Separation of the geodetic consequences of past and present ice-mass change: influence of topography with application to Svalbard (Norway)

Polar regions such as Greenland, Svalbard and Antarctica are deforming today because of both the present-day ice-mass (PDIM) change of glaciers and the glacial isostatic adjustment (GIA) following the Pleistocene deglaciation. Observations handled in these areas contain both the contributions from the PDIM change and GIA. This study aims at separating them by considering two specific gravity variation-to-vertical displacement ratios. We first review the case of the viscoelastic rebound (GIA) subsequent to the Pleistocene deglaciation leading to a ratio C^v. The outcome of previous studies is that C^v is approximately equal to −0.15 μGal/mm and almost independent of the deglaciation history, ice geometry and viscosity profile of the mantle. Similarly we consider the elastic deformation resulting from PDIM change which leads to a second ratio C^e,N. Several studies have shown that C^e,N ≈ −0.26μGal/mm if one assumes that the changing glaciers are thin layers over the surface of a spherical Earth model. In this case, we show that the separation between the contributions from PDIM change and GIA is unique if both gravity and height changes observations are available at the same station. Next, we focus on C^e,N and show that according to the deglaciation/glaciation context and from colocated gravity variation and ground vertical velocity measurements one can deduce a range of possible values for C^e,N. Studying the influence of the topography on C^e,N we first show that it tends to positive values if most of surrounding ice-mass changes above the altitude of the observation site and to values lower than −0.26 μGal/mm if changes are below. We next apply our general formalism to the case of the past and PDIM changes in Svalbard, Norway. We compute the ratio C^e,N at the geodetic observatory at Ny-Ålesund and show the influence of the topography of the surrounding glaciers on the measured gravity and uplift rates. We show that if the ice-mass change is spatially uniform, C^e,N does not depend on the speed of ice-mass change, and hence the separation of the contributions from PDIM changes and GIA can still be done univocally. However, if the ice-mass change is not spatially uniform, C^e,N depends on both the speed of ice-mass change and the volume of ice-change rate.