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

The basal topography is largely unknown beneath most glaciers and ice caps, and many attempts have been made to estimate a thickness field from other more accessible information at the surface. Here, we present a two-step reconstruction approach for ice thickness that solves mass conservation over single or several connected drainage basins. The approach is applied to a variety of test geometries with abundant thickness measurements including marine- and land-terminating glaciers as well as a 2400-km2 ice cap on Svalbard. The input requirements are kept to a minimum for the first step. In this step, a geometrically controlled, non-local flux solution is converted into thickness values relying on the shallow ice approximation (SIA). In a second step, the thickness field is updated along fast-flowing glacier trunks on the basis of velocity observations. Both steps account for available thickness measurements. Each thickness field is presented together with an error-estimate map based on a formal propagation of input uncertainties. These error estimates point out that the thickness field is least constrained near ice divides or in other stagnant areas. Withholding a share of the thickness measurements, error estimates tend to overestimate mismatch values in a median sense. We also have to accept an aggregate uncertainty of at least 25-% in the reconstructed thickness field for glaciers with very sparse or no observations. For Vestfonna ice cap (VIC), a previous ice volume estimate based on the same measurement record as used here has to be corrected upward by 22-%. We also find that a 13-% area fraction of the ice cap is in fact grounded below sea level. The former 5-% estimate from a direct measurement interpolation exceeds an aggregate maximum range of 6-23-% as inferred from the error estimates here.This study received primary funding from the German Research Foundation (DFG) under grant number FU1032/1-1. Results presented in this publication are based on numerical simulations conducted at the high-performance computing centre of the Regionales Rechenzentrum Erlangen (RRZE) of the University of Erlangen-Nuremberg. The reconstruction approach also benefits from co-development work of the Elmer/Ice team at the CSC-IT Center for Science Ltd. (Finland). The velocity analysis on Svalbard was funded by DFG within the priority programme 1158 Antarctic Research with Comparable Investigations in Arctic Sea Ice Areas under contract number BR2105/9-1 and received financial support from the Helmholtz Association of the German Research Centres (HGF) Alliance on Remote Sensing and Earth System Dynamics. Thickness data collection in Wedel Jarlsberg Land was funded by the Spanish R&D projects C11093001 and C150954001, NCBiR/PolarCLIMATE-2009/2-2/2010 from the Polish National Centre for R&D, by IPY/269/2006 from the Polish Ministry of Science and Higher Education, by Polish-Norwegian funding through the AWAKE (PNRF-22-AI-1/07) project, by the EU FP7 ice2sea programme (grant number 226375) and by funds of the Leading National Research Centre (KNOW) received by the Centre for Polar Studies of the University of Silesia, Poland. The DEM generation inWedel Jarlsberg Land received financial support from the European Research Council (grant 320816) and from ESA (project Glaciers CCI, 4000109873/14/I-NB). TanDEM-X data were provided under AO XTIGLAC6770. The WRF-SMB field was produced within the PERMANOR project funded by the Norwegian Research Council (255331)