Temporal changes in the debris flow threshold under the effects of ground freezing and sediment storage on Mt. Fuji

. Debris flows are one of the most destructive sediment transport processes in mountainous areas because of their large volume, high velocity, and kinematic energy. Debris flow activity varies over time and is affected by changes in 10 hydrogeomorphic processes in the initiation zone. To clarify temporal changes of debris flow activities in cold regions, the rainfall threshold for the debris flow occurrence was evaluated in Osawa failure at a high elevation on Mt. Fuji, Japan. We conducted field monitoring of the ground temperature near a debris flow initiation zone to estimate the presence or absence of seasonally frozen ground during historical rainfall events. The effects of ground freezing and the accumulation of channel deposits on the rainfall threshold for debris flow occurrence were analyzed using rainfall records and annual changes in the 15 volume of channel deposits since 1969. Statistical analyses showed that the intensity-duration threshold during frozen periods was clearly lower than that during unfrozen periods. A comparison of maximum hourly rainfall intensity and total rainfall also showed that debris flows during frozen periods were triggered by a smaller magnitude of rainfall than during unfrozen periods. Decreases in the infiltration rate due to the formation of frozen ground likely facilitated the generation of overland flow, triggering debris flows. During unfrozen periods, the rainfall threshold was higher when the volume of channel deposits was 20 larger. Increases in the water content in channel deposits caused by the infiltration of rainfall is likely important for the debris flow occurrence during unfrozen periods. The results suggest that the occurrence of frozen ground and the sediment storage volume need to be monitored and estimated for better debris flow disaster mitigation in cold regions.

hydrogeomorphic processes in the initiation zone. To clarify temporal changes of debris flow activities in cold regions, the rainfall threshold for the debris flow occurrence was evaluated in Osawa failure at a high elevation on Mt. Fuji, Japan. We conducted field monitoring of the ground temperature near a debris flow initiation zone to estimate the presence or absence of seasonally frozen ground during historical rainfall events. The effects of ground freezing and the accumulation of channel deposits on the rainfall threshold for debris flow occurrence were analyzed using rainfall records and annual changes in the 15 volume of channel deposits since 1969. Statistical analyses showed that the intensity-duration threshold during frozen periods was clearly lower than that during unfrozen periods. A comparison of maximum hourly rainfall intensity and total rainfall also showed that debris flows during frozen periods were triggered by a smaller magnitude of rainfall than during unfrozen periods.
Decreases in the infiltration rate due to the formation of frozen ground likely facilitated the generation of overland flow, triggering debris flows. During unfrozen periods, the rainfall threshold was higher when the volume of channel deposits was 20 larger. Increases in the water content in channel deposits caused by the infiltration of rainfall is likely important for the debris flow occurrence during unfrozen periods. The results suggest that the occurrence of frozen ground and the sediment storage volume need to be monitored and estimated for better debris flow disaster mitigation in cold regions.

Introduction
Debris flows are one of the most destructive sediment transport processes in mountain areas because of their large volume and 25 high velocity and kinematic energy (Scott et al., 2004;Theule et al., 2018;Song et al., 2019). Debris flow risks are increasing in cold mountainous regions under climate change due to changes in hydrological processes on hillslopes, increases in the magnitude of rainfall events, and those in sediment supply activity in their initiation zones (Stoffel and Huggel, 2012;Stoffel et al., 2014). Because debris flows are usually triggered by heavy rainfall events (Scott et al., 2004;Sidle and Chigira, 2004; https://doi.org/10.5194/esurf-2021-41 Preprint. Discussion started: 26 May 2021 c Author(s) 2021. CC BY 4.0 License. Dowling and Santi, 2014;Zhang et al., 2019), estimation of the rainfall thresholds triggering debris flows is essential for debris 30 flow hazard mitigation measures, such as the installation of early warning systems (Pan et al., 2018;Hürlimann et al., 2019).
Many studies have attempted to determine rainfall thresholds by analyzing rainfall records in periods with and without a debris flow (e.g., Cannon et al., 2011;Hürlimann et al., 2019). The intensity-duration (ID) threshold is one of the most commonly used rainfall thresholds (Caine, 1980;Guzzetti et al., 2008;Staley et al., 2012;Zhou and Tang, 2014). Other factors, such as cumulative rainfall depth and the return time of rainfall, have also been used to estimate rainfall thresholds (Fiorillo 35 and Wilson, 2004;Imaizumi et al., 2006). Although many studies have calculated a single rainfall threshold for each torrent and region, the threshold varies with time and is affected by changes in hydrological processes and the volume of debris flow material (Jakob et al., 2005;Schlunegger et al., 2009;Chen et al., 2012;Theule et al., 2012). Therefore, temporal changes in the rainfall threshold need to be understood to evaluate future risks of debris flows under climate change.
Debris flow activity is controlled by hydrological characteristics on hillslopes and debris flow material (i.e., channel deposits 40 and talus slopes) in debris flow initiation zones (Bovis and Dagg, 1988;Staley et al., 2014;Loye et al., 2016). Wildfires decrease the infiltration rate of rainfall into the ground, resulting in the generation of overland flow that leads to debris flows (Cannon et al., 2001;Shakesby and Doerr, 2006;Ebel et al., 2012;Staley et al., 2014). The hydraulic conductivity of debris flow material also controls the initiation of debris flows (Bovis and Dagg, 1988). Ground freezing changes hydrological processes in watersheds, with the infiltration rate generally low in periods with a frozen soil layer (Blackburn et al., 1990;45 Iwata et al., 2010). Thus, the discharge of shallow runoff during the frozen period is higher than during the unfrozen period (Shanley and Chalmers, 1999;Coles and McDonell, 2018). However, the effect of ground freezing on the rainfall threshold of debris flow remains poorly understood.
The volume of debris flow material in the initiation zones of debris flow is controlled by the sediment supply from hillslopes and the evacuation of sediment by debris flows and fluvial processes (Imaizumi et al., 2006;Berger et al., 2011a;Theule et al., 50 2012;Imaizumi et al., 2019). Debris flow frequency is generally high in torrents with high sediment supply activity (May, 2002;Jakob et al., 2005). Bovis and Jakob (1999) classified debris flow basins into weathering-limited basins, which require a long sediment recharge period for the occurrence of a debris flow, and transport-limited basins, in which the debris flow occurrence is primarily controlled by hydroclimatic events. These studies imply that the volume of debris flow material in the watershed needs to be interpreted to improve the accuracy of debris flow prediction. 55 Mount Fuji, which is the most famous mountain of Japan, has frequently experienced severe debris flow disasters, as well as slush avalanches, which are mixtures of water and snow that erode large amounts of sediment as they move downstream (Hanaoka et al., 2007). Sediment accumulated in gully bottoms, which is eroded by overland flow during rainfall events, is the main source of debris flow material. Many disasters around Mt. Fuji have occurred in spring and late autumn, despite precipitation in those seasons being lower than in summer and early autumn (Hanaoka et al., 2007). Although previous 60 interpretations have implied that seasonal ground freezing affects temporal changes in the rainfall threshold of debris flow (Anma, 2007), this has not been supported by quantitative analyses due to the lack of field monitoring data. On Mt. Fuji, the https://doi.org/10.5194/esurf-2021-41 Preprint. Discussion started: 26 May 2021 c Author(s) 2021. CC BY 4.0 License. sediment storage volume in debris flow torrents has also changed over time because of the sediment supply from hillslopes and the evacuation of sediment by debris flows (Hanaoka et al., 2007).
The overall aim of this study was to clarify temporal changes in the rainfall threshold for the debris flow occurence in a cold 65 region under the effects of seasonal ground freezing and changes in the sediment storage volume. We conducted field monitoring of ground temperatures on Mt. Fuji to estimate the ground freezing conditions during historical rainfall events that triggered or did not trigger debris flows and slush avalanches. The specific objectives of the study were to estimate periods of ground freezing over 50 years using an empirical model based on field monitoring, calculate the rainfall thresholds in periods with and without frozen ground given changes in the sediment storage volume, and understand the hydrological processes 70 triggering debris flows in relation to the formation of frozen ground and the volume of debris flow material.

Study site
Osawa failure, which is a huge gully (length 2.1 km, width 500 m, and depth 150 m), is the most active debris flow torrent on Mt. Fuji. The Osawa failure is located on the western slope of Mt. Fuji (Figs. 1a,1b), where a westerly wind dominates. Results of age determination using C 14 indicated that this gully started to form circa 3,000 years ago (Iwatsuka and Machida, 1962). 75 The Osawa failure increased in size following a catastrophic failure circa 1,000 years ago (Hanaoka et al., 2007). The total volume of sediment derived from the gully is estimated to be 75,000,000 m 3 . The west side of Mt. Fuji is underlain by an alternation of scoria and basaltic lava, whereas thick tephra layers occur on the east side (Miyaji, 1998). Unconsolidated scoria layers have been actively eroded by freeze-thaw activity, overland flows, and strong winds. As the erosion of basal scoria layers proceeds, the lava outcrop becomes unstable due to overhanging, resulting in episodic failure of the outcrop of up to 30 80 m in thickness. Between 1970 to 2004, the estimated total volume of sediment evacuated from the Osawa failure was 5,020,000 m 3 (Hanaoka et al., 2007).
The Osawa failure has a cold climate due to its high elevation. The monthly average air temperature around the debris flow initiation zone (3,200 m a.s.l.) is lower than 0°C from November to April (Fig. 2). The maximum daily air temperature is also below 0°C from November to April, facilitating the development of seasonally frozen ground. The average annual precipitation 85 from 2010 to 2019 was 2,737 mm. Heavy rainfall (>100 mm) occurs during the "Baiu" rainy season (i.e., monsoon season from June to July) and during typhoon crossings (August to October). Precipitation in winter (December to February) accounts for only 8% of the annual precipitation.
In the Osawa failure, the slope gradients of the scoria and lava layers are 35-50° and 40-90°, respectively. Talus slopes,    Fig. 1a). Some debris flows were just monitored at one or two observatories because of the absence of monitoring devices, problems encountered during monitoring, or the short travel distance of the debris flows. The MLIT has also distinguished slush avalanches from debris flows based on field surveys just after each event and the presence or absence of snow in the flow as captured by video cameras. A total of 35 debris flows 115 and eight slush avalanches were monitored from 1969 to 2019 (Fuji Sabo Office, 2017; Fuji Sabo Office, 2020). The maximum total discharge of the debris flows, which was estimated with a video camera, ultrasonic water level gauge, and Doppler flowvelocity sensor at Iwadoi observatory, was 3 × 10 5 m 3 (Fuji Sabo Office, 2017).

Ground temperature monitoring 120
A depth profile of the ground temperature was obtained at an elevation of 3,220 m a.s.l. along the northern boundary of the Osawa failure (TM in Fig. 1d). The elevation of the monitoring point was selected based on the known initiation points of many debris flows, which were determined in an analysis of aerial photographs and airborne Light Detection and Ranging (LiDAR) digital elevation models (DEMs). A 2-m-deep hole was drilled in welded scoria. Then, temperature sensors (TMC-HD, Onset) were installed at 10 different depths (ground surface, 0.1, 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, and 2 m vertically) 125 and connected to data loggers (U12-008, Onset). Errors in temperature measurement after calibration of the sensors were within ± 0.1°C. Monitoring was conducted from September 30, 2017 to September 17, 2019, with temperature recorded at intervals of 1 hr. The sensor at the ground surface was covered by pebbles to match its albedo to that of the natural ground surface.
The occurrence of diurnal freeze-thaw activity and the formation of seasonally frozen ground were determined based on 130 observed ground temperature data. The period with diurnal freeze-thaw activity was determined to be the period during which the ground surface temperature rose above and fell below 0°C within 1 day, whereas the period with seasonal ground freezing was determined to be the period during which the ground temperature was equal to or below 0°C over multiple days.

Estimation of frozen periods
To estimate the presence or absence of seasonally frozen ground during rainfall events before the monitoring of ground 135 temperature began, the downward progress of the freezing and thawing fronts at the debris flow initiation zone since 1969 was estimated using air temperature records for the summit of Mt. Fuji (3,775 m a.s.l.), which were provided by the Japan Meteorological Agency (JMA). Because the ground-freezing period is spatially variable and affected by slope orientation, elevation, and snow distribution (e.g., Bayard et al., 2005;Kneisel et al., 2015), it is difficult to precisely estimate the frozen https://doi.org/10.5194/esurf-2021-41 Preprint. Discussion started: 26 May 2021 c Author(s) 2021. CC BY 4.0 License. period at an exact debris flow initiation point, which differs among debris flow events inside the Osawa failure. Therefore, we 140 estimated the frozen period at TM using the simple degree-day method to conduct an initial evaluation of the effect of ground freezing on the debris flow occurence.
First, the ground surface temperature at the debris flow initiation zone was estimated using a regression equation for the relationship between air temperature at the summit station and the monitored ground surface temperature from September 30, 2017 to September 17, 2019 (R 2 =0.94). Then, the downward progress of the freezing and thawing fronts was obtained from 145 freezing degree days and thawing degree days, respectively, which were calculated from the estimated ground surface temperature (Yamazaki, 1998;Miao et al., 2019;Walvoord et al., 2019) as follows: where Df is the depth of the freezing front, T is the daily average temperature, Dm is the depth of the thawing front, and cf and cm are coefficients. The coefficients cf and cm, which reflect temporal changes in the freezing and thawing depths as calculated from monitoring data, were used for the estimation of the freezing and thawing fronts before field monitoring began.
Air temperature at the Fuji City meteorological station (20 km south of the Osawa failure), which is also maintained by the 155 JMA, was used to estimate the ground temperature in the period for which data from the summit station were unavailable (0.9% of 1969-2019), although the elevation of this station (66 m a.s.l.) is much lower than that of the debris flow initiation zone. The regression equation for the relationship between the air temperature at the Fuji City station and ground surface temperature at the debris flow initiation zone (TM) was used to estimate the freezing and thawing lines in a depth-time graph (R 2 =0.93). In this study, the periods between freezing and thawing lines are referred to as frozen periods, whereas the periods 160 between thawing and subsequent freezing lines are referred to as unfrozen periods.
Except for the gully bottom, snow cover in the Osawa failure is generally shallow or absent, even in mid-winter, due to its slope orientation (windward side of Mt. Fuji), steep topography, and low precipitation (Fig. 2). Therefore, we did not consider snow cover to estimate the freezing and thawing lines.

Rainfall monitoring 165
From May 1, 1969, the MLIT has observed precipitation at 2,330 m a.s.l. using a tipping-bucket rain gauge, with a precision of 1 mm, close to the Osawa failure. The rain gauge, which has an internal heating system, can also monitor winter precipitation.
The observation of precipitation was occasionally interrupted by problems with the monitoring system in winter (mainly from December to April) until 2012, because of difficulties with maintenance. Hence, we could not obtain precipitation data associated with seven debris flows and one slush avalanche. Rainfall thresholds appropriately separating rainfall events with and without debris flows were determined by calculating the critical successful index (CSI) using the following equation (e.g., Liao et al., 2011;Formetta et al., 2016;Staley et al., 2017): where tp is the number of true positive events, fp is the number of false positive events, and fn is the number of false negative events. In this study, the ID threshold, a widely used concept (e.g., Guzzetti et al., 2008;Hürlimann et al., 2019), was employed to determine the importance of intensity and duration on the debris flow occurence. The rainfall threshold was also obtained by comparing the maximum hourly intensity and total rainfall to further improve our understanding of the debris flow initiation 180 mechanism. Appropriate rainfall thresholds were determined under various conditions in the debris flow initiation zone, such as the presence or absence of a frozen layer and large or small volumes of sediment storage. Debris flows and slush avalanches were likely to occur in the period with and without a snowpack in their initiation zones, respectively. We did not distinguish between debris flows and slush avalanches to obtain rainfall thresholds, because the presence or absence of a snowpack during rainfall events was unclear, especially during events without significant sediment transfer. Rainfall events with a total rainfall 185 <10 mm were not analyzed in this study, because they appeared unrelated to the occurrence of debris flows and slush avalanches. The time period used to separate different rainfall events was set to 24 h, which was longer than in many other studies (e.g., Bezak et al., 2016;Imaizumi et al., 2017). This was because the time required for flood concentration in the Osawa failure is likely longer than for many other debris flow torrents due to the large catchment area. Fiji Sabo Office (2020) estimated the volume of channel deposits inside the Osawa failure using a DEM in November 2000, when channel deposits were absent due to evacuation by debris flows, thus determining the base topography of the channel bed (Fig. 3). In the 1974-1975, 1979-1980, and 1998-1999 periods, when topography was measured using aerial photographs, the loss of a large volume of channel deposits (>100,000 m 3 ) was estimated despite there being no debris flow signals at the 205 Otaki, Iwadoi, and Osawagawa Bridge observatories. Errors in the estimation of sediment volume as well as the occurrence of debris flows terminating in the section between the Osawa failure and the observatories possibly affected the evaluated loss of channel deposits. Hence, our analysis of the volume of channel deposits contains some inherent errors for the period in which data were obtained using aerial photography surveys.

Changes in the volume of channel deposits
In this study, we obtained rainfall thresholds for two volume classes of channel deposits: ≥350,000 m 3 and <350,000 m 3 . 210 The boundary of the two classes was set to 350,000 m 3 to ensure that a statistically sufficient number of debris flow events could be allocated to both volume classes.

Changes in ground temperature
In the shallower part of the ground (i.e., ≤0.25 m deep), diurnal freeze-thaw activity was frequently observed in autumn and 235 spring, when the diurnal amplitude of the ground surface temperature was evident, whereas seasonally frozen ground was observed in winter (Figs. 4 and 5). At depths between 0.25 to 1.25 m, seasonally frozen ground occurred over long periods up to four months (Fig. 5). The ground below 1.75 m was not frozen in both the 2017-2018 and 2018-2019 frozen periods.
Temporal patterns in the ground temperature were different between the 2017-2018 and 2018-2019 frozen periods (Fig. 4).
In 2017-2018, ground temperature above a depth of 1.5 m rapidly increased during a heavy rainfall event on March 5 (total 240 rainfall and maximum hourly rainfall of 89 mm and 18 mm h -1 , respectively), which triggered a slush avalanche. Although the seasonally frozen layer was retained for more than 1 month after the rainfall event, the ground temperature at a depth >0.5 m did not fall much below 0°C. In spring 2019, when heavy rainfall events were not observed, the ground temperature below 0.5 m was lower than that in spring 2018. After ground warming on March 20-21 and April 20-24, 2019, ground cooling was observed, because the spring was colder than in the previous year. In both winters, seasonally frozen ground to a depth of 1.25 245 m persisted until mid-June in 2018 and early July in 2019 (Fig. 4).    The rapid and simultaneous increase in ground temperature from negative values to the melting point (Fig. 4) indicated that thawing of the porous volcanic ground was controlled by not only heat conduction but also heat advection. Taking this into account, we calculated the coefficient cm as an empirical value rather than a physical parameter. The empirical cm was 6.8 when Eq. (2) best reproduced the thawing of the depths between 0.75 and 1.25 m (Fig. 5). In this study, periods of ground freezing 265 could be roughly estimated from the time when the freezing front started to progress downward from the ground surface and the time when the estimated thawing front reached a depth of 1.25 m (Fig. 5).

Changes in channel bed topography
Channel bed topography clearly changed with time and was affected by the sediment supply from hillslopes and the evacuation of channel deposits by debris flows (Fig. 6). From September 2013 to October 2014 (Fig. 6a), no debris flow was monitored 270 at the observatories. During this period, aggradation of the channel bed of up to 5 m in association with sediment supply from the surrounding hillslopes was evident. From September to November of 2011, the channel deposit zone was significantly eroded by a debris flow that occurred on November 9, 2011 (Fig. 6b). During this period, debris flows occurred in some  tributaries without any failure of the surrounding hillslopes (Fig. 6b). Sediment produced by the failure of basaltic lava outcrops was deposited just below the outcrops without evolving into a debris flow. Hence, past debris flows in the Osawa failure were 275 mainly caused by the evacuation of channel deposits rather than the direct mobilization of landslide sediment.  Figure 7a shows the influence of rainfall intensity and duration on sediment transfer (i.e., debris flows and slush avalanches), which tended to occur during the conditions represented in the upper-right quadrant of all plots. This indicated that the 285 magnitude of rainfall events that triggered sediment transfer was larger than that of an ordinary rainfall event. However, the distributions of rainfall events that did or did not trigger sediment transfer could not be completely separated. The CSI for the ID threshold was significantly low (0.21). When ID diagrams were plotted for the frozen and unfrozen periods, respectively, the distribution of rainfall events that triggered sediment transfer during frozen periods was positioned further to the lowerleft side than in the corresponding diagram for unfrozen periods (Figs. 7b, 7c). Thus, the ID threshold in frozen periods was 290 lower than that in unfrozen periods. The CSI values of the ID thresholds in the frozen and unfrozen periods were 0.42 and 0.15, respectively. Therefore, the CSI in frozen periods was substantially improved compared to the CSI for all periods. Slush Rainfall thresholds for the occurrence of sediment transfer were also obtained by comparing total rainfall and maximum 295 hourly rainfall intensity (Fig. 7d). The total rainfall and maximum rainfall intensity that produced the highest CSI value were 314 mm and 42 mm h -1 , respectively. However, the distributions of rainfall events that did or did not trigger sediment transfer could not be completely separated (CSI = 0.15). As with the ID diagrams, rainfall events in the frozen and unfrozen periods were plotted separately (Figs. 7e, 7f). In frozen periods, the threshold values of total rainfall and maximum hourly rainfall were 120 mm and 22 mm h -1 , respectively. In unfrozen periods, the threshold values of total rainfall and maximum hourly 300 rainfall were higher than those in the frozen periods (314 mm and 42 mm h -1 , respectively). Both of the debris flows triggered by a maximum hourly rainfall <30 mm in unfrozen periods occurred within the 10-day period prior to the estimated subsequent frozen period. Thus, it is possible that the ground was frozen when these debris flows occurred. The CSI values of the rainfall thresholds in the frozen and unfrozen periods (0.38 and 0.27, respectively) were better than that obtained using all rainfall events (0.15). 305 https://doi.org/10.5194/esurf-2021-41 Preprint. Discussion started: 26 May 2021 c Author(s) 2021. CC BY 4.0 License.

Effects of the volume of channel deposits on the conditions required to initiate a debris flow 315
During frozen periods, the ID threshold was not very different between periods with large and small volumes of channel deposits (Fig. 8). The CSI values of the thresholds for small and large volumes of channel deposits were 0.45 and 0.38, respectively. Therefore, the CSI was not improved from when the ID threshold was determined without considering the volume of channel deposits (0.42, Fig. 7b). During unfrozen periods, the ID threshold in periods with a large volume of channel deposits was clearly higher than that in periods with a small volume of channel deposits (Fig. 8b). The CSI values for both 320 volume groups (0.20 and 0.14 for small and large volumes of channel deposits, respectively) were not significantly higher than the value obtained without considering the volume of channel deposits (0.15, Fig. 7c).
As with the ID threshold, the maximum hourly intensity and total rainfall that triggered debris flows were not clearly affected by the volume of channel deposits during the frozen periods (Figs. 9a, 9b, Table 2). By contrast, the thresholds in the unfrozen periods were very different and were dependent on the volume of channel deposits (Figs. 9c, 9d, Table 2). A larger hourly 325 rainfall intensity and total rainfall were needed for the debris flow occurence in periods with a large volume of channel deposits.
Many rainfall events that exceeded the rainfall threshold in periods with a small volume of deposits did not trigger debris flows in periods with a large volume of deposits. The CSI of the rainfall thresholds obtained separately for each sediment volume class (0.30 and 0.60 for large and small volumes of channel deposits, respectively) was improved from that calculated for all rainfall levels, regardless of the sediment volume (0.27, Fig. 7f).

Discussion
Our simple model could roughly reproduce the period of ground freezing at site TM (Fig. 5), although subsurface heterogeneity, infiltration of rainfall, and upward movement of sensible heat were not considered in the model. The snowpack, which affects 350 the period of ground freezing in many cold regions (e.g., Zhang, 2005;Luo, 2018), was not considered important to the formation of frozen ground at the monitoring point, because diurnal changes in the ground surface temperature (Fig. 4) indicated that the snowpack was never sufficiently deep to prevent ground cooling in the observed winters. The shallow snow depth in winter due to the strong wind and steep topography around the Osawa failure likely resulted in the limited influence of the snowpack on the period of ground freezing. 355 The rainfall threshold was significantly different between the frozen and unfrozen periods (Fig. 7). Therefore, the formation of frozen ground is a critical factor affecting the initiation of a debris flow. Bovis and Dagg (1988) implied that the hydraulic conductivity of channel deposits affects temporal changes in debris flow activity. Based on constant head permeability tests in the laboratory, Nanzaka and Iwata (1989) reported that the hydraulic conductivity of frozen deposits in the Osawa failure (3 to 22 mm h -1 ) was lower than that of unfrozen deposits (720 mm h -1 ). Decreases in the infiltration rate due to ground freezing, 360 which result in the occurrence of overland flow, have been reported in other regions (Blackburn et al., 1990;Iwata et al., 2010;Coles and McDonell, 2018). Consequently, the generation of overland flow affected by the low infiltration rate of deposits in frozen periods likely resulted in the debris flow occurence during smaller rainfall events (Fig. 7). The effect of the volume of channel deposits on the rainfall threshold was unclear in the frozen periods (Figs. 8,9), suggesting that debris flows in these periods were triggered by hydrological processes near the ground surface rather than the saturation of entire channel deposits 365 (Fig. 10a). Increasing in the debris flow frequency due to decreasing in the infiltration rate has also been reported in the regions affected by wild fire (Staley et al., 2017;McGuire et al., 2018;Rengers et al., 2020). Because a rainfall index representing the total water supply to the basin (i.e., total rainfall) was also an important factor in the triggering of debris flows (Fig. 7e), a sufficient amount of stream discharge may also be needed for the occurrence of debris flow. As with the Osawa failure, slush avalanches and debris flows have been recorded in other cold regions (Decaulne and 370 Saemundsson, 2006;Decaulne, 2007). In contrast to a debris flow, the presence of a snowpack is necessary for the occurrence of a slush avalanche (Decaulne, 2007;Eckerstorfer and Christiansen, 2012). The magnitude of rainfall events triggering slush avalanches were smaller than those that triggered debris flows (Fig. 7). Because snow in a slush avalanche sometimes melts as it moves to lower elevations due to the increasing temperature (Anma, 2007), some sediment transfer events classified as debris flow would originally be slush avalanches in the initiation zone. That could be one of the reasons why the distributions 375 of slush avalanches and debris flows according to rainfall factors overlapped in Fig. 7.

380
In contrast to the frozen periods, overland flow rarely occurred in the unfrozen periods because of the high infiltration rate of the deposits. Therefore, an increase in the groundwater level in channel deposits would likely influence the occurrence of debris flows (Fig. 10b). The slope of the ID threshold in environments in which the rainfall duration was important was steeper than in environments in which rainfall intensity was important (Guzzetti et al., 2008). A steeper threshold line in the unfrozen periods relative to the frozen periods (Fig. 8) indicated that rainfall duration was the important factor in the unfrozen periods. 385 A large rainfall magnitude was needed for the occurrence of debris flows when a large volume of sediment was stored in the initiation zone (Figs. 8,9). The relationship between the rainfall threshold and the volume of sediment stored was different from that reported in weathering-limited debris flow basins (Bovis and Jakob, 1999;Larsen et al., 2006). Because debris flows occurred even in periods with a small volume of channel deposits (Fig. 3), the threshold of sediment volume needed for the occurrence of a debris flow, which has been reported in weathering-limited basins (Bovis and Jakob, 1999), was not clear in 390 the Osawa failure. The relationship between the rainfall threshold and the storage volume in the Osawa failure was also different from that in transport-limited basins, in which the rainfall threshold can be given as a constant value regardless of the storage volume (Bovis and Jakob, 1999;Schlunegger et al., 2009). Channel deposits in the Osawa failure had a thickness of up to 10 m in some periods and were also characterized by a high infiltration rate. The ratio of thickness of the saturated layer to the entire thickness of the deposits is a factor controlling the movement of cohesionless deposits in steep channels (Imaizumi 395 et al., 2016, 2017). A large water supply is needed for the movement of thick deposits. Hence, the volume of channel deposits likely has a negative effect on the debris flow occurence in unfrozen periods.
Plots of rainfall events with and without debris flow events overlapped to a certain extent, even after consideration of the frozen periods and volume of channel deposits (Figs. 8,9). The magnitude of some rainfall events that triggered debris flows in unfrozen periods was as low as those in the frozen periods (Fig. 7), indicating that it is difficult to accurately estimate when 400 frozen periods occur. Because periods of ground freezing differ with slope aspect and elevation, it was difficult to determine if the ground was frozen at the initiation point for all events. Another potential factor reducing the CSI was the spatial variability of precipitation in the Osawa failure, which has a difference of elevation of up to 1,500 m. The ID threshold for the Osawa failure was higher than those measured for many other torrents globally (e.g., Guzzetti et al., 2008;Bezak et al., 2016;Hürlimann et al., 2019). Although the lower limit for debris flow in the Osawa failure was not far from the ID thresholds for 405 other regions, rainfall levels above the lower limit without the debris flow occcurence pushed the threshold upward. In general, the lower-limit lines for debris flow are lower than the lines separating rainfall events with and without debris flows (Cannon et al., 2008;Bezak et al., 2016). Because the debris flow threshold is often the lower-limit line (Cannon et al., 2008;Guzzetti et al., 2008), the threshold in the Osawa failure gully is higher. The observatories are located far from the debris flow initiation zone, resulting in debris flows just a short distance away being missed. This might have also affected the higher threshold line. 410

Summary and Conclusion
To determine the effects of frozen ground on temporal changes in the rainfall threshold for the occurrence of debris flows and slush avalanches, we estimated periods of seasonal ground freezing based on field monitoring conducted close to the initiation zone in the Osawa failure on Mt. Fuji. We also evaluated the influence of sediment storage volume in the debris flow initiation 415 zone on the rainfall threshold. The ID threshold in periods of ground freezing was clearly lower than in periods without ground freezing. A comparison of the maximum hourly rainfall intensity and total rainfall during rainfall events also showed that debris flows occurred during periods of seasonal ground freezing with rainfall events of a smaller magnitude. Decreases in the infiltration rate due to the formation of frozen ground facilitated the generation of overland flow, which triggered debris flows.
The volume of channel deposits also affected the rainfall threshold, especially during unfrozen periods. The rainfall 420 threshold in periods with large volumes of channel deposits was higher than that in periods with small volumes of channel deposits, indicating that a large water supply is needed for the debris flow occurrence when channel deposits are thick.
Increases in the water content in channel deposits caused by the infiltration of rainfall are important for the debris flow occurence during unfrozen periods, whereas hydrological processes near the ground surface are more important in frozen periods. 425 Our study determined that the rainfall threshold is variable even in the same torrent due to the influence of the formation of frozen ground and changes in sediment storage volume. Therefore, the occurrence of frozen ground and the sediment storage https://doi.org/10.5194/esurf-2021-41 Preprint. Discussion started: 26 May 2021 c Author(s) 2021. CC BY 4.0 License. volume need to be monitored and estimated to improve debris flow disaster mitigation in cold regions. Because periods of ground freezing and the sediment supply ratio are strongly affected by climatic conditions, future changes in the debris flow threshold should be carefully monitored for continuous sediment flow-associated disaster mitigation under climate change. 430

Data availability
The data that support the findings of this study are available from the corresponding author, Fumitoshi Imaizumi, upon reasonable request and agreement by Ministry of Land, Infrastructure, Transport and Tourism, Japan.