Simultaneous Estimation of Microphysical Parameters and Atmospheric State with Radar Data and Ensemble Square-root Kalman Filter . Part I : Sensitivity Analysis and Parameter

The possibility of estimating fundamental parameters common in single-moment ice microphysics schemes using radar observations is investigated, for a model-simulated supercell storm, by examining parameter sensitivity and identifiability. These parameters include the intercept parameters for rain, snow and hail/graupel, and the bulk densities of snow and hail/graupel. These parameters are closely involved in the definition of drop/particle size distributions of microphysical species but often assume highly uncertain specified values. The sensitivity of pure model forecast as well as model state estimation to the parameter values, and the solution uniqueness of the estimation problem are examined. The ensemble square-root filter (EnSRF) is employed for model state estimation. Both forecast and assimilation sensitivity experiments show that the errors in the microphysical parameters have a larger impact on model microphysical fields than on wind fields; radar reflectivity observations are therefore preferred over those of radial velocity for microphysical parameter estimation. Among the three intercept parameters, the pure forecast is most (least) sensitive to rain (snow) intercept while the sensitivity to hail density is generally lager than that to snow density. The analyzed model state in the assimilation sensitivity experiments is, however, found to be most (least) sensitive to hail (rain) intercept, and there is a larger sensitivity to hail density than to snow density. The time scales of analysis response to errors in individual parameters are also investigated. The results suggest that a successful estimation of the parameters can be expected within the typical lengths of assimilation window needed for state estimation. The response functions calculated for the forecast as well as assimilation sensitivity experiments for all five individual parameters show concave shapes, with unique minima occurring at or very close to the true values; therefore true values of these parameters can be retrieved at least in these cases where only one parameter contains error at a time. The identifiability of multiple parameters together is evaluated from their correlations with forecast reflectivity. Significant levels of correlations are found that can be interpreted physically. As the number of uncertain parameters increases, both the level and the area coverage of significant correlations decrease, implying increased difficulties with multiple-parameter estimation. The details of the estimation procedure and the results of a complete set of estimation experiments will be presented in Part II of this paper. _____________________________

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