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Abstract Assimilating polarimetric radar data within a double-moment microphysics scheme requires that both hydrometeor mixing ratios and number concentrations be updated simultaneously to effectively utilize the radar information. This study directly assimilates polarimetric radar data in a fraternal twin observing system simulation experiment (OSSE) using both mixing ratios and number concentrations as analysis variables within a variational approach. A newly developed set of parameterized forward operators for polarimetric radar data, incorporating a new continuous melting model, is employed. To address challenges in minimizing the cost function, a power transformation function is applied to the analysis variables of mixing ratios and number concentrations. This approach alleviates issues arising from the very large dynamic range of number concentrations and the highly nonlinear relationship between the model’s hydrometeors and radar variables. Results from several groups of sensitivity experiments show that updating number concentrations using an appropriate power transformation function together with mixing ratios of hydrometeors reduces the analysis errors of radar variables and improves the analysis of polarimetric radar signatures. Updating number concentrations proves to be quite sensitive when assimilating differential reflectivity, while the additional assimilation of specific differential phase yields smaller analysis errors for reflectivity and mixing ratios of water vapor and rainwater compared to differential reflectivity assimilation alone. Experiments with smaller observation errors provide better analyses of the radar variables but also increase model variable analysis errors. Among the threshold values tested for reflectivity and polarimetric variables, assimilating polarimetric variables at grids where reflectivity exceeds 15 dBZprovides the best qualitative analysis. 

Abstract To cover its large dynamic range, radar reflectivity factors have historically been displayed and used on a logarithmic scale, that is, decibels of reflectivity (dBZ). Logarithmic reflectivity has also been used for data assimilation without being questioned or well validated. However, fundamental limitations exist with directly assimilating logarithmic reflectivity, such as strong nonlinearity of the observation forward operator and the fact that the impacts of small reflectivity values are amplified, leading to exaggerated increments when mapped back into physical space. In this study, we power‐transform both reflectivity and hydrometeor mixing ratios to alleviate the aforementioned issues with using conventional logarithmic reflectivity. Forecast evaluation across eight severe convection events demonstrates that applying the Box‐Cox power transformations to both reflectivity and hydrometeor mixing ratios effectively reduces the nonlinearity between the observations and control variables. This approach significantly improves analyses of model hydrometeor variables and forecasts of composite reflectivity and hourly precipitation.