Environmental Engineering Reference
In-Depth Information
TABLE 18.1 Potential runoff coefficients of the WetSpa model for different land-use, soil type and slope.
Land-
Slope
Sand
Loamy
Sandy
Loam
Silt
Silt
Sandy clay
Clay
Silty clay
Sandy
Silty
Clay
use
(%)
sand
loam
loam
loam
loam
loam
clay
clay
Forest
< 0.5
0.03
0.07
0.10
0.13
0.17
0.20
0.23
0.27
0.30
0.33
0.37
0.40
0.5-5
0.07
0.11
0.14
0.17
0.21
0.24
0.27
0.31
0.34
0.37
0.41
0.44
5-10
0.13
0.17
0.20
0.23
0.27
0.30
0.33
0.37
0.40
0.43
0.47
0.50
> 10
0.25
0.29
0.32
0.35
0.39
0.42
0.45
0.49
0.52
0.55
0.59
0.62
Grass
< 0.5
0.13
0.17
0.20
0.23
0.27
0.30
0.33
0.37
0.40
0.43
0.47
0.50
0.5-5
0.17
0.21
0.24
0.27
0.31
0.34
0.37
0.41
0.44
0.47
0.51
0.54
5-10
0.23
0.27
0.30
0.33
0.37
0.40
0.43
0.47
0.50
0.53
0.57
0.60
> 10
0.35
0.39
0.42
0.45
0.49
0.52
0.55
0.59
0.62
0.65
0.69
0.72
Crop
< 0.5
0.23
0.27
0.30
0.33
0.37
0.40
0.43
0.47
0.50
0.53
0.57
0.60
0.5-5
0.27
0.31
0.34
0.37
0.41
0.44
0.47
0.51
0.54
0.57
0.61
0.64
5-10
0.33
0.37
0.40
0.43
0.47
0.50
0.53
0.57
0.60
0.63
0.67
0.70
> 10
0.45
0.49
0.52
0.55
0.59
0.62
0.65
0.69
0.72
0.75
0.79
0.82
Bare
< 0.5
0.33
0.37
0.40
0.43
0.47
0.50
0.53
0.57
0.60
0.63
0.67
0.70
soil
0.5-5
0.37
0.41
0.44
0.47
0.51
0.54
0.57
0.61
0.64
0.67
0.71
0.74
5-10
0.43
0.47
0.50
0.53
0.57
0.60
0.63
0.67
0.70
0.73
0.77
0.80
> 10
0.55
0.59
0.62
0.65
0.69
0.72
0.75
0.79
0.82
0.85
0.89
0.92
IMP
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
TABLE 18.2 Average degree of imperviousness for different
urban land-use classes: default values and estimates derived from
IKONOS data and Landsat ETM+ data for the Woluwe case study.
where Q [L 3 T 1 ]istheflowrate, x [L] is the distance along
the flow direction, t [T] is the time, c i [LT 1 ]isanadvective
velocity and d i [L 2 T 1 ] is the diffusion coefficient. The advective
velocity is a function of the flow velocity, which is calculated
using Manning's equation. The diffusion coefficient is a function
of the flow velocity, the hydraulic radius and the slope of the cell.
For a unit impulse input, the solution to Equation 18.3 at the
grid cell outlet, assuming open boundary upstream and closed
boundary downstream is a first passage time distribution as given
by (Eagleson, 1970):
Land-use
Default degree of
IKONOS-
Landsat-
classes
imperviousness
derived value
derived
value
Low density
built-up
0.30
0.12
0.12
High density
built-up
0.50
0.57
0.61
2 πd i t 3 exp
( c i t l i ) 2
4 d i t
l i
u i ( t )
=
(18.4)
City center
0.70
0.45
0.38
Infrastructure
0.50
0.58
0.60
where u i ( t )[T 1 ] is the cell impulse response function at time t
(Fig. 18.3b) and l i [L] is the length of the cell. After determining
the cell impulse response function using Equation 18.4, the
flow path response is determined using a linear routing by
successively applying the convolution integral. Assuming that
the path response is also a first passage time distribution, an
approximate numerical solution for the convolution integral is
given by De Smedt, Liu and Gebremeskel (2000). Equation 18.5
shows the convolution integral and its numerical solution.
Roads
0.50
0.36
0.31
Industry
0.70
0.84
0.86
increasing soil moisture content. In general, the model accounts
for the effect of slope, soil type, land-use, soil moisture, rainfall
intensity and its duration on the production of surface runoff in
arealisticway.
18.4.2 Flow routing
exp
N
t i ) 2
2 σ i tt 1
1
2 πσ i t 3 t 3
( t
U i ( t ) =
u i ( t ) =
(18.5)
In WetSpa, flow routing is carried out at a grid cell, flow path and
catchment level as shown in Fig. 18.3(a). Assuming the grid cell
as a reach with one-dimensional unsteady flow and neglecting
the acceleration terms of the St. Venant equation and combining
it with the continuity equation yields the diffusive wave equation,
which is the basis for the flow routing in the grid cell (Miller and
Cunge, 1975; Jobson, 1989):
i
j
=
1
i
where U i ( t )[T 1 ] is the path response function (Fig. 18.3c), the
subscript i denotes the cell where the input occurs, j refers to the
cell connecting cell i with the outlet, N is the total number of
cells along the flow path, t i [T] is the mean flow time from the
input cell to the end of the flow path, and σ i [T] is the standard
deviation of the flow time.
The flow path input response function is used to determine
the flow response at the end of a flow path by convoluting the
∂x d i 2 Q
∂Q
∂t + c i ∂Q
= 0
(18.3)
∂x 2
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