Initialization of ice-sheet forecasts viewed as an inverse Robin problem
As simulations of 21st-century climate start to include components with longer timescales,
such as ice sheets, the initial conditions for those components will become critical to the forecast.
This paper describes an algorithm for specifying the initial state of an ice-sheet model, given spatially
continuous observations of the surface elevation, the velocity at the surface and the thickness of the
ice. The algorithm can be viewed as an inverse procedure to solve for the viscosity or the basal drag
coefficient. It applies to incompressible Stokes flow over an impenetrable boundary, and is based upon
techniques used in electric impedance tomography; in particular, the minimization of a type of cost
function proposed by Kohn and Vogelius. The algorithm can be implemented numerically using only the
forward solution of the Stokes equations, with no need to develop a separate adjoint model. The only
requirement placed upon the numerical Stokes solver is that boundary conditions of Dirichlet, Neumann
and Robin types can be implemented. As an illustrative example, the algorithm is applied to shear flow
down an impenetrable inclined plane. A fully three-dimensional test case using a commercially available
solver for the Stokes equations is also presented.