Many weather radar networks in the world have now provided polarimetric radar data (PRD) that have the potential to improve our understanding of cloud and precipitation microphysics, and numerical weather prediction (NWP). To realize this potential, an accurate and efficient set of polarimetric observation operators are needed to simulate and assimilate the PRD with an NWP model for an accurate analysis of the model state variables. For this purpose, a set of parameterized observation operators are developed to simulate and assimilate polarimetric radar data from NWP model-predicted hydrometeor mixing ratios and number concentrations of rain, snow, hail, and graupel. The polarimetric radar variables are calculated based on the T-matrix calculation of wave scattering and integrations of the scattering weighted by the particle size distribution. The calculated polarimetric variables are then fitted to simple functions of water content and volume-weighted mean diameter of the hydrometeor particle size distribution. The parameterized PRD operators are applied to an ideal case and a real case predicted by the Weather Research and Forecasting (WRF) model to have simulated PRD, which are compared with existing operators and real observations to show their validity and applicability. The new PRD operators use less than one percent of the computing time of the old operators to complete the same simulations, making it efficient in PRD simulation and assimilation usage.

Polarimetric radar data (PRD) have potential to be used in numerical weather prediction (NWP) models to improve convective-scale weather forecasts. However, thus far only a few studies have been undertaken in this research direction. To assimilate PRD in NWP models, a forward operator, also called a PRD simulator, is needed to establish the relation between model physics parameters and polarimetric radar variables. Such a forward operator needs to be accurate enough to make quantitative comparisons between radar observations and model output feasible, and to be computationally efficient so that these observations can be easily incorporated into a data assimilation (DA) scheme. To address this concern, a set of parameterized PRD simulators for the horizontal reflectivity, differential reflectivity, specific differential phase, and cross-correlation coefficient were developed. In this study, we have tested the performance of these new operators in a variational DA system. Firstly, the tangent linear and adjoint (TL/AD) models for these PRD simulators have been developed and checked for the validity. Then, both the forward operator and its adjoint model have been built into the three-dimensional variational (3DVAR) system. Finally, some preliminary DA experiments have been performed with an idealized supercell storm. It is found that the assimilation of PRD, including differential reflectivity and specific differential phase, in addition to radar radial velocity and horizontal reflectivity, can enhance the accuracy of both initial conditions for model hydrometer state variables and ensuing model forecasts. The usefulness of the cross-correlation coefficient is very limited in terms of improving convective-scale data analysis and NWP.