Abstract
We develop a Bayesian model for estimating ice thickness given sparse observations coupled with estimates of surface mass balance, surface elevation change, and surface velocity. These fields are related through mass conservation. We use the Metropolis-Hastings algorithm to sample from the posterior probability distribution of ice thickness for three cases: a synthetic mountain glacier, Storglaci\aren, and Jakobshavn Isbr\ae. Use of continuity in interpolation improves thickness estimates where relative velocity and surface mass balance errors are small, a condition difficult to maintain in regions of slow flow and surface mass balance near zero. Estimates of thickness uncertainty depend sensitively on spatial correlation. When this structure is known, we suggest a thickness measurement spacing of one to two times the correlation length to take best advantage of continuity based interpolation techniques. To determine ideal measurement spacing, the structure of spatial correlation must be better quantified.
Highlights
Bed elevation is required to model glacier dynamics
Many widely used digital elevation models (DEMs) of subglacial topography are based upon classical geostatistical techniques such as Kriging (Bamber et al, 2013)
Such DEMs tend to induce immediate modeled surface elevation changes from dynamical models that are implausibly larger than observations of surface elevation change (Seroussi et al, 2011; Bindschadler et al, 2013)
Summary
Bed elevation is required to model glacier dynamics. Because modeling often requires a thickness field, reliable methods of interpolation between observations are valuable. Many widely used digital elevation models (DEMs) of subglacial topography are based upon classical geostatistical techniques such as Kriging (Bamber et al, 2013). Such DEMs tend to induce immediate modeled surface elevation changes from dynamical models that are implausibly larger than observations of surface elevation change (Seroussi et al, 2011; Bindschadler et al, 2013). In an effort to minimize these spurious model transients, contemporary DEMs incorporate physical constraints on interpolated fields. The procedure is conceptually simple and fits neatly into the general framework of geophysical inversion theory: formulate a cost functional that quantifies the misfit between the field of interest and observations, subject to the constraint that the field be compatible with a forward model
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