基于主成分分析和Copula函数的灌溉用水效率评价方法

灌区灌溉用水效率评价,对推行最严格的水资源管理制度具有重要意义。该文在构建评价指标体系的基础上,尝试将Copula函数应用于灌溉用水效率评价。针对多元变量导致Copula函数参数求解困难的问题,采用主成分分析法(principal component analysis,PCA)提取主成分因子,形成新的指标体系,从而建立PCA-Copula评价方法,对灌溉用水效率进行综合评价。对7个灌区灌溉用水效率为例进行评价,从灌区地形地貌、规模大小、供水类型、降雨多少、作物结构以及灌溉成本几方面分析评价值的影响因素。根据各灌区灌溉水有效利用系数的高低,经过Spearman等级相关系数检验,表明PCA-Copula评价方法的评价结果与熵值法以及突变理论评价方法的结果排序相差不超过2个名次的比例为100%,评价结果具有一致性,能够客观反映灌区灌溉用水效率的高低。同时,PCA-Copula评价方法的评价值在0~1之间分布均匀,最大差值为0.622,明显高于另外2种方法,且相邻排序的综合评价值梯度明显,有利于更直观地区别灌区灌溉用水效率的高低。

Evaluation method for irrigation-water use efficiency based on principle component analysis and Copula function

Abstract: Water use efficiency is an important parameter used for assessing quality of irrigation water system. This paper proposed a principle component analysis (PCA)-Copula method to comprehensively evaluate irrigation water use efficiency. Six indexes including water utilization coefficient of canal system, ratio of effective irrigated farmland, irrigation water use of unit area, water utilization coefficient of field, ratio of grain crop and yield of unit irrigation water were selected to estimate the water use efficiency. These indexes were normalized using mean and standard deviation. Two mutually independent principal factors were extracted from the normalized indexes by principal component analysis, and then incorporated into the Copula function to evaluate water use efficiency. Two mutually independent factors rather than six indexes decreased the dimension of copula function and thus overcame the difficulty of parameter estimation for multivariate copula. Five types of marginal distribution functions, i.e., Normal distribution, Exponential distribution, Extreme Maximum Type I distribution, Extreme Minimum Type I distribution and Gamma distribution, were used to fit the principal factors and Kolmogorov-Smirnov test was utilized for estimating the fitness of marginal distribution function. Finally, Akaike Information Criterion (AIC) and root-of-mean-square error (RMSE) were used for the selection of marginal distribution. Seven irrigation districts were chosen as the case study and the evaluation results of proposed PCA-Copula evaluation method were compared with those of Entropy Value Method (EVM) and Mutation Theory Evaluation Method (MTEM). The water use efficiencies of 7 irrigation districts were evaluated and ranked by the three methods, respectively. The results showed that the Spearman's rank coefficients between the results of PCA-Copula and those of EVM and MTEM were 0.857 and 0.75, respectively, which were above the threshold value of 0.714 and illustrated that the results of PCA-Copula method is consistent with those of EVM and MTEM. And the correlation coefficients between the effective irrigation water utilization coefficient and the results based on the PCA-Copula method, EVM and MTEM were 0.875, 0.875 and 0.768, respectively, revealing that the PCA-Copula method and EVM are superior over MTEM. In addition, the value of water use efficiencies evaluated by PCA-Copula method was evenly distributed over 0, 1] with the difference between maxima and minima of 0.622, rather than concentrated near 0.1 (the difference between maxima and minima of 0.037 based on EVM) or 1 (the difference between maxima and minima of 0.024 based on MTEM), implying a higher resolution ratio of PCA-Copula method over the other two methods. Therefore, the PCA-Copula method can assess the irrigation water use efficiently and lead to great convenience to the practice of water resources management. The water use efficiencies of 7 irrigation districts have been all increased by adopting water saving irrigation. By using the proposed method, water use efficiency was highest and greatly improved by water saving strategy in Zhanghe irrigation district, followed by Dujiangyan district. And, the water use efficiency and improvement of Zekou district and Shimen district were relatively low, only better than Dongfeng district, Yahekou district and Pingyuan district. In addition, Partial correlation analysis was used between water use efficiency evaluation based on PCA-Copula method and irrigation scale, precipitation and irrigation cost and the results implied: 1) water use efficiency was increased with increasing irrigation scale; 2) water use efficiency was low for the area with high precipitation; and 3) water use efficiency increased with increasing irrigation cost. These implications can be used for the adjustment of water resources management policies.