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ABSTRACT
Nearly 332 days of current, wave, wind, and sea-level measurements were
obtained at two locations in the inner and outer Añasco Bay Shelf. One station was
located at the shelf break on the northern tip of Manchas Exteriores (18 12' 39" latitude
and 67 14' 36" longitude) and the other about half a mile west of El Maní Community
(18° 14' N and 67° 10' 56" W). These data were examined for the average conditions and
seasonal cycles of water circulation. Spectral estimates were calculated for all
measurements to define the principal forces responsible for the circulation. Current
ellipses were determined for the diurnal and semidiurnal band. Drogues were deployed at
different locations inside the bay. The long term average flow offshore El Mani was
about 5.4 0.85 cm/s toward the southeast (111°-149°). The average flow at Manchas
Exteriores was 10.41 2.35 cm/s in a south-southeastward direction (163°-175°). The
data showed no indication of a seasonal current pattern throughout the year. The long
term average wind direction was from the east (83°-119°). Orientation of current ellipses
at El Maní revealed a stronger north-south component (v). This back and forth motion of
the current fluctuations primarily along the north-south axis is due to the local
bathymetry. Spectral estimates of El Maní indicate a strong influence of the tide in
generating the fluctuations in current speed of u and v. Strong sea and land breeze
patterns contribute to current fluctuations along the East-West component (v).
RESUMEN
Medidas de corriente, oleaje, velocidad del viento y nivel del mar fueron tomadas
aproximadamente durante 332 dias en dos localidades dentro de la plataforma de la Bahía
de Añasco. Una estación fue localizada en el borde de la plataforma, en la punta norte de
Manchas Exteriores (latitud 18 12' 39" N, longitud 67 14' 36" O) y la otra
aproximadamente a 0.5 millas al oeste de la Comunidad El Maní ( 18° 14' N and 67° 10'
56" O). Se examinó la data para establecer condiciones promedio y ciclos estacionales de
la circulación. Se calcularon estimados espectrales de todas las medidas para tratar de
identificar las fuerzas responsables de la circulación. Se determinaron los elipses de
corriente para la banda semidiurna y diurna. Se usaron anclajes lagranjianos (“drogues”)
en diferentes localidades dentro de la Bahía. El flujo promedio a largo plazo, en las
afueras de El Maní, fue de 5.4 0.85 cm/s hacia el sureste (111°-149°). El flujo
promedio en Manchas Exteriores fue de 10.41 2.35 cm/s moviéndose en dirección sur-
sureste (163°-175°). A largo plazo la dirección promedio del viento fue del este (83°-
119°). Los datos no mostraron patrón estacional alguno. La orientación de los elipses
indica que el componente norte-sur (v) es más fuerte. Este movimiento rectilíneo en una
dirección y luego en otra a lo largo de un eje norte-sur se debe a la batimetría local.
Estimados espectrales de las corrientes en El Maní reflejan mayormente la influencia de
la marea en generar las fluctuaciones en los componentes u y v. Patrónes fuertes de brisa
marina contribuyen a crear fluctuaciones en el componente este-oeste (v).
To Hortensia and Lucy
ACKNOWLEDGMENTS
Acknowledgment is due to Dr. José M. Lopez for providing direction throughout
this work and my professional training. Credit is also due to Capt. Dennis Corales, his
labor made possible the gathering of all this data.
Acknowledgment is due to Kurt Grove who continued the sampling for additional
six months to complete the year record. Thanks to Dr. Manuel Hernández Avila who
provided me with his field assistant, Marcos Rosado, as diving partner. My appreciation
is extended to Angel Dieppa, Deborah Parrilla, Gretchen Colón and Alfredo Vélez who
participated in the diving operations.
Acknowledgment is due to Prof. Aurelio Mercado and Dr. Jorge Capella who
provided me with the basics for processing of oceanographic data.
Support of this work was provided by a NASA training grant (NGT-70238) for
three years (1992-1994).
TABLE OF CONTENTS
Chapter Title Page
LIST OF TABLES viii
LIST OF ILLUSTRATIONS ix
1 INTRODUCTION 1
Site Description 6
2 REVIEW OF LITERATURE 9
Previous investigations conducted in Añasco Bay 12
3 FIELD METHODS AND DATA ANALYSIS 18
A: Field Methods 18
1. Current Meters 18
2. Tide-gauge 24
3. Wind Station 25
4. Drogues 26
B: Data Analysis 32
1. Relative Annual Transport 32
2. Monthly Mean Vectors 34
3. Spectral Estimates 35
4. Current Ellipses 36
4 RESULTS 40
Current Ellipses 50
Spectral Estimates 67
Monthly Mean Vectors 85
Drogues 88
5 CONCLUSIONS AND RECOMMENDATIONS 109
BIBLIOGRAPHY 114
LIST OF TABLES
Table No. Page
2.1. Previous Research Conducted in Añasco Bay. 13
4.1. M2 tidal ellipse characteristics between January
to December 1993. 60
4.2. K1 tidal ellipse characteristics between January
to December 1993. 60
4.3. Observed periodicity in the spectra of component u and v. 84
4.4. Observed periodicity in the spectra of sea-level height. 84
LIST OF ILLUSTRATIONS
Figure No. Page
1.1. Study area and location of current meters, tide-gauge and wind station. 7
2.1. Location of current meters for the Metcalf and Eddy study. 14
3.1. Study area and location of current meters, tide-gauge and wind station. 19
3.2. Concrete mooring and arrangement of the instruments. 22
3.3. Buoy and window shade drogue used at depths of 10 and 30 meters. 29
3.4. Buoy and cruciform drogue used at depths of 1, 3 and 5 meters. 30
3.5. Drogue deployments during December, 1993. 31
3.6. Current vector hodograph and the ellipse parameters. The tip of current
vector W traces the ellipse. 39
4.1 . One year time series of currents, wind stress and surface elevation for
Añasco Bay. 41
4.2 . Significant wave height and wave direction at Manchas Exteriores Reef
for 1993. 42
4.3. Monthly current direction rose from Manchas Exteriores Reef for the
first six months 44
4.4. Monthly current direction rose from Manchas Exteriores Reef for the
last six months. 45
4.5 Monthly wind rose from Añasco for JAN-JUN. 46
4.6. Monthly wind rose from Añasco for JUL-DEC 1993. 47
4.7. Relative transport for one year at Manchas Exteriores. 48
4.8. Relative transport for one year offshore El Maní.
From hourly values of current speed and direction. 49
4.9. Current components in a positive north and positive east direction,
v and u. Sample of the band pass filter used to extract the
semidiurnal component M2. 51
4.10. Semidiurnal (M2) components u and v for Manchas Exteriores
Reef. Current ellipse for the M2 constituent. 52
4.11. Current components in a positive north and positive east direction,
v and u. Sample of the band pass filter used to extract the diurnal
component K1. 53
4.12. Diurnal (K1) components u and v for Manchas Exteriores Reef.
Current ellipse for the K1 constituent. 54
4.13. Horizontal current components u and v . Sample of the bandpass
filter used to extract the semidiurnal component M2. 55
4.14. Semidiurnal (M2) components u and v for Offshore El Maní.
Current ellipse for the M2 constituent. 56
4.15 Horizontal current components u and v . Sample of the bandpass
filter used to extract the semidiurnal component K1. 57
4.16. Diurnal (K1) components u and v for Offshore El Maní.
Current ellipse for the K1 constituent. 58
4.17. Moon phase and lunar declination with respect to celestial
equator and its influence over the Mayaguez tide. 61
4.18. Current vector and hourly wind stress for August. 62
4.19. Sample of the diurnal portion of the mixed tide that occurs
during maximun declination of the moon during August 13th. 1993. 64
4.20. Another example of the diurnal behavior of the mixed tide
on August 25th. 1993 offshore El Mani. 65
4.21. Semidiurnal part of the mixed tide occured when the declination
was zero and three days after new moon. 66
4.22. Spectral estimate for current speed offshore El Maní. 68
4.23. Spectral estimate for u component. 69
4.24. Spectral estimate for v component. 70
4.25. Spectral estimate for current speed offshore El Maní
between April and October. 71
4.26. Spectral estimate for u component. Effective new sampling
time of 24 hr. after decimate. 72
4.27. Spectral estimate for v component. Effective new sampling
time of 24 hr. after decimate. 73
4.28. Spectral estimate for u component. Data sampling was
every three hours. 76
4.29. Spectral estimate for v component. Data sampling was
every three hours. 77
4.30. Spectral estimate for height at Manchas Exteriores Reef.
Each sample consisted of a 9 min. average taken every three hours. 78
4.31. Spectral estimate for sea surface height offshore El Maní.
Sampling time every five minutes. 79
4.32. Spectral estimate for height offshore El Maní. Data was
decimated to one hour samples and a low pass filter was
applied allowing events larger than 2.5 days. 80
4.33. Spectral estimate for horizontal component u of wind stress. 81
4.34. Spectral estimate for horizontal component v of wind stress. 82
4.35. Spectral estimate of hourly atmospheric pressure data from
San Juan (JUL-DEC 1993). 83
4.37. Montly mean vectors of currents and wind stress for Manchas
Exteriores Reef. 86
4.38. Monthly mean vectors of currents and wind stress offshore El Maní. 87
4.39. Drogue tracks on December 5, 1993 from 1039 until 1420. 89
4.40. Profile of drogue speeds (cm/s) for 1, 3, 5, 10 and 30 meters
from surface. Current direction and speed measured by the
S4 current meter the same day. 90
4.41. Stick plot of currents for 24 hours on DEC 5 1993.
Wind direction compass for the same period. 91
4.43. Height of tide in feet during December 5-6 1993. 92
4.44. Drogue tracks from 1205 until 1550 on December 6, 1993
at the following depths: 1, 3 ,5, 10, 30 meters. 93
4.45. Profile of drogue speeds (cm/s) for 1, 3, 5, 10 and 30 meters
from surface. Current direction and speed measured by the S4
current meter on the same day. 94
4.46. Stick plot of currents for 24 hours on DEC 6 1993. Wind direction
compass for the same period. 95
4.47. Drogue tracks from 0816 until 1126 on December 21, 1993. 97
4.48. Velocity profiles from drogue speeds on December 21, 1993. 98
4.49. Tide, wind speed and direction for December 21, 1993. 99
4.50. Drogue tracks from 0756 until 1208 (local time) on December 23, 1993. 100
4.51. Velocity profiles from drogue speeds on December 23, 1993. 101
4.52. Velocity profiles from drogue speeds on December 23, 1993. 102
4.53. Tide, wind speed and direction on December 23, 1993. 103
4.54. Drogue tracks from 0758 until 1155 (local time) on December 28, 1993. 105
4.55. Velocity profiles from drogue speeds on December 28, 1993. 106
4.56. Velocity profiles from drogue speeds on December 28, 1993. 107
4.57. Tide, wind speed and direction on December 28, 1993. 108
1
CHAPTER 1
INTRODUCTION
Physical oceanographers have dedicated a great deal of effort to the understanding
of the motion of the waters in the world oceans. This motion ranges from powerful
currents like the Gulf Stream to small swirls and eddies. To study water circulation in the
marine environment requires the analysis of the different motion components and of the
forces responsible for each of them.
Currents can be divided into two main groups: Oceanic Currents and Shelf
Currents. The last group is defined as all the water motions present over the continental
or insular shelves. These shelves are regions of relatively shallow water extending
offshore for distances that can vary with the geographical location, but are typically in the
order of 50-150 km (much smaller for insular shelves). The sea floor slopes gently
across the continental shelf from the coast to water depths of about 200 m, where an
abrupt increase in the slope generally occurs at the shelf break. The term “shelf
circulation” includes all the currents between the surf zone and the foot of the continental
slope. The shelf circulation is influenced by the shelf’s bottom topography, the density
stratification, the offshore current regime, the local and remote wind patterns, the tidal
regime, the discharge of fresh water by rivers and by the presence of a coastline.
Currents offshore of the continental platforms are considered oceanic.
2
Shelf circulation studies are important because oceanographic conditions on the
shelf influence several important oceanic processes such as the influx of nutrients
necessary for phytoplankton growth (Corredor et al., 1984; Burton et al., 1988). Most of
the biological primary productivity of the oceans takes place in the waters of the
continental shelves. Sediment transport and pollutant dispersion are strictly affected by
the shelf circulation. Also, the impact of man’s activities on shelf waters is more direct
than in the oceans.
In the last two decades many studies about shelf circulation have been conducted
in many regions of the world. The knowledge of coastal currents and shelf circulation is
based largely on direct measurements of the currents and hydrographic surveys of the
distribution of water properties. Measurements are usually collected for a few months
interval, or even for a whole year. But there are some long term studies (larger than 1
year) of the U.S. Eastern Continental Shelf such as that of Mayer et al. (1979) in the
Middle Atlantic Shelf and the work of Atkinson et al. (1985) in the Southeastern U.S.
continental shelf. Current measurements made on continental shelves have shown that
the nature of the flow in different shelf regions can vary considerably. Major variations
in the flow appear to be due in part to differences in the shelf width, the nature of the
local and nearby coastal winds, and the influence of offshore currents. But in spite of
differences there is a similarity in the characteristics of the flow, specially in the
dominant time scales observed in the fluctuations of the flow. In all regions, currents
vary with periods from a few days to a few weeks (see Huyer, 1990). Sometimes they
vary seasonally. These time scales are similar to those observed in the variations of the
3
winds. The motions occurring at longer periods than the tidal periods but less than a
month are related to the direct meteorological forcing. The subinertial variability caused
by atmospheric forcing over the shelf waters can be explained in terms of coastal-trapped
waves. Shelf waves are responsible for fluctuations in the alongshore current velocity.
These waves use the continental slope as a waveguide and respond to the coriolis
parameter, relative vorticity and depth. Ocean currents variations respond with longer
periods, usually of the order of months. Variations in the shelf flow with this time scale
are associated to the forcing due to deep ocean currents for which the shelf acts like a
boundary layer. Also there is a possible forcing from the runoff of large river systems
which can change the density field (Winant, 1980).
Islands in the Caribbean have a narrower shelf platform than along the continents;
usually of the order of 1 to 20 km. These shelves are characterized by steeply sloping
bottoms and irregular topography. Also, the shelf edge is very irregular and follows the
shape of the coastline. In terms of modeling the shelf circulation, the platform is assumed
to be straight and uniform. But there is an advantage in having a smaller shelf platform,
we can study in detail the variability and the forces responsible for water motion with
much less effort than in a continental shelf.
The Caribbean Region is a great place for the study of shelf circulation. Day-
periodic processes such as the local sea-breeze and land-breeze patterns dominate our
climate, in contrast to the higher latitudes where these diurnal cycles in the wind regime
are less evident than seasonal changes of it. Also, the Caribbean Region is affected with
the regular passage of low pressure waves and cold fronts. All these phenomena account
4
for periodic changes in the atmospheric pressure and in the wind stress of the order of a
few days. Considering that, it is reasonable to expect to see a similar order of variability
in the current fluctuations along the insular shelf. Periodic wind stress changes can
generate shelf waves that can be trapped around an island using the shelf slope as a
waveguide. The circular traveling permits in principle to easily identify such waves from
the current and sea-level spectra (Mysak, 1980).
The passage between some of the islands offer a pathway for the interchange of
different water masses (Gordon, 1967; Wüst, 1963; Molinari et al., 1980). These currents
are passing between the narrow insular shelf of each of the islands and could drive the
shelf mean flow and low frequency fluctuations of the order of months.
I decided to study the circulation over an insular shelf as a continuation of
previous studies conducted in other regions to determine its temporal variability. The
goal of this study is to understand the time scales in the fluctuations of the shelf currents
over an insular platform and interpret them in perspective to the local conditions affecting
our region. To accomplish this goal I must achieve the following objectives.
1. To determine the mean shelf flow over the insular platform during one year;
2. To estimate the temporal variability in the shelf circulation;
3. To discern possible generation mechanisms of the stronger current fluctuations;
4. To determine if seasonal changes are present in the current record;
5. To determine the role of the local wind regime in the observed fluctuations;
After the completion of the above objectives we will have a better understanding
of the time scales of shelf currents variability over the insular platforms of the Caribbean
5
Islands. One practical reason for the study of shelf circulation is that it can help to
evaluate the potential impact of projects and natural phenomena affecting a paticular area.
For example dredging projects, sanitary discharges, river discharges or constructions over
the littoral zone.
6
SITE DESCRIPTION
Physical Description
This study is focused on the coastal area near Mayagüez, Puerto Rico and was
limited to the Añasco Bay area (see fig. 1.1). The Bay is located at the leeward side of the
Island. It covers about 53 square kilometers. Añasco Bay is bounded at the north by
Punta Cadena, the westward part of a small mountain chain, at the southeast by Punta
Algarrobo, and at the southwest by a discontinuous barrier of shelf reefs (Manchas
Exteriores and Manchas Interiores).
The Añasco Bay Shelf extends from Punta Cadena to Punta Algarrobo following
the coastline. Water depth at the shelf break is about 20 m. Using the 20 m isobath,
offshore of Punta Cadena the shelf extends for about 1.3 Km, from this point the shelf
begins to broaden down to Offshore El Maní where it reaches 4.1 Km in width. The
northern portion of the shelf slope is very steep and gradually decreases as you move
south.
Manchas Exteriores and Manchas Interiores are submerged barrier reef systems
located at the shelf edge. The mean shallow water is 6 meters. Both reefs form a barrier
of 3.1 Km along a northwest-southeast azimuth. This barrier and the coastline forms a
channel with a northwest-southeast axis. Mid-channel depths are about 10 meters. The
entrance to the channel is north of the Manchas Exteriores northern tip and exits between
the southern tip of Manchas Interiores and Punta Algarrobo. Due to this configuration
most of the wave energy reaching Añasco Bay comes from the northwest.
7
Fig. 1.1. Study area and location of current meters, tide-gauge and wind station.
8
Añasco River discharges onto the narrow insular shelf of the bay and produces a
wide distribution of terrigenous sediments (Morelock et al., 1983). Seasonal fluctuations
in rainfall result in maximum river discharge from May to November (rainy season).
Average monthly discharge in May is 12 m3/sec. The discharge peak is in October with
24 m3/sec (Rickher, 1970). Two smaller water bodies, Caño Boquilla and Caño La
Puente, contributes with fresh water and sediment, especially during flood stages.
Añasco Bay experiences greater amount of precipitation than others parts of
Puerto Rico. This is due to the convergence between the afternoon sea breeze and the
easterly winds. The convergence produces a greater frequency of afternoon showers and
results in a larger annual mean precipitation of 70 inches.
The water motion inside Añasco Bay, as in any bay, is controlled by a
combination of different types of aperiodic and periodic movements. These periodic
movements could be of the order of hours, days or weeks depending of which was the
generating mechanism and/or the bay geometry and depth. The main motion components
are: tidal, effects of oceanic circulation, wave induced, wind driven, seiching, density
gradients and currents associated with run-off (MHR Research Associates Inc., 1993).
9
CHAPTER 2
REVIEW OF LITERATURE
In the last few decades many studies of shelf circulation have been conducted on
different parts of the world such as Washington, Oregon, the Atlantic coast of the
northeastern and southeastern United States, the coast of Peru, and the southeast coast of
Australia among others. Particular features of shelf circulation are summarized in review
articles by Winant (1980), Allen (1980), Mysak(1980), Brink(1991), and Huyer (1990).
Before 1960 all knowledge of shelf circulation was based on hydrographic surveys of the
water properties. A rope wire with bottles and reversing thermometers located at discrete
depths were used to collect water samples and temperature of the water. Salinity was
estimated in the laboratory from the water samples. Using temperature and salinity it was
possible to calculate the density distribution and pressure fields. From this data it was
possible to estimate the steady or slowly varying components of the velocity field. Now
its possible to obtain continuous salinity and temperature profiles with the help of CTD
(conductivity, temperature, depth) instrumentation. These hydrographic surveys require
observations at different sites and are completed in a few days or weeks. These
techniques usually are applied to calculate large scale circulation such as currents present
in a particular basin.
Nowadays moored current meters are capable to collect nearly continuous velocity
data. These instruments are located in specially selected sites and collect data for a period
of months or even a year. This kind of instrumentation is expensive, so there is a limit in
10
the number of current meters you can have to study a particular area. Usually, in studies
of shelf circulation, the current meter data are recorded a few times per hour, these
measurements are then filtered to remove high-frequency noise (from waves and mooring
motion) and decimated (i.e. to resample it) to hourly values. To remove higher
frequencies fluctuations due to tidal motion, the data is low-pass filtered again. The
filtered data are removed of the diurnal, semidiurnal tides, and of inertial currents if the
measurements were made in higher latitudes. After this process the record still shows
considerable variability. Examples of this type of data processing can be found in
Stabeno et al. (1987), Mayer et al. (1982) and Lee et al. (1985).
There are similarities in the characteristics of the flow over most continental
shelves. One of this similarities is that currents vary over periods ranging from a few
days to a few weeks (5 to 30 days) (Huyer, 1990), and even vary throughout the seasons.
These time scales are similar to those of variations in the wind, but different from those
of currents in the open ocean, which typically vary over periods between 25 and 150 days
(Stabeno et al., 1987).
Winant (1980) classifies currents that fluctuate on time scales of the order of a
few weeks to a year into three classes depending on the generating forces. These classes
are: meteorological forcing, forcing due to deep ocean steady circulation and deep ocean
waves, and forcing from the runoff of large river systems.
Currents over the shelf can be divided in two components: the steady or seasonal
component and the fluctuating component. Huyer (1990) makes a good review of these
11
two components and some generalizations of what’s being found about them in different
regions. She explains the steady component observed in continental platforms is due to
the influence of the general circulation of the oceans. For example, continental shelves
along the eastern coasts of the continents are influenced by the stronger western boundary
currents and for that reason they do not present substantial seasonal variation. On the
contrary, along the eastern boundaries of the ocean, the oceanic currents are weaker and
the steady component of the shelf currents changes with seasonal variations in the local
winds. These seasonal variations in the wind patterns intensify and change the direction
of the Ekman transport during certain periods. In terms of the fluctuating components,
Huyer (1990) says that all continental platforms experience currents with fluctuations of
3 to 15 days and that they tend to be anisotropic (i.e., alongshore component “v” greater
than the cross-shore component “u”); to be quasibarotropic; to be correlated with local
sea level at the coast; to have the alongshore component in geostrophic balance; to decay
with offshore distance and to propagate along the coast.
According to Allen (1980) the alongshore wind stress is responsible for energetic
fluctuations in the shelf velocity field at the two to ten-day scales. He writes that the
same time scales are observed in the variability of atmospheric storms and synoptic scale
wind effects. In his work he reviewed some models of wind-driven currents over the
continental shelf with emphasis on the temporal variability with time scales of several
days to several weeks.
Changes in the alongshore wind stress are responsible in the generation of shelf
waves according to Gill and Schumann (1974). These perturbations propagate along the
12
continental slope, out of the forcing region in which they were generated. This
mechanism explains observed current fluctuations ( time scales of days) by changes in
the wind stress in a location hundred of kilometers apart. Mysak (1980) describes the
theory and generation mechanisms of this kind of wave and of the other two types of
topographic waves: Kelvin waves and edge waves.
Previous investigations conducted in Añasco Bay
Investigations of coastal currents have been previously conducted in Mayaguez
and Añasco Bay by Colón (1971), Puerto Rico Department of Public Works (1971-72),
Geocon Inc. (1975), R. M. Guzmán Associates (1974), Morelock et al. (1983), Metcalf &
Eddy Inc. (1985), and MHR Research Associates Inc. (1993). Currents were measured in
these studies using various methods, including: current meters, drogues and fluorescent
dyes. Some of the above mentioned investigations were conducted near our study area.
Table 2-1 shows a list of the investigator, number of days to complete the field
measurements, the method of measurement, and the location.
Geocon Inc. (1975) found that mean resultant currents north of Añasco River
mouth, at a depth of 11 meters, were moving in a northeast direction at a speed of 8 cm/s
(7-day mean). PRDPW (1971) found south of the river mouth, at a depth of 4 meters,
currents moving to the northwest with speeds of 9 cm/s (1-day mean). At a depth of 12
and 24 meters currents averaged 3 cm/s (1-day mean) in a southeastern direction.
13
Table-2.1. Previous Research Conducted in Añasco Bay
INVESTIGATOR METHOD DEPTH
(METERS)
LOCATION
MHR Research
(1993)
current
meter1
5 Offshore Maní
5 days drogues 1,2,3 Pta. Algarrobo
Metcalf & Eddy
(1985)
current
meter2
3, 9.1 A.A.A. sewage
outfall
14-31 days 3.6, 13 Manchas Exterior.
6.4 Manchas Interior
Geocon, Inc.
(1974)
current
meter
11 North Añasco
River Mouth
7 days
P.R.D.P.W.
(1971)
current
meter
4,12,24 South Añasco
River Mouth
1 day
R.M. Guzman and
Associates (1971)
current
meter
surface, 1.5, 3 Punta Algarrobo
1 day
According to Morelock et. al. (1983) currents measured on the Bay ranged
between 2 to 38 cm/s. Surface speeds had a range of 13 to 38 cm/s and there is a vertical
velocity gradient with mean surface speeds of 23 cm/s at the surface and 3 cm/s at a depth
of 10 meters. In their study they found that variability in wind direction and velocity and
in the tidal currents are not strong enough to generate the transport of bottom sediments.
They established that waves coming from the northwest have the necessary energy to
move sediments over the shelf.
According to the latest reports for the study area (Metcalf & Eddy, 1985; MHR
Research Associates Inc., 1993) the circulation is controlled mainly by tidal currents and
wave energy contributes to the littoral circulation patterns in the Bay. Both reports
coincide in the high variability of the water circulation. Metcalf & Eddy set up three
1 S4 Electromagnetic Current Meter
2 Endeco 105 Continuous Recording Current Meter
14
Fig. 2.1. Location of current meters for the Metcalf and Eddy study.
15
stations: CM1 located off EL Mani, CM2 on Manchas Exteriores and CM3 at Manchas
Interiores (see fig. 2.1). Endeco 105 continuous recording current meters recording every
30 minutes, were installed at every station. Station CM1 had two current meters located
at a depth of 3 meters and 9.1 meters and station CM2 at a depth of 3.6 and 13 meters.
For station CM3 they had just one instrument at a depth of 6.4 meters. The period of data
gathering was between January 5 to the 19th, 1985. The second period, was during the
wet season, between May 13 to June 13, 1985. (See Metcalf & Eddy supplement p. 3-2).
Measured directions in CM1 at the top meter were northwest and southwest
during ebb and flood tides, respectively. The average net drift current (31-day mean) at
the top meter was 5.5 cm/s along north-northwest direction (fig. IIB3.9 of their report).
The corresponding drift at the bottom was in a northerly direction (fig. IIB3.10 of their
report) at approximately 4.5 cm/s (14-day mean). Current speeds ranged between 0-27
cm/s (fig. IIB3.4 of their report) for the top meter and 0-18 cm/s for the bottom meter (fig.
IIB3.5 of their report).
Measured directions in CM2 at the top current meter were generally to the
northwest and southeast during ebb and flood tides, respectively. The average net drift
(14-day mean) at the top and bottom meters was to the northwest at approximately 2 cm/s
and 3.3 cm/s (fig. IIB3.11-12 of their report), respectively. Current speeds ranged
between 0-28 cm/s for the top and 0-26 cm/s for the bottom current meter (fig. IIB3.6-7
of their report). They suggested that the higher bottom velocities in CM2 are are due to
the hydrographic effect induced by Manchas Exteriores.
16
Measured directions in CM3 at mid-depth were generally to the north and
northwest during ebb tide, and to the south and southwest during flood tide. The
progressive vector plot (Lagrangian point of view ) revealed a rotary current: south net
drift from (Jan. 5-11), north and northwest from (Jan. 11-19) (fig. IIB3.13 of their report).
Current speeds ranged between zero and 20 cm/s for mid-depth (fig. IIB3.8 of their
report).
The frequency distribution of the current velocity measured at each station
reveals that the lowest ten percentile current value was 2.1 cm/s and the highest 10
percentile was 16.6 cm/s. The predominant 50 percentile was 6.5 cm/s.(Table IIB4.1 &
3.1 from the Supplement).
According to Metcalf and Eddy the available current data is not extensive enough
to allow for the statistical analyses necessary to establish correlation between seasonal
wind patterns and coastal circulation.
Lagrangian current measurements and current meter data from offshore El Mani
were collected by MHR Associates for a period of four days. They used drifting drogues
at a depth of 1,2 and 3 meters. Figure C-4 to C-21 of their report shows the drogue's
tracks for the three days of the experiment. They observed the surface flow is mainly
controlled by the wind at the surface layers and the tide dominates below 3 meters,
especially during low wind conditions. The mean speeds for the drogues were from 3.4
to 8.6 cm/s at the surface (table C-3 of their report). From the current meter data they
found that the flow of water is toward the southeast at relative high speeds (max. 31.6
17
cm/s) during the ebb stage of the tide. During the slack time of the tide they recorded 1.2
cm/s .
All the available oceanographic studies of the area are short term (less than a
month) and were undertaken to fulfill the specific requirements of environmental impact
statements or project feasibility studies. In addition, the sizes of the studied areas were
usually small. They were limited to the project development area. Therefore the
available information is not enough to derive a scheme of the Bay circulation and its
variability throughout the year.
18
CHAPTER 3
FIELD METHODS AND DATA ANALYSIS
A: Field Methods
1. Current Meters
Two continuous recording in-situ current meters, were located in two strategic
locations over the Añasco Bay Shelf; one nearshore and one offshore near the shelf edge
(see fig. 3.1). For the task two S4 current meters from InterOcean Systems Inc. were used
(Trageser et al., 1990). The S4 is a solid state electromagnetic current meter housed in a
25 cm diameter spherical enclosure with no protruding sensors. The instrument may be
programmed and data retrieved via a standard RS232C serial connection to a computer.
The S4 is a true averaging instrument, sampling at a one half second rate (2 Hertz). The
user may program the averaging period, on time duration and the recording duration. The
instrument is capable to log to internal memory and data may retrieved several days after
the measurements. Both were indispensable for the continuous measurement of the
subsurface circulation inside the Bay (Hemsley et al., 1991).
One of the instruments was located at the northern tip of Manchas Exteriores
Reef at a depth of 5 meters (bottom depth is 6m) and the other about half a mile offshore
El Maní Community at a depth of 10 meters (bottom depth 11 m). The precise location
was at the northernmost shallow point of Manchas Exteriores (18 12' 39" latitude & 67
14' 36" longitude).
19
Fig. 3.1. Study area and location of current meters, tide-gauge and wind station.
20
The second S4 was located about a half nautical mile from the shore ( 18° 14' N and 67°
10' 56" W), between the fisherman’s village at the southern end of El Maní and Punta
Algarrobo. On the west side, it was bounded by Manchas Interiores Reef. These
locations were selected taking in consideration the following factors:
1) The Añasco shelf-edge has a maximum seaward extension of 4 kilometers at the
northern tip of Manchas Exteriores;
2) Near the shelf edge is easier to detect the influence of oceanic currents on the shelf
circulation;
3) Near the shelf edge is easier to measure the arrival of deep water waves and
fluctuations in the current associated with topographically-trapped waves;
4) The 10 m isobath at low tide is considered the boundary between the littoral and
offshore zone in the shelf (Brown et al., 1991);
5) The instrument located offshore El Maní is at the center of a channel delimited at both
sides by Manchas Interiores and the coastline;
6) The instrument was located near Punta Algarrobo because the literature review
suggests that north and south of this point we should expect differences in water motions,
one associated with the Añasco Bay current patterns (north or northeast) and at the south
the one associated with Mayaguez Bay (Metcalf & Eddy, 1985; MHR Research
associates, 1993);
7) Mayaguez Bay is surrounded by Manchas Grandes & Escollo Rodriguez line of reefs
(4 to 5 meters deep). Therefore, its possible the deeper water flow that goes into
Mayaguez Bay is restricted to pass through the ship channel or between Manchas
21
Interiores and Punta Algarrobo (i.e. coming from Añasco Bay) where the depths are about
10 meters. Another possibility could be that water from the ship channel goes into
Añasco Bay passing through Algarrobo Point. In conclusion, both scenarios justified the
location of the S4 in that spot;
8) As a summary, the S4 located on Manchas Exteriores could measure the flow passing
by through the north into Añasco Bay and the other one the flow coming from the south.
The use of these instruments required certain mooring considerations. The
relative motion of the instrument to the water mass must be minimized. Since the S4
measures water speed and direction and depth relative to itself, it cannot distinguish
between instrument movement and absolute water movement. To fix that problem a rigid
bottom mounting is recommended. For each current meter, we constructed a concrete
anchor (size 1m x 1m x 10 cm) with a 4 inch PVC tube attached to it (see fig. 3.2.) This
PVC tube kept the instrument 1 meter above the sea floor.
The instrument located offshore El Maní was programmed to record 1 minute
averages of the half second sample rate. Every half a second a measure of component u
and v of the current is recorded. It means that 120 samples are averaged every 1 minute.
The instrument turns on for one minute and then turns off for another minute. For every
hour the current meter collected 30 averages. Since this means a two-minute interval
between each average (h=.033 hours), we can detect current fluctuations with frequencies
up to 15 cycles per hour (Nyquist frequency=15 cph).
22
Fig. 3.2. Concrete mooring and arrangement of the instruments.
S4 Current meter
Seabird SBE 26
Tide-gauge
Sea Floor
Concrete
Anchor
PVC
Tube
4 “
1 meter
1 meter
1 meter
Electromagnetic
Sensors
Pressure sensor
3 “ Bolts
10 cm
23
This interval between measurements makes it possible to resolve fluctuations in the
current due to shallow water harmonics of the tide with periods of less than six hours and
seiches with periods of less
than half an hour. This high resolution allow us to describe in detail the current ellipses
of the diurnal and semidiurnal tide constituents.
The instrument located at Manchas Exteriores had wave height measurement
capabilities (S4DW) and measured wave induced pressure variations and direction at the
Añasco Bay shelf edge. Wave characteristics were calculated from bursts of nine minutes
collected at a frequency of 2 Hertz. Each burst was repeated every three hours. Also we
measured subsurface current velocities in east- west direction components during the nine
minutes burst. Each 9-minute burst consisted of 1080 values of current and pressure. For
each burst we averaged the 1080 samples to obtain the average current components and
pressure every three hours. To convert the 3-hour pressure time series to water elevation,
we used the hydrostatic equation (P=gH). Then we calculated the mean lower low water
and using that as reference level we found the sea-level height. The 3-hour current time
series can resolve fluctuations up to 0.167 cph. This means it can show fluctuations due
to tides and longer period phenomena.
Approximately every 21 days the two stations were visited and the instruments
recovered. This time limit respond to the following limitations: battery life of the
instruments, internal memory capacity and problems of biofouling over the sensors. Each
visit was conducted aboard the R/V Sultana. At least two divers were necessary for each
24
deployment and recovery operations. After the data was gathered, the instruments were
cleaned and deployed immediately to their respective moorings. Data was collected from
January 19, 1993 until December 17, 1993. This long record can help us to correlate
seasonal variations in the shelf circulation due to seasonal variations in wind stress. It will
be possible to detect low frequency fluctuations of time scales of days and weeks
produced by the atmospheric forcing.
2. Tide-gauge
Due to the poor resolution of the pressure transducer in the current meter located
offshore El Maní, we installed a tide and wave meter from Seabird Electronics in the S4
mooring (see fig. 3.2). The SBE 26 Seagauge has a Paroscientific Digiquartz pressure
sensor capable of measuring tides and water level with high resolution. For tide and
water level monitoring the pressure sensor output is continuously integrated to average
out wave action. The integration interval is user programmable with a minimum of one
minute and a maximum of 500 hours. After recovering the instrument the data is
transferred to a computer via a RS-232C data link.
Our integration interval was five minutes. It means 12 one-minute averages per
hour. A sampling frequency of 12 cph allow us to see sea-level oscillations with
frequencies up to 6 cph. Sea level oscillations due to the tide and seiches will be clearly
seen. Sea-level data on this station was collected from July 8, 1993 until December 17,
1993. But the sea-level data collected at Manchas Exteriores covers the whole year.
25
3. Wind Station
The wind station was located about 200 meters north of the Añasco River Mouth
(18° 16’ 12” N and 67° 11’ 15” W) and 100 meters inland (see fig. 3.1). The Añasco
River watershed is approximately 40 km long and 11 km wide, consisting of 517 square
kilometers. The station was located at the seaward edge of the Añasco Valley. The
valley is surrounded by foothills with heights between 61-122 meters, but Pico Atalaya
(north of the station) reaches 362 meters. The mountains to the east provide shelter from
much of the trade winds. There are sugar cane fields east of the station that can reach
high between 3 to 4 meters during their mature stage. Palm trees to the north of the
station and along the beach have an approximate height of 15 meters. Aquaculture ponds
and the Añasco River are to the south and the area is clear of trees.
The anemometer and wind vane are located about 10 meters high from the sea
level. The anemometer is about 8.5 meters from ground level. Height of ground level
from sea level was estimated using the pond’s water level (between 1-2 meters), because
the pond is less than 30 meters from the sea. At this distance the water table height is
close to the sea level height. The data collection instrument used was a Zond
Windrunner, model WRC 986. The instrument is designed to collect and record
integrated hourly wind speed averages, primary wind direction during that hour, a 16
point wind-rose based on seconds of wind direction measurements, and a 16 point wind-
rose based on wind speed averages occurring simultaneously with wind direction data.
Hourly average wind speed data is continuously collected (no sampling), and digitally
integrated. Wind direction was recorded at a rate of once per second. Data retrieval is
26
handled by a simple battery powered lap computer. Visits to the station were
approximately every three weeks. Data was collected for the whole year.
To convert wind velocity into wind-stress the following steps were completed:
1) Wind speed expressed as miles per hour (MPH) was converted to meters per sec.(m/s).
2) The wind-stress coefficient was obtained from
C10= (0.8 + .065 U10) x 10-3
(eq. 1)
where C10 is the wind-stress coefficient and U10 is the wind velocity measured at 10 m
above the sea surface. This empirical formula proposed by Wu (1982) is applicable from
breeze to hurricane winds.
3) The wind-stress was calculated using
= C10 (U10)2 (eq. 2)
where is the wind-stress acting on the sea surface (units are Pascal) and is the density
of air. For our study we used air=1.2 kg/m3 .
4) Finally, wind-stress expressed in Pascal units was converted to dynes/cm2 .
4. Drogues
A total of 24 Lagrangian drift measurements were conducted on five cruises, at
different levels in the water column. The depth for each drogue was selected according to
the depth of the stratified layers. Based on preliminary studies of the stratification in
Añasco I chose depths of 1m, 2m, 5m, 10m and 30m. Our drogues tried to follow the
next two guidelines: First, a buoy large enough to support a flagpole and to provide
sufficient excess buoyancy to offset the negative buoyancy of the drogue. Second, the
drogue itself should in comparison to the buoy, present a large cross-sectional area to the
27
flow and have sufficient negative buoyancy to keep the buoy mast upright and to keep the
connecting wire essentially vertical (Monahan and Monahan, 1973).
Cruciform and "window-shade" forms were our main options for the draft design
of the drogues. I used cruciform drogues for the following depths: 1m, 3m and 5m.
Window shade forms were used for 10m and 30m. The window shade drogues had an
area of 1.858 square meters and were constructed with zinc sheets (see fig. 3.3). The
buoy had an unwetted cross sectional area of 0.06 square meters and the wetted cross
sectional area was 0.1 square meters (Fornshell and Capella, 1984). The cruciform
drogues were made of 2 mm aluminum sheets and had an area of 0.21 square meters.
The buoy had an unwetted surface area of .04 square meters and the wetted area was .038
square meters (fig. 3.4).
Drogues were deployed from the stern of the R/V Sultana (42 ft vessel) on the 5th
and 6th of December and from an 17 feet Skiff AquaSport™ for the 21st, 23rd and 28th
of the same month. Drogues were deployed through all the Bay area (see fig. 3.5) The
positions and time were acquired by GPS (Global Position System) during the
deployment and recovery operations. To know the exact position of the drogue the vessel
went beside each drogue and took the reading from its GPS system. Once you know the
total displacement of the drogue and the time required to cover that distance, you can
estimate the drogue speed. We deployed four drogues at different depths in the same
location and we recovered them after four hours. For the last three deployments (Dec.
21st., 23rd and 28th.) we decided to take drogue positions every hour to estimate hourly
velocities.
28
29
Fig. 3.3. Buoy and window shade drogue used at depths of 10 meters and 30 meters.
Lead Weight
Zinc Sheet
Bridle
Spar Buoy
Window Shade Drogue
10 or 30 meters of 1/4
inch propylene line
Foam Sea surface
wood
Wetted Area=0.1 square meters
Unwetted Area=0.06 square
meters
Drogue Area= 1.858 m2
Flag
30
Fig. 3.4. Buoy and cruciform drogue used at depths of 1, 3 and 5 meters.
Cruciform Drogue
Buoy
y
Flag
1,3 or 5 meters of nylon cord
2 mm
Aluminum Sheets
Bridle
Unwetted Area= 0.04 m2
Wetted Area= 0.038 m2
Drogue Area= 0.21m2
31
Fig. 3.5. Drogue deployments during December, 1993.
32
B: Data Analysis
1. Relative Annual Transport
Relative transport is the mass flowing per second in one direction relative to the
total water mass moving into all directions. For this study a 24-point current rose was
created in which each bin consisted of a 15° arc sector. The transport of water going
through each sector relative to the sum of the transport along all 24 sectors (total
transport) is
MM
Mrelative
BIN
total
1 (eq.1)
where MBIN1 is the total mass transport going through sector 1 (BIN1), i.e.,
M U dz u dz u dz u dz
U u u u u
BIN BINh
BINh
BINh
BINh
BIN BIN BIN BIN BIN
N
N
1 1 1 1 1
1 1 1 1 1
1 2
1 2 3
( ) ( ) ( )
( ) ( ) ( ) ( )
... ...
... ... (eq.2)
The subscripts in BIN1 (1,2,3 up to N), indicate the number of speed events along sector
1. Here h is a specific water depth and is the surface level. is the density of water
and UBIN1 is the sum of all the speed events in time within sector 1, i.e.,
U u u u uBIN BIN BIN BIN BIN N1 1 1 1 11 2 3 ( ) ( ) ( ) ( )... ...
(eq.3)
and MTOTAL is the total mass transport going through all sectors, i.e.,
M M M M MTOTAL BIN BIN BIN BINN 1 2 3 ... ...(eq.4)
If we apply equation 2 and 4 to the first equation, we obtain
33
MU dz
U dz U dz U dzrelative
BINh
BINh
BINh
BINh
1
1 2 3 ... (eq.5)
If we assume a fix surface level and a constant density (=const.), eq. 5 can be
simplified into the following form
MU
U U U Urelative
BIN
BIN BIN BIN BIN N
1
1 2 3 ... ...(eq.6)
This equation defines the relative transport in sector one in terms of the ratio between the
sum of all speed events within that particular sector and the sum of the speeds in all
sectors.
To calculate relative transport in Manchas Exteriores and offshore El Maní
equation 6 was used. For example, offshore El Maní current velocities were taken every
minute throughout all the year and all the speed events in each sector were added up.
Once you have the MBIN for each sector, it was divided by the sum of all the speeds
measured (in all directions) during that year. The same procedure was applied to the
current data from Manchas Exteriores.
34
2. Monthly Mean Vectors
We have computed overall means for each current record (from Manchas Exteriores
and El Maní) and 30-day averages of current velocity, for seasonal and monthly
comparisons. Current meter sampling intervals were either 1 min. or 3 hours. The
following steps were taken to calculate the 30-day means:
1) Outliers were removed from the whole record. Any values that deviated from the mean
by 3 standard deviations or more were removed.
2) The year-record, sampled every minute, was decimated to hourly values. To decimate
the data these steps were followed: First, the edited data were smoothed out with a 8th
order lowpass Chebyshev Type I filter which filters the time series in both the forward and
reverse directions to remove all phase distortion, effectively doubling the filter order.
Finally, the data was resampled hourly. This step was not applied to the 3-hour sampled
data from Manchas Exteriores.
3) Once the data were decimated, a recursive IIR (Infinite Impulse Response) digital filter
was applied allowing frequencies lower than 0.4 cpd (periods greater than 2.5 days).
Matlab Signal Processing Toolbox from the MathWorks Inc. provides a function called
Yulewalk that performs this procedure. After this process is finished, the time series is
very smooth and only fluctuations larger than 2.5 days are present.
4) The lowpassed time series was decimated for a second time to a new sampling time of
24 hours.
35
5) The lowpassed time series (after step four was completed) was averaged every 30 days
(samples) to obtain the mean speed and direction for every month. The monthly means
were averaged to obtain the overall mean speed and direction.
3. Spectral Estimates
Spectral Analysis was applied to the current data to find in which frequencies
most of the kinetic energy was concentrated throughout the year. The same analysis was
applied to the sea-level time series, to the wind time series and to the atmospheric
pressure time series.
To estimate the power spectral density (PSD) of each time series the Welch’s
Method was used. The method consists in the following steps:
1) The time series is sectioned in non-overlaping sections of size N/3 or N/4 (where N is
the total number of samples). Each section is linearly detrended.
2) A non-rectangular window (Hanning Window) is applied to each section. This
window diminishes the spectral leakage while increases the degrees of freedom n (n=2q,
where q is the number of sections).
3) Fast Fourier Transform (FFT) is calculated for each section. The square magnitude of
the result is the power spectral density (PSD)of each section.
4) From ensemble averaging across all sections, we obtain the PSD for the complete time
series. This average spectral estimate is smoother and the statistical confidence of the
spectral peaks was increased.
To study the low frequency fluctuactions in the time series, a lowpass filter was
applied to it before estimating the power spectral density. This process results in a
36
smoother spectral estimate but reduces the spectral resolution. A lowpass filter allowing
frequencies lower than 0.4 cpd was applied to the current time series (same as in step 3
and 4 of section 2 “Monthly Averages”). Current fluctuations with those frequencies are
associated with atmospheric forcing, for this reason it is called the Atmospheric Band.
This band was also studied in the sea-level time series from El Maní.
Currents and the wind-stress were resolved into east-going and north-going
components, u and v . Spectral estimates for each component were taken, to see how the
energy was distributed in longshore and crosshore directions.
4. Current Ellipses
Tidal currents usually are represented by a current vector hodograph, i.e. the
figured traced out by the tip of a vector representing the current at specific time intervals.
To construct such tidal ellipse, the currents were resolved into east-going and north-going
components, u and v respectively. Once we had the time series for each horizontal
component, a digital bandpass filter was applied to each one. Two bandpass filters were
created, one centered in the diurnal frequency (.04 cph) and the other centered in the
semidiurnal frequency (.08 cph). This procedure allowed us to keep the 12-hour or 24-
hour fluctuations in the u and v component. In that way, it was possible to study currents
produced by the diurnal and semidiurnal tidal constituents. Once the time series of the
horizontal components are filtered for each tidal band, a fast fourier transform was
applied. The result may be expressed as
U
a jbFourier Transform of u
1 1
2 (eq.1)
37
V
a jbFourier Transform of v
2 2
2 (eq.2)
where the a’s and b’s are the Fourier Coefficients. The parameters of the ellipse may be
expressed as a function of the Fourier coefficients (O’Brien, 1974). The length of the
semi-major axis and the semi-minor are
semi major A C
semi or A C
min (eq.3)
where A and C are expressed in terms of the Fourier coefficients
A a b a b
C a b a b
1 2
1 2
1 2
2
2 1
2 1 2
1 2
2
2 1
2 1 2
/ [( ) ( ) ]
/ [( ) ( ) ]
/
/ (eq.4)
The orientation of the major axis with respect to the real axis u is
orientation
( )
2 (eq.5)
where are in terms of the Fourier coefficients are
tan
tan
1 2 1
1 2
1 2 1
1 2
a b
a b
a b
a b
(eq.6)
The sense of rotation of the ellipse is determined by the two following conditions:
A C Anticlockwise
A C Clockwise
>
<
These parameters allowed us to construct the diurnal and semi-diurnal ellipses (see fig.
3.6).
38
39
Fig. 3.6. Current vector hodograph and the ellipse parameters. The tip of current vector
W traces the ellipse.
A+C
A-C
w u (real)
jv (imaginary)
40
CHAPTER 4
RESULTS
Nearly 332 days of current, wave, wind and sea surface elevation were collected
from January 19, 1993 until December 17, 1993. Fig. 4.1 and fig.4.2 shows time series
of currents (cm/s), wind stress (dynes/cm2), sea surface elevation (m) above mean lower
low water (MLLW), wave height and direction (i.e., the direction the waves are coming
from) for Manchas Exteriores Reef during all year. Using the figures we can observe an
average current around 10 cm/s pointing mainly toward the south. Events of a larger
magnitude between 20 and 40 cm/s appear at the beginning and end of the year. These
events coincide with a considerable increase of up to one meter in significant wave
height, as you can see in fig. 4.2 . Wind stress oscillated between .05 and .5 dynes/cm2.
Wind stress was larger during February, April and May. Note that appropriate space was
left for missing data in all measurements. Comparing measured sea level on Manchas
Exteriores above MLLW versus the prediction for Mayaguez Harbor you can see big
differences on the first three months (January, February, March). Also on October you
can see a fall of around 0.2 meters. Sampling time h was 3 hours, except for the wind
stress time series (h=1 hr.). Also the wind stress series was for the full year (365 days).
If we stratify the original time series of Manchas Exteriores Reef ‘s currents in
monthly bins as shown in fig. 4.3 and 4.4, and produce current roses, the most frequent
41
Fig 4.1 . One year time series of currents, wind stress
3 and surface elevation for Añasco Bay. Sampling
rate for Manchas Exteriores currents and surface elevation is 3-hour . Wind data was one hour averages.
3 Due to the large number of samples the x-axis is compressed and the sticks does not show the true wind
direction.
42
Fig. 4.2 . Significant wave height and wave direction at Manchas Exteriores Reef for 1993. Sampling rate
was 9 min. bursts every three hours. Tide prediction for Mayaguez Harbor during 1993.
43
direction (darker portion of each rose) on each month was between 165° and 195° or in
another way, 180°15°. Currents are stronger for the six months between October and
April and weaker for the remaining of the year. In July and August, currents averaged 7
cm/s, the weaker currents of the year. Stronger currents with a maximum speed of 34
cm/s were measured on January. Wind roses for each month are displayed in fig. 4.5 -
4.6. Speeds are expressed as miles per hour (M.P.H.) and each bar represents the
direction the wind is coming from. Two main directions are repeated in every wind rose,
these are 058° and 238°. Both are separated by 180 degrees and during most part of the
year show stronger speeds than along any other directions. Taking in account the above
conditions and that we were located on a leeward coast, these stronger components must
be the sea-land breeze pattern. Winds were weaker on September and October with
maximum speeds around 10 M.P.H. Stronger winds were measured around 15 M.P.H.
from about 013° on January and February. These are the northeast winds produced by the
cold fronts during winter. Keep in mind the wind speeds and directions are one hour
averages.
Relative transport was estimated from the complete current record of Manchas
Exteriores and offshore El Maní, these are shown in fig. 4.7 and 4.8 respectively. Most of
the transport is toward south at Manchas Ext. Near 50% of the transport is between 165°
and 210°. Offshore El Mani (fig.4.8) is a total different story. The two main directions of
transport are between 0°-30° and 150°-180°.
44
Fig. 4-3. Monthly current direction rose from Manchas Exteriores Reef for the first six months. Each
vector represents an average of a 9-minute burst taken every three hours.
45
Fig. 4-4. Monthly current direction rose from Manchas Exteriores Reef for the last six months. Each
vector represents an average of a 9-minute burst taken every three hours.
46
00
5
5
10
10
15
15
20
20
00 55 1010 1515 202090
o
75o
60o
45o
30o
15o0
o
345o
330o
315o
300o
285o
270o
255o
240o
225o
210o
195o
180o 165
o
150o
135o
120o
105o
January 1993
00
5
5
10
10
15
15
20
20
00 55 1010 1515 202090
o
75o
60o
45o
30o
15o0
o
345o
330o
315o
300o
285o
270o
255o
240o
225o
210o
195o
180o 165
o
150o
135o
120o
105o
February 1993
00
4
4
8
8
12
12
16
16
00 44 88 1212 161690
o
75o
60o
45o
30o
15o0
o
345o
330o
315o
300o
285o
270o
255o
240o
225o
210o
195o
180o 165
o
150o
135o
120o
105o
March 1993
00
5
5
10
10
15
15
20
20
00 55 1010 1515 202090
o
75o
60o
45o
30o
15o0
o
345o
330o
315o
300o
285o
270o
255o
240o
225o
210o
195o
180o 165
o
150o
135o
120o
105o
April 1993
00
5
5
10
10
15
15
20
20
00 55 1010 1515 202090
o
75o
60o
45o
30o
15o0
o
345o
330o
315o
300o
285o
270o
255o
240o
225o
210o
195o
180o 165
o
150o
135o
120o
105o
May 1993
00
5
5
10
10
15
15
00 55 1010 151590
o
75o
60o
45o
30o
15o0
o
345o
330o
315o
300o
285o
270o
255o
240o
225o
210o
195o
180o 165
o
150o
135o
120o
105o
June 1993
Fig. 4.5 Monthly wind rose for Añasco for JAN-JUN. Wind Vane is around 10 meters from sea surface.
Each vector represents one hour average (M.P.H.).
47
00
5
5
10
10
15
15
20
20
00 55 1010 1515 202090
o
75o
60o
45o
30o
15o0
o
345o
330o
315o
300o
285o
270o
255o
240o
225o
210o
195o
180o 165
o
150o
135o
120o
105o
July 1993
00
5
5
10
10
15
15
20
20
00 55 1010 1515 202090
o
75o
60o
45o
30o
15o0
o
345o
330o
315o
300o
285o
270o
255o
240o
225o
210o
195o
180o 165
o
150o
135o
120o
105o
August 1993
00
2.5
2.5
5.0
5.0
7.5
7.5
10.0
10.0
12.5
12.5
00 2.52.5 5.05.0 7.57.5 10.010.0 12.512.590
o
75o
60o
45o
30o
15o0
o
345o
330o
315o
300o
285o
270o
255o
240o
225o
210o
195o
180o 165
o
150o
135o
120o
105o
September 1993
00
2.5
2.5
5.0
5.0
7.5
7.5
10.0
10.0
12.5
12.5
00 2.52.5 5.05.0 7.57.5 10.010.0 12.512.590
o
75o
60o
45o
30o
15o0
o
345o
330o
315o
300o
285o
270o
255o
240o
225o
210o
195o
180o 165
o
150o
135o
120o
105o
October 1993
00
5
5
10
10
15
15
20
20
00 55 1010 1515 202090
o
75o
60o
45o
30o
15o0
o
345o
330o
315o
300o
285o
270o
255o
240o
225o
210o
195o
180o 165
o
150o
135o
120o
105o
November 1993
00
5
5
10
10
15
15
20
20
00 55 1010 1515 202090
o
75o
60o
45o
30o
15o0
o
345o
330o
315o
300o
285o
270o
255o
240o
225o
210o
195o
180o 165
o
150o
135o
120o
105o
December 1993
Fig. 4.6. Monthly wind rose for Añasco for JUL-DEC 1993. Wind Vane is around 10 meters from sea
surface. Each bar indicates the direction the wind is coming from.
48
00
5
5
10
10
15
15
20
20
00 55 1010 1515 202090
o
75o
60o
45o
30o
15o0
o
345o
330o
315o
300o
285o
270o
255o
240o
225o
210o
195o
180o 165
o
150o
135o
120o
105o
% Percent
% p
erc
en
t
Relative transport for one year
Fig. 4.7. Relative transport for one year at Manchas Exteriores.
49
00
2.5
2.5
5.0
5.0
7.5
7.5
10.0
10.0
12.5
12.5
00 2.52.5 5.05.0 7.57.5 10.010.0 12.512.590
o
75o
60o
45o
30o
15o0
o
345o
330o
315o
300o
285o
270o
255o
240o
225o
210o
195o
180o 165
o
150o
135o
120o
105o
% Percent
% P
erc
en
t
Relative transport for one year
Fig. 4.8 Relative transport for one year offshore El Maní. From hourly values of current speed and
direction. Each bar indicates the direction transport is moving to.
50
Current Ellipses
Current ellipses were calculated for the two principal astronomical constituents
M2 and K1 . For that purpose, currents were resolved into north-south (v) and east-west
(u) components, as shown on fig. 4.9 for Manchas Exteriores Reef. Looking at the east-
west component figure is clear u has a stronger magnitude than the north-south
component v. The same figure shows the frequency response of the band-pass filter that
will be applied to u and v, allowing frequencies of .08 cycles per hour (C.P.H.) . Once
they are filtered (fig. 4.10) its easy to see the modulation due to the M2 constituent acting
over u and v. The ellipse orientation is 080° with respect north and rotates in a clockwise
sense. Also you can see that it is very elongated with a semimajor axis of 11 cm/s and a
semiminor axis of 0.02 cm/s. More than an ellipse it is a to-and-fro motion in the east-
west direction. Fig. 4.11. displays the filter response of the band pass filter used to
consider only such frequencies associated with the diurnal constituent K1. The diurnal
ellipse for Manchas Exteriores (fig. 4.12) rotates in anticlockwise sense and has an
orientation of 154° with respect to the north . It also has an ellipse axis ratio of 6.88. The
semiminor and semimajor axes are 13 cm/s and 0.9 cm/s respectively. The semimajor
axis is oriented along the shelfbreak.
The M2 current ellipse for offshore El Maní has an orientation of 174° from north
(fig. 4.14). It has the strongest semimajor axis of all the ellipses: 23 cm/s and a very
weak semiminor axis of .0101 cm/s. It rotates in a anticlockwise sense. The K1 ellipse
has about half the semimajor speed of the M2 (fig. 4.15). Its orientation is similar to the
M2.
51
Fig. 4.9. Current components in a positive north and positive east direction, v and u. Sample of the band
pass filter used to extract the semidiurnal component M2.
52
Fig.4.10. Semidiurnal (M2) components u and v for Manchas Exteriores Reef. Current ellipse for the M2
constituent. Arrows indicate sense of rotation.
53
Fig. 4.11. Current components in a positive north and positive east direction, v and u. Sample of the band
pass filter used to extract the diurnal component K1.
54
Fig. 4.12. Diurnal (K1) components u and v for Manchas Exteriores Reef. Current ellipse for the K1
constituent. Arrows indicate sense of rotation.
55
Fig. 4.13. Horizontal current components u and v . Sample of the bandpass filter used to extract the
semidiurnal component M2 .
56
Fig. 4.14. Semidiurnal (M2) components u and v for Offshore El Maní. Current ellipse for the M2
constituent. Arrows indicate sense of rotation.
57
Fig. 4.15 Horizontal current components u and v . Sample of the bandpass filter used to extract the
semidiurnal component K1.
58
Fig. 4.16. Diurnal (K1) components u and v for Offshore El Maní. Current ellipse for the K1 constituent.
Arrows indicate sense of rotation.
59
Both ellipses are oriented along the coast but have opposite sense of rotation. Discussed
descriptions are presented on table 4-1 and table 4-2. Components v are stronger than u
for both diurnal and semidiurnal case.
In the case of the tide at Mayaguez, the tides with a one day period, diurnal tides
(produced by constituents K1 , O1 , etc.), are similar in magnitude to the semidiurnal tides
(produced by constituents M2 , S2 , etc.) . This composite type of tidal regime is called a
mixed tide, the relative importance of the semidiurnal and the diurnal components
changing throughout the month are as plotted at bottom of Figure 4.17 for the month of
August 1993. The diurnal tides are most important when the moon’s declination is
greatest (August 13th and August 25th), and reduce to zero when the moon is passing
through the equatorial plane, where it has zero declination (August 20th). The
semidiurnal tides are most important between two and three days after full or new moon,
August 6th and 20th respectively. At the bottom of figure 4.18 we can observe the wind
stress values for the month of August, mostly ranging between 0.1 to 0.3 dynes/cm2 .
These low wind conditions permit us to study the effect of each part of the mixed tide
over the currents. The top of the same figure shows a stick plot diagram of currents
sampled every three hours, but the sampling time is too large to easily resolve the
changing currents due to the tide. El Mani currents were sampled every 2 minutes and
measured in great detail the changes in direction through the tidal cycle. Fig. 4.19 shows
a stick plot of the 24th hour current time series for August 13th, during maximum lunar
declination (21° 40’ 57’’). At the lower low water of that day currents are minimum
(slack water), measuring about 1 cm/s in a southeast direction. As the level rises it
60
Table-4.1. M2 tidal ellipse characteristics between January to December 1993
Location Semimajor
axis
Semiminor
axis
Ellipse axis
ratio*
Ellipse
orientation†
Rotation
Manchas
Exterior
10.9823 0.0174 0.16 80° clockwise
Offshore
Mani
22.5855 0.0101 0.045 174° anti-
clockwise
Table-4.2. K1 tidal ellipse characteristics between January to December 1993
Location Semimajor
axis
Semiminor
axis
Ellipse axis
ratio
Ellipse
orientation
Rotation
Manchas
Exteriores
12.7810 0.8794 6.88 154° anti-
clockwise
Offshore El
Mani
12.9143 0.0903 0.70 010° clockwise
* semi-minor / semi-major x 100
† Angle of semi-major axis clockwise positive from v (north).
61
Fig. 4.17. Moon phase and lunar declination with respect to celestial equator and its influence over the
Mayaguez tide.
62
Fig. 4.18. Current vector and hourly wind stress4 for August. Each current vector represents a 9 min.
average taken every three hours.
4 Due to the large number of samples the x-axis is compressed and the sticks does not show the true wind
direction.
63
changes to the north and increases in speed up to a maximum of 4 cm/s during the first
one third of the high water. Soon after that, currents begin to turn to the west and
decrease in speed. At high water the currents are barely noticed. Then currents begin to
turn more southwesterly and increase in speed (up to 7 cm/s) during the first third of the
decrease in water height. Just at the middle between high and low water the flow is to the
south (6 cm/s) and near low water, currents begin to turn more easterly (slowly decreasing
in speed). At low water they are pointing in a southeasterly direction with speeds
between 1 and 2 cm/s. In conclusion, during the diurnal portion of the tide currents
offshore El Maní turn in a counterclockwise sense during that day. Fig 4.20 shows
another day of currents when the diurnal cycle prevails during minimum lunar
declination. This time the anticlockwise pattern seems to be distorted by a higher tidal
harmonic. Fig 4.21 shows the current pattern when the semidiurnal frequency prevails.
From high water to low water, currents going to the south (max. speed 7 cm/s) begin to
turn westerly and at low water point directly to the west. Then as the tide starts to
increase the weak west current turns more northerly and about half the way, points
directly to the north (max. speed 8 cm/s). Just before high water currents turn more
easterly and at high tide they point to the east but are very weak (less than 1 cm/s). In
conclusion, current ellipse for the semidiurnal frequency has a clockwise rotation.
64
Fig. 4.19. Sample of the diurnal portion of the mixed tide that occurs during maximun declination of the
moon during August 13th. 1993.
65
Fig. 4.20. Another example of the diurnal behavior of the mixed tide on August 25th. 1993 offshore El
Mani.
66
Fig. 4.21. Semidiurnal part of the mixed tide occured when the declination was
zero and three days after new moon.
67
Spectral Estimates
Spectral estimate of currents offshore El Maní (fig. 4.22) reveals the frequency
bands in which the kinetic energy of the current speed fluctuations are concentrated. In
fig. 4.22 four peaks are clearly seen in the following frequencies in cycles per hour:
0.0422 cph (23.7 hrs), 0.0809 cph (12.4 hrs), 0.1606 cph (6.22 hrs), and 0.25 cph (4 hrs).
These frequencies correspond respectively to the diurnal, semidiurnal, fourthdiurnal and
sixthdiurnal period. A peak in the inertial frequency (0.026 cph for our latitude) was not
revealed in the spectrum. In the low frequency part of the spectrum there is one peak at
0.003 cph (13.88 days) and a distinct band between 0.006 cph to 0.008 cph (7 to 5 days).
In the high frequency end there are two peaks at 1.9 cph and 3 cph, 31 and 20 minutes
respectively. The current data used for this spectrum was sampled every one minute. We
separate the data in u and v components and take the power spectrum of each (fig. 4.23
and fig.4.24). The spectra of u shows the diurnal, semidiurnal and fourthdiurnal but the
sixthdiurnal is missing. Also the diurnal peak is the largest one and the fortnightly stills
present (.03 cph). For the v component (fig. 4.24) the semidiurnal peak is larger than the
diurnal one and the fourthdiurnal and sixthdiurnal are present. The fortnightly is lost but
the 20 min. and 31 min. fluctuations are present.
Fig. 4.25 shows the spectral estimate for the 24-hour lowpassed speed data. It
permit us to resolve in the low frequency part of the spectrum. The spectra of u (fig.
4.26) reveals a peak at 0.036 cycles per day (27.7 days), 0.065 cpd (15 days), 0.08 cpd
(13 days), 0.11 cpd (9 days) and 0.14 cpd (7 days). In contrast in fig. 4.27 the v spectra
reveals only the 15 and 7 days fluctuations. Figure 4.28 shows the spectral estimate for
68
Fig. 4.22. Spectral estimate for current speed offshore El Maní. Data consists of one minute averages
taken every one minute (30 samples per hour). Data was detrended and outliers were removed.
23.7 hr. 12.4 hr.
6.22 hr.
4 hr. 7.7 hr. 13.88 days
7- 5 days
20 min.
69
Fig. 4.23. Spectral estimate for u component. Data sampling was every one minute.
70
Fig. 4.24. Spectral estimate for v component. Data sampling was every one minute.
71
Fig. 4.25. Spectral estimate for current speed offshore El Maní between April and October. Data was
decimated to one hour samples and a low pass filter was applied allowing events larger than 2.5 days.
Finally it was decimated to 24 hr. samples. Frequency in cycles per day (C.P.D.)
72
Fig.4.26. Spectral estimate for u component. Effective new sampling time of 24 hr. after decimate.
73
Fig.4.27. Spectral estimate for v component. Effective new sampling time of 24 hr. after decimate.
74
the u component at Manchas Exteriores. It has less resolution than the spectra of El Maní
because the sampling time was every three hours. The three largest peaks correspond to
the semidiurnal, diurnal and fourthdiurnal period. The v spectra has less energy in the
diurnal band but the semidiurnal and fourthdiurnal band remain strong (fig. 4.29).
Sea level oscillations are revealed by the spectral estimate of surface height at
Manchas Exteriores (fig. 4.30) and offshore El Maní (fig. 4.31). In Manchas Exteriores
most of the energy is concentrated in the semidiurnal and diurnal bands. Other peaks are
present in the fourthdiurnal and Lunar monthly band (27 days). El Mani reveals energy
spread over more bands: semidiurnal, diurnal, fourthdiurnal, sixdiurnal, fortnightly and in
the high frequency oscillations of 20 and 31 minutes. For both locations the semidiurnal
peak is the largest one. Low pass of surface elevations (fig. 4.32) at El Maní show energy
oscillations with the following periods: 6, 7, 13, 25 and 50 days.
Spectral estimates for wind stress components u and v are presented in fig. 4.33
and fig. 4.34. Component u has more energy in the semidiurnal and diurnal bands but
component v has energy in the following frequencies: 0.003 cph (13.88 days), 0.006 cph
(7 days) and 0.0085 cph (5 days). Energy in the diurnal and semidiurnal band is less than
in u. Table 4.3 and 4.4 summarize the results.
Spectral estimate of the hourly atmospheric pressure in San Juan is shown in fig.
4.35. It reveals the strong semidiurnal (12 hr.) pressure oscillations due to the solar
semidiurnal atmospheric tide S2 . These pressure oscillations are conspicuously apparent
in the pressure records of the tropics. According to the literature (Hastenrath, 1991) the
diurnal atmospheric tide S1 (24 hr.) is more prevalent in the higher latitudes and
75
negligible in the tropics, but our spectral estimate reveals a peak at the corresponding
frequency (0.042 cph). In the low frequency section of the spectrum there are peaks with
periods of 2.6, 4 and 5 days. A peak with period of 5 days, had also been found in the
wind stress spectrum of component v.
76
Fig. 4.28. Spectral estimate for u component. Data sampling was every three hours.
77
Fig. 4.29. Spectral estimate for v component. Data sampling was every three hours.
78
Fig. 4.30. Spectral estimate for height at Manchas Exteriores Reef. Each sample consisted of a 9 min.
average taken every three hours.
79
Fig. 4.31. Spectral estimate for sea surface height offshore El Maní. Sampling time every five minutes.
80
Fig.4.32. Spectral estimate for height offshore El Maní. Data was decimated to one hour samples and a low
pass filter was applied allowing events larger than 2.5 days. Finally it was decimated to 24 hr. samples.
Frequency in cycles per day (C.P.D.).
81
Fig.4.33. Spectral estimate for horizontal component u of wind stress.
82
Fig.4.34. Spectral estimate for horizontal component v of wind stress.
83
Fig. 4.35. Spectral estimate of hourly atmospheric pressure data from San Juan (JUL-DEC 1993).
S2
5 days
S1
2.6
days
84
Table-4.3. Observed periodicity in the spectra of component u and v.
Location Component u Component v
Currents at El Mani 24 hr., 12 hr., 6 hr.,
13.88 days
24 hr., 12 hr., 6 hr.,
4 hr., 31 min., 20 min.
Low Passed Currents at El
Mani
27.7 days, 15 days,
7 days, 9 days, 13.8 days
15 days, 7 days
Currents Manchas Ext. 24 hr., 12 hr., 6 hr. 12 hr., 6 hr.
Wind Stress at Añasco 24 hr., 12 hr. 13.88 days, 7 days,
5 days
Table-4.4. Observed periodicity in the spectra of sea-level height.
Location Period of observed oscillations
Sea-level at El Mani 24 hr., 12 hr., 6 hr.,
4 hr., 31 min., 20 min., 13.8 days
Low pass sea-level at El Mani 50 days, 25 days, 13 days, 7 days
Sea-level at Manchas Exteriores 24 hr., 12 hr., 6 hr.,
13.88 days, 27.7 days
Atmospheric pressure in San Juan 24 hr., 12 hr., 2.6 days, 5 days
85
Monthly Mean Vectors
Thirty-day means (monthly means) were computed for the current data at each
site. Before computing the means we applied a low pass filter to both data sets allowing
frequencies lower than 0.4 cpd (2.5 days). Fig. 4.37 illustrates the monthly mean vectors
of currents throughout the year for Manchas Exteriores. It shows a consistent
southeasterly flow with maximum values on January (14 cm/s) and December (14 cm/s).
Monthly mean speeds ranged between 8 and 14 cm/s throughout the year. A compass of
the monthly wind stress vectors is at the bottom of the same figure. Average wind
throughout the year was from the east with maximum values for January and May, 0.04
and 0.05 dynes/cm2, respectively. Minimum mean wind stress was observed in
September. Wind in January was from the northeast and in September from the
southeast. Monthly mean wind stress values were extremely low throughout the year
ranging from 0.005 to 0.05 dynes/cm2.
Monthly mean vectors of currents at El Mani (fig. 4.38) also point in a
southeasterly direction but are a little more deflected to the east. The mean flow went
parallel along a passage formed by the barrier reefs (Manchas Exteriores and Manchas
Interiores) and the coastline between Añasco River and Punta Algarrobo. Maximum
values on August (5 cm/s) and September (5 cm/s). Average speeds were much less than
in Manchas Exteriores and had a smaller range. Monthly mean speeds ranged between 3.5
and 5 cm/s throughout the year.
86
4.37. Montly mean vectors of currents and wind stress for Manchas Exteriores Reef. Original sampling
interval was 3 hr. But data was decimated to 24 and then averaged for the whole month. Low pass of
events larger than 2.5 days.
87
Fig. 4.38. Monthly mean vectors of currents and wind stress offshore El Maní.
88
Drogues
Drogues were deployed on December 1993 at different locations around the bay.
On December 5, we deployed 5 drogues about 2 miles west of Añasco River at the
following depths: 1, 3, 5, 10 and 30 meters. Location and tracks of drogues are shown in
figure 4.39. The deployment (1039) and recovery (1420) interval of time is 3.5 hours.
Deeper drogues (10 and 30 m) moved to the southeast and the 1 m and 5 m drogue moved
to the northwest. Average velocities for this period (fig. 4.40) ranged between 3.8 cm/s
and 8.6 cm/s. Maximum speed was attained by the 30 meters drogue. Figure 4.40 also
displays a 24-hour time series of current speed and direction for the S4 current meter
located offshore El Maní. This instrument measured the current at a depth of 10 meters.
The time axis for the graphs of currents, wind speed and wind direction, are expressed on
Greenwich Mean Time (GMT) . That means you have to look at the record between 1439
to 1820. That correspond just before and after the high water (fig. 4.43) occurring at 1330
local time (1730 GMT). During that period currents were very erratic (see top fig. 4.41)
and decreased in strength as the slack water approached. Low wind speeds between 1 and
5 M.P.H. coming mostly from the east were present all day (bottom fig. 4.41).
On December 6, the same array of drogues were deployed at the same location
between 1205 and 1557 (fig. 4.44). Average velocities for that period ranged between
0.86 cm/s up to 4.29 cm/s. The calculated highest speed was found in the 1 meter drogue.
All drogues moved southeast and parallel to the coastline. We observed a more regular
current pattern than the day before in the tracks (fig. 4.46) and in the corresponding stick
89
18.25
18.26
18.27
18.28
-67.230 -67.215 -67.200 -67.185
drogue 3m 1039 to 1413drogue 5m 1039 to 1412drogue 1m 1039 to 1411
Añasco River
D point of deploymentR point of recovery
RR
D
Longitude
Latit
ude
Drogue tracks at Añasco Bay on December 5, 1993
18.25
18.26
18.27
18.28
-67.230 -67.215 -67.200 -67.185
drogue 30m 1039 to 1420drogue 10m 1039 to 1410
R
D
Añasco River
D point of deploymentR point of recovery
Longitude
Latit
ude
Drogue tracks at Añasco Bay on December 5, 1993
Fig. 4.39. Drogue tracks on December 5, 1993 from 1039 until 1420.
90
Drogue speeds on December 5, 1993
3.7937894
5.3179062
3.8447699
4.0854179
8.6382889
0 1 2 3 4 5 6 7 8 9
1
3
5
10
30
Dep
th (
m)
Speed (cm/s)
Current speed offshore El Maní on December 5, 1993
0
2
4
6
8
10
12
14
16
0:0
2
2:0
2
4:0
2
6:0
2
8:0
2
10:0
2
12:0
2
14:0
2
16:0
2
18:0
2
20:0
2
22:0
2
Hour (G.M.T.)
Sp
eed
(cm
/s)
Current direction offshore El Maní on December 5,
1993
0
100
200
300
400
0:0
2
2:0
2
4:0
2
6:0
2
8:0
2
10:0
2
12:0
2
14:0
2
16:0
2
18:0
2
20:0
2
22:0
2
Hour (G.M.T.)
Co
mp
ass R
ead
ing
(°)
Fig. 4.40. Profile of drogue speeds (cm/s) for 1, 3, 5, 10 and 30 meters from surface. Current direction
and speed measured by the S4 current meter the same day.
91
Wind speed for Añasco on December 5
1993
0.00
1.00
2.00
3.00
4.00
5.00
6.00
1 3 5 7 9 11 13 15 17 19 21 23 25
Sample
Sp
eed
(M
PH
)
Wind direction for Añasco Bay on
December 5, 1993
0
100
200
300
400
1 4 7 10 13 16 19 22 25
Sample
Dir
ecti
on
(deg
rees)
Fig. 4.41 Stick plot of currents for 24 hours on DEC 5 1993. Wind direction compass for the same period.
Hour (GMT)
Hour (GMT)
92
Predicted tide for December 5 1993
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.80
0:0
0.0
01:1
5.0
02:3
0.0
03:4
5.0
05:0
0.0
06:1
5.0
07:3
0.0
08:4
5.0
10:0
0.0
11:1
5.0
12:3
0.0
13:4
5.0
15:0
0.0
16:1
5.0
17:3
0.0
18:4
5.0
20:0
0.0
21:1
5.0
22:3
0.0
23:4
5.0
Hour (local time)
He
igh
t (f
ee
t)
Predicted height of tide for Añasco Bay on December 6 1993
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
00:0
0.0
02:0
0.0
04:0
0.0
06:0
0.0
08:0
0.0
10:0
0.0
12:0
0.0
14:0
0.0
16:0
0.0
18:0
0.0
20:0
0.0
22:0
0.0
Hour (local time)
He
igh
t (f
t.)
Fig. 4.43. Predicted height of tide in feet during December 5-6, 1993
93
18.255
18.260
18.265
18.270
-67.225 -67.200 -67.175
drogue 30m 1205 to 1557drogue 10m 1205 to 1547drogue 5m 1203 to 1549drogue 3m 1203 to 1550drogue 1m 1203 to 1541
R
D
D point of deploymentR point of recovery
Añasco River
Longitude
La
titu
de
Drogue tracks at Añasco Bay on December 6, 1993
Fig. 4.44. Drogue tracks from 1205 until 1550 (local time) on December 6, 1993 at the following depths:
1, 3 , 5, 10, 30 meters.
94
Drogue speeds on December 6, 1993
4.29
1.66
0.86
1.76
2.88
0 1 2 3 4 5
1
3
5
10
30
Dep
th (
m)
Speed (cm/s)
Current speed offshore El Maní on December 6, 1993
0
5
10
15
0:0
2
2:0
2
4:0
2
6:0
2
8:0
2
10:0
2
12:0
2
14:0
2
16:0
2
18:0
2
20:0
2
22:0
2
Hour (G.M.T.)
Sp
eed
(cm
/s)
Current direction offshore El Maní on December 6,
1993
0
100
200
300
400
0:0
2
2:0
2
4:0
2
6:0
2
8:0
2
10:0
2
12:0
2
14:0
2
16:0
2
18:0
2
20:0
2
22:0
2
Hour (G.M.T.)
Co
mp
ass R
ead
ing
(°)
Fig. 4.45. Profile of drogue speeds (cm/s) for 1, 3, 5, 10 and 30 meters depths. Current direction and
speed measured by the S4 current meter on the same day.
95
Wind speed for Añasco on December 6
1993
0.00
1.00
2.00
3.00
4.00
5.00
1 3 5 7 9 11 13 15 17 19 21 23
Sample
Sp
eed
(M
PH
)
Wind direction for Añasco Bay on
December 6, 1993
0
100
200
300
400
1 4 7 10 13 16 19 22
Sample
Dir
ecti
on
(deg
rees)
Fig. 4.46. Stick plot of currents for 24 hours on DEC 6, 1993. Wind direction compass for the same
period.
Hour (GMT)
Hour (GMT)
96
plots. A northwest wind with speeds between 2 and 3 M.P.H. and the ebb tide (fig. 4.43)
were present when drogues were in the water (1605-1957 GMT). (bottom fig. 4.46).
On December 21, the drogues were deployed near Punta Cadena on the northern
side of Añasco Bay (fig. 4.47). Low tide was approaching at 0900 (see top fig. 4.49) and
drogues speeds were slowing down. Figure 4.48 presents a sequence of vertical profiles
of drogue speeds for each hour. At 0915 speeds remained uniform throughout the water
column with speeds around 12 cm/s. The 30 meter drogue had already lost most of its
energy. But looking at the 1015 speed profile it seems that the energy loss by the upper 5
meters water layer was transferred to the 10 and 30 meter drogues. Then at 1115 the 10
and 30 meter drogues were moving much slower (1 cm/s) than the 1m, 3m and 5m
drogues (4-8 cm/s). It seems that the energy of the 10 and 30 meter drogue was lost at a
greater rate by bottom friction. The direction of motion remained the same, pointing
northwesterly. Wind conditions on that day are shown on figure 4.49.
On December 23, drogues were deployed in the channel north of the Manchas
Exteriores tip, not far from the S4 current meter location (fig. 4.50). Drogues remained
about four hours in the water. Approximate water depth was 30 meters. Fig. 4.53 shows
the tide and wind conditions during that period. Time of low water was 1030 and light
winds were present (3 MPH). Figure 4.51 and fig. 4.52 show the average drogue speeds
for every hour. Between deployment time and 0850 drogues moved in a southwesterly
direction with uniform speeds but the 30 meter drogue was moving slowly to the
northwest at 2.28 cm/s. At 0950 all drogues reduced their speed by an amount of 6 cm/s
97
18.27
18.28
18.29
18.30
18.31
-67.23 -67.22 -67.21
drogue 30m 0825 to 1126
drogue 10m 0825 to 1120
drogue 5m 0816 to 1115
drogue 3m 0816 to 1114
drogue 1m 0816 to 1112
Wind:Calm; 1020-SW <3mph
Swell: < 1ft
D point of deployment
R point of recovery
R
D
Punta Cadena
Longitude
Latitude
Drogue tracks at Añasco Bay on December 21, 1993
Fig. 4.47. Drogue tracks from 0816 until 1126 on December 21, 1993.
L
a
t
i
t
u
d
e
98
Profile of drogue speeds around 0915
on December 21, 1993
13.83
12.93
11.85
11.85
4.21
0 5 10 15
1
3
5
10
30
Dep
th (
m)
Speed(cm/s)
Profile of drogue speeds around 1015
on December 21, 1993
12.09
9.66
9.37
13.51
7.36
0 5 10 15
1
3
5
10
30
Dep
th (
m)
Speed(cm/s)
Profile of drogue speeds around 1115
on December 21, 1993
4.06
6.49
7.33
1.08
1.10
0 2 4 6 8
1
3
5
10
30
Dep
th (
m)
Speed(cm/s)
Fig. 4.48. Velocity profiles from drogue speeds on December 21, 1993.
99
Predicted height of tide for Añasco Bay on
December 21, 1993
0
0.2
0.4
0.6
0.8
1
1.2
00:0
0
02:0
0
04:0
0
06:0
0
08:0
0
10:0
0
12:0
0
14:0
0
16:0
0
18:0
0
20:0
0
22:0
0
Hour
Heig
ht
(ft.
)
Wind speed for Añasco on December 21
1993
0.00
1.00
2.00
3.00
4.00
1 3 5 7 9 11 13 15 17 19 21 23
Sample
Sp
eed
(M
PH
)
Wind direction for Añasco Bay on
December 21, 1993
0
100
200
300
400
1 4 7 10 13 16 19 22
Sample
Dir
ecti
on
(deg
rees)
Fig. 4.49. Tide, wind speed and direction on December 21, 1993.
Hour (GMT)
Hour (GMT)
Hour (local time)
100
18.22
18.23
18.24
18.25
18.26
-67.225 -67.200 -67.175
drogue 30m 7:56 to 12:03drogue 10m 7:56 to 11:59drogue 5m 7:47 to 11:55drogue 3m 7:47 to 11:54drogue 1m 7:47 to 11:54
D point of deploymentR point of recovery
D
El Maní
PuntaAlgarrobo
Añasco River
D point of deploymentR point of recovery
Longitude
La
titu
de
Drogue tracks at Añasco Bay on December 23, 1993
Fig. 4.50. Drogue tracks from 0756 until 1208 on December 23, 1993.
101
Profile of drogue speeds around 0850
on December 23, 1993
17.39
17.39
16.17
10.23
2.28
0 5 10 15 20
1
3
5
10
30
Dep
th (
m)
Speed(cm/s)
Profile of drogue speeds around 0950
on December 23, 1993
10.25
10.09
9.42
4.88
2.74
0 5 10 15
1
3
5
10
30
Dep
th (
m)
Speed(cm/s)
Fig. 4.51. Velocity profiles from drogue speeds on December 23, 1993.
102
Profile of drogue speeds around 1050
on December 23, 1993
14.78
14.78
14.16
13.04
9.50
0 5 10 15
1
3
5
10
30
Dep
th (
m)
Speed(cm/s)
Profile of drogue speeds around 1155
on December 23, 1993
15.12
14.90
14.54
14.17
13.22
12 13 14 15 16
1
3
5
10
30
Dep
th (
m)
Speed(cm/s)
Fig. 4.52. Velocity profiles from drogue speeds on December 23, 1993.
103
Wind speed for Añasco on December 23
1993
0.00
1.00
2.00
3.00
4.00
5.00
1 3 5 7 9 11 13 15 17 19 21 23
Sample
Sp
eed
(M
PH
)
Wind direction for Añasco Bay on
December 23, 1993
0
100
200
300
400
1 4 7 10 13 16 19 22
Sample
Dir
ecti
on
(deg
rees)
Fig. 4.53. Tide, wind speed and direction on December 23, 1993.
Hour (GMT)
Hour (GMT)
104
with the exception of a little increase on the 30 m drogue. By 1050 all drogues were
moving in a northwesterly track with an increase in speed at all depths. By 1150 all
drogues were still moving to the northwest with a an average uniform speed of 14.4 cm/s.
From this sequence it is clear that the deeper drogues (10m, 30m) respond to the changing
tide.
On December 28, the drogues were deployed near Punta Algarrobo on the south
side of Añasco Bay (fig. 4.54). Drogues were in the water around four hours, from 0758
to 1155. High tide was at 0830 and low tide at 1430 (fig. 4.57). Wind conditions
between 1200 GMT (0800 local time) and 1600 GMT (1200 local time) were increasing
(from 2 to 8 MPH) from the east (fig. 4.57 bottom). At 0853 speeds were uniform at all
depths (fig. 4.55). Then at 0951 drogues pick up speed. The surface drogue felt the wind
and turned a little to the west. At 1053 the 3,5, and 10 meter drogue increased its speed
by 3 cm/s (fig. 4.56). At 1150 all drogues decreased their speeds.
To summarize, I present some of the findings of the above lagrangian drift
measurements:
1) Drogues during the flood tide moved to the southeast.
2) Drogues during the ebb tide moved to the northwest.
3) The 30-meter and 10-meter drogues accelerated (change in speed and direction) sooner
than the rest of the drogues when approaching high or low tide.
4) During the high or low tide, currents were weak (less than 2-3 cm/s) and the 1m, 3m
and 5m drogues went in different directions than the 10m and 30m drogues.
5) Drogue tracks most of the time moved parallel to the coastline.
105
18.21
18.22
18.23
-67.185 -67.170 -67.155
drogue 10m 0758 to 1148drogue 5m 0758 to 1150drogue 3m 0758 to 1153drogue 1m 0758 to 1155
D point of deploymentR point of recovery
R
D
YagüezRiver
PuntaAlgarrobito
PuntaAlgarrobo
Longitude
La
titu
de
Drogue tracks at Añasco Bay on December 28, 1993
Fig. 4.54. Drogue tracks from 0758 until 1155 on December 28, 1993.
106
Profile of drogue speeds around 0853
on December 28, 1993
6.38
6.97
6.97
6.97
6 6.2 6.4 6.6 6.8 7
1
3
5
10
Dep
th (
m)
Speed(cm/s)
Profile of drogue speeds around 0951
on December 28, 1993
10.84
8.41
8.41
8.41
0 5 10 15
1
3
5
10
Dep
th (
m)
Speed(cm/s)
Fig. 4.55. Velocity profiles from drogue speeds on December 28, 1993.
107
Profile of drogue speeds around 1053
on December 28, 1993
10.94
11.78
11.81
10.47
9.5 10 10.5 11 11.5 12
1
3
5
10
Dep
th (
m)
Speed(cm/s)
Profile of drogue speeds around 1150
on December 28, 1993
5.39
3.30
1.89
7.59
0 2 4 6 8
1
3
5
10
Dep
th (
m)
Speed(cm/s)
Fig. 4.56. Velocity profiles from drogue speeds on December 28, 1993.
108
Predicted height of tide for Añasco Bay on
December 28, 1993
0
0.5
1
1.5
2
00:0
0
02:0
0
04:0
0
06:0
0
08:0
0
10:0
0
12:0
0
14:0
0
16:0
0
18:0
0
20:0
0
22:0
0
Hour
Heig
ht
(ft.
)
Wind speed for Añasco on December 28
1993
0.00
2.00
4.00
6.00
8.00
10.00
1 3 5 7 9 11 13 15 17 19 21 23
Sample
Sp
eed
(M
PH
)
Wind direction for Añasco Bay on
December 28, 1993
0
100
200
300
400
1 4 7 10 13 16 19 22
Sample
Dir
ecti
on
(deg
rees)
Fig. 4.57. Tide, wind speed and direction on December 28, 1993
Hour (GMT)
Hour (GMT)
Hour (local time)
109
CHAPTER 5
CONCLUSIONS AND RECOMMENDATIONS
The principal objectives undertaken in this investigation were, first to document
the long term average currents over one year period on Añasco Bay, second to determine
any periodicity of the fluctuating components and finally, to determine the forces which
are responsible for their behavior and variability.
First, let summarize the conclusions derived from the observed mean flow at both
stations. The long term average flow 0.5 nautical miles offshore El Mani is about 5.4
0.85 cm/s toward the southeast (111°-149°). The average flow at Manchas Exteriores is
10.41 2.35 cm/s slightly toward east of south (163°-175°). Manchas Exteriores had
almost twice the speed than at El Mani. These differences can be explained because the
S4 located at Manchas Exteriores near the shelf break was exposed to stronger currents
offshore the shelf break. The monthly mean current vectors did not show any indication
of a seasonal current pattern; they kept pointing approximately along the same direction
throughout all year in both stations. The mean flow direction (to the southeast) of El
Maní, can be explained in terms that the flow was steered along a passage between the
barrier reefs (Manchas Interiores and Manchas Exteriores) and the coastline of El Maní.
Orientation of current ellipses at El Maní revealed a stronger north-south
component (v). Also most of the observed periodicity in the current fluctuations are in
110
the v spectra. This back and forth motion of the current fluctuations primarily along the
north-south axis is due to the local bathymetry. This tendency to be anisotropic (i.e. to
have a preferred orientation) alongshore or along-isobath has been observed in most of
the continental shelf currents (Huyer, 1990).
In spite of the steering by bottom topography and bay geometry the average flow
moves southward as revealed by the monthly means of Manchas Exteriores. This flow
may be the result of residual tidal currents or the result of a North-South current along the
Mona Passage. We discarded the first option because a mean flow between 5.4 cm/s and
10.41 cm/s can not be explained in terms of a residual current generated by tidal currents
ranging between 1 cm/s and 17 cm/s. Usually the magnitude of the tidal residual currents
are expected to be one or two orders of magnitude less than the tidal currents themselves.
Residual currents, nor the mean local wind stress, can explain the observed mean flow.
The long term average wind direction was from the east (83°-119°) and the average wind
stress near the coast was 0.03 dynes/cm2. From the above facts and taking in
consideration that the shelf is very narrow it is reasonable to attribute the observed mean
flow to the influence of an offshore oceanic current.
Spectral estimates of currents at El Maní indicate a strong influence of the tide in
generating the fluctuations in current speed of u and v. But fluctuations in wind stress
might have a role on the enhancement of some particular frequencies. For example, the
spectra of wind stress component v shows peaks at diurnal and semidiurnal frequencies
that could be responsible on the increase of the diurnal over the semidiurnal band in the u
component (east-west) of currents at El Maní. Also 7- day wind stress fluctuations
111
probably are responsible for the peak observed at the same frequency in the low passed
current data of El Mani. Spectral estimates of the east-west wind stress show energy
concentration in the diurnal and semidiurnal band. This 24-hour and 12-hour fluctuation
is associated with the daily sea breeze-land breeze pattern common in this coast. The sea-
land breeze pattern is caused by the semidiurnal atmospheric tide S2 and the local
atmospheric circulation. The atmospheric tidal constituent S2 consists of a 12-hourly
progressive pressure wave. This pressure wave has its largest amplitude of over 1mb at
the equator and travels from East to West in such a way that at any location maxima are
experienced around 1000 and 2200 and minima around 0400 and 1600 local time. The
spectral estimate of the atmospheric pressure data from San Juan revealed this pressure
wave.
The inertial period for our latitude is 38.5 hours but no significant peak was
observed for that band. Probably because the average depth of Añasco Bay is about 40
feet (12.2 m) and friction slows down currents in a short period.
Sea level oscillations reveal the strong semidiurnal (M2) and diurnal (K1)
constituents of the tide plus shallow water harmonics with fourthdiurnal and sixthdiurnal
constituents.
112
The nonlinear terms in the equation of motion:
U/t + U U/x + V U/y -f V + g /x - 1/ x/z = 0
V/t + U V/x + V V/y +f U + g /y - 1/ y/z = 0
A B C D E F
where B, C and D give rise to this shallow water harmonics. The sixthdiurnal and
fourthdiurnal component, M6 and M4 respectively, are the second and third harmonics
generated by the semidiurnal constituent (M2).
Higher frequency components of 1.9 cph (31 min.) and 3.0 cph (20 min.) are
present in the sea level oscillations and in the current speed fluctuations. Merian’s
formula for open basin oscillations gives the resonant period, T, of the shelf as :
T= 4*L/(g *d)1/2
where L is the shelf width, d the shelf depth (assumed to be uniform), and g the
gravitational acceleration. For a section normal to the shelf break and passing through the
tide gauge located offshore El Mani (.5 nm of the shore), L4630 m (2.5 nautical miles)
and d12.192 m (40 feet), giving T32 minutes. This corresponds quite closely with one
of our peaks.
Drogue deployments during low wind conditions gave us an insight of the vertical
transfer of momentum during the tidal cycle. The deeper drogues in all occasions were
the first to respond to the changing tide. They changed speed and the direction, expected
for that part of the cycle, first than the drogues above. At the bottom velocities are easier
to change than in the surface because the friction is greater and can remove faster the
inertia gained by the drogues from the previous part of the tidal cycle. As a general rule,
113
tidal currents go from south to north on the flood tide and from north to south on the ebb.
The sense of rotation of the current will depend on the relative importance between the
semidiurnal and diurnal components of the mixed tide.
In this study, just the temporal variability was described. It is recommended that
further studies on the spatial variability of the shelf currents be undertaken. To
accomplish that, current meters and tide-gauges must be located alongshore the
continental shelf and the data analyzed for coherence between the alongshore currents and
sea-level. This could give us an insight into the spatial scale of the topographically
trapped waves. Cross-correlation and cross-spectral analysis of alongshore current
measurements could give us the speed of propagation of these waves. Once we know
these information it would be easier to describe which type of waves are responsible of
the current fluctuations observed in the Bay.
It is also recommended that further studies of the seiches observed in the high
frequency part of the sea-level and current spectra be undertaken to compare these with
similar findings of studies currently in progress on the south coast of Puerto Rico. It will
be helpful to understand the generating mechanism responsible for these seiches.
It is not recommended to locate current meters near the same locations chosen in
this study; they should be located at other sites around the bay in order to compare and
search for similarities or differences with our observations. We suggest to locate a
current meter off the shelf (out in deep water) and far from the influence of the coast.
This information will be helpful to corroborate if the currents in the Mona Passage move
from north to south and the time scales of variability present.
114
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