3-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. 

Haigh, J.D., and J.A. Pyle, Ozone perturbation experiments in a two-dimensional circulation model. Quart J Roy Meteor Soc 108, 551, 1982. 

Meridional circulation in two-dimensional stratospheric models has been specified based on observations or general circulation model calculations recendy efforts have been undertaken to calculate circulations from first principles, within the stratospheric models themselves. An important limitation of using models in which circulations are specified is that these caimot be used to study the feedbacks of changing atmospheric composition and temperature on transport, factors which may be important as atmospheric composition is increasingly perturbed. 

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... 

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. 

We conclude this section with a brief overview of some of the 3-dimensional, dynamic coupled physical-biological models that were developed in the 1990s. There is a historic spht in the practice of ocean biogeochemical modefing, i.e., the field has been divided into large-scale global box and later circulation models with... 

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... 

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. 

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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