Em[ssion, Scattering and Absorption of Radiation

The effect that cirrus clouds have upon the radiation emitted to space from the earth-atmosphere system is studied theoretically using a matrix method for computing the transfer of radiation in model cloud layers. The matrix method, which in essence is a generalization of a multi-streams approximation, is used to obtain the thermal radiation emitted by the clouds as well as their transmissivities to radiation from below. However, in order to perform these computations it is necessary to determine some of the physical characteristics of the clouds such as the form, size, and orientation of the ice crystals, the ice concentration, temperature distribution, etc. By studying photographs of ice crystals collected in cirrus clouds, information with respect to the size and form of the crystals is obtained. Deductions from visual optical phenomena and laboratory studies of falling bodies which simulate ice crystals falling in air lead to the conclusion that the crystals are randomly oriented in any horizontal plane in the cloud but are not random in all three dimensions. The long axes of hexagonal columns tend to align themselves more with the horizontal plane than with any other plane. Utilizing this information about the ice crystals, the angular patterns of the radiation scattered by the indivi.dual crystals are obtained. For the infrared wavelengths studied and the sizes of the crystals involved, it is concluded that refraction through the crystals is negligible and that the scattering patterns could be well approximated by Kirchhoff diffraction and surface reflection. It is further shown that if the ice crystals were approximated by circular cylinders, the diffraction pattern for crystals randomly oriented in either a plane or in three dimensions would be nearly identical to that for spheres which scatter the same total amount of energy as that scattered by the crystals. In the case that radiation in the visible portion of the spectrum is scattered, refraction must be taken into account and therefore the above spherical approximations are not valid. For this radiation, a method is described for computing the angular pattern of radiation scattered by hexagonal crystals which makes use of the laws of geometric optics. It is shown that by tracing the paths of a large number of parallel rays through the crystals, the scattering pattern is sufficiently determined.