water
Article A Proposed Simultaneous Calculation Method for Flood by River Water, Inland Flood, and Storm Surge at Tidal Rivers of Metropolitan Cities: A Case Study of Katabira River in Japan
Naoki Koyama 1,* and Tadashi Yamada 2
1 Civil, Human and Environmental Engineering Course, Graduate School of Science and Engineering, Chuo University, 1-13-27, Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan 2 Department of Civil and Environmental Engineering, Faculty of Science and Engineering, Chuo University, 1-13-27, Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan; [email protected] * Correspondence: [email protected]; Tel.: +81-3-3817-1805
Received: 6 May 2020; Accepted: 18 June 2020; Published: 22 June 2020
Abstract: All metropolitan cities in Japan are located in low-lying areas that surround ports. Accordingly, significant floods that occur in these cities will trigger the simultaneous occurrence of flooding by river water and inland flooding. However, existing studies have focused on the impact of flooding by river water, inland flooding, and high tide in tidal rivers, and disaster mitigation measures focused on detailed flooding processes in such flooding areas have not been conducted thus far. This study focused on a tidal river, i.e., Katabira River of Yokohama city, one of Japan’s metropolitan cities, to construct a simultaneous occurrence model of flooding by river water and inland flooding, including the impact of a high tide. Numerical analysis was conducted using this model, and the results show that the flooded area significantly changed from 0.004 to 0.149 km2 according to the tide level of the estuary. Moreover, by simultaneously solving the calculation of flooding by river water and inland flooding, we found that there was a difference of 50 min between the occurrences of these floods. Therefore, we found that there is a possibility that, if evacuation is not conducted at the time of occurrence of inland flooding, evacuation during subsequent river-water flooding may not be possible. Based on these results, our proposed method was found to be useful for tidal rivers of metropolitan cities.
Keywords: simultaneous calculation method; flood by river water; inland flood; storm surge; tidal river; mitigation measures; inundation; metropolitan Japanese cities
1. Introduction Flooding is one of the most frequently occurring natural disasters and impacts many people every year in the world [1]. Large-scale flooding can significantly impact local societies and their economies [1,2]. For example, economic damage from flooding in the United States has cost $260 billion (approximately ¥28 trillion) per year from 1980 to 2013 [3]. Similarly, between 1970 and 2008, floods caused at least 87 billion euros (approximately ¥10.4 trillion) in economic losses in Europe [4]. In Japan, the cost of damage from flooding between 1993 and 2002 was approximately ¥2.4 trillion. This amount can be broken down into approximately ¥1.1 trillion damage from inland flooding and roughly ¥1.3 trillion from river-water flooding [5]. If it is limited to the Tokyo Metropolitan area as the largest city, the damage cost of inland flooding accounts for approximately 80% of the total [5]. Based on these data, it is clear that inland flooding causes significant economic damage in Japan. Moreover, all large cities in Japan, in which the country’s population is concentrated (Tokyo, Yokohama, Osaka, Fukuoka, Nagoya,
Water 2020, 12, 1769; doi:10.3390/w12061769 www.mdpi.com/journal/water Water 2020, 12, 1769 2 of 18 etc.), are all located in low-lying areas that surround ports [5]. Japan’s land can be broadly categorized into mountainous areas, hilly areas, plateau, low-lying areas, and inland water areas. When these area ratios are compared, mountainous and hilly areas represent roughly 70%; the population and properties are concentrated on plateau and low-lying areas that account for the remaining 30%. For this reason, Japan’s land is susceptible to receive inland flooding and high-tide damage. So-called urban flooding, which occurs in cities, has been occurring globally in recent years [6,7], and rapid urbanization is impacting the scale and frequency of such flooding [8–12]. Due to the progression of urbanization, rainwater that used to either seep into the ground or stagnated on the ground surface has started flowing directly downstream as surface water, thus increasing flooding damage in low-lying areas. Extreme changes in meteorological phenomena due to climate change are considered a global issue and are increasing the danger within cities [10–14]. In addition, climate change will raise sea levels and increase the risk of storm surges in coastal areas [15,16]. In addition, short torrential downpours known as guerrilla rainstorms are becoming frequent in Japanese cities. Specifically, the review of long-term changes in annual rainfall over time in Japan indicates a tendency toward increases in heavy rain, with more than 50 or 80 mm of hourly rainfall being observed [17]. Tropical cyclone activity is also increasing; it is said that high tides caused by the attacks of super typhoons will cause significant flood damages at Osaka Bay surrounding Osaka City, at Ise Bay surrounding Nagoya, and at Tokyo Bay surrounding Tokyo [2]. Based on the above factors, to respond to flood damage that may occur in the future in cities, it is necessary to shift to flood damage countermeasures that also consider the increase in external forces such as typhoons due to climate change. In the case of cities, rainwater is discharged into rivers via sewers. However, when heavy rainfall exceeds the external force envisaged by the design, river-water flooding occurs when the retention capacity of a river is exceeded, and inland flooding occurs when the discharge capacity of sewers is exceeded. A city is protected from flooding by these two systems working in balance. To accurately calculate/predict urban flooding, a model that can simultaneously calculate/analyze river-water flooding and inland flooding is needed. Furthermore, as discussed above, metropolitan cities in Japan are located in the places surrounding ports. Thus, there is a situation where the water level at the estuary rises due to storm surges and water flowing upstream, rendering the river unable to discharge its water into the sea. We must consider this kind of situation may occur [18,19]. Accordingly, what is necessary is a calculation method that takes the effect of a storm surge into account, in addition to river-water flooding and inland flooding. Multiple previous studies have been conducted on creating methods that integrally calculate the flooding of sewers and river water in cities [20,21]. These include the method that integrally calculates river-water/inland flooding and analyzes flooding damage using differences in total rainfall and rainfall intensity [20]. In addition, a proposed model enables real-time river-water/inland flooding prediction simulation for the approximately 620 km2 of 23 wards of Tokyo Metropolis [21]. In addition, previous studies have conducted numerical calculations on the effect of storm surge and wind on water levels in estuaries for coastal areas [22–25]. Pinheiro et al. simulated the effect of storm surge on river water levels [22], Oliveira, H. analyzed the effect of wind on water levels in coastal areas [23]. In addition, Ullman, D.S. et al. simulated the ocean and estuary response to storm surge and rainfall from hurricanes [24]. Cavallaro, L. et al. analyzed the effect of mobile gates on river water level during high tides and floods using numerical analysis [25]. However, no calculation method that takes the impact of a storm surge into account, in addition to river-water and inland flooding, has been proposed in previous studies. Thus, in this paper, we propose a method that takes into account the effect of a storm surge on river-water/inland flooding. This method is applicable to large cities. We also suggest the importance of considering a storm surge by analyzing its results. The objective of this paper is to discuss disaster mitigation measures taking concrete inundation processes into account. Water 2020, 12, 1769 3 of 18
2. The Basin Area of Interest Water 2020, 7, x FOR PEER REVIEW 3 of 20 Water 2020, 7, x FOR PEER REVIEW 3 of 20 2.1. Overview2. The Basin of Katabira Area of RiverInterest (Yokohama City) 2. The Basin Area of Interest This paper is aimed at the Katabira River basin, which flows through Yokohama City, one of the 2.1. Overview of Katabira River (Yokohama City) largest2.1. cities Overview in Japan. of Katabira Yokohama River (Yokohama Station City) is located at the estuary of the Katabira River, and flood This paper is aimed at the Katabira River basin, which flows through Yokohama City, one of the damages frequentlyThis paper is have aimed occurred at the Katabira in the River area basin, around which Yokohama flows through Station, Yokohama mostly City, one due ofto the typhoon largest cities in Japan. Yokohama Station is located at the2 estuary of the Katabira River, and flood damagelargest [26]. cities The basinin Japan. area Yokohama of Katabira Station River is locat is 57.9ed at km the ,estuary and the of lengththe Katabira of the River, main and river flood channel is damages frequently have occurred in the area around Yokohama Station, mostly due to typhoon 17.3 km.damages Figure frequently1 shows anhave elevation occurred mapin the (Figure area around1a) and Yokohama a pipeline Station, network mostly map due (Figureto typhoon1b) in the damage [26]. The basin area of Katabira River is 57.9 km2, and the length of the main river channel is damage [26]. The basin area of Katabira River is 57.9 km2, and the length of the main river channel is Katabira17.3 Riverkm. Figure basin. 1 shows The estuary an elevation faces map Tokyo (Figure Bay, 1a) and and the a pipeline tidal area network is up map to 4(Figure km from 1b) in the the estuary. 17.3 km. Figure 1 shows an elevation map (Figure 1a) and a pipeline network map (Figure 1b) in the As shownKatabira in FigureRiver basin.1b, there The estuary are di fffaceserent Tokyo types Bay, of an sewaged the tidal systems area is withinup to 4 km the from Katabira the estuary. River basin. Katabira River basin. The estuary faces Tokyo Bay, and the tidal area is up to 4 km from the estuary. In the upstream area, the system comprises separate sewers where the rainwater line and sewage AsAs shown shown in in Figure Figure 1b, 1b, there there areare differentdifferent types of sewagesewage systemssystems within within th the eKatabira Katabira River River basin. basin. line areInIn the separated, the upstream upstream while,area, area, the the in system system the downstream comprisescomprises separate area, sewerssewers the system where where the the is rainwaterequipped rainwater line line with and and sewage combined sewage line line sewers whereare rainwaterare separated, separated, and while, while, sewage in in the the flow downstreamdownstream through area, the samethe systemsystem single isis equipped pipe.equipped When with with viewingcombined combined from sewers sewers the where where entire basin, the combinedrainwaterrainwater sewersand and sewage sewage are usedflow flow throughthrough in approximately thethe same single 30% pipe.pipe. of the WhenWhen total viewing viewing area. from Infrom addition, the the entire entire facilitiesbasin, basin, the the such as combined sewers are used in approximately 30% of the total area. In addition, facilities such as floodwayscombined for discharging sewers are used overflowing in approximately rainwater 30%during of the total a flood area. and In addition, drainage facilities pumping such stations as for floodways for discharging overflowing rainwater during a flood and drainage pumping stations for controllingfloodways the flow for discharging of rivers areoverflowing equipped rainwater in the during basin. a Figure flood and2a showsdrainage an pumping aerial photostations of for the tidal controllingcontrolling the the flow flow of of rivers rivers areare equippedequipped in the basin.basin. FigureFigure 2a 2a shows shows an an aerial aerial photo photo of of the the tidal tidal area ofareaarea Katabira of of Katabira Katabira River River River basin basin basin and and and Figure FigureFigure2 b2b shows shows aa photo photo of of of Katabira Katabira Katabira River River River (u (upperpper (upper stream stream stream from from Bridge fromBridge Bridge B in FigureB Bin in Figure Figure1a). The1a). 1a). The tidalThe tidal tidal area area area is a isis completely aa completelycompletely urbanized urbanized areaarea area and and and Katabira Katabira Katabira River River River is is concrete-lined. concrete-lined. is concrete-lined.
(a) (b) (a) (b) Figure 1. Overview of Katabira River basin: (a) elevation map; and (b) pipeline networks map. FigureFigure 1. Overview 1. Overview of Katabiraof Katabira River River basin:basin: ( (aa)) elevation elevation map; map; and and (b) (pipelineb) pipeline networks networks map. map.
(a) (b) (a) (b) FigureFigure 2. Overview 2. Overview of of the the tidal tidal area: area: ( a)) aerial aerial photo; photo; and and (b) photo (b) photo of Katabira of Katabira River. River. Figure 2. Overview of the tidal area: (a) aerial photo; and (b) photo of Katabira River. 2.2. The Relationship between Weather Conditions and Increased Water Level in Katabira River
2.2.1. The Relationship between Total Rainfall and Maximum Water Level Deviation Figure 3 shows the relationship between the peak rainfall intensity and water level deviation (Figure3a) and between the total rainfall and water level deviation Figure3b, at Bridge A (as shown Water 2020, 7, x FOR PEER REVIEW 4 of 20
2.2. The Relationship between Weather Conditions and Increased Water Level in Katabira River Water 2020, 12, 1769 4 of 18 2.2.1. The Relationship between Total Rainfall and Maximum Water Level Deviation in Figure1Figurea, 2.1 km3 shows upstream the relationship from the estuary)between inthe the peak 1205 rainfall rainfall intensity events and that water occurred level deviation for 11 years between(Figure 2008 3a) and and2018. between Here, the total water rainfall level and deviation water level indicates deviation the Figure value 3 obtained(b), at Bridge by A subtracting (as shown the astronomicalin Figure tide1a, 2.1 level km upstream at the estuary from the from estuary) the observed in the 1205 water rainfall level. events Astronomical that occurred tidefor 11 level years is the predictedbetween tide 2008 level and and 2018. is calculated Here, water based level on deviation the tide indicates levels observed the value in obtained the past, by and subtracting this tide the level is astronomical tide level at the estuary from the observed water level. Astronomical tide level is the not influenced by the weather. The maximum tide level deviation indicates the value where the tidal predicted tide level and is calculated based on the tide levels observed in the past, and this tide level level deviation became the highest during a rainfall event. At the water level observation station of is not influenced by the weather. The maximum tide level deviation indicates the value where the interest,tidal it level can be deviation concluded became that the there highest is less during correlation a rainfall between event. At peak the water rainfall level intensity observation and waterstation level deviationof interest, (Figure it can3a), be while concluded there that is correlation there is less betweencorrelation the between total rainfallpeak rainfall and waterintensity level and deviationwater (Figurelevel3b). deviation Moreover, (Figure many 3a), of thewhile events there withis correlation maximum between water the level total deviations rainfall and are water rainfall level events causeddeviation by typhoons. (Figure The3b). Moreover, Katabira Rivermany basinof the isevents relatively with largemaximum as an wa urbanter level river, deviations approximately are 60 kmrainfall2; thus, events it is considered caused by typhoons. to be more The susceptible Katabira Ri tover typhoon basin is rainfall relatively than large short-term as an urban concentrated river, rainfallapproximately such as heavy 60 km guerrilla2; thus, it rainfall. is considered Moreover, to be more it is susceptible considered to thattyphoon the waterrainfall levelthan short- deviation becomestermlarge concentrated due to rainfall the storm such surge as heavy when guerrilla a typhoon rainfall. makes Moreover, landfall it is considered because the that Katabira the water River level deviation becomes large due to the storm surge when a typhoon makes landfall because the basin is located at the estuary and influenced by the tide level. However, there are variations in the Katabira River basin is located at the estuary and influenced by the tide level. However, there are maximum water level deviations of events with similar total rainfalls. variations in the maximum water level deviations of events with similar total rainfalls.
(a) (b)
FigureFigure 3. (a) Relationship3. (a) Relationship between between peak rainfallpeak rainfall intensity inte andnsity water and levelwater deviation; level deviation; and (b )and relationship (b) betweenrelationship total rainfall between and total water rainfall level and deviation. water level deviation.
2.2.2.2.2.2. The RelationshipThe Relationship between between Water Water Level Level Deviation Deviation and Weather Weather Conditions Conditions In SectionIn Section 2.2.1 ,2.2.1, it is found it is found that the that possibility the possibility that weather that weather conditions conditions may influence may influence the variations the variations in water level deviations. To validate this possibility, Figure 4 presents the relationship in water level deviations. To validate this possibility, Figure4 presents the relationship between between water level deviation and weather conditions at the time when Typhoon Phanfone made water level deviation and weather conditions at the time when Typhoon Phanfone made landfall in landfall in 2014, showing that the total rainfall and the maximum water level deviation were both 2014,significant. showing thatThethe observed total rainfall value andof tide the level maximum deviation water changes level deviation(increases) werewith bothchanges significant. in The observedatmospheric value pressure, of tide wind level direction, deviation and changes wind spee (increases)d. The value with of changes tide level in deviation atmospheric (the value pressure, windobtained direction, by and subtracting wind speed. astronomical The value tide oflevel tide from level the deviation observed (thewater value level) obtained showed an by increase subtracting astronomicalin water tidelevel level due to from rainfall. the observed While there water were level) few changes showed in an either increase atmospheric in water pressure level due or towind rainfall. Whilespeed there during were few this changes rainfall inevent, either the atmospheric water level increased pressure orthe wind mostspeed at the duringtime when this rainfallthe wind event, the waterdirection level changed increased to thea southeast most at direction. the time whenFor this the re windason, it direction is clear that changed accurate to asimulation southeast is direction. not For thispossible reason, without it is clearincluding that the accurate tide level simulation at the estuary is not in possiblecalculation without conditions. including Furthermore, the tide while level at the water level was not affected when rain with a rainfall intensity of 10 mm/h continued to fall, the the estuary in calculation conditions. Furthermore, while the water level was not affected when rain water level rose when the rainfall intensity exceeded 30 mm/h. with a rainfall intensity of 10 mm/h continued to fall, the water level rose when the rainfall intensity exceeded 30 mm/h. In Section 2.2.1, it is noted that water level deviation can differ even though the total rainfall is approximately the same. Therefore, the relationship between water level and weather conditions for two rainfall events whose total rainfall was approximately 270 mm (Typhoon Saola on 19 October 2017 and a heavy rain event on 5 June 2014) were compared. Figure5 organizes the water level deviations and weather conditions of the two events. Figure5a shows the water level deviation during the typhoon rainfall event. It is clear that atmospheric pressure, wind direction, and wind speed affected impacts. While rain with a strength of approximately 40 mm/h fell, it did not influence the Water 2020, 12, 1769 5 of 18 water level deviation as this occurred during low tide. Moreover, the atmospheric pressure decreased approximately 50 hPa once the typhoon made landfall. Considering a 1-hPa decrease in atmospheric pressure causes an approximately 1-cm increase in water level due to the static sucking effect [27], an approximately 50-cm increase in tide level is inferred to have occurred due to a reduction in atmospheric pressure. Furthermore, the wind speed increased as the atmospheric pressure decreased and the wind direction changed to southeast, hitting the estuary. Thus, it can be concluded that the tide level increased approximately 100 cm due to the effects of atmospheric pressure, wind direction, and wind speed. In addition, the arrival of the typhoon coincided with full tide, further increasing the water level deviation. Next, we present the case of a rainfall event caused by heavy rain (Figure5b). As this was not a typhoon-related rainfall event, there was hardly any change in atmospheric pressure or wind, and the water level changed only due to the amount of rainfall. Since this event involved rain continuing over a long period of time, it is inferred that it did not cause a significant increase in water level. Accordingly, it was interpreted that the water level increase of a river at its estuary was significantly influenced by weather conditions, atmospheric pressure, wind direction, wind speed, and the timing of tidal changes. In addition to precipitation, these factors play a role in whether flooding Water 2020, 7, x FOR PEER REVIEW 5 of 20 is triggered.Water 2020, 7, x FOR PEER REVIEW 5 of 20
Figure 4. The relationship between water level deviation and weather conditions (at the time of FigureFigure 4. The 4. relationshipThe relationship between between waterwater level deviation deviation and and weather weather conditions conditions (at the (attime the of time of TyphoonTyphoon Phanfone Phanfone making making landfall landfall in in 2014). 2014). Typhoon Phanfone making landfall in 2014).
(a) (b) (a) (b) Figure 5. The relationship between water level deviation and weather conditions: (a) at the time of Figure 5. The relationship between water level deviation and weather conditions: (a) at the time of FigureTyphoon 5. The relationship Saola making betweenlandfall in water2017; and level (b) during deviation a heavy and rain weather event inconditions: 2014. (a) at the time of TyphoonTyphoon Saola Saola making making landfall landfall in in 2017; 2017; andand (b)) during during a aheavy heavy rain rain event event in 2014. in 2014. In Section 2.2.1, it is noted that water level deviation can differ even though the total rainfall is In Section 2.2.1, it is noted that water level deviation can differ even though the total rainfall is approximately the same. Therefore, the relationship between water level and weather conditions for approximately the same. Therefore, the relationship between water level and weather conditions for two rainfall events whose total rainfall was approximately 270 mm (Typhoon Saola on 19 October two2017 rainfall and aevents heavy whose rain event total onrainfall 5 June was 2014) approx wereimately compared. 270 mmFigure (Typhoon 5 organizes Saola the on water 19 October level 2017deviations and a heavy and weather rain event conditions on 5 June of the2014) two were even compared.ts. Figure 5a Figure shows 5 theorganizes water levelthe water deviation level deviationsduring the and typhoon weather rainfall conditions event. ofIt isthe clear two th evenat atmosphericts. Figure 5apressure, shows windthe water direction, level and deviation wind duringspeed the affected typhoon impacts. rainfall While event. rain withIt is cleara strength that ofatmospheric approximately pressure, 40 mm/h wind fell, direction, it did not influenceand wind speedthe wateraffected level impacts. deviation While as rain this with occurred a strength during of approximatelylow tide. Moreover, 40 mm/h the fell,atmospheric it did not pressureinfluence thedecreased water level approximately deviation as50 thishPa onceoccurred the typhoon during lowmade tide. landfall. Moreover, Considering the atmospheric a 1-hPa decrease pressure in decreasedatmospheric approximately pressure causes 50 hPa an approximatelyonce the typhoon 1-cm made increase landfall. in water Considering level due to a the1-hPa static decrease sucking in atmosphericeffect [27], pressurean approximately causes an 50-cmapproximately increase 1-cmin tide increase level is in inferred water level to have due tooccurred the static due sucking to a effectreduction [27], anin approximatelyatmospheric pressure. 50-cm increaseFurthermore, in tide the level wind is speedinferred increased to have as occurred the atmospheric due to a reductionpressure indecreased atmospheric and the pressure. wind direction Furthermore, changed the to southeast,wind speed hitting increased the estuary. as the Thus, atmospheric it can be pressure decreased and the wind direction changed to southeast, hitting the estuary. Thus, it can be
Water 2020, 7, x FOR PEER REVIEW 6 of 20 concluded that the tide level increased approximately 100 cm due to the effects of atmospheric pressure, wind direction, and wind speed. In addition, the arrival of the typhoon coincided with full tide, further increasing the water level deviation. Next, we present the case of a rainfall event caused by heavy rain (Figure 5b). As this was not a typhoon-related rainfall event, there was hardly any change in atmospheric pressure or wind, and the water level changed only due to the amount of rainfall. Since this event involved rain continuing over a long period of time, it is inferred that it did not cause a significant increase in water level. Accordingly, it was interpreted that the water level increase of a river at its estuary was significantly influenced by weather conditions, atmospheric Waterpressure,2020, 12wind, 1769 direction, wind speed, and the timing of tidal changes. In addition to precipitation,6 of 18 these factors play a role in whether flooding is triggered.
3. Creating A River-Water/Inland River-Water/Inland Water SimultaneousSimultaneous AnalysisAnalysis ModelModel thatthat ConsidersConsiders HighHigh TideTide 3.1. Structure of the Simultaneous Analysis Model 3.1. Structure of the Simultaneous Analysis Model In this study, a calculation model was built using NILIM2.0 software, programmed by the In this study, a calculation model was built using NILIM2.0 software, programmed by the National Institute for Land and Infrastructure Management (March 2012 released) [28]. Figure6 National Institute for Land and Infrastructure Management (March 2012 released) [28]. Figure 6 shows the conceptual diagram of the river-water/inland water simultaneous analysis model. The shows the conceptual diagram of the river-water/inland water simultaneous analysis model. The model calculated the process from rainfall outflow to flooding by dividing it into five sections and model calculated the process from rainfall outflow to flooding by dividing it into five sections and estimated the inundation height and flood locations by combining the calculation results of these five estimated the inundation height and flood locations by combining the calculation results of these five sections, where (I) is the process of rainfall flowing into the river, calculated using the synthesized sections, where (I) is the process of rainfall flowing into the river, calculated using the synthesized rational formula, and (II) is the process of the outflowing river water flowing downstream, calculated rational formula, and (II) is the process of the outflowing river water flowing downstream, calculated using the one-dimensional unsteady flow analysis. For these factors, the outflow obtained through using the one-dimensional unsteady flow analysis. For these factors, the outflow obtained through rainfall–runoff calculation was given as the boundary condition to the upper reach, and the tide rainfall–runoff calculation was given as the boundary condition to the upper reach, and the tide level level that took the influence of high tide into account was given as the boundary condition to the that took the influence of high tide into account was given as the boundary condition to the downstream end. Furthermore, (III) is the process of the rainwater being collected through manholes, downstream end. Furthermore, (III) is the process of the rainwater being collected through manholes, calculated using the kinematic wave method, and (IV) is the sewage tracking calculation that obtained calculated using the kinematic wave method, and (IV) is the sewage tracking calculation that the flow of water collected through the manholes inside the sewers and was calculated using the obtained the flow of water collected through the manholes inside the sewers and was calculated using dynamic wave method. (III) and (IV) were calculated only for the downstream basin, where there was the dynamic wave method. (III) and (IV) were calculated only for the downstream basin, where there an effect of high tide. (V) is the process of the expansion of inland flooding caused by overflow from was an effect of high tide. (V) is the process of the expansion of inland flooding caused by overflow manholes and river-water flooding caused by overflow from levees; a horizontal two-dimensional from manholes and river-water flooding caused by overflow from levees; a horizontal two- unsteady flow equation was used for the ground surface flooding calculation necessary to calculate it. dimensional unsteady flow equation was used for the ground surface flooding calculation necessary The respective calculation methods for the above-noted conditions are provided below. to calculate it. The respective calculation methods for the above-noted conditions are provided below.
Figure 6. Conceptual diagram of simultaneous analysis model of internal and external water. Figure 6. Conceptual diagram of simultaneous analysis model of internal and external water. 3.1.1. Calculation of Outflow into the River (I) 3.1.1. Calculation of Outflow into the River (I) To calculate outflow into the river, the synthesized rational formula, commonly used for the planning of small- and medium-sized rivers or sewers was used; this was because the basin area under study was only roughly 60 km2 [29]. The synthesized rational formula is shown in Equation (1): (t tn)H[t tn] (t (tn + tr))H[t (tn + tr)] − − h − − i − − ave x x qn(t) = rn v t tn v H t tn v (1) − − −x −h − x i t (tn + tr) H t tn + tr − − v − − v Water 2020, 12, 1769 7 of 18
However, it is ( 1 (x > a) H(x a) = (2) − 0 (x < a) ave Here, q is the runoff ratio [mm/h], n is the calculation time, x is the slope length [m], rn is the average rainfall amount [mm/h], tn is the start time of rainfall, tr is the duration of rainfall, v is the cross-sectional average flow velocity [m/s], x/v is the flood concentration time, and H is the Heaviside step function.
3.1.2. River Channel Tracking Calculation (II) The one-dimensional unsteady flow was used for river channel tracking calculation. Equation (3) and Equation (4) represent continuous and momentum equations, respectively, which were the fundamental equations used in this calculation.
∂A ∂Q + = q (3) ∂t ∂x
∂Q ∂β ∂A βQ2 ∂A ∂H A A + Q2 2βQ + gA2 + τ = 0 (4) ∂t ∂x − ∂x − A ∂x ∂x ρ However, it is: Q Q τ = ρgA (5) | | !2 P A 2 i R 3 ni i i=1 Here, A is the water conduction cross-sectional area, R is the hydraulic mean depth, Q is the flow amount [m3/s], q is the horizontal inflow per unit width [m2/s], n is the roughness coefficient of Manning, h is the water depth, β is the synthesized coefficient of the high and low water channels, g is the gravitational acceleration, ρ is water density, x is the distance [m], and t is time [s]. To calculate levee overflow amount Qb, the levee overflow amount equation [30] proposed by the Public Works Research Institute was used. When h2/h1 < 2/3: ∂A ∂Q + = q (6) ∂t ∂x
When h2/h1 = 2/3: r P = dd (7) h 1 When |P| 5 0.84 and P > 0: q Q = (0.6 0.3 P) (h + r ) 2g(h h ) (8) b − · · 2 dd · 1 − 2 When |P| 5 0.84 and P 5 0: q q = (0.6 0.4 P)h 2g(h h ) (9) − · 2 · 1 − 2 When |P| > 0.84: q q = 0.91 h 2g(h h ) (10) · 2 · 1 − 2 Figure7 shows a conceptual diagram of the equation of the above-noted levee breach amount. h1 and h2 are the water depths of the inland and outland areas of the embankment, respectively, as measured from the embankment height. P is the ratio of levee height rdd to the river water level from the levee height. Water 2020, 7, x FOR PEER REVIEW 8 of 20
When |P| ≦ 0.84 and P > 0:
Qbdd0.6 0.3Phr21 2 gh (8)
When |P| ≦ 0.84 and P ≦ 0:
qPhghh0.6 0.4212 2 (9)
When |P| > 0.84:
qhghh0.91212 2 (10)
Figure 7 shows a conceptual diagram of the equation of the above-noted levee breach amount. h1 and h2 are the water depths of the inland and outland areas of the embankment, respectively, as Watermeasured2020, 12 ,from 1769 the embankment height. P is the ratio of levee height rdd to the river water level8 from of 18 the levee height.
Figure 7. Figure 7.The The conceptualconceptual diagramdiagram forfor derivingderiving the the levee levee breach breach degree. degree. 3.1.3. Rainwater Collection Calculation (III) 3.1.3. Rainwater Collection Calculation (III) The kinematic wave method was used to calculate rainwater collection. The water collection area allocatedThe kinematic to each wave manhole method was was set used by substituting to calculate therainwater water collectioncollection. area The ofwater a manhole collection with area a rectangularallocated to slope. each Furthermore,manhole was by set setting by substituting the equivalent the water roughness collection coeffi cientarea andof a slope manhole inclination with a atrectangular the water slope. collection Furthermore, area based by on setting the land the equi usagevalent situation roughness there, coefficient the surface and flow slope amount inclination was calculated.at the water The collection fundamental area equationsbased on the of the land kinematic usage situation wave method there, canthe besurface found flow below. amount was calculated. The fundamental equations of the kinematic wave method can be found below. ∂h ∂q hq+ = r (11) ∂t ∂x r (11) tx h = K qp (12) × Here, h is the depth of water on the slope, q is the flowp per unit width of the slope, r is the effective(112 hKq rainfall strength, R the hydraulic mean depth, and K and p are the constants. The values defined by) TOYOKUNIHere, h et is al. the [31 depth] (Table of1 )water were usedon the as slope, the parameters q is the flow of K perand unitp. width of the slope, r is the effectiveTable1. rainfallEquivalent strength, roughness R the coe hydraulicfficient and mean slope inclination depth, and corresponding K and p are to thethe land constants. usage category. The values defined by TOYOKUNI et al. [31] (Table 1) were used as the parameters of K and p. Equivalent Roughness Slope Code Category Coefficient Inclination 3.1.4. Sewer Pipeline CalculationMountain (IV) 1 forest/abandoned Rice paddy 0.70 Farmland/Mountain The diffusion wave equationland, was etc. used to calculate the sewer line. The continuous equation, forest Farm/Other 0.001 which is 2the fundamental operation in Equation (13), depends on the2.00 state inside the pipeline, and is purposes either open3 water channel flow or pressure flow, as shown in Equation0.03 (14), while Equation (15) is 4 Plot under development the momentum Developmentequation. 0.02 5 Empty plot 6 Industrial site Common low-rise 0.36 7 Residential land housing area 0.01 Housing area Dense low-rise 8 housing area Medium/high-rise 9 housing area 0.011 10 Land for common public facility 11 Land for roads 0.1 0.031 Land for common 12 Park/Green area, etc. 0.001 public facility 0.3 13 Other common public facility 14 River/Lake, etc. 15 Others 17 Ocean 18 Outside the subject area
3.1.4. Sewer Pipeline Calculation (IV) The diffusion wave equation was used to calculate the sewer line. The continuous equation, which is the fundamental operation in Equation (13), depends on the state inside the pipeline, and is either open water channel flow or pressure flow, as shown in Equation (14), while Equation (15) is the momentum equation. ∂A ∂Q + = q (13) ∂t ∂x in Water 2020, 12, 1769 9 of 18
∂h C2 ∂u C2 + = qin (14) ∂x g ∂x qA0 ! ∂h n2 k Q2 = S S = S + (15) 0 f 0 4 2 ∂x − − R 3 2gL A However, it is; ! 1 L sin ϕ A 2 C = g 0 (16) N AL
Here, A is the water conduction cross-sectional area, θ the flow amount, qin is the horizontal inflow amount, n is the roughness coefficient, R the hydraulic mean depth, S0 is the water channel floor inclination, h is the water depth, A0 is the pipeline cross-sectional area, Al is the pipeline cross-sectional area, L is the pipeline length, ϕ the connection angle, N is the number of attached pipes, C is the pressure wave velocity, and Sf is the friction loss inclination and k the local loss factor.
3.1.5. Ground Surface Flooding Calculation (V) Two-dimensional unsteady flow was used to calculate ground surface flooding. The same equation was employed for both river water flooding and inland flooding. Equation (17) is the continuous equation and Equation (18) is the momentum equation, which constitute the fundamental equations used. ∂h ∂M ∂N + + = 0 (17) ∂t ∂x ∂y
∂M ∂(uM) ∂(vM) ∂H 1 + + + gh + τx = 0 ∂t ∂x ∂y ∂x ρ (18) ∂N + ∂(uN) + ∂(vN) + ∂H + 1 = ∂t ∂x ∂y gh ∂y ρ τy 0
ρgn2u √(u2+v2) τx = 1 h 3 (19) ρgn2v √(u2+v2) τx = 1 h 3 Here, H is the water level, h is the depth of inundation, u and v are the flow speed in the x and y directions, g is the gravitational acceleration, ρ is the water density, M and N are the flow flux of the x and y directions (M = uh, N = vh), τx(b), τy(b) the shearing force in the x and y directions, u¯ and v are the average of the flow speed at the current time and previous time and n is the bottom roughness coefficient (n0 is the synthesized equivalent roughness coefficient, and θ is the building occupancy (%). Moreover, Equation (20) was used for bottom roughness and Equation (21) was used for the bottom roughness coefficient of meshes other than buildings. [28]
2 2 θ 4 n = n + 0.020 h 3 (20) 0 × 100 θ × − 2 2 2 n A + n A2 + n A3 2 1 1 2 3 n0 = (21) (A1 + A2 + A3) Here, the calculation was conducted with n as the bottom roughness coefficient, n as the bottom roughness coefficient of the areas other than buildings, θ as the building occupancy (%), h as the depth of inundation (m), A1 as the farm area, A2 as the road area, A3 as the area other than the farm or road, n1 as the farm roughness coefficient (=0.060), n2 as the road roughness coefficient (=0.047), and n3 as the roughness coefficient of the area other than farms or roads (=0.050) [28]. Water 2020, 12, 1769 10 of 18
3.2. Verifying the Accuracy of the Constructed Model The calculations of runoff into the river, river water flooding and inland flooding were individually conducted in order to examine the accuracy of the river water/inland simultaneous flooding analysis model that takes high tide into account
3.2.1. Verifying the Accuracy of the Calculation Method of Runoff into the River The section that is upstream from the confluence of the main stream of the Katabira River and its branches was divided into four catchments in order to calculate the runoff into the river, and the result of the calculation was examined. However, as downstream from the confluence of the Katabira River and the Imai River is the area where combined sewers are used and rainwater is discharged through them, calculation of the runoff into the river was not conducted for this area and rainwater collection calculation and sewer pipeline calculations were conducted instead. The division of catchments is shown in Figure8, with the area and runo ff ratio of each catchment shown in Table2. The flood concentration time was uniformly set to 1 h. The operational standard established by Kanagawa prefecture, which has been in use since 2004, was employed for the branching point of the Katabira River and its floodway, and the ratio of the runoff amount between the diversion channel and main stream was set at 8:2 until the flow through the floodway reached 260 m3/s. After that point, every runoff was set to flow into the main stream. When conducting the river channel calculation, the flow amount was given as the boundary condition to the upstream end of the Imai River and upstream from the confluence of the Imai and Katabira Rivers (the point indicated with a red star in Figure8), and the tide level was given as the boundary condition to the downstream end of the Katabira River. The roughness coefficient n was set at n = 0.034 uniformly throughout the area [30]. A verification of the accuracy of the river channel runoff calculation was conducted by comparing the real measurement of the water level and the calculation result. The rainfall event used for the calculation was typhoon Saola from 2017 at the point of its arrival; the two days between 0:00 on October 27, 2017 and 24:00 on October 28, 2017 were studied. The rainfall data observed by the ground rain gauge were used for the examination. The accumulated rainfall during this event was 193 mm. Figure9 shows the comparison of the calculation result and measurement. The measurement was reproduced at Bridge A, located 1.8 km from the river mouth, and at Bridge B, located 1.6 km from the river mouth (see Figure8). Water 2020, 7, x FOR PEER REVIEW 12 of 20
FigureFigure 8.8. Catchment division diagram.
Figure 9. Comparison of the calculation result of the river channel water level analysis and measurement.
3.2.2. Accuracy Examination of the River Water Flooding Calculation Method While it is desirable to compare the calculation result of this method and the real measurement data of flooding from the past in order to verify the accuracy of the river water flooding calculation method, in reality it is common that the inundation area or inundation depth are not studied unless large-scale flooding occurs. Thus, in this accuracy verification, the calculation was conducted by using the same condition and rainfall data used for producing the river water hazard map of the Katabira River, and the verification was conducted by comparing the calculation result, inundation area and inundation depth shown in the hazard map. The rainfall event used for the calculation was typhoon Rolly from 2004 at the point of its arrival, with the 11 h between 11:00 on October 9, 2004 and 22:00 on October 9, 2004 being studied. The rainfall data observed by the ground rain gauge was used for the examination. The cumulative rainfall of this event was 198 mm. Moreover, the tide level at the downstream end was obtained by combining the peak of the river water level of the downstream basin and that of high tide, as this was expected to occur during the spring high tide, as was the case for the conditions on whose basis the hazard map was produced. Figure 10 shows a
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Table 2. Area and runoff ratio of catchments.
Basin Area (km2) Runoff Ratio Basin 1 22.6 0.9 Basin 2 3.4 0.8 Basin 3 116.1 0.9 Basin 4 7.5 0.8 Figure 8. Catchment division diagram.
FigureFigure 9.9.Comparison Comparison of theof calculationthe calculation result ofresult the river of the channel river water channel level analysiswater level and measurement.analysis and 3.2.2.measurement. Accuracy Examination of the River Water Flooding Calculation Method
3.2.2.While Accuracy it is desirableExamination to compare of the River the calculationWater Flooding result Calculation of this method Method and the real measurement data of flooding from the past in order to verify the accuracy of the river water flooding calculation While it is desirable to compare the calculation result of this method and the real measurement method, in reality it is common that the inundation area or inundation depth are not studied unless data of flooding from the past in order to verify the accuracy of the river water flooding calculation large-scale flooding occurs. Thus, in this accuracy verification, the calculation was conducted by using method, in reality it is common that the inundation area or inundation depth are not studied unless the same condition and rainfall data used for producing the river water hazard map of the Katabira large-scale flooding occurs. Thus, in this accuracy verification, the calculation was conducted by River, and the verification was conducted by comparing the calculation result, inundation area and using the same condition and rainfall data used for producing the river water hazard map of the inundation depth shown in the hazard map. The rainfall event used for the calculation was typhoon Katabira River, and the verification was conducted by comparing the calculation result, inundation Rolly from 2004 at the point of its arrival, with the 11 h between 11:00 on October 9, 2004 and 22:00 area and inundation depth shown in the hazard map. The rainfall event used for the calculation was on October 9, 2004 being studied. The rainfall data observed by the ground rain gauge was used for typhoon Rolly from 2004 at the point of its arrival, with the 11 h between 11:00 on October 9, 2004 the examination. The cumulative rainfall of this event was 198 mm. Moreover, the tide level at the and 22:00 on October 9, 2004 being studied. The rainfall data observed by the ground rain gauge was downstream end was obtained by combining the peak of the river water level of the downstream basin used for the examination. The cumulative rainfall of this event was 198 mm. Moreover, the tide level and that of high tide, as this was expected to occur during the spring high tide, as was the case for the at the downstream end was obtained by combining the peak of the river water level of the conditions on whose basis the hazard map was produced. Figure 10 shows a comparison of the river downstream basin and that of high tide, as this was expected to occur during the spring high tide, as water flooding calculation result and the hazard map. Both the inundation area and inundation depth was the case for the conditions on whose basis the hazard map was produced. Figure 10 shows a were faithfully reproduced.
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Watercomparison2020, 12, 1769 of the river water flooding calculation result and the hazard map. Both the inundation12 of 18 area and inundation depth were faithfully reproduced.
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comparison of the river water flooding calculation result and the hazard map. Both the inundation area and inundation depth were faithfully reproduced.
(a) (b)
FigureFigure 10. Comparison10. Comparison of of the the river river water water floodingflooding calculation calculation result result and and analysis analysis result result in the in report the report on floodingon flooding hazard hazard map map production: production: ((aa)) riverriver water water flooding flooding an analysisalysis result; result; and and(b) report (b) report on the on the floodingflooding hazard hazard map map production. production.
3.2.3. Verifying the Accuracy of the Inland Flooding Calculation Method
It is necessary to first adjust the parameters used for the rainwater collection calculation, sewer tracking calculation and(a ground) surface flooding calculation and then(b) examine them in order to construct an inland flooding calculation method. The area where the inland flooding calculation Figure 10. Comparison of the river water flooding calculation result and analysis result in the report method wason flooding applied hazard is the map downstream production: basin,(a) river which water flooding is an estuary analysis and result; feature and (b combined) report on the sewers (see Figure 11).flooding hazard map production.
Figure 11. Subject area for calculation.
3.2.3. Verifying the Accuracy of the Inland Flooding Calculation Method It is necessary to first adjust the parameters used for the rainwater collection calculation, sewer tracking calculation and ground surface flooding calculation and then examine them in order to construct an inland flooding calculation method. The area where the inland flooding calculation method was applied is the downstream basin, which is an estuary and feature combined sewers (see Figure 11). For the rainwater collectionFigure calculation,Figure 11. 11.Subject Subject the collection area for for calculation. calculation.area was defined by conducting a Voronoi tessellation on the subject area for each manhole of the pipeline, with equivalent roughness and slope inclinationsFor3.2.3. the Verifying rainwater given the in collectionAccuracy order to solveof calculation, the usingInland the Flooding the kinematic collection Calculation wave area method. wasMethod defined The values by conductingof the equivalent a Voronoi tessellationroughnessIt is on necessary and the subjectslope to inclination first area adjust for eachwere the parameters manholeset at ni = of 0.01used the and for pipeline, ithe = 0.360, rainwater with respectively, equivalent collection in calculation, roughnessaccordance sewer andwith slope inclinationsthetracking aforementioned given calculation in order Tableand to ground1. solve The roughness usingsurface the flooding kinematiccoeffici calculationent within wave and method.the pipelinethen examine The for values the them sewer of in the trackingorder equivalent to calculation was set to 0.013, considering the length of approximately 192.5 km of pipeline and 10,009 roughnessconstruct and an slope inland inclination flooding calculation were set at method.ni = 0.01 The and areai = where0.360, the respectively, inland flooding in accordance calculation with manholes within the basin [24]. For the operation of the pump station, the operating conditions of the aforementionedmethod was applied Table is the1. Thedownstream roughness basin, coe whicfficienth is an within estuary theand pipelinefeature combined for the sewersewers tracking(see threeFigure pump 11). stations were considered. For the ground surface flooding calculation, the lattice size of calculation was set to 0.013, considering the length of approximately 192.5 km of pipeline and 10,009 the calculationFor the rainwater result was collection set to 5 calculation, m mesh, and the a collection numerical area map was of defined5 m mesh by wasconducting also used a Voronoi for the manholes within the basin [24]. For the operation of the pump station, the operating conditions of tessellation on the subject area for each manhole of the pipeline, with equivalent roughness and slope threeinclinations pump stations given were in order considered. to solve using For thethe groundkinematic surface wave method. flooding The calculation, values of the the equivalent lattice size of the calculationroughness and result slope was inclination set to 5 mwere mesh, set at and ni = a 0.01 numerical and i = 0.360, map ofrespectively, 5 m mesh in was accordance also used with for the altitudethe [aforementioned32]. Moreover, Table for the 1. bottomThe roughness roughness coeffici coeentfficient within of the the pipeline areas other for the than sewer buildings, tracking it was postulatedcalculation that anywherewas set to 0.013, other considering than buildings the length were of road, approximately as was the 192.5 case withkm of the pipeline river waterand 10,009 flooding analysismanholes calculation, within withthe basin 0.047 [24]. taken For to the hold operation uniformly of the throughout pump station, the the basin operating area [27 conditions]. As there of is no three pump stations were considered. For the ground surface flooding calculation, the lattice size of the calculation result was set to 5 m mesh, and a numerical map of 5 m mesh was also used for the
Water 2020, 7, x FOR PEER REVIEW 14 of 20
Wateraltitude2020 [32]., 12, 1769 Moreover, for the bottom roughness coefficient of the areas other than buildings, 13it was of 18 postulated that anywhere other than buildings were road, as was the case with the river water flooding analysis calculation, with 0.047 taken to hold uniformly throughout the basin area [27]. As realthere measurement is no real measurement data that can data be usedthat can for verifyingbe used for the verifying inland flooding the inland calculation, flooding as calculation, was the case as withwas the the case river with water the flooding river water calculation, flooding thecalculat calculationion, the wascalculation conducted was usingconducted the same using conditions the same andconditions rainfall and data rainfall used to data produce used theto produce inland water the inland hazard water map, withhazard the map, examination with the conducted examination by comparingconducted by the comparing calculation the result calculation and inundation result and area inundation and the inundation area and the depth inundation shown depth in the shown inland waterin the hazardinland map.water The hazard rainfall map. event The used rainfall the sameeventevent used asthe that same described event as in th Sectionat described 3.2.2. Figure in 3.2.2. 12 showsFigure the12 shows comparison the comparison of the inland of floodingthe inland calculation flooding resultcalculation and inland result waterand inland hazard water map. hazard When examiningmap. When the examining inundation the situationinundation of thesituation area around of the area Yokohama around Station, Yokohama indicated Station, with indicated a white with dot, botha white the dot, inundation both the areainundation and inundation area and depthinundation were mostlydepth were reproduced. mostly reproduced. However, the However, calculation the resultcalculation of the result area aroundof the area National around Route National 1 showed Route a deeper1 showed inundation a deeper depth inundation than that depth of the than inland that hazardof the inland map. hazard This was map. due This to the was fact due that to the inlandfact that hazard the inland map hazard does not map represent does not the represent inundation the situationinundation of situation main roads. of main Thus, roads. the validity Thus, the of the validity calculation of the resultcalculation could result not be could assessed. not be assessed.
(a) (b)
Figure 12. ComparisonComparison of inland flooding: flooding: ( a)) inland inland water water analysis analysis result; and ( b) report on the inland water hazard mapmap production.production.
4. Results and Discussion 4.1. The Effect of High Tide on River Water Flooding 4.1. The Effect of High Tide on River Water Flooding There is a possibility that flooding from a river caused by rainfall and an increase in the tide There is a possibility that flooding from a river caused by rainfall and an increase in the tide level at the estuary occur simultaneously when a typhoon hits [33]. Anticipating such a scenario, level at the estuary occur simultaneously when a typhoon hits [33]. Anticipating such a scenario, the the effect of high tide on river water flooding was analyzed. Two sets of conditions, namely when effect of high tide on river water flooding was analyzed. Two sets of conditions, namely when the the tide level is high and when it is low were given as the boundary conditions for the downstream tide level is high and when it is low were given as the boundary conditions for the downstream end. end. The conditions were given by postulating that the case when the tide level at the downstream The conditions were given by postulating that the case when the tide level at the downstream end is end is high and that for when it is low would occur simultaneously for the peak water level of the high and that for when it is low would occur simultaneously for the peak water level of the calculation calculation of runoff into the river at this point. The maximum anticipated tide level was set to 2.3 m of runoff into the river at this point. The maximum anticipated tide level was set to 2.3 m (high (high astronomical tide level + storm surge), which is the maximum planned tide level, and this was astronomical tide level + storm surge), which is the maximum planned tide level, and this was given given so as to be synchronized with the peak water level of the runoff. The maximum planned tide so as to be synchronized with the peak water level of the runoff. The maximum planned tide level is level is set by the port administration by anticipating the occurrence of storm surge during high tide in set by the port administration by anticipating the occurrence of storm surge during high tide in the the spring tide season. The minimum tide level was given by setting it at the low tide level during spring tide season. The minimum tide level was given by setting it at the low tide level during the the neap tide season, which is the lowest tide level throughout the year, and synchronizing it to the neap tide season, which is the lowest tide level throughout the year, and synchronizing it to the peak peak water level of the runoff. The rainfall event used the same event as that described in Section 3.2.2. water level of the runoff. The rainfall event used the same event as that described in 3.2.2. Figure 13 Figure 13 shows the comparison of the inundation situation when the maximum anticipated high tide shows the comparison of the inundation situation when the maximum anticipated high tide and and flooding occurred simultaneously and the inundation situation when low tide and flooding both flooding occurred simultaneously and the inundation situation when low tide and flooding both occurred. It was determined that when high tide occurs during full tide in the spring tide season, the effect of the downstream tide level is transmitted to the river water level, causing flooding on the Water 2020, 7, x FOR PEER REVIEW 15 of 20 Water 2020, 12, 1769 14 of 18 occurred. It was determined that when high tide occurs during full tide in the spring tide season, the effect of the downstream tide level is transmitted to the river water level, causing flooding on the downstream side, and that when low tide occurs duringduring the neap tide season, the river water level is not influencedinfluenced by the tide level, causing floodingflooding on the upstream side. Moreover, from the fact that the inundation area significantlysignificantly didiffersffers dependingdepending onon thethe heightheight ofof thethe tidetide level,level, itit was found not to be possiblepossible toto accuratelyaccurately anticipateanticipate thethe flooding flooding situation situation of of a a tidal tidal river river if if the the eff effectect of of the the high high tide tide is notis not included. included.
(a) (b)
Figure 13. ComparisonComparison of ofthe the maximum maximum and and minimum minimum inun inundationdation situations situations obtained obtained through through river riverwater water flooding flooding analysis: analysis: (a) when (a) high when tide high occurs tide occursduring duringfull tide full in the tide spring in the tide spring season; tide and season; (b) andwhen (b low) when tide low occurs tide duri occursng the during neap the tide neap season. tide season.
4.2. Result of River Water/Inland Water/Inland SimultaneousSimultaneous FloodingFlooding CalculationCalculation When conducting the riverriver waterwater/inland/inland simultaneoussimultaneous floodingflooding calculation,calculation, a postulatedpostulated casecase wherewhere 7575 mmmm/h/h rainrain fell continuously for one hour on the subject area was given as the the rain rain condition. condition. This isis thethe rainfallrainfall that that is is said said to to occur occur in in the the subject subject area area at aat probability a probability of once of once every every 30 years. 30 years. The realThe tidereal leveltide level measured measured during during the arrival the arrival of Typhoon of Typhoon Lan inLan 2017 in 2017 was usedwas used as the as downstream the downstream end tideend level.tide level. The The calculation calculation time time was was set toset four to four hours hours from from the startthe start of the of rainfall.the rainfall. Figure Figure 14 shows 14 shows the calculationthe calculation result. result. Inundation Inundation caused caused by inland by inland flooding flooding occurred occurred near near Yokohama Yokohama Station Station 20 min 20 aftermin theafter rainfall the rainfall began. began. This floodingThis flooding started started with thewith overflow the overflow from thefrom branches the branches connected connected to the to main the linemain instead line instead of an overflowof an overflow from the from main the sewage main line.sewage After line. 50 After min, river50 min, water river flooding water occurredflooding atoccurred the flooding at the pointflooding of thepoint river of the and river the inundationand the inundation area continued area continued to expand to asexpand the time as the passed. time Itpassed. was found It was that found the that flooding the flooding water gathered water gathered at a low at altitude a low altitude area as the area time as the passed, time andpassed, that and the expansionthat the expansion of the inundation of the inundation area stopped area stopped around 140 around min after140 min the after start ofthe the start rain, of the and rain, about and 1 h about after the1 h rainafter hadthe rain stopped. had stopped. The verificationverification results of river waterwater/inland/inland simultaneous floodingflooding calculation are summarized inin TableTable3 3..
Table 3. Verification results.
Verification Result The effect of high tide on river water flooding. (1) The location of the flooding changes. (From Section 4.1) (2) The maximum inundation height changes from 3.02 to 3.85 m. (3) The area of the flooding changes from 0.004 to 0.149 km2. Differences in inundation onset time by river (1) Inland flooding begins after 20 min. water/inland simultaneous flooding calculation. (2) River water flooding begins after 50 min. (From Section 4.2) (3) The difference between the time an inland flooding and a river water flooding begins is 30 min.
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FigureFigure 14. Inundation 14. Inundation process process obtained obtained through through the constructedthe constructed river river water water and inlandand inland flooding flooding analysis. analysis. 4.3. Inundation Process during A Simultaneous Occurrence of River Water/Inland Flooding Table 3. Verification results. It was clarified in Section 4.2 that there is a time gap between the occurrence of river water flooding and inland flooding,Verification and that inland flooding occurs first. Thus,Result the flooding process was analyzedThe byeffect focusing of high tide on theon river chronological water flooding. change 1) ofThe inundation location of the depth flooding at the changes. point where it was deepest.(From Figure Section 15 shows 4.1) the chronological change of2) inundationThe maximum depth inundation at the deepest height changes point (indicated from 3.02 to 3.85 m. with the red dot). The inundation depth of the inland flooding started to increase approximately 3) The area of the flooding changes from 0.004 40 min from the start of the calculation and reached its deepest inundation depth (about 0.2 m) after to 0.149 km2. approximatelyDifferences 70 in min. inundation In contrast, onset thetime inundation by river depth1) Inland of the flooding river begins water floodingafter 20 min. started to rapidly increasewater/inland after about simultaneous 90 min and flooding its water level increased2) River by water some flooding 0.6 m in begins approximately after 50 min. 20 min. As a result,calculation. the 0.8 m inundation depth at this point was3) anticipated The difference to bebetween from thethe time flooding an inland of the inland and river(From water. section Upon 4.2) examination of the protocolflooding for issuing and evacuationa river water informationflooding begins in is Japan 30 [34], it was found that it is in principle issued in responsemin. to river water levels and does not consider inland flooding. As inland flooding commonly starts with the overflow of, for instance, manholes, the expansion4.3. Inundation speed Process of floodwater during A Simultaneous is not very Occurrence fast, although of River thatWater/Inland depends Flooding on the inclination of the terrain. Thus,It was it clarified is considered in Section to have 4.2 that little there effect is a on time evacuation. gap between However, the occurrence if inland of andriver river water water floodingflooding occur and simultaneously, inland flooding, aand situation that inland where flood peopleing occurs cannot first. evacuate Thus, the due flooding to inland process floodwater was and thenanalyzed get caughtby focusing in floodwater on the chronological from subsequent change riverof inundation flooding depth could at be the envisaged. point where Especially it was in largedeepest. cities, there Figure are 15 many shows underground the chronological and commercial change of facilities,inundation and depth there at is athe high deepest probability point that (indicated with the red dot). The inundation depth of the inland flooding started to increase inland floodwater flows in and inundates underground facilities. Moreover, with respect to the doors approximately 40 min from the start of the calculation and reached its deepest inundation depth of buildings, it is understood that doors that open outwards can no longer be opened when the depth (about 0.2 m) after approximately 70 min. In contrast, the inundation depth of the river water flooding of inundationstarted to reachesrapidly increase 26 cm,while after doorsabout 90 that min open and inwards its water can level no increased longer open by some when 0.6 the m depth in of inundationapproximately reaches 20 47 min. cm As [35 a]. result, Thus, the there 0.8 ism alsoinundation a possibility depth at that this one point cannot was anticipated evacuate ato building be whenfrom floodwater the flooding reaches of the certain inland depths. and river Furthermore, water. Upon the examination flow speed of and the depthprotocol that for would issuing allow an adult male to walk safely through water is considered to be less than 1 m/s when the water depth is no more than 0.4 m [35]. Thus, if a person does not immediately evacuate when inland flooding occurs, it is possible that s/he will lose his/her life from subsequent river flooding. In light of the factors Water 2020, 7, x FOR PEER REVIEW 17 of 20
evacuation information in Japan [34], it was found that it is in principle issued in response to river water levels and does not consider inland flooding. As inland flooding commonly starts with the overflow of, for instance, manholes, the expansion speed of floodwater is not very fast, although that depends on the inclination of the terrain. Thus, it is considered to have little effect on evacuation. However, if inland and river water flooding occur simultaneously, a situation where people cannot evacuate due to inland floodwater and then get caught in floodwater from subsequent river flooding could be envisaged. Especially in large cities, there are many underground and commercial facilities, and there is a high probability that inland floodwater flows in and inundates underground facilities. Moreover, with respect to the doors of buildings, it is understood that doors that open outwards can no longer be opened when the depth of inundation reaches 26 cm, while doors that open inwards can no longer open when the depth of inundation reaches 47 cm [35]. Thus, there is also a possibility that one cannot evacuate a building when floodwater reaches certain depths. Furthermore, the flow speed Water 2020, 12, 1769 16 of 18 and depth that would allow an adult male to walk safely through water is considered to be less than 1 m/s when the water depth is no more than 0.4 m [35]. Thus, if a person does not immediately evacuate when inland flooding occurs, it is possible that s/he will lose his/her life from subsequent discussed above, it can be inferred that in a large city, river water flooding may take place after the river flooding. In light of the factors discussed above, it can be inferred that in a large city, river water occurrence of inland flooding. Therefore, it can be said that unless the occurrence of inland flooding is flooding may take place after the occurrence of inland flooding. Therefore, it can be said that unless predictedthe occurrence and evacuation of inland information flooding is predicted is issued and at thatevacuation point ininformation time, a situation is issued whereat that point subsequent in evacuationtime, a wouldsituation be where difficult subsequent can be anticipated.evacuation would be difficult can be anticipated.
FigureFigure 15. 15.Chronology Chronology of ofinundation inundation depth depthduring the during simultaneous the simultaneous occurrence of river occurrence water/inland of river waterflooding./inland flooding.
5. Conclusions5. Conclusions 1) This1) This study study investigated investigated the the Katabira Katabira River, River, which which is the is the tidal tidal river river of Yokohama of Yokohama City, one City, of one of thethe main main large large citiescities of of Japan, Japan, to toconstruct construct a simu a simultaneousltaneous occurrence occurrence model of model river water of river and inland water and inlandflooding flooding that that incorporates incorporates the influence the influence of high oftide. high Its accuracy tide. Its was accuracy then examined was then and examined the flooding and the floodingphenomena phenomena predicted predicted in the insubject the subjectarea were area anal wereyzed. analyzed. With the Withresults the of resultscalculations, of calculations, it was determined that the occurrence location of river water flooding differs depending on whether it is it was determined that the occurrence location of river water flooding differs depending on whether it during the planned maximum tide level or during low tide, and that the inundation areas are also is during the planned maximum tide level or during low tide, and that the inundation areas are also significantly different. From this, it can be stated that taking high tide into consideration is important significantlywhen conducting different. flooding From this, simulation it can bes of stated tidal rivers that takingin large highcities tide. Moreover, into consideration it was discovered is important that whenthe conducting tide level is flooding influenced simulations by atmospheric of tidal pressu riversre, inwind large direction, cities. Moreover,and wind speed, it was and discovered therefore that the tideimprovement level is influenced in prediction by atmosphericaccuracy is directly pressure, linked wind to the direction, results of flooding and wind predictions. speed, and therefore improvement2) It was in prediction discovered accuracy that at the is Katabira directly River linked basin, to the inland results flooding of flooding occurs predictions.first, followed by 2)river Itwas water discovered flooding, when that they at the occur Katabira simultaneously River basin,. In addition, inland inundation flooding occurs by river first, water followed occurs by river water flooding, when they occur simultaneously. In addition, inundation by river water occurs extremely quickly, suggesting the possibility that unless one evacuates before the commencement of inland flooding, one may not be able to evacuate at all. From these findings, it can be argued that it is urgent to revise the issuing protocol for evacuation information based on river water flooding, as has been practiced in Japan thus far, and to issue new protocols of evacuation information that also take inland flooding into account. In order to realize this, the development of a faster and easier calculation method for the simultaneous occurrence of river water and inland flooding that takes high tide into account is necessary, and we aim to improve on our method in the future.
Author Contributions: Conceptualization, N.K. and T.Y.; methodology, N.K.; software, N.K.; validation, N.K., T.Y.; formal analysis, N.K.; writing—original draft preparation, N.K.; writing—review and editing, T.Y.; and supervision, T.Y. All authors have read and agreed to the published version of the manuscript. Funding: This research was supported by Unit for Research and Application Solution of Water-Related Disaster Science and Information of Research and Development Initiative (RDI), Chuo University. Acknowledgments: We would like to thank City of Yokohama and Tokyu Construction Co., Ltd. for assisting with data collection. Conflicts of Interest: The authors declare no conflict of interest. Water 2020, 12, 1769 17 of 18
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