Explicit Generation of Orthogonal Grids for Ocean Models

Abstract

Several explicit methods are proposed for generating global orthogonal curvilinear grids for ocean modelling. The methods are based on the conformal properties of stereographic and Mercator map projections and have been developed with the specific object of removing the North Pole from the ocean domain. Some of the configurations, in addition to overcoming the pole problem, have very attractive resolution properties in the polar regions. Two of the constructions are geometrical in nature, while a third is based on the superposition of potential fields generated by discrete coordinate poles. The methods described here differ from those commonly employed in engineering problems in that grid line control is exercised by the placement of a finite number of singularities, and no specific condition is placed upon the fitting of coordinate lines to physical boundaries. The grids produced are accordingly of global construction and have smooth variations in grid size. Being of analytical or semi-analytical formulation, the grids may be generated quickly and without the need for advanced software.