Three-dimensional circulation model

Pitari G. and Visconti G., Global transport of volcanic aerosol from El Chichon eruption studied with a three-dimensional circulation model. Geofisica Internacional , (to appear) 1984. 

Pacanowski and Philander, 1981 Peters et al., 1988). More sophisticated methods are based on prognostic equations for the turbulent kinetic energy k and a second quantity, which is either the dissipation rate e or a length scale in the turbulent flow see Burchard (2002) for a recent review and applications of two-equation turbulence closures for onedimensional water column models. A two-equation turbulent closure has been applied by Omstedt et al. (1983) and Svensson and Omstedt (1990) for the Baltic Sea surface boundary layer under special consideration of sea ice, whereas the application in three-dimensional circulation models is described by Burchard and Bolding (2002) and Meier et al. (2003). 

To simulate the transport of sedimentary material in the water column over realistic topography, it is necessary to run a three-dimensional circulation model, which is extended by submodels describing the surface waves, (Schwab et al., 1984), the shear forces within the bottom boundary layer, and the resulting deposition and erosion processes at the seabed. 

In the Eulerian approach (Jankowski et al., 1996 Lou and Ridd, 1997 Holt and James, 1999 Ribbe and Holloway, 2001 Christiansen et al., 2002), a transport equation is solved for the sediment concentration. Recent studies (Kuhrts et al., 2004, 2006 Seifert et al., 2007) describe moving sedimentary material as a tracer variable in a three-dimensional circulation model. This approach combines a wave boundary layer (Grant and Madsen, 1979) and a friction layer (Smith and McLean, 1977) to compute the wave-induced and the current-induced contribution to the skin friction acting on the seabed. 

Such models describe the life history of animals as propagation through the different size or mass classes and need a sophisticated formulations of predator-prey interaction. There are several approaches to describe life histories of copepods by models (Carlotti et al., 2000). A new theoretical formulation to allow the consistent embedding of dynamical copepod models into three-dimensional circulation models was given in Fennel (2001). Examples of simulations for the Baltic were given in Fennel and Neumann (2003). The basic idea is that both biomass and abundance of different stages or mass classes are used as state variables, while the process control is related to mean average individuals in each mass class, that is the ratio of biomass over abundance. 

Although many important features of oceanic and atmospheric circulation can be explicitly resolved in three-dimensional gridpoint models, there will always be many processes that occur on the sub-gridscale level that cannot. The effects of these sub-gridscale processes must be parameterized, i.e., summarized in a statistical fashion in a way related to the large-scale flow. The purpose of parameterization is to describe the combined effect of sub-gridscale processes on the larger-scale... 

Three-dimensional models offer more realism, at least apparently, but with the cost of greater complexity, a more limited number of simulations, and a higher probability of crucial regional errors in the base solutions, which may compromise direct, quantitative model-data comparisons. Ocean GCM solutions, however, should be exploited to address exactly those problems that are intractable for simpler conceptual and reduced dimensional models. For example, two key assumptions of the 1-D ad-vection-diffusion model presented in Figure 2 are that the upwelling occurs uniformly in the horizontal and vertical and that mid-depth horizontal advection is not significant. Ocean GCMs and tracer data, by contrast, show a rich three-dimensional circulation pattern in the deep Pacific. 

A. Ungan and R. Viskanta, Three dimensional Numerical modelling of circulation and heat transfer in a glassmelting tank Part I. Mathematical formulation, Glastechnische Berichte. 60, 1987, page 71-78... 

The containment pressure transient calculation uses the transient energy release from the break, and includes submodels for dousing, containment air coolers, fission product and hydrogen transport, and natural and forced circulation, as well as models for containment impairments such as open ventilation dampers. Multinode two or three fluid one dimensional containment models have been used for this analysis recently three dimensional containment models have been applied to study the local distribution of hydrogen after a LOCA + LO ECC. 

Roelofs, G.J., Lelieveld, J., and van Dorland, R. (1997) A three-dimensional chemistry/general circulation model simulation of anthropogenically derived ozone in the troposphere and its radiative climate forcing, J. Geophys. Res. 102,23389-23401. 

Hyppanen, T Lee, Y. Y., and Rainio, A. A three-dimensional model for circulating fluidized bed combustion, in Circulating Fluidized Bed Technology III (P. Basu, M. Horio and M. Hasatani, eds.), pp. 563-568. Pergamon Press, 1991. 

Applications of three-dimensional Baltic Sea circulation models, which encompass both synoptic scales and slowly varying long-term processes, were reported in Lehmann (1995), Lehmann and Hinrichsen (2000), Neumann et al. (2002), Schrum et al. (2003), and Lehmann et al. (2004). Long-term simulations covering the last century have been carried out by Meier... 

Circulation models are based on the equations of motion of the geophysical fluid dynamics and on the thermodynamics of seawater. The model area is divided into finite size grid cells. The state of the ocean is described by the velocity, temperature, and salinity in each grid cell, and its time evolution can be computed from the three-dimensional model equations. To reduce the computational demands, the model ocean is usually incompressible and the vertical acceleration is neglected, the latter assumption is known as hydrostatic approximation. This removes sound waves in the ocean from the model solution. In the horizontal equations, the Boussinesq approximation is applied and small density changes are ignored except in the horizontal pressure gradient terms. This implies that such models conserve... 

Andrejev, O., Myrberg, K., Alenius, P., Lundberg, P. A., 2004. Mean circulation and water exchange in the Gulf of Finland a study based on three-dimensional modelling. Boreal Environment Research, 9, 1-16. 

Blumberg, A. F, Mellor, G. L., 1987. A description of a three-dimensional coastal ocean circulation model. In Heaps N. S. (Ed.), Three-Dimensional Coastal Ocean Models. American Geophysical Union,Washington, DC, pp.1-16. 

Stevens, D. P., 1990. On open boundary conditions for three dimensional primitive equation ocean circulation models. Geophysical and Astrophysical Fluid, Dynamics, 51, 103-133. 

Daimon M, Shiota T, Gillinov AM, et al. Percutaneous mitral valve repair for chronic ischemic mitral regurgitation a realtime three-dimensional echocardiographic study in an ovine model. Circulation 2005 111 2183—9. 

Three-dimensional models which provide solutions to some form of the primitive equations outlined in Section 3.3 are called general circulation models (GCMs). These models can provide insight on the coupling between dynamical and radiative processes in the atmosphere. They resolve large-scale waves and synoptic eddies, and include state-of-the-... 

Rasch, P.J., B.A. Boville, G.P. Brasseur, A three-dimensional general circulation model with coupled chemistry for the middle atmosphere. J Geophys Res 100, 9041, 1995. 

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