A generalized vertical coordinate for 3D marine models

Vertical coordinate transformation is used in ocean modelling to provide good representation of the flow near bottom and free surface boundaries and to allow the concentration of grid points in regions of high gradient. A natural treatment of impermeability boundary conditions is achieved by considering transformations which fit the surface and bottom boundaries. This paper develops the governing equations of shallow sea hydrodynamics for a generalised vertical coordinate transformation, which embraces all formulations commonly used in ocean modelling, and allows greater freedom to concentrate grid points in regions of high gradient. In addition to the popular sigma coordinates, various hybrid "sigma-z" coordinate transformations, defined for ad hoc applications, are reviewed. Conservative formulations are proposed for the governing equations, including the pressure gradient and horizontal diffusion terms

Un modèle simple pour comprendre pourquoi la couche de glace à la surface d'un plan d'eau tend à rester relativement mince = A simple model to understand why the layer of ice on the surface of water level tends to remain relatively thin

The ice covering salty or fresh water tends to remain rather thin, even if the air temperature is low for a long time. This is due to the insulating role of the ice cover itself, which slows down the transfer to the atmosphere of the heat produced by the solidification of the water. A simple thermodynamic model is developed to investigate the heat transfer processes associated with ice accretion. It is seen that the ice thickness tends to increase as the square root of the time elapsed and that the temperature profile in the ice layer is approximately linear. The stability of the solution obtained is examined. Finally, the simple model is applied to sea ice in the Arctic and Antarctic. The magnitude of the oceanic heat flux is shown to be partially responsible for the ice cover being generally thicker in the Arctic than in the Antarctic

Du rôle de la dispersion horizontale de quantité de mouvement dans les modèles marins tridimensionnels

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On the time to tracer equilibrium in the global ocean

An important issue for the interpretation of data from deep-sea cores is the time for tracers to be transported from the sea surface to the deep ocean. Global ocean circulation models can help shed light on the timescales over which a tracer comes to equilibrium in different regions of the ocean. In this note, we discuss how the most slowly decaying eigenmode of a model can be used to obtain a relevant timescale for a tracer that enters through the sea surface to become well mixed in the ocean interior. We show how this timescale depends critically on the choice between a Neumann surface boundary condition in which the flux of tracer is prescribed, a Robin surface boundary condition in which a combination of the flux and tracer concentration is prescribed or a Dirichlet surface boundary condition in which the concentration is prescribed. Explicit calculations with a 3-box model and a three-dimensional ocean circulation model show that the Dirichlet boundary condition when applied to only part of the surface ocean greatly overestimate the time needed to reach equilibrium. As a result regional-"injection" calculations which prescribe the surface concentration instead of the surface flux are not relevant for interpreting the regional disequilibrium between the Atlantic and Pacific found in paleo-tracer records from deep-sea cores. For tracers that enter the ocean through air-sea gas exchange a prescribed concentration boundary condition can be used to infer relevant timescales if the air-sea gas exchange rate is sufficiently fast, but the boundary condition must be applied over the entire ocean surface and not only to a patch of limited area. For tracers with a slow air-sea exchange rate such as 14C a Robin-type boundary condition is more relevant and for tracers such as d18O that enter the ocean from melt water, a Neumann boundary condition is presumably more relevant. Our three-dimensional model results based on a steady-state modern circulation suggest that the relative disequilibrium between the deep Atlantic and Pacific is on the order of "only" 1200 years or less for a Neumann boundary condition and does not depend on the size and location of the patch where the tracer is injected

What is wrong with isopycnal diffusion in world ocean models?

Coarse grid Ocean General Circulation Models (OGCMs) take into account the effect of unresolved mesoscale eddies by means of a rotated mixing operator which diffuses tracers (such as temperature or salinity) along surfaces of constant potential density called isopycnals. In spite of its profitable physical aspects, the discrete version of the isopycnal mixing parameterization can produce oscillations in the tracer fields, which disagrees with the well-known properties of diffusion operators. The causes of this non-monotonic behaviour of a diffusion operator are highlighted. The location and magnitude of these over-/under-shootings are examined in the results of an OGCM

A two-compartment model for understanding the simulated three-dimensional circulation in Prince William Sound, Alaska

A two-compartment model of Prince William Sound (PWS), Alaska, is developed. One compartment, corresponding to the southern PWS, represents advective phenomena, while the other is dominated by diffusion. This simple model is shown to reproduce rather well the temporal evolution of the mass of a passive tracer contained in PWS simulated by a complex, three-dimensional model under five types of surface forcing. The three parameters of the box-model have clear physical meanings, which helps to understand the hydrodynamics of PWS. In particular, the fraction of the flow entering the northern PWS is estimated, as well as the turnover time of the two regions considered