Gridpoint model

The simplest kind of gridpoint model is one where only one spatial dimension is considered, most often the vertical. Such one-dimensional models are particularly useful when the conditions are horizontally homogeneous and the main transport occurs in the vertical direction. Examples of such situations are the vertical distribution of CO2 within the ocean (except for the downwelling regions in high latitudes, Sie-genthaler, 1983) and the vertical distribution of... 

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... 

In gridpoint models, transport processes such as speed and direction of wind and ocean currents, and turbulent diffusivities (see Section 4.8.1) normally have to be prescribed. Information on these physical quantities may come from observations or from other (dynamic) models, which calculate the flow patterns from basic hydrodynamic equations. Tracer transport models, in which the transport processes are prescribed in this way, are often referred to as off-line models. An on-line model, on the other hand, is one where the tracers have been incorporated directly into a d3mamic model such that the tracer concentrations and the motions are calculated simultaneously. A major advantage of an on-line model is that feedbacks of the tracer on the energy balance can be described... 

A related issue is that the potential can be very sensitive to grid points very near the cavity surface, where die dielectric constant is changing instantaneously. By construction, die cavity is actually defined only to within the grid-point spacing. The van der Waals radii defining the cavity surface that determines whedier a given gridpoint is inside or outside the solute may either be chosen arbitrarily or optimized for a particular computational model (see, for example, Banavali and Roux 2002). 

The more desirable alternative is to use an adaptive numerical algorithm which changes and adapts the number and distribution of the gridpoints and the length of every time step dependent on the shape of the solution to achieve an user specified accuracy. This guarantees that the solution is not dependent on the used numerical solution method but only on the model equations considered. 

Fig. 10. Model calculations of the time development of transient T iring patterns in a batch reactor using the six-variable model of reactions (l)-(3) and (10). [MA]o = 3 x 10 M, [Llo = 8.2 X 10 M, [ClO lo = 1 X 10 M, [S]o = 0.1 M. Length is 5 mm shown horizontally. Total time is 30 minutes shown vertically. Number of gridpoints is 400. Rate constants and diffusion coefficients are in the fourth column of Table II.

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