5.3 Toward Detecting the Influence of Climate on Topography and
Erosion Rates
Remote analysis of channel steepness patterns can provide a preliminary
means to detect whether the climate may be influencing river profiles in
a landscape, and whether transient adjustment to a change in climate may
be ongoing. For landscapes well-described by the SPM, discrepancies
between rainfall conditions experienced by trunk and tributary basins
should cause systematic differences in trunk and tributaryksn (Figures 5&6; Gasparini & Whipple, 2014),
but not in ksn-q . As illustrated in Figure 10c,
the expected contrast in trunk and tributary ksnis most developed at steady state, but it begins manifesting immediately
during transient adjustment as differences in localksn at confluences that migrate upstream (Figure
10c, Movie S5). In contrast, precise agreement between trunk and
tributary ksn-q is expected at steady state, and
it is approximately maintained even during periods of adjustment to a
change in rainfall pattern. Agreement between trunk and tributaryksn-q that weakens upstream from confluences may
also be an important indication of ongoing transient adjustment that may
be difficult detect from the ksn pattern alone
(Figure 10c, e.g., as discussed in section 5.2.2). Therefore, comparison
of ksn and ksn-q patterns
may be a useful way to diagnose and further assess the potential extent
of influence by rainfall gradients, provided the pattern of discharge
accumulation can be reasonably estimated (e.g., using high spatial
resolution satellite rainfall or nested stream gauge data).
Following topographic analysis, our results have additional implications
for designing effective catchment-averaged erosion rate sampling
strategies. Broadly, sampling strategies can be grouped into two
classes: nested and distributed, described below. Nested, or
hierarchical, sampling strategies comprise multiple samples from the
same river basin where some or all samples are collected along the trunk
river, and where averages typically integrate over very large
(102–105 km2)
drainage areas (e.g., Abbühl et al., 2010; Henck et al., 2011; Portenga
et al., 2015; Reinhardt et al., 2007; Safran et al., 2005; Whittaker et
al., 2007; Willenbring et al., 2013; Wittmann et al., 2016). In
principle, such strategies can allow researchers to assess
reproducibility of individual measurements, test sediment mixing models,
and sub-divide basins into different sectors to identify along-stream
variations in erosion rates. Given the complex along-stream patterns of
erosion rate we observe in response to changing rainfall patterns and
widely disparate responses between trunk and tributary profiles,
however, our results suggest that caution is warranted in interpreting
patterns of erosion rates collected in a nested fashion. In particular,
this includes datasets that compile measurements from along trunk rivers
and tributary catchments, but also those that compare samples from
different large catchments that experience different mean climates and
rainfall patterns, even at quasi-steady-state, because how each reflects
and experiences variations in rainfall may be fundamentally different.
Furthermore, because we find that along-stream variations in erosion
rate due to changes in rainfall pattern are characteristically muted
along the trunk profile (e.g., Figure 10a), nested strategies may not be
appropriate in many settings, especially if the goal is to measure the
influence of climate on fluvial incision.
The other widely used strategy, which we refer to as a distributed
sampling strategy, targets single samples from catchments that are
distributed across a landscape or mountain front, and typically –
though certainly not always – comprises relatively smaller
(100-102 km2)
catchments (e.g., Adams et al., 2020; Binnie et al., 2008; Carretier et
al., 2013; DiBiase et al., 2010; Godard et al., 2014; Morell et al.,
2015; Ouimet et al., 2009; Scherler et al., 2014). This type of strategy
generally allows more freedom to carefully select preferable catchments
(relatively uniform channel steepness, rainfall, lithology), with the
limitation that spatial variations in erosion at the sub-catchment scale
are not resolvable with single measurements. In contrast to muted
spatial variations in erosion noted for nested strategies, our model
results suggest distributed strategies inherently record a more direct
signal of climatic influences than nested approaches, consistent with
previous findings by Han et al. (2015). However, if inter-catchment
variations in rainfall and therefore erosional efficiency are not
accounted for, or transient conditions are not recognized, this
sensitivity may cause significant dispersion or distortion in measured
relationships among landscape metrics, as shown forksn –Eavg relationships
(Figures 5b & 6b), and/or lead to misleading spatial patterns in
erosion rate and ksn (Figure 10).
Lastly, we note that transient adjustments in response to changes in
rainfall pattern do not significantly affect apparent erosional
efficiency in ksn-q –Eavgrelationships where no variations in rock properties exist, even in
response to the dramatic shifts in rainfall patterns that we model,
regardless of sampling strategy. Indeed, transient deviations from
expected steady state relationships modelled in any location are
generally well within the analytical uncertainty of measured
catchment-average erosion rates from natural landscapes (Figures 5 and
6). Exceptions to this appear to be limited to scenarios where
landscapes experience a shift toward arid climates. Nevertheless,
transient, spatially variable patterns of erosion caused by changes in
rainfall pattern are reflected in ksn-q patterns
with good accuracy in our model (Figure 10c, Movie S3-S5). As such,ksn-q may be used to recognize ongoing adjustment
to changes in climate where ksn can be ambiguous.
We suggest that ksn-q , or a different metric that
encompasses the spatial distribution of rainfall (runoff), may be vital
component for future efforts to detect climate’s influence on and from
topography and erosion rates in mountain landscapes where rainfall is
inherently spatially variable.