Environmental Engineering Reference
In-Depth Information
Therefore, most studies have focused on testing or
calibrating algorithms for individual geomorphic pro-
cesses, most commonly fluvial incision and transport.
The method usually used is to compare 1-D model
predictions with landscape (most often fluvial profile)
forms for which the driving forces and boundary and
initial conditions are reasonably well constrained, in what
Tucker (2009) recently termed 'natural experiments in
landscape evolution' (Figure 19.4). Natural settings can
be either in a steady state or transient. Steady-state land-
scapes are easier to study because the initial conditions
do not need to be known and the landscape form should
contain information on model parameters and the sensi-
tivity of the landscape to their variation. However, several
studies (e.g., Whipple and Tucker, 2002; Whipple, 2004;
Lague et al ., 2005) have shown that steady-state river
profiles cannot be used to discriminate between different
fluvial incision models, as all predict slope-area scaling
that is comparable, within the resolution of the data,
to that observed in natural settings. Such discrimina-
tion requires applying the models to transient systems,
for which initial conditions (and preferably intermediate
states) should thus be known. Fluvial terraces or vol-
canic flows that fossilize palaeoprofiles can inform the
estimation of these initial and intermediate states.
Known or supposed steady-state fluvial profiles have
been extensively used to fit stream-power incision mod-
els and constrain the sensitivity of stream profile form to
tectonic uplift rate and lithology (see Wobus et al ., 2006
for a review). Single profiles can only provide constraints
on the ratio of the exponents m and n in Equation 19.7,
which is generally found to be consistent with incision
rates being proportional to either unit stream power or
shear stress. Inferring absolute values for these parameters
requires comparing streams undergoing variable incision
or underlain by variable bedrock lithologies. Several of
these studies have come up with 'unrealistic' values for m
and n , i.e. values that are not readily explained by either
total stream power, unit stream power or shear stress
models (in particular values of n 1). These have been
interpreted as implying a significant threshold shear stress
for fluvial incision combined with a stochastic distribu-
tion of floods (Snyder et al ., 2003a) and/or breakdown of
hydraulic scaling in rapidly incising reaches (Duvall et al .,
2004). Tomkin et al . (2003) have attempted to use the
steady-state profile of the Clearwater River (NW USA) to
test different fluvial incision algorithms but found that
the approach was nondiscriminatory; none of the models
was able to describe the observed fluvial profile form
satisfactorily and no one performed significantly better
than the others. Brocard and van der Beek (2006) used
observations of fluvial profile form (in particular the pres-
ence or absence of lithogenic knickpoints) and valley-flat
width in supposedly steady-state rivers of SE France
to calibrate a combined detachment/transport limited
stream power model (as conceptualized by Whipple and
Tucker, 2002), but did not test alternative sediment-flux-
dependent models.
Fewer studies have addressed transient systems, prob-
ably because the required knowledge of initial conditions
limits the number of potentially suitable study sites. Stock
and Montgomery (1999) used rivers in Hawaii, California,
Japan and Australia to calibrate the detachment-limited
stream-power model. Whereas all profiles could be fit-
ted with 'reasonable' values for m (
.
1),
fitting the highly variable incision rates in the differ-
ent settings studied required a five-orders-of-magnitude
variation in the value of K in Equation 19.7. Van der
Beek and Bishop (2003) used the 20-My record of inci-
sion in the Lachlan River (New South Wales, Australia)
to test six fluvial incision algorithms (detachment and
transport-limited stream power, threshold shear stress,
undercapacity and tools models). They found that either
a simple detachment-limited stream power model or
an undercapacity model that incorporated an explicit
description of spatial variations in channel width provided
most reasonable fits to the observations (Figure 19.4).
The fits significantly improved when spatial variability
in bedrock resistance to incision was taken into account,
implying close to detachment-limited conditions. Loget
et al . (2006) used the Messinian incision of the Rh one
Valley (SE France) to calibrate the parameters in the
undercapacity-like incision law of Crave and Davy (2001;
see also Davy and Lague, 2009). They found that the
strongly concave form of the incision profile required a
very small characteristic length compared to the profile
length, implying close to transport-limited conditions.
Valla et al . (2010) have recently reached a similar con-
clusion for much smaller scale bedrock gorges incising
glacial hanging valleys in the western Alps and also
showed that this unexpected result could be due to strong
hillslope-channel coupling and significant sediment sup-
ply from gorge sidewalls to the channel. Finally, Attal
et al . (2008) used the well-constrained uplift and incision
history for footwall blocks of normal faults in central Italy
(cf. Whittaker et al ., 2007) to calibrate a detachment-
limited stream power model including a threshold and
incision-dependent scaling of channel width.
Although the above studies have not as yet reached
a consensus as to what is a suitable fluvial incision
0
4) and n (
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