Improvement to microphysical schemes in WRF Model based on observation data, part I: size distribution function

In this study, we evaluated the performance of size distribution functions (SDF) with 2- and 3-moments in fitting the observed size distribution of rain droplets at three different heights for improving the microphysics schemes in meso-scale models, such as Weather Research and Forecast (WRF). Rain droplets were observed during eight periods of different rain types at three stations on the Yellow Mountain in East China. The SDF in this study were M-P distribution with a fixed shape parameter in Gamma SDF(FSP). Where the Gamma SDFs were obtained with three diagnosis methods with the shape parameters based on Milbrandt_2010(DSPM10), Milbrandt_2005(DSPM05) and Seifert_2008(DSPS08) for solving the shape parameter(SSP) and Lognormal SDF. Based on the preliminary experiments, three ensemble methods deciding Gamma SDF was also developed and assessed.

The result showed that the magnitude of average relative error caused by FSP was 10^-2 for fitting 0-order moment of observed rain droplet distribution, and the magnitude of average relative error changed to 10^-1 and 10⁰ respectively for 1-4 order moments and 5-6 order moments. To different extent, DSPM10, DSPM05, DSPS08, SSP and ensemble methods could improve fitting accuracies for 0-6 order moments, especially the one coupling SSP and DSPS08 methods, which provided a average relative error 6.46% for 1-4 order moments and 11.90% for 5-6 order moments, respectively. Besides, although Lognormal SDF also could also be used to build a three equation group s to predict three parameters, its relative error of fitted moment was much larger than that of Gamma SDF.

For the properties of SSP method, the threshold value of shape parameter ranged from 0 to 8, because values beyond this range could cause overflow of calculation. When average diameter of rain droplets was less than 2mm, the possibility of unavailable shape parameter value(USPV) increased with a decreasing droplet size. There was strong sensibility of moment group in fitting accuracy. When ensemble method coupling SSP and DSPS08 was used, 1-3-5 moment group presented a better fix ability than 0-3-6 moment group.