Formation of evenly spaced ridges and valleys

Abstract

Seen from above, it's clear that in many hilly landscapes the ridges and valleys appear uniformly spaced. Current physically based models of landscape evolution produce realistic looking topography, but cannot predict the 'wavelength' typical of evenly spaced ridges and valleys in natural landscapes. Taylor Perron and colleagues use equations of mass conservation and sediment transport to derive a characteristic length scale that is directly proportional to the ridge–valley wavelength in models of landform evolution and at five field study sites across the United States, including Nappa Valley in California and Point of the Mountain in Utah. The findings provide a quantitative explanation for one of the most widely observed characteristics of landscapes and suggest that valley spacing records the effects of material properties and climate on erosional processes. Ridges and valleys in many landscapes are uniformly spaced, but no theory has predicted this fundamental topographic wavelength. A characteristic length scale is now derived from equations of mass conservation and sediment transport; it is found to be directly proportional to the valley spacing in models of landform evolution, and to the measured valley spacing at five study sites in the USA. One of the most striking examples of self-organization in landscapes is the emergence of evenly spaced ridges and valleys1,2,3,4,5,6. 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 realistic7,8,9, 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. The findings also imply that valley spacing is a fundamental topographic signature that records how material properties and climate regulate erosional processes.