The frequent occurrence of typhoons causes geological disasters, such as debris flow and landslide, by bringing extreme rainfall events. Due to the lack of data collection on extreme rainfall events caused by typhoons, the relationship between rainfall patterns and debris flow has not been deeply studied. Therefore, based on hourly rainfall data during typhoons in Wenzhou from 1980 to 2017, this study used a variety of methods to classify the rainfall events and analyze the characteristics of typhoon-induced rainfall events and their impacts on the probability of debris-flow occurrence. Three classification techniques, including dynamic time warping, K-Means cluster, and self-organizing maps, are applied with two ways to normalize rainfall records, including dimensionless rainfall density curves and dimensionless rainfall cumulation curves, for extracting rainfall patterns from recorded 1 h rainfall data. The rainfall patterns are then used for the estimation of typhoon-induced debris-flow occurrence probability. Results show that different methods present different rainfall patterns. The probability of debris flows varies with different patterns of rainfall events. The research results help deepen the understanding of typhoon rainfall events and debris-flow disaster prevention in the region and contribute to regional flood control and disaster reduction.

  • Different rainfall pattern classification methods present distinct rainfall patterns.

  • For refined rainfall patterns, the dimensionless density curve is more suitable than the dimensionless cumulation curve for rainfall pattern classification methods.

  • Although different classification methods yield diverse rainfall patterns, the overall probabilities of debris-flow occurrence are close.

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.

The hourly rainfall data during typhoons used in this study were collected from 89 meteorological stations (refer to Figure 1). The distances between adjacent stations are from 1.63 to 20.59 km, adhering to the standards set by the Chinese government.
Figure 1

89 meteorological stations in Wenzhou.

Figure 1

89 meteorological stations in Wenzhou.

Close modal
A flowchart of the framework in this study is shown in Figure 2, which includes the main steps of the methodology.
Figure 2

Framework of this study.

Figure 2

Framework of this study.

Close modal

Statistical analysis of rainfall events

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.

An entropy-based temporal concentration () of precipitation (Li et al. 2017) is employed to quantify the variations among different rainfall patterns. The formula to compute the temporal concentration is given by the following equation:
formula
(1)
where N represents the number of time steps in the rainfall patterns ( in this study), denotes the (dimensionless) rainfall depth at the th time step, and represents the fraction of rainfall depth of the th time step. The range of Q spans from 0 (indicating a uniform rainfall pattern) to 1 (indicating a completely concentrated rainfall pattern).

Methods for the classification of rainfall patterns

In this study, rainfall patterns characterize the relative rainfall intensity over dimensionless time intervals and normalized rainfall depth. As shown in Figure 3, the rainfall pattern will be presented in both density and cumulation form. The dimensionless density curve (DC) is represented in Equation (2), and the dimensionless cumulation curve (CC) is represented in Equation (3):
formula
(2)
formula
(3)
where represents the dimensionless rainfall depth (proportion of the total rainfall depth) at the dimensionless time interval; d denotes the total duration of rainfall events; represents the dimensionless interval corresponding to the observation time t, ; is the total rainfall depth; is the cumulative rainfall depth; and corresponds to the dimensionless cumulative rainfall depth, . Each rainfall event's duration can be equally divided into intervals . In this study, .
Figure 3

Dimensionless rainfall DC and dimensionless rainfall CC of a rainfall event.

Figure 3

Dimensionless rainfall DC and dimensionless rainfall CC of a rainfall event.

Close modal

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.

Table 1

The initial matrix for the DTW

Rainfall patterns
Advanced pattern 7/23 6/23 4/23 3/23 2/23 1/23 
Delayed pattern 1/26 2/26 3/26 6/26 8/26 6/26 
Central pattern 1/20 4/20 7/20 5/20 2/20 1/20 
Uniform pattern 3/21 4/21 3/21 4/21 3/21 4/21 
Two-peak (advanced and delayed) 5/20 3/20 1/20 2/20 5/20 4/20 
Two-peak (advanced and central) 4/18 2/18 3/18 5/18 3/18 1/18 
Two-peak (central and delayed) 2/23 3/23 7/23 4/23 2/23 5/23 
Rainfall patterns
Advanced pattern 7/23 6/23 4/23 3/23 2/23 1/23 
Delayed pattern 1/26 2/26 3/26 6/26 8/26 6/26 
Central pattern 1/20 4/20 7/20 5/20 2/20 1/20 
Uniform pattern 3/21 4/21 3/21 4/21 3/21 4/21 
Two-peak (advanced and delayed) 5/20 3/20 1/20 2/20 5/20 4/20 
Two-peak (advanced and central) 4/18 2/18 3/18 5/18 3/18 1/18 
Two-peak (central and delayed) 2/23 3/23 7/23 4/23 2/23 5/23 

Note: In the above table, the numerator represents the percentage of rainfall, and the denominator represents the total rainfall.

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).

Figure 4 shows all potential rainfall patterns that may be identified by the aforementioned classification methods. The advanced patterns (A1, A2, and A3, representing rainfall peaks on the first, second, and third periods, respectively) and delayed patterns (D1, D2, and D3, representing rainfall peaks on the fourth, fifth, and sixth periods, respectively) exhibit one prominent peak (comprising more than 50% of the total rainfall depth) and are differentiated by the position of this peak. The central pattern (C) is distinguished by a low and prolonged rainfall peak. The rainfall depth percentage of the central pattern in the third and fourth periods exceeds 50%, which closely resembles the peaks of other rain patterns with significant rainfall peaks. The uniform pattern exhibits even distribution across each period, with slight decreases observed in the first and last periods. The two-peak pattern is particularly distinctive due to the presence of two rainfall peaks, occurring during the second and last periods. The gradually increased (GI) pattern and gradually decreased (GD) pattern are characterized by rainfall events exhibiting an evident trend of increasing or decreasing rainfall intensity, respectively.
Figure 4

Dimensionless DC of different rainfall patterns.

Figure 4

Dimensionless DC of different rainfall patterns.

Close modal

Triggering thresholds of debris flow: intensity–duration rainfall curve

The intensity–duration (ID) rainfall curve is a robust and effective simplification of triggering thresholds for debris flow (Caine 1980). The applicability of the ID rainfall curve has been proven across a range of rainfall duration from 10 min to 10 days (Caine 1980; Ozturk et al. 2018). The ID rainfall curve is a statistical relationship between rainfall intensity and duration, as expressed in the following equation:
formula
(4)
where I represents the rainfall intensity and D represents the duration (h). A and B are the curve parameters that vary with the geological features of the study area.

Given its statistical nature, the application of the ID 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).

Stochastic generation of rainfall events and Monte-Carlo experiments

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.

The procedure of Monte-Carlo experiments is briefly described as follows:
  • 1. Generation of rainfall depth and duration of typhoon-induced extreme rainfall events: There are 100,000 pairs of rainfall depths and durations being generated in this step. The rainfall depths for the simulated 1a–100a return period typhoon-induced extreme rainfall events follow the Pearson III distribution, as shown in Figure 5. The rainfall duration follows a uniform distribution.

  • 2. Generation of time series of rainfall events with depth, duration, and pattern: The 100,000 pairs of rainfall depth and duration are used in combination with various rainfall patterns to generate rainfall event time series.

  • 3. Probability estimation of debris-flow occurrence: This step involves comparing the ID curve with the rainfall time series to ascertain whether debris flow will occur. Given that each generated rainfall event may exhibit several potential rainfall patterns (i.e., each pair of rainfall depth and duration), this step returns the probability of debris-flow occurrence for all generated rainfall events.

Figure 5

The Pearson III distribution of rainfall depth based on 64 extreme rainfall events.

Figure 5

The Pearson III distribution of rainfall depth based on 64 extreme rainfall events.

Close modal

Statistics of typhoon-induced extreme rainfall events

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).

Table 2

Statistics of typhoon-induced extreme rainfall events

Rainfall depth (mm)Average rainfall intensity (mm/h)Maximum rainfall intensity (mm/h)Duration (h)
Maximum 691 55 109.10 94 
95% 404.40 11.90 58.10 68 
75% 232.50 6.19 33.30 49 
50% 130.50 4.29 22.40 35 
25% 74.85 3.00 15.40 21 
Rainfall depth (mm)Average rainfall intensity (mm/h)Maximum rainfall intensity (mm/h)Duration (h)
Maximum 691 55 109.10 94 
95% 404.40 11.90 58.10 68 
75% 232.50 6.19 33.30 49 
50% 130.50 4.29 22.40 35 
25% 74.85 3.00 15.40 21 

Classification of rainfall patterns

Figure 6 illustrates the classification of rainfall patterns extracted by DTW, K-Means, and SOM from dimensionless rainfall DCs and dimensionless rainfall CCs, while Tables 35 present characteristics of the rainfall patterns. According to Figure 6, it is evident that the classification of rainfall patterns can significantly vary depending on different classification methods. The number of patterns ranges from 4 to 9 across the different classification methods. The DTW-CC method failed to identify advanced and delayed patterns, indicating a limitation in its classification capability. Additionally, the same rainfall pattern obtained through different classification methods exhibits distinct characteristics. For example, in the case of the A1 pattern, the percentage of rainfall depth in the first period ranges from 40% (K-Means-CC) to 60% (SOM-CC), whereas the percentage of rainfall depth in the first and second periods ranges from 60% (K-Means-DC) to 80% (SOM-CC). Notably, only SOM-CC recognizes all one-peak patterns (A1, A2, A3, D1, D2, and D3).
Table 3

Rainfall pattern characteristics based on the DTW

Rainfall patternProportion (%)
Average rainfall intensity (mm/h)
Average rainfall depth (mm)
Rainfall duration (h)
Temporal concentration
DCCCDCCCDCCCDCCCDCCC
8.12 32.17 4.41 4.81 152.67 179.89 34.62 37.36 0.3767 0.3815 
GI 24.37 20.36 4.94 4.64 183.98 164.68 37.27 35.47 0.3934 0.4074 
GD 13.24 25.11 4.42 4.28 161.53 140.83 36.53 32.94 0.4211 0.3917 
A1 5.27 3.41 83.59 24.54 0.4447 
30.06 22.36 5.03 4.93 179.23 177.27 35.66 35.99 0.3900 0.4013 
D1 9.28 4.63 161.71 36.26 0.4360 
2P 9.65 4.04 144.28 35.74 0.4250 
Rainfall patternProportion (%)
Average rainfall intensity (mm/h)
Average rainfall depth (mm)
Rainfall duration (h)
Temporal concentration
DCCCDCCCDCCCDCCCDCCC
8.12 32.17 4.41 4.81 152.67 179.89 34.62 37.36 0.3767 0.3815 
GI 24.37 20.36 4.94 4.64 183.98 164.68 37.27 35.47 0.3934 0.4074 
GD 13.24 25.11 4.42 4.28 161.53 140.83 36.53 32.94 0.4211 0.3917 
A1 5.27 3.41 83.59 24.54 0.4447 
30.06 22.36 5.03 4.93 179.23 177.27 35.66 35.99 0.3900 0.4013 
D1 9.28 4.63 161.71 36.26 0.4360 
2P 9.65 4.04 144.28 35.74 0.4250 
Table 4

Rainfall pattern characteristics based on the K-Means

Rainfall patternProportion (%)
Average rainfall intensity (mm/h)
Average rainfall depth (mm)
Rainfall duration (h)
Temporal concentration
DCCCDCCCDCCCDCCCDCCC
18.20 4.29 148.94 34.68  0.4034 
GI 26.42 4.73 176.67 37.36 0.3584  
A1 6.28 7.17 3.63 3.73 95.40 89.81 26.29 24.06 0.4408 0.4310 
A2 18.78 22.31 4.49 4.60 157.24 169.29 35.02 36.83 0.4036 0.4195 
A3 18.62 4.87 191.07 39.22 0.4146  
19.04 5.04 185.98 36.91  0.4081 
D2 17.14 13.61 4.66 4.74 169.48 176.22 36.35 37.16 0.4081 0.4495 
D3 12.76 19.67 4.98 4.94 153.42 181.46 30.78 36.72 0.4133 0.4020 
Rainfall patternProportion (%)
Average rainfall intensity (mm/h)
Average rainfall depth (mm)
Rainfall duration (h)
Temporal concentration
DCCCDCCCDCCCDCCCDCCC
18.20 4.29 148.94 34.68  0.4034 
GI 26.42 4.73 176.67 37.36 0.3584  
A1 6.28 7.17 3.63 3.73 95.40 89.81 26.29 24.06 0.4408 0.4310 
A2 18.78 22.31 4.49 4.60 157.24 169.29 35.02 36.83 0.4036 0.4195 
A3 18.62 4.87 191.07 39.22 0.4146  
19.04 5.04 185.98 36.91  0.4081 
D2 17.14 13.61 4.66 4.74 169.48 176.22 36.35 37.16 0.4081 0.4495 
D3 12.76 19.67 4.98 4.94 153.42 181.46 30.78 36.72 0.4133 0.4020 
Table 5

Rainfall pattern characteristics based on the SOM

Rainfall patternProportion (%)
Average rainfall intensity (mm/h)
Average rainfall depth (mm)
Rainfall duration (h)
Temporal concentration
DCCCDCCCDCCCDCCCDCCC
14.98 4.29 153.78 35.88  0.4075 
GI 22.10 4.76 178.02 37.42 0.3963  
GD 18.09 12.61 4.52 4.17 178.81 139.45 39.56 33.44 0.4087 0.4115 
A1 5.43 2.95 3.48 3.66 87.14 66.62 25.06 18.18 0.4459 0.4697 
A2 6.12 9.81 4.21 4.18 103.77 139.01 24.62 33.25 0.4323 0.4344 
A3 8.76 4.98 184.18 37.00 0.4480  
12.55 42.77 5.02 5.11 187.28 190.36 37.32 37.24 0.4296 0.3752 
D1 8.49 6.17 4.59 4.98 163.89 169.20 35.73 33.97 0.4394 0.4559 
D2 9.76 10.71 4.67 4.42 171.41 171.09 36.68 38.75 0.4326 0.4327 
D3 8.70 4.89 153.45 31.37 0.4325  
Rainfall patternProportion (%)
Average rainfall intensity (mm/h)
Average rainfall depth (mm)
Rainfall duration (h)
Temporal concentration
DCCCDCCCDCCCDCCCDCCC
14.98 4.29 153.78 35.88  0.4075 
GI 22.10 4.76 178.02 37.42 0.3963  
GD 18.09 12.61 4.52 4.17 178.81 139.45 39.56 33.44 0.4087 0.4115 
A1 5.43 2.95 3.48 3.66 87.14 66.62 25.06 18.18 0.4459 0.4697 
A2 6.12 9.81 4.21 4.18 103.77 139.01 24.62 33.25 0.4323 0.4344 
A3 8.76 4.98 184.18 37.00 0.4480  
12.55 42.77 5.02 5.11 187.28 190.36 37.32 37.24 0.4296 0.3752 
D1 8.49 6.17 4.59 4.98 163.89 169.20 35.73 33.97 0.4394 0.4559 
D2 9.76 10.71 4.67 4.42 171.41 171.09 36.68 38.75 0.4326 0.4327 
D3 8.70 4.89 153.45 31.37 0.4325  
Figure 6

Rainfall patterns classified with DTW, K-Means, and SOM.

Figure 6

Rainfall patterns classified with DTW, K-Means, and SOM.

Close modal

Tables 35 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 35), aligning with the temporal distribution of rainfall concentration in summer and autumn in South China (Fu et al. 2023).

Estimation of the probability of debris-flow occurrence

Probability estimation for debris-flow occurrence is performed on the generated rainfall events. Figure 7 illustrates the correlation between the probability of debris flow and characteristics of rainfall patterns, such as average rainfall depth and temporal concentration. In Figure 7, the A1 patterns derived by different classification methods are clustered in the bottom-right corner of the graph, which are characterized by higher temporal concentration and lower rainfall depth, resulting in higher probabilities of debris flow. Conversely, the other patterns exhibit comparable ranges of temporal concentration, average rainfall depth, and probabilities of debris flow. Upon excluding A1, the correlation coefficient between temporal concentration and the probability of debris-flow occurrence is 0.14, while the correlation coefficient between the average rainfall depth and the probability of debris-flow occurrence is 0.07.
Figure 7

Comparison of the temporal concentration of precipitation and the probability of debris flow.

Figure 7

Comparison of the temporal concentration of precipitation and the probability of debris flow.

Close modal

Table 6 shows the probability of debris flow induced by typhoon extreme rainfall events of various patterns as determined by the ID 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%.

Table 6

Probability of debris flow based on I–D curves

Probability of debris-flow occurrenceDTW
K-Means
SOM
DCCCDCCCDCCC
34.42% 35.06% 37.57% 35.23% 
GI 34.90% 34.88% 35.27% 35.10% 
GD 34.77% 34.48% 34.63% 33.21% 
A1 40.49% 39.95% 42.94% 40.33% 43.72% 
A2 34.26% 34.48% 36.13% 34.79% 
A3 34.06% 33.86% 
34.29% 34.05% 34.12% 33.65% 32.72% 
D1 36.01% 36.09% 37.71% 
D2 36.22% 37.08% 36.25% 35.00% 
D3 33.97% 34.87% 33.78% 
2P 37.87% 
SUM 35.34% 34.65% 35.15% 36.01% 35.15% 34.24% 
Probability of debris-flow occurrenceDTW
K-Means
SOM
DCCCDCCCDCCC
34.42% 35.06% 37.57% 35.23% 
GI 34.90% 34.88% 35.27% 35.10% 
GD 34.77% 34.48% 34.63% 33.21% 
A1 40.49% 39.95% 42.94% 40.33% 43.72% 
A2 34.26% 34.48% 36.13% 34.79% 
A3 34.06% 33.86% 
34.29% 34.05% 34.12% 33.65% 32.72% 
D1 36.01% 36.09% 37.71% 
D2 36.22% 37.08% 36.25% 35.00% 
D3 33.97% 34.87% 33.78% 
2P 37.87% 
SUM 35.34% 34.65% 35.15% 36.01% 35.15% 34.24% 

Figure 8 illustrates the distribution of debris-flow occurrence time, representing the duration from the onset of rainfall to the occurrence of debris flow. The occurrence of fast debris flow (with an occurrence time of <10 h) is less frequent in the experiments conducted using the DTW-DC and DTW-CC methods compared to the other methods.
Figure 8

Distribution of debris-flow time obtained by six classification methods.

Figure 8

Distribution of debris-flow time obtained by six classification methods.

Close modal

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 ID 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.

Aryal
N. R.
&
Jones
O. D.
2021
Spatial-temporal rainfall models based on Poisson cluster processes
.
Stochastic Environmental Research and Risk Assessment
35
(
12
),
2629
2643
.
https://doi.org/10.1007/s00477-021-02046-5
.
Caine
N.
1980
The rainfall intensity: Duration control of shallow landslides and debris flows
.
Geografiska Annaler: Series A, Physical Geography
62
(
1/2
),
23
27
.
https://doi.org/10.1080/04353676.1980.11879996
.
Cao
Z.
,
Zhu
D.
,
Li
R.
,
Wu
Z.
,
Fu
L.
&
Zhao
Y.
2024
Influence of typhoons on the spatiotemporal variation in rainfall erosivity in the Pearl River Basin
.
Theoretical and Applied Climatology
155
(
2
),
1019
1034
.
https://doi.org/10.1007/s00704-023-04676-x
.
Cen
G.
,
Shen
J.
&
Fan
R.
1998
Research on rainfall pattern of urban design storm
.
Advances in Water Science
9
(
1
),
41
46
(in Chinese)
.
Chang
W. J.
,
Chou
S. H.
,
Huang
H. P.
&
Chao
C. Y.
2021
Development and verification of coupled hydro-mechanical analysis for rainfall-induced shallow landslides
.
Engineering Geology
293
,
106337
.
https://doi.org/10.1016/j.enggeo.2021.106337
.
Chen
W.
2019
Study on Characteristics and Regularities of Slope Geological Hazard Induced by Torrential Rainfall in Wenzhou
.
Master's Thesis
,
Wenzhou University
,
China
(in Chinese)
.
Chen
J.
,
Chen
H.
&
Guo
S.
2018
Multi-site precipitation downscaling using a stochastic weather generator
.
Climate Dynamics
50
(
5
),
1975
1992
.
https://doi.org/10.1007/s00382-017-3731-9
.
Dai
L.
,
Cheng
T. F.
&
Lu
M.
2020
Summer monsoon rainfall patterns and predictability over southeast China
.
Water Resources Research
56
(
2
),
e2019WR025515
.
https://doi.org/10.1029/2019WR025515
.
Fang
J.
,
Wahl
T.
,
Fang
J.
,
Sun
X.
,
Kong
F.
&
Liu
M.
2021
Compound flood potential from storm surge and heavy precipitation in coastal China: Dependence, drivers, and impacts
.
Hydrology and Earth System Sciences
25
(
8
),
4403
4416
.
https://doi.org/10.5194/hess-25-4403-2021
.
Fu
S.
,
Zhang
H.
,
Zhong
Q.
,
Chen
Q.
,
Liu
A.
,
Yang
J.
&
Pang
J.
2023
Spatiotemporal variations of precipitation concentration influenced by large-scale climatic factors and potential links to flood-drought events across China 1958–2019
.
Atmospheric Research
282
,
106507
.
https://doi.org/10.1016/j.atmosres.2022.106507
.
Garcia
G. A.
&
Aranda
O. E.
1993
A stochastic model of dimensionless hyetograph
.
Water Resources Research
29
(
7
),
2363
2370
.
https://doi.org/10.1029/93WR00517
.
Hao
R.
,
Xu
Y.
&
Chiang
Y.
2021
Identification of the controlling factors for hydrological responses by artificial neural networks
.
Hydrological Processes
35
(
11
),
e14420
.
https://doi.org/10.1002/hyp.14420
.
Hill
M. O.
,
Harrower
C. A.
&
Preston
C. A.
2013
Spherical k-means clustering is good for interpreting multivariate species occurrence data
.
Methods in Ecology and Evolution
4
(
6
),
542
551
.
https://doi.org/10.1111/2041-210X.12038
.
Hong
H.
,
Li
S.
&
Duan
Z.
2016
Typhoon wind hazard estimation and mapping for coastal region in mainland China
.
Natural Hazards Review
17
(
2
),
04016001
.
https://doi.org/10.1061/(ASCE)NH.1527-6996.0000210
.
Huff
F. A.
1967
Time distribution of rainfall in heavy storms
.
Water Resources Research
3
(
4
),
1007
1019
.
https://doi.org/10.1029/WR003i004p01007
.
Katz
R. W.
1977
Precipitation as a chain-dependent process
.
Journal of Applied Meteorology and Climatology
16
(
7
),
671
676
.
https://doi.org/10.1175/1520-0450(1977)016 < 0671:PAACDP > 2.0.CO;2
.
Keifer
C. J.
&
Chu
H. H.
1957
Synthetic storm pattern for drainage design
.
Journal of the Hydraulics Division
83
(
4
),
1332-1
1332-25
.
https://doi.org/10.1061/JYCEAJ.0000104
.
Kohonen
T.
1998
The self-organizing map
.
Neurocomputing
21
(
1–3
),
1
6
.
https://doi.org/10.1016/S0925-2312(98)00030-7
.
Li
H.
,
Zhai
P.
,
Lu
E.
,
Zhao
W.
,
Chen
Y.
&
Wang
H.
2017
Changes in temporal concentration property of summer precipitation in China during 1961–2010 based on a new index
.
Journal of Meteorological Research
31
,
336
349
.
https://doi.org/10.1007/s13351-017-6020-y
.
Ma
J.
,
Yao
Y.
,
Wei
Z.
,
Meng
X.
,
Zhang
Z.
,
Yin
H.
&
Zeng
R.
2024
Stability analysis of a loess landslide considering rainfall patterns and spatial variability of soil
.
Computers and Geotechnics
167
,
106059
.
https://doi.org/10.1016/j.compgeo.2023.106059
.
MacQueen
J.
1967
Some methods for classification and analysis of multivariate observations
.
Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability
1
,
281
297
.
Nayak
S.
&
Takemi
T.
2020
Typhoon-induced precipitation characterization over northern Japan: A case study for typhoons in 2016
.
Progress in Earth and Planetary Science
7
,
39
.
https://doi.org/10.1186/s40645-020-00347-x
.
Ni
H.
&
Song
Z.
2020
Response of debris flow occurrence to daily rainfall pattern and critical rainfall condition in the Anning River–Zemu River Fault Zone, SW China
.
Bulletin of Engineering Geology and the Environment
79
,
1735
1747
.
https://doi.org/10.1007/s10064-019-01667-z
.
Ozturk
U.
,
Wendi
D.
,
Crisologo
I.
,
Riemer
A.
,
Agarwal
A.
,
Vogel
K.
,
López-Tarazón
J. A.
&
Korup
O.
2018
Rare flash floods and debris flows in southern Germany
.
Science of the Total Environment
626
,
941
952
.
https://doi.org/10.1016/j.scitotenv.2018.01.172
.
Pilgrim
D. H.
&
Cordery
I.
1975
Rainfall temporal patterns for design floods
.
Journal of the Hydraulics Division
101
(
1
),
81
95
.
https://doi.org/10.1061/JYCEAJ.0004197
.
Ran
Q.
,
Hong
Y.
,
Li
W.
&
Gao
J.
2018
A modelling study of rainfall-induced shallow landslide mechanisms under different rainfall characteristics
.
Journal of Hydrology
563
,
790
801
.
https://doi.org/10.1016/j.jhydrol.2018.06.040
.
Serrà
J.
&
Arcos
J. L.
2014
An empirical evaluation of similarity measures for time series classification
.
Knowledge-Based Systems
67
,
305
314
.
https://doi.org/10.1016/j.knosys.2014.04.035
.
Tang
G.
,
Huang
J.
,
Sheng
D.
&
Sloan
S. W.
2018
Stability analysis of unsaturated soil slopes under random rainfall patterns
.
Engineering Geology
245
,
322
332
.
https://doi.org/10.1016/j.enggeo.2018.09.013
.
Tavenard
R.
&
Amsaleg
L.
2015
Improving the efficiency of traditional DTW accelerators
.
Knowledge and Information Systems
42
,
215
243
.
https://doi.org/10.1007/s10115-013-0698-7
.
Wang
X. J.
,
Wu
S. J.
,
Tsai
T. L.
&
Yen
K. C.
2023
Modeling probabilistic-based reliability assessment of gridded rainfall thresholds for shallow landslide occurrence due to the uncertainty of rainfall in time and space
.
Journal of Hydroinformatics
25
(
3
),
706
737
.
https://doi.org/10.2166/hydro.2023.124
.
Yang
S.
&
Duan
Y.
2020
Extremity analysis on the precipitation and environmental field of typhoon Rumbia in 2018
.
Journal of Applied Meteorological Science
31
(
3
),
290
302
.
https://doi.org/10.11898/1001-7313.20200304
.
Yang
P.
,
Xu
Z.
,
Yan
X.
&
Wang
X.
2024
Establishing a rainfall dual-threshold for flash flood early warning considering rainfall patterns in mountainous catchment, China
.
Natural Hazards
.
https://doi.org/10.1007/s11069-024-06493-5
.
Yin
S.
,
Lin
X.
&
Yang
S.
2022
Characteristics of rainstorm in Fujian induced by typhoon passing through Taiwan Island
.
Tropical Cyclone Research and Review
11
(
1
),
50
59
.
https://doi.org/10.1016/j.tcrr.2022.04.003
.
Yuan
W.
,
Lu
L.
,
Song
H.
,
Zhang
X.
,
Xu
L.
,
Su
C.
,
Liu
M.
,
Yan
D.
&
Wu
Z.
2022
Study on the early warning for flash flood based on random rainfall pattern
.
Water Resources Management
36
,
1587
1609
.
https://doi.org/10.1007/s11269-022-03106-3
.
Zhang
S.
,
Xu
C.
,
Wei
F.
,
Hu
K.
,
Xu
H.
,
Zhao
L.
&
Zhang
G.
2020
A physics-based model to derive rainfall intensity-duration threshold for debris flow
.
Geomorphology
351
,
106930
.
https://doi.org/10.1016/j.geomorph.2019.106930
.
Zhao
Y.
,
Meng
X.
,
Qi
T.
,
Li
Y.
,
Chen
G.
,
Yue
D.
&
Qing
F.
2022
AI-based rainfall prediction model for debris flows
.
Engineering Geology
296
,
106456
.
https://doi.org/10.1016/j.enggeo.2021.106456
.
Zhu
M.
,
Li
Y.
,
Zhang
X.
,
Sun
J.
&
Jia
C.
2024
Spatiotemporal evolution of tropical cyclone precipitation in China from 1971 to 2020
.
Natural Hazards
.
https://doi.org/10.1007/s11069-024-06479-3
.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/).