Velocity estimation of glaciers with physically-based spatial regularization - Experiments using satellite SAR intensity images

Glaciers are an important climate indicator due to their sensitive dependence upon local and regional climate variables, which makes them worthwhile research subjects. A comprehensive description of the glaciers' interaction with the environment and their dynamical behavior requires complex physical models and the measurement of relevant parameters. In-situ data acquisitions are costly and often spatially sparse due to the large extent of glaciers; however, satellite-based sensors offer timely data with complete ground coverage, making them a good choice for continuous monitoring of glaciers. Synthetic aperture radar (SAR) allows a nearly weather-independent monitoring of glacier motion, which is beneficial for often cloudy regions like Alaska or Patagonia. This paper presents a new workflow for the automatic extraction of glacier surfaces from SAR intensity images and the determination of their velocities involving a fluid mechanics model. An initial motion estimation is obtained from intensity tracking on SAR image pairs and subsequently corrected by a physics-based spatial regularization. The surface velocity is approximated by the two-dimensional Navier-Stokes equation for incompressible fluids. The regularization is formulated as a data assimilation problem in which the final solution is a proper solution of the Navier-Stokes equation and simultaneously fitted to the observed velocity. This partial differential equation (PDE) constrained optimization is solved with adjoint models using finite element methods. The proposed method is evaluated on the Taku Glacier, AK, an outlet glacier of the Juneau Icefield. Our presented approach is independent from the type of sensor as long as initial velocity estimates can be obtained. The final results can be used as input to methods estimating ice volume and thickness.