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One of the most striking examples of self-organization in landscapes is the emergence of evenly spaced ridges and valleys (1-6). 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 realistic (7-9), 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 time-scales 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., The spacing between adjacent ridges and valleys is a fundamental dimension of hilly topography (1-6). Even a casual observer can see from an aeroplane window that ridges and valleys in [...]

Author(s): William E. Dietrich (corresponding author) [1]; J. Taylor Perron [1] Do biota affect landscape form and evolution? One way to think about this question is to imagine a very [...]