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period ( being the sampling interval).
Th
e terms of the ocean-lagoon
exchange time series during any
n
th time step (
TNt
total
=⋅∆∆
t
nN
=
1,
) can then be obtained as
[
]
n
n
n
avg
∆
h
=
∆
h
−
∆
t
⋅
(
Q
+
Q
−
Q
)
S
,
(6.20)
inf
low
avg
riv
prc
evp
lag
where is the average lagoon surface area, which is a time-dependent function
of the level variation
S
lag
avg
Sht
lag
avg
(())
. The volume inflow and flux are then easily calculated
∆
h
inflow
from
by summation of positive terms only as:
∑
∆
avg
n
V
=⋅
S
h
(),
+ =
n
1
,
N
(6.21)
inf
low
lag
inf
low
and
QV
=
T
inf
low
inf
low
total
Ocean-lagoon water exchange estimates and dominant periods of oscillation can
also be obtained through spectral analysis. At first, the time-dependent level variation
function is decomposed into harmonic series, after subtracting the linear
trend. A trend in local water-level measurements may be the result of a water-level
trend in the adjacent ocean, of a geological subsidence of the coastline over yearly
time scales, or simply an erroneous functioning of the tide gauge.
Once the local trend is removed from the series, the water-level time series can
be reduced to its Fourier harmonic components as
∆
ht
inf
()
low
∆
h
()
t
=⋅
∆
h
sin
(
ωϕ
⋅ +
t
),
k
=
1
,
K
inf
low
k
k
k
where are the amplitude, the frequency, and the period of
the
k
th harmonic, respectively. In this case, the harmonic frequencies are limited by
the Nyquist frequency (or minimum period,
∆
h
,
ωπ
=⋅
2
/
T
,
and
T
k
k
k
k
T
K
), given by
w
K
=
(2
∆
t
)
-1
, where
∆
t
is the sampling interval.
Assuming that the wet surface area change with water level
Sh
lag
avg
()
∆
is not
V
k
inflow
significant, the volume corresponding to one period of ocean-lagoon inflow
and its flux
q
inflow
due to the
k
th harmonic term at period
T
k
is given by
k
avg
∆
V
=⋅ ⋅
2
S
∆
h
inf
low
lag
k
(6.22)
k
k
q
=
∆
V
T
inf
low
inf
low
k
where the multiplication by 2 takes into account the fact that an integral over half
of a period of harmonic function sin equals 2.
Finally, the total average seawater inflow flux during the period
T
total
is
∑
k
Q
=
q
,
k
=
1
,
K
(6.23)
inf
low
inf
low
q
inflow
The comparison of the magnitudes of provides information on which
oscillation period constitutes the main input into ocean-lagoon water exchange.
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