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Application of projection pursuit method in assessment and prediction of water resources carrying capacity
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摘要: 为解决区域水资源承载力综合评价中指标数据高维、非线性的问题，构建基于最大信息熵原理的投影寻踪水资源承载力评价方法，将该方法应用于2015年安徽省16个地级市水资源承载力的空间分布评价中；最后对2005—2015年安徽省全省水资源承载力进行动态评价，将该评价结果与灰色GM(1,1)模型结合，对2018—2020年安徽省区域水资源承载状况进行预测。结果表明：2015年，安徽省水资源承载空间分布状况整体表现为皖南地区优于皖中地区，皖中地区优于皖北地区；2005—2015年期间，全省水资源承载力虽基本处于临界超载状态，但年际间承载状况逐年好转。预测结果表明，2018—2020年全省水资源承载力保持良好的发展态势，总体向可载趋势发展。Abstract: In order to solve the problem of high-dimensional and non-linearity of index data in the comprehensive assessment of regional water resources carrying capacity, the method of projection pursuit was adopted in this study for assessing water resources carrying capacity based on the principle of maximum information entropy, and this method was further applied to assess the spatial distribution in 16 cities of Anhui Province in 2015, and finally the dynamic assessment of Anhui Province from 2005 to 2015 was carried out. The assessment results were combined with the GM (1,1) model to predict the regional water resources carrying capacity in Anhui Province from 2018 to 2020. The results show that in terms of the overall spatial distribution of water resources carrying capacity in 2015, the water resources carrying capacity in southern Anhui was better than that in central Anhui, which was further better than that in northern Anhui. The water resources carrying capacity of the province was basically at a critical point of overload from 2005 to 2015. But the inter-annual carrying capacity was improved year by year. The forecast results show that the water resources carrying capacity of the province maintains a good development momentum from 2018 to 2020, and the overall development trend is toward the excellent capability of loading.
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图 1 安徽省水资源承载力分布
Figure 1. Distribution of water resources carrying capacity in Anhui Province
表 1 水资源承载力状态等级[18-20]
Table 1. Status of water resources carrying capacity[18-20]
等级 承载状态 水资源承载社会经济状况 Ⅰ级 可载 区域水资源量足以承载当下社会经济规模需求且富余，水资源系统的承载状况良好 Ⅱ级 临界超载 区域水资源系统基本满足当地当下规模的社会经济的发展，水资源系统的承载状况一般 Ⅲ级 超载 区域水资源量、质与当地社会经济发展规模不相适应，水资源达到了可供给量的上限，水资源短缺成为阻碍当地进一步发展的因素 
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表 2 水资源承载力空间分布评价指标体系及等级标准[19]
Table 2. Evaluation index system and grade standard of spatial distribution of water resources carrying capacity[19]
目标层 子系统 子系统权重 指标层 评价标准 权重 可载 临界超载 超载 水资源承载力 水资源支撑力
子系统0.4 人均水资源量（m3） ≥1 670 1 670~1 000 <1 000 0.133 2 产水模数（104m3/km2） ≥80 80~50 <50 0.133 2 人均供水量（m3/(人·年）） ≥450 450~350 <350 0.105 6 植被覆盖率（%） ≥40 40~25 <25 0.028 0 水资源压力
子系统0.4 人均日生活用水量（L/(人• d)） ≤70 70~180 >180 0.039 6 万元GDP用水量（m3/万元） ≤100 100~400 >400 0.079 2 万元工业增加值需水量（m3/万元） ≤50 50~200 >200 0.059 6 人口密度（人/km2） ≤200 200~500 >500 0.079 2 城市化率（%） ≤50 50~80 >80 0.063 2 农田灌溉定额（m3/亩） ≤250 250~400 >400 0.079 2 水资源调控力
子系统0.2 水资源开发利用率（%） ≤40 40~70 >70 0.058 2 人均GDP（元/人） ≥24 840 24 840~6 624 <6 624 0.048 4 污水排放达标率（%） ≥90 90~70 <70 0.028 8 水功能区达标率（%） ≥95 95~70 <70 0.045 4 生态用水率（%） ≥5 1~5 <1 0.019 2
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表 3 灰色GM(1,1)预测模型精度等级[15-16]
Table 3. Precision grade of grey GM(1,1) prediction model[15-16]
模型精度等级 小误差概率 后验比 模型精度等级 小误差概率 后验比 1级（好） P ≥0.95 C ≤0.35 3级（一般） 0.70≤P<0.80 0.50<C≤0.65 2级（合格） 0.80≤P<0.95 0.35<C≤0.50 4级（不合格） P<0.70 C >0.65
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表 4 安徽省2005—2015年动态评价与预测结果
Table 4. Dynamic evaluation and forecast results of Anhui Province from 2005 to 2015
年份 投影特征值 原始序列 GM(1,1)预测序列 相对误差/% 年份 投影特征值 原始序列 GM(1,1)预测序列 相对误差/% 2005 0.100 9 0.100 9 0.100 9 0 2011 0.121 3 0.121 3 0.120 4 -0.72 2006 0.100 1 0.100 1 0.104 3 4.18 2012 0.123 8 0.123 8 0.123 9 0.12 2007 0.105 5 0.105 5 0.107 3 1.73 2013 0.125 3 0.125 3 0.127 6 1.81 2008 0.111 1 0.111 1 0.110 5 −0.57 2014 0.129 0 0.129 0 0.131 3 1.78 2009 0.115 7 0.115 7 0.113 7 −1.74 2015 0.135 2 0.135 2 0.135 1 −0.05 2010 0.124 1 0.124 1 0.117 0 −5.71
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