Effects of rainfall pattern classification methods on the probability estimation of typhoon-induced debris-flow occurrence

Debris flow is one of the major disaster types caused by the extreme rainfall events induced by typhoons. Typhoon-induced sudden extreme rainfall events can easily trigger debris flows. Typhoon-induced extreme rainfall events exhibit greater suddenness and unpredictability compared to those induced by other meteorological elements. Significant variations exist in typhoon-induced extreme rainfall events from year to year (Zhu et al. 2024). Empirical rainfall thresholds, calibrated using physical models for specific slope conditions, have the potential to predict the debris-flow occurrences (Zhang et al. 2020; Zeng et al. 2023). According to the percolation model and the slope stability model of unsaturated soil slope, advanced-, delayed-, intermediated-, and uniform-pattern rainfall events exhibit different failure probabilities and times under unsaturated slope conditions (Ran et al. 2018; Tang et al. 2018; Chang et al. 2021). Classifying rainfall patterns based on observed rainfall events enhances the accuracy of predicting debris-flow occurrence through the application of stochastic rainfall models (Garcia & Aranda 1993). Additionally, it has also been confirmed that the prediction accuracy of debris flow can be improved by using a greater variety of rainfall patterns (Zhao et al. 2022). Classifying rainfall patterns based on debris-flow events can effectively identify the contribution of various rainfall patterns to the occurrence of debris flow (Ni & Song 2020). However, few quantitative studies focus on the effects of rainfall classification methods on debris-flow prediction. Indeed, the foundation of quantitative studies has been laid. Many scholars have studied the rainfall pattern classification techniques, such as Pilgrim & Cordery, K-Means, dynamic time warping (DTW), self-organizing maps (SOM), the Chicago method, and the Huff method (Keifer & Chu 1957; Huff 1967; Pilgrim & Cordery 1975; Serrà & Arcos 2014; Gao et al. 2018). A study of typhoon-induced extreme rainfall prediction shows that tens of attributes are needed to build usable models for specific sites (Wei & Chou 2020). The limitation of data collection regarding typhoon rainfall events has historically hindered in-depth studies of the relationship between rainfall patterns and debris-flow occurrences. However, leveraging data from multiple stations or remote sensing can effectively discern the characteristics of typhoon-induced extreme rainfall events (Nayak & Takemi 2020; Wei & Chou 2020; Yang & Duan 2020; Fang et al. 2021). Furthermore, based on the knowledge of rainfall patterns and classifications, numerous stochastic rainfall models have been proposed (Katz 1977; Chen et al. 2018; Aryal & Jones 2021; Ma et al. 2024). Stochastic rainfall models considering temporal structures (i.e., rainfall patterns) can accurately simulate rainfall duration, depth, and rainfall patterns and can be effectively extended to ungauged sites (Gao et al. 2018). This concept has been successfully employed in the simulation of flash flood events, while the different rainfall patterns significantly affected the simulation and evaluation results (Yuan et al. 2022). Nevertheless, the aforementioned techniques have not been introduced to studies on debris-flow prediction. By considering the classification of the same original rainfall data into multiple rainfall patterns (Yang et al. 2024), the accuracy of forecasting disaster events (floods, debris flow, etc.) can be improved.

Therefore, this study aims to (1) compare the methods of rainfall pattern classifications when applied to typhoon-induced extreme rainfall events and (2) investigate the influence of different methods of rainfall pattern classifications on the estimation of debris-flow occurrence probabilities. In this study, rainfall data from 89 meteorological stations were utilized. Three classification techniques and two normalized ways for rainfall events were employed, resulting in six distinct ways of the classification of rainfall patterns. The probabilities based on six ways of classification were compared.

Wenzhou, with a total land area of 12,110 km², is the southeast prefecture of Zhejiang Province, East China. Wenzhou's terrain is complex, with its seaboard bordering the East China Sea. Consequently, Wenzhou is one of the areas most heavily impacted by typhoons, which constitute one of the primary drivers of geological hazards in Wenzhou.

In this study, the rainfall pattern, depth, and duration are utilized for both description and stochastic generation of rainfall events. The typhoon-induced extreme rainfall events are identified based on the criteria defined by the China Meteorological Administration: (1) rainfall depth for 1 h ≥16 mm; (2) rainfall depth for continuous 12 h ≥30 mm; or (3) rainfall depth for continuous 24 h ≥50 mm. A period of two consecutive hours without rainfall is selected as the cut-off point for defining rainfall events. Typhoon-induced extreme rainfall events from all meteorological stations are aggregated to compensate for data scarcity. The statistical analysis, based on the aforementioned aggregated sample, illustrates the statistical characteristics of rainfall events at each meteorological station during typhoon passage, as elaborated in Table 2.

The distribution of rainfall depth is obtained from the representative rainfall events of each typhoon. The representative rainfall events correspond to the highest rainfall depth observed at 89 stations during each typhoon (see Figure 5). The rainfall characteristics, including rainfall depth, average rainfall intensity, maximum rainfall intensity, and duration, for all stations were extracted from the extreme rainfall events induced by typhoons, as elaborated in section 4.1, Table 2.

The rainfall pattern classification techniques employed in this study include DTW (Cen et al. 1998; Tavenard & Amsaleg 2015), K-Means clustering (MacQueen 1967; Hill et al. 2013; Gao et al. 2018), and SOM (Kohonen 1998; Dai et al. 2020; Hao et al. 2021), representing classical expert knowledge-based techniques, data mining-based techniques, and machine/deep learning-based techniques, respectively. An iterative process is used to ensure that the DTW can find the most suitable rainfall pattern. The initial pattern matrix is shown in Table 1 (Cen et al. 1998). In this study, the six cluster centers of the K-Means were selected by trial-and-error experiments.

This study combines three aforementioned classification techniques and two ways for transforming rainfall events into dimensionless curves, resulting in a total of six distinct classification methods for rainfall patterns (DTW-DC, DTW-CC, K-Means-DC, K-Means-CC, SOM-DC, and SOM-CC).

Given its statistical nature, the application of the I–D rainfall curve necessitates sufficient data to calibrate the curve parameters (A and B). In this study, the values of A and B are 72 and 0.668, respectively, as determined by 27 debris-flow events in Wenzhou spanning from 1990 to 2016 (Chen 2019).

A Monte-Carlo experiment is designed to elucidate the impact of rainfall classification methods on debris-flow occurrence prediction. Stochastic rainfall events for typhoons are generated in the Monte-Carlo experiment.

Rainfall event generation encompasses pattern, duration, and rainfall depth. Generally, these characteristics of rainfall events are interrelated, necessitating consideration of their relationships during event generation (Gao et al. 2018; Wang et al. 2023). Nevertheless, typhoon-induced rainfall depth correlates with the distance between the ground station and the typhoon center, while the duration of the typhoon-induced rainfall events is associated with typhoon movement speed (Wei & Chou 2020; Cao et al. 2024). The moving speed and the diameter of typhoons can be seen as independent (Hong et al. 2016). Thus, in this study, the duration and depth of typhoon-induced rainfall are generated independently.

In this study, for each typhoon, the most extreme rainfall events from all 89 meteorological stations (as detailed in Section 2) are utilized for subsequent analysis. In total, adhering to the definition of extreme rainfall events, 1,896 typhoon-induced extreme rainfall events are selected for pattern and duration generation, while 64 rainfall events are utilized for rainfall depth generation. Monte-Carlo experiments are devised to investigate how rainfall pattern classification methods affect the probability estimation of debris-flow occurrence.

Table 2 shows the maximum and 95th, 75th, 50th, and 25th percentile values for the rainfall characteristics of extreme rainfall events induced by typhoons in Wenzhou. As shown in Table 2, the hourly rainfall intensity is high, and there is significant fluctuation in duration. Generally, large rainfall depth is observed. These findings align with the results of correlation studies in the surrounding region, indicating that the typhoon-induced extreme rainfall, influenced by topography, exhibits high intensity, extensive coverage, and large rainfall depth (Yin et al. 2022).

Tables 3–5 outline the characteristics of the rainfall patterns extracted by the six classification methods, laying the groundwork for further interpretation of the results and methods. With the exception for the A1 and A2 patterns, the rainfall patterns exhibit similar ranges of rainfall depth, intensity, and duration,. The A1 pattern, representing the smallest proportion (2.95%, SOM-CC to 7.17%, K-Means-CC), exhibits the lowest rainfall depth (66.62 mm, SOM-CC to 95.40 mm, K-Means-DC) along with the least rainfall intensity (3.41 mm/h, DTW-DC to 3.73 mm/h, K-Means-CC) and the shortest duration (18.18 h, SOM-CC to 26.29 h, K-Means-DC). While not as pronounced as the A1 pattern, the difference between the A2 pattern and the other rainfall patterns is notable. The temporal concentration ranges from 0.35 to 0.5 (as shown in Tables 3–5), aligning with the temporal distribution of rainfall concentration in summer and autumn in South China (Fu et al. 2023).

Table 6 shows the probability of debris flow induced by typhoon extreme rainfall events of various patterns as determined by the I–D curve. The overall probabilities of debris-flow occurrence, calculated using rainfall pattern classifications of different methods, are similar, ranging from 34.3 to 36.2%.

This study analyzes the variations among rainfall pattern classification methods and their impact on estimating the probability of debris flow. The results show that classifying the sudden and unpredictable extreme rainfall events induced by typhoons is beneficial for estimating the probability of debris flow. Among the assessed methods, the DTW-DC method emerges as the most special option since it is the only method capable of distinguishing the two-peak pattern. The K-Means-CC method exhibits the highest probability of debris-flow occurrence. More rainfall patterns are identified under the dimensionless DC in comparison to the dimensionless CC in the classification of rainfall events among the three rainfall pattern classification methods.

Based on the results and discussion above, the following conclusions can be drawn from this study:

• (1) Although the classification techniques used in this paper are all widely acknowledged and have demonstrated success across various domains, they yield divergent results when applied to the classification of rainfall patterns.

• (2) Variations in the estimated probability of debris-flow occurrence for different rainfall patterns cannot be solely attributed to a single rainfall characteristic, such as temporal concentration or rainfall depth. The A1 pattern is special due to its lower rainfall depth, shorter duration, and higher probability of debris-flow occurrence.

• (3) The overall probabilities of debris-flow occurrence derived from different classification methods are similar, ranging from 34.24–36.01%. However, the DTW-DC and DTW-CC methods underestimated the occurrence probability of fast debris flow (with an occurrence time of <10 h).

However, the I–D rainfall curve utilized in this study for debris flows induced by extreme rainfall events does not consider minor yet significant physical factors such as rainfall infiltration, hydrologic convergence in the vicinity, and subsurface flow. Future studies should integrate physically based debris-flow models with rainfall pattern classification methods.

The authors are grateful for the hard work provided by the Wenzhou Hydrology Management Center for collecting the data used in this study.

All authors contributed to the study conception and design. Material preparation, data collection, and data organization were performed by Z.B., L.L., and Y.Y. Conceptualization, methodology, and funding acquisition were performed by Z.B. The first draft of the manuscript was written by Z.B. and Y.Y., and project management, supervision, and review were performed by L.G.. All authors read and approved the final manuscript.

This work is supported by the Zhejiang Natural Science Foundation (LZJWY22D010001) and the Zhejiang Xinmiao Talents Program (2022R429A029).

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.