Interpreting catchment-mean erosion rates from in situ
produced cosmogenic

Measurement of in situ produced cosmogenic

In contrast to point measurements, where a clear framework exists for
converting

The pixel-by-pixel skyline-shielding algorithm of Codilean (2006) results in
the largest topographic shielding corrections, and has gained popularity due
to its ease of implementation in the software packages TopoToolbox
(Schwanghart and Scherler, 2014) and CAIRN (Mudd et al., 2016), the latter
of which was used to recalculate published

Here I model the shielding of incoming cosmic radiation flux responsible for spallogenic production at both the surface and at depth for a simple catchment geometry to evaluate, as a function of catchment slope and relief, the total effect of topographic shielding on surface nuclide concentrations and the partitioning of shielding into surface skyline shielding and changes to the effective mass attenuation length. I then apply this framework to catchments that have a net dip (i.e., dipping plane fit to boundary ridgelines) and compare calculations of total shielding to those from typical pixel-by-pixel skyline-shielding corrections.

The incoming cosmic ray intensity,

For a horizontal surface sample (

Equation (3) has two implications for interpreting exposure ages or erosion
rates from cosmogenic nuclide concentrations of samples partially shielded
by skyline topography (

The importance of accounting for both changes in surface production rate,

For stream sediment samples that require calculating cosmogenic nuclide
production rates across an entire catchment, solving Eq. (3) as a function
of depth is presently too computationally intensive to be practical.
Consequently, numerical implementations of topographic shielding
calculations at the catchment scale make the simplifying assumption that

Throughout the analysis below, both the effective mass attenuation length,

Model catchment setup, showing

Dipping catchment shielding geometry, illustrated using
example from the San Gabriel Mountains, California, USA. Image is centered
on 34.20

Catchment geometry is simplified as an infinitely long v-shaped valley with
width

Total shielding factor,

After applying Eq. (6) to a hillslope, it is straightforward to calculate
the surface skyline-shielding component,

Although spallogenic production of cosmogenic nuclides following Eq. (1) is
well-described by an exponential decrease with depth for horizontal
unshielded surfaces, this is not true in general for shielded samples (Dunne
et al., 1999). The effective vertical mass attenuation length,

Plots of

Plot of normalized production rate relative to horizontal
unshielded surface as a function of normalized vertical depth for a
60

Although the above framework accounts for variations in catchment relief and
hillslope angle,

Plots showing mean total shielding factor,

For the catchment geometry shown in Fig. 1, the local shielding factor,

The normalized effective attenuation length,

The combined effect of the decrease in surface production (Fig. 4a) and the
increase in effective attenuation length (Fig. 4b) leads to a pattern
whereby the total effective shielding factor,

For the case of dipping catchments (Fig. 2), the sensitivity of the mean
effective shielding parameter to catchment dip,

For the two example catchments in the San Gabriel Mountains (Fig. 2), the
mean total effective shielding factor,

The above results indicate that no correction factor for topographic
shielding is needed to infer catchment-mean erosion rates from

For catchments with spatially variable quartz content or erosion rate, a
spatially distributed total effective shielding factor,

The modeling approach above assumes a simplified angular distribution of
cosmic radiation flux (Eq. 1) and only accounts for cosmogenic nuclide
production via spallation. In actuality, the cosmic radiation flux does not
go to zero at the horizon, and becomes increasingly collimated (higher

Overall, the effect of topographic shielding corrections on interpreting
catchment erosion rates is small compared to typical assumptions inherent to
detrital cosmogenic nuclide methods. In particular, the assumption of steady
lowering is likely to be increasingly inappropriate for rapidly eroding
landscapes characterized by a significant contribution of muonogenic
production or slowly eroding landscapes where

The simplified model presented here for catchment-scale topographic shielding of incoming cosmic radiation highlights the two competing effects of slope and skyline shielding. As catchment relief increases, surface production rates are reduced due to increased skyline shielding. However, for shielded samples radiation is increasingly collimated, and for sloped surfaces oblique radiation pathways increase nuclide production at depth. Both of these effects lead to deeper effective vertical mass attenuation lengths, which offset the reduction in surface production when inferring erosion rates from cosmogenic nuclide concentrations. At the catchment scale, the mean total effective shielding factor is 1 for a large range of catchment geometries, suggesting that topographic shielding corrections for catchment samples are generally not needed, and that applying commonly used topographic shielding algorithms leads to underestimation of true erosion rates by up to 20 %. Although these corrections are typically small compared to other methodological uncertainties, they vary systematically with slope and relief. Consequently, misapplication of shielding correction factors could influence interpretations of relationships between topography and erosion rate.

MATLAB codes used to generate Figs. 3, 4,
and 6 are included as Supplement and available at:

The supplement related to this article is available online at:

The author declares that there is no conflict of interest.

This project was supported by funding from National Science Foundation grant EAR-160814, and benefited from discussions with Kelin Whipple, Alexander Neely, Paul Bierman. Review comments from Greg Balco, Dirk Scherler, and an anonymous reviewer helped improve the manuscript. Edited by: Jane Willenbring Reviewed by: Greg Balco and one anonymous referee