To date, assimilation of observations into large-scale ice models hasconsisted predominantly of time-independent inversions of surface velocitiesfor basal traction, bed elevation, or ice stiffness, and has relied primarilyon analytically derived adjoints of glaciological stress balance models. Toovercome limitations of such "snapshot" inversions – i.e., their inability toassimilate time-dependent data for the purpose of constraining transient flowstates, or to produce initial states with minimum artificial drift andsuitable for time-dependent simulations – we have developed an adjoint of atime-dependent parallel glaciological flow model. The model implements ahybrid shallow shelf–shallow ice stress balance, solves the continuityequation for ice thickness evolution, and can represent the floating,fast-sliding, and frozen bed regimes of a marine ice sheet. The adjoint isgenerated by a combination of analytic methods and the use of algorithmicdifferentiation (AD) software. Several experiments are carried out withidealized geometries and synthetic observations, including inversion oftime-dependent surface elevations for past thicknesses, and simultaneousretrieval of basal traction and topography from surface data. Flexiblegeneration of the adjoint for a range of independent uncertain variables isexemplified through sensitivity calculations of grounded ice volume tochanges in basal melting of floating and basal sliding of grounded ice. Theresults are encouraging and suggest the feasibility, using real observations,of improved ice sheet state estimation and comprehensive transientsensitivity assessments.
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