Unsteady polynya flux model solutions incorporating a parameterization for the collection thickness of consolidated new ice

This paper develops a time-dependent, two-dimensional model for the opening of a coastal polynya. The model incorporates a parameterization for the collection thickness of frazil ice at the polynya edge that is given in terms of (a) the depth of frazil ice arriving at the polynya edge, (b) the component normal to the polynya edge of the frazil ice velocity relative to the consolidated new ice velocity, and (c) a constant depth term (hw) associated with wave radiation stress. The last term depends upon the wavelength of surface waves that are most readily generated by the wind stress, and for coastal polynyas is shown to be of the order of 5 cm. The inclusion of hw also removes possible cases of the parameterization being non-robust in the unsteady problem. Polynya opening solutions are calculated adjacent to a straight coastal barrier of finite length D, by numerically integrating Charpitʹs equations, a generalisation of the method of characteristics. Polynya opening times are compared with those in a constant collection depth model, when both models open to polynyas with identical steady-state area. For “long” islands (D≫alongshore adjustment length scale La), the opening time T obeys T>Tc, where Tc is the constant collection depth opening time; when D≪La, the inequality is reversed. Finally, month by month simulations of the opening of the St. Lawrence Island Polynya (SLIP) are presented, for which satellite-derived steady-state areas are available. In most simulations, the simulated steady-state area falls within the 90% confidence limits of the observed area.