A variational scheme for retrieving ice cloud properties from combined radar, lidar, and infrared radiometer

A variational method is described for retrieving profiles of visible extinction coefficient, ice water content and effective radius in ice clouds using the combination of ground-based or spaceborne radar, lidar and infrared radiometer. The forward model includes effects such as non-Rayleigh scattering by the radar and molecular and multiple scattering by the lidar. By rigorous treatment of errors and a careful choice of state variables and associated a priori estimates, a seamless retrieval is possible between regions of the cloud detected by both radar and lidar and regions detected by just one of these two instruments. Thus, when the lidar signal is unavailable ( for reasons such as strong attenuation), the retrieval tends toward an empirical relationship using radar reflectivity factor and temperature, and when the radar signal is unavailable ( such as in optically thin cirrus), accurate retrievals are still possible from the combination of lidar and radiometer. The method is tested first on simulated profiles from aircraft data and then on real observations taken in West Africa. It would be straightforward to expand the approach to include other measurements simply by including a forward model for them.