Tomographic reconstruction of 3D convective clouds is a large and challenging inverse problem that can benefit from a reasonably good initial guess. In this study, we use synthetic and real MISR data to demonstrate a robust and highly efficient determination of the effective outer shape of a 3D cloud, one slice at a time. Although time will tell, we believe this will constitute a viable initial guess for the full 3D cloud tomography.
In our methodology, the outer boundary of a 2D slice from a 3D cloud along any convenient direction (say N-S) is represented as an irregular n-sided off-grid polygon with the lowest facet (i.e., cloud base) being constrained to remain horizontal.
Radiance emerging from each facet (except the base) is modeled with a radiosity-type angular distribution inspired by asymptotic radiative transfer theory; this function has at most two free parameters. In total, 2n-1+2(n-1) = 4n-3 parameters need to be determined by fit to the MISR data. We found that n = 8 is a reasonable balance for a wide range of cloud sizes, in view of the coarse nature of the cloud boundary model. Thus, a nonlinear minimization problem is solved to estimate the 29 parameters per 2D slice, 15 of which will be used in the subsequent full 3D cloud tomographic reconstruction to construct an initial guess. This preliminary fitting problem also calls for an initial guess that we distill out of cloud masks for the nadir and most oblique views.