The Cryosphere Discuss., 7, 2845-2890, 2013
© Author(s) 2013. This work is distributed
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This discussion paper has been under review for the journal The Cryosphere (TC). Please refer to the corresponding final paper in TC.
Parameter and state estimation with a time-dependent adjoint marine ice sheet model
D. N. Goldberg and P. Heimbach
Earth, Atmospheric and Planetary Science, M.I.T., Cambridge, USA

Abstract. 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 diagnostic ice velocity models. To overcome limitations of such "snapshot" inversions, i.e. their inability to assimilate time-dependent data, 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, involves a prognostic 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.

Citation: Goldberg, D. N. and Heimbach, P.: Parameter and state estimation with a time-dependent adjoint marine ice sheet model, The Cryosphere Discuss., 7, 2845-2890, doi:10.5194/tcd-7-2845-2013, 2013.
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