Retrieval of lower-order moments of the drop size distribution using CSU-CHILL X-band polarimetric radar: a case study

Abstract

Abstract. The lower-order moments of the drop size distribution (DSD) have generally been considered difficult to retrieve accurately from polarimetric radar data because these data are related to higher-order moments. For example, the 4.6th moment is associated with a specific differential phase and the 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 for the DSD. Many double-moment “bulk” microphysical schemes predict the total number concentration (the 0th moment of the DSD, 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, 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 by 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 correction of measured reflectivity Zh using the total Φdp constraint, i.e., 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 about 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 from radar 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 <15 % in magnitude, with Pearson’s correlation coefficient >0.9. Both radar measurement and parameterization errors were estimated rigorously. We show that the temporal variation of the radar-retrieved mass-weighted mean diameter with M0 resulted in coherent “time tracks” that can potentially lead to studies of precipitation evolution that have not been possible so far.

Testing the Drop-Size Distribution-Based Separation of Stratiform and Convective Rain Using Radar and Disdrometer Data from a Mid-Latitude Coastal Region

“…Dm' depends on two (chosen) reference DSD moments. In Reference [35], where X-band polarimetric radar retrievals were successfully carried out, the chosen reference moments were the third and the sixth moments. We use a similar approach here, except the frequency is now S-band.…”

Retrieving Rain Drop Size Distribution Moments from GPM Dual-Frequency Precipitation Radar

“…Algorithm errors are sometimes referred to as parameterization errors. Bringi et al [31] considered an additional source of uncertainty, namely those due to radar measurement errors. They found that, for lower-order moments, the parameterization error dominates the overall uncertainties, whereas the radar-measurement errors dominate those for higher-order moments.…”

“…Recently, retrieval of DSD moments from ground-based polarimetric radar measurements has been evaluated using X-band data, with special emphasis on the prediction of lower-order moments. Two examples are [30,31]. In both cases, the procedure initially entailed the retrieval of two "reference" moments, in both cases [M 3 , M 6 ], followed by reconstructing the DSDs and calculating other moments assuming a specific function to represent the underlying shape (denoted h(x), as explained in the next section).…”

“…In both cases, the procedure initially entailed the retrieval of two "reference" moments, in both cases [M 3 , M 6 ], followed by reconstructing the DSDs and calculating other moments assuming a specific function to represent the underlying shape (denoted h(x), as explained in the next section). In [30], the two reference moments are estimated using the co-polar reflectivity (Z h for horizontal polarization), differential reflectivity (Z dr ), and the specific differential propagation phase (K dp ), whereas in [31], they are estimated using Z h , Z dr , and specific attenuation, A h .…”

Testing the Drop-Size Distribution Based Separation of Stratiform and Convective Rain Using Radar and Disdrometer Data from a Midlatitude Coastal Region

“…Dm' depends on two (chosen) reference DSD moments. In [32], where X-band polarimertic radar retrievals were successfully carried out, the chosen reference moments were the 3 rd and the 6 th moments. We use a similar approach here, except the frequency is now S-band.…”