[en] The sigma-transformation is a widely used coordinate change that maps the actual depth-varying sea onto a computational domain, the depth of which is constant. The advantages of this technique are numerous. It permits an efficient use of computer resources, a simple treatment of the surface and bottom boundary conditions, and an accurate representation of the bathymetry. However, if the range of the depth is too large, or when the depth varies too rapidly, as in the shelf break region, it may be shown that the sigma-transformation leads to severe numerical errors. In the application of GHER's three-dimensional model to the Western Mediterranean, the occurrence of those numerical errors is avoided by the introduction of a two-fold sigma-coordinate system in the deep sea.
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Bibliography
Arakawa, Suarez (1983) Vertical differencing of the primitive equations in sigma coordinates. Mon. Weather Rev. 111:34-45.
Beckers (1988) Modélisation Mathématique et Numérique de la Méditerranée Occidentale. Engineering Dissertation , University of Liège, Liège; 184.
Beckers (1991) Application of the GHER 3D general circulation model to the Western Mediterranean. J. Mar. Syst. 1:315-332.
Blumberg, Mellor (1987) A description of a three-dimensional coastal ocean circulation model. Three-Dimensional Coastal Ocean Models , N.S. Heaps, American Geophysical Union, Washington, D.C; 1-16.
Deleersnijder (1989) Upwelling and upsloping in three-dimensional marine models. Appl. Math. Modelling 13:462-467.
Deleersnijder, Nihoul (1988) General Circulation in the Northern Bering Sea. ISHTAR Annual Progress Report , University of Liège; 392.
Deleersnijder, Wolanski (1990) Du rôle de la dispersion horizontale de quantité de mouvement dans les modéles marins tridimensionnels. Journées Numériques de Besançon 1990—Courants Marins , J.-M. Crolet, P. Lesaint, Publications Mathématiques de Besançon, Besançon; 39-50.
De Kok (1992) A 3-D finite difference model for the computation of near field and far-field transport of suspended matter near a river mouth. Cont. Shelf Res. 12:625-642.
Dutton The Ceaseless Wind , Mc-Graw-Hill, New York; 1986, 617.
Freeman, Hale, Danard (1972) A modified sigma equations' approach to the numerical modeling of Great Lakes hydrodynamics. Journal of Geophysical Research 77:1050-1060.
Gal-Chen, Somerville (1975) On the use of a coordinate transformation for the solution of the Navier-Stokes equations with topography. J. Comput. Phys. 17:276-310.
Gary (1973) Estimate of truncation error in transformed coordinate primitive equation atmospheric models. Journal of the Atmospheric Sciences 30:223-233.
Haney (1991) On the pressure gradient force over steep topography in sigma coordinate ocean models. Journal of Physical Oceanography 21:610-619.
Janjic (1977) Pressure gradient force and advection scheme used for forecasting with steep and small scale topography. Contrib. Atmos. Phys. 50:186-199.
Kasahara (1974) Various vertical coordinate systems used for numerical weather predictions. Monthly Weather Review 102:509-522.
Mellor, Blumberg (1985) Modeling vertical and horizontal diffusivities with the sigma coordinate system. Monthly Weather Review 113:1379-1383.
Mesinger (1982) On the convergence and error problems of the calculation of the pressure gradient force in sigma coordinate models. Geophys., Astrophys. Fluid Dyn. 19:105-117.
Nihoul (1984) A three-dimensional general marine circulation model in a remote sensing perspective. Ann. Geophys. 2:433-442.
Nihoul, Deleersnijder, Djenidi (1989) Modelling the general circulation of shelf seas by 3D k − ϵ models. Earth-Sci. Rev. 26:163-189.
Nihoul, Djenidi (1987) Perspective in three-dimensional modelling of the marine system. Three-Dimensional Models of Marine and Estuarine Dynamics , J.C.J. Nihoul, B.M. Jamart, Elsevier, Amsterdam; 1-33.
Nihoul, Waleffe, Djenidi (1986) A 3D-numerical model of the Northern Bering Sea. Environ. Softw. 1:76-81.
Owen (1980) A three-dimensional model of the Bristol Channel. J. Phys. Oceanogr. 10:1290-1302.
Pedlosky Geophysical Fluid Dynamics , Springer-Verlag, New York, N.Y; 1982, 624.
Peyret, Taylor Computational Methods for Fluid Flows , Springer-Verlag, New York, N.Y; 1983, 358.
Phillips (1957) A coordinate system having some special advantages for numerical forecasting. Journal of Meteorology 14:184-185.
Pielke, Martin (1981) The derivation of a terrain-following coordinate system for use in a hydrostatic model. J. Atmos. Sci. 38:1707-1713.
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