Determining optimal probability distributions for gridded precipitation data based on L-moments

Understanding the probability distributions of precipitation is crucial for predicting climatic events and constructing hydraulic facilities. To overcome the inadequacy of precipitation data, regional frequency analysis was commonly used by "trading space for time". However, with the increasing availability of gridded precipitation datasets with high spatial and temporal resolutions, the probability distributions of precipitation for these datasets have been less explored. We used L-moments and goodness-of-fit criteria to identify the probability distributions of annual, seasonal, and monthly precipitation for a 0.5° × 0.5° dataset across the Loess Plateau (LP). We examined five 3-parameter distributions, namely General Extreme Value (GEV), Generalized Logistic (GLO), Generalized Pareto (GPA), Generalized Normal (GNO), and Pearson type III (PE3), and evaluated the accuracy of estimated rainfall using the leave-one-out method. We also presented pixel-wise fit-parameters and quantiles of precipitation as supplements. Our findings indicated that precipitation probability distributions vary by location and time scale, and the fitted probability distribution functions are reliable for estimating precipitation under various return periods. Specifically, for annual precipitation, GLO was prevalent in humid and semi-humid areas, GEV in semi-arid and arid areas, and PE3 in cold-arid areas. For seasonal precipitation, spring precipitation mainly conforms to GLO distribution, summer precipitation around the 400 mm isohyet prevalently follows GEV distribution, autumn precipitation primarily meets GPA and PE3 distributions, and winter precipitation in the northwest, south, and east of the LP mainly conforms to GPA, PE3 and GEV distributions, respectively. Regarding monthly precipitation, the common distribution functions are PE3 and GPA for the less-precipitation months, whereas the distribution functions of precipitation for more-precipitation months vary substantially across different regions of the LP. Our study contributes to a better understanding of precipitation probability distributions in the LP and provides insights for future studies on gridded precipitation datasets using robust statistical methods.