Tuesday, 11 January 2005
Retrieval of Drop Size Distribution from Simulated Dual-Frequency Radar Measurements
As part of NASA’s precipitation measurement mission, the performance of retrieval of raindrop size distribution (DSD) from simulated dual-frequency radar measurements has been tested employing disdrometer observations collected at different climatic regimes of the world. Reflectivities at 13.6 GHz and 35 GHz frequencies were calculated from disdrometer measurements through Mie scattering for 0° C with an assumption of spherical raindrops as they appear when observed at vertical cross-section. Integral rainfall parameters of rain rate, liquid water content, and mean mass diameter were also calculated from disdrometer measurements. A three parameter gamma function in the form of N(D) = N0 Dm exp (-LD), where N0 , L, and m are intercept, slope, and shape parameters, respectively, was used for the retrieval of the DSD. Unfortunately, there is no analytical solution for the parameters of the gamma distribution and therefore we seek numerical solutions for a fixed shape parameter. At a given shape parameter, the ratio of two reflectivity measurements (DFR = Z13.6/Z35) had three different regions where no, one, and two solutions were available for slope parameter. The intercept parameter, which is not a function of DFR, was then solved for using either reflectivity. Integral rainfall parameters were recalculated from gamma fitted distributions for a range of shape parameters. Best shape parameter was then determined for the lowest bias and mean absolute error between observed and retrieved integral rainfall parameters. We applied this retrieval algorithm for averaged disdrometer measurements that were grouped by 2 dBZ13.6 intervals. Best shape parameters ranged from 2 to 12 where either one or two solutions were available for slope parameter. Where two solutions existed for slope parameter, the second (higher) solution was better at less than 25 dBZ13.6 and vice-versa. Best shape parameters were nearly identical for two sites in the central Pacific Ocean, while the continental tropical and mid-latitude sites showed differences in best shape parameter reflecting the regional differences of the DSD. The best shape parameter in the Florida Keys, where precipitation originated in mountainous Cuba, more closely resembled continental than oceanic sites. A table of best shape parameters as a function of simulated reflectivity measurements at 13.6 GHz was developed for each site where potential application is the use of similar technique for the upcoming NASA Global Precipitation Measurement (GPM) dual-frequency radar measurements. We also applied our algorithm for instantaneous (1-minute), 3-, 6-, and 10-minute running average disdrometer measurements, using the table of shape parameters determined previously. Regardless of running average, one-solution cases had the lowest bias and mean absolute error for integral rainfall parameters. For two-solution cases, the higher value of L was correct for reflectivities below ~20 dBZ13.6, and the lower value of L was correct above ~30 dBZ13.6. In between the correct solution varied, and no reliable predictor of the best solution could be found as a function of reflectivity measurements. For the no-solution cases, a solution could be obtained for a shape parameter greater than the value given by the table that was obtained using reflectivity-averaged measurements. The effect of averaging over time increased the number of one-solution cases at the expense of no- and two-solution cases.