Uncertainty estimation of basal friction using a game theoretical approach

Abstract:

Basal conditions are a major control of ice sheet dynamics but remain poorly understood. Over the past three decades, there has been an exponential growth in observations of ice sheet surface conditions. However, very few direct observations of the ice sheet base exist to this day. Most of our knowledge of the basal conditions comes from sounding radar observations and assimilation of surface conditions in ice flow models. Data assimilation has been extensively used to constrain basal friction and initialize ice sheet models, albeit with large uncertainties that have not yet been quantified. Estimating uncertainties that arise from such an approach is challenging but necessary to further constrain future climate projections.

In this work, we propose to use a novel game theoretical approach to estimate and quantify the uncertainty of the basal friction at the base of ice sheets, and assess its impact of projections of ice sheet evolution over the coming decades. When applied to a parameterized family of models, the proposed approach identifies a distribution over models identified as a (minmax) optimal strategy for a game where Player I selects the true model, Player II observes data produced by the model selected by Player I and must predict a quantity of interest that is a function of the model selected by Player I. This optimal distribution is computationally approximated by (1) generating a finite number of copies of the parametrized model and (2) iteratively altering the weights and parameters of each copy (via gradient descent). We will apply this technique to Helheim Glacier in Southwest Greenland to understand the impact of uncertainty in basal friction on sea level projections and compare them to other sources of uncertainty.

This work was performed at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Funding was provided by the JPL Strategic Research and Technology Development Program.