Geology Reference
In-Depth Information
the pace of landscape change. In such instances,
one cannot simply operate on the numerical
landscape with a transport rule - which might
lead to diffusive behavior - but must as well
embed in the model a rule, or mathematical rep-
resentation, for the generation of regolith (see
the next section; Anderson and Humphrey, 1989).
In such circumstances, one therefore needs a
rule for what sets the rate at which regolith is
produced. Once produced from bedrock, parti-
cles are moved down slopes, first on hillslopes
and then in channels. One must, therefore,
determine where the channels lie within a land-
scape, how effective they are in transporting
sediment, and, if bare bedrock is exposed in the
channel, how fast the bedrock is being eroded.
world, because the weathering rates are far too
low to measure on human time scales. Hope has
emerged, however, with the aid of cosmogenic
radionuclides in constraining the constants in at
least a few geological and climatic settings - see,
e.g., Pavich and Hack (1985), Pavich (1986), and
McKean
et al
. (1993), who use garden-variety
10
Be, and Heimsath
et al
. (1997, 1999, 2000) and
Small
et al
. (1999), who use
10
Be and
26
Al
produced
in situ
; see also Chapter 3 on dating
for a discussion of these methods.
Hillslopes
Material is moved down hillslopes by a number
of processes, whose types and rates are modu-
lated by the local climate and slope materials.
All hillslope transport processes are dictated
to some degree by the local slope angle. The
simplest model rule is therefore something like:
Regolith production
Our understanding of the long-term controls on
the conversion of bedrock to regolith is incom-
plete. In fact, this lack of understanding has led
to the establishment of a number of experimental
sites in both the United States and Europe,
dubbed Critical Zone Observatories, in which
both the processes and rates of regolith produc-
tion, and the ecological and hydrologic services
that they perform, are targets of investigation
(Anderson
et al
., 2008). To first order, we would
expect that, the wetter the climate, the faster will
be the weathering of rock. Gilbert (1877) hypoth-
esized that, within any particular landscape (he
was then considering arid landscapes of the
Henry Mountains in Utah), the regolith produc-
tion rates should be a strong function of the
regolith thickness as well. Bare bedrock can
effectively shed water, thereby protecting itself
from chemical attack, whereas even a thin
regolith cover should allow significant chemical
attack of the underlying rock. Beyond a given
thickness, however, the bedrock lies at such a
great depth beneath the surface that wetting
events may not penetrate, and the conversion
rate might be expected to diminish. A mathemat-
ical statement of this conceptual picture has
been incorporated in a number of numerical
landscape evolution models within the last few
decades. Although appealing, this conceptual
picture has been difficult to document in the real
∂
∂
z
Qk
x
=−
(11.2)
where
∂z
/
∂x
is the local gradient of the
topography, or the slope, in the
x
direction. The
constant
k
reflects the long-term efficiency of
sediment motion, which might be expected
to be a function of the climate. A major goal
of modern geomorphology is to explore the
dependence of this hillslope transport efficiency
on aspects of the climate and on the material
properties of the regolith (e.g., Dietrich
et al
.,
2003; Anderson, 2002). This arena has seen
much recent progress, with considerable
attention to specific transport processes. Gabet
(2000) and Heimsath
et al
. (2002) have proposed
rules that acknowledge the roles of biological
transport actors; Anderson (2002) has proposed
a plausible rule for transport by frost creep.
Roering (2008) has summarized several poten-
tial rules and has explored the impact of the
choice of rule on the look of the resulting
modeled topography. Several workers (e.g.,
Anderson and Humphrey, 1989; Roering
et al
.,
2001; Roering, 2008) have modified this rule
(Eqn 11.2) in order to mimic regolith landslides
by enhancing the transport nonlinearly as a
threshold slope angle is approached (Fig. 11.7B).
