Cloud tomography: Role of constraints and a new algorithm

Retrieving spatial distributions of cloud liquid water content from limited‐angle emission data (passive microwave cloud tomography) is ill‐posed, and a small inaccuracy in the data and/or numerical treatments may result in a large error in the retrieval. Proper handling of the ill‐posedness is an ongoing challenge to the atmospheric remote sensing community. In this paper we first analyze the major regularization methods that each apply a single but different constraint to their retrievals and extend these methods to allow for multiple constraints. We then develop a new iterative algorithm that can also incorporate complex physical constraints with great flexibility. To understand the influences of different constraints on the retrievals, we use the new iterative algorithm with various combinations of constraints to retrieve a stratocumulus cloud simulated with a large‐eddy‐simulation model. For this relatively homogeneous cloud case, the standard least squares method with no constraints, as expected, performs very poorly, and yields a very large retrieval error, making this method nearly useless. Adding a nonnegativity constraint reduces the mean retrieval error by a factor of 6 but the internal structure of the cloud is still not reproduced in the retrieval. Adding a smoothness constraint dramatically improves the retrieved spatial structure of the cloud, and brings the mean error down further, although the retrieved cloud top edges are still considerably blurred. Further adding the so‐called double‐side constraint (based on scaled adiabatic profiles) produces the best result; the retrieval faithfully reproduces the cloud water structure with a mean retrieval error of only one third of that of the nonnegativity and smoothness constrained method.