The radiative interaction of two blackbodies Body 1 and 2, can in a simplified version of this model be described as a system of the form

dT1/dt = R T2 - R T1 = R (T2 - T1), dT2/dt = R T1 - R T2 = - R (T2 - T1)

with T1 and T2 the temperatures of the two bodies (or with R T1 replaced by R T1^4 and R T2 by R T2^4 to connect to Stefan-Boltzmann's Radiation Law), and R is a radiation constant. Here the term R T2 in the equation for T1 represents heat absorbed from Body 2 while emitting R T1, and vice versa.

Adding the equations, we find the balance d(T1 + T2)/dt = 0 and conclude that T1 + T2 stays constant, irrespective of the strength R of the interaction.

This connects to the discussion in the comments to the previous post Thermodynamics of Global Climate 2 about the size of the "backradiation" from the atmosphere, which connects to the size of R in the model. Clearly, in the model you can assign any value to R, strong or weak interaction, without affecting the mean value T1 + T2.

As indicated in the above formulas, one can also view the net exchange R (T1 - T2 ) to work on the difference T1 - T2 rather the absolute values T1 and T2, which may be closer to a reality

of radiation.

The above argument is intended to support to the idea that "circulating radiation" and "backradiation" is fictional rather than real.

Backradiation is hardly fictional, it can by directly measured (look up "pyrgeometer" for instance, though any infrared spectrometer will do).

SvaraRaderaAlso your equations here only work if the heat capacities of your two black bodies are the same. dQ = C dT remember.

But if T1 and T2 are similar, then yes you can linearize the Planck functions involved in the exchange and for many frequency values in the real atmosphere the net heat flow associated with radiation really does vary as (T1 - T2). As I noted in a comment on your earlier post, which you seem not to have read carefully.

Because, one serious problem with this approximation for Earth is there are some frequencies at which T2 is effectively absolute zero (transmission through the atmosphere into space). The part of outgoing radiation that is never absorbed by the atmosphere cannot be neglected if you are trying to assess the importance of that absorption.

I agree that some radiation is escaping directly into space, but what we are

SvaraRaderatalking about is the one absorbed and "reradiated" in some form of "circulating radiation", right?

Not "circulating" exactly - 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.

SvaraRaderaThe reason you can't treat it that way in the real atmosphere though is because air is very far from that "high absorption" limit - and in particular (why I keep raising this) some is not absorbed at all. One of the effects of adding greenhouse gases is to narrow the window of non-absorbed radiation.

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SvaraRaderaOK Arthur, what is then the present effect on the Earth surface temperature of atmospheric CO2? And how is it determined?

SvaraRaderaI had a rather long comment in response which just was lost, but essentially CO2 controls the entire greenhouse effect on Earth - I recommend this talk from Richard Alley:

SvaraRaderahttp://www.easterbrook.ca/steve/?p=1121

How it is determined is through theory, models and observations, particularly the basic spectroscopy (radiation effects) and studies of many different indicators of ancient atmosphere and climate properties.

Alley speaks a lot but does not say much/anything about radiation physics. If there is a greenhouse gas effect, there should be some physics formulated in equations demonstrating such an effect quantitatively, not justqualitatively saying that CO2 must have a warming effect (or possibly cooling effect or no effect at all). Where is this physics written down?

SvaraRaderaIf you are looking for some single equation or a simple set of them going from the basic quantum behavior of CO2 to the amount of predicted warming, there is no such thing. The reason for this is that several of the steps in the chain of logic involve high complexity: hundreds of thousands of individual absorption lines, pressure dependence and response issues dependent on the detailed profile of Earth's atmosphere. And climate modeling requires accounting for the detailed distribution of land and ocean on our planet as well. So there can be no simple equation or small set of them giving the result; any simple representation must be an approximation (of which the "sensitivity" relationship of about 3 K per doubling of CO2 usually discussed is the most useful).

SvaraRaderaBut the details of the physics are generally known and accounted for with great precision; the issue is more that one needs to handle hundreds of thousands or millions of input parameters from spectroscopy observations etc, which requires computers to do the theory work properly (models).

Where this is "written down" in full is in model documentation - for example NCAR's community climate model has excellent details on the equations it uses. Or for a more general overview, there are the textbooks a David Archer has one with freely available online video lectures here:

http://geoflop.uchicago.edu/forecast/docs/lectures.html

And Ray Pierrehumbert is also coming out with a new textbook sometime this year which I've already used in draft form myself, it's very clear on how things work.

We seem to agree that there is no "fundamental physics" explanation of

SvaraRaderaa greenhouse effect in quantitative terms, beyond a simple ad hoc relation of the form dQ = 4 dT from Stefan-Boltzmann. Yet this seems to be the basis of IPCC climate alarmism with a climate sensitivity of 1 C. What would happen to climate alarmism if it is acknowledged that that there is no "fundamental physics" basis to this postulate? If it is only an ad hoc assumption, or the outcome of a complex computation with unknown ingredients?

dQ = 4 dT *DOES NOT COME FROM STEFAN-BOLTZMANN* !!!

SvaraRaderaAs far as I can tell, this is in fact a meaningless equation (what are the units of Q, T, for example?) Do you have *ANY* citation of any source for having used it? It is certainly *NOT* the basis for "IPCC climate alarmism with a climate sensitivity of 1 C".

As I just said, there is *extensive* fundamental physics behind estimates of climate sensitivity - it is very straightforward physics, but it is highly complex and contingent on the properites of CO2 and Earth. It is most certainly not "ad hoc" and has absolutely no dependence on some "Stefan-Boltzmann" assumption. It is indeed the outcome of a complex computation but essentially all the ingredients are quite well known, not "unknown". The only real unknowns are a few of the response issues - which is why the results include a level of uncertainty. Those unknowns are, at least, known and quantified. Unlike your equation.

In a similar fashion there is no "fundamental physics" explanation of, for example, the relation between stress and motion of, say, the Empire State Building. Nevertheless, such a relation can be assessed through basic theory, through computer and scale models, and through actual observations.

All of these same approaches apply equal well to the response of our planet to changes in atmospheric constituents.

What you refer to is not science: to say that it is "straightforward physics"

SvaraRaderawhich is "highly complex" is contradictory fog. If the Empire State Building

rested on the same foundation, it would not stand up. Concerning dQ = 4 dT, I have shown in a sequence o posts how this follows from SB with certain data and how it conforms with the 1 C from 4 Watts radiative forcing from doubled CO2 = the basic postulate of climate alarmism. I have also shown that SB cannot be used in this way, and thus the basic postulate lacks solid scientific support.

(A) It is "straightforward physics" in the sense that it was first developed in rough form over 100 years ago; the complexity comes from the high degree of computational intensity to actual turn the basic physics into a result relevant for our planet and atmosphere. That conditional complexity is hardly unique to climate. I provided an engineering example, but going from the "straightforward physics" of, for example, the standard model of particle physics to the basic properties of interaction of atoms and molecules is similarly exceedingly computationally intensive, and is certainly not captured by just writing down a couple of equations. Nevertheless the foundations of chemistry in quantum physics have been proved time after time with detailed computations compared with observations.

SvaraRaderaThere is no contradiction between physics that is at heart simple, and having an exceedingly difficult time calculating meaningful numbers from that physics. If you haven't run into it yourself, your familiarity with physics must be very limited.

(B) I didn't ask whether *you* had said anything about dQ = 4 dT before, I asked whether it ever appeared in any work of climate science, for example something cited by the IPCC. You claim it is the basis for the IPCC's conclusions on sensitivity, but I have read both the assessment reports and many of the articles cited and I have never run across any claim of the sort.

Even so, fundamentally that relation has to be wrong. Post a URL where you show that it "follows from SB" and we can discuss further.

See posts on climate sensitivity including

SvaraRaderahttp://claesjohnson.blogspot.com/2010/05/fenics-and-climate-modeling.html

Ok, let's review what you are claiming in that URL.

SvaraRaderaIn the "derivation" of your dQ=4dT, you start from

Q = c T^4

But you don't explain what Q (or T) is. The only place in Earth's climate system a relation of this sort applies is if Q is the *total* outgoing thermal radiation (not the net radiative heat flow suggested by the label Q) from the surface at a temperature T. The constant c then is the product of the local emissivity (usually very close to 1) and the Stefan-Boltzmann constant sigma which is 5.67x10^-8 W/m^2K. You then claim Q = 288 W/m^2 and T = 288 K. 288 K is the actual average surface temperature, although the approximation that all radiation leaves at that temperature isn't quite right.

But more seriously, where did Q = 288 come from? It's not supported by your starting diagram, which has 390. 390 is also the number you get plugging in the actual Stefan-Boltzmann constant as c. You seem to be pulling numbers out of thin air to justify your claim.

Worse than that, the argument makes no sense. What are you thinking it proves? Total upwelling radiation from the surface is almost irrelevant to the level of warming if there is strong infrared absorption in the atmosphere - because however high the outgoing number is from the surface, the nearby atmosphere is almost as warm, and radiates almost as much back down. What matters radiatively in determining warming of the surface is what gets off the planet completely - ie. if any simplistic Stefan-Boltzmann calculation is relevant it needs to be from high in the atmosphere, not the surface. But wavelength dependence of emissivity makes that all much more complicated anyway. Which is why computer calculations are needed to get it right.

The argument is intended to show how a basic climate sensitivity of 1 C

SvaraRaderafrom "radiative forcing" of 4 Watts/m2 by IPCC claimed to result form doubled CO2, comes out from a (trivial) application of SB. As far as I can understand this is what is referred to as the "basic physics" behind climate alarmism: 1 C + feedback gives 3 C = alarm!

I question the basis of 1 C from SB. What is your derivation of basic climate sensitivity and how big is it, if it is not 1 C from SB?

First, "radiative forcing" is a very different thing from "outgoing radiative energy flow from the surface" which your calculation appears to start from. For one thing, the energy flow change is calculated not at the surface, but at the tropopause. Surface energy flow changes will generally be very different from changes at the tropopause - not least because convection is involved as well as radiation, within the troposphere. This is something non-scientists like Monckton seem to be frequently confused about, but I thought somebody like you would have studied the subject a bit and understood at least this.

SvaraRaderaThe approximation that makes "radiative forcing" a useful comparative concept at all is the 1-dimensional so-called "radiative convective" approach, first outlined in a paper by Ramanathan and Coakley (1978). Under that approximation, changes in solar forcing, aerosols, or GHGs all essentially manifest themselves through a change in radiative energy flux through the tropopause, and then given that number, the surface responds the same way to each forcing (I.e. Feedbacks work the same way for anynforcing change). It is a convenient way to divide the problem into two more tractable components: the raw effect of the CO2 change itself, and the response of the rest of the planet.

But note this is only an approximation used to better understand the problem, it is never in practice used to actually make the calculation - with models that is done by actually making the GHG changes in model atmospheres, for example.

When you ask what is the "basic climate sensitivity" you seem to be adopting this forcing/response separation and asking for the bare response, but how would you define that bare response? The paper by Bony et al which I cited in an earlier comment does this by assuming the bare response is a uniform change in temperatures through the troposphere, with atmospheric composition held constant. This gives a value for the Planck response which is remarkably consistent across all the calculations that have been done - about 3.2 W/m^2K. Which implies the bare temperature change associated with a forcing change of the order 4 W/m^2 would be about 1.2 K.

Excellent! From where did you get 1.2 K?

SvaraRadera4 W/m^2 (actually slightly less than 4) divided by 3.2 W/m^2 K gives slightly more than 1.2 K.

SvaraRaderaThe reference on this is:

Sandrine Bony et al, Journal of Climate 19:3445 (2006), "How Well Do We Understand and Evaluate Climate Change Feedback Processes?"

See Appendix A, "How are Feedbacks Defined?"

The value of 3.2 W/m^2 K for the (negative) Planck response comes from Brian J. Soden and Isaac M. Held, Journal of Climate 19:3354 (2006) (an issue or two before the Bony paper) - see the first column of Table 1 which shows the value from a variety of models, ranging from 3.13 to 3.26 in value.

Are you joking? From where do you get 4 W/m2 to divide by 3.2?

SvaraRaderaFrom Bony et al

SvaraRaderahttp://journals.ametsoc.org/doi/full/10.1175/JCLI3819.1#sa1

it is clear that the basis of IPCC climate alarmism is the "Planck response" of 3.8 W/m2 from SB blackbody radiation formula, which gives a climate sensitivity of about i 1 C, which you seem to accept.

My point is that this cannot be taken as starting point for various feedbacks, because the internal response of the Earth with atmosphere is not described by the SB formula. If the basic climate sensitivity is instead 0.15 C, as a I argue, unthinkable feedback factors of size 10-30 would be required. Right?

The 4 W/m2 is what you quoted above for the "radiative forcing from doubling CO2". That comes from a completely separate calculation - see for example Modtran which does this:

SvaraRaderahttp://geoflop.uchicago.edu/forecast/docs/Projects/modtran.orig.html

Why did you change the tightly-constrained "3.2" to "3.8" in your second comment? I do not accept that change; please remember this is based on energy flow *at the tropopause*, not at the surface. There is no convection or latent heat flow through the tropopause, by definition that's where the temperature gradient is zero. So considerations of convection or latent heat cannot have any effect on this basic number. Your argument is nonsense.

I agree: I presented this argument to show that the basis of climate alarmism of a climate sensitivity of 1 C based on SB, is nonsense.

SvaraRadera