Stochastic Variations in Transport Capacity and its Role in 'Long- Runout' Gravel Progradation in Alluvial Basins

Sediment transport in gravel-bed rivers requires a critical shear stress. Several recent studies have used the critical shear stress criterion, together with measurements of median grain size and channel depth in ancient fluvial deposits, to infer the paleoslopes of alluvial basins in the western United States. In some applications of this method, inferred paleoslopes are sufficiently large that tectonic tilting must be invoked in order for the sediments to have been transported to their present locations. In this paper, we evaluate the robustness of the paleoslope-estimation method within the context of a coupled numerical model for the postorogenic topographic decay of a mountain belt coupled to a coarse-grained foreland sedimentary basin. In the model, critical slopes for entrainment are varied stochastically in time (to represent fluctuations in flow depth and local deviations from an equilibrium channel geometry) with a lognormal distribution characterized by a constant mean and variance equal to the values measured in a large dataset of gravel bed rivers in North America. The model shows that when critical slope values vary stochastically, foreland basin sediments can persistently prograde at slopes far below the minimum value predicted by paleoslope-estimation theory. As such, the model suggests that coarse-grained 'long-runout' gravels do not necessarily require steep slopes to form, especially in hydroclimatic regions characterized by flashy discharges, climatic changes, local deviations from channel equilibrium, and in cases when deposition occurs over long spans of geologic time. The model also suggests that postorogenic topographic decay is characterized by three distinct phases: an initial phase characterized by knickpoint retreat in the mountain belt and proximal deposition in the adjacent foreland basin (lasting ~5 Myr), a second phase in which erosion and deposition balance to maintain a constant basin aspect ratio (~5 to 10 Myr) and a third phase of gradual isostatic rebound of the mountain belt and adjacent basin, reworking of sediments from the proximal to the distal foreland basin, and basin thinning by episodic transport (~10 to 100 Myr). This sequence adds further refinement to the classic two-stage model of gravel progradation in foreland basins.