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Article Hydraulic Evaluation of the Levee System Evolution on the Kurobe Alluvial Fan in the 18th and 19th Centuries

Tadaharu Ishikawa 1,* and Hiroshi Senoo 2

1 Tokyo Institute of Technology, Tokyo 152-8552, Japan 2 TOKEN C. E. E. Consultants Co., Ltd., Tokyo 170-0004, Japan; [email protected] * Correspondence: [email protected]

Abstract: The development process and flood control effects of the open-levee system, which was constructed from the mid-18th to the mid-19th centuries, on the Kurobe Alluvial Fan—a large alluvial fan located on the Japan Sea Coast of Japan’s main island—was evaluated using numerical flow simulation. The topography for the numerical simulation was determined from an old pictorial map in the 18th century and various maps after the 19th century, and the return period of the flood hydrograph was determined to be 10 years judging from the level of civil engineering of those days. The numerical results suggested the followings: The levees at the first stage were made to block the dominant divergent streams to gather the river flows together efficiently; by the completed open-levee system, excess river flow over the main channel capacity was discharged through upstream levee openings to old stream courses which were used as temporary floodways, and after the flood peak, a part of the flooded water returned to the main channel through the downstream levee openings. It is considered that the ideas of civil engineers of those days to control the floods exceeding river channel capacity, embodied in their levee arrangement, will give us hints on how to control the extraordinary floods that we should face in the near future when the scale of storms will increase due to the global climate change. Citation: Ishikawa, T.; Senoo, H. Hydraulic Evaluation of the Levee Keywords: open-levee system; alluvial fan; flood control; early modern times (Edo period); System Evolution on the Kurobe numerical flow simulation; hydraulic function of levee systems Alluvial Fan in the 18th and 19th Centuries. Energies 2021, 14, 4406. https://doi.org/10.3390/en14154406 1. Introduction Academic Editor: Michele La Rocca After more than a hundred years of turmoil, Japan entered a stable era of 250 years under one administration from the beginning of the 17th century to the middle of the Received: 18 May 2021 19th century, which is called the Edo period. During the first century of this period, Accepted: 12 July 2021 Published: 21 July 2021 the population increased from 10 million to 30 million as a result of the expansion of farmlands and by the growth of commerce and industry. This population remained almost

Publisher’s Note: MDPI stays neutral constant during the succeeding one and a half centuries. In addition, a variety of arts, with regard to jurisdictional claims in hobbies, forms of entertainment and types of food, which are now recognized as unique to published maps and institutional affil- Japan, were developed by townspeople. iations. That social development was supported by flood control benefits of river improvement works, which were actively carried out on alluvial plains in the 17th and 18th centuries. As continuous high levees could not be built at that time, fragmentary levees were arranged to disperse the impact of river overflow in consideration of the micro-topography and the land use conditions on floodplains at the beginning, and they were gradually integrated Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. into a levee system. According to researchers who studied the development process of This article is an open access article those works from the viewpoint of engineering history by analyzing old documents and distributed under the terms and drawings, many of the river improvement works in Edo period were successful, and some conditions of the Creative Commons of them were in use until quite recently (for example, [1–4]). Attribution (CC BY) license (https:// However, the actual hydraulic effects of those river works are not fully understood creativecommons.org/licenses/by/ from engineering history studies. Hydraulic model tests were carried out to examine the 4.0/). functions of individual hydraulic structures, but they could not clarify the total effects

Energies 2021, 14, 4406. https://doi.org/10.3390/en14154406 https://www.mdpi.com/journal/energies Energies 2021, 14, 4406 2 of 17

of the river works as a system due to the scale limitation (for example, [5,6]). With the recent progress of computers, on the other hand, numerical simulation of flood flows in a wide area has become a powerful tool to clarify the hydraulic effects of those old river works as well as to understand the flood control strategy in the Edo period when the engineers lacked the knowledge of modern hydraulics and advanced techniques for levee construction (for example, [7–11]). This study carried out a numerical flow simulation to evaluate the development of levee system construction from the mid-18th to the mid-19th centuries on the Kurobe Alluvial Fan, a large alluvial fan located on the Japan Sea’s coast of Honshu, Japan’s main island. The improved levee systems on alluvial fans were behind those on the alluvial floodplain due to the difficulty caused by the unsteadiness of rapid rivers. As an alluvial fan is a conical steeply sloped terrain formed by sedimentation due to water flow spreading from the outlet of a canyon in a mountainous region, the paths of swift currents tend to branch and change their course frequently. Therefore, it is considered that the river works on alluvial fans took a long time, starting by cutting off branch streams to gather the river flows together. A pictorial map drawn in 1785 was used to estimate the topographic condition at the early state of levee construction after compensating for geometrical distortion. A map of levee lines obtained from surveys in 1894 was used to determine the configuration of the completed levee system. Hereafter, the former is called the 18th-C levee and the latter is called the 19th-C levee. Using a shallow water flow model, inundation flow fields were examined numerically for three levee conditions: no levee, the 18th-C levee, and the 19th-C levee, with the same calculation conditions for topography and river flow rate. Based on the hydraulic evaluation results and the literature [12], summarizing information written in old documents, the flood control strategy in the Edo period, when civil engineering was still inadequate to fully control large floods, is discussed. It is expected that the ideas of civil engineers of those days, embodied in their levee arrangement, might give us hints on how to control the extraordinary floods that we could face in the near future when the scale of storms increases due to global climate change.

2. Study Site The Kurobe River is one of the most rapid rivers in Japan, flowing from Japan’s central mountain range, with an elevation of 3000 m, to the Japan Sea via a deep canyon about 80 km long, and carrying a large volume of sediment. The river forms a vast alluvial fan on the Japan Sea’s coast, with a sector radius of 13 km, a slope of 1/100, and an apex angle of 90 degrees [13]. Figure1 shows the topography of the alluvial fan. The contour lines accompanied by elevation in meters are almost concentric except at the coastline, where they are distorted by a local imbalance between the sediment supplied by the river and the erosion caused by coastal currents and waves. The sky-blue bands represent the old river courses, the black line represents the position of the levees surveyed in 1894, and the small numbers with “K” are the distances from the river mouth along the current river channel center line in kilometers (1K is one km). The J-, M-, and F-plane with colored open arrows are the remaining parts of old alluvial fans formed in the diluvial epoch. A trunk highway, called “Hokurikudo”, connects the important cities along the Japan Sea’s coast and branches into two routes on the Kurobe Alluvial Fan, as shown with green lines in the figure. The main highway takes the course near the coast, which is level and short in distance, but it sometimes is inundated from the flooding of the Kurobe River. Therefore, the secondary highway, a route with a bridge over the exit from the canyon at the top of the alluvial fan, was built for use during flood seasons. One of the objectives of stabilizing the Kurobe River was to reduce the risk of flooding on the main highway for the convenience of travelers [12]. The three place names marked with squares indicate the location of large settlements in the Edo period. Energies 2021, 14, x FOR PEER REVIEW 3 of 17

stabilizing the Kurobe River was to reduce the risk of flooding on the main highway for the convenience of travelers [12]. The three place names marked with squares indicate the Energies 2021, 14, x FOR PEER REVIEW location of large settlements in the Edo period. 3 of 17

According to a survey of ancient dwelling ruins, people have lived on F-plane and M-plane for more than 5000 years. Paddy rice production on the present alluvial fan began stabilizing the Kurobe River was to reduce the risk of flooding on the main highway for thearound convenience the of 1sttravelers century [12]. The BC three along place thenames cliffs marked of with old squares alluvial indicate fans the which are rich in spring locationwater, of largeand settlements then at inthe the skirt Edo period. of the alluvial fan where subterranean streams spring. The ruinsAccording of a largeto a survey plantation of ancient mana dwellinggement ruins, people office have in thelived 9th on F-planeto 10th and centuries were found near M-plane for more than 5000 years. Paddy rice production on the present alluvial fan began aroundthe coastthe 1st ofcentury Nyuzen. BC along However, the cliffs of full-scaleold alluvial fanspaddy which field are rich development in spring in the center part of water,the andalluvial then at fan the skirtwas of finally the alluvial started fan where in the subterranean Edo period streams when spring. the The flow path of the Kurobe ruinsRiver of a largebecame plantation stable, mana andgement many office dispersed in the 9th to 10th vill centuriesages, as were shown found innear Photo 1, were formed. Energies 2021, 14, 4406 the coast of Nyuzen. However, full-scale paddy field development in the center part3 ofof 17 the alluvial fan was finally started in the Edo period when the flow path of the Kurobe River became stable, and many dispersed villages, as shown in Photo 1, were formed.

FigureFigure 1. 1.KurobeKurobe Alluvial Alluvial Fan. Fan. According to a survey of ancient dwelling ruins, people have lived on F-plane and Figure 2 is a cross-sectional view of the old and the present alluvial fans with the M-plane for more than 5000 years. Paddy rice production on the present alluvial fan began origin at the exit from the canyon. The datum level for altitude measurements is the Tokyo aroundFigure the 1. 1st Kurobe century Alluvial BC along theFan. cliffs of old alluvial fans which are rich in spring water, Bay average sea level (Tokyo Peil). All elevation values in this paper are in meters above and then at the skirt of the alluvial fan where subterranean streams spring. The ruins of a the Tokyo Peil. Carbon-14 dating showed that the order of terrain formation was large plantation management office in the 9th to 10th centuries were found near the coast J→M→F→FigureG (present), 2 is which a cross-sectional coincides with the orderview of ofthe theslope old angle. and As the the ground present in alluvial fans with the of Nyuzen. However, full-scale paddy field development in the center part of the alluvial thisfanorigin region was finally atis thetilted started exit toward infrom the the Edo thesea period ascanyon. a resu whenlt Theof the an flow datumorogeny, path of levelthe the older Kurobe for terrain altitude River became became measurements is the Tokyo steeper.stable,Bay averageThe and dissection many dispersedsea of level the villages,F-plane (Tokyo by as shownthe Peil). G-plane in All Photo started elevatio 1, were about formed.n 10,000values years in ago. this The paper are in meters above geological unconformities under the seabed found by a sounding survey, shown with theFigure Tokyo2 is a cross-sectionalPeil. Carbon-14 view of thedating old and theshowed present alluvialthat fansthe with order the origin of terrain formation was crossesat the in exit the from figure, the canyon.are just on The the datum extensio leveln forof the altitude F-plane measurements on the land. isThe the lines Tokyo of BayF- planeaverageJ→ Mand→ seaG-planeF→ levelG (present), (Tokyointersect Peil). at awhich All point elevation 45 coincides m above values sea inwith thislevel, paperthe showing order are in that meters of erosionthe above slope has the angle. As the ground in occurredTokyothis Peil.region on the Carbon-14 upper is tilted half dating and toward showed deposition that the has the sea occurred order as of a terrainon resu the formationlowerlt of half an was [13]. orogeny,J →M→F→ theG older terrain became (present),steeper. which The coincides dissection with theof orderthe F-plane of the slope by angle. the AsG-plane the ground started in this regionabout 10,000 years ago. The is tilted toward the sea as a result of an orogeny, the older terrain became steeper. The dissectiongeological of the unconformities F-plane by the G-plane under started the about seabed 10,000 found years ago. by The a geologicalsounding survey, shown with unconformitiescrosses in the under figure, the seabed are foundjust byon a the sounding extensio survey,n shownof the with F-plane crosses inon the the land. The lines of F- figure, are just on the extension of the F-plane on the land. The lines of F-plane and G-plane intersectplane atand a point G-plane 45 m above intersect sea level, at showing a point that erosion45 m hasabove occurred sea on level, the upper showing that erosion has halfoccurred and deposition on the has upper occurred half on the and lower deposition half [13]. has occurred on the lower half [13].

Figure 2. Radial section profiles of alluvial fans.

FigureFigure 2. Radial 2. Radial section section proﬁles of profiles alluvial fans. of alluvial fans.

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Energies 2021, 14, 4406 3. Estimation of Past Topography 4 of 17 3.1. Analysis of Pictorial Map from the Late 18th Century 3.Figure Estimation 3 shows of Past the Topography old maps used in this study, which all have the same northern orientation,3.1. Analysis as ofshown Pictorial in Map the from upper the Late right 18th corner Century of (c). Panel (a) is a pictorial map drawn in 1785, Figurewhich3 showsshows the branching old maps usedflow inpaths this study,(thick which curved all havelines), the discrete same northern short levees (dotted orientation,belts), village as shown names, in the and upper highways right corner [12] of. Panel (c). Panel (b) (a) shows is a pictorial the levee map drawnarrangement ob- tainedin 1785, from which the advanced shows branching survey ﬂow carried paths (thickout in curved 1894 under lines), discretethe direction short levees of Johannis de (dotted belts), village names, and highways [12]. Panel (b) shows the levee arrangement Rijke,obtained an engineer from the from advanced the surveyNetherlands carried out [14] in 1894. Panel under (c) the is directionthe first of 1/50,000 Johannis scale de modern mapRijke, published an engineer by the from Japanese the Netherlands government [14]. Panel in (c)1910, is the in ﬁrstwhich 1/50,000 houses, scale streets, modern and village namesmap are published plotted. by theHowever, Japanese governmentsince the location in 1910, ins of which levees houses, were streets, not andvery village clear, the levee locationsnames in are (b) plotted. were However, added by since hand. the locationsHereafte ofr, levees these were three not maps very clear,are called the levee Map (a), Map locations in (b) were added by hand. Hereafter, these three maps are called Map (a), (b), Mapand (b),Map and (c), Map respectively, (c), respectively, for for convenience. convenience.

Figure 3.Figure Old maps 3. Old used maps usedin this in thisstudy. study. (a ()a Pictorial) Pictorial mapmap drawn drawn in 1785;in 1785; (b) levee (b) levee lines measured lines measured in 1894; (c in) 1/50,000 1894; (c scale) 1/50,000 scale map publishedmap published in 1910. in 1910. Figure4, hereafter called Map (d), is a special map named “landform classification mapFigure for flood 4, hereafter control” and called was issued Map recently(d), is bya special the Geospatial map Informationnamed “lan Authoritydform ofclassification mapJapan for flood [15]. In control” this map, theand ground was issued surface isrecently classified by into the landforms Geospatial such asInformation floodplains, Authority of Japanold river [15]. channel In this traces, map, terraces, the ground natural levees, surface wetlands, is classified and sand into dunes. landforms Although such the as flood- old river channel traces are often fragmentary, they possibly correspond to the locations of plains, old river channel traces, terraces, natural levees, wetlands, and sand dunes. Alt- stream paths depicted in Map (a). hough theComparing old river Map channel (a) with traces Map (c),are it often can be fr seenagmentary, that Map they (a) has possibly a large amountcorrespond to the locationsof distortion. of stream Therefore, paths Map depicted (b) was in geometrically Map (a). corrected using the thin plate spline method [16], and the positions of flow paths and levees in Map (a) were mapped onto Map (c) using the following four assumptions: (1) The stream paths in Map (a) nearly correspond to the old river channel traces depicted in Map (d); (2) Comparatively long levees drawn in Map (a) remain as parts of the levee system depicted in Map (b); (3) The positions of village names in Map (a) roughly correspond to the locations of village centers in Map (c); (4) The position of the highway is the same in Maps (a) and (c).

Figure 4. Landform classification map for flood control.

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3. Estimation of Past Topography 3.1. Analysis of Pictorial Map from the Late 18th Century Figure 3 shows the old maps used in this study, which all have the same northern orientation, as shown in the upper right corner of (c). Panel (a) is a pictorial map drawn in 1785, which shows branching flow paths (thick curved lines), discrete short levees (dotted belts), village names, and highways [12]. Panel (b) shows the levee arrangement obtained from the advanced survey carried out in 1894 under the direction of Johannis de Rijke, an engineer from the Netherlands [14]. Panel (c) is the first 1/50,000 scale modern map published by the Japanese government in 1910, in which houses, streets, and village names are plotted. However, since the locations of levees were not very clear, the levee locations in (b) were added by hand. Hereafter, these three maps are called Map (a), Map (b), and Map (c), respectively, for convenience.

Figure 3. Old maps used in this study. (a) Pictorial map drawn in 1785; (b) levee lines measured in 1894; (c) 1/50,000 scale map published in 1910.

Figure 4, hereafter called Map (d), is a special map named “landform classification map for flood control” and was issued recently by the Geospatial Information Authority of Japan [15]. In this map, the ground surface is classified into landforms such as floodplains, old river channel traces, terraces, natural levees, wetlands, and sand dunes. Alt- Energies 2021, 14, 4406 hough the old river channel traces are often fragmentary, they possibly5 of 17 correspond to the Energies 2021, 14, x FOR PEER REVIEWlocations of stream paths depicted in Map (a). 5 of 17

Comparing Map (a) with Map (c), it can be seen that Map (a) has a large amount of distortion. Therefore, Map (b) was geometrically corrected using the thin plate spline method [16], and the positions of flow paths and levees in Map (a) were mapped onto Map (c) using the following four assumptions: (1) The stream paths in Map (a) nearly correspond to the old river channel traces depicted in Map (d); (2) Comparatively long levees drawn in Map (a) remain as parts of the levee system depicted in Map (b); (3) The positions of village names in Map (a) roughly correspond to the locations of village centers in Map (c); (4) The position of the highway is the same in Maps (a) and (c). FigureFigure 4.InLandform 4. the Landform identification classification classification map of for landmarks, flood map control. for flood some control. subjective judgment is unavoidable, but the resultsIn the shown identification in Figure of landmarks, 5a were some obtained subjective judgmentby aiming is unavoidable, for overall but consistency. the In the figure, resultsthe blue shown lines in Figure are5 streama were obtained paths byand aiming the forred overall lines consistency. are the 18th-C In the figure, levees that were drawn in theMap blue (a) lines in are 1785. stream The paths red and lines the red in lines Figure are the 5b 18th-C indicate levees the that 19th-C were drawn levees in that were drawn in Map (a) in 1785. The red lines in Figure5b indicate the 19th-C levees that were drawn in MapMap (b) (b) in 1894. in 1894. Many branchMany streamsbranch were streams cut off bywere the 19th-Ccut off levees by and,the as19th-C a result, levees and, as a result, thethe river river flow flow was finally was concentratedfinally concentrated in a narrow band in a bounded narrow by band levees. bounded by levees.

FigureFigure 5. Mapping 5. Mapping of the stream of the paths stream in 1785 paths (blue lines)in 1785 to the (blue map oflines) 1910. to (a) the The redmap lines of are 1910. (a) The red lines are leveeslevees in 1785. in 1785. (b) The (b red) The lines red are leveeslines in are 1894. levees in 1894. 3.2. Topography in the 18th Century 3.2.The Topography topography ofin alluvial the 18th fans Century in the 18th century was estimated as follows from the latest groundThe topography surface elevation of map alluvial with a fans spatial in resolution the 18th of 5century m, which was is hereafter estimated as follows from called LP data [17]. the latest ground surface elevation map with a spatial resolution of 5 m, which is hereafter called LP data [17]. The LP data map shows that the current riverbed is considerably below the bankside floodplain. This suggests that the channel bed was eroded by an increase in bed load transport caused by the concentration of river flow after the construction of the 19th-C levees. Therefore, for the sake of convenience, the elevation data for the channel bed portion were changed to the elevation obtained by linear interpolation of the elevation at both banks for each cross section. In addition, man-made land elevation changes, such as for road and railway construction on the ground after the 20th century, were eliminated by interpolation from the flat ground elevation on both sides. After that, local ground undulations were smoothened by averaging the elevations of adjacent grid cells to determine the basic topography of the alluvial fan. The color contour map in Figure 6 shows the topography of the alluvial fan obtained by the abovementioned data processing, in which the blue lines are the stream paths obtained in the previous section, and the dark spots show the locations of

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The LP data map shows that the current riverbed is considerably below the bankside floodplain. This suggests that the channel bed was eroded by an increase in bed load transport caused by the concentration of river flow after the construction of the 19th-C levees. Therefore, for the sake of convenience, the elevation data for the channel bed portion were changed to the elevation obtained by linear interpolation of the elevation at both banks for each cross section. Energies 2021, 14, x FOR PEER REVIEW 6 of 17 In addition, man-made land elevation changes, such as for road and railway construction on the ground after the 20th century, were eliminated by interpolation from the flat ground elevation on both sides. After that, local ground undulations were smoothened by Energies 2021, 14, x FOR PEER REVIEWaveraging the elevations of adjacent grid cells to determine the basic topography6 of 17 of the village centers (large ones) and individual houses (small ones) indicated on Map (c) in alluvial1910. fan. The color contour map in Figure6 shows the topography of the alluvial fan obtained by the abovementioned data processing, in which the blue lines are the stream villagepaths obtainedcenters (large in theones) previous and individual section, houses and the (small dark ones) spots indicated show the on locationsMap (c) in of village 1910.centers (large ones) and individual houses (small ones) indicated on Map (c) in 1910.

FigureFigureFigure 6.6. Topography6.Topography Topography of Kurobe of of Kurobe Kurobe Alluvi Alluvialal Alluvi Fan in Fanal the Fan in18th the in century. the 18th 18th century. century.

TheTheThe terrain terrain terrain in inFigure in Figure Figure 6 after6 after 6 removing after removing removing all the all ground theall the ground undulations ground undulations undulations is almost is smooth. almost is almost smooth. smooth. However, the flow paths must have been naturally lower than their surroundings. As However, the flow paths must have been naturally lower than their surroundings. shownHowever, by the examplesthe flow in paths Figure must 7, the havetraces ofbeen old rivernaturally channels lower indicated than in their the “land- surroundings. As formAsshown shown classification by bythe the examples map examples for flood in inFigure Figurecontrol” 7,7 the ,(Figure the traces traces 4) ofare of old slightly old river river lower channels channels than indicatedtheir indicated sur- in in the the “land- roundings.“landformform classification classification map map for forflood flood control” control” (Figure (Figure 4)4 )are are slightly slightly lower thanthan theirtheir sur- surroundings.roundings.

Figure 7. Examples of ground depression of old river channel trace. Upper: landform classification map. Blue hatched area is the old river channel trace. Lower: cross-section profile along the red line in the upper figure.

FigureFigureTherefore, 7. 7.Examples Examples the cross of of ground sectionground depression of depression each river of segment oldof old river river shown channel ch annelin trace.Figure trace. Upper: 5a wasUpper: landform determined landform classification classification asmap.map. follows Blue Blue from hatched hatched the corresponding area area is is the the old old rivertrace river channelof channelthe old trace. river trace. Lower: shown Lower: cross-section in Figurecross-section 4. First, profile profilethe along chan- along the red the line red line nelinin the widththe upper upper was figure. determinedfigure. from a part of the trace which had a clear outline. Next, based on classical river regime theory [18], the following equation was adopted to estimateTherefore, the bankfull the crossdischarge: section of each river segment shown in Figure 5a was determined as follows from the corresponding trace of the old river shown in Figure 4. First, the chan- / nel width was determined from𝐵𝛼 a part 𝑄 of, the trace which had a clear outline.(1) where Next,B is the based channel on widthclassical (m), river Q is regimethe bankfull theory discharge [18], the (m following3/s), and the equation recom- was adopted mendedto estimate range thefor αbankfull is 3.5~7.0 discharge: [19]. Here, a mean α value of 5.25 was used. The channel depth was estimated based on the Manning uniform flow formula for a wide rectangular cross section, and is given by 𝐵𝛼/ 𝑄 , (1)

where B is the channel width (m), Q is the bankfull discharge (m3/s), and the recom-

mended range for α is 3.5~7.0 [19]. Here, a mean α value of 5.25 was used. The channel depth was estimated based on the Manning uniform flow formula for a wide rectangular cross section, and is given by

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𝑛𝑄 / (2) ℎ , 𝐵𝑆

where h is the channel depth, S is the channel slope, and the roughness coefficient n was assumed to be 0.04.

3.3. Topography in the Middle 20th Century Energies 2021, 14, 4406 7 of 17 For numerical simulation of inundation flow to examine whether the 19th-C levee system still remained effective even under changes in sedimentation, the topographic con- ditionTherefore, in the the mid-20th cross section century of each river wa segments determined shown in Figureas described5a was determined below. as followsFigure from the 8 correspondingshows the tracelongitudinal of the old river profile shown inof Figure the 4riverbed. First, the channelmeasured in 1963 together width was determined from a part of the trace which had a clear outline. withNext, the based present on classical profiles river regimefor both theory riverbanks [18], the following obtained equation from was the adopted LP data. Both sets of data toare estimate plotted the bankfull from discharge:the high water level at each section, so as to see the differences easily. Several centuries ago, when the river branched into many streams, the elevation differ- B = α Q1/2, (1) ence between the river bank and riverbed was not very large, but later increased, probably wheredueB tois thea change channel widthin bed (m), loadQ is the caused bankfull by discharge the flow (m3 /s),concentration and the recommended by the levees. range for α is 3.5~7.0 [19]. Here, a mean α value of 5.25 was used. The channel depth was estimatedThe based line on of the the Manning channel uniform bed flow intersects formula for those a wide rectangularof the riverbanks cross section, around 6 km from the andriver is given mouth. by According to the contour map in Figure 1, the ground elevation of the allu- 3/10 n2Q2 vial fan in this location is habout= 45 m above, sea level, corresponding (2) to the intersection point of the long-term topographicB2S change shown in Figure 2. These data suggest that whereconcentratingh is the channel the depth, flowS isinto the channela single slope, narrow and the roughnesschannel coefficientenlargedn wasthe vertical topographic assumed to be 0.04. change and that the deformation of river channel bed shown in Figure 3b probably started 3.3.after Topography the construction in the Middle 20th of Centurythe levee system. ForThe numerical topographic simulation data of inundation for the flow20th to century examine whetherwere determined the 19th-C levee from the LP data with a system still remained effective even under changes in sedimentation, the topographic conditionresolution in the of mid-20th 5 m as century follows: was determinedbecause largescale as described below.riverbed degradation was caused by the constructionFigure8 shows of the high longitudinal dams in profile the upstream of the riverbed canyon measured after in the 1963 1960s together and bed sediment exca- withvation the present for building profiles for materials both riverbanks [12], obtained the LP from data the LPwere data. corrected Both sets of by data adding the amount of are plotted from the high water level at each section, so as to see the differences easily. Severaltransversely centuries ago, averaged when the channel river branched bed into degradation many streams, measured the elevation after difference 1963. In addition, the re- betweencently the constructed river bank and fills riverbed for wasrailways not very and large, highways but later increased, were probablyeliminated due from the LP data by tointerpolation a change in bed loadfrom caused the bysurrounding the flow concentration ground. by the levees.

FigureFigure 8. Longitudinal 8. Longitudinal proﬁles ofprofiles riverbed of and riverbed river banks. and river banks.

The line of the channel bed intersects those of the riverbanks around 6 km from the river4. Methodology mouth. According for to the Flood contour Simulation map in Figure 1, the ground elevation of the alluvial fan4.1. in thisNumerical location is Model about 45 m above sea level, corresponding to the intersection point of the long-term topographic change shown in Figure2. These data suggest that concentrating the ﬂowA into two-dimensional a single narrow channel shallow enlarged water the vertical model, topographic which change was and obtained that the from the integral of deformationthe three-dimensional of river channel bed equations shown in Figure of 3motionb probably fr startedom the after ground the construction to the water surface under of the levee system. theThe assumptions topographic data of an for incompressible the 20th century were fluid determined and a hydrostatic from the LP data pressure with field, was used for anumerical resolution of flood 5 m as follows:flow simulation: because largescale riverbed degradation was caused by

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the construction of high dams in the upstream canyon after the 1960s and bed sediment excavation for building materials [12], the LP data were corrected by adding the amount of transversely averaged channel bed degradation measured after 1963. In addition, the recently constructed ﬁlls for railways and highways were eliminated from the LP data by interpolation from the surrounding ground.

4. Methodology for Flood Simulation 4.1. Numerical Model A two-dimensional shallow water model, which was obtained from the integral of the three-dimensional equations of motion from the ground to the water surface under the assumptions of an incompressible fluid and a hydrostatic pressure field, was used for numerical flood flow simulation: ∂h ∂(Uh) ∂(Vh) + + = 0 (3) ∂t ∂x ∂y

∂(Uh) ∂(UUh) ∂(UVh) ∂t + ∂x + ∂y ( ) ( ) (4) = −gh ∂H + ∂ hτUU + ∂ hτUV − τ0 √ U ∂x ∂x ∂y ρ U2+V2 ∂(Vh) ∂(UVh) ∂(VVh) ∂t + ∂x + ∂y ( ) ( ) (5) = −gh ∂H + ∂ hτUV + ∂ hτVV − τ0 √ V ∂y ∂x ∂y ρ U2+V2 where U and V denote the velocity components in the x- and y- directions, respectively, h is the water depth, H is the free water surface elevation, ρ is the density of water, and g is the acceleration of gravity. τ0 denotes the bed shear stress and τUU, τUV, and τVV are the horizontal components of stress tensor expressed following Wu [20] as:

ρg(U2+V2) τ = ρU 2 = n2 , 0 f h1/3 ∂U 2 ∂U ∂V ∂V 2 (6) τUU = 2ε ∂x − 3 k, τUV = ε ∂y + ε ∂x , τVV = 2ε ∂y − 3 k, 1 2 ε = 6 κUf h, k = 2.07Uf

where Uf is the friction velocity, n is Manning’s roughness coefﬁcient, ε is the vertically averaged eddy viscosity, k is the turbulent kinetic energy, and κ (=0.41) is the von Karman constant. The expression for k in the equation was proposed by Nezu and Nakagawa [21]. The ﬂow rate over the levees was calculated using the following formula proposed by Honma [22]: ( p 0.35h1 2gh1 if h2/h1 ≤ 2/3 = q p (7) 0.91h2 2g(h1 − h2) otherwise

where q is the flow rate per unit width over the levee and h1 and h2 represent the water surface heights upstream and downstream, respectively, of the overflow from the levee crown. To model the motion of the inundation front, the Eulerian method proposed by Brufau et al. [23] was adopted to avoid the so-called C-property collapse at the interface between a wet cell and a dry bed cell. This method temporarily sets the ground elevation of the dry bed cells adjacent to the wet area as equal to the water surface level in the neighboring wet cell. These differential equations were converted to finite difference equations using the finite volume method with an unstructured triangular mesh system. More details relating to the finite difference equations and their solver can be found in the report by Roe [24]. The mesh system was generated from the lines of the river banks and levees using Ansys ICEM computational fluid dynamics software [25]. Energies 2021, 14, x FOR PEER REVIEW 9 of 17

and around the river channel, and those in the region far-off from the channel were around 200 m. In all, 71,384 computational grids were created for the whole calculation area.

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Figure9 shows the triangular meshes for the ﬂow simulation corresponding to the and around the river19th-C channel, levees. The and order those of triangle in the side region length far-off was around from 20 the m for channel the ﬁne mesheswere in around 200 m. In andall, around71,384 thecomputational river channel, and grids those were in the created region far-off for the from whole the channel calculation were around area. 200Figure m. In all, 9. 71,384Triangular computational mesh grids system. were created for the whole calculation area.

4.2. Flood Hydrograph Figure 10 is a hydrograph of the flood observed at the exit of the canyon in 1969 normalized by the peak discharge (6700 m3/s) [12]. This was the largest flood in the history of recorded observations, and its return period was estimated as 100 years, as shown in the probability plot in Figure 11 [12]. However, because the frequency of river overflow to the floodplain in the late Edo era was about once every 7 years according to an old local document [12], the scale of target flood for the design of 19-C levee was considered smaller than that of the flood observed in 1969. Therefore, in this study, a numerical flood simulation was carried out for a flood with a return period of 10 years. According to the probability plot in Figure 11, the peak discharge of this flood is 3000 m3/s and the hydrograph Figure 9. Triangular meshin Figure system.Figure 10 normalized 9. Triangular mesh system.by this value was used. The green vertical dotted line in Figure 4.2.10 Flood shows Hydrograph the time of inspection for constructing the flow field figures when the flood peak 4.2. Flood Hydrograph reachesFigure 10 the is a downstream hydrograph of the channel flood observed section, at the exit which of the canyonwill be in 1969discussed in Section 5. Figure 10 is anormalized hydrograph by the of peak the discharge flood ob (6700served m3/s) at [12 the]. This exit was of the the largest canyon flood inin the1969 history normalized by the ofpeak recorded dischargeThe observations, numerical (6700 m and3/s) itssimulation [12]. return This period was was wasthe estimated largest carried flood as 100 out in years, the fo history asr shownthe five in conditions listed in Table 1. of recorded observations,theThe probability effect and its plot of return in18th-C Figure period 11 [levees12 ].was However, estimatedwas becauseevaluated as the100 frequency years, by comparisonas of shown river overflow in of the results for Cases (a) and the probability plotto in the Figure floodplain 11 in[12]. the However, late Edo era because was about the once frequency every 7 years of river according overflow to an old local(b). document The effect [12], the of scale 19th-C of target levees flood for thewas design evaluated of 19-C levee by was comparison considered of the results for Cases (b) to the floodplain in the late Edo era was about once every 7 years according to an old local smallerand than(c). thatCase of the (d) flood examined observed in 1969. whether Therefore, 19th-C in this study, levees a numerical worked flood well even after the riverbed document [12], thesimulation scale of target was carried flood outfor th fore adesign flood with of 19-C a return levee period was ofconsidered 10 years. Accordingsmaller to than that of the floodthedeformed probabilityobserved plot indue 1969. in Figureto Therefore, the 11 flow, the peak in concentration this discharge study, of a this numerical floodin the is 3000 channel.flood m3 /ssimu- and In the addition, Case (e) examined the lation was carried hydrographoutresponse for a flood in Figureof with flooding 10 anormalized return toperiod by riverb this of value 10ed wasyears. deformation used. According The green verticalto so the as dottedprob- to lineinduce an overflow to the right in Figure 10 shows the time of inspection for constructing the flow field figures when the 3 ability plot in Figurefloodbankside, 11, peak the reaches peak the discharge the purpose downstream of this of channel floodwhich section, is 3000 will which m be/s will describedand be the discussed hydrograph later. in Section 5. in Figure 10 normalized by this value was used. The green vertical dotted line in Figure 10 shows the time of inspection for constructing the flow field figures when the flood peak reaches the downstream channel section, which will be discussed in Section 5. The numerical simulation was carried out for the five conditions listed in Table 1. The effect of 18th-C levees was evaluated by comparison of the results for Cases (a) and (b). The effect of 19th-C levees was evaluated by comparison of the results for Cases (b) and (c). Case (d) examined whether 19th-C levees worked well even after the riverbed deformed due to the flow concentration in the channel. In addition, Case (e) examined the response of flooding to riverbed deformation so as to induce an overflow to the right bankside, the purpose of which will be described later.

Figure 10. Normalized ﬂood hydrograph. Figure 10. Normalized flood hydrograph.

Figure 10. Normalized flood hydrograph.

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FigureFigure 11. Probability 11. Probability plot of annual plot maximum of annual discharge. maximum discharge. The numerical simulation was carried out for the five conditions listed in Table1. The effect of 18th-C levees was evaluated by comparison of the results for Cases (a) and (b). TheTable effect of1. 19th-CCase leveesof numerical was evaluated simulation. by comparison of the results for Cases (b) and (c). Case (d) examined whether 19th-C levees worked well even after the riverbed deformed due to theCase flow concentrationLevee in the channel. condition In addition, Case (e) examined the response Topography of flooding(a) to riverbed deformationNo so levee as to induce an overflow to the right bankside,Late 18th-C the purpose of which will be described later. (b) 18th-C levee Late 18th-C Table 1. Case of numerical simulation. (c) 19th-C levee Late 18th-C Case(d) Levee19th-C Condition levee Topography Mid 20th-C (a) No levee Late 18th-C (e)(b) 18th-C 19th-C levee levee Late 18th-C Channel bed deformation (c) 19th-C levee Late 18th-C (d) 19th-C levee Mid 20th-C 5. Results(e) of Numerical 19th-C Simulation levee Channel bed deformation

5.5.1. Results Hydraulic of Numerical Effect Simulation of 18th-C Levees 5.1. HydraulicFigure Effect 12a of 18th-C shows Levees the inundation depth distribution at the inspection time after the Figure 12a shows the inundation depth distribution at the inspection time after theflood ﬂood peakpeak (t (t = 41= h41 in h Figure in Figure8) obtained 8) forobtained Case (a), thefor condition Case (a), of nothe lev- condition of no levees. The ees.locationsThe locations of 18th-Cof 18th-C levees levees are are shown shown by black by black dotted linesdotted for the lines reference for the reference only. Villages only. Villages and highways are also indicated by dark spots and thin lines, respectively. Figureand 12 highwaysb shows the same are kindalso of indicated map obtained by for Casedark (b), spots in which and the locationsthin lines, of respectively. Figure 12b 18th-Cshows levees the are same drawn kind with black of map solid obtained lines, and for for reference Case only,(b), thein which locations the of locations of 18th-C levees 19-Care levees drawn are depicted with byblack dotted solid lines. lines, and for reference only, the locations of 19-C levees are depicted by dotted lines. Many of the 18th-C levees were discrete and short, designed to protect individual villages from direct flood impacts. However, some of the relatively long levees on the right bank appear to have been intended to block the divergent stream, and in fact they became part of the 19th-C embankment system. This fact suggests the possibility that the hydraulic engineers had a rough plan of a levee system to prevent flooding on the right bank of the floodplain (north half of the alluvial fan) by cutting off branch streams. On the left bank, in contrast, a double embankment was only built in the uppermost stream reach near the canyon outlet to suppress the spread of the flow. One branch stream, which had flowed from the upstream right bank to the coast on the north side, as shown in Case (a), was cut off in Case (b). As a result, the area indicated with (A) became free from flooding by that stream. The branch streams that had flowed into the area indicated by (B) became weakened by the long levee at the middle river reach. As a result, the frequency of flood damage to nearby villages and highways probably decreased.

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However, in the area near the coast indicated by (C) and the area on the left bank indicated by (D), where only short and discrete levees were installed, no big difference can be seen in inundation conditions between the two figures. By actually experiencing the effects of levee changes in this way, the engineers those days might have learned that a systematic arrangement of longer levees to cut the branch streams off was required to Energies 2021, 14, 4406 reduce the flood risk. However, there is no evidence of their actual thinking, because11 of 17 the engineering techniques at that time were handed down not in public textbooks but by an unwritten transmission of proficiency based on unwritten practice.

(a) (b)

(c)

FigureFigure 12. (a) 12. Inundation(a) Inundation depth depth distribution distribution Case Case (a): (a): elapsed elapsed time time = = 41 41 h.h. ((bb)) InundationInundation depth depth distribution distribution Case Case (b): (b): elapsedelapsed time = time 41 h. = ( 41c). h. Inundation (c). Inundation depth depth distribution distribution Case Case (c): (c): elapsed elapsed time time = 41 h.h.

5.2. HydraulicMany Effect of the of 18th-C 19th-C levees Levees were discrete and short, designed to protect individual villages from direct flood impacts. However, some of the relatively long levees on the right The black solid lines in Figure 12c indicate the 19th-C levees. The locations of some bank appear to have been intended to block the divergent stream, and in fact they became of thepart right of the bank 19th-C levees embankment were the system. same as This thos facte suggestsof the 18th-C the possibility levees shown that the in hydraulic Figure 12b. In contrast,engineers the had left a roughbank levees, plan of which a levee had system not to existed prevent in flooding the 18th on century, the right were bank completed of the beforefloodplain the late (north 19th halfcentury, of the but alluvial the fan)order by and cutting the offtiming branch of streams. construction On the were left bank, not recorded.in contrast, It should a double be noted embankment that the left was bank only builtlevees in theappear uppermost to consist stream of reachthree nearparts: the short leveescanyon overlapping outlet to suppressone another the spread at a downstre of the flow.am connection, a long continuous levee in the midstream,One branch and stream,short discrete which hadlevees flowed upstream. from the upstream right bank to the coast onThe the colors north in side, the asfigure shown show in Casethe inundation (a), was cut depth off in distribution Case (b). As at a the result, inspection the area time indicated with (A) became free from flooding by that stream. The branch streams that had obtained for Case (c). It can be seen that there is almost no flooding of the right bank flowed into the area indicated by (B) became weakened by the long levee at the middle floodplain.river reach. The As flooding a result, of the the frequency left bank of begins flood damage at the upstream to nearby levee villages openings and highways and flows downprobably the old decreased. river channel outside the long continuous levee. Finally, the flow splits into two streams,However, one inof thewhich area returns near the to coast the river indicated channel by (C) among and the the area downstream on the left bankoverlap- pingindicated short levees, by (D), and where the other only short flows and down discrete further levees to the were wetlands installed, in no front big differenceof the coastal dunes.can be seen in inundation conditions between the two figures. By actually experiencing the effects of levee changes in this way, the engineers those days might have learned that a systematic arrangement of longer levees to cut the branch streams off was required to reduce the flood risk. However, there is no evidence of their actual thinking, because the engineering techniques at that time were handed down not in public textbooks but by an unwritten transmission of proficiency based on unwritten practice. Energies 2021, 14, 4406 12 of 17

5.2. Hydraulic Effect of 19th-C Levees The black solid lines in Figure 12c indicate the 19th-C levees. The locations of some of the right bank levees were the same as those of the 18th-C levees shown in Figure 12b. In contrast, the left bank levees, which had not existed in the 18th century, were completed Energies 2021, 14, x FOR PEER REVIEW 12 of 17 before the late 19th century, but the order and the timing of construction were not recorded. It should be noted that the left bank levees appear to consist of three parts: short levees overlapping one another at a downstream connection, a long continuous levee in the midstream, and short discrete levees upstream. The colors in the figure show the inundation depth distribution at the inspection time obtainedFigure for Case (c). 13 It canshows be seen the that flow there is velocity almost no flooding vectors of the in right the bank region of the green rectangle in Fig- floodplain. The flooding of the left bank begins at the upstream levee openings and flows downure the 12c. old river It can channel be outside seen the that long continuousthe streams levee. Finally, are following the flow splits into the trace of the old river channel. As twoleveling streams, one technology of which returns towas the river already channel among developed the downstream in overlappingthe Edo period, it is considered that they short levees, and the other flows down further to the wetlands in front of the coastal dunes. knewFigure the13 shows ground the flow undulation velocity vectors inof the the region old of theriver green channel rectangle in well. Therefore, they possibly con- Figure 12c. It can be seen that the streams are following the trace of the old river channel. Assidered leveling technology the old was river already channel developed as in the a Edotemporary period, it is consideredfloodway that when the river discharge from the theycanyon knew the exceeded ground undulation the of main the old riverchannel channel capaci well. Therefore,ty. This they possibly is considered again later. considered the old river channel as a temporary floodway when the river discharge from the canyonThis exceeded point the main is discussed channel capacity. again This is considered below. again later.

FigureFigure 13. Overﬂow 13. Overflow and return ﬂow and through return levee openings flow (Casethro (c)).ugh levee openings (Case (c)). This point is discussed again below.

5.3.5.3. Function Function of 19th-C Leveesof 19th-C in the 20th Levees Century in the 20th Century Figure 14 shows the calculation results for Case (d), where the 19th-C levees are superimposedFigure on the 14 topography shows of the the 20th calculation century. As mentioned results above, for dueCase to the (d), where the 19th-C levees are su- riverperimposed flow concentration on caused the bytopography the 19th-C levees, of the the riverbed 20th should cent haveury. been As de- mentioned above, due to the river formed from that described in Section 3.2 to that described in Section 3.3. The purpose of thisflow section concentration is to examine whether caused the flood flowby patternthe 19th-C changed fromlevees, that obtained the riverbed for should have been deformed Casefrom (c) depending that described on the riverbed in degradation. Section As mentioned3.2 to that above, duedescribed to the concen- in Section 3.3. The purpose of this tration of flow by the 19-C embankment, the riverbed should have been transformed from whatsection was found is into Section examine 3.2 to what whether was found inthe Section flood 3.3. flow pattern changed from that obtained for Case (c) depending on the riverbed degradation. Another purpose is to verify the inundation simulation results using the data for the flooding pattern in 1934, the peak discharge of which was around 3000 m3/s, almost equal to the peak discharge we used in the above simulations. Compared with Figure 12c, although the mainstream position in the river channel is different due to the bed topography change, the patterns of inundation on the left bank are similar to each other. The area of the inundation became slightly smaller, because the volume of floodwater decreased due to upstream riverbed erosion, as shown in Figure 8. Figure 15 shows the flood flow path and inundation areas estimated based on the reports of damage from the 1934 flood [4]. Although Figure 14 shows the flow pattern at the moment just after the flood peak and Figure 15 shows the overall image of flooding, they are very similar in their basic flood patterns—that is, excess river water overflows from the upstream levee openings, flows down through the old river channel outside the left levee and partially returns to the river channel through the gaps between the short overlapping levees. From the above results, it is supposed that the designers of the 19th-C levees expected their design concept of using the old river channel as a temporary floodway would be preserved even if the channel bed was deformed.

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FigureFigure 14.14.Inundation Inundation depth distributiondepth distribution Case (d): elapsed Case time (d): = 41 h.elapsed time = 41 h.

Another purpose is to verify the inundation simulation results using the data for the flooding pattern in 1934, the peak discharge of which was around 3000 m3/s, almost equal to the peak discharge we used in the above simulations. Compared with Figure 12c, although the mainstream position in the river channel is different due to the bed topography change, the patterns of inundation on the left bank are similar to each other. The area of the inundation became slightly smaller, because the volume of floodwater decreased due to upstream riverbed erosion, as shown in Figure8. Figure 15 shows the flood flow path and inundation areas estimated based on the reports of damage from the 1934 flood [4]. Although Figure 14 shows the flow pattern at the moment just after the flood peak and Figure 15 shows the overall image of flooding, they are very similar in their basic flood patterns—that is, excess river water overflows from the upstream levee openings, flows down through the old river channel outside the left levee and partially returns to the river channel through the gaps between the short FigureoverlappingFigure 15. Inundation levees.14. Inundation flow in depth 1934 estimated distribution by Teramura Case (d): [4]. elapsed time = 41 h.

5.4. Flooding over the Right Bank Induced by Virtual Riverbed Deformation The numerical flow simulation in Figures 12c and 14 showed river overflow only at the left bank, one reason for which is considered to be due to the flow center in the upstream river channel being located near the left bank. However, the channel bed deformation could change the position of the flow center and cause overflow of the right bank. Thus, to examine the characteristics of inundation over the right bank, the riverbed was intentionally deformed to change the flow center from the left bank to the right bank. Figure 16 shows the calculation results for inundation depth. Overflow at the right bank occurred on the levee where the flow center attacked. Figure 17 shows the flow ve-

locity vectors in the region of the green rectangle in Figure 16. The floodwater flows down theFigure Figureold 15. riverInundation 15. channel Inundation ﬂow in 1934just estimated outside flow by in Teramurathe 1934 right [estimated4]. levee, and by aTeramura part of the [4]. flow returns to the river channelFrom through the above results, the gaps it is supposed between that thethe designers overlapp of theing 19th-C levees. levees expectedIn comparison with Figure 13, althoughtheir design the concept flood of usingflow the became old river weaker channel as by a temporary the reduced ﬂoodway overflow would be volume due to channel preserved5.4. Flooding even if the channel over bedthe wasRight deformed. Bank Induced by Virtual Riverbed Deformation bed degradation,The numerical the flow flow patterns simulation for both bank in Figures are verys 12c similar and 14to theshowed pattern river seen overflowon only at the left bank in Figure 13. Therefore, it is presumed that such levee placement was decided on bythe engineers left bank, at thatone timereason as a fortypica whichl method is consider of flood controled to be for due steep to rivers. the flow center in the upstream river channel being located near the left bank. However, the channel bed deformation could change the position of the flow center and cause overflow of the right bank. Thus, to examine the characteristics of inundation over the right bank, the riverbed was intentionally deformed to change the flow center from the left bank to the right bank. Figure 16 shows the calculation results for inundation depth. Overflow at the right bank occurred on the levee where the flow center attacked. Figure 17 shows the flow velocity vectors in the region of the green rectangle in Figure 16. The floodwater flows down the old river channel just outside the right levee, and a part of the flow returns to the river channel through the gaps between the overlapping levees. In comparison with Figure 13, although the flood flow became weaker by the reduced overflow volume due to channel bed degradation, the flow patterns for both banks are very similar to the pattern seen on Figurethe 16. left Inundation bank in depthFigure distribution 13. Therefore, Case (e): it elapsed is presumed time = 41 thath. such levee placement was decided on by engineers at that time as a typical method of flood control for steep rivers.

Figure 16. Inundation depth distribution Case (e): elapsed time = 41 h.

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Figure 14. Inundation depth distribution Case (d): elapsed time = 41 h.

Figure 15. Inundation flow in 1934 estimated by Teramura [4].

5.4. Flooding over the Right Bank Induced by Virtual Riverbed Deformation

Energies 2021, 14, 4406 The numerical flow simulation in Figures 12c and 14 showed14 of 17 river overflow only at the left bank, one reason for which is considered to be due to the flow center in the upstream river channel being located near the left bank. However, the channel bed defor- 5.4.mation Flooding could over the change Right Bank the Induced position by Virtual of Riverbed the flow Deformation center and cause overflow of the right bank. Thus,The numericalto examine flow simulation the characteristics in Figures 12c and of 14 showedinundation river overflow over only the at right the bank, the riverbed was left bank, one reason for which is considered to be due to the flow center in the upstream riverintentionally channel being deformed located near theto change left bank. the However, flow the center channel from bed deformation the left bank to the right bank. could changeFigure the 16 position shows of the the flow calculation center and cause results overflow for of theinundation right bank. Thus, depth. Overflow at the right to examine the characteristics of inundation over the right bank, the riverbed was inten- tionallybank deformedoccurred to changeon the the levee flow center where from the left flow bank center to the right attacked. bank. Figure 17 shows the flow ve- locityFigure vectors 16 shows in the the calculation region results of the for green inundation rect depth.angle Overflow in Figure at the 16. right The floodwater flows down bank occurred on the levee where the flow center attacked. Figure 17 shows the flow velocitythe old vectors river in channel the region ofjust the outside green rectangle the right in Figure levee, 16. The and floodwater a part flowsof the flow returns to the river downchannel the old through river channel the just gaps outside between the right levee,the overlapp and a part ofing the levees. flow returns In tocomparison with Figure 13, thealthough river channel the through flood the flow gaps became between the weaker overlapping by levees.the reduced In comparison overflow with volume due to channel Figure 13, although the flood flow became weaker by the reduced overflow volume due to channelbed degradation, bed degradation, the the flow flow patterns patterns for both for banks both are verybank similars are to very the pattern similar to the pattern seen on seenthe on left the bank left bank in in Figure Figure 13 13.. Therefore, Therefore, it is presumed it is presumed that such levee that placement such waslevee placement was decided decided on by engineers at that time as a typical method of flood control for steep rivers. on by engineers at that time as a typical method of flood control for steep rivers.

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FigureFigure 16. Inundation16. Inundation depth distribution depth Casedistribution (e): elapsed timeCase = 41(e): h. elapsed time = 41 h.

FigureFigure 17. Overﬂow 17. Overflow and return and ﬂow return through leveeflow openings through (Case levee (e)). openings (Case (e)).

6. Process of Levee Development on the Kurobe Alluvial Fan As described in the previous section, the picture drawn in 1785 and survey map drawn in 1894 were used with a shallow water flow model to numerically estimate the flood control function of the levee system on the Kurobe Alluvial Fan at the two time points. This section discusses the overall process of levee development and considers the flood control strategies of that era using the above results and the literature [12], summarizing information written in old documents. In the past, the Kurobe River, after flowing out from the canyon, branched into many streams that changed their course freely to develop the conical terrain of the Kurobe Al- luvial Fan. That river condition was called “Kurobe 48 shallows”. Prior to the 17th century, a group of predominant streams flowed down along the cliffs of the F-plane (see Figures 1 and 4) to the coast north of the alluvial fan. The dominant group of streams gradually moved west and reached the center of the alluvial fan in the 18th century (as shown in Figure 6). The deviation of the present coastline from the concentric contour lines began in this age due to an imbalance between the sediment supply from river flows and coastal erosion by waves and drift currents from the north to the west. With the formation of a stable society in the Edo period after the 17th century, short embankments were installed discretely to protect individual villages from flooding of the Kurobe River. However, due to the frequent displacement of stream paths on the alluvial fan, the short discrete embankments are thought to have lost their functionality in a short period of time. It is probable, therefore, that local engineers tried to unite the flow of the Kurobe River by blocking its stream branches with relatively long levees in upstream and mid-stream areas. The pictorial map in Figure 3a was probably drawn at an early stage of levee construction under that strategy, in which a relatively long levee to block the divergent streams and short discrete embankments to protect the villages co-existed. The levee construction started from the right bank, probably because the engineers were afraid that the Kurobe River would return to the old river courses, around which agricultural fields and villages, as well as the main highway, had already developed. On the left bank (south side) of the group of flows, in contrast, a relatively wide and strong flow existed, as can be seen in Figures 3a and 4, but it was not blocked with a long levee during the early efforts, probably due to the limits of civil engineering technology at that time. The date of completion and the order of construction of the 19th-C levees are not clear, but considering that construction was not possible during the heavy snowfall season in winter and the flood season in summer, the large extension from the 18th-C levees probably took a considerable amount of time. Flooding possibly occurred many times during that period, and as a result, the engineers were able to re-evaluate their work frequently, observing the effects of the partially completed embankment on flood control. Through their actual experience, they possibly thought of how to use the old river channel next to the levees.

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6. Process of Levee Development on the Kurobe Alluvial Fan As described in the previous section, the picture drawn in 1785 and survey map drawn in 1894 were used with a shallow water flow model to numerically estimate the flood control function of the levee system on the Kurobe Alluvial Fan at the two time points. This section discusses the overall process of levee development and considers the flood control strategies of that era using the above results and the literature [12], summarizing information written in old documents. In the past, the Kurobe River, after flowing out from the canyon, branched into many streams that changed their course freely to develop the conical terrain of the Kurobe Alluvial Fan. That river condition was called “Kurobe 48 shallows”. Prior to the 17th century, a group of predominant streams flowed down along the cliffs of the F-plane (see Figures1 and4) to the coast north of the alluvial fan. The dominant group of streams gradually moved west and reached the center of the alluvial fan in the 18th century (as shown in Figure6). The deviation of the present coastline from the concentric contour lines began in this age due to an imbalance between the sediment supply from river flows and coastal erosion by waves and drift currents from the north to the west. With the formation of a stable society in the Edo period after the 17th century, short embankments were installed discretely to protect individual villages from flooding of the Kurobe River. However, due to the frequent displacement of stream paths on the alluvial fan, the short discrete embankments are thought to have lost their functionality in a short period of time. It is probable, therefore, that local engineers tried to unite the flow of the Kurobe River by blocking its stream branches with relatively long levees in upstream and mid-stream areas. The pictorial map in Figure3a was probably drawn at an early stage of levee construction under that strategy, in which a relatively long levee to block the divergent streams and short discrete embankments to protect the villages co-existed. The levee construction started from the right bank, probably because the engineers were afraid that the Kurobe River would return to the old river courses, around which agricultural fields and villages, as well as the main highway, had already developed. Embankment construction began on the right bank side. On the left bank (south side) of the group of flows, in contrast, a relatively wide and strong flow existed, as can be seen in Figures3a and4, but it was not blocked with a long levee during the early efforts, probably due to the limits of civil engineering technology at that time. The date of completion and the order of construction of the 19th-C levees are not clear, but considering that construction was not possible during the heavy snowfall season in winter and the flood season in summer, the large extension from the 18th-C levees probably took a considerable amount of time. Flooding possibly occurred many times during that period, and as a result, the engineers were able to re-evaluate their work frequently, observing the effects of the partially completed embankment on flood control. Through their actual experience, they possibly thought of how to use the old river channel next to the levees.

7. Conclusions The findings in this study are summarized as follows: 1. In the early stage settlement on the Kurobe Alluvial Fan, short levees were built to protect individual groups of houses from the direct impacts of flood streams. With the progress of levee construction technology in the middle of the 18th century, the branch streams were blocked by construction of longer levees to unify the river flow for the full-scale development of the Kurobe Alluvial Fan. 2. The capacity of the united river channel corresponded to the seven-year return period flood. River flow over the channel capacity was diverged intentionally through the upstream levee openings to old river courses, which were a little bit lower than the surroundings and used as temporary floodway. A part of flood flow in the old river courses returned to the main river channel through the downstream levee openings at the river flow receding phase. Energies 2021, 14, 4406 16 of 17

The abovementioned levee design and construction procedure seems to have been reasonable even from the viewpoint of modern hydraulics, and here we must consider the reason why such excellent work was possible in Edo period when the technology was limited. As survey technology based on angle measurement was not available in the Edo period, accurate ground drawings were only possible for a relatively narrow range of manmade objects, and these consisted only of right angles and parallel lines. For a ground design over a wide area, such as river improvement works, civil engineers only had “pictorial maps”, which were much less accurate than the maps that we are accustomed to today. In addition, they were not equipped with the knowledge of modern hydraulics, not even the concept of “flow rate balance” [9]. Therefore, it can be said that the hydraulic engineers had almost no tools for “engineering design” in the modern sense. The reasoning behind the levee development process described in the previous section suggested that they did not have a blueprint for the 19th-C levees at the beginning. It seems impossible even at the present to foresee the hydraulic effects of the final form of the levee system one century ahead. In addition, it would have been very dangerous to carry out large-scale trial-and-error experiments on the rapid stream of the Kurobe River with insufficient embankment technology. Therefore, it is considered that the 19th-C levee system, which had excellent performance, was not the result of a blueprint prepared in advance nor simple trial and error, but might have involved an evolutionary development process, a so-called “designoid method [26]”, which is the systematic accumulation of small, lucky successes. An increase in intense rain storm events is anticipated due to global climate change. How to control large floods that exceed a river’s channel capacity is now under discussion in Japan, and one possible measure is premeditated river overflow to a running water type retarding basin [27]. Similar to the temporary floodway of the Kurobe River, this facility flattens the flood hydrograph, making use of the difference in flow velocity between the river channel and the floodplain. The point is how to control the inundation flow safely based on the condition of micro-topography, land cover, and land use on the floodplain. However, because some flood damage will occur on the floodplain to some extent, facilities need to be built carefully by monitoring incremental installation results. Although the flood control facilities of today are always built based on blueprints and budgets prepared in advance, this method is unsuitable for developing the final forms of facilities for premeditated overflow. The authors think that a designoid process may be needed. Although the designoid process took a lot of time in the Edo period, because today’s engineers have a variety of numerical simulation techniques, a wealth of digital map information, advanced flood observation technology as well as high-speed computers, they will be able to carry out the process more quickly.

Author Contributions: Conceptualization, T.I.; methodology, T.I. and H.S.; numerical simulation, H.S.; validation, T.I. and H.S.; investigation, T.I. and H.S.; writing—original draft preparation, T.I.; writing—review and editing, T.I. Both authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest. Energies 2021, 14, 4406 17 of 17

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