Jesse V. Johnson
Department of Computer Science
University of Montana
Missoula, Montana, USA
The velocity of ice flow can be measured using interferometric techniques
on satellite images. Such data have proven remarkably useful for critical
investigations of the mass balance of ice sheets, ice sheet response to
perturbation, and as a constraint on ice sheet models. When used for mass
balance, an area is defined at the mouths of major outlet glaciers and the
velocity times that area provides the flux of ice moving into the ocean.
Measurements of this sort produce the lowest uncertainty we currently have
on the mass balance of Antarctica and Greenland. Time series of surface
velocity measurements reveal that changes in the position of the calving
front and seasonal surface melting are strongly correlated with increases
in the surface velocity. These correlations, in turn, allow investigators
to form hypotheses on the key mechanisms responsible for ice dynamical
changes. Used as a constraint for ice sheet models, model output is
brought into agreement with surface velocity observation, often using
adjoint based assimilation methods. The agreement between model and
observation is achieved through manipulation of the basal traction field,
an unknown of considerable interest because it reveals something about the
interaction between ice, rock, sediment, and basally generated melt water.
Given the high importance of these data, it is critical that they be
presented in the best way possible. However, as they now exist, there are
numerous visible artifacts and large gaps in the coverage. The artifacts
arise from different tracks being followed by satellites, and slightly
different processing occurring within each track. Sharp discontinuities
appear between the tracks. Gaps in the data emerge in regions of high snow
accumulation or high surface slope, where interferometric analysis
struggles to lock on key features for comparison. The problems in the data
are most critical to the model assimilation work, where surface artifacts
produce artifacts in basal traction.
Here, I present an optimization technique which preserves the essential nature of the data while smoothing over artifacts and filling in gaps in the coverage. The technique involves solving the differential form of the continuity equation for ice to determine the ice speed. Placed in an adjoint framework for optimization, I minimize the differences between computed and observed speeds by using the snowfall driven accumulation of ice as a control variable. Observed ice flow directions are assumed to be correct, and the guessed to be downhill in regions where there are no observations. The results are 1) within the stated uncertainties of the velocity observations, 2) continuous over the entire domain, 3) consistent with the conservation of mass, and 4) providing reasonable estimates of the velocity in regions of no coverage. They should be of assistance to all those involved with the interpretation of interferometrically derived surface velocity data. The values of the control variable, accumulation, are also instructive, as they reveal inaccuracies in other data used, in particular the thickness of ice.