Estimation of Total Nitrogen and 

Phosphorus in New England Streams Using 

Spatially Referenced Regression Models

By Richard Bridge Moore, Craig M. Johnston, Keith W. Robinson, and 

Jeffrey R. Deacon

U.S. Department of the Interior

U.S. Geological Survey

In cooperation with the

New England Interstate Water Pollution Control Commission and

U.S. Environmental Protection Agency

Scientific Investigations Report 2004-5012
U.S. Department of the Interior

Gale A. Norton, Secretary

U.S. Geological Survey

Charles G. Groat, Director

For sale by U.S. Geological Survey, Information Services

Box 25286, Denver Federal Center

Denver, CO 80225

For more information about the USGS and its products:

Telephone: 1-888-ASK-USGS

World Wide Web: http://www.usgs.gov/

Any use of trade, product, or firm names in this publication is for descriptive purposes only and does not imply 

endorsement by the U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to

reproduce any copyrighted materials contained within this report.

U.S. Geological Survey, Pembroke, New Hampshire: 2004
 iii

Acknowledgments

The authors thank Richard A. Smith, Richard B. Alexander, and Gregory E. Schwarz of the

U. S. Geological Survey (USGS), who developed the SPARROW modeling technique and made this 

work possible by providing computer code, assistance, and reviews. We especially acknowledge 

the efforts of Richard Alexander for patiently answering questions regarding the computer code, 

and to Gregory E. Schwarz, who has written the most recent version of the SPARROW computer 

code and provided assistance with the update. We thank Mary Chepiga and Gerard McMahon of 

the USGS for their thoughtful reviews of this report, and those who provided assistance during the 

course of the project, including Stephen Preston, Elaine Trench, Thor Smith, Laura Medalie,

James Shanley, John Brakebill, Lance Ostiguy, Peter Steeves, and Laura Hayes, from the USGS. 

We thank and acknowledge the essential support, encouragement, and reviews provided by 

Alison Simcox, Matthew Liebman, and Henry Walker of the U.S. Environmental Protection Agency, 

and Bethany Card and Laura Blake of the New England Interstate Water Pollution Control

Commission.

 v

Contents

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .i

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

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Purpose and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Description of the SPARROW Modeling Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Description of Data Used in the New England Sparrow Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Hydrologic Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Channel-Transport Characteristics Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Stream Nutrient-Load Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Nutrient-Source Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Physical Watershed Characteristics Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Climatic Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Land-Surface Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Spatially Referenced Regression Models for Nutrients in New England Streams . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Phosphorus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Model Assumptions and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Model Estimates of Nutrient Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Phosphorus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Use of SPARROW Model Results in Water-Resources Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Determining Sources and Transport of Nutrient Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Determining Nutrient Concentrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Determining Nutrient Loads Delivered to Coastal Waters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Selected References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
vi 

Figures

1. Map showing location of basins in, or draining into, New England. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2. Diagram showing features of the SPARROW stream network. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5

3-5. Maps showing—

3. Spatial detail of the New England SPARROW model with 42,000 National Hydrography

Dataset (NHD) reach catchments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

4. Nutrient-load measurement sites used in the New England SPARROW models. . . . . . . . . . . . . 10

5. Permitted municipal and pulp and paper wastewater-discharge locations in 

New England. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

6-7. Graphs showing—

6. Relation of predicted and observed total nitrogen load values from the calibration

of the New England SPARROW model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

7. Relation of predicted and observed total phosphorus load values from the calibration

of the New England SPARROW model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

8-11. Maps showing—

8. Predicted total nitrogen catchment yield from the New England SPARROW model

based on source loads from 1992-93 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

9. Contribution predicted by the New England SPARROW model of total nitrogen 

catchment yield from (A) atmospheric deposition of nitrogen, (B) developed land 

areas, (C) agricultural land-use areas, and (D) primary sources of nitrogen loads 

in the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

10. Predicted total phosphorus catchment yield from the New England SPARROW

model based on source loads from 1992-93 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

11. Contribution predicted by the New England SPARROW model of total phosphorous

catchment yield from (A) forested land-use areas, (B) developed land areas, 

(C) agricultural land-use areas, and (D) primary sources of phosphorus loads

in the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

12. Diagrams and map showing example from the Connecticut River Basin of total maximum

daily load applications of the results from the New England SPARROW model for total nitrogen. . . 33

13. Maps showing New England SPARROW model mean-annual flow-weighted concentration

predictions of (A) nitrogen and (B) phosphorus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

14. Map and graphs showing ecoregions (A) identified by U.S. Environmental Protection Agency

for nutrient-criteria management activities. Cumulative frequency diagrams and tables for

SPARROW-predicted total mean-annual flow-weighted (B) nitrogen and (C) phosphorus

concentrations by ecoregion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

15. Graph and map showing nitrogen loads to the New England coast predicted by the

New England SPARROW model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
 vii

Tables

1. Sources of data used in the New England SPARROW models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7

2. Categories, subcategories, and codes of the National Land Cover Dataset. . . . . . . . . . . . . . . . . . . . . . . . 12

3. Calibration results and bootstrap estimates for the New England SPARROW model for

total nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4. Calibration results and bootstrap estimates for the New England SPARROW model for

total phosphorus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

5. Summary of predicted nitrogen loads by state from the New England SPARROW model for

total nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

6. Predicted nitrogen loads by major basin and state from the New England SPARROW model

for total nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

7. Comparison of predicted nitrogen loads from the New England SPARROW model with five

other nitrogen-load prediction studies for selected major river basins in New England . . . . . . . . . . . . 25

8. Comparison of predicted nitrogen loads from the New England SPARROW model with the

Boyer nitrogen-load prediction model for selected river basins in New England . . . . . . . . . . . . . . . . . . 26

9. Summary of predicted phosphorus loads by state from the New England SPARROW model

for total phosphorus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

10. Predicted phosphorus loads by major basin and state from the New England SPARROW model

for total phosphorus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

11. Comparisons of predicted phosphorus loads from the New England SPARROW model with

predictions from other studies for selected major river basins in New England . . . . . . . . . . . . . . . . . . . . 31

12. Distribution of New England SPARROW model predictions of nitrogen concentrations for

undeveloped reference reaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

13. Distribution of New England SPARROW model predictions of phosphorus concentrations for

undeveloped reference reaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

14. New England SPARROW model predictions of nitrogen concentrations for small and

large streams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

15. New England SPARROW model predictions of phosphorus concentrations for small and

large streams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
viii 

Conversion Factors and Abbreviations

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows:

°C = (°F - 32) / 1.8

ABBREVIATIONS USED IN THIS REPORT

d-1 = per day

cm/h = centimeter per hour

cm/yr = centimeter per year

kg/km2/yr = kilograms per kilometer squared per year

mg/L = milligrams per liter

CLI = Canada Land Inventory

DMR = discharge-monitoring report

GIS = geographic information system

HSPF = Hydrologic Simulation Program Fortran

NED = National Elevation Dataset

NEWIPCC = New England Interstate Water Pollution Control Commission

NHD = National Hydrography Dataset

NLCD = National Land Cover Data

NOAA = National Oceanic and Atmospheric Administration

NPDES = National Pollutant Discharge Elimination System

NRCS = Natural Resources Conservation Service

p = probability level

PCS = Permit Compliance System

PRISM = Parameter-elevation Regressions on Independent Slopes Model

SPARROW = Spatially Referenced Regressions on Watershed attributes

STATSGO = State Soil Geographic data

TMDL = total maximum daily load

USDA = U.S. Department of Agriculture

USEPA = U.S. Environmental Protection Agency

USGS = U.S. Geological Survey

Multiply By To obtain

Length

centimeter (cm) 0.3937 inch (in.)

meter (m) 3.281 foot (ft)

kilometer (km) 0.6214 mile (mi)

Area

hectare (ha) 2.471 acre (a)

square kilometer (km2) 0.3861 square mile (mi2)

Weight

metric tons 1.1 tons
Estimation of Total Nitrogen and Phosphorus in 

New England Streams Using Spatially Referenced 

Regression Models

By Richard Bridge Moore, Craig M. Johnston, Keith W. Robinson, and Jeffrey R. Deacon

Abstract

The U.S. Geological Survey (USGS), in cooperation with 

the U.S. Environmental Protection Agency (USEPA) and the 

New England Interstate Water Pollution Control Commission 

(NEWIPCC), has developed a water-quality model, called 

SPARROW (Spatially Referenced Regressions on Watershed 

Attributes), to assist in regional total maximum daily load 

(TMDL) and nutrient-criteria activities in New England. 

SPARROW is a spatially detailed, statistical model that uses 

regression equations to relate total nitrogen and phosphorus 

(nutrient) stream loads to nutrient sources and watershed characteristics. The statistical relations in these equations are then 

used to predict nutrient loads in unmonitored streams. 

The New England SPARROW models are built using a 

hydrologic network of 42,000 stream reaches and associated 

watersheds. Watershed boundaries are defined for each stream 

reach in the network through the use of a digital elevation model 

and existing digitized watershed divides. Nutrient source data 

is from permitted wastewater discharge data from USEPA’s 

Permit Compliance System (PCS), various land-use sources, 

and atmospheric deposition. Physical watershed characteristics 

include drainage area, land use, streamflow, time-of-travel, 

stream density, percent wetlands, slope of the land surface, and 

soil permeability. 

The New England SPARROW models for total nitrogen 

and total phosphorus have R-squared values of 0.95 and 0.94, 

with mean square errors of 0.16 and 0.23, respectively. Variables that were statistically significant in the total nitrogen 

model include permitted municipal-wastewater discharges, 

atmospheric deposition, agricultural area, and developed land 

area. Total nitrogen stream-loss rates were significant only in 

streams with average annual flows less than or equal to

2.83 cubic meters per second. In streams larger than this, there 

is nondetectable in-stream loss of annual total nitrogen in New 

England. Variables that were statistically significant in the total 

phosphorus model include discharges for municipal wastewater-treatment facilities and pulp and paper facilities, developed 

land area, agricultural area, and forested area. For total phosphorus, loss rates were significant for reservoirs with surface 

areas of 10 square kilometers or less, and in streams with flows 

less than or equal to 2.83 cubic meters per second. 

Applications of SPARROW for evaluating nutrient loading in New England waters include estimates of the spatial distributions of total nitrogen and phosphorus yields, sources of the 

nutrients, and the potential for delivery of those yields to receiving waters. This information can be used to (1) predict ranges 

in nutrient levels in surface waters, (2) identify the environmental variables that are statistically significant predictors of nutrient levels in streams, (3) evaluate monitoring efforts for better 

determination of nutrient loads, and (4) evaluate management 

options for reducing nutrient loads to achieve water-quality 

goals.

Introduction

Excessive nutrient (nitrogen and phosphorus) concentrations are common in rivers and lakes throughout the United 

States and New England and frequently result in water-resource 

impairments (U.S. Environmental Protection Agency, 2000a 

and 2000b). Although nitrogen and phosphorus are essential for 

healthy plant and animal life, elevated concentrations of these 

nutrients can cause eutrophication of waterbodies. Elevated 

amounts of phosphorus are the common cause of eutrophic 

freshwater rivers and lakes that often exhibit dense growths of 

algae or other nuisance aquatic plants, depressed dissolved oxygen levels, loss of fish and submerged aquatic vegetation, and 

foul odors. More than 30 percent of the lakes in New England 

were classified by State and Federal agencies as eutrophic in 

2000 (U.S. Environmental Protection Agency, 2000b). 

Eutrophication of coastal waters from excessive nitrogen loadings is also common in the United States and locally in New 

England (National Research Council, 2000; U.S. Environmental Protection Agency, 2000b). 

Sources of phosphorus and nitrogen to rivers, lakes, and 

coastal waters include permitted and unpermitted wastewater 

discharges (termed point sources), and runoff from the land surface, ground waters, and the atmosphere (a source primarily for 

nitrogen only) that collectively are called nonpoint sources. 

Agricultural and urban land uses are major sources of nutrients 
2 Estimation of Total Nitrogen and Phosphorus in New England Streams Using Spatially Referenced Regression Models

(Carpenter and others, 1998) and are typically a greater source 

of nutrients than wastewater discharges (Howarth and others, 

1996). 

Numerous studies have assessed nutrient discharges to 

coastal waters of the eastern United States because of coastal 

eutrophication concerns. Many of these studies are summarized 

by the National Research Council (2000). Howarth and others 

(1996) report that riverine discharges of nitrogen to coastal 

waters have increased 5 to 20 times since pre-industrial times 

and that the increased human population, use of nitrogen fertilizers, increased imports of human food and animal feed, and 

atmospheric deposition are the principal sources of the increasing levels of nitrogen to coastal waters. Nitrogen levels during 

the later years of the 20th century in forested watersheds of the 

northeastern United States continued to increase in contrast to 

urbanized rivers that have experienced stable nitrogen levels 

(Roman and others, 2000). Roman and others (2000), Robinson 

and others (2003), and Litke (1999) show that phosphorus concentrations in streams have declined since the 1960s as a result 

of phosphate detergent bans and improved wastewater treatment at municipal sewage facilities. Nutrient loads to coastal 

waters of New England were characterized by the National 

Oceanic and Atmospheric Administration (NOAA) (1987). 

Boyer and others (2002) and Mullaney and others (2002) estimated the loads of nitrogen to coastal waters of the eastern 

United States and to Long Island Sound from Connecticut, 

respectively, and the relative importance of point and nonpoint 

sources to the total loads. 

Managing and reducing nutrient loads to rivers has been a 

major water-pollution-control activity of individual states and 

U.S. Environmental Protection Agency (USEPA) under the 

Clean Water Act since the 1970s. In the 1990s, the USEPA 

implemented two programs to facilitate the management of 

nutrients in the Nation’s waters. The Nutrient Criteria program 

was designed to create waterbody-specific nutrient-concentration criteria for rivers, lakes, and estuaries. The Total Maximum Daily Load (TMDL) program was designed to assess and 

manage contaminant loads to waterbodies with designated-use 

impairment. Numeric criteria for concentrations of nitrogen 

and phosphorus to protect the designated uses of waterbodies 

are being generated by ecoregions and USEPA regions by the 

individual states and the USEPA (1998a). Available nutrient 

data for waterbodies also are being analyzed and new data are 

being collected during the process of creating the nutrient criteria. 

USEPA implements the TMDL program for waterbodies 

not meeting designed uses because of some form of contamination. TMDLs define the amount of contaminant allowable in 

the waterbody so that designated uses are met, and allocate 

allowable pollutant loadings from point and nonpoint sources 

that contribute the contaminants (U.S. Environmental Protection Agency, 2003). States and the USEPA are charged with 

identifying streams, rivers, and other waterbodies that have 

nutrient levels causing designated-use impairment and may 

require management action. In New England, nearly 2,000 

waterbodies do not meet designated uses due to nutrient and 

organic enrichment, noxious aquatic plants, and low dissolved 

oxygen (U.S. Environmental Protection Agency, 2003). 

Because water-quality data for New England waterbodies 

are limited for generating nutrient criteria and TMDLs, generating new data through field sampling or modeling to characterize nutrient levels is needed. Statistical modeling that relates 

nutrient conditions in waterbodies to watershed characteristics 

is an approach recommended by the National Research Council 

(2001) for the TMDL program. Such models can include measures of model prediction uncertainty, which can be useful 

when developing and implementing TMDLs (National 

Research Council, 2001; Shabman, 2002). The National 

Research Council study also recommended that approaches to 

TMDL development incorporate physical (deterministic) characteristics along with stochastic models that provide estimates 

of the errors involved in the predictions. 

The spatially referenced regression model SPARROW 

(Spatially Referenced Regressions on Watershed attributes), by 

Smith and others (1997), provides a modeling approach recommended by the National Research Council for water-quality 

assessments, including assessments needed for the TMDL program. The SPARROW model is designed to characterize nutrient loads in rivers based on a regression equation that includes 

terms for nutrient sources, land-to-water delivery of nutrients, 

and riverine transport and loss. The model also relies on geographic information system (GIS) technology to link river segments (termed reaches) and contributing drainage areas 

together. The SPARROW modeling technique has been successfully applied for predicting total nitrogen and phosphorus 

loads for streams in the continental United States (Smith and 

others, 1997) and New Zealand (Alexander and others, 2002), 

and for estimating total nitrogen loads for the Chesapeake Bay 

watershed in the eastern United States (Preston and Brakebill, 

1999) and in the Albemarle-Pamlico watersheds in North Carolina (McMahon and others, 2003). 

Purpose and Scope

This report describes results of two New England SPARROW models—one each for total nitrogen and total phosphorus 

—that have been developed for assisting water-resources managers with TMDL and nutrient-criteria development in New 

England. The models were developed by the U.S. Geological 

Survey (USGS), in cooperation with the New England Interstate Water Pollution Control Commission (NEIWPCC) and the 

USEPA. The New England models for total nitrogen and total 

phosphorus are calibrated for the early to mid-1990s and 

designed to refine national SPARROW results (Smith and others, 1997) by providing enhanced spatial detail and calibrated 

models on the basis of regional data. These enhancements are 

desirable because of national-model limitations that include

(1) coarse stream resolution for parts of New England; (2) an 

inability to accurately predict nutrient loads in watersheds less 

than 65 km2 (Focazio and others, 1998); (3) the use of only agricultural and non agricultural land-use categorizations; and
Introduction 3

(4) older county-level point-source data from the late 1970s and 

early 1980s. This report also provides a basic understanding of 

the New England SPARROW model technique, a description of 

the New England SPARROW model input data, and examples 

of SPARROW results and applications for use by waterresources managers in TMDL and nutrient-criteria development efforts. 

The study area for the New England SPARROW models 

includes watersheds that drain to Long Island Sound, the Gulf 

of Maine, Lake Champlain, and the New England portions of 

the Hudson and St. Francois River watersheds (fig. 1). The area 

includes 172,000 km2

 and covers all of New Hampshire,

Vermont, Massachusetts, Connecticut, Rhode Island, most of 

Maine, and parts of New York and Canada (fig. 1). Major urban 

areas within the study area include Boston, Springfield, and 

Worcester, Mass.; Hartford, Waterbury, and New Haven, 

Conn.; Providence, R.I.; Manchester, N.H.; Burlington, Vt.; 

and Portland, Maine. Major river basins include the Connecticut, Merrimack, Saco, Androscoggin, Kennebec, Penobscot, 

and parts of the St. Croix, and Upper St. John River Basins. 

Parts of the St. John and St. Croix River Basins in Canada were 

not included because of incomplete model input data for these 

areas.

Description of the SPARROW Modeling Technique

SPARROW is a statistical modeling technique that relates 

stream-nutrient loads to upstream sources and land-surface 

characteristics and then makes predictions for locations with no 

nutrient-load data. The SPARROW modeling technique, as 

described by Smith and others (1997), has several important 

features. Data for in-stream nutrient loads at monitoring sites, 

nutrient sources, and land-surface characteristics are assigned 

to each stream reach in a digital stream-reach network that provides continuity between upstream and downstream loads. The 

stream-reach network consists of individual, hydrologically 

linked stream reaches and associated catchments (figs. 2 and 3). 

Catchments are the drainage areas that contribute flow directly 

to each stream reach (not including flow from upstream 

reaches). 

The New England SPARROW models for nitrogen and 

phosphorus loads are the first SPARROW models to utilize the 

detail of the National Hydrography Dataset (NHD) as the 

underlying stream-reach network. Nutrient sources are evaluated as a function of location, magnitude, and the interaction of 

the sources with watershed characteristics. Nutrient transport 

and loss are modeled simultaneously through this network.

(1)

where

Load i

 = nutrient load in reach I, measured in kilograms per year;

n, N = source index where N is the total number of individual sources;

J(i) = the set of all reaches upstream and including reach i, except those containing or 

upstream of, monitoring stations upstream of reach i;

β n = estimated source coefficient for source n;

S n, j = nutrient mass from source n in drainage to reach j;

α = estimated vector of land-to-water delivery coefficients;

Z j

 = land-surface characteristics associated with drainage to reach j;

δ = estimated vector of in-stream-loss coefficients;

Ti, j = channel transport characteristics;

ε = error; and

e = base for the natural logarithm (approximately equal to 2.7183).

Loadi Sn j, βn e

α′ Zj ( )

n = 1

N

∑ e

δ′ Ti j , ( ) –

jε J i( )

∑ ⎩ ⎭ ⎨ ⎬ ⎧ ⎫

e

ε i ( )

=

Load Sources

Sn j , βn

Land-to-water 

delivery

α′ Zj

In-stream 

loss

δ′ Ti j , –

Error

ε i
4 Estimation of Total Nitrogen and Phosphorus in New England Streams Using Spatially Referenced Regression Models

New

Hampshire

Maine

Vermont

Massachusetts

Connecticut Rhode

Island

Quebec

New

Brunswick

New

York

Connecticut

River

Basin

Kennebec

River Basin

Upper St. John

River Basin

Penobscot

River Basin

Androscoggin

River Basin

Saco River

and Coastal

Basins

Merrimack

River Basin

Lake

Champlain

Basin

Upper

Hudson

River Basin

St. Francois

River Basin

Gulf of Maine

Atlantic Ocean

Quebec

Boston

Albany

Concord

Augusta

Montreal

Hartford

Portland

New Haven

Waterbury

Worcester

Montpelier

Providence

Manchester

Burlington

Springfield

Canada

United States

Long Island Sound

St. Lawrence River

MassachusettsRhode Island

Coastal Basins

Connecticut

Coastal Basins

Connecticut

Coastal Basins

St. Croix River

and Maine

Coastal Basins 

St. Croix River

and Maine

Coastal Basins 

U.S. political boundaries from 1:2,000,000-scale U.S. Geological Survey digital line graph data, 1990-1994; Canadian 

provincial boundaries from 1:3,000,000-scale Environmental System Research Institute ArcWorld data, 1999; shaded 

relief from U.S. Geological Survey 30-meter national elevation dataset, 1999; major hydrologic basins from 1:24,000-scale 

U.S. Department of Agriculture National Resource Conservation Service watershed boundary dataset, 2002

0 100 MILES 50

0 50 100 KILOMETERS

72 ̊ 70 ̊ 68 ̊ 74 ̊

48 ̊

46 ̊

44 ̊

42 ̊

Figure 1. Location of basins in, or draining into, New England.
Introduction 5

The mathematical form of the SPARROW models is that 

of a nonlinear regression model in which nutrient loads are 

related to nutrient-source data, which are weighted by estimates 

of loss as a result of land-surface and in-stream processes (equation 1) (Smith and others, 1997). In-stream nutrient loads 

(model-dependent variables) are evaluated as nonlinear functions of independent variables for nutrient sources (such as permitted wastewater releases; atmospheric deposition of nitrogen; 

and forest, agricultural, and developed land uses), for landdelivery processes (such as slope and precipitation), and for instream nutrient processes (such as travel times and reservoirsettling factors). 

Model parameters are estimated for each of the independent variables to evaluate the statistical significance of that variable for explaining the spatial variation in-stream nutrient loads. 

Source parameters (βn) are included and tested to determine the 

statistical significance of nutrient sources (Sn,j) in explaining 

the variation of loads among stream reaches. 

The land-to-water delivery coefficients (α) are used to 

determine the statistical significance of different types of landsurface characteristics (Z) for increasing or decreasing the 

delivery of nutrients from the land surface to the stream reach. 

For example, large percentages of developed land use, with 

accompanying impermeable surface areas, could potentially 

increase delivery of water and nutrients from the land surface to 

stream reaches. Developed lands could not only act as a nutrient source, but could increase the delivery of nutrients from 

atmospheric deposition to the streams. Land-to-water coefficients that were considered in the New England SPARROW 

models include air temperature, precipitation, runoff per unit of 

area, land-surface slope, soil permeability, stream density, wetland area, percent urban, percent forest, percent wetland, and 

percent open water. Delivery of wastewater-discharge loads to 

stream reaches was assumed to be unaffected by land-surface 

characteristics, and the value of the land-delivery term (e(α ′ Zj)) 

for these sources is set equal to one because the discharges are 

delivered directly into the streams. 

Estimating in-stream-loss and reservoir-loss parameters 

(equation 1) is important for relating upstream sources to downstream loads because some nutrients may be lost through stream 

and reservoir processes, such as denitrification (for nitrogen 

only), biological uptake, and sedimentation. These losses may 

be important for determining the importance of upstream nutrient sources to eventual receiving waters such as Long Island 

Sound and the Gulf of Maine. Although there are a variety of 

chemical, biological, and physical processes that contribute to 

in-stream loss of nutrients, the SPARROW models do not 

attempt to distinguish or identify individual nutrient loss processes because adequately detailed information on these processes generally is not available. The SPARROW model 

requires that estimates of mean-annual flow and associated 

mean velocities be assigned to each stream reach in the NHD. 

In-stream-loss variables are included in the model and tested to 

see whether they are statistically significant predictors of nutrient loads and whether nutrient loads significantly decrease with 

increased residence time. Stream residence time is estimated by 

dividing reach length by mean velocity. Additionally, the reciprocal hydrologic load (the ratio of the water-body surface area 

divided by the outflow) is used to determine if estimated nutrient loss in reservoirs is statistically significant. A coefficient for 

this variable (calculated by calibrating the model) is the areal 

hydraulic load, which is mathematically equivalent to the ratio 

of depth to water residence time (Chapra, 1997). 

Fortran programs (Richard Alexander, U.S. Geological 

Survey, written commun., 2002) are used to simulate the downstream movement of nutrients. SAS computer software programs (Richard Alexander, written commun., 2002; 

Gregory Schwarz, U.S. Geological Survey, written commun., 

2002, 2003) are used to calibrate and apply the model. Arc-Info 

GRID (Environmental Systems Research Institute, Inc., 1999) 

was used for storage of spatial data.

A bootstrap analysis was conducted to assess the errors 

associated with the predictions and to confirm calibration 

results. Bootstrap analysis uses a single dataset to derive an 

empirical distribution of the coefficients in the model that 

approximates their true distribution (Efron, 1982). Bootstrap 

analysis is useful when multiple datasets are not available to 

compute multiple sets of model coefficients and has been used 

in previous SPARROW models (Smith and others, 1997; 

Preston and Brakebill, 1999). For the SPARROW models the 

bootstrap analysis permits the computation of 200 sets of model 

coefficients, based on a single input dataset. The bootstrap 

analysis involves a parametric simulation in which Monte Carlo 

methods are used to generate 200 sets of bootstrap samples. 

This method is based on the assumption that the coefficients are 

distributed multivariate normal with the mean and the covariance matrix given by the original parametric model results 

(Gregory Schwarz, written commun., 2003). The final model 

predictions and prediction intervals are based on the parametric 

Monte Carlo bootstrap procedure.

Upstream monitoring 

 station

Point source

Reach segment 

 nonpoint-source 

 contributing area 

 "catchment"

Reach segment

Downstream 

 monitoring station

Subbasin divide

Figure 2. Features of the SPARROW stream network (modified from Schwarz (1998)).
6 Estimation of Total Nitrogen and Phosphorus in New England Streams Using Spatially Referenced Regression Models 74 ̊ 72 ̊ 70 ̊ 68 ̊ 42 ̊44 ̊ 46 ̊ 0 100 MILES 50 0 50 100 KILOMETERS Base from U.S. Geological Survey Digital line graph, 1:2,000,000 scale, 1990-94 EXPLANATION National Hydrography Dataset reach catchments Extent of basins not modeled Topographic map Base from U.S. Geological Survey Center Lovell and North Waterford quadrangles, 1:24,000 scale, 1989 70 ̊52'30" Reach catchment divideSubbasin divide 44 ̊15' NHD stream reach Saco River Basin Kezar Lake subbasin Subbasin divide Kezar Lake subbasin NHD stream reach NHD water-body center line NHD water-body center line reach

Figure 3. Spatial detail of the New England SPARROW model with 42,000 National Hydrography Dataset (NHD) reach catchments.
Description of Data Used in the New England Sparrow Models 7

Criteria for inclusion of the predictor variables in the 

model included (1) a probability level (p) (for coefficients equal 

to zero) of less than or equal to 0.05 or (2) p is less than or equal 

to 0.15 and the variable and the coefficient makes sense in terms 

of physical processes involved. This method is consistent with 

the method used by other SPARROW models (Smith and others, 1997; Preston and Brakebill, 1999).

A nested model was applied to determine whether the 

results for total nitrogen in streams in New England differ significantly between the national and New England nutrient 

SPARROW models. In the nested model, the New England 

data were run simultaneously with the national model data to 

allow direct comparison of the benefit of different model coefficients that would improve the understanding of model results. 

National SPARROW model stream reaches were used outside 

of New England and the more detailed New England stream 

reaches were used in New England. This approach allowed 

direct comparison between national and New England coefficients, provided an enhanced understanding of the New 

England model results, evaluated the adequacy of the calibration data, and identified whether in-stream processes and loss 

rates in New England differ from the nation as a whole. 

Description of Data Used in the New 

England Sparrow Models 

The New England nutrient SPARROW models were calibrated to data collected primarily during the years 1992-93. 

This was done to maximize the amount of nutrient load and predictor variable datasets available for analysis. Sections that follow describe the types of data that were used in developing the 

models. Data sources are summarized in table 1.

Table 1. Sources of data used in the New England SPARROW models.

[USGS, U.S. Geological Survey; NWIS, National Water Information System; USEPA, U.S. Environmental Protection Agency; NHD, National Hydrography

Data; NRCS, Natural Resources Conservation Service; HUCs, Hydrologic Unit Codes; NED, National Elevation Dataset; NRPI, National Pollution Release

Inventory; NLCD, National Land Cover Data; STATSGO, State Soil Geographic Data; PRISM, Parameter-elevation Regressions on Independent Slopes Model]

Data type category Data type determined for each 

reach, except * Source

LOADS

*Annual total nitrogen and 

phosphorus loads

Calculated at nutrient-load measurement sites using the ESTIMATOR (Cohn and others, 

1989) program, and basic data from the USGS NWIS database, numerous databases 

from state agencies (Isabell Moran, ENSR Corporation, written commun., January 

2000), the USEPA, and from research hydrologists (Gene Likens, Institute of Ecosystem 

Studies, Millbrook, N.Y., written commun., 2001; James Shanley, U.S. Geological Survey, written commun., 2001).

STREAM 

NETWORK

River reaches The NHD, 1:100,000 scale (U.S. Geological Survey, 1999c); Canada’s National Topographic Data Base, 1:50,000 scale, (Natural Resources Canada, 2000).

Mean-annual streamflows Calculated from Randall (1996), using NHD catchments.

Watersheds (called “catchments”) for each reachNRCS 12 digit HUCs (Donald Richard and Reed Sims, Natural Resources Conservation 

Service, written commun. 2000), and generated using the NED (U.S. Geological Survey, 

1999b).

Reach slope Reach slope is the change in reach elevation (calculated using the catchments and NED 

data) divided by the reach length (from the NHD).

Travel times Calculated from the reach length and regional estimation equations for average stream 

velocity (Jobson, 1996).

Surface area size of lakes and 

reservoirs

NHD stream network (U.S. Geological Survey, 1999c).

TESTED 

NUTRIENT 

SOURCES

Permitted wastewater

discharges

(Stephen Rubin, U.S. Environmental Protection Agency, written commun., 2000; Canadian NRPI database (accessed 2002, at http://www.ec.gc.ca/pdb/npri/npri_home_e.cfm).

Land use (forest, agricultural, 

urban, wetland)

United States - NLCD circa 1992 (U.S. Geological Survey, 2000, 2002); Canada – 

(Brenna Beaulieu, Quebec Ministry of the Environment, written commun., 2001).

Atmospheric nitrogen

deposition

Ollinger and others (1993).

Population 1990 census, U.S. Census Bureau, 1996 Canadian Census.

TESTED 

DELIVERY 

FACTORS

Soil permeability STATSCO (U.S. Department of Agriculture, 1994; Schwarz and Alexander, 1995).

Surface slope Calculated using NED.

Stream density Calculated using NHD stream network.

Precipitation and air temperaturePRISM (Daley and Taylor, 2000a and b).
8 Estimation of Total Nitrogen and Phosphorus in New England Streams Using Spatially Referenced Regression Models

Hydrologic Network

The SPARROW model requires a hydrologically connected representation of a stream network through which nutrient loads are transported from an upstream reach to the next 

reach downstream, thus relating upstream sources to monitored 

load data (fig. 3). The hydrologic network used for the New 

England SPARROW models was the National Hydrography 

Dataset (NHD) (U.S. Geological Survey, 1999c). The NHD is 

produced by the USGS, in cooperation with the USEPA, at an 

initial scale of 1:100,000. The NHD is a digital hydrographicdata model represented in ARC/INFO, a GIS software package 

(Environmental Systems Research Institute, Inc., 1994). Basic 

characteristics, such as reach length, have been assigned to each 

stream reach including the identification of the upstream and 

downstream reaches in a series of related tabular databases. 

This link between upstream and downstream reaches is vital to 

the SPARROW model. 

Previous SPARROW models in the United States (Smith 

and others, 1997; Alexander and others, 2002; Preston and 

Brakebill, 1999; McMahon and others, 2003) were based on 

USEPA’s River Reach File 1 (RF1) (DeWald and others, 1985). 

RF1 is a 1:500,000-scale, digital stream dataset that has 

attributes for stream-reach length, average stream discharge, 

and average flow velocity. The need for improved resolution in 

the New England models resulted in the selection of the NHD 

at a 1:100,000 scale. For comparison, in New England there are 

2,462 RF1 catchments (mean size 75.6 km2

) and 42,000 NHD 

catchments (mean size 4.4 km2

). 

The SPARROW model required a number of modifications to the NHD. As a result of inconsistencies in the resolution of intermittent streams across New England in the NHD, 

these streams were not included in the New England SPARROW models. New reaches also were added for watersheds 

with contributing drainage in Canada. These watersheds 

included parts of the Connecticut Rivers and the Lake Champlain Basins on the basis of 1:50,000-scale digital hydrography 

data obtained from Natural Resources Canada’s National Topographic Data Base (NTDB) (Natural Resources Canada, 2000). 

These stream reaches were integrated into the NHD by selecting 

and generalizing them to match the density of the NHD. Canadian reaches were not added for the Upper St. John and

St. Croix River Basins in Maine because of lack of existing data 

required for input to SPARROW. In addition, editing of the 

NHD was required before it could be used for modeling. For 

example, connector reaches were added manually to connect 

gaps in the NHD network, and corrections were made to the 

relational flow tables, which identify which reach flows into 

which, to ensure hydrographic continuity throughout all watersheds in the model. Tidal reaches are included in the network 

(no differentiation is made between tidal and nontidal in the 

NHD) but all nutrient-load measurement sites are upstream of 

the head of tide. Tidal reaches have been identified by a combination of National Elevation Dataset (NED) (U.S. Geological 

Survey, 1999b) data and known tidal ranges along the New 

England coast.

The catchment for each reach in the network (fig. 3) was 

determined using the NED, the NHD stream network, and the 

12-digit hydrologic unit watersheds delineated by the Natural 

Resources Conservation Service (NRCS) (Donald Richard and 

Reed Sims, NRCS, written commun., 2000). The NRCS watershed delineations were subdivided by use of the 30-meter NED 

dataset and surface modeling in the ARC/INFO Grid software 

(Environmental Systems Research Institute, Inc., 1999). An 

ARC/INFO AML program called AGREE (Hellweger and 

Maidmont, 1997) was used in this process. AGREE forces the 

NED to conform to the NHD stream network because drainage 

inferred from the NED may not match stream locations in the 

NHD. A similar process developed for this study forced compatibility between the NRCS watershed boundaries (where they 

exist) to the surface-modeled watershed boundaries generated 

from the NED. An example of the spatial detail on the resultant 

stream reaches and catchments used in the New England SPARROW hydrologic network is shown in figure 3.

Throughout this report, catchment refers to the local drainage area directly contributing to a stream reach. Watersheds are 

the total upstream drainage area, and the term “basin” refers to 

large named watersheds such as the Connecticut River Basin.

Channel-Transport Characteristics Data

The New England SPARROW models require that estimates of mean-annual flow, stream velocity, and retention or 

settling effects of impoundments and lakes be assigned to each 

reach of the NHD. Mean-annual flow was determined by 

applying data from a streamflow-runoff map of the northeastern 

United States by Randall (1996) to the drainage area of each 

reach catchment. Mean-annual flow was calculated as the sum 

of the runoff from each catchment and all upstream catchments. 

Results of this process compared favorably with measured data 

from 211 active USGS stream-gaging stations. The estimates 

for 53 percent of the sites compared (112 stations) had errors 

less than 5 percent of the reported mean-annual flow; 30 percent 

of the sites (64 stations) had errors between 5 and 10 percent of 

the reported flow; 10 percent of the sites (20 stations) were 

between 10 and 15 percent of the reported flow; and the remaining 7 percent (15 stations) were between 15 and 28 percent of 

the reported flow. 

In addition to the total streamflow in each stream reach, the 

SPARROW models require a time-of-travel or residence time 

in each reach. This residence time was generated for all stream 

reaches by applying a regression equation for stream velocity 

from Jobson (1996, equation 12) and dividing the reach length 

by the velocity. To estimate velocity, Jobson’s equation 

requires flow, reach slope, and total drainage area for each 

stream reach. A comparison of velocity estimates to measured 

velocity data was made using mean-annual flow conditions for 

five selected (relatively unregulated) New Hampshire stream 

reaches (Thor Smith, U.S. Geological Survey, written commun., 2002). These comparisons indicate that the velocity estimates may have as much as a 40 percent error. Further compar-
Description of Data Used in the New England Sparrow Models 9

ison of these estimates to RF1 velocity estimates reveal an 

improvement over the estimates associated with the RF1 network.

The parameter used by SPARROW in testing for loss of 

nutrients in lakes and reservoirs is defined as the “reciprocal 

areal hydraulic load,” which is the ratio of water-surface area to 

outflow discharge in units of years per meter (Alexander and 

others, 2002). Lakes and reservoirs were identified on the basis 

of the size of the waterbody polygon identified in the NHD. 

Reaches passing through waterbody polygons with surface 

areas greater than or equal to 2 km2

 were classified as lake or 

reservoir reaches. 

Stream Nutrient-Load Data

In-stream total nitrogen and total phosphorous loads serve 

as the dependent variables in the SPARROW models. The 

loads were estimated from stream discharge and water-quality 

data collected at monitoring sites throughout the New England 

model study area by a variety of agencies and researchers. 

Nutrient data were obtained from the USGS, numerous databases from state agencies (Isabell Moran, ENSR Corporation, 

written commun., January 2000), the USEPA, from researchers 

at Sleepers River Watershed in Vermont (James Shanley, U.S. 

Geological Survey, written commun., 2001), and from the Lake 

Champlain Long-Term Water Quality and Biological Monitoring Program in Vermont and New York (Laura Medalie, U.S. 

Geological Survey, written commun., 2001). Nutrient data 

from stream-monitoring sites were compiled for 1974 through 

1999. 

Nutrient-load values were generated from stream-discharge and water-quality data through the use of a log-linear 

regression model called ESTIMATOR (Cohn and others, 

1989). The ESTIMATOR model estimates daily concentration 

values on the basis of available concentration data, flow, season, and temporal load trends for a specified period. Estimated 

daily load values were calculated by ESTIMATOR from estimated daily concentrations and long-term average daily flows. 

The long-term average daily flow data are used in the analysis 

to prevent an error resulting from random spatial variations in 

precipitation and flow during any given year. Estimated daily 

load values were subsequently summed to calculate an annual 

stream load. Annual loads were averaged to calculate a meanannual load. In most cases, the mean-annual load, which was 

representative of the early 1990s, was used for load prediction. 

Some sites did not have data to generate loads for the early 

1990s; therefore, mean-annual loads from the available time 

period were used. The use of these data allowed for the inclusion of more sites in the model. Where flow data were not available at the water-quality monitoring site, estimates were made 

by applying drainage-area adjustments to streamflow data from 

a nearby station. For the remainder of this report, stream loads 

that were derived from ESTIMATOR are referred to as “observation loads” to distinguish them from those predicted by the 

SPARROW models. 

Nutrient-concentration data from many of the 123 sites 

with data were eliminated for use in the study because the data 

were considered inadequate for annual-load estimation. Sites 

had inadequate data if (1) the time period for collection of 

water-quality data did not overlap with the collection of flow 

data, (2) there was insufficient water-quality data to estimate an 

annual load, or (3) the error terms in the computed-load estimates were considered too high (greater than 60-percent error). 

Of the 72 sites with total nitrogen data and 95 sites with total 

phosphorus data, 65 and 67 sites, respectively, had appropriate 

stream-loading data and were included in the models (fig. 4). 

Nutrient-Source Data

The SPARROW models require information on specific or 

potential point and nonpoint sources of nutrients. All potential 

sources were georeferenced and allocated to the appropriate 

NHD catchments.

Municipal and industrial wastewater discharges of nitrogen or phosphorus for the New England SPARROW models 

were based on a USEPA permitted wastewater-discharge 

dataset (Steven Rubin, U.S. Environmental Protection Agency, 

written commun., January 2000). This dataset includes estimates of nutrient loads and other pollutants as average yearly or 

monthly estimates of total nitrogen or total phosphorus. Loads 

were estimated by USEPA using a methodology developed by 

NOAA to characterize wastewater loads to coastal waters and 

watersheds (National Oceanic and Atmospheric Administration, 1993). These provided estimates were based on a hierarchy of data sources. The highest priority source was derived 

from data from the USEPA's National Pollutant Discharge 

Elimination System (NPDES) program as reported in each 

facility's discharge monitoring report (DMR). When this information was not available, permitted discharge limits set for the 

facility were used. If neither monitoring nor permit pollutant 

data were available, engineering values, associated with either 

the facility's industrial activity or level of wastewater treatment, 

were used for the estimate (National Ocean and Atmospheric 

Administration, 1993). Spot checking of the estimates, with a 

more recent nitrogen dataset for Connecticut and a phosphorus 

dataset for western Vermont, showed some large discrepancies. 

However, the wastewater discharge estimates were used in the 

models because they were the best available information covering the entire New England model area.

Estimates of total nitrogen and total phosphorous loads 

from permitted wastewater discharges in Canada were provided 

by the Quebec Ministry of the Environment (Jacques Dupont, 

Quebec Ministry of the Environment, written commun., 2001). 

A total of 2,300 permitted wastewater discharges of nutrients 

were present on 1,506 stream reaches. Of these, 403 stream 

reaches had discharges from municipal wastewater-treatment 

facilities, and 73 reaches had discharges from paper and pulp 

industries (fig. 5). The remaining reaches had nutrient discharges from other industries.
10 Estimation of Total Nitrogen and Phosphorus in New England Streams Using Spatially Referenced Regression Models

Connecticut River

Thames River

Housatonic River

Taunton River

Merrimack River

Atlantic Ocean

Saco River

Presumpscot River

Androscoggin River

Kennebec River

Penobscot River

Providence River

Blackstone/ Charles

River

Moosehead

Lake

Lake

Winnipesaukee

74 ̊

72 ̊

70 ̊

68 ̊

42 ̊

44 ̊

46 ̊

0 100 MILES 50

0 50 100 KILOMETERS

EXPLANATION

Load sites

 Nitrogen

 Phosphorous

 Nitrogen and phosphorous

Base from U.S. Geological Survey

Digital line graph, 1:2,000,000 scale, 1990-94

National Hydrography Dataset, 1:100,000 scale, 2002

MAINE

NEW

HAMPSHIRE

VERMONT

MASSACHUSETTS

CONNECTICUT

RHODE

ISLAND

NEW

YORK

CANADA

Lake

Champlain

Figure 4. Nutrient-load measurement sites used in the New England SPARROW models.
Description of Data Used in the New England Sparrow Models 11

74 ̊

72 ̊

70 ̊

68 ̊

42 ̊

44 ̊

46 ̊

0 100 MILES 50

0 50 100 KILOMETERS

EXPLANATION

Permitted wastewater discharge

 Municipal sewer system

 Pulp and paper facility

Base from U.S. Geological Survey

Digital line graph, 1:2,000,000 scale, 1990-94

National Hydrography Dataset, 1:100,000 scale, 2002

MAINE

NEW

HAMPSHIRE

VERMONT

MASSACHUSETTS

CONNECTICUT

RHODE

ISLAND

NEW

YORK

CANADA

Figure 5. Permitted municipal and pulp and paper wastewater-discharge locations in New England.
12 Estimation of Total Nitrogen and Phosphorus in New England Streams Using Spatially Referenced Regression Models

Disperse (nonpoint) nutrient sources are characterized in 

the SPARROW models through land-use data and measures of 

agricultural activities, population density, and atmospheric deposition. Land use was defined by using the National Land 

Cover Data (NLCD) that is available for the early 1990s at a

30-m resolution grid (U.S. Geological Survey, 2000; 2002). 

Major land-use categories include water, developed, barren, 

forest, shrubland, non-natural woody, agricultural, and wetlands; although there are a total of 18 subcategories within the 

model area (table 2). A similar land-cover dataset in Canada at 

a 25-m resolution was integrated for areas in Canada (Brenna 

Beaulieu, Quebec Ministry of the Environment, written commun., 2001). 

The New England SPARROW model study area is

75.7 percent forested, 7.9 percent agricultural, 5.8 percent 

developed, 4.9 percent wetland, 4.3 percent water, and

1.4 percent barren land.

County and state-based estimates of the nitrogen and phosphorus contents of fertilizers applied to agricultural lands and 

from livestock manure wastes also were considered as predictors in the models (Alexander and Smith, 1990; Soil Conservation Service, 1992). These data, however, were not used in the 

models because of apparent discrepancies in the reporting procedures used from state to state. 

Atmospheric deposition of nitrogen is known to be a significant contributor of total nitrogen to streams (Smith and others, 1997; Valigura and others, 2001). Atmospheric deposition 

of phosphorus is considered minor (Smith and others, 1997) and 

was not considered as a phosphorus source in the model. Estimates from an existing spatial model of atmospheric deposition 

of total nitrogen in the northeastern United States (Ollinger and 

others, 1993) were used for the New England SPARROW 

model for total nitrogen. In the model by Ollinger and others 

(1993), total nitrogen deposition is a function of latitude, longitude, and total precipitation. Contoured data from Ollinger and 

others (1993) were extended into Canada using a shaded relief 

map as a general guide for extrapolating the atmospheric-deposition contours for the New England SPARROW model area 

into Canada. In the New England SPARROW model area, 

atmospheric deposition of total nitrogen is shown to range from 

320 kg/km2

/yr in the northeastern part to 1,030 kg/km2/yr in the 

southwestern part and on the higher mountains such as Mount 

Washington in New Hampshire (Ollinger and others, 1993).

Human population density was characterized and tested in 

the New England SPARROW models by use of the 1990 census 

map data available in ARC INFO format. The U.S. Bureau of 

the Census data are available at the block group level (townwide 

or even more detailed for populous municipalities). Population 

was assumed to be evenly distributed within each block. Population for all blocks and partial blocks in each catchment were 

summed to estimate the population in each catchment. Canadian population data were from the 1996 Statistics Canada data 

at the enumeration-area level, which is comparable to the U.S. 

Census block group (Brenna Beaulieu, Quebec Ministry of the 

Environment, written commun., 2001). The population, in 

1990, for the entire model area was 11,800,000.

Physical Watershed Characteristics Data

Meteorological and land-surface characteristics data were 

compiled for each catchment from a variety of datasets. Each 

of the variables was considered to be a potentially important 

factor in controlling the delivery of nutrients from the land surface to streams. 

Table 2. Categories, subcategories, and codes of the National 

Land Cover Dataset.

[U.S. Geological Survey, 2000; Model runs were conducted in all combinations, with and without the main category of which it is a part, and with and 

without each subcategory within the main category; --, negligible in model area]

Category and subcategory name Percent of model 

area

Water 4.3

Open water1

Developed 5.8

Low-intensity residential1

High-intensity residential1

Commercial/industrial/transportation

Urban/recreational grasses1

Barren 1.4

Bare rock/sand/clay

Quarries/strip mines/gravel pits

Transitional

Forest 75.7

Deciduous forest1

Evergreen forest1

Mixed forest1

Shrubland --

Shrubland

Non-natural woody --

Orchards/vineyards/other1

Agricultural 7.9

Pasture/hay

Row crops

Small grains

Wetlands 4.9

Woody wetlands

Emergent herbaceous wetlands

1

Subcategories tested in the models.
Spatially Referenced Regression Models for Nutrients in New England Streams 13

Climatic Factors

The climatic variables of mean-annual air temperature and 

precipitation were compiled for the New England SPARROW 

models. Air temperature can affect the amount of nitrogen that 

reaches streams by affecting the rate of biological processes 

such as denitrification. Precipitation affects delivery by determining the volume and rate of runoff in areas of the watershed. 

Estimates of mean-annual temperature and precipitation for use 

in the New England SPARROW models came from the Parameter-elevation Regressions on Independent Slopes Model 

(PRISM) developed by Oregon State University as part of the 

USDA-NRCS Spatial Climate Mapping Project (Daley and 

Taylor, 2000a, 2000b). Climate data for Canada was estimated 

by extending PRISM data contours into Canada using a shaded 

relief map as an elevation factor guide along with Canadian climate observation station data from State of the Environment 

(Jacques Dupont, Quebec Ministry of the Environment, written 

commun., 2001). Within the model area, mean-annual precipitation, averaged by catchment, ranged from a low of 79.4 centimeters per year (cm/yr) to a high of 244 cm/yr, with an average 

catchment precipitation of 114 cm/yr. Mean-annual temperature ranged from a low of 1.6oC to a high of 11.1oC, with an 

average mean-annual catchment temperature of 6.7oC.

Land-Surface Characteristics

Land-surface characteristics tested in the New England 

SPARROW models include soil permeability, surface slope, 

stream density, and percent wetlands. Soil permeability information (given in units of centimeters per hour) is contained in 

the 1:250,000-scale NRCS State Soil Geographic (STATSGO) 

data (U.S. Department of Agriculture, 1994; Schwarz and Alexander, 1995) and is based on generalized soils maps. Detailed 

county-level digitized soils data were not available throughout 

much of New England; therefore, the more generalized 

STATSGO data was used to characterize soils. Canadian soils 

data were integrated with STATSGO using 1:250,000-scale 

Canada Land Inventory (CLI) data (Agriculture and Argi-Food 

Canada, 1998). CLI data did not have a measure of permeability, but did have several attributes such as texture and wetness 

describing the soil suitability for agriculture. A comparison 

with adjacent soils in the United States was used to assign a 

mean permeability to each soil type. High soil permeability is 

an indication of increasing percolation to ground water that can 

influence nutrient delivery to streams. Within the model area, 

soil permeability averaged by catchment ranged from a low of 

0.0 cm/h to a high of 46.1 cm/h, with an average of 11.3 cm/h.

Average slope of the land surface was determined for each 

catchment by use of the 30-m NED, which is available for all of 

New England and parts of Canada (U.S. Geological Survey, 

1999b). Steep slopes can potentially cause increased delivery 

of nutrients to streams. Stream density for each catchment was 

calculated as the ratio of channel length to drainage area. The 

channel lengths used to calculate these values were those 

depicted in the 1:100,000-scale NHD. High stream densities 

may indicate a shortened flow path of nutrients to streams, less 

loss, and high delivery rates. Within the model area, the landsurface slope, averaged by catchment and measured as a percent-change elevation relative to horizontal distance, ranged 

from a 0.0 to 52.6 percent, with an average of 8.2 percent.

Spatially Referenced Regression Models for 

Nutrients in New England Streams

The calibration and bootstrap New England SPARROW 

models are presented in this section. Total nitrogen and total 

phosphorus loads (referred to as simply nitrogen and phosphorus) are dependent variables in the two separate models. Model 

applications and the comparison of model results to those from 

other nutrient assessments are provided.

Nitrogen

Calibration and bootstrap results for the New England 

SPARROW model for nitrogen are presented in table 3. Significant predictor variables were found to include (1) nitrogen 

loadings from permitted municipal wastewater discharge,

(2) atmospheric deposition of total nitrogen, (3) the area of agricultural land, and (4) the area of developed urban and suburban 

land. Parameter-coefficient estimates and standard errors of the 

estimates are given in table 3. In general, the nitrogen load predicted by the model closely matches the observation load as 

indicated by a coefficient of determination (R2) of 0.95, and a 

mean-squared error of 0.16 (fig. 6). The coefficient of determination is a measure of the fraction of variance in the load data 

(expressed in natural log units) that was accounted for by the 

independent variables used in the regression model. The nitrogen model accounted for a large proportion of the variance

(95 percent) in the load data. For comparison, the national 

SPARROW model for nitrogen had an R2 of 0.88 and a meansquared error of 0.43 (Smith and others, 1997). 

The coefficients estimated for the nitrogen model (table 3) 

have various physical interpretations. The coefficient of 1.11 

for discharges from municipal wastewater-treatment facilities 

indicates that for each estimated kilogram of nitrogen discharged into the rivers at the wastewater-discharge locations, 

the model is predicting 1.11 (+ 0.36) kg of nitrogen at the monitoring stations. The coefficient of 0.37 for atmospheric deposition indicates that for each estimated kilogram of nitrogen that 

falls on the land surface, the model is predicting that an average 

of 0.37 (+ 0.06) kg are delivered to streams. In other words, the 

results of the model indicate that two thirds of the mass of nitrogen from atmospheric deposition is either retained in the watershed or returned to the atmosphere. 

The coefficient for agricultural lands indicates that, per 

year, there are 895 (+ 335) kg of nitrogen in streams for each 

square kilometer of agricultural land. This value can be
14 Estimation of Total Nitrogen and Phosphorus in New England Streams Using Spatially Referenced Regression Models

Table 3. Calibration results and bootstrap estimates for the New England SPARROW model for total nitrogen.

[kg/km2/y, kilograms per kilometer squared per year; d-1, per day; m/s, meters per second; ft3/s, cubic feet per second; R-squared = 0.95; 

mean-square error = 0.16]

Significant predictor variables

(coefficient units)

Calibration model 

coefficient

Standard error 

of coefficient

Bootstrap 

estimate of 

coefficient

Standard error of 

bootstrap 

coefficient

Sources:

Municipal wastewater-treatment facilities1 1.11 0.36 1.13 0.36

Atmospheric deposition1 .37 .06 .36 .07

Cultivated agricultural land (kg/km2/y) 895 335 910 362 

Developed urban and suburban land (kg/km2/y) 1,032 366 988 385

Delivery variable:

Natural log of soil permeability1 0.37 .14 .36 .14

Loss variable:

Stream loss for small streams2

 (d-1) .78 .49 .71 .52

2Dimensionless.

3

Small streams with mean-annual flow less than or equal to 2.83 m3/s (100 ft3/s).

8 9 10 11 12 13 14 15 16 17

8

9

10

11

12

13

14

15

16

17

OBSERVATION

NATURAL LOG OF NITROGEN LOAD, IN KILOGRAMS PER YEAR

PREDICTION FROM MODEL

NATURAL LOG OF NITROGEN LOAD, IN KILOGRAMS PER YEAR

Figure 6. Relation of predicted and observed total nitrogen load values from the calibration 

of the New England SPARROW model.
Spatially Referenced Regression Models for Nutrients in New England Streams 15

compared to an average export coefficient of 760 kg/km2/yr of 

agricultural land determined for the State of Connecticut and 

the Connecticut Watershed Model Project’s Hydrologic Simulation Program Fortran (HSPF) Model (Paul Stacey, Connecticut Bureau of Water Management, written commun., 2003). 

The Connecticut export coefficient for agricultural land 

includes the contribution from atmospheric deposition. 

SPARROW model results indicate that an average of 276 kg/

km2

/yr is related to atmospheric deposition in Connecticut. If 

this amount from atmospheric deposition is removed from

760 kg/km2/yr, then the SPARROW and Connecticut HSPF 

results can be directly compared. Export rates obtained for agricultural lands from the New England SPARROW model are 

about twice that of the Connecticut Watershed Model Project 

results (895 kg/km2

/yr for the SPARROW model compared to 

484 kg/km2

/yr for the Connecticut HSPF model).

The coefficients for developed lands indicate that about 

1,032 (+ 366) kg of nitrogen occur in streams for each square 

kilometer of developed land upstream per year. This value is 

greater than a coefficient of 785 kg/km2/yr for urban lands computed by the Chesapeake Bay Watershed SPARROW model 

(Preston and Brakebill, 1999, p. 8), and similar to an average 

export coefficient of 1,064 kg/km2/yr of urban land determined 

for the State of Connecticut by the Connecticut Watershed 

Model Project (Paul Stacey, written commun., 2003). For comparison, the Connecticut Watershed Model export was adjusted 

for atmospheric deposition by subtracting the average SPARROW-estimated atmospheric deposition in Connecticut to 

derive 1,064 kg/km2/yr.

The natural log of the soil permeability was the only delivery variable found to be significant in the SPARROW model for 

nitrogen. The positive coefficient (table 3) indicates that for 

New England, high soil permeability (increased percolation to 

ground water) is associated with increased nitrogen delivery to 

streams. 

The coefficient for stream loss indicates that nitrogen is 

removed from small streams (with mean-annual flows of

2.83 m3/s or less (100 ft3/s) (table 3). About 86 percent of the 

stream reaches in the New England SPARROW model have 

mean-annual flows less than or equal to 2.83 m3/s. Presumably, 

the ability to identify this loss in small streams was enhanced by 

using the detailed NHD stream network. The modeled loss thus 

applies to about 86 percent of the stream reaches in the model. 

The coefficient of 0.77 d-1 equates to a half-life of about 0.9 

days; for example, for each 0.9 days of transport in streams with 

flows less than 2.83 m3/s, about half of the nitrogen load is lost. 

This coefficient of 0.77 (or 0.71 for the bootstrap model) can be 

compared to a coefficient of 0.38 from the national nitrogen 

model for streams less than 28.3 m3/s (1,000 ft3/s) (Smith and 

others, 1997. The loss/decay half-life of 0.9 days for the New 

England nitrogen SPARROW model compares to 1.8 days for 

the national model (Smith and others, 1997).

An important model result was a lack of statistically significant loss for large streams with flows greater than 2.83 m3/s 

and for reservoirs. When introduced into the model, a variable 

for time-of-travel within any stream reach with flows greater 

than 2.83 m3

/s had an insignificant coefficient with the wrong 

sign, which, if significant, would have indicated nitrogen gain, 

not loss. For reservoir loss, an insignificant coefficient representing loss from all reservoirs was computed to be

1.8 (+2.9) m/yr. This finding is contrary to the findings of the 

national and the more southern regional SPARROW models 

developed to date (Smith and others, 1997; Preston and

Brakebill, 1999; McMahon and others, 2003). The lack of identified loss of in-stream annual nitrogen loads in large streams 

and reservoirs may be the result of inadequate data as input to 

the model or it may be from an actual lack of significant nitrogen loss. Different physical features and processes in New 

England, as compared to other areas of the Nation such as relatively cool temperatures during the spring season when the bulk 

of the nitrogen load is released from the terrestrial environment, 

may inhibit nitrogen loss. 

To determine how the New England and National SPARROW results for in-stream nitrogen loss differ, a direct comparison between national and New England nitrogen model coefficients was made with a nested SPARROW model. In the nested 

model, the New England data were run simultaneously with the 

national data to provide an enhanced understanding of the New 

England model results, evaluate the adequacy of the calibration 

data, and identify whether in-stream processes and loss rates in 

New England differ from the nation as a whole. Conclusions 

reached from the nested SPARROW model are as follows:

1. For streams in New England, with flows less than

2.83 m3/s, the nitrogen loss is higher than that of the 

national RF1 reaches (0.8 d-1 as opposed to 0.3 d-1 for the 

national model stream reaches outside New England). 

2. The nitrogen loss on an annual basis for New England 

streams with flows greater than 2.83 m3/s (grouped as a 

whole) is negligible at a 90-percent confidence level. If 

the 2.83–28.3 m3/s streamflow category is tested 

separately, there still appears to be negligible loss. 

Outside of New England, results for the national model 

reaches indicate that for the 2.83–28.3 m3

/s category, 

there is significant loss (with a coefficient of 0.34 +

0.00). For New England streams, in this 2.83-28.3 m3

/s 

category, the loss coefficient is not statistically 

significantly different from zero (0.05 + 0.29). 

Therefore, nitrogen loss was not included for streams 

with flows greater than 2.83 m3

/s in the New England 

nitrogen model. 

3. Results for nitrogen reservoir loss, however, is 

inconclusive. The New England reservoir coefficient 

(2.2 + 5.0) was not statistically significantly different 

from either zero or the coefficient for the national dataset 

of 5.3. This indicates a lack of data (monitoring sites) 

regarding reservoir loss of nitrogen in New England. 

This is an area where additional data-collection activities 

could be useful.
16 Estimation of Total Nitrogen and Phosphorus in New England Streams Using Spatially Referenced Regression Models

Phosphorus

Calibration and bootstrap results for the phosphorus New 

England SPARROW model are presented in table 4. Significant predictor variables include (1) phosphorus from permitted 

municipal and pulp and paper wastewater discharges, (2) area of 

forested land, (3) area of agricultural land, (4) the area of developed urban and suburban land, (5) a reservoir loss variable for 

small lakes and reservoirs with surface area less than 10 km2

, 

and (6) an exponential loss term for streams with flows less than 

or equal to 2.83 m3

/s (100 ft3/s). Parameter coefficient estimates and standard errors of the estimates are given in table 4. 

A comparison of the observations and model predictions for 

phosphorus is shown in figure 7. In general, the model results 

fit the observation load data, with a coefficient of determination 

(R2) of 0.94, and a mean-squared error of 0.23. For comparison, 

the national phosphorus SPARROW model had an R2 of 0.81 

and a mean-squared error of 0.71 (Smith and others, 1997). 

The p value for the reservoir loss variable was 0.096 in the 

calibration model, and 0.04 in the bootstrap model. These levels of significance, together with the initial coefficient and the 

bootstrap coefficient estimates being similar (109 and 105, 

respectively), provide justification for the inclusion of the reservoir loss as a predictor in reservoirs or lakes with surface 

areas less than 10 km2

. The p value for in-stream loss in small 

streams, with mean-annual flows less than or equal to 

2.83 m3/s (100 ft3/s), was 0.27 in the calibration model but was 

0.125 in the bootstrap model. Although statistically, this variable is only marginally significant (p = .125) in predicting phosphorus loads, further justification for inclusion is found in the 

coefficient estimates and in previous SPARROW model results. 

In previous SPARROW phosphorus models, phosphorus loss 

was significant in small rivers and streams (Smith and others, 

1997; McMahon and others, 2003). 

In the phosphorus model (table 4), the coefficient of 1.27 

for discharges from municipal wastewater-treatment facilities 

and pulp and paper discharges indicates that for each estimated 

kilogram of phosphorus discharged into the rivers at the wastewater-discharge locations, the model is predicting an average of 

1.27 (+ 0.22) kg of phosphorus at the monitoring stations. The 

coefficients for forested lands indicate that about 13.4 (+ 3.8) kg 

of phosphorus are estimated as entering streams for each square 

kilometer of forested land upstream per year. Likewise, the 

coefficients for agricultural lands indicate that about 108

(+ 26) kg of phosphorus are estimated as entering the river system for each square kilometer of agricultural land upstream per 

year. The coefficients for developed lands indicate that about 

38.9 (+ 13.7) kg of phosphorus are modeled as entering the river 

system for each square kilometer of developed land upstream 

per year. Unlike with nitrogen, there is no Connecticut HSPF 

phosphorus model with which to compare model coefficients.

None of the variables that were used to test for phosphorus 

loss on the landscape (such as soil permeability) were significant predictors of phosphorus loads (at either 85- or 95-percent 

confidence levels). It is presumed that the land-delivery losses 

are factored into the source coefficients for forested, agricultural, and developed land areas where phosphorus is applied or 

distributed to the land area. Percent wetland was the land-delivery factor that performed the best, but it had a p value greater 

than 0.60. 

The coefficients for reservoir and stream loss indicate that 

phosphorus is removed from small reservoirs and small streams 

(table 4). As with other studies, the reservoir loss coefficient of 

109 m/yr in the calibration model, quantifies the length of the 

water column from which nutrients are removed per unit of time 

by benthic processes, including the settling and burial of particulates (Alexander and others, 2002; Chapra, 1975; Molot and 

Dillon, 1993; Kelly and others, 1987). The coefficient of

0.48 d-1 for loss in small streams equates to a half-life of about 

1.5 days. This means that for each 1.5 days of transport in 

streams with flows less than 2.83 m3/s, about half of the phosphorus load is lost, most likely from sedimentation or biological 

processes. This coefficient of 0.48 can be compared to a coefficient of 0.27 (2.6-day half-life) from the national phosphorus 

model for streams less than 28.3 m3

/s (Smith and others, 1997); 

and to a coefficient of 11.2 from a New Zealand phosphorus 

model for streams less than 1 m3/s (1.5-hour half-life)

(Richard Alexander, written commun., 2003). 

Model Assumptions and Limitations

The SPARROW model is based on assumptions that 

define the form and context of a multiple regression analysis. 

These assumptions are (1) the functional form of the model is 

correct in terms of the variables included and their role in the 

model; (2) the error term is independent across the range of 

observations implying that there is no correlation in the errors 

among the monitored streams (Smith and others, 1997); (3) the 

residuals of the model are normally (or near normally) distributed; and (4) the residuals are homoscedastic; that is, the distribution of the residuals are similar throughout the range of predicted values. In addition, the bootstrap analysis is designed to 

provide robust coefficient estimates, model predictions, and 

prediction intervals in relation to the characteristics of both the 

model and sampling errors (Smith and others, 1997).

Preliminary analysis of the residuals for each model has 

been conducted. This analysis indicates that the residuals 

appear to be randomly distributed across the New England 

region with no spatial grouping of over- and under-predictions. 

But, statistically, the residuals are slightly positively skewed. 

Additional analyses of residuals as related to watershed characteristics and nutrient sources may help to define factors influencing the residuals. 

As with any model, there are strengths and weaknesses 

associated with the model and its results. Strengths of the New 

England SPARROW models are the high R2 and relatively 

good precision of most parameter coefficients obtained with the 

models. These results support the use of these models as waterquality-assessment tools. Other strengths of the models include 

the ability to provide regionally consistent characterizations of 

nutrient conditions and sources in streams, and the transport and
Spatially Referenced Regression Models for Nutrients in New England Streams 17

Table 4. Calibration results and bootstrap estimates for the New England SPARROW model for total phosphorus.

[kg/km2/yr, kilograms per kilometer squared per year; m/yr, meters per year; d-1, per day; km2, square kilometers; m3/s, cubic meters per second; ft3/s, cubic feet 

per second; R-squared = 0.94; mean-square error = 0.23]

Significant predictor variables

(coefficient units)

Calibration 

model 

coefficient

Standard error 

of coefficient

Bootstrap 

estimate of 

coefficient

Standard error 

of bootstrap 

coefficient

Sources:

Municipal wastewater-treatment facilities and pulp and paper facilities1 1.27 0.22 1.28 0.22

Forested land (kg/km2/yr) 13.4 3.8 12.7 4.1

Agricultural land (kg/km2

/yr) 108 25.7 110 27.5

Developed urban and suburban land (kg/km2/yr) 38.9 13.7 37.8 14.3

Loss variables:

Reservoir loss variable for small lakes and reservoirs2 (m/yr) 109 64.5 105 59.7

Stream loss for small streams3 .48 d-1 .43 .42 .41

4

Dimensionless.

5

Small lakes and reservoirs with surface area less than or equal to 10 km2.

6

Small streams with mean-annual flow less than or equal to 2.83 m3/s (100 ft3/s).

OBSERVATION

NATURAL LOG OF PHOSPHORUS LOAD, IN KILOGRAMS PER YEAR

PREDICTIONFROM MODEL

NATURAL LOG OF PHOSPHORUS LOAD, IN KILOGRAMS PER YEAR

4

5

6

7

8

9

10

11

12

13

14

15

4 5 6 7 8 9 10 11 12 13 14 15

Figure 7. Relation of predicted and observed total phosphorus load values from the calibration of the New England SPARROW model.
18 Estimation of Total Nitrogen and Phosphorus in New England Streams Using Spatially Referenced Regression Models

loss of nutrients within watersheds, and to show prediction or 

confidence intervals associated with these assessments. Previously, these forms of data have not been available for most New 

England stream reaches.

Weaknesses of the model and results can be linked to the 

modeling process and the data used to calibrate and provide predictions of nutrient conditions. Smith and others (1997) note 

that the SPARROW model structure inherently oversimplifies 

nutrient transport processes. Many factors locally and regionally affect the transport and loss of nutrients in streams, many 

of which cannot be accounted for in the SPARROW model. 

However, model results do indicate that certain transport processes are regionally important. Also, there are limitations with 

the data used in the modeling process. These limitations 

include the following:

1. The model requires long-term water-quality datasets that 

include multiple samples per year. Because of this 

requirement, the models only incorporate data from limited number of sites throughout the entire New England 

region. Load datasets, with a greater number of load sites 

than were used in the existing SPARROW models, may 

increase the ability to identify statistically significant 

explanatory variables.

2. Predictor variables may be coarse (such as land uses) or 

of relatively poor quality (such as point source loads). 

These data sets may introduce error in the ability of the 

model to explain and predict the effect of these data on 

stream water quality. Because of the regional nature of 

the model, only data that were available for the entire 

study area could be used. This restriction prevents the 

use of many locally more precise data or data that 

characterize other nutrient source or transport processes. 

3. Model results also have more uncertainty in smaller 

watersheds that tend to be further away from monitoring 

sites. This reflects a lack of monitoring data in New 

England for watersheds under 25-40 km2. (There are 

only 2 sites in the nitrogen and phosphorus datasets with 

watersheds less than 25 km2 and only 4 sites with 

watersheds less than 40 km2.)

4. Finally, the models only predict mean-annual conditions, 

not necessarily critical conditions such as low-flow 

conditions that may be of more concern to water-quality 

managers and scientists.

Model Estimates of Nutrient Loads

The calibrated SPARROW models allow for the prediction 

of nutrient loads for nearly 42,000 unmonitored stream reaches 

throughout New England. The spatial variability of nutrient 

loads is an important consideration for water-resources managers and planners in prioritizing areas for management actions. 

Nutrient loads are predicted by applying the SPARROW 

regression equation to each reach catchment. Starting at the 

headwater catchments, the regression equation is applied and 

predicted nutrient loads from that catchment are used as sources 

in the calculation of the load prediction for the next reach downstream. This process continues downstream until the terminal 

reach at the mouth of the river is encountered. Reach-level 

catchment predictions of nutrient loads obtained from SPARROW-model runs are shown in figures 8 and 9. Considerable 

spatial detail from the use of the NHD can be observed in the 

predicted results. These predictions represent source-load conditions from 1992-1993.

Several other deterministic and stochastic nutrient models 

have been used to estimate nutrient balances in New England 

watersheds. Although these studies have different time frames 

and use different techniques, they are available for comparison 

with the New England SPARROW model predictions. 

Nitrogen

The predicted nitrogen load generated by each of the 

42,000 reach-catchment areas is expressed as a nitrogen yield 

(delivered to the catchment outlet) by dividing the predicted 

load generated from within each catchment (including only 

sources from within the catchment) by the area of the catchment. (Thus, yields are loads normalized by area.) Median 

catchment yield of nitrogen for the entire study area is

336 kg/km2/yr with the 10- and 90-percent quantiles at 134 and 

782 kg/km2/yr, respectively. The relative contributions from 

the various source inputs are also predicted by the SPARROW 

model. The contributions from these sources that go into the 

catchment yield (fig. 8) are apparent by comparing predicted 

catchment yield with predicted yield from atmospheric deposition of nitrogen (fig. 9a); predicted developed-land nitrogen 

yield (fig. 9b); and predicted agricultural-land nitrogen yield 

(fig. 9c). Because discharge is localized and not a distributed 

yield, the permitted wastewater discharge is not shown in

figure 9. 

The primary, or largest, contributing nitrogen source for 

each catchment is identified in figure 9d. Catchments having 

permitted municipal wastewater discharge as the primary nitrogen source are also typically in the highest yield category of 

nitrogen shown in figure 8 (over 1,000 kg/km2/yr). These 

yields are especially high because the wastewater from a given 

sewer system is discharged to a single stream reach. 

For the entire model area, SPARROW estimates that 

86,100 metric tons (86.1 million kilograms) of nitrogen enter 

New England rivers and streams per year. Of this total, 50 percent (42,700 metric tons/year) is estimated to be from atmospheric deposition; 21 percent (18,000 metric tons/year) is estimated to be discharged from permitted municipal wastewater 

discharges; 15 percent (13,000 metric tons/year) is estimated to 

be from other developed land sources; and 14 percent

(12,400 metric tons/year) is estimated to be from agricultural 

lands. The large contributions of atmospheric deposition to 

nitrogen loads in New England is a major finding of the New 

England SPARROW model for nitrogen. Model estimates of
Model Estimates of Nutrient Loads 19

74 ̊

72 ̊

70 ̊

68 ̊

42 ̊

44 ̊

46 ̊

0 100 MILES 50

0 50 100 KILOMETERS

EXPLANATION

Total nitrogen yield, in kilograms 

 per square kilometer per year

 Less than 200

 200 to 300

 301 to 400

 401 to 1,000

 Greater than 1,000 

Base from U.S. Geological Survey

Digital line graph, 1:2,000,000 scale, 1990-94

Figure 8. Predicted total nitrogen catchment yield from the New England SPARROW model based on source loads from 

1992-93.
20 Estimation of Total Nitrogen and Phosphorus in New England Streams Using Spatially Referenced Regression Models 74o 72o 70o 68o 44o 42o 46o 0 100 MILES 50 0 50 100 KILOMETERS Base from U.S. Geological Survey Digital line graph, 1:2,000,000 scale, 1990-94 EXPLANATION Atmospheric deposition yield of nitrogen, in kilograms per square kilometer per year Less than 135 135 to 172 173 to 222 223 to 274 275 to 312 313 to 356 Greater than 356 74o 72o 70o 68o 44o 42o 46o A. B. EXPLANATION Developed land yield of nitrogen, in kilograms per square kilometer per year Less than 1 1 to 25 26 to 100 101 to 250 251 to 500 Greater than 500
Model Estimates of Nutrient Loads 21

74o

72o

70o

68o

42o

44o

46o

Base from U.S. Geological SurveyDigital line graph, 1:2,000,000 scale, 1990-94

EXPLANATION

Agricultural land-use yield of nitrogen, in kilograms per square kilometer per year Less than 1 1 to 29 30 to 72 73 to 197 198 to 335 Greater than 335

74o

72o

70o

68o

42o

44o

46o

C. D.

EXPLANATION

Primary sources of nitrogen Atmospheric Developed land Agricultural land Point source

0 100 MILES 500 50 100 KILOMETERS

Figure 9. Contribution predicted by the New England SPARROW model of total nitrogen catchment yield from (A) atmospheric deposition of nitrogen, (B) developed land areas, 

(C) agricultural land-use areas, and (D) primary sources of nitrogen loads in the model.
22 Estimation of Total Nitrogen and Phosphorus in New England Streams Using Spatially Referenced Regression Models

the nitrogen loads and the percentages related to the various 

sources by State are summarized in table 5. The SPARROW 

model estimates of nitrogen loads for 13 major basins in New 

England are summarized in table 6, along with the relative contributions by each State within each basin, and the percentages 

related to the various sources for each State.

There are several other deterministic and stochastic models that have been used to estimate nitrogen loads in New 

England basins. Although five of these models have different 

time frames and use different techniques, they can be compared 

with the New England SPARROW model predictions (table 7). 

These models include the (1) national SPARROW (Smith and 

others, 1997); (2) National Coastal Pollutant Discharge Inventory conducted by the National Oceanic and Atmospheric 

Administration (NOAA) (Percy A. Pacheco, NOAA, written 

commun., 1994); (3) Long Island Sound TMDL Study, an analysis to achieve water-quality standards for dissolved oxygen in 

Long Island Sound (New York Department of Environmental 

Conservation/Connecticut Department of Environmental Protection, 2000; Paul Stacey, Connecticut Bureau of Water Management, written commun., 2003); (4) HSPF deterministic 

model for the State of Connecticut (Paul Stacey, written commun., 2003); and (5) a regression model used to relate watershed characteristics to nutrient loads by Mullaney and others 

(2002). All of these compare nitrogen estimates at the mouth of 

selected rivers

Predictions are also available for comparison with a study 

of the anthropogenic nitrogen sources and relations to riverine 

nitrogen export in the Northeast (Boyer and others, 2002)

(table 8). These predictions, however, are for the farthest downstream USGS water-quality stations, and not at the mouth of the 

river. 

The New England SPARROW model predictions selected 

for major river basins (table 7) generally have an average of

+ 30 percent difference from those of other models presented in 

table 7, with a maximum difference of 127 percent for the 

Charles River in Massachusetts. The Charles River Basin is 

considered an outlier and was excluded from the average of

+ 30 percent. The national SPARROW model predicted more 

than twice (127 percent more) the nitrogen load that the New 

England SPARROW model predicted for the Charles River 

Basin. This is largely because the offshore municipal-wastewater discharge for metropolitan Boston is not considered part of 

the basin nitrogen load in the New England model. However, 

the national model includes this point source as part of the 

Charles River model prediction. When compared to the predictions from the model by Boyer and others (2002), the New 

England SPARROW model predictions have an average of

+ 35 percent of the other predictions, with a maximum difference (111 percent) at the Penobscot River water-quality station 

(table 8). The cause for this large difference is not known.

Phosphorus

Reach-level predictions of the phosphorus loadings by 

stream catchment are shown in figures 10 and 11. Median 

catchment yield of phosphorus for the entire study area is

17.6 kg/km2/yr with the 10- and 90-percent quantiles at 11.5 

and 41.0 kg/km2/yr, respectively. 

The relative contributions from the various source inputs 

are apparent by a comparison of figure 10 with its source components—predicted yield from forested areas (fig. 11a), predicted yield from developed areas (fig. 11b), and predicted yield 

from agricultural areas (fig. 11c). The permitted wastewater 

discharges are not shown because these are localized and not a 

distributed yield. The primary, or largest, contributing source 

for each catchment is shown in figure 11d. Catchments where 

discharges from permitted municipal and pulp and paper wastewater discharges are the primary source are identified in black 

in figure 11d. These are also catchments within the highest 

yield category shown in figure 10 (over 118 kg/km2 of phosphorus per year). 

For the entire model area, SPARROW estimates that

7,380 metric tons (7.38 million kilograms) of phosphorous 

enter New England rivers and streams per year. Of this amount, 

52 percent (3,860 metric tons/year) is estimated to be from permitted municipal and pulp and paper wastewater discharges;

Table 5. Summary of predicted nitrogen loads by state from the New England SPARROW model for total nitrogen.

[km2, square kilometers; values not adjusted for the stream loss downstream of the reach of nutrient origin]

State Drainage area

(km2

)

Total nitrogen 

(metric tons)

Predicted percent of nitrogen load from

Atmospheric 

deposition Agricultural lands Developed lands

Municipal 

wastewater

Maine 79,071 20,476 68 16 7 9

Massachusetts 19,402 20,481 32 6 25 37

New Hampshire 24,009 12,862 59 12 12 16

Connecticut 12,644 11,660 39 12 28 21

Vermont 23,565 11,420 55 30 6 10

Rhode Island 2,561 3,729 24 3 19 54
Model Estimates of Nutrient Loads 23

Table 6. Predicted nitrogen loads by major basin and state from the New England SPARROW model for total nitrogen.

[km2, square kilometers; values not adjusted for the stream loss downstream of the reach of nutrient origin]

River or lake basin

State/Province

Drainage area 

(km2

)

Total nitrogen 

(metric tons)

Predicted percent of nitrogen load from

Atmospheric 

deposition

Agricultural 

lands

Developed 

lands

Municipal 

wastewater

Connecticut: 29,172 18,489 49 14 14 23

Vermont 10,162 4,367 65 21 4 9

New Hampshire 7,941 3,568 66 16 7 12

Massachusetts 7,048 6,470 37 10 15 38

Connecticut 3,726 3,978 35 12 28 25

Quebec 294 96 65 30 4 0

Maine 1 0 100 0 0 0

Merrimack: 12,944 10,796 39 9 19 32

New Hampshire 9,840 6,250 52 12 15 20

Massachusetts 3,105 4,546 22 5 24 50

Lake Champlain: 19,212 9,851 51 32 6 11

Vermont 10,766 5,726 47 36 6 11

New York 7,102 3,518 60 22 4 14

Quebec 1,344 607 43 50 7 0

Providence: 2,251 4,913 15 3 14 68

Rhode Island 1,258 2,987 16 2 15 67

Massachusetts 993 1,913 18 4 14 65

Penobscot:

Maine 21,866 4,299 78 8 4 10

Kennebec (excluding Androscoggin):

Maine 15,320 4,552 65 18 5 12

Housatonic: 5,036 3,880 45 16 18 21

Connecticut 3,185 2,762 41 14 20 26

Massachusetts 1,294 816 53 17 18 11

New York 557 302 60 34 7 0

Androscoggin: 9,135 3,546 66 16 6 12

Maine 7,284 2,960 62 18 7 13

New Hampshire 1,851 585 87 3 2 8

Thames: 3,807 2,591 50 19 16 15

Connecticut 3,006 2,038 52 21 16 10

Massachusetts 644 490 39 10 17 34

Rhode Island 156 63 82 12 5 0
24 Estimation of Total Nitrogen and Phosphorus in New England Streams Using Spatially Referenced Regression Models

Saco: 4,397 1,981 73 13 6 8

Maine 2,148 1,088 63 18 9 11

New Hampshire 2,249 892 85 7 3 5

Piscataqua (Portsmouth Harbor): 2,608 1,802 46 13 20 21

New Hampshire 1,977 1,414 44 12 21 22

Maine 630 388 52 15 16 16

Taunton:

Massachusetts 1,392 1,646 31 4 30 36

Charles:

Massachusetts 767 844 31 5 44 21

Table 6. Predicted nitrogen loads by major basin and state from the New England SPARROW model for total nitrogen.—Continued

[km2, square kilometers; values not adjusted for the stream loss downstream of the reach of nutrient origin]

River or lake basin

State/Province

Drainage area 

(km2

)

Total nitrogen 

(metric tons)

Predicted percent of nitrogen load from

Atmospheric 

deposition

Agricultural 

lands

Developed 

lands

Municipal 

wastewater
Model Estimates of Nutrient Loads 25

Table 7. Comparison of predicted nitrogen loads from the New England SPARROW model with five other nitrogen-load prediction 

studies for selected major river basins in New England.

[Predictions are for the rivers at the mouth. NOAA, National Oceanic and Atmospheric Administration; HSPF, Hydrologic Simulation Program Fortran; 

--, no data available]

River basin

 Predicted nitrogen load 

(metric tons per year for entire basins)

New England 

SPARROW

National 

SPARROW1 NOAA2 Long Island 

Sound study3

Connecticut 

HSPF4 Mullaney5

Modeled years

1992-93 1987 1982 1991-95 1991-95 1988-98

Connecticut 16,215 18,550 -- 16,243 13,307 11,051

Merrimack 9,575 4,536 9,165 -- -- --

Kennebec (includes 

Androscoggin)

7,438 11,027 7,729 -- -- --

Providence 4,549 1,725 -- -- -- --

Penobscot 3,637 1,092 -- -- -- --

Housatonic 3,386 3,849 -- -- -- 1,996

Androscoggin 3,181 3,353 2,349 -- -- --

Thames 2,278 2,112 -- -- -- --

Winooski 1,219 2,018 -- -- -- --

Saco 1,710 1,970 1,003 -- -- --

Piscataqua 1,463 824 997 -- -- --

Taunton 1,342 691 -- -- -- --

Charles 723 1,641 -- -- -- --

Presumpscot 666 691 -- -- -- --

1

Smith and others, 1997.

2Percy A. Pacheco, National Oceanic and Atmospheric Administration, written commun., 1994.

3New York Department of Environmental Conservation/Connecticut Department of Environmental Protection, 2000; and Paul Stacey, Connecticut 

Bureau of Water Management, written commun., 2003.

4Paul Stacey, Connecticut Bureau of Water Management, written commun., 2003.

5

Mullaney and others, 2002.
26 Estimation of Total Nitrogen and Phosphorus in New England Streams Using Spatially Referenced Regression Models

Table 8. Comparison of predicted nitrogen loads from the New England SPARROW model with

the Boyer nitrogen-load prediction model for selected river basins in New England.

[Predictions are for the U.S. Geological Survey stream-gaging stations that are furthest downstream, not at the

mouth of the river.]

River basin Drainage area 

(km2

)

Predicted nitrogen load 

(metric tons per year)

Boyer and others 

(2002) New England SPARROW

Modeled years

1988-93 1992-93

Connecticut 25,019 13,460 12,786

Merrimack 12,005 5,990 7,922

Kennebec 13,994 4,660 3,502

Blackstone 1,077 1,228 1,690

Penobscot 20,109 6,374 3,014

Androscoggin 8,451 3,414 2,868

Saco 3,349 1,302 1,471

Charles 475 306 587

Table 9. Summary of predicted phosphorus loads by State from the New England SPARROW model for total phosphorus.

[km2, square kilometers; values not adjusted for the lake and reservoir and stream loss downstream of the reach of nutrient origin]

State Drainage area 

(km2

)

Total phosphorus 

(metric tons)

Predicted percent of phosphorus load from

Forested lands Agricultural lands Developed lands

Wastewater 

(municipal and

pulp and paper)

Maine 79,071 2,111 42 22 3 34

Massachusetts 19,402 1,604 11 9 10 71

Connecticut 12,644 1,495 7 10 7 76

Vermont 23,565 943 27 49 3 22

New Hampshire 24,009 853 32 20 5 43

Rhode Island 2,561 769 3 2 3 93

5 percent (391 metric tons/year) is estimated to be from other 

developed land sources; 19 percent (1,380 metric tons/year) is 

estimated to be from agricultural lands; and 24 percent

(1,750 metric tons/year) is estimated to be from forested lands. 

Phosphorus loads predicted for each state by the New England 

SPARROW model and the percentages related to the various 

sources are shown in table 9. SPARROW model estimates of 

phosphorus loads for 13 major basins in New England, the relative contributions by state within each major basin, and the 

percentages related to the various sources for each state are 

shown in table 10. 

Two other model studies for selected basins in New 

England are available for comparison of phosphorus load predictions from the New England SPARROW model (table 11). 

These models are (1) the national SPARROW (Smith and others, 1997), and (2) the National Coastal Pollutant Discharge 

Inventory conducted by NOAA (Percy A. Pacheco, written 

commun., 1994).
Model Estimates of Nutrient Loads 27

74 ̊

72 ̊

70 ̊

68 ̊

42 ̊

44 ̊

46 ̊

0 100 MILES 50

0 50 100 KILOMETERS

EXPLANATION

Total phosphorus yield, in kilograms 

per square kilometer per year

 Less than 13

 13 to 15

 16 to 21

 22 to 185

 Greater than 185

Base from U.S. Geological Survey

Digital line graph, 1:2,000,000 scale, 1990-94

Figure 10. Predicted total phosphorus catchment yield from the New England SPARROW model based on source loads 

from 1992-93.
28 Estimation of Total Nitrogen and Phosphorus in New England Streams Using Spatially Referenced Regression Models 74o 72o 70o 68o 42o 44o 46o Base from U.S. Geological Survey Digital line graph, 1:2,000,000 scale, 1990-94 EXPLANATION Forested land-use yield of phosphorus, in kilograms per square kilometer per year Less than 8.0 8.0 to 10.0 10.1 to 11.0 11.1 to 12.0 12.1 to 13.0 Greater than 13.0 74o 72o 70o 68o 44o 42o 46o A. B. EXPLANATION Developed land yield of phosphorus, in kilograms per square kilometer per year Less than 1.0 1.0 to 4.0 4.1 to 7.0 7.1 to 13.0 13.1 to 19.0 Greater than 19.0 0 100 MILES 50 0 50 100 KILOMETERS
Model Estimates of Nutrient Loads 29

EXPLANATION

Agricultural land-use yield of phosphorus, in kilograms per square kilometer per year Less than 5.0  5.1 to 13.0 13.1 to 24.0 24.1 to 40.0 40.1 to 63.0 Greater than 63.0

74o

72o

70o

68o

44o

42o

46o

Base from U.S. Geological SurveyDigital line graph, 1:2,000,000 scale, 1990-94

74o

72o

70o

68o

42o

44o

46o

C. D.

EXPLANATION

Primary sources of phosphorus Forest Agricultural land  Developed land Point source

0 100 MILES 500 50 100 KILOMETERS

Figure 11. Contribution predicted by the New England SPARROW model of total phosphorous catchment yield from (A) forested land-use areas, (B) developed land areas, (C) agricultural land-use areas, and (D) primary sources of phosphorus loads in the model.
30 Estimation of Total Nitrogen and Phosphorus in New England Streams Using Spatially Referenced Regression Models

Table 10. Predicted phosphorus loads by major basin and state from the New England SPARROW model for total phosphorus.

[km2, square kilometers; values not adjusted for the reservoir and stream loss downstream of the reach of nutrient origin]

River or lake basin

State/Province

Drainage area

(km2

)

Total 

phosphorus 

(metric tons)

Predicted percent of phosphorus load from

Forested lands Agricultural 

lands

Developed 

lands

Wastewater 

(municipal and

pulp and paper)

Connecticut: 29,172 1,790 18 17 4 61

Connecticut 3,726 662 4 7 5 83

Massachusetts 7,048 572 12 12 5 70

Vermont 10,162 310 39 38 2 21

New Hampshire 7,941 238 39 27 3 31

Quebec 295 8 44 53 2 0

Maine 1 0 99 1 0 0

Lake Champlain: 19,212 872 22 51 2 24

Vermont 10,766 535 19 56 3 22

New York 7,102 275 29 36 2 33

Quebec 1,344 62 19 78 3 0

Providence: 2,251 957 2 1 2 94

Rhode Island 1,258 700 2 1 2 95

Massachusetts 993 257 3 3 4 90

Merrimack: 12,944 840 16 12 7 65

Massachusetts 3105 424 6 6 8 81

New Hampshire 9,840 417 26 19 7 49

Penobscot:

Maine 21,866 617 41 9 1 49

Kennebec (excluding 

Androscoggin):

Maine 15,320 428 39 28 2 30

Housatonic: 5,036 407 12 19 6 64

Connecticut 3,185 323 9 14 6 71

Massachusetts 1,294 64 20 26 8 46

New York 557 20 29 67 4 0

Androscoggin: 9,135 394 27 15 2 56

Maine 7,284 341 24 17 2 57

New Hampshire 1,851 53 45 3 1 51

Thames: 3,807 240 15 22 6 57

Connecticut 3,006 203 14 22 5 59

Massachusetts 644 32 18 19 9 53

Rhode Island 156 3 64 32 4 0

Piscataqua (Portsmouth Harbor): 2,611 117 22 19 9 49

New Hampshire 1,977 92 21 18 9 51

Maine 630 25 27 23 8 43
Model Estimates of Nutrient Loads 31

Table 11. Comparisons of predicted phosphorus loads from the New England SPARROW model with

predictions from other studies for selected major river basins in New England.

[Predictions are for the rivers at the mouth. NOAA, National Oceanic and Atmospheric Administration; --, no data available]

River basin

Predicted phosphorus load

(metric tons per year for entire basins)

New England SPARROW National SPARROW1 NOAA2

Modeled years

1992-93 1987 1982

Connecticut 1,510 1,091 --

Merrimack 789 339 1,477

Kennebec (includes the Androscoggin) 530 447 523

Providence 295 314 --

Penobscot 443 474 --

Housatonic 331 227 --

Androscoggin 271 128 253

Thames 170 133 --

Taunton 37 115 --

Saco 88 77 131

Charles 13.5 392 --

Piscataqua 72 121 336

Presumpscot 66 45 --

Winooski 102 89 --

6Smith and others, 1997.

7Percey A. Pacheco, National Oceanic and Atmospheric Administration, written commun., 1994.

Saco: 4,397 107 49 23 3 25

Maine 2,148 65 37 29 4 30

New Hampshire 2,249 43 67 13 2 18

Taunton:

Massachusetts 1,393 86 13 7 16 64

Charles:

Massachusetts 767 26 20 14 46 20

Table 10. Predicted phosphorus loads by major basin and state from the New England SPARROW model for total phosphorus.

—Continued

[km2, square kilometers; values not adjusted for the reservoir and stream loss downstream of the reach of nutrient origin]

River or lake basin

State/Province

Drainage area

(km2

)

Total 

phosphorus 

(metric tons)

Predicted percent of phosphorus load from

Forested lands Agricultural 

lands

Developed 

lands

Wastewater 

(municipal and

pulp and paper)
32 Estimation of Total Nitrogen and Phosphorus in New England Streams Using Spatially Referenced Regression Models

The New England SPARROW phosphorus model predictions have an average of + 43 percent difference from that of the 

national SPARROW model predictions, with a maximum difference of 211 percent for the Taunton River Basin, and have an 

average of + 88 percent difference from the NOAA predictions, 

with a maximum difference of 367 percent for the Piscataqua 

River Basin (table 11). As with nitrogen, comparisons for the 

Charles River Basin are not valid because the offshore municipal-wastewater discharge for metropolitan Boston is excluded 

from the basin in the New England SPARROW model but 

included in the national SPARROW model prediction. Phosphorus loads estimated by NOAA are higher in three of the five 

basins compared. These higher estimates may be due to higher 

phosphorus concentrations in New England streams in the 

1970s and 1980s (Robinson and others, 2003).

Use of SPARROW Model Results in WaterResources Management

The SPARROW models can be used by water-resources 

managers as tools in water-quality assessment and management 

activities such as TMDL studies, nutrient-criteria development, 

and determination of nutrient loadings to coastal waters. Examples of how SPARROW model results can be used for these 

specific water-quality activities are provided. 

Determining Sources and Transport of Nutrient Loads

SPARROW model results can increase understanding of 

nutrient transport, load distributions, and relative effects of various nutrient sources in large river basins that are difficult and 

costly to model with deterministic models. This ability to estimate contaminant loads relative to watershed characteristics, 

complete with statistical estimates of the error, can be an important tool for TMDL studies. 

Nitrogen-model results for the Connecticut River Basin 

serve as an example of how SPARROW results are useful for 

TMDL studies. The SPARROW model provides an estimation 

of the nitrogen loading delivered from any selected stream 

reach to the mouth of the river. For the Connecticut River 

Basin, this information can be used in estimating the total nitrogen contributions to Long Island Sound from any location in the 

entire basin. SPARROW results from just two reaches, the 

mouth of the Connecticut River where it enters Long Island 

Sound, and the reach where the Connecticut River leaves New 

Hampshire and Vermont, indicate that 41 percent of the nitrogen load entering Long Island Sound originated upstream of the 

point where the Connecticut River leaves New Hampshire and 

Vermont (fig. 12). SPARROW results also indicate that, of the 

nitrogen load in the Connecticut River leaving New Hampshire 

and Vermont, 11 percent is from municipal wastewater-treatment facilities; 6 percent is from developed land; 20 percent is 

from agricultural lands; and the remaining 63 percent is from 

atmospheric deposition. The model shows no statistically significant loss of nitrogen load, on an annual basis, as the load is 

transported down the Connecticut River from New Hampshire 

and Vermont to Long Island Sound. Nitrogen loss is only 

observed in small streams.

Determining Nutrient Concentrations

Currently (2004), the USEPA (1998a, 2000a) is developing nutrient (nitrogen and phosphorus) concentration criteria for 

rivers, lakes, and estuaries. The USEPA is identifying which 

streams, rivers, and other waterbodies have nutrient levels causing water-quality impairment, determining what concentrations 

cause impairment, and then relating these levels to management 

actions to improve water-quality conditions. SPARROW 

model results can provide information on the estimated nutrient 

concentrations throughout the New England region. A meanannual, flow-weighted concentration (in milligrams per liter) is 

derived from the mean-annual loads predicted by the SPARROW model (converted to milligrams per year) divided by the 

mean-annual flows (estimated as a SPARROW input dataset 

and converted to liters per year). The SPARROW-predicted 

mean-annual flow-weighted concentrations (in milligrams per 

liter) for nitrogen are shown in figure 13a and for phosphorus in 

figure 13b. Although these concentrations do not represent the 

variability of nutrient concentrations throughout the year, these 

predictions can be used as a guide for water-resource managers 

to set priorities. McMahon and others (2003) demonstrated for 

watersheds in North Carolina how SPARROW-predicted concentrations can be used in conjunction with the associated errors 

of the predictions to determine probability of exceeding (on an 

annual basis) threshold concentrations of interest for water 

management.

The USEPA is developing nutrient criteria specific to 

ecoregions or areas suspected of having similar natural or reference nitrogen and phosphorus levels based on geology, vegetation, and land uses (U.S. Environmental Protection Agency, 

1999). Reference levels are defined as nutrient concentrations 

in stream reaches having little or no nutrient contributions from 

urban or agricultural sources. The five ecoregions in the model 

area are shown in figure 14a along with the cumulative distribution of the SPARROW-predicted mean-annual flow-weighted 

concentrations by ecoregion for nitrogen (fig. 14b) and for 

phosphorus (fig. 14c). The Laurentian Plains and the Northeast 

Highlands have low median concentrations of nitrogen (0.26 

and 0.48 mg/L, respectively) compared to the Eastern Great 

Lakes and Hudson Lowlands ecoregion surrounding Lake 

Champlain (0.88 mg/L). The median concentration of

1.32 mg/L for the Atlantic Coastal Pine Barrens (fig. 14b) is 

especially high because of the effective delivery of the nutrients 

to the streams associated with the high soil permeability. For 

the Laurentian Plains, the low nitrogen concentrations are the 

result of less atmospheric deposition of nitrogen. In the Eastern 

Great Lakes and Hudson Lowlands ecoregion, average concentrations of phosphorus (fig. 14c) are higher than in the other
Use of SPARROW Model Results in Water-Resources Management 33

41 percent

59 percent

EXPLANATION

Predicted total nitrogen 

 loads to Long Island Sound

 New Hampshire- 

 Vermont

 Massachusetts-

 Connecticut

EXPLANATION

Primary sources of nitrogen 

 in the Connecticut River 

 as it leaves New Hampshire

 and Vermont

 Atmospheric 

 Developed land

 Agricultural land

 

 Point source 20 percent

Connecticut River

Atlantic Ocean

Long Island Sound

63 percent

11 percent

6 percent

72 ̊

42 ̊

44 ̊

0 100 MILES 50

0 50 100 KILOMETERS

EXPLANATION

 Connecticut River Basin

Base from U.S. Geological Survey

Digital line graph, 1:2,000,000 scale, 1990-94

National Hydrography Dataset, 1:100,000 scale, 2002

Maine

Vermont

New Hampshire

Massachusestts

Connecticut

New York

Rhode

Island

Canada

Figure 12. Example from the Connecticut River Basin of total maximum daily load applications of the results from the New 

England SPARROW model for total nitrogen.
34 Estimation of Total Nitrogen and Phosphorus in New England Streams Using Spatially Referenced Regression Models 74o 72o 70o 68o 42o 44o 46o Base from U.S. Geological Survey Digital line graph, 1:2,000,000 scale, 1990-94 EXPLANATION Total nitrogen mean-annual concentration, in milligrams per liter per year Less than 0.25 0.25 to 0.50 0.51 to 0.65 0.66 to 1.50 Greater than 1.50 74o 72o 70o 68o 42o 44o 46o A. B. EXPLANATION Total phosphorus mean-annual concentration, in milligrams per liter per year Less than 0.015 0.015 to 0.020 0.021 to 0.035 0.036 to 0.075 Greater than 0.075 0 100 MILES 50 0 50 100 KILOMETERS Figure 13. New England SPARROW model mean-annual flow-weighted concentration predictions of (A) nitrogen and (B) phosphorus.
Use of SPARROW Model Results in Water-Resources Management 35

74 ̊

72 ̊

70 ̊

68 ̊

42 ̊

44 ̊

46 ̊

0 100 MILES 50

0 50 100 KILOMETERS

EXPLANATION

Ecoregion

 Northeast Highlands

 Northeast Coastal Zone

 Laurentian Plains

 Hudson Lowlands and Eastern Great Lakes

 Atlantic Coastal Pine Barrens

Base from U.S. Geological Survey

Digital line graph, 1:2,000,000 scale, 1990-94

0 0.2 0.4 0.6

1.00

0.75

0.50

0.25

CUMULATIVE FREQUENCY

0

PHOSPHORUS CONCENTRATION BY ECOREGION,

IN MILLIGRAMS PER LITER

C.

0123

1.00

0.75

0.50

0.25

CUMULATIVE FREQUENCY

0

NITROGEN CONCENTRATION BY ECOREGION,

IN MILLIGRAMS PER LITER

B.

NITROGEN MEAN ANNUAL CONCENTRATION 

BY ECOREGION, IN MILLIGRAMS PER LITER

Quantile, Ecoregion

 in percent

 90 0.49 0.79 1.74 1.48 2.46

 75 0.36 0.63 1.15 1.17 1.86

 50 (median) 0.26 0.48 0.80 0.88 1.32

 25 0.20 0.32 0.61 0.68 0.94

 10 0.16 0.22 0.51 0.56 0.78

PHOSPHORUS MEAN ANNUAL CONCENTRATION 

BY ECOREGION, IN MILLIGRAMS PER LITER

Quantile, Ecoregion

 in percent

 90 0.049 0.044 0.051 0.065 0.205

 75 0.033 0.034 0.035 0.048 0.133

 50 (median) 0.023 0.025 0.025 0.036 0.089

 25 0.017 0.020 0.020 0.028 0.051

 10 0.013 0.018 0.017 0.023 0.036

A.

Figure 14. Ecoregions (A) identified by U.S. Environmental Protection Agency for nutrient-criteria management activities. 

Cumulative frequency diagrams and tables for SPARROW-predicted total mean-annual flow-weighted (B) nitrogen and (C) 

phosphorus concentrations by ecoregion.
36 Estimation of Total Nitrogen and Phosphorus in New England Streams Using Spatially Referenced Regression Models

ecoregions. Median phosphorus concentration for this ecoregion is 0.089 mg/L, which compares to a median low concentration of 0.023 mg/L for the Laurentian Plains (fig. 14c). These 

high concentrations of phosphorus for the Eastern Great Lakes 

and Hudson Lowlands are partly the result of agricultural activity in the Lake Champlain Basin.

SPARROW-predicted reference levels can be also examined by selecting a subset of the predicted nutrient concentrations. A subset was selected for the entire model area and for 

each ecoregion (tables 12 and 13). Data presented in these 

tables were developed by use of a selection criteria that also has 

been used by the USEPA Nutrient Criteria program for defining 

reference levels (Matthew Liebman, U.S. Environmental Protection Agency, written commun., 2003); these criteria include 

stream reaches with (1) drainage areas with less than 1 percent 

developed land, (2) drainage areas with less than 5 percent agricultural land use, and (3) drainage areas with population densities less than 20 humans per square mile. When all three conditions are met, then the stream reach was selected as representing 

relatively undeveloped reference conditions. No stream 

reaches in the Atlantic Coastal Pine Barrens ecoregion met 

these criteria.

Nitrogen reference levels vary widely depending on the 

ecoregion. The effects of atmospheric deposition of nitrogen 

contribute to this variability. Phosphorus reference levels, however, are remarkably similar between ecoregions, except in the 

Hudson Lowlands and Eastern Great Lakes ecoregion, which 

has higher concentrations than the reference stream reaches in 

the other ecoregions. This exception, however, may be a result 

of the small number of stream reaches (10) in that ecoregion 

that meet the criteria for reference conditions.

Streams can also be categorized as small, wadeable (potentially periphyton-dominated), and large (phytoplankton-dominated) streams. A mean-annual streamflow of 2.83 m3/s can be 

used as an approximation of this division between small and 

large streams. The statistical distributions of the predicted 

nitrogen concentrations of these two stream categories shows 

less than a 15-percent difference between quantiles (table 14). 

However, for phosphorus, the statistical distributions of the predicted concentrations of these two stream categories show differences. Although, both large and small streams have similar 

median concentrations of 0.27 or 0.28 mg/L of phosphorus, the 

10-percent quantile concentration for large streams is 47 percent lower than in the small streams, and the 90-percent quantile 

concentration for large streams is 29 percent higher than in the 

small streams.

Table 13. Distribution of New England SPARROW model predictions of phosphorus concentrations for undeveloped

reference reaches.

[Reach predictions, in milligrams per liter total phosphorus; column: A, entire study area; B, Northeast Highlands; C, Laurentian Plains; 

D, Northeast Coastal Zone; E, Hudson Lowlands and Eastern Great Lakes]

Quantile 

(percent)

Predicted phosphorus concentration in reference reach

ABCDE

Number of reaches 12,504 7,816 4,672 6 10

90 0.025 0.025 0.025 0.022 0.052

75 .023 .023 .022 .021 .047

50 .020 .020 .019 .020 .038

25 .017 .017 .015 .018 .035

10 .013 .015 .009 .018 .028

Table 12. Distribution of New England SPARROW model predictions of nitrogen concentrations for undeveloped

reference reaches.

[Reach predictions, in milligrams per liter total nitrogen; column: A, entire study area; B, Northeast Highlands; C, Laurentian Plains; 

D, Northeast Coastal Zone; E, Hudson Lowlands and Eastern Great Lakes]

Quantile 

(percent)

Predicted nitrogen concentration in reference reach

ABCDE

Number of reaches 12,504 7,816 4,672 6 10

90 0.46 0.51 0.28 0.47 0.82

75 .34 .40 .24 .47 .80

50 .25 .30 .20 .46 .63

25 .20 .22 .17 .45 .54

10 .16 .19 .14 .36 .38
Summary 37

Determining Nutrient Loads Delivered to Coastal 

Waters

The transport of nitrogen from freshwaters to coastal 

waters has resulted in environmental concerns, such as eutrophication and depletion of oxygen, in coastal ecosystems (New 

York Department of Environmental Conservation/Connecticut 

Department of Environmental Protection, 2000). Because of 

the significance and complexity of the nutrient-enrichment 

problems within coastal waters, an active area of scientific 

research has emerged and nationwide strategies to assess waterquality conditions and management options are under consideration (National Research Council, 2000). The New England 

SPARROW model provides estimates of mean-annual nutrient 

loadings to coastal waters (fig. 15). This information can help 

identify the relative contributions of different river basins to 

nutrient loads to the coast and where potential eutrophication 

may occur. Estimated nitrogen loads to the coast are greatest 

from the Connecticut, Merrimack, and Kennebec Rivers, which 

is partly related to their large drainage size. Large annual nitrogen loads from the Connecticut, Providence, and the Housatonic Rivers make Long Island Sound especially vulnerable to 

nitrogen enrichment and eutrophication (New York Department 

of Environmental Conservation/Connecticut Department of 

Environmental Protection, 2000).

Summary

Excessive nutrient (nitrogen and phosphorus) concentrations in water can potentially affect human health and the health 

of aquatic ecosystems. Although nitrogen and phosphorus are 

essential for healthy plant and animal life, elevated concentrations of these nutrients can degrade water quality or cause 

human health problems. Managing and reducing nutrient loads 

to rivers has been a major activity under the Clean Water Act 

since the 1970s. Currently (2004), the U.S. Environmental

Protection Agency (USEPA) has two major programs to help 

address nutrient management. One program is the Nutrient

Criteria Program, which is designed to develop nutrientconcentration criteria for rivers, lakes, and estuaries. The other 

program is the Total Maximum Daily Load (TMDL) program, 

which attempts to understand and manage nutrient loads that 

result in designated-use impairment. To provide analysis that 

can help water-resources managers with these efforts, the U.S. 

Geological Survey, in cooperation with the USEPA and the 

New England Interstate Water Pollution Control Commission, 

has developed water-quality models called the New England 

SPARROW (Spatially Referenced Regressions on Watershed 

Attributes) models. 

SPARROW is a spatially detailed, statistical model that 

uses regression equations to relate total nitrogen and phosphorus (nutrient) stream loads to nutrient sources and watershed 

characteristics. These statistical relations are then used to predict nutrient loads in unmonitored streams. The study area for 

the New England SPARROW models for total nitrogen and 

total phosphorus includes river basins that drain to Long Island 

Sound, the Gulf of Maine, Lake Champlain, and the New 

England parts of the Hudson and St. Francois River Basins. The 

area includes 172,000 km2

 and covers all of New Hampshire, 

Vermont, Massachusetts, Connecticut, Rhode Island, most of 

Maine, and parts of New York and Canada. 

The New England SPARROW models are based on a 

hydrologic network of 42,000 stream reaches and associated 

watersheds. The hydrologic network used was primarily the 

National Hydrography Dataset (NHD) at a scale of 1:100,000 

(Canadian streams had to be added). Watershed boundaries are 

defined for each stream reach in the network through the use of 

a digital elevation model and available digitized watershed 

divides. Nutrient-source data are from permitted wastewaterdischarge data, from USEPA’s Permit Compliance System 

(PCS), various land-use sources, and atmospheric deposition. 

The dependent variables in the SPARROW models are instream total nitrogen and total phosphorous loads. The loads 

were estimated from stream discharge and water-quality data 

collected at monitoring locations throughout the study area by a 

variety of agencies and researchers. The required streamTable 14. New England SPARROW model predictions of nitrogen concentrations for small and large streams.

[Concentrations are in milligrams per liter. Small streams are defined as having flows less than 2.83 cubic meters per second and large streams are defined as having flows greater than or equal to 2.83 cubic meters per second]

Quantile 

(percent)

Predicted nitrogen concentration

Small streams Large streams

90 1.12 1.01

75 .74 .69

50 .52 .47

25 .31 .27

10 .21 .18

Table 15. New England SPARROW model predictions of phosphorus concentrations for small and large streams.

[Concentrations are in milligrams per liter. Small streams are defined as having flows less than 100 cubic meters per second and large streams are defined 

as having flows greater than or equal to 100 cubic meters per second]

Quantile 

(percent)

Predicted phosphorus concentration

Small streams Large streams

90 0.056 0.072

75 .040 .046

50 .028 .027

25 .021 .016

10 .017 .009
38 Estimation of Total Nitrogen and Phosphorus in New England Streams Using Spatially Referenced Regression Models

74 ̊

72 ̊

68 ̊

42 ̊

44 ̊

0 100 MILES 50

0 50 100 KILOMETERS

Base from U.S. Geological Survey

Digital line graph, 1:2,000,000 scale, 1990-94

National Hydrography Dataset, 1:24,000 scale, 2002

EXPLANATION

Nitrogen load sites, 

 in metric tons per year

 30 to 100

 101 to 250

 251 to 1,000

 1,010 to 3,000

 3,010 to 8,000

 8,010 to 16,200

Connecticut River

Thames River

Housatonic River

Providence Rive

Blackstone/

r

Taunton River

Charles

River

Atlantic Ocean

Merrimack River

Saco River

Presumpscot River

Androscoggin River Kennebec River

Penobscot River

New

Hampshire

Vermont

Massachusetts

Maine

Connecticut

Rhode

Island

New

York

Nitrogen load predicted by the New England SPARROW model

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

NITROGEN LOAD, 

IN METRIC TONS PER YEAR

RIVER BASIN

CONNECTICUT

MERRIMACK

KENNEBEC (INCLUDES ANDROSCOGGIN)

PROVIDENCE/BLACKSTONE

PENOBSCOT

HOUSATONIC

ANDROSCOGGIN

THAMES

TAUNTON

SACO

CHARLES

PRESUMPSCOT

18,000

Figure 15. Nitrogen loads to the New England coast predicted by the New England SPARROW model.
Summary 39

loading data for inclusion in the SPARROW models were available from 65 total nitrogen and 67 total phosphorus sites. 

Predictor variables of total nitrogen loads in streams 

include (1) atmospheric deposition of total nitrogen, (2) nitrogen loadings from permitted wastewater discharges (EPA estimates for municipal wastewater-treatment facilities), (3) area of 

agricultural land, and (4) the area of developed land. In general, 

the model results fit the observation load data as indicated by a 

coefficient of determination (R2

) of 0.95, and a mean-squared 

error of 0.16. To estimate prediction intervals, a bootstrap analysis was conducted. 

For the entire model area, SPARROW estimates that 

86,100 metric tons (86.1 million kilograms) of total nitrogen 

enters New England rivers and streams per year based on data 

from 1992 to 1993. Fifty percent (42,700 metric tons/year) is 

estimated to be from atmospheric deposition; 21 percent 

(18,000 metric tons/year) is estimated to be discharged from 

municipal wastewater-treatment facilities; 15 percent

(13,000 metric tons/year) is estimated to be generated from 

other developed land sources; and 14 percent (12,400 metric 

tons/year) is estimated to be generated from agricultural lands. 

The coefficient for nitrogen stream loss indicates that 

nitrogen is removed from the streams with mean-annual flows 

less than or equal to 2.83 m3

/s. About 86 percent of the stream 

reaches in New England streams modeled with SPARROW 

have mean-annual flows less than or equal to 2.83 m3

/s. Presumably, the ability to identify this loss in small streams was 

enhanced by using a detailed stream network. The coefficient 

of 0.77 from the bootstrap model is equivalent to a half-life of 

about 0.9 days.

An important model result was a lack of statistically significant annual modeled attenuation of nitrogen for larger streams 

with flows greater than 2.83 m3/s and for reservoirs. This finding is contrary to the findings of the national and other regional 

SPARROW models developed to date. To determine how the 

estimates for nitrogen in the New England and national SPARROW models differ for streams in New England, a direct comparison between the nitrogen model coefficients was made by 

applying a nested model. In the nested model, the New England 

data was run simultaneously with the national data to allow 

direct comparison of national and New England specific model 

coefficients. Conclusions reached from nesting the New 

England model within the national model are (1) for streams in 

New England with flows less than 2.83 m3/s, the nitrogen loss 

is higher than that of the national model stream reaches (0.8 d-1

as opposed to 0.3 d-1 for the national model stream reaches outside New England); (2) for streams in New England with flows 

greater than 2.83 m3/s (grouped as a whole), the nitrogen loss 

on an annual basis is negligible at a 90-percent confidence level; 

and (3) there is a lack of data regarding reservoir loss of nitrogen in New England. 

Significant predictor variables of total phosphorus loads in 

streams were found to include (1) phosphorus from wastewater 

discharges (USEPA estimates for permitted municipal and pulp 

and paper wastewater discharges), (2) area of forested land,

(3) area of agricultural land, (4) area of developed land, (5) a 

reservoir loss variable for small reservoirs less than 10 km2

 in 

surface area, and (6) a stream loss variable for streams with 

flows less than or equal to 2.83 m3

/s. 

In general, the model results fit the phosphorus observation load data, as indicated by an R2

 of 0.94 and a mean-squared 

error of 0.23. The bootstrap coefficients for reservoir and 

stream loss indicate that phosphorus is removed within the 

smaller reservoirs and streams. The coefficient of 0.48, for the 

stream loss variable for small streams from the bootstrap model, 

is equivalent to a half-life of about 1.5 days.

For the entire model area, SPARROW estimates that

7,380 metric tons (7.38 million kilograms) of total phosphorous 

enter New England rivers and streams per year. Of this amount, 

52 percent (3,860 metric tons/year) is estimated to be discharged from municipal wastewater-treatment facilities or the 

paper industry; 5 percent (391 metric tons/year) is estimated to 

be from other developed land sources; 19 percent (1,380 metric 

tons/year) is estimated to be from agricultural lands; and 24 percent (1,750 metric tons/year) is estimated to be from forested 

lands.

As with any model, the New England SPARROW models 

have strengths and weaknesses. Strengths of the New England 

SPARROW models include the high R2 values and relatively 

good precision of most parameter coefficients. Other strengths 

include (1) the ability to provide regionally consistent characterizations of nutrient conditions and sources of the nutrients in 

streams, (2) to characterize the transport and loss of nutrients 

within watersheds, and (3) to show prediction intervals associated with nutrient load estimates. Weaknesses of the models 

include (1) the models only incorporate monitored-load data 

from limited number of sites with long-term data; (2) predictor 

variables may be coarse (such as land uses) or of relatively poor 

quality (such as point source loads); and (3) the models only 

predict mean-annual conditions, not necessarily critical conditions such as low-flow conditions.

There are several other deterministic and stochastic models that have been used to estimate nitrogen loads in New 

England basins. Although five of these models have different 

time frames and use different techniques, they can be compared 

with the New England SPARROW model predictions. Excluding one outlier basin (Charles River), the New England Basins 

SPARROW model predictions have an average of + 30 percent 

of the other model predictions, with a maximum difference of 

70 percent. For phosphorus, there are only two other model 

studies available for comparison. Excluding the Charles River 

Basin, the New England SPARROW phosphorus model predictions have an average of + 43 percent of the national SPARROW model predictions (with a maximum difference of

211 percent for the Taunton River Basin) and are within an 

average of + 88 percent of the NOAA predictions (with a maximum difference of 367 percent for the Piscataqua River Basin). 

Comparisons for the Charles River Basin are not valid because 

the offshore municipal wastewater discharge for metropolitan 

Boston is excluded from the basin in the New England SPARROW model but included in the basin in the national SPARROW model. 
40 Estimation of Total Nitrogen and Phosphorus in New England Streams Using Spatially Referenced Regression Models

The SPARROW models can be used as tools by waterresources managers in water-quality assessment and management activities such as TMDL studies, nutrient-criteria development, and nutrient loadings to coastal waters. The ability to 

estimate contaminant loads relative to watershed characteristics, complete with statistical estimates of the error involved, 

can be an important tool available to the TMDL program. 

Nitrogen-model results for the Connecticut River Basin serve as 

an example of how SPARROW results are useful in assessing 

the contributions to Long Island Sound from any location in the 

entire watershed. SPARROW results provide an estimate that 

41 percent of the total nitrogen load entering Long Island Sound 

originated upstream of the point where the Connecticut River 

leaves New Hampshire and Vermont. Further, SPARROW 

estimates also indicate that, of the load leaving New Hampshire 

and Vermont, 11 percent is from municipal wastewater-treatment facilities, 6 percent is from developed land, 20 percent is 

from agricultural lands, and the remaining 63 percent is from 

atmospheric deposition. 

SPARROW results provide useful information relative to 

nutrient-criteria goals. The mean flow-weighted concentrations 

can be computed from the annual loads (total load at the downstream end of each stream reach, predicted by SPARROW) 

divided by the mean-annual flows. Model results do not show 

the variability of concentrations throughout the year; however, 

these predictions can be used as a guide for water-resources 

managers to identify management priorities. Nitrogen concentrations for the Laurentian Plains and the Northeast Highlands 

have, on average, lower concentrations of nitrogen than do the 

other ecoregions, and the Atlantic Coastal Pine Barrens has the 

highest concentrations. For the Laurentian Plains, the low 

nitrogen concentrations can be attributed to less atmospheric 

deposition of nitrogen because the ecoregion is farther away 

from sources in the industrial Midwest United States. The Eastern Great Lakes and Hudson Lowlands ecoregion (surrounding 

Lake Champlain) appear to have high concentrations of phosphorus, which is partially the result of intense agricultural activity in the Lake Champlain Basin.

The large estimated contributions of atmospheric deposition to total nitrogen loads in New England is a major finding of 

this New England SPARROW modeling effort. For the entire 

study area, the model results indicate that 50 percent of the 

nitrogen loads come from atmospheric deposition. The percentage increased for western parts of the model area; SPARROW 

results indicate that 63 percent of the nitrogen load leaving New 

Hampshire and Vermont from the Connecticut River is from 

atmospheric deposition. 

A product of the New England SPARROW models is the 

estimation of the nutrient loading delivered from each stream 

reach to the mouth of the river. This information can be used in 

estimating the nutrient contributions to estuaries and the ocean 

from upstream sources. SPARROW model results have been 

used to estimate the total nitrogen loads to New England coastal 

waters. This information can help estimate the relative contributions of different river basins of nutrient loads to the coast and 

can help identify where potential eutrophication may occur.

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