Simultaneous Estimation of Microphysical Parameters and the Atmospheric State Using Simulated Polarimetric Radar Data and an Ensemble Kalman Filter in the Presence of an Observation Operator Error

The impacts of polarimetric radar data on the estimation of uncertain microphysical parameters are investigated through observing system simulation experiments when the effects of uncertain parameters on the observation operators are also considered. Five fundamental microphysical parameters (i.e., the intercept parameters of rain, snow, and hail and the bulk densities of snow and hail) are estimated individually or collectively using the ensemble square root Kalman filter. The differential reflectivity ZDR, specific differential phase KDP, and radar reflectivity at horizontal polarization ZH are used individually or in combinations for the parameter estimation while the radial velocity and ZH are used for the state estimation. In the process, the parameter values estimated in the previous analysis cycles are used in the forecast model and in observation operators in the ensuing assimilation cycle. Analyses are first performed that examine the sensitivity of various observations to the microphysical parameters with and without observation operator error. The results are used to help interpret the filter behaviors in parameter estimation. The experiments in which either a single or all five parameters contain initial errors reveal difficulties in estimating certain parameters using ZH alone when observation operator error is involved. Additional polarimetric measurements are found to be beneficial for both parameter and state estimation in general. It is found that the polarimetric data are more helpful when the parameter estimation is not very successful with ZH alone. Between ZDR and KDP, KDP is found to produce larger positive impacts on parameter estimation in general while ZDR is more useful in the estimation of the intercept parameter of hail. In the experiments that attempt to correct errors in all five parameters, the filter fails to correctly estimate the snow intercept parameter and the density with or without polarimetric data, seemingly due to the small sensitivity of the observations to these parameters and complications involving the observation operator error. When these two snow parameters are not corrected during the estimation process, the estimations of the other three parameters and of all of the state variables are significantly improved and the positive impacts of polarimetric data are larger than that of a five-parameter estimation. These results reveal the significant complexity of the estimation problem for a highly nonlinear system and the need for careful sensitivity analysis. The problem is potentially more challenging with real-data cases when unknown sources of model errors are inevitable.