A robust and computationally efficient model of a two-dimensional coastal polynya Ian Walkington a , M.A. Morales Maqueda b, * , A.J. Willmott b a School of Computing and Mathematics, Keele University, Keele, Staffordshire ST5 5BG, UK b Proudman Oceanographic Laboratory, 6 Brownlow Street, Liverpool L3 5DA, UK Received 25 May 2006; received in revised form 4 December 2006; accepted 4 December 2006 Available online 8 January 2007 Abstract A two-dimensional polynya model incorporating a new computationally efficient parameterisation for the collection thickness of frazil ice at the polynya edge, H, is presented. The new parameterisation is designed to overcome the lack of robustness associated with the parameterisation of [Biggs, N.R.T., Morales Maqueda, M.A., Willmott, A.J. 2000. Poly- nya flux model solutions incorporating a parameterisation for the collection thickness of consolidated new ice. J. Fluid. Mech. 408, 179–204], in which H depends on the relative orientation of the polynya edge with respect to the flow of ice. As a result of this dependence, steady state polynya edge solutions exist that support seemingly unrealistic corners and that cannot be attained by evolving the polynya equations from an initial state in which the polynya is closed. The new parameterisation, removes the dependence of H on the orientation of the polynya edge by averaging the collection thickness of Biggs et al. (2000) along the polynya edge over length scales much smaller than the length of the polynya edge but much larger than the diameter of individual ice floes. The new parameterisation is robust in that steady state two- dimensional polynya solutions can now always be attained starting from a closed polynya state. Ó 2006 Elsevier Ltd. All rights reserved. 1. Introduction Wind-driven polynya flux models calculate the location of the polynya edge by equating the fluxes of upwind frazil ice and downwind consolidated new ice at the polynya edge, thus ensuring the conservation of ice volume. In one dimension, this flux balance is given by Ou (1988) h c u c  dX dt   ¼ H U c  dX dt   ; ð1Þ where h c and u c are the volume per unit area and the velocity of frazil ice arriving at the polynya edge, respec- tively, X is the location of the polynya edge, and H and U c are the collection thickness of frazil ice and the velocity of consolidated new ice at X, respectively. The condition that u c > U c is required throughout the 1463-5003/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ocemod.2006.12.001 * Corresponding author. Tel.: +44 151 795 4851; fax: +44 151 795 4918. E-mail address: mamm@pol.ac.uk (M.A. Morales Maqueda). Ocean Modelling 17 (2007) 140–152 www.elsevier.com/locate/ocemod