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**Extra info for Atmospheric Radiation: Theoretical Basis**

**Sample text**

The important practical question is the extent to which the absorption coefficient and the source function can be changed from their equilibrium values by the action of the incident radiation. Since the discussion now involves disequilibrium states, we can no longer use thermodynamic arguments but, instead, we must employ a THEORY OF RADIATIVE TRANSFER 31 microscopic statistical model. In this section, we shall follow the consequences of this model to the point of understanding the conditions under which Kirchhoff s and Planck's laws fail.

We may, therefore, regard Planck's and Boltzmann's laws as interchangeable; conditions leading to one lead to the other, and vice versa. We shall go further and demonstrate that a one-to-one relationship exists between the source function and the state populations and, therefore, that our task is simply to calculate the state populations. Now, it is known that collisions acting alone will bring about a Boltzmann distribution and, consequently, a Planck source function. But, in a collisionless medium, radiation can bring about almost any population of energy levels and Planck's law need not be obeyed.

The energy density is Iv dca/c and the rate of gain of photons by the radiation field is [dlv(s)/ds] dca. 54) is because spontaneous emission is isotropic. Induced emission, on the other hand, is identical in all respects to the incident radiation and all induced photons fall within the solid angle dm. 17) we find, as matters of definition, that the absorption coefficient and source function are where the overbars again indicate an equilibrium state. 57) are rarely used without approximations. One approximation is acceptable for all atmospheric bands except for the water vapor rotation band.