The stream power law model has been widely used to represent erosion by rivers but does not take into account the role played by sediment in modulating erosion and deposition rates. Davy and Lague (2009, https://doi.org/10.1029/2008JF001146) provide an approach to address this issue, but it is computationally demanding because the local balance between erosion and deposition depends on sediment flux resulting from net upstream erosion. Here, we propose an efficient (i.e., O(N) and implicit) method to solve their equation. This means that, unlike other methods used to study the complete dynamics of fluvial systems (e.g., including the transition from detachment‐limited to transport‐limited behavior), our method is unconditionally stable even when large time steps are used. We demonstrate its applicability by performing a range of simulations based on a simple setup composed of an uplifting region adjacent to a stable foreland basin. As uplift and erosion progress, the mean elevations of the uplifting relief and the foreland increase, together with the average slope in the foreland. Sediments aggrade in the foreland and prograde to reach the base level where sediments are allowed to leave the system. We show how the topography of the uplifting relief and the stratigraphy of the foreland basin are controlled by the efficiency of river erosion and the efficiency of sediment transport by rivers. We observe the formation of a steady‐state geometry in the uplifting region, and a dynamic steady state (i.e., autocyclic aggradation and incision) in the foreland, with aggradation and incision thicknesses up to tens of meters.

The evolution of a fluvial landscape is a balance between tectonic uplift, fluvial erosion, and sediment deposition. The erosion term can be expressed according to the stream power model, stating that fluvial incision is proportional to powers of river slope and discharge. The deposition term can be expressed as proportional to the sediment flux divided by a transport length. This length can be defined as the water flux times a scaling factor ζ. This factor exerts a major control on the river dynamics, on the spacing between sedimentary bedforms, or on the overall landscape erosional behavior. Yet, this factor is difficult to measure either in the lab or in the field. Here, we propose a new formulation for the deposition term based on a dimensionless coefficient, G, which can be estimated at the scale of a landscape from the slopes of rivers at the transition between a catchment and its fan. We estimate this deposition coefficient from 29 experimental catchment–alluvial fan systems and 68 natural examples. Based on our data set, we support the idea of Davy and Lague (2009) that G is a relevant parameter to characterize the erosional and transport mode of a fluvial landscape, which can be field calibrated, with a continuum from detachment-limited (G = 0) to transport-limited behavior (G >0.4 from the studied examples).

Among the most urgent challenges in future climate change scenarios is accurately predicting the magnitude to which precipitation extremes will intensify. Analogous changes have been reported for an episode of millennial-scale 5 °C warming, termed the Palaeocene-Eocene Thermal Maximum (PETM; 56 Ma), providing independent constraints on hydrological response to global warming. However, quantifying hydrologic extremes during geologic global warming analogs has proven difficult. Here we show that water discharge increased by at least 1.35 and potentially up to 14 times during the early phase of the PETM in northern Spain. We base these estimates on analyses of channel dimensions, sediment grain size, and palaeochannel gradients across the early PETM, which is regionally marked by an abrupt transition from overbank palaeosol deposits to conglomeratic fluvial sequences. We infer that extreme floods and channel mobility quickly denuded surrounding soil-mantled landscapes, plausibly enhanced by regional vegetation decline, and exported enormous quantities of terrigenous material towards the ocean. These results support hypotheses that extreme rainfall events and associated risks of flooding increase with global warming at similar, but potentially at much higher, magnitudes than currently predicted.

The grain-scale morphology and size distribution of sediments are important factors controlling the erosion efficiency, sediment transport and the aquatic ecosystem quality. In turn, characterizing the spatial evolution of grain size and shape can help understand the dynamics of erosion and sediment transport in coastal, hillslope and fluvial environments. However, the size distribution of sediments is generally assessed using insufficiently representative field measurements, and determining the grain-scale shape of sediments remains a real challenge in geomorphology. Here we determine the size distribution and grain-scale shape of sediments located in coastal and river environments with a new methodology based on the segmentation and geometric fitting of 3D point clouds. Point cloud segmentation of individual grains is performed using a watershed algorithm applied here to 3D point clouds. Once the grains are segmented into several sub-clouds, each grain-scale morphology is determined by fitting a 3D geometrical model applied to each sub-cloud. If different geometrical models can be tested, this study focuses mostly on ellipsoids to describe the geometry of grains. G3Point is a semi-automatic approach that requires a trial-and-error approach to determine the best combination of parameter values. Validation of the results is performed either by comparing the obtained size distribution to independent measurements (e.g., hand measurements) or by visually inspecting the quality of the segmented grains. The main benefits of this semi-automatic and non-destructive method are that it provides access to (1) an un-biased estimate of surface grain-size distribution on a large range of scales, from centimeters to meters; (2) a very large number of data, mostly limited by the number of grains in the point cloud data set; (3) the 3D morphology of grains, in turn allowing the development of new metrics that characterize the size and shape of grains; and (4) the in situ orientation and organization of grains. The main limit of this method is that it is only able to detect grains with a characteristic size significantly greater than the resolution of the point cloud.