Toward Cloud Tomography from Space using MISR and MODIS: The Physics of Image Formation for Opaque Convective Clouds

Abstract

3D convective cloud images form via two intertwined radiative diffusion processes. Sunlight starts in the anti-solar direction and ends in toward-sensor ones, but repeated forward-peaked scattering smears the well-collimated beams across_direction_ space. This loss of directional memory in the cloud's "outer shell" (OS) is modeled as a random walk (RW) on the sphere. We show that, for typical cloud phase functions, 5 or 6 scatterings suffice for severe degrading of directionality. Simultaneously, a RW unfolds in_standard_ 3D space where steps are angularly-correlated, hence a drift in the original direction and an associated lateral dispersion. Any distinctive cloud image "feature" originates in the OS, and the shallower the better. That is also why we previously found that the optical depth of the "veiled core" (VC) is ~5. Significant amounts of sunlight thus arrive at the VC as a diffuse irradiance, and leave it even more isotropic. The diffusion limit of 3D radiative transfer (RT) is therefore valid inside the VC. Consequently, the underlying RW in the VC unfolds in 3D space, now with isotropic steps since extinction is scaled back to account for forward scattering. We show that the VC optical thickness controls cloud-scale brightness contrast between the illuminated and self-shaded sides of the cloud. Full cloud image formation thus involves diffusions (i.e., RWs) in both Euclidian and spherical/direction spaces. 3D cloud tomography based on MISR and MODIS multi-angle/-spectral data is an emerging technique in passive VNIR-SWIR sensing that will make judicious use this spatial separation of RT regimes to accelerate forward modeling without significant loss in accuracy.