Modeling Concepts - Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development - page 293

numerical methods terminology, 42 the terms neglected from the equations are the
source of nonremovable errors in the solution, while the terms conserved are the
source of numerical errors. These restrictions are now discussed in some detail.

6.5.1.1 Physical Restrictions

Physical equations constitute the heart of any numerical model. It is generally
admitted that the physical background of most problems in marine sciences, includ-
ing hydrology, hydrodynamics, oceanology, or climatology, are well investigated,
especially when dealing with “averaged” dynamics and excluding turbulent or non-
linear processes. This physical background is well incorporated into the equations
of matter, momentum, and energy conservation, and the nature of the driving forces
is well understood. 41
In some instances, the physics of a model is simplified by neglecting some terms
that are thought to be “insignificant” in the equations. This is done in order to reduce
the computational resources otherwise needed by a complex problem. However, in
doing so, the question of whether the neglected terms are really “insignificant”
remains unchecked. 41 Therefore, considering the capacity of modern computer
resources and the availability of state-of-the-art models, it is now advisable to choose
a numerical model that includes a complete physical background in order to solve
any problem under consideration. It must be remembered that computer resources
will only improve and very rapidly so. 41
For example, a physical approach widely used for the study of lagoon hydro-
dynamics has been the shallow-water vertically integrated approach. The correspond-
ing 2D numerical model has the following basic assumptions:

• The simulated variables (e.g., currents or density) have a homogenous
vertical distribution in the water column
• Each point of the studied area has one water layer whose thickness is time
dependent
• The flow is time dependent and vertically integrated through the whole
layer
• The bathymetry varies slowly
• The water depth is small compared to the horizontal scale of the process

under study (e.g., in comparison to the wavelength or the length of
domain)

However, in some instances, this 2D approach may not be suitable for some
lagoons. For example, when a wind blows along the major axis of a lagoon, the
surface level at the downwind end is set up and an upwind return will occur near
the bottom when the lagoon depth is on the order of a few meters. In this case, the
numerical model should clearly incorporate the physics of 3D motion. In summary,
a 3D numerical model is recommended for the study of lagoons where a deep basin
(e.g., 5 m) can be found. For shallower lagoons, the 3D model can always be
simplified to a 2D model during the simulation set-up by assigning only one layer
in the vertical direction.