40
Working out a system-oriented model, as well as interpreting its results, generally poses
several mathematical problems, which may sometimes be addressed with the help of simpler,
test-oriented models. Some of these problems are considered below.
For example, the numerical scheme selected for solving the equations of the model must
provide accurate results. To do so, the algorithm must be, at least, consistent and stable. In
most cases, consistency is easily checked. On the other hand, verifying that the numerical
scheme associated with a system-oriented model is stable often presents insurmountable
difficulties, for the equations are very complex. The usual approach is then to analyse sub-sets
of the whole algorithm, especially those that are likely to be the least stable. Properly choosing
the reduced sets of equations is thus the key problem. Any inappropriate choice may give rise to
unpleasant surprises, as exemplified in Section 3 (see also Beckers and Deleersnijder, 1993).
Another significant problem is the well-foundedness of the pararneterizations. No numerical
model is able to cover all the time-space scales of marine phenomena. Once the resolution of the
model is chosen, the effect of the processes having smaller scales than the time-space
discretization grid, the so-called sub-grid scale phenomena, must be parameterized by
appropriate formulae. A parameterization is merely an approximation, hopefully providing a
reasonably good account of the process it addresses. It is thus conceivable that, for a given subgrid scale phenomenon, several parameterizations may be considered. The formulation to be
selected must obviously be capable of realistically representing the effect it addresses. More
importantly, perhaps, it must also be well-conditioned, i.e., when introduced into the model, it
must enable the model to produce well-behaved solutions. The latter property does not
necessarily ensue from the parameterization being sufficiently realistic, as will be shown in
Section 4 (see also Deleersnijder and Luyten, 1994).
Complex marine models routinely output millions, or even billions, of real numbers, the
analysis and interpretation of which are far from straightforward. In fact, understanding such a
large amount of information is a real challenge. Simple models may be helpful for interpreting
the results of a complex one. Most quantities computed by marine models are four-dimensional,
i.e., they depend on time and three space coordinates. Since the vast majority of the graphical
tools are two- or three-dimensional, the graphical representation of the model results requires
appropriate mapping onto a two- or three-dimensional space. This may be carried out in
numerous ways by means of existing graphical packages. One must however bear in mind that
the role of computer graphics is not just to produce attractive pictures, but to help gain insight
into the physics of the marine flow under study. In other words, physical intuition and
reasoning are also needed if profound understanding of the flow mechanisms is sought.
Schematically, this may be expressed by the following relation: quality of the interpretation =
(Physical skill) x (computer graphics skill). This implies, for instance, that the best graphical
software will probably prove useless if operated by someone having no idea of ocean
dynamics! An example of an interpretation method based on little graphical skill but
considerable physical skill is given in Section 5, where the vertical velocity field produced by a
hydrodynamic model of the region of the Bering Strait is analyzed (see also Deleersnijder
1994a).
Finally, in Section 6, some results of a World Ocean model are given. Its equations are
similar to those used at smaller scales, but the nature of the phenomena is completely different.
A coordinate system is designed in such a way that the whole World Ocean, including the
Arctic Ocean, can be represented without facing any singularity problem - as would happen,
Working out a system-oriented model, as well as interpreting its results, generally poses
several mathematical problems, which may sometimes be addressed with the help of simpler,
test-oriented models. Some of these problems are considered below.
For example, the numerical scheme selected for solving the equations of the model must
provide accurate results. To do so, the algorithm must be, at least, consistent and stable. In
most cases, consistency is easily checked. On the other hand, verifying that the numerical
scheme associated with a system-oriented model is stable often presents insurmountable
difficulties, for the equations are very complex. The usual approach is then to analyse sub-sets
of the whole algorithm, especially those that are likely to be the least stable. Properly choosing
the reduced sets of equations is thus the key problem. Any inappropriate choice may give rise to
unpleasant surprises, as exemplified in Section 3 (see also Beckers and Deleersnijder, 1993).
Another significant problem is the well-foundedness of the pararneterizations. No numerical
model is able to cover all the time-space scales of marine phenomena. Once the resolution of the
model is chosen, the effect of the processes having smaller scales than the time-space
discretization grid, the so-called sub-grid scale phenomena, must be parameterized by
appropriate formulae. A parameterization is merely an approximation, hopefully providing a
reasonably good account of the process it addresses. It is thus conceivable that, for a given subgrid scale phenomenon, several parameterizations may be considered. The formulation to be
selected must obviously be capable of realistically representing the effect it addresses. More
importantly, perhaps, it must also be well-conditioned, i.e., when introduced into the model, it
must enable the model to produce well-behaved solutions. The latter property does not
necessarily ensue from the parameterization being sufficiently realistic, as will be shown in
Section 4 (see also Deleersnijder and Luyten, 1994).
Complex marine models routinely output millions, or even billions, of real numbers, the
analysis and interpretation of which are far from straightforward. In fact, understanding such a
large amount of information is a real challenge. Simple models may be helpful for interpreting
the results of a complex one. Most quantities computed by marine models are four-dimensional,
i.e., they depend on time and three space coordinates. Since the vast majority of the graphical
tools are two- or three-dimensional, the graphical representation of the model results requires
appropriate mapping onto a two- or three-dimensional space. This may be carried out in
numerous ways by means of existing graphical packages. One must however bear in mind that
the role of computer graphics is not just to produce attractive pictures, but to help gain insight
into the physics of the marine flow under study. In other words, physical intuition and
reasoning are also needed if profound understanding of the flow mechanisms is sought.
Schematically, this may be expressed by the following relation: quality of the interpretation =
(Physical skill) x (computer graphics skill). This implies, for instance, that the best graphical
software will probably prove useless if operated by someone having no idea of ocean
dynamics! An example of an interpretation method based on little graphical skill but
considerable physical skill is given in Section 5, where the vertical velocity field produced by a
hydrodynamic model of the region of the Bering Strait is analyzed (see also Deleersnijder
1994a).
Finally, in Section 6, some results of a World Ocean model are given. Its equations are
similar to those used at smaller scales, but the nature of the phenomena is completely different.
A coordinate system is designed in such a way that the whole World Ocean, including the
Arctic Ocean, can be represented without facing any singularity problem - as would happen,