Error sources in basal yield stress inversions for Jakobshavn Isbræ, Greenland, derived from residual patterns of misfit to observations

ABSTRACTThe basal interface of glaciers is generally not directly observable. Geophysical inverse methods are therefore used to infer basal parameters from surface observations. Such methods can also provide information about potential inadequacies of the forward model. Ideally an inverse problem can be regularized so that the differences between modeled and observed surface velocities reflect observational errors. However, deficiencies in the forward model usually result in additional errors. Here we use the spatial pattern of velocity residuals to discuss the main error sources for basal stress inversions for Jakobshavn Isbræ, Greenland. Synthetic tests with prescribed patterns of basal yield stress with varying length scales are then used to investigate different weighting functions for the data-model misfit and for the ability of the inversion to resolve details in basal yield stress. We also test real-data inversions for their sensitivities to prior estimate, forward model parameters, data gaps, and temperature fields. We find that velocity errors are not sufficient to explain the residual patterns of real-data inversions. Conversely, ice-geometry errors and especially simulated errors in model simplifications are capable of reproducing similar error patterns and magnitudes. We suggest that residual patterns can provide useful guidance for forward model improvements.

The basal speed of valley glaciers: an inverse approach

Geophysical inverse methods are used to calculate the basal motion of a glacier. They are applied to a one-dimensional forward model that can be linearized to make the analysis simpler. The inverse method finds a solution that fits the data within a given error. It selects for smooth solutions to discriminate against unrealistic oscillations. The method is applied to a simple model glacier of uniform shape and thickness to test how well a given basal motion field can be reconstructed. It shows, as expected, that optimizing for smoothness lowers maxima and increases minima of the solution. A step change in basal velocity is drawn out in the inversion over a distance that is given by the half-width of a resolving function. This is typically about three times the ice thickness, but is also affected by the sampling rate of the data. The method is then applied to two glaciers where suitable data are available: Brown Glacier on Heard Island, southern Indian Ocean, and McCall Glacier in the Brooks Range, Alaska, U.S.A. The McCall results agree well with earlier estimates of basal motion.