes up, and dew reforms, The weather that controls the movement of energy through the atmosphere is not in any kind of equilibrium ever. Any model predictions have to take these small scale, but highly effective, accurately mechanisms into account. All the current GCM’s assume a positive feedback effect from an increase in water vapor from increased temperature. With all the small scale effects going on in the atmosphere, many of which would be negative feedbacks, the actual facts are totally “up in the air”.

The logical way to estimate how much a doubling of CO2 would affect the temperature is to go back to the basic observations. With deference to T.J.Nelson, a linear increase in temperature requires an exponential increase in CO2. Each doubling of CO2 will cause the same temperature increase. Although CO2 hasn’t doubled since 1900, we can calculate a proportion based on the observed CO2 and temperatures. Between 1900 and 2000 CO2 increased from 295 ppm to 365 ppm. The temperature increase about .57 degC. In proportion:
ln(365/285)= k x .57
k=.3735
doubling CO2
ln(2)=.693
dT=.693/.3735= 1.85 deg. C as an upper limit for temperature change due to a doubling of CO2.

You can take this kind of calculation further by using and effective CO2 level that includes other green house gases, which reduces the temperature increase to around 1.02 deg.C.

Assuming the correlation between CO2 and temperature really shows causation and that a degree or so C doesn’t cause dramatic changes in the mechanisms working in radiation absorption and in the atmosphere, it appears that not much is going to happen to the climate.

72. […] Part One – Responses – answering some questions about Part One […]