Interpreting erosion rates from cosmogenic radionuclide concentrations measured in rapidly eroding terrain

A combination of numerical analysis and ¹⁰Be concentrations measured in sediment samples from the high-relief Torrente catchment, southern Spain, allows us to investigate the sampling requirements for determining erosion rates using cosmogenic nuclides in high-relief, landslide-dominated terrain. We use simple modelling to quantify the effect of particle spalling and/or landsliding on erosion rates determined using a cosmogenic in-situ produced isotope. Analytical results show that the cosmogenic nuclide concentration of a surface experiencing regular detachment of a grain or block may be considered to be in steady state, and 'in-situ' erosion rates estimated, when an appropriate number of spatially independent samples are amalgamated. We present equations that enable calculation of the number of bedrock samples that must be amalgamated for the estimation of mean erosion rates on an outcrop experiencing regular detachment of a grain or chip of thickness L every T years. Our findings confirm that mean catchment erosion rates may be reliably estimated from ¹⁰Be concentrations in fluvial sediment in high-relief rapidly eroding terrain. These catchment-wide integrated erosion rates can be calculated where erosion is primarily accomplished through shallow (<3 m) spalling processes; where deep-seated (>3 m) landslides are the dominant mode of erosion only minimum erosion rates can be determined. Lastly, we present erosion rate measurements from the Torrente catchment that reveal variation of two orders of magnitude (0-03-1-6 m ka^-1) quantifying the high degree of spatial variation in erosion rates expected within rapidly uplifting catchments.