Introduction

As one of the widespread geological disasters in mountainous areas around the world, debris flows are characterized by fast and turbulent flows of rock debris within steep river channels or gullies, which seriously threaten the lives and property of local residents1. Rainfall, especially short-duration heavy rainfall, has been identified as one of the most important triggering factors for the occurrence of debris flows2,3,4,5,6,7,8,9,10,11,12,13. It is therefore critical to investigate the relationship between rainfall and debris flow events and to establish effective warning systems5,6,14,15,16,17,18.

Different from other passively monitoring methods19, such as pore water pressure, ground vibration20, infrasound21, flow velocity, and depth22, the rainfall monitoring is an effective method to predict the occurrence of debris flows before their actual occurrences23,24. Currently, there are two means to determine the rainfall thresholds, one is the mathematical statistics15,16,25,26,27,28,29,30 and the other is the physical simulation31,32,33.

The statistical method is much more popular to determine the threshold values based on the relationship between rainfall characteristics (or rainfall indices) and debris flow events33. Therefore, how to accurately capture rainfall characteristics becomes critically important. Rainfall characteristics considered in theoretical models generally include the average intensity, maximum intensity, triggering intensity, peak intensity of the rainfall. Moreover, the duration, antecedent effective amount, daily amount, average amount, as well as the average area amount of rainfall should also be well accounted for10,15,25,34,35,36,37,38,39,40,41. Traditional prediction models for rainfall are generally the average rainfall intensity-duration threshold model. However, the monitoring and warning work for debris flow disasters in the arid and semi-arid regions of northwest China mainly relied on the traditional threshold models (i.e., rainfall duration and rainfall intensity). The higher false alarm rate (i.e., 74.54%.) significantly disrupts the normal lives of local residents. Proposing a new monitoring and warning model with acceptable accuracy is crucial for the local area.

It has been well noted that the triggering rainfall and antecedent effective precipitation (AEP) are two factors significantly affecting the formation of debris flows42. Among them, the role played by the AEP is to enhance surface runoff during the occurrence of rainfall43,44. Moreover, the AEP somehow reduces the shear strength of the loose in debris flow channels, associated with the increases of solid material required for debris flow formation45. On the other hand, the AEP makes it easy to carry soil by runoff, accelerating the occurrence of the debris flow. Most importantly, the AEP significantly influences the parameters α and β in the I-D threshold curve46. It is therefore believed that considering the influence of AEP on the rainfall threshold models can improve the accuracy of debris flow prediction.

The threshold of rainfall can be the constant values for the certain rainfall, which is generally related to the cumulative rainfall, hourly rainfall intensity, or the AEP47. Sometimes, it can also be expressed by two curves of rainfall parameters, such as the rainfall intensity-duration threshold curve25 and the rainfall intensity-antecedent rainfall curve32. One of the most popular models is the intensity (I) and duration (D) curve19. The relationship between daily rainfall and antecedent rainfall was also investigated by scholars48. Moreover, the combined impact of daily rainfall intensity and duration on rainfall thresholds was also previously evaluated40. It is evident that previous research predominantly focused on the binary threshold curves. Although some scholars have quantified the influence of the AEP on thresholds or the impact of AEP on I-D threshold curves46, it failed to integrate it into the mudslide threshold judgement formula, while AEP is only a part of the pre-excitation rainfall. In this study, the direct pre-excitation rainfall and AEP were integrated into the total effective rainfall prior to mudslide excitation (EREP) used to create the mudslide I-D-E rainfall threshold judgement model (Supplementary information).

In this study, we take the debris flow in General Gully as an example and consider that in the arid and semi-arid areas, the rainfall in the short and medium term has a greater impact on the occurrence of debris flow disasters. We form a new threshold judgement model by integrating the factors of the total amount of effective rainfall in the early period on the basis of the former I-D threshold judgement formula. The purpose of this paper is to put forward a threshold judgement model that is applicable to the arid and semi-arid areas, and is more accurate and rich in the consideration of factors compared to the former model. The purpose of this paper is to propose a threshold judgment model that is applicable to the arid and semi-arid areas and is more accurate and rich in factor consideration than the previous model. At the same time, the multifactor threshold judgment model developed in this study can provide a technical reference for monitoring and prediction of debris flow in arid and semi-arid areas.

Geological conditions of the research area

Jiangjungou, a typical gully located along the eastern side of Jiangjun Mountain in Altay City, Northwest China, is of the erosion and denudation tectonic. Belonging to the low mountain landform, the overall terrain of Jiangjungou is higher in the east and lower in the west with a length of 7 km and a drainage area of 16 km2. Note that the Kran River crosses the gully at the altitude of 1314 m to 800 m (Fig. 1). The regional tectonic movement of the research area (N88°03′–88°18′, E47°49′–47°52′) is intense. The study area is located in the climate zone of the middle temperate sub-arid region and the arid region, it is a typical temperate continental cold climate, summers are hot and dry, and winters are bitterly cold. The weathering effect is relatively strong, 85% of which is exposed rocks with obvious fractures and poor integrity. Because that the main rocks distributed in this area are mica, slate, and sandstone, some fractured rocks are widely distributed on slopes when they are exposed and affected by fragmentation and weathering. The estimated accumulation of loose deposites in the research region is over 2.4 × 106 m3 in total, as reported by the No.2 Hydrogeological and Engineering Geological Brigade of Xinjiang, China.

Fig. 1
figure 1

Overview of the research area (Cartography with arcgis 9.2 https://www.arcgis.com/index.html).

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Rainfall data collection and processing

Rainfall data collection

The rainy season of the research area generally starts from May to October), the precipitation of which accounts for 65.3% of the overall annual total. As reported, there were 18 debris flow events that occurred during the rainy season, in particular, ranging from the July and August. There were 2 debris flow during the snow season (from the November to March of the next year), the snowfall during which accounts for 30.1% of the annual snowfall. From 1954 to 2022 that 34 heavy rain, snow-melt flood, and debris flow events occurred, resulting in cumulative impacts on 106,047 people and a 729.5 km2 area. The rainfall data analyzed in the present research range from 1984 to 2022, most of which were obtained from the Hydrological Survey Bureau and Meteorological Bureau before the implementation of on-site monitoring equipment in 2010. After the installation of two rainfall monitoring devices at the mouth and middle section of Jiangjungou in 2021 by the Xinjiang Institute of Geological and Environmental Monitoring, the high-resolution rainfall data (with a rainfall resolution of 0.1 mm and an observation interval of 1 min) were also put into consideration.

Rainfall data processing

It has been well noted that debris flows are typically triggered by specific rainfall (Fig. 2), which may be the short-term high-intensity rainfall or long-term and low-intensity rainfall. Analyzing the relationship between debris flows and rainfall parameters including the intensity (I), duration (D), antecedent effective precipitation (AEP) (\(R_{{\text{a}}}\)) and rainfall before the outbreak of the day (\(D_{{\text{q}}}\)) becomes critical. Based on the analysis of debris flows occurred in Jiangjungou, the outbreak of which is the attributed to the combined effects of antecedent rainfall and short-term intense rainfall. That is, the rainfall during the whole debris flow event can be categorized into antecedent rainfall before the occurrence of the debris flow, rainfall that triggers the debris flow, as well as the continuous rainfall after the debris flow event.

Fig. 2
figure 2

Schematic Diagram of Rainfall Process.

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Currently, there is no unified standard for the interval between rainfall events. For example, Jan and Lee49 defined it as rainfall not exceeding 4 mm in the hour before the occurrence of the rainfall event, while Zhou and Tang50 defined it as rainfall not exceeding 1 mm in the six hours before the occurrence of the rainfall event. Therefore, in previous studies, the standards of the Ji-Ji earthquake disaster area in Taiwan were mostly adopted51,52,53.

Because of significant regional climate differences, existing standards are not applicable to evaluate the rainfall in Altay. In arid and semi-arid areas, rainfall is mostly intermittent short-term heavy rainfall. This paper refers to the standard of Taiwan Jiji earthquake disaster area and combines the arid and semi-arid climate of the study area with the small amount of rainfall, which is intermittent and other characteristics. The modified baseline was established for Jiangjungou subjected to short-term and high-intensity rainfall, That is, the initiation of rainfall is defined as the point when the rainfall intensity exceeds 0.1 mm/h for five consecutive hours, while the cessation of which corresponds to the intensity drops below 0.1 mm/h. In the present research, 18,812 sets of rainfall data and 24,020 sets of sediment data obtained from Jiangjungou were compared and investigated (Fig. 3), from which 100 effective rainfall events and 22 rainfall-triggered debris flow events were identified from May 2021 to December 2023.

Fig. 3
figure 3

On-site rainfall monitoring data for the study area from 2021 to 2023.

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Critical parameters of rainfalls (e.g., the rainfall duration, triggering rainfall intensity/daily maximum rainfall intensity, cumulative rainfall intensity, antecedent rainfall before triggering as well as the daily rainfall) were extracted by the MATLAB program. The antecedent rainfall amount, which affects the initial soil moisture content and surface runoff54, was subsequently determined. For ease of reference, the antecedent rainfall and daily rainfall amount are denoted as Ra and R0, i.e. \(R_{{\text{a}}}\) usually refers to effective rainfall prior to the day of the mudslide events respectively. Considering that the moisture stored in the soil decreases during the evapotranspiration and drainage processes, it is the effective antecedent rainfall rather than the cumulative antecedent rainfall was adopted. As per the suggestion by Bruce and Clark55, the value of Ra can be calculated by the following equation:

$${R}_{\propto }=\sum_{i=1}^{n}{k}^{i}{R}_{i}$$
(1)

where, \({R}_{i}\) represents the daily rainfall amount before the occurrence of debris flow, n is a number of days to be accounted for, and K represents the decay factor.

Herein, the value of the decay factor is directly affected by the evaporation, vegetation coverage, as well as the hydrological characteristics of the weathered layer. Referring to the research conducted by Xawkat et al.56, the recommended value of the decay factor ranges from 0.80 to 0.85, which is based on the research in Tianshan mountain range. In arid and semi-arid areas, the evaporation effect is obvious, and the vegetation is sparse and mostly bare land, so the value of K should be selected as 0.8. In this paper, according to the local government part of the prevention and warning needs, in order to make the calculated warning value is bigger in order to in the actual process of mudslide early warning, for the crowd to escape time, so the K value was adjusted, according to the previous warning experience will be adjusted from 0.8 K value to 0.81. The in-depth analysis of historic records in Altay, revealed that the short-term heavy rainfall is the main factor resulted in the occurrence of debris flow.Rainfall in the study area is mostly short-term heavy rainfall, showing intermittent, small rainfall, evapotranspiration, etc.. After the event division, it was found that the duration of continuous rainfall in the study area is mostly within 3 days and after the rainfall intensity is reduced by greater than 3 days, the rainfall amount of retention is relatively small. Therefore, the time period of 3 days is adopted to calculate the value of Ra in the present research.

Rainfall characteristics

Figure 5 depicts monthly and daily information on rainfall periods for the 122 rainfall events., suggesting that about 90% of the rainfall events and all debris flow events occurred between the April and October, Among them, 30% of debris flows occurred in June between 04:00 and 08:00 and 14:00–20:00, which generally agreed with the occurrence of rainfall events (12:00–14:00 and 16:00–18:00). As illustrated in Figs. 4, 5, it is obvious that the intensity of rainfall events triggering debris flows is significantly higher than that of rainfall events not triggering debris flows, further demonstrated that the rainfall event is the trigger to debris flows.

Fig. 4
figure 4

Rainfall Event Characteristic Relationship Diagram (red marker: DF events and “blue marker: non-DF events).

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Fig. 5
figure 5

Distribution of Rainfall Events from 2021 to 2023: (a) monthly and (b) hourly.

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Establishment of the theoretical model

To determine whether rainfall events will trigger debris flows, widely-used models (e.g., XGBoost, support vector machines, Bayesian models, and logistic regression) were selected for comparative analysis. Notice that the SPSS software was employed to build a binary classification predictive model, in which the rainfall parameters are adopted as the input variables while the occurrence of debris flow events is determined as the response variable. To evaluate the performance of theoretical models’ threshold, a confusion matrix was utilized. As defined by Peirce57 and Townsend58, four key metrics were given in below, which are the accuracy, true positive rate (TPR), false positive rate (FPR), and F1 score.

$$Accuracy=\frac{TP+TN}{TP+TN+FP+FN}$$
(2)
$$True positive rate(TPR)=\frac{TP}{TP+FP}$$
(3)
$$False positive rate(FPR)=\frac{FP}{FP+TN}$$
(4)
$$F1-Score=\frac{2\times precision\times recall}{percision+recall}=\frac{2TP}{2TP+FN+FP}$$
(5)

in which, TP represents the number of True Positives while the FP denotes False Positives. FN and TN are the numbers of False Negatives and True Negatives, respectively. Note that the values of TPR, FPR, and F1 Score range from 0 to 1, the larger value of which indicates excellent model fitting or superior predictive capability.

Test results

The 22 rainfall triggered debris flow events were brought into each of the four models to produce four confusion matrices (Fig. 6). The XGBoost accuracy is 84%, precision is 86.67%, recall is 84%, and f1-score is 0.79; the plain Bayesian accuracy is 72%, precision is 69.762%, recall is 72%, and f1-score is 0.71; the support vector machine accuracy is 80%, precision is 64%, and recall is 80%, and f1- score is 0.71; logistic regression model has an accuracy rate of 76%, precision rate of 72.121%, recall rate of 76% and f1-score of 0.732. These results show that XGBoost outperforms the other three models overall, in terms of accuracy, precision, recall, and F1 score.

Fig. 6
figure 6

Confusion Matrix for different Models: (a) XGBoost; (b) Naive Bayes; (c) Support Vector Machine; (d) Logistic Regression Model.

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Significance of rainfall characteristics

The bivariate correlation analysis was conducted with IBM SPSS statistics software (version No. 26, https://www.ibm.com/software) to explore the positive correlations between rainfall metrics and the occurrence of debris flows. Calculated results demonstrated that the Early effective rainfall (Ra) positively correlated the occurrence of debris flows (r = 0.0442, P < 0.01). Moreover, Triggered hourly rainfall (I), and duration of rainfall (D) exhibited a stronger positive correlation (r = 0.384, P < 0.01). Similarly, direct rainfall before excitation (Dq) is also positively correlated with the debris flow (r = 0.0442, P < 0.01). Overall speaking, all parameters proposed in this study significantly positively correlated to the occurrence of the debris flow.

When the XGBoost model with higher accuracy was selected for further calculated, it can be seen that the duration of rainfall (D) and direct rainfall before excitation (Dq) before the occurrence of debris flow are two major factors to be considered, the weights of which contributes to 58 and 24% respectively. Differently, the weights of Triggered hourly rainfall (I) and early effective rainfall (Ra) are only 13 and 5%, respectively (Fig. 7).

Fig. 7
figure 7

Importance Plot of XGBoost Model.

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Characteristics of debris flow events and non-debris flow events are much different, which can be seen from Fig. 8. It is obvious that debris flows generally happens if the rainfall duration exceeds 8 h. The other obvious observation is the threshold values of the direct rainfall amount (Dq). If Dq > 7.1, the rainfall will easily triggered debris flows and vice versa. The likelihood of debris flows also increases, when the values of the rainfall intensity or the maximum rainfall (I) is equal to 2.35, or the value of effective rainfall (Ra) exceeds 13.19. These above patterns suggests that the occurrence of debris flows is positively correlated with effective rainfall prior to the occurrence, rainfall density and rainfall duration, which agrees well with previous investigation.

Fig. 8
figure 8

Boxplot of Rainfall Characteristics.

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Determination of rainfall thresholds

The widely accepted thresholds of rainfall are based on the relationship between the empirical rainfall intensity and rainfall duration, as documented by Guzzetti et al.5,6, Baum and Godt16, and Lee et al.59. The general expression of the I-D threshold is as follows:

$$I=c+\propto {D}^{\beta }$$
(6)

in which, I and D represent the rainfall intensity and rainfall duration, respectively. Other parameters, such as \({\text{c}}\)、\(\alpha\) and \(\beta\) are the constant values.

To accurately simulate the empirical relationship between I and D, these two variables are plotted in Fig. 9 for further comparison. It can be seen from Fig. 9 that approximately 70% of the rainfall events triggered debris flows in Jiangjungou predominantly ranges from three to six hours.

Fig. 9
figure 9

(a) Risk zoning map of rainfall duration versus rainfall intensity, (b) Risk zoning map of EREP versus rainfall intensity (red marker: DF events and “blue marker: non-DF events).

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With reference to the statistical model adopted by Jiang et al.’s60, the probability curves of debris flow events for 122 rainfall events were calculated in MATLAB using the least squares and plain Bayesian methods according to Eq. 6 The boundary equation for the occurrence of debris flow is listed in below:

$$I=1.8669{D}^{-0.8383}+0.907$$
(7)

The median threshold in this Equation was derived from the Naive Bayesian probability analysis, in which the probability curve corresponding to the point with 50% chance of occurring was adopted. This equation can not only demonstrate the relationship between rainfall intensity and duration, but also predict the occurrence of debris flows.

Subsequently, the 90% probability curve in the graph was calculated, where the equation for the 90% threshold was derived via the equation of

$$I=23.4575{D}^{-0.978}+4.647$$
(8)

The graph is divided into high-risk zone, medium risk zone and low risk zone by these two thresholds. The high-risk area is above the 90% curve, which signifies a very high likelihood of debris flow occurrence. The medium-risk area lies between the 90% and 50% curves, for which there is a comparatively lower probability of debris flow within the intensity (I) and duration (D) curves.

Traditionally, both the monitoring and early warning systems for debris flows highly depend on a single equation related to rainfall intensity, duration, or prior effective rainfall, resulting in frequent false alarms or missed alerts. In the present research, a new evaluation system with the application of the Naive Bayes model was developed to perform a statistical analysis of the EREP (EREP = Dq + Ra) based on 122 debris flow events. Once the threshold curves were plotted, both the equation for the median threshold and a 90% probability curve of debris flow occurrence can be obtained and three risk zones are consequently marked (see Fig. 9).

The critical rainfall amounts, denoted as \({I}_{{E}_{50}}\)、\({I}_{{D}_{50}}\)、\({I}_{{E}_{90}}\) and \({I}_{{D}_{90}}\), are obtained based on the derived threshold formulas for debris flow events and non-debris flow events. According to the feature weight results calculated by XGBoost, the impact parameters of I and D are obtained based on factors such as rainfall duration, antecedent effective rainfall, and directly preceding-day rainfall.That is, the total effective rainfall in the previous period: rainfall duration is 0.29 (0.24 + 0.05): 0.58 = 1: 2, through the ratio of the two to derive the total effective rainfall in the previous period and the rainfall duration of the impact of the weight of the combined rainfall intensity threshold. This allows for the determination of the comprehensive rainfall intensity limit, expressed as:

$${I}_{A}=\frac{1}{3}{I}_{E}+\frac{2}{3}{I}_{D}$$
(9)

Combining Eq. (8) with the previously mentioned curve threshold formulas yields two additional formulas (Fig. 10). The median threshold surface (i.e., the probability surface where there is a 50% chance of a debris flow occurring) can be expressed as:

$${I}_{{A}_{50}}=1.442{D}^{-0.8383}-0.0367E+3.283$$
(10)

and the lowest threshold surface (i.e., the surface representing a 90% probability of occurrence) can be expressed as:

Fig. 10
figure 10

Threshold judgement surfaces with different probabilities: (a) Threshold judgement surfaces with a 50% probability of mudslide events; (b) Threshold judgement surfaces with a 90%probability of mudslide events.

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$${I}_{{A}_{90}}=15.6383{D}^{-0.978}-0.0123E+5.1603$$
(11)

The real-time rainfall intensity I recorded by monitoring instruments is compared with the comprehensive rainfall intensity boundary to calculate the differences, \({C}_{50}\) (Difference between real-time rainfall intensity and threshold rainfall intensity for a 50 per cent probability surface) and \({C}_{90}\) (Difference between real-time rainfall intensity and threshold rainfall intensity for 90 per cent probability surface) (see Fig. 11). Based on these differences, the corresponding judgment criteria are set: if \({C}_{50}\le 0\), the debris flow event is classified as low risk; if \({C}_{90}\le 0<{C}_{50}\), it is classified as medium risk; and if \(0<{C}_{90}\), it is classified as high risk.

Fig. 11
figure 11

Warning Model Diagram.

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Validation of proposed model

As depicted in Fig. 12, a total of 36 instances, for which the values of \({C}_{50}\) exceeded zero, were identified, when historical debris flow events are adopted for regression validation. Among them, there are 18 debris flow that actually occurred, with the accuracy of 50%. The reason for the missed rate of 18.2% in predicting debris flow is primarily affected by the snow melting in March. Moreover, there are eight debris flows successfully confirmed, which is among nine recorded events with \({C}_{90}\) greater than zero.

Fig. 12
figure 12

Monitoring and Early Warning Model Validation Diagram (a), Monitoring and Early Warning Model Validation Diagram (b) (red marker: DF events and “blue marker: non-DF events).

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Discussion

Theoretical analysis

Feature extraction from rainfall monitoring data revealed that the rainfall duration of debris flow events in Jiangjungou is always 8 h or even longer, while the value of the EREP generally exceeded 20.29, while the rainfall intensity is usually 2.35 mm/h. This observation aligns well with the weights given in the XGBoost model. That is, the rainfall duration has the greatest impact, followed by the EREP and rainfall intensity. Thus, the total effective prior rainfall (EREP) significantly contributes to the likelihood of debris flow occurrence and lowers the debris flow warning threshold, which are consistent with previous studies conducted by Chen et al.61, Zhao et al.62, and Hirschberg et al.24.

Four machine learning methods (i.e., the XGBoost, Support Vector Machines, Naive Bayes and logistic regression) were adopted to determine the optimal weights of rainfall variables on debris flow occurrence. These variables included rainfall duration, effective prior rainfall, rainfall on the day before the trigger, and hourly/maximum rainfall intensity. By combining antecedent effective rainfall with the direct rainfall on a given day, the concept of total antecedent effective rainfall (EREP) was proposed in the present research. Furthermore, the proposed EREP factor was incorporated into the rainfall intensity-duration threshold empirical formula. This integration yielded a novel ternary threshold determination formula associated with a refined curve to assess rainfall thresholds for debris flow.

It is since 2021 that the false alarm rate of debris flows is about 74.54%, the data of which was provided by the on-site monitoring equipment installed by the Xinjiang Geological Environment Monitoring Institute. When the multiple models developed in this research was adopted, 18 debris flow were successfully predicated among 36 cases with an occurrence probability exceeding 50%. Furthermore, 8 out of 9 instances with a probability above 90% were verified, the false alarm rate of which is about 11.1%. It is thus apparent that the modified theoretical model is much more accurate, which is much suitable for the debris flow monitoring and early predication in Altay.

Looking ahead

In this study, on the basis of the previous I-D threshold formula, according to the climate of arid and semi-arid regions and the characteristics of mudslide disaster outbreaks, a new rainfall event classification standard is adopted, and the EREP factor is introduced so as to establish the I-D-E threshold judgement model, i.e.\(I = \alpha D^{ - \beta } - \delta E + c\),\(I\), where is the rainfall intensity; \(D\) is the rainfall duration;\(E\) is the total effective rainfall in the previous period;\(\alpha\),\(\beta\) and \({\text{c}}\) are other parameters. When applied in other areas with different climatic and geological conditions, the relationship between the characteristics of rainfall events and the occurrence of disasters needs to be determined, and then the rainfall event data should be fitted according to a simplified formula to derive a threshold judgement surface applicable to the local situation. Data This study on the one hand found that the occurrence of mudslide events is mostly related to snowmelt, while the monitoring and warning of mudslides pay less attention to the amount of snowfall and snowmelt. During the snowmelt period, the monitoring error of rainfall is larger, which is the main reason for the larger error of the model in this paper, so it is necessary to further study the monitoring and warning and risk assessment of mudslides during the snowmelt and snowfall periods, which is especially important for high-altitude and high-latitude areas. In this study, only the rainfall threshold for mudflow was established, and in the future, the rainfall monitoring threshold can be combined with the mud level monitoring threshold to form a more accurate and comprehensive monitoring and warning model.

On the other hand, it was found in the study that it is necessary to carry out multiple monitoring for monitoring and early warning of mudslides, and multiple monitoring means can confirm the accuracy of the data, so it is recommended that the governmental part and relevant practitioners should adopt multiple monitoring means in the process of monitoring mudslides, and at the same time make a good record of the long-time disaster of mudslides, which will be more conducive to the further study of monitoring and early warning of mudslides.·

Conclusions

The large database of historical rainfall records in Jiangjungou was adopted to explore the triggering conditions of debris flows. The modified theoretical model was also established in the present research, which contributes to the outcomes listed in below:

  • (1) Four theoretical models (i.e., the naive Bayes, support vector machine, logistic regression, and XGBoost) are applied to determine the weight of rainfall characteristics extracted from the database, suggesting that the most significant factor is rainfall duration, followed by the total antecedent effective rainfall.

  • (2) The concept of the total antecedent effective rainfall total (EREP), the primary factor affecting the occurrence of debris flow, was proposed and incorporated into the empirical formula for rainfall intensity-duration threshold, resulting in a new ternary threshold determination formula and judgment surface with superior accuracy.

  • (3) The probability curves of rainfall intensity-duration (I-D) and intensity-EREP (I-E) thresholds were obtained by the least squares method with Bayesian modelling, which were integrated and weighted according to the optimal weights to generate the probability surfaces and warning zones of the mudslides. A general formula for the associated I-D-E surface is proposed:.(4) In this paper, the rainfall threshold judgement curves for the study area are as follows: the median threshold surface: and the lowest threshold surface: . The accuracy of the modified model for the debris flow occurrence is superior than existing model, the false alarm rate of which is within 11.1%.