Abstract
Abstract. Hybrid models, or depth-integrated flow models that include the effect of both longitudinal stresses and vertical shearing, are becoming more prevalent in dynamical ice modeling. Under a wide range of conditions they closely approximate the well-known First Order stress balance, yet are of computationally lower dimension, and thus require less intensive resources. Concomitant with the development and use of these models is the need to perform inversions of observed data. Here, an inverse control method is extended to use a hybrid flow model as a forward model. We derive an adjoint of a hybrid model and use it for inversion of ice-stream basal traction from observed surface velocities. A novel aspect of the adjoint derivation is a retention of non-linearities in Glen's flow law. Experiments show that in some cases, including those nonlinearities is advantageous in minimization of the cost function, yielding a more efficient inversion procedure.
Highlights
Direct observations of many parameters crucial to behavior of glaciers and ice sheets are practically impossible and those that are feasible are logistically challenging and usually confined to specific locations
Including the nonlinear terms in Eqs. (10) and (12) does not change the solution of the inversion; it can only affect whether the inversion scheme finds a minimum of Eq (5) and the speed of convergence
In this sense the flowline inversions demonstrated a clear advantage in including these terms
Summary
Direct observations of many parameters crucial to behavior of glaciers and ice sheets are practically impossible (e.g. history of ice-sheet-wide surface temperature and precipitation, ice fabric) and those that are feasible are logistically challenging and usually confined to specific locations (e.g. basal sediments, subglacial water pressure). The SSA balance is of lower computational dimension than the First Order or Full Stokes balances (Greve and Blatter, 2009), and easier to solve It does not account, though, for the effect of vertical shear, which has an effect on the nonlinear Glen’s Law viscosity (Glen, 1955) and the basal velocity used in flow laws, and which can be nonnegligible where basal traction is high. Bueler and Brown (2009) heuristically combine the results of an SSA solution with an SIA solution, while Pollard and DeConto (2009), Schoof and Hindmarsh (2010), and Goldberg (2011) use depth-integrated forms of the horizontal stress terms While these hybrid models account for all of the stress terms in the First Order balance, they have a computational advantage in that the elliptic solve (the most expensive step) is not resolved in the vertical. Special attention is paid to the effects of including the nonlinearities mentioned above in the adjoint model on the convergence of the inversion scheme
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
