Radiative Heat Flow vs Fluid Flow

To remove some of the mystery surrounding the radiative energy balance of the Earth + atmosphere, it is useful to think of a fluid model consisting of two connected water reservoirs 1 and 2 at different altitudes A_1  > A_2 , with inlet I_1 to 1 (from rain in the mountains) and outlet O_2 from 2 into the ocean. We assume that the flow of water F_12 in the connecting water pipe is proportional to the pressure pressure drop A_1 - A_ 2 and the pipe diameters normalized to 1, so that

• F_12 = C x (A_1 - A_2)     (*)

where C is a positive coefficient. In equilibrium in stationary state we have by conservation of water

• I_1 =  C x (A_1 - A_2) = O_3.

By measuring A_1, A_2 and O_3 the constant C can be determined to give the formula (*) for prediction of F_12 from measurements of A_1 and A_2, which can be used for planning purposes.

We understand that this can be viewed as a simple model of the radiative heat transfer between the Earth surface as 1, the atmosphere as 2, with A_1 the temperature of the surface, A_2 that of the atmosphere and C a coefficient of emissivity/absorptivity between the surface and atmosphere.

We see that in this model there is no DLR or back radiation: The flow of water is always one-way from higher to lower level. To get back flow pumps have to be introduced, but Nature does not have such pumps.