Some mathematical problems associated with the development
and use of marine models
*
**
Eric DELEERSNIJDER ,Jean-Marie BECKERS , Jean-Michel CAMPIN,
*
***
Mohammed EL MOHAJIR, Thierry FICHEFET and Patrick LUYTEN
Institut d'Astronomie et de Geophysique G. Lemaitre
Universire Catholique de Louvain
2 Chemin du Cyclotron, B-1348 Louvain-Ia-Neuve, Belgium
1. Introduction
"Science is now a tripartite endeavour with simulation added to the two classical
components, experiment and theory (Robinson, 1987). The routine use of numerical
"simulation in scientific research (numerical experimentation, sensitivity and process studies,
etc.) is thought by many to represent the first major step forward in the basic scientific method
since the seventeenth century" (Robinson, 1987).
Marine sciences, as many other fields of scientific research, now intensively use
mathematical and numerical models. There might even be a tendency, among some
oceanographers, to overly rely on the predictions of the models, which are, in fact, no more
than artefacts, i.e., man-made objects. The models, however complex they may be, provide, at
, best, a reasonable estimate of the behaviour of the system under study.
" Numerical models are now so appealing that one might progressively forget that they are no
suqstitute to reality. To avoid such "alienation", it is helpful to realized that there are several
types of models, with different objectives. According to Nihoul (1994) one may distinguish:
- The test-oriented models, which are needed for "testing mathematical and numerical methods
and their software implementation". These models are based on a reduced set of equations and,
hence, are generally not intended to realistically simulate the reality.
- The process-oriented models, which focus on a few dominant or important processes. This
often implies sacrificing some of the realism of the results, but allows detailed analysis of the
mechanisms driving the system under study to be carried out.
- The system-oriented models, which are "called upon to tackle a practical situation", such as
the management of the resources of the seas. The results of these models must be as realistic as
possible, which usually requires appropriate data assimilation procedure to operate together
with the prognostic model (Bennett, 1992). Encompassing a large number of processes,
system-oriented models are generally very complex, so that they are probably not the best
suited tool for investigating or "explaining" processes .
.. Research Associate, National Fund for Scientific Research (8elgium)
.... Senior Research Assistant, National Fund for Scientific Research (Belgium); GHER, University of
Liege, Sart Tilman 85, 8-4000 Liege, Belgium
...... MUMM, Gul/edel/e 100, B-1200 Brussels, Belgium
NATO ASI Series. Vol. I 48
The Mathematics of Models for Climatology
and Environment
Edited by Jesus I1defonso Diaz
© Springer-Verlag Berlin Heidelberg 1997
and use of marine models
*
**
Eric DELEERSNIJDER ,Jean-Marie BECKERS , Jean-Michel CAMPIN,
*
***
Mohammed EL MOHAJIR, Thierry FICHEFET and Patrick LUYTEN
Institut d'Astronomie et de Geophysique G. Lemaitre
Universire Catholique de Louvain
2 Chemin du Cyclotron, B-1348 Louvain-Ia-Neuve, Belgium
1. Introduction
"Science is now a tripartite endeavour with simulation added to the two classical
components, experiment and theory (Robinson, 1987). The routine use of numerical
"simulation in scientific research (numerical experimentation, sensitivity and process studies,
etc.) is thought by many to represent the first major step forward in the basic scientific method
since the seventeenth century" (Robinson, 1987).
Marine sciences, as many other fields of scientific research, now intensively use
mathematical and numerical models. There might even be a tendency, among some
oceanographers, to overly rely on the predictions of the models, which are, in fact, no more
than artefacts, i.e., man-made objects. The models, however complex they may be, provide, at
, best, a reasonable estimate of the behaviour of the system under study.
" Numerical models are now so appealing that one might progressively forget that they are no
suqstitute to reality. To avoid such "alienation", it is helpful to realized that there are several
types of models, with different objectives. According to Nihoul (1994) one may distinguish:
- The test-oriented models, which are needed for "testing mathematical and numerical methods
and their software implementation". These models are based on a reduced set of equations and,
hence, are generally not intended to realistically simulate the reality.
- The process-oriented models, which focus on a few dominant or important processes. This
often implies sacrificing some of the realism of the results, but allows detailed analysis of the
mechanisms driving the system under study to be carried out.
- The system-oriented models, which are "called upon to tackle a practical situation", such as
the management of the resources of the seas. The results of these models must be as realistic as
possible, which usually requires appropriate data assimilation procedure to operate together
with the prognostic model (Bennett, 1992). Encompassing a large number of processes,
system-oriented models are generally very complex, so that they are probably not the best
suited tool for investigating or "explaining" processes .
.. Research Associate, National Fund for Scientific Research (8elgium)
.... Senior Research Assistant, National Fund for Scientific Research (Belgium); GHER, University of
Liege, Sart Tilman 85, 8-4000 Liege, Belgium
...... MUMM, Gul/edel/e 100, B-1200 Brussels, Belgium
NATO ASI Series. Vol. I 48
The Mathematics of Models for Climatology
and Environment
Edited by Jesus I1defonso Diaz
© Springer-Verlag Berlin Heidelberg 1997