Parameter and state estimation with a time-dependent adjoint marine ice sheet model

Abstract

Abstract.To date, assimilation of observations into largescale ice models has consisted predominantly of timeindependent 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 shelfshallow 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 timedependent 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.

Inferred basal friction and surface mass balance of the Northeast Greenland Ice Stream using data assimilation of ICESat (Ice Cloud and land Elevation Satellite) surface altimetry and ISSM (Ice Sheet System Model)

“…Several studies have demonstrated the usefulness of such an approach for steady-state ice-flow model inversions (MacAyeal, 1993;Morlighem et al, 2010;Vieli et al, 2006;Arthern and Gudmundsson, 2010), and our results suggest this extends to transient ice-flow models as well. Here, as previously alluded to by Heimbach and Bugnion (2009) and explored in Goldberg and Heimbach (2013), a combined approach should be entertained, in which both surface velocity and height be used to invert for the state of the ice at the ice-bedrock interface and at the surface. This puts serious constraints on the rate at which surface velocities from SAR platforms should be collected, but the emergence of satellites such as TerraSAR-X or Sentinel, which can provide high-repeat pass observations -in combination with continuous coverage from altimetry by CryoSat-2, sub-meterresolution stereo imaging from Worldview-2 (Shean et al, 2012) and in the coming years ICESat-2 -shows a highdegree of promise.…”

“…This can be somewhat higher (but still fixed) for overloaded-operator approaches, which are not computationally as efficient. AD tools have been leveraged extensively in the oceanic context for state-of-the art ocean models (Marotzke et al, 1999;Heimbach et al, 2002;, and more recently to ice-sheet models (Heimbach and Bugnion, 2009;Goldberg and Heimbach, 2013).…”

“…For example, new approaches are emerging, based on time-dependent adjoint modeling Goldberg and Heimbach, 2013), which show great promise in potentially enabling sophisticated data assimilation of disparate data sets into ice-sheet models. Here, we propose one such approach, based on algorithmic differentiation of the Ice Sheet System Model (ISSM), to improve assimilation of surface altimetry data (over the entire ICESat time period) into a transient reconstruction of the ice-flow dynamics of the Northeast Greenland Ice Stream (NEGIS).…”

<i>Albany/FELIX</i>: a parallel, scalable and robust, finite element, first-order Stokes approximation ice sheet solver built for advanced analysis

“…Recently, these approaches have been extended to simultaneously optimize both model parameter fields and uncertain initial condition fields, while also accounting for forcing from climate models in order to minimize transient shocks when coupling to climate forcing (Perego et al, 2014). Other recent and noteworthy optimization improvements include the assimilation of time-dependent observations (e.g., Goldberg and Heimbach, 2013) and the estimation of formal uncertainties for optimized parameter fields (Petra et al, 2015).…”

“…A primary development focus has been on improving the representation of the momentum balance equations over the "shallow ice" (SIA; Hutter, 1983) and "shallow-shelf" (SSA; Morland, 1987) approximations through the inclusion of both vertical shear and membrane stresses over the entire model domain (e.g., Pattyn, 2002). These approaches include "hybrid" models (a combination of SIA and SSA; Bueler and Brown, 2009;Pollard and Deconto, 2009;Goldberg and Sergienko, 2011), socalled "higher-order" models (Pattyn, 2003), "full" Stokes models Leng et al, 2012;Gagliardini et al, 2013), and combinations of a range of approximations up to and including full Stokes . By accounting for both vertical and horizontal stress gradients, the aforementioned models allow for more realistic and accurate simulations of outlet glaciers, ice streams, and ice shelves, as well as modeling of the transfer of perturbations from marginal to inland regions.…”