The last step follows from the assumption that each individual equivalent width is small compared to A. Note that when the sum of the equivalent widths is small compared to A, this expression reduces to the previous expression given for individual or non-overlapping lines.
The line parameters laid out above - position, width,strength and temperature scaling - lie at the heart of most real-gas radiative transfer calculations. There being thousands of spectral lines for dozens of substances of interest in planetary climate, teasing out the data one needs from the original literature is a daunting task. Fortunately, a small but dedicated group of spectroscopists 4 have taken on the task of validating, cross-checking and assembling the available line data into a convenient database known as HITRAN. It is suitable for most planetary calculations, though it must sometimes be supplemented with information on absorption that is not associated with spectral lines (the continuum absorption), and with additional data on weak lines which are important in the extremely hot, dense atmosphere of Venus. Instructions for obtaining the HITRAN database, along with sources for additional spectral data of use on Venus, Titan and Jupiter, are given in the references section at the end of this chapter, and the software supplement to this book provides a simple set of routines for reading and performing calculations with the HITRAN database.
4 May they live forever!
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