Modeling Concepts - Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development - page 289

In both types of models, the typical length of a cell is on the order of magnitude
of the width. This does not mean that detailed bathymetric information is not
required. In fact, in order to obtain realistic results, the geometry used in the model
must represent the lagoon bathymetry. To accomplish that, every critical cross section
must be defined as a cross section in the model (a section can be critical because it
may be wider or narrower than the adjacent one).

6.4.1.2 Horizontal Resolution Models

Horizontal resolution models can be depth integrated (2D) or fully 3D. Here, the
computational grid representing the modeled area is formed by rectangular cells in
finite-difference methods and by triangles in finite-element methods. The depth is
specified in the center of the grid or at the corners and is obtained by interpolation
of hydrographic depth soundings or other sources of digitized bathymetry. The
horizontal resolution in horizontally resolving models is much higher than that of
laterally integrated models, and more detailed bathymetric information is required.
In general, “grid-generating programs” create these computational grids. These
programs require the supply of a detailed coastline and they compute the depth of
each cell by averaging/interpolating a digitized bathymetry. When the information
is scarce, special care has to be taken when verifying the depth generated for each
model cell.
In the case of 3D models, once a horizontal grid is generated with a corresponding
depth distribution, a vertical discretization has to be defined. Two discretizations can
be easily defined: (1) sigma coordinates or (2) Cartesian coordinates. In Cartesian
coordinates, the layers are horizontal and except for the surface layer, they maintain
the same thickness in time. The surface layer thickness will depend on the free surface
position. The bottom layers progressively disappear as the water becomes shallower.
In the case of sigma coordinates, the water column is divided into layers of variable
thickness (in space and time) in such a way that the ratio between the thickness of a
layer and the local depth remains constant in space and time. In other words, in sigma-
type models, the vertical resolution and the number of layers are independent of the
local depth. This is convenient in systems where density effects play a secondary role
compared to topographic effects. Special care must, however, be taken in intertidal
areas, where the thickness of each layer approaches zero during the drying procedure.
The consideration of two sigma domains in the water column can be a solution.

6.4.2 I NITIAL C ONDITIONS

Initial conditions must be supplied for each state variable (velocity and levels,
temperature, salinity, nutrients, etc.). This information has to be obtained from field
data measured synoptically. Unfortunately, information on most variables is
unknown or available only for a few points, so that assumptions have to be made
about initial conditions. For that purpose, properties can be grouped into rapidly
dissipative and slowly (or non-) dissipative properties.
Dissipative properties rapidly “forget” the information related to the initial condi-
tions and become dependent in time only on the boundary conditions. Hydrodynamic