Semidiurnal and Diurnal Tidal Constituents
in Florida Bay
by
Ned P. Smith
Patrick A. pitts
Harbor Branch Oceanographic Institutlon
5600 N. U.S. Highway 1
Fort pierce, Florida 34946
The First Report in Connection with
Cooperative Agreement CA 5280-4-9022
800
::.:..
-t.o +26"0
.
.
~;i<l\%¥'-f~~fi~\
0;:::..:::::
N
..
~~:(,!......
" :-
-:..
__ s .
I
o
1
I
50
J
i
1
10Q-Km:
Figure 1. Map of Florida Bay, showing the study area between
the southern tip of the Florida Peninsula and the
Florida Keys.
-1-
INTRODUCTION
Florida Bay lies directly south of the southern tip of the
Florida peninsula (Figure 1).
south by the Florida Keys.
The bay is bounded on the east and
On the western side, the bay is open to
the Gulf of Mexico, and there is no topographically defined boundary between the Gulf and the Bay.
Taking the 81°05'W meridian as
the boundary, however, the surface area of Florida Bay is approxiApproximately 1,645 km 2 of Florida Bay, 77% of
mately 2,140 km2 •
the total, lies within Everglades National Park.
Water depth along
the 81°05' meridian averages about 3 m; within the bay, the water
depth is characteristically 0.5 to 1.0 m.
islands
define
a
series
of
sub-basins
Mud banks and mangrove
that
are
connected
by
channels.
The tides of Florida Bay represent the interaction of tidal
conditions in the eastern Gulf of Mexico and southwestern North
Atlantic Ocean.
Given the dominance of semidiurnal tidal constit-
uents in the Atlantic and the dominance of diurnal constituents
throughout much of the Gulf, tidal conditions in the Florida Keys
are spatially variable--an interesting mix of Gulf tidal waves
moving toward the Atlantic, and Atlantic tidal waves moving toward
the Gulf of Mexico.
The combined effect of shallow water, mangrove
islands and mud banks, however, is to damp the ebb and flood of the
semidiurnal and diurnal tide, leaving the interior of
th~ ~ayvir­
tually tideless and dominated, by the seasonal-sea ,level cycle and
low-frequency wind effects.
Nevertheless, in much of the bay, and
certainly around the fringe, tidal processes play an important role
by providing a baseline level of circulation and flushing.
-2-
Previous studies of tides that focused on the eastern Gulf of
Mexico included little from Florida Bay in particular.
Marmer
(1954) listed harmonic constants from 40 stations surrounding the
Gulf, but included:nothing between Key West and Baron River, near
Cape Romano.
Similarly, Zetler and Hansen (1970) provided harmonic
constants from Key West, the Dry Tortugas and Naples on the Gulf
side of Florida Bay, and Miami on the Atlantic side, but nothing
from Florida Bay proper.
gional perspective.
Still, these early studies provided a re-
Tidal conditions in the eastern Gulf of Mexico
were shown to be mixed, semidiurnal--in contrast to the predominantly diurnal tides found in the western Gulf.
Tidal character-
istics of Florida Bay were described in a qualitative way and without supportive data by Jones
(1973), who stated that individual
tidal patterns at any given location can be extremely complex.
The
data base available for characterizing tidal conditions was very
small at that time, however.
In addition to poor spatial resolution in the vicinity of
Florida Bay,
previous studies were restricted largely to semi-
diurnal and diurnal constituents.
Analyses of longer time series
needed to quantify the fortnightly, monthly, semiannual and annual
tidal constituents were made only for primary tide stations at
Miami and Key West.
This was a consequence of the difficulty of
obtaining long time series with older generations of recording.
. .
instrumentation.
Marmer (1954), however, quatltified the seasonal
variability of water level in the Gulf of Mexico, and his findings
apply equally well to Florida Bay.
Whitaker (1977) went one step
further by investigating the steric expansion and contraction of
-3-
the water column over annual time scales.
Steric effects make a
significant contribution to the annual, Sa, and semiannual, Ssa,
tidal constituents, but harmonic constants were not quantified.
While water level measurements in Florida Bay itself were almost nonexistant until 1988, numerous time series were obtained by
the National Ocean Service from both short- and long-term studies
on the Gulf side of the Florida Keys.
Unpublished data from Na-
tional Ocean Service studies conducted over the past three decades
include harmonic constants from 174 locations between Miami Beach
and the Dry Tortugas,
28 of which relate to the present study.
Harmonic constants are available for three semidiurnal and two
diurnal tidal constituents at each stationi most records are too
short to calculate harmonic constants of the longer period tides.
The importance of understanding the tides of Florida Bay stems
from the role tides play in exchanging water between the bay and
adjacent Atlantic and Gulf shelf waters.
In addition to this peri-
odic flushing action around the fringe of the bay, Wang,
et ale
(1994) have suggested that a set-up of water levels in the western
part of the bay arises from the frictional damping of progressive
tidal waves and produces a flushing action by forcing water through
the bay and out into the Atlantic through tidal channels separating
the Florida Keys.
Smith (1994) has documented a long-term net out-
flow through several tidal channels in the Middle Keys.
The purpose of this report is to
surnrnari~
recent analyses of
long time series collected by National Park Service personnel from
the interior of Florida Bay, and to incorporate these findings into
the growing data base of water levels in Florida Bay.
Data col-
-4-
lected by the National Park Service have been used to determine the
harmonic constants (amplitudes and local phase angles) of the principal tidal constituents.
Amplitudes and local phase angles are
combined in the form of co-amplitude and co-phase charts, respectively, to provide a clearer picture of the magnitude and movement
of semidiurnal and diurnal tides in Florida Bay.
Results confirm
complex patterns in the sense that amplitudes and phase angles for
a given tidal constituent are spatially variable.
Amplitudes are
damped rapidly as tidal waves enter the bay from the Gulf of Mexico
and from the Atlantic through tidal channels along the southeast
perimeter.
As a result, a virtually tideless region appears in the
interior of the bay.
There, only long-period tidal constituents
and nontidal processes provide the forcing needed to effect transport and flushing.
DATA
The National
Park Service maintains water level
recorders
within Florida Bay proper and in freshwater areas directly connected to the bay.
Table 1 is a listing of National Park Service
water level stations, and the segments of water level records that
were found to be suitable for use in this report.
The criteria for
retaining any segment of water level record involved both timing
errors and water depth errors.
A record was dropped from further
consideration if the t i.mi.nq. error exceeded -5 minutes or if the
water depth error exceeded 3 ern.
Data from all National
Park
Service study sites have been used in this study; however only 11
stations
provided
harmonic
constants
used
in
constructing
co-
-5-
Table 1. Summa~ of the National Park Service water level records used
to quantify tidal harmonic constants and construct analog plots. Times
are in Eastern Standard Time. The column labelled 'Obs'ns' contains the
number of hourly data points in each record.
End Time
Date
Obs'ns
Study Site
Filename
Start Time
Blackwater
Sound
DBS9193
DBS93A
DBS94
1305 Oct. 22, 1991
1705 Oct. 06, 1993
1105 Jan. 04, 1994
0905 Feb. 11, 1993
1505 Nov. 15, 1993
1005 Jan. 24, 1994
11,469
959
480
Bob Allen
Key
DBA9092
DBA9293
DBA9394
1105 Jan. 03, 1990
1005 Apr. 17, 1992
1205 June 25, 1993
1005 Mar. 19, 1992
1705 May 26, 1993
1605 Jan. 25, 1994
19,344
9,704
5,141
Buoy Key
DBK9091
DBK9192
DBK92A
DBK9293
DBK9394
1705
1405
1305
1205
0805
Jan.
Apr.
Apr.
Oct.
June
03,
08,
01,
13,
25,
1990
1991
1992
1992
1993
1505
1605
0005
1105
1405
Mar.
Mar.
Oct.
May
Jan.
15,
19,
08,
21,
20,
1991
1992
1992
1993
1994
10,463
8,307
4,548
5,280
5,023
Broad
River
DBR90A
DBR9091
DBR91A
DBR91B
DBR9192
DBR93A
DBR9394
1305
1305
1405
1405
1605
1405
0705
Jan.
Nov.
Mar.
June
Dec.
Mar.
June
18,
13,
20,
19,
18,
09,
20,
1990
1990
1991
1991
1991
1993
1993
1105
1005
1005
1205
1305
1105
1305
Oct.
Feb.
May
Sep.
July
Apr.
Jan.
12,
14,
15,
19,
22,
30,
11,
1990
1991
1991
1991
1992
1993
1994
6,407
2,230
1,341
2,207
5,206
1,246
4,927
Butternut
,
Key
DBN9091
DBN9192
DBN9293
DBN93A
DBN93B
DBN9394
1004
1605
1505
0905
0505
0705
Jan.
Nov.
Apr.
Mar.
June
Nov.
03,
21,
13,
12,
15,
20,
1990
1991
1992
1993
1993
1993
1505
0905
1405
1505
1605
1305
Oct.
Mar.
Mar.
May
Nov.
Jan.
17,
30,
11,
27,
11,
24,
1991
1992
1993
1993
1993
1994
15,654
3,114
7,920
1,831
3,684
1,567
Cane Patch
DCN90A
DCN9091
DCN9192
DCN93A
DCN9394
1705
1505
1405
1405
1105
Jan.
Sep.
July
Jan.
June
19,
01,
19,
08,
20,
1990
1990
1991
1993
1993
1005
1505
1405
1405
1505
July
June
July
Apr.
Jan.
24,
19,
22,
30,
11,
1990
1991
1992
1993
1994
4,458
6,985
8,857
2,689
4,925
Duck Key
DDK90A
DDK9192
DDK9293
DDK9394
1104
1505
1505
1005
Jan.
Nov.
Sep.
Aug.
OS, 1990
19, 1991
15, 1992
06, 1993
1404
1405
1305
1105
Apr.
Aug.
May
Jan.
30,
17,
18,
12,
1990
1992
1993
1994
2,764
6,528
5,879
3,818
Highway
Creek
DHC9091
DHC9192
DHC9293
DHC93A
DHC9394
1105
1805
1305
1205
1405
Jan. 04, 1990
Mar. 22, 1991
Oct~ 19, 1992
Mar. 17, 1993
June 14, 1993
1705 Mar.
1205_..Sep .'
1405 Mar.
1105 May
1405 Jan.
21,
15,
10,
18,
21,
1,99.1
1992
1993
1993
1994
10,591
13,027
. 3,410
1,488
5,305
&
Date
&
-6-
Joe Bay
DJB9091
DJB91A
DJB92A
DJB9293
DJB9394
Jolmson
"Key
DJK8990
DJK90A
DJK9091
DJK9192
DJK93A
DJK93B
DJK93C
;
."
1405
1005
1305
1005
1105
Jan.
Oct.
Jan.
July
June
04,
21,
23,
20,
14,
1990
1991
1992
1992
1993
1405
1405
1505
0805
1205
Mar.
Dec.
July
May
Jan.
19,
16,
16,
24,
12,
1991
1991
1992
1993
1994
10,537
1,349
4,203
7,391
5,090
1805
1405
1705
1505
1205
1305
1405
Nov.
Mar.
Sep.
Oct.
Feb.
Mar.
Sep.
28,
26,
08,
23,
10,
24,
09,
1989
1990
1990
1991
1993
1993
1993
1305
2105
1305
1205
0505
1005
2005
Feb.
Aug.
Sep.
May
Mar.
May
Oct.
09,
04,
17,
13,
13,
26,
25,
1990
1990
1991
1992
1993
1993
1993
1,748
3,152
8,973
4,870
738
1,510
1,111
Little
Blackwater
Sound
DLB9192
DLB9293
DLB9394
1505 Sep. 11, 1991
1305 Apr. 14, 1992
1105 June 13, 1993
1005 Mar. 30, 1992
1305 Mar. 10, 1993
1105 Jan. 24, 1994
4,820
7,921
5,401
Little
Madeira
Bay
DLM9092
DLM93A
DLM9394
1605 Jan. 04, 1990
1505 Feb. 16, 1993
1505 Sep. 07, 1993
1105 Dec. 31, 1992
0805 May, 19, 1993
1505 Jan. 13, 1994
26,204
2,202
3,073
Little
Rabbit
Key
DLR9093
DLR93A
DLR93B
DLR9394
1405
1105
1105
1505
Long Sound
DLS9092
DLS9293
DLS9394
1205 Jan. 04, 1990
1205 Nov. 20, 1992
1205 June 14, 1993
Murray Key
DMK93A
DMK93B
DMK93C
DMK9394
1305
1105
0905
0905
Feb.
Apr.
June
Nov.
10,
26,
25,
12,
1993
1993
1993
1993
0405
1005
0105
1505
Mar.
May
Oct.
Jan.
13,
26,
31,
20,
1993
1993
1993
1994
736
720
3,065
1,663
North
River
DNR90A
DNR9091
DNR9i92
DNR93A
DNR93B
DNR93C
DNR9394
1705
0605
1105
1405
1205
1305
1405
Feb.
July
Mar.
Jan.
Mar.
June
Sep.
03,
03,
20,
12,
16,
20,
15,
1990
1990
1991
1993
1993
1993
1993
0805
1505
1105
0605
1505
1705
1605
June
Feb.
July
Mar.
Apr.
Aug.
Jan.
19,
14,
22,
13,
27,
04,
11,
1990
1991
1992
1993
1993
1993
1994
3,256
5,434
11,761
1,433
1,012
1,085
2,835
Peterson
Key
DPK9091
DPK9192
DPK92A
DPK9293
DPK9394
1505
1105
1205
0505
1105
Jan.
Nov.
Aug.
Nov.
June
OS, 1990
18,
14,
27,
25,
1991
1992
1992
1993
0505
0205
0905
1605
1505
Nov. 14,
July 17,
Nov. 25,
May 26,
Jan. ; 25,
1991
1992
1992
1993
1994
16,263
5,700
2,470
4,332
5,141
Taylor
River
DTR9091
DTR91A
DTR9192
DTR92A
DTR9293
DTR93A
1005
1105
0705
1505
0905
1005
June
June
Dec.
Mar.
May
July
12,
17,
14,
20,
17,
27,
1990
1991
1991
1992
1992
1993
1105
1105
1305
1205
1205
1305
1991
1991
1992
1992
1993
1993
7,610
4,273
1,999
1,342
8,164
3,556
Jan.
Mar.
June
Dec.
03,
24,
25,
27,
1990
1993
1993
1993
1993
1993
1993
1994
27,936
1,517
3,361
696
1305 Apr. 14, 1992
1005 May 18, 1993
1205 Jan. 24, 1994
19,946
4,295
5,377
1305
1505
1105
1405
Mar.
May
Nov.
Jan.
12,
26,
12,
25,
,
_e.
Apr.
Dec.
Mar.
May"
Apr.
Dec.
"25,
12,
06,
15,
22,
22,
-7-
Terrapin
Bay
DTB91A
DTB9193
DTB93A
DTB9394
1991
1991
1993
1993
1405
1205
1105
1705
Dec.
Mar.
May
Jan.
12,
19,
06,
27,
1991
1993
1993
1994
2,186
11,068
1,085
5,196
Trout Cove
DTC90A
1305 Jan. 04, 1990
DTC9092 . 1505 Nov • 08, 1990
DTC92A
1405 Sep. 03, 1992
DTC92B
1140 Nov. 23, 1992
DTC93A
1105 Feb. 12, 1993
DTC93B
1105 Apr. 23, 1993
DTC93C
0905 June 14, 1993
DTC9394
1205 Nov. 10, 1993
0805
1405
2305
1140
1105
1305
0705
1405
Oct.
July
Oct.
Dec.
Mar.
May
Oct.
Jan.
09,
16,
02,
30,
11,
17,
21,
12,
1990
1992
1992
1992
1993
1993
1993
1994
6,668
14,784
706
889
649
579
3,095
1,515
1505 Mar. 12, 1993
1205 May 19, 1993
1005 Jan. 25, 1994
27,891
1,466
5,140
1305
0905
0705
0605
Sep.
Dec.
Mar.
June
12,
14,
22,
25,
"
Whipray
Basin
DWB9093
DWB93A
DWB9394
1305 Jan. OS, 1990
1105 Mar. 19, 1993
0705 June 25, 1993
-8-
amplitude and co-phase charts.
water level records from upland
study sites (including North River, Cane Patch, Broad River, Taylor
River and Highway Creek) and from isolated bodies of water (including Joe Bay, Long S9und, Blackwater Sound, Little Blackwater Sound
and Terrapin Bay) are far enough removed from Florida Bay proper to
justify excluding them from the co-phase and co-amplitude charts.
Water levels are recorded using a float and counterweight system and a Telog potentiometric recorder.
Water level is recorded
every second, and averaged over la-minute time periods.
Ten-minute
averages are well suited for resolving high-frequency events, such
as water level fluctuations occurring in response to rapid changes
in wind speed and direction.
Ten -minute averages are not appropri-
ate for harmonic analysis of tidal periodicities, however.
Prior
to analysis for tidal harmonic constants, water level time series
were edited to retain only the la-minute averages from the top of
the hour to 10 minutes after the hour.
These values were assigned
a time of five minutes past the hour to avoid introducing a 1.2 0
and 2.4 0 phase shift in diurnal and semidiurnal tidal constituents
phase angles, respectively.
The effect of averaging on amplitudes
is negligible--well within the precision of the Telog recorder--and
was therefore ignored.
The data used to construct the table of harmonic constants of
the principal tidal constituents (Table 2) are restricted to data
collected by National Park Service personneL.-since 1990.
In all
cases, data collected since that time are sufficient for determining representative harmonic constants.
The data base used to con-
struct the co-amplitude and co-phase charts goes well beyond that
-9-
Table 2. Harmonic constants of the principal diurnal and semidiurnal tidal constituents for National Park Service water level
data from study sites in Florida Bay. Amplitudes (~) are in em
S-l and phase angles (lC) are in degrees.
Asterisks ( * ) indicate
amplitudes less than 0.5 em S-l and, therefore, unreliable phase
angles~
I Study Site
Bob Allen Key
I~
11
lC
Buqy Key
11
lC
Butternut Key
11
lC
Duck Key
11
lC
Highway Creek
Joe Bay
~
lC
11
1C
Johnson Key
11
lC
Little Madeira Bay
11
1C
Little Rabbit Key
11
1C
Long Sound
11
1C
Peterson Key
11
1C
Taylor River
11
1C
Trout Cove
11
lC
Whipray Basin
11
1C
~
I S2 I
N2
I
K1
I
01
I
P1
4.3
312
0.9
333
0.9
290
1.3
348
1.6
341
0.2
351
2.3
169
0.7
198
0.5
140
1.8
089
1.8
076
0.7
107
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
4.2
129
2.3
096
6.6
019
5.8
012
1.8
027
*
*
14.2
110
*
*
0.5
033
*
*
*
*
*
*
*
*
. 1.5
113
0.5
173
*
*
2.2
045
2.3
030
0.8
057
0.6
091
*
*
*
*
6.8
299
1.3
333
*
*
*
*
0.5
228
*
*
*
*
*
1.5
282
1.9
328
2.6
327
0.5
336
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
1.3
093
1.2
081
0.5
103
*
*
*
*
I
-10-
assembled by the National Park Service, however (Figure 2).
In-
cluded in these figures are results from the National Ocean Service
data base,
and results obtained from the water level or bottom
pressure records collected by Harbor Branch personnel over the past
four years.
The expanded data base was needed to characterize ade-
quately tidal conditions along the western and southeastern fringes
of Florida Bay.
The NOS data base, for example, describes tidal
conditions along the keys and tidal channels; the Harbor Branch
data base characterizes tidal conditions in the unprotected waters
of the western side of the bay.
Together with National Park Ser-
vice data from the interior of Florida Bay, the combined data base
is sufficient to describe semidiurnal and diurnal tidal constituents throughout the bay,
both within and outside Everglades Na-
tional Park.
METHODS
Harmonic constants
(amplitudes and local phase angles) were
quantified by one of two computer programs, depending on the length
of the record.
When the time series was shorter than a full year,
a series of 29-day analyses (Dennis and Long 1971) provided several
amplitude and phase angle pairs for each tidal constituent that
could be vector averaged to provide harmonic constants more representative of the entire time series.
Only the diurnal, semidiur-
nal and shorter period tidal constituents con l.d be. quantified in
these cases.
When time series were one year in length,
a least
squares analysis of one-year segments (Schureman 1"958) provided information on the longer period consituents, as well as on the diur-
-11-
• Study SitQS
.BK
TC
..
SA.
• ;:'..
3749 ..... 3 7.111
3752·
1'-+
WK .•. .
3807 ...~-,,.. 3776
}=
·C
•
397;;;;rr0
..•.. • :.
•
'-h'l
.w-
~
949
<>
~
c$.
3852 . ~J3
/.
P
d.
~
o
I
Figure 2.
~ .(~Y3808
PK.
NDBC. KML ••
h~C5C2
LKC~' .
3918~··· ·
.
3899
3921...
·s
~
AS
20km
Composite of National Park Service (NPS), National
Ocean Service (NOS) and Harbor Branch Oceanographic
Institution (HBOI) water level recording stations.
NOS stations are identified by four-digit codes;
"NDBC" identifies the C-MAN station operated by the
National Data Buoy Center. NPS and HBOI stations are
identified by one-, two - a n d three-letter codes .
-12-
Tidal constituents of particu-
nal and semidiurnal constituents.
lar interest included M2, S2'
N2, K lI 0 1 ,
P1 , Mf, MSf, MIn, Ssa and
Sa.
The movement of individual tidal constituents through Florida
Bay can be inferred using co-amplitude and co-phase charts.
Iso-
pleths of local phase angles can be interpreted to provide information'on the speed and direction of tidal wave propagation;
iso-
pleths of amplitude provide information on how tidal waves are
damped as they move through the bay.
Co-phase charts a n this study
have been constructed with contour intervals of 30°.
For semidiur-
nal constituents, a 30° phase lead or lag corresponds very closely
to a one-hour time lead or lag.
Thus neighboring isopleths in the
M2 co-phase chart show the relative movement of wave forms over a
one-hour time period.
The spacing of the isopleths is therefore
d i r ect.Ly related to the speed of propagation:
The greater the
separation of two adjacent lines, the further and thus the faster
the tidal wave form has to move in an hour.
For diurnal tidal con-
stituents, the 30° contour interval corresponds closely to a twohour time difference.
One must interpret co-phase and co-amplitude charts with caution if there is a chance that tidal waves are being reflected to
produce a standing wave pattern, or if waves from two source regions are interacting.
Bay is probably slight,
The reflection of tidal waves in Florida
alth0~gh
the shallow water of the bay does
offer considerable resistance to wave propagation.
Parts of the
bay do appear to experience an interaction of tidal waves originating in the Atlantic Ocean and in the Gulf of Mexico.
-13RESULTS
Table 2 summarizes amplitudes and local phase angles of the
diurnal and semidiurnal tidal constituents
for 23
locations at
which historical water level records have been obtained.
Values
are included in the table only where amplitudes are 0.5 em or
greater.
Amplitudes less than 0.5 em are within the precision of
the water level recorder.
Also, it is difficult to determine the
phase angles of a very low-amplitude tidal wave with confidence.
A listing of harmonic constants summarizes results of calculations,
but it is not well suited for establishing spatial patterns.
For
this purpose, co-amplitude and co-phase charts have been constructed.
The M2 , K1 and
01
constituents have been selected for presen-
tation in this way.
Figure 3 is a co-amplitude chart for the M2 tidal constituent,
the
pr~ncipal
semidiurnal constituent for the bay.
Highest M2 am-
plitudes of just over 35 cm are found in the northwest corner of
Florida Bay,
south of East Cape.
The data show a west-to-east
decrease in amplitude of about 2 em km- 1 , as the M2 constituent is
damped by the shallow water and numerous mud banks and mangrove
islands.
In the northern and northeastern parts of the bay, the M2
tide is virtually absent.
Isolated pockets of locally higher M2
amplitude are found along the southeastern fringe of Florida Bay
where tidal channels permit tidal waves to enter from Hawk Channel
on the Atlantic side of the keys.
M2 amplitudes of 27 em have been
recorded along the reef tract at Tennessee Reef, although the highest amplitudes recorded in tidal channels are approximately 18 em.
The interaction of tidal waves entering Florida Bay from both
-l4-
I
I
I
I
I
I
I
I
,:
\
35
25l
\
\
1
1
I
I
-1
I
:I 15
1
I
I'
I
I
I
I
I
I
,I
,
I
I
I
I
I
I
5
\
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I
o
I
Figure 3.
20km
,
Co-amplitude chart for the M2 tidal constituent in
Florida Bay.
Isopleths of amplitude are in centimeters. The chart is constructed---from National Park
Service, National Ocean Service and Harbor Branch
Oceanographic Institution data obtained at 35 study
sites_
-15the Gulf of Mexico and the Atlantic Ocean results in a complex cophase chart (Figure 4).
The west-to-east increase in phase angle
in the northwest corner of the bay shows that semidiurnal M2 waves
enter Florida Bay from the Gulf of Mexico.
Using the spacing of
the isopleths to infer the speed of propagation of the tidal wave
form, one finds that propagation speed is initially 10-12 km h- 1 in
the northwest corner of the bay, then it slows to 3-4 km h- 1 in the
interior of the bay.
Isopleths are compressed in the southern part
of the bay, probably representing the superposition of tidal waves
of Gulf and Atlantic origin.
Just north of Long Key, the spacing
of the isopleths suggests a propagation of speed on the order of 1
km h- 1 •
The 5 km separation of the 60 0 and 240 0 isopleths indicates
that the M2 tide is 180 0 out of phase, and thus high and low tide
occur simultaneously at locations separated by as little as 5 km.
TQe co-amplitude and co-phase charts for the K1 constituent
are shown in Figure 5.
Amplitudes (upper figure) are as large as
15 em in the northwestern corner of the bay; the 1 em isopleth is
oriented approximately northwest-southeast in the northeast corner
of the bay.
Amplitudes east of that line are all a fraction of a
centimeter,
except in the immediate vicinity of tidal channels.
Co-phase lines (bottom figure) indicate a convergent pattern with
tidal waves moving into the northern part of the bay.
The more
closely spaced lines in the eastern side of the bay indicate that
tidal waves move northward
m~re
slowly than tidal waves move east-
ward from the western side of the bay.
speed
1S
The northward propagation
on the order of 1 km hr- 1 , while the eastward propagation
speed at the western end of the bay is on the order of 3 km hr- 1 ,
-16-
- .'
~:';""
M2 Phase Angle
( 0 l...:::~llW~::~~;~~~f.ii.!~:~~i::::
.
... -.
.. . .
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::.
....••••,:::..
...........
.::.:::. :::.:-::.:.-..
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.
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'.
.:
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' .. : ..: .~.~.;~ ·:::i:::.:::: :-..: -, : .. : ::::.::-:.:..:.::::
".
..:-c:
."..... ~:'.: '. ~ .. :~ :.:.: : : :. -. ~ :.: :.: .
. :"::::.::.:.; ::........
-:.:c.:=:.:.~: :::-:-" .. -.
:·::jf~:.:.i~:~·:~.::~::~~ {:::::::::.:.::.:.:.~;:{ '\
"," .
:'.::'
:::::.~
::.;.::::..::..:.. :.:~. :: .:::.~
.......
.
1'50 \
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:
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,,'\
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1/,"/
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ti
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I"
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,
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...---_
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/..---.....
/~d
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I:/~,// 24'.
,~ ',//1
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",/ .,
II,
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II,
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30
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Figure 4.
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90 "\' \\"I 210
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,,120\
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.-:
0
20km
I
Co-phase chart for the M2 tidal constituent ~n Florida
Bay. Isopleths -of local phase angle are in degrees.
The chart is constructed from Natlonal Park Service,
National Ocean Service and Harbor ·Br a n c h Oceanographic
Institution data obtained at 35 study sites.
-17-
15
,,r
I
/'
"./
10 5,
.•
,
\
I
i
f>y
/fP
~J
'~
20km
20km
Figure 5.
Co-amplitude chart (top) and co-phase chart (bottom)
for the K1 tidal constituent in Florida Bay.
Isopleths of amplitude are in centimeters; isopleths of
local phase angles are in degrees. The charts are
constructed from National Park Service, National Ocean
Service and Harbor Branch Oceanographic Institution
water level records obtained at 35 study sites.
-18decreasing to 1 km nr"
in the interior.
Figure 6 contains the co-amplitude (top) and co-phase (bottom)
charts for the 0 1 tidal constituent.
Several of the general fea-
tures seen in Figure 4 are repeated here.
Again, highest ampli-
tudes appear in the northwest corner of the bay, although 01 amplitudes do not exceed 12 em.
The 01 constituent has amplitudes less
than 1 em in the northeast corner of the bay, and thus is virtually
absent in that area.
Isolated pockets of slightly higher 0 1 ampli-
tude occur on the bay side of two tidal channels.
pear if
I
touring.
Others would ap-
for example, the 2 em isopleth had been selected for conThe co-phase chart shows
the convergence of 0 1
waves into the northern part of the bay.
tidal
Propagation speeds are on
the order of a few kilometers per hour and thus similar to values
calculated for other tidal constituents.
Again,
the arrival of
Atlantic tidal waves through channels separating the keys reduces
phase angles along the southeast fringe of the bay.
The form number, F, is sometimes used to characterize the diurnal or semidiurnal nature of the tide at a given location. The
form number is obtained by dividing the sum of the K1 and 0 1 amplitudes by the sum of the M2 and 8 2 amplitudes.
F has been cal-
culated for each station in Florida Bay, however values do not fall
into a coherent pattern.
Results are not presented on a plan-view
map, however some generalities are appropriate.
Along the western
fringe of the bay, form numbers are around O. 7""at most study sites,
indicating mixed, semidiurnal tides.
In the interior of the bay,
form numbers increase to over 2.0 at several stations, indicating
a dominance of diurnal tidal constituents.
Values are lower along
-19-
., 5··,
\""-.
,i -,
,/
.... / / /
/'
'5-.::--/
T~;'
20km
Figure 6.
Co-amplitude chart (top) and co-phase chart (bottom)
for the 0 1 tidal constituent in Florida Bay.
Isopleths of amplitude are in centimeters; isopleths of
phase are in degrees. The charts are constructed from
National Park Service, National Ocean Service and
Harbor Branch Oceanographic Institution water level
records obtained at 35 study sites.
-2athe southeast fringe of the bay, just behind the keys, indicating
the effect of semidiurnal tidal waves entering the bay through
tidal channels.
Form numbers in the northeast corner of the bay
are highly variable_, probably indicating that the tidal amplitudes
used in the calculations are approaching the precision of the water
level recorders.
Water level records from Cane Patch,
Broad River and North
River must be treated as special cases, because they lie outside
Florida Bay proper,
and because they are heavily influenced by
freshwater outflow.
Figure 7 shows a 3-month water level record
from Cane Patch during fall and winter months,
this time period,
1993-94.
During
water level reaches its annual maximum,
decreases irregularly through the rest of the record.
data are not available, but it
1S
then
Discharge
likely that annual maximum sur-
face runoff occurs during this time as well.
This interpretation
is supported by the temporal variations in tidal period fluctuations in water level.
In general, during periods of relatively
high water level, the tidal signal decreases significantly.
During
the third and fourth weeks of October, for example, the tidal fluctuation virtually disappears.
Harmonic analysis of a 29-day record
starting in early October shows M2 , K1 and 0 1 amplitudes all around
0.6 em.
Harmonic analysis of the last 29 days of the record indi-
cate that all amplitudes have increased by at least a
four.
factor of
One possible explanation is that tida-l waves are signifi-
cantly damped as they move upstream against strong freshwater outflow.
In early November, as water level falls
(and presumably as
freshwater outflow decreases), tidal ranges increase dramatically.
-21-
150
140
,.....,
E
0
130
c
"--'
<J.)
>
<J.)
--J
1.-
110
~I
<J.)
.......
ro
S
100
90
80 -rnrlTT'l~rTTTI'TTTTTTTTTTTTTT"I'TTT"ITTT"ITTT"I"TTT'1CTTT"1"TTT'T"TTT'TTTT"I'"1'TT'1"TTT'1"TTT'1r1TT'lrlTT'll'TT'rrTTTTTTTTTTTTTTT'1
3
10 17 24 31 7
14 21 28 5
12 19 26 2
9
. OCT
NOV
DEC
JAN
Cane Patch Water Level Data, 1993-1994
Figure 7.
Hourly water levels (em) recorded at the Cane Patch
study site in Whitewater Bay by the National Park
Service from October 3, 1993 to January 11, 1994 .
-22-
By the end of the time series in late December and early January,
water levels have fallen 20-30 em below October values,
tidal range has increased to about 10 em.
and the
Because amplitudes of
the major tidal constituents vary substantially as a function of
water level,
it is impossible to suggest representative values.
Therefore these three stations appear in Table 2 only to be formally excluded.
Seasonal variations in water level appear in the
related report dealing with long-period tides and seasonal cycles
of water level, however.
Although this report focuses on the analysis of water level
data collected by National Park Service personnel,
it is appro-
priate to note that an integration of current meter and bottom
pressure data collected by Harbor Branch personnel at Channel Marker 5, southwest of Flamingo, suggests that the M2 , K1 and 0 1 tides
enter the northwest corner of Florida Bay as mostly progressive
waves.
Harmonic analysis of current meter and bottom pressure
records reveals that strongest M2 flood current speeds lead highest
water levels by 35 0 in phase,
time (Figure 8).
and thus 1 hour and 12 minutes in
For comparison,
for a purely progressive wave,
strongest flood currents and highest water levels would coincide,
and harmonic analysis would reveal a 00 phase lead.
For a standing
wave, maximum flood currents would have a 90 0 phase lead over highest water levels.
The largely progressive, partially standing wave
nature of the M2 tide indicates that shallow water and complex
bottom topography act to impede the movement of the tidal wave
entering the bay.
'I'he distinction between progressive and standing
waves is important, because volume transport occurs with progress-
-23-
/
40
High TIde
-....::::
.-..
E
0
.......-
..A:::-
20
Strongest Flood
<D
>
<D
.....J
1..-
0
ill
........
ttl
S
(\J
-20
2
I
I
I
I
-40
-30
-20
-10
I
o
I
I
I
1
10
20
30
40
M2 Current Speed (em
Figure 8.
S-l)
Plot relating water level with current speed over one
complete M2 tidal cycle at Channel Marker 5 in the
northwest corner of Florida Bay (see Fig. 2). Arrows
within the ellipse indicate a counter-clockwise rotation; arrows outside the ellipse show that the phase
lead of strongest flood currents ·over highest water
levels is 35° (corresponding to 1 hour and 12 minutes) .
-24-
lve waves, while no transport is associated with standing waves.
Harmonic analyses of the K1 and 0 1 waves (results not shown) produced similar phase leads of strongest flood currents over highest
water levels.
tidal
The tentative conclusion is that each of these three
constituents
as
capable
of
transporting
water
into
the
northwest corner of Florida Bay.
DISCUSSION
This report of semidiurnal and diurnal tidal constituents in
Florida Bay not only brings to light tidal conditions in the interior of the bay, it also integrates NOS data from the Florida Keys
with Harbor Branch data from the northwestern and southeastern
fringes of the bay.
Thus, this report constitutes the first com-
plete summary of regional
tidal conditions.
The picture that
emerges reveals a rapid fringe-to-interior damping of the semidiurnal and diurnal tidal constituents, and a large interior region
which is virtually tideless in terms of the
ents.
M2 ,
K1 and 0 1 constitu-
Significant water level fluctuations occur in the interior
of the bay, but they are associated with the long-period tides and
nontidal forcing.
Around the fringe of Florida Bay, the tide can
be characterized as mixed, semidiurnal.
In the interior of the bay
the tide becomes more diurnal in character, but tidal amplitudes
decrease to the point that tidal processes in general are of negligible importance.
While tidal waves converge into the northern part of the bay
from both the west and the southeast,
it is apparent that tidal
waves entering the bay from the Gulf of Mexico are the dominant
-25-
feature of the co-phase charts.
Tidal waves entering the bay
through tidal channels along the southeast margin are of local
importance,
but the constrictions afforded by even the largest
tidal channels prevent these exchanges from impacting larger areas
of the bay.
Previous studies of Florida Bay have used the term "complex"
to describe tidal conditions.
A better term might be "spatially
variable."
lS
Spatial variability
an expected characteristic when
tidal waves entering the bay from the Gulf of Mexico to the west
interact with tidal waves enter the bay through tidal channels
along the southeastern fringe of the bay.
This study shows that
when tidal constituents are treated individually,
and when data
from many stations are assembled on co-amplitude and co-phase
charts, results form a coherent picture.
As tidal amplitudes decrease in the interior of the bay, phase
angles become harder to quantify with confidence.
For example,
when M2 water levels fall, then rise only 1-2 ern In several hours,
it is difficult to determine exactly when low tide occurred.
When
the maximum or minimum water level is hard to pinpoint, the phase
angle is correspondingly hard to define.
In these cases, very long
water level records are needed to construct co-phase charts, and it
is fortunate that so many uninterrupted water level records are
available in the historical data base.
It is appropriate to include some thoughts regarding follow-up
studies that could be based on results presented here.
One such
study would be designed to improve spatial resolution.
Although
data from a total of 35 stations were available for characterizing
-26-
the tides of Florida Bay, additional data from the western fringe
and especially the southern part of the bay are needed for improving station density in an area where spatial gradients are greatest.
Also, although of secondary importance, additional data are
needed from the immediate vicinity of tidal channels, where tidal
waves enter the bay from Hawk Channel on the Atlantic side of the
keys.
Undoubtedly, the most important follow-up to the observational
work described here is a modeling study designed to improve spatial
resolution throughout the bay, and to add information on tidal currents.
This report provides the foundation on which modeling work
can proceed.
While information presented in this report stands
alone as a description of Florida Bay tides, it also serves as the
data base necessary to validate hydrodynamic models designed to
simulate tidal motions and tidal transport through the bay.
Model-
ers often verify simulations according to their model's ability to
reproduce the timing and magnitude of high and low water levels
over a single tidal cycle.
With the data presented here, a sig-
nificantly more rigorous test can be applied.
Harmonic constants
are available for the principal tidal constituents, and model simulations that extend over time periods of a synodic month (29 days)
can be used to calculate harmonic constants for comparison.
A hy-
drodynamic model that can reproduce harmonic constants is clearly
validated.
A validated hydrodynamic
mode I. can
then
take
the
present study an important step further by quantifying the tidal
transport associated with the tidal period fluctuations in water
level.
This study is not an end in itself.
Rather, it should be
-27-
used in support of follow-up studies designed to apply hydrodynamic
models to important management decisions.
Acknowledgements
While this study was designed to be an analysis of historical
watei level data collected by National Park Service personnel, it
was logical to incorporate results from all relevant sources.
In
the final analysis, National Park Service data accounted for only
one-third of the data base utilized in the construction of the coamplitude and co-phase charts.
Three other ongoing projects con-
tributed data and thus harmonic constants.
Bottom pressure records
from Florida Bay waters adjacent to Tavernier Creek and Snake Creek
were collected as part of a NURC contract to investigate flow
through tidal channels in the Upper Keys.
from Oxfoot Bank,
Bottom pressure records
Sprigger Bank and Arsensic Bank,
and a water
level record from the Keys Marine Lab on Long Key were obtained
through the SEAKEYS program,
Foundation.
Bottom pressure
with the support of the MacArthur
records
from
stations
along
the
81°05'W meridian were obtained with the support of the Florida Department of Environmental Protection under Contract MR020.
Special
thanks to go Ms. Carolyn Petrie, who worked on the raw data files
during the summer of 1993.
-28-
LITERATURE CITED
Dennis,
R.
and E.
Long.
A user's guide to a
1971.
computer
program for harmonic analysis of data a tidal frequencies.
NOAA Tech. Rept., U.S. Dept. Commerce 41: 31 pp
Jones, J.I.
1973.
Physical oceanography of the Northeast Gulf of
Mexico and Florida continental shelf area
Marmer,
H.A.
1954. Tides and sea level in the Gulf of Mexico.
Fishery Bull. Fish wildl. Servo U.s. 55:101-118.
Schureman, P.
tides.
1958.
Spec.
Manual of harmonic analysis and prediction of
Publ. No.
98,
rev.
ed.,
U.s.
Govt.
Printing
Off., Washington, D.C., 317 pages.
Wang, J.D., J.C. van de Kreeke, N. Krishnan and D. Smith.
Wind and tide response in Florida Bay.
1994.
Bull. mar Sci. 54:579-
601.
Whitaker, R.E.
1971.
Seasonal variations of steric and recorded
sea level of the Gulf of Mexico.
Ref. 71-14T, Texas A & M
Univ. Research Foundation, College Station Texas, 110 pp.
Zetler, B. and D. Hansen.
1970.
Tides in the Gulf of Mexico--a
review and a proposed program.
'.
'\
\.
Bull. mar. Sci. 20:57-69.