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Assessing regional flood vulnerability based on catastrophe theory
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摘要: 从洪灾脆弱性组成结构出发，选取11个指标构建洪灾脆弱性评价指标体系，建立了基于突变理论的区域洪灾脆弱性评价方法，并应用于全国重点地区防洪保护区——怀洪南片防洪保护区洪灾脆弱性评价中，结果表明：区内大部分地区的洪灾脆弱性程度偏高，其中特脆弱性等级的乡镇为头铺镇、沫河口镇、曹老集镇；重脆弱性等级的乡镇为大新镇、新集镇；中脆弱性等级的乡镇为新马桥镇、王庄镇、吴小街镇、曹顾张乡、浍南镇; 轻脆弱性等级的乡镇为小蚌埠镇、梅桥镇、临北回族乡；微脆弱性等级的乡镇为怀远县城关镇、魏庄镇。并与基于熵权模糊优选法进行对比，二者评价结果基本一致，进一步表明了方法的合理性和有效性。研究成果对于降低防洪保护区内各乡镇的洪灾脆弱性具有指导作用，对防洪保护区的减灾投资及洪灾管理具有重要意义。Abstract: Based on the structure of the flood vulnerability, 11 indexes are chosen to establish the flood vulnerability evaluation index system. Then the regional flood vulnerability evaluation method based on catastrophe theory is established and applied to evaluate the flood vulnerability of the Huaihongnanpian (HHNP) flood protection area, which is a national key flood protection area. The results show that the flood vulnerability degree is high in most areas of the HHNP flood protection area. The townships with the first level of flood vulnerability are Toupu, Mohekou and Caolaoji, with the second level of flood vulnerability are Daxin and Xinji, with the third level of flood vulnerability are Xinmaqiao, Wangzhuang, Caoguzhangxiang, Wuxiaojie and Kuainan, with the fourth level of flood vulnerability are Xiaobengbu, Meiqiao and Linbeihuizu, with the last level of flood vulnerability are Huaiyuanxianchengguan and Weizhuang. And compared with the fuzzy optimization method based on entropy weight, the results of the two evaluations are basically the same, which further demonstrates the rationality and effectiveness of the method. The research results have a guiding role in reducing the flood vulnerability of each township in the flood protection area, which is of great significance to the flood disaster reduction investment and flood disaster management.
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Key words:
- flooding /
- vulnerability /
- catastrophe theory /
- flood protection area
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表 1 三类常用的初等突变模型
Table 1. Three commonly used models of elementary catastrophe
突变模型 控制变量维数 状态变量维数 势函数 分歧集 尖点突变 2 1 ${V_{ab}}\left( x \right) = \frac{1}{4}{x^4} + \frac{1}{2}a{x^2} + bx $ $a = - 6{x^2}, b = 8{x^3} $ 燕尾突变 3 1 ${V_{abc}}\left( x \right) = \frac{1}{5}{x^5} + \frac{1}{3}a{x^3} + \frac{1}{2}b{x^2} + cx $ $\begin{array}{l} a = - 6{x^2}, b = 8{x^3}, \\ c = - 3{x^4} \end{array} $ 蝴蝶突变 4 1 ${V_{abcd}}\left( x \right) = \frac{1}{6}{x^6} + \frac{1}{4}a{x^4} + \frac{1}{3}b{x^3} + \frac{1}{2}c{x^2} + dx $ $\begin{array}{l} a = - 10{x^2}, b = 20{x^3}\\ c = - 15{x^4}, d = 4{x^5} \end{array} $ 
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表 2 洪灾脆弱性评价指标体系
Table 2. Evaluation index system of flood vulnerability
目标层 准则层 指标层(及其说明) (A)洪灾脆弱性评价指标体系 (B1)暴露度 (C1)单位面积GDP(取单位面积上农业、工业、第三产业的生产总值) (C2)人口密度(取单位面积上的人口数) (C3)居民地密度(取单位面积上居民地的面积) (C4)生命线工程密度(取单位面积上生命线的长度) (B2)敏感性 (C5)平均高程(取各乡镇平均高程) (C6)农业人口占比(指各乡镇农业人口占总人口的百分比) (C7)土地利用敏感指数(采用文献[22]中定义，将各乡镇土地利用类型分为耕地、居民地、园地、林地及牧草地五类，计算土地利用敏感性指数) (C8)女性人口占比(指各乡镇女性人口占总人口的百分比) (B3)防灾减灾能力 (C9)人均GDP (C10)避难所密度(指各乡镇单位面积上可以容纳受灾群众的大中型场地的个数，如学校、大型商场、酒店等) (C11)医疗救助机构密度(指各乡镇单位面积上医疗救助机构的个数)
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表 3 研究区评价指标原始数据
Table 3. Original data of evaluation index in study area
乡镇 单位面积GDP/(万元·km-2) 人口密度/ (人·km-2) 居民地密度/(km2·km-2) 生命线工程密度/(km·km-2) 农业人口占比/% 平均高程/m 土地利用敏感指数 女性人口占比/% 人均GDP/ (万元·人-1) 避难所密度/(个·km-2) 医疗救助机构密度/ (个·km-2) 浍南镇 904.597 296.004 0.014 0.407 0.964 18.176 4.119 0.468 2.663 0.288 0.090 新集镇 1 351.741 449.046 0.021 0.482 0.941 16.136 4.063 0.470 2.640 0.030 0.296 头铺镇 1 043.725 505.887 0.023 0.593 0.962 15.076 4.200 0.478 1.882 0.101 0.172 大新镇 1 160.379 461.485 0.022 0.512 0.964 16.625 3.275 0.473 2.219 0.146 0.255 曹顾张乡 1 152.572 184.241 0.007 0.271 0.828 17.446 4.336 0.485 6.256 0.083 0.193 临北回族乡 531.921 185.198 0.007 1.620 0.862 17.257 3.265 0.465 2.872 0.081 0.228 新马桥镇 1 285.729 359.764 0.014 0.631 0.946 19.193 4.270 0.475 3.274 0.061 0.155 王庄镇 1 047.172 355.156 0.013 0.343 0.968 18.905 4.167 0.466 2.774 0.037 0.203 梅桥镇 3 926.926 805.851 0.000 0.685 0.930 17.277 3.623 0.459 4.873 0.298 0.265 曹老集镇 2 652.742 530.141 0.021 0.473 0.951 17.288 3.967 0.477 5.004 0.104 0.166 吴小街镇 17 638.226 757.459 0.031 1.258 0.700 16.991 3.662 0.501 21.843 0.474 0.422 小蚌埠镇 62 040.981 1 217.154 0.051 1.843 0.336 17.656 3.146 0.506 44.590 1.834 0.386 沫河口镇 3 567.112 707.183 0.029 0.604 0.947 17.492 4.367 0.478 4.749 0.347 0.163 魏庄镇 254.260 125.800 0.010 1.027 0.967 18.281 2.847 0.470 1.038 0.108 0.118 怀远县城关镇 14 918.667 691.251 0.053 2.324 0.220 18.670 2.831 0.493 10.435 1.226 0.200
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表 4 各乡镇洪灾脆弱性指标值
Table 4. Flood vulnerability index values of each township
乡镇名称 暴露度 敏感性 防灾减灾能力 突变理论值 突变理论值等级 模糊熵权值 模糊熵权值等级 怀远县城关镇 0.572 6 0.323 4 0.828 6 0.799 1 Ⅰ 0.322 9 Ⅰ 魏庄镇 0.392 8 0.634 4 0.987 9 0.827 7 Ⅰ 0.304 9 Ⅰ 小蚌埠镇 0.934 6 0.705 3 0.191 3 0.839 4 Ⅱ 0.544 0 Ⅲ 梅桥镇 0.513 5 0.628 1 0.910 7 0.849 9 Ⅱ 0.410 5 Ⅱ 临北回族乡 0.464 0 0.756 9 0.947 8 0.859 8 Ⅱ 0.276 3 Ⅰ 新马桥镇 0.601 7 0.695 0 0.971 7 0.884 8 Ⅲ 0.536 3 Ⅲ 王庄镇 0.525 1 0.867 0 0.946 5 0.888 2 Ⅲ 0.504 0 Ⅲ 曹顾张乡 0.601 1 0.728 4 0.959 9 0.888 3 Ⅲ 0.565 5 Ⅳ 浍南镇 0.586 0 0.792 6 0.977 0 0.895 1 Ⅲ 0.532 0 Ⅲ 吴小街镇 0.778 9 0.857 3 0.544 3 0.897 1 Ⅲ 0.553 2 Ⅳ 大新镇 0.643 5 0.826 5 0.935 5 0.908 1 Ⅳ 0.449 1 Ⅱ 新集镇 0.642 9 0.886 0 0.922 1 0.914 1 Ⅳ 0.567 9 Ⅳ 曹老集镇 0.672 0 0.856 3 0.958 9 0.919 6 Ⅴ 0.596 1 Ⅴ 头铺镇 0.648 7 0.950 8 0.969 5 0.927 0 Ⅴ 0.673 9 Ⅴ 沫河口镇 0.716 9 0.866 9 0.944 6 0.928 7 Ⅴ 0.682 0 Ⅴ
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