Research on an effective rainfall model for geological disaster early warning in Fujian Province, China
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摘要: 降雨是诱发地质灾害最主要的外部因素之一，在中国东南沿海中低山丘陵区强降雨诱发的地质灾害集群发生，造成了大量人员伤亡和财产损失。以福建省为例，深入挖掘多年历史地质灾害案例的降雨实况资料，以县级行政区为统计单元，基于定量化降雨估测对诱发群发性地质灾害的典型降雨过程进行相关性研究，并基于地质环境的量化指标进行了偏相关分析验证，建立了福建省有效降雨模型并通过现场监测和预警应用进行了验证。研究表明：福建地区地质灾害的发生与灾害发生3日内降雨相关，且以0.79为折减系数逐日折减，据此建立了福建地区有效降雨模型；将福建地区有效降雨模型应用于地质灾害气象预警，可以在保证地质灾害命中率的前提下，减少预警区面积、降低预警等级、缩短预警持续时间，提高地质灾害气象预警的精准性。研究结果有助于准确把握降雨特征，可为区域地质灾害气象预警中降雨因子的合理评估提供科学依据。Abstract: Rainfall is one of the most important external factors inducing geological disasters, especially prominent in China’s mountainous regions. Many group-occurring geological disasters induced by heavy rainfall occurred in southeast China’s middle and low mountainous regions, causing many casualties and property losses. Taking Fujian Province as an example, we carefully examined the actual rainfall data of historical geological disaster cases and conducted correlation studies on typical rainfall processes inducing group-occurring geological disasters based on quantitative rainfall estimation with county-level administrative districts as the statistical unit. We also carried out a partial correlation analysis based on quantitative indicators of the geological environment for verification. The result shows that the occurrence of geological disasters in Fujian correlates with adequate rainfall within three days, and it is reduced by a reduction coefficient of 0.79 daily. Based on that finding, we established an effective rainfall model for Fujian Province and verified it through field monitoring and early warning applications. Applying this rainfall model to geological disaster early warning in Fujian can reduce the warning area, lower the warning level, shorten the warning duration, and improve the accuracy of geological disaster early warning by maintaining the hit ratio. The results of the study can help to characterize the rainfall accurately and can provide a scientific basis for the reasonable assessment of rainfall factors in regional geological disaster early warning.
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图 2 福建省构造分区图（韦德光等，1997）
Figure 2. Tectonic zones in Fujian（Wei et al., 1997）
图 4 地质灾害与月平均降雨量关系图（2010—2019年）
Figure 4. Relationship between monthly rainfall and geological disaster (2010–2019)
图 5 福建省降雨诱发地质灾害分布图（2010—2019年）
Figure 5. Distribution of the rainfall-induced geological disasters in Fujian（2010–2019）
图 6 有效降雨系数−相关系数变化曲线
Figure 6. Variation curve of effective rainfall coefficient with correlation coefficient
图 7 降雨入渗现场监测示意图
Figure 7. Schematic diagram showing the site monitoring of rainfall infiltration
图 11 2021年6月28日—7月3日福建南平地区降雨分布图
Figure 11. Rainfall distribution in Nanping, Fujian from June 28 to July 3, 2021
图 12 6月28日预警结果
a—原模型预警结果 b—新模型预警结果
Figure 12. Warning results of June 28
(a) Results of the original model; (b) Results of the new model
图 13 7月1日预警结果
a—原模型预警结果；b—新模型预警结果
Figure 13. Warning results of July 1
(a) Results of the original model; (b) Results of the new model
表 1 福建省典型群发性地质灾害发生数量统计表（2010—2019年）
Table 1. Group-occurring geological disasters in Fujian（2010–2019）
年份 降雨时间 降雨情况 地质灾害数量/起 典型案例 2010 6月13日—27日 全省大部分县市降雨量超过100 mm，59个县（市、区）的733个乡镇降雨量超过250 mm，26个县（市、区）的158个乡镇降雨量超过500 mm，以建宁樱桃岭的875 mm最大 1574 南平市“6·14”滑坡灾害（造成24人死亡失踪） 2011 8月29日—
9月3日台风“南玛都”在福建登陆，福建东部局部地区出现了大暴雨 85 2012 8月2日—3日 台风“苏拉”在福建登陆，北部局部区域和西部大部分区域出现暴雨、大暴雨 41 2015 5月18日—21日 中南部地区出现大范围的大暴雨，局地特大暴雨 107 2016 5月7日—9日 西部的三明、南平两市发生的特大暴雨，多处雨量站点监测实况雨量大于150 mm/d，成片区出现大暴雨量级及以上等级的降雨 43 福建泰宁“5·8”特大型泥石流灾害（造成36人死亡失踪，直接经济损失600 万元 2019 7月6日—9日 福建大部有暴雨，局地有大暴雨，累计雨量100～250 mm 22 
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表 2 地质灾害有效降雨量计算模型一览表（Crozier and Eyles，1980；李长江等，2011；唐红梅等，2013；狄靖月等，2019；刘艳辉等，2019）
Table 2. Summary of the effective rainfall calculation models for geological disasters (Crozier and Eyles, 1980; Li et al., 2011; Tang et al., 2013; Di et al., 2019；Liu et al., 2019 )
时间 提出者 计算方法 衰减系数 计算时间/天 参数说明 研究区 1980 Crozier M J
Eyles R J${P}_{ {a0} }=\displaystyle \sum _{i=1}^{10}{K}^{i}{R}_{i}$ 0.84 10 Pa0为前期有效降雨量，mm；i为计算时间，d； K为衰减系数； Ri为第i日的日降雨量， mm 美国(渥太华) 1985 濑微克美 ${P}_{ {a0} }=\displaystyle \sum _{i=1}^{14}{\alpha }_{i}{R}_{i}$ 0.5i/T 14 Pa0为前期有效降雨量， mm； i为计算时间，d； $ {\alpha }_{i} $为衰减系数； Ri为计算日前第i日的日降雨量， mm；T为半衰期 日本 1991 谭万沛 ${P}_{ {a0} }=\displaystyle \sum _{i=1}^{14}{\alpha }_{i}{R}_{i}$ 0.5i/2 14 中国(四川、云南、
西藏4条泥石流沟)1993 谢正伦等 ${P}_{ {a0} }=\displaystyle \sum _{i=1}^{7}{\alpha }_{i}{R}_{i}$ 0.5i/T 7 中国(台湾) 2000 中国科学院水利部成都山地
灾害与环境研究所${P}_{ {a0} }=\displaystyle \sum _{i=1}^{20}{K}^{i}{R}_{i}$ 0.8 20 Pa0为前期有效降雨量， mm； i为计算时间，d； K为衰减系数； Ri为第i日的日降雨量， mm 中国(云南) 2001 王礼先等 ${P}_{ {a0} }=\displaystyle \sum _{i=1}^{20}{K}^{i}{R}_{i}$ 0.8 15 中国(北京) 2004 詹钱登等 ${P}_{ {a0} }=\displaystyle \sum _{i=1}^{7}{\alpha }_{i}{R}_{i}$ 0.8 7 Pa0为前期有效降雨量， mm； i为计算时间，d； $ {\alpha }_{i} $为衰减系数； Ri为计算日前第i日的日降雨量， mm 中国(台湾) 2005 Zezere ${P}_{ {a0} }=\displaystyle \sum _{i=1}^{30}{\alpha }_{i}{R}_{i}$ 0.9 30 葡萄牙 2013 唐红梅等 ${P}_{ {a0} }=\displaystyle \sum _{i=1}^{4}{K}^{i}{R}_{i}$ 0.6 4 Pa0为前期有效降雨量， mm； i为计算时间，d； K为衰减系数； Ri为第i日的日降雨量， mm 中国(重庆) 2019 刘艳辉等 $ {T}_{i}=\displaystyle \sum _{x=1}^{m}{k}^{x}{T}_{ix} $ 0.84 7 Ti为有效雨量， mm； i为预警单元编号； m为有效降雨时间，d； k为衰减系数； Tix为前x天的降雨量， mm； x为预警当日向前计算的时间 中国(四川) 2019 狄靖月等 ${P}_{ {a0} }=\displaystyle \sum _{i=0}^{10}{K}^{i}{R}_{i}$ 0.8 15 Pa0为前期有效降雨量， mm； i为计算时间，d； K为衰减系数； Ri为第i日的日降雨量， mm 中国(东南地区)
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表 3 地质灾害发生数量与日降雨量相关性分析
Table 3. Correlation between the number of geological disasters and daily rainfall
日降雨量/mm 当日 前1日 前2日 前3日 前4日 前5日 前6日 前7日 前8日 前9日 相关系数 0.290** 0.463** 0.137* −0.066 0.046 −0.057 −0.049 −0.051 −0.058 −0.085 注：**—在0.01 水平（双侧）上显著相关；*—在0.05 水平（双侧）上显著相关
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表 4 地质灾害发生数量与日降雨量偏相关分析
Table 4. Partial correlation between the number of geological disasters and daily rainfall
日降雨量/mm 当日 前1日 前2日 前3日 前4日 前5日 前6日 前7日 前8日 前9日 偏相关系数 0.293** 0.464** 0.137* −0.067 0.048 −0.057 −0.049 −0.052 −0.059 −0.087 注：**—在0.01 水平（双侧）上显著相关；*—在0.05 水平（双侧）上显著相关
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表 5 地质灾害发生数量与有效降雨量相关性分析
Table 5. Correlation between the number of geological disasters and effective rainfall
有效降雨系数 k=0.77 k=0.78 k=0.79 k=0.80 k=0.81 k=0.82 k=0.83 k=0.84 相关系数 0.53404** 0.53408** 0.53409** 0.53406** 0.53401** 0.53392** 0.53380** 0.53365** 注：**—在0.01 水平（双侧）上显著相关
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表 6 发灾情况一览表
Table 6. List of geological disasters
发生日期 发生时间 发灾地点 灾害类型 灾害规模
/m3造成人员伤亡
/人直接经济损失
/万元主要诱因 2021-6-28 13时 南平市建阳区书坊乡松坑村南木溪10号 泥石流 3000 0 2 特大暴雨 2021-6-28 12时 南平市建阳区建阳区书坊乡饶坝村 滑坡 8000 3 10 特大暴雨 2021-7-1 9时 南平市浦城县九牧镇中垄村 崩塌 50 0 0.2 降雨 2021-7-1 10时 南平市邵武市水北镇三都村下洪源组 滑坡 600 0 0.1 暴雨
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表 7 预警结果对比一览表
Table 7. Comparison list of the early warning results
预警日期 预警等级 预警区面积/km2 地质灾害命中率/% 原模型 新模型 原模型 新模型 原模型 新模型 6月28日 橙色预警 橙色预警 5275 4925 100 100 6月29日 橙色预警 橙色预警 5950 4900 − − 6月30日 橙色预警 橙色预警 9875 9675 − − 7月1日 红色预警 橙色预警 8775 4875 100 100 7月2日 红色预警 橙色预警 9475 2275 − − 7月3日 橙色预警 无预警 7725 0 − − 7月4日 橙色预警 无预警 4950 0 − − 7月5日 黄色预警 无预警 475 0 − −
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