基于Copula函数的人民胜利渠灌区地下水埋深与TDS联合分布分析  

Jointed Distribution Analysis of Groundwater Depth and TDS in the Peoples Victory Canal Irrigation Area Based on Copula Function

作　　者：刘中培[1,2] 阿长松 冯邵依 李鑫 韩宇平[1,2] 曹润祥[1] 冷静 LIU Zhongpei;A Zhangsong;FENG Shaoyi;LI Xin;HAN Yuping;CAO Runxiang;LENG Jing(North China University of Water Resources and Electric Power,Zhengzhou 450046,China;Henan Key Laboratory of Water Resources Conservation and Intensive Utilization in the Yellow River Basin,Zhengzhou 450046,China)

机构地区：[1]华北水利水电大学,河南郑州450046 [2]河南省黄河流域水资源节约集约利用重点实验室,河南郑州450046

出　　处：《人民黄河》2023年第12期88-95,共8页Yellow River

基　　金：国家自然科学基金资助项目(42072287)

摘　　要：为了查明不同埋深区域地下水溶解性总固体(TDS)变化规律,选择人民胜利渠灌区为研究区,根据地下水TDS值将灌区划分为高值区域、过渡区域和低值区域,采用AIC准则筛选出最优Copula函数,采用最优Copula函数构建不同区域地下水埋深与TDS之间的联合分布,对两者的关系进行分析。结果表明:不同区域地下水埋深与TDS之间均具有较强的正相关关系,高值区域地下水埋深和TDS最优边缘分布均为Gamma分布,过渡区域和低值区域地下水埋深最优边缘分布均为Weibull分布、TDS最优边缘分布均为Gamma分布。各典型观测井埋深-TDS最优联合分布函数均为Frank Copula函数。根据联合概率等值线可得当地下水埋深与TDS增大时,联合概率值也增大;当联合概率值一定时,TDS随着地下水埋深的增大而降低,并趋于稳定;联合概率等值线也可以反映任意埋深下TDS所发生的概率,以及同一概率下不同埋深与TDS之间可能出现的组合。In order to find out the variation law of total dissolved solids(TDS)in groundwater in different buried depth areas,this paper took the Peoples Victory Canal Irrigation Area as the research area,and divided into high value area,transition area and low value area according to TDS value,the optimal Copula function was selected by AIC criterion,the optimal Copula function was used to build the joint distribution between groundwater depth and TDS in different regions and analyze the relationship between the two.The results show that there is a strong positive correlation between groundwater depth and TDS in different regions,the optimal edge distribution of groundwater depth and TDS in the high value area is Gamma distribution,the optimal edge distribution of groundwater depth in transition area and low value area is Weibull distribution,and the optimal edge distribution of TDS is Gamma distribution.The optimal joint distribution function of the burial depth of each typical observation well and TDS is the Frank Copula function.According to the joint probability contour,when the groundwater depth and TDS increase,the joint probability value also increases;When the joint probability value is constant,TDS decreases with the increase of groundwater depth and tends to be stable;The joint probability contour can also reflect the probability of TDS under any groundwater depth,and the possible combination between different groundwater depths and TDS under the same probability.

关 键 词：地下水埋深 TDS COPULA函数 联合概率 人民胜利渠灌区 

分 类 号：P641.3[天文地球—地质矿产勘探]