Emma Jayne Harrison, Brandon McElroy, Jane Willenbring 

Measuring rates of valley head migration and determining the timing of canyon-opening are insightful for the evolution of planetary surfaces. Spatial gradients of in situ-produced cosmogenic nuclide concentrations along horizontal transects provide a framework for assessing the migration of valley networks and similar topographic features. We developed a new derivation for valley head retreat rates from the concentration of in situ produced cosmogenic radionuclides in valley walls. The retreat rate is inversely proportional to the magnitude of the spatial concentration gradient and proportional to local nuclide production rates. By solving for a spatial gradient in concentration along a valley parallel transect, we created an expression for the explicit determination of valley head retreat, which we refer to herein as unzipping. We applied this expression to a seepage-derived drainage network developing along the Apalachicola River, Florida, USA. Sample concentrations along a valley margin transect varied systematically from 2.9x105 atoms/g to 3.5x105 atoms/g resulting in a gradient of 160 atoms/g/m, and from this value a valley head retreat rate of 0.025 m/y was found. The discrepancy between overall network age and current rates of valley head migration suggests intermittent network growth which is consistent with glacial-interglacial precipitation variations during the Pleistocene. This method can be applied to a wide range of Earth-surface environments. For the 10Be system, this method should be sensitive to unzipping rates bounded between 10-6 m/y and 100 m/y.