RADIATIVE-TRANSFER IN CIRRUS CLOUDS .4. ON CLOUD GEOMETRY, INHOMOGENEITY, AND ABSORPTION

The effects of cloud geometry and inhomogeneity on the radiative prope rties of cirrus clouds are investigated by using the successive orders of scattering (SOS) approach for radiative transfer. This approach is an integral solution method that can he directly applied to specific geometry and inhomogeneous structure of a medium without the requireme nt of solving the basic differential radiative transfer equation. A sp ecific interpolation scheme is developed for the intensity and source function iterations to reduce the computation effort, and its accuraci es are checked with existing results from the plane-parallel adding-do ubling method, a number of two-dimensional models, and the three-dimen sional Monte Carlo method. The SOS approach is shown to be particularl y useful for cirrus clouds with optical depths less than about 5. Some demonstrative results show that the importance of the cloud-side scat tering is dependent on the cloud horizontal dimension relative to the vertical thickness and that the cloud inhomogeneity can play a signifi cant role in determining the domain-averaged solar reflection and tran smission patterns. By employing the optical depth retrieved from AVHRR radiances and the ice crystal size distribution derived from replicat or soundings during FIRE-II-IFO, Kansas, November-December 1991, a mea ns by which a 3D extinction coefficient held for cirrus clouds can be constructed is demonstrated. The SOS model is applied to finite, inhom ogeneous cirrus clouds to investigate deviations of the radiation fiel ds computed from the pixel by pixel (PBP) plane-parallel approximation . The authors show that the PBP approach is a good approximation for c omputing the domain-averaged reflected and transmitted fluxes if the c loud horizontal dimension is much larger than the vertical thickness. However, the PBP bidirectional reflectance patterns computed from the plane-parallel method deviate substantially from those from the 3D mod el because of the horizontal radiative energy exchanges coupled with t he cloud optical inhomogeneity. For finite clouds, the authors derive a physical equation using the Cartesian coordinates to define cloud ab sorption in terms of the absorbed solar flux per volume associated wit h the 3D flux divergence. The cloud absorption so defined is governed by the incident solar fluxes on three sides and reflection and transmi ssion at the cloud top and bottom as well as radiation leakages out of the four sides. Using a solar wavelength of 2.22 mu m as an example, it is shown that anomalous cloud absorption can occur if specific clou d geometries are involved, for example, cubic clouds with an oblique s olar zenith angle. Compatibilities between radiometric measurements fr om aircraft and theoretical calculations are further discussed. To res olve the anomalous cloud absorption issue from the physical perspectiv e, it is essential that the cloud geometrical structure and cloud micr ophysics including aerosols be determined concurrently with radiometri c measurements from the air.