Dispelling the Smoke Screen

I am delighted to find the following paper by Joseph Reynen. Although I don't quite agree with the main conclusion of the paper, I think its Ansatz is very sound and instructive and in certain respects similar to the model I proposed in the post "A Discrete Model Atmosphere". Given this ground work I therefore believe we could be just a skip and a hop away from altogether ridding the climate discussion from one of its most stupidifying elements. I'm talking about the mysterious notion of "backradiation".

What is backradiation? I don't know. The first guess would be that it is the occurrence of electromagnetic radiation directed downwards in the atmosphere. In that case I guess we could all agree that it exists. However, some people claim that "backradiation" violates the second law of thermodynamics. What they probably mean is that the heating of a warmer object by a colder object through backradiation violates the second law. But what about obstruction to cooling through backradiation, does that violate the second law? Certainly a colder object can slow down the cooling of a warmer object. Let me give an example:

If I go outside when the temperature is 20 degrees C I loose heat at a slower rate than if I go outside when the temperature is -10 degrees C. Why is it so? In both cases my body temperature is higher than the surrounding temperature. 

Models versus reality

The exact microphysical processes that determine the rate of cooling of objects are presently unknown to humans, any attempt to model this from first principles would be a tremendously difficult task, (yet climate scientists think they can do it). Instead we usually resort to empirical studies and heuristic arguments. Empirical evidence tells us that the rate of cooling is proportional to the temperature difference. How can we explain this? One way to think about it is that each object have a certain thermal "impact" on its surrounding proportional to its temperature, but, in the competition the warmer object wins with a margin proportional to the temperature difference. This "impact" is of course composed of several elements, but there is no ground to argue that radiation cannot be part of this.

From a mathematical point of view one can of course ask the question. Why do you represent the heat flow as a two-stream model instead of a one-stream model? A fair question, but there may be technical reasons for this as I will try to explain later. But the important thing to remember is that neither the two-stream model nor the one-stream model has any direct relation to the actual microphysical processes. 

Smoke screens

What has caused this obsession with backradiation? Part of the reason I think are two smoke screens

1. Cartoons

2. Simplified mathematical models

In the cartoons the supposedly non-trivial contribution to the thermodynamics by greenhouse gases are respresented by a downward arrow often called backradiation. Hence, If you don't believe that greenhouse gases add anything non-trivial as regards to thermodynamics it is therefore natural to question the downward arrow. This is, however, a trap. First of all you should never even consider arguing about a cartoon. Whenever a greenhouse defender shows you a cartoon you say:

Please, show me the equations for the temperature profile of the entire atmosphere!

As regards the simplified mathematical models, which you can find even in supposedly rigorous books like that of Goody and Yung, the trap mainly lies in wrongly or vaguely specified boundary conditions. But this is a bit too technical to be covered here. Just recently, after having dug in the literature for quite some time, and after some creative work of my own I think I finally understood what the Greenhouse Gas Hypothesis (GGH) really is.

Why does the GGH violate the second law of thermodynamics? 

In my opinion, not all the specific cases included in the GGH violate the second law. At least not in a loose sense. One example of this is the so called "grey" atmosphere. Why do I think so? Because in the grey gas model there is no cooling of the upper atmosphere. The most flagrant violation of the second law, I think, is the simultaneous warming of the lower atmosphere together with the cooling of the upper atmosphere that supposedly occurs in a "real" atmosphere. After having read Pierrehumbert's text on the subject I can perhaps guess how this occurs in the model. It is because an uneven distribution of carbon dioxide and water vapor. Water, (due to the formation of clouds?), resides mainly the lower part of the atmosphere. The upper part, however, populated by CO2 backradiates in the CO2 spectrum to the lower part, which in turn, cunningly, radiates the energy back mainly in the H2O spectrum which CO2 cannot absorb. Wicked!

So in summary: 

The grey gas model does not violate the second law (in a loose sense)

Yet...

The grey gas model is built on a two-stream model

Consequence:

People think that GGH violates the second law (because of the cooling of the upper atmosphere). The grey gas model is kept hidden. People look at cartoons and see a downward arrow. People draw the conclusion that the downward arrow violates the second law.

Gotcha!!!

Unfortunately, however, people have now invested so much prestige in this "back-radiation" issue that I'm not sure if we can get out of this mess in the near future, though I am hopeful. 

What traps heat?

Let's look upon it this way. What is heat? Answer: It is microscopic motion. What traps motion? Answer: Mass. If you through a tennis ball into the wall the ball bounces back. If there is no wall the ball continues. Why? Because a massive object can absorb a lot of momentum without at the same time absorb a lot of energy. This is because momentum scales linearly with the velocity but energy scales with the velocity squared. Radiation obeys the law of conservation of momentum. QED.

Solution?

I think that the grey gas model can actually be useful, after one major adjustment: Replace the absorption coefficient related to the greenhouse concentration with the total mass. In doing so, the grey gas model violates the second law even less, because now it looks as a straight forward heat transport problem.

Why is the two-stream model useful?

The usefulness primarily lies in that it facilitates the modelling of the escape of heat to outer space. Please have a look at "A Discrete Model Atmosphere". If anyone comes up with a "one-stream" representation for this problem: Be my guest, I won't complain. But personally I don't think that it matters that much.

  

A stepwise axiomatic approach

This, I guess, is in part a response to Postma's latest article which I find well written and addresses several key questions concerning the GE. In particular I like the approach which starts off with simple reasoning and simple equations, adding details when necessary, rather than a heavy first principles approach from the very start. I will not go into direct polemic, instead I will try to summarize my own thoughts in what I call a "stepwise axiomatic approach". The present version of it is probably not the most succinct, but I think that this or similar approaches could be helpful in disentangling disagreements, to see where the viewpoints really depart.

Consider the following set of assumptions (axioms), each of which may be subject to amendments or cancellation. (Some are inconsistent with each other and are therefore numbered.)

A.  For the atmosphere the ideal gas law T = PV/nR holds true with an accuracy sufficient for our considerations. 

B. Thermometers measure temperature with an accuracy sufficient for our considerations.

C. There is always a (net) heat flow from higher to lower temperature

D1. The incoming sunlight is a heat flow

D2. The incoming sunlight is not a heat flow but should instead be considered as an energy source (thereby functionally equivalent to a radiator, burning of fuel. radioactive decay and so on)

Axiom C is one formulation of the second law of thermodynamics. Obviously we have to choose between D1 and D2 so lets start with D1.

Consider the set of assumptions (A, B, C, D1). Here we encounter a problem. Since the upper atmosphere is colder than the surface (B) assumption C says that there must be a net heat flow between the surface and the upper atmosphere. However, D says that there is no such net heat flow. (We have neglected the fact that the sunlight is asymmetrically distributed, but adding the asymmetry doesn't help, think about it.) So how do we resolve this? A significant number of people resolve this by an amendment to the second law of thermodynamics, stating that in a gravity field there need not be a net heat flow from higher to lower temperature. In the end they usually arrive at the following formula for the lapse rate:

The details of the reasoning behind this, and its problems, can not be covered here, instead I refer to other articles (for example on this blog). An alternative is to abandon D1 in favour of D2.

Consider the set of assumptions (A,B,C,D2).  In this case the lapse rate simply pops out in the form of the heat equation:

where F is the solar forcing. If this simple observation has evaded you until now don't be ashamed. It took me months. The heat equation I think provides a powerful tool to analyze certain topics infected with misunderstandings. I believe for example that back-radiation (in the most general sense) is neatly incorporated in the left hand side of the above equation, see for example my post "The heat equation revisited". It is not necessary to incorporate back-radiation for example in the following way:

where B is a fictitious extra forcing term supposedly arising from back-radiation. Moreover, if we test one of the predictions of the GE theory, namely that an atmosphere without greenhouse gases becomes isothermal. Given the set of assumptions (A,B,C,D2) that would correspond to an atmosphere with infinite thermal conductivity. Now ask yourself the question: Does dry air have infinite thermal conductivity?

It should also be noted that the formula for the adiabatic lapse rate may become useful also under the set of assumptions (A,B,C,D2) but then in the context of the limit it puts on convection, see previous posts. 

In summary, I think that an approach like this can resolve many misunderstandings. Try it! 

Pierrehumbert explains the cooling of the Stratosphere

Upon further reading of Pierrehumbert's "Principles of Planetary Climate" I found the following passage explaining the cooling of the stratosphere:

Note especially that he writes 

"Moreover, as the optical thickness of the atmosphere is increased, the stratosphere actually

becomes colder than even the semigrey skin temperature; this contrasts with the grey case, where

the temperature of the uppermost part of the atmosphere always approaches the skin temperature, regardless of how optically thick the rest of the atmosphere is."

The boldfaced statement seems to be what I concluded myself in the previous post "A discrete model atmosphere", thus it is not news to Pierrehumbert. However, there are a lot of questions urging for an answer now. For example:

1. In my very first post "What is the greenhouse effect" I calculated the temperature profile using the formulas provided by Goody and Yung where the stratospheric cooling fell out quite simply apparently without any assumption about a "grey" or "non-grey" atmosphere. Hence, are these formulas valid at all? Are there several greenhouse effects, in that case, which is the IPCC one? 

2. If there is no cooling of the stratosphere for a "grey" atmosphere, then why is it generally portayed as a triviality, taking as an example Spencers "blanket analogy". (Maybe we have to assume a non-grey blanket?) 

3. Where is the observational evidence for all these claims? As far as I can see, the stratospheric temperature of most planets can be calculated from the incident solar energy without any special consideration of the spectral properties of the constituent gases.

A Discrete Model Atmosphere

(A few additional comments since this post seems to have attracted certain attention. Although it might look odd, in reality it describes an ordinary diffusion process. The corresponding differential equation is described on the post "A new attempt". Here, the thermal conductivity k is normalized to 1 but if you want to vary it all you have to do is to divide the forcing vector F by k. The derivation of this I leave to the reader.)


This post is a bit technical but if you bear with me I hope it might shed some light on certain important topics. The reason why I have constructed a discrete model is that by doing so I have avoided the tricky problem of specifying the boundary conditions, which you are invariably faced with if you formulate the model in terms of differential equations. The model which I am going to present admittedly bear some SUPERFICIAL ressemblance with the greenhouse effect, but one of the questions I am asking is if it ACTUALLY reproduces the greenhouse effect. Take a look at the diagram below:

The atmosphere has been discretized into a finite number of layers each having its own "weight" w1, w2 and so on. The arrows may represent either a "real" or a "formal/mathematical" energy flow. What do I mean by this? There is actually a point in not specifying this at the moment. It could be interpreted as if the "weight" of the atmospheric layer is simply a function of the amount of greenhouse gases present and that the arrows represent upward or downward radiation. On the other hand, if we allow a certain "flexibility" in our thinking, the "weight" could be interpreted as a function of the actual weight (mass) of the layer and the arrows merely illustrate a "formal" energy conserving representation of the obstruction to cooling caused by these layers. Although that may sound like mumbo-jumbo in your ears, somehow we have to account for the eventual energy loss to outer space, and I haven't found any better way to do it than this. Now for the technicalities:

The amount of energy absorbed per unit time by each layer is the amount of incident energy times its wight. (Hence, the wight must be less than 1). Each layer loses energy per unit time proportional to its temperature AND weight. This loss is equally distributed upwards and downwards. Keep in mind that the energy that is not absorbed by the layer is free to pass on to the next and so on. (This is accounted for by inserting a factor (1-w) for each intermediate layer). Below is a Mathematica worksheet where the energy balance equations for the STATIONARY state of a model with four layers are written down and solved. Staionary means that all of the layers have reached energy balance, hence, the amount of energy lost per unit time equals the amount of energy absorbed per unit time. The left hand sides represents the energy lost and the right hand sides contains the absorbed energy.

This model is linear in temperature, unlike mainstream climatology where one is instead obsessed with the SB-law. A linear dependence on temperature may very well be physically motivated, especially if we are dealing with ideal gases, though admittedly, here it is primarily employed for computational efficiency, things would become very much more cumbersome with a T4-dependence. If the wight of the layers are assumed to decline exponentially with altitude, from the analytical and numerical solutions we see not only the formation of a stratosphere but we can also infer with almost certainty (although I have no strict proof for this) that the temperature approaches the finite value F/2 at the top of the atmosphere, where F is the solar forcing at the surface. This can be verified also with a numerical algorithm solving the equations for a model atmosphere discretized in 60 layers as is shown below (The Python-script for this is appended at the end)

What is then the main conclusion to be drawn from this. The most obvious one is that this model does not predict a cooling of the stratosphere upon an increases in the weight-function. On the contrary it either produces a warming of the entire atmosphere upon an increase in the weight or solar forcing, or conversely a cooling of the entire atmosphere upon a decrease in solar forcing or weight. In other words, the temperature gradient does not pivot, and this holds true even if the weight is interpreted as the amount of greenhouse gases present. (Admittedly it also somewhat contradicts some of my previous statements/guesses, which the reader can verify on his/her own.) 

How the cooling of the stratosphere comes about in the mainstream models is very obscure. From the most simple equations I can see that this follows from foolishly applying a Dirichlet boundary condition at the surface rather than at the top of the atmosphere, but how it emerges in their time-stepping algorithms remains a mystery to me. One of the lessons to be learned, however, is that there is much mathematical subtlety involved and that any "wordy" explanations from people like Roy Spencer must now be replaced by reproducible algorithms/equations.

Moving on, one could now ask if the model presented above could actually be useful as a model atmosphere. My answer to that is: Yes maybe, if the weight is interpreted as a function of the TOTAL MASS. The reason why I believe this is that:

1. It predicts an elevation in surface temperature as a function of atmospheric mass

2. It predicts the formation of a stratosphere whose temperature is a function of solar forcing alone

3. It can easily be extended so as to reproduce a thermosphere higher up if you add solar forcing terms to the uppermost layers.


Below is the Python code for your enjoyment:

***

import numpy as np
import matplotlib.pyplot as plt

interval = 6
meshsize = 0.1
N = int (interval/meshsize)

weight = np.zeros(N)
weight[0] = 1


for idx in range(1,N):

    weight[idx] =  np.exp(-idx*meshsize)*meshsize
    


A = np.zeros([N,N])
    
for idx1 in range(N):
    for idx2 in range(N):
        if idx1 == idx2: 
            if idx1 == 0:
                A[idx1,idx2] = -1
            else:
                A[idx1,idx2] = -2
            
        else:
            A[idx1,idx2] = weight[idx2]

            if idx2>idx1:

                for idx3 in range(idx1+1, idx2):
                    A[idx1,idx2] = A[idx1,idx2]*(1-weight[idx3])

            else:
                for idx3 in range(idx2+1, idx1):
                    A[idx1,idx2] = A[idx1,idx2]*(1-weight[idx3])    
            
F = np.zeros(N)
F[0] = 1



temp = np.linalg.solve(A,-F)
print temp

x = np.arange(0,interval,meshsize)

plt.plot(x, temp)
plt.ylabel('Temperature')
plt.xlabel('Position')
plt.show()

***

Ray Pierrehumbert explains the Radiative Transfer Equations

In order to elucidate the reasoning behind the differential equation yielding the "grey atmosphere" radiative lapse rate I now take the liberty to present some extracts from Ray Pierrehumbert's first online distribution of the book "Principles of Planetary Climate" dating November 11, 2009. In my view, this is the only understandable derivation that I have found. Take special notice of the formulas (4.6), (4.7), (4.8) and (4.29). Try to reproduce these with your own hand. I believe I have verified that, assuming that the net radiative flux q_T = (I+) - (I-) is independent of altitude, formula (4.29) yields the differential equation appearing first in the Ramanthan/Coakley review paper, except for some numerical factor which probably comes from some angular integral.

A 1978 review paper

Some day ago I came across the following review paper from 1978. Compared to other papers on the subject it appears to be relatively accessible and it contains a lot of references. In particular notice the very first formula describing radiative equilibrium of a "grey" atmosphere. Apparently it originates from a 1958 paper by a guy called Ambartsumyan. That you didn't know, did you?

I am personally convinced that the devil lies somewhere in the equations, and climatologists have indeed made a very good job making these equations as inaccessible as possible, so that virtually nobody can quote them, even less interpret them. But I'll see what information I can extract from it.

An Atmospheric Model

When looking at the planetary data it seems as if the tropopause appears typically at a pressure of 100 mB and that the temperature at this reference pressure raised to the power of 4 is roughly proportional to the sum of the solar and internal heat forcings. It is primarily Jupiter and Saturn that has substantial internal heat sources. We could therefore test the following conjecture:

Recall the formula for a bouyant layer of air

where theta is a constant and p_0 is the reference pressure. Based on the observational evidence we put the reference pressure to

 Finally the constant theta is given by

where F_s is the solar forcing, F_i is the internal forcing and k is the only "phenomenological" parameter in the model. If I remember correctly, in SI units it is roughly equal to 6e-7. 

Obviously the temperature follows the pressure, but, one should be careful not to immediately infer that the pressure is the sole "cause" of the elevation in air temperature. It is merely one of the factors in a bigger picture. In a way one could say that the pressure puts a limit to the rate of convective cooling due to bouyancy. 

The outer boundary

In a previous post I attempted to build an elementary atmospheric model based on the heat equation. By assuming that the heat absorbing capability of the gas depended monotonically on the mass one could predict a stratosphere, (or a tropopause), at a point where the density had decreased below a certain value. Here we will not focus so much on the stratosphere as such but instead assume that there is some tropopause somewhere and give it a temperature. Following the heat equation reasoning one could speculate on a boundary condition of the form:

Where the first term on the right hand side is simply the temperature of "outer space". If we assume that this is zero we obtain the missing boundary condition:

Upon inspection of the planetary data this seems to be a reasonable way forward.

PS

Upon more careful inspection it appears as if you get a better fit by assuming

F_s = T^4/constant

Thus bringing us back to the "blackbody" law.

Backradiation resolved?

Why is it that the greenhouse discussion doesn't seem to get anywhere? I believe that all parties are partly to blame for this. The people who could give an authoritative account of the effect are hiding and instead leaving the job to politicians like Al Gore and Lord Monckton. Since neither of these two know what the greenhouse effect is, they redefine it to be the Thyndall gas effect. However, in a recent exchange, Lindzen now claims that the Thyndall gas effect of Al Gore is not quite the same Thyndall gas effect as that Lord Monckton supports. I agree with Lindzen on two points though, the discussion has become quite bizarre and I think greenhouse skeptics should take much more care checking the relevant sources before confronting climatologists. Two of the major obstacles that I see in front of me are the following:

1. If the greenhouse hypothesis is not true then the "atmospheric problem" remains unsolved.

2. People have a very hard time managing "back-radiation".

The first obstacle could be dealt with principles well known to lawyers but apparently unknown to scientists, namely that it is the responsibility of the prosecutor to prove the guilt of the defendant, not the other way around. Hence, you can be sharp when scrutinizing the greenhouse hypothesis while beeing tentative when presenting your own ideas. There are promising observations and alternative theories, but they are not complete and we shouldn't pretend that they are. 

The second obstacle possibly stems from the frustration and numbness that can follow from having watched too many cartoons. I think, however, that it could be tackled with a little bit of mathematics, but not too much. There is a problem facing the greenhouse skeptics: 

If there is indeed some kind of thermodynamic "atmospheric effect", is it then completely out of the question that part of this effect is carried out by IR-radiation?

Let me restate the simplest mathematical representation of the basic radiative equilibrium that I have found in the litterature:

The first of these expresses the ground temperature as a function of solar heating Fs and an absorption coefficient a0. The second equation describes the lapse rate, but notice that the latter formula does not depend on Fs. Let me now constrast this with the classic heat equation:

Ok, so what has this got to do with back-radiation? Well, the heat equation can be motivated with a "back-radiation" argument. Imagine that you have two plates radiating against each other proportional to its respective temperature with proportionality constant k. Then the net heat transfer from hot to cold will be simply the temperature difference times k. Hence, when you discuss back-radiation you must specify what you are actually aiming for. Is it that the heat equation is wrong, that the derivation of the heat equation is wrong or is it that the boundary condition (first formula) is misapplied. I belong to the latter category. Instead of fixing the surface temperature at a particular value (also known as a Dirichlet boundary condition) it seems to me much more natural to impose an open boundary condition at the surface (also known as a Neumann boundary condition).

Is this what the back-radiation debate is really about? 

The arbitrary constant

In a previous post "A new attempt" I sketched a model which could possibly explain the atmospheric lapse rate as the solution of a relatively simple heat equation, which of course in the end must also take into account convection. However, the solution had an arbitrary constant which in normal cases is taken care of through boundary conditions. I am now speculating whether this constant should instead be fixed using a somewhat different reasoning. Let Fa be the total amount of heat absorbed by the atmosphere.

The temperature could then be fixed using an energy argument in combination with the gas law:

Total energy = Fa = 3/2Nk_bTa,

where Ta is some suitably averaged temperature of the atmosphere. A note of caution however! It could be that we should instead put:

Total energy = Fa = 5/2Nk_bTa,

since according to statistical physics the heat capacity of the gas increases in a gravitational field. But this requires further thinking.

The thermodynamics of Fred Singer

Fred Singer attacks greenhouse effect deniers in a recent article entitled "Climate Deniers are giving us skeptics a bad name". The main argument addressing the deniers read:

"Now let me turn to the deniers.  One of their favorite arguments is that the greenhouse effect does not exist at all because it violates the Second Law of Thermodynamics -- i.e., one cannot transfer energy from a cold atmosphere to a warmer surface.  It is surprising that this simplistic argument is used by physicists, and even by professors who teach thermodynamics.  One can show them data of downwelling infrared radiation from CO₂, water vapor, and clouds, which clearly impinge on the surface.  But their minds are closed to any such evidence."

I'm not sure if I belong to the category of "deniers" that Singer refers to although I do plead guilty to having introduced the somewhat bad name "lukewarmer" to the category of "skeptics" that Singer belongs to. One of the favourite twistings of the lukewarmers is that they present neither the greenhouse effect nor the second law of thermodynamics in a way that allows for a serious scientific discussion. I shall also admit that many skeptics fail to notice these twistings and often fall into futile discussions about the existence of "back-radiation". 

First of all, as I recollect the second law of thermodynamics it reads something like this:

The spontaneous tendency of a thermodynamic system to reach equilibrium can only be reversed if at the same time some organized energy is transformed into heat.

How does this apply to the greenhouse effect? If people check the sources or read the relevant articles of for example Roy Spencer, which I reckommend them to do, it becomes clear that the greenhouse gases alone are responsible for turning an isothermal atmosphere, which by definition is in equilibrium, to an atmosphere with a very steep temperature gradient, which by definition is not in equilibrium. The same happens in your refrigerator: turn the electricity off and the beer gets isothermal with the kitchen. What is the difference? The refrigerator uses electricity, which is a form of organized energy.

Fred Singer then, of course, twists things again when he equalizes the greenhouse effect with the existence of "back-radiation". The question is now, is Singer serious?

A new attempt

This is an attempt to incorporate the density using a slightly different reasoning.

Let F be the total stationary heat flux. Each segment of the atmosphere will not absorb the total flux, however, but we assume that the absorbed flux is proportional to the mass density. Assuming an exponential decay in density the heat equation becomes:

where m is a phenomenological parameter proportional to but not identical to the atmospheric mass. The solution is of course:

which smoothly approaches a zero lapse rate, but where the boundary condition still needs to be specified.

Does heat insolation lower the ouside temperature?

Dr Roy Spencer elaborates further on the greenhouse effect in a recent post. I think that I can follow his arguments to a certain extent although I disagree with him on some fundamental issues. Let's begin with a thought experiment. The main issue here is the cooling of the stratosphere, something that Roy Spencer tries to explain with a "blanket analogy", the same analogy which is often used to explain the elevation of the surface temperature.

Suppose that your house is heated by a constant heat source, that is, there is no thermostat regulating the temperature in the house. In this case, it is widely acknowledged that if you increase the insolation in your house the inside temperature will increase. But will it lower the outside temperature?

My answer to that is no. When the new stationary state is reached, the same amount of energy will be emitted from your house to the ouside, there is no way this heat could disappear. In other words, a squirrel living just beneath your roof will not suffer from your insolation, apart maybe for a certain amount of time while the new stationary state is reached.

I agree with Roy Spencer that back-radition exists, and that this downwelling radiation taken alone probably reduces the rate of cooling of the earth. But so does any downward motion of the atmospheric particles.

But

I disagree with Roy on the following issues:

1. I believe that any gas can cool radiatively, just check Maxwell's equations for accelerating charged particles.

2. I have not found, despite my best efforts, any arguments to show why an increased IR absorption/emission destabilizes the atmosphere, that is, increases the lapse rate (check out my simple radiative transfer models). I challenge anyone to demonstrate it mathematically using a bottom-up model.

3. I believe that the sunlight destabilizes the atmosphere.

4. I believe that the total atmospheric mass is the primary parameter that determines the heat insolation, there are microscopic arguments supporting this, the best I can think of is Newtons third law together with the fact that radiation carries momentum.

5. Increased heat insolation does not cool any part of the system, in the sense that when the new stationary state is reched the temperature will be higher everywhere.

The Lukewarmers

"And ye shall know the truth, and the truth shall make you free." John 8:32

Why do I talk so much about the greenhouse gas hypothesis on this blog? The simple and somewhat provocative answer is that this is precisely what the lukewarmers don't want me to do. If they had indeed wanted it then the would have done it themselves on their highly frequented internet forums, wouldn't they?

I will stop here for the moment and define the term lukewarmer. Here I do not refer to any person, layman or scientist, who at some point in their life believed that greenhouse gases elevate the surface temperature by some small amount through the so called greenhouse effect. Neither do I refer to Roy Spencer, although I guess he is an archetype of what could be called a "scientific lukewarmist". The people I am referring to are perhaps more accurately denoted the lukewarmist gatekeepers, and then you probably know which people I am talking about: Lord Monckton, Judith Curry, Anthony Watts, Willis Eschenbach, and well known in Sweden, Peter Stilbs. To name a few. Rarely do you excite the same amount of fury and contempt as when you approach any of these with theories such as that of Nikolov and Zeller, or even worse, if you mention the name Hans Jelbring. Try it, and you will see for yourself. Depending on the particular personal characteristics of the lukewarmer you get a somewhat different reaction though, but the motive is the same. Mission: Save the greenhouse effect! Which greenhouse effect they want to save is not clear though, since none of them are capable of defining it. It is more the public belief in something which is to be called the greenhouse effect.

As a corollary to this we may then ask, who is the real enemy? Is Al Gore really dangerous or is he perhaps merely an inconvenience that has to be dealt with for a certain amount of time. True, if it hadn't been for Al Gore and the IPCC few of us would have been involved in this.

Now imagine you are a lukewarmer, how do you proceed? Most of the methods they employ, to a great sucess in some cases, I believe fall under the category Cognitive Disruption. The first insight that hits the lukewarmist could be the following: Al Gore is going to loose. It is not what perhaps many less politically sophisticated people think: Al Gore might win. The scope of the political project is simply so huge that it is only a matter of time before the Fargo collapses, and when it does we need to have a narrative in place for the public which explains this monumental failure. The Lukewarmist Narrative.

You all know what I'm talking about:

The natural greenhouse effect is real, (since it is written down in nice analytical formulas using greek letters in books that no one has bothered to check for 100 years), but then evil Al Gore came along with his evil computer models and screwed everything up. The actual warming effect upon a doubling of CO2 can be any number between 0 and 1, because the (undefined) greenhouse effect is counteracted by negative feedbacks. These feedbacks also happen to be undefined.

Upon careful inspection any reasonable person realizes that this narrative is devoid of any real scientific analysis, it is purely emotional. Apart from constantly hammering this narrative in to the public mind, there are a number of other ways by which they distract peoples attention away from the greenhouse effect and its weak points.


1. Make people think about something else, the sun, the decadal pacific oscillation, the uncertainty of whether forecasts, and so on. This is accomplished by keeping controle of the priviledge of problem formulation. The question is not whether the GE hypothesis is correct, but instead what are the causes of climate change. This is sufficient for most people.

For those who anyway insist on discussing the basics of the GE there are some further strategies:

2. Redefine the GE. Make it appear as if the GE is equivalent to the Thyndall gas effect. Of course it is not, but in order to discover this you need to dig into the sources which most people don't do. Replace formulas with cartoons, because critisism of cartoons is harmless. "Come on, it's just a cartoon".

3. Be deliberately vague on the temperature lapse rate. Say that it is caused by gravity, people will not discover the inconsistency with the cooling of the stratosphere anyway.

4. Don't mention the cooling of the stratosphere. And if you have to, say that "the greenhouse gases in the stratosphere cools the earth", that should do the trick.

5. Be deliberately vague on whether the thermodynamic system is in equilibrium or not. This is another reason for always making the discussion be about the surface temperature. That way you can make it appear as if the GE is an obstuction to cooling, like a blanket, and hence do not a priori violate the second law of thermodynamics. Though make sure to attack any alternative explanation on the basis of the second law.

6. Make sure you are always in the attacking position. This is accomplished by never clearly defining your own standpoint.


So there you have it. Sophisticated? Not really, but it appears to have worked remarkably well up to this point. The politicians and the public are slowly but securely loosing interest in global warming and instead beginning to slipp down into the nice and cosy lukewarmist fog, ideally suited for people with lukewarm characters and intellects. So I guess the only thing I can do is to congratulate the lukewarmers for this masterful deception.

Or could perhaps the course of history take another turn?  
  

Des Pudels Kern

In Liou's book we are provided the following formula for the calculation of a steady state "radiative equilibrium":

In Goody and Yung they present the following formula:

The latter I guess corresponds to choosing the kernel function:

However, Liou is not very explicit on how to construct this function and GY do not motivate their choise either. So where do we go from here? Maybe some expert on radiative transfer could help us here.

One of the most important observations that I would like to point out is that, if using the GY formula the lapse rate becomes independent of the heat source Fs, in contrast to what would be the default assumption in conventional thermodynamics:

Where k is the conductivity. Regarding the "convective adjustment" Liou writes:

"For applications to one-dimensional climate models, the critical lapse rate,.., is usually assumed to be 6.5 K /km for the globally averaged condition. This number is based on the fact that the climatological atmospheric temperature profile in the troposphere has a lapse rate close to this value."

If this is the level of sophistication we are working at here, I wonder why they don't just let the computer adjust the lapse rate to the one they want from the very beginning.

The Greenhouse Effect according to Liou

Below are some excerpts from Liou's "An Introduction to Atmospheric Radiation" relevant to the ongoing debate.

Roy explains the Greenhouse Effect

I would like to congratulate Roy Spencer for yet another excellent and accurate account of the greenhouse effect. A good read for all those greenhouse effect deniers out there who more or less deliberately obscure matters so that ordinary people cannot think clearly. Spencer writes

"One of the first things you discover when putting numbers to the problem is the overriding importance of infrared radiative absorption and emission to explaining the atmospheric temperature profile. These IR flows would not occur without the presence of “greenhouse gases”, which simply means gases which absorb and emit IR radiation. Without those gases, there would be no way for the atmosphere to cool to outer space in the presence of continuous convective heat transport from the surface.

Indeed, it is the “greenhouse effect” which destabilizes the atmosphere, leading to convective overturning. Without it, there would not be weather as we know it. The net effect of greenhouse gases is to warm the lowest layers, and to cool the upper layers. The greenhouse effect thus continuously “tries” to produce a lapse rate much steeper than the adiabatic lapse rate, but convective overturning occurs before that can happen, cooling the lower troposphere and warming the upper troposphere through a net convective transport of heat from lower layers to upper layers."

Now for some comments. The convective overturning results in a bouyant layer of air characterized by a constant potential temperature, which, as far as I know, is not identical to the "adiabatic lapse rate". This could be a source of confusion, and it is of utmost importance for everyone to clearly understand how the convective "lapse rate" of Roy Spencer differs from for example that of H. Jelbring and others. For Roy Spencer it is the MAXIMUM lapse rate that a convective layer can TOLERATE. Greenhouse gases would like to steepen it further though. For H. Jelbring the dry adiabatic lapse rate is the lapse rate that an air parcel MOST HAPPILY installs itself into, because that is its most relaxed state. 

Put in more technical terms, they differ through their interpretation of the thermodynamic system as either beeing very far from equilibrium, or rather close to equilibrium. In previous post though, I have tried to expose how the greenhouse hypothesis is very ambiguous indeed on whether it is in equilibrium or out of equilibrium. But that is another story that I will leave for now. I would though like to propose some intermediate solution:

Could it be that it is the sunlight, and not the greenhouse gases that destabilizes the atmosphere. It is so simple that it sounds almost silly.

Moreover, could Spencer or someone else come up with BOTTOM-UP description of how the greenhouse gases actually destabilize the atmosphere. I tried to construct my own radiative transfer model in the posts "A simple radiation model", "The heat equation revisited", which were initially critisized for not taking into account a variable thickness of the atmosphere, which I did in, "It's the density, stupid". The latter did not alter my previous conclusions, but as far as I can see strengthened them.

But finally, I think we should accept Spencers challenge and try to put numbers into our models. I will be busy with other things for a while, but maybe there is some young talent out there who can perform it, who knows.

Tallbloke's buzzing Talkshop

Some week ago I discovered Tallbloke's Talkshop which has feautured several posts and discussions on for example Hans Jelbring's 2003 paper "Greenhouse Effect as a function of Atmospheric Mass" and a more recent paper of Nikolov and Zeller. These authors are courageous in the sense that they propose new theories raising important questions about apparent correlations between atmospheric pressure and temperature open for anyone to discuss and critizise. Proponents of the "official" greenhouse theory seldom offer us the same curtesy, since they almost never mention any sources of the often quoted 1C "no feedback sensitivity" from a doubling of CO2 for us to check and scrutinize. Moreover, many of them shamelessly support inconsistent statements on the reason why the temperature decreases with height in the first place. Since it is the IPCC and not Hans Jelbring who dictates climate policies, sometime I would like the table turned, and we could all contribute to this happening.

Nevertheless, I would like to air some of my own thought about the Jelbring hypothesis and those similar to it.

1. As far as I can see it is incomplete as regards to the boundary conditions. It doesn't predict any specific surface temperature as a function of atmospheric mass. One could argue that for certain physical reasons the surface temperature should have a certain value, and then temperatures at other altitudes will be recovered by following the adiabat. Or, you could argue that the temperature at 10km height should have a specific value, and then the surface temperature is recovered accordingly. This is not specified.

A correction: Nikolov and Zeller do indeed provide a formula for the surface temperature, but I still think it would be desirable to justify the fitted parameters with boundary conditions.

2. As far as I can see there are no conclusive arguments from either statistical mechanics nor Navier-Stokes equations supporting the conjecture that the equilibrium configuration of the atmosphere should be adiabatic rather than isothermal. But this does of course not exclude the possibility that our thermometers measure the wrong temperature almost everywhere, or that any of the physical models referred to are invalid.

3. It does not predict the existence of a stratosphere. One reason that could be raised is that the lapse rate is reversed at a certain altitude because of the absoption of UV-light by ozone. But if this explanation is proposed then you could equally well argue that the surface maintains a higher temperature because of the absorption of sunlight at lower frequencies. 

Which leads to my last point. What would happen to the temperature in your house during winter if you were to double the thickness of your walls. It would probably increase because a thicker wall slows down the cooling. Now think about it, a thicker wall means a more massive wall, and there you have it: Greenhouse Effect as a function of Atmospheric Mass. This is of course just a conjecture that needs the same scrutiny as any other theory. But I believe that this is an approach that has until now been largely neglected.

Some questions to Gerhard Kramm et al.

Professor Gerhard Kramm at the University of Alaska stands out as one of few meteorologists who publicly express doubts about the validity of the so called greenhouse effect, most recently done in a paper coauthored with Ralph Dlugi, where in the abstract they state that

"..it is time to acknowledge that the atmospheric greenhouse effect and especially its climatic impact are based on meritless conjectures."

 The main argument of the paper appears to be that the temperature difference of 33 degrees C between the measured surface temperature and that of a hypothetical earth without an atmosphere modelled as a blackbody in equilibrium with the incoming solar radiation, lacks rationale and that therefore any explanation of this temperature difference, for example as a result of greenhouse gases, also lacks rationale. 

The very definition of the greenhouse effect seems to be elusive. There can be no doubt that the canonical version not only attempts to explain why the surface temperature is higher than the hypothetical equilibrium temperature but also why the temperature at higher altitudes, for example at the tropopause, is lower.

On Wikipedia you can find the following information on Prof. Kramm

"Since 2003 Kramm has served as an associate faculty at the College of Natural Science and Mathematics, UAF, where he has taught atmospheric dynamics, atmospheric radiation, physics of the atmospheric boundary layer, and turbulence."

Given this I thought it would be interesting to ask the following questions to Prof. Kramm:

1. Where is the TOA ("Top of the Atmosphere") and why is it situated where it is?

2. Is the difference in average temperature between the surface and the tropopause fictitious, and if not, what is the reason for its existence?

3. To your knowledge, does there exist any "sophisticated radiative transfer model" moving beyond the simple formulas that you can find in for example Goody and Yung chapter 9, and in that case where can I find it?