Analytical long-profile models of fluvial incision are fundamental in geomorphology, however, analogous models are missing for glaciers, despite the fact that glaciers are an important and widespread agent of physical erosion. We introduce a new analytical solution for coupled glacial-fluvial networks under steady-state climate and uplift. We then integrate this solution into a critical wedge orogen theory to explore the effect of glaciation on the balance between climate, erosion and orogen geometry. We find that the relief is closely tied to the equilibrium line altitude (ELA) and that the geometry and average uplift rate can respond significantly more sensitively to changes in climate than critical wedge orogens dominated by fluvial erosion. Using this observation, we suggest that the global lower ELA during glacial maximums over the last few millions years could trigger narrowing of critical orogens, with an associated increase in uplift rates within the active orogen core.

Sediment transport in rivers near the threshold of grain motion is characterized by rare but large transport events. This intermittency makes it difficult to relate average sediment flux to average flow conditions, or to define an unambiguous threshold for grain entrainment. Although intermittent sediment transport can be observed and characterized, its origins are unclear. In this study we investigate bedload sediment transport near the threshold of grain motion in an experimental flume to examine the origins of intermittency. We apply image-processing techniques to high-speed video of grains in a narrow flume, which allows us to track individual particles and measure statistics of particle motion. Bedload sediment transport near the threshold of grain motion is very low, allowing us to approximate the time evolution of the sediment flux via a polynomial expansion, including a linear growth rate and a nonlinear term which saturates the growth. We introduce a noisy coefficient to the linear growth rate term (“multiplicative noise”), rather than adding the noise to the equation, to model the inherent fluctuations in the system. We demonstrate that multiplicative noise near the threshold of grain motion can account for the observed intermittency. We use analytical results from bifurcation theory in the presence of multiplicative noise to analyze our experimental results, quantifying the noise responsible for the intermittency and calculating the critical shear stress for grain entrainment in a novel way that is consistent with the physics of grain motion at low transport stages.