Overview of the Bergen Ocean Model

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The Bergen Ocean Model (BOM) is a sigma coordinate numerical ocean model that allows development for time stepping, pressure gradient, advection and sub grid- parameterizations and is initiated in FOTRAN 90. The numerical foundation for the model is governed by the equations of motion, continuity (conservation of mass) and thermodynamics, the derivatives of the model include the velocity field, temperature, salinity, density and pressure.

The first version of the model was implemented in 1995. This version used the implicit method to predict the depth integrated shallow water equations. A second version introduced the averaging Coriolis term to avoid instabilities, this version also allowed for time-split to be described and implemented (1998). A third version (1990) presented a method whereby the 2D time steps were changed, with the implicit method replacing the forward-backward method. The latter two versions offer different representations of the heat transport than the first version.

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The BOM is continually improving and there have been further advances and updated versions to date.

Ocean numerical system codes are used as a research tool around the world by many scientists and can be used to simulate many processes in oceanography such as remote sensing, climatological, hydrological and gridding data. System codes can be adapted to fit the purpose of research by adjusting the numerical algorithms, such as boundary conditions, resolution and derivatives.

A sigma (topography following vertical) coordinate model is suited for specific types of problems and BOM has been used regionally to simulate the continental shelf break, coastal areas and estuaries in small scales. However, BOM codes can be used successfully in a wide range of applications including larger scales, such as basin to global scales and codes are readily available on-line.

Processes studied include shallow water waves, 3D coastal ocean circulation, global ocean and atmospheric circulation, turbulence, fresh water driven primary production in a fjord, circulation effects of storm flows and continental shelf.

Truncation errors occur when discretization transfers functions, equations and variables into discreate counterparts. Finite changes are placed on a staggered grid in the vertical by the discretization in sigma coordinates. According to s= z/h(X,Y) each grid function is spaced equally by subdividing the vertical resolution into equal points and is processed one step at a time. The shorter the distance between the two points the better the interpolation.

The sigma coordinate spatial resolution is very high and offers a true image over the margins of continents and other shallow water depths in the oceans, seas or lakes. When a time-step limitation occurs due to exceptional spacing of the vertical grid then the implicit scheme should be used. The vertical resolution in shallow areas can be very fine.

To be suitable for statistical calculation BOM assumes hydrostatic assumption (although there is the choice to add the effect of non-hydrostatic pressure when necessary) and Boussinesq approximation.

In sigma coordinates, the pressure gradient force (PGF) is the quantity of two conditions and when the near topography is steep these terms are large. The two conditions are of the same size in magnitude although if an error (however small) is computed then a big error would occur in the total PGF. If the hydrostatic consistency is not correct then the finite difference will be classed as inconsistent hydrostatically and non-convergent.

Advantages of the model include a natural representation of the bottom boundary layer and a precise image of the equation of state (EOS).

Disadvantages include problems to the natural contours of the horizontal pressure gradient (PG) and in tracer diffusion and advection in the inclined neutral surfaces.

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