Research on the I-D-M threshold model for regional rainfall-induced landslide hazard early warning at a regional scale
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摘要:
区域滑坡灾害降雨预警是近年来研究的热点问题，其难点在于拟定降雨阈值模型。基于逐时雨量数据引入峰值雨量（
M ），构建了滑坡灾害的三维表征降雨阈值模型，可为区域滑坡灾害降雨预警提供科学依据。在浙江省宁波市慈溪市、江北区、镇海区北部3区2010−2022年期间的104处降雨型滑坡事件基础上开展了研究。首先，利用泰森多边形划分单元网格方法划定与灾害相关联的雨量站空间分布，揭示滑坡灾害的有效降雨特征信息；其次，基于滑坡事件编录构建灾害发生时的逐时降雨强度−降雨历时（I -D ）阈值模型，并采用分位数回归方法划分临界阈值曲线；最后，针对I -D 阈值模型不足引入峰值雨量（M ）改进提出I -D -M 模型。以受试者工作特征曲线（receiver operating characteristic，简称ROC）和滑坡实例对比检验上述2种模型精度，据此确定最优阈值模型作为本地区降雨预警判据。结果表明，考虑峰值雨量（M ）的I -D -M 阈值模型相比于I -D 模型具有更高的预警精度，滑坡发生概率黄色预警提高8%，橙色预警提高17%，红色预警提高16%，表明峰值雨量对滑坡的发生具有重要影响；基于分位数回归的I -D -M 阈值模型可作为本地区滑坡灾害红、橙、黄三级降雨预警的判据。研究成果提出的三维表征降雨阈值模型对区域滑坡灾害降雨预警具有理论指导意义。Abstract:Objective Regional early warning of rainfall-induced landslide has been a research hotpot in recent years, with the primary challenge being the formulation of rainfall threshold models. Based on hourly rainfall data, this study introduces peak rainfall (
M ) to construct a three-dimensional characterization model, which can provide a scientific basis for regional rainfall-induced landslide early warning.Methods The research was conducted using data from 104 rainfall-induced landslide events recorded between 2010 and 2022 in the three northern districts of Ningbo City (Cixi, Jiangbei, and Zhenhai). Firstly, the spatial distribution of rainfall stations associated with landslides was delineated using Voronoi diagram method to reveal the effective rainfall characteristic information of landslide hazards. Secondly, the rainfall intensity-rainfall duration (
I -D ) threshold model was established based on landslide inventory, with critical threshold curves defined using quantile regression. Finally, to address the limitations of theI -D model, peak rainfall (M ) was incorporated to propose an improvedI -D -M model. The accuracy of both models was evaluated and compared using ROC curves and historical landslide cases to identify the optimal threshold model for regional early warning.Results The results demonstrate that the
I -D -M model, incorporating peak rainfall (M ), achieves higher warning accuracy than the conventionalI -D model. Probability of landslide occurrence increased by 8% for yellow warnings, 17% for orange warnings, and 16% for red warnings, indicating the significant role of peak rainfall on landslide initiation. The quantile regression-basedI -D -M threshold model can be effectively applied as a criterion for implementing three-tiered (red, orange, yellow) rainfall landslide early warning in the study area.Conclusion The proposed three-dimensional rainfall threshold model provides theoretical and practical insights for improving regional landslide early warning systems, demonstrating enhanced predictive capability and operational applicability.
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图 1 研究区滑坡点分布及泰森多边形
Figure 1. Distribution of the recorded landslides and Voronoi diagram in the study area
图 2 研究区(2010−2022年)月平均降雨量与滑坡灾害频次图
Figure 2. Monthly average rainfall and landslide frequency in the study area (2010−2022)
图 3 2012年6月降雨事件划分示意图
Figure 3. Schematic diagram of rainfall event identification in June 2012
图 4 研究区滑坡发生时峰值雨量分布图（2010-2022年66起滑坡，下同）
Figure 4. Distribution of the peak rainfall at the time of landslide occurrence in the study area
图 5 研究区滑坡发生时峰值雨量与平均降雨强度
Figure 5. Peak rainfall and average rainfall intensity of the landslide in the study area
图 6 研究区降雨强度−降雨历时(I-D)降雨阈值曲线
Figure 6. Curve of the I-D rainfall threshold in the study area
图 8 I-D-M和I-D阈值ROC曲线
AUC. 受试者工作特征曲线（ROC）下面积
Figure 8. ROC curves of the I-D-M and I-D threshold model
表 1 不同预警等级降雨阈值方程
Table 1. Rainfall threshold equations for different warning levels
等级划分 分位数回归方程 黄色预警（滑坡发生概率25%） $ {52.76D}^{-0.604} $ 橙色预警（滑坡发生概率50%） $ {71.23D}^{-0.642} $ 红色预警（滑坡发生概率75%） $ {92.68D}^{-0.637} $ 注：D. 降雨历时，h；下同 
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