Variational Retrieval of Rain Microphysics and Related Parameters from Polarimetric Radar Data with a Parameterized Operator

Abstract

Abstract A variational retrieval of rain microphysics from polarimetric radar data (PRD) has been developed through the use of S-band parameterized polarimetric observation operators. Polarimetric observations allow for the optimal retrieval of cloud and precipitation microphysics for weather quantification and data assimilation for convective-scale numerical weather prediction (NWP) by linking PRD to physical parameters. Rain polarimetric observation operators for reflectivity ZH, differential reflectivity ZDR, and specific differential phase KDP were derived for S-band PRD using T-matrix scattering amplitudes. These observation operators link the PRD to the physical parameters of water content W and mass-/volume-weighted diameter Dm for rain, which can be used to calculate other microphysical information. The S-band observation operators were tested using a 1D variational retrieval that uses the (nonlinear) Gauss–Newton method to iteratively minimize the cost function to find an optimal estimate of Dm and W separately for each azimuth of radar data, which can be applied to a plan position indicator (PPI) radar scan (i.e., a single elevation). Experiments on two-dimensional video disdrometer (2DVD) data demonstrated the advantages of including ΦDP observations and using the nonlinear solution rather than the (linear) optimal interpolation (OI) solution. PRD collected by the Norman, Oklahoma (KOUN) WSR-88D on 15 June 2011 were used to successfully test the retrieval method on radar data. The successful variational retrieval from the 2DVD and the radar data demonstrate the utility of the proposed method.