Continuous probability threshold for rainfall-type landslides in Zigui County, Hubei Province
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摘要:
确定降雨阈值是开展滑坡危险性评价和气象风险预警的重要基础。针对临界降雨阈值空间分辨率低，区分降雨过程精度较差的问题，以湖北省秭归县为例，根据472处滑坡和58个雨量站数据，构建了有效降雨量−持续时间（
E -D ）临界降雨阈值；运用逻辑回归方法，以不同临界降雨阈值对应的有效降雨量（E ）和持续时间（D ）为自变量，时间概率（P ）为因变量，拟合了区内降雨型滑坡的连续概率阈值；最后，通过历史滑坡事件和危险性评价结果，从时空2方面对阈值模型精度进行了分析和验证。结果表明：①区内滑坡以中小型浅层堆积层滑坡为主，降雨与滑坡事件存在显著正相关性，86.63%的滑坡发生在雨季；②连续概率阈值非线性拟合方程为$ 1/P= 1+ $$ {{\mathrm{e}}}^{2.0792+0.24156\times D-0.04072\times E} $，拟合度达0.9497 ；③基于验证集滑坡样本，滑坡发生概率为60%时，连续概率阈值模型预测精度提高17.4%，危险性评价中的4处已知滑坡危险等级均有提高。连续概率阈值对研究区滑坡灾害的预警精度和空间辨识度更优，可为地方政府开展滑坡风险预警提供科学理论参考。Abstract:Determining rainfall thresholds is a crucial foundation for landslide hazard assessments and meteorological risk early warnings.
Objective To address the limitations of low spatial resolution and poor accuracy in distinguishing rainfall processes of traditional critical rainfall thresholds,
Methods this study takes Zigui County, Hubei Province as a case. Based on data from 472 landslides and 58 rainfall stations, an effective rainfall-duration (
E -D ) critical rainfall threshold was established; logistic regression was employed, with effective rainfall (E ) and duration (D ) as the independent variables and time probability (P ) as the dependent variable, to fit the continuous probability thresholds for rainfall-induced landslides within the study area; finally, the accuracy of the threshold model was analyzed and validated from both temporal and spatial perspectives using historical landslide events and hazard assessment results.Results The results indicate: ① Landslides in the region are primarily small to medium-sized shallow-deposited layer landslides, with a significant positive correlation between rainfall and landslides occurrences, with 86.63% of landslides occurring during the rainy season; ②The nonlinear fitting equation for the continuous probability threshold is $ 1/P=1+{{\mathrm{e}}}^{2.0792+0.24156\times D-0.04072\times E} $, with a fitting degree of
0.9497 ; ③ Using validation set of landslide samples, when the probability of landslide occurrence reaches 60%, the prediction accuracy of the continuous probability threshold model improves by 17.4%, and the hazard levels of four known landslides in the hazard assessment all increase.Conclusion The continuous probability threshold demonstrates superior accuracy in landslide disaster warning and spatial resolution for the study area, providing a scientific theoretical reference for local governments to conduct landslide risk warnings.
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图 1 研究区地理位置与滑坡分布
Figure 1. Geographical location and landslide distribution in the study area
图 3 2024年7月初滑坡灾害与累计降雨量空间分布图
Figure 3. Landslide hazard and spatial distribution of cumulative rainfall in early July 2024
图 6 剔除前后滑坡样本点空间分布图
Figure 6. Spatial distribution of landslide sample points before and after exclusion
图 8 滑坡发生前每日不同降雨等级占比图
Figure 8. Map of percentage of different rainfall classes for each day before the landslide
图 9 临界E-D阈值曲线
E20%，E40%，E60%，E80%分别为滑坡发生时间概率为20%，40%，60%，80%的有效降雨量值，下同
Figure 9. Critical E-D threshold curve
图 11 基于临界降雨阈值的滑坡危险性验证结果
Figure 11. Validation results of landslide hazard based on critical rainfall threshold
图 12 各事件当天滑坡发生时间概率（P）分布图
Figure 12. Probability distribution of occurrence time of landslides on the day of each event
图 13 基于滑坡连续概率阈值的危险性分级图
Figure 13. Hazard classification diagram based on landslide continuum probability threshold
表 1 滑坡类型、规模、厚度及其数量占比
Table 1. Type, scale, thickness of landslides and their quantity ratios
分类依据 数量/处 占比/% 类型 堆积层滑坡 806 94.27 岩质滑坡 42 4.91 岩土混合滑坡 7 0.82 规模/
104m3<10（小型） 265 30.99 [10, 100)（中型） 416 48.66 [100, 1000 )（大型）150 17.54 [ 1000 ,10000 )（特大型）23 2.69 > 10000 （巨型）1 0.12 厚度/
m<10（浅层） 567 66.31 [10, 25)（中层） 236 27.60 [25, 50)（深层） 49 5.73 >50（超深层） 3 0.36 
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表 2 样本集和验证集滑坡类型、规模、厚度、坡度及其数量占比
Table 2. Type, scale, thickness, slope of landslides of sample set and validation set and their quantity ratios
分类依据 数量/处 占比/% 样本集 验证集 样本集 验证集 类型 堆积层滑坡 293 58 97.67 92.06 岩质滑坡 6 3 2.00 4.76 岩土混合滑坡 1 2 0.33 3.18 规模/
104m3<10（小型） 121 18 40.33 38.57 [10, 100)（中型） 140 31 46.67 48.21 ≥100（大型及以上） 39 14 13.00 13.22 厚度/
m<10（浅层） 228 37 76.00 71.73 [10, 25)（中层） 61 20 20.33 22.75 ≥25（深层及以上） 11 6 3.67 5.52 坡度/(°) ＜25 103 23 34.33 36.51 [25, 35) 138 31 46.00 49.21 ≥35 59 9 19.67 14.28
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表 3 研究区典型滑坡变形破坏前的降雨特征
Table 3. Rainfall characteristics before typical landslides deformation and damage in the study area
滑坡名称 发生时间 变形前降雨特征 别家坡滑坡 1979-07-20 7月11日-当日一次暴雨
累计降雨量达93.7 mm胡家院子滑坡 1983-07-02 6月26日-当日累计降雨量133.8 mm 谭家岭滑坡 1991-06-30 发生当日降雨量137.5 mm 后头坪滑坡 1996-07-04 滑坡发生当日及前2 d
累计降雨量200.2 mm百日场（谭大坝）
滑坡1996-07-07 7月2日-7月4日累计降雨量200.2 mm 桐子沟滑坡 1998-07-01 6月29日降雨量189.6 mm 水田坝乡龙口村1组
云盘居民点2014-09-02 发生当日及前4 d累计降雨量237 mm 泄滩乡白家河
村2组池塘坪2016-07-07 6月24日-当日一次暴雨
累计降雨量达159 mm茅坪镇陈家冲
村3组向家坝2016-07-10 发生当日及前2 d累计降雨量153.3 mm 磨坪乡天井坪
村2组水井湾2017-10-06 发生当日及前9 d累计降雨量247.5 mm 院墙坡滑坡 2020-06-29 发生当日及前8 d累计降雨量144.4 mm 归州镇向家店村5组
小岩头变形体2020-07-27 发生当日及前9 d累计降雨量149.9 mm 柏树嘴滑坡 2024-07-10 7月3日-7月4日累计降雨量165 mm，
7月9日降雨量135 mm湾水田滑坡 2024-07-17 7月15日降雨量242.8 mm，
7月9日降雨量159 mm
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表 4 秭归县不同天数降雨因子与滑坡因子相关性分析
Table 4. Correlation analysis between rainfall factors of different days and landslide factors at Zigui County
降雨因子 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 相关系数 0.593** 0.601** 0.546** 0.495** 0.463** 0.449** 0.435** 0.420** 0.418** 0.392** 偏相关性系数 0.601** 0.614** 0.542** 0.489** 0.459** 0.452** 0.437** 0.419** 0.417** 0.387** 注：P1. 以滑坡灾害事件当日00:00至24:00期间的雨量作为滑坡灾害的当日降雨量；P2. 以当日与前1 d降雨量之和作为该滑坡灾害事件的2 d累计降雨量；P3～P10以此类推；**. 在0.01显著性水平下，显著相关；下同
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表 5 滑坡发生前每日不同降雨等级占比
Table 5. Percentage of different rainfall classes for each day before the landslide
时间 降雨等级占比/% 无降雨 小雨 中雨 大雨 暴雨 大暴雨 当日 5.19 15.41 16.09 17.96 19.86 25.48 前1 d 7.90 34.66 8.80 18.48 19.26 10.90 前2 d 23.02 40.41 14.00 10.38 6.77 5.42 前3 d 28.22 40.18 22.80 6.32 2.48 0 前4 d 26.64 50.56 10.16 11.96 0.68 0 前5 d 38.60 41.53 7.00 8.45 4.42 0 前6 d 38.83 30.47 8.13 18.51 4.06 0 前7 d 31.18 26.95 22.61 14.97 4.06 0.23 前8 d 49.89 28.22 17.38 3.61 0.68 0.23 前9 d 59.82 23.02 11.29 4.74 1.13 0 前10 d 41.96 31.38 11.51 6.44 1.58 1.13 注：无降雨、小雨、中雨、大雨、暴雨、大暴雨为根据累计降雨量划分的降雨等级，其累计降雨量分别为0，(0，10)，[10，25)，[25，50)，[50，100)，≥100 mm，下同
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表 6 不同衰减系数下前7 d有效降雨量与滑坡间的相关性
Table 6. Correlation between effective rainfall in the first 7 days and landslides with different attenuation coefficients
衰减系数α 1 0.9 0.8 0.7 0.6 0.5 相关性系数 0.718** 0.726** 0.745** 0.684** 0.636** 0.589** 偏相关性系数 0.717** 0.724** 0.747** 0.681** 0.633** 0.584**
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表 7 滑坡E-D阈值曲线方程
Table 7. Equations for landslide E-D threshold curves
预警等级 P/% 宏观阈值曲线 8 d降雨量/mm 有效 实际 蓝色预警 20 E20%=29D0.381 63.91 110.24 黄色预警 40 E40%=37.7D0.381 83.08 129.53 橙色预警 60 E60%=47.2D0.381 104.02 179.46 红色预警 80 E80%=73D0.381 160.88 276.55 注：E. 有效降雨量；D. 降雨持续时间；P. 滑坡发生时间概率；下同
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表 8 不同时间概率下的前期有效降雨量及降雨持续天数
Table 8. Effective rainfall and rainfall duration days in the previous period with different temporal probabilities
P/% E/mm D=1 d D=2 d D=3 d D=4 d D=5 d D=6 d D=7 d D=8 d D=9 d D=10 d 0 9.5 12.4 14.4 16.1 17.5 18.8 19.9 20.9 21.9 22.8 5 17.8 23.2 27.0 30.1 32.8 35.2 37.3 39.2 41.0 42.7 10 21.0 27.3 31.9 35.6 38.7 41.5 44.0 46.3 48.4 50.4 15 24.7 32.1 37.5 41.8 45.5 48.8 51.7 54.4 56.9 59.3 20 29.0 37.7 44.0 49.1 53.5 57.3 60.7 63.9 66.8 69.6 30 34.2 44.5 51.9 57.9 63.0 67.6 71.6 75.4 78.8 82.0 40 37.7 48.4 56.5 63.0 68.6 73.5 77.9 82.0 85.7 89.2 50 42.7 55.6 64.8 72.3 78.7 84.4 89.4 94.1 98.4 102.4 60 47.2 61.4 71.7 79.9 87.0 93.2 98.9 104.0 108.8 113.2 70 64.0 83.3 97.2 108.4 118.0 126.4 134.1 141.0 147.5 153.5 80 73.0 95.0 110.8 123.6 134.6 144.2 152.9 160.9 168.2 175.1 90 90.5 117.8 137.4 153.3 166.8 178.8 189.6 199.4 208.6 217.1 100 108.7 141.5 165.0 184.1 200.4 214.7 227.7 239.6 250.5 260.8
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表 9 2种模型验证集滑坡点分布情况
Table 9. Distribution of landslide sites in the validation set of the two models
滑坡发生时间概率P/% <20 [20,40） [40,60） [60,80） ≥80 临界降雨阈值模型 滑坡数量/个 6 8 14 23 12 滑坡占比/% 9.5 12.7 22.2 36.5 19.1 连续概率阈值模型 滑坡数量/个 1 5 11 23 23 滑坡占比/% 1.6 7.9 17.5 36.5 36.5
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表 10 典型降雨型滑坡的降雨数据和基于临界降雨阈值的发生时间概率
Table 10. Rainfall data and probability of occurrence time for typical rainfall-induced landslides based on critical rainfall threshold
发生时间 滑坡 坡度/(°) 规模 厚度/m R0/mm R1/mm R2/mm R3/mm R4/mm R5/mm R6/mm R7/mm E/mm D/d P/% 危险性等级 2014-08-05 沙湾子滑坡 25 中型 13 72.7 35.2 23.4 10.3 6.4 0 0 0 123.73 5 80 极高 2016-07-10 向家院子滑坡 40 大型 15 38.3 39.7 49.4 21.2 16.6 0 0 0 119.33 5 60 高 2016-07-19 店子坪滑坡 37 中型 5 69.6 44.5 7.6 6.7 30.1 5.2 2.1 0 128.08 6 60 高 2017-07-20 归州老城滑坡 25 大型 15 40.9 24.4 37.3 0.1 0 0 0.1 66.2 98.25 3 60 高 2020-07-03 王大洲屋前滑坡 32 小型 7 63.1 18.2 15.9 13.8 39.9 0 0 0 111.24 5 60 高 2024-07-09 张家红屋场滑坡 35 中型 5 152.1 0 0 2.9 0.5 154.6 34.6 0.4 213.64 1 80 极高 注：R0. 当日降雨量；R1. 前1 d降雨量；R2. 前2 d累计降雨量；R3～R7以此类推
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表 11 典型降雨型滑坡基于连续概率阈值的发生时间概率
Table 11. Probability of occurrence time for typical rainfall-induced landslides based on continuous probability threshold
发生时间 滑坡 E/mm D/d P/% 易发性值 连续概率
危险性值危险性
等级2014-08-05 沙湾子滑坡 123.73 5 96.7 0.923 0.893 极高 2016-07-10 向家院子滑坡 119.33 5 93.4 0.899 0.840 极高 2016-07-19 店子坪滑坡 128.08 6 95.1 0.863 0.821 极高 2017-07-20 归州老城滑坡 98.25 3 89.8 1 0.898 极高 2020-07-03 王大洲屋前滑坡 111.24 5 91.3 0.972 0.887 极高 2024-07-09 张家红屋场滑坡 213.64 1 99.9 0.983 0.982 极高
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