基于降维思想的水资源脆弱性非线性评估模型及其应用

摘要

利用微分方程建模技术构建一种通用的水资源脆弱性非线性评估模型,在对指标进行降维的基础上,研究水资源脆弱性和指标之间的非线性关系.首先,基于投影寻踪技术建立降维模型,对多维指标进行降维处理,然后采用拉格朗日函数法求解最优投影方向;其次根据评估函数具备的性质和特点建立水资源脆弱性微分方程模型;最后求解方程估计未知参数,模拟水资源脆弱性与指标之间的非线性函数模型.利用所建模型定量研究北京市1979-2012年的水资源脆弱性变化规律,筛选影响北京市水资源脆弱性的敏感因子,研究结果符合北京市实际情形,说明模型的适用性.在水资源供需平衡分析的基础上,对2020年北京市水资源脆弱性进行评价,研究结果表明:当不考虑外调水和再生水时,2020年北京市在1956-2012年来水条件下的水资源脆弱性值均约为0.88,水资源均处于极度脆弱状态;利用再生水和南水北调水后,2020年在不同来水条件下的水资源脆弱性均有所降低,平均下降幅度仅为17.2％.本文建立的水资源脆弱性非线性评估函数模型可以避免人为的干扰,具备单调性、有界性和变化的连续平稳性等性质,能定量模拟和刻画水资源脆弱性与指标之间的变化关系.%This study focuses on building a general nonlinear assessment model for water resources vulnerability analysis using a differential function modeling technique.This paper studies the nonlinear relation between water resources vulnerability and its indicators after performing dimension reduction.The major steps were as follows.First,a dimension reduction model was built based on projection pursuit,and the optimal projection direction was searched by Lagrange function.Second,a differential function model was established on the basis of the characters and features of an assessment function.Finally,a nonlinear function model of water resources vulnerability and its indicators were simulated by computing the equation and estimating the parameters.The model was used to study the variation tendency of water resources vulnerability of Beijing during the period 1979-2012 and the sensitive impact factors of water resources vulnerability were selected.The results were consistent with the situation of Beijing,proving that the model was reliable.After performing an analysis of balance between water supply and water demand,water resources vulnerability in 2012 was evaluated.Under different scenarios of inflows,all the values for water resources vulnerability in 2020 is about 0.88 and water resources of Beijing are in the state of extreme vulnerability without considering transferred and reclaimed water use.After using transferred and reclaimed water,all the values of vulnerability are reduced,but the average reduction rate is only 17％.Our model is free of artificial disturbances,and it is characterized by monotony,boundedness and continuous stationarity.The model can simulate and describe the relation between water resources vulnerability and its indicators quantitatively.