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

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.