Abstract
The formulation and the algorithm of solving an ocean model for the prediction and assimilation of the observed data which makes it possible to reconstruct the circulation in the deep-water parts of the sea and at a shallow water shelf, as well as to describe the large time–space variability in the surface level, are considered. The model uses a vertical hybrid σ–z coordinate system: the several upper tens of meters of the ocean are described in the σ-coordinate system and the rest of the water column is described in the z coordinates. Such hybridization extends the possibilities of models for reconstructing thermo-hydrodynamic processes in different sea basins and the World Ocean. The differential formulation of the model in the σ–z coordinate system is presented; the simplified records of several operators that are allowable in the case of a small thickness of the ocean σ-layer are described. The construction of a computational grid, approximation of the bottom topography on it, and discretization of equations and boundary conditions of the models are considered; an approach to describing the bottom friction at shallow waters is offered. The results of the comparative experiments in the z and σ–z coordinate models are analyzed.
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References
J. Willebrand, B. Barnier, C. Böning, et al., “Circulation characteristics in three eddy-permitting models of the North Atlantic,” Prog. Oceanogr. 48, 123–161 (2001).
E. P. Chassignet, H. Arango, D. Dietrich, et al., “DAMEE-NAB: The base experiments,” Dyn. Atmos. Oceans 32, 155–184 (2000).
S. G. Demyshev, “A numerical model of online forecasting Black Sea currents,” Izv., Atmos. Ocean. Phys. 48 (1), 120–132 (2012).
S. Griffies, Elements of the Modular Ocean Model (MOM) (2012 release), GDFL Ocean Group technical report No. 7 (2012).
R. D. Smith, J. K. Dukowicz, and R. C. Malone, “Parallel ocean general circulation modeling,” Phys. D (Amsterdam) 60, 38–61 (1992).
J. Marshall, A. Adcroft, C. Hill, et al., “A finite-volume, incompressible Navier–Stokes model for studies of the ocean on parallel computers,” J. Geophys. Res. 102 (C3), 5753–5766 (1997).
S. J. Marsland, H. Haak, J. H. Jungclaus, et al., “The Max-Planck-Institute global ocean/sea ice model with orthogonal curvilinear coordinates,” Ocean Modell. 5, 91–127 (2003).
V. B. Zalesny, Modeling Large-Scale Motions in the World Ocean (Department of Numerical Mathematics, USSR Acad. Sci., Moscow, 1984) [in Russian].
N. A. Diansky, Modeling the Ocean Circulation and Study of Its Response to Short- and Long-Period Atmospheric Influences (Fizmatlit, Moscow, 2013) [in Russian].
A. V. Gusev and N. A. Diansky, “Numerical simulation of the world ocean circulation and its climatic variability for 1948–2007 using the INMOM,” Izv., Atmos. Ocean. Phys. 50 (1), 1–12 (2014).
A. Blumberg and G. L. Mellor, “A description of a threedimensional coastal ocean circulation model,” in Three- Dimensional Coastal Ocean Models, Ed. by N. S. Heaps (American Geophysical Union, Washington, D.C., 1987). doi 10.1029/CO004p0001
G. L. Mellor, T. Ezer, and L.-Y. Oey, “The pressure gradient conundrum of sigma coordinate ocean models,” J. Atmos. Ocean. Technol. 11 (4), 1126–1134 (1994).
G. L. Mellor, L.-Y. Oey, and T. Ezer, “Sigma coordinate pressure gradient errors and the seamount problem,” J. Atmos. Ocean. Technol. 15 (5), 1122–1131 (1998).
E. P. Chassignet, H. E. Hurlburt, O. M. Smedstad, et al., “Generalized vertical coordinates for eddy-resolving global and coastal ocean forecasts,” Oceanography 19 (1), 118–129 (2006).
G. Madec, F. Lott, P. Delecluse, and M. Crépon, “Large-scale preconditioning of deep-water formation in the northwestern Mediterranean sea,” J. Phys. Oceanogr. 26 (8), 1393–1408 (1996).
C. N. Barron, A. B. Kara, P. J. Martin, et al., “Formulation, implementation and examination of vertical coordinate choices in the Global Navy Coastal Ocean Model (NCOM),” Ocean Modell. 11 (3), 347–375 (2006).
H. Hasumi, Documentation for CCSR Ocean Component Model (COCO), version 4.0, 2007. http://ccsraoriu-tokyoacjp/~hasumi/COCO/indexhtml.
R. A. Ibrayev, “Model of enclosed and semi-enclosed sea hydrodynamics,” Russ. J. Numer. Anal. Math. Modell. 16 (4), 291–304 (2001).
R. A. Ibraev, Mathematical Modeling of Thermodynamic Processes in the Caspian Sea (GEOS, Moscow, 2008) [in Russian].
R. A. Ibrayev, E. Ozsoy, C. Schrum, and H. I. Sur, “Seasonal variability of the Caspian Sea three-dimensional circulation, sea level and air–sea interaction,” Ocean Sci. 6, 311–329 (2010).
V. V. Kalmykov and R. A. Ibrayev, “The overlapping algorithm for solving shallow water equations on massively- parallel architectures with distributed memory,” Vestnik UGATU 17 (5), 252–259 (2013).
A. S. Sarkisyan, R. A. Ibrayev, and N. G. Iakovlev, “High-resolution and four-dimensional analysis as a prospect for ocean modeling,” Russ. J. Numer. Anal. Math. Modell. 25 (5), 477–496 (2010).
P. D. Killworth, D. Stainforth, D. J. Webb, and S. Paterson, “The development of a free surface Bryan–Cox–Semtner model,” J. Phys. Oceanogr. 21, 1333–1348 (1991).
G. L. Mellor and A. F. Blumberg, “Modeling vertical and horizontal diffusivities with the sigma coordinate system,” Mon. Weather Rev. 113, 1380–1383 (1985).
A. Sarkisyan and J. Sündermann, Modelling Ocean Climate Variability (Springer, Berlin, 2009).
A. Arakawa, Design of the UCLA general circulation model, Tech. Rep. No. 7, Department of Meteorology, University of California, Los-Angeles (1972).
A. Arakawa and V. R. Lamb, “Computational design of the basic dynamical processes of the UCLA general circulation model,” in Computational Physics (Academic Press, New York, 1977), Vol. 17, pp. 173–265.
M. L. Batteen and Y.-J. Han, “On the computational noise of finite-difference schemes used in ocean models,” Tellus 33 (4), 387–396 (1981).
S. M. Griffies, Fundamentals of Ocean Climate Models (Princeton University Press, Princeton, 2004).
Vl. V. Voevodin, S. A. Zhumatii, S. I. Sobolev, et al., “The Lomonosov supercomputer practice,” Otkrytye Sist., No. 7, 36–39 (2012).
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Original Russian Text © R.A. Ibrayev, G.S. Dyakonov, 2016, published in Izvestiya Rossiiskoi Akademii Nauk, Fizika Atmosfery i Okeana, 2016, Vol. 52, No. 4, pp. 514–526.
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Ibrayev, R.A., Dyakonov, G.S. Modeling of ocean dynamics with large variations in sea level. Izv. Atmos. Ocean. Phys. 52, 455–466 (2016). https://doi.org/10.1134/S000143381604006X
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DOI: https://doi.org/10.1134/S000143381604006X