Variational Inference at Glacier Scale

TL;DR

This paper introduces a scalable variational inference method using Gaussian processes and eigenfunctions to estimate the joint posterior of ice sheet parameters from surface speed data, effectively handling large-scale glacier models.

Contribution

It presents a novel scalable variational inference approach with Gaussian process priors for glacier-scale ice sheet modeling, capturing parameter uncertainty and mutual indeterminacy.

Findings

Method accurately recovers known parameters in synthetic tests.

Scales effectively to glacier-sized problems.

Uncertainty remains high in slow-flow regions regardless of noise model.

Abstract

We characterize the complete joint posterior distribution over spatially-varying basal traction and and ice softness parameters of an ice sheet model from observations of surface speed by using stochastic variational inference combined with natural gradient descent to find an approximating variational distribution. By placing a Gaussian process prior over the parameters and casting the problem in terms of eigenfunctions of a kernel, we gain substantial control over prior assumptions on parameter smoothness and length scale, while also rendering the inference tractable. In a synthetic example, we find that this method recovers known parameters and accounts for mutual indeterminacy, both of which can influence observed surface speed. In an application to Helheim Glacier in Southeast Greenland, we show that our method scales to glacier-sized problems. We find that posterior uncertainty in regions of slow flow is high regardless of the choice of observational noise model.