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基于Copula函数的流域水文动静态相似度融合方法

A fusion method of dynamic and static similarity in watershed hydrology using Copula function

  • 摘要: 流域水文相似度计算准确率的提高对解决无资料及缺资料地区的水文模拟具有重要的意义。该研究构建了一种融合静态特征与动态时序的流域水文综合相似度计算模型:采用基于伪标签的机器学习方法,借助沙普利可加性解释(shapley additive explanations,SHAP)降维物理属性指标、量化指标权重,以改进传统相似流域静态识别框架,并引入降雨时间序列相似的动态分析维度,采用基于数值符号和形态特征的时间序列距离(numerical symbolic and shape feature measure,NSM)度量动态相似度,最终基于Copula函数为两种维度下的异构相似度动态分配权重,实现动静态水文相似度的协同融合。以山西省汾河流域中小尺度的82个子流域为研究区域,分别计算上、中、下游三个分区流域对的综合相似度,在此基础上构建土壤和水分评估模型(soil and water assessment tool,SWAT)模拟各流域年尺度径流,计算流域径流相似度,进行相似流域识别结果的验证分析。结果表明:1)基于伪标签的机器学习特征指标选择方法所识别的水文相似性核心影响因子,与各分区的气候条件、下垫面格局及水文产汇流机制高度契合,26种相似性指标中,汾河上游流域相似性核心影响因子为年平均降雨量、地形起伏度和草地占比,权重累计0.66。中游为砂粒占比、年平均降雨量和流域面积,权重累计0.56。下游为高程变异系数、砂粒占比与不透水面占比,权重累计0.42;2)流域对静态主导及动静双维度均衡匹配是高水文相似性的核心驱动,高相似组中静态主导型流域对和动静均衡型流域对累计占比81%,显著高于低相似组的39%。同时流域对动态主导是低水文相似性的关键成因,低相似组中,动态主导型流域占比61%,显著高于高相似组的19%;3)对比SWAT模型径流模拟计算出的径流相似度,在与其差值阈值为0.05的前提下,汾河上、中、下游综合相似度模型计算的流域相似度准确率为分别为54%、84%、69%,而静态相似度计算的流域相似度准确率分别为31%、55%、29%,综合相似度模型的整体准确率为71%,静态相似度整体准确率为39%,综合相似度模型整体准确率相对提高了82%。综合相似度模型突破了传统相似度评估中指标选择主观性强、动态与静态信息割裂的局限,能够更客观地捕捉流域间在多维度上的相似性,为提升无(缺)资料地区水文相似流域识别的准确性提供了新的技术途径。

     

    Abstract: Improving the calculation accuracy of watershed hydrological similarity is of great significance for hydrological simulation in ungauged and data-insufficient regions. This study constructed a comprehensive calculation model of watershed hydrological similarity that integrates static characteristics and dynamic time series. A pseudo-label-based machine learning method was adopted to improve the traditional static identification framework for similar watersheds, in which the Shapley Additive Explanations (SHAP) was used to reduce the dimension of physical attribute indicators and quantify indicator weights. Meanwhile, a dynamic analysis dimension of rainfall time series similarity was introduced, and the Numerical Symbolic and Shape Feature Measure (NSM) distance was employed to measure dynamic similarity. Finally, the Copula function was used to dynamically assign weights to heterogeneous similarities under the two dimensions, realizing the synergistic fusion of dynamic and static hydrological similarities. Taking 82 medium and small-scale sub-basins in the Fenhe River Basin of Shanxi Province as the study area, the comprehensive similarity of watershed pairs in the upper, middle and lower reaches was calculated respectively. On this basis, the Soil and Water Assessment Tool (SWAT) model was constructed to simulate annual runoff of each watershed, and the watershed runoff similarity was calculated to verify and analyze the identification results of similar watersheds. The results demonstrated that: 1) The core drivers of hydrological similarity identified by the pseudo-label-based machine learning feature selection method are highly consistent with the climatic conditions, underlying surface patterns and runoff mechanisms of each sub-region. Among 26 indicators, the key factors for the upper, middle and lower Fenhe River basin are mean annual precipitation, terrain relief and grassland coverage (cumulative weight 0.66); sand content, mean annual precipitation and watershed area (0.56); and elevation coefficient of variation, sand content and impervious surface coverage (0.42), respectively. 2) Static dominance and balanced matching of static-dynamic dual dimensions for basin pairs are the core drivers of high hydrological similarity. The cumulative proportion of static-dominant and static-dynamic balanced basin pairs in the high-similarity group reaches 81%, which is significantly higher than 39% in the low-similarity group. Meanwhile, dynamic dominance of basin pairs is the key cause of low hydrological similarity. The proportion of dynamic-dominant basins in the low-similarity group is 61%, remarkably higher than 19% in the high-similarity group. 3) Using a difference threshold of 0.05 against the SWAT-derived runoff similarity benchmark, the accuracy rates of the proposed comprehensive similarity model for the upper, middle, and lower reaches were 54%, 84%, and 69%, respectively. These rates substantially exceeded those of the static similarity model alone, which were 31%, 55%, and 29%. The overall accuracy of the comprehensive model reached 71%, representing an 82% relative improvement over the 39% overall accuracy of the static model. In conclusion, the developed comprehensive similarity fusion method effectively addresses critical bottlenecks in traditional assessment approaches, such as strong subjectivity in indicator selection and the isolation of dynamic and static information. It provides a more objective means to capture multi-dimensional similarities between watersheds, offering a new and effective technical pathway for improving the accuracy of hydrological similar-watershed identification in ungauged or data-scarce regions.

     

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