Evaluation scheme and application of regional water resources carrying capacity based on heat transfer subtraction set pair potential
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摘要:
为有效评估区域水资源承载力系统演变特征并诊断脆弱性影响因素,引入物理学热传递思想,在集对分析传统减法集对势基础上进一步深化确定性项和不确定项之间的势差概念,构建了基于热传递减法集对势的区域水资源承载力评价方法,并应用于安徽省江淮丘陵区。结果表明:2011—2018年安徽省江淮丘陵区除合肥市外,其余地市水资源承载力水平整体有所改善,合肥市水资源承载力等级较低;人均水资源量、产水模数、生态用水率等因素是影响安徽省江淮丘陵区水资源承载力变化的重要脆弱性因素。整体而言,本文计算分析结果与传统减法集对势及半偏减法集对势计算结果基本一致,这表明构建的基于热传递减法集对势的水资源承载力评价方法计算结果合理有效,且丰富和发展了集对势的内涵,可为开展区域水资源承载力评价及脆弱性因素识别提供新的研究途径。
Abstract:Effective evaluation of the evolution characteristics of regional water resources carrying capacity system and diagnosis of vulnerability influencing factors, introducing the idea of physical heat transfer, further deepening the concept of potential difference between deterministic items and uncertain items on the basis of set pair analysis of traditional subtraction set pair potential, and constructing an evaluation method of regional water resources carrying capacity based on heat transfer subtraction set pair potential, and an empirical application study is carried out in Jianghuai hilly area of Anhui Province. The results show that from 2011 to 2018, except Hefei, the water resources carrying capacity of other cities in Jianghuai hilly region of Anhui Province showed an overall upward trend, and the level of water resources carrying capacity in Hefei was low, and the factors such as per capita water resources, water production modulus and ecological water use rate were important fragile factors affecting the change of water resources carrying capacity in Jianghuai hilly region of Anhui Province. On the whole, the calculation and analysis results of this paper are basically consistent with those of traditional subtraction and semi-partial subtraction set pair potential, which shows that the calculation results of the water resources carrying capacity evaluation method based on heat transfer subtraction set pair potential are reasonable and effective, and further enrich and develop the rich connotation of set pair potential, which can provide a new research way for regional water resources carrying capacity evaluation and vulnerability factor identification.
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水资源是人类、经济社会发展和生态环境保护的基础,水资源承载力是指一个特定区域在一定时间范围内,经综合考虑水资源数量和质量、环境承载力及经济社会因素后,所能承载的水资源利用量和质的上限,是制定水资源管理政策和水利规划的重要依据[1-2]。可根据水资源承载力进行水资源管理,在管理中落实可持续性原则,从而达到合理调配、协调开发、维持平衡的目的[3]。近年来,区域水资源承载力研究方法有主成分分析法[4]、模糊综合评价法[5]、系统动力学法[6]、灰色关联法[7]、投影寻踪法[8]、集对分析法[9-21]等。其中,集对分析法[17-21]因能定量评估水资源承载力,准确反映评价指标和评价标准之间的确定性和不确定性关系,开始应用于水资源承载力分析评价中。Zhou等[12]通过将熵理论和联系数相结合,构建了水资源承载力预警模型;Pan等[13]提出了基于联系熵的变化环境下水资源系统脆弱性评价方法;Cui等[14]综合熵权法和改进的层次分析法确定水资源承载力评价指标的权重,建立了基于联系数的区域水资源承载力评价和诊断模型;Jiao等[15]根据区域用水的实际情况,提出了一种基于集对分析的评价标准构建方法;Lu等[16]通过熵权集对理论来评估所涉及的不确定性,对地区水资源可持续利用进行了评价;金菊良等[17]在联系数基础上提出了减法集对势这一伴随函数,并将其应用于水资源承载力脆弱性指标识别中;吴凡等[18]构建了模糊集对评价模型,结合五元减法集对势对新疆15个地州水资源承载力进行评价并诊断其发展态势;金菊良等[19]提出引力减法集对势,应用于水资源承载力分析评价。上述关于集对势计算原理及其应用的现有研究成果,未能考虑确定性项和不确定性项之间转化时的势差影响,即确定性项和不确定性项之间量的差距。
本文在传统减法集对势的基础上,考虑联系数中不确定性项转化到确定性项上的可能难度,认为不确定性项和确定性项的转化存在势差的影响。基于物理学中热传递的转化理论,将不确定性项向确定性项的转化值视为物体间相互传递的热量,将两者间可能存在的势差视为物体间的温度差,提出基于热传递减法集对势的区域水资源承载力评价方法,并于安徽省江淮丘陵区开展实证应用研究,将现有不同类型集对势方法计算结果与本文提出的方法计算结果进行对比分析,验证热传递减法集对势计算方法的有效性。
1. 热传递减法集对势
热传递公式Q=αAΔT[22],是根据热传导定律,通过对传热介质的温度差、热导率和导热面积等因素的量化描述,来计算热传递过程中的热量传递量;其中α为导热系数,A为导热面积,ΔT为物体之间的温度差。
集对分析法[9]以联系数从同、异、反三个方面,探讨水资源承载力中评价样本与等级标准间的不确定性关系,而集对势[9]是联系数的一种伴随函数,能描述集对分析联系数中研究对象在宏观上的确定性状态及相对确定性发展趋势,可根据集对势识别诊断评价结果中的脆弱性指标,分析发展态势。
金菊良等[17]提出了三元减法集对势:
$$ {s_1}(u) = (a - c)(1 + b) = a - c + ba - bc $$ (1) 式中:减法集对势是根据a、c所占比重将b转化为a和c,本文考虑不确定性项转化到确定性项上的可能难度,认为不确定性项和确定性项的转化存在势差的影响,基于物理学中热传递的转化理论,将不确定性项向确定性项的转化值视为物体间相互传递的热量,将两者之间可能存在的势差视为物体之间的温度差,进一步提出热传递减法集对势:
$$ {s_2}(u) = a - c + ba{\left[{(a - b)^2} + {\left(1 - \frac{b}{{a + b}}\right)^2}\right]^{0.5}} - bc{\left[{(c - b)^2} + {\left(1 - \frac{b}{{c + b}}\right)^2}\right]^{0.5}} $$ (2) 式中:考虑不确定性项和确定性项之间的势差因素,将不确定性项和确定性项之间的转化值类比于热传递过程中的热量传递量,以差异度项转化为同一度项这部分为例,其中a对应a/(a+b+c),表示为b向a的转化率,可类比为导热系数α;b为待转化值,可类比为导热面积A;文献[14]中采用$ \left| {a - b} \right| $作为状态间的距离值,本文则认为同一度项和差异度项处于一坐标轴上,a和b分别为同一度项和差异度项的竖向长度,考虑将$ \left| {a - b} \right| $当作平面上不确定性项和同一度项间的纵向势差,b/(a+b)表示b所占比重,同一项a和差异度项b之间的横向距离为1,以1−b/(a+b)作为横向势差,再根据勾股定理公式,得$ {[{(a - b)^2} + {(1 - b/(a + b))^2}]^{0.5}} $,作为a和b状态之间的势差值,类比传热介质之间的温度差,然后三部分依次相乘,最终得到差异度项b向同一度项a的转化值,类比于热传递公式中的热流量Q=αAΔT。同理可得差异项度b向对立度项c的转化值$ bc{[{(c - b)^2} + {(1 - b/(c + b))^2}]^{0.5}} $,根据原有减法集对势,最终构建了热传递减法集对势的计算公式。
由式(2)可知,热传递减法集对势取值范围为[−1, 1],参考减法集对势的均分原则[23-25],划分为5个势级:反势∈[−1.0, −0.6),偏反势∈[−0.6, −0.2),均势∈[−0.2, 0.2],偏同势∈(0.2, 0.6],同势∈(0.6, 1.0]。依据热传递减法集对势值的大小,判断其所处势级状态,进而判断该指标是否是导致区域水资源承载力变低的主要因素,并且可判断该指标是否需要进行重点调控。与减法集对势相比,热传递减法集对势考虑到不确定性转化到确定性的可能性,增加势差这一项值,类比于物理中热传递的思想,考虑更加细化、完整,有助于丰富减法集对势的内涵。本文将热传递减法集对势分别与减法集对势、半偏减法集对势两种方法进行模拟计算对比,计算出两者之间平均绝对误差,计算公式如下:
$$ {d_1} = \sum\limits_{m = 1}^M {\left| {{s_2}({u_m}) - {s_1}({u_m})} \right|} $$ (3) $$ {d_2} = \sum\limits_{m = 1}^M {\left| {{s_2}({u_m}) - {s_3}({u_m})} \right|} $$ (4) 式中:M为模拟联系数次数;s1(um)、s2(um)、s3(um)分别表示减法、热传递减法和半偏减法集对势。本文模拟104、105和106次时,其平均绝对误差d1和d2分别约2.6%和2.7%,这说明了热传递减法集对势公式的合理性。
2. 区域水资源承载力分析评价模型
参考现有的集对分析理论及方法,建立基于热传递减法集对势的水资源承载力分析评价模型[26],其建模包含以下4个步骤:
(1)建立水资源承载力评价指标体系,确定相应评价等级标准[27-32]。结合研究区域的实践调研、专家咨询、文献统计等相关成果,建立区域水资源承载力评价指标体系{xj|j=1, 2, …, nj},评价指标样本数据集为{xij|i=1, 2,…, ni;j=1, 2,…, nj},其中,xij为评价样本x中评价指标j的值,ni为评价样本数目,nj为评级指标数目。本文区域水资源承载力划分等级标准为{skj|k=1, 2, …, nk;j=1, 2, …, nj},将水资源承载力分为3个等级:可载(1级)、临界超载(2级)和超载(3级)[26-33],可载代表该地区的水资源承载力情况较好,临界超载代表地区水资源承载力情况一般,超载代表地区水资源承载力接近饱和,未来可能会出现水资源短缺情况。
(2)将评价指标值与等级标准两个集合构成集对,根据两集合接近程度这一可变模糊集,计算出评价单指标联系数。具体公式如下:
$$ {u}_{ij1}=\left\{ \begin{aligned} &1,正向指标{x}_{ij}\leqslant {s}_{1j}或反向指标{s_{1j}} \leqslant {x_{ij}}\\ &1-2({x}_{ij}-{s}_{1j})/({s}_{2j}-{s}_{1j}),正向指标{s}_{1j} < {x}_{ij}\leqslant {s}_{2j}或反向指标{s_{2j}} \leqslant {x_{ij}} < {s_{1j}}\\ &-1,正向指标{x}_{ij} > {s}_{2j}或反向指标{x}_{ij} < {s}_{2j}\end{aligned} \right. $$ (5) $$ {u}_{ij2}=\left\{ \begin{aligned} & 1-2({s}_{1j}-{x}_{ij})/({s}_{1j}-{s}_{0j}),正向指标{x}_{ij}\leqslant {s}_{1j}或反向指标{s_{1j}} \leqslant {x_{ij}}\\ &1,正向指标{s}_{1j} < {x}_{ij}\leqslant {s}_{2j}或反向指标{s_{2j}} \leqslant {x_{ij}} < {s_{1j}}\\ &1-2({x}_{ij}-{s}_{2j})/({s}_{3j}-{s}_{2j}),正向指标{s}_{2j} < {x}_{ij}\leqslant {s}_{3j}或反向指标{s_{3j}} \leqslant {x_{ij}} < {s_{2j}}\\ &-1,正向指标{x}_{ij} > {s}_{3j}或反向指标{x}_{ij} < {s}_{3j}\end{aligned} \right. $$ (6) $$ {u}_{ij3}=\left\{ \begin{aligned} &-1,正向指标{x}_{ij}\leqslant {s}_{1j}或反向指标{s_{1j}} \leqslant {x_{ij}}\\ &1-2({s}_{2j}-{x}_{ij})/({s}_{2j}-{s}_{1j}),正向指标{s}_{1j} < {x}_{ij}\leqslant {s}_{2j}或反向指标{s_{2j}} \leqslant {x_{ij}} < {s_{1j}}\\ &1,正向指标{s}_{2j} < {x}_{ij}\leqslant {s}_{3j}或反向指标{s_{3j}} \leqslant {x_{ij}} < {s_{2j}}\end{aligned} \right. $$ (7) 式中:s0j、s3j分别是各指标的1级和3级评价标准等级值的另一端临界阈值;s1j、s2j分别是3个标准等级之间的阈值。对应的相对隶属度v*ijk的计算公式如下:
$$ v_{ijk}^* = 0.5 + 0.5{u_{ijk}} (i=1, 2, …, n_{i}; j=1, 2,…, n_{j}; \;\;k=1,2,3) $$ (8) $$ 归一化处理,得联系数分量:\qquad\qquad\qquad\qquad\qquad{v_{ijk}} = v_{ijk}^*/\sum\limits_{k = 1}^3 {v_{ijk}^*} \qquad\qquad\qquad\qquad\qquad\qquad\;\;\;\;$$ (9) $$ 评价指标值联系数:\qquad\quad\qquad\qquad\qquad\qquad\qquad\quad{u_{ij}} = {v_{ij1}} + {v_{ij2}}I + {v_{ij3}}J \qquad\qquad\qquad\qquad\quad\;\;\;$$ (10) $$ 评价样本i的指标值联系数:\qquad\qquad\qquad\qquad\qquad\quad{u_i} = {v_{i1}} + {v_{i2}}I + {v_{i3}}J \qquad\qquad\qquad\qquad\qquad\;\;\;\;$$ (11) 式中:$ {v_{i1}} = \sum\limits_{j = 1}^{{n_j}} {{w_j}{v_{ij1}}} $;$ {{v_{i2}} = \sum\limits_{j = 1}^{{n_j}} {{w_j}{v_{ij2}}} } $;$ {{v_{i3}} = \sum\limits_{j = 1}^{{n_j}} {{w_j}{v_{ij3}}} } $。
(3)使用级别特征值法计算对应样本$ i $的等级值:
$$ {h}(i) = \sum\limits_{k = 1}^3 {{v_{ik}}k}$$ (12) (4)将上述求得的评价指标值联系数、综合联系数值代入热传递减法集对势计算公式(2),得到热传递减法集对势值,分析评估水资源承载力发展态势、诊断辨识脆弱性指标。
3. 实例分析
安徽省江淮丘陵地区属亚热带向暖温带过渡气候区,南北气流在此交汇,降水年际变化大,年内分配不均,是水旱灾害频发地带;水资源空间分布不均匀,且水资源供应不足,水资源短缺问题长期存在,水资源安全存在一定风险。因此合理准确评价水资源承载力,为水资源管理和调控措施制定提供科学支撑,是亟需解决的问题。
本文将基于热传递减法集对势的水资源承载力分析评价模型应用于安徽省江淮丘陵区下辖的合肥、滁州、六安、安庆等四市。根据区域水资源承载支撑力、承载压力、承载调控力相作用形成区域水资源承载状态这一机理,参考金菊良等[23,26-28]研究构建安徽省江淮丘陵区水资源承载力评价指标体系、等级标准,运用基于加速遗传算法的模糊层次分析法确定指标权重[32],如表1所示。相关数据来源于《安徽省统计年鉴》和《安徽省水资源公报》(2011—2018年四市所需评价指标数据,部分数据需要处理)。将上述数据代入式(5)~(12)计算出各市各年的联系数分量、评价等级值,然后将各市各年的联系数分量代入式(1)和式(2),结果如表2所示,同时将表2的四市集对势结果值绘制成图(见图1)。为识别四市水资源承载力评价中的脆弱性指标,计算出2011—2018年各指标的减法和热传递减法集对势值,结果见表3(由于篇幅限制,故所列出指标仅为各市部分样本指标)。
表 1 安徽省江淮丘陵区水资源承载力评价指标体系及等级标准和权重Table 1. Evaluation index system and grade standard and weight of water resources carrying capacity in Jianghuai hilly region of Anhui Province目标层 子系统 指标层 指标含义 评价标准 指标
权重1级 2级 3级 (可载) (临界可载) (超载) 水资源承载力评价 承载支撑力 人均水资源量g1/m3 水资源总量/常住人口总数 ≥1 670 [1 000, 1 670) <1 000 0.133 产水模数g2/(万m3/km2) 多年平均水资源总量/区域面积 ≥80 [50, 80) <50 0.132 人均供水量g3/(m3/(人·a)) 供水总量/常住人口总数 ≥450 [350, 450) <350 0.106 植被覆盖率g4/% 森林面积/土地总面积 ≥40 [25, 40) <25 0.028 承载调控力 水资源开发利用率g5/% 供水总量/水资源总量 ≤40 (40, 70] >70 0.093 人均GDPg6/(元/人) 总GDP/总人口数 ≥24 840 [6 624, 24 840) <6 624 0.077 生态用水率g7/% 生态环境用水量/用水总量 ≥5 [1, 5) <1 0.031 承载压力 人均日生活用水量g8/L 居民生活日用水量/常住人口总数 ≤70 (70, 180] >180 0.040 万元GDP用水量g9/m3 用水总量/万元GDP ≤100 (100, 400] >400 0.079 万元工业增加值用水量g10/m3 用水总量/万元工业增加值 ≤50 (50, 200] >200 0.060 人口密度g11/(人/km2) 常住人口总数/区域面积 ≤200 (200, 500] >500 0.079 城市化率g12/% 城镇人口/总人口 ≤50 (50, 80] >80 0.063 农田灌溉定额g13/(m3/hm2) 灌溉用水量/灌溉面积 ≤3 750 (3 750, 6 000] >6 000 0.079 表 2 安徽省江淮丘陵区水资源承载力评价联系数分量、评价等级、集对势值及态势结果Table 2. Connection number component, evaluation grade, set pair potential value and situation result of water resources carrying capacity evaluation in Jianghuai hilly region地市 年份 联系数分量[26] 等级值 热传递减法集对势 减法集对势 半偏减法集对势 a b c 结果值 态势 结果值 态势 结果值 态势 合肥 2011 0.212 0.429 0.360 2.149 −0.184 均势 −0.212 偏反势 −0.203 偏反势 2012 0.216 0.429 0.356 2.140 −0.173 均势 −0.200 均势 −0.191 均势 合肥 2013 0.234 0.418 0.349 2.116 −0.143 均势 −0.163 均势 −0.155 均势 2014 0.241 0.442 0.318 2.078 −0.095 均势 −0.111 均势 −0.106 均势 2015 0.243 0.443 0.314 2.072 −0.088 均势 −0.103 均势 −0.098 均势 2016 0.341 0.462 0.198 1.857 0.177 均势 0.210 偏同势 0.201 偏同势 2017 0.266 0.38 0.354 2.089 −0.110 均势 −0.122 均势 −0.115 均势 2018 0.282 0.403 0.316 2.035 −0.042 均势 −0.048 均势 −0.045 均势 滁州 2011 0.212 0.466 0.322 2.110 −0.135 均势 −0.161 均势 −0.154 均势 2012 0.203 0.451 0.346 2.144 −0.177 均势 −0.208 偏反势 −0.199 均势 2013 0.235 0.455 0.311 2.077 −0.094 均势 −0.111 均势 −0.106 均势 2014 0.296 0.475 0.230 1.935 0.081 均势 0.097 均势 0.094 均势 2015 0.326 0.482 0.192 1.866 0.165 均势 0.199 均势 0.191 均势 2016 0.356 0.481 0.162 1.807 0.238 偏同势 0.287 偏同势 0.277 偏同势 2017 0.327 0.436 0.238 1.911 0.110 均势 0.128 均势 0.122 均势 2018 0.395 0.446 0.160 1.766 0.290 偏同势 0.340 偏同势 0.327 偏同势 六安 2011 0.182 0.462 0.356 2.174 −0.214 偏反势 −0.254 偏反势 −0.244 偏反势 2012 0.221 0.484 0.295 2.074 −0.091 均势 −0.110 均势 −0.105 均势 2013 0.252 0.487 0.261 2.010 −0.011 均势 −0.014 均势 −0.013 均势 2014 0.325 0.491 0.184 1.860 0.172 均势 0.209 偏同势 0.202 偏同势 2015 0.352 0.480 0.168 1.817 0.226 偏同势 0.272 偏同势 0.262 偏同势 2016 0.437 0.470 0.094 1.658 0.424 偏同势 0.504 偏同势 0.491 偏同势 2017 0.399 0.451 0.150 1.751 0.308 偏同势 0.362 偏同势 0.349 偏同势 2018 0.446 0.445 0.109 1.664 0.417 偏同势 0.487 偏同势 0.472 偏同势 安庆 2011 0.257 0.477 0.266 2.010 −0.011 均势 −0.013 均势 −0.013 均势 2012 0.336 0.485 0.178 1.843 0.194 均势 0.235 偏同势 0.226 偏同势 2013 0.344 0.489 0.168 1.824 0.216 偏同势 0.262 偏同势 0.253 偏同势 2014 0.396 0.482 0.122 1.727 0.337 偏同势 0.406 偏同势 0.394 偏同势 2015 0.394 0.478 0.129 1.736 0.326 偏同势 0.392 偏同势 0.379 偏同势 2016 0.455 0.438 0.107 1.652 0.432 偏同势 0.501 偏同势 0.485 偏同势 2017 0.442 0.447 0.111 1.669 0.411 偏同势 0.480 偏同势 0.465 偏同势 2018 0.432 0.451 0.117 1.685 0.390 偏同势 0.457 偏同势 0.443 偏同势 由图1和表2可知:(1)级别特征值法计算的江淮丘陵区域四市的水资源承载力大多处于2级(临界可载),等级值在2左右波动。其中,滁州市、六安市和安庆市的等级值逐渐降低,表明三市的水资源承载力状况逐渐改善,但尚未达到1级(可载)状态,仍需关注并采取措施。合肥市2011—2018年的评级大多处于2—3级之间,表明水资源承载力超载情况严重。2011—2016年评价等级值有所下降,但幅度较小,水资源承载力状况较差;而2016年开始评价等级值又突然上升,突破2级阈值,水资源承载力较差,这表明合肥市急需采取措施改善水资源承载力状况。同时热传递减法集对势方法得出的评价结果和变化趋势与其他两种方法基本一致,表明该方法较为符合实际。(2)从评价态势看,热传递减法集对势方法在四市的评价结果与其他两种方法存在细微差别。例如,2011年合肥市热传递减法集对势的结果值和态势与其他方法有所不同;2016年合肥市的评价态势也略有差异。(3)从评价结果看,当集对势值大于0时,热传递减法集对势的曲线位于其他两条曲线下方;而当集对势值小于0时,其曲线则位于上方。这表明热传递减法集对势方法在表达良好状况时较为悲观,而在表达恶劣状况时则较为乐观。这种表达方式反映了保守的评价态度,对于水资源承载力的分析较为有利。可见,该方法是一种合理有效的方法。
由表3可知:(1)合肥市人均水资源指标集对势值在2011—2018年始终小于−0.400,最小值达到−0.942,判断为合肥市水资源承载力的脆弱性指标,这说明合肥市近几年发展迅速,但人均水资源量已明显不足,需加强引水工程的建设;水资源开发利用率指标在2013年之前集对势值小于−0.600,2014年开始波动上升,且波动幅度较大,这说明合肥市政府采取了一定措施进行调控,但措施的实施并不严谨;城市化率指标的集对势值在2011—2018年间呈下降趋势,且在2018年低于−0.400,这说明合肥城镇化进程过快,水资源不足以支撑,急需改善调整。(2)滁州市人均水资源量指标从2014年集对势值开始波动,且具有反复性,需要注意并适当调整,产水模数和生态用水率指标在8年间一直小于−0.300,属于偏反势和反势态势,可判断为脆弱性指标,需要列为调控对象。(3)六安市产水模数指标2014—2018年波动幅度较大,需适当进行关注,人均GDP和万元GDP用水量集对势值呈总体上升趋势,但人均GDP指标值小于−0.200,态势为偏反势,判断为脆弱性指标。(4)安庆市生态用水率指标虽然2014年和2015年有所回暖,但随后3年波动下降,判断为脆弱性指标。产水模数和人口密度指标虽有所波动,但总体呈上升趋势,故适当做出改善调整。(5)四市部分指标集对势值的变化趋势和波动幅度基本一致,这说明热传递减法集对势对脆弱性指标的诊断识别比较合理,对水资源承载力的分析评价是合适的。
表 3 2011—2018年各市部分指标热传递减法集对势值和减法集对势值Table 3. Potential value of heat transfer subtraction set and potential value of subtraction set for some indicators in cities from 2011 to 2018合肥市 年份 人均水资源量g1 水资源开发利用率g5 城市化率g12 本文方法 减法集对势 本文方法 减法集对势 本文方法 减法集对势 2011 −0.922 −0.939 −0.684 −0.795 0.016 0.020 2012 −0.904 −0.929 −0.666 −0.781 −0.057 −0.070 2013 −0.927 −0.942 −0.687 −0.797 −0.114 −0.140 2014 −0.780 −0.858 0.052 0.064 −0.167 −0.205 2015 −0.789 −0.863 −0.312 −0.381 −0.221 −0.270 2016 −0.431 −0.523 0.654 0.772 −0.289 −0.353 2017 −0.877 −0.914 −0.643 −0.764 −0.359 −0.438 2018 −0.766 −0.849 −0.041 −0.050 −0.410 −0.499 滁州市 年份 人均水资源量g1 产水模数g2 生态用水率g7 本文方法 减法集对势 本文方法 减法集对势 本文方法 减法集对势 2011 −0.534 −0.645 −0.769 −0.851 −0.874 −0.913 2012 −0.694 −0.802 −0.839 −0.893 −0.822 −0.883 2013 −0.694 −0.801 −0.837 −0.891 −0.802 −0.871 2014 −0.328 −0.400 −0.741 −0.833 −0.737 −0.830 2015 0.064 0.079 −0.687 −0.796 −0.750 −0.839 2016 0.446 0.541 −0.640 −0.762 −0.720 −0.819 2017 −0.438 −0.532 −0.750 −0.839 −0.688 −0.797 2018 0.340 0.415 −0.645 −0.766 −0.391 −0.476 六安市 年份 产水模数g2 人均GDPg6 万元GDP用水量g9 本文方法 减法集对势 本文方法 减法集对势 本文方法 减法集对势 2011 −0.741 −0.833 −0.411 −0.500 −0.599 −0.720 2012 −0.713 −0.814 −0.412 −0.501 −0.371 −0.452 2013 −0.722 −0.821 −0.414 −0.504 −0.265 −0.324 2014 −0.475 −0.576 −0.386 −0.470 −0.127 −0.155 2015 0.082 0.100 −0.308 −0.376 −0.222 −0.271 2016 0.631 0.755 −0.304 −0.372 0.154 0.189 2017 −0.644 −0.765 −0.324 −0.395 0.198 0.243 2018 −0.001 −0.001 −0.306 −0.373 0.290 0.354 安庆市 年份 产水模数g2 生态用水率g7 人口密度g11 本文方法 减法集对势 本文方法 减法集对势 本文方法 减法集对势 2011 −0.639 −0.761 −0.473 −0.574 −0.433 −0.526 2012 0.098 0.121 −0.473 −0.574 −0.209 −0.256 2013 −0.091 −0.112 −0.502 −0.608 −0.212 −0.260 2014 0.500 0.605 −0.239 −0.293 −0.210 −0.257 2015 0.619 0.744 −0.230 −0.281 0.042 0.051 2016 0.854 0.902 −0.410 −0.499 0.032 0.039 2017 −0.013 −0.016 −0.416 −0.506 0.028 0.035 2018 −0.225 −0.275 −0.410 −0.499 0.034 0.042 4. 结 语
本文在减法集对势的基础上,引入物理学中热传递的思想,通过类比公式提出了热传递减法集对势,具有一定的合理性,丰富了集对势的计算方式。上述方法在安徽省江淮丘陵区不同地市水资源承载力评价计算的实证应用结果表明:
(1)热传递减法集对势的计算公式相比于减法集对势,表达了确定性和不确定性之间的势差关系,含义丰富、内容完整、解释合理。
(2)2011—2018年江淮丘陵区域四市水资源承载力状况除合肥市外,整体呈上升趋势,说明各市采取措施调整了相关产业结构,使得水资源承载力状况有所改善。合肥市的水资源承载力状况不容乐观,存在下降趋势,急需采取一定措施进行调控。
(3)热传递减法集对势和减法集对势的指标态势分析变化趋势基本一致,能够诊断识别出四市中水资源承载力评价的脆弱性指标,例如:合肥市人均水资源、滁州市产水模数和生态用水率、六安市人均GDP和万元GDP用水量,都需要列为重点调控指标。同时说明热传递减法集对势方法有效,为准确识别水资源承载力评价中脆弱性指标提供了新方式,有助于丰富集对势的内涵,为水资源承载力分析评价提供了新途径。
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表 1 安徽省江淮丘陵区水资源承载力评价指标体系及等级标准和权重
Table 1 Evaluation index system and grade standard and weight of water resources carrying capacity in Jianghuai hilly region of Anhui Province
目标层 子系统 指标层 指标含义 评价标准 指标
权重1级 2级 3级 (可载) (临界可载) (超载) 水资源承载力评价 承载支撑力 人均水资源量g1/m3 水资源总量/常住人口总数 ≥1 670 [1 000, 1 670) <1 000 0.133 产水模数g2/(万m3/km2) 多年平均水资源总量/区域面积 ≥80 [50, 80) <50 0.132 人均供水量g3/(m3/(人·a)) 供水总量/常住人口总数 ≥450 [350, 450) <350 0.106 植被覆盖率g4/% 森林面积/土地总面积 ≥40 [25, 40) <25 0.028 承载调控力 水资源开发利用率g5/% 供水总量/水资源总量 ≤40 (40, 70] >70 0.093 人均GDPg6/(元/人) 总GDP/总人口数 ≥24 840 [6 624, 24 840) <6 624 0.077 生态用水率g7/% 生态环境用水量/用水总量 ≥5 [1, 5) <1 0.031 承载压力 人均日生活用水量g8/L 居民生活日用水量/常住人口总数 ≤70 (70, 180] >180 0.040 万元GDP用水量g9/m3 用水总量/万元GDP ≤100 (100, 400] >400 0.079 万元工业增加值用水量g10/m3 用水总量/万元工业增加值 ≤50 (50, 200] >200 0.060 人口密度g11/(人/km2) 常住人口总数/区域面积 ≤200 (200, 500] >500 0.079 城市化率g12/% 城镇人口/总人口 ≤50 (50, 80] >80 0.063 农田灌溉定额g13/(m3/hm2) 灌溉用水量/灌溉面积 ≤3 750 (3 750, 6 000] >6 000 0.079 表 2 安徽省江淮丘陵区水资源承载力评价联系数分量、评价等级、集对势值及态势结果
Table 2 Connection number component, evaluation grade, set pair potential value and situation result of water resources carrying capacity evaluation in Jianghuai hilly region
地市 年份 联系数分量[26] 等级值 热传递减法集对势 减法集对势 半偏减法集对势 a b c 结果值 态势 结果值 态势 结果值 态势 合肥 2011 0.212 0.429 0.360 2.149 −0.184 均势 −0.212 偏反势 −0.203 偏反势 2012 0.216 0.429 0.356 2.140 −0.173 均势 −0.200 均势 −0.191 均势 合肥 2013 0.234 0.418 0.349 2.116 −0.143 均势 −0.163 均势 −0.155 均势 2014 0.241 0.442 0.318 2.078 −0.095 均势 −0.111 均势 −0.106 均势 2015 0.243 0.443 0.314 2.072 −0.088 均势 −0.103 均势 −0.098 均势 2016 0.341 0.462 0.198 1.857 0.177 均势 0.210 偏同势 0.201 偏同势 2017 0.266 0.38 0.354 2.089 −0.110 均势 −0.122 均势 −0.115 均势 2018 0.282 0.403 0.316 2.035 −0.042 均势 −0.048 均势 −0.045 均势 滁州 2011 0.212 0.466 0.322 2.110 −0.135 均势 −0.161 均势 −0.154 均势 2012 0.203 0.451 0.346 2.144 −0.177 均势 −0.208 偏反势 −0.199 均势 2013 0.235 0.455 0.311 2.077 −0.094 均势 −0.111 均势 −0.106 均势 2014 0.296 0.475 0.230 1.935 0.081 均势 0.097 均势 0.094 均势 2015 0.326 0.482 0.192 1.866 0.165 均势 0.199 均势 0.191 均势 2016 0.356 0.481 0.162 1.807 0.238 偏同势 0.287 偏同势 0.277 偏同势 2017 0.327 0.436 0.238 1.911 0.110 均势 0.128 均势 0.122 均势 2018 0.395 0.446 0.160 1.766 0.290 偏同势 0.340 偏同势 0.327 偏同势 六安 2011 0.182 0.462 0.356 2.174 −0.214 偏反势 −0.254 偏反势 −0.244 偏反势 2012 0.221 0.484 0.295 2.074 −0.091 均势 −0.110 均势 −0.105 均势 2013 0.252 0.487 0.261 2.010 −0.011 均势 −0.014 均势 −0.013 均势 2014 0.325 0.491 0.184 1.860 0.172 均势 0.209 偏同势 0.202 偏同势 2015 0.352 0.480 0.168 1.817 0.226 偏同势 0.272 偏同势 0.262 偏同势 2016 0.437 0.470 0.094 1.658 0.424 偏同势 0.504 偏同势 0.491 偏同势 2017 0.399 0.451 0.150 1.751 0.308 偏同势 0.362 偏同势 0.349 偏同势 2018 0.446 0.445 0.109 1.664 0.417 偏同势 0.487 偏同势 0.472 偏同势 安庆 2011 0.257 0.477 0.266 2.010 −0.011 均势 −0.013 均势 −0.013 均势 2012 0.336 0.485 0.178 1.843 0.194 均势 0.235 偏同势 0.226 偏同势 2013 0.344 0.489 0.168 1.824 0.216 偏同势 0.262 偏同势 0.253 偏同势 2014 0.396 0.482 0.122 1.727 0.337 偏同势 0.406 偏同势 0.394 偏同势 2015 0.394 0.478 0.129 1.736 0.326 偏同势 0.392 偏同势 0.379 偏同势 2016 0.455 0.438 0.107 1.652 0.432 偏同势 0.501 偏同势 0.485 偏同势 2017 0.442 0.447 0.111 1.669 0.411 偏同势 0.480 偏同势 0.465 偏同势 2018 0.432 0.451 0.117 1.685 0.390 偏同势 0.457 偏同势 0.443 偏同势 表 3 2011—2018年各市部分指标热传递减法集对势值和减法集对势值
Table 3 Potential value of heat transfer subtraction set and potential value of subtraction set for some indicators in cities from 2011 to 2018
合肥市 年份 人均水资源量g1 水资源开发利用率g5 城市化率g12 本文方法 减法集对势 本文方法 减法集对势 本文方法 减法集对势 2011 −0.922 −0.939 −0.684 −0.795 0.016 0.020 2012 −0.904 −0.929 −0.666 −0.781 −0.057 −0.070 2013 −0.927 −0.942 −0.687 −0.797 −0.114 −0.140 2014 −0.780 −0.858 0.052 0.064 −0.167 −0.205 2015 −0.789 −0.863 −0.312 −0.381 −0.221 −0.270 2016 −0.431 −0.523 0.654 0.772 −0.289 −0.353 2017 −0.877 −0.914 −0.643 −0.764 −0.359 −0.438 2018 −0.766 −0.849 −0.041 −0.050 −0.410 −0.499 滁州市 年份 人均水资源量g1 产水模数g2 生态用水率g7 本文方法 减法集对势 本文方法 减法集对势 本文方法 减法集对势 2011 −0.534 −0.645 −0.769 −0.851 −0.874 −0.913 2012 −0.694 −0.802 −0.839 −0.893 −0.822 −0.883 2013 −0.694 −0.801 −0.837 −0.891 −0.802 −0.871 2014 −0.328 −0.400 −0.741 −0.833 −0.737 −0.830 2015 0.064 0.079 −0.687 −0.796 −0.750 −0.839 2016 0.446 0.541 −0.640 −0.762 −0.720 −0.819 2017 −0.438 −0.532 −0.750 −0.839 −0.688 −0.797 2018 0.340 0.415 −0.645 −0.766 −0.391 −0.476 六安市 年份 产水模数g2 人均GDPg6 万元GDP用水量g9 本文方法 减法集对势 本文方法 减法集对势 本文方法 减法集对势 2011 −0.741 −0.833 −0.411 −0.500 −0.599 −0.720 2012 −0.713 −0.814 −0.412 −0.501 −0.371 −0.452 2013 −0.722 −0.821 −0.414 −0.504 −0.265 −0.324 2014 −0.475 −0.576 −0.386 −0.470 −0.127 −0.155 2015 0.082 0.100 −0.308 −0.376 −0.222 −0.271 2016 0.631 0.755 −0.304 −0.372 0.154 0.189 2017 −0.644 −0.765 −0.324 −0.395 0.198 0.243 2018 −0.001 −0.001 −0.306 −0.373 0.290 0.354 安庆市 年份 产水模数g2 生态用水率g7 人口密度g11 本文方法 减法集对势 本文方法 减法集对势 本文方法 减法集对势 2011 −0.639 −0.761 −0.473 −0.574 −0.433 −0.526 2012 0.098 0.121 −0.473 −0.574 −0.209 −0.256 2013 −0.091 −0.112 −0.502 −0.608 −0.212 −0.260 2014 0.500 0.605 −0.239 −0.293 −0.210 −0.257 2015 0.619 0.744 −0.230 −0.281 0.042 0.051 2016 0.854 0.902 −0.410 −0.499 0.032 0.039 2017 −0.013 −0.016 −0.416 −0.506 0.028 0.035 2018 −0.225 −0.275 −0.410 −0.499 0.034 0.042 -
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