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

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.

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

Interpreting catchment-mean erosion rate from in situ produced cosmogenic 10Be concentration in stream sands 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 effect of 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 to calculate the spatial variation in surface skyline shielding, effective mass attenuation length, and the total effective shielding factor for catchments with mean slopes ranging from 0° to 80°. For flat catchments (i.e., uniform elevation of bounding ridgelines), the increase in effective attenuation length as a function of hillslope angle and skyline shielding leads to a catchment-mean total effective shielding factor of one, implying that no topographic shielding factor 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 total effective shielding factor is also one, except for cases of extremely steep range-front catchments, where the shielding correction is counterintuitively greater than one. These results indicate that in most cases, topographic shielding corrections are inappropriate for calculating catchment-mean erosion rates, and only needed for steep catchments with non-uniform distribution of quartz and/or erosion rate. By accounting only 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.

The CAIRN method: automated, reproducible calculation of catchment-averaged denudation rates from cosmogenic nuclide concentrations

We report a new program for calculating catchment-averaged denudation rates from cosmogenic nuclide concentrations. The method (Catchment-Averaged denudatIon Rates from cosmogenic Nuclides: CAIRN) bundles previously reported production scaling and topographic shielding algorithms. In addition, it calculates production and shielding on a pixel-by-pixel basis. We explore the effect of sampling frequency across both azimuth (Δθ) and altitude (Δϕ) angles for topographic shielding and show that in high relief terrain a relatively high sampling frequency is required, with a good balance achieved between accuracy and computational expense at Δθ = 8° and Δϕ = 5°. CAIRN includes both internal and external uncertainty analysis, and is packaged in freely available software in order to facilitate easily reproducible denudation rate estimates. CAIRN calculates denudation rates but also automates catchment averaging of shielding and production, and thus can be used to provide reproducible input parameters for the CRONUS family of online calculators.

The CAIRN method: Automated, reproducible calculation of catchment-averaged denudation rates from cosmogenic radionuclide concentrations

The use of cosmogenic radionuclides to calculate catchment-averaged denudation rates has become a widely adopted technique in the last two decades, yet the methodology varies between studies and is not always reproducible. We report a new program for calculating catchment-averaged denudation rates from cosmogenic radionuclide concentrations. The method (Catchment-Averaged denudatIon Rates from cosmogenic Nuclides: CAIRN) bundles previously reported production scaling and topographic shielding algorithms. In addition, it calculates production and shielding on a pixel-by-pixel basis. We explore the sampling frequency across both azimuth (Δθ) and altitude (Δφ) angles for topographic shielding and show that in high relief terrain a relatively high sampling frequency is required, with a good balance achieved between accuracy and computational expense at Δθ = 8° and Δφ = 5°. The method includes both internal and external uncertainty analysis, and is packaged in freely available software in order to facilitate easily reproducible denudation rate estimates. CAIRN calculates denudation rates but also automates catchment averaging of shielding and production, and thus can be used to provide reproducible input parameters for the CRONUS family of online calculators.

Long-term shoreline retreat rates on Whidbey Island, Washington, USA

Long-term retreat rates of Puget Sound's unconsolidated sediment shorelines have been difficult to quantify, and little systematic research has been completed to constrain retreat in this area. We put forward a new application of cosmogenic 10Be exposure dating to assess long-term shoreline retreat on Whidbey Island, WA by dating lag boulders exposed on the shore platform as the shoreline erodes. Production of 10Be in shoreline boulders is modulated by both tidal submergence and topographic shielding from the retreating bluff. By modeling the combined effect of these variables on 10Be production, the timing of exposure can be determined and used to calculate long-term (103–104 yr) bluff retreat rates. In rare cases, retreat rates are underestimated due to inherited 10Be. Within the study area, average retreat rates ranged between 0 and 8 cm yr− 1. Our results demonstrate the utility of cosmogenic nuclides for determining long-term shoreline retreat rates in areas with thick sediment cover, where large numbers of samples can be collected, and where the pre-depositional history of the boulders is uncomplicated.

Physical and topographic factors as related to short-period wind noise

abstract Median values of seismic noise in the period range of 0.3 to 1.3 sec were obtained from recordings at vaults of the Pole Mountain and WMSO arrays. Interquartile ranges were used to measure dispersions about the medians. Medians of the noise at Pole Mountain ranged from 0.91 mµ to 2.20 mµ in November 1962. The former value was obtained for a vault that was located in dense granite at the base of a massive granite outcrop; the latter value was obtained for a vault in a slab of dense granite located on a grassy plain. This indicated that topographic shielding from wind rather than density of bedrock affected noise. As a test of this idea, wind protection numbers were assigned to vaults Z1 through Z9 of the WMSO array based on comparative topographic shielding with respect to a known wind direction. Noise values increased as wind numbers decreased. Topographic protection and vault construction limited wind noise at WMSO.