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The assimilation of reflectivity ( Z ) within 3DVar or hybrid ensemble-3DVar (En3DVar) requires the adjoint of the  Z  observation operator. With the 3DVar or En3DVar method, previous studies often use  Z  operators consistent with a single-moment microphysics scheme even when the forecast model uses a double-moment scheme. As such, only the mixing ratios of hydrometeors are directly updated by the data assimilation (DA) system, leading to inconsistency between the analyzed microphysics state variables and the microphysics scheme in the prediction model. In this study, we formulated a  Z  operator consistent with the double-moment Thompson microphysics used in the numerical integrations; in the operator the snow and graupel reflectivity components are simplified using functions fitted to T-matrix simulation results. This operator and its adjoint are implemented within the GSI hybrid En3DVar DA system to enable direct assimilation of  Z  with a consistent operator. The impacts of this new operator on convective storm analysis through DA cycles, and on the ensuing 3-h forecasts are first examined in detail for a tornado outbreak case of 16 May 2017 in Texas and Oklahoma, and then for five additional thunderstorm cases. Forecast reflectivity, hourly precipitation, and updraft helicity tracks are subjectively evaluated, while neighborhood ETSs and performance diagrams are examined for reflectivity and/or precipitation. Compared to experiments using a  Z  operator consistent with a single-moment microphysics scheme, the  Z  operator consistent with double-moment Thompson microphysics used in the forecast model produces better forecasts of reflectivity, hourly precipitation, and updraft helicity tracks with smaller biases, and the improvement is somewhat larger for a higher  Z  threshold.

Use of a Reflectivity Operator Based on Double-Moment Thompson Microphysics for Direct Assimilation of Radar Reflectivity in GSI-Based Hybrid En3DVar