10Be concentrations constraining surface age and valley growth rate in a seepage-derived drainage network in the Apalachicola River basin, Florida

<p class="Head1"><span><span>Measuring rates of valley head migration and determining the timing of canyon-opening are insightful quantifications for the history and evolution of planetary surfaces.  Horizontal spatial gradients of <em>in situ-</em>produced cosmogenic nuclide concentrations provide a framework for assessing the migration of these and similar topographic features. We developed a theoretical model for the concentration of <em>in situ</em> produced cosmogenic radionuclides in valley walls during retreat of a valley head. The retreat rate is inversely proportional to the magnitude of the spatial concentration gradient and proportional to local nuclide accumulation 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, termed unzipping.  We applied this theory to a developing seepage-derived drainage network along the Apalachicola River, Florida, USA.  Sample concentrations along a valley margin transect vary systematically from 2.9 x 10⁵ atoms/g to 3.5 x 10⁵ 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 is 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.</span></span></p>