## söndag 6 juni 2010

### Basic Climate Sensitivity = 0.15 C

by radiation at a mean surface temperature of 15 C, and 120 Watts by convection coupled with evaporation/condensation.  By Stefan-Boltzmann's radiation law the 60 Watts radiated corresponds to a temperature drop of about 15 C, which is in accordance with a radiation temperature of 0 C of the stratopause.

Suppose now the radiative properties of the atmosphere is changed by 1%, which is the estimated effect of doubled CO2. This could require an extra 0.6 Watts to be radiated,  which by Stefan-Boltzmann would correspond to an increase of surface temperature 0.15 C.

This argument suggests a climate sensitivity 0.15 C. With an even more simplistic argument based on Stefan-Boltzmann, IPCC suggests instead 1 C, which is elevated by feedbacks
to an alarming 3 C. Starting instead with 0.15 C gives no reason for alarm.

Which argument do you think is more correct? Both are simplistic and do not require more than  common sense to evaluate.

#### 24 kommentarer:

1. Consider this: http://is.gd/cEU9S

Your budget starts at the wrong point. What temperature corresponds to 60 W outgoing longwave radiation?

Suppose we go with

60 W/m^2 = emissivity * sigma * T^4

then the emissivity works out to .15

However, the emissivity of the surface is very near 1.0, and the easily measured outbound infrared radiation at a random point on the surface is on the order of 390 W/m^2 .

So you are off by a factor of about 6.5, which brings us back to the right neighborhood.

It happens that Arthur has the classical radiation budget picture up on his blog in his most recent article.

http://is.gd/cEV1p

Typically, if one finds oneself in first order disagreement with IPCC WG I on an elementary matter of phsyics, one can be confident that one is wrong. IPCC is not infallible by any means but it is not capable of being as wrong as you suggest on matters of this sort.

Please study the chart on Arthur's page. The various components of this budget are known with a few watts per square meter by direct measurement. I emphasize, these are observational and not theoretical quantities.

The sensitivity question is more subtle, since we are essentially looking at derivatives of these quantities with respect to forcing (and, in practice, to time). If you begin by getting the budget grossly wrong, you are not proposing an alternative that is worth discussing.

2. No, the net radiation between the Earth surface at 288 K and the stratopause at 273 K is determined by sigma (288^4 - 273^4).

3. My numbers are roughly consistent with http://is.gd/cEV1p:

161 absorrbed by the Earth surface of which 63 net is radiated and 98 convected by thermals and evapo/transp. Right?

4. The stratopause is not a black body. In fact, it is not even a body. Admittedly you are correct if you substitute "atmosphere" for "tropopause" in your 11.28 comment.

I am not sure that is quibbling. We come back to the fact that the equilibration of the system, though relatively straightforward in principle, is irreducibly complex in practice.

The "1 %" in question is an extra input of somewhere between 3 and 4 W/m^2. The change as a consequence of the 4 W is the issue. If you say 4 W is 1 % as compared to 340 W and then switch to talking about 1 % of 60 W net difference between the surface and the atmosphere it seems to me that you are presuming that the whole setup is linear for large changes. Which it certainly isn't.

5. What we are speaking of is a marginal change of radiative properties, say
1%, and as first approximation that could be estimated to come down to
a 1% change of the 60 W transported to space by radiation. The part transported by convection should not be involved since only radiative
properties are changed (by CO2). Right?

6. Some questions and comments: Quoting from Arthurs page:

In the limit of very high absorption the behavior of the radiation becomes diffusive - a random walk. Which is also the microscopic behavior of molecules and electrons conducting heat, so conductivity and radiative heat flow become functionally similar in that limit.

Suppose we would reach this limit in our atmosphere, what would then prevent the atmosphere from becoming isothermal? Compare with Roy Spencers article:

http://wattsupwiththat.com/2010/01/02/spencer-earths-sans-greenhouse-effect-what-would-it-be-like/

Second question: If we are not in the high absorption limit, that is the radiation is no longer a "random walk" but rather a momentum transfer with specified direction. Why is it then treated as a heat transfer and not as a radiation pressure?

7. I don't understand Spencer's idea that without greenhouse gases there would be no weather. To me a pot of water on the stove heated from below generating convection and cooling on top, represents a weather

8. This is not to say that there is no greenhouse effect helping to maintain
a vertical temperature gradient. The question is how big the net effect is,
which connects to (basic) climate sensitivity. Is it 1 C or 0.1 C?

9. Claes, without greenhouse gases there wouldn't be any cooling on top of the atmosphere, which is the main point of Spencer's article.

10. Of course the top could be cooling by radiation into space, with heat
transported there by convection without radiation.

Isn't it strange that we discuss what seems to be elements, as if these questions have not been answered since long?

11. If we consider the incoming sunlight as a relevant heatflow, then one could argue that the atmosphere is neither heating nor cooling at the "top of the atmosphere" but rather is thermally equilibrated to it. Depending on how you define the system there is indeed room to argue that the atmosphere should be isothermal (with or without greenhouse gases).

Suppose you expose a bucket of water with uniformly distributed radiation which is eventually reradiated at equilibrium, is there a temperature gradient in the water?

A note on Spencers article, he explicitly states that conduction has the function that it transports heat from higher to lower temperature and thereby seeks to erradicate temperature differences. It therefore seems to me that according to Spencer the greenhouse effect would be offset in the high absorption limit.

12. To me the atmosphere is being heated from below and cools on top with a temperature gradient maintained by gravity - convection - evapor/condens. With only radiation the atmosphere could probably be isothermal.

13. Claes - you seem not to understand the very first basic issue with radiation:

*not everything radiates according to the Stefan-Boltzmann equation*

You attack the IPCC for using a "simplistic argument" when they never make such claims at all - you have never provided a reference on this. You are attacking a straw man with fake numbers.

When you state "Of course the top could be cooling by radiation into space, with heat
transported there by convection without radiation. "

That is simply not true. What defines the "top"? I've asked you this over and over and you seem not to get it.

Emission of radiation is intimately coupled to absorption - this is a very basic rule, Kirchoff's law of radiation:

"At thermal equilibrium, the emissivity of a body (or surface) equals its absorptivity."

The emissivity is the factor that multiplies the basic Planck-law radiation value (which leads to the Stefan-Boltzmann law when integrated over all wavelengths). So outgoing radiation is reduced by the degree to which the emissivity is low, which means to the degree the absorptivity is low.

That means that a body, such as the stratosphere, that is nearly transparent to all forms of radiation also cannot emit very much radiation. The "stratopause" which you take as your "top" is not a solid surface and so has identically zero emissivity and absorptivity.

For wavelengths in the "window" that is transmitted directly from surface to space, the absorptivity of the atmosphere is also essentially zero so there is no emissivity from anywhere in the atmosphere for those wavelengths - the heat involved doesn't go via the atmosphere at all, obviously, it goes directly into space.

This is something you just have to understand to understand the greenhouse effect at all.

Your argument about "1%" is also obviously wrong as Michael Tobis has outlined - the "1%" is based on a detailed calculation that comes to 4 W/m^2 *at the tropopause*, not the surface. So you are cherrypicking values you like (1%) and ignoring ones you don't (4) and comparing completely out of context (at the surface, not tropopause).

Thanks to Michael for the link to my summary article which puts together the various comments I've made here in more coherent form, by the way - here's the direct URL:

http://arthur.shumwaysmith.com/life/content/more_climate_change_basics

14. OK, if basic climate sensitivity of about 1 C according to IPCC does not come from a direct application of SB, from where does it then come?

15. As I've explained repeatedly (follow the link at the end of my comment for details on what I've said), the standard climate response comes from an actual application of Planck's law with appropriate absorptivity/emissivity defined by the constituents of the atmosphere. Planck's law only gives the same result as Stefan-Boltzmann if emissivity (and absorptivity) == 1 for all wavelengths.

Emissivity = 1 everywhere is very close to true for Earth's surface.

It is *very far from true* for the atmosphere. You need to apply the correct physics. Stefan Boltzmann at the stratopause is very definitely wrong.

16. I agree. Plancks law is also incorrect physics, because the climate physics is not only radiation.

17. And yet your critique is based solely on radiation arguments (and false ones at that). Why? The IPCC numbers regarding radiation-only issues are perfectly correct, and your straw-man apples-to-boulders comparison has no argument against it.

But IPCC and standard climate science also includes much more than radiation in assessing the response of the planet to changes in atmospheric composition. As I explained in my comments here, and the summary post referenced above. Read it, and then explain your argument again, trying not to get anything so obviously wrong this time?

Remember, the stratopause is not a black body and does not radiate to space according to Stefan-Boltzmann, its outgoing radiation is much much less because of its low emissivity (and absorptivity) at thermal wavelengths. Most radiation going to space comes from lower in the atmosphere at lower temperatures than the stratopause; some comes directly from the surface (at higher temperatures).

And one other note - the effect of increased CO2 or any other GHG is a *decrease* in the importance of radiation relative to other heat transport methods within the atmosphere. So the "60 W/m^2" at the surface would *decrease*, not increase, as CO2 went up. Think about that a bit, and what it means for your logic.

18. You are right that increased GHG will shift heat transport from radiation to convection, possibly with very little effect on temperature = small climate sensitivity = no alarm. What climate alarmists have to show is the physics of high sensitivity and this is missing.

19. Claes,

Varför flåsar hundar mer än människor? Därför att dom har mindre förmåga än oss att förlora värme genom strålning. Varför skulle högre strålningsförmåga hos atmosfären leda till ökad yttemperatur?

20. Claes - no, the effect of shifting heat transport from radiation to convection is to decrease the rate at which the surface can cool. That causes warming. There is an imbalance in Earth's energy budget caused by the increased CO2. The planet is absorbing more, and radiating less. Things are warming up. Observably.

21. Another good online discussion of this very basic issue of where the actual outgoing radiation comes from is "Science of Doom's" part 3 here:

http://scienceofdoom.com/2010/03/21/the-earth%E2%80%99s-energy-budget-%E2%80%93-part-three/

although this doesn't get into the surface heat flow you seem to be interested in.

22. GHG do not change the amount that goes in = what goes out. It is only
a question of temperature gradient required for the heat transport,
which is a combination of convection and radiation. Our discussion illustrates the confusion concerning the physics of this combination
in climate science. We are currently investigating the role of turbulent convective heat transport which may be more important than radiation.
In any case, discussion is needed. Thanks for your contributions.

23. As a preface to my comment, please note that you may mean something different by "convection" than atmospheric scientists do. We typically reserve that word for the cumulus process of vertical convection triggered by profiles that are unstable to latent heat releases. Other processes where motion carries properties are referred to as "advective" rather than "convective". "Turbulent convection" is thus meaningless in our jargon.

You began this latest dialogue by talking about dissipating turbulent energy into heat. If you are talking about transfer of properties across pressure surfaces outside of moist convective regions, this term is generally considered negligible on large spatial scales. (It may be important to cumulus microphysics.) If you can show otherwise that would be a major contribution.

To do so, though, you will have to find a much more detailed model. A one dimensional model simply will not do. There can be no simple formula for the one-dimensional global mean temperature profile as a function of forcing applicable across a wide range of forcings.

Probably the dominant reason that a 1-D global vertical profile is not a well-constrained function of forcing is the crucial importance of water phase changes to the energy budget. Moist convection depends crucially on local profiles and not on a globally averaged one, which is necessarily stable to moist convection.

Of course, such 1-D models can be constructed for observed conditions. But they necessarily have observationally based estimated bulk parameterizations, the applicability of which cannot be established in conditions other than those observed. Lacking a vast array of planets to play with, we are reduced to deriving bulk parameters in 1-D models in hypothetical forcing situations from complex 3-D models.

I have often said that there "can be no Newton or Maxwell or Einstein of climate science"; there is no fundamental missing physical insight, no missing equation. The system is just large in an irreducible dynamical sense.

I will be pleased to be proven wrong on this, but I imagine that if such a thing were possible, such a breakthrough will be from someone who is very familiar with the known principles and quantitative properties of the Earth's atmosphere and oceans.

24. I agree that simple models are simple, but 3d Navier-Stokes with phase change under gravitation may capture reality and we are now preparing
computations with this model which may reveal some of the real thermodynamics of an atmosphere.