Analysis of the influence of dimensional unity in landslide susceptibility assessment
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摘要:
以往的区域性滑坡易发性评价研究多以对比不同评价模型结果和改进模型为主，而忽视了所选致灾因子的信息保留以及因子量纲如何统一的问题。为探究致灾因子的相关性和量纲对易发性评价结果的影响，以甘肃省靖远县北部地区作为研究区，选取高程、坡度、坡向和地形起伏度等12个因子，利用主成分分析提取的新因子参与易发性评价，并采用数据标准化、滑坡密度和信息量值替代法统一致灾因子的量纲，最后基于GIS平台绘制研究区滑坡易发性分区图。通过ROC曲线评估各模型的易发性评价结果精度。结果表明：在信息量模型、逻辑回归模型和感知机模型中，经主成分分析处理的因子得到的模型评价结果精度更高，采用信息量值替代法统一因子的量纲能够进一步提升逻辑回归和感知机模型的评价结果精度；同时，3种评价模型中感知机模型的结果精度最高(AUC = 0.936 7)，优于信息量模型(AUC = 0.917 3)和逻辑回归模型(AUC = 0.927 2)，是该研究区滑坡易发性评价的理想模型，应优先考虑。研究结果可为类似地区的防灾减灾工作提供基础数据和理论参考。
Abstract:Previous studies on the susceptibility assessment of regional landslides mainly focused on comparing and improving the results of different evaluation models, while neglected the preservation of information on selected disaster-causing factors and the issue of how to unify factor dimensions. To explore the correlation and dimensionality of disaster causing-factors and their impact on susceptibility assessment, this study selected 12 factors such as elevation, slope, aspect, and terrain undulation, and used new factors extracted from principal component analysis in susceptibility assessment in the northern Jingyuan County. Data standardization, landslide density, and information quantity substitution methods were used to unify the dimensionality of disaster-causing factors. The landslide susceptibility zoning map was drawn based on the GIS platform in the study area. The accuracy of the susceptibility assessment of each mode was evaluated by the receiver operating characteristic curve. The results show that among the information model, the logistic regression model, and the perceptron model, the accuracy of the model evaluation obtained by the factors processed by principal component analysis is the highest. Using the information value substitution method to unify the dimensions of factors can further improve the accuracy of the evaluation of the logistic regression model and the perceptron model. The perceptron model has the highest accuracy (AUC=0.936 7), which is superior to the information model (AUC=0.917 3) and the logistic regression model (AUC=0.927 2). This is an ideal model for the landslide susceptibility assessment in the study area and should be given priority. The results can provide the basic theoretical information for disaster prevention and mitigation in similar areas.
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表 1 各致灾因子的信息量值
Table 1. Information value of each disaster-causing factor
致灾因子 类别 信息量值 致灾因子 类别 信息量值 高程/m [1 280, 1 560] 1.469 年均降雨量/（mm·a−1） [106, 135] 0.473 (1 560, 1 800] −0.410 (135, 150] 0.213 (1 800, 2 020] −0.396 (150, 165] −0.224 (2 020, 2 330] 0.060 (165, 180] 0.311 (2 330, 3 010] −2.167 (180, 223] −2.520 坡度/（°） [0, 9] −2.063 距河流距离/m 200 2.198 (9, 17] −0.369 400 0.091 (17, 25] 0.897 800 0.757 (25, 33] 1.555 1 600 −0.733 (33, 63] 1.332 3 200 −0.282 坡向 平地 −2.126 土地类型 农田 −0.120 北 −0.601 建筑用地 0.349 东北 0.132 果园 0.054 东 0.869 旱地 −0.688 东南 0.544 草地 0.152 南 −0.371 乔木林地 −0.799 西南 −0.029 水体 −1.658 西 0.195 裸土地 2.142 西北 −0.167 灌木丛 −0.570 地形起伏度 [0, 13.4] −2.043 径流强度指数（SPI） [−13.8, −9.3] −3.545 (13.4, 22.5] 0.182 (−9.3, −5.8] −0.117 (22.5, 31.6] 1.153 (−5.8, −1.8] −2.476 (31.6, 43.5] 1.576 (−1.8, 1.8] 0.569 (43.5, 137.6] 0.913 (1.8, 12.0] −0.071 距沟谷距离/m 50 2.476 距公路距离/m 100 2.800 100 3.345 200 2.396 200 3.003 400 0.943 400 1.123 600 −0.601 800 −1.288 800 −0.465 1 600 −1.223 1 000 −1.332 >1 600 −2.007 >1 000 −0.811 地形粗糙度 [1, 1.05] −1.219 $ {{F}}_{{1}} $ [−4.65, −1.50] −2.452 (1.05, 1.10] 0.935 (−1.50, −0.72] −1.451 (1.10, 1.25] 1.458 (−0.72, 0.60] 0.136 (1.25, 1.35] 1.592 （0.60, 2.24] 1.506 (1.35, 2.22] 1.345 (2.24, 12.09] 1.732 地形湿度指数（TWI） [2.6, 4.5] 0.941 $ {{F}}_{{2}} $ [−3.90, −1.00] −0.305 (4.5, 5.7] 0.701 (−1.00, 0.00] 0.200 (5.7, 7.5] −0.327 （0.00, 1.30] −0.135 (7.5, 10.4] −1.370 (1.30, 2.80] 0.579 (10.4, 26.8] −1.693 (2.80, 7.43] −3.332 
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表 2 致灾因子的皮尔逊相关系数
Table 2. Pearson correlation coefficient of disaster-causing factors
影响因子 坡向 土地类型 距公路距离 距河流距离 距山沟距离 年均降雨量 地形粗糙度 地形起伏度 TWI 高程 坡度 SPI 坡向 1.00 土地类型 0.13 1.00 距公路距离 0.03 0.20 1.00 距河流距离 −0.08 −0.07 0.10 1.00 距沟谷距离 −0.07 −0.13 0.20 0.01 1.00 年均降雨量 −0.02 0.19 0.18 0.19 −0.02 1.00 地形粗糙度 0.16 0.24 0.11 −0.09 −0.02 0.03 1.00 地形起伏度 0.26 0.35 0.15 −0.08 −0.07 0.04 0.91 1.00 TWI −0.33 −0.32 −0.13 0.04 0.05 −0.01 −0.49 −0.65 1.00 高程 0.01 0.22 0.20 0.46 0.07 0.73 0.21 0.24 −0.17 1.00 坡度 0.26 0.35 0.15 −0.08 −0.07 0.05 0.91 0.98 −0.68 0.24 1.00 SPI 0.10 0.02 −0.02 −0.01 −0.06 0.03 0.19 0.21 0.23 0.03 0.22 1.00
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表 3 特征值及方差
Table 3. Characteristic values and variances
主成分 初始特征值 提取载荷平方和 总计 方差百分比 累积/% 总计 方差百分比 累积/% F1 3.787 63.117 63.117 3.787 63.117 63.117 F2 1.490 24.836 87.953 1.490 24.836 87.953 F3 0.428 7.130 95.083 F4 0.226 3.763 98.846 F5 0.059 0.982 99.828 F6 0.010 0.172 100.000
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表 4 成分系数
Table 4. Composition coefficient values
标准化因子 主成分 $ {F}_{1} $ $ {F}_{2} $ $ {Z}_{1} $ 0.911 0.167 $ {Z}_{2} $ 0.964 0.214 $ {Z}_{3} $ −0.792 −0.270 $ {Z}_{4} $ 0.964 0.219 $ {Z}_{5} $ −0.473 0.812 $ {Z}_{6} $ −0.500 0.797
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表 5 各逻辑回归模型的AUC值
Table 5. AUC values for each logistic regression model
消除因子相关方法 标准化数据 滑坡密度 信息量值 剔除相关因子 0.898 2 0.920 1 0.926 2 PCA降维 0.898 2 0.925 3 0.927 2
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表 6 各感知机模型的AUC值
Table 6. AUC values for each perceptron model
消除因子相关方法 标准化数据 滑坡密度 信息量值 剔除相关因子 0.920 8 0.505 1 0.933 0 PCA降维 0.930 8 0.820 3 0.936 7
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表 7 各模型的滑坡易发性分区的统计结果
Table 7. Statistical results of landslide susceptibility zoning for each model
模型 易发性分区 滑坡面积/m2 分区面积/m2 滑坡面积密度/10−5 分区百分比/% 分区滑坡百分比/% 信息量值 信息量模型 非易发区 2 571 547 969 365 0.47 21.41 0.28 −6.26 低易发区 39 502 815 045 498 4.85 31.85 4.30 −2.89 中易发区 147 158 959 176 506 15.34 37.48 16.02 −1.23 高易发区 729 606 236 878 631 308.01 9.26 79.40 3.10 逻辑回归模型 非易发区 24 537 1 462 113 826 1.68 57.13 2.67 −4.42 低易发区 72 297 636 718 143 11.35 24.88 7.87 −1.66 中易发区 115 994 237 569 020 48.83 9.28 12.62 0.44 高易发区 706 009 222 669 011 17.07 8.71 76.84 3.14 感知机模型 非易发区 18 888 1 766 670 263 1.07 69.04 2.06 −5.07 低易发区 57 285 366 837 348 15.62 14.33 6.23 −1.20 中易发区 86 797 183 517 408 47.30 7.17 9.45 0.40 高易发区 755 867 242 044 981 312.28 9.46 82.26 3.12
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