Coastal Current Regime in Añasco Bay -...

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



4.53. 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



4.57. 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.

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).

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

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315o

300o

285o

270o

255o

240o

225o

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195o

180o 165

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150o

135o

120o

105o

January 1993

00

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February 1993

00

4

4

8

8

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12

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16

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60o

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210o

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180o 165

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150o

135o

120o

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March 1993

00

5

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10

10

15

15

20

20

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75o

60o

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30o

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330o

315o

300o

285o

270o

255o

240o

225o

210o

195o

180o 165

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150o

135o

120o

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April 1993

00

5

5

10

10

15

15

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20

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60o

45o

30o

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150o

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May 1993

00

5

5

10

10

15

15

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75o

60o

45o

30o

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345o

330o

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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 Exte

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