Geology Reference
In-Depth Information
This type of rule is not capable of treating
such potentially important processes as
bedrock-involved landsliding. Unfortunately, in
some rapidly eroding landscapes (Burbank
et al
.,
1996b), this process is the dominant means of
pulling rock from the adjoining hillslopes toward
the bounding channels. Algorithms that attempt
to capture this process come in several flavors.
The simplest is one in which there is assumed to
be a threshold bedrock slope angle above which
a slope cannot be maintained; any material found
above an envelope that points in a “V” upward
from the channel at the threshold slope angle
is, therefore, shaved off and delivered instantly
to the channel. Another algorithm essentially
modifies the hillslope efficiency,
k
, such that it
increases rapidly as an angle of repose is
approached from lower angles (Anderson and
Humphrey, 1989; Howard, 1994, 1997; see dis-
cussion in Roering, 2008). Yet other approaches
explicitly employ failure thresholds that entail
both local slope and height and incorporate an
assumed rock-mass strength (Densmore
et al
.,
1998; Schmidt and Montgomery, 1995, 1996). In
these latter cases, the failed masses must then be
distributed in the landscape in a realistic manner,
capturing the material properties of the masses
subsequent to failure.
choice of the channel initiation threshold or to
the balance between advective and diffusive
processes is explored in detail through numeri-
cal models by Whipple and Tucker (1999) and
Perron
et al
. (2008).
Bedrock incision
Our knowledge of the complex process by which
rivers etch into bedrock has only recently been
addressed by field and modeling studies. The
physical processes include abrasion by particles
entrained in the flow, plucking of blocks from the
bed, and cavitation (Hancock
et al
., 1998). Most
model rules that purport to capture the essence
of this suite of processes use a stream-power
argument (Howard and Kerby, 1983; Rosenbloom
and Anderson, 1994; Seidl and Dietrich, 1992) -
see also the review in Whipple (2004), and chap-
ter 13 in Anderson and Anderson (2010). This
simplification is often abstracted further to a rule
in which the rate of erosion is dependent on the
local channel slope,
S
, and the drainage area at
that point,
A
, i.e., the slope-area product:
∂
∂
z
c
=
dSA
(11.3)
t
where
d
is a coefficient of erosion. This equation
is undoubtedly only a crude approximation of
bedrock channel behavior. For instance, the
coefficient
d
collapses any number of sins,
including the resistance of the rock, the effective
discharge of the river, the runoff efficiency, and
so on, into a single model parameter, as dis-
cussed for example in Hancock
et al
. (1998).
Channel initiation
Most models of landscape evolution embed
some rule for where in the landscape the chan-
nels initiate. As shown convincingly in map and
field analysis by Montgomery and Dietrich
(1988, 1989, 1992), channels begin wherever a
stream-power threshold has been exceeded.
This threshold is thought to reflect the material
strength at the channel head and both the water
discharge and resultant shear stresses at that
point. This initial incision point is usually cap-
tured in the numerical models by embedding
a threshold product of the local slope,
S
, with
the local drainage area,
A
, thereby producing a
slope-area product in which upstream area is a
proxy for discharge. Nodes at which this prod-
uct is greater than some constant are considered
channels, whereas all others remain hillslopes.
The sensitivity of the landscape character to the
Alluvial transport
Many transport rules have been used in
geomorphic models. We can only touch on a
couple of classes here. Most model rules embed
the observation that sediment transport increases
with the boundary shear stress of the flow, or
the discharge of the water, above some entrain-
ment threshold. The simplest such statement is
the DuBoys equation, relating sediment flux per
unit width of flow,
Q
s
, to the local boundary
shear stress,
t
b
:
Q
s
=
b
(
t
b
−
t
c
)
(11.4)
