Environmental Engineering Reference
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where:
where:
=
q
s
is unit sediment load
α
,
β
,
γ
,
δ
are constants
the cumulative probability function of a
standard normal deviate
T
=
a constant
and:
S
T
=
the coefficient of variation of T (assumed
constant)
ω
=
ρ
·
g
·
S
·
q
S
τ
b
=
the coefficient of variation of
τ
b
(assumed
where:
constant)
ω
=
stream power
ρ
=
density of water
and:
g
=
gravitational acceleration
τ
b
=
150
·
ρ
·
g
·
h
·
S
S
=
energy slope
q
=
unit discharge of water
where:
ρ
=
density of water
If the sediment concentration of the water on the cell
exceeds its transport capacity, deposition occurs. This is
calculated using a version of equation 12 in Lei
et al
.
(1998), which assumes deposition to be a linear function
of the difference between sediment load and transport
capacity. Note that no consideration is made of different
settling times for each size fraction of the deposited
sediment, or of differences in properties (for example,
bulk density, erodibility) between re-entrained and newly
eroded sediment.
Whereas outflow velocity and transport capacity are
both determined by the energy gradient, it is assumed to
be the soil surface gradient which controls detachment.
In RillGrow 2, detachment occurs only if both energy
gradient and soil surface gradient are downhill. If the soil
surface gradient is uphill, then the energy gradient-driven
outflow is assumed to be merely hydrostatic levelling.
Where detachment does occur, its value is calculated
using a probabilistic equation by Nearing (1991), which
assumes that detachment is controlled by the probability
of occurrence of random turbulent bursts and the differ-
ence between soil strength and the shear stress generated
by these bursts. The relationship used in RillGrow 2 is a
reformulation of equation 10 in Nearing (1991):
gravitational acceleration
h
=
water depth
S
g
=
=
energy slope.
RillGrow 2, while still relatively simple, is thus a devel-
opment of the earlier RillGrow model in that it explicitly
attempts to reproduce, in a true time domain, the effects
of several processes that are involved in rill formation.
4.4.2.1 Results from RillGrow 2
During a series of twelve laboratory-based experiments
at the University of Leicester (Lascelles
et al
., 2000, 2002)
simulated rainfall (from an overhead sprinkler system)
was applied to a sandy soil in a 4
75 m flume. A
range of slope angles and rainfall intensities were used
(Table 4.2). Each experiment lasted for 30 minutes, dur-
ing which surface flow, discharge, sediment removal and
flow velocities were measured. Prior to and following each
experimental run, digital photogrammetry was used to
create digital elevation models (DEMs) of the soil's sur-
face. The initial (pre-experiment) DEMs and other data
were then used as inputs to RillGrow 2. For one exper-
iment only (X11: Table 4.2), measured flow velocities,
discharge and sediment yield were also used to calibrate
the model with respect to soil roughness and erodibil-
ity. Once calibrated, the model's inputs were not further
adjusted when simulating the other eleven experiments.
Full results are given in Favis-Mortlock
et al
. (2000),
however measured and simulated discharge and sediment
delivery for all experiments are compared in Figure 4.6.
While both total discharge and sediment loss were well
simulated in all cases, sediment loss was consistently
underestimated for the low-gradient experiments. This
result arose from the relatively loose coupling between
the splash and flow components of the model: the
nonspatial representation of the exchange of sediment
×
1
.
e
=
K
·
S
·
u
·
P
(4.2)
where:
e
=
detachment
K
=
a constant
u
=
outflow speed
and:
T
−
τ
b
P
=
1
−
S
T
2
+
S
τ
b
2
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