Geology Reference
In-Depth Information
Table 5.2
Operating equations of EUROSEM (from Quinton, 1997, where details of the sources cited in column 4 can be found).
No.
Model subroutine and key equation
Definition of terms
Source
1
Interception I
c
=
RP
c
I
c
is the depth of rainfall intercepted (mm),
R
the rainfall (mm) and
P
c
the
percentage canopy cover expressed as a ratio.
R
I
c
x
2
Interception storage
=-
I
I
(1
e
)
I
s
is the interception storage (mm),
I
x
the maximum interception storage (mm)
and
R
c
the cumulative rainfall (mm).
Merriam (1973)
s
x
3
Stemflow for grasses S
f
=
0.5T
if
(cos. P
a
.
sin
2
P
a
)
a
is the average acute angle (degrees) of the plant stems to the ground surface
and
T
if
(mm) is the temporarily intercepted throughfall.
van Elewijck (1989a,b)
4
and for other plant species S
f
=
0.5 T
if
(cos. P
a
)
5
Infiltration f
c
=
K
s
(1 −
e
−
F
/
B
)
−1
f
c
is the infiltration capacity (mm h
−1
),
F
the amount of rain already absorbed
into the soil (mm), and
K
s
is the saturated hydraulic conductivity (mm h
−1
);
B
and
G
are defined below.
Smith & Parlange (1978)
6
where B
=
G
(
q
s
−
q
i
)
(
q
s
−
q
i
) is the saturation deficit and
G
is the capillary drive (mm).
0
1
()()
7
and
G
=
ò
K
yy
d
K(
y
)
is a hydraulic conductivity function and
y
is the soil matric potential.
K
s
¥
8
Modification of infiltration by vegetation
K
sv
=
K
s
(1 −
P
b
)
P
b
is the plant basal area ratio,
K
sv
is the modified value of saturated hydraulic
conductivity.
Holtan (1961)
9
Surface runoff rating equation Q
=
a h
m
Q is
discharge (m
2
s
−1
) and
h
is the depth of flow (m)
a
and
m
are defined below.
Woolhiser
et al
(1989)
0.5
s
10
where
a
=
s
is the slope (m m
−1
) and
n
the value of Manning's
n
n
5
3
11
and
m
=
12
Surface runoff continuity equation
q
is the lateral inflow rate (m
3
s
−1
).
Woolhiser
et al
. (1989)
¶
+=
¶¶
hQ
q
t
()
xt
,
x
13
Soil detachment by raindrop impact D
s
=
kK
e
e
−
bh
K
e
is the kinetic energy of the rain reaching the ground surface (J m
−2
),
k
the
detachability of the soil (g J
−1
),
h
is the depth of surface water (m) and
b
is an
exponent (1 to 3).
14
Kinetic energy: of direct throughfall
K
e
(DT)
=
8.95
+
(8.44 log I)
K
e
(DT)
represents the kinetic energy (J m
−2
) per mm of direct throughfall and
I
is
the rainfall intensity (mm h
−1
).
Brandt (1989)
15
of leaf drainage
K
e
(LD)
=
(15.8.P
h
0.5
)- 5.87
K
e
(LD
) is the kinetic energy (J m
−2
) per mm of leaf drainage and
P
h
the height of
the plant canopy (m).
Brandt (1989)
16
Soil detachment by flow D
F
=
b
wv
s
(C
m
−
C)
C
m
is the equilibrium sediment concentration in the flow,
C
the actual sediment
concentration,
b
the resistance of the soil to detachment, and
v
s
the settling
velocity of the particles (m s
−1
).
Smith
et al
. (1995)
17
where C
m
=
a
(Su
−
0.4)
g
S
is the slope of the land (m m
−1
),
u
is the flow velocity (m s
−1
) and
α
and
γ
are
coefficients which vary with the median particle size of the soil
Govers (1990)
18
Sediment continuity equation
()()
() ()
A
is the cross-sectional area of the flow (m
2
),
q
s
is the lateral input or extraction
of sediment per unit length of flow (m
3
s
−1
),
e
is the net pick-up rate of
sediment from the bed per unit length of flow (m
3
s
−1
) and
x
is the horizontal
distance (m).
Bennett (1974), Kirkby (1980),
Woolhiser
et al
. (1989)
¶
AC
¶
QC
ext
,
q xt
,
+
-
=
t
x
s
¶
¶
