In 3DVAR data assimilations, a cost function, measuring the departure of a state vector from a background forecast and the observations, weighted by the inverse of their respective error covariances, is minimized to obtain a mathematically optimal analysis (subject to certain assumptions). This analysis is, however, not necessarily optimal physically when we directly analyze radar reflectivity data in the absence of additional physical constraints in the cost function, because of the non-uniqueness of the solution when multiple hydrometeor spices are to be analyzed. Furthermore, the nonlinearity associated with the observation operator for the reflectivity in dBZ can also create difficulties in finding the true minimum of the cost function.
In this study, we applied 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, snow and hail first from the reflectivity, based on physical considerations. The temperature and vertical velocity in the background forecast are used to help determine the rainwater (qr), snow (qs) and graupel (qg) mixing ratios found in the WSM6 (WRF single-moment 6-class) microphysics scheme. When the temperature is higher than 0 °C, Z is related to qr. While the temperature is lower than 0 °C, the hydrometeor is in the form of snow and graupel, depending on if the magnitude of the vertical wind is smaller or larger than 1 m/s. To simplify the implementation within an existing version of WRF 3DVAR which does not include analysis variables for the hydrometeors, we carry all three hydrometeors using a single variable while distinguishing the types using the above criteria. When the derived mixing ratios are analyzed, reduced spatial correction scales are used.
Ten-minute analysis cycles are performed over a one-hour assimilation window, on a 4 km grid nested inside a 20 km one. 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.