
科学技术与工程

中国技术经济学会
Progress of Compensatory Assessment of Runoff Abundance and Depletion in Water Diversion and Transfer Project Based on Copula Function
Fei YAO , Dan-yi ZHANG , Ping CHEN , Pei GAO , Xian-qun HU , Xiu-qin YANG
Science Technology and Engineering ›› 2026, Vol. 26 ›› Issue (17) : 7111 -7122.
The establishment and solution methods for the assessment model of runoff high-low flow compensation in inter-basin water diversion projects, based on the Copula function, were summarized. The calculation and application of the assessment indicators for runoff high-low flow compensation were also summarized. The conclusions are as follows: existing research primarily focuses on establishing two-dimensional Copula function assessment models using runoff or precipitation data from a single water source area and a single water receiving area of a diversion project. The correlation index method and the maximum likelihood method were commonly used to fit parameters, with the Clayton, Frank, and Gumbel Copula functions identified as the most applicable distributions. The high-low flow encounter probabilities under nine combined scenarios (high-normal-low) were calculated based on runoff series classified by the assurance rate method. The high-low flow compensation capability was quantitatively assessed by the combined probabilities of synchronous/asynchronous high-low flows and favorable/unfavorable conditions for water diversion. It is determined that major water diversion projects in China, such as the South-to-North Water Diversion Project, the Hanjiang-to-Weihe River Water Diversion Project, and the Central Yunnan Water Diversion Project, all possess a certain degree of high-low flow compensation capacity. Recommendations are proposed as follows: the free and open-source Copula toolbox MhAST is suggested for parameter fitting and uncertainty analysis of two-dimensional Copula functions. The anomaly percentage method is employed to classify the flood and drought levels of runoff sequences, ensuring the obtained probabilities of flood-drought occurrences, synchronous and asynchronous flood-drought combinations, and favorable versus unfavorable water transfer combinations can clearly express the compensation relationship between water source and receiving regions. The high-high encounter event should be regarded as a favorable condition for water diversion, and its occurrence probability should be incorporated into the combined probability of favorable diversion.
Copula function / water diversion project / runoff abundance compensation / evaluation indexes
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