Methodology for Estimating Nutrient Loads Discharged from the

East Coast Canals to Biscayne Bay, Miami-Dade County, Florida

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 99-4094

Prepared as part of the

U.S. Geological Survey South Florida Ecosystem Program
U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 99-4094

Methodology for Estimating Nutrient Loads

Discharged from the East Coast Canals to

Biscayne Bay, Miami-Dade County, Florida

Prepared as part of the

U.S. Geological Survey South Florida Ecosystem Program

By A.C. LIETZ

Tallahassee, Florida

1999
U.S. DEPARTMENT OF THE INTERIOR

BRUCE BABBITT, Secretary

U.S. GEOLOGICAL SURVEY

Charles G. Groat, Director

For additional information write to: Copies of this report can be purchased

from:

U.S. Geological Survey

Branch of Information Services

Box 25286

Federal Center

Denver, CO 80225

The use of firm, trade, and brand names in this report is for identification purposes only and does not constitute 

endorsement by the U.S. Geological Survey.

District Chief

U.S. Geological Survey

Suite 3015

227 North Bronough Street

Tallahassee, FL 32301
Contents iii

CONTENTS

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

Introduction ........................................................................................................................................................................... 2

Purpose and Scope....................................................................................................................................................... 4

Background on Nutrients............................................................................................................................................. 4

Historical Surface-Water-Quality Data........................................................................................................................ 5

Previous Studies .......................................................................................................................................................... 5

Acknowledgments ....................................................................................................................................................... 6

Description of Study Area ..................................................................................................................................................... 6

Environmental Setting ................................................................................................................................................. 7

Hydrologic Setting....................................................................................................................................................... 9

Data-Collection Methods and Procedures............................................................................................................................... 10

Sample Collection and Processing .............................................................................................................................. 11

Quality Assurance Samples ......................................................................................................................................... 12

Determination of Instantaneous Discharge.................................................................................................................. 13

Estimation of Nutrient Loads and Water-Quality Analyses .................................................................................................. 14

Distribution of Nutrient Concentrations ...................................................................................................................... 14

Water-Quality Cross-Section Surveys ......................................................................................................................... 21

Statistical Comparisons of Point (Grab) and Depth-Integrated Samples .................................................................... 24

Model Development .................................................................................................................................................... 27

The Estimator Program...................................................................................................................................... 27

Nutrient Loads Estimation Models.................................................................................................................... 29

Model Usage and Limitations............................................................................................................................ 30

Summary and Conclusions .................................................................................................................................................... 33

Selected References............................................................................................................................................................... 34

FIGURES

1. Map showing location of the east coast canal sites and subregions in Miami-Dade County ................................. 3

2. Bar graph showing average annual rainfall in Miami, 1966-95.............................................................................. 6

3. Map showing physiographic features of Miami-Dade County ............................................................................... 8

4. Graph showing population of Miami-Dade County, 1960-94................................................................................. 9

5. Pie chart showing approximate land-use percentages in the developed area of Miami-Dade County ................... 9

6. Schematic showing hydraulic connection between gaining and losing canals ....................................................... 11

7. Diagram showing depth-integrated sample collected by use of the equal-width-increment method ..................... 12

8-13. Box plots showing:

8. Total organic nitrogen concentrations among land-use categories................................................................. 17

9. Total ammonia concentrations among land-use categories ............................................................................ 18

10. Total nitrate concentrations among land-use categories................................................................................. 19

11. Total nitrite plus nitrate concentrations among land-use categories .............................................................. 20

12. Total phosphorus concentrations among land-use categories ........................................................................ 21

13. Orthophosphate concentrations among land-use categories........................................................................... 22

14-18 Graphs showing:

14. Vertical profiles of dissolved-oxygen concentration in Snapper Creek Canal at site S-22 at various 

distances from left bank looking downstream................................................................................................ 23

15. Depth profiles of total phosphorus and total nitrogen concentrations from midstream in Snapper 

Creek Canal at site S-22 ................................................................................................................................. 24
iv Contents

16. Comparison of grab and depth-integrated (DI) samples for total phosphorus concentrations from 

midstream at sites S-21, S-25B, and S-28 as defined by the line of organic correlation............................... 26

17. Total nitrogen load as a function of discharge at the east coast canal sites in Miami-Dade County ............. 31

18. Total phosphorus load as a function of discharge at the east coast canal sites in Miami-Dade County........ 32

TABLES

1. Operational description of the east coast canal sites in Miami-Dade County ........................................................ 7

2. Summary of nutrient concentrations determined at the east canal sites in Miami-Dade County........................... 16

3. Statistical interpretation of total nitrogen and total phosphorus concentrations at the east coast canal 

sites in Miami-Dade County................................................................................................................................... 25

4. Regression models for the estimation of total nitrogen and total phosphorus loads at site S-26 developed 

from the ESTIMATOR program............................................................................................................................. 28

5. Summary statistics for the estimation of total nitrogen and total phosphorus loads at site S-26 computed

 by the ESTIMATOR program for water years 1987-96 ........................................................................................ 28

6. Results of regression analyses relating load to discharge at the east coast canal sites in Miami-Dade County..... 29
Abstract 1

Methodology for Estimating Nutrient Loads

Discharged from the East Coast Canals to 

Biscayne Bay, Miami-Dade County, Florida

By A.C. Lietz

Abstract

Biscayne Bay is an oligotrophic, subtropical 

estuary located along the southeastern coast of 

Florida that provides habitat for a variety of plant 

and animal life. Concern has arisen with regard to 

the ecological health of Biscayne Bay because of 

the presence of nutrient-laden discharges from the 

east coast canals that drain into the bay. This concern, as well as planned diversion of discharges for 

ecosystem restoration from the urban and agricultural corridors of Miami-Dade County to Everglades National Park, served as the impetus for a 

study conducted during the 1996 and 1997 water 

years to estimate nutrient loads discharged from 

the east coast canals into Biscayne Bay.

Analytical results indicated that the highest 

concentration of any individual nutrient sampled 

for in the study was 4.38 mg/L (milligrams per 

liter) for nitrate at one site, and the lowest concentrations determined were below the detection 

limits for orthophosphate at six sites and nitrite at 

four sites. Median concentrations for all the sites 

were 0.75 mg/L for total organic nitrogen, 

0.10 mg/L for ammonia, 0.02 mg/L for nitrite, 

0.18 mg/L for nitrate, 0.20 mg/L for nitrite plus 

nitrate nitrogen, 0.02 mg/L for total phosphorus, 

and 0.005 mg/L for orthophosphate. The maximum total phosphorus concentration of 0.31 mg/L 

was the only nutrient concentration to exceed U.S. 

Environmental Protection Agency (1986) waterquality criteria. High concentrations of total phosphorus usually reflect contamination as a result of 

human activities. Five sites exceeded the freshwater quality standard of 0.5 mg/L for ammonia 

concentration as determined by the Miami-Dade 

County Department of Environmental Resources 

Management. Median total organic nitrogen concentrations were higher in urban and forested/wetland areas than in agricultural areas; median 

concentrations of nitrite, nitrate, and nitrite plus 

nitrate nitrogen were higher in agricultural areas 

than in urban and forested/wetland areas; and 

ammonia, total phosphorus, and orthophosphate 

concentrations were higher in urban areas than in 

agricultural and forested/wetland areas. These 

results coincide with expected differences in nutrient concentrations based on knowledge of point 

and nonpoint source influences and nutrient 

cycling.

The Wilcoxon signed ranks test (WSRT) 

was used to compare differences between point 

(grab) samples and depth-integrated samples for 

total nitrogen and total phosphorus concentrations 

at 12 east coast canal sites. Statistically significant 

differences (alpha level of 0.025) in total phosphorus concentrations between point (grab) samples 

collected 1.0 meter deep and depth-integrated 

samples were detected at three sites. One site also 

showed statistically significant differences in total 

phosphorus concentrations between point (grab) 

samples collected 0.5 meter deep and depth-integrated samples. There were no statistically significant differences in total nitrogen and total 

phosphorus concentrations between point (grab) 

samples collected 0.5 meter deep and 1.0 meter 

deep for all the sites. Results of the line of organic 

correlation, a fitting procedure used to compare 
2 Methodology for Estimating Nutrient Loads Discharged from the East Coast Canals to Biscayne Bay, Miami-Dade County, Florida

point (grab) and depth-integrated samples where 

statistically significant differences exist as defined 

by the WSRT, indicated that point (grab) samples 

underestimate total phosphorus concentrations 

when compared to depth-integrated samples. This 

underestimation probably can be attributed to the 

reduced suspended-sediment concentrations near 

the surface during periods of flow as compared to 

those near the streambed.

Predictive models were developed to estimate total nitrogen and total phosphorus loads by 

means of an ordinary least-squares regression technique. Instantaneous discharge was used as the 

independent variable, and total phosphorus load or 

total nitrogen load represented the dependent variable. A software program called Estimator was 

used to develop the regression models and to compute total nitrogen and total phosphorus loads at 

site S-26 along Miami Canal. The coefficients of 

determination (R2) were adjusted to conform with 

the number of degrees of freedom in the model. 

The adjusted R2 for total nitrogen load models 

ranged from 0.69 to 0.99, and the adjusted R2 for 

total phosphorus load models ranged from 0.23 to 

0.99. The average adjusted R2 for total nitrogen 

load models and the average adjusted R2 for total 

phosphorus load models were 0.87 and 0.76, 

respectively. All but two of the models were 

statistically significant at an alpha level of 0.05. 

One total phosphorus load model was statistically 

significant at an alpha level of 0.10 (site G-58), and 

the other total phosphorus load model was not 

statistically significant at either 0.05 or 0.10 

(site S-21A).

INTRODUCTION

A major concern in many coastal areas across the 

Nation is the ecological health of bays and estuaries. 

One common problem in many of these areas is nutrient 

enrichment as a result of agricultural and urban activities. Nutrients are essential compounds for the growth 

and maintenance of all organisms and especially for the 

productivity of aquatic environments. Nitrogen and 

phosphorus compounds are especially important to seagrass, macroalgae, and phytoplankton. However, heavy 

nutrient loads transported to bays and estuaries can 

result in conditions conducive to eutrophication and the 

attendant problems of algal blooms and high phytoplankton productivity. Additionally, reduced light 

penetration in the water column because of phytoplankton blooms can adversely affect seagrasses, which many 

commercial and sport fish rely on for their habitat.

Biscayne Bay, a shallow subtropical estuary 

along the southeastern coast of Florida, provides an 

aquatic environment that is habitat to a diversity of 

plant and animal species. Increased nutrient loads in 

discharges from the east coast canals in southern Florida (fig. 1), as a result of agricultural and urban activities, are a potential threat to the health of Biscayne Bay. 

Dissolved-oxygen concentrations average about 5 mg/L 

(milligrams per liter) in Biscayne Bay, but hypoxic conditions along with nutrient enrichment exist in the east 

coast canals. Plans are being formulated by water-management officials to reestablish natural flow to Everglades National Park (ENP) by diverting water that now 

flows through the agricultural/urban corridor and then 

discharges by way of canals to Biscayne Bay.

An understanding of nutrient loading to Biscayne 

Bay is needed for both an assessment of the ecological 

health of the bay as well as an evaluation of the waterquality impact of the diverted water to ENP. The U.S. 

Geological Survey (USGS) began a study in April 1996 

to: (1) develop methodology for the purpose of estimating nutrient loads in Biscayne Bay, and (2) determine 

whether point (grab) samples, historically collected at 

0.5 and 1 m (meter) below the surface near the centroid 

of flow, accurately represent water quality in the stream 

cross section. The study was done as part of the South 

Florida Ecosystem Program, which is a collaborative 

effort by the USGS; various other Federal, State, and 

local agencies; and Indian Tribes to provide earth science information needed to resolve land-use and water 

issues in southern Florida.

For planning purposes, Biscayne Bay is divided 

into three subregions; namely, north bay, central bay, 

and south bay (Alleman, 1995). North bay extends from 

about 5 mi (miles) north of the Dade/Broward County 

boundary to the Miami shoreline, central bay extends 

from the Miami shoreline to the featherbed banks east 

of Model Land Canal, and south bay extends from the 

featherbed banks east of Model Land Canal to Barnes 

Sound (fig. 1). Certain areas of north bay exhibit 

severely degraded water quality that largely is attributed to heavy loads of nutrients and toxicants from the 

tributary canals, including Arch Creek, Snake Creek, 

Biscayne Canal, and Little River Canal. Hypoxic 
Introduction 3

Figure 1. Location of the east coast canal sites and subregions in Miami-Dade County.
4 Methodology for Estimating Nutrient Loads Discharged from the East Coast Canals to Biscayne Bay, Miami-Dade County, Florida

conditions exist in the canals and high concentrations of 

ammonia, total phosphorus, and trace elements are 

common. Water quality in the central bay region ranges 

from pristine to highly degraded. Miami Canal, flowing 

through a highly urbanized area, contributes heavy discharges of pollutants to Biscayne Bay. Tributary or 

coastal canals that drain into central bay, such as Miami 

Canal, Coral Gables Canal, and Snapper Creek Canal, 

tend to be nutrient enriched and contribute toxicants to 

Biscayne Bay. Canals draining into south bay receive 

nutrient enrichment from agricultural activities. Black 

Creek Canal contains high levels of ammonia as a result 

of leachate from the south Miami-Dade landfill.

Purpose and Scope

The purpose of this report is to present methodology that can be used to estimate nutrient loads discharged from the east coast canals into Biscayne Bay in 

southeastern Florida. Graphical summaries have been 

created to compare medians and evaluate the distribution of nutrient concentrations in the east coast canal 

system based on land-use categories in the Biscayne 

Bay watershed. Vertical depth profiles of dissolvedoxygen, total phosphorus, and total nitrogen concentrations have been constructed to document horizontal and 

vertical variability within the canal system. A statistical 

approach is used to compare differences between point 

(grab) and depth-integrated samples (from the east 

coast canal sites) for total nitrogen and total phosphorus 

concentrations. A modeling technique is used for developing equations through simple linear regression analyses in order to estimate nutrient loads based on 

discharge. The nitrogen and phosphorus species 

described in this report include total organic nitrogen, 

ammonia, nitrite, nitrate, nitrite plus nitrate nitrogen, 

total phosphorus, and orthophosphate. Most of the data 

presented in this report were collected from the east 

coast canal sites during the 1996 and 1997 water years. 

Data from one site (S-26 along Miami Canal) were collected from 1966 to 1996.

Background on Nutrients

The ecological health of Biscayne Bay is dependent on nutrient loads. An understanding of the processes that control nutrient loads to the bay is needed to 

properly develop restoration efforts in southern Florida. 

Nutrients fall into three categories − macronutrients, 

micronutrients, and trace nutrients. The macronutrients 

(generally represented as nitrogen, phosphorus, and 

carbon species) are required in the greatest amounts and 

are major components in the cells of all organisms. 

Nitrogen and phosphorus compounds are important to 

free-floating type plants, such as algae (Hem, 1985, 

p.128). Micronutrients consist of trace elements such as 

manganese, copper, and zinc.

Nitrogen, phosphorus, and carbon species can 

exist in both organic and inorganic forms. The most 

common inorganic forms of nitrogen are ammonia, 

nitrite, and nitrate. Total organic nitrogen can exist as 

particulate or nonparticulate organic nitrogen. Most of 

the nitrogen compounds in surface-water bodies exist in 

an oxidized form as nitrate and nitrite. The U.S. Environmental Protection Agency (1986) has established 

water-quality standards or guidelines for nitrate, nitrite, 

nitrite plus nitrate nitrogen, and ammonia. Nitrate, 

nitrite, and ammonia in concentrations above established standards or guidelines can be detrimental to the 

health of humans, and ammonia is toxic to aquatic 

organisms.

Phosphorus exists inorganically as soluble reactive phosphorus and in the particulate inorganic and 

nonparticulate inorganic states. Soluble reactive phosphorus is commonly referred to as orthophosphate. 

Particulate inorganic phosphorus consists mostly of 

phosphate minerals, such as apatite. Nonparticulate 

inorganic phosphorus includes condensed phosphates, 

such as those found in detergents. Phosphorus exists 

organically as particulate organic and nonparticulate 

organic phosphorus. Particulate organic phosphorus 

exists in plants, animals, and organic detritus. Nonparticulate organic phosphorus comprises mainly dissolved or colloidal organic compounds (Chapra, 1997, 

p. 523). 

Nutrients exist in water bodies as a result of both 

natural and anthropogenic (manmade) sources, 

although contributions from natural sources are minimal. Anthropogenic contributions might be significant, 

however, and can result from agricultural activities, 

domestic and animal waste, municipal wastewater, and 

byproducts of manufacturing processes. Phosphorus 

generally is lower in concentration than other nutrients 

because it does not naturally occur in the atmosphere 

nor is it abundant in the earth’s crust. Phosphorus also 

tends to strongly adsorb to sediments and fine-grained 

particles, causing its removal from the water column. 

Nitrogen differs from phosphorus in that it naturally 

occurs in the atmosphere and does not adsorb as 

strongly to particulate matter. Additionally, denitrification acts as a removal mechanism for nitrogen under 

anaerobic conditions.
Introduction 5

The nitrogen cycle principally is a series of oxidation and reduction reactions catalyzed by bacteria, 

mostly the Nitrobacter and Nitrosomonas species 

(Lawrence, 1996, p. 9). Under aerobic and anaerobic 

conditions, total organic nitrogen catalyzed by bacteria 

is decomposed to amine groups in a process called 

deamination. This reaction continues under aerobic 

conditions to produce ammonia (ammonification) as 

well as nitrite and nitrate (nitrification). The process is 

expressed below:

Total organic nitrogen ⇒Amines ⇒ Ammonia ⇒ 

Nitrite ⇒ Nitrate

Furthermore, the microbes use nitrogen under aerobic 

conditions by consuming electrons in the oxygen molecule. However, during reducing conditions (usually 

when dissolved-oxygen concentration is below 1.0 

mg/L), the microbes use electrons from oxygen in the 

nitrate molecule. With this process, the nitrate ion is 

depleted of oxygen (denitrification), resulting in the formation of nitrous oxide or gaseous nitrogen (Lawrence, 

1996, p. 10). The nitrogen atom eventually is reduced 

by reacting with hydrogen ions to form ammonia in a 

process called nitrate reduction. The process is 

expressed below:

Nitrous oxides or nitrogen gas ⇐ Nitrate ⇒ 

Nitrite ⇒ Ammonia

Most nitrogen compounds in surface-water bodies exist 

as nitrate because of prevailing aerobic conditions.

Eutrophication is defined as a natural or artificial 

addition of nutrients to a water body (Hackney and others, 1992, p. 693) and is the principal threat to lakes, 

estuaries, or streams that receive excessive total nitrogen and total phosphorus loads. Nutrient enrichment 

can result in inordinate algal production, known as cultural eutrophication, and produces an undesirable taste 

and odor problems to a water supply. Many other undesirable chemical effects also could be attributed to 

eutrophication. Algal dieoffs result in an increase in the 

amount of organic matter available for consumption by 

bacteria, resulting in oxygen depletion. If oxygen is 

depleted faster than it is replenished by photosynthesis 

or absorption from the atmosphere, hypoxic or anoxic 

conditions can ensue, thus adversely affecting aquatic 

species and ultimately resulting in fish kills. The consequences of oxygen depletion include changes in redox 

states, especially as they apply to certain trace elements. 

Sulfate reduction and methanogenesis can occur, iron 

sulfides can form in the sediments, and soluble iron can 

be transferred to the water column. Additionally, the 

release of phosphate to the water column from 

iron/phosphate complexes (because of changes in 

iron/sulfur oxidation states) could further accelerate the 

eutrophication process.

Historical Surface-Water-Quality Data

A considerable amount of historical surfacewater-quality data exists from the east coast canal system in southern Florida, much of it having been collected intermittently for many years by the USGS for 

determination of concentrations of nutrients and major 

inorganic constituents. Since 1940, a voluminous 

amount of salinity monitoring data has been collected 

from the east coast canal sites. In 1974, the USGS began 

a program called the National Stream Quality Accounting Network (NASQAN), which was designed to determine long-term water-quality trends associated with 

major drainage basins throughout the Nation. Concentrations of major inorganic constituents and physical 

characteristics, nutrients, trace elements, suspended 

sediment, selected organic compounds, and bacteriological and biological constituents were determined at 

one NASQAN east coast canal site (S-26 along Miami 

Canal). Water samples from this site were collected 

monthly from October 1974 to September 1981 and 

quarterly from October 1981 to September 1994. Data 

that were collected under other programs since 1966 

also exist. The Miami-Dade County Department of 

Environmental Resources Management (DERM) has 

collected surface-water-quality data from the east coast 

canals since 1979. Much of the same data, as determined under the NASQAN program, also were collected by DERM under a variety of programs. Most of 

the DERM data were collected as part of the Biscayne 

Bay Monitoring Program, General Canal Monitoring 

Program, or Intensive Canal Monitoring Program.

Previous Studies

Previous studies involving the development of 

models based upon linear regression techniques are 

numerous. Smith and others (1982) studied trends in 

total phosphorus measurements at NASQAN stations 

based upon concentration/discharge models. Cohn and 

others (1989) studied the problem of retransformation 

bias, which can result when log-linear regression 

models are used to estimate constituent loads. Gilroy 

and others (1990) studied mean square errors of regression-based constituent transport estimates. Cohn and 

others (1992) evaluated the validity of a minimum vari-
6 Methodology for Estimating Nutrient Loads Discharged from the East Coast Canals to Biscayne Bay, Miami-Dade County, Florida

ance unbiased estimator (MVUE) to estimate fluvial 

constituent loads. Watts (1993) and Ries (1994) used 

regression models to estimate monthly water-level 

changes in the Closed Basin Division of the San Luis 

Valley in Colorado and low-flow deviation discharges 

in Massachusetts, respectively. Belval and others 

(1994) estimated loads of water-quality constituents in 

the James and Rappahonnock Rivers in Virginia based 

upon multiple-regression techniques. Stoker and others 

(1995) used an ordinary least-squares technique to 

describe loading characteristics of McKay Bay, 

Delaney Creek, and East Bay in Tampa, Fla. 

Acknowledgments

The author gratefully acknowledges the assistance and cooperation of the South Florida Water Management District (SFWMD) field offices in Miami and 

Homestead, with special thanks to Dawn Browning and 

Ron Dempsey, who gained access for the USGS to perform water sampling and collect hydrologic data at the 

control structures from the east coast canal sites in 

Miami-Dade County. Thanks also is extended to the 

National Oceanic and Atmospheric Administration for 

providing Miami-Dade County climatological data; to 

Frank McCune, environmental planner with MiamiDade County, who supplied the land-use component of 

the Miami-Dade County Comprehensive Development 

Master Plan; and to Rick Alleman of the SFWMD for 

use of the map of Biscayne Bay showing subregions. 

The author gratefully acknowledges the assistance of 

hydrologic technicians Elizabeth Debiak and John 

Goebel and former civil engineering student trainee 

Frank Panellas of the USGS Miami Subdistrict office, 

all of whom collected much of the data for the study.

DESCRIPTION OF STUDY AREA

Miami-Dade County, located on the southeastern 

tip of peninsular Florida (fig. 1), encompasses an area of 

about 2,000 mi2

 (square miles). The county is bounded 

by the Atlantic Ocean on the east, Broward County on 

the north, Collier and Monroe Counties on the west, and 

the Florida Keys (Monroe County) on the south. The 

area is characterized as a subtropical, marine environment with long, hot, wet summers and mild, dry winters. 

Seasonal variation in rainfall is pronounced; about 75 

percent of areal rainfall occurs during the 5-month wet 

season from June through October. Long-term records 

(1966-95) indicate that average annual rainfall in Miami 

is about 59 in. (inches), ranging from as low as 39 in. in 

1975 to as high as 83 in. in 1968 (fig. 2).

Figure 2. Average annual rainfall in Miami, 1966-95.
Description of Study Area 7

A total of 15 east coast canal sites in 

Miami-Dade County (fig. 1) were selected for 

the study; 13 sites are gated spillways and 2 sites 

are gated culverts. All east coast canal sites that 

have automatic gate operation contain an overriding mechanism that closes the gates to prevent 

saltwater intrusion when the headwater and tailwater differential reaches a certain level. The 

operational description of the 15 east coast canal 

sites in table 1 is condensed from recently published reports by the U.S. Army Corps of 

Engineers (1995) and by Swain and others 

(1997).

Environmental Setting

Physiographic features (fig. 3) have significantly 

controlled the environment, drainage, and ultimately 

the land use in Miami-Dade County (Fish and Stewart, 

1991, p. 4). The Atlantic Coastal Ridge, 2 to 10 mi in 

width, forms the highest ground in the county. Elevations along the ridge range from about 8 to 15 ft (feet) 

above sea level, but are 20 ft above sea level or greater 

in some places. West of Homestead, elevations of the 

Atlantic Coastal ridge are from 5 to 8 ft above sea level. 

The Atlantic Coastal Ridge is a natural barrier to drainage of the interior, except where it is breached by 

shallow sloughs or rivers.

Table 1. Operational description of the east coast canal sites in Miami-Dade County

[High and low ranges in stage, as indicated at specific sites, depend on field conditions and agricultural needs. Operational purpose: 1, control flooding; 2, 

prevent saltwater intrusion. Type of control: 4B-CMPC, four-barrel, corrugated metal-pipe culverts; RCGS, reinforced-concrete gated spillway; 1B-CMPC, 

single-barrel, corrugated metal-pipe culvert. Other notes: N/A, not applicable]

Site No. Local identification 

number

Operational 

purpose

Type of control Number and 

type of gates

Stage, in feet above sea level

Level at which 

gates automatically open

Level at which 

gates become 

stationary

Level at which 

gates automatically close

G-58 255406080094600 1 4B-CMPC Four flap gates N/A N/A N/A

G-93 02290560 2 RCGS Two vertical 

lift gates N/A N/A N/A

S-20 252129080223500 2 RCGS One vertical 

lift gate 1.4 1.2 1.0

S-20F 02290725 2 RCGS Three vertical 

lift gates 1.4 or 2.2 1.2 or 2.0 1.0 or 1.8

S-20G 252922080204800 2 RCGS One vertical 

lift gate 1.4 or 2.2 1.2 or 2.0 1.0 or 1.8

S-21 02290711 2 RCGS Three vertical 

lift gates 2.0 or 2.4 1.5 or 1.9 1.0 or 1.5

S-21A 253110080204700 2 RCGS Two vertical 

lift gates 1.4 or 2.2 1.2 or 2.0 1.0 or 1.8

S-22 02290700 2 RCGS Two vertical 

lift gates 3.5 2.9 2.5

S-25 02290520 2 1B-CMPC One circular 

sluice gate 2.2 2.0 1.8

S-25B 254735080154800 2 RCGS Two vertical 

lift gates 3.0 2.8 2.0

S-26 02288600 2 RCGS Two vertical 

lift gates 2.8 2.5 2.3

S-27 02286380 2 RCGS Two vertical 

lift gates 1.9 1.7 1.6

S-28 02286340 2 RCGS Two vertical 

lift gates 2.1 1.8 1.5

S-29 02286300 2 RCGS Four vertical 

lift gates 2.5 2.0 1.5

S-123 02290704 2 RCGS Two vertical 

lift gates 2.4 or 3.5 2.0 or 3.0 1.6 or 2.5
8 Methodology for Estimating Nutrient Loads Discharged from the East Coast Canals to Biscayne Bay, Miami-Dade County, Florida

Figure 3. Physiographic features of Miami-Dade County.
Description of Study Area 9

The Sandy Flatlands in northeastern Miami-Dade 

County is lower in elevation (6-18 ft above sea level) 

than the Atlantic Coastal Ridge, and prior to development was poorly drained. The Everglades, by far the 

largest feature, is slightly lower than the Sandy Flatlands, and before development, was wet in most years 

and subject to seasonal flooding. Drainage was slow 

and generally to the south and southwest, channeled 

behind the higher Atlantic Coastal Ridge. The Everglades forms a natural trough in north-central, central, 

and southwestern Miami-Dade County. Elevations 

range from about 9 ft above sea level in the northwestern corner to about 3 ft above sea level in southwestern 

Miami-Dade County, except for tree islands or hammocks which may be a few feet higher than the 

surrounding land. Most of the eastern part of the 

Everglades within the county is used for agriculture, 

rock quarrying, or urban development.

A small part of the Big Cypress Swamp occupies 

northwestern Miami-Dade County where elevations 

range from 7 to 10 ft above sea level. Coastward from 

the Everglades and the Atlantic Coastal Ridge lie 

coastal marshes and mangrove swamps at elevations 

that generally range from 0 to 3 ft above sea level. This 

description of the physiographic features in MiamiDade County was taken from a published report by Fish 

and Stewart (1991, p. 4).

One of the principal factors influencing the 

development of southern Florida water control is the 

rapid population growth along the lower east coast. 

According to the 1990 census, the population in MiamiDade County doubled every 10 years between 1910 and 

1960 (Metropolitan Dade County, 1995, p. I-79). 

Although the rate of population slowed over the next 

Figure 4. Population of Miami-Dade County, 1960-94.

two decades, there still was a significant growth in population, with about 1.3 and 1.7 million people in 1970 

and 1980, respectively (fig. 4). Immigration accounted 

for 78 percent of the population growth from 1960 to 

1990; as of 1994, Miami-Dade County had attained a 

population of about 2.0 million people.

As of 1985, about 205,827 (16.5 percent) and 

1,045,162 acres (83.5 percent) of total land area in 

Miami-Dade County was classified as developed and 

undeveloped land, respectively (Metropolitan Dade 

County, 1988, p. 39). The major land-use categories in 

the developed area include residential, transportation, 

parks and recreation, industrial, and commercial and 

institutional (fig. 5). The residential category comprises 

the highest percentage of land use in the developed area 

of Miami-Dade County. The undeveloped land area in 

Miami-Dade County includes agriculture, barren/urban 

open land, and forested/wetland.

Hydrologic Setting

A rapidly expanding population in the urban and 

agricultural areas of southern Florida has resulted in an 

extensive water-management system that has evolved 

over the years. This system of canals, levees, pump 

stations, and gated water-control structures was constructed over the last century, initially for the purpose of 

draining the wetlands and for flood control. The earliest 

attempt at water management occurred in 1905 with the 

Florida Legislature’s creation of the Everglades Drainage District. This resulted in the construction of North 

Figure 5. Approximate land-use percentages in the 

developed area of Miami-Dade County.
10 Methodology for Estimating Nutrient Loads Discharged from the East Coast Canals to Biscayne Bay, Miami-Dade County, Florida

River Canal and Miami Canal by 1913, and the construction of Hillsboro Canal and West Palm Beach 

Canals (north of the study area) shortly thereafter. By 

1921, all four canals had hurricane gates at the Lake 

Okeechobee end. Many of the canals along the east 

coast of southern Florida were completed by the 1930’s 

for the purpose of flood protection, but were uncontrolled and did not impede saltwater intrusion.

 During 1943-45, saltwater intrusion became a 

serious threat to the water supplies of southern Florida 

because of severe drought conditions. The need for a system of gated control structures on the primary east coast 

canals was realized and came to fruition with the creation 

in 1948 of the Central and Southern Florida Flood Control Project, designed by the U.S. Army Corps of Engineers (USACE). Operational control of this project came 

under the direction of the Central and Southern Flood 

Control District, now known as the SFWMD, which was 

created in 1949 by the Florida Legislature. An extensive 

series of levees was constructed, eventually resulting in 

the formation of major water-conservation areas used to 

supply water for ENP and to store water for recharging 

the Biscayne aquifer. Most of these water-conservation 

areas were completed by the early 1960’s. As a result of 

this highly managed system, the hydrology of southern 

Florida has been altered. Recent plans have focused on 

“replumbing” the water-management system to restore 

more natural flow to ENP.

The water-management system provides flood 

protection during the wet season (June-October) by 

storing excess water in the water-conservation areas 

and by discharging water through the east coast canals 

when flood events occur. During the dry season 

(November-May), replenishment of ground-water supplies along the east coast is accomplished by conveying 

water through the primary canals from the water-conservation areas. All of the major tributary canals along 

the east coast contain gated control structures that are 

opened during flood situations to permit discharge of 

excess water, and are closed during dry periods to maintain high freshwater heads, recharge ground water, and 

retard saltwater intrusion.

A key element in the operation of the watermanagement system is the communications and control 

system, which is a sophisticated electronic system that 

relies on remote acquisition and control units to operate 

control structures and to record hydrologic and meteorological data. These data are transmitted by way of 

telemetry to the operations control center in West Palm 

Beach, Fla. (north of Broward County), where decisions are made regarding water-management needs.

The close hydraulic connection that exists 

between ground and surface water in southern Florida is 

due to the highly transmissive nature of the Biscayne 

aquifer, the sole source of drinking water for residents 

of Miami-Dade County. Depending on the relation of 

the canal stages to the surrounding water table, water is 

exchanged from surface water to ground water or vice 

versa, and canals can be classified as either “gaining” or 

“losing” (fig. 6). At the east coast canal sites, the gates 

are opened during the wet season to discharge excess 

water to the Atlantic Ocean and are closed during the 

dry season to prevent saltwater intrusion. When the 

gates are opened during the wet season, canal stages 

generally become lower than the surrounding water 

table, inducing ground-water flow to the canals (gaining) and eventual discharge to tide. During the dry season, the gated control structures are closed to prevent 

saltwater intrusion; however, the ground-water hydraulic gradient is generally seaward, and the inland reaches 

of the coastal canals continue to collect ground water 

and transport it downstream to the coastal controls. The 

stages at the gated control structures are generally 

higher than the surrounding ground-water levels, and 

the canals (losing) recharge the aquifer and retard saltwater intrusion.

Canal-aquifer relations can also affect water 

quality. During dry periods when there is no flow, the 

canals tend to be chemically and physically stratified, 

resembling long lakes. During periods of flow, mixing 

occurs in the canals and ground-water seepage contributes highly mineralized water devoid of oxygen to the 

canals. Recharge to the tributary canals can be the result 

of rainfall, surface runoff, inflow from secondary 

canals, seepage through levees, and in some cases, 

releases from water-conservation areas or from Lake 

Okeechobee (by way of Miami Canal), all of which 

provide water of varying quality. The canals also 

provide a permanent surface for evaporation.

DATA-COLLECTION METHODS 

AND PROCEDURES

During periods of flow, water samples were 

collected for the determination of nitrogen and phosphorus species that truly represent the stream cross 

section. This was accomplished by collecting depth-
Data-Collection Methods and Procedures 11

integrated samples and point (grab) samples from midstream at 0.5- and 1.0-m depths for comparison. These 

samples were collected mostly upstream of the gated 

control structures at locations where most of the historical data were collected. Additionally, hydrologic data 

were collected concurrent with each sampling event for 

use in the determination of instantaneous discharge. 

Based on these data, statistical comparisons were made 

between point (grab) and depth-integrated samples, and 

models were developed to estimate total nitrogen and 

total phosphorus loads.

Figure 6. Hydraulic connection between gaining and losing canals.

Sample Collection and Processing

Depth-integrated and point (grab) samples for 

nutrients were collected from the gated control structures at the east coast canal sites in Miami-Dade 

County during periods of flow. Most of the samples 

were collected near low tide when the gates at the sites 

usually are open. Depth-integrated samples were collected by means of the equal-width-increment method 

(fig. 7), which commonly is used when a discharge 

measurement is not made before sampling. In this 
12 Methodology for Estimating Nutrient Loads Discharged from the East Coast Canals to Biscayne Bay, Miami-Dade County, Florida

method, the width of the stream is subdivided into 

equal-width intervals with a sampling vertical associated with each interval.

In each cross section for the study, 8 to 10 verticals were used. The first vertical selected was half the 

distance of the first interval from the edge of the stream 

bank, and the other verticals were equally spaced apart 

across the stream from the first vertical. Because flow 

velocities of the east coast canals in Miami-Dade 

County are nearly always less than 2 ft/s (feet per 

second), the weighted-bottle method was used to collect 

each sample. The weighted bottle does not sample isokinetically (nozzle velocity equal to stream velocity); 

however, it can be used during low flows and when differences in water quality across the stream are believed 

to be insignificant (Shelton, 1994, p. 11). In the initial 

step, the vertical with the greatest velocity is selected; 

the weighted bottle is then lowered and raised at a constant rate so that it is not overfilled when returned to the 

surface. For each specific site, this transit rate was 

maintained throughout for all the verticals in the cross 

section, and a sample from each vertical was composited in a churn splitter for processing. The transit rate as 

well as the nozzle size was varied for each specific site 

in order to prevent overfilling of the bottle.

During sample processing, the water in the churn 

was stirred by the churn disc at a rate of about 9 in/s 

(inches per second) to minimize error, with care being 

exercised to prevent the churn disc from breaking the 

surface. A total of 125 mL (milliliters) of this composite 

sample was siphoned off into an amber polyethylene 

bottle, chilled immediately, and within 48 hours was 

shipped to the USGS Water Quality Service Unit in 

Ocala, Fla., for analysis according to the procedures 

described by Fishman and Friedman (1989). The constituents determined were total organic nitrogen, 

Figure 7. Depth-integrated sample collected by use of the 

equal-width-increment method.

ammonia, nitrite, nitrate, nitrite plus nitrate nitrogen, 

total phosphorus, and orthophosphate.

A point (grab) sample was collected concurrently with each depth-integrated sample. Point (grab) 

samples, depending on the site, were collected at 0.5 

or 1.0 m below the surface near the centroid of flow by 

using a Niskin bottle. This bottle is spring loaded so 

that a messenger can trip it shut at the appropriate 

depth. After collection of the point (grab) sample, 

125 mL of the sample was transferred from the Niskin 

bottle into an amber polyethylene bottle, chilled, and 

shipped for analysis according to protocol (Fishman 

and Friedman, 1989).

Before each sampling trip, the Niskin bottle, 

weighted bottle, and churn splitter were cleaned with 

a dilute nonphosphate detergent and then rinsed with 

tap water followed by deionized water. Two rinses 

with native water were required for the samplers 

before sample collection at each east coast canal site. 

Between sampling sites, the samplers were rinsed with 

deionized water before being rinsed with native water.

Quality Assurance Samples

To ensure the integrity of the field data collected 

for the study, quality assurance samples (equipment 

blanks, field blanks, and split samples) were used extensively in the data-collection phase. Blank solutions 

essentially are samples free of the analytes being determined in the environmental samples. An equipment 

blank is a blank solution that is processed through all of 

the equipment used in the collection and processing of 

the environmental samples. Field blanks are actually 

equipment blanks done in the field and are subject to all 

aspects of the data-collection efforts as the environmental samples, including processing, preservation, transport, and laboratory handling. Two types of field and 

equipment blanks were used: one for the Niskin bottle 

and the other for the weighted bottle and churn splitter. 

These two field blank solutions consisted of inorganic 

blank water prepared at the USGS Water Quality 

Service Unit and were processed and analyzed according to protocol. Analytical results from the equipment 

blanks and field blanks indicated that most of the 

concentrations for the individual nitrogen and phosphorus species were below the detection limits for the 

analytical methods.
Data-Collection Methods and Procedures 13

Split samples were collected concurrently by the 

USGS and DERM to verify interlaboratory accuracy. 

The sampling data consisted of point (grab) samples 

that were collected from the same Niskin bottle by 

both agencies. The samples were sent to the USGS 

Water Quality Service Unit and to the DERM laboratory for analysis.

Determination of Instantaneous Discharge

During 1960-61, the USACE performed a study 

on a 1:16 scale physical model of a typical SFWMD 

gated east coast canal site (U.S. Army Corps of Engineers, 1963). Test results indicated that four possible 

flow regimes exist: submerged orifice flow, submerged 

weir flow, free orifice flow, and free weir flow. The 

USACE developed theoretical flow equations for the 

stage-discharge relations for the gated spillway east 

coast canal sites under these regimes. In their laboratory 

analyses, the USACE determined experimental values 

for the discharge coefficients for the equations under 

these flow regimes, relating the coefficients and pertinent variables in plots (U.S. Arms Corps of Engineers, 

1963). Since then, the SFWMD has applied the USACE 

equations and calibrated them for each east coast canal 

site (Otero, 1994).

Because only experimental discharge coefficients 

existed for gated spillways and culverts for the various 

flow regimes, a study was conducted to develop discharge-coefficient ratings based on actual field conditions (Swain and others, 1997). The dischargecoefficient ratings were determined from field measurements made by an Acoustic Doppler Current Profiler 

(ADCP). The ADCP uses the Doppler shift in reflected 

acoustic signals to determine the velocity of moving 

water (RD Instruments, 1989). A discharge measurement can be made rapidly at low, irregular flow conditions, which often exist for the east coast canal sites. 

The discharge-coefficient ratings developed by this 

methodology were used in the determination of instantaneous discharge for each sampling event. The 

upstream and downstream stages and gate readings 

were recorded before and after each sampling event. 

The gates were held stationary during the sampling 

periods. Discharge-related data collected during each 

sampling event were used in the following equations to 

compute discharge for the submerged orifice and weir 

flow regimes.

Submerged orifice flow for gated spillways is 

expressed by the equation (Collins, 1977):

, (1)

where Q is discharge, in cubic feet per second; Cgs is the 

discharge coefficient relative to the function of a gate 

opening and submergence; L is length of gate sill, in 

feet; g is acceleration of gravity, in feet per square second; H, is headwater height above sill, in feet; and h is 

tailwater height above sill, in feet. Cgs can be derived 

from field measurements by rearranging equation 1 as:

. (2)

Submerged weir flow for gated spillways is 

expressed by the equation (U.S. Army Corps of Engineers, 1963):

, (3)

which can be rearranged in the form:

, (4)

where Cws is a discharge coefficient for submerged weir 

flow. Cgs should approach Cws as the gate opening 

approaches submerged weir flow conditions.

Ratings for gated culverts include multiple flow 

conditions depending on submergence of the upstream 

and downstream ends. The standard rating equation for 

a submerged culvert used in southern Florida originates 

from the orifice-flow equation:

, (5)

where K is a flow coefficient which accounts for the 

entrance, friction, and exit losses; v = Q/A, the mean 

flow velocity; and A is the open area of the gate. With 

some manipulation, equation 5 becomes (Swain and 

others, 1997, p. 7):

Q Cgs = Lh 2gH h ( ) –

Cgs

Q

Lh 2gH h ( ) – = -----------------------------------

Q Cws = Lh 2gH h ( ) –

Q

Lh 2g ----------------- = Cws H h –

H h – K v2

2g = -----
14 Methodology for Estimating Nutrient Loads Discharged from the East Coast Canals to Biscayne Bay, Miami-Dade County, Florida

, (6)

where Cc is a submerged culvert coefficient. Cgs, Cws, 

and Cc are the discharge coefficients determined under 

actual field conditions for submerged orifice flow 

(gated spillways), submerged weir flow (gated spillways), and submerged culvert flow, respectively.

ESTIMATION OF NUTRIENT LOADS AND 

WATER-QUALITY ANALYSES

Water samples were collected from the gated 

control structures at the east coast canal sites in 

Miami-Dade County (fig. 1) for the purpose of developing models that could be used to estimate nitrogen 

and phosphorus loads. Box plots were constructed 

(shown later) to show differences in the median concentration of the individual nutrient species at each 

site. Additionally, field measurements of selected 

water-quality constituents (specific conductance, pH, 

water temperature, and dissolved oxygen) were made 

at specific intervals to describe vertical and horizontal 

variability of an east coast canal site (S-22). Plots 

have been constructed for site S-22 (shown later) to 

determine whether total nitrogen and total phosphorus 

concentrations increase with depth.

Statistical comparisons also are made to determine differences between point (grab) samples collected at 0.5 and 1.0 m deep and depth-integrated 

samples collected from the east coast canal sites. 

Finally, a least-squares regression analysis technique 

is used to determine the relation between nutrient 

loads and instantaneous discharge. By use of this 

technique, the total number of samples required to 

attain a certain level of precision in load estimates is 

reduced and error in load estimates is minimized 

because models are based on complete data sets and 

not daily observations, which are subject to sampling 

errors of a single observation.

The constituent load at any given time can be 

determined if the constituent concentration and the 

discharge at the time of sampling is known. The load is 

computed as follows:

, (7)

where L is the constituent load, in short tons per day; C

is the constituent concentration, in milligrams per liter; 

Q is discharge at time of sampling, in cubic feet per 

second; and 0.002697 is a conversion factor to short 

tons per day.

Distribution of Nutrient Concentrations

More than 200 depth-integrated samples were 

collected for this study during a range of flow conditions to determine nutrient concentrations in the east 

coast canal waters of Miami-Dade County. The individual nitrogen and phosphorus species (depth-integrated samples) that were analyzed for the study are 

summarized in table 2. The box plots presented and 

discussed herein show concentrations of nutrients 

among three land-use categories: forested/wetland, 

agricultural, and urban. Forested/wetland areas are 

considered to be the land-use category with the lowest 

level of human activities whereas the agricultural and 

urban areas are the highest (Ham and Hatzell, 1996, 

p. 12). The results coincide with expected differences 

in nutrient concentrations based on knowledge of 

point and nonpoint source influences and nutrient 

cycling.

The median total organic nitrogen concentration for all the east coast canal sites was 0.75 mg/L, 

which represents the highest median concentration 

of any nutrients sampled for in this study. The box 

plot in figure 8 indicates that median total organic 

nitrogen concentrations generally were higher in 

forested/wetland and urban areas than in agricultural 

areas. The minimum total organic nitrogen concentration of 0.20 mg/L was detected at site S-21A 

along Princeton Canal, and the maximum total 

organic nitrogen concentration of 1.7 mg/L was 

detected at site S-26 along Miami Canal. Miami 

Canal is one of five canals that distributes water 

from Lake Okeechobee to the highly urbanized 

southeastern coast of Florida. The entire reach of the 

canal traverses forested/wetland, agricultural, and 

urban areas. Agricultural and urban runoff and 

sewage effluent discharges contribute to the waterquality degradation in Miami Canal.

Q ACc = 2gH h ( ) –

L CQ = × × 0.002697
Estimation of Nutrient Loads and Water-Quality Analyses 15

Table 2. Summary of nutrient concentrations determined at the east canal sites in Miami-Dade County

[All units in milligrams per liter as nitrogen or as phosphorus]

Category

Total 

organic 

nitrogen

Ammonia Nitrite Nitrate Total nitrite 

plus nitrate

Total nitrogenTotal

phosphorus

Orthophosphate

Site G-58

Mean 0.55 1.27 0.020 0.090 0.11 1.92 0.23 0.17

Median .55 1.20 .020 .080 .10 1.95 .24 .17

Maximum .60 1.50 .047 .154 .20 2.10 .31 .26

Minimum .50 1.10 <.001 .020 .02 1.70 .13 .09

No. of samples 6 6 6 6 6 6 4 6

Site G-93

Mean .58 .39 .036 .360 .39 1.37 .05 .02

Median .52 .25 .035 .300 .35 1.30 .05 .02

Maximum 1.00 .80 .081 .570 .60 2.20 .08 .04

Minimum .40 .05 .003 .017 .02 .61 .04 .01

No. of samples 10 10 10 10 10 10 10 10

Site S-20

Mean 1.05 .06 .003 .004 .007 1.12 .007 .002

Median 1.10 .05 .003 .004 .008 1.10 .007 .001

Maximum 1.20 .10 .006 .007 .010 1.30 .010 .010

Minimum .83 .04 .002 .002 .002 .88 .006 <.001

No. of samples 11 11 11 11 11 11 11 11

Site S-20F

Mean .32 .04 .016 1.21 1.23 1.58 .010 .004

Median .32 .04 .016 1.19 1.20 1.50 .010 .002

Maximum .47 .10 .020 1.38 1.40 1.90 .020 .010

Minimum .21 .03 .014 .99 1.00 1.40 .007 <.001

No. of samples 10 10 10 10 10 10 10 10

Site S-20G

Mean .40 .06 .017 .780 .79 1.21 .025 .008

Median .40 .06 .019 .930 .95 1.30 .02 .006

Maximum .50 .10 .028 1.180 1.20 1.70 .08 .020

Minimum .23 .02 .004 .056 .06 .51 .01 <.001

No. of samples 7 8 8 8 8 7 8 8

Site S-21

Mean 0.58 0.19 0.019 0.37 0.39 1.16 0.012 0.006

Median .56 .20 .022 .46 .50 1.20 .010 .004

Maximum .75 .30 .037 .69 .70 1.70 .030 .020

Minimum .41 .10 <.001 .07 .07 .62 .007 <.001

No. of samples 17 17 17 17 17 17 17 17

Site S-21A

Mean .30 .03 .021 3.69 3.7 4.04 .006 .002

Median .30 .03 .020 3.69 3.7 4.10 .005 .001

Maximum .42 .07 .028 4.38 4.4 4.70 .010 .004

Minimum .20 .01 .014 2.88 2.9 3.30 .004 <.001

No. of samples 7 7 7 7 7 7 7 7
16 Methodology for Estimating Nutrient Loads Discharged from the East Coast Canals to Biscayne Bay, Miami-Dade County, Florida

Site S-22

Mean .78 .08 .010 .12 .12 .97 .010 .004

Median .75 .09 .009 .11 .12 .97 .010 .004

Maximum 1.10 .20 .024 .19 .20 1.20 .020 .008

Minimum .55 .01 .004 .07 .08 .75 .006 .002

No. of samples 21 21 21 21 21 21 21 21

Site S-25

Mean .76 .21 .015 .13 .14 1.10 .049 .023

Median .75 .10 .013 .08 .09 1.00 .045 .014

Maximum 1.10 .50 .037 .28 .30 1.50 .100 .060

Minimum .50 .06 .006 .07 .08 .81 .030 .004

No. of samples 14 14 14 14 14 14 14 14

Site S-25B

Mean .79 .07 .022 .35 .37 1.20 .02 .007

Median .79 .07 .020 .29 .32 1.20 .02 .004

Maximum 1.00 .20 .056 .59 .60 1.40 .03 .040

Minimum .55 .01 .001 .24 .25 .89 .01 .001

No. of samples 20 20 20 20 20 20 20 20

Site S-26

Mean 1.05 0.60 0.032 0.170 0.20 1.8 0.020 0.004

Median 1.00 .61 .020 .110 .15 1.7 .020 .003

Maximum 1.70 1.10 .100 .460 .56 2.8 .050 .020

Minimum .70 .03 .006 .002 .01 1.3 .008 .001

No. of samples 19 19 19 19 19 19 19 19

Site S-27

Mean .79 .64 .028 .190 .22 1.6 .04 .02

Median .70 .65 .030 .180 .21 1.7 .04 .02

Maximum 1.10 .96 .040 .300 .33 1.9 .05 .03

Minimum .55 .41 .010 .060 .07 1.4 .03 .01

No. of samples 17 17 17 17 17 17 16 17

Site S-28

Mean .86 .16 .011 .110 .110 1.10 .04 .014

Median .86 .15 .009 .070 .080 1.10 .03 .010

Maximum 1.20 .47 .036 .260 .300 1.50 .07 .020

Minimum .66 .02 .002 .001 .002 .83 .03 .008

No. of samples 18 18 18 17 18 18 18 18

Table 2. Summary of nutrient concentrations determined at the east canal sites in Miami-Dade County--(Continued)

[All units in milligrams per liter as nitrogen or as phosphorus]

Category

Total 

organic 

nitrogen

Ammonia Nitrite Nitrate Total nitrite 

plus nitrate

Total nitrogenTotal

phosphorus

Orthophosphate
Estimation of Nutrient Loads and Water-Quality Analyses 17

Site S-29

Mean 1.02 .29 .021 .19 .22 1.51 .020 .003

Median 1.00 .30 .020 .18 .20 1.51 .020 .002

Maximum 1.30 .50 .064 .48 .50 2.10 .030 .007

Minimum .85 .03 <.001 .06 .06 1.60 .008 <.001

No. of samples 17 17 17 17 17 17 17 17

Site S-123

Mean .37 .16 .004 .13 .13 .58 .03 .014

Median .39 .09 .005 .08 .09 .56 .02 .004

Maximum .47 .70 .01 .40 .40 .87 .12 .07

Minimum .26 .03 <.001 .01 .01 .31 .02 .002

No. of samples 7 8 8 8 8 7 8 8

Table 2. Summary of nutrient concentrations determined at the east canal sites in Miami-Dade County--(Continued)

[All units in milligrams per liter as nitrogen or as phosphorus]

Category

Total 

organic 

nitrogen

Ammonia Nitrite Nitrate Total nitrite 

plus nitrate

Total nitrogenTotal

phosphorus

Orthophosphate

Figure 8. Total organic nitrogen concentrations among land-use categories.
18 Methodology for Estimating Nutrient Loads Discharged from the East Coast Canals to Biscayne Bay, Miami-Dade County, Florida

Protection Agency, 1986). However, five sites (G-58, 

G-93, S-26, S-27, and S-123) had concentrations that 

exceeded the Miami-Dade County DERM waterquality freshwater standard of 0.5 mg/L for ammonia.

Nitrite is an intermediate species in the nitrification process by which ammonia is transformed into 

nitrate under aerobic conditions which exist in most 

canals. The median nitrite concentration for all the 

east coast canal sites was 0.02 mg/L, which is below 

USEPA maximum contaminant level of 1.0 mg/L 

(U.S. Environmental Protection Agency, 1986). The 

maximum contaminant level is the maximum permissible level of a contaminant in water which is delivered to any user of a public water system. Median 

nitrite concentrations tend to be higher in agricultural 

areas than in urban and wetland areas. The minimum 

nitrite concentration of less than 0.001 mg/L was 

Total organic nitrogen is transformed by the 

process of ammonification to ammonia. The median 

ammonia concentration for all the east coast canal 

sites was 0.10 mg/L. The box plot in figure 9 indicates 

that median ammonia concentrations tend to be higher 

in urban areas than in agricultural and forested/wetland areas. The minimum ammonia concentration of 

0.01 mg/L was detected at sites S-21A, S-22, and 

S-25B. The maximum ammonia concentration of 

1.5 mg/L was detected at site G-58 along Arch Creek. 

The upper Arch Creek watershed is highly contaminated as a result of possible landfill leachate and 

industrial waste (Alleman, 1995, p. 20). The highest 

ammonia concentration detected was well below the 

U.S. Environmental Protection Agency (USEPA) 

maximum concentration of 2.1 mg/L for chronic 

exposure to aquatic organisms (U.S. Environmental 

Figure 9. Total ammonia concentrations among land-use categories.
Estimation of Nutrient Loads and Water-Quality Analyses 19

detected at sites G-58, S-21, S-29, and S-123, and the 

maximum nitrite concentration of 0.10 mg/L was 

detected at site S-26 (table 2).

Nitrate represents the end product of the nitrification process. The median nitrate concentration for 

all the east coast canal sites was 0.18 mg/L. The 

box plot in figure 10 indicates that median nitrate concentrations tend to be higher in agricultural areas than 

in forested/wetland and urban areas. The minimum 

nitrate concentration of 0.001 mg/L was detected at 

site S-28; the maximum nitrate concentration of 

4.38 mg/L was detected at site S-21A (table 2), which 

is well below the maximum contaminant level of 

10.0 mg/L (U.S. Environmental Protection Agency, 

1986). The maximum nitrate concentration, which 

was the highest maximum concentration of any nutriFigure 10. Total nitrate concentrations among land-use categories.

ents sampled for in this study, was probably the result 

of agricultural runoff.

Total nitrogen, which represents the sum of total 

organic nitrogen, ammonia, nitrite, and nitrate concentrations, ranged from 0.31 to 4.7 mg/L for all the east 

coast canal sites (table 2). The maximum total nitrogen 

concentration of 4.7 mg/L was detected at site S-21A 

in an agricultural area, with nitrate comprising 93 percent of this maximum concentration. The minimum 

total nitrogen concentration of 0.31 mg/L was detected 

at site S-123.

The median nitrite plus nitrate nitrogen concentration for all the east coast canal sites was 0.20 mg/L. 

The box plot in figure 11 indicates that median nitrite 

plus nitrate concentrations tend to be higher in agricul-
20 Methodology for Estimating Nutrient Loads Discharged from the East Coast Canals to Biscayne Bay, Miami-Dade County, Florida

tural areas than in forested/wetland and urban areas. 

The minimum nitrite plus nitrate concentration of 

0.002 mg/L was detected at sites S-20 and S-28; the 

maximum nitrite plus nitrate concentration of 4.4 

mg/L was detected at site S-21A, which is below the 

maximum contaminant level of 10.0 mg/L (U.S. Environmental Protection Agency, 1986). 

The median total phosphorus concentration for 

all the east coast canal sites was 0.02 mg/L. The box 

plot in figure 12 indicates that median total phosphorus 

concentrations generally were higher in urban areas 

than in forested/wetland and agricultural areas. The 

minimum total phosphorus concentration of 

Figure 11. Total nitrite plus nitrate concentrations among land-use categories.

0.004 mg/L was detected at S-21A; the maximum total 

phosphorus concentration of 0.31 mg/L was detected at 

site G-58 (table 2), which is above the recommended 

upper concentration limit of 0.10 mg/L to control 

eutrophication (U.S. Environmental Protection Agency, 

1986). Additionally, the maximum total phosphorus 

concentration of 0.12 mg/L at site S-123 (table 2) 

slightly exceeded the recommended upper concentration limit. High concentrations of total phosphorus usually reflect contamination as a result of human 

activities, such as from point or nonpoint source discharges.
Estimation of Nutrient Loads and Water-Quality Analyses 21

The median orthophosphate concentration for all 

the east coast canal sites was 0.005 mg/L, which is the 

lowest median concentration of any nutrients sampled 

for in this study. The box plot in figure 13 indicates that 

median orthophosphate concentrations generally were 

higher in urban areas than in forested/wetland and agricultural areas. The minimum orthophosphate concentration of less than 0.001 mg/L was detected at sites 

S-20, S-20F, S-20G, S-21, S-21A, and S-29, and the 

maximum orthophosphate concentration of 0.26 mg/L 

was detected at site G-58 (table 2). High concentrations 

of orthophosphate as well as total phosphorus are usually indicative of human activities, such as from point or 

nonpoint source discharges.

Figure 12. Total phosphorus concentrations among land-use categories.

Water-Quality Cross-Section Surveys

Water-quality cross-section surveys for specific 

conductance, pH, water temperature, and dissolved 

oxygen were conducted to document water-quality 

cross-section homogeneity in the east coast canal 

system. On October 7, 1997, field measurements of 

these constituents were made (from near the surface at 

1-ft intervals to the streambed) at site S-22 along Snapper Creek Canal from seven verticals about 10 ft equidistant from each other in the cross section. During the 

field measurements, instantaneous discharge was determined to be 414 ft3/s (cubic feet per second). The only 

water-quality constituent to show any variation with 

depth was dissolved oxygen.
22 Methodology for Estimating Nutrient Loads Discharged from the East Coast Canals to Biscayne Bay, Miami-Dade County, Florida

Plots of dissolved-oxygen concentration for the 

seven vertical profiles at site S-22 along Snapper Creek 

Canal (from the left bank looking downstream) were 

constructed and are shown in figure 14. Dissolved-oxygen concentration decreased with increasing depth for 

all but one vertical. The vertical 46.2 ft from the left 

bank showed no variation with depth, which probably 

can be attributed to complete mixing in the vertical. In 

June and July 1996, preliminary water-quality surveys 

at three verticals in the cross section were performed at 

sites S-22, S-25B, S-26, and S-28. Results were similar 

to those for the water-quality survey done at site S-22 in 

October 1997, with dissolved-oxygen concentration 

decreasing with depth.

During the same October 1997 period when a 

water-quality cross-section survey was made at site 

Figure 13. Orthophosphate concentrations among land-use categories.

S-22, total nitrogen and total phosphorus concentrations 

also were determined at the same location. Water samples were collected midstream at a depth of 1 ft below 

the surface and at 2-ft intervals thereafter, until near the 

streambed at a depth of 15 ft. The plots in figure 15 indicate that both total nitrogen and total phosphorus 

concentrations increased with depth. Additionally, 

point (grab) samples at 1.0 m deep near midstream and 

depth-integrated samples were collected for analysis of 

suspended-sediment concentration. Significant differences in suspended-sediment concentration were 

detected between the point (grab) and depth-integrated 

samples (1.0 and 3.0 mg/L, respectively). This is plausible because suspended-sediment concentrations usually are higher near the streambed during periods of 

flow than near the surface and would not be “captured” 

by a point (grab) sample.
Estimation of Nutrient Loads and Water-Quality Analyses 23

Figure 14. Vertical profiles of dissolved-oxygen concentration in Snapper Creek Canal at site S-22 at various distances 

from left bank looking downstream (LEW). Instantaneous discharge is 414 cubic feet per second. LEW represents left 

edge of water.
24 Methodology for Estimating Nutrient Loads Discharged from the East Coast Canals to Biscayne Bay, Miami-Dade County, Florida

Statistical Comparisons of Point (Grab) 

and Depth-Integrated Samples

Statistical tests were used in this study to 

compare differences between point (grab) and depthintegrated samples for total nitrogen and total phosphorus concentrations from the east coast canal sites in 

Miami-Dade County. A matched-pair approach using 

the Wilcoxon signed ranks test (WSRT), a nonparametric statistical test, was used to compute differences 

between sample pairs and to rank the absolute values of 

the nonzero differences. Each rank was assigned a 

negative sign if the original difference is negative and a 

positive sign otherwise. Because of the small sample 

sizes, the exact form of the test statistic (W+) was used 

rather than the large sample approximation (Helsel and 

Hirsch, 1992, p. 144). The W+ statistic is the sum of all 

the ranks having a positive sign. The p-value (Helsel 

and Hirsch, 1992, table B6) is the attained significance 

level and must be less than the alpha or significance 

level to reject the null hypothesis of no difference in 

medians between the data sets. The significance (or 

Figure 15. Depth profiles of total phosphorus and total 

nitrogen concentrations from midstream in Snapper Creek 

Canal at site S-22. Instantaneous discharge is 414 cubic 

feet per second.

alpha level) for a one-sided WSRT is 0.05 and indicates 

that there is a 5 percent, or a 1 in 20, probability of 

incorrectly rejecting the null hypothesis when it is actually true. When a two-sided WSRT is used (x is either 

larger or smaller than y), the significance (or alpha 

level) then becomes 0.025. The WSRT was used in this 

study because the null hypothesis of normality is difficult to reject for small sample sizes, and water-quality 

data frequently assume a non-normal or asymmetric 

distribution.

Table 3 presents the results of the WSRT for total 

nitrogen and total phosphorus concentrations for 12 of 

the east coast canal sites by comparing: (1) differences 

between point (grab) samples collected at 1.0 m deep 

and depth-integrated samples, (2) point (grab) samples 

collected at 0.5 m deep and depth-integrated samples, 

and (3) point (grab) samples collected at 0.5 and 1.0 m 

depths. There were no statistically significant differences in total nitrogen concentration between point 

(grab) samples collected at 1.0 m deep and depth-integrated samples; however, there were statistically significant differences in total phosphorus concentration for 

the same comparisons at sites S-21, S-25B, and S-28. 

No sites showed any statistically significant differences 

in total nitrogen concentration between point (grab) 

samples collected at 0.5 m deep and depth-integrated 

samples, and only one site (S-21) showed statistically 

significant differences in total phosphorus concentration. At none of the sites were statistically significant 

differences detected in total nitrogen and total phosphorus concentrations between point (grab) samples collected at 0.5 m and 1.0 m depths. Based on these 

statistical results, depth-integrated samples probably 

provide a more realistic representation of total phosphorus concentrations in the stream cross section than do 

the point (grab) samples.

The WSRT, like all hypothesis tests, only indicates which differences are statistically significant and 

does not describe the relation between the variables. For 

this reason, differences between point (grab) and depthintegrated samples that were indicated by the WSRT 

were further examined by using the line of organic correlation (LOC). This fitting procedure, first proposed in 

hydrology by Kritskiy and Menkel (1968), is also 

known as the reduced major axis, unique solution, or 

equivalence line and is represented by the equation:

y , (8) ˆ y r( )Sy

Sx = + sgn -----( ) x x –
Estimation of Nutrient Loads and Water-Quality Analyses 25

where is the estimated value of y, is the average 

of y values, is the average of x values, Sy is the standard deviation of y values, Sx is the standard deviation 

of x values, and sgn (r) is the sign of correlation coefficient (1 if r is greater than 0, 0 if r = 0, and -1 if r is 

less than 0).

The LOC is basically a geometric method as it 

minimizes the sum of the areas of right triangles formed 

by the horizontal and vertical lines from data points to the 

fitted line (Hirsch and Gilroy, 1984, p. 707). Unlike an 

ordinary least-squares regression technique, the LOC is 

useful in describing the relation between two variables,

yˆ y

x

 

Table 3. Statistical interpretation of total nitrogen and total phosphorus concentrations at the east coast canal sites in MiamiDade County

[Significant level (a) = 0.05/2 = 0.025; P values from Helsel and Hirsch (1992, table B6); DI, depth integrated; >, greater than the value; N/A, not applicable]

Site No. Constituent

Statistical difference between samples

Grab samples collected at 1.0-meter 

depth and DI samples

Grab samples collected at 0.5-meter 

depth and DI samples

Grab samples collected at 0.5-meter and 

1.0-meter depths

No. of 

sample 

pairs

No. of 

nonzero 

differences

W+

 statistic

P

value

No. of 

samples

No. of 

nonzero 

differences

W+

 statistic

P

value

No. of 

sam

-ples

No. of 

nonzero 

differences

W+

statistic

P

value

G-58 Total nitrogen 6 4 3.5 >0.312 N/A N/A N/A N/A N/A N/A N/A N/A

Total phosphorus 6 4 4 >.312 N/A N/A N/A N/A N/A N/A N/A N/A

G-93 Total nitrogen 10 8 15 >.191 4 3 4 .375 4 4 7.5 >0.188

Total phosphorus 10 2 1.5 >.375 4 0 0 >.375 4 1 1 >.375

S-21 Total nitrogen 17 15 56 >.151 8 7 11 >.188 8 7 17.5 >.188

Total phosphorus 17 14 94 .003 8 7 25.5 .023 8 4 2 >.312

S-21A Total nitrogen 7 7 15 >.188 5 5 10 >.219 5 4 8 >.188

Total phosphorus 7 4 8 .188 5 1 1 >.375 5 4 2 >.312

S-22 Total nitrogen 21 14 80 .045 N/A N/A N/A N/A N/A N/A N/A N/A

Total phosphorus 21 7 14.5 >.188 N/A N/A N/A N/A N/A N/A N/A N/A

S-25 Total nitrogen 14 9 29 >.180 N/A N/A N/A N/A N/A N/A N/A N/A

Total phosphorus 14 6 14 >.219 N/A N/A N/A N/A N/A N/A N/A N/A

S-25B Total nitrogen 20 13 63 .122 N/A N/A N/A N/A N/A N/A N/A N/A

Total phosphorus 20 10 55 .001 N/A N/A N/A N/A N/A N/A N/A N/A

S-26 Total nitrogen 18 8 10.5 >.191 N/A N/A N/A N/A N/A N/A N/A N/A

Total phosphorus 18 6 17 .109 N/A N/A N/A N/A N/A N/A N/A N/A

S-27 Total nitrogen 17 7 10.5 >.188 N/A N/A N/A N/A N/A N/A N/A N/A

Total phosphorus 17 4 4 >.312 N/A N/A N/A N/A N/A N/A N/A N/A

S-28 Total nitrogen 18 11 44 >.160 N/A N/A N/A N/A N/A N/A N/A N/A

Total phosphorus 18 6 21 .016 N/A N/A N/A N/A N/A N/A N/A N/A

S-29 Total nitrogen 17 11 38.5 >.160 N/A N/A N/A N/A N/A N/A N/A N/A

Total phosphorus 17 7 18 >.188 N/A N/A N/A N/A N/A N/A N/A N/A

S-123 Total nitrogen 7 6 19 .047 N/A N/A N/A N/A N/A N/A N/A N/A

Total phosphorus 7 4 10 .062 N/A N/A N/A N/A N/A N/A N/A N/A

STATISTICALLY SIGNIFICANT DIFFERENCES BETWEEN GRAB AND DEPTH-INTEGRATED SAMPLES

Equation from line of organic correlation is Grab = 0.2973 DI + 0.0057. Direction of bias of grab is low.

Equation from line of organic correlation is Grab = 0.25 DI + 0.00625. Direction of bias of grab is low.

Equation from line of organic correlation is Grab = 0.8255 DI − 0.0018. Direction of bias of grab is low.

Equation from line of organic correlation is Grab = 1.093 DI − 0.008. Direction of bias of grab is low.
26 Methodology for Estimating Nutrient Loads Discharged from the East Coast Canals to Biscayne Bay, Miami-Dade County, Florida

and thus, was used in this study to describe the relation 

between point (grab) and depth-integrated samples. The 

LOC eliminates variance reduction in estimates by 

eliminating the correlation coefficient from the slope. 

The variances of the LOC estimates are then in proportion to the variances of the original data (Helsel and Hirsch, 1992, p. 278).

Statistically significant differences for total 

nitrogen and total phosphorus between point (grab) and 

depth-integrated samples collected from sites S-21, 

S-25B, and S-28, as defined by the LOC (the same 

samples and sites as defined by the WSRT in table 3), 

are shown in figure 16. As illustrated, point (grab) 

samples collected from 0.5- and 1.0-m depths underestimate total phosphorus concentrations compared to 

Figure 16. Comparison of grab from midstream and depth-integrated (DI) samples for total phosphorus 

concentrations at sites S-21, S-25B, and S-28 as defined by the line of organic correlation.

depth-integrated samples. Because of the affinity of 

total phosphorus to adsorb to particulate matter, underestimation of concentrations by point (grab) samples 

probably is due to the reduced suspended-sediment concentrations near the surface compared to concentrations 

near the streambed during periods of flow. The suspended-sediment concentration determined from a 

point (grab) sample during the October 1997 waterquality cross-section survey at site S-22 was only onethird the concentration determined from the depth-integrated sample collected concurrently. However, suspended-sediment concentrations in southern Florida 

canals are low; for example, the average concentration 

based on 108 samples collected from site S-26 along 

Miami Canal over a 20-year period was 6.7 mg/L. 
Estimation of Nutrient Loads and Water-Quality Analyses 27

Additionally, other factors contributing to differences 

between sample types could be related to the degree of 

mixing at the sample location based upon physical characteristics of the channel, such as distance upstream or 

downstream from the control structures and configuration of the channel.

Model Development

An ordinary least-squares regression technique 

was used to develop predictive equations for the purpose of estimating total nitrogen and total phosphorus 

loads discharged from the east coast canals to Biscayne 

Bay. The predictive equations can be used to estimate 

the value of a dependent variable from observations on 

a related or independent variable. In this study, load was 

used as the dependent or response variable and discharge as the independent or explanatory variable. 

Because discharge is used in the computation of load, 

linearity and the best fit equation can be established or 

developed more easily by relating load to discharge 

rather than concentration to discharge.

Using more than one independent variable, such 

as stage, rainfall, gate opening, and discharge, multiple 

linear regression was attempted to improve the predictive equations. However, because discharge is computed from stage and gate openings and is based upon 

rainfall, collinearity between independent variables 

precluded this approach. A smoothing procedure, called 

locally weighted scatterplot smooth (LOWESS), was 

used by plotting load as a function of discharge to determine the degree of linearity between the two variables. 

When it was deemed necessary to improve the linear 

relation between load and discharge, transformations of 

the independent variable were made based upon the 

relation of the curve to the Mosteller and Tukey bulging 

rule (Helsel and Hirsch, 1992, p. 229).

Improvement in the models was based on 

increases in the adjusted coefficient of determination 

(R2), which explains the amount of variation in the load 

determined by discharge and reduction in the predicted 

error sums of squares (PRESS) statistic. The models 

selected were those having the highest adjusted R2

 and 

the lowest PRESS statistic as well as the lowest root 

mean square error or standard error of the regression. 

The null hypothesis of no linear relation between load 

and discharge was rejected at the 0.05 significance level 

(α level) when the attained significance level (p-value) 

was less than 0.05.

An important part of model development is residuals analysis. Two assumptions of an ordinary leastsquares regression are: (1) variance of the residuals is 

constant (homoscedastic) over the range of values, and 

(2) residuals are independent. Plots of predicted values 

against residuals were examined, and where nonconstant variance (heteroscedasticity) over the range of 

values was observed, log transformations of the 

response variables were made. Because of errors in 

comparing log space with real space, no comparisons 

were made with this analogy between transformed and 

nontransformed models based on the adjusted R2 or 

PRESS statistics.

A key element in model development is regression diagnostics. Basing model adequacy solely on the 

adjusted R2

 may prove to be inadequate because there 

may be no indication as to whether the data have been 

well fitted. Examination of data points for leverage, 

influence, or outliers was required to verify model adequacy. Outliers in the x direction were determined to be 

significant if they exceeded 3 p/n where p is the number 

of coefficients and n equals the number of samples 

(Helsel and Hirsch, 1992, p. 247). Studentized residuals 

were used to examine outliers in the y direction, and 

Cook’s D was used to determine influence from outliers. Observations were considered to have high influence if Cook’s D exceeded the value for the F

distribution for p +1, n − p at α = 0.1 (Helsel and Hirsch, 

1992, p. 249). Numerous data values demonstrated high 

leverage, but only a few data values showed both high 

leverage and high influence.

The ESTIMATOR Program

Because continuous discharge data are currently 

being computed and long-term water-quality data are 

available at site S-26 along Miami Canal, a software 

program, called ESTIMATOR, was used in the development of nitrogen and phosphorus load models and for 

the estimation of loads at the site. The ESTIMATOR 

program develops models and computes loads based on 

mean daily discharge and water-quality data files. This 

program was used at site S-26 (formerly part of the 

NASQAN network as previously discussed) because of 

the continuous discharge data available and the requirement that about 50 water samples should have been collected over at least a 2-year period. The ESTIMATOR 

program consists of a seven-parameter log/linear model 

employing the following regressors: a constant, a quadratic fit to the natural logarithm of discharge, a quadratic fit to time, and a sinusoidal first-order Fourier 
28 Methodology for Estimating Nutrient Loads Discharged from the East Coast Canals to Biscayne Bay, Miami-Dade County, Florida

function to compensate for seasonality. The model is 

written as:

, (9)

where ln is the natural logarithm, L is load, β0 is the 

constant, β1 to β6 are the coefficients, Q is discharge, T

is decimal time, T2 is decimal time squared, and sin2πT

+ cos2πT are periodic functions.

The ESTIMATOR program employs a minimum variance unbiased estimator for the elimination 

of bias in the transformation of log space to real space. 

Regression models for total nitrogen and total phosphorus loads and coefficients statistically significant 

at the 95 percent confidence intervals for site S-26 are 

presented in table 4. In addition to the constant, both 

the logarithms of discharge and discharge squared 

were significant for the total nitrogen load model, 

whereas only the logarithm of discharge was significant for the total phosphorus load model. The program estimates monthly and annual mean daily loads. 

Maximum and minimum monthly mean daily and 

annual daily loads computed by the ESTIMATOR 

program at site S-26 for water years 1987 through 

1996 are summarized in table 5.

lnL β0 β1 Q β2 + Q β3T β4 + +

2 T2 = + ln ln

+β5 2πT β6 sin + 2 cos πT

Table 4. Regression models for the estimation of total 

nitrogen and total phosphorus loads at site S-26 developed 

from the ESTIMATOR program

[See equation 9 in text. The coefficients of determination (R2) for both total 

nitrogen and total phoshorus models are 0.99. A total of 152 and 188 observations were used in the total nitrogen load and total phosphorus load models, respectively]

Constituent Coefficient Value

Total nitrogen

Total phosphorus

β0 -10.151

 -13.811

Total nitrogen

Total phosphorus

β1 1.0031

.99951

Total nitrogen

Total phosphorus

β2 .00111

 -.0019

Total nitrogen

Total phosphorus

β3 .0034

 -.0018

Total nitrogen

Total phosphorus

β4 .0005

-.0014

Total nitrogen

Total phosphorus

β5 -.0540

-.0403

Total nitrogen

Total phosphorus

β6 -.0532

 -.0914

1

Statistically significant at 95 percent confidence interval.

Table 5. Summary statistics for the estimation of total nitrogen and total phosphorus loads at 

site S-26 computed by the ESTIMATOR program for water years 1987-96

Water 

year

Constituent

Maximum monthly 

mean daily load

(tons per day)

Minimum monthly 

mean daily load

(tons per day)

Annual daily load

(tons per year)

1987 Total nitrogen

Total phosphorus

 0.72

 .008

 0.011

 1.85 x 10-4

 78.2

 .70

1988 Total nitrogen

Total phosphorus

 1.68

 .021

 .004

 6.32 x 10-4

 190

 2.47

1989 Total nitrogen

Total phosphorus

 .54

 .007

 .00

 .00

 46.5

 .61

1990 Total nitrogen

Total phosphorus

 1.01

 .012

 .00

 .00

 85.5

 1.11

1991 Total nitrogen

Total phosphorus

 1.60

 .018

 .013

 2.21 x 10-4

 144

 1.81

1992 Total nitrogen

Total phosphorus

 2.63

 .028

 .040

 6.55 x 10-4

 261

 2.98

1993 Total nitrogen

Total phosphorus

 1.04

 .012

 .008

 1.38 x 10-4

 188

 2.18

1994 Total nitrogen

Total phosphorus

 .77

 .008

 .018

 2.48 x 10-4

 127

 1.45

1995 Total nitrogen

Total phosphorus

 2.00

 .019

 .00

 .00

 268

 2.71

1996 Total nitrogen

Total phosphorus

 1.72

 .016

 .00

 .00

 199

 2.19
Estimation of Nutrient Loads and Water-Quality Analyses 29

Nutrient Loads Estimation Models

Measured nutrient loads were used to develop 

equations through simple linear regression analyses in 

order to estimate computed loads based on discharge. 

The measured data were mainly based on data collected 

from depth-integrated samples. The nutrient loads 

and/or discharge were occasionally transformed before 

simple linear regression techniques were employed to 

develop the “best fit” models used to estimate the 

loads. Results of the regression analyses relating load 

to discharge at the east coast canal sites are presented 

in table 6. The coefficients of determination (R2) in 

table 4 were adjusted to conform with the number of 

degrees of freedom in the model.

Table 6. Results of regression analyses relating load to discharge at the east coast canal sites in Miami-Dade County

[Data based on depth-integrated samples, except for sites S-20, S-20F, and S-20G in which data are based on grab samples. Significant level (α) = 0.05; 

Annotations: ACD, adjusted coefficient of determination; N, nitrogen load, in tons per day; P, phosphorus load, in tons per day; Q, discharge, in cubic feet 

per second; ln, natural logarithm. Models are valid for discharges greater than zero]

Site No.

Discharge 

range

(cubic feet 

per second)

Predictive equation No. of 

samples

ACD

(R2)

Root mean 

square 

error

pvalue

95 percent confidence intervals 

of the coefficient

Upper limit Lower limit

G-581 10 - 66

N = 0.013 + 4.45 × 10-3Q 6 0.99 0.01 0.00 5.07 × 10-3 3.83 × 10-3

P = -0.013 + 9.14 × 10-3lnQ 4 .77 .004 .082 2.10 × 10-2 -2.73 × 10-3

G-93 30 - 237 N = 1.5 × 10-3 + 3.68 × 10-3Q 10 .84 .113 .00 4.92 × 10-3 2.44 × 10-3

LnP = -5.69 + 1.16 × 10-2Q 10 .81 .39 .00 1.58 × 10-2 7.37 × 10-3

S-20 143 - 237 N = -0.12 + 3.76 × 10-3Q 10 .69 .073 .00 5.64 × 10-3 1.88 × 10-3

P = 5.1 × 10-4 + 9.4 x 10-8Q2 10 .79 .0005 .00 1.00 × 10-6 5.80 × 10-8

S-20F 346 - 1,080 N = -13.8 + 2.58lnQ 9 .91 .26 .00 3.25 1.92

P = 5.08 × 10-4 + 2.43 × 10-5Q 9 .91 .001 .00 3.05 × 10-5 1.80 × 10-5

S-20G 286 - 429 N = 0.225 + 9.8 × 10-6Q2 5 .71 .046 .046 1.93 × 10-5 3.00 × 10-7

P = 2.76 × 10-4 + 5.53 × 10-5Q 5 .97 .0005 .00 7.00 × 10-5 4.05 × 10-5

S-21 202 - 1,740 N = -0.38 + 3.77 × 10-3Q 17 .88 .45 .00 0.004 0.003

P = -7.38 + 10-4 + 4.27 × 10-8Q2 17 .89 .01 .00 0.004 0.003

S-21A 223 - 387 N = 0.85 + 2.56 × 10-5Q2 7 .85 .33 .00 3.64 × 10-5 1.47 × 10-5

LnP = 4.72 - 1.71lnQ 7 .23 .24 .193 1.30 -4.71

S-22 133 - 576 LnN = -1.32 + 3.25 × 10-3Q 21 .83 .14 .00 3.97 × 10-3 2.54 × 10-3

LnP = -6.11 + 3.81 × 10-3Q 21 .61 .29 .00 5.52 × 10-3 2.39 × 10-3

S-25 21 - 82 N = 3.61 × 10-2 + 3.87 × 10-5Q2 14 .86 .32 .00 4.80 × 10-5 2.94 × 10-5

LnP = -6.22 + 3.18 × 10-4Q2 14 .78 .35 .00 4.20 × 10-4 2.16 × 10-4

S-25B 214 - 781 N = 1.46 × 10-2 + 3.17 × 10-3Q 20 .82 .197 .00 3.88 × 10-3 2.46 × 10-3

P = -0.014 +7.81 × 10-5Q 20 .50 .01 .00 1.15 × 10-4 4.16 × 10-5

S-27 127 - 524 N = -0.46 + 4.60 × 10-3Q 17 .93 .13 .00 5.30 × 10-3 3.91 × 10-3

P = 4.05 × 10-3 + 1.20 × 10-4Q 16 .80 .006 .00 1.54 × 10-4 8.75 × 10-5

S-28 165 - 857 N = -0.26 + 3.76 × 10-3Q 18 .89 .206 .00 4.45 × 10-3 3.07 × 10-3

LnP = -4.26 + 2.40 × 10-3Q 18 .58 .31 .00 3.43 × 10-3 1.37 × 10-3

S-29 333 - 1,440 N = -17 + 3.09lnQ 17 .95 .35 .00 3.49 2.71

LnP = -4.93 + 1.87 × 10-3Q 17 .79 .36 .00 2.38 × 10-3 1.35 × 10-3

S-123 514 - 1,330 N = -1.10 + 3.11 × 10-3Q 7 .93 .24 .00 4.01 × 10-3 2.20 × 10-3

P = 6.7 × 10-4 + 5.34 × 10-5Q 7 .99 .001 .00 5.59 × 10-5 5.09 × 10-5

1

Upper and lower limits at site G-58 based on 90 percent confidence intervals of the coefficient.

2Statistically significant at (α) = 0.10. 3

Not statistically significant for phosphorus load.
30 Methodology for Estimating Nutrient Loads Discharged from the East Coast Canals to Biscayne Bay, Miami-Dade County, Florida

The adjusted R2 for the total nitrogen load models 

ranged from 0.69 to 0.99 (table 4), indicating that from 

69 to 99 percent of the variation in total nitrogen load is 

explained by discharge. The maximum adjusted R2

 of 

0.99 was determined for sites G-58 (table 6) and S-26 

(table 4), both in urban areas, and the minimum adjusted 

R2

 of 0.69 was determined for site S-20 (table 6) in a forested/wetland area. The average adjusted R2

 for all the 

total nitrogen load models was 0.87. Models for five 

sites (S-20F, S-20G, S-21A, S-25, and S-29) required 

transformation of the independent variable (discharge) to 

improve linearity, and models for one site (S-22) 

required log transformation of the dependent variable 

(total nitrogen load) due to nonconstant variance of the 

residuals (heteroscedasticity). All of the total nitrogen 

load models had p-values less than 0.05, indicating they 

were statistically significant at an alpha level of 0.05. 

Plots showing total nitrogen load as a function of discharge at the east coast canal sites are shown in figure 17.

The adjusted R2 for the total phosphorus load 

models ranged from 0.23 to 0.99 (table 6), indicating 

from 23 to 99 percent of the variation in total phosphorus 

load is explained by discharge. The maximum adjusted 

R2

 of 0.99 was determined for sites S-123 (table 6) and 

S-26 (table 4) located in urban areas, and the minimum 

adjusted R2

 of 0.23 was determined for site S-21A in an 

agricultural area (table 6). The average adjusted R2 for 

all the total phosphorus load models was 0.76, which is 

lower than that for the total nitrogen load models. Models for five sites (G-58, S-20, S-21, S-21A, and S-25) 

required transformation of the independent variable (discharge) to improve linearity, and models for six sites 

(G-93, S-21A, S-22, S-25, S-28, and S-29) required log 

transformation of the dependent variable (total phosphorus load) due to heteroscedasticity. Most of the total 

phosphorus load models had p-values less than 0.05; 

however, the predictive model for site G-58 had a pvalue of 0.08, indicating that it is statistically significant 

only at an alpha level of 0.1. Thus, upper and lower limits of the slope coefficient for site G-58 represents the 90 

percent confidence intervals, indicating less predictive 

power for the model. The total phosphorus load model 

for site S-21A, indicating an inverse relation between 

total phosphorus concentration and discharge was not 

statistically significant at either an alpha level of 0.05 or 

0.10 and should not be used for estimating loads. Plots 

showing total phosphorus load as a function of discharge 

at the east coast canal sites are presented in figure 18.

Variation in constituent concentration relative to 

discharge generally is attributed to two physical processes: dilution or washoff (or a combination of both). 

Dilution usually occurs as constituents enter a stream or 

canal from a point source or because of ground-water 

seepage during discharge. This is reflected as an inverse 

relation between constituent concentration and discharge, and is common among the major ions. Washoff 

generally occurs as nutrients enter a stream because of 

surface runoff from urban or agricultural areas, and in 

this case, reflects an increase in constituent concentrations with discharge. Variation in phosphorus concentrations, however, is commonly the result of both the 

dilution and washoff processes. The low adjusted R2

 for 

some total phosphorus load models could be attributed to 

dilution and washoff occurring simultaneously, resulting 

in the poor linear relations between load and discharge.

Model Usage and Limitations

The models with the greatest predictive power 

are those with the highest adjusted R2

 and the lowest 

root mean square error. Because of project time constraints, data collected during this study span only 

2 water years. The predictive power of the models 

might be enhanced if data were collected for a longer 

time period, such as 5 or 10 years, because a more representative range of hydrologic conditions is likely to 

occur over a longer time period. The small number of 

samples that were collected at some sites reflects the 

fact that the gates at the control structures rarely open, 

except during extreme rainfall events. Additionally, 

loads estimated by the models represent loads computed at the gated control structures on the canals. At 

some sites, such as S-25, S-25B, and S-26, the canal 

reaches (fig. 1) consist of several miles of ungaged sections to which both point and nonpoint source nutrient 

loads could be contributed before the terminus of the 

reaches at Biscayne Bay. This is particularly true of 

Miami River, downstream of S-26 along Miami Canal, 

which drains the urban and commercial areas of downtown Miami. Other processes, such as ground-water 

seepage, direct surface drainage, and precipitation, can 

also contribute nutrient loads to Biscayne Bay.

The upper and lower limits of the 95 percent confidence intervals of the slope coefficient for the total 

nitrogen and total phosphorus load models are presented in table 6. The significance of the 95 percent 

confidence intervals and the relation to the predictive 

power of the models is demonstrated by the following 

example. If the mean daily discharge at site S-28 along 

Biscayne Canal were 300 ft3

/s, the model-predicted 

total nitrogen load would range from 3.20 to 4.76 tons/d 

(tons per day) based on the lower and upper limits of the 

95 percent confidence interval for the slope coefficient.
Estimation of Nutrient Loads and Water-Quality Analyses 31

Figure 17. Total nitrogen load as a function of discharge at the east coast canal sites in Miami-Dade County.
32 Methodology for Estimating Nutrient Loads Discharged from the East Coast Canals to Biscayne Bay, Miami-Dade County, Florida

Figure 18. Total phosphorus load as a function of discharge at the east coast canal sites in Miami-Dade County.
Summary and Conclusions 33

A problem can arise with the use of log-transformed models in estimating the mean load for several 

time periods. If the log-transformed values are summed 

for a period and the mean is then transformed back into 

the original units, the estimates tend to be biased low 

and more closely resemble the median and not the 

mean. This can be overcome by use of the “smearing 

estimator” described in Helsel and Hirsch (1992) by the 

following equation:

, (10)

where Yi

 is the response variable; f -1 is the inverse of 

selected transformation; bo is the intercept; bi

 is the 

slope coefficient; Xi

 is the value of x for which y is to be 

estimated, ei

 represents residuals, in original units; and 

n is the number of samples. Use of this equation 

requires that the residuals be independent and heteroscedastic. As previously mentioned, the ESTIMATOR program (used at site S-26) employs a minimum 

variance unbiased estimator for the elimination of bias 

in transforming from log space to real space.

SUMMARY AND CONCLUSIONS

Biscayne Bay, located along the southeastern 

coast of Florida, is an oligotrophic, shallow, subtropical 

estuary that provides habitat for a variety of plant and 

animal life. In recent years, the ecological health of 

Biscayne Bay has become a matter of concern due to the 

presence of nutrient-laden discharges from coastal 

canals that drain into the bay. This concern, as well as 

planned diversion of discharges for ecosystem restoration from the urban and agricultural corridors of MiamiDade County to Everglades National Park, served as the 

impetus for a study to develop a method for estimating 

nutrient loads discharged from the east coast canals into 

Biscayne Bay. More than 200 depth-integrated samples 

were collected for analysis of total organic nitrogen, 

ammonia, nitrite, nitrate, nitrite plus nitrate nitrogen, 

total phosphorus, and orthophosphate concentrations 

during the 1996 and 1997 water years. At 15 east coast 

canal sites in Miami-Dade County, a comparison of 

nutrient concentrations by land-use category was made.

Yi

f –1 b0 bi Xi ei ( ) +++

i = 1

n

∑

n = -------------------------------------------------------------

Analytical results indicated that the highest concentration of any nutrients sampled for in this study was 

4.38 mg/L for nitrate (as nitrogen) at one site, and the 

lowest concentrations determined were below the 

detection limits for orthophosphate at six sites and 

nitrite at four sites. Total organic nitrogen concentrations ranged from 0.20 to 1.7 mg/L, with a median 

concentration of 0.75 mg/L for all of the east coast canal 

sites. The 0.75-mg/L value was the highest median 

concentration of any nutrients sampled for in this study. 

Ammonia concentrations ranged from 0.01 mg/L to 

1.5 mg/L, with a median concentration of 0.10 mg/L for 

all the sites. Five sites had concentrations that exceeded 

the Miami-Dade County DERM freshwater standard of 

0.5 mg/L for ammonia. Nitrite concentrations ranged 

from less than 0.001 mg/L to 0.10 mg/L, with a median 

concentration of 0.02 mg/L for all the sites. Nitrate concentrations ranged from 0.001 to 4.38 mg/L, with a 

median concentration of 0.18 mg/L for all the sites. 

Nitrite plus nitrate nitrogen concentrations ranged from 

0.002 to 4.4 mg/L, with a median concentration of 

0.20 mg/L for all the sites.

Total phosphorus concentrations ranged from 

0.004 to 0.31 mg/L, with a median concentration of 

0.02 mg/L. The maximum total phosphorus concentration of 0.31 mg/L was the only nutrient concentration to 

exceed water-quality standards or guidelines of 

0.10 mg/L for control of eutrophication. High concentrations of total phosphorus usually reflect contamination as a result of human activities. Orthophosphate 

concentrations ranged from less than 0.001 mg/L to 

0.26 mg/L, with a median concentration of 0.005 mg/L 

for all the sites. The 0.005 mg/L value was the lowest 

median concentration of any nutrients sampled for in 

this study.

Median concentrations of nitrite, nitrate, and 

nitrite plus nitrate nitrogen tended to be higher in agricultural areas than in forested/wetland and urban areas. 

Median concentrations of ammonia, total phosphorus, 

and orthophosphate tended to be higher in urban areas 

than in forested/wetland and agricultural areas. Median 

total organic nitrogen concentrations generally were 

higher in forested/wetland and urban areas than in 

agricultural areas. These results coincide with expected 

differences in nutrient concentrations based on knowledge of point and nonpoint source influences and nutrient cycling.

A water-quality cross-section survey conducted 

at site S-22 along Snapper Creek Canal during an 

instantaneous discharge of 414 ft3

/s in October 1997 

indicated that dissolved-oxygen concentrations 
34 Methodology for Estimating Nutrient Loads Discharged from the East Coast Canals to Biscayne Bay, Miami-Dade County, Florida

decreased with increasing depth. Water samples collected incrementally from the middle of the canal 

between the surface and the streambed at site S-22, 

demonstrated an increase in total nitrogen and total 

phosphorus concentrations with depth. Additionally, 

point (grab) samples at 1.0 m deep and depth-integrated 

samples were collected for analysis of suspended-sediment concentration. Significant differences in concentration were detected between point (grab) and depthintegrated samples (1.0 and 3.0 mg/L, respectively). 

Suspended-sediment concentrations generally were 

higher near the streambed during flow conditions than 

near the surface.

The Wilcoxon signed ranks test (WSRT) was 

used to compare differences between point (grab) and 

depth-integrated samples for total nitrogen and total 

phosphorus concentrations from 12 east coast canal 

sites. There were no statistically significant differences 

in total nitrogen concentration between point (grab) 

samples collected at 1.0 m deep and depth-integrated 

samples, but statistically significant differences in total 

phosphorus concentration between the samples were 

apparent at 25 percent of the sites. No sites showed any 

statistically significant differences in total nitrogen concentration between point (grab) samples collected at 

0.5 m deep and depth-integrated samples, and only one 

site showed statistically significant differences in total 

phosphorus concentration. Statistically significant differences in total nitrogen and total phosphorus concentrations between point (grab) samples collected at 0.5- 

and 1.0-m depths were not detected at any sites.

A fitting procedure, referred to as the line of 

organic correlation (LOC), was used to compare point 

(grab) and depth-integrated samples where statistically 

significant differences exist as defined by the WSRT. 

Results of the LOC indicated that point (grab) samples 

at 0.5- and 1.0-m depths underestimate total phosphorus 

concentrations when compared to depth-integrated 

samples. Because total phosphorus tends to adsorb to 

particulate matter, this underestimation is attributed to 

the reduced suspended-sediment concentrations near 

the surface as compared to those near the streambed 

during periods of flow. The suspended-sediment concentration determined from a point (grab) sample was 

only one-third the concentration determined from a 

depth-integrated sample. Physical factors, such as distance upstream or downstream from the control structures and configuration of the sampling cross section, 

could influence the degree of mixing and contribute to 

differences between point (grab) and depth-integrated 

samples.

Models were developed to estimate nutrient loads 

in the east coast canals of Miami-Dade County. The 

measured loads were mainly based on data collected 

from depth-integrated samples. Discharge was used as 

the independent or explanatory variable, and total phosphorus load or total nitrogen load represented the 

dependent or response variable. The coefficients of 

determination (R2

) were adjusted to conform with the 

number of degrees of freedom in the model. The 

adjusted R2 for total nitrogen load models ranged from 

0.69 to 0.99, indicating that from 69 to 99 percent of the 

variation in total nitrogen load is explained by discharge. The average adjusted R2

 for all the total nitrogen load models was 0.87. The adjusted R2

 for the total 

phosphorus load models ranged from 0.23 to 0.99 and 

averaged 0.76, which was lower than that for the total 

nitrogen load models. All of the models, except for two 

total phosphorus load models, were statistically significant at an alpha level of 0.05. Some models for total 

nitrogen and total phosphorus loads required transformation of the independent variable (discharge) to 

enhance linearity, and a few models required log transformation of the dependent variable (load) due to heteroscedastic residuals. Because long-term water-quality 

data exist and continuous discharge is computed at site 

S-26 along Miami Canal, a software program, ESTIMATOR, was used to estimate total nitrogen and total 

phosphorus loads at that site.

Models that have the greatest predictive power 

are those with the highest adjusted R2 and the lowest 

root mean square error or standard error of the regression. Because of time constraints, data were collected 

over a period of 2 consecutive water years (1996-97). 

Data collected over longer time periods, such as 5 to 10 

years, would enhance the predictive power of the models and would more accurately represent long-term 

hydrologic conditions in southern Florida.

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