Evaluation of Fast Flood Diffusion through a Drainage Channel : A Flood Disaster Case Study of Japan ’ s Kinugawa River , September 10 , 2015

On September 10, 2015, unprecedented flood was occurred in Kinugawa River basin located on eastern Japan. It inundated 40 km of flood plain in Joso city, Ibaraki Prefecture, and more than 4000 people there called for help despite supposedly having sufficient time to evacuate. Some said that small initial flood before main severe flood arrived made them make a mistake in deciding whether to evacuate or stay there, despite having to actually evacuate in reality. This study focused on flood behaviour in this area, in particular, the effect of a small drainage channel lying on the flood plain which caused fast flood diffusion in case of occurring huge overflowing. Field investigations starting on time of the disaster with high-resolution positioning system were conducted to obtain spatial maps of flood depth and height. For appropriate modelling of the effect of small channel, we applied simulation model coupling 1-dimensional (1D) and 2-dimensional (2D) hydraulic scheme on the field and compared results from the 1D/2D coupled model and model without 1D scheme. The models provided information that the flood could reach 4 hours earlier to the city central of Joso city comparing in case of model without 1D scheme. The water depth rose irregularly and it was more confusing and difficult for the victims to make appropriate evacuation act.


Introduction
Japan is located in a monsoon zone and, thus, is one of the rainiest countries in the world.Most of Japan's cities lie on alluvial plains in which the flood risk is relatively high, so historically we have suffered a large number of floods.Many flood protection measures have been implemented, including structural countermeasures, alert systems and evacuation planning and procedures.However, recently, we experienced incredibly strong rainfalls, perhaps as a result of global climate change, resulting in extremely severe disasters in Yamaguchi in 2013, Hiroshima and Izu-Oshima in 2014, to name a few.In Yamaguchi, a continual downpour of two hours that exceeded 130 mm/hour inundated the town of Susa very quickly and completely.Hiroshima experienced more than 100 mm/hour of severe rainfall, and a number of debris flows struck hillside residences, resulting in eight victims losing their lives.And it is feared that extremely heavy rainfalls such as these will increase in the future.These unprecedented rainfalls brought flood patterns we had never before experienced.Therefore, it is important to learn as much as possible about them to determine whether existing flood protection facilities, warning systems and evacuation schemes remain effective.
On September 9, 2015, an especially severe rainfall was brought on by two strong typhoons, Nos. 17 (Kilo) and 18 (Etan), in Kanto and the South Tohoku region, in eastern Japan.Serious flooding occurred in the Kinugawa River basin, located in the prefectures of Tochigi and Ibaraki in the Kanto region (Figure 1(a) and Figure 1(b)).Due to the severe flood, a levee failure and flood overtopping happened, and they inundated around 40 km 2 area of the flood plain in the city of Joso, Ibaraki Prefecture (Figure 1(c) and Figure 2(a) and Figure 2(b)).In this disaster, one of the most remarkable facts is that more than 4000 inhabitants in the city needed to be rescued from their homes even though they might have had enough time to evacuate without assistance, because Joso's city center is 10 km away from the riverbank failure point.In fact, there was little flooding in the city center before arrival of the main flood.Some residents said that this minimal initial flooding made them think the flood was smaller than they anticipated, and they decided to stay home, not realizing that they were actually facing unprecedented severe flood.In the flood plain, a drainage waterway called Hachikenbori-gawa Channel lies as shown in Figure 1(c) and Figure 2(c).It can be assumed that the flood water bumped into the channel and diffused downstream very quickly considering its high water depth.This accelerated diffusion of the flood through the channels or pipes has been discussed in inland flooding, especially in urban areas [1] [2] [3].Though huge volume flows such as those caused by riverbank failures have not been a focus of much discussion, the effect of this fast diffusion can be significant.
To evaluate the interaction between channel facilities and floodplain properly, a 1D/2D coupled hydraulic model is effective [4] [5].In particular, that kind of hydrodynamic model was applied to urban area using several commercial software applications for integrated flood simulation [4] [6].In general, modeling of flood diffusion on flood plain is developed on the 2D field.Although computation performance has improved day by day, calculation grid size was set several meters long in practice, which is not enough to resolve geometry (width and volume) of small channel like we discussed.Including point of view of simulation According to this background, we studied the process of the flood diffusion, especially in focusing on acceleration by small channel, based on the case study of the unprecedented flood occurred in Kinugawa River basin, 2015.Essential information of the flood, site location, rainfall and flood intensity and official waring and evacuation, were provided for the first introduction.Flooding process was investigated from beginning of the flood, and inundation depth and absolute water level were also surveyed with high accurate positioning equipment.A simulation model capable 1D/2D model integration was applied to the field for appropriate modeling of small channels lying on broad flood plain.
From the results after the model validation, we discussed the properties of the Journal of Water Resource and Protection flood, shorter arriving time of flood, irregularity of flood depth rise and water balance, and future direction to the flood protection we should do.

Site Location
The Kinugawa River basin is located in eastern Japan's Kanto region (Figure 1(a) and Figure 1(b)).The Kinugawa is one of the largest branches of the Tonegawa River, which has the widest watershed in Japan.The Kinugawa River is 177 km in length and drains into a 1760 km 2 watershed area.Four multipurpose dams and many check dams were installed in its upper reach.About 65% of the basin is covered with mountainous landscape, and the remaining 35% is alluvial plain.In the middle reach, the river bed mainly consists of grain, and its width is considerable (about 700 m), but not particularly braided.Due to abundance supply of sediment, natural banks, riverside sand hills, and a wide flood plain formed in the lower middle reach, where the width of the river is smaller (300 m) than it is in the upper middle reach.
The inundated area is a flood plain on the left side of Kinugawa River in the lower middle reach.It is surrounded by a natural levee or sand hill formed by Kinugawa River and Kokaigawa River (Figure 1(c)).The urban area has mainly on a slightly higher elevation.Joso's city center, called the Mitsukaido area, is also on the higher land, but the residential area has been expanding into the The pumping station, which can drain 30 m 3 /sec, is installed at the most downstream point of the channel.The channel also branches in the Mitsukaido area, and the sub-channel is called Old Hachikenbori-gawa Channel.Also, several small drainage are installed in the Hachikenbori-gawa Channel, however, many of their gates unintentionally were not closed during the disaster.

Rainfall
Typhoon No.18 appeared in southern Japan in the northern Pacific (N20˚25'32", E136˚4'52") on September 7, 2015.It moved northward and reached the Atsumi Peninsula, Aichi Prefecture at 10:00 on September 9. Then it became an extratropical typhoon in the Sea of Japan at 15:00.Unfortunately, Typhoon No.17 also retained its intensity in the Pacific Ocean, east of Japan.In combination, the two typhoons brought increasing humidity and forceful winds.As a result, a continuous linear rainfall band that stretched in a north-south direction developed in the North Kanto and Tohoku regions.The accumulated rainfall total

Injuries and Property Damage
Table 1 presents a summary of the human toll and property damage caused by this disaster.According to this data from the Cabinet Office [7] and local government [8], the number of deaths and seriously injured people in the Ibaraki Prefecture was three and 51, respectively.In terms of property damage, the number of partially and fully collapsed buildings, and those with flooding above ground level are 54, 5486, 185 and 3767, respectively.The number of injuries and deaths was not as devastating as in past flood disasters in our history, but the property damage was extensive sewers using several commercial software applications for integrated flood simulation [9].Finally, an official evacuation directive and an official evacuation call were issued to approximately 34,000 persons.Nonetheless, many residents were stranded in their homes: 1339 persons required rescue by helicopter and 2919 were rescued by boat.Road washouts, railway disruptions and other such transportation complications were the main causes for these extreme measures.

Evacuation
Pumping got underway to resolve the inundation, but despite considerable helps, it took about 10 days for the water to recede.

Methods
To evaluate the channel's effect on flooding, we conducted a field survey and integrated hydrodynamic simulation.We investigated the distribution of the inundation depths and levels by measuring hundreds of high water marks using high resolution positioning system called RTK-GNSS (Real-Time Kinematic Global Navigation Satellite System).The geometry of the bank height along the channels was also measured in the field.The 1D/2D coupled hydraulic simulation model was applied to the inundated field for determining the effect of small channels that drive flood water downstream quickly.In this study, MIKE 2016, commercial hydrodynamic simulation software including MIKE FLOOD module capable model coupling of 1D model (MIKE 11) and 2D model (MIKE 21) was used.

Field Investigation
Field surveys for the investigation of flood characteristics were conducted several times.In the first survey on September 10, the day the flood occurred; we inspected the flood area and found that the initial inundation occurred in the Mitsukaido district, as shown in the photo in Figure 3. Secondary surveys were done to identify flood behavior and characteristics.Many flood marks were measured from the ground to their ultimate height.Some were also measured at their elevation with a portable and high-accuracy positioning system called network type RTK-GNSS with Virtual Reference Station (VRS) method (Trimble R4, Trimble R6 and TOPCON HiPerV GGDM) which has an approximately ±4 cm height margin of error.In this system, initial estimation data are adjusted in real time by information of VRS location and its correction status via mobile phone network.The system also has advantage in portability which is able to treat by one worker and one set of equipment in a few minutes.Although we can obtain flood depth distribution data by conventional way, the new equipment enable to collect absolute level data easily and efficiently and deploy it on GIS software immediately.Finally, we collected 307 and 133 data elements of flood depth and flood elevation including data shared by [10].To investigate the flooding process, we interviewed area residents and collected their photos of the disaster to extract information of water level under the disaster.

Governing Equations
The main governing equations of the 1D (MIKE11) and 2D (MIKE21) modules are briefly discussed here, as are the solution procedures.The governing equation of the 1D model is the Saint-Venant equation based on several assumed factors: incompressible and homogeneous fluid, uniform velocity and horizontal water level in cross-section, small bottom slope and small longitudinal variation in hydrostatic pressure distribution.The equations are conservation of mass and momentum as given in Equations ((1) and ( 2)), respectively.
Solutions of the equations of continuity and momentum are based on an implicit finite difference scheme.The scheme is structured in order to be independent of the wave description specified (i.e., kinematic, diffusive or dynamic).In this simulation, we used a dynamic wave approximation scheme.
The MIKE 21 modelling system is based on the numerical solution of the depth-averaged Navier-Stokes equations describing the conservation of mass and momentum in two horizontal directions.These equations can be written in simplified form as shown in Equations (3) through (5).
These equations are solved using finite difference approximations and an Alternating Direction Implicit (ADI) scheme that include unconditional stability in the linear sense where there is no stability limit on the time step.
To connect the MIKE 11 and MIKE 21 model calculations, we applied the lateral link function in the MIKE FLOOD module, which calculates flow interaction based on the structure equation and water level of MIKE 11 and MIKE 21 on the pre-defined links.Concretely, water levels inside (on 1D) and outside (on 2D) of channel and bank height were compared.If the MIKE 11 water level was higher than the others, the discharge flowing from MIKE11 to MIKE21 was estimated by following Honma's weir formula, shown in Equation ( 6).This can more accurately expresses the exchange of volumes via embankment.
Note the flow through the link is distributed into several MIKE 11 computational points to obtain water level h, and the method do not guarantee momentum conservation.

Calculation Setting
As shown in Figure 4(a) and Figure 4(b), the calculation area was set to cover the flooding area.In this calculation we modeled Hachikenbri-gawa Channel and its branches with 1D model and the other field with 2D.Inflow rate onto the 2D field occurred by levee failure and overflowing were considered as boundary conditions.Because of their uncertainty, these inflow input and roughness parameters were calibrated to fit to observed inundation depth and level and water level on the channel.The calculations were carried out from 5:00 on September 10 through 8:00 on September 11 (JST).
In the 2D calculation field, 25,000 (125 × 200) rectangular computational grids (50 m × 100 m) were applied.Needless to say, finer grids or unstructured cells could also provide reliable results; however, it is not necessary and not reasonable in situation like our site that boundary condition remains uncertainty.
Flow rate input at the grids for the bank breach (21 km) and overtopping (25 km) were obtained as shown in Figure 4(c) for boundary condition.Overtopping actually occurred at two points, but we considered them as one at 25.0 km.
Note that these data are just hypothetical value obtained by following estimation: elongating the observed water level data at near Kamaniwa Station (27.3 km) as the peak attached to the high water mark level at the overtopping and bank breach points, applying the weir formula of Honma and calibrating to fit the maximum depth to the observed in situ flood mark depth.The accumulation of input volume is about 44 million m 3 , which is similar to the other estimation [10], however, the inflow data needs further discussion of its validity.The bathymetry for the calculation was obtained by generating 5 m mesh DEM (digital elevation model) data.It is customary to provide a mesh-averaged value, but we took the maximum value −0.6 m to mesh over major road and railway to consider the blocking effects by embankment.Model parameter of roughness, Manning's n, was set at 0.10 in urban areas and 0.06 which is the range usually used, respectively.Precipitation on the site during the calculation period was ignored because it enough weak (Figure 3).

Model Validation
For model validation, we show results obtained by the 1D/2D coupled model in Figure 5 and Figure 6.At 17:00, we found that the main flood moved along the right bank of the channel, and the water depth was higher than that on the left bank.It indicated that the Hachikenbori-gawa Channel bank significantly affected the flood behavior.At 19:00, the flood reached the Mitsukaido area and completely inundated it.On the west side of the Hachikenbori-gawa Channel, where the deepest inundation was observed concequently, the flood had not yet arrived.However, the waters went not only northward upstream, but they also travelled downstream.

Flooding Process
Between 23:00 and midnight, nearly the entire flood plain was partially submerged, except at the natural levee.Comparing the simulated maximum depth produced by the two models, we did not find any significant difference; however, the existence of a small channel lying on the flood plain changed the flood propagation pattern.

Flood Diffusion on Channel
As formerly mentioned in Figure 6, the water level at the upstream and downstream stations on the Hachikenbori-gawa Channel rose almost simultaneously at 12:00 indicates the flood wave along the channel quickly diffused downstream.
After 15:00, the water-level increase became moderate.At that point, overtopping occurred through the Old-Hachikenbori-gawa Channel and its drainage canals.In fact, the bank height along the Old-Hachikenbori-gawa Channel was lower than the water level then.We were able to reproduce this water level change well with our model.
Photo analysis, shown as yellow-hatched marks in Figure 6, pinpointed the start of inundation in this stage.At that time, flood mark levels on the flood plain were lower than those in the Hachikenbori-gawa Channel, meaning that inflow from the channel to the flood plain actually occurred.After the initial inundation, the flood water level drastically increased at 19:00 due to the arrival of the main flood wave.At this stage, the flood plain was also completely inundated (see also Figure 7).Careful examination showed that the water level on the flood plain was slightly higher than the Hachikenbori-gawa Channel's water level.This proves that flood water should move from the flood plain to the channels.
Moreover, it can be assumed that the Hachikenbori-gawa Channel bank worked to prevent flood waters from flowing into the channel.

Water Balance Analysis
Mass balance in each channel in the calculation is shown in

Figure 1 .
Figure 1.Example of a figure caption (figure caption).(a) and (b) study site of Kinugawa River basin, (c) map of the flood's extent on 9/10/2015 in Kinugawa.
lower flood plain due to population increases.The first inflow of flood water by overtopping occurred in the Wakamiyado area (25.35 km and 24.75 km from Tonegawa River, Figure 2(a)) at 6:30 on Sep. 10 and the Misakacho area (21.0 km from Tonegawa R., Figure 2(b)) at 12:50 by riverbank failure.A small channel, the Hachikenbori-gawa Channel, lies in the flood plain (Figure 1(c) and Figure 2(c)).It divides the flood plain into east and west sections.The channel was digged for agricultural drainage during the 16 th Century.

Figure 3
Figure3shows time series data of rainfall and evacuation advisories for heavy rainfall (JMA: Japan Metrological Agency), flood disaster (rainfall based, JMA) and specific river flooding (water level based, MLIT: Ministry of Land, Infrastructure, Transport and Tourism) around Joso city.The first heavy-rain advisory was announced on September 8 at 13:29 and it was raised to a heavy rain warning on September 9 at 16:36.A flood advisory was released on September 9 at 5:00 from JMA and it changed to warning at 16:36.In terms of Kinugawa River flood information, MLIT released an advisory at 20:40 on September 9 because the water level at Kinugawa-Mitsukaido Station triggered a flood caution at 23:00, followed by a flood warning at 0:15 on September 10.Approximately six hours later on the 10 th , overtopping occurred on the left bank in the Wakamiyado area and flood occurrence information was released at 6:30.After that, an emergency rainfall warning was issued at 7:45, signifying that residents should take immediate survival actions.At 12:50, a left riverbank failure occurred in the Misakacho area.These two severe flooding occurrences inundated the entire flood plain.Joso's city hall, located in the Mitsukaido area, saw its administrative functions paralyzed.

Figure 3 .
Figure 3. Timeline of disaster-information dissemination in the Kinugawa River basin.

Figure 4 .
Figure 4. (a) and (b) Maps of calculation bathymetry, channel branch, boundary condition and observed inundation depth.Colored mesh and blue lines indicate 2D land height and 1D channel branch location, respectively and colored circles indicate classed high water mark depth.(c) and (d) Time series data of input flow rate for boundary condition onto 2D mesh and 1D region indicating discharge at overtopping and bank collapse points in 2D, and upstream runoff and pumping rate in the 1D model.(e) Model geometry of the 1D model based on level observations using RTK-GNSS.

The
1D open channel model includes Hachikenbori-gawa Channel, Old Hachikenbori-gawa Channel and two small drainage canals attached to the flood plain.Distributed discharge and point sink at the pump station were considered as a boundary condition as shown in Figure 4(d).Initial flow rate and water level were determined to adjust to the condition before the flood water flowing into the channel.The pumping status was decided according to the official report.All the end of the branches was closed, which the mass interaction to 2D region occurred only via the lateral links.The geometry of the 1D branch was based on the observations with RTK-GNSS shown as in Figure 4(e).Manning's n of the channels and drainage canals was uniformly set at 0.05 considering its vegetation.

Figure 5
Figure 5 and Figure 6.Figure 5 shows a comparison between maximum depth in calculation and high water depth obtained by flood mark investigation.The data were stratified into upper, middle and lower areas, shown in Figure 4(a).

Figure 5 .
Figure 5. Model validations with comparing water depth.The colored marks correspond to the areas displayed in Figure 3.

Figure 6 .
Figure 6.Time series of observed (marks) and calculated (lines) water level including data analyzed from photos taken under the flood.

Figure 7
Figure 7 indicates estimations of water depth and velocity distribution at each time and in maximum given by the 1D/2D coupled model (Figure 7(a)) and the model using 2D instead of 1D part (2D-only) (Figure 7(b)).From the figure, we see that the flooding gradually propagated southward along the Hachikenbori-gawa Channel.Figure 7(a) shows that on September 10 at 11:00, overtopping flow from Wakamiyado reached the right bank of Hachikenbori-gawa Channel and went south along the height bank.At 15:00 after the bank failure, shown in the top middle image of Figure 7(a), the flow from the bank breach point also reached to the Hachikenbori-gawa Channel.The flood entered the channel and

Figure 7 .
Figure 7. Distributions of depth and velocity in calculation.(a) Results of 1D/2D coupled model and (b) 2D-only model.

Figure 8 Figure 8 .
Figure 8 shows time series changes of flood water depth at certain grids in the 1D/2D coupled model (Figure 8(a)) and the 2D-only model (Figure 8(b)) extracted at several meshes shown in Figure 8(c).Here we also found a difference in the initial inundation in the Mitsukaido area, indicated by blue line C and purple line D in Figure 7(a) and Figure 7(b).The 1D/2D coupled model produced a stepwise rising pattern, but the 2D-only model produced a simple gradation.The coupled model showed the start time of the Mitsukaido area flood to be around 14:00, with moderate rises in water depth from 15:00 to 18:00.The 2D-only model, however, does not indicate this.After that, the water depth rapidly increased due to the arrival of the main flood wave at 19:00.In the area on the left side of Hachikenbori-gawa Channel (point E, depicted by the green line) at which maximum inundation depth was observed, the arrival of the flood was

Figure 9 .
figure, inflow from flood plain to channels is defined as plus.The fluctuating values indicate net volume-per-unit time through each channel in m 3 /sec unit.

Figure 9 .
Figure 9.Time series of calculated mass balance across the 1D and 2D connection.Grey hatch indicates out of calculation.

Table 1 .
Summary of damage and evacuation in Ibaraki Prefecture.