Observational operators for dual polarimetric radars in variational data assimilation systems (PolRad VAR v1.0)

We implemented two observational operators for dual polarimetric radars in two variational data assimilation systems: WRF Var, the Weather Research and Forecasting Model variational data assimilation system, and NHM-4DVAR, the nonhydrostatic variational data assimilation system for the Japan Meteorological Agency nonhydrostatic model. The operators consist of a space interpolator, two types of variable converters, and their linearized and transposed (adjoint) operators. The space interpolator takes account of the effects of radar-beam broadening in both the vertical and horizontal directions and climatological beam bending. The first variable converter emulates polarimetric parameters with model prognostic variables and includes attenuation effects, and the second one derives rainwater content from the observed polarimetric parameter (specific differential phase). We developed linearized and adjoint operators for the space interpolator and variable converters and then assessed whether the linearity of the linearized operators and the accuracy of the adjoint operators were good enough for implementation in variational systems. The results of a simple assimilation experiment showed good agreement between assimilation results and observations with respect to reflectivity and specific differential phase but not with respect to differential reflectivity.