Hydrology of Laguna Joyuda, Puerto Rico

By Luis Santiago-Rivera and Vicente Quinones-Aponte

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 93-4135

Prepared in cooperation with the

CENTER FOR ENERGY AND ENVIRONMENT RESEARCH and 

THE UNIVERSITY OF PUERTO RICO, MAYAGUEZ CAMPUS

San Juan, Puerto Rico 

1995
U.S. DEPARTMENT OF THE INTERIOR 

BRUCE BABBITT, Secretary

U.S. GEOLOGICAL SURVEY 

Gordon P. Eaton, Director

For additional information write to:

District Chief

U.S. Geological Survey

GSA Center

651 Federal Drive, Suite 400-15

Guaynabo, Puerto Rico 00965

Copies of this report can be purchased from:

U.S. Geological Survey 

Earth Science Information Center 

Open-File Reports Section, MS 517 

Box 25286, Denver Federal Center 

Denver, CO 80225
CONTENTS

Abstract................................................................................................................................................................ 1

Introduction.........................................................................................._^

Description of study area............................................................................................................................... 2

Acknowledgments .........................................................................................................................................5

Hydrology of Laguna Joyuda............................................................................................................................... 5

Rainfall and evaporation................................................................................................................................5

Surface water.................................................................................................................................................5

Ground water................................................................................................................................................. 8

Tidal flow.....................................................................................................................................................13

Tidal-cycle studies................................................................................................................................ 13

Application of an unsteady-flow model................................................................................................ 14

Model schematization..................................................................................................................... 14

Model calibration and verification ................................................................................................. 16

Sensitivity analysis......................................................................................................................... 19

Hydrologic budget and flushing rate of the lagoon..................................................................................... 22

Summary............................................................................................................................................................25

References.......................................................................................................................................................... 26

Contents III
FIGURES

1. Map showing location of Laguna Joyuda, drainage canal, streamflow stations, and

drainage basins ....................................................................................................................................3

2. Map showing location of hydrologic stations in the study area...............................................................4

3. Diagram showing bathymetry of Laguna Joyuda, January 20, 1988....................................................... 6

4. Graph showing monthly rainfall at Laguna Joyuda, December 1985 to April 1988............................... 7

5. Graph showing stage-discharge relation for Quebrada Mamey at Joyuda (50130320)........................... 8

6. Map showing potentiometric surface in the Laguna Joyuda area, December 17,

1986..............................................................................................................................................^

7. Graph showing water-level fluctuations in observation piezometer 6 and monthly

rainfall at Laguna Joyuda from May 1986 to April 1988.................................................................. 11

8. Graph showing stage data from the lagoon and the sea gages at Laguna Joyuda,

May 11-24, 1986................................................................................................................................ 13

9. Schematization of Laguna Joyuda drainage canal for the branch-network flow

model................................................................................................................................................. 15

10-15. Graphs showing:

10. Model-simulated and measured discharges at station 50130340 and measured 

water-surface elevation at station 50130350 during May 1-2, 1986, 

tidal-cycle study ...................................................................................................................... 16

11. Model-simulated and measured discharges at station 50130340 and measured 

water-surface elevation at station 50130350 during August 5-6, 1987, 

tidal-cycle study....................................................................................................................... 17

12. Relation of simulated and measured discharges and the root mean square

difference range for the verification run of August 5-6, 1987, tidal-cycle 

study......................................................................................................................................... 18

13. Relation of simulated and measured discharges for the specific duration time 

of the measurement and the root mean square difference range of the longterm verification from February 1987 to April 1988............................................................... 19

14. Relative sensitivity analysis for cross-sectional area and roughness coefficient.......................... 21

15. Hydrologic budget of Laguna Joyuda, December 1985 to April 1988.........................................23

TABLES

1. Physical characteristics of Laguna Joyuda and drainage basin................................................................ 2

2. Estimates of transmissivity and hydraulic conductivity at Laguna Joyuda............................................. 9

3. Physical characteristics for piezometers and wells at Laguna Joyuda................................................... 12

4. Lithology of observation piezometers constructed in the vicinity of Laguna Joyuda........................... 12

5. Model-generated accumulated flow volume for August 1987 at station 50130340.............................. 20

6. Effects of errors in best methods of measurement on calculation of the water balance

of Laguna Joyuda............................................................................................................................... 24

IV Hydrology of Laguna Joyuda, Puerto Rico
CONVERSION FACTORS, ABBREVIATED WATER-QUALITY UNITS, AND ACRONYMS

Multiply By To obtain

centimeter (cm) 0.3937 inch

cubic meter (m3 ) 35.31 cubic foot

cubic meter per day (m3/d) 264.2 gallon per day

cubic meter per second (m3/s) 35.31 cubic foot per second

kilometer (km) 0.6214 mile

meter (m) 3.281 foot

meter per day (m/d) 3.281 foot per day

meters squared per day (m2/d) 10.76 feet squared per day

millimeter (mm) 0.03937 inch

million cubic meters (Mm3 ) 35.31 million cubic feet

pascal (Pa) 0.01 millibars

square kilometer (km2) 0.3861 square mile

square meter (m2 ) 10.76 square foot

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows: °C = 5/9 (°F - 32)

Abbreviated water-quality units used in this report:

milligrams per liter (mg/L)

microsiemens per centimeter at 25 °C (jiS/cm)

Acronyms used in this report:

Center for Energy and Environment Research (CEER)

Mean Sea Level (MSL)

Root Mean Square Difference (RMSD)

U.S. Geological Survey (USGS)

Conversion Factors, Abbreviated Water-Quality Units, and Acronyms
Hydrology of Laguna Joyuda, Puerto Rico

By Luls Santlago-RJvera, anc/Vicente Quinones-Aponte

Abstract INTRODUCTION

A study was conducted by the U.S. Geological Survey 

to define the hydraulic and hydrologic characteristics of 

the Laguna Joyuda system (in southwestern Puerto Rico) 

and to determine the water budget of the lagoon. This 

shallow-water lagoon is connected to the sea by a single 

canal. Rainfall and evaporation, surface-water, groundwater, and tidal-flow data were collected from December 

1,1985, to April 30,1988. A conceptual hydrologic model 

of the lagoon was developed and discharge measurements and modeling were undertaken to quantify the 

different flow components. The water balance during the 

29-month study period was determined by measuring and 

estimating the different hydrologic components: 4.14 

million cubic meters rainfall; 5.38 million cubic meters 

evaporation; 1.18 million cubic meters surface water; and 

0.34 million cubic meters ground water. A total of 18.9 

million cubic meters ebb flow (tidal outflow) was 

discharged from the lagoon and 14.4 million cubic meters 

flood flow (tidal inflow) entered through the canal during 

the study. Seawater inflow accounted for 71 percent of 

the water into the lagoon. The storage volume of the 

lagoon was about 1.55 million cubic meters. The lagoon's 

hydrologic-budget residual was 4.22 million cubic meters, 

whereas the sum of the estimated errors for the different 

hydrologic components amounted to 4.51 million cubic 

meters. Average flushing rate for the lagoon was 

estimated at 72 days. During the study, the specific 

conductance of the lagoon water ranged from 32,000 to 

52,000 microsiemens per centimeter at 25 degrees 

Celsius, whereas the specific conductance of local 

seawater is about 45,000 to 55,000 microsiemens.

Laguna Joyuda is a small saltwater lagoon located in 

southwestern Puerto Rico (fig. 1). The lagoon is the 

habitat of many protected plants and animal species and is 

a natural reserve relatively undisturbed by the urban or 

industrial developments that affect many coastal 

ecosystems in Puerto Rico. To increase the understanding 

of the processes, which account for the productivity of 

lagoons and the interest in exploring Laguna Joyuda as a 

coastal processes pilot-study model; in 1985, the U.S. 

Geological Survey (USGS), in cooperation with the 

Center for Energy and Environment Research (CEER) 

and the University of Puerto Rico at Mayagiiez initiated a 

hydrologic study of Laguna Joyuda.

The purpose of this report is to define the hydraulic 

and hydrologic characteristics of the Laguna Joyuda 

system. The principal objective of the USGS hydrologic 

investigation was to define the hydrologic budget of 

Laguna Joyuda. A conceptual hydrologic model of the 

lagoon was developed and the component parts were 

determined as follows:

 Rainfall was measured using two rainfall gages, 

and evaporation was estimated using specificconductance and water-temperature data 

collected at the stage-measurement station 

located at the lagoon (fig. 2), in conjunction with 

a nearby meteorological station and applying 

Kuznetzov's formula (Shnitnikov, 1974),

Introduction
 Surface water contribution into the lagoon was 

quantified by three streamflow gaging stations 

(one continuous-record and two partial-record 

sites) and regression equations developed relating 

their discharges,

 Ground-water interchange with the lagoon was 

estimated by determining transmissivity by 

applying the slug test technique in four wells 

located within the area (fig. 2) and using Darcy's 

law,

 Tidal influence was determined by monitoring the 

specific conductance and temperature of water in 

the lagoon and of ground water,

 Interchange of water between the sea and the 

lagoon was determined by constructing and 

calibrating a one-dimensional flow model that 

simulated tidal flow in and out of the lagoon 

through the drainage canal (fig. 1) that connects 

the lagoon to the sea.

Description of Study Area

Laguna Joyuda is on the southwestern coast of Puerto 

Rico, about 5.1 km northwest of Cabo Rojo, 8.0 km south 

of Mayagiiez, and about 115 km southwest of San Juan 

(fig. 1). Laguna Joyuda is bounded to the east by the 

Cordillera Sabana Alta, to the west by a narrow land 

barrier comprised of sand bars, and to the south by 

orchards, marshy lowlands, and Joyuda village.

A general geologic description of the study area is 

given on the basis of the geologic map of the Mayagiiez, 

Puerto Real and Rosario quadrangles (Curet, 1986). The 

lagoon area is underlain by intrusive and extrusive 

volcanic rocks, predominately serpentinite of Jurassic 

age. These rocks are overlain by quartz-sand deposits of 

Tertiary and Quaternary age that have been weathered and 

eroded by ephemeral streams. In turn, these deposits are 

overlain by deposits of silt, sand, and clay of Holocene 

age. Swamp deposits are present along the southern and 

southwestern shorelines of the lagoon. The coastline 

along the Mona Passage is composed predominately of 

beach deposits of Holocene age.

Laguna Joyuda was formed about 500 years ago by the 

accretion of two sand bars that enclosed a small

embayment (Comer, 1969). This saltwater lagoon is 

separated from the sea by a narrow land barrier about 3.0 

km long and 0.12 to 0.50 km wide (fig. 1). The lagoon is 

in a drainage basin with an area of 5.83 km2 , including the 

lagoon's surface area of 1.41 km2 (table 1). The lagoon is 

relatively shallow and has a mean depth of 1.1 m. The 

specific conductance of the lagoon water ranged from 

32,000 to 52,000 |LlS/cm during the study period. The 

lagoon is connected to the sea by a tidal-influenced canal 

located at the southern boundary of the lagoon. The canal 

is 488 m long, with an average width of 6.7 m and an 

average depth of 0.6 m. Occasionally, the mouth of the 

canal is blocked by sediment. About 50 percent of the 

land area within the lagoon's drainage basin is in pasture 

and is used for raising livestock. Little land is under 

cultivation. The remaining land area is covered by 

mangrove, with different species of trees and bushes. 

Fishing and water-sport activities are minimal within the 

lagoon.

Results of a bathymetric survey of Laguna Joyuda 

conducted on January 20, 1988, were used to determine 

the lagoon's storage volume of 1.55 Mm3 at a watersurface elevation of about 0.14 m above mean sea level. 

Computations were performed using the "Range Method" 

described by the U.S. Soil Conservation Service (1983).

Table 1. Physical characteristics of Laguna Joyuda and 

drainage basin

Physical characteristics Quantity

Lagoon area

volume

mean depth

maximum depth

maximum length

maximum width

perimeter

Canal length

mean width

mean depth

Basin drainage area

perimeter

maximum drainage 

basin elevation

1.41

1.55

1.1

2.59

2.1

1.1

7.1

488

6.7

.6

5.83

11.5

105

square kilometers

million cubic meters

meters

meters

kilometers

kilometers

kilometers

meters

meters

meter

square kilometers

kilometers

meters

Hydrology of Laguna Joyuda, Puerto Rico
67°ir 67-10' 67°09'30"

18°08'30"

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Base from U.S. Geological Survey 

Mayaguez and Puerto Real, 

topographic quadrangles Puerto Rico. EXPLANATION

50130300 SURFACE-WATER MEASUREMENT 

A SITE AND NUMBER

50130320 A SURFACE-WATER GAGINGA STATION AND NUMBER

DA - 0 98 DRAINAGE AREA, IN SQUARE - w-w KILOMETERS

 DRAINAGE DIVIDE

 Line of equal elevation referenced 

to mean sea level. 

Contour interval 5 meters.

Figure 1. Location of Laguna Joyuda, drainage canal, streamflow stations, and drainage basins.

Introduction
67 11' 67°10' 67°09'30"

18°08'30"

18°08'

18°07'

18°06'30"

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Base from U.S. Geological Survey 

Mayagtlez and Puerto Real, 

topographic quadrangles Puerto Rico EXPLANATION

50130320 A SURFACE-WATER CONTINUOUS-RECORD

A GAGING STATION AND NUMBER

50130330 A SURFACE-WATER MEASUREMENT

^^ SITE AND NUMBER

50130340i A STAGE-MEASUREMENT STATION

 +> RAIN GAGE WITH RECORDER

<^ RAIN GAGE DAILY OBSERVATION

(D) 7 PIEZOMETER AND NUMBER

O14 STOCK-WATER SUPPLY WELL AND NUMBER

AND NUMBER

Figure 2. Location of hydrologic stations in the study area.

4 Hydrology of Laguna Joyuda, Puerto Rico
Depths and distances were measured using a fathometer 

coupled to a current meter mounted on a moving boat 

(Smoot and Novak, 1969). A total of 13 ranges were 

surveyed to develop a bathymetric map of the lagoon 

(fig. 3). Bearings were tied to land reference points.

Acknowledgments

The authors gratefully acknowledge Dennis Corales 

and other members of the Center for Energy and 

Environment Research staff for their assistance in the 

collection of field data during the study. We also thank 

Luis Toro-Rosa, a local resident, who recorded the daily 

rainfall observations.

HYDROLOGY OF LAGUNA JOYUDA

The hydrology of Laguna Joyuda was determined by 

first formulating a conceptual hydrologic model of inflow 

and outflow to and from the lagoon. Data were collected 

to quantify the water budget of the lagoon and to calibrate 

and verify models for inflow and outflow that could not 

be determined directly. Inflow to the lagoon included 

rainfall, surface water via streamflow, ground water, and 

tidal flow. Outflow included evaporation and ebb flow.

Rainfall and Evaporation

The west coast of Puerto Rico is characterized by a 

relatively dry season from February to April, increased 

rainfall from May to July, and a relatively wet season 

from August to January. Total rainfall during the 

29-month study period (December 1, 1985, to April 30, 

1988) was 2,941 mm, equivalent to a yearly average of 

1,215 mm. Monthly rainfall varied from a maximum of 

316 mm in May 1986 to a minimum of 14 mm in 

February 1988 (fig. 4). Rainfall data were recorded using 

an automatic-digital recorder with 15-minute readings and 

daily readings by an observer at a standard rain gage. The 

total rainfall contribution of 4.14 Mm3 to the lagoon was 

determined by multiplying the depth of measured rainfall 

by the surface area of Laguna Joyuda. Direct evaporation 

from the lagoon surface was estimated using data 

collected at a temperature station located at the lagoon

and at a meteorological station located at the Lajas 

Experimental Station, Lajas, nine miles southeast of 

Laguna Joyuda, and applying Kuznetzov's empirical 

formula (Shnitnikov, 1974):

E = 0.88E,. -^2-,

e n -

(1)

where 

E

e2

is the lagoon evaporation, in millimeters per 

day;

is the standard pan evaporation, in millimeters 

per day;

is the water vapor pressure at the lagoon water 

temperature of 28.4 °C, in pascals;

is the water vapor pressure at the evaporation 

pan temperature, in pascals;

is the water vapor pressure at a height of 2 m 

above the lagoon surface and at a temperature

of 25.5 °C.

Equation (1) was used to estimate an average 

evaporation value because of the small variability of the 

water and air temperatures, the small changes in 

atmospheric pressure, and the lack of detailed information 

needed to compute a more accurate energy balance. An 

average yearly evaporation value of 1,582 mm was used 

to estimate the total evaporation of 5.38 Mm3 for the 

lagoon for the study period.

Surface Water

Streamflow to Laguna Joyuda is from intermittent and 

ephemeral streams originating in the Cordillera Sabana 

Alta. The flow fluctuates in response to periods of intense 

rainfall (normally May and August through November). 

During the dry season (February through April), 

streamflow is reported by local residents often to cease 

completely. The principal sources of runoff to the lagoon 

are: Quebrada Mamey, an intermittent stream with a 

drainage area of 0.98 km2; Quebrada Mango, an 

intermittent stream with a drainage area of 0.88 km2 ; 

Quebrada Palma, an ephemeral stream with a drainage 

area of 0.39 km2; and Quebrada Indio, an ephemeral 

stream with a drainage area of 0.14 km2 (fig. 1).

Hydrology of Laguna Joyuda
67"! TOO" 67°10'00"

18°08'30"

18°08'00"

18°07'00"

300 

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600

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1,200 FEET

EXPLANATION

 0.9 LINE OF EQUAL WATER DEPTH, IN METERS. 

eoo METERS Depth interval is variable. Water-surface 

_J elevation is 0.14 meter above mean sea level.

Figure 3. Bathymetry of Laguna Joyuda, January 20, 1988.

6 Hydrology of Laguna Joyuda, Puerto Rico
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and

Dalrymple, 1967; Shearman, 1976). Daily-mean 

discharges at Quebrada Mango were estimated on the 

basis of a discharge correlation using 85 pairs of 

concurrent discharge measurements made at Quebrada 

Mamey and Quebrada Mango. The ordinary least square 

regression method yielded the following equation:

Q, = -0.0002 + Q2(0.7522), (2)

Figure 4. Monthly rainfall at Laguna Joyuda, 

December 1985 to April 1988.

is the discharge, in cubic meters per second, at 

Quebrada Mango,

is the discharge, in cubic meters per second, at 

Quebrada Mamey,

X intercept = -0.0002 m3/s,

slope = 0.7522, and

correlation coefficient = 0.94.

Streamflow data were collected at Quebrada Mamey, 

Quebrada Mango, and Quebrada Palma. Discharge 

measurements at Quebrada Mamey (the only continuousrecord station) and Quebrada Mango were made three 

times a month using the methods described by Buchanan 

and Somers (1969). Twelve streamflow measurements 

were made at Quebrada Palma during the study period. 

Measurements were not possible at Quebrada Indio 

because it is an ephemeral stream for which runoff ceases 

almost immediately after rainfall stops. Daily-mean 

discharges were computed for Quebrada Mamey for a 

period of record extending from December 1985 to April 

1988. The automatic data processing methods of 

Kennedy (1983) were used to compute the daily-mean 

discharge data.

A stage-discharge relation (fig. 5) at Quebrada Mamey 

was developed using the methods described by Carter and 

Davidian (1965). The lower part of the rating curve was 

defined using discharge measurements, and the upper part 

was defined using step-backwater modeling (Benson and

To estimate the discharge contribution of Quebrada 

Palma, the daily-mean discharges of Quebrada Mamey 

and Quebrada Mango were divided by their respective 

drainage areas. The resulting values, in cubic meters per 

second per square kilometer, were plotted as the ordinate 

and each stream drainage area, in square kilometers, as 

the abscissa to develop a relation curve. The drainage 

area of Quebrada Palma was entered into the relation 

curve to derive a daily-mean discharge value. This value 

was then multiplied by the total number of days for the 

study period. Most of the remaining 2.03 km2 that are not 

lagoon or the delineated drainage basins serves as a 

recharge area to the ground-water flow system. During 

high intensity rainfall, however, this remaining drainage 

basin can contribute some sheet flow (overland flow) to 

the lagoon. Sheet flow was not considered in this study 

because high intensity rainfall is infrequent in the study 

area. The total surface-water contribution to the lagoon 

from Quebrada Mamey, Quebrada Mango, and Quebrada 

Palma during the study period was estimated at 1.18 Mm3 .

Hydrology of Laguna Joyuda
10

C/D 

DC 

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 DISCHARGE MEASUREMENTS 

A STEP-BACKWATER ANALYSIS

0.001 0.01 0.1 1 

DISCHARGE, IN CUBIC METERS PER SECOND

10

Figure 5. Stage-discharge relation for Quebrada Mamey at Joyuda (50130320).

Ground Water

Ground water in the study area is in unconsolidated 

alluvial-valley deposits and in faulted or fractured 

volcanic rocks in the upland areas of Cordillera Sabana 

Alta. Water generally moves from the uplands toward the 

lagoon, except in the vicinity of Quebrada Mamey and 

Quebrada Mango. These streams are perennial along their 

reaches that extend from the lagoon to about 1 km 

upstream. The streams flows are sustained by aquifer 

discharge.

An estimate of the contribution of ground-water flow 

to the water budget of the lagoon was made using Darcy's 

equation

where 

Q

T

I

is the discharge, in cubic meters per day; 

is the aquifer transmissivity (11.2 m2/d); 

is the hydraulic gradient (3.05 m/177 m); and

8 Hydrology of Laguna Joyuda, Puerto Rico
L is the distance along line A-A' (see fig. 6), 

3,048 m, which is an approximation of the 

length of the aquifer containing fresh ground 

water that flows perpendicular to the 7.6-m 

potentiometric-surface contour.

This simple form of Darcy's law can be applied only to 

areas where the aquifer characteristics are uniform and 

vertical and lateral components are negligible (one 

dimensional). Therefore, the estimate was made only for 

that part of the aquifer contained between the 4.6-m and 

7.6-m potentiometric-surface contours (fig. 6). Groundwater level fluctuations between 1.5 and 3.5 m above 

mean sea level (fig. 7) precluded the application of 

Darcy's equation to estimate ground-water flow through 

the lower part of the watershed. This is because Darcy's 

equation is based on the assumption of steady-laminar 

flow, and these ground-water fluctuations may be due to 

nonsteady flow. It appears from figure 7 that these 

fluctuations can be explained by local rainfall patterns. 

An estimate of the ground-water flow through the lower 

part of the watershed is not needed because the specific 

conductance of water in test wells 3, 8, 9, and 10 with 

depths of 1.6 to 17.2 meters, is similar to values typical 

for local seawater (45,000 to 55,000 jiS/cm). This 

indicates that fresh ground water from the uplands does 

not discharge beneath the lagoon and into the sea.

To apply Darcy's equation, the three terms on the right 

side of equation 3 need to be determined. A 

transmissivity value was estimated using

where 

K is the hydraulic conductivity, in meters per day; 

and

is the aquifer thickness, in meters.

A hydraulic conductivity value representative of the 

simplified ground-water flow system was estimated as the 

geometric mean of K values (table 2) based on four slug

tests that were conducted at wells 4,6, 12, and 13 (see fig. 

6). These wells were used because they were within the 

area of estimate. Physical characteristics of the 

piezometers and wells are presented in table 3. Results of 

the slug tests were analyzed using the technique described 

by Papadopulos (1973). A representative aquifer 

thickness (b) of 15.2 m was assigned on the basis of 

lithologic information (see table 4). The transmissivity 

value was estimated at 11.2 m2/d. Because of the 

uniformity of the potentiometric contours on the upper 

part of the watershed, a representative hydraulic gradient 

(3.05 m/177 m) was used. The simple geometry of the 

aquifer, the uniform configuration of the potentiometric 

contours, and the small variability of water levels in wells 

at the part of the aquifer contained between the 4.6-m and 

7.6-m potentiometric contours (fig. 6), support the 

application of Darcy's equation to estimate ground-water 

flow to the lagoon. The total fresh ground-water flow to 

the lagoon was estimated at 380 m3/d, which is equivalent 

to 0.34 Mm3 for the study period.

Table 2. Estimates of transmissivity and hydraulic 

conductivity at Laguna Joyuda

[m2/d, meters squared per day; m/d, meters per day; , no data 

available]

Piezometer 

or well 

number

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Depth 

(meters 

below 

land 

surface)

1.89

1.52

1.55

3.57

8.32

8.23

5.18

2.13

7.01

17.37

3.66

4.57

7.62

9.14

9.14

Length of 

screen 

interval 

(meters)

0.61

0.61

0.61

0.61

3.05

1.22

.46

.61

.61

2.74

1.52

1.52

4.57

4.57

4.57

T 

m2/d

31.60

6.04

.09

.08

-

4.83

.05

4.18

8.18

5.76

2.14

K 

m/d

51.82

9.91

.15

.07

7.92

.08

2.74

1.79

1.26

.47

Hydrology of Laguna Joyuda
67° 10' 67°09'30"

18°08'30"

18°08'

18°07

18'06'30"

 >^ 0

1 

0

.5 1 KILOMETER

.5 1 MILE /

Base from U.S. Geological Survey 

Mayaguez and Puerto Real, 

topographic quadrangles Puerto Rico. EXPLANATION

_ 7.5__ WATER-TABLE CONTOUR-Shows elevation 15 

of potentiometric surface. Dashed where 

approximately located. Contour interval in 0.65 

meters and variable. Datum is mean sea level.

<D> PIEZOMETER A A' 

O STOCK-WATER SUPPLY WELL

PIEZOMETER OR WELL NUMBER

WATER LEVEL IN METERS ABOVE 

MEAN SEA LEVEL

LINE ACROSS WHICH TOTAL GROUNDWATER FLOW WAS CALCULATED

DIRECTION OF GROUND-WATER FLOW

Figure 6. Potentiometric surface in the Laguna Joyuda area, December 17, 1986.

10 Hydrology of Laguna Joyuda, Puerto Rico
CO 

DC 

LU

H 

LU

2

z 

<

350

300

250

200

150

100

50

0

m

m

m

LU

3.5

2.5

LLJ 

>

LLJ

LLJ 

CO

LU 

^ 

LU

O 

CO

CO 

DC 

LU

H

LJJ

? 0.5

O

I

LLJ

1.5

-0.5

OBSERVATION PIEZOMETER 6

Mean Sea Level

LU > o i- i- > o

ID O- O O LU

Z Q

< LU

CD DC DC > LU >-

D_ 

<

O

0- O

I- >

< LU

CD DC DC

< 0- 

<

1986 1987 1988

Figure 7. Water-level fluctuations in observation piezometer 6 and monthly rainfall at Laguna Joyuda from May 

1986 to April 1988.

Hydrology of Laguna Joyuda 11
Table 3. Physical characteristics for piezometers and wells at Laguna Joyuda 

[e, estimated]

Piezometer Latitude 

or well and 

number longitude

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

18°08'27"

18°08'25"

18°08'23"

18°07'23"

18°07'35"

18°07'50"

18°08'16"

18°07'20"

18°07'21"

18°07'22"

18°07'24"

18°07'32"

18°07'31"

18°08'17"

18°08'36"

67°10'51"

67°10'48"

67°10'45"

67°10'36"

67°10'25"

67°10'12"

67°10'31"

67° 11 '02"

67° 11 '02"

67° 11 '02"

67°10'38"

67°10'26"

67°10'05"

67°10'29"

67°10'42"

Elevation, in

Measuring 

point

2,

1

1

2,

2,

4,

3,

2,

2.

2.

1.

2.

8.

10,

1.

.62

.62

.85

.85

.80

.56

.08

.29

.08

.20

.73

.91

.71

.10

.37

meters above or below mean sea level

Land 

surface

1.77

0.70

0.36

1.84

1.98

3.72

2.16

1.50

1.48

1.41

1.12

2.76

8.19

9.65

1.07

Bottom 

of well

-0.12

-0.82

-1.20

-1.72

-6.34

-4.51

-3.02

-0.64

-5.54

-15.96

-2.54

-1.82

0.57

0.50

-8.08

Top of to] 

screen

0.49

-0.21

-0.59

-1.11

-3.29

-3.29

-2.56

-0.03

-4.92

-13.22

-1.01

-0.29

5.14e

5.07e

-3.50

Length of casing to Casing 

p of screen, in meters diameter, in 

below land surface centimeters

1 .28

0.91

0.94

2,

5,

7,

4,

1,

6

14.

2.

3.

3.

4.

4.

.96

.27

.01

.72

.52

.40

.63

,13e

.05e

.05e

.57e

,57e

10

10

10

10

10

10

10

10

10

10

7,

10

15,

10.

7.

.16

.16

.16

.16

.16

.16

.16

.16

.16

.16

.62e

.16

.24

.16e

.62

Table 4. Lithology of observation piezometers constructed in the vicinity of Laguna Joyuda

Piezometer Date Depth of piezometer 

number drilled (meters below

land surface)

General lithology

(values are in meters below land surface)

9

10

3/25/86

3/25/86 

3/25/86

3/25/86 

3/25/86

3/26/86 

3/26/86 

3/27/86

3/27/86 

3/27/86

1.89

1.52

1.55

3.57

8.32

5.18

2.13

7.01

17.37

0-0.6 Light-brown sand mixed with rocks (fill); 0.6-1.5 light-brown 

coarse sand; 1.5 water; 1.5-1.9 light-grey coarse sand.

0-0.3 Grey coarse sand; 0.3-1.5 light-grey coarse sand.

0-0.9 Brown rocky clay road fill; 0.9-1.2 light-grey medium-size wet 

sand; 1.2-1.6 dark-grey medium-size sand.

0-0.6 Dark-grey heavy clay; 1.5 water; 0.6-3.6 dark-grey heavy wet 

clay.

0-2.1 Dark-brown fine sand; 2.1-3.7 yellow dark wet sand 3.7-4.3 

yellow sandy clay; 4.3-4.9 brownish, sandy clay; 4.9-6.7 yellow sandy 

clay; 7.6 water; 6.7-8.3 yellow heavy wet clay.

0-0.6 Dark-brown sandy loam topsoil; 0.6-1.2 light-brown mediumsize sand; 1.2-3.7 brown sandy clay (water); 3.7-5.2 brown wet clay; 

5.2-8.2 brown wet heavy clay.

0-0.6 Clayey very fine sandy loam topsoil; 0.6-2.1 brown clay, damp 

crumbly; 2.1-3.7 reddish-brown clay; 3.7-5.2 reddish-brown soupy 

sandy clay.

0-0.3 Rocky clay fill; 0.3-.6 dark grey clay with shell fragments 

(swamp soil); 0.6-2.1 (1.2 water) dark grey clay and sand with 

shell fragments.

0-0.6 Rocky clay fill; 0.6-7.0 dark grey clay and sand with shell 

fragments.

0-0.6 Rocky clay fill; 0.6-6.7 grey soupy sandy clay (shell hash); 

6.7-8.2 hard clay; 8.2-15.8 (9.8-11.3 water) reddish-brown sandy 

clay; 15.8-17.4 reddish soupy sandy clay and shell fragments.

12 Hydrology of Laguna Joyuda, Puerto Rico
Tidal Flow

Cross sections surveyed along the canal connecting 

Laguna Joyuda to the sea reveal a relatively uniform canal 

geometry. Flood and ebb currents dominate flow through 

the canal, except during periods when infrequent runoff 

becomes the dominant flow. When extreme rainfall 

causes an accumulation of large volumes of freshwater in 

the lagoon, the direction of flow in the canal is seaward 

and prevent the entrance of seawater into the lagoon over 

substantial periods of time. One such rainfall occurred 

during May 11-24, 1986 (fig. 8). This type of rainfall may 

occur once or twice a year. Seawater inflow accounted 

for 71 percent of the water into the lagoon. Any 

obstruction or interference with the free flow of water 

through the tidal canal would alter the hydraulic condition 

of the lagoon system.

Discharge in the canal was simulated using the 

branch-network unsteady-flow model of Schaffranek and 

others (1981). A detailed description of the modeling 

procedures is presented in the section of this report titled 

"Application of an Unsteady Flow Model." During the 

period of study, an estimated total of 14.4 Mm3 of water 

entered the lagoon, and 18.9 Mm3 discharged seaward.

Tidal-Cycle Studies

Tidal-cycle measurements were made every hour 

during a 25-hour period to quantify flood and ebb flows 

through the canal. Flood flow is the quantity of water 

that flows in the upstream direction (into the lagoon) and 

ebb flow is the quantity of water that flows in the 

downstream direction (out of the lagoon). Stage was 

normally recorded at a staff gage and related to the local

Stage at Lagoon Station (50130340)

Stage at Sea Station (50130350)

Mean Sea Level

11 12 13 14 15 16 17 18 19 20 21 22 23 24

Figure 8. Stage data from the lagoon and the sea gages at Laguna Joyuda, May 11-24, 1986.

Hydrology of Laguna Joyuda 13
mean sea level datum. Average velocities were 

determined from discharge measurements using standard 

USGS procedures (Buchanan and Somers, 1969).

The first set of tidal-cycle measurements began at 

0700 hours on May 1, 1986, and ended at 0800 hours on 

May 2, 1986. Total ebb and flood flows measured were 

31,200 m3 and 14,200 m3 , respectively. The difference of 

17,000 m3 represents the net flow out of the lagoon for the 

complete tidal cycle. Specific-conductance measurements 

in the canal ranged from 48,600 to 51,500 |iS/cm during 

the first tidal-cycle measurement. This range is similar to 

the range of specific conductance for local seawater 

(45,000 to 55,000 |iS/cm), indicating that lateral 

contributions of freshwater to the canal were insufficient 

to affect the specific conductance of the water in the 

lagoon.

A second tidal-cycle measurement began at 0700 

hours on August 5, 1987, and ended at 0800 hours on 

August 6, 1987. Total ebb flow measured during this 

period was 51,000 m3 , whereas 22,700 m3 entered the 

lagoon on the flood tide. Therefore, there was a net ebb 

flow of 28,300 m3 . During this tidal-cycle measurement, 

the specific conductance in the canal ranged from 42,000 

to more than 50,000 |iS/cm.

Application of an Unsteady-Flow Model

The branch-network unsteady-flow model (BRANCH) 

(Schaffranek and others, 1981) was used to simulate 

discharge in the Laguna Joyuda canal based on watersurface elevations at each end of the canal. By using the 

model, total inflow and outflow to and from the lagoon 

can be quantified by summing the continuous flow 

computed on the basis of the continuous-record of watersurface elevation at the boundaries represented by two 

canal gaging stations. The BRANCH model is based on 

an implicit finite-difference formulation of the continuity 

and momentum flow equations. The model 

implementation is supported by a data-base system that 

provides computer programs to compute cross-section 

geometry and to process time-dependent and boundaryvalue data.

Model Schematization

A schematization of the canal system of Laguna 

Joyuda is shown in figure 9. The network system 

consists of one branch. Two external junctions delimit 

the upstream and downstream boundaries. Two cross 

sections were used for model computations. The 

segment length was determined by measuring the 

distance along the thalweg of the canal. To simulate 

flow, stage data were specified at the upstream and 

downstream boundaries. Stage data were obtained at 

gaging stations 50130340 and 50130350 (fig. 2). These 

stations were referenced to the local mean sea level 

datum. Stage-recording synchronization was maintained 

by using USGS solid-state timers.

A convergence study was done to demonstrate that 

the model can achieve convergence in space and time 

using only two computational cross sections. 

Convergence in space is demonstrated by operating the 

model with two or more sets of computational cross 

sections and examining those computational nodes 

common to both sets of model results and verifying that 

the model is not sensitive to the distance step. 

Convergence in time is demonstrated by varying the 

computational time step and examining the impact on 

model output. In the convergence test, distance steps of 

244 m (three cross sections) and 122 m (four cross 

sections) and a time step of 5 minutes (300 seconds) were 

sufficient to achieve convergence of the model using the 

May 1986 and August 1987 tidal-cycle measurements. 

For all the previously mentioned distance steps, the 

predicted discharges changed very little when the time 

step of 15 minutes (900 seconds) is changed to 5 minutes 

(300 seconds). The convergence test indicates that the 

values used in the model for the distance step and time 

step are appropriate to provide numerical stability.

Conveyance and storage characteristics for the reach 

were defined by the cross-sectional canal geometry, 

segment length, roughness coefficient, and momentum 

coefficient. Cross-sectional geometry and segment 

length were measured directly, whereas the other factors 

initially were approximated and subsequently refined 

during model calibration.

14 Hydrology of Laguna Joyuda, Puerto Rico
LAGUNA JOYUDA

/External Branch Junction

Cross Section

Branch

Flood Flow (Negative)

Ebb Flow (Positive)

Thalweg

External Branch Junction

50 100

MONA PASSAGE 

150 METERS

100 200 300 400 FEET

Figure 9. Schematization of Laguna Joyuda drainage canal for the branch-network flow model.

Hydrology of Laguna Joyuda 15
Cross-sectional geometry was measured by a leveling 

survey of the canal. Eleven cross sections were surveyed. 

The canal has a uniform geometry, with a cross-sectional 

width of 16 m at the upstream boundary and 14 m at the 

downstream boundary. Due to the reach length and 

uniformity of the canal sections, only two cross sections 

were used in model computation. The step-backwater 

computer program by Benson and Dalrymple (1967) was 

used to compute the cross-sectional properties. The 

geometry data were prepared in the form of stage-areawidth tables for model input. Points along the canal 

center line, right and left edges of water, canal bottom, 

overbanks, water-surface elevation, and cross sections 

were surveyed to determine the canal geometry.

Flow through the canal consists of longitudinal ebb 

and flood currents that constantly affect the water-surface 

slope. The canal is 488 m long, has a mean width of 6.7 

m, and a mean depth of 0.6 m. The canal bottom is 

composed of sand and sparse gravel. Thick mangrove 

roots are present along both banks of the canal at the

waters edge. Heavy mangrove along the banks protects 

the canal flow from wind disturbance; hence, wind was 

not considered a forcing function in the model.

Model Calibration and Verification

Calibration of the flow model was accomplished by 

using a 25-hour tidal-cycle measurement performed on 

May 1-2, 1986. The roughness coefficient was adjusted 

until model results were similar to measured discharges 

(fig. 10). A roughness coefficient of 0.042 resulted in the 

best fit to calibrate the model.

Results from a second 25-hour tidal-cycle 

measurement performed on August 5-6, 1987, were used 

to verify the calibrated model. None of the model 

parameters were adjusted during verification. Simulated 

and measured discharges compared well (fig. 11).

Differences between simulated and measured 

discharge from the verification run were evaluated using 

the root mean square difference (RMSD).

Measured discharge 

Simulated discharge 

Line of zero flow 

Water-surface elevation

19 

TIME, IN HOURS

Figure 10. Model-simulated and measured discharges at station 50130340 and measured water-surface elevation at 

station 50130350 during May 1-2, 1986, tidal-cycle study.

16 Hydrology of Laguna Joyuda, Puerto Rico
Q

2 

O

o

UJ 

CO 

DC 

UJ 

CL

CO 

DC

UJ

UJ 

^ 

O 

CO

D 

O

LU 

O 

DC 

<

I 

O 

CO

Q

Measured discharge 

Simulated discharge 

Line of zero flow

19 

TIME, IN HOURS

Figure 11. Model-simulated and measured discharges at station 50130340 and measured water-surface elevation at 

station 50130350 during August 5-6, 1987, tidal-cycle study.

The RMSD is determined by the equation:

where

N

Qs

RMSD =

N

is the number of measurements (25);

is the simulated discharge, in cubic meters per 

second; and

is the measured discharge, in cubic meters per 

second.

The analysis of the differences between simulated 

and measured discharges indicates that the model 

accurately simulated unsteady flow in the canal in the 

range of measured discharges. Application of equation 

4 to the verification data resulted in a RMSD of 0.08 

m3/s (fig. 12). For the calibration period, RMSD was 

0.11 m3/s.

During the study, 42 discharge measurements were 

made in the canal from February 1987 through April 

1988. These measurements were compared with 

corresponding discharges simulated by the model (fig. 

13). Discharge measurements were made during time 

periods ranging from 25 to 40 minutes, and the resulting 

discharge values represent the average discharge during

Hydrology of Laguna Joyuda 17
2.0

Q

Z

O

CO

DC 

LLJ 

Q_

CO 

DC 

LLJ

LLJ

O 

00

o o.o

CO

1.0

0.5

.05 U ' D

LLJ

CD 

DC 

<

O

§ -1.0

Q 

LLJ

I - 1 '5

-2.0

Root mean square difference range = 0.08 m /s

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 

MEASURED DISCHARGE, IN CUBIC METERS PER SECOND

Figure 12. Relation of simulated and measured discharges and the root mean square difference range for the 

verification run of August 5-6, 1987, tidal-cycle study.

the measurement period. For the present study, modeled 

discharges were generated every 15 minutes. Model 

values concurrent to the time duration of each 

measurement were averaged to better represent the actual 

measurement conditions. Tidal surge in the canal is 

greater during flood flow than during ebb flow. Flow 

reversals and their time duration also affect the accuracy 

of measured flow. Tidal surge and flow reversals are 

factors that will increase the volume error of 

measurements made during these periods. It is suspected 

that volume errors caused the model simulated values to

depart from measured values (fig. 10) and contributed to 

the scatter in the plot of measurements during flood flow 

shown in figure 13.

A flow-volume summary of the interchange between 

lagoon and sea waters is provided by the BRANCH 

model. An output sample (table 5) lists ebb (positive) 

and flood (negative) volumes computed in cubic meters 

for successive tidal cycles for the Laguna Joyuda canal at 

station 50130340. Flood volume is the total quantity of 

water that flows in the upstream direction (into the 

lagoon) and ebb volume is the total quantity of water that

18 Hydrology of Laguna Joyuda, Puerto Rico
2.0

O 

O

LJJ 

C/)

DC 

LU 

Q_

C/) 

DC 

LJJ hLU

^ 

O 

CD

o o.o

=) 

1

C/)

1.5

1.0

0.5

-0.5

LJJ 

O 

DC

I 

O

§ -1.0

Q 

LJJ

-1.5

-2.0

Root mean square difference range = 0.13 m /s

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 

MEASURED DISCHARGE, IN CUBIC METERS PER SECOND

Figure 13. Relation of simulated and measured discharges for the specific duration time of the measurement and 

the root mean square difference range of the long-term verification from February 1987 to April 1988.

flows in the downstream direction (out of the lagoon). 

The discharge in one direction is accumulated by the 

model until the flow reverses.

The first volume listed for any given day is the volume 

of water accumulated from the beginning of the day to the 

first reversal, and the last volume listed is the volume of 

water accumulated from the last reversal to the end of the 

day (table 5). The approximated time of the flow reversal 

also is identified in the monthly flow-volume summary. 

These flow-volume summaries were useful in estimating 

total flood and ebb flows for the study period.

Sensitivity Analysis

A sensitivity analysis was performed to identify ranges 

within which parameters could be changed without 

substantially affecting the calibrated model results. The 

analysis also indicated which parameters were the most 

important to determine.

The relative sensitivity approach developed by Simon 

(1988) was used because it provides a way to compare 

parameters that have different physical meaning and 

magnitudes by presenting these parameters in a 

normalized form. In the relative sensitivity approach, the 

model parameters are varied by different percentages (25,

Hydrology of Laguna Joyuda 19
Table 5. Model-generated accumulated flow volume for August 1987 at station 50130340 

[Rev., reverse; Vol., volume; flood flow is negative, ebb flow is positive]

August 1987 Flow volume in cubic meters at station 50130340

Day Flow Rev. Flow Rev. Flow 

no. vol. time vol. time vol.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

-4,418

-3,110

824

25,253

37,685

34,361

36,955

35,794

-558

-2,911

-3,877

-5,055

-5,707

-4,534

-3,067

76

419

19,501

-374

-1,866

-827

-980

-1,940

-3,118

-3,073

-2,758

-2,892

-3,475

-2,892

-3,019

30,240

0215

0200

0130

1245

1500

1530

1615

1730

0030

0145

0200

0245

0245

0215

0200

0015

0045

1400

0045

0215

0115

0100

0130

0230

0200

0200

0130

0200

0145

0215

1200

18,496

23,353

-272

-6

-23,231

-24,398

-23,710

-21,860

9,037

8,924

9,193

9,062

9,663

14,460

16,624

-1,130

-352

-16,273

2,387

23

2,571

1,827

2,240

1,399

4,483

6,684

0

9,074

11,815

13,155

-11,699

1115

1215

0145

1300

2245

2245

2330

0700

0715

0800

0830

0845

1015

1100

0115

0115

2245

0330

0230

0430

0345

0430

0415

0630

0630

0145

0730

0845

0915

1815

-11,056

-13,313

439

575

1,631

1,552

212

-2,175

-3,271

-5,859

-11,705

-15,032

-14,622

-16,822

289

436

153

0

-99

-2,594

-190

-7,241

-10,232

-10,637

-232

-198

-82

-18,306

-18,878

9,026

Rev. 

time

1700

1830

0215

1315

0845

1000

1130

1345

1615

1700

1845

0145

0200

2315

0345

0245

0715

0415

1015

1100

1245

0645

0200

0745

1715

1700

Flow 

vol.

7,168

7,754

-252

-88

19,575

18,564

13,594

9,136

6,324

6,250

4,021

-618

-139

-464

377

354

12,568

374

9,057

8,420

7,683

113

7,601

210

178

13,013

Rev. 

time

2215

0230

1330

1800

1845

1915

1945

2030

2145

2215

0230

0215

2345

0400

0330

1515

0500

1630

1715

1745

0715

0700

0815

1730

Flow 

vol.

-1,934

23,738

235

-23,545

-18,130

-15,517

-11,792

-6,941

-3,158

-142

17,646

813

252

-586

-2,733

-23,367

-4,494

-22.602

-20,526

-17,575

-11,651

-14,678

-15,896

-133

Rev. 

time

1300

1400

2230

1145

0300

2400

0445

0630

0900

1330

1400

1545

1745

Flow Change in storage 

vol. in the lagoon

-13,325

-19,275

855

-19,238

-218

-48

14,336

13,735

11,710

7,556

5,675

3,203

835

8,256

14,684

11,152

6,694

16,085

11,515

13,457

13,934

2,334

3,176

-2,466

-10,354

-11,693

-1,604

1,469

-2,975

959

3,121

16,140

9,414

-11,649

8,247

-20,486

-24,057

-19,119

-288

-4,492

-6,966

-8,503

4,271

27,567

(-) Volume gain

50, and 75 in this case) of their calibrated values. Each of 

the selected model parameters is varied individually while 

keeping the others unchanged. An objective function is 

used to represent the overall change in model results due 

to a change in the calibrated parameter value. The RMSD 

(equation 4) was chosen as the objective function because 

it provides a good representation of the overall changes in 

model results. Finally, the ratio of the relative change in 

the parameter value is computed by

in which

SREL; =

ASRj

APR;

(5)

ASR; =

APR; =

(SS; -SST) 

SST

(PR.-PRJ 

PR,

and where

(6)

(7)

SS;

is the index;

is the value of the objective function modified 

by the change in the parameter value;

20 Hydrology of Laguna Joyuda, Puerto Rico
SST is the objective function value for the calibrated 

parameter, computed using the field measured 

values as reference;

PR; is the modified parameter value; 

PRC is the calibrated parameter value;

ASR; is the relative change in the objective function; 

and

APR; is the relative change of the parameter.

The relative changes in the objective function and the 

parameter value for changes of plus 50 and plus 75 percent 

from the calibrated parameter value are defined by

ASR; =

SST

(8)

and

APR; =

(PRi-PR,,)

PR, (9)

The following terminology is used to classify the 

behavior of the parameters as they are changed from their 

calibration value and as an aid for the interpretation of the 

analysis results:

1. Active parameter a parameter that significantly 

affect model results;

2. Inactive parameter a parameter that does not significantly affect model results; and

3. Nuisance parameter a parameter for which model 

results do not indicate a functional behavior, such as 

increasing and decreasing without a defined pattern.

In this study, the activity of a parameter was 

represented by the relative sensitivity value of the 

objective function. The level of activity of a parameter 

increases as the relative sensitivity value increases (fig. 

14). Relative sensitivity values will decrease as the 

percentage change in parameter value approaches that of 

the calibrated parameter value.

The cross-section geometry and roughness 

coefficient were determined to be the only significant 

parameters in the model. The cross-section geometry 

includes cross-sectional area and section width. 

Changes in the cross-sectional area were made by 

changing the section width. The results of the relative 

sensitivity analysis indicate that when the values of the 

parameters are increased a slight increase in their 

activity is noted (fig. 14). This is true for both the 

cross-section geometry and the roughness coefficient. 

For the roughness coefficient, however, the change is 

less, and actually decreases when the parameters were 

increased by 75 percent. When the parameters were 

decreased by 25 percent, the roughness coefficient was

1,000

100

10

a - cross-sectional area 

n - roughness coefficient

1

-75 -50 -25 0 25 50 75

PERCENT CHANGE IN CALIBRATED PARAMETER VALUE

Figure 14. Relative sensitivity analysis for cross-sectional 

area and roughness coefficient.

Hydrology of Laguna Joyuda 21
more active than the cross-section geometry. Both 

parameters (cross-section geometry and roughness 

coefficient) increased in activity at a relatively high rate 

when they were decreased to 50 percent of their calibrated 

values, although the roughness coefficient still remained 

more active. A large decrease in the activity of both 

parameters occurred when the parameters were decreased 

in value from 50 to 75 percent of their calibrated value 

(fig. 14). Consequently, the cross-section geometry is 

more important when the parameters are overestimated 

whereas the roughness coefficient is more important when 

the parameters are underestimated.

Hydrologic Budget and Flushing Rate 

of the Lagoon

The hydrologic budget was determined by estimating 

the inflows and outflows of Laguna Joyuda. Inflows to 

the lagoon included rainfall, surface water via streamflow, 

ground-water flow, and flood flow (tidal in-flow) and 

totaled 20.06 Mm3 . Outflows considered were 

evaporation and ebb flow (tidal out-flow) and totaled 

24.28 Mm3 .

The hydrologic budget is summarized in figure 15. 

Rainfall contributed 4.14 Mm3 , and the estimated 

evaporation was 5.38 Mm3 . Surface-water contributed 

1.18 Mm3 to the lagoon, and the estimated ground-water 

contribution was 0.34 Mm3 . Ebb flow leaving the lagoon 

was estimated to be 18.9 Mm3 , and flood flow entering 

the lagoon was estimated to be 14.4 Mm3 . The waterbudget residual, or the difference between total inflow 

and total outflow for Laguna Joyuda was 4.22 Mm3 .

Errors in measuring and estimating hydrologic 

components interacting with impounded water bodies can 

have a significant effect on calculations of water 

balance. The errors are particularly important if one or 

more components are calculated as a residual term, and 

the errors in the measured components are not considered 

in interpretation of that residual term. Errors can be 

broadly classified into those of measurement and 

regionalization (interpretation or scale errors). 

Measurement errors result from trying to measure a 

quantity using imperfect instruments and inadequate

sampling design and data-collection procedures. 

Regionalization errors result from estimating quantities 

in a time-space continuum from point data (Winter, 

1981).

Two sets of error estimates presented by Winter 

(1981, table 7, p. 109) were considered for this study. 

The first set summarizes errors associated with the "best" 

methods of measurement and interpretation, and the other 

set summarizes errors associated with more "commonly 

used" methods. Methods of measurements and their 

respective estimates of error, which are based on values 

discussed in this report, are listed in table 6. The error 

measurement strategy is to determine the residual that 

consists solely of errors in hydrologic estimates and to 

compare that result to the water-budget residual of the 

lagoon. The water-balance equation, including the error 

terms, was used to estimate the residual term for the 

measured hydrologic components. The water-balance 

equation is:

SI±eSI + CI±eCI = E±eE + CO±eco (10)

where

P is the precipitation, in million cubic meters;

E is the evaporation, in million cubic meters;

SI is the stream in-flow, in million cubic meters;

CI is the canal in-flow, in million cubic meters;

CO is the canal out-flow, in million cubic meters;

G is the ground-water flux, in million cubic 

meters; and

ex is the residual error in each component, in 

million cubic meters, where x is the six 

respective component in table 6.

This water-budget residual is related to errors 

associated with the methods used to measure the 

hydrologic components. To evaluate the effect of these 

errors on the calculations of the water balance, the error 

of each hydrologic component measured or estimated 

was analyzed and interpreted using the procedure

22 Hydrology of Laguna Joyuda, Puerto Rico
EVAPORATION 

5.38

PRECIPITATION 

4.14

LAGUNA JOYUDA 

Volume

SURFACE 

WATER

1.18 

\ \

 Quebrada Mamey 

Quebrada Mango .. "_ - -_

EXPLANATION

1.55 VOLUME OF WATER 

IN MILLIONS OF 

CUBIC METERS

Figure 15. Hydrologic budget of Laguna Joyuda, December 1985 to April 1988.

Hydrology of Laguna Joyuda 23
Table 6. Effects of errors in best methods of measurement on calculation of the water balance of Laguna Joyuda

Component Estimated error 

Percent

Quantity of water 

for each component 

Million cubic meters

Quantity of water represented by the

error in the given methodology

Million cubic meters

PRECIPITATION

Gage 

(Using recording gage at lagoon)

EVAPORATION

NWS Class A Pan 

(Using National Weather Service 

data from nearest gage)

STREAMFLOW IN

Stage Discharge Rel. 

(Using recording stage gages)

CANAL FLOW IN

Stage Discharge Rel. 

(Using recording stage gages)

CANAL FLOW OUT

Stage Discharge Rel. 

(Using recording stage gages)

GROUND WATER

+ 2

+ 15

+ 10

+ 10

+ 10

4.14

5.38

1.18

14.4

18.9

0.34

+ 0.08

+ 0.81

+ 0.12

+ 1.44

+ 1.89

Slug Tests + 50 

(Using Piezometers)

Total Error

+ 0.17 

+ 4.51

presented by Winter (1981). The product of the estimated 

error in each term and the component value is equal to the 

residual of the given component. The maximum error in 

the overall water balance is the sum of absolute errors of 

each of the water-balance equation components entering 

and leaving the lagoon.

The sum of the input error values is

e,N = ep + eg, + eci + eG (11)

- 0.0828 + 0.1180+1.4400 + 0.1700 

= 1.8108 Mm3 , 

and the sum of the output error value is

eOUT eE "*" eCO (12)

- 0.8070+ 1.8900 

= 2.6970 Mm3 ,

where the estimated maximum possible error is

(13)

 eIN + eOUT

= 1.8108 + 2.6970

= 4.5078 Mm3 .

Then, potential overall error, according to the 

magnitude and direction of the input and output error 

terms, is

(+) + (+) = 4.5078

(+) + (-) = -0.8862

(-) + (-) = -4.5078

(-) + (+) - 0.8862

24 Hydrology of Laguna Joyuda, Puerto Rico
Replacing the inflow and outflow computed values for 

each hydrologic component in equation 10, the lagoon's 

water-budget residual (er) becomes

4.14+1.18+14.4 + 0.34±eIN =5.38 +18.9±eOUT, 

20.06 + e1N = 24.28 + eOUT, 

CIN + COUT = 24.28 - 20.06, and 

er = 4.22 Mm3 .

When the maximum overall estimated error residual 

(emax) of 4.51 Mm3 was compared to the hydrologicbudgel residual (er) of 4.22 Mm3 , the error residual was 

greater than the budget residual by 0.29 Mm3 . This 

indicates that the water-budget residual (er) of the lagoon 

is within the range of the maximum error estimated of 

4.51 Mm3 for the hydrologic components.

The flushing rate can be defined as the ratio between 

the annual discharge into a lake and the lake volume. 

Flushing rates are important in studies on lake hydraulics 

and eutrophication of lakes. For Laguna Joyuda, the 

definition becomes the ratio between total ebb flow from 

the lagoon and volume of the lagoon. The flushing rate of 

the lagoon was estimated at 72 days, or 12 flushing cycles 

during the 29-month study period. To estimate the 

flushing rate, the storage volume of the lagoon (1.55 

Mm3 ) was divided by the average discharge (21,425 m3/d) 

of the total ebb flow (18.9 Mm3 ). The volume of seawater 

entering and exiting the lagoon through the canal is the 

major factor in the lagoon's high flushing rate.

SUMMARY

From December 1985 to April 1988, the USGS studied 

the hydrologic characteristics of Laguna Joyuda (a 

shallow lagoon in southwestern Puerto Rico) and 

hydraulic characteristics of its tidally affected canal to 

determine the water budget of the lagoon. A conceptual 

model was developed, and estimates of rainfall and 

evaporation, surface water, ground water, and tidal flow 

were used to define the hydrologic characteristics of the 

lagoon. For the 29-month study period total rainfall on 

the lagoon's surface area was about 4.14 Mm3 , and direct 

evaporation from the lagoon was about 5.38 Mm3 . For

the same period, the total freshwater streamflow 

contribution to the lagoon was about 1.18 Mm3 , whereas 

ground water contributed about 0.34 Mm3 .

The hydraulic characteristics of the lagoon's 

drainage canal normally follows the prevailing tides. 

Tidal flow through the drainage canal consists of ebb and 

flood currents. To simulate flow, the branch-network 

unsteady-flow model was applied to the 488-m reach of 

the drainage canal. The model provides a means to 

compute continuous discharge given the boundary data on 

the water-surface elevation. Model calibration and 

verification were accomplished using two 25-hour tidalcycle studies and 42 discharge measurements. For the 

study period, total ebb flow estimated by the model was 

18.9 Mm3 leaving the lagoon and 14.4 Mm3 flood flow 

entering the lagoon.

A sensitivity analysis was performed to identify the 

relative sensitivity of the model to changes in parameter 

values. Cross-sectional area and the roughness coefficient 

were successively increased and decreased by 25, 50, and 

75 percent of their calibrated values. Consequently, the 

cross-section geometry is more important when the 

parameters are overestimated whereas the roughness 

coefficient is more important when the parameters are 

underestimated.

The lagoon contains 1.55 Mm3 of water at a watersurface elevation of 0.14 m above mean sea level. The 

volume of seawater that enters and leaves the lagoon 

through the canal depends on the high or low water 

elevation of the tides. Seawater inflow accounted for 71 

percent of the water into the lagoon. Tidal influx reaches 

all parts of the lagoon, resulting in well-mixed waters. 

During the study, specific conductance in the lagoon 

ranged from 32,000 to 52,000 jiS/cm, which is about 

equal to the local seawater specific conductance of about 

45,000 to 55,000 jiS/cm. When extreme rainfall causes 

an accumulation of large volumes of freshwater in the 

lagoon, the direction of flow in the canal is seaward and 

prevent the seawater to enter the lagoon over substantial 

periods of time. Any obstruction or interference with the 

free flow of water through the canal would alter the 

hydraulic condition of the lagoon system.

Summary 25
The hydrologic budget was determined by estimating 

the inflows and outflows of Laguna Joyuda. Inflows 

included rainfall (4.14 Mm3), surface water (1.18 Mm3), 

ground water (0.34 Mm3), and flood flow (14.4 Mm3). 

The outflows included evaporation (5.38 Mm3), and ebb 

flow (18.9 Mm3). Total outflow (24.28 Mm3) was greater 

than the total inflow (20.06 Mm3) by 4.22 Mm3 . The 

lagoon's hydrologic-budget residual was 4.22 Mm3 , 

whereas the maximum overall estimated sum of the errors 

estimated for the hydrologic components amounted to 

4.51 Mm3 . The difference between the budget residual 

and the estimated errors for the different components 

residual is 0.29 Mm3 , indicating that the lagoon's waterbudget residual is within the range of the estimated 

maximum error for the hydrologic components.

The flushing rate of the lagoon was estimated at 72 

days (about 12 flushing cycles occurred during the 29- 

month study). To estimate the flushing rate, the storage 

volume of the lagoon (1.55 Mm3 ) was divided by the 

average discharge (21,425 m3/d) of the total ebb flow 

(18.9 Mm3). The volume of seawater entering and exiting 

the lagoon through the canal is the major factor in the 

lagoon's high flushing rate.

REFERENCES

Benson, M.A., and Dalrymple, Tate, 1967, General field 

and office procedures for indirect measurements: U.S. 

Geological Survey Techniques of Water-Resources 

Investigations, Book 3, Chap. Al, 30 p.

Buchanan, T.J., and Somers, W.P., 1969, Discharge 

measurements at gaging stations: U.S. Geological 

Survey Techniques of Water-Resources 

Investigations, Book 3, Chap. A8, 64 p.

Carter, R.W., and Davidian, Jacob, 1965, Discharge 

ratings at gaging stations: U.S. Geological Survey 

Techniques of Water-Resources Investigations, Book 

l,Chap. 12, 33 p.

Comer, J.B., 1969, Sedimentology and physical-chemical 

environment of a tropical lagoon, western Puerto Rico: 

Geologic Society American Abstract, 30 p.

Curet, A.F., 1986, Geologic map of the Mayagiiez and 

Rosario quadrangles, Puerto Rico: U.S. Geological 

Survey, Map 1-1657.

Kennedy, E.J.. 1983, Computation of continuous records 

of streamflow: U.S. Geological Survey Techniques 

Water-Resources Investigations, Book 3, Chap. A13, 

51 p.

Papadopulos, S.S., 1973, On the analysis of 'slug test 1 

data: Water-Resources Research, v. 9. no. 4, p. 1087- 

1089.

Schaffranek, R.W., Baltzer, R.A., and Goldberg, D.E., 

1981, A model for simulation of flow in singular and 

interconnected channels: U.S. Geological Survey 

Techniques of Water-Resources Investigations, Book 

7, Chap. C3, 110 p.

Shearman, J.O., 1976, Computer applications for stepbackwater analyses: U.S. Geological Survey OpenFile Report 76-499, 103 p.

Shnitnikov, A.V., 1974, Current methods for the study 

of evaporation from water surfaces and 

evapotranspiration: Hydrological Sciences-Bulletin, 

XIX, p. 85-97.

Simon, E., 1988, Parameter sensitivity analysis for 

hydrologic simulation models: Water International, 

v. 13, p. 46-56.

Smoot, F.G., and Novak, E.G., 1969, Measurement of 

discharge by the moving boat method: U.S. 

Geological Survey Techniques of Water-Resources 

Investigations, Book 3, Chap. Al 1, 22 p.

U.S. Soil Conservation Service, 1983, National 

engineering book, section 3, chapter 7, Field 

Investigation and Surveys: U.S. Soil Conservation 

Service, Washington, D.C., p. 7-41.

Winter, T.C., 1981, Uncertainties in estimating the water 

balance of lakes: Water-Resources Bulletin, v. 17, no. 

1, p. 82-115.

26 Hydrology of Laguna Joyuda, Puerto Rico