Environmental Fluid Mechanics

, Volume 19, Issue 5, pp 1295–1307 | Cite as

Assessment of flood risk management in lowland Tokyo areas in the seventeenth century by numerical flow simulations

  • Tadaharu IshikawaEmail author
  • Ryosuke Akoh
Original Article


Numerical simulations using the shallow water model on an unstructured triangular mesh system were conducted to elucidate the hydraulic functions of the Nihon levee system, which was built in the seventeenth century to protect the city of Edo (present-day Tokyo) against flooding. Because numerical data related to the topography and hydrology of that era do not exist, simulation conditions were inferred from records from the beginning of twentieth century and recent GIS elevation data and flood records. In the simulation results, floodwaters spread over the floodplain surrounded by the levee system, and the inundation areas expanded gradually through a canal to rice paddies in the adjacent river basin. Furthermore, the rise in the water level induced by the levee system produced a steeper water surface slope in the downstream channel, causing a high-rate discharge to Tokyo Bay, where the water level was practically constant. These results suggest that the river engineering of Japan in the seventeenth century was based on a levee design technique with the aim not of restraining floodwaters with levees but of generating water head differences to divert flood flow from urban areas.


Historic flood control strategy Levee system design Early modern period Shallow water model 

1 Introduction

With the current level of global climate change, the frequency of large rains producing runoff exceeding the capacity of the conventional flood control measures has become a concern in Japan. However, increasing the capacity of river channels is often not practical because of budgetary restrictions as well as inconsistencies with levees that have already been completed under the current standard. Therefore, the possibility of constructing a flood control system as a countermeasure against extraordinary floods, in which inundation is admitted to some degree and flood damage is mitigated by appropriately controlling the flow on floodplains, is now under investigation [1].

In the early modern period of Japan when river flooding was more frequent because large continuous embankments had not been constructed, a variety of levee arrangements were designed and constructed on floodplains to disperse the impact of river overflow in consideration of topographic, hydrological, and land use conditions [2]. Although the civil engineers of the day lacked modern knowledge of hydraulics, some of their works were still in use until quite recently. The reevaluation of those flood control facilities from the viewpoint of modern hydraulics may provide inspiration for modern-day measures to mitigate damage from extraordinary floods.

Recently, the hydraulic function of some historical levee systems and the flood control strategies employed in the early modern period have been investigated by estimating the topographic and hydrological conditions from various types of available data and utilizing existing numerical flow simulation models. Nemoto et al. [3] have studied a levee system constructed in the sixteenth century along a river channel called the Midai River, which flows on a steep alluvial fan, using a two-dimensional (2D) shallow water model with a rectangular grid system and concluded that the system provided good stabilization for the steep river channel on one side of the alluvial fan. Ishikawa et al. [4] have studied the flow capacity of a series of earth and masonry dikes located at the head of a seventeenth-century floodway named the Hyakken River by applying the 2D shallow water model with unstructured triangular grid system and discussed the roles of the dikes at each stage of flood. Ishikawa et al. [5] have extended this model to simulate the inundation flow from the Hyakken River and estimated the increase in the flood discharge safety level in a nearby castle city. Senoo and Ishikawa [6] applied the same numerical model to investigate the function of a series of discontinuous levees located along a river channel named the Kurobe River in the early nineteenth century. They concluded that the levee openings in the upper river reach were intended to diverge part of the river flow to old river channels and the openings in the lower river reach were intended to return the inundated water to the river channel after the flood had receded.

The variety of flood control facilities described above depended on the site conditions, including the topographic, hydrologic, and land use conditions. Therefore, the most difficult point in this type of research is how to determine the conditions for numerical simulations, which are typically not readily available, and researchers must make considerable efforts to obtain the information required for the calculation conditions in addition to preparing an appropriate numerical simulation model. In addition, the research target of such studies is not simply to obtain the calculation results but also to understand the considerations made by civil engineers of the day in the design of each facility under the conditions of each site, which are not well-documented in literature from the early modern period. Therefore, further hydraulic studies of individual facilities are necessary to understand the flood control strategies used in the early modern age.

The present study discusses the hydraulic function of a set of levees, designated herein as the Nihon levee system, which were built in 1624 on the alluvial lowland along the lower Arakawa River, also called the Sumida River, to protect urban areas of the city of Edo (present-day Tokyo) from flooding. The levee system survived until 1927, when the Arakawa River Floodway was constructed to discharge flood waters directly into Tokyo Bay. Edo became the administrative capital of Japan in 1603, when the Tokugawa Shogunate was established, although the Imperial Family continued to reside in Kyoto. Consequently, the period of rule by the Tokugawa Shogunate (1603–1868) is often called the Edo Era. The political center of Edo, including the castle and the residential area used by the ruling classes, was built on the diluvial plateau close to Edo Bay. However, along with growth in commerce and industry in the seventeenth century, the business area run by townspeople expanded rapidly into the eastern alluvial lowland, through which the Sumida River flowed. The Nihon levee system was built just upstream of the business area.

Existing studies on the civil engineering history of Japan have relied on the assumption that the levee system functioned to store flood water in a detention basin upstream of Edo [7, 8] without providing any quantitative analysis to support this assumption. However, levees in the Edo Era were usually less than three meters in height because of technological limitations, and the Arakawa River is one of the biggest rivers in Japan, having a catchment area of more than 1000 km2. This study originated from simply questioning this assumption about the motivations of the civil engineers of the day; damming up a large volume of flood water from the Arakawa River immediately upstream of the capital city with an earth levee of only three meters in height would have been very dangerous.

In this study, a series of numerical flow simulations were conducted to elucidate the hydraulic function of the Nihon levee system using the shallow water model with an unstructured triangular mesh system, in which levee overtopping and inundation front motion were incorporated [9]. Because of the absence of numerical data for ascertaining the Edo Era conditions for the simulation, geographic information system (GIS) elevation data [10] and recent flood records were used as the basis for topographic and hydrological assumptions in the numerical simulations, and these data were modified considering the records available at the beginning of the twentieth century, when the conditions of the city and the land around Tokyo had not yet changed substantially from those of the Edo Era.

Basic flood flow characteristics and the correlation between the inundation areas with the land use layout were discussed based on the simulation results. The water volume balance during a flood in the calculation area was analyzed to estimate the ratio of water flow components and water storage in the retention basin surrounded by the Nihon levee system. Finally, on the basis of these results, the flood risk management strategy for the Edo district in the seventeenth century was discussed.

2 Study site

Figure 1a shows part of a map of Edo drawn in 1859, near the end of the Edo Era. Three levees indicated by green lines were arranged in a funnel shape to dam floodwater in the upstream basin. The region south of the Nihon levee was part of Edo; the gray and red sections were residential areas and temples or shrines, respectively. The wide orange areas in the north side were paddy fields. The Ayase River was connected to a bending section of the Sumida River with a short canal to facilitate water transportation across the river basins.
Fig. 1

Study site. Levee arrangement along the Sumida River

Figure 1b shows the first accurate map of the Tokyo area based on modern surveying but without elevation data, published in 1886 when the city and land around Tokyo had not yet changed substantially since the Edo Era. The area depicted in Fig. 1a is indicated by a red rectangle in this map. Embankments are shown as green lines with their respective names, and the thick brown line shows the edge of the diluvial plateau. The names of the major waterways are written in blue. According to a report by the river administration office [8], there was a nameless levee extending eastward from the downstream end of Sumida levee, and it is simply referred to as the “low levee” in this report. Edo Castle was located in the southern part of the diluvial plateau. The dark colored areas on the banks of the Sumida River represent downtown Edo. This was the economic center of Japan in the Edo Era, as the Sumida River was the main artery of water transportation for the capital city connecting the riverside marketplaces to Tokyo Bay and the eastern inland areas through many canals and rivers. The names of some places in downtown Edo are written in black.

Figure 2 shows the difference between the elevation data in the first modern map published at the beginning of the twentieth century and the GIS elevation map (2015). The Nihon levee connected slightly elevated areas at the foot of the diluvial plateau in the west and a river bank in the east, as shown in the GIS map. The levee was 3 m in height with respect to the ground elevation at its base. The greatest difference between the two maps is the Arakawa River Floodway, completed in 1924, which discharges flood water from the upper Arakawa River directly to Tokyo Bay through the watershed of the old Naka River. Other topographic changes included the deformation of the coastline because of land reclamation, the creation of embankments for railways and highways, and the removal of old levees.
Fig. 2

Change in land conditions. The colored dots in (a) show the elevation difference in comparison with (b)

In addition, remarkable ground subsidence took place in the area between the Sumida River and the Naka River because of a large amount of groundwater pumping for industrial water use in the twentieth century. The colored dots in Fig. 2a show the ground subsidence during the twentieth century obtained from the differences between the elevation data shown on the two maps.

3 Methods

3.1 Numerical model

Two-dimensional shallow water models have been increasingly used in the numerical simulation of inundation flow, and they are obtained by integrating the three-dimensional (3D) equations of motion from the ground to the water surface under the assumptions of incompressible fluid and hydrostatic pressure field as follows:
$$ \frac{\partial h}{\partial t} + \frac{{\partial \left( {Uh} \right)}}{\partial x} + \frac{{\partial \left( {Vh} \right)}}{\partial y} = 0 $$
$$ \begin{aligned} & \frac{{\partial \left( {Uh} \right)}}{\partial t} + \frac{{\partial \left( {UUh} \right)}}{\partial x} + \frac{{\partial \left( {UVh} \right)}}{\partial y} \\ & \quad = - \,gh\frac{\partial H}{\partial x} + \frac{{\partial \left( {h\tau_{UU} } \right)}}{\partial x} + \frac{{\partial \left( {h\tau_{UV} } \right)}}{\partial y} - \frac{{\tau_{0} }}{\rho }\frac{U}{{\sqrt {U^{2} + V^{2} } }} \\ \end{aligned} $$
$$ \begin{aligned} & \frac{{\partial \left( {Vh} \right)}}{\partial t} + \frac{{\partial \left( {UVh} \right)}}{\partial x} + \frac{{\partial \left( {VVh} \right)}}{\partial y} \\ & \quad = - \,gh\frac{\partial H}{\partial y} + \frac{{\partial \left( {h\tau_{UV} } \right)}}{\partial x} + \frac{{\partial \left( {h\tau_{VV} } \right)}}{\partial y} - \frac{{\tau_{0} }}{\rho }\frac{V}{{\sqrt {U^{2} + V^{2} } }} \\ \end{aligned} , $$
where U and V respectively denote the x- and y-components of the velocity, h is the water depth, H (= h + ground level) is the water surface level, ρ is the water density, and g is the acceleration due to gravity. Additionally, τ0 denotes the bed friction force, and τUU, τUV, and τVV are the horizontal shear stresses, which are expressed respectively following Wu [11] in this report:
$$ \begin{aligned} \tau_{0} & = \rho U_{f}^{2} = n^{2} \frac{{\rho g\left( {U^{2} + V^{2} } \right)}}{{h^{1/3} }}, \\ \tau_{UU} & = 2\varepsilon \frac{\partial U}{\partial x} - \frac{2}{3}k,\quad \tau_{UV} = \varepsilon \frac{\partial U}{\partial y} + \varepsilon \frac{\partial V}{\partial x},\quad \tau_{VV} = 2\varepsilon \frac{\partial V}{\partial y} - \frac{2}{3}k. \\ \end{aligned} $$
Here Uf is the friction velocity, n is Manning’s roughness coefficient, ε is the vertically average eddy viscosity, and k is the turbulent kinetic energy. The eddy viscosity and turbulent kinetic energy are respectively expressed as
$$ \varepsilon = \frac{1}{6}\kappa U_{f} h,\quad k = 2.07U_{f}^{2} , $$
where κ (= 0.41) is the von Karman constant. The expression for k in Eq. (5) was proposed by Nezu and Nakagawa [12].

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 [13]. Triangular meshes were generated from the lines of the river banks and levees using ANSYS ICED CFD software [14].

The flow rate over the levees was calculated using the following formula proposed by Honma [15]:
$$ q = \left\{ {\begin{array}{*{20}l} {0.35h_{1} \sqrt {2gh_{1} } } \hfill & {if\quad h_{2} /h_{1} \le 2/3} \hfill \\ {0.91h_{2} \sqrt {2g\left( {h_{1} - h_{2} } \right)} } \hfill & {otherwise} \hfill \\ \end{array} ,} \right. $$
where q is the flow rate per unit width over the levee, and h1 and h2 represent the water surface heights upstream and downstream of the overflow from the levee crown, respectively.

To model the motion of the inundation front, the Eulerian method proposed by Brufau et al. [16] 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.

3.2 Simulation conditions

3.2.1 Topography

The numerical flow simulation covered the lowlands between the diluvial plateau in the west and the Naka River in the east along the channel of the Sumida River for up to 24 km from the river mouth. The GIS elevation map (2015) was modified to simulate the flood flow around Edo as follows: the embankments of railways and highways and the Arakawa River Floodway were removed by ground level interpolation across them. The effect of ground subsidence caused by groundwater pumping was eliminated by adding a contour map of the amount of sinking obtained from the interpolation of the data presented in Fig. 2a.

The longitudinal profiles of the crown height of the Nihon, Kumagaya, and Sumida levees were inferred based on the values recorded on the map published in 1909 and the values given in the literature [8]. The heights of other levees were estimated by considering the surrounding topography. Because the channel course and width of Sumida River have changed little since the Edo Era, as shown in Figs. 1b and 2b, the river channel topography was derived from cross-sectional survey data obtained in 2015 by the Tokyo Metropolitan Government. Rectangular cross sections were assumed for the old Naka River and the Ayase River because of the absence of surveying data.

3.2.2 Flood hydrograph

The flood flow capacity of the lower Arakawa River channel was 90,000 shaku3/s in the flood control plan issued in 1911 when the Arakawa River Floodway did not yet exist. The shaku is an old unit of length in Japan and equals approximately 30 cm; thus, this capacity corresponds to 2500 m3/s in SI units. This value is much smaller than both the present design of the flood discharge (6200 m3/s) and the basic high water discharge (11,900 m3/s). Because no continuous levee existed along the upper and middle reaches of the Arakawa River, the flood hydrograph was flattened by inundation before reaching Edo at the most downstream river reach, which explains the reason for this smaller capacity.

All flood waters from the Arakawa River were discharged through the floodway. They stopped flowing into the Sumida River after floodway construction. Therefore, the present channel of the Sumida River is almost identical to that in 1886 (see Figs. 1b, 2b). The present official channel capacity is 2100 m3/s, including that provided by a levee freeboard. These facts suggest that the flood discharge volume in the Edo Era was approximately 2500 m3/s.

The blue line in Fig. 3 is the flood hydrograph observed in the lower Arakawa River in 2007, the peak discharge of which was 5285 m3/s. The red hydrograph used in the numerical simulations (Case 1) was obtained by flattening the observed hydrograph so that the peak discharge became 2500 m3/s while maintaining the total water volume. The green hydrograph (Case 2) was obtained by doubling the flood duration from Case 1. The sky-blue hydrograph (Case 3) has the same total water volume as Case 1, but the peak discharge is 4000 m3/s. The basic characteristics of the flood flow were examined in Case 1, which was regarded as representing the standard conditions used for this study. The effects of different flood durations and peak discharges were examined respectively in Cases 2 and 3. The vertical red dotted lines in Fig. 4 show the inspection times at which the flow conditions were examined for the three phases of flooding in each calculation case.
Fig. 3

Flood hydrographs used in the numerical simulation

Fig. 4

Times for inspection of the calculation results

4 Results and discussion

4.1 Case 1 (standard conditions)

The inundation depths at the three times presented in Fig. 4 are depicted in Fig. 5, where the waterways and embankments are indicated with red and black lines, respectively. The names of the waterways and embankments are given in Fig. 5a, and a rough classification of the land use is indicated in yellow. Overflow from the Arakawa River channel originated from the upstream reach in the initial phase of the flood, but inundation expansion to the downstream was blocked by the Nihon levee at the flood peak phase. Instead, the inundation area expanded to the paddy fields to the north of the Kumagaya levee and the east of the Sumida levee through the opening to the Ayase River after the retention basin was almost filled with flood water. The inundation area became much wider during the flood receding phase. The flood waters to the east were eventually discharged into the Naka River. The urban areas on both sides of the Sumida River were protected from flooding by the Nihon levee and the low levee, which extended from the east bank of the Sumida River to the bank of the Naka River.
Fig. 5

Instantaneous distribution of the inundation depth (Case 1)

Figure 6 shows the discharge components obtained from the water balance analysis. The total outflow (red line) is the sum of the outflows to the lower Sumida River and the Ayase River, the latter of which carries water to rural areas in the adjacent Naka River Basin. The storage rate (sky-blue line) represents the variation in the water volume in the retention basin, which was positive in the rising phase and negative in the receding phase. This result demonstrates that the outflow, especially to the lower Sumida River, was the dominant component of the water balance.
Fig. 6

Results of water balance analysis (Case 1)

The reason for the large outflow to the lower Sumida River can be understood from Fig. 7, where the longitudinal water surface profile at the flood peak (red line) is shown along with that before the flood (blue line) and the levee crown heights. KP denotes the distance from the present-day river mouth. Actually, the river mouth in the Edo Era was located at 2 KP, and the water surface level was thus kept constant at this location in the simulations. A steep water surface slope occurred in the lower Sumida River because of the water surface rise induced by the Nihon levee. Consequently, the river discharge became far larger than that under normal conditions, and the large discharge slowed the rising of the water surface on the upstream side of the Nihon levee.
Fig. 7

Water surface profiles with levee heights (Case 1)

The function is reminiscent of the gateless outlet of a flood mitigation dam, which increases the outflow as the water level rises [17]. However, the volume of water storage achievable by the Nihon levee system was dependent mainly on the horizontal expansion of the water surface, whereas water storage usually depends on the vertical displacement of the water surface in a flood mitigation dam.

4.2 Case 2 (long flood duration)

The inundation depth distributions obtained from the Case 2 calculation are displayed in Fig. 8 in the same manner as in Fig. 5. The total flood water volume was doubled from that in Case 1 to simulate an inflow with a long duration. Therefore, the inundation depth was slightly larger than that in Fig. 5. However, the depth increase was not doubled for two reasons: the expansion rate of the inundation area was higher, and the outflow to the lower Sumida River increased as the water surface in the retention basin rose.
Fig. 8

Instantaneous distribution of the inundation depth (Case 2)

The results clearly demonstrate that the function of the Nihon levee system was not only to store flood water in the upstream lowlands, as assumed by previous studies on the civil engineering history of Japan [7, 8], but also to increase the discharge rate in the lower Sumida River to Tokyo Bay and to divert flood flow to paddy fields in neighboring rural areas. The simulation results indicate that this system was effective even for floods of a far longer duration if a balance was established between the inflow and the outflow, whereas a modern dam reservoir loses its effectiveness when the total inflow volume during a long-duration flood exceeds the water storage capacity.

4.3 Case 3 (large flood peak)

Figure 9 shows the inundation depth distributions at the three times indicated in Fig. 4 for Case 3, in which the flood duration was shorter but the peak inflow rate was higher than in Case 1. The total flood water volume was the same as that in Case 1 and half that of Case 2. The retention basin upstream from the Nihon levee was already nearly full during the rising phase. The flooding reached the downtown area south of the Nihon levee at the flood peak. The flood water did not overtop the Nihon levee but overflowed at the lower part of the Nikko Highway running near the slope of the diluvial plateau.
Fig. 9

Instantaneous distribution of the inundation depth (Case 3)

These results demonstrate that the Nihon levee system would have failed if the flood hydrograph was sharp enough that the inundation area expansion to the adjacent rural area could not respond with sufficient speed. Therefore, it can be inferred that the Nihon levee system was valid under the hydrological conditions prevailing during the Edo Era, when the flood hydrograph was flattened by wide inundation in upstream river reaches where continuous levees had not been prepared.

5 Conclusions

In this study, numerical flow simulations were conducted to investigate the hydraulic function of the Nihon levee system, which has existed for about 300 years from the beginning of the seventeenth century to protect the urban area of Edo (present-day Tokyo) against flooding. The exact topographic and hydrological conditions under which the system was established are not available from historical records. The results and discussion therefore include some uncertainty, but the following conclusions were obtained, as illustrated in Fig. 10.
Fig. 10

Illustration of the function of the Nihon levee system

The retention basin surrounded by the levee system functioned similarly to a gateless flood mitigation dam, allowing flood waters to discharge through two outlets with the flow rate depending on the water level in the basin. One outlet was the channel of the lower Sumida River to Tokyo Bay. The channel length was only 6 km. Therefore, the water surface slope became much steeper because of the upstream surface rise of two meters, which caused a highly efficient discharge of flood water to the sea without a large increase in the water level in the channel through the urban areas.

The other outlet was the opening to the Ayase River, which was used for water transportation under normal flow conditions, through which flood waters were dispersed to paddy fields in adjacent rural areas. Expansion of the inundation area enlarged the flood retention capacity of the levee system without greatly increasing the water surface level in the retention basin, thereby preventing the flood water from overtopping the levees. Transfer of flooding from urban areas to paddy fields was considered because the economic loss attributable to inundation was far less for paddy fields than for urban areas.

Because of the time lag between the inflow rate increase and the water surface rise in the retention basin, the discharge rate could not increase sufficiently quickly to match a sharp increase in the inflow. Perhaps for that reason, the levee system might have failed when the flood hydrograph was very sharp. Therefore, the Nihon levee system design was based on the hydrological conditions of the Edo Era, when the flood hydrograph was flattened by the inundation of the upper reaches of the Arakawa River.

Reviewing the development of Edo City after the seventeenth century reveals that the flood risk management strategies for diverting flood waters to the paddy fields in the Naka River watershed showed considerable foresight. The city of Edo expanded steadily to the lowlands along the Sumida River and grew to become the largest city in the world, eventually having a population of one million in the mid-eighteenth century. The city became the economic center of Japan, as well as its political center, as commerce and industry became more important to the national economy than agriculture. Because of the economic development of Edo, the official capital of Japan (along with the Emperor’s residence) was relocated from Kyoto to Tokyo after the Tokugawa Shogunate was abolished.

Edo Era civil engineers lacked modern knowledge of hydraulics and even the idea of river flow rates, and the height of embankments was restricted by the availability of construction equipment and materials. However, they were able to conduct level surveying with high accuracy to construct irrigation channel networks in the sixteenth century. Therefore, it is considered that the river engineering and levee construction in the Edo Era were not intended to hold back flood waters but to generate a water head difference to divert the flood waters to areas where less damage would occur.

According to present flood risk management policy in Japan, a fixed level of flood risk is considered acceptable for each river basin based on occurrence probabilities, although the land conditions change along the channel. However, recent changes in the global climate might increase the frequency of flood water volumes that exceed the channel capacity determined for river improvement works. Therefore, to reduce the total flood damage from extraordinary floods, inundation flow should be controlled by considering the distribution of land cover and properties. Reevaluation of past civil engineering works, which effectively dealt with flooding without requiring large-scale construction, can contribute to the development of new approaches to the risk management of extreme floods in the near future.



We would like to thank Emeritus Professor Hideo Kikkawa of the Tokyo Institute of Technology for his valuable suggestions pertaining to this study. We would also like to thank the Arakawa-Karyu River Office and the Tokyo Metropolitan Government Bureau of Construction for providing field survey data for this study. This study was supported by a Grant from the River Foundation (No. 27-1212-006).


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Professor EmeritusTokyo Institute of TechnologyTokyoJapan
  2. 2.Graduate School of Environmental and Life ScienceOkayama UniversityOkayamaJapan

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