Sensitivity analysis of DSD retrievals from polarimetric radar in stratiform rain based on the mu-Lambda relationship

Raindrop size distributions (DSDs) play a crucial role in quantitative rainfall estimation using weather radar. Thanks to dual polarization capabilities, crucial information about the DSD in a given volume of air can be retrieved. One popular retrieval method assumes that the DSD can be modeled by a constrained gamma distribution in which the shape (mu) and rate (Lambda) parameters are linked together by a deterministic relationship. In the literature, mu-Lambda relationships are often taken for granted and applied without much critical discussion. In this study, we take another look at this important issue by conducting a detailed analysis of mu-Lambda relations in stratiform rain and quantifying the accuracy of the associated DSD retrievals. Crucial aspects of our research include the sensitivity of mu-Lambda relations to the temporal aggregation scale, drop concentration, inter-event variability, and adequacy of the gamma distribution model. Our results show that mu-Lambda relationships in stratiform rain are surprisingly robust to the choice of the sampling resolution, sample size, and adequacy of the gamma model. Overall, the retrieved DSDs are in a rather decent agreement with ground observations (correlation coefficient of 0.57 and 0.74 for mu and D-m). The main sources of errors and uncertainty during the retrievals are calibration offsets in reflectivity (Z(hh)) and differential reflectivity (Z(dr)). Measurement noise and differences in scale between radars and disdrometers also play a minor role. The raindrop concentration (N-T) remains the most difficult parameter to retrieve, which can be off by several orders of magnitude. After careful data filtering and removal of problematic Z(hh)/Z(dr) pairs, the correlation coefficient for the retrieved N-T values remained low, only slightly increasing from 0.12 into 0.24.