Preprints
https://doi.org/10.5194/gmd-2021-321
https://doi.org/10.5194/gmd-2021-321

Submitted as: development and technical paper 29 Sep 2021

Submitted as: development and technical paper | 29 Sep 2021

Review status: this preprint is currently under review for the journal GMD.

A new sampling capability for uncertainty quantification in the Ice-sheet and Sea-level System Model v4.19 using Gaussian Markov random fields

Kevin Bulthuis and Eric Y. Larour Kevin Bulthuis and Eric Y. Larour
  • Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA

Abstract. Assessing the impact of uncertainties in ice-sheet models is a major and challenging issue that needs to be faced by the ice-sheet community to provide more robust and reliable model-based projections of ice-sheet mass balance. In recent years, uncertainty quantification (UQ) has been increasingly used to characterize and explore uncertainty in ice-sheet models and improve the robustness of their projections. A typical UQ analysis involves first the (probabilistic) characterization of the sources of uncertainty followed by the propagation and sensitivity analysis of these sources of uncertainty. Previous studies concerned with UQ in ice-sheet models have generally focused on the last two steps but paid relatively little attention to the preliminary and critical step of the characterization of uncertainty. Sources of uncertainty in ice-sheet models, like uncertainties in ice-sheet geometry or surface mass balance, typically vary in space and potentially in time. For that reason, they are more adequately described as spatio(-temporal) random fields, which account naturally for spatial (and temporal) correlation. As a means of improving the characterization of the sources of uncertainties in ice-sheet models, we propose in this paper to represent them as Gaussian random fields with Matérn covariance function. The class of Matérn covariance functions provides a flexible model able to capture statistical dependence between locations with different degrees of spatial correlation or smoothness properties. Samples from a Gaussian random field with Matérn covariance function can be generated efficiently by solving a certain stochastic partial differential equation. Discretization of this stochastic partial differential equation by the finite element method results in a sparse approximation known as a Gaussian Markov random field. We solve this equation efficiently using the finite element method within the Ice-sheet and Sea-level System Model (ISSM). In addition, spatio-temporal samples can be generated by combining an autoregressive temporal model and the Matérn field. The implementation is tested on a set of synthetic experiments to verify that it captures well the desired spatial and temporal correlations. Finally, we demonstrate the interest of this sampling capability in an illustration concerned with assessing the impact of various sources of uncertainties on the Pine Island Glacier, West Antarctica. We find that both larger spatial and temporal correlations lengths will likely result in increased uncertainty in the projections.

Kevin Bulthuis and Eric Y. Larour

Status: open (until 24 Nov 2021)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse

Kevin Bulthuis and Eric Y. Larour

Data sets

A new sampling capability for uncertainty quantification in the Ice-sheet and Sea-level System Model v4.19 using Gaussian Markov random fields -- Datasets and results Kevin Bulthuis and Eric Larour https://doi.org/10.5281/zenodo.5532710

Model code and software

A new sampling capability for uncertainty quantification in the Ice-sheet and Sea-level System Model v4.19 using Gaussian Markov random fields -- Software Kevin Bulthuis and Eric Larour https://doi.org/10.5281/zenodo.5532775

Kevin Bulthuis and Eric Y. Larour

Viewed

Total article views: 191 (including HTML, PDF, and XML)
HTML PDF XML Total BibTeX EndNote
148 38 5 191 1 1
  • HTML: 148
  • PDF: 38
  • XML: 5
  • Total: 191
  • BibTeX: 1
  • EndNote: 1
Views and downloads (calculated since 29 Sep 2021)
Cumulative views and downloads (calculated since 29 Sep 2021)

Viewed (geographical distribution)

Total article views: 186 (including HTML, PDF, and XML) Thereof 186 with geography defined and 0 with unknown origin.
Country # Views %
  • 1
1
 
 
 
 
Latest update: 22 Oct 2021
Download
Short summary
We discuss a new method to sample spatially and temporal varying uncertain input parameters in ice sheet models, like the ice thickness or the surface mass balance. We represent these source of uncertainty of Gaussian random fields with Matérn covariance function. We generate random samples of this random field using an efficient computational approach based on solving a stochastic partial differential equation.