On the limit to resolution and information on basal properties obtainable from surface data on ice streams

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Abstract
An optimal estimation method for simultaneously determining both basal slipperiness and basal topography from variations in surface flow velocity and topography along a flow line on ice streams and ice sheets is presented. We use Bayesian inference to update prior statistical estimates for basal topography and slipperiness using surface measurements along a flow line. The methods requires no smoothing of surface data. Our main focus here is on how errors and spacing of surface data affects estimates of basal quantities and on possibly aliasing/mixing between basal slipperiness and basal topography. We find that the effects of spatial variations in basal topography and basal slipperiness on surface data can be accurately separated from each other, and mixing in retrieval does not pose a serious problem. For realistic surface data errors and density, small-amplitude perturbations in basal slipperiness can only be resolved for wavelengths larger than about 50 times the mean ice thickness. Bedrock topography is well resolved down to horizontal scale equal to about one ice thickness. Estimates of basal slipperiness are not significantly improved by accurate prior estimates of basal topography. Retrieval of basal slipperiness is found to be highly sensitive to unmodelled errors in basal topography.
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