Environmental Engineering Reference
In-Depth Information
parameter
b
represents the effect of increasing erosion by removing topsoil in the process of erosion, and
the parameter
f
represents the effect of vegetation controlling erosion. Figure 2.31 shows that once the
top soil is removed the slope suffers from accelerating soil erosion in a red soil area in southern China.
Combining Eqs. (2.12) and (2.11) the coupled differential equations for the vegetation-erosion interaction
under the action of ecological stresses are obtained as (Wang et al., 2003a)
d
V
½
aV
cE
K
G
()
t
°
V
inst
0
R
d
d
d
t
E
(2.13)
bE
fV
E
R
¿
t
In the equations, the dimension of patameter
b
is [1/time
-1
] with the units yr
-1
, the dimensions of
f
and
E
R
are [mass/(area·time
2
)] with the units of t/(km
2
yr
2
). The parameters
a
,
c
,
b
,and
f
are important and they
are functions of climate, precipitation, soil, topography, and morphology. For any watershed or area the
parameters can be determined by applying a trial and error method and using data on vegetation, erosion,
and human activities.
Fig. 2.31
A slope suffers from accelerating soil erosion because the top soil is removed in a red soil area in
southern China (See color figure at the end of this topic)
The differential equations are non-homogeneous and linear and may be solved theoretically as follows:
ª
d
V
º
§
·
Vc
e
mt
c
e
mt
e
mt
³
e
mt mt
e
³
e
mt
W
bVcE t
d
d
t
(2.14)
1
2
1
1
2
2
«
¨
¸
»
1
2
W
W
d
t
©
¹
¬
¼
am
am
ª
§
d
E
·
º
1
mt
2
m t
mt
³
mt
m t
³
m t
W
Ec
e
c
e
e
e
e
e
aE fV t t
d
d
(2.15)
1
2
1
«
1
2
2
¨
¸
»
1
2
W
W
c
c
d
t
©
¹
¬
¼
in which
VKt
G
()
¾
V
W
inst
R
(2.16)
EE
¿
W
R
The exponents
m
1
and
m
2
are given as follows:
1
ª
º
2
¼
(2.17)
m
(
a
r
b
)
(
a
b
)
(
ab
cf
)
1, 2
¬
2
c
1
and
c
2
are integration constants to be determined by the boundary conditions. For any watershed if the
ecological stresses are known the vegetation and erosion processes can be theoretically described by
Eqs. (2.14) and (2.15).
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