Development of a Viscoelastic Ice-flow Model for Process-based Prediction of Ice-Sheet Evolution

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).

Alley 0909335

Pennsylvania State University

The glaciology community lacks a quantitatively predictive understanding of sliding and bed deformation. The PIs propose a modeling effort to develop viscoelastic ice-flow models overlying a viscous-plastic bed and associated techniques for data assimilation to help constrain basal flow laws describing this bed. For ice, the Maxwell model (consisting of a spring and dashpot in series) is anticipated to prove sufficient when the standard Newtonian (linear) dashpot is replaced by one obeying Glen's (nonlinear) flow law. The Maxwell model allows instantaneous elastic response, as well as stress relaxation, in which the stress required to sustain a given strain rate in the material diminishes over time. Thus, the Maxwell model is well-suited to materials for which viscous and elastic behavior are relatively independent, so that changing a model from viscous to Maxwell viscoelastic may be viewed as adding an elastic 'overlay' to the existing model. Prior success in modeling tidal forcing of a purely elastic ice stream lends support to this approach. However, should the Maxwell model prove inadequate, the PIs are prepared to investigate a Burgers model, which consists of a Maxwell unit in series with a Kelvin unit (itself consisting of a spring and dashpot in parallel). In addition to the viscous and instantaneous elastic behavior of the Maxwell model, the Burgers model also displays delayed elastic response to forcing at certain frequencies. At the longer timescales of interest for glacial flow, though, the PIs expect that any lag between forcing and (nonlocal) response will result from the finite propagation speed of elastic waves. They plan to begin by adding Maxwell viscoelastic behavior to a depth-integrated, width-averaged ice stream-ice shelf model. This type of one-dimensional model allows for relatively straightforward incorporation of new physics, yet is sophisticated enough to assess the effects of ice shelf buttressing and basal melting.