On the calculation of normalized viscous–plastic sea ice stresses

Abstract

Calculating and plotting the normalized states of stress for viscous–plastic sea ice models is a common diagnostic for evaluating the numerical convergence and the physical consistency of a numerical solution. Researchers, however, usually do not explain how they calculate the normalized stresses. Here, we argue that care must be taken when calculating and plotting the normalized states of stress. A physically consistent and numerically converged solution should exhibit normalized stresses that are inside (viscous) or on (plastic) the normalized yield curve. To do so, two possible mistakes need to be avoided. First, when using an implicit solver, normalized stresses should be computed from viscous coefficients and replacement pressure calculated using the previous numerical iterate and the strain rates at the numerator calculated from the latest iterate. Calculating the stresses only from the latest iterate falsely indicates that the solution has numerically converged. Second, for both implicit and explicit (i.e., the EVP) solvers, the stresses should be normalized by the ice strength and not by the replacement pressure. Using the latter, normalized states of stress only lie on the yield curve (i.e., falsely indicating there are no viscous states of stress).