Biological and Environmental Research - Earth and Environmental System Sciences
Earth and Environmental System Modeling

Parameter and State Estimation with a Time-Dependent Adjoint Marine Ice Sheet Models

TitleParameter and State Estimation with a Time-Dependent Adjoint Marine Ice Sheet Models
Publication TypeJournal Article
Year of Publication2013
AuthorsGoldberg, D N., and Heimbach P
JournalThe Cryosphere
Volume7
Number6
Pages1659-1678
Abstract / Summary

To date, assimilation of observations into large-scale ice models has consisted predominantly of time-independent inversions of surface velocities for basal traction, bed elevation, or ice stiffness, and has relied primarily on analytically derived adjoints of glaciological stress balance models. To overcome limitations of such "snapshot" inversions – i.e., their inability to assimilate time-dependent data for the purpose of constraining transient flow states, or to produce initial states with minimum artificial drift and suitable for time-dependent simulations – we have developed an adjoint of a time-dependent parallel glaciological flow model. The model implements a hybrid shallow shelf–shallow ice stress balance, solves the continuity equation for ice thickness evolution, and can represent the floating, fast-sliding, and frozen bed regimes of a marine ice sheet. The adjoint is generated by a combination of analytic methods and the use of algorithmic differentiation (AD) software. Several experiments are carried out with idealized geometries and synthetic observations, including inversion of time-dependent surface elevations for past thicknesses, and simultaneous retrieval of basal traction and topography from surface data. Flexible generation of the adjoint for a range of independent uncertain variables is exemplified through sensitivity calculations of grounded ice volume to changes in basal melting of floating and basal sliding of grounded ice. The results are encouraging and suggest the feasibility, using real observations, of improved ice sheet state estimation and comprehensive transient sensitivity assessments.

URLhttps://doi.org/10.5194/tc-7-1659-2013
DOI10.5194/tc-7-1659-2013
Journal: The Cryosphere
Year of Publication: 2013
Volume: 7
Number: 6
Pages: 1659-1678
Publication Date: 11/2013

To date, assimilation of observations into large-scale ice models has consisted predominantly of time-independent inversions of surface velocities for basal traction, bed elevation, or ice stiffness, and has relied primarily on analytically derived adjoints of glaciological stress balance models. To overcome limitations of such "snapshot" inversions – i.e., their inability to assimilate time-dependent data for the purpose of constraining transient flow states, or to produce initial states with minimum artificial drift and suitable for time-dependent simulations – we have developed an adjoint of a time-dependent parallel glaciological flow model. The model implements a hybrid shallow shelf–shallow ice stress balance, solves the continuity equation for ice thickness evolution, and can represent the floating, fast-sliding, and frozen bed regimes of a marine ice sheet. The adjoint is generated by a combination of analytic methods and the use of algorithmic differentiation (AD) software. Several experiments are carried out with idealized geometries and synthetic observations, including inversion of time-dependent surface elevations for past thicknesses, and simultaneous retrieval of basal traction and topography from surface data. Flexible generation of the adjoint for a range of independent uncertain variables is exemplified through sensitivity calculations of grounded ice volume to changes in basal melting of floating and basal sliding of grounded ice. The results are encouraging and suggest the feasibility, using real observations, of improved ice sheet state estimation and comprehensive transient sensitivity assessments.

DOI: 10.5194/tc-7-1659-2013
Citation:
Goldberg, DN, and P Heimbach.  2013.  "Parameter and State Estimation with a Time-Dependent Adjoint Marine Ice Sheet Models."  The Cryosphere 7(6): 1659-1678.  https://doi.org/10.5194/tc-7-1659-2013.