See Climate System Modeling by Kevin Trenberth.
The relation dQ = 4 dT comes from Stefan-Boltzmann's Radiation Law, which cannot be disputed as such.
However, the application of the Radiation Law by IPCC to motivate that dQ = 4 dT with dT the warming of the surface of the Earth, can be disputed. This is what I do in the previous posts on Climate Sensitivity and in the related article A New Approach to Climate Sensitivity with a model study indicating instead a basic climate sensitivity of 0.15 C without feed backs.
The resaon the Radiation Law does not determine the temperature of the surface of the Earth to its value of 15 C, is that the Earth is one part of the coupled Earth-atmosphere system with radiation exchange between the parts. The Radiation Law determines the temperature of the surface of the system, the stratopause, to 0 C, but not the Earth surface temperature.
Comments are wellcome.
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Could you explain the origin of the "alpha*T" term in your equation (1), please. Is this from Newton's cooling law or does it arise in another way?
SvaraRaderaAlso, is your equation (1) a new model as far as you know, or has it been used in previous analyses?
Thank you very much in advance.
The alpha T term models absorption/emission and is set = 0 in the
SvaraRaderaargument, which relies on convection (beta) and evaporation/condensation (q) . The epsilon is the Newton/Fourier heat diffusion coefficient with heat flow =- epsilon T_x
Thanks for your reply, Claes. I'm not an expert in this subject, but I am very curious to understand as best I can and I enjoyed your analysis very much. I have read about the importance of convection and evaporation for climate in several articles by Richard Lindzen and others.
SvaraRaderaI can see that your epsilon term originates in the heat equation and that the beta term originates in the convection equation. However, although I have seen the alpha term in several different places, I am still unsure which basic equation it comes from. Can you help me, please?