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

Abstract

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

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.

Figures/Tables 13

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Tab. 1

Tab. 2

Fig. 6

Tab. 3

Test results of samples from 2021 to 2023"

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

Tab. 3

Tab. 4

Fig. 7

Tab. 5

Fig. 8

References 44

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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

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

Probability of landslide disasters induced by rainfall based on Bayesian formula correction

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