Modeling Concepts - Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development - page 267

1000

9

6

5

4

3

2

100

9

7

6

5

4

3

2

10

9

1.0 10.0 100.0 1000.0

Period, day

FIGURE 6.15 Convergence of flushing times as longer period harmonics are added to
Equation (6.37).

than the initial data random error (1 cm) were also excluded, leaving 286 terms in
the Fourier series. These terms were finally used to calculate the marine water inflow
(Equation (6.36)) and the corresponding ventilation time (Equation (6.37)).
Figure 6.15 shows results obtained from Equations (6.36) through (6.37) indicat-
ing that the flushing time for the Vistula Lagoon is

19 days. This is the time
necessary to reduce any conservative pollutant concentration to 37% of its initial
value. This figure also shows that the initial concentration will diminish to 10% over
2.3

τ flush ≈

⋅τ flush ≈ 43-44 days, and to 1% over 4.6 ⋅τ flush ≈ 87-88 days.

6.3.3.1.2 Local Flushing Time
It is instructive to distinguish between the integral flushing time and the local
flushing time (Zimmerman 9 ) for some applications, which means using the same
approach but applied not only to total lagoon volume but also to any compartment
of a lagoon, even to any grid cell.
Consider a lagoon of volume V 0 , continuously flushed by a stationary volume
flux Q including a river discharge (if any) at the upstream boundary and tidal prism
at the ocean boundary. The integral flushing time of the lagoon has been defined
above as Equation (6.32). This expression implicitly assumes that the marine water
added to the lagoon through its open boundaries is completely and instantaneously