基于贝叶斯公式修正的降雨型滑坡灾害概率研究

doi:10.12118/j.issn.1000-6060.2025.425

摘要/Abstract

摘要：

以改进降雨诱发滑坡灾害时空概率算法，提高预报预警能力为研究目标，基于2001—2020年山西省滑坡灾害与同期降雨资料，剔除冻融期及无明显降雨诱发的滑坡灾害样本，重构样本集。采用逻辑回归方法，构建了以累积有效降雨量、降雨间隔历时为变量的降雨致灾概率模型。结合下垫面影响因子空间分布特征，将山西省划分为5个片区，应用贝叶斯公式对逻辑回归模型进行修正，建立空间概率模型。通过接受者操作特征曲线（ROC）获得降雨致灾最佳临界值，最后应用2021—2023年样本进行检验，经插值获得各片区降雨致灾阈值曲线。结果表明：（1）山西省南部冻融期结束时间在5月上旬，而北部则可持续到6月中旬。（2） ROC曲线表明逻辑回归模型、贝叶斯公式修正模型均有一定的预测能力，且后者更佳，临界致灾概率分别为61.51%、60.37%。（3）逻辑回归模型、贝叶斯公式修正模型准确率分别为86.44%、93.22%，贝叶斯公式修正效果显著。（4）山西省各片区均表现为随着降雨间隔时长的增加，所需阈值逐渐递减，就空间分布而言，山西省滑坡灾害隐患点阈值呈现从西南到东北逐渐降低的特点。

关键词: 冻融期与非冻融期, 降雨, 滑坡灾害, 逻辑回归, 贝叶斯公式, 阈值

Abstract:

To improve the spatiotemporal probability algorithm for rainfall-induced landslide disasters and improve early warning accuracy, the dataset of rainfall and landslide events in Shanxi, China form 2001 to 2020 was reconstructed by removing samples from the freeze-thaw period and landslides not clearly rainfall-induced. A disaster probability model was developed using logistic regression based on accumulated effective rainfall and rainfall duration. Shanxi Province was divided into five subregions according to the spatial distributions of underlying surface factors; the probability model was corrected using a Bayesian formula to obtain a spatial probability model. The receiver operating characteristic curve (ROC) was applied to determine the critical value of landslide disasters, and the models were validated with data from 2021 to 2023. Finally, interpolation was used to derive the disaster threshold curves for different subregions. The conclusions are as follows: (1) The freeze-thaw period ends in early May in southern Shanxi Province but lasts until mid-June in the north. (2) The ROC curve shows that both the logistic regression and Bayesian formula correction models predict accurately, with the latter performing better; critical probabilities are 61.51% and 60.37%, respectively. (3) The accuracies of the logistic regression and Bayesian formula correction models are 86.44% and 93.22%, respectively, indicating significant improvements with the Bayesian formula correction. (4) Threshold curves across subregions of Shanxi Province decrease with rainfall duration increases. Spatially, landslide thresholds decrease from southwest to northeast across Shanxi Province.

Key words: freeze-thaw period and non-freeze-thaw period, rainfall, landslide disaster, logistic regression, Bayesian formula, threshold

卢盛栋, 王文春, 郝小栋, 孙立军, 张华明. 基于贝叶斯公式修正的降雨型滑坡灾害概率研究[J]. 干旱区地理, 2026, 49(5): 917-927.

LU Shengdong, WANG Wenchun, HAO Xiaodong, SUN Lijun, ZHANG Huaming. Probability of landslide disasters induced by rainfall based on Bayesian formula correction[J]. Arid Land Geography, 2026, 49(5): 917-927.

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主要影响因子		北太行山片区	晋南片区	太岳山片区	北吕梁山片区	南吕梁山片区
坡度/(°)	(0.00, 12.64)	54.50	59.16	53.31	42.89	34.75
	[12.64, 31.78)	39.51	34.67	43.34	53.09	57.80
	[31.78, 78.80)	5.99	6.17	3.35	4.01	7.45
NDVI	(0.076, 0.460)	1.91	1.97	1.45	1.96	0.62
	[0.460, 0.732)	40.80	27.98	29.55	52.76	30.10
	[0.732, 0.920)	57.29	70.05	68.99	45.28	69.28
TWI	[-1.62, 6.42)	43.45	43.63	45.44	48.05	50.95
	[6.42, 15.44)	56.16	56.07	54.18	51.62	48.78
	[15.44, 26.19)	0.39	0.31	0.38	0.33	0.27
工程地质岩组	土体	43.25	44.27	47.86	60.60	39.51
	岩体	56.08	55.56	52.06	39.27	60.49
	其他（水体等）	0.07	0.18	0.08	0.13	0.00
隐患点高程/m	[0, 1000)	28.46	62.12	29.84	32.23	31.37
隐患点高程/m	[1000, 2800]	71.54	37.78	70.16	67.77	68.63

变量	短期降雨			中期降雨			中长期降雨
变量	较少	较多	特别多	较少	较多	特别多	较少	较多
P(C₁\|B,L)	0.00	100.00	100.00	0.00	75.00	100.00	30.00	7.69
P(C₁\|B)	36.36	66.67	100.00	23.81	41.18	100.00	30.77	7.69
P(C₂\|B,L)	0.00	100.00	100.00	0.00	100.00	100.00	10.00	19.23
P(C₂\|B)	18.18	100.00	100.00	4.76	100.00	100.00	7.69	19.23
P(C₃\|B,L)	0.00	100.00	100.00	0.00	25.00	100.00	15.00	11.54
P(C₃\|B)	9.09	100.00	100.00	33.33	11.76	100.00	11.54	11.54
P(C₄\|B,L)	0.00	100.00	100.00	0.00	100.00	100.00	10.00	19.23
P(C₄\|B)	36.36	100.00	100.00	9.52	100.00	100.00	7.69	19.23
P(C₅\|B,L)	100.00	100.00	100.00	0.00	100.00	100.00	35.00	42.31
P(C₅\|B)	100.00	100.00	100.00	28.57	100.00	100.00	42.31	42.31

样本序号	累积有效降雨量/mm	降雨历时/d	是否发生滑坡灾害	逻辑回归概率/%	贝叶斯公式修正概率/%	样本序号	累积有效降雨量/mm	降雨历时/d	是否发生滑坡灾害	逻辑回归概率/%	贝叶斯公式修正概率/%
1	56.46	15	是	96.68	100.00	30	93.79	12	否	99.66	99.66
2	162.21	14	是	100.00	100.00	31	33.23	7	否	16.71	16.71
3	59.81	10	是	86.83	100.00	32	1.97	1	否	0.14	0.00
4	175.51	14	是	100.00	100.00	33	18.38	7	否	4.94	0.00
5	299.01	11	是	100.00	100.00	34	0.60	2	否	0.17	0.00
6	302.90	12	是	100.00	100.00	35	19.18	9	否	10.26	0.00
7	142.38	11	是	99.99	99.99	36	9.10	7	否	2.18	0.00
8	98.57	12	是	99.78	100.00	37	51.14	6	否	41.72	41.72
9	69.73	10	是	94.21	94.21	38	34.29	4	否	7.02	7.02
10	99.42	4	是	96.59	96.59	39	15.40	1	否	0.46	0.46
11	48.25	7	是	44.04	93.62	40	14.74	2	否	0.62	0.93
12	28.31	16	是	76.28	63.10	41	16.11	15	否	42.56	35.21
13	116.75	10	是	99.91	99.91	42	41.68	11	否	64.45	53.31
14	103.24	11	是	99.80	99.80	43	44.76	11	否	70.58	58.38
15	107.92	4	是	98.40	98.40	44	10.90	1	否	0.31	0.31
16	127.28	11	是	99.98	99.98	45	106.93	8	否	99.58	99.58
17	94.57	5	是	96.30	96.30	46	29.50	2	否	2.33	2.33
18	112.94	5	是	99.28	99.28	47	1.30	2	否	0.18	0.18
19	172.05	10	是	100.00	100.00	48	56.92	6	否	54.77	54.77
20	112.37	11	是	99.91	99.91	49	43.78	8	否	42.85	42.85
21	206.98	14	是	100.00	100.00	50	27.09	11	否	32.45	31.64
22	91.73	11	是	99.42	99.42	51	16.35	6	否	2.93	0.00
23	41.55	14	是	83.98	69.47	52	20.58	6	否	4.25	4.25
24	37.05	11	是	54.34	44.95	53	5.89	8	否	2.33	0.00
25	217.32	4	是	100.00	100.00	54	29.40	1	否	1.63	1.63
26	145.05	7	是	99.98	99.98	55	23.40	2	否	1.35	1.35
27	84.35	9	是	97.73	97.73	56	51.26	7	否	50.87	50.87
28	32.92	13	是	62.57	81.36	57	40.33	11	否	61.60	60.06
29	213.07	4	是	100.00	100.00	58	47.10	2	否	10.58	15.88

类型	预测未发生		预测发生
类型	逻辑回归模型	贝叶斯公式修正模型	逻辑回归模型	贝叶斯公式修正模型
实际未发生	24	27	5	2
实际发生	2	1	27	28

降雨历时/d	北吕梁山片区	北太行山片区	晋南片区	南吕梁山片区	太岳山片区
3	57.10	30.70	56.81	42.67	35.81
7	47.23	29.36	49.59	40.84	33.89
10	40.96	28.39	44.78	39.52	32.52