A variational method to retrieve the extinction profile in liquid clouds using multiple-field-of-view lidar

Liquid clouds play a profound role in the global radiation budget, but it is difficult to retrieve their vertical profile remotely. Ordinary narrow-field-of-view (FOV) lidars receive a strong return from such clouds, but the information is limited to the first few optical depths. Wide-angle multiple-FOV lidars can isolate radiation that is scattered multiple times before returning to the instrument, often penetrating much deeper into the cloud than does the single-scattered signal. These returns potentially contain information on the vertical profile of the extinction coefficient but are challenging to interpret because of the lack of a fast radiative transfer model for simulating them. This paper describes a variational algorithm that incorporates a fast forward model that is based on the time-dependent two-stream approximation, and its adjoint. Application of the algorithm to simulated data from a hypothetical airborne three-FOV lidar with a maximum footprint width of 600 m suggests that this approach should be able to retrieve the extinction structure down to an optical depth of around 6 and a total optical depth up to at least 35, depending on the maximum lidar FOV. The convergence behavior of Gauss-Newton and quasi-Newton optimization schemes are compared. Results are then presented from an application of the algorithm to observations of stratocumulus by the eight-FOV airborne Cloud Thickness from Off-Beam Lidar Returns (THOR) lidar. It is demonstrated how the averaging kernel can be used to diagnose the effective vertical resolution of the retrieved profile and, therefore, the depth to which information on the vertical structure can be recovered. This work enables more rigorous exploitation of returns from spaceborne lidar and radar that are subject to multiple scattering than was previously possible. © 2012 American Meteorological Society.