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where h is the substantial water depth on the slope, q the discharge per
unit width on the slope, b the slope width, θ the slope gradient, r the
rainfall intensity, k the hydraulic conductivity, γ theeffectiveporosity, n the
roughness coecient, D the superficial A -layer depth, and m is the constant
value of 5/3. The obtained runoff discharge at the downstream end of each
slope is given to the flood-prone area as the boundary condition.
In the flood-prone area, two-dimensional (2D) inundation flow analysis,
based on the “unstructured mesh model”, 3 is conducted.
∂h
∂t + ∂M
+ ∂N
∂y
= r,
∂x
gn 2 M u 2 + v 2
h 4 / 3
∂M
∂t
+ ( uM )
∂x
+ ( vM )
∂y
gh ∂H
=
∂x
,
gn 2 N u 2 + v 2
h 4 / 3
∂N
∂t
+ ( uN )
∂x
+ ( vN )
∂y
gh ∂H
=
∂y
,
where h is water depth, M , N are the x -and y -directional discharge per unit
width, respectively, u , v are x -and y -directional flow velocity, respectively,
and H is water stage (= h + z b , z b is the ground elevation). The rainwater
given to the flood-prone area is drained through pump stations and its
drained water is given to the river channel as the lateral inflow.
3.2. Application to the Isahaya low-lying area
The computational reach of the Hommyo River is 5.2 km (from Urayama
to Shiranui), and that of the Hanzou River is 3.1 km (from Umetsu to the
confluence with the Hommyo River). The spatial interval of discretization
x is 200 m, and the value of roughness coecient is 0.030 for the Hommyo
River and 0.045 for the Hanzou River.
The steep slopes used in the hillside area are adjacent areas to the flood-
prone area as shown in Fig. 4. The values of the parameters used here are:
k is 0.002 (m/s), γ is 0.15, n is 0.3 (m 1 / 3 s) and D is 0.5 (m).
The computational meshes used in the flood-prone area (shown in Fig. 4)
are divided into four categories: urban areas, channels, streets, and culti-
vated areas. The values of roughness coecient of them are 0.067, 0.020,
0.043, and 0.025, respectively.
As the simulation conditions, the flow discharge at Urayama and
Umetsu, and the water level at Shiranui observed at the disaster of 1999
are given to the river channel. The temporal change of rainfall intensity
observed at the disaster of 1999 (see Fig. 2) is uniformly given to the whole
computational area. The computational time step ∆ t is set to be 0.05 s.
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