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Radar reflectivity (Z) data are either directly assimilated using 3DVar, 4DVar, or ensemble Kalman filter, or indirectly assimilated using, for example, cloud analysis that preretrieves hydrometeors from Z. When directly assimilating radar data variationally, issues related to the highly nonlinear Z operator arise that can cause nonconvergence and bad analyses. To alleviate the issues, treatments are proposed in this study and their performances are examined via observing system simulation experiments. They include the following: 1) When using hydrometeor mixing ratios as control variables (CVq), small background Z can cause extremely large cost function gradient. Lower limits are imposed on the mixing ratios (qLim treatment) or the equivalent reflectivity (ZeLim treatment) in Z observation operator. ZeLim is found to work better than qLim in terms of analysis accuracy and convergence speed. 2) With CVq, the assimilation of radial velocity (Vr) is ineffective when assimilated together with Z data due to the much smaller cost function gradient associated with Vr. A procedure (VrPass) that assimilates Vr data in a separate pass is found very helpful. 3) Using logarithmic hydrometeor mixing ratios as control variables (CVlogq) can also avoid extremely large cost function gradient, and has much faster convergence. However, spurious analysis increments can be created when transforming the analysis increments back to mixing ratios. A background smoothing and a lower limit are applied to the background mixing ratios, and are shown to be effective. Using CVlogq with associated treatments produces better reflectivity analysis that is much closer to the observation without resorting to multiple analysis passes, and the cost function minimization also converges faster. CVlogq is therefore recommended for variational radar data assimilation.

Direct Variational Assimilation of Radar Reflectivity and Radial Velocity Data: Issues with Nonlinear Reflectivity Operator and Solutions