E3S Web of Conferences 415, 05030 (2023)
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https://doi.org/10.1051/e3sconf/202341505030

Probabilistic Prediction Method of Erosion Volume andDeposition Area from Rainfall Observation DataKazuki Yamanoi1*, Kaori Shikakura2, Kenji Kawaike1, and Satoru Oishi3
1Kyoto University, Disaster Prevention Research Institute, 8128235, Yoko-oji Shimomisu Higashinokuchi, Fushimi, Kyoto, Japan
2Kyoto University, Graduate School of Engineering, 8128235, Yoko-oji Shimomisu Higashinokuchi, Fushimi, Kyoto, Japan
3RIKEN Center for Computational Science, 6500047, Minatojima-Minamimachi, Chuo-ku, Kobe, JapanAbstract. We propose a methodology to estimate the spatial distribution of the probability of sedimentdeposition due to debris flow from rainfall data by combining the probability prediction of erosion volume
based on an ordinal logistic regression and a sediment transport simulation. By using the Receiver Operating
Characteristic (ROC) curve and Area Under Curve (AUC) we have selected the best combination of shortand long-term rainfall indices used as explanatory variables in the ordinal logistic model. The results showedthat the regression model using 60-minute and 48-hour rainfall indices performed well and that theregression model using three events improved the predictability of local disasters in 2014. Furthermore, weperformed Monte Carlo debris-flow simulations using rainfall data from 2014 using the model. We
confirmed that the spatial distribution of disaster probability is consistent with the actual damage.

1 Backgrounds
Generally, the prediction method of sediment-related
disasters can be divided into real-time rainfall-based
prediction (alerting) and affected-area prediction byusing the empirical or physically-based method (hazardmapping). Both methods are already implemented insociety. In Japan, sediment disaster alert estimated fromSWI (soil water index) calculated by a tank model
having three vertical tanks and 60 min rainfall[1]. The
warning is mainly issued to the residents in thevulnerable area specified as the sediment disaster(special) precaution zone. However, the false alert rateis large because sediment movement does not take placein all warning areas when the warning is issued, andthere are areas within an area where debris flows are
relatively difficult to reach[2], resulting in differences inhazards.
It is still difficult to accurately predict the sedimentdisaster occurrence and affected area from the rainfall
observation because geological structure is complicated.
However, the spatial distribution of the damage
possibility can be valuable information to minimize thehuman damage and risk evaluation. This study proposesa methodology to quantify the damage possibility by
combining the statistically-based yield volume
prediction and sediment transport simulation based on
the stony debris flow model.

2 Statistic prediction of the erosion
volume2.1 Stochastic prediction of the debris-flow
erosion volume by employing ordinal logistic
regression
We set the target area as Hiroshima prefecture, Japan,
where two recent large-scale sediment disasters
happened. The first one, which occurred in 2014,
includes 107 debris flows and 59 shallow slides, whichcaused 44 injuries and 74 deaths [3]. The second one
caused 624 sediment movements in a wider area in
Hiroshima prefecture compared to the first event [4].
Total erosion volume is important in evaluating andsimulating debris flow. This study selected it as theregression model's objective variable, as in the previous
study [5]. The airborne lidar precisely measure thevolume by comparing the surface elevation in twoperiods, usually before and after the debris flow
occurrence. This study mainly uses the surface
difference data for the 2018 event. This data wasobtained by comparing the 1-m DEM taken before theevent and taken two-three weeks after the event. Due tothe few debris flows that occurred before the 2018 eventand the lack of significant rainfall after the event until
the measurement, the negative volumes in thisdifferential data can be considered as the amount oferosion caused by debris flow. However, since data wereunavailable for some traces of the 2018 event and alltraces of the 2014 event, this study also used a methodof estimating erosion volume using only trace data forthe area where data were unavailable. In the method, theline at the 12 degrees of surface slope [6] divided thetrace into erosion area and deposition area. We assumed* Corresponding author: yamanoi.kazuki.6s@kyoto-u.ac.jp© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0(https://creativecommons.org/licenses/by/4.0/).

E3S Web of Conferences 415, 05030 (2023)
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https://doi.org/10.1051/e3sconf/202341505030

Fig. 1. Estimated erosion volume levels.
Table 1. AUC value predicting the 2014 event’s erosion volume magnitudes.
Magnitude

10m-24hSmall
0.9875
Medium 0.9873
Large
0.994710m-48h0.98520.98570.994

10m-72h0.98440.9851
0.9936

AUC for "short-term RI" - "long-term RI"
30m-24h30m-48h30m-72h60m-24h
0.96250.98540.9846
0.94820.98150.98650.986
0.9866
0.98950.99480.99450.9967that the area whose slope is larger than 12 degrees has a
1m erosion depth. To treat the erosion volumes andprecipitation variables in same resolution, wesummarized the erosion volume in the 250m-resolution
cells which are same as the radar-based rainfall
observation.
The ordinal logistic regression is a regression
method to predict the ordinal value. In this study, wecategorized the erosion volume in the mesh system V
into three ranks Y, small Y=1 (0<V<980 [m3]), medium
Y=2 (980<V<2695 [m3]), and Y=3 large (V>2695 [m3]),
which are the objective variables. The estimatedcategories for 2018 and 2014 events are shown in Fig. 1.
The thresholds were set at the top 10% and 30% of theerosion volumes in the 2018 event.
For the explanatory variables, we employed a meanslope gradient and two rainfall-related indexes, theshort-term rainfall index (SRI) and the long-term
rainfall index (LRI). In this study, we selected themaximum 10min, 30min, and 60 min rainfall as SRI,
and 24 h, 48 h, and 72 h rainfall when the SRI reachedthe maximum as explanatory variables.
In this study, 2018 data trained the logistic model,
and 2014 data tested it. The regression employing ninesets of SRI and LRI yielded the nine ordinal logistic
models.

60m-48h0.9616
0.9876
0.996760m-72h0.95530.9871
0.9966

Fig .2. ROC curve for 2014 event by using logistic model
employing 60-min and 48-hour rainfall.

accurately divide the positive and negative states. Fig.2shows the example of the ROC curve of the prediction
model created by the 2018 disaster date and applied tothe 2014 disaster, which adopts the 60-minute and 48hour rainfall as SRI and LRI, respectively.
The AUC value is listed in table 1. According to thistable, the pair of 60-minute and 48-hour rainfall showed
the best score among all pairs predicting medium andlarge-scale sediment yield. Therefore, we selected thispair to generate the debris-flow simulation input. Notethat the precipitation area in 2014 is limited in the target
area, thus the FPR can be small with large sensitivity,resulting high AUC value. Also, the all precipitationindexes (i.e. 10 min, 30 min, 60 min, 24 hour, 48 hour,and 72 hour rainfall) around the damaged area werelarger than the indexes in the other area. This is thereason why all AUC values exceed 0.94.

2.2 Evaluation of the regression model
We applied the ROC (Receiver Operating
Characteristic) curve and AUC (Area Under Curve) toevaluate the performance of the nine logistic models
employing the multiple pair of SRI and LRI. ROC is therelationship curve between the sensitivity (True PositiveRate) and 1-specificity (False Positive Rate) in changing
the threshold to divide the positive and negative states.
The large AUC, the area under the ROC curve, indicatesthe high performance of the prediction model, which can2

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(b)

(c)

Fig. 3. Estimated occurrence probability of the small (a), medium (b), and large (c) scale of erosion in the 2014 event employing 60
min and 48-hour rainfall.

Fig. 4. Examples of the debris flow simulation input and outputs, generated initial debris flow mass (a), calculated maximum waterlevel (b), and deposition depth (c). (d) and (d') are the preliminary hazard as a relative frequency for the area larger than 0.01 mdeposition. (e) is the current practical hazard map for reference.

3

E3S Web of Conferences 415, 05030 (2023)
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3 Monte-Carlo debris flow runout
simulation inputting the predictederosion volume

LRI using the 2018 disaster data. The ROC curve and
AUC in the 2014 disaster prediction evaluated themodels' performances. The regression model using 60minute and 48-hour rainfall recorded relatively higher
performance than the other models. We generated 100
patterns of sediment production (debris flow mass) datain the 2014 event condition to execute a Monte Carlodebris flow simulation. As a result, the relative
frequency of deposition area, which is regarded as thehazard possibility with several assumptions, wasobtained. Real time execution of this method estimates
the hazard probability in the practical hazard area at anytime, contributing to advancing the warning andevacuation systems.

Using the observed rainfall in 2014, the regression
model yielded the probability of occurrence of threescale erosion, as shown in fig. 3. Although the higher
area of the small-scale probability is much broader thanthe occurred area, as shown in fig.1, the area with thehigher probability of large-scale erosion is consistent
with it.
We converted the probability distribution into thedebris flow mass by comparing the pseudo-random
numbers generated for each grid and three probabilitiescalculated by the logistic model. Assuming the massaccumulates in the center of the grid, the mass volume
was translated into the depth, shown in Fig.4. (a) as anexample. Inputting the depth as the initial condition, weperformed the debris-flow simulation [7] based on
Takahashi's stony debris flow model [8]. The simulation
calculated the maximum water (and sediment) level (b)and deposition depth (c). Since the generated volume
includes the erosion volume in the stream channels, weneglected the erosion process in the transportation. Notethat the logistic model evaluates the possibility ingenerating the mass from rainfall and topographicalindexes neglecting the land use. Therefore, the strangeshaped debris mass was also generated in the city area
as a result. On the contrary, the water level anddeposition depth around the mountainous valley outlet,
where the actual damage was observed, seems
consistent with the actual phenomena.
We iterated the mass generation 100 times andconducted a 100-case Monte-Carlo runout simulation,
producing 100 patterns of the deposition depth andwater level maps. Although there is no convincedmethod to determine the degree of hazard frompredicted variables such as deposition depth and waterlevel, this study regard the area whose deposition depth
is greater than the representative grain size (0.01m),
which is the input parameter, as the affected area ofdebris flow. Thus, we organized the 100 patterns into therelative frequency for the deposition depth greater than
0.01 m. The frequency distribution is shown in fig. 4 (d)and (d'). Assuming that there is no other uncertainty thanthe location and volume of the initial debris-flow mass,and the 0.01m deposition can be a hazard to thepopulation or buildings, this frequency is equivalent to
the hazard possibility. This method can estimate thedistribution of the quantitative hazard possibility (i.e.
preliminary hazard) inside the practical hazard area, as
shown in fig.4 (e). Additionally, since this methodology
can be applied by employing real-time rainfall
observation, such information can be expected to greatly
enhance the existing evaluation system, for example,
when selecting evacuation shelters.

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4 Conclusions
In this study, we developed an ordinal logistic model toestimate the probability distribution for the sedimentyield (erosion) scale by changing the pair of SRI and4

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