Generation of Stochastic Daily Precipitation for China Based on Empirical Orthogonal Function Analysis

Historical precipitation data are crucial for assessing the risks associated with natural disasters such as droughts and floods. However, some extreme precipitation scenarios may not have been included in historical records, particularly in China where the observed precipitation time series is relatively short compared to the return periods of rare extremes. This limitation poses a considerable challenge in disaster risk assessment, because the absence of data on certain extreme events can lead to risk underestimation. Therefore, the generation of spatially correlated stochastic precipitation events based on historical data is a key issue in disaster risk assessment. Current methodologies tend to focus on generating stochastic precipitation events for either a single site or a small number of sites. However, methods designed to generate stochastic precipitation events on large-scale grids have not yet been fully developed. To address this gap, we aimed to explore a method for generating daily stochastic precipitation events set at a 0.1° grid scale nationwide based on empirical orthogonal function (EOF) analysis and probabilistic fitting of principal component coefficients. We applied the EOF analysis method to decompose daily precipitation data for China from 1961 to 2022 (62 years). For each day of the year, 62 spatial modes and their corresponding mode coefficients were generated. Multiple probability distribution functions were used to fit the probability distributions of the mode coefficients for each day, with the optimal fitting function selected for each day. Based on these probability distributions, thresholds were set using twice the maximum and minimum values of the historical mode coefficients as the upper and lower boundaries, respectively. Monte Carlo sampling of daily precipitation scenarios was conducted using the 62-year historical data (1961-2022). Finally, using 62-year historical data (1961-2022), we performed Monte Carlo sampling to generate daily precipitation scenarios. To compare the consistency and differences between historical and stochastic precipitation characteristics, 5000 years of simulated daily precipitation events were generated. A comparative analysis was conducted using five statistical metrics: maximum value, mean, standard deviation, typical return period precipitation, and spatial correlation. The analysis results show that: (1) The stochastic precipitation adequately preserved the intensity-probability characteristics of historical precipitation, with the average difference between the two at the grid scale being less than 0.9 mm, which is considered negligible. The differences in the precipitation intensities for return periods of 10, 20, and 50 years were all less than 15%, and the differences in their standard deviations were all less than 8%. (2) The stochastic precipitation effectively extended the upper bound of the annual maximum values, with the maximum value in the grid with the greatest difference being 36% higher than the historical precipitation. (3) The stochastic precipitation maintained a good spatial correlation, with the daily Moran's index and Pearson correlation coefficient for all grids across the country having minimum values greater than 0.96 and 0.95, respectively. The national daily precipitation stochastic event set, based on empirical orthogonal decomposition, provides a robust data foundation for subsequent quantitative disaster risk assessments.