Radiative Transfer in Cirrus Clouds. Part IV: On Cloud Geometry, Inhomogeneity, and Absorption

Abstract

The effects of cloud geometry and inhomogeneity on the radiative properties 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 em be directly applied to specific geometry and inhomogeneous structure of a medium without the requirement of solving the basic differential radiative transfer equation. A specific interpolation scheme is developed for the intensity and source function iterations to reduce the computation effort, and its accuracies are checked with existing results from the plane-parallel adding-doubling method, a number of two-dimensional models, and the three-dimensional Monte Carlo method. The SOS approach is shown to be particularly useful for cirrus clouds with optical depths less than about 5. Some demonstrative results show that the importance of the cloud-side scattering is dependent on the cloud horizontal dimension relative to the vertical thickness and that the cloud inhomogeneity can play a significant role in determining the domain-averaged solar reflection and transmission patterns. By employing the optical depth retrieved from AVHRR radiances and the ice crystal size distribution derived from replicator soundings during FIRE-II IFO, Kansas, November-December 1991, a means by which a 3D extinction coefficient field for cirrus clouds can be constructed is demonstrated. The SOS model is applied to finite, inhomogeneous cirrus clouds to investigate deviations of the radiation fields computed from the pixel by pixel (PBP) plane-parallel approximation. The authors show that the PBP approach is a good approximation for computing the domain-averaged reflected and transmitted fluxes if the cloud 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 model because of the horizontal radiative energy exchanges coupled with the cloud optical inhomogeneity. For finite clouds, the authors derive a physical equation using the Cartesian coordinates to define cloud absorption in terms of the absorbed solar flux per volume associated with the 3D flux divergence. The cloud absorption so defined is governed by the incident solar fluxes on three sides and reflection and transmission at the cloud top and bottom as well as radiation leakages out of the four sides. Using a solar wavelength of 2.22 µm as an example, it is shown that anomalous cloud absorption can occur if specific cloud geometries are involved, for example, cubic clouds with an oblique solar zenith angle. Compatibilities between radiometric measurements from aircraft and theoretical calculations are further discussed. To resolve the anomalous cloud absorption issue, from the physical perspective, it is essential that the cloud geometrical structure and cloud microphysics including aerosols be determined concurrently with radiometric measurements from the air.