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Raindrop size distributions (DSD) and rain rate have been estimated from polarimetric radar data using different approaches with the accuracy depending on the errors both in the radar measurements and the estimation methods. Herein, a deep neural network (DNN) technique was utilized to improve the estimation of the DSD and rain rate by mitigating these errors. The performance of this approach was evaluated using measurements from a two-dimensional video disdrometer (2DVD) at the Kessler Atmospheric and Ecological Field Station in Oklahoma as ground truth with the results compared against conventional estimation methods for the period 2006-17. Physical parameters (mass-/volume-weighted diameter and liquid water content), rain rate, and polarimetric radar variables (including radar reflectivity and differential reflectivity) were obtained from the DSD data. Three methods--physics-based inversion, empirical formula, and DNN--were applied to two different temporal domains (instantaneous and rain-event average) with three diverse error assumptions (fitting, measurement, and model errors). The DSD retrievals and rain estimates from 18 cases were evaluated by calculating the bias and root-mean-squared error (RMSE). DNN produced the best performance for most cases, with up to a 5% reduction in RMSE when model errors existed. DSD and rain estimated from a nearby polarimetric radar using the empirical and DNN methods were well correlated with the disdrometer observations; the rain-rate estimate bias of the DNN was significantly reduced (3.3%in DNN vs 50.1%in empirical). These results suggest that DNN has advantages over the physics-based and empirical methods in retrieving rain microphysics from radar observations. [ABSTRACT FROM AUTHOR]