Test of Power Transformation Function to Hydrometeor and Water Vapor Mixing Ratios for Direct Variational Assimilation of Radar Reflectivity Data

Assimilating radar reflectivity into convective-scale NWP models remains a challenging topic in radar data assimilation. A primary reason is that the reflectivity forward observation operator is highly nonlinear. To address this challenge, a power transformation function is applied to the WRF model’s hydrometeor and water vapor mixing ratio variables in this study. Three 3-D variational data assimilation experiments are performed and compared for five high-impact weather events that occurred in 2019: (i) a control experiment that assimilates reflectivity using the original hydrometeor mixing ratios as control variables, (ii) an experiment that assimilates reflectivity using power-transformed hydrometeor mixing ratios as control variables, and (iii) an experiment that assimilates reflectivity and retrieved pseudo-water vapor observations using power-transformed hydrometeor and water vapor mixing ratios (qv) as control variables. Both qualitative and quantitative evaluations are performed for 0–3-hour forecasts from the five cases. The analysis and forecast performance in the two experiments with power-transformed mixing ratios is better than the control experiment. Notably, the assimilation of pseudo-water vapor with power-transformed qv as an additional control variable is found to improve the performance of the analysis and short-term forecasts for all cases. In addition, the convergence rate of the cost function minimization for the two experiments that use the power transformation is faster than that of the control experiments.