Ice Clouds. Ice clouds forming at high altitudes contain predominantly nonspherical crystals and, hence, the Mie scattering code hsphr is unsuitable for calculating extinction and absorption coefficients. For example, cirriform clouds are composed mainly of hexagonal-column crystals several hundred micrometers long at a concentration of 0.1 to 1 cm 3. To estimate the transmissivity through these cloud types, we relied upon existing observational measurements and the rather limited number of available theoretical treatments. A number of authors have measured the transmissivity of various cloud types at different wavelengths. Few, however, have simultaneously measured the cloud thickness so that /3ex can be estimated. For those instances where the cloud thickness is known, we have plotted the transmissivity at 11 gm as a function of cloud thickness for various cirriform clouds in Fig. 7. The upper curve is a least-squares fit to the measurements of Kuhn and Weickmann (39) for cirrus clouds. Cirrus-cloud measurements of other references are in close agreement with this curve. The theoretical calculation of Liou (41) is for randomly-oriented ice cylinders having a mean length of 200 gm, a mean radius of 30 gim, and a mean concentration of 0.05 cm'3. This gives a frozen water density of 0.0283 g/m3. Because Liou did not attempt to incorporate a size distribution model into his calculations, this theoretical estimate must be taken only as a rough approximation to the transmissivity properties of an actual cirrus cloud. Denser cirriform clouds, such as cirrostratus, are more opaque to infrared radiation even though their average thickness is generally less than for cirrus clouds. Unlike many water-based cloud types occurring at lower altitudes, dense cirriform clouds may attenuate more strongly at 11 gm than at shorter wavelengths (36, 40, 44), although this effect amounts to a difference in transmissivity of perhaps 20% at most. Rain. For large, homogeneous, and spherical droplets such as rain, light absorption and extinction can be approximated by geometrical optics (19): Equation 2 was derived assuming hralX > 1 and (n' - 1) < 1, which holds for most rains with the exception of fine mists. The absorption efficiency factor is likewise given by
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