Ensemble probability distribution of annual runoff for the past 70 years in two main watersheds of China

ABSTRACT Water resources in China, especially in the major basins of the Songhua and Yangtze rivers, are characterized by uneven distribution both temporally and spatially, leading to notable challenges in per capita water availability. In this study, we investigate the ensemble probability distribution of annual runoff over the past 70 years in two of China's major watersheds: the Songhua River and the Yangtze River. By dividing each basin into several regions from upstream to downstream, based on annual mean discharge as a proxy for annual runoff, we observed a significant correlation between the annual runoff of the control sections and those of the upstream and downstream regions in these large watersheds. Consequently, this study establishes the probability distribution of annual runoff for each region within the basins, anchored on the design annual runoff of the control sections, using the joint bivariate logarithmic normal distribution of two interrelated random variables. Furthermore, we developed a relationship between the conditional probability distribution and correlation diagram data, and a regression equation correlating regional annual runoff with the watershed control section's runoff. This investigation into the historical patterns of runoff over the past 70 years provides a comprehensive understanding of the dynamics in these critical watersheds.