A Least Squares Collocation Method for Modeling Ice, Water and Sediment Transport

We present a new least squares collocation method for computational simulation of ice related flow processes on a three dimensional topographic surface. The collocation approach is predicated on 1) irregular, cell-based discretization of the topographic surface, 2) local second-order polynomial approximation of the bed topography and ice surface, and 3) Runge-Kutta time marching. The ice flow is simulated in 2D planform using a second- order shallow-ice approximation (SOSIA). Hence, higher order asymptotics, including contributions from longitudinal stress gradients and ice surface curvatures, are addressed. The collocation approach leads to a general and highly parallel algorithm based on discrete cell interactions, which is well suited for simulating also other types of surface flow processes, such as fluvial and hillslope related sediment transport. The inherent benefit of the method thus relates primarily to the ease with which several types of earth surface processes may be simulated simultaneously. Using this new integrated modeling platform, it is our objective to study landform generation by simulating glacial and fluvio-glacial erosion, sediment transport, and deposition. The dynamics of the ice and of the processes acting under glaciers must to some degree be manifested by the landforms produced by glaciers, and we wish to test quantitatively the potential of established sub-glacial dynamical relations for explaining well known large scale glacial landforms such as U-shaped valleys and cirques.