Geology Reference
In-Depth Information
A
parallel retreat
knickpoint reach
τ
c
>
τ
t
3
t
2
t
Fig. 8.9
Models for knickpoint
migration.
Models for knickpoint migration or
formation based on stream-table
analyses. Here
t
c
is the threshold
stress to initiate erosion of the bed;
and
t
is the actual bed shear stress.
A. Parallel retreat of the knickpoint
through time with the initial shape
being maintained. A resistant rock
unit caps the units that are being
incised. B. Knickpoint propagation
in uniformly resistant rocks with
slope replacement during migration.
C. Knickpoint formation due to
differential erosion of strata with
contrasting resistance to erosion.
No propagation is required here.
Modified after Gardner (1983).
t
0
1
very resistant
strata
τ
c
<<
τ
knickpoint reach
ultimate profile
τ
c
<
τ
slope replacement
B
t
3
t
2
t
1
uniformly resistant
strata
t
0
τ
c
<
τ
knickpoint reach
differential erosion
without propagation
C
τ
c
>
τ
τ
c
<
τ
resistant
strata
t
0
t
1
t
2
t
3
Modes of Migration
weakly resistant
strata
relation to faulting events. Rates of knickpoint
propagation in bedrock-floored rivers are
generally poorly known, but recent studies of
knickpoint migration in channels carved into
Hawaiian basalts suggest long-term upstream
propagation rates of more than 2 mm/yr
(Seidl
et al
., 1994), whereas migration rates a
thousand times faster (~2 m/yr) are estimated for
knickpoints in the weak forearc mudstones and
siltstones of northeast New Zealand (Crosby and
Whipple, 2006) (Fig. 8.7). Rates as high as 300 m/
yr have been observed for the knickpoint caused
by the Chi-Chi earthquake in 1999 (Fig. 8.7C).
Calculations of knickpoint migration rates
depend both on interpretations of the geomorphic
history and on dating the sequential migration.
The study in Hawaii relied on cosmogenic nuclide
exposure dating of bedrock exposed along chan-
nels to determine how rapidly incision and trans-
lation have occurred in the past, whereas the
New Zealand study exploited dated volcanic
ashes preserved in terraces that pre- and post-date
knickpoint migration. Without such dating, rates
of knickpoint migration in most geomorphic
settings remain speculative. Moreover, in natural
settings, the original shape of the knickpoint or
how that shape has been modified as it propa-
gated is commonly impossible to document. Is
the original shape simply translated through the
landscape or is it smoothed and flattened during
translation? What controls the speed of migration?
Under circumstances where natural settings reveal
little about the geomorphic processes of interest,
sometimes useful insights on these processes can
be obtained through small-scale experiments and
modeling that attempt to reproduce key aspects
of the natural setting.
Experimental responses
to base-level lowering
Using a long, narrow flume with a steady input
flow of water to a pre-carved shallow channel,
Gardner (1983) explored temporal and spatial
changes in shape and flow parameters across a
knickpoint. A comparison of the threshold shear
stress (
t
c
) needed to initiate erosion with the
actual bed shear stress (
t
) serves to predict
how and where erosion may occur. Above a
knickpoint's lip, the channel was observed to
become steeper, narrower, and deeper, such that
the bed shear stress (as predicted by Eqn 8.2)
steadily increased to a maximum at the lip
and promoted rapid erosion at this point.
