Geology Reference
In-Depth Information
(e.g. Ciesiolka & Rose, 1998), or else inferred
from other data. Yu
et al
. (1999) showed that
consistent values of erodibility parameters are
obtained if: (i) an effective runoff rate is calcu-
lated from a measured hydrograph; (ii) a
hydrograph is estimated from rainfall rate and
total runoff amount; or (iii) scaling techniques
using peak rainfall intensity and a gross runoff
coefficient are used.
1
V =
2/3
1/ 2
R
S
(11.4)
n
where
S
is the land slope (the sine of the slope
angle), and
R
the hydraulic radius (m). For rills of
different shapes, analytical expressions for
R
are
given in Yu and Rose (1999).
Other than for perfect plane geometry of flow,
when
R
D
, the flow depth, there is no straight-
forward analytical solution to determine the
water depth for a given unit discharge. Water
depth, however, is determined numerically (using
Newton's method) to solve the continuity equa-
tion (Equation (11.3) ):
=
11.3
Theory Outline for GUEST (Type B)
This theory outline is for the Type B version of
GUEST which provides a physically meaningful
erodibility parameter (
b
) provided that runoff-
driven processes are dominant, which has been
shown to be the case on steeplands (Rose
et al
.,
1997). If other erosion processes contribute sig-
nificantly to soil loss, or plots are not bare of
vegetation, then the physical interpretation of
the value of
b
is less certain, although it is still
useful in describing the erodibility of the meas-
urement plot (assumed to be essentially planar,
although if rilling is observed, its effects are
recognized).
Under steady-state conditions, for a given run-
off rate,
Q
(mm h
−1
), the unit discharge (or volu-
metric discharge per unit slope width),
q
(m
2
s
−1
),
is determined by
A(D) V(D)
-
q = 0
W
(11.5)
r
Once the water depth is determined, hydraulic
radius and flow velocity can be computed, and
the stream power per unit area,
Ω
(W m
−2
), calcu-
lated from:
W
=
r
g S R V
(11.6)
e
where
r
e
is the density of water and sediment
mixture. Soil erosion due to flow-driven proc-
esses occurs only when stream power exceeds a
threshold value
Ω
0
(about 0.008 W m
−2
for culti-
vated soils (Proffitt
et al
., 1993b) ).
A key assumption in the GUEST theory is that
a certain fraction,
F
, of the excess stream power
(
Ω
0
) is involved in maintaining the sediments
in suspension. A value of
F
Ω
−
q
=
LQ/3600000
(11.2)
0.1 is used in GUEST,
although values as high as 0.2 have been meas-
ured at low stream powers (Proffitt
et al
., 1993b).
Supported by direct observation (Heilig
et al
.,
2001), a layer of previously eroded and deposited
sediment quickly develops which sits on top of
the original uneroded soil matrix. This depos-
ited layer, whilst providing some degree of pro-
tection to the soil matrix from entrainment by
the eroding agent, also provides a ready source
of easily erodible material, due to its low or neg-
ligible strength. The sediment concentration
would be expected to be at a maximum when
this weak deposited layer completely covers the
soil matrix, and an equilibrium sediment con-
centration would be achieved when the rate of
=
where
L
is the slope length (m). Rill geometry, if
rilling occurs, can be defined by its average spac-
ing,
W
r
(m), bottom rill width,
W
b
(m) and the side
slope of rills,
z
(defined as the horizontal incre-
ment per unit vertical increment).
The continuity equation for the surface runoff
is given by:
r
q = A V
W
(11.3)
where
A
is the cross-sectional area (m
2
), and
V
(m s
−1
) the mean flow velocity. In effect, an aver-
age catchment area of
W
r
L
is assumed for each
rill. The velocity is determined using Manning's
formula:
