Investigation of stochastic-threshold incision models across a climatic and morphological gradient

Abstract

Abstract. Long-term landscape evolution is controlled by tectonic and climatic forcing acting through surface processes. Rivers are the main drivers of continental denudation because they set the base level of most hillslopes. The mechanisms of fluvial incision are thus a key focus in geomorphological research and require accurate representation and models. River incision is often modeled with a stream power model (SPM) based on the along-stream evolution of drainage area and channel elevation gradient but can also incorporate more complex processes such as threshold effects and statistical discharge distributions, which are fundamental features of river dynamics. Despite their importance in quantitative geomorphology, such model formulations have been confronted with field data only in a limited number of cases. Here we investigate the behavior of stochastic-threshold incision models across the southeastern margin of the French Massif Central, which is characterized by significant relief and the regular occurrence of high-discharge events. Our study is based on a new dataset combining measurements of discharge variability from gauging stations, denudation rates from 34 basins from 10Be cosmogenic radionuclide (CRN) concentration measurements in river sediments, morphometric analysis of river long profiles, and field observations. This new dataset is used for a systematic investigation of various formulations of the SPM and to discuss the importance of incision thresholds. Denudation rates across the SE margin of the Massif Central are in the 20–120 mm kyr−1 (equivalent to mm/ka in the figures) range, and they positively correlate with slope and precipitation. However, the relationship with the steepness index is complex and supports the importance of taking into account spatial variations in parameters (D50, discharge variability k, runoff) controlling the SPM. Overall, the range of denudation rate across the margin can mainly be explained using a simple version of the SPM accounting for spatially heterogeneous runoff. More complex formulations including stochastic discharge and incision thresholds yield poorer performances unless the spatial variations in bedload characteristics controlling incision thresholds are taken into account. Our results highlight the importance of the hypotheses used for such a threshold in SPM application to field studies and notably the impact of actual constraints on bedload size.

Stochastic in Space and Time: 2. Effects of Simulating Orographic Gradients in Daily Runoff Variability on Bedrock River Incision

“…There are now many studies testing the utility of the STIM (e.g., Campforts et al., 2020; Desormeaux et al., 2022; DiBiase & Whipple, 2011; Forte et al., 2022; Marder & Gallen, 2023; Scherler et al., 2017). However, we believe this paper is the first attempt to modify a longitudinal profile version of STIM to allow for stochastic events in space as well as time, which we refer to as spatial‐STIM.…”

“…However, if erosional thresholds matter, nonlinearity is also linked to the temporal variability of streamflow (Lague, 2014; Lague et al., 2005; Tucker, 2004). As such, there has been increasing interest in examining how such stochastic‐threshold models (stochastic‐threshold incision models (STIM)) of river incision can be applied to empirical relationships between equilibrium channel steepness and long term erosion rates (Campforts et al., 2020; Desormeaux et al., 2022; DiBiase et al., 2010; Forte et al., 2022; Marder & Gallen, 2023; Scherler et al., 2017). Yet there has been less attention given to how orographic gradients in temporal dynamics may similarly alter predictions from simple stream power.…”

Stochastic in Space and Time: Part 1, Characterizing Orographic Gradients in Mean Runoff and Daily Runoff Variability

“…Regardless of how stochastic processes are represented, these early efforts prompted a large number of studies to take a closer look at whether relationships between long-term erosion rates and river morphology can be better explained using stochastic-threshold models of river incision (Campforts et al, 2020;Desormeaux et al, 2022;DiBiase & Whipple, 2011;Forte et al, 2022;Scherler et al, 2017). While success is decidedly mixed, the general outcome of using stochastic-threshold models has been to provide an alternative interpretation to nonlinear relationships between river channel morphology and long-term erosion rates (Harel et al, 2016;Marder & Gallen, 2023).…”

New remote method to systematically extract bedrock channel width of small catchments across large spatial scales using high‐resolution digital elevation models

“…Deriving this reference flow, however, can be challenging at ungauged locations. Previous studies have used satellite‐based measurements of mean annual precipitation (MAP) as a proxy for calculating discharge at ungauged locations (Desormeaux et al, 2022; Rossi et al, 2016). Comparing MAP – calculated by averaging the mean annual precipitation between 1963 and 1995 obtained from the PRISM data set (PRISM Climate Group, 2022) across the respective location's drainage basin – to the MAQ at the known USGS gauging locations reveals that MAP is a good proxy ( r 2 = 0.82) for predicting MAQ in Puerto Rico when assuming a power‐law relationship (Figure 5, Supporting Information Figure S1).…”