Sediment load determines the shape of rivers.

Understanding how rivers adjust to the sediment load they carry is critical to predicting the evolution of landscapes. Presently, however, no physically based model reliably captures the dependence of basic river properties, such as its shape or slope, on the discharge of sediment, even in the simple case of laboratory rivers. Here, we show how the balance between fluid stress and gravity acting on the sediment grains, along with cross-stream diffusion of sediment, determines the shape and sediment flux profile of laminar laboratory rivers that carry sediment as bedload. Using this model, which reliably reproduces the experiments without any tuning, we confirm the hypothesis, originally proposed by Parker [G. Parker, J. Fluid Mech 89, 127-146 (1978)], that rivers are restricted to exist close to the threshold of sediment motion (within about 20%). This limit is set by the fluid-sediment interaction and is independent of the water and sediment load carried by the river. Thus, as the total sediment discharge increases, the intensity of sediment flux (sediment discharge per unit width) in a river saturates, and the river can transport more sediment only by widening. In this large discharge regime, the cross-stream diffusion of momentum in the flow permits sediment transport. Conversely, in the weak transport regime, the transported sediment concentrates around the river center without significantly altering the river shape. If this theory holds for natural rivers, the aspect ratio of a river could become a proxy for sediment discharge-a quantity notoriously difficult to measure in the field.

Simple Rules Govern the Patterns of Arctic Sea Ice Melt Ponds.

Climate change, amplified in the far north, has led to rapid sea ice decline in recent years. In the summer, melt ponds form on the surface of Arctic sea ice, significantly lowering the ice reflectivity (albedo) and thereby accelerating ice melt. Pond geometry controls the details of this crucial feedback; however, a reliable model of pond geometry does not currently exist. Here we show that a simple model of voids surrounding randomly sized and placed overlapping circles reproduces the essential features of pond patterns. The only two model parameters, characteristic circle radius and coverage fraction, are chosen by comparing, between the model and the aerial photographs of the ponds, two correlation functions which determine the typical pond size and their connectedness. Using these parameters, the void model robustly reproduces the ponds' area-perimeter and area-abundance relationships over more than 6 orders of magnitude. By analyzing the correlation functions of ponds on several dates, we also find that the pond scale and the connectedness are surprisingly constant across different years and ice types. Moreover, we find that ponds resemble percolation clusters near the percolation threshold. These results demonstrate that the geometry and abundance of Arctic melt ponds can be simply described, which can be exploited in future models of Arctic melt ponds that would improve predictions of the response of sea ice to Arctic warming.