Inversion of basal boundary conditions for a thermomechanically coupled nonlinear Stokes ice sheet model

Modeling the dynamics of polar ice sheets is critical for projections of future sea level rise. Yet, there remain large uncertainties in the boundary conditions at the base of the ice sheet. Thus, we target the inversion for basal boundary conditions and the basal geothermal heat flux using surface velocity measurements. The flow of ice sheets and glaciers is modeled as a sheer thinning, viscous incompressible fluid with temperature-dependent viscosity via a thermomechanically coupled Stokes model. The inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that contains the misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well-posed and account for observational and model errors. We use an infinite-dimensional adjoint-based inexact Newton method for the solution of this least squares optimization problem. Results for a three-dimensional model problem demonstrate the ability of inverting for a smoothly varying basal sliding coefficient and geothermal heat flux. This capability will be incorporated into a state-of-the-art continental-scale ice sheet dynamics model.