Abstract
Abstract. We propose a new approach to indirectly estimate basal properties of ice streams, i.e. bedrock topography and basal slipperiness, from observations of surface topography and surface velocities. We demonstrate how a maximum a posteriori estimate of basal conditions can be determined using a Bayesian inference approach in a combination with an analytical linearisation of the forward model. Using synthetic data we show that for non-linear media and non-linear sliding law only a few forward-step model evaluations are needed for convergence. The forward step is solved with a numerical finite-element model using the full Stokes equations. The Fréchet derivative of the forward function is approximated through analytical small-perturbation solutions. This approximation is a key feature of the method and the effects of this approximation on model performance are analyzed. The number of iterations needed for convergence increases with the amplitude of the basal perturbations, but generally less than ten iterations are needed.
Highlights
The goal of geophysical inverse methods is to make quantitative inferences about Earth characteristics from indirect observations (e.g., Gouveia and Scales, 1998)
In Bayesian inference, a priori information about the basal properties is expressed as a probability density function and combined with the surface measurements to give a posteriori probability distribution describing the final uncertainty of the estimate
The transfer functions T are analytical solutions for linear rheology describing the effects of small-amplitude variations in bed topography and basal slipperiness on surface fields (Gudmundsson, 2003, 2008)
Summary
2005) to estimate bedrock topography and basal slipperiness under ice streams from surface velocities and surface geometry. Gudmundsson: Non-linear inversion of synthetic data transfer functions (Gudmundsson, 2003) These transfer functions describe the effects of small-amplitude perturbations in basal properties (bedrock profile and slipperiness) on surface fields in the case of Newtonian rheology and linear sliding law. The case studies presented allow us to explore the performance of the proposed inverse procedure and in particular to assess the practicality of approximating the Frechet derivative of the forward function using analytical small-amplitude solutions. Joughin et al (2004) used a similar method to arrive at estimates of basal stress for ice streams flowing over a perfectly plastic bed These inverse procedures use forward models that solve a reduced set of the Stokes equations.
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