Environmental Engineering Reference
In-Depth Information
L fb = 20 km
L fb = 100 km
L fb = 200 km
150
150
150
100
100
100
50
50
50
0
0
0
0
50
0
50
0
50
km
km
km
0.0
0.2
0.4
Elevation [km]
0.6
0.8
1.0
Figure 19.3 Planform view of topography and drainage patterns predicted after 10 My of escarpment retreat into an initially flat
plateau at an elevation of 1 km, dropping down to base level on one side. The model used is the same as in Figure 20.2 and results are
shown for different values of the 'characteristic length' for fluvial incision L f as defined in Equation 20.11. Small values of L f
approximate transport-limited conditions while large values correspond to detachment-limited conditions. Other parameter values
for these models are:
10 2 my 1 (Adapted with permission from van der Beek, P.A. and Braun, J. (1998)
Numerical modelling of landscape evolution on geological time-scales: A parameter analysis and comparison with the south-eastern
highlands of Australia. Basin Research , 10, 49-68).
1m 2 y 1 ; K s =
κ =
0
.
calibre, leads to an expression of the form:
controls bedrock-incision rates. Lague (2010) has recently
proposed an incision algorithm that combines both the
static (sediment-thickness) and dynamic (sediment-flux)
effects, leading to an expression of the form:
Q s
h
Q s
t = k 1
k 2
τ c
1 1 / 2
τ c
1 2
(19.13)
D 3 / 2
s
k exp
exp
(
h
t =
Q s
Q eq
h s
ξ D s
υ
τ τ c )
(19.14)
τ c are nondimensional forms of the shear
stress and critical shear stress, respectively, and D s is the
mean grain diameter. Lamb et al . (2008) have recently
further extended this model to include abrasion by sus-
pended load. An alternative approach to model the cover
effect was suggested by Howard (1998) and implemented
by Hancock and Anderson (2002), in which the mean sed-
iment thickness on the bed rather than the sediment flux
τ and
where
where
is a dynamic cover factor, h s is the mean sediment
thickness on the bed and
ν
is a static cover factor. Although
several studies have investigated the implications of the
different sediment-flux dependent incision models for
river long-profile evolution (Whipple and Tucker, 2002;
Sklar and Dietrich, 2006; Turowski et al . 2007; Lague,
ξ
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