Radiation Parameterization for Three-Dimensional Inhomogeneous Cirrus Clouds: Application to Climate Models

The effects of cirrus clouds on the radiation budget of the earth and the atmosphere, and hence their impact on weather and climate processes, have been articulated by Liou (1986, 1992). Cirrus clouds are frequently finite and highly inhomogeneous based on satellite and replicator sounding observations (Ou et al. 1995; Heymsfield and Miloshevich 1993). Potential effects of the cloud geometry and inhomogeneity on the transfer of radiation must be carefully studied to understand their impact on the radiative properties of the atmosphere as well as to perform proper interpretations of radiometric measurements from the ground, the air, and space. Most of the approaches to three-dimensional (3D) radiative transfer employ the Monte Carlo method. For application to cirrus clouds, Liou and Rao (1996) have used the successive orders of scattering (SOS) approach, which can be directly applied to specific geometry and inhomogeneous structure of a medium. Ou and Liou (1982) presented a spherical harmonic method in multiple dimensions, based on which the diffusion approximation for 3D radiative transfer can be developed (Liou 1992). However, the requirement of computer resources remains the primary obstacle in the modeling of 3D radiative transfer. In conjunction with our objective of understanding the effects of 3D inhomogeneous cirrus on radiative flux and heating rate profiles in the atmosphere and of providing a physical basis for parameterization in climate models, we have developed a 3D inhomogeneous radiative transfer model based on a modified diffusion approximation employing Cartesian coordinates.