自然災害科学 J. JSNDS 38 特別号 97 -108（2019 ）Numerical Simulation of Pluvial Inundation Considering Gate
Operation
Herman MUSUMARI1, Nakagawa HAJIME2, Kenji KAWAIKE3 and Rocky TALCHABHADEL4

Numerical Simulation of Pluvial Inundation
Considering Gate Operation
Herman MUSUMARI1, Nakagawa HAJIME2,
Kenji KAWAIKE3 and Rocky TALCHABHADEL4
Abstract
The implementation of river embankments to mitigate fluvial flooding inadvertently
impacts on the occurrence of pluvial inundation. Receiving rivers and tributaries are linked
by gates whose operation becomes crucial when the water level of the main river rises
considerably. This study considered a one-dimensional kinematic wave and dynamic wave
model for hills and mountains alongside a two-dimensional inundation model based on
unstructured meshes applied to lowland areas. It also took into account the interaction between
tributaries and the main channel at the downstream boundary as well as gate operation. This
resulted in a more realistic simulation of the pluvial inundation that occurred in July 2018
in Oe Town, Kyoto Prefecture. The simulated results were in good agreement with observed
data although they revealed a small underestimation. The risk of not operating the gates (ontime) was also investigated. In our case, not operating the gates yielded an increase of 40
cm of inundation depth in comparison to the case where the gates were closed on time. We
believe that the developed model can be used to effectively assess the mitigation effect ofcountermeasures such as pumping stations in the coming days.
Key words：Pluvial inundation, ﬂuvial ﬂood countermeasures, gate operation

1

2

3

Masterʼs Student, Dept. of Civil and Ear th Resources
Engineering, Kyoto University, Japan
Prof., Disaster Prevention Research Institute (DPRI),
Kyoto University, Japan

4

97

Assoc. Prof., DPRI, Kyoto University, Japan
Researcher, DPRI, Kyoto University, Japan

98

Numerical Simulation of Pluvial Inundation Considering Gate Operation

1. INTRODUCTION

punctuated the period spanning from the end of

Flood-related disasters pose a serious threat

June to the middle of July 2018 with widespreadin Japan. The mountain-dominated topography anddamage and hundreds of casualties in the western

rapid growth of cities have induced over half of thepart of Japan. Fig. 1 shows 10 daysʼ cumulated

population to settle in ﬂood-prone areas. This highrainfall exceeding in some zones the annual aver-

exposure to ﬂood proneness accompanied by local

age rainfall of the country.

torrential rainfall renders flood disasters a common occurrence in Japan (Kawaike et al., 2018).

The dynamism of land use characterized bya signiﬁcant reduction in pervious area alongside

In addition, these disasters are likely to in-heavy rainfall triggered a rapid increase in thecrease as a result of the rising issue of climate

water level at several receiving rivers. Consequenc-

change affecting the frequency and intensity ofes pertaining to this high water level are at least

rainfall patterns (Dale et al., 2015; Shephard et al.,twofold. Firstly, the discharge from tributaries

2014). Recently, extraordinar y downpours havebecomes difﬁcult to drain into the main receiving

Fig. 110 days of rainfall across Japan, July 2018 (Source: Japan Meteorological Agency).

99

自然災害科学 J. JSNDS 38 特別号（2019 ）channels. Secondly, the water level of tributaries

on ﬂood scale and intensity.

also rises as a result of the backwater effect, which
threatens the stability of contiguous dykes and2. STUDY AREA AND DATA

heightens the risk of ﬂuvial ﬂoods by overtopping.

The target area of this study is Oe Town locat-

Unlike in Kurashiki City (located in Okaya-

ed in Fukuchiyama City on the northwestern side

ma Prefecture), which witnessed dramatic fluvialof Kyoto Prefecture. With a total catchment area

inundation due to several levee breaches, seriousof 4.9 km 2 (including the mountainous zone up-

pluvial inundations occurred in Fukuchiyama City

stream), it is drained by three small rivers ﬂowing

in Kyoto Prefecture and some other cities in Kochi.

into Yura River, a ﬁrst-class river bending along the

While numerous researchers have relied oncity (Fig. 2).

numerical models to analyze and reproduce ﬂood

The studied area under went serious pluvial

extension using catchment characteristics, less at-inundation triggered by two consecutive rainy days

tention has been devoted to the operation of gates(July 6th and 7th of 2018) whose hyetograph pro-linking the tributaries to the main channels. In

vided by AMeDAS at Sakaura station, the closest

fact, although the implementation of embankments

to our area, is illustrated in Fig. 3. Yura River rose

aids in reducing the frequency of river overﬂows,

considerably, causing the three gates connecting

they adversely affect the drainage of the connect-

the Yura to its tributaries to be constrained closed.

ing tributaries, especially when the water level

The importance of pumping stations is recognizedbecomes sensibly high. Due to this fact, soundin such circumstances to alleviate the inundation

flood management requires steady control of theand buffer damage by artiﬁcially draining water.

water level on both sides of embankments and the

Nevertheless, pumps have not yet been im-

prompt operation of gates in order to resolve theplemented in Oe Town. As a result, the small town

potential backwater effect and avoid the intrusion

turned into a reservoir with no outgoing ﬂow dis-of discharge from the main rivers that may exacer-

charge.

bate the inundation damage. Gate operation con-

As shown on the elevation map, Fig. 2, thesists of keeping gates open when the water level inarea is divided into two major parts: the moun-the receiving channel is lower in comparison to its

tainous area from which we estimated the flow

tributaries and to shut them when the water level

discharge, and the lowland area into which the dis-

becomes equal or higher.

charge ultimately ﬂowed.

In order to analyze and reproduce inundation

In addition, two essential zones are distin-with regard to gate operation, the timing of gate

guished within the lowland area: the residential

closure is of signiﬁcant importance. However, thearea starting at the toe of the mountains, and thetime distribution for the operation of gates is rarely

paddy field located between the embankment

available due to certain policies.

bearing the railway and the one contiguous to Yura

As gate operation directly impacts on theRiver, Fig. 2.

condition of the downstream boundary in the nu-

The former embankment delineates the res-merical model, our study will focus on different

idential side from the paddy field. Based on this,patterns of operation. We will ﬁrstly trace back the

34,090 triangular meshes were constructed with an

most likely time of closure based on which pluvial

edge size ranging from 1 meter to 10 meters, andinundation will be reproduced, and secondly inves-

five mesh categories were defined to account for

tigate the effects of delayed or early gate operation

river streams, roads, railway, the residential area

100

Fig. 2

Numerical Simulation of Pluvial Inundation Considering Gate Operation

Target area and the topography of the catchment (including the mountainous area and the inundation
zones) provided by 5m x 5m DEM data.

Fig. 310 minutesʼ rainfall distribution observed at Sakaura station.

101

自然災害科学 J. JSNDS 38 特別号（2019 ）(with buildings), and paddy ﬁeld. To each catego-

applied respectively for slope units, and the mainry, a different roughness coefﬁcient was assigned.

streams. The details are well explained by Takahashi et al. (2001).

3. METHODOLOGY

The inundation calculation on the downstream

Numerical methods constitute an essential
tool for the depiction and analysis of event-based

area is based on 2D shallow-water equations withthe following governing equations:inundation. Many models, ranging from the sim（1）plest conceptual approach to the highly complex
physically based models, have been developed andapplied to analyze pluvial flooding in many areas（2）

throughout the world. In the case of highly urbanized areas with sophisticated channel networks,
Lee et al. (2014) applied an integrated model that（3）

accounts for the interaction of the sewerage pipe
and the overland flow. In contrast, Prasad et al.
(2016) focused on pluvial inundation analysis from（4）

the perspective of tuning a hazard map with respect to given return periods.
The model used in this paper consists of the
conjunction of a 1D kinematic and dynamic wave

（5）

model with a 2D unstructured mesh model for theinundation propagation applied respectively to theHere, g is the acceleration due to gravity, u and v

upstream and downstream zones of the target area.

are velocities in the x and y directions respectively,

To assess the effectiveness of our numerical model

M=uh and N=vh represent the flux in the x and yin representing the studied event, our team visited

directions respectively, h is the ﬂow depth, ρ is the

Oe Town after the disaster and recorded floodspeciﬁc density of water, and β is the momentum

marks at several points (Table 1).

correction coefficient. τbx and τby are the bottom

3. 1

shear stress along x and y respectively, and qrain des-Numerical model

ignates the source term from the rainfall.

For the mountainous area, the kinematic wave

A finite-volume method derived from equa-model and the dynamic wave models have been

tions 1, 2, and 3 based on the leapfrog scheme andTable 1

Observed water depth/level at the residential area−

Flood Mark5 m DEM

Water level−

Flood Mark5 m DEM

Water level11.60 m12.50 m14.10 m10

2.30 m12.00 m14.30 m2

2.00 m11.80 m14.10 m11

2.20 m11.80 m14.00 m3

1.70 m12.30 m14.00 m12

2.30 m11.70 m14.00 m4

2.60 m11.40 m14.00 m13

2.50 m11.50 m14.00 m5

1.60 m12.40 m14.00 m14

2.60 m11.40 m14.00 m6

2.20 m11.80 m14.00 m15

2.70 m

11.10 m13.80 m7

1.80 m

12.10 m13.90 m16

1.50 m12.50 m14.00 m8

1.40 m12.80 m14.20 m170.60 m10.80 m11.40 m9

2.10 m12.00 m14.10 m102

Numerical Simulation of Pluvial Inundation Considering Gate Operation

applied to triangular unstructured meshes yields:

fall was turned into runoff by using a 1D kinematicwave approximation. The outﬂow discharge of each（6）

slope ser ved as a lateral input to the main channels (channel 1, 2, and 3) whose ﬂow routing wascomputed based on the 1D dynamic wave model.
The calibrated Manning coefﬁcients for slopes and（7）

river channels were respectively 0.1 and 0.02. The
simulated discharge obtained from the mountainous area was thus given as the upstream boundary（8）

condition for the inundation modeling (Fig. 5) andthe rainfall shown in Fig. 3 is considered as a later-

Owing to Fig. 4, ML and NL are the x and y flux

al input for the entire inundation domain.

computed at the middle point of the edge shared

The basin of channel 2 and 3 being respec-by mesh i and j, di and dj are the distance of cen-tively 55474 m 2 and 66600 m 2, the two channels

troids of mesh i and j to that point, respectively. M1

exhibit a similar discharge pattern that is highly

and M2 (resp. N1 and N2), which represent the sec-

dependent on their basinʼs size. The downstream

ond and third convection terms of the momentum

boundar y, however, largely depends on the con-equation, are estimated using the components ofdition at the gates and the subsequent operation.

the horizontal and vertical flux at the centroid of

Because of the unavailability of the real operation

the computed cell and these fluxes are averaged

gates mentioned earlier, Fig. 6 encapsulates differ-using the flux at the three edges of the mesh.

ent cases considered at the gate boundary, whichMore details on the formulation of this approach

will allow us to trace back the most likely gate op-

are presented in Kawaike et al. (2000).

eration and reproduce the inundation event of July
6th to 7th. As the timing of closure is unknown, we

3. 2

Boundary conditions

run as a first step a simulation by assuming that

The mountainous area was split into a series

the water level of Yura River remains lower thanof rectangular lumped hillslopes in which the rain-

the water level of the three tributaries and that theFig. 4Control volume (left) and interpolation between meshes (right).

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自然災害科学 J. JSNDS 38 特別号（2019 ）gates stayed open. This ﬁrst case helps to estimate
the theoretical timing of gate operation.

Finally, we considered different patterns of
the gate operation to represent delayed or early

For the second and third case, we embed into

closing in order to assess the impact of these oper-

the model the interaction between the main river

ations on the inundation scale/intensity (focusing

and the tributaries at the gate meshes. Dependingon the residential area).

on

4. RESULTS AND DISCUSSION（9）

Case 1, based on the assumptions that thewater level of Yura River remained lower in comparison to its tributaries and that all gates opened（10）

throughout the simulation time, revealed that therainfall of July 6th and 7th, 2018 would not havebeen enough to trigger inundation if the water lev-（11）

el of the main river did not rise signiﬁcantly as happened on July 6th and 7th, 2018. As illustrated inFig. 7, the residential area is quasi-non-inundated.
The simulated water level at the gates meshes from case 1 alongside the observed water level

the drainage/over flow discharge exchanged atof Yura River allowed us to trace back the theoreti-

gates q were computed. Subscripts Y and g refer tocal closure timing expressed by the intersection of

Yura River and its tributaries, respectively. H is thethe two curves (Fig. 8).

water level, h represents the water depth, z the bot-

This timing at which gates are supposed to be

tom elevation, and ht=hg and hd=min{hg,hY}. Coef-closed to avoid the backwater effect is roughly 12

ﬁcients C0=0.38, C1=0.35, and C2=0.91 are validated

hours counted from the beginning of the simula-by Kawaike et al. (2018).

tion time.

Fig. 5

Discharge given as the upstream boundary condition.

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Numerical Simulation of Pluvial Inundation Considering Gate Operation

Case 2 served in reproducing the event thatthe simulation.

occurred in July 2018 and considered the previous

The simulated result is shown in Fig. 9a withtiming as well as the interaction between the maina noticeable increase in the ﬂood extent and water

river and its tributaries. At time t=12 hours, alldepth throughout the domain. There was no signif-

gates are assumed to shut down simultaneously in

icant change in the inundation pattern with respect

Fig. 6

Schematic representation of different cases.

Fig. 7

Inundation distribution from case 1.

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自然災害科学 J. JSNDS 38 特別号（2019 ）to different closure timing for each gate depending on the respective water level time series (notshown here).
A slight underestimation is observed in the setof points (1, 8, 9, 10, 12, 13, and 14) in comparison
to the ﬁeld data (Fig. 9d), and this may be justiﬁed
by some inaccuracies pertaining to the quality of
DEM data. However, the variability is both conser ved and reasonable. The inundated domain
behaved like a reservoir and the ﬂow progressively

Fig. 9Fig. 8

Wa t e r l e v e l t i m e s e r i e s a l l o w i n gestimation of the closure timing.

(a) Case 2 simulation considering the interaction of rivers and the closing time; (b) case 3 simulationconsidering the interaction of rivers without operating gates; (c) spatial distribution of the difference
between case 2 and case 1; (d) comparison between simulated cases and the field data.

106

Numerical Simulation of Pluvial Inundation Considering Gate Operation

9c where an increase of 40 cm in both the inundat-

ﬁlled depression zones as time evolved.
Consequently, the quality of topographicaled residential area and the paddy ﬁeld is noticed.

data becomes of utmost importance to precisely

Taking the theoretical closure timing (12 hours)

assess the water depth throughout the domain andas a reference, two sets of four cases are run. In

especially in the residential area.

the ﬁrst group, gates are closed 1, 2, 3, and 4 hours

Although the result of case (3) seems closeprior to the reference time. The second groupin some points (1, 8, 9, 10, 12, 13, and 14) to theconsiders the other four cases in which gates areobserved data, the root mean square error (RMSE)

operated after the reference time.

showed that this case greatly deviated from theFig. 10 shows that operating the gates withinreference (ﬁeld data) with an overestimation trend.

4 hours prior to the reference time has similar con-

The RMSE of case (3) was 0.423, deviating mostly

sequences to not operating them the next 4 hours

towards high values, while the RMSE of case (2)after that time. An increase in the average inunda-

was 0.3 with a deviation towards lower values.

tion depth is noticed when we move away from theAnother explanation behind the underestimationreference point, considered here as the theoreticalexhibited in case (2) is related to the real timing ofclosure timing (12 hours). The gradients of theclosure, which might be greater than the theoreti-

first and second limb around the reference point

cal timing (12 hours) derived from Fig. 8.

are highly dependent on the rainfall pattern andthe evolution of the water level in the main river,（12）

respectively. However, the sound operation of thegates should intervene as close as possible to theHere, sim^ stands for the simulated values, ob^s des-reference time, which corresponds to the mini-

ignates the observed values, and n is the number

mum inundation depth computed.

of points. When gates are not operated, the ﬂood
the observed data in some points (5, 6, and 7) as

5. CONCLUSIONS AND RECOMMENDATIONS

shown in Fig. 9d. The spatial distribution of the

We analyzed a case of pluvial flooding influ-

difference between case 2 and 3 is shown in Fig.

enced by the conditions at gates joining Yura Riveris more prominent and even signiﬁcantly exceeds

Fig. 10 Average inundation water depth related to different closure timing in theresidential area.

107

自然災害科学 J. JSNDS 38 特別号（2019 ）with its tributaries. A 1D model for rainfall runoff

gineers - Engineering Sustainability, 170(4), 214-

process and a 2D model for runoff inundation were

224.
Kawaike, K., Inoue, K., & Toda, K. (2000). Inundation
modeling in urban area based on unstructured
meshes. Hydrosoft, Hydraulic engineering software, WIT Press, 457-466.

used in conjunction. The interaction between themain river and its tributaries and the consideration of gate operation allowed us to realisticallysimulate the inundation intensity as well as the its
scale with results that were in good agreement.
This study highlighted the importance of operating
gates on time, especially when the water level onboth sides of the gates becomes equal. Due to theunavailability of the closure timing, we could traceback the most likely time (theoretical time) by
combining the observed and the simulated data ofthe main channel and tributaries, respectively. The
results show that delayed interventions resulted inhigher inundation depth in comparison to early interventions and that the optimum intervention corresponds to the theoretical closure timing. Future
study will incorporate countermeasures such as
pumping stations or diversion channels (Niroshinie
et al., 2016) into the model and evaluate their effectiveness in the mitigation of damage to a desired
level.

References
Dale, M., Luck, B., Fowler, H.J., Blenkinsop, S., Gill, E.,
Bennett, J., Kendon, E., & Chan, S. (2015). New
climate change rainfall estimates for sustainabledrainage. Proceedings of the Institution of Civil En-

要

Kawaike, K., Zhang, H., Sawatani, T., & Nakagawa,H. (2018). Modeling of stormwater drainage/
overﬂow processes considering ditches and theirrelated structures. Journal of Natural Disaster
Science, 39(2), 35-48.
Lee, S., Nakagawa, H., Kawaike, K., & Zhang, H.
(2014). Urban inundation simulation incorporating sewerage system without structure effect.
Annuals of DPRI, Kyoto Univ., 57(B), 407-414.
Niroshinie, M.A.C., Nihei, Y., Ohtsuki, K., & Okada, S.
(2016). The countermeasures for ﬂood mitigation
evaluated by 1D and 2D coupled models. In 11th
ISE, (pp. 1-5), Melbourne, Australia.
Prasad, J., Kumar, R., & Mani, P. (2016). Combined
ﬂuvial and pluvial ﬂood inundation modelling fora project site. Procedia Technology, 24, 93-100.
Shephard, M.W., Mekis, E., Morris, R.J., Feng, Y.,
Zhang, X., Kilcup, K., & Fleetwood, R. (2014).
Trends in Canadian short-duration extreme rainfall: Including an intensity-duration-frequency
perspective. Atmosphere - Ocean, 52(5), 398-417.
Takahashi, T., Nakagawa, H., & Satofuka, Y. (2001).
Estimation of debris-flow hydrographs in the
Camuri Grande river basin, Journal of Natural
Disaster Science, 23, 41-50.
（投 稿 受 理：2019年 4 月 5 日
訂正稿受理：2019年 7 月 3 日）

旨

京都府北部を流れる由良川では，河道からの洪水氾濫対策として本川堤防の整備が進められてきたが，かえってそれが内水氾濫の発生を助長してしまっている。支川とその流下先の本川との合流部には樋門が設置されており，本川水位が上昇した際にはこの樋門の操作が極めて重要になる。本研究では，上流山地部で 1 次元モデルを考慮し，さらに下流低平地部では 2 次元氾濫モデルを適用した解析を行った。また，下流端境界においては，樋門操作とともに支川と本川の水位による相互作用を考慮した。このモデルを用いることで，平成30年 7 月豪雨において福知山市大江町で発生した内水氾濫をより現実に即してシミュレーションすることができた。
解析結果は，やや過小評価になったものの，実測データとよく一致した。さらに本研究では，
樋門操作を（適切なタイミングで）行わないリスクについても検討した。解析によると，適切な

108

Numerical Simulation of Pluvial Inundation Considering Gate Operation

タイミングで樋門を閉鎖した場合に比較して，樋門を閉鎖しなかった場合には浸水深が40 cm
大きくなる結果となった。本モデルは，ポンプ設置などの将来的な浸水軽減対策の効果を評価するのに用いることも可能であると考えられる。
キーワード：内水氾濫，門の操作，洪水氾濫対策