Approximate methods for finding CO₂ 15‐μm band transmission in planetary atmospheres

Abstract

The CO 2 15‐μm band provides an important source of thermal opacity in the atmospheres of Venus, Earth, and Mars. Efficient and accurate methods for finding the transmission in this band are therefore needed before complete, self‐consistent physical models of these atmospheres can be developed. In this paper we describe a hierarchy of such methods. The most versatile and accurate of these is an “exact” line‐by‐line model (Fels and Schwarzkopf, 1981). Other methods described here employ simplifying assumptions about the structure of the 15‐μm band which significantly improve their efficiency. Because such approximations can reduce the accuracy of a model, as well as its computational expense, we established the range of validity of these simpler models by comparing their results to those generated by the line‐by‐line model. Pressures and absorber amounts like those encountered in the atmospheres of Venus, Earth, and Mars were used in these tests. Physical band models based on the Goody (1952) random model compose the first class of approximate methods. These narrow‐band models include a general random model and other more efficient techniques that employ the Malkmus (1967) line‐strength distribution. Two simple strategies for including Voigt and Doppler line‐shape effects are tested. We show that the accuracy of these models at low pressures is very sensitive to the line‐strength distribution as well as the line shape. The second class of approximate methods is represented by an exponential wideband model. This physical band model is much more efficient than those described above, since it can be used to find transmission functions for broad sections of the CO 2 15‐μm band in a single step. When combined with a simple Voigt parameterization, this method produces results almost as accurate as those obtained from the more expensive narrow ‐ band random models. The final class of approximate methods tested here includes the empirical logarithmic wideband models that have been used extensively in climate‐modeling studies (Kiehl and Ramanathan, 1983; Pollack et al., 1981). These methods are very efficient, but their range of validity is more limited than that of the other methods tested here. These methods should therefore be used with caution.

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