G Jp1 Mgp0 T0

For a pure one-component atmosphere, (M/MG)qG = 1 and one simply uses the self-broadened absorption coefficients in preparing the distribution H(k), rather than going through the intermediary of defining asel f for each band.

Because the scaling of absorption coefficient with pressure and temperature is only approximate, it is important to compute H for a reference pressure and temperature that is characteristic of the general range of interest for the atmosphere under consideration, so as to minimize the amount of scaling needed. Typically, one might use a half or a tenth of the surface pressure as the reference pressure, and a mid-tropospheric temperature as the reference temperature; if one were primarily interested in stratospheric phenomena, or if one were computing OLR on a planet like Venus where most of the OLR comes from only the uppermost part of the atmosphere, pressures and temperatures characteristic of a higher part of the atmosphere would be more appropriate.

Modern professionally-written radiative transfer codes attempt to get around the inaccuracies of temperature and pressure scaling by using an extension of the exponential-sums method known as correlated-k. The basic idea behind this method is to explicitly compute a database of absorption distribution functions H covering the range of pressure and temperature values encountered in the atmosphere, rather than generating them from rescaling of a single distribution function. The mathematical justification of the way these distribution functions are used to compute the transmission is poor, but the method reduces to exponential sums when scaling is valid. It is thus guaranteed to be no worse than exponential sums, and comparisons with detailed line-byline calculations indicate that it commonly performs well, though it is hard to say when the method should work and when it shouldn't. The exponential sums approach suffices to give the reader an understanding of the basic principles of real-gas radiative effects, so we will use that method as the basis of most of our further discussion of the subject. The reader wishing to learn how to make use of the correlated-k method is directed to the reference given in the Further Readings section of this chapter.

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