Modeling Concepts - Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development - page 295

One way of reducing residual errors resulting from parameterization is to choose
the spatial grid size such that the Nyquist wave number falls within a trough
(minimum) of the energy cascade spectrum. This will ensure a distinct separation
between motions determined deterministically and parametrically. 43
Further constraints arise when assigning values to the diffusion coefficients.
Usually, these values are not assigned from diffusion-dispersion field experiment
results but rather from model numerical stability considerations or from model-data
calibration tests.

6.5.1.4 Input Data Restrictions

A first type of input data restriction applies to initial conditions . How long does a
solution “remember” its initial condition? The answer depends on the retention time
of the system, which, in turn, depends on the boundary conditions. The retention
time is the average time molecules of incoming waters remain in the system. 4b
Normally, a lagoon system will “forget” its initial conditions and will tend toward
a state of equilibrium with the boundary conditions. The initial conditions influence
the solution only during an initial period of about one to five times the retention
time, 44 and then they are “flushed out” rather quickly by advection or mixing.
So, initial conditions can be specified from common sense (average values, for
example) or simple balance estimations. Their influence on the solution lasts a
limited period that can easily be determined. Therefore, field measurement require-
ments for initial conditions are minimal. It is sufficient to know an order of magnitude
of the values of the required initial parameters.
In some instances, the initial conditions can be important, for example, during
short-term emergency forecast simulations or in such specific cases when inflow and
outflow are balanced and an initial error in the absolute water-level estimations is
conserved during further studies of the system. 44 The initial conditions are also
important in systems with long retention times as in some lakes or estuaries, espe-
cially if sediment dynamics is included in the simulation (the residence time of
contaminants in sediment is extremely long). 44
Finally, since a numerical model has a short “initial condition memory,” initial
values can be specified outside a critical range that could otherwise generate numer-
ical instabilities. Practically speaking, after the corresponding initial estimations are
“washed out,” 44 it is always possible to discard them from the solution.
A second type of input data restrictions is related to boundary conditions . Bound-
ary conditions are the driving forces that cause circulation and water quality changes
in a lagoon. Boundary conditions cannot be simulated within a model and must be
specified. They include wind stresses and heat fluxes at the air-water interface and
inflows, outflows, and difference in water-surface elevations across horizontal water
boundaries, as a function of time. In some cases, a boundary condition can be a
relationship between two dependent variables, such as flow vs. depth in a rating curve
for an estuary. 4c
Open boundaries of a model domain must not be located near regions of the grid
where predictions are critically required. 4a This is to avoid the propagation of boundary
errors to that region of interest. For example, when attempting to model fluxes through
a lagoon entrance, open boundaries must be located far offshore, into the sea.