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 forsnEavg 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-qEavgrelationships 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.