Direct Assimilation of Radar Reflectivity Data in Logarithmic Scale or Power Transform?

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.