基于Copula函数的三峡库区万州段蓄水前后降雨量-径流量关系分析

三峡水库蓄水对其库区降雨量-径流量关系变化的影响程度对于库区水资源规划有着重要意义。选用万县水文站1977-2017共计41 a的降雨量和径流量实测值，确定了各蓄水阶段降雨量和径流量的分布情况，引入Copula函数模型计算各阶段的联合分布函数，定量分析水库调蓄对两者关系的影响，预测了2017年后水文情势。结果表明：采用Copula函数联合分布数学模型能较好计算三峡库区万州段不同阶段的降雨量-径流量关系。万州段从天然河道变为库区河道后，降雨量-径流量关系发生了较大变化。在天然河道阶段，降雨量和径流量均采用皮尔逊III型分布最为合理；三峡水库工程施工期和初步蓄水阶段，降雨量变为Gumbel分布，径流量变为对数正态分布；试验性蓄水阶段，降雨量变为对数正态分布，径流量恢复至皮尔逊III型分布。年降雨量和年径流量在施工期及初步蓄水阶段较天然河道阶段均有所减少，年降雨量变幅区间减小38.4%，年径流量变幅区间减小20.6%；试验性蓄水阶段的年降雨量增多，变幅区间增大24.5%，而年径流量减少，变幅区间减小57%。通过该数学模型预测三峡库区万州段今后年径流量不小于3 490×10⁸ m³（±5%），最大不超过4 055×10⁸ m³（±5%）；年降雨量不小于1 048 mm（±5%），最大值不超过1 842 mm（±5%）。该研究可为三峡库区万州段流域水资源开发利用与水文序列的重构工作等提供科学依据，也可为其他库区内河道的水文特性变化关系的研究提供参考。

Analysis of rainfall-runoff relationship before and after impoundment of Three Gorges Reservoir Wan County section based on Copula function

The impoundment of the Three Gorges Reservoir affects the changes of rainfall-runoff relationship in reservoir area, so the water resources planning of the reservoir area has to take this effect into consideration. In this paper, the measured rainfall-runoff value of 41 a (1977-2017) from Wan County Hydrological Station was selected to study the distribution of rainfall-runoff at each water storage stage, then the joint distribution function of each water storage stage was calculated using the Copula function model to quantatively analyze the effect of reservoir impoundment on its relationships, based on which the hydrological situation in this area after 2017 was predicted. Research indicates that the Copula function joint distribution mathematical model is applicable to the caculation of rainfall-runoff relationship of different stages in Wan County section of the Three Gorges Reservoir. The rainfall- runoff relationship of Wan County section of the Three Gorges Reservoir has changed greatly after it was converted from a natural river course to a part of reservoir course. At the natural river course stage, the marginal distributions of rainfall and runoff in this area were better described using Pearson III distribution. Whereas the rainfall changed to Gumbel distribution and the runoff changed to lognormal distribution during the construction period and preliminary impoundment stage. At the experimental stage, the rainfall became lognormal distribution, and the runoff returned to the Pearson III distribution. Compared to the natural river course stage, during the construction period and preliminary impoundment stage the annual rainfall decreased by 38.4%, the annual runoff decreased by 20.6%, whereas the annual rainfall increased by 24.5%, and the annual runoff decreased by 57% at the experimental stage. According to the prediction results of this mathematical model, the annual runoff of this area will be no less than 349.0×10⁹ m³ (±5%), but no more than 405.5×10⁹ m³ (±5%), the annual rainfall will be no less than 1 048 mm (±5%), but will not exceed 1 842 mm (±5%). This research can provide a theorectical support for the development and utilization of water resources and the reconstruction of hydrological sequences in the Wan County section of the Three Gorges Reservoir area. It can also provide some reference for the research of hydrological characteristics changes of river channels in other reservoir areas.