Formation of evenly spaced ridges and valleys

Abstract

One of the most striking examples of self-organization in landscapes is the emergence of evenly spaced ridges and valleys. Despite the prevalence of uniform valley spacing, no theory has been shown to predict this fundamental topographic wavelength. Models of long-term landscape evolution can produce landforms that look realistic, but few metrics exist to assess the similarity between models and natural landscapes. Here we show that the ridge-valley wavelength can be predicted from erosional mechanics. From equations of mass conservation and sediment transport, we derive a characteristic length scale at which the timescales for erosion by diffusive soil creep and advective stream incision are equal. This length scale is directly proportional to the valley spacing that emerges in a numerical model of landform evolution, and to the measured valley spacing at five field sites. Our results provide a quantitative explanation for one of the most widely observed characteristics of landscapes. They also imply that valley spacing is a fundamental topographic signature that records how material properties and climate regulate erosional processes.