Hydraulic function of the kasumi levee systemon the Kurobe Alluvial Fan of the 19th century
Hiroshi SENOO1 and Tadaharu ISHIKAWA2
1TOKEN C. E. E. Consultants Co., Ltd., Tokyo, 174-0004, JapanTokyo Institute of Technology, Kanagawa, 226-8503, Japan

2Abstract. Kasumi levees are a type of discontinuous levee system thatwas used in early-modern times of Japan, but few records remain of thehydraulic design of the levee construction. Results of numerical flow
simulation are presented for the hydraulic functioning of the Kasumi leveesystem along the Kurobe River that flows on a steep alluvial fan. Historical
records from the 19th century to the present were used to simulate the flow
through a levee system.. The computational results suggest that the floodcontrol strategy was such that old river paths were utilized for temporary
floodways and a portion of this diverted flow was returned to the mainriver channel through funnel-shaped levee openings located along themiddle reach to prevent inundation of the alluvial fan.

1. Introduction
A variety of discontinuous levee systems, that are now typically called “kasumi (meaninghaze) levees”, were built from the 17 to mid-19th centuries to mitigate the impact of riverflooding. The most common perception of the kasumi levee system is a series of funnelshaped levees opening upstream as shown in Fig. 1: Storm water, exceeding the river
channel capacity, was spread backwards, reducing the river discharge, returning to thechannel when the flood receded. According to Okuma [1], the design of these levees varied
depending on the geographical and hydrological conditions with the major hydraulicfunction depending on the ground slope.
Non-flood flow

Flood detention

Fig. 1. Typical kasumi levee arrangement

1

Corresponding author: senoo-h@tokencon.co.jp

DrainageIn this study, hydraulic role of the discontinuous levee system constructed on theKurobe Alluvial Fan in the 19th century was studied by numerical flood simulation using
shallow flow model on unstructured triangular grids [2], and the strategy of flood risk
management on the alluvial fan in those days was discussed.
Due to the absence of historical topographical and hydrological data, the simulation
parameters were determined from a combination of some 19th century flood damage records,a levee map drawn at the end of 19th century, flood hydrographs observed in the middle of
20th century, modern river channel measurements and GIS elevation floodplain data.

2. Study Site
The Kurobe River flows down 85 km with an elevation drop of 3,000m, from the central
mountains of Japan’s Main Island to the Japan Sea. The large volume of sediment carriedby the canyon river formed an alluvial fan with a radius of 13 km, a top angle of 60°, andan average slope of 1/100 at the downstream river reach (see Fig. 2).
Fig. 2b shows a contour map of the alluvial fan in which the light blue bands represent
the old river courses before the 19th century. The contour lines are almost concentric except
near the coast. The zone of transition from erosion to sedimentation is located at around the50 m above sea level [3] and geological evidence suggest that the river channel moved
during the recent geomorphic process.
In the early 19th century, the branching streams were aligned into a single channel byconstructing the levee system shown by the black lines in the Fig. 2b. The "K" suffix valuesindicate the distance from the river mouth in kilometers. This realignment of the channel
caused the northeast coast to erode due to the absence of sediment supply and river delta toprogressively move further out to the sea [4].

Hokurikudo(Highway in the19th century)

old rivercourses

NW

ES

0K
1K
2K
3K

4K

5K

6K
7K

10m

20m 30m

40m

8K
50m

9K
60m

70m

80m
90m 100m

10K
110m

11K
12K
110m

Fig. 2. Topography of Kurobe Alluvial Fan

Fig. 3 shows the longitudinal profiles of the river channel bed and the ground level ofboth banks measured from the present high-water level. The channel bed is lower than thenearby ground in the upstream reach, while higher in the downstream reach as a result ofgeomorphic dissection, which was magnified in the narrowly fixed river channel. By
comparing Fig. 2 and Fig. 3, we can see an overall correlation between the leveearrangements and the ground level differences as follows: Levees were doubled or tripled in
the downstream reach as typical kasumi levee arrangement where the channel bed is higher
than the nearby ground (KP < 5 at the left bank and KP < 7 at the right bank). On the other
hand, the levees had wide openings in the upstream reach where the channel bed was nothigher than the nearby ground.

横断平均河床高

堤内地盤高(左岸)

堤内地盤高(右岸)

Elevation relative tothe high water (m)2.0high water level

0.0

channel bed

-2.0
-4.0
(right bank)(left bank) ground level

-6.0
0.0

2.0

4.0

6.0

8.0

河口からの距離[km]Distance fromriver mouth (KP)

10.0

12.0

Fig. 3. Longitudinal bed profiles relative to the high water level

Fig. 4 shows the probability of annual maximum discharge for the last 56 years. The
largest recorded discharge was 6,700 m3/s in 1969 that corresponds to a return period ofabout 100 years. According to a historical record, villages along the river were affected byriver overflow ten times during the 68 years from 1828 to 1895. The flood frequency
corresponds to a 2,700 m3/s river discharge as indicated by green in the figure.
99.5
9998

Largest recorded
6,700 m3/s (1969)

Probability smaller (%)

95
90

6/7=86 %

80
70
60
50
4030
20

Log-normal
distribution

1051

2,700 m3/s
1001000

10000

Annual maximum discharge (m3/s)

Fig. 4. Probability plot of annual maximum discharge

3. Methodology
3.1. Numerical model
A set of shallow water equations was adopted for the numerical simulation model.
(1)
(2)

(3)

where (U, V) are the velocity components in (x, y) coordinates, h is the water depth, H is thewater surface level (= h + ground level), ρ is the water density, and g is the gravitationalacceleration. τ0 is the bed friction force, and τUU, τUV and τVV are the horizontal shear stresses,
which are expressed by the following equations:(4)
where Uf is the friction velocity, n is Manning’s roughness coefficient, ε is the verticallyaveraged eddy viscosity, k is the turbulent kinetic energy, and κ is the Karman constant.
The differential equations were converted to difference equations by the finite volume
method on the unstructured triangular mesh system. The equation forms and solving
process are described in Akoh et al. [2].
The flow rate over the banks was calculated by the formula presented by Honma [5]:(5)where q is the flow rate over the unit length, and h1 and h2 are the water depths on theupstream and downstream sides, respectively.
3.2. Calculation condition
Because of the absence of data for the alluvial fan topography in the 19th century, the GIS
elevation data published in 2015 (grid size; 5 m) were used for the numerical simulations.
Local elevation changes due to the construction of roads and railways were removed byinterpolation from surrounding elevation values. The Hokuriku-do (a 19th century highway)
indicated by green lines in Fig. 2 was assumed as a low embankment 60 cm higher than thesurrounding ground.
Due to the high sediment load from the upstream canyons, the river channel bed iscovered by a pattern of moving sand bars that continually propagate downstream (see thephotograph in Fig. 2). The standard deviation from the transversely averaged bed elevation
undulations is approximately 1 m. In addition, the bed bathymetry is strongly affected,
since 1960, by the construction of a high dam in the upstream canyon as well as bed
sediment excavation for construction aggregates. Therefore, the longitudinal profile of thetransversely averaged bed topography, measured in 1963, was adopted for the simulations
Fig. 5 shows the design flood hydrograph, adopted in 1969 for the present river
improvement works. Hydrographs used in the numerical simulation were simple
magnifications of that shown in Fig. 5, uniformly scaled to reflect a peak discharge listed at
the left side of the figure. The peak flow in Case 1 was just over the channel capacity(indicated by green in Fig. 4), and the other two cases were extraordinary floods that would
cause significant damage along the river.
Relative discharge (Q/Qp)

1.2

The largest recorded flood(in 1969; Qp= 6,700 m3/s)

1.0
0.8

Inspection ofinundation area

0.6

Channel capacity(2,700 m3/s)

0.4
0.2
0.0

02040

Elapse time (hour)Fig. 5. Design flood hydrograph (1969)60

Qp= 3,000 m3/s (Case-1)
4,000 m3/s (Case-2)
5,000 m3/s (Case-3)

4. Results and discussions
4.1. Results of numerical simulation
Fig. 6 shows the inundation depth at the flood peak and the receding phase for the case of
Qp = 3,000 m3/s. River water overflowed to the left-side floodplain through a levee openingaround 9 K and flowed down the old river channel along the backside of levees (see Fig. 2).
During the receding phase, a portion of the flood water returned to the river channel
through levee openings located from 3 K to 5 K.
(b) Receding phase(T=41 hours)(a) Flood peak
(T=39 hours)

1K

1K

2K
3K

4K

5K

6K

2K

Overflow

3K

4K

5K

7K

Return flow

6K
7K

8K

8K

9K

9K

10K

10K

11K

11K

Fig. 6. Water depth (Case-1), at flood peak (left) and during the receding phase (right)

Fig. 7 (a) show the velocity vectors in the area indicated with the red rectangle in Fig. 6(b). Fig. 7 (b) shows the hydrograph at the upstream boundary (blue), the rate of overflow
through the levee opening at 9 K (green), and the rate of returning flow through the levee
openings from 3 K to 5 K (red). The peak of returning flow had a time lag of two hours
from the flood peak, when the river discharge was already receding.
Velocity(m/s)

3,500

0.25

0.10(a)Returning flow field(Case-1:Receding phase)

Flow rate (m3/s)

0.50

3,000 m3/s

3,0001.00

River discharge

2,500(b)Time lag ofreturning flow
(Case-1)

2,000
1,500

2 hours

1,000500

overflow
253035Return flow
4045

Elapse time (hour)

50

Fig. 7. Returning flow during the receding phaseFig. 8 shows the course of flood flow estimated by Teramura [6] for the 1934 flood (Qp~ 3,000 m3/s). It shows the same tendency as the calculated flood flow: river water
overflowed to the left-side floodplain around 9 K, flowed along the levee backside, andpartially returned to the river channel through the openings near 5 K.
Flood flow route
Inundation areaFig. 8. Inundation record from 1934 (Teramura, [6])Fig. 9 (a) shows the inundation depth at the receding phase obtained for Qp = 5,000 m3/s
and Fig. 9 (b) shows the velocity vectors in the area indicated with red rectangles in Fig. 9(a). The flooding area was almost within the old river channel as for the case of Qp = 3,000
m3/s, although the inundation volume became larger with increasing river discharge. The
levee openings between the long doubled levees around 3 K did not drain the landsidewater, but the levees prevented overflow from the river channel to the flat lowland at theleft bank side.
(b)Returning flow field(Case-3:Receding phase)

Depth (m)(a)Inundation depth(Case-3:Receding phase)

Velocity(m/s)
1.00

1K
2K
3K

4K

5K

0.50
6K
7K

0.25

8K
9K
10K

11K

0.10

3

Fig. 9. Flow field during receding phase (Case-3: Qp = 5,000 m /s)

4.2. Hydraulic function of right bank levees
In the above-mentioned calculation, river overflow happened only to the left-sidefloodplain. However, this does not prove that the right-side floodplain was always safe
from river overflow. As mentioned earlier, the channel bed is covered by multiple bars
having large amplitude, which implies that levee overtopping could have occurred due to achannel bed rise near the right bank. The long, doubled levees below 7 KP might be themost effective measure against river overflow to the old river channel.
An experiment was performed to examine the function of the right bank leveearrangement by inducing a river overflow to the right-side floodplain. The river channel
bed was raised by 1 m to induce overflows on both sides of the channel. Three back leveesof the doubled levee sections (red lines in Fig. 10) were removed to examine the flow fieldchanges over the floodplain from the original levee arrangement.
0K
1K
2K
3K

4K

5K

6K
7K
8K
9K
10K

Fig. 10. Experimental conditions for long back levee

11K
12K

Fig. 11 shows the water depth and velocity field calculated for the original leveearrangement (Case-A) during the flood receding phase, and Fig. 12 shows those for themodified levee arrangement (Case-B). River water overtopped the right bank levees around
8 K, and flowed down the old river channel. In Case-A for the original levee alignment, thelong back levee located around 6K interrupted the flood flow and returned a portion of theflow to the main channel. As a result, the two villages located at a slightly higher elevation
area were not inundated, while the villages were inundated by a strong current in Case-B.

Depth (m)Itaya Village
Sasahara Village

Fig. 11. Flooding due to channel bed rise of 1 m with original levee lengths
Depth (m)Fig. 12. Flooding due to channel bed rise of 1 m with three levees removed.

4.3. Strategy of flood risk management in the early 19th century
The numerical results discussed above can be used to formulate the flood risk management
strategy on the Kurobe Alluvial Fan in the early 19th century as follows (see Fig. 13): Civil
engineers utilized old river channels as temporary floodways and located levee openings toinduce flow divergence as indicated with green arrows in the figure because the leveeheight of 3 m could not confine the large volume of runoff water in the river channel. Whenthe overflow rate exceeded the capacity of the old river channels, long back levees guided
the excess water to return to the main channel as indicated with red arrows in Fig. 13. In
addition, because the flood duration of Kurobe River was short (see Fig. 5), the floodwaterin the old river channel could be drained to the main channel at the flood receding phasethrough the funnel-shaped levee openings located in the middle reach of the river.

0K
1K
2K
3K

4K

5K

6K
7K10m20m 30m

40m

8K
50m

9K
60m

70m

Fig. 13. Flood control strategy for the early 19th century

80m
90m 100m

10K
110m

11K
12K
110m

5. Conclusions
The exact topographical and hydrological conditions when the system was established were
not available for numerical simulation, and the results and discussions thus contain someuncertainties, but the following conclusions may be obtained:(1) During periods of floods larger the channel capacity, excess water overflowed to theleft side floodplain. The floodwater flowed down the old river channel without
spreading widely and a portion of the flow returned to the main river channel throughfunnel-shaped levee openings located around 5K. This agrees with the flood record in1934 presented by Teramura [6].
(2) Because the computations with the transversely averaged river bed elevation did notindicate a river overflow to the right-side floodplain, an experiment was conductedwith a 1 m river bed rise to examine the hydraulic function of the kasumi leveealignment on the right bank. The result shows that the floodwater flowed into theright-side old river channel from 8K, and that a portion of the flood flow returned tothe main river channel guided by the long back levees and funnel-shaped openings
around 6K, thereby protecting the downstream villages from inundation.
(3) The results suggest that the 19th century flood control strategy for the alluvial fan was
as follows. During large rain runoff, the old river channels were utilized as temporary
floodways by locating levee openings at the channel heads. In order to prevent
inundation from spreading on the alluvial fan, funnel-shaped levee openings werelocated to return a portion of the flood flow exceeding the old channel capacity to themain river channel.
Acknowledgement. Authors would like to thank Professor Jorg Imberger for helping to edit themanuscript.

References
1.
2.
3.
4.
5.
6.

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R. Akoh, T. Ishikawa, T. Kojima, M. Tomaru and S. Maeno, Nat. Hazards Earth Syst.
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S. Fujii, Earth Sci., 78, 11 -20 (1965) (in Japanese)
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