Environmental Engineering Reference
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0.7
Values from individual stations
(a)
0.6
Averages within soil-moisture classes
0.5
0.4
0.3
0.2
λ
= 0.524 s + 0.0031
R
2
= 0.67
0.1
0.2
0.4
0.6
0.8
1
s
(b)
Values from individual stations
26
Averages within soil-moisture
classes
21
16
11
6
1
0.2
0.4
0.6
s
0.8
1
Figure 4.18. Dependence between average soil moisture (top 50 cm) and (a) average
storm frequency
at 27 rainfall stations uniformly distributed across
Illinois (three stations for each climate division). The solid dots indicate
λ
and (b) depth
α
λ
and
α
values at individual stations, and the squares represent statewide averages (i.e.,
λ
and
) within soil-moisture classes. The solid lines represent a linear fit (after
D'Odorico and Porporato
,
2004
).
α
L
(
s
) are null when soil moisture is below field capacity
s
fc
, whereas, when
s
>
s
fc
,
leakage is modeled (
Laio et al.
,
2001
)as
K
s
e
β
(1
−
s
fc
)
{
e
β
[
s
(
t
)
−
s
fc
]
L
(
s
)
=
K
(
s
)
=
}
,
[
s
fc
<
s
(
t
)
≤
1]
,
(4.24)
where
is a parameter of the soil-water retention curves (
Laio et al.
,
2001
), and
K
s
is the saturated hydraulic conductivity. The parameters
β
,
K
s
,and
s
fc
depend on only
the soil properties. We may obtain total losses by combining Eqs. (
4.23
)and(
4.24
),
ρ
β
(
s
)
=
[
E
(
s
)
+
L
(
s
)]
/
nZ
r
(Fig.
4.17
).
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