Calculation of the cosmogenic nuclide production topographic shielding scaling factor for large areas using DEMs

Abstract

The recent surge of applications using terrestrial cosmogenic nuclides (TCNs) to calculate catchment-averaged erosion rates from isotopic concentrations in fluvial sediment, and the prospect of coupling TCN production functions with numerical surface process models (SPMs), necessitate a fast and accurate algorithm for the calculation of topographic shielding. Topographic shielding refers to the proportion of the incoming cosmic radiation that is shielded by the surrounding topography, the scaling factor being defined as the ratio of the unshielded (total minus shielded) to the total (or maximum) cosmic ray flux (i.e. the flux received by a horizontal, unobstructed surface). Topography contributes to the reduction of TCN production by obstructing a certain proportion of the incoming flux and by modifying the angle of incidence. Available algorithms calculate the proportion of obstructed radiation by dividing the horizon as seen by the sample (a grid cell in the case of a DEM), into arc segments (usually of equal length) for which the average obstruction heights expressed as zenith angles are calculated. The use of these methods is feasible only when dealing with a small number of isolated samples, since the identification of obstructions when dealing with an entire area is computationally very intensive. This paper describes a method that uses a relief shadow modelling technique to identify those areas of a DEM that are under shadow (i.e. shielded), and thus to account for the obstructed radiation. This method produces results that are very similar to those obtained using a direct implementation of available methods (maximum difference between results of c. 0·1). The method based on relief shadow modelling is also faster than a direct implementation of any available method and can be readily implemented in any GIS system with raster capabilities.

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

“…We adopt the method of Codilean (2006), in which both the effect of dipping sample surfaces and shielding by topography blocking incoming cosmic rays are computed. The Codilean (2006) method is spatially distributed: each pixel in a digital elevation model (DEM) has its own topographic shielding correction that varies from 0 (completely shielded) to 1 (no topographic shielding). These correction values are calculated by modeling shadows cast upon each pixel in the DEM from every point in the sky.…”

“…These again are spatially distributed and so authors reporting catchmentaveraged denudation rates frequently report averaged shielding values. Although software packages do exist for calculating spatially averaged topographic shielding (e.g., Codilean, 2006) and snow shielding (e.g., Schildgen et al, 2005), results from these models are not integrated with spatially varying production rates. Finally, in landslide dominated terrain, removal of thick layers of sediment can dilute cosmogenic nuclide concentrations in river sediment (Niemi et al, 2005;Yanites et al, 2009;West et al, 2014).…”

Effects of terrain smoothing on topographic shielding correction factors for cosmogenic nuclide‐derived estimates of basin‐averaged denudation rates

“…While this is an attractive theory, we believe that it is too simplistic, and that the calculation of basin-averaged shielding factors is necessary. Basin-averaged shielding factors are calculated from DEMs (Codilean, 2006), digital representations of ground surface topography or terrain. The most common structure for a DEM is a regular array of squares of equal size, and hence equal area.…”

“…This in contrast to the alternative method of using relief-shadow modelling to account for topographic shielding. Codilean (2006) found that both methods produce similar results. An algorithm was developed that calculates the elevation angle for each grid cell within the drainage basin to every other cell of the digital elevation model for each 5° azimuth bin.…”

“…Therefore, an accurate assessment of topographic shielding would include measurement of the angle to the horizon in all directions from every point in the basin. While this poses a prohibitive field problem, it can be solved in a geographical information system (GIS) by determining the inclination to the horizon in all directions from every pixel in a watershed using digital elevation models (DEMs) (Codilean, 2006). In this way, a representative topographic shielding factor can be calculated, and the production rate scaled accordingly.…”