On the errors involved in ice-thickness estimates I: ground-penetrating radar measurement errors

Abstract

ABSTRACT. This is the first (Paper I) of three companion papers focused respectively, on the estimates of the errors in ice thickness retrieved from pulsed ground-penetrating radar (GPR) data, on how to estimate the errors at the grid points of an ice-thickness DEM, and on how the latter errors, plus the boundary delineation errors, affect the ice-volume estimates. We here present a comprehensive analysis of the various errors involved in the computation of ice thickness from pulsed GPR data, assuming they have been properly migrated. We split the ice-thickness error into independent components that can be estimated separately. We consider, among others, the effects of the errors in radio-wave velocity and timing. A novel aspect is the estimate of the error in thickness due to the uncertainty in horizontal positioning of the GPR measurements, based on the local thickness gradient. Another novel contribution is the estimate of the horizontal positioning error of the GPR measurements due to the velocity of the GPR system while profiling, and the periods of GPS refreshing and GPR triggering. Their effects are particularly important for airborne profiling. We illustrate our methodology through a case study of Werenskioldbreen, Svalbard.

Subglacial topography, ice thickness, and bathymetry of Kongsfjorden, northwestern Svalbard

“…We used standard analytical error propagation methods (Lapazaran et al, 2016;Taylor, 1996) to calculate the error in subglacial elevation for each data point:…”

“…bandwidth) and the digitization frequency. The range resolution for the data collected in this study was estimated at 8.5 m. We also included the vertical resolution, by taking the inverse of the radar frequency (Lapazaran et al, 2016). This results in values of between 8.5 (thin ice) and 30.5 m (thick ice) with a mean value of 14.3 m and standard deviation of 4.2 m (Fig.…”

“…5a). We 15 calculated the positioning error at each data point depending on the bed slope angle along the profile, following the method by Lapazaran et al (2016). We assumed a helicopter-travel speed of 40 km h (Fig.…”

Application of a two-step approach for mapping ice thickness to various glacier types on Svalbard

“…Therefore, the early icecore information was discarded here because it only gives information at three additional points and because it is not evident how to reliably estimate surface elevation changes since the early 1990s. For WSB, the GPR measurement error was analysed in depth accounting for positioning-related icethickness uncertainty (Lapazaran et al, 2016). Measurement errors fall into a range of 3.3 to 6.8 m with an average value of 4.5 m. These error values ignore a known uncertainty term originating from 2-D data migration (Moran et al, 2000).…”

“…2.2.5 and 2.3.2. First, the Dirichlet conditions on the error on the WSB and THPB thickness measurement δH is set to 5 m (Lapazaran et al, 2016). For VIC, we prescribe 10 and 25 m for the ground and airborne RES data, respectively .…”