Abstract
Regional ocean models usually utilize orthogonal curvilinear grids that are fit to the coastline of the modeled regions. While the orthogonality of the grid is required from the perspective of the numerical algorithms, the alignment to the irregular coastlines improves the characterization of the land-sea distribution and the ocean simulation. In this article, we carry out fractal analysis of two representative coastal regions and discuss the trade-offs between the orthogonality and coastline alignment during the grid generation of these regions. A new grid generation method based on Schwarz-Christoffel conformal mappings is proposed, with automatic coastal boundary retrieval algorithm that generates resolution dependent boundary for grid generation and alleviates the human efforts involved in traditional methods. We show that for the southeastern Pacific region, the coastline is smooth with low fractal dimension and there exists effective trade-off with a coastline boundary that adjusts to the desired grid resolution. On the contrary, there is no effective trade-off for southeast China seas where the coastline is of higher fractal dimension, and a coarser coastline boundary is recommended for better orthogonality with little loss in coastline alignment. Further numerical study of coastal trapped Kelvin waves for the typical regions demonstrate that the new coastline-fitting grids achieve smaller error in numerical dispersion and higher accuracy. Through analysis, we conclude that for grid generation for regional ocean modeling, modelers should bring into consideration of the multi-scale fractal characteristics of the coastline.
Highlights
This article is part of the Topical Collection on the 8th International Workshop on Modeling the Ocean (IWMO), Bologna, Italy, 7–10 June 2016Responsible Editor: Tal EzerThe grid system is the basis of the spatial discretization for geophysical fluid dynamic models
With the increase of the offset, the standard deviation of θO generally decreases, while that of θA grows. This is a result of that with a larger offset, a more smooth coastline boundary which is further from the coastline and of less details of the coastline is adopted for the grid generation
We evaluate the effect of the alignment of grid lines to coastlines in the new grids, by simulating typical baroclinic Kelvin waves that propagate along the coastal areas of the southeast Pacific ocean (SEP) and Southeast China Seas (SECS) regions
Summary
This article is part of the Topical Collection on the 8th International Workshop on Modeling the Ocean (IWMO), Bologna, Italy, 7–10 June 2016. In order to overcome the singularity caused by the North Pole, people usually adopt dipolar or tripolar grids that displace the North Pole onto lands, as in Murray (1996) These global grids are usually generated based on an analytical formulation, such as confocal curves. Since the coastal boundary as used for the grid generation has to be chosen manually, for highresolution model grids, the human work and the potential effort in tuning the resulting grid could be prohibitive Since it is not practical for the subjective and manual choosing process of the boundary, to simplify this process, modelers usually adopt large-scale coastlines with a limited number of control points, which are usually smooth with respect to the spatial scale of the grid resolution.
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