Journal of Natural Disaster Science, Volume 39，Number 2，2018，pp35-48

Modeling of Stormwater Drainage/Overflow Processes Considering Ditches
and their Related Structures
Kenji KAWAIKE*, Hao ZHANG**, Takumi SAWATANI***and Hajime NAKAGAWA**Disaster Prevention Research Institute, Kyoto University**Faculty of Science and Technology, Kochi University***Research and Development Center, Nippon Koei Co., Ltd(Received: Oct. 18, 2018 Accepted: Dec. 12, 2018)

Abstract

We propose a revised inundation flow model for urban areas in which storage effects of ditches
are incorporated into stormwater drainage and overflow processes. Ditches are assumed to be on
both sides of every street. Simulations were performed for two cases, i.e., considering and notconsidering ditches, and a significant difference was observed between the results for the twocases. However, the simulation results obtained by including the volume capacity of ditches inthe volume of stormwater drainage boxes in the authors’ conventional model are almost the sameas the results obtained using our revised model. Consequently, while the volume of ditches has asignificant effect on the inundation results, the stormwater drainage process can be simplified in
the simulation model.
Keywords: pluvial inundation, ditch, stormwater drainage box, numerical simulation

1. INTRODUCTION
In recent years, pluvial inundation disasters have occurred frequently in urban areas worldwide.
In Japan, such pluvial inundations are caused by short-time local torrential rainfall and long-term
rainfall events. In certain cases, the high water level of external rivers makes it difficult to drain
pluvial inundation water from residential areas. Consequently, pluvial inundation has led to highwater depth and severe economic damage in a few cases. It has become more important topredict local risks of pluvial inundation with greater accuracy, which requires the improvementof simulation models.
One of the difficulties in simulating urban inundation is the complex system of drainage
facilities. Several structures are involved in this system, such as storm drains, drainage boxes,
ditches, connecting pipes, and sewer pipes. The scale of these structures is relatively smaller thanthat of overland structures, and detailed data of their locations and configurations are notavailable. Thus, in typical models, the drainage and overflow processes are simplified byomitting some of these structures.
For example, Takeda et al. (2007) assume that the inundation water on a ground surface
is drained into sewer pipes through manholes with no covers and estimated drainage discharge isbased on the weir equation. Chen et al. (2007) combine a 1D sewer model and a 2D overland

35

K.KAWAIKE, H.ZHANG, T.SAWATANI, H.NAKAGAWA

inundation model with grids containing manholes, and interaction discharge is calculated using
the weir and orifice equations.
Our research group has developed and improved numerical models for urban pluvial
inundation, considering the interaction process between overland surfaces and sewerage systems.
In the first model (Kawaike et al., 2004), pump capacity is allocated to every computationalmesh in its catchment area, which is equivalent to the maximum drainage discharge from themesh. In the second model (Kawaike et al., 2010), storm drains are assumed along a sewer pipewith equal interval spacing and interaction discharge is calculated using the step-down andoverflow equations. In the third model (Lee et al., 2013), storm drains are assumed at the centerof every street mesh and interaction discharge is calculated using the weir and orifice equations.
However, comparisons of the simulation results obtained using these models and actual
measurement results show that simulated inundation areas are typically overestimated,particularly in the cases of small inundation events. This may be because stormwater is not
drained before reaching the storm drain inlets in the simulation and computational meshes witheven a small depth of stormwater are regarded as inundated areas.
In this study, our numerical model of urban inundation is revised in terms of thestormwater drainage or overflow processes between an overland surface and a sewerage system,and ditches and their related structures are incorporated into the model. Ditches are set on bothsides of every street mesh, and stormwater on the overland surface is expected to drain into theditches more easily.

2. COMPUTATIONAL MODEL
We think that ditch capacity has a significant effect on the urban inundation process though it isusually neglected in numerical simulations. In this study, based on the conventional model for
pluvial urban inundation, we improved the interaction part between 1D and 2D sub-models by
incorporating ditches in the drainage/overflow process (revised model). Another method of
improvement is incorporating ditch capacity into the drainage box capacity of the conventionalmodel (simplified model). We compared the simulation results of these three models: theconventional model, the revised model, and the simplified model.
2.1 Model for pluvial inundation (Conventional model)
The numerical model for pluvial inundation that we developed (Lee et al., 2013; Lee et al., 2016)is an integration of a 2D model of overland inundation flow and a 1D model of sewer pipe flow.
An overland surface is divided into triangular unstructured meshes to delineate the border
between streets and buildings, and the meshes are categorized into streets, buildings, vacant
spaces, etc.
We assume that all street meshes possess a drainage box and calculate the interaction
discharge between the drainage box and overland surface and between the drainage box andsewer pipe depending on their water levels or piezometric heads (Fig. 1(a)). The weir and orificeequations (equivalent to Eqs. (9), (11) and (10), (12), respectively, described later) are employed
for this calculation. Such an integrated model and the coefficient values contained in theequations have already been validated through physical experiments (Lee et al., 2013).

36

Journal of Natural Disaster Science, Volume 39，Number 2，2018，pp35-48

rainfallOverland surface meshStreet meshStreet mesh

Drng.
box

Drng.
box

Sewer pipe(a) Stormwater drainage/overflow processes in the conventional model
rainfallOverland surface meshStreet mesh

Drng.
box

ditch

Street mesh
Drng.
box

ditch

Drng.
box

Sewer pipe(b) Stormwater drainage/overflow processes in the revised model

Drainage box in the revised model
Ditch in the revised model
Drainage box in the conventional model

streetbuilding
vacant area(c) Location of drainage boxes and ditches in the conventional and revised models
Fig. 1 Schematic view of the conventional and revised models
37

K.KAWAIKE, H.ZHANG, T.SAWATANI, H.NAKAGAWA

In this model, while the length and the width of a drainage box are assumed as 20 m and 0.5 m,
respectively, the height is determined by substituting the capacity of the connecting pipe (thediameter is assumed as 20 cm) between the drainage box and sewer pipe.
2.2 Revised model
In the above-mentioned numerical model for pluvial inundation, the stormwaterdrainage/overflow processes between the overland surface and sewer pipe are revised as shownin Fig. 1(b). Ditches, which are typically located on the border between streets and residential
blocks, are not necessarily prepared as a dataset of their coordinate positions, elevations, crosssectional configurations, and potential discharge capacities as sewerage network data. In thisstudy, we assume that ditches are located along the border between the street meshes and themeshes of other categories and drainage boxes are located at both ends of the ditches. We
propose a new model (hereinafter ‘revised model’) considering the drainage/overflow processes
through the ditches. The stormwater on a street mesh flows into a ditch, then to the drainage
boxes at both ends of the ditch, and finally to the sewer pipe closest to the drainage boxes. If thepiezometric head of the sewer pipe is higher than the surface elevation, the stormwater overflows
on the overland surface in the opposite order to the above-mentioned drainage process: a sewer
pipe, a drainage box, a ditch, and a street mesh. Figure 1(c) shows the locations of drainage
boxes in the conventional model and the locations of ditches and drainage boxes in the revised
model. The simulation results are sensitive to the width and height of ditches and drainage boxes,
and these parameters are discussed in Section 3.2.
The interaction discharges of the respective processes are calculated as follows:
Interaction discharge between a street mesh and a ditch
We assume that ditches are located along the border line of street meshes. A ditch is notdivided in the longitudinal direction, and its storage volume is only calculated using its length,
width, and height in the simulation. The bottom elevation of the ditch is determined bysubtracting its height from the surface elevation of the neighboring street mesh. In reality, aportion of the ditch is covered with lids, which regulate interaction discharge. However, theeffects of lids are disregarded in this study for simplicity. This implies that the entire surface ofthe ditch is open.
--

Drainage process (ℎ𝑠𝑠 ≤ ℎ𝑟𝑟 )𝑄𝑄𝑒𝑒 = 𝐶𝐶1 𝐴𝐴𝑡𝑡 �2𝑔𝑔ℎ𝑟𝑟 ∶ ℎ𝑠𝑠 ⁄ℎ𝑟𝑟 ≤ 2⁄3(1)

𝑄𝑄𝑒𝑒 = 𝐶𝐶2 𝐴𝐴𝑑𝑑 �2𝑔𝑔(ℎ𝑟𝑟 − ℎ𝑠𝑠 ) ∶ ℎ𝑠𝑠 ⁄ℎ𝑟𝑟 > 2⁄3(2)

𝑄𝑄𝑒𝑒 = −𝐶𝐶1 𝐴𝐴𝑡𝑡 �2𝑔𝑔ℎ𝑠𝑠 ∶ ℎ𝑟𝑟 ⁄ℎ𝑠𝑠 ≤ 2⁄3(3)

Overflow process (ℎ𝑠𝑠 > ℎ𝑟𝑟 )𝑄𝑄𝑒𝑒 = −𝐶𝐶2 𝐴𝐴𝑑𝑑 �2𝑔𝑔(ℎ𝑠𝑠 − ℎ𝑟𝑟 ) ∶ ℎ𝑟𝑟 ⁄ℎ𝑠𝑠 > 2⁄3(4)

where Qe is the interaction discharge, Hr and Hd are the water levels of a street mesh and a ditch,
respectively, zr is the surface elevation of the street mesh, hr and hs are the overflow depth of thestreet mesh and the ditch, respectively (ℎ𝑟𝑟 = 𝐻𝐻𝑟𝑟 − 𝑧𝑧𝑟𝑟 , ℎ𝑠𝑠 = 𝐻𝐻𝑑𝑑 − 𝑧𝑧𝑟𝑟 , ℎ𝑟𝑟 ≥ 0, ℎ𝑠𝑠 ≥ 0), At is theattachment water area of the street mesh (𝐴𝐴𝑡𝑡 = 𝐿𝐿𝑑𝑑 ∙ ℎ𝑟𝑟 ), Ad is the smaller attachment water area38

Journal of Natural Disaster Science, Volume 39，Number 2，2018，pp35-48(𝐴𝐴𝑑𝑑 = 𝐿𝐿𝑑𝑑 ∙ min(ℎ𝑟𝑟 , ℎ𝑠𝑠 )), Ld is the attachment length between the street mesh and ditch, and C1and C2 are coefficients (C1 = 0.35, C2 = 0.91) validated by Lee (2013).
Interaction discharge between a ditch and a drainage box--

Drainage process (ℎ𝑠𝑠 ≤ ℎ𝑑𝑑 )Overflow process (ℎ𝑠𝑠 > ℎ𝑑𝑑 )𝑄𝑄𝑒𝑒 = 𝐶𝐶1 𝐴𝐴𝑏𝑏 �2𝑔𝑔ℎ𝑑𝑑(5)

𝑄𝑄𝑒𝑒 = −𝐶𝐶1 𝐴𝐴𝑏𝑏 �2𝑔𝑔ℎ𝑠𝑠(7)

𝑄𝑄𝑒𝑒 = 𝐶𝐶2 𝐴𝐴𝑏𝑏 �2𝑔𝑔(ℎ𝑑𝑑 − ℎ𝑠𝑠 )(6)

𝑄𝑄𝑒𝑒 = −𝐶𝐶2 𝐴𝐴𝑏𝑏 �2𝑔𝑔(ℎ𝑠𝑠 − ℎ𝑑𝑑 )(8)where Hb is the water level of a drainage box, zd is the bottom elevation of the ditch, hd and hs are
the overflow depth of the ditch and the drainage box, respectively, (ℎ𝑑𝑑 = 𝐻𝐻𝑑𝑑 − 𝑧𝑧𝑑𝑑 , ℎ𝑠𝑠 = 𝐻𝐻𝑏𝑏 −𝑧𝑧𝑑𝑑 , ℎ𝑑𝑑 ≥ 0, ℎ𝑠𝑠 ≥ 0) and Ab is the attachment water area between the ditch and drainage box.
Interaction discharge between a drainage box and a sewer pipe-

Drainage process (ℎ𝑝𝑝 ≤ ℎ𝑏𝑏 )2

𝑄𝑄𝑒𝑒 = 3 𝐶𝐶𝑑𝑑𝑑𝑑 𝐿𝐿𝑝𝑝 �2𝑔𝑔�ℎ𝑏𝑏 − ℎ𝑝𝑝 �-3⁄2∶ �ℎ𝑏𝑏 − ℎ𝑝𝑝 � ≤ 𝐵𝐵0⁄2

𝑄𝑄𝑒𝑒 = 𝐶𝐶𝑑𝑑𝑑𝑑 𝐴𝐴𝑢𝑢 �2𝑔𝑔�ℎ𝑏𝑏 − ℎ𝑝𝑝 � ∶ �ℎ𝑏𝑏 − ℎ𝑝𝑝 � > 𝐵𝐵0⁄2

Overflow process (ℎ𝑝𝑝 > ℎ𝑏𝑏 )2

𝑄𝑄𝑒𝑒 = − 3 𝐶𝐶𝑑𝑑𝑑𝑑 𝐿𝐿𝑝𝑝 �2𝑔𝑔�ℎ𝑝𝑝 − ℎ𝑏𝑏 �3⁄2∶ �ℎ𝑝𝑝 − ℎ𝑏𝑏 � ≤ 𝐵𝐵0⁄2

𝑄𝑄𝑒𝑒 = −𝐶𝐶𝑑𝑑𝑑𝑑 𝐴𝐴𝑢𝑢 �2𝑔𝑔�ℎ𝑝𝑝 − ℎ𝑏𝑏 � ∶ �ℎ𝑝𝑝 − ℎ𝑏𝑏 � > 𝐵𝐵0⁄2

(9)
(10)
(11)
(12)

where Hp is the piezometric head of a sewer pipe, zb is the bottom elevation of a drainage box, hb
is the water depth of the drainage box (ℎ𝑏𝑏 = 𝐻𝐻𝑏𝑏 − 𝑧𝑧𝑏𝑏 ), hp is the piezometric height of the sewer
pipe higher than zb ( ℎ𝑝𝑝 = 𝐻𝐻𝑝𝑝 − 𝑧𝑧𝑏𝑏 ), Lp is the perimeter length of a connecting pipe, Au is the
cross-sectional area of the connecting pipe, B0 is the diameter of the connecting pipe, and Cdw
and Cdo are the coefficients of the weir and the orifice equations, respectively (Cdw = 0.48, Cdo =0.57).
2.3 Simplified model
Instead of considering the detailed drainage/overflow processes in the revised model, we
consider ditch capacity in a simpler manner. The effects of ditches are simply represented byincorporating the equivalent capacity of ditches into the capacity of drainage boxes in theconventional model (hereinafter ‘simplified model’). The simplified model proposed here is thesame as the conventional model except for the increased capacity of the drainage boxes.

39

K.KAWAIKE, H.ZHANG, T.SAWATANI, H.NAKAGAWA

3. APPLICATION TO AN ACTUAL URBAN AREA
3.1 Target area
The target area of this study is the Mikazuki district, which is one of the sewer drainage areas in
Kochi, Japan. This area is between Kuma River and Kosui River, and it experiences severe
inundation damage caused by heavy rainfall. The Mikazuki district is shown in Fig. 2; its area is
1.94 km2. This target area is divided into 73,305 unstructured meshes, which are categorized into
mountains, drainage channels, vacant spaces, buildings, and streets. The representative mesh size
is approximately 10 m, and the representative divided length of the sewer pipes is approximately
3 m. The surface elevation and the five categories with different roughness of computational
meshes are shown in Figs. 3 and 4, respectively. In this study, 77 sewer pipes and 78 manholes
are considered, which are shown in Fig. 5. A pumping station with three pumps is located at thedownstream end of this sewer pipe network. The outlet of the station faces Kosui River. The total
capacity of the three pumps is 15.667 m3/s.

Kuma
River

Kochi Express way

Target area
Kochi Sta.
Kosui
River

Kochi Castle
Kochi City Hall

Kagami River

01km

Fig. 2 Target area of the simulation

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Journal of Natural Disaster Science, Volume 39，Number 2，2018，pp35-48

Fig. 3 Surface elevation of the target area

Buildings
Vacant spaces
Streets
Drainage channels
Mountains
Fig. 4 Categories of the computational meshes

41

K.KAWAIKE, H.ZHANG, T.SAWATANI, H.NAKAGAWA

Mikazuki
Pumping Station
01km

Fig. 5 Sewer pipes and the location of Mikazuki Pumping Station

This target area experienced inundation damage on August 3, 2014. The rainfall observedat the pumping station, the estimated overflow discharge from Kuma River and Kosui River, andthe actual inundated area are shown in Figs. 6, 7, and 8 (Kochi Prefecture, 2014), respectively.
This inundation event is the target for simulation in this study. No inflow or outflow discharge inthe target area is considered other than the above-mentioned observed rainfall, the estimatedoverflow discharge from Kuma River and Kosui River, and the drainage discharge from thepumping station. In the simulation, the effective rainfall is given to the surface of the target area,
and the effective rainfall is derived from the observed rainfall multiplied by runoff ratio, 0.55
(Kochi Prefecture, 2014). The stormwater on the meshes other than street is not drained before it
reaches any street meshes (conventional model) or ditches (revised model).
The computational duration is 48 hours, from 00:00 August 2 to 00:00 August 4.

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Journal of Natural Disaster Science, Volume 39，Number 2，2018，pp35-48

rainfallFig. 6 Hyetograph from 2 to 3 August, 2014 (Kochi Pref., 2014)(The red line in the figure denotes the designated rainfall intensity of the seweragesystem in Kochi city, which is 77 mm/hr = 12.8 mm/10 min.)

Kuma River
Kosui River

Fig. 7 Estimated overflow discharge from Kuma River and Kosui River on 3 August, 2014
(Kochi Pref., 2014)

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K.KAWAIKE, H.ZHANG, T.SAWATANI, H.NAKAGAWA

Fig. 8 Actual inundation area and the measurement points of inundation water depth(Kochi Pref., 2014)

3.2 Configuration of ditches and drainage boxes
It is necessary to determine the configurations (length, width, and height) of ditches and drainage
boxes for the simulation. However, the positions of ditches and drainage boxes are hypothetical.
Even if the precise positions could be reflected in the simulation, it would be difficult to assign
individual configurations to ditches and drainage boxes. We assume a uniform configuration for
all ditches and drainage boxes installed in the target area. We consider seven configuration cases,
as shown in Table 1.

Table 1 Configuration of ditches and drainage boxes (unit: m)
Ditch
Drainage box
width height width length height
Case 1
0.4
0.4
0.5
0.5
0.7
Case 2
0.5
0.5
0.5
0.6
0.8
Case 3
0.6
0.6
0.5
0.7
0.9
Case 4
0.7
0.7
0.5
0.8
1.0
Case 5
0.8
0.8
0.5
0.9
1.1
Case 6
0.9
0.9
0.5
1.0
1.2
Case 7
1.0
1.0
0.5
1.1
1.3

The maximum inundation depths at 11 points (indicated in Fig. 8) obtained through thesimulation are compared with the measured depth. The measured depth, computed depth, and theaveraged difference between them at 11 points are shown in Table 2. The minimum difference
appears in Case 6, and the computed depths are close to the measured values in Cases 4, 5, and 7.
Hereinafter, the configuration of Case 4 is regarded as the basic configuration because theinundated area is the closest to the actual area in Cases 4 and 5 and because the uniform crosssection of 0.9 m × 0.9 m in Case 6 appears to be considerably larger than the actual section size.

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Journal of Natural Disaster Science, Volume 39，Number 2，2018，pp35-48

Table 2 Comparison between the measured depth and calculated maximum depth(unit: m)

Measured
depth
Case 1Case 2
Case 3
Case 4
Case 5
Case 6
Case 7

P1

P2

P3

P4

P5

P6

P7

P8

P9

P10

P11

0.40

0.80

0.55

0.70

0.38

0.28

0.50

0.65

0.60

0.45

1.12

Averageddifference
from themeasured
depth
－

0.690
0.672
0.661
0.633
0.625
0.598
0.569

0.928
0.908
0.894
0.862
0.853
0.820
0.783

0.667
0.647
0.633
0.601
0.593
0.561
0.524

0.662
0.644
0.633
0.605
0.597
0.570
0.541

0.661
0.644
0.633
0.605
0.597
0.570
0.542

0.288
0.272
0.260
0.232
0.224
0.196
0.168

0.551
0.537
0.528
0.509
0.499
0.477
0.458

0.647
0.636
0.629
0.616
0.606
0.588
0.572

0.918
0.910
0.906
0.897
0.893
0.886
0.879

0.458
0.450
0.446
0.437
0.434
0.427
0.420

1.199
1.192
1.188
1.180
1.178
1.172
1.167

0.120
0.113
0.110
0.102
0.101
0.098
0.102

Table 3 Maximum depth calculated using the revised and conventional models(unit: m)

Measured depth
Revised model(Case 4)Conv. model
No ditch volume

Simplified modelwith ditch volume

P1
P2
P3
P4
P5
P6
P7
P8
P9
P10
P11
0.40 0.80 0.55 0.70 0.38 0.28 0.50 0.65 0.60 0.45 1.12
0.633 0.862 0.601 0.605 0.605 0.232 0.509 0.616 0.897 0.437 1.180
0.678 0.919 0.659 0.648 0.649 0.276 0.537 0.630 0.902 0.444 1.188
0.617 0.853 0.594 0.587 0.589 0.216 0.492 0.596 0.877 0.418 1.164

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K.KAWAIKE, H.ZHANG, T.SAWATANI, H.NAKAGAWA

3.3 Comparison between the conventional model and revised model
As mentioned in the previous section, the configuration of Case 4 is applied to ditches anddrainage boxes in the simulation of the revised model. In the simulation of the ‘conventionalmodel’ in this section, the configuration of Case 4 is adopted for drainage boxes and the capacityof the connecting pipes between sewer pipes and drainage boxes is neglected though it was
included in the drainage box capacity in the original ‘conventional model’ (Lee et al., 2016).
The maximum water depths at 11 points for both models are shown in Table 3. The
temporal changes in the water volumes of the overland surface, sewer pipes, ditches, anddrainage boxes for the models are shown in Fig. 9. The inundation water volume at the peak timediffers significantly between the two models. The water volume on the overland surface in therevised model considering the processes of ditches is considerably smaller than that in theconventional model. The drainage box capacity in the conventional model is sufficiently small.
However, in the revised model, the capacities of ditches and drainage boxes, which store a water
volume equivalent to one quarter that of the overland inundation water, have significant effects
on the inundation water volume on the overland surface.
Water volume [m3]

Revised model
Conventional model

OverlandOverlandSewer pipes
Sewer pipes

Ditches + drainage boxes
Drainage boxes (no ditch volume)Fig. 9 Comparison between the revised and conventional models without ditch volume(Water volume of the overland surfaces, sewer pipes, ditches and drainage boxes)
The water volumes of sewer pipes in the two models are almost the same before 16:00. On thecontrary, the water volume of overland inundation is always larger in the conventional model.
This implies that inundation water is stored or drained in ditches in the revised model. After
16:00, the difference between the overland inundation water volume for the models decreases
while the difference between the water volume of sewer pipes for the models increases. This
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Journal of Natural Disaster Science, Volume 39，Number 2，2018，pp35-48

implies that overland inundation water stagnates at ditches or drainage boxes and it takes longer
to reach sewer pipes.
3.4 Comparison between the revised model and simplified model
In the simulation of the simplified model, the height and length of drainage boxes are fixed as
0.3 m and 5.0 m, respectively, and the width is calculated as 1.83 m from the total capacity of theditches and the drainage boxes of Case 4.
The maximum water depths at 11 points for both models are shown in Table 3. The
temporal changes in the water volumes of the overland surface, sewer pipes, ditches, anddrainage boxes for the models are shown in Fig. 10. The overland inundation water volume
around the peak time is almost the same for both models, while it is larger in the simplified
model before and after the peak time. This implies that the maximum inundation depth obtained
through the simulation of the simplified and revised models is almost the same at several points.
However, the simulation results of the detailed inundation/drainage processes at depths otherthan the peak depth are different between the two models. That difference might be caused by thelocation and the surface area of storm drains in both models, which could be regarded as theeffects of lids over the ditches. This requires further investigation.
Water volume [m3]

Revised model
Simplified model

OverlandOverlandSewer pipes
Sewer pipes

Ditches + drainage boxes
Drainage boxes (with ditch volume)Fig. 10 Comparison between the revised and simplified models with ditch volume(Water volume of the overland surfaces, sewer pipes, ditches and drainage boxes)

4. CONCLUSIONSIn this study, we revised an inundation flow model with the effects of ditches in the stormwaterdrainage/overflow processes. The conclusions obtained from the study are summarized below.
47

K.KAWAIKE, H.ZHANG, T.SAWATANI, H.NAKAGAWA-

Assuming that ditches exist on every border between the street mesh and other meshes, theeffect of ditch capacity on the inundation water volume on the overland surface cannot be
neglected.
- The conventional model without ditch capacity overestimates the peak volume of theinundation water on the overland surface.
- The conventional model can represent almost the same inundation situation at the peak timeas the revised model simply by considering the ditch effects by incorporating ditch capacity
into the capacity of drainage boxes.
In conclusion, ditch capacity has significant effects on overland inundation, and thesimplified model, incorporating the ditch capacity into the capacity of drainage boxes, issufficient if the purpose is to assess the inundation depth at the peak time.

Acknowledgement
This work was supported by JSPS KAKENHI Grant-in-Aid for Young Scientists (A) 16H06100
and a grant (17CTAP-C095650-03) from the Infrastructure and Transportation Technology
Promotion Program funded by the Ministry of Land, Infrastructure and Transport of the Korean
government.

REFERENCES
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