In 3DVAR data assimilation, a cost function, which quantifies the departure of a state vector from a background forecast and the observations, is minimized to obtain a mathematically optimal analysis (subject to certain assumptions). The cost function is weighted by the inverse of error covariance matrix. This analysis is, however, not necessarily physically optimal when we directly analyze radar reflectivity data in the absence of additional physical constraints in the cost function. This is caused by the fact that nonlinearities associated with the observation operator for reflectivity (dBZ) can create difficulties in finding the true minimum of the cost function.

In this study, we apply a modified version of the WRF (Weather Research and Forecast) 3DVAR system to the 12-13 May 2005 precipitation case over the Central Great Plains, by assimilating data from six WSR-88D radars. Instead of assimilating reflectivity data in dBZ directly, we derive hydrometeor mixing ratios for rainwater from the reflectivity on the condition above 0 degree C. Moreover, we use the simplified constrained gamma function for the rain drop size distribution. Therefore, rain microphysics is also based on that distribution and the modifications of rain-related terms like cloud water and temperature are also related to that distribution.

Ten-minute analysis cycles are performed over a one-hour assimilation window, on a 4 km grid nested within the outer domain with a 20 km grid. Forecasts are performed from the resulting analysis and the results are compared with runs without the use of radar data, and with the direct assimilation of reflectivity.