An Elastic–Viscous–Plastic Model for Sea Ice Dynamics

TLDR

Sea ice is typically represented as a visco‑plastic material that flows plastically under normal stresses but behaves as a nearly rigid, linear viscous fluid at low strain rates, necessitating implicit numerical methods that are time‑consuming, poorly scalable, and ill‑suited to parallel computation. The authors aimed to overcome these limitations by developing and testing two new computational approaches. They implemented a preconditioned conjugate‑gradient solver based on a symmetric, negative‑definite matrix representation of the rheology, and introduced an elastic‑wave mechanism that replaces the viscous‑plastic response at short timescales while retaining it at longer wind‑forcing timescales, yielding a fully explicit scheme. The resulting elastic‑viscous‑plastic model delivers more accurate short‑timescale ice responses, reproduces viscous‑plastic behavior at longer scales, and achieves superior computational efficiency, especially on parallel machines, compared to the standard viscous‑plastic formulation.

Abstract

The standard model for sea ice dynamics treats the ice pack as a visco–plastic material that flows plastically under typical stress conditions but behaves as a linear viscous fluid where strain rates are small and the ice becomes nearly rigid. Because of large viscosities in these regions, implicit numerical methods are necessary for time steps larger than a few seconds. Current solution methods for these equations use iterative relaxation methods, which are time consuming, scale poorly with mesh resolution, and are not well adapted to parallel computation. To remedy this, the authors developed and tested two separate methods. First, by demonstrating that the viscous–plastic rheology can be represented by a symmetric, negative definite matrix operator, the much faster and better behaved preconditioned conjugate gradient method was implemented. Second, realizing that only the response of the ice on timescales associated with wind forcing need be accurately resolved, the model was modified so that it reduces to the viscous–plastic model at these timescales, whereas at shorter timescales the adjustment process takes place by a numerically more efficient elastic wave mechanism. This modification leads to a fully explicit numerical scheme that further improves the model’s computational efficiency and is a great advantage for implementations on parallel machines. Furthermore, it is observed that the standard viscous–plastic model has poor dynamic response to forcing on a daily timescale, given the standard time step (1 day) used by the ice modeling community. In contrast, the explicit discretization of the elastic wave mechanism allows the elastic–viscous–plastic model to capture the ice response to variations in the imposed stress more accurately. Thus, the elastic–viscous–plastic model provides more accurate results for shorter timescales associated with physical forcing, reproduces viscous–plastic model behavior on longer timescales, and is computationally more efficient overall.