Retrieval of Lower-Order Moments of the Drop Size Distribution using CSU-CHILL X-band Polarimetric Radar: A Case Study

Abstract. The lower order moments of the drop size distribution (DSD) have generally been considered as difficult to retrieve accurately from polarimetric radar data because these are related to higher order moments. For example, the 4.5th moment is associated with specific differential phase, 6th moment with reflectivity and ratio of high order moments with differential reflectivity. Thus, conventionally, the emphasis has been to estimate rain rate (3.67th moment) or parameters of the exponential or gamma distribution. Many double-moment bulk microphysical schemes predict the total number concentration (the 0th moment or M0) and the mixing ratio (or equivalently, the 3rd moment M3). Thus, it is difficult to compare the model outputs directly with polarimetric radar observations or, given the model outputs, to forward model the radar observables. This article describes the use of double-moment normalization of DSDs and the resulting stable intrinsic shape that can be fitted to the generalized gamma (G-G) distribution. The two reference moments are M3 and M6 which are shown to be retrievable using the X-band radar reflectivity, differential reflectivity and specific attenuation (from the iterative ZPHI method). Along with the climatological shape parameters of the G-G fit to the scaled/normalized DSDs, the lower order moments are then retrieved more accurately than possible hitherto. The importance of measuring the complete DSD from 0.1 mm onwards is emphasized using, in our case, an optical array probe with 50 µm resolution collocated with a two-dimensional video disdrometer with 170 µm resolution. This avoids small drop truncation and hence the accurate calculation of lower order moments. A case study of a complex multi-cell storm which traversed an instrumented site near the CSU-CHILL radar is described for which the moments were retrieved and compared with directly computed moments from the complete spectrum measurements using the aforementioned two disdrometers. Our detailed validation analysis of the radar-retrieved moments showed relative bias of the moments M0 through M2 was  0.9. Both radar measurement and parameterization errors were estimated rigorously. We show that the temporal variation of the radar-retrieved characteristic diameter with M0 resulted in coherent time tracks that can potentially lead to studies of precipitation evolution that have not been possible so far.