Theoretical performance bounds for the estimation of drop size distribution and rain rate
Reed, Jenny Lynn
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Radar is an indispensable tool in the observation, analysis, and prediction of weather. The Weather Surveillance Radar 1988-Doppler (WSR-88D) is the primary source of weather radar data in the United States (U.S.), providing dual-polarimetric (dual-pol) radar measurements for the inference of meteorological phenomena. A classic estimation problem in radar meteorology is the estimation of rain rate. Taking this problem one step further, a number of approaches have been suggested for estimating the parameters of the drop size distribution (DSD) of rain (or clouds). While various methodologies have been suggested for rain rate and DSD estimation, and numerous studies have evaluated these estimators, no fundamental limit has yet been established for how well these estimators could perform given the available dual-pol data. This dissertation derives fundamental performance bounds for the variance of any unbiased estimator of the DSD parameters, given the dual-pol measurements recorded by operational weather radars, e.g., the WSR-88D. This dissertation further establishes similar bounds for the estimation of rain rate and liquid water content (LWC). These bounds and their implications are examined in detail to infer the efficacy of the dual-pol measurements provided by the WSR-88D for the estimation of the DSD parameters, rain rate, and LWC.