Studies have shown that the assimilation of radar data is helpful for convective-scale numerical weather prediction. So far, the assimilation of reflectivity data has been achieved using either ensemble Kalman filter or indirect methods such as complex cloud analysis or via pre-retrieval of hydrometeors. To directly assimilate radar data within variational framework, some issues associated with the nonlinearity of the reflectivity operator arise When using hydrometeor mixing ratios as the control variables (CVq), the gradient of the cost function can become dominantly large, making the assimilation of reflectivity in storm regions and of radial velocity ineffective. To address this issue, a lower limit on hydrometeor mixing ratios or equivalent reflectivity (qLim or ZeLim) is imposed on the reflectivity observation operator. In addition, a separate analysis pass (VrPass) is used to assimilate radial velocity. When logarithmic hydrometeor mixing ratios are used as the control variables (CVlogq) instead, the issue of the extremely large gradient is avoided. However, the analysis increments are inappropriately spread. As a solution, a lower limit is added to the background when converting the log(q) increment to q increment(XbLim).
Through perfect-model observing system simulation experiments for a simulated supercell storm, the capability of directly assimilating radial velocity and reflectivity within 3DVar or En3DVar frameworks using CVq and CVlogq are examined. The results indicate that the analysis and forecast from En3DVar using CVq with ZeLim treatment are closest to the truth. The 3DVar using CVlogq with XbLim produces better analyses of the storm intensity and has faster minimization convergence speed than using CVq. However, with the VrPass treatment, the storm analyses of 3DVar using CVq are greatly improved, and its prediction of storm location is better than using CVlogq.