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Gravity based subtractive set pair potential method for dynamic evaluation of water resources carrying capacity
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摘要: 为动态分析水资源承载力变化状况、准确识别脆弱性指标，采用万有引力和阻尼系数的思想，构造了用以反映集对事件的联系程度及态势的引力减法集对势。将引力减法集对势应用于水资源承载力动态分析评价中，并与现有的减法集对势进行对比分析。结果表明：引力减法集对势对安徽省水资源承载力的动态分析及态势分析的结果与现有的减法集对势结果相一致，这两种集对势之间的相关系数接近1.0；引力减法集对势诊断出以下指标—植被覆盖率、人口密度、入河污水排放达标率、水功能区水质达标率和生态用水率是安徽省2005—2015年水资源承载力评价的脆弱性指标，需重点调控，其他指标需注意做好改善工作。因此，引力减法集对势方法运用于安徽省水资源承载力动态评价与诊断是可行的；该方法解释性强、计算简便、结果符合实际、适用性强，为判断集对事件的当前状态及发展趋势提供了新途径，在系统动态分析评价中具有应用前景。Abstract: In order to dynamically analyze the change of water resources carrying capacity and accurately identify the vulnerable indexes, the idea of universal gravitation and damping coefficient is used for reference to construct gravity based subtractive set pair potential, which can reflect the relation and situation of set pair events. The method of gravity based subtractive set pair potential was applied to the dynamic analysis of the water resources carrying capacity evaluation, and compared with the existing subtractive set pair potential. The results show that the dynamic analysis of the water resources carrying capacity of Anhui province by the gravity based subtractive set pair potential and the comparison of the situation analysis of subtractive set pair potential are consistent, and the correlation coefficient between the two kinds of set pair situation is close to 1.0; according to the gravity based subtractive set pair potential, the indexes of vegetation coverage rate, population density, sewage discharge reaching the standard, water quality reaching the standard and ecological water use rate in the water functional area in 2005-2015 are the vulnerability indexes of water resources carrying capacity evaluation in Anhui province, which should be mainly controlled. And other indicators need to be improved. Therefore, the gravity based subtractive set pair potential is feasible for the dynamic evaluation and diagnosis of water resources carrying capacity in Anhui province; and gravity based subtractive set pair potential has strong potential interpretation, simple calculation, practical results and strong applicability. The method provides a new way for judging the current condition and development trend of the set pair events, and has application prospect in system dynamic analysis and evaluation.
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图 1 安徽省水资源承载力代表性指标引力减法集对势和减法集对势2005—2015年计算值
Figure 1. Calculation values of gravity based subtractive set pair potential and subtractive set pair potential of representative indicators of water resources carrying capacity in Anhui province from 2005 to 2015
图 2 安徽省水资源承载力评价指标引力减法集对势和减法集对势2005—2015年计算值
Figure 2. Calculation value of gravity based subtractive set pair potential and subtractive set pair potential in Anhui province from 2005 to 2015
表 1 安徽省水资源承载力动态评价指标体系、等级标准和权重[17]
Table 1. Dynamic evaluation index system, grade standard and weight of water resources carrying capacity in Anhui province[17]
目标层 子系统 权重 指标层 评价标准 权重 可载(1级) 临界可载(2级) 超载(3级) 水资源承
载力评价承载支撑力
子系统0.4 人均水资源量x1/m3 ≥1670 1670~1000 <1000 0.1332 产水模数x2/(万m3·km−2) ≥80 80~50 <50 0.1332 人均供水量x3/(m3/(人·a)) ≥450 450~350 <350 0.1056 植被覆盖率x4/% ≥40 40~25 <25 0.0280 承载压力
子系统0.4 人均日生活用水量x5/L ≤70 70~180 >180 0.0396 万元GDP用水量x6/m3 ≤100 100~400 >400 0.0792 万元工业增加值需水量x7/(m3/万元） ≤50 50~200 >200 0.0596 人口密度x8/(人·km−2） ≤200 200~500 >500 0.0792 城市化率x9/% ≤50 50~80 >80 0.0632 农田灌溉定额x10/(m3·hm−2） ≤3750 3750~6000 >6000 0.0792 承载调控力
子系统0.2 水资源开发利用率x11/% ≤40 40~70 >70 0.0582 人均GDP x12/（元/人） ≥24840 24840~6624 <6624 0.0484 入河污水排放达标率x13/% ≥90 90~70 <70 0.0288 水功能区水质达标率x14/% ≥95 95~70 <70 0.0454 生态用水率x15/% ≥5 5~1 <1 0.0192 
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表 2 各年安徽省水资源承载力评价的平均联系数、引力减法集对势和减法集对势计算值
Table 2. Average connection number, gravity based subtractive set pair potential and subtractive set pair potential of water resources carrying capacity evaluation in Anhui province in each year
年份 平均联系数 引力减法集对势 减法集对势 结果值 态势 结果值 态势 2005 0.132 8+0.536 0I+0.331 2J −0.339 偏反势 −0.305 偏反势 2006 0.128 1+0.413 1I+0.458 8J −0.481 偏反势 −0.467 偏反势 2007 0.164 3+0.542 1I+0.293 6J −0.223 偏反势 −0.199 均势 2008 0.176 3+0.651 7I+0.172 0J 0.009 均势 0.007 均势 2009 0.156 3+0.648 0I+0.195 7J −0.081 均势 −0.065 均势 2010 0.199 5+0.687 2I+0.113 3J 0.189 均势 0.145 均势 2011 0.114 9+0.644 4I+0.240 7J −0.256 偏反势 −0.207 偏反势 2012 0.129 1+0.765 3I+0.105 6J 0.059 均势 0.041 均势 2013 0.114 8+0.587 0I+0.297 8J −0.338 偏反势 −0.291 偏反势 2014 0.149 0+0.851 0I+0J 0.443 偏同势 0.276 偏同势 2015 0.165 6+0.834 4I+0J 0.477 偏同势 0.304 偏同势
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