Short communication: Increasing vertical attenuation length of cosmogenic nuclide production on steep slopes negates topographic shielding corrections for catchment erosion rates

Abstract

Abstract. Interpreting catchment-mean erosion rates from in situ produced cosmogenic 10Be concentrations in stream sediments requires calculating the catchment-mean 10Be surface production rate and effective mass attenuation length, both of which can vary locally due to topographic shielding and slope effects. The most common method for calculating topographic shielding accounts only for the reduction of nuclide production rates due to shielding at the surface, leading to catchment-mean corrections of up to 20 % in steep landscapes, and makes the simplifying assumption that the effective mass attenuation length for a given nuclide production mechanism is spatially uniform. Here I evaluate the validity of this assumption using a simplified catchment geometry with mean slopes ranging from 0 to 80∘ to calculate the spatial variation in surface skyline shielding, effective mass attenuation length, and the total effective shielding factor, defined as the ratio of the shielded surface nuclide concentration to that of an unshielded horizontal surface. For flat catchments (i.e., uniform elevation of bounding ridgelines), the effect of increasing vertical attenuation length as a function of hillslope angle and skyline shielding exactly offsets the effect of decreasing surface production rate, indicating that no topographic shielding correction is needed when calculating catchment-mean vertical erosion rates. For dipping catchments (as characterized by a plane fit to the bounding ridgelines), the catchment-mean surface nuclide concentrations are also equal to that of an unshielded horizontal surface, except for cases of extremely steep range-front catchments, where the surface nuclide concentrations are counterintuitively higher than the unshielded case due to added production from oblique cosmic ray paths at depth. These results indicate that in most cases topographic shielding corrections are inappropriate for calculating catchment-mean erosion rates, and are only needed for steep catchments with nonuniform distributions of quartz and/or erosion rate. By only accounting for shielding of surface production, existing shielding approaches introduce a slope-dependent systematic error that could lead to spurious interpretations of relationships between topography and erosion rate.

OCTOPUS: an open cosmogenic isotope and luminescence database

“…Cosmogenic nuclide exposure dating is based on the study of rare isotopes produced by high-energy cosmic radiation breaking up the atoms that make up the minerals and rocks at the Earth's surface. The term "in situ" is used to distinguish these isotopes from those that are produced through the same cosmic-ray-induced nuclear reactions in the atmosphere -termed "meteoric" (Dunai, 2010;Granger et al, 2013). Several of the in situ cosmogenic nuclides, including the stable 3 He and 21 Ne, and the radioactive 10 Be, 26 Al, and 36 Cl, are now routinely measured and have been used in geomorphological studies for the last three decades (Bierman and Nichols, 2004;von Blanckenburg, 2005;Dunai, 2010;Granger and Schaller, 2014).…”

“…The term "in situ" is used to distinguish these isotopes from those that are produced through the same cosmic-ray-induced nuclear reactions in the atmosphere -termed "meteoric" (Dunai, 2010;Granger et al, 2013). Several of the in situ cosmogenic nuclides, including the stable 3 He and 21 Ne, and the radioactive 10 Be, 26 Al, and 36 Cl, are now routinely measured and have been used in geomorphological studies for the last three decades (Bierman and Nichols, 2004;von Blanckenburg, 2005;Dunai, 2010;Granger and Schaller, 2014). Of these nuclides, however, 10 Be produced in quartz is the workhorse for in situ applications, and most in situ cosmogenic nuclide studies have used 10 Be either alone or in conjunction with other cosmogenic nuclides such as 26 Al and 21 Ne.…”

Growing topography due to contrasting rock types in a tectonically dead landscape

“…More sophisticated versions of the stream power model may explicitly account for different controls in K (e.g. DiBiase and Whipple, 2011;Campforts et al, 2020;Zondervan et al, 2020b), yet such an approach requires specific data of an adequate resolution, such as river hydraulic geometry, rock strength measurements, and hydrological data to resolve spatial and temporal runoff variability, which are not readily available.…”

Escarpment retreat rates derived from detrital cosmogenic nuclide concentrations

“…Cosmic ray shielding generally reduces surface production rate ' ( , ) but extends the free path attenuation length by the change of irradiation geometry (Dunne et al, 1999). DiBiase ( 2018) evaluated the counter-effects of shielding on catchment-wide production rate (via spallation) and attenuation length, although he found that the combined shielding effect on surface production rate (via spallation) and free path attenuation length is negligible when the valley surface slope is less than 30 degrees (DiBiase, 2018). In general, shielding calculations for detrital CRN data are not very important as most shielding is local, i.e.…”