Numerical studies of ice flow over subglacial geothermal heat sources at Grímsvötn, Iceland, using Full Stokes equations

The importance of studying geothermal heat sources under glaciers lies in: (1) the potential for jökulhlaups from such sites; (2) the potential for enhanced sliding of ice masses caused by meltwater lubrication of the ice-bedrock interface; and (3) the potential to gain a deeper understanding of the interaction between the geothermal system and the overlying ice. We study the temporal evolution of an elongated depression on the eastern side of the geothermally active Grimsvötn caldera through numerical 2-dimensional forward modeling, solving the full Stokes equation. The 100-150 m deep depression formed gradually between 1998 and 2004. The model results show that heat flux estimates based on depression volume are strongly dependent on the value of the rate factor A in Glen's flow law. If flow of ice into the depression is not taken into account, heat flux underestimates of 15-75% occur, corresponding to rate factors of 10-68 × 10^-16 s^-1 kPa^-3. The estimated heat flux at the study site was 260-390 W m^-2, with the best estimate being 280 W m^-2, obtained from the best estimate of A = 23 × 10^-16 s^-1 kPa^-3. The total power of the modeled site was 250-300 MW, about one tenth of the total heat output of Grimsvötn. This heat flux is of comparable magnitude to that of other powerful subglacial geothermal areas. Finally, as the maximum modeled strain rates (1 × 10^-7 s^-1) are within the range of the applicability of Glen's flow law, this suggests that the full Stokes approach should be valid for the study of many subglacial geothermal areas.