E3S Web of Conferences 415, 05005 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341505005

A novel downstream Flood Hazard Grade Index incorporating
upstream Hydrograph Characteristics to predict Debris Flow
Runoff
Norio Harada1*, Kana Nakatani2, Masamitsu Fujimoto3, and Yoshifumi Satofuka3
1Mitsui Consultants Co., Ltd., 5520007 Minatoku, Osaka, Japan
2Forest and Biomass dep., University of Kyoto, 6068502, Kyoto, Japan
3Engineering dep., University of Ritsumeikan, 5258577, Kusatsu city, Shiga, JapanAbstract. The July 2020 debris flow in Japan caused enormous damage, and briefing sessions on disasterprevention have prompted demands for detailed explanations and predictions of such phenomena in highrisk areas. It is necessary to obtain four-dimensional risk information, which considers temporal changes indisaster risk, rather than limiting the analysis to conventionally static information. In this study, wedeveloped a method for setting the boundary conditions necessary for debris flow prediction via a fourdimensional hazard map using various types of digital information. To understand the effects of hydrographcharacteristics from the upstream, flow discharge was analysed under different flow conditions, such as
topography-driven riverbed shear stress, using a one-dimensional numerical model that considers water andsediment flow. Our results suggested that characteristics of the upstream inflow hydrograph affect flood
runoff processes downstream; therefore, we developed a separate downstream flood hazard grade index thatuses characteristics of the upstream inflow hydrograph as input.

1 Introduction
With the broad application of detailed threedimensional (3D) model data, such as satellite
topographical data [1], further development of models
that utilize digital information to predict hazard
susceptibility is expected in Japan [2] [3]. For example,
landslide disaster countermeasure models offer detailed
predictions of disaster risks based on rainfall andlandslide forecasting information [4].
A debris flow in Atami City, Shizuoka Prefecture,
Japan in July 2020 caused enormous damage [5],resulting in nationwide interest in risks associated withlandslides such as debris flows. Subsequent briefing
sessions based on disaster prevention hazard maps haveprompted demand for detailed explanations andpredictions of such phenomena in high-risk areas.
Therefore, to further improve understanding ofdisaster risks among the general population, wedeveloped the iHazard map project, which includes
simple explanations of disaster phenomena using
visualizations, as shown in Figure 1. For this purpose, itis necessary to obtain four-dimensional (4D) risk
information, which considers temporal changes, rather
than limiting the analysis to conventionally staticinformation [6]. In this study, we developed a method
for setting the boundary conditions necessary for debris
flow prediction, to create 4D hazard maps using various
types of digital information.
To understand the effects of upstream hydrographcharacteristics, debris flow discharge was analyzed
under different flow conditions, such as topographydriven riverbed shear stress, using a one-dimensional(1D) numerical model [7] that considers debris flow.
Finally, a new index was developed to represent flood
hazard in downstream areas caused by debris flow.

■: Special sediment-related
disaster hazard area■: Sediment-related disaster warning area

Debris flow direction

Fig. 1. Example virtual reality-based debris flow simulation
results.

* Corresponding author: harada@mccnet.co.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, 05005 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341505005

The erosion/deposition velocity ib is calculated as :2 Numerical analysis of debris flow
runoffprocesses
affectedbyhydrographic characteristics

Erosion: C < C∞ib   e2.1 Governing equations
ib   d

The continuity equation for the total volume of adebris flow is:C (2)(9)

 tan w

   tan  tan w (10),where θw is the water-surface gradient and φ is theinternal frictional angle of the sediment.
The generation and development of debris flow arecalculated using a staggered scheme and arrangement
variables.

the continuity equation for the volume of sediment in thedebris flow isCh Chu
 ibC* ,txC  C q,
C* h

where C∞ is the equilibrium sediment concentration, q
is the unit width flow discharge, δe is the coefficient oferosion, and δd is the coefficient of deposition. Theequilibrium sediment concentration C ∞ for the debris
flow is(1)h uh ib ,
t
x(8)Deposition: C ≥ C∞

A 1D numerical model considering debris flow [7] wasused in this study.
The momentum in the flow direction under depthaverage velocity is calculated as follows:uuH  b .
 u  gtx
x hC  C q,C*  C d(3)and the continuity equation for the riverbed level isz ib  0 ,t

2.2 Calculation conditions(4)

Debris flow runoff processes affected by upstream
inflow hydrograph characteristics were estimated underpreviously described ideal conditions [7], as shown in
Table 1. Flood runoff processes affected by the riverwidth, riverbed gradient, and sediment concentration of
the volume flow were analyzed.
To understand the effect of upstream inflow
hydorograph characteristics on flood runoff processes,
we used numerical models to analyzed sevensignificantly different hydrograph geometries, as shownin Figure 2.

where u is the average velocity in the flow direction, t istime, x is the flow distance, g is the acceleration due togravity, τb is the riverbed shear stress, H is the flow
surface level (H = z + h), ρ is the interstitial fluid density,
h is the flow depth, ib is the erosion/deposition velocity,
C is the sediment concentration of the volume flow, C*
is the sediment concentration by volume in the movable
bed layer, and z is the riverbed height.
Various sediment transport types affected by changes
in bed slope are observed in the downstream segmentsof debris flows. Therefore, the riverbed shear stresses offlow τb were classified into three types according to thesediment characteristics of the debris flow [7], stonedebris flow, immature debris flow, and bed loadtransport, which are represented by the following
equations:

Table 1. Parameters used in the calculation.

Stone debris flow: C ≥ 0.4C*



(5)

Flow discharge Q (m3/s)

2Immature debris flow: 0.01 < C < 0.4C*

b1 d2uu
h 0.49 h 3(6)Bed load transport: h/d ≥ 30 or C ≤ 0.01
2

x (m)

ρ (kg m-3)

nm (m-1/3s)

d (m)

0.001

10.0

1.1

0.05

0.1

60d uub,3h 8h C  1  C  /  C* / C 1/ 3  1 2

 b gnm u u,hh4/3t (s)

CASE1-1
CASE1-4
CASE1-750

CASE1-2
CASE1-5

CASE1-3
CASE1-6

40
30

20
1060

ΣQ85
0600

1200

1800

2400Time(s)

3000

3600

4200

(7)
Fig. 2. Hydrograph analysis results for various inflow

where ρ is the interstitial fluid density, σ is the bulk thedensity of sediment, d is the particle diameter of thesediment, and nm is Manning’s riverbed roughness
coefficient.

conditions.

2E3S Web of Conferences 415, 05005 (2023)
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https://doi.org/10.1051/e3sconf/202341505005

2.3 Factors affected by upstream hydrographcharacteristics

consideration of upstream inflow hydrographcharacteristics altered the peak flow discharge comparedto the results shown in Figure 2.
Next, we analyzed peak flow discharge for different
river widths, keeping other variables constant, i.e., flow
distance from the observation point (L = 1,500 m),
riverbed gradient (I = 0.04), and flow sedimentconcentration (C = 0), as shown in Figure 5. Figure 5
shows the relationship between river width and nondimensional peak flow discharge. Again, theconsideration of upstream inflow hydrographcharacteristics altered the peak flow discharge comparedto the results shown in Figure 2.

To understand the debris flow processes affected by
upstream inflow hydrograph characteristics, weanalyzed the peak outflow discharge at different
observation points (different flow distances) usinghydrographs (cases 1-1, 1-2, 1-3, and 1-4) as shown in
Figure 2. Other variables were kept constant, i.e.,riverbed gradient (i = 0.04), river width (B = 10 m), andsediment concentration of the volume flow (C = 0), as
shown in Figure 3. Relationship between flow distanceand peak flow discharge for various flow distances. In
Figure 3, the y-axis is the non-dimensional peak flow
discharge at each observation point (i.e., the peakoutflow discharge at each observation point divided by
the maximum outflow discharge; Q0max = 40 m3 s-1), andthe x-axis is the flow distance between the boundary of
the upstream and the observation point.
The peak flow discharge of each hydrograph shownin Figure 2 changed as a result of upstream inflow. To
evaluate upstream effects on downstream sedimentconcentrations, we first focused on floods without
sediment. In addition, the results shown in Figure 3
suggest that downstream ratios of peak outflow
discharge were nearly unchanged over distances of >500 m.

Peak flow discharge
Q*= Qmax / Q0 max

1.0

Peak flow discharge
Q*= Qmax / Q0 max

NO.2

0.4
0250

NO.4
1000

0.2

1-1
1-3

CASE
CASE

10 B (m)

1-2
1-4
1520

Finally, flow discharge was analyzed for various
flow sediment concentrations, while other variables
were kept constant, i.e., flow distance at the observation
point (L = 1,500 m), riverbed gradient (i = 0.04), andriver width (B = 10 m), as shown in Figure 6. Figure 6
shows the relationship between flow sedimentconcentration and non-dimensional peak flow
discharge. A comparison of Figure 6 with Figures 2–4
indicates that sediment concentrations were not affectedby upstream hydrograph characteristics. We assume thatthese simulation results are representative of thebehavior of actual debris flows.

NO.3

500

CASE
CASE

Fig. 5. Relationships between river width and nondimensional flow discharge for cases 1-1, 1-2, 1-3, and 14), where L = 1,500 m, i = 0.04, and C = 0.

NO.1

CASE 1-1
CASE 1-2
CASE 1-3
CASE 1-40.4

L = 1500m, i = 0.04, C = 0.

NO.0

0.6

0.6

51.00.80.8

1500Distance L(m)i = 0.04, B = 10 m, C = 0.

Fig. 3. Relationships between flow distance and nondimensional peak flow discharge for cases 1-1, 1-2, 13, and 1-4), where i = 0.04, B = 10 m, and C = 0.

0.8

Peak flow discharge
Q*= Qmax / Q0 max

Peak flow discharge
Q*= Qmax / Q0 max

1.0
0.8
0.6
0.4

CASE 1-1
CASE 1-3

0.2
0.02

0.04

i ( H/L )0.06

CASE 1-2
CASE 1-4
0.08

0.6
0.4
0.2

CASE 1-1
CASE 1-3

0.0
0.1

0.2 C
*CASE 1-2
CASE 1-4
0.30.4

L = 1500m, i = 0.04, B = 10m.

i = 0.04, B = 10 m, C = 0.

Fig. 6. Relationships between flow sediment concentrationand non-dimensional flow discharge for cases 1-1, 1-2, 13, and 1-4), where L = 1,500 m, i = 0.04, and B = 10 m.

Fig. 4. Relationships between riverbed gradient and nondimensional flow discharge for cases 1-1, 1-2, 1-3, and1-4), where i = 0.04, B = 10 m, and C = 0.

2.4 Evaluation of the effects of upstreamhydrographic
characteristics
ondownstream flood runoff

Peak flow discharge was analyzed for various
riverbed gradients, with other variables held constant,i.e., flow distance from the observation point (L = 1,500m), river width (B = 10 m), and flow sedimentconcentration (C = 0), as shown in Figure 4. Figure 4
shows the relationship between the riverbed gradientand the non-dimensional peak flow discharge. TheThe effects of the upstream inflow hydrographcharacteristics on debris flow processes were evaluated3

E3S Web of Conferences 415, 05005 (2023)
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https://doi.org/10.1051/e3sconf/202341505005

3 Summaryby trial and error using the ratio of the flow discharge
difference shown in Figure 3. The resulting relationshipbetween flow discharge and inflow hydrographcharacteristics is as follows:Qmax    Q0 max  Q85 ,In this study, we used a 1D numerical model toinvestigate the effects of upstream inflow hydrographcharacteristics (e.g., landslide dam installation) on
downstream debris flow runoff processes. As a result,
we developed a new debris flow hazard index fordownstream areas based on upstream inflow hydrographcharacteristics.

(11)

where Qmax is the downstream debris flow discharge, Q0max is the upstream inflow discharge (Figure 7), and ΣQ85
is the proposed new index obtained through sensitivity
analysis, with 15% of the lower flow discharge
subtracted from the whole flow discharge (Figure 7),
where α and β are correction coefficients. This newindex is proposed as a downstream debris flow hazard
degree index that considers the upstream inflowhydrograph characteristics, as follows:
FH    Q0 max

1/ 2 Q85,

References
1.

(12)

2.

where FH is the proposed new index, assuming that α =1.0. If FH is larger, then the debris flow hazard is greater
downstream. Our analysis results yielded a correlation
coefficient of 0.89, with β = 0.5 (Figure 8). Further study
is needed to improve the accuracy of the new index.

3.

4.
5.

Flow discharge Q (m3/s)

Peak flow discharge
Q0 max (m3/s)

6.
ΣQ85

Q0 max×0.15(m3/s)

7.
Time(s)Fig. 7. Schematic used to calculate the proposed new index FH.

Peak flow discharge
Q*= Qmax / Q0 max

0.8

0.6
0.4

R² = 0.801

0.20020406080

Hydro Factor ( α・Q0max1/2・ΣQ85 )100

Fig. 8. Relationship between the new index and nondimensional peak flow discharge.

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