Estuary Processes and Managment - River Dynamics and Integrated River Management - page 488

Fig. 8.24 Schematic diagram for flushing analysis of a semi-enclosed water body: a) one-segment system; b) two-
segment system

the system from the exterior, the decrease of tracer mass due to tidal flushing is given by (Thomann and
Mueller, 1987):

e QVt MMe (8.2)

In order to derive systematically the flushing time from numerical tracer experiments, we may adopt a
definition of the flushing time as “the average lifetime of a particle in the given volume of water body”
(Officer and Kester, 1991). For the tracer experiment, flushing time can be represented by the following
equation:

0

1

f

³

T t M d (8.3)

f

M

0

0

Solving Eqs. (8.2) and (8.3) gives the flushing time:

V

T

f

(8.4)

Q

e

While the volume V can be readily obtained from field measurements, the net tidal exchange Q e is
affected by many factors including freshwater runoff, tidal flow, and salinity distribution, and cannot be
directly measured. Hence, for a complex coastal embayment, traditionally, highly simplified methods
based on readily available data (such as salinity or tide levels) are often applied - e.g., the “fraction of
freshwater method” and “tidal prism method”.
The tidal prism method is a classical approach to estimate flushing time in tidal systems when only
basin geometry and tidal range information are available. By assuming that the flood flow entering the
semi-enclosed inlet behaves like a jet, while the flow leaving the bay during ebb tide is a sink-type of flow
(Ketchum, 1951; Stommel and Farmer, 1952), an analytical model of the tidal exchange characteristics
between the inlet and its exterior can be obtained. Based on measurements of tidal cycles, the tidal prism
method calculates the flushing time as:

VT

T

bP

(8.5)

f

1

where, V is the mean volume, T is the tidal period, P is the tidal prism equal to the difference in the
volume of water between low and high tides, and b is the return ratio (fraction of ebb water returning to
the embayment during the subsequent flood). The tidal prism method tacitly assumes complete mixing
within the defined segments, and hence tends to produce overly optimistic flushing rates.
The tidal prism method cannot be applied to embayments with substantial freshwater inflow, because
an increase of freshwater inflow leads to a decrease of the portion of the tidal prism volume. In such
situations, the fraction of freshwater method is often used (Dyer, 1973; Fischer et al., 1979). Describing