Mechanisms of Initiation, Runout, and Rainfall Thresholds of Extreme-Precipitation-Induced Debris Flows

The frequency of unprecedented extreme precipitation events is increasing, and consequently, catastrophic debris ﬂows occur in regions world-wide. Rapid velocity and long-runout distances of debris ﬂow induce massive loss of life and damage to infrastructure. Despite extensive research, understanding the initiation mechanisms and deﬁning early warning thresholds for extreme-precipitation-induced debris ﬂows remain a challenge. Due to the nonavailability of extreme events in the past, statistical models cannot determine thresholds from historical datasets. Here, we develop a numerical model to analyze the initiation and runout of extreme-precipitation-induced runoﬀ-generated debris ﬂows and derive the Intensity-Duration (ID) rainfall threshold. We choose the catastrophic debris ﬂow on 6 August 2020 in Pettimudi, Kerala, India, for our analysis. Our model satisfactorily predicts the accumulation thickness (7 m to 8 m) and occurrence time of debris ﬂow compared to the benchmark. Results reveal that the debris ﬂow was rapid, traveling with a maximum velocity of 9 m/s for more than 9 minutes. The ID rainfall threshold deﬁned for the event suggests earlier thresholds are not valid for debris ﬂow triggered by extreme precipitation. The methodology we develop in this study is helpful to derive ID rainfall thresholds for debris ﬂows without historical data. g and h show the continued accumulation of sediments but with a reduced velocity.


Abstract
The frequency of unprecedented extreme precipitation events is increasing, and consequently, catastrophic debris flows occur in regions worldwide. Rapid velocity and long-runout distances of debris flow induce massive loss of life and damage to infrastructure. Despite extensive research, understanding the initiation mechanisms and defining early warning thresholds for extreme-precipitation-induced debris flows remain a challenge. Due to the nonavailability of extreme events in the past, statistical models cannot determine thresholds from historical datasets. Here, we develop a numerical model to analyze the initiation and runout of extreme-precipitation-induced runoff-generated debris flows and derive the Intensity-Duration (ID) rainfall threshold. We choose the catastrophic debris flow on 6 August 2020 in Pettimudi, Kerala, 1 *Corresponding author(s). E-mail(s): bhatia.u@iitgn.ac.in; India, for our analysis. Our model satisfactorily predicts the accumulation thickness (7 m to 8 m) and occurrence time of debris flow compared to the benchmark. Results reveal that the debris flow was rapid, traveling with a maximum velocity of 9 m/s for more than 9 minutes. The ID rainfall threshold defined for the event suggests earlier thresholds are not valid for debris flow triggered by extreme precipitation. The methodology we develop in this study is helpful to derive ID rainfall thresholds for debris flows without historical data.
Keywords: Debris flows, initiation, runout, numerical modeling, ID thresholds Most of the studies for debris flows in India, as mentioned above, analyzed the runout of debris flows with seldom importance given to the initiation and triggering conditions. Both the DAN3D and RAMMS programs require the user to define an initial volume of failure mass assuming that the failure has already occurred and then simulate only the runout of the debris over a terrain (Van Asch et al. 2010 State of the art studies in the past decades gives an understanding of initiation mechanisms of debris flows. Iverson (1997) gave insights on the physics of debris flow initiation and runout on a catchment scale and emphasized three processes: (a) widespread coulomb failure, (b) partial or complete liquefaction, and (c) conversion of landslide translational energy to internal vibrational energy ). Meanwhile, Reid et al. (1997) performed debris-flow initiation experiments using diverse hydrologic triggers and provided exceptionally complete data on conditions preceding and accompanying slope failure and debris-flow mobilization. Later, Imaizumi et al. (2006), through performing in-situ observations of numerous debris flows in a steep channel (>20 deg) in the Ohya landslide area, central Japan, explored the role of partial saturation of sediments. Their work proposed the critical conditions for the movement of unsaturated materials by equating shear stress with solid friction of the channel bed and assessed the mechanism of hydrogeomorphic processes in the debris flow initiation zones.    . Pettimudi village is located deep within the "Shola forests" and covers many tea estates surrounding the area (Fig. 1a).
The site is within the west draining slopes of the Rajamalai range. Settlements mostly of laborers of the tea estate were present very near to the confluence of the second-order stream with the main flowing Anaimudi river channel. A To address the challenge mentioned above, we attempt numerical modeling to We organize the rest of the manuscript as follows. Section 2 introduces the characteristics of the disastrous debris flow event that occurred in Pettimudi, Kerala, India. Section 3 first details the data and methods we adopt in this study, including the rainfall data and other site-specific information. Then, the numerical model explanation is presented, focusing on the improvements made in this study compared to the original model by Van Asch et al. (2014). After this, we detail the ID threshold method we adopt in this study. Section 4 comprises the results of the numerical modeling and ID threshold analysis. We discuss the recent increasing occurrences of debris flow events in the Western Ghats of Kerala, India, and highlight the improvements needed in ID threshold analysis in Section 5. We explicitly mention the limitations of the study. Finally, in Section 6, we conclude the main findings of this study and imply 3 Data and methods 3.1 Rainfall and other site-specific data/information Achu et al. (2021) report the rainfall data available nearest to the disaster site from Nyamakad estate station (Fig. 3a), located 8 km away from Pettimudi. The rainfall record at Nyamakad estate station exhibits an enormous downpour (600 mm/day) on the day of the disaster, 6 August 2020. In addition to to be around 280500 m 3 , and the total area of the event was about 70125 m 2 (Achu et al. 2021).
The initiation of debris flows took place within the steep Shola forests. Above the initiation zone, a hollow region with barren soil and rock might supply an enormous amount of runoff water through the first-order stream. The debris flow fan that spread over the river is more than 120 m in length. The total travel distance of the debris flow is 1250 m. After crossing several embankments of the estate road, the debris flow traveled downward (Fig. 2a), damaging the nearby settlements (Fig. 1b). Besides, most of the settlements (more than four rows of continuous housing blocks) were located just before the stream's confluence with the Anaimudi river. These settlements are destroyed and washed out thoroughly (Fig. 2), resulting in more than 60 casualties. The geology in this area is predominant of Precambrian crystallines of Southern Granulite Terrain (SGT). The principal rock types are granite and migmatitic gneiss (Achu et al. 2021). Within the initiation zone, unconsolidated overburden (2 -5 m thick), mostly of soil and slope debris, was present above the moderately weathered granitic gneiss (GSI, 2020). Water absorption of weathered granitic soil could be a causal factor of such kind of heavy rainfall-induced debris flows (Furuichi et al. 2018, Zhu et al. 2020). The initiation zone of the debris flow is around 2100 m a.s.l. (above sea level) while the deposition zone is approximately 1595 m a.s.l. (Fig. 2c). The debris flow volume is estimated network of one-line (single lane) estate roads connects these settlements with the uphill tea plantations. We delineate the extent of the debris flows from the February 2021 (post-event) Google earth imagery. Superimposing the debris flow boundary over the February 2020 (pre-event) boundary reveals the debris flow intersects multiple times ( Fig. 1a) with the one-line estate roads. A firstand the second-order stream is also visible from the pre-event imagery, which follows the same path as the debris flow (Fig. 1a). Preliminary investigations suggested that the debris flow traveled through the first-order and secondorder drainages of the catchment transporting a large amount of eroded and entrained materials. Across the first-and second-order drainage, tea plantations and cut slopes were present (Achu et al. 2021). This study uses remote sensing products, numerical analysis, and interpretations to understand the mechanism of initiation and runout of the debris flow. We find that the debris flows traveled through tea plantation areas, across many single-lane roads on the hillslopes, collapsing embankments, and taking the materials through drainage that connects the main river (see Fig. 1b).  this site-specific data, we collect station-wise rainfall data from India Meteorological Department (IMD). These data are monitored by IMD through stations (see Fig. 3b for locations) at different towns within the Idukki district, viz. Peermade, Thodupuzha, Munnar, Idukki, and Myladumpara (shown in Fig.  4a and b).
Preliminary reports classify this rainfall event as a cloudburst (Achu et al. 2021, Sajinkumar et al. 2020). Other places within the district, i.e., Peermade, Thodupuzha, Munnar, Idukki, and Myladumpara (see Fig. 1b for locations), also record heavy rainfall during the months from June to August 2020. However, none of the station's daily rain exceeds 250 mm/day on 6 August 2020. Besides, the cumulative rainfall from June to August is between 1500 mm and 2500 mm among these four stations, almost 75 % of the total annual rain  2019) to study the roles of loose co-seismic materials, grain sizes, and vegetation in the post-earthquake settings. We use the PCRaster platform based on a geographical information system (GIS) and model the governing equations using script/python-based command line (Deursen 1995). The model requires a digital elevation model (DEM), and the resolution of DEM is the mesh size. Other spatial derivatives, i.e., slope and local drainage direction, are computed for the hydrological and erosion analyses based on DEM. For our study and research, we use the freely available 12.5 m resolution ALOS-PALSAR DEM. Other spatial inputs such as the total area of the catchment, where R u is the overland flow runoff (m/s), and I (m/s) is the infiltration.
where ASW denotes the available surface water (m/s) calculated from the where P r is the precipitation (m/s), and k s (m/s) is the hydraulic conductivity of soil at saturation. Along with the calculation of ASW, the model estimates the surface runoff generated from each pixel and routes towards the neighboring pixels based on the concept of Hortonian overland flow (Horton 1933, Corradini et al. 1994, 1998 where R ui * is the upstream contributed water that can infiltrate into the soil (m/s), and R uu is the runoff from upstream contributed runoff water (m/s), which is a sum of all the infiltration excess runoff water from the upstream pixels. The available water for infiltration I (m/s) can infiltrate the soil/bed depending on the hydraulic conductivity and initial moisture content conditions. The model computes the infiltration in the soil based on the percolation where P e is the percolation in soil layer (mm/day), θ is the volumetric water content of soil (m 3 /m 3 ), θ res is the residual volumetric water content of soil (m 3 /m 3 ), θ sat is the volumetric water content of the soil at saturation (m 3 /m 3 ), and ∆t is the incremental time step. The volumetric water content at complete water saturation is equal to the porosity of the soil, and the model considers a fraction of this maximum as the volumetric water content at a residual degree of saturation. All liquid water storage and fluxes are in units of volume of water. At any time during the numerical simulation, the model can convert this value into a relative degree of saturation to make it convenient for calculating the percolation/infiltration within an unsaturated soil. The degree The value of S r varies between 0 and 1, respectively, at soil's residual (θ res ) where P e is the percolation in the soil layer (m/s), θ is the volumetric water where δ e is the coefficient of erosion rate which is non-dimensional and back- The model accounts for deposition rate i (m/s) of debris flow following where δ d is a non-dimensional coefficient of deposition rate obtained through back-analysis and p (< 1)is a non-dimensional coefficient to describe the initiation of the depositing process. Takahashi  We run the numerical model with the input parameters specified in Table  1   The initial moisture content is 0.05 m 3 /m 3 , considering a dry spell before the rainfall. The total duration of the numerical analysis is set as 12 days, starting from 28-07-2020 to 11-08-2020. The time step is seconds (1036800 seconds = 12 days) for convergence purposes. The model used a Courant-Friedrichs-Lewy (CFL) condition (De Moura & Kubrusly 2013) to check the mass balance and convergence at every timestep. The model tracks the volumetric water content response, erosion, and deposition at different locations within the catchment. We estimate debris-flow volumes at each timestep by tracking the materials transported through the first-and second-order streams at an elevation close to the river. The model also provides velocity (m/s) and thickness of debris flow (m) outputs at each timestep. Due to the practicality and global usage of this approach, in this study, we use numerical modeling to identify the intensity and duration of the debris flow that occurred on 6 August 2020. Numerical simulations modeling the initiation and runout of debris flows can serve as the best alternative to identify the triggering rainfall thresholds where historical data is unavailable (Van Asch et al. 2014, 2018). Once we calibrate the numerical model using the methods given in the above section, we run ten numerical simulations with constant rainfall magnitudes ranging 10mm/hr., 15 mm/hr., 20 mm/hr., 25 mm/hr., 30 mm/hr., 35 mm/hr., 40 mm/hr., 45 mm/hr., 50 mm/hr., and 90 mm/hr. For each set of numerical simulations, the model observes the arrival

Results
The response of the numerical model under given rainfall boundary conditions is tracked for volumetric water content and degree of saturation (averaged throughout the pixels of the catchment, see Fig. 5). The long duration of heavy rain slowly increases the moisture content of the beds, and the beds are entirely saturated on 6 August 2020, resulting in an enormous amount of runoff which might have subsequently triggered the debris flow. The simulated volume of debris flow is 284500 m 3 (shown in Fig. 6), similar to the volume reported by (Achu et al. 2021).  The numerical model simulates the arrival of the debris-flow fan at the confluence on 6 August 2020. The volume of debris flow is also close to the measured value. The numerical results suggest, initiation of debris flows started around 22:55, and the peak flow was achieved before 23:15, as shown in (Fig.  6c and d). The model suggests the soil/bed might have reached complete saturation on the day of debris flow (see average moisture content and degree of saturation plots in Fig. 6a and b. The observation from the model is similar to the observation reported by (Achu et al. 2021). The numerical model tracks the velocity of the moving mass during the flow process. Fig. 7 shows  Fig. 7a. Within 60 seconds, the moving mass of debris flow propagated at an increased velocity ranging from 0 -9 m/s flowing through the first-order stream (Fig. 7b) towards the lower parts of the slope. Due to entrainment effects, the velocity at lower parts of the slopes might have decreased slightly, but the debris flow mass spread through the first-and second-order stream and further moved downstream (Fig. 7c and d). After around 10 minutes of debris flow initiation, further substantial erosion took place at the crest of the slope with a velocity ranging from 0 -4 m/s (Fig. 7e). We infer this to be the slope failure induced by excess pore water pressure and runoff. Strictly at 23:08, further eroded materials got deposited downstream (areas with settlements) with a maximum velocity of 9 m/s (Fig.  7f). The deposition continued until 23:10 but with a lower propagating speed ( Fig. 7g and h).  in the calibration (see Fig. 10).
Out of the ten numerical simulations we perform for the rainfall threshold analysis, debris flow occurs under nine rainfall intensities except for 10 mm/hr. These intensities and durations are plotted in a two-dimensional plane, as shown in Fig. 10. Threshold, especially high-intense rainstorms, is not available from the literature for this study area (Yunus et al. 2021). Previous studies Through this, we calibrate the numerical model for this particular debris flow event. To analyze the intensity-duration thresholds of debris flow, we run the numerical model with constant rainfall input conditions ranging from 10mm/hr., 15 mm/hr., 20 mm/hr., 25 mm/hr., 30 mm/hr., 35 mm/hr., 40 mm/hr., 45 mm/hr., 50 mm/hr., and 90 mm/hr. Fig. 9 shows the difference in arrival of debris flow against all the constant rainfall intensities analyzed. As the intensity of rainfall increases, the triggering time of debris flow decreases. Under a given rainfall intensity (I) in mm/hr., the duration of the debris flow arrives at the river is considered D (hours). Thus, we obtain an ID threshold for this particular debris flow event under the same material parameters used maximum thickness of the debris flow deposits at 23:08 is 9 m. The reported thickness of the debris flow was between 3 m to 7m. Fig 8 g and h show the continued accumulation of sediments but with a reduced velocity.   2019) reported ID thresholds primarily for short-intensity long-duration rainfall events, different from the Pettimudi case. We find previously established thresholds in the Idukki district are unsuitable to predict debris flows triggered by high-intensity, short-duration rainfall.   , through performing fieldwork and using advanced monitoring systems. In future works, we aim to achieve in situ monitoring to understand the dynamics and controlling factors of debris flows in the Western Ghats. This study has explored the first-order controls of the Pettimudi event despite the above limitations.
• The erosion equation used in this study is a simplified representation of various erosion mechanisms that could take place in loose materials deposited