Geology Reference
In-Depth Information
5.0
A
B
C
1.0
0.5
Stream Power
versus Erosion Rate
Annual Rainfall
versus Erosion Rate
Channel Slope
versus Erosion Rate
ER = 0.05(±0.03) SSP 0.71(±0.20)
r 2 = 0.84
ER = 2.2(±0.3) PPT 0.3(±0.1)
r 2 = 0.66
ER = 48(±0.31) Slope 2.0(±0.6)
r 2 = 0.68
0.1
100 200
Specific Stream Power (watts/m 2 )
50
400
0.1
0.2
Channel Slope (m/m)
0.3
0.4
2.0
4.0
0.05
0.1
1.0
Annual Rainfall (m/yr)
0.5
Fig. 8.3 Himalayan erosion rates as a function of stream power, channel slope, and rainfall.
Average catchment-wide erosion rates derived from analysis of detrital cosmogenic nuclide concentrations in the
Himalaya and Tibet are compared with variables expected to influence erosion rates. A. Specific stream power
incorporates spatial variability in rainfall distributions and provides the strongest correlation ( r 2 = 0.84) with erosion
rates. B, C: As separate variables, either channel slope (B) or rainfall (C) predict two-thirds of the variability in erosion
rates, but explain about 25% less of the variability than does specific stream power (A). Compilation courtesy of Bodo
Bookhagen.
m ~ 0.5 because E ~ Q /width, and width is
typically considered to vary as a function of Q 0.5
(Whipple, 2004).
The proposition that greater discharge, steeper
channel slopes, or greater stream power would
lead to higher rates of erosion makes intuitive
sense. Until recently, however, few data were
available to provide a clear demonstration of
a  linkage between erosion rates and these
quantities. As discussed in the previous chapter
(Fig. 7.18), compilations of erosion rates at time
scales of centuries to a few millennia have
recently emerged from studies of cosmogenic
nuclide concentrations in detrital sediments
(Granger et al ., 1996; von Blanckenburg, 2006).
Because these concentrations are interpreted
to  represent the average erosion rate in the
catchment upstream of the sampling site, the rates
are expected to be responsive to the catchment-
averaged rainfall, channel slope, or specific stream
power. Detrital cosmogenic data from the
Himalaya and Tibet, for example, show quite
strong correlations of erosion with each of
these  variables (Fig. 8.3). Variations in specific
stream power predict over 80% of the variance in
erosion  rates, whereas variations in rainfall or
channel slope predict about two-thirds of the
variance. In this Himalayan region, remotely
sensed rainfall data with a high spatial resolution
(5 × 5 km) show very strong orographic control:
topography modulates rainfall distributions, such
that five- to 10-fold gradients in rainfall over a
few tens of kilometers are not uncommon
(Bookhagen and Burbank, 2010). Hence, the
summed rainfall over a catchment is a much
more reliable predictor of discharge than is
catchment area in the Himalaya. Not surprisingly,
then, for these Himalayan data, discharge based
on area is a considerably weaker predictor of
erosion ( r 2 = 0.48) than is rainfall ( r 2 = 0.66). In
assessing these correlations (Fig. 8.3), keep in
mind two caveats: such correlations provide little
insight on the actual process of erosion; and cor-
relation does not necessarily indicate causation.
It is possible that all of these factors (slopes, rain-
fall, erosion rates) are driven by another variable,
such as rates of rock uplift or variations in rock
strength. Nonetheless, if the correlation of
specific stream power with erosion rates could
be shown to be broadly applicable, the increas-
ing availability of digital topography and remotely
sensed rainfall would underpin far more efficient
comparisons of spatial variations in erosion
across tectonically active regions.
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