Fuzzy comprehensive evaluation and its validation for shallow groundwater vulnerability in Jianghan Plain
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摘要: 为开展江汉平原浅层地下水防污性能评价，以江汉平原沙洋-旧口地区浅层地下水为研究对象，针对传统DRASTIC模型评价指标存在关联性、权重主观性强、评分值缺乏连续性以及评价结果缺乏实测数据验证等缺点，考虑研究区实际条件，建立了基于改进DRASTIC模型的模糊综合评价模型，并利用研究区浅层地下水关键污染因子Cl-、NO3-和NH4+实测数据验证了模型的准确性和可靠性。该模型使用包气带黏性土厚度代替包气带介质指标，含水层厚度代替含水层介质指标、土壤饱和渗透系数代替土壤介质指标，采用全定量评价指标体系，评价指标更加客观、合理；采用三标度层次分析方法确定各评价指标权重，减少了传统DRASTIC模型人为确定权重的主观性；在改进的DRASTIC模型基础上，引入模糊数学理论，以隶属度函数代替传统DRASTIC模型固定评分值，克服了传统DRASTIC模型使用定额评分带来的不连续性。模糊综合评价结果表明：研究区浅层地下水防污性能整体表现为差-较差，占研究区总面积的76.53%。研究结果可为平原地区开展浅层地下水脆弱性评价提供方法参考，为江汉平原浅层地下水污染防治工作提供科学依据。Abstract: Taking shallow groundwater of shayang-jiukou area in Jianghan plain as the research object to evaluate shallow groundwater vulnerability of Jianghan plain, is directed against the shortcomings of the traditional DRASTIC model, suchas strong relevance and weight subjectivity of evaluation indexes, discontinuity of the scoring values, and absence of measured data verification to the evaluation result. Considering the reality in the study area, a fuzzy comprehensive evaluation model is established on the basis of the improved DRASTIC model, and the accuracy and reliability of the model are verified by key pollution factors such as Cl-, NO3- and NH4+ in shallow groundwater. In this model, a new quantitative evaluation index system was built to make the evaluation indexes more objective and reasonable, which the impact of the vadose zone media, aquifer media and soil media were replaced by the thickness of cohesive soil in vadose zone, thickness of aquifer and soil saturated hydraulic conductivity respectively. The three-scale AHP method was adopted to determine the weight of each index, which reduced the subjectivity of the index weights from the traditional DRASTIC model. Based on the improved DRASTIC model, a fuzzy mathematics method was introduced, and the fixed scoring values of the indexes were replaced by the subordinating degree function to overcome the discontinuity of traditional DRASTIC model for using the quota scoring. The fuzzy comprehensive evaluation result showed that vulnerability evaluation of shallow groundwater in the study area is poor or comparatively poor on the whole, accounting for 76.53% of the study area. This research can provide method reference for shallow groundwater vulnerability evaluation in plain regions and scientific evidence for the prevention and control of shallow groundwater pollution in Jianghan Plain.
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图 1 研究区第四系地质及地理位置图
Figure 1. Quaternary geological map and location map of the study area
图 3 改进的DRASTIC模型各指标分区图
Figure 3. Partition map of each estimation factor for improved DRASTIC model
图 4 地下水防污性能评价结果验证图
a.改进的DRASTIC模型；b.模糊综合评价模型
Figure 4. Verification of groundwater vulnerability estimation
表 1 改进的DRASTIC模型各指标分级及评分
Table 1. Ranges and scoring of each estimation factor for improved DRASTIC model
评分 地下水位埋深/m 包气带黏性土厚度/m 土壤饱和渗透系数/(cm·s-1) 净补给量/mm 含水层厚度/m 含水层渗透系数/(cm·s-1) 地形坡度/(°) 1 > 6 > 9 (10-11, 10-8] (0，55] > 45 (10-4, 5×10-4] > 18 2 (5，6] (8，9] (10-8, 5×10-6] (55，110] (40，45] (5×10-4, 10-3] (16, 18] 3 (4，5] (7，8] (5×10-6, 10-4] (110，147] (35，40] (10-3, 3×10-3] (14, 16] 4 (3，4] (6，7] (10-4, 5×10-4] (147，184] (30，35] (3×10-3, 5×10-3] (12, 14] 5 / (5，6] (5×10-4, 10-3] (184，220] (25，30] (5×10-3, 10-2] (11, 12] 6 (2，3] (4，5] (10-3, 3×10-3] (220，249] (20，25] (10-2, 5×10-2] (9, 11] 7 / (3，4] (3×10-3, 5×10-3] (249，278] (15，20] (5×10-2, 10-1] (8, 9] 8 (1，2] (2，3] (5×10-3, 10-2] (278，308] (10，15] (10-1, 5×10-1] (6, 8] 9 / (1，2] (10-2, 1] (308，330] (5，10] (5×10-1, 1] (5, 6] 10 (0，1] (0，1] > 1 > 330 (0，5] > 1 [0, 5] 参考依据 文献[19] 文献[22] 文献[18] 文献[20] 文献[24] 
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表 2 三标度层次分析法比较矩阵K{ij}及间接判断矩阵D{ij}
Table 2. Comparison matrix K{ij} and indirect judgment matrix D{ij} of tri-scale analytic hierarchy process
地下水位埋深 包气带黏性土厚度 净补给量 含水层厚度 含水层渗透系数 土壤饱和渗透系数 地形坡度 地下水位埋深 1(1) 1(1) 2(2.091) 2(3.182) 2(3.182) 2(4.273) 2(5) 包气带黏性土厚度 1(1) 1(1) 2(2.091) 2(3.182) 2(3.182) 2(4.273) 2(5) 净补给量 0(0.478) 0(0.478) 1(1) 2(2.091) 2(2.091) 2(3.182) 2(3.909) 含水层厚度 0(0.314) 0(0.314) 0(0.478) 1(1) 1(1) 2(2.091) 2(2.818) 含水层渗透系数 0(0.314) 0(0.314) 0(0.478) 1(1) 1(1) 2(2.091) 2(2.818) 土壤饱和渗透系数 0(0.234) 0(0.234) 0(0.314) 0(0.478) 0(0.478) 1(1) 2(1.727) 地形坡度 0(0.2) 0(0.2) 0(0.256) 0(0.355) 0(0.355) 0(0.579) 1(1) 注：括号外数值为比较矩阵K{ij}，括号内为间接判断矩阵D{ij}
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表 3 三标度层次分析法指标权重
Table 3. Index weight of three-scale analytic hierarchy process
指标 地下水位埋深(D) 包气带黏性土厚度(I) 净补给量(R) 含水层厚度(A) 含水层渗透系数(C) 土壤饱和渗透系数(S) 地形坡度(T) 权重 0.282 0.282 0.138 0.089 0.089 0.066 0.054
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表 4 平均随机一致性指标RI与n关系
Table 4. Relationship between average random consistency index RI and n
n 2 3 4 5 6 7 8 9 10 RI 0 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.49
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表 5 标准值矩阵及相对隶属度矩阵
Table 5. Standard value matrix and relative membership matrix
级别 1 2 3 4 5 6 7 8 9 10 地下水位埋深/m 9(1) 8(0.889) 7(0.778) 6(0.667) 5(0.556) 4(0.444) 3(0.333) 2(0.222) 1(0.111) 0(0) 包气带黏性土厚度/m 9(1) 8(0.889) 7(0.778) 6(0.667) 5(0.556) 4(0.444) 3(0.333) 2(0.222) 1(0.111) 0(0) 净补给量/(mm·a-1) 0(1) 55(0.833) 110(0.667) 147(0.555) 184(0.442) 220(0.333) 249(0.245) 278(0.158) 308(0.067) 330(0) 含水层厚度/m 45(1) 40(0.889) 35(0.778) 30(0.667) 25(0.556) 20(0.444) 15(0.333) 10(0.222) 5(0.111) 0(0) 含水层渗透系数/(cm·s-1) 0.000 1(1) 0.000 5(0.999) 0.001(0.999) 0.003(0.997) 0.005(0.995) 0.01(0.990) 0.05(0.950) 0.1(0.900) 0.5(0.500) 1(0) 土壤饱和渗透系数/(cm·s-1) 10-11 (1) 10-8 (0.999) 5×10-6 (0.999) 10-4 (0.999) 5×10-4(0.999) 10-3(0.999) 3×10-3(0.997) 5×10-3(0.995) 10-2(0.990) 1(0) 地形坡度/(°) 18(1) 16(0.889) 14(0.778) 12(0.667) 11(0.611) 9(0.500) 8(0.444) 6(0.333) 5(0.278) 0(0) 注：括号外数据为各指标对于10个级别的标准值，括号内数据为各指标对极难污染级别的相对隶属度
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表 6 地下水防污性能评价结果
Table 6. Results of groundwater vulnerability estimation
模型 防污性能分区 好 较好 较差 差 改进的DRASTIC模型 DI < 5.4 [5.4, 6.7) [6.7, 8.0) ≥8.0 分布面积/km2 0.5 53.88 334.31 484.61 分区面积占比/% 0.06 6.17 38.28 55.49 模糊综合评价模型 F < 5.4 [5.4, 6.7) [6.7, 8.0) ≥8.0 分布面积/km2 0 204.99 473.12 195.19 分区面积占比/% 0 23.47 54.18 22.35
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表 7 地下水防污性能评价分区水质点分布统计
Table 7. Distribution of water quality points for each partition in groundwater vulnerability estimation
模型 分区统计/防污性能 好 较好 较差 差 改进的DRASTIC模型 未污染类点数量及比例/% 1(100) 5(83.3) 12(17.1) 5(7.6) 轻度污染点数量及比例/% 0 1(16.7) 12(17.1) 21(31.8) 重度污染点数量及比例/% 0 0 46(65.8) 40(60.6) 污染点数量及比例/% 0 1(16.7) 58(82.9) 61(92.4) 模糊综合评价模型 未污染类点数量及比例/% / 13(81.3) 10(13.5) 0(7.9) 轻度污染点数量及比例/% / 0 29(39.2) 5(9.4) 重度污染点数量及比例/% / 3(18.7) 35(47.3) 48(90.6) 污染点数量及比例/% / 3(18.7) 64(86.5) 53(100)
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表 8 地下水防污性能评价分区水质点分布密度统计
Table 8. Density distribution of water quality point for each partition in groundwater vulnerability estimation
模型 分区统计/防污性能 好 较好 较差 差 改进的DRASTIC模型 分布面积/km2 0.5 53.88 334.51 484.61 未污染点分布密度/(个·km-2) 2 0.093 0.036 0.010 污染点分布密度/(个·km-2) 0 0.019 0.138 0.083 模糊综合评价模型 分布面积/km2 / 204.99 473.12 195.19 未污染点分布密度/(个·km-2) / 0.063 0.021 0 污染点分布密度/(个·km-2) / 0.015 0.135 0.272
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