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 in situ-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 in situ 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.

Beryllium extraction was performed at the University of Pennsylvania cosmogenic lab between April and May of 2011. The chemical blank ratio (¹⁰Be/⁹Be) run with this sample was 4x10^-15; 3.4x10³ atoms of ¹⁰Be were added to the samples via the chemical blank. The quartz samples were spiked with 250 ml of a 10^-3 g/g ⁹Be solution from CEREGE, Aix-en-Provence, France before dissolution. An adaption of the Kohl and Nishiizumi (1992) chemical procedure was used for quartz purification and Be extraction. The ratio of cosmogenic to native (carrier) Beryllium was measured via AMS at PRIME Lab at Purdue University during January of 2012.

Six samples were collected from a vertical profile at the channel head to a depth of 2 m. An additional sample was collected at a depth of 5 m below the upland surface by excavating horizontally ~1 m. This sample was considered shielded from spallation production and was used to determine the inherited concentration for the site. Using the CRONUS-Earth calculator (Balco et al., 2008), a production rate for the surface in these locations was found to be 4.1 atoms/g/y including modern topographic shielding. The sediment bulk density is 1.6 g/cm3. 

A series of 5 samples were collected from a 460 m long transect of the southwestern slope of a valley axis. Samples were collected on valley slopes approximately 5 m below the upland surface and from 0.3 m beneath the ground surface. The average production rate in this interval was 3.2 atoms/g/y.

Most samples were approximately 1-2 kg of material. Sample elevations are all 60±10 m.