onsdag 29 februari 2012

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?

tisdag 28 februari 2012

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.

More conductivity

måndag 27 februari 2012

Conductivity and diffusivity

It appears as if I have in some previous posts confused myself, and possibly some others, by not making an appropriate distinction between heat conductivity k and diffusivity D. According to Fourier's law, under stationary conditions the heat flux F is given by

F = -k*dT/dx.

The diffusivity D is proportional to k but also inversely proportional to the density. In particular this means that my attemps to motivate the existence of a stratosphere through a reduction in air density does not follow directly from the heat equation. (A note of caution is perhaps appropriate here, since I think that the heat equation was first formulated for solids and not gases). However, I think that the overall "thickness" of the atmosphere must come into play somehow. How to motivate this seems to be an open question and what is perhaps lacking is an adequate theory for heat conduction in the atmosphere.

This article could perhaps provide some information though.

söndag 19 februari 2012

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.


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.

torsdag 9 februari 2012

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?  

onsdag 1 februari 2012

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.