Uncertainties of Landslide Susceptibility Modeling under Different Environmental Factor Connections and Prediction Models
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摘要: 拟深入探讨滑坡与其环境因子间的非线性联接计算以及不同数据驱动模型等因素，对滑坡易发性预测建模不确定性的影响规律.以江西省瑞金市为例共获取370处滑坡和10种环境因子，通过概率统计（probability statistics，PS）、频率比（frequency ratio，FR）、信息量（information value，Ⅳ）、熵指数（index of entropy，IOE）和证据权（weight of evidence，WOE）等5种联接方法分别耦合逻辑回归（logistic regression，LR）、BP神经网络（BP neural networks，BPNN）、支持向量机（support vector machines，SVM）和随机森林（random forest，RF）模型共构建出20种耦合模型，同时构建无联接方法直接将原始数据作为输入变量的4种单独LR、BPNN、SVM和RF模型，预测出总计24种工况下的滑坡易发性；最后分别使用ROC曲线、均值、标准差和差异显著性等指标分析上述24种工况下易发性结果的不确定性.结果表明：（1）基于WOE的耦合模型预测滑坡易发性的平均精度最高且不确定性较低，基于PS的耦合模型预测精度最低且不确定性最高，基于FR、Ⅳ和IOE的耦合模型介于两者之间；（2）单独数据驱动模型易发性预测精度略低于耦合模型，且未能计算出环境因子各子区间对滑坡发育的影响规律，但其建模效率高于耦合模型；（3）RF模型预测精度最高且不确定性较低，其次分别为SVM、BPNN和LR模型.总之WOE是更优秀的联接法且RF模型预测性能最优，WOE-RF模型预测的滑坡易发性不确定性较低且更符合实际滑坡概率分布特征.Abstract: This study aims to explore the influences of some modeling factors including the non-linear correlation calculation between landslides and environmental factors and the different data-based models on the uncertainty law of landslide susceptibility prediction (LSP) modeling. The Ruijin City of Jiangxi Province in China with investigated 370 landslides and 10 environmental factors is used as study case. Accordingly, a total of 20 types of different coupling modeling conditions are proposed for LSP with five different connection methods(probability statistics (PS), frequency ratio (FR), information value (Ⅳ), index of entropy (IOE) and weight of evidence (WOE)) and four different data-based models including logistic regression (LR), back propagation neural networks (BPNN), support vector machines (SVM) and random forest (RF). Meanwhile, four single LR, BPNN, SVM and RF models with the original data as input variables are also proposed, as a whole, a total of 24 types of modeling conditions for LSP are obtained based on the above 20 types of coupling conditions and 4 types of single models. Finally, the uncertainty characteristics in the LSP modeling are assessed using the area under the receiver operation curve (ROC), mean value, standard deviation and significance test, respectively. Results show follows. (1) WOE-based models have the highest LSP accuracy and low uncertainty while PS-based models have the lowest LSP accuracy and the highest uncertainty, and the FR, Ⅳ and IOE-based models are in between. (2) The single data-based models have slightly lower LSP accuracies than those of the coupling models on the whole and cannot calculate the influence law of each sub-interval of environmental factors on landslide evolution, however, the single data-based models have higher modeling efficiency than those of the coupling models. (3) Among all the data-based models, RF model has the highest LSP accuracy and relatively low uncertainty, followed by the SVM, BPNN and LR models, respectively. It is concluded that the WOE is a very excellent correlation method and the RF model predicts the optimal LSP performance, the LSP results of WOE-RF model have the lowest uncertainties and the predicted landslide susceptibility indexes are more consistent with the actual landslides distribution characteristics.
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图 3 环境因子(a~h) (高度和地形起伏度未列入)
Fig. 3. The environmental factors (a-h) (elevation and topographic relief are not included)
图 4 基于数据驱动模型的滑坡易发性制图
a1.单独LR模型；a2.单独BPNN模型；a3.单独SVM模型；a4.单独RF模型；b1~b4.FR-based模型；c1~c4.WOE-based模型
Fig. 4. Landslide susceptibility maps of data-based models
图 5 基于RF模型的易发性制图
a.单独RF模型；b. PS-RF模型；c.FR-RF模型；d.Ⅳ -RF模型；e.IOE-RF模型；f.WOE-RF模型
Fig. 5. Landslide susceptibility maps
图 6 不同组合工况下的滑坡易发性建模ROC曲线
Fig. 6. ROC curves of LSP under different conditions
a.LR; b.BPNN; c.SVM; d.RF models
图 7 基于数据驱动模型和基于WOE-based模型的ROC曲线
a.Data-based模型；b.WOE-based模型
Fig. 7. ROC curves of data-based and WOE-based models
图 8 滑坡易发性分布
a1~a3.单独模型；b1~b3.WOE-based模型
Fig. 8. Landslide susceptibility index distributions
图 9 基于RF的滑坡易发指数分布
a.单独RF；b.PS-RF；c.FR-RF；d.Ⅳ-RF；e.IOE-RF；f.WOE-RF
Fig. 9. Susceptibility index distributions
表 1 瑞金市滑坡易发性预测数据源
Table 1. Ruijin landslide susceptibility prediction data source
数据集 空间分辨率 时间 数据用途 数据来源 滑坡编录数据库 2014-12-30 瑞金市滑坡分布 江西省自然资源厅 DEM 30 m 2016-06-06 地形因子 来源于网站http://solargis.cn/imaps/ Landsat 8 TM 多光谱30 m 2013-10-15 NDVI, MNDWI, NDBI 中科院对地观测中心http://ids.ceode.ac.cn/index.aspx 地层岩性分布图 1∶50 000 2014-12-30 岩土类型 江西省自然资源厅 
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表 2 各环境因子的联接值计算
Table 2. The connection values of environmental factors
环境因子 变量值 全区栅格数 滑坡栅格数 PS FR Ⅳ WOE IOE 高度(m)
(连续性)139~293 730 572 1 939 0.354 1.332 0.124 0.414 0.035 293~308 647 032 1 563 0.285 1.212 0.084 0.260 308~373 558 257 964 0.176 0.866 -0.062 -0.178 373~446 369 863 587 0.107 0.796 -0.099 -0.260 446~534 231 817 254 0.046 0.550 -0.260 -0.640 534~642 121 414 98 0.018 0.405 -0.393 -0.932 642~780 66 004 44 0.008 0.334 -0.476 -1.113 780~1118 25 732 33 0.006 0.643 -0.191 -0.445 坡度(°)
(连续性)0~3.6 569 695 51 0.009 0.045 -1.348 -3.328 0.083 3.6~7.0 490 091 537 0.098 0.550 -0.260 -0.693 7.0~10.6 532 865 1 396 0.255 1.315 0.119 0.352 10.6~14.0 438 190 1 442 0.263 1.651 0.218 0.634 14.0~17.6 338 424 1 074 0.196 1.592 0.202 0.553 17.6~21.6 221 097 613 0.112 1.391 0.143 0.366 21.6~26.8 121 534 300 0.055 1.239 0.093 0.225 26.8~52.0 38 795 69 0.013 0.892 -0.049 -0.116 坡向
(连续性)-1.0 499 0 0 0 0 0 0.054 0~22.5
337.5~360.0324 822 668 0.122 1.032 0.014 0.035 22.5~67.5 297 924 585 0.107 0.985 -0.006 -0.017 67.5~112.5 354 479 943 0.172 1.335 0.125 0.340 112.5~157.5 359 791 816 0.149 1.138 0.056 0.150 157.5~202.5 332 830 695 0.127 1.048 0.020 0.053 202.5~247.5 332 143 620 0.113 0.937 -0.028 -0.075 247.5~292.5 378 011 655 0.119 0.869 -0.061 -0.161 292.5~337.5 370 192 500 0.091 0.678 -0.169 -0.439 平面曲率
(连续性)0~10.2 448 550 1 544 0.282 1.727 0.237 0.700 0.07 10.2~18.8 523 511 1 430 0.261 1.371 0.137 0.407 18.8~27.8 429 580 1 002 0.183 1.170 0.068 0.189 27.8~37.7 347 255 632 0.115 0.913 -0.039 -0.104 37.7~48.2 272 547 343 0.063 0.631 -0.200 -0.500 48.2~59.1 223 692 126 0.023 0.283 -0.549 -1.327 59.1~70.6 205 059 121 0.022 0.296 -0.529 -1.274 70.6~81.4 300 497 284 0.052 0.474 -0.324 -0.810 剖面曲率
(连续性)0~1.5 671 767 858 0.157 0.641 -0.193 -0.556 0.009 1.5~3.2 695 534 1 628 0.297 1.174 0.070 0.221 3.2~4.8 534 972 1 244 0.227 1.167 0.067 0.195 4.8~6.6 378 519 827 0.151 1.096 0.040 0.107 6.6~8.7 243 529 507 0.092 1.045 0.019 0.048 8.7~11.0 138 110 258 0.047 0.937 -0.028 -0.068 11.0~14.4 68 229 134 0.024 0.985 -0.006 -0.015 14.4~30.4 20 031 26 0.005 0.651 -0.186 -0.432 地形起伏度(°)
(连续性)0~5.5 588 993 151 0.028 0.129 -0.891 -2.266 0.061 5.5~11.0 611 553 1 116 0.204 0.916 -0.038 -0.113 11.0~16.1 562 924 1 572 0.287 1.401 0.147 0.447 16.1~21.3 428 304 1 289 0.235 1.510 0.179 0.512 21.3~26.8 287 508 718 0.131 1.253 0.098 0.256 26.8~33.4 170 550 411 0.075 1.209 0.082 0.204 33.4~42.6 80 923 204 0.037 1.265 0.102 0.244 42.6~93.8 19 936 21 0.004 0.529 -0.277 -0.642 地层岩性
(离散型)变质岩 1 218 584 3 249 0.593 1.338 0.126 0.603 0.259 碎屑岩 503 748 1 593 0.291 1.587 0.201 0.603 岩浆岩 899 363 359 0.065 0.200 -0.698 -1.939 碳酸盐 107 442 136 0.025 0.635 -0.197 -0.469 水域 21 554 145 0.026 3.376 0.528 1.240 NDVI
(连续性)0~0.014 15 215 13 0.002 0.429 -0.368 -0.851 0.029 0.014~0.120 51 765 38 0.007 0.368 -0.434 -1.012 0.120~0.190 104 953 144 0.026 0.688 -0.162 -0.386 0.190~0.243 233 124 546 0.100 1.175 0.070 0.178 0.243~0.284 487 817 1 149 0.210 1.182 0.073 0.207 0.284~0.322 723 461 1 508 0.275 1.046 0.019 0.061 0.322~0.363 734 588 1 503 0.274 1.027 0.011 0.035 0.363~1 399 768 581 0.106 0.729 -0.137 -0.362 NDBI
(连续性)< 0 473 698 651 0.119 0.690 -0.161 -0.435 0.009 0~0.061 820 803 1 550 0.283 0.948 -0.023 -0.077 0.061~0.126 616 979 1 541 0.281 1.253 0.098 0.302 0.126~0.201 339 466 873 0.159 1.290 0.111 0.297 0.201~0.286 225 388 496 0.090 1.104 0.043 0.109 0.286~0.374 145 844 262 0.048 0.901 -0.045 -0.110 0.374~0.482 90 590 95 0.017 0.526 -0.279 -0.659 0.482~1 37 923 14 0.003 0.185 -0.732 -1.699 距水系距离(m)
(离散型)< 150 508 453 2 135 0.389 2.107 0.324 1.036 0.150 150~300 464 069 1 573 0.287 1.701 0.231 0.685 300~450 420 058 480 0.088 0.573 -0.242 -0.632 > 450 1 358 111 1 294 0.236 0.478 -0.320 -1.152
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表 3 各工况下LR系数和常数项
Table 3. Logistic regression coefficients and constant terms
环境因子 单独LR PS-LR FR-LR Ⅳ-LR IOE-LR WOE-LR 高度 -0.005 4.103 1.534 3.093 11.803 1.166 坡度 0.139 5.187 1.238 1.843 13.144 0.724 坡向 -0.001 5.366 1.074 2.384 10.451 0.911 剖面曲率 -0.015 4.798 0.775 1.553 6.533 0.588 平面曲率 0.017 1.124 0.663 0.872 6.062 0.319 地形起伏度 -0.019 0.031 0.299 0.288 2.850 0.105 地层岩性 -0.434 1.977 1.135 1.848 10.465 0.616 NDVI 0.807 -0.767 0.170 -0.224 1.259 -0.085 NDBI 2.579 1.723 1.160 2.554 9.973 0.987 水系距离 0 5.191 0.794 2.012 5.474 0.594 常数 2.598 -6.018 -9.805 -0.003 -10.337 -0.178
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表 4 基于不同联接方法和数据驱动模型的AUC值
Table 4. AUC values of different connection methods and original value under different data-based models
预测模型 AUC值 RF模型 SVM模型 BPNN模型 LR模型 平均AUC 无联接 0.922 0.809 0.838 0.781 0.838 PS 0.906 0.817 0.806 0.779 0.827 FR 0.905 0.836 0.840 0.832 0.853 Ⅳ 0.907 0.838 0.838 0.838 0.855 IOE 0.905 0.837 0.839 0.833 0.854 WOE 0.896 0.839 0.843 0.838 0.857
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表 5 基于不同连接方式和不同数据模型下的平均值和标准差
Table 5. Mean and standard deviation of different connection methods and original value under data-based models
预测模型 RF模型 SVM模型 BPNN模型 LR模型 平均值 标准差 平均值 标准差 平均值 标准差 平均值 标准差 原始 0.263 0.240 0.355 0.233 0.358 0.189 0.385 0.215 PS 0.279 0.250 0.344 0.247 0.398 0.161 0.383 0.211 FR 0.278 0.254 0.331 0.252 0.376 0.173 0.337 0.242 Ⅳ 0.278 0.255 0.335 0.249 0.367 0.182 0.331 0.251 IOE 0.278 0.254 0.330 0.250 0.367 0.189 0.336 0.246 WOE 0.283 0.261 0.334 0.249 0.359 0.193 0.331 0.251
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表 6 各建模工况下易发性指数的平均秩
Table 6. Mean rank of different connection methods under different data-based models
预测模型 平均秩 RF模型 SVM模型 BPNN模型 LR模型 PS 8.77 13.12 16.87 15.82 FR 8.69 11.87 16.08 12.58 Ⅳ 8.64 12.38 15.39 11.90 IOE 8.64 11.85 15.30 12.43 WOE 8.97 12.48 14.79 12.06 原始数据 8.08 13.74 14.65 14.90
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