Journal cover Journal topic
Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
Geosci. Model Dev., 8, 3471-3485, 2015
https://doi.org/10.5194/gmd-8-3471-2015
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.
Development and technical paper
29 Oct 2015
On the use of Schwarz–Christoffel conformal mappings to the grid generation for global ocean models
S. Xu1, B. Wang1,2, and J. Liu2 1Ministry of Education Key Laboratory for Earth System Modeling, Center for Earth System Science (CESS), Tsinghua University, Beijing, China
2State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China
Abstract. In this article we propose two grid generation methods for global ocean general circulation models. Contrary to conventional dipolar or tripolar grids, the proposed methods are based on Schwarz–Christoffel conformal mappings that map areas with user-prescribed, irregular boundaries to those with regular boundaries (i.e., disks, slits, etc.). The first method aims at improving existing dipolar grids. Compared with existing grids, the sample grid achieves a better trade-off between the enlargement of the latitudinal–longitudinal portion and the overall smooth grid cell size transition. The second method addresses more modern and advanced grid design requirements arising from high-resolution and multi-scale ocean modeling. The generated grids could potentially achieve the alignment of grid lines to the large-scale coastlines, enhanced spatial resolution in coastal regions, and easier computational load balance. Since the grids are orthogonal curvilinear, they can be easily utilized by the majority of ocean general circulation models that are based on finite difference and require grid orthogonality. The proposed grid generation algorithms can also be applied to the grid generation for regional ocean modeling where complex land–sea distribution is present.

Citation: Xu, S., Wang, B., and Liu, J.: On the use of Schwarz–Christoffel conformal mappings to the grid generation for global ocean models, Geosci. Model Dev., 8, 3471-3485, https://doi.org/10.5194/gmd-8-3471-2015, 2015.
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Short summary
This article applies Schwarz-Christoffel (SC) conformal mappings for single-connected and multiple-connected regions to the generation of general orthogonal grids for OGCMs, to achieve 1) the enlarged lat-lon proportion, 2) the removal of landmass and easier load balancing, 3) better spatial resolution on continental boundaries, and 4) alignment of grid lines to large-scale coastlines. The generated grids could be readily utilized by the majority of OGCMs that support general orthogonal grids.
This article applies Schwarz-Christoffel (SC) conformal mappings for single-connected and...
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