Direct Assimilation of Radar Reflectivity without Tangent Linear and Adjoint of the Nonlinear Observation Operator in the GSI-Based EnVar System: Methodology and Experiment with the 8 May 2003 Oklahoma City Tornadic Supercell

AGSI-based EnVar data assimilation system is extended to directly assimilate radar reflectivity to initialize convective-scale forecasts. When hydrometeor mixing ratios are used as state variables (method mixing ratio), large differences of the cost function gradients with respect to the small hydrometeor mixing ratios and wind prevent efficient convergence. Using logarithmic mixing ratios as state variables (method logarithm) fixes this problem, but generates spuriously large hydrometeor increments partly due to the transform to and from the logarithmic space. The tangent linear of the reflectivity operators further contributes to spuriously small and large hydrometeor increments in method mixing ratio and method logarithm, respectively. A new method is proposed by directly adding the reflectivity as a state variable (method dBZ). Without the tangent linear and adjoint of the nonlinear operator, the new method therefore avoids the aforementioned problems. The newly proposed method is examined on the analysis and prediction of the 8 May 2003 Oklahoma City tornadic supercell storm. Both the probabilistic forecast of strong low-level vorticity and maintenance of strong updraft and vorticity in method dBZ are more consistent with reality than in method logarithm and method mixing ratio. Detailed diagnostics suggest that a more realistic cold pool due to the better analyzed hydrometeors in method dBZ than in other methods leads to constructive interaction between the surface gust front and the updraft aloft associated with the midlevel mesocyclone. Similar low-level vorticity forecast and maintenance of the storm are produced by the WSM6 and Thompson microphysics schemes in method dBZ. The Thompson scheme matches the reflectivity distribution with the observations better for all lead times, but shows more southeastward track bias compared to the WSM6 scheme.