A Method for Fitting Full Raindrop Size Distribution Based on Generalized Gamma Model

The raindrop size distribution (RSD) plays a crucial role in study of microphysical processes related to precipitation. Discrepancies in the derived microphysical characteristics of precipitation arise when different models are adopted to fit RSD, thereby affecting accuracy of precipitation microphysical studies. Consequently, a comprehensive examination of RSD fitting models is warranted. Due to limitations of the instrument, the disdrometer is prone to underestimating small raindrops and medium-size raindrops.The full RSD is constructed through the combination and observations from micro rain radar and disdrometer at Mêdog (4 April, 13 September and 29 September in 2021) and Longmen (10 May, 9 June and 10 June in 2022). Generalized Gamma model is implemented to characterize full RSD, with comparative analyses being conducted against the standard Gamma model. Results indicate that rain rates calculated from full RSD are better agreement with the ground rain gauge measurements, exhibiting higher correlation coefficients and smaller biases. Based on full RSD data of different rainfall intensities obtained from different regions, double-moment normalization is adopted by choosing the 3rd and the 6th moments to achieve the fitting of generalized Gamma model with two shape parameters(μ and c). The raindrop number concentration N(D), generalized diameter parameter D'm and rain rate obtained are shown to be closer to observations than those fitted by standard Gamma model, and it can be used to describe the drizzle pattern, the precipitation pattern, and the region between them simultaneously. Judging from results of quantitative comparison, it shows that the fitting of generalized Gamma model demonstrates a smaller bias and a higher model efficiency coefficient compared to standard Gamma model. Based on the raindrop size distribution of precipitation influenced by various microphysical processes (diameter-controlled type and quantity-controlled type) at Mêdog and Longmen, the fundamantal shape h(x) of the raindrop size distribution is derived through double-moment normalization. Even for raindrop size distributions that exhibit significant microphysical differences, the function h(x) continues to demonstrate remarkable stability. Especially in the central part of the normalized diameter range, this relative stability is demonstrated to have important practical application value for the retrieval of raindrop size distribution from dual-polarization weather radar data by applying the generalized Gamma model.