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See discussions, stats, and author profiles for this publication at: A Generalization of a Sigma Coordinate Ocean Model and an Intercomparison of Model Vertical Grids Chapter · January 2002 DOI: 10.1007/978-3-662-22648-3_4 CITATIONS 106 READS 194 4 authors , including: Some of the authors of this publication are also working on these related projects: Gulf Stream View project Sea Level Rise and Variability View project George L. Mellor Princeton University 90 PUBLICATIONS 7,848 CITATIONS SEE PROFILE Tal Ezer Old Dominion University 113 PUBLICATIONS 3,596 CITATIONS SEE PROFILE All content following this page was uploaded by Tal Ezer on 30 October 2014. The user has requested enhancement of the downloaded file.
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4 A Generalization of a Sigma Coordinate Ocean Model and an Intercomparison of Model Vertical Grids G EORGE M ELLOR 1 , S IRPA H ÄKKINEN 2 , T AL E ZER 1 AND R ICHARD P ATCHEN 3 1 Atmospheric and Oceanic Sciences Program Princeton University, Princeton, NJ 2 NASA Goddard Space Flight Center, Greenbelt, MD 3 Dynalysis of Princeton, Princeton N.J. 4.1 Introduction Numerical ocean models increasingly make use of σ - coordinate systems. A paper by Gerdes (1993) shows that these coordinate systems can be more general; he termed the generalized form an "s - coordinate" system. The main advantage of the σ or s - system is that, when cast in a finite difference form, a smooth represen- tation of the bottom topography is obtained; one can also easily incorporate a bot- tom boundary layer as well as a surface boundary layer in those coordinate systems. This is intuitively appealing and Gerdes has shown that superior numeri- cal results are obtained relative to a z - level system. However, in regions of steep topography and crude resolution - a limiting case would be a seamount represented by a single grid point surrounded by a flat bottom - the so-called sigma coordinate pressure gradient error exists (Haney 1991, Mellor et al. 1994, 1998) and at least locally a z - level coordinate system might be preferred. On the other hand, in a recent study, Bell (1997) has shown that the step structure of z - level models lead to vorticity errors and consequent errors in the barotropic component of the flow which, he reports, cause rather large temperature errors (3 to 4° C) on a 1° x 1° grid of an Atlantic Ocean model after 3 months of integration. And it is difficult to model bottom boundary layers in a z - level model (Winton et al. 1998). The pioneer Bryan-Cox model (Bryan 1969, Cox 1984) is a z - level model. A modification by Spall and Robinson (1993) is termed a "hybrid" coordinate system; they describe it as a z - level system in the region, 0 > z > - z c = constant, and a σ system when z c > z > - H(x, y) where the transformed sigma equations apply. Pre- sumably, this system is adopted so that surface mixed layers, which do not scale on depth, may be best represented. However, the hybrid system would appear to require separate numerical implementations for the two regions; their objectives can be realized more simply with the s - coordinate system described here.
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  • Summer '17
  • idk
  • Atlantic Ocean, Polar coordinate system, Coordinate systems, Sigma Coordinate Ocean Model

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