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Josef M. Oberhuber

Abstract

A diabatic ocean general circulation model based on primitive equations is described. It uses isopycnals as Lagrangian coordinates in the vertical and predicts a free surface. Prognostic fields of temperature and salinity enter the dynamics as active tracers through a realistic equation of state. The surface boundary layer is parameterized by a detailed mixed-layer model. A sea ice model with a viscous-plastic rheology is coupled to the mixed layer. Thermal forcing, wind stress, and surface input of turbulent kinetic energy are determined from monthly mean values of atmospheric quantities, while the freshwater flux still is parameterized by a Newtonian relaxation towards the observed surface salinity.

The model equations are written in layer formulation. Each interface represents an isopycnal. As the equations are written in flux form, the mass flux and the content of mass, heat, and salt are conserved in the model domain. A potential vorticity conserving scheme is included. Except for the mixed layer, all layers are kept at a prescribed potential density that is different for each layer. In the uppermost layer, potential density is allowed to develop arbitrarily. A method is developed that treats vanishing layers by making the horizontal boundaries time dependent in each layer. The time integration scheme consists of a predictor-corrector technique combined with a semi-implicit scheme. The model is formulated in spherical coordinates with variable, but still orthogonal, grid resolution in longitude and latitude and allows for any irregular geometry.

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Josef M. Oberhuber

Abstract

An ocean general circulation model (OGCM) formulated on isopycnal coordinates is used to model the circulation of the Atlantic. The model domain is bounded meridionally at 30°S and the North Pole and extends zonally from 100°W to 50°E with cyclic boundary conditions in the Arctic basin. The Atlantic sector of the Arctic basin is included in order to obtain a more realistic exchange of water masses between the North Atlantic and the Arctic. For the purpose of achieving a sufficient resolution of the high-latitude current systems, the grid spacing is made variable with a 2° × 2° resolution in the entire equatorial and North Atlantic and a steadily increasing resolution in the Greenland-Iceland-Norwegian seas towards about 1° zonally and 0.5° meridionally. The model is integrated over 100 years, with acceleration of the deeper layers during the fist 50 years. Initial conditions are observed annual mean temperature and salinity. After the adjustment period the ocean approaches a cyclo-stationary state, except for the deep ocean where temperature and salinity have not become stationary.

The model yields realistic equatorial currents and also simulates the separation of the Gulf Stream and the complex current structure in the Greenland-Iceland-Norwegian seas. Heat and freshwater fluxes and the seasonal variation of the mixed-layer depth agree reasonably with observations. The stratification of the upper ocean demonstrates the capability of an isopycnal model with thermodynamics to reproduce the thermohaline circulation. Finally, the simulated sea ice cover is considered in order to discuss the coupling among sea ice, mixed layer, and the deep ocean.

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Michael Herzog, Josef M. Oberhuber, and Hans-F. Graf

Abstract

The presented turbulence scheme was developed for the Active Tracer High-Resolution Atmospheric Model (ATHAM) to parameterize the effect of subgrid-scale turbulence. In contrast to the commonly used assumption of local isotropy in high-resolution atmospheric modeling, this scheme differentiates between horizontal and vertical turbulent exchange to represent the strong influence of buoyancy forces and vertical transports. Its computational efficiency is similar to classical turbulent kinetic energy approaches while preserving one of the main feature of higher-order schemes. The present extensions to include anisotropic effects in a turbulent kinetic energy approach do not need any ad hoc assumptions and are equivalent to the classical formulation in the isotropic limit.

The presence of high tracer concentrations in a particle-laden plume is taken into account, as well as supersonic effects at low Mach numbers. The turbulent exchange coefficients used in the equations of motion are derived from a set of three coupled differential equations for the horizontal and vertical turbulent energy and the turbulent length scale. No turbulent equilibrium is assumed. All turbulent quantities are treated prognostically.

Numerical simulations of convective plumes of a typical Plinian volcanic eruption with the nonhydrostatic plume model ATHAM reveal that a complex treatment of turbulent quantities is necessary in order to capture the bulk characteristics of the plume, such as the plume height, the horizontal extent, and plume development in time. Anisotropic effects of turbulence have a significant impact on the stability and internal structure of the plume. For the first time, results from a fully three-dimensional simulation of a volcanic plume are presented.

Because of its general formulation the presented turbulence scheme is suitable for a wide range of atmospheric applications.

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