Prepared in cooperation with the Massachusetts Department of Environmental Protection

Nutrient and Metal Loads Estimated by Using Discrete, 

Automated, and Continuous Water-Quality Monitoring 

Techniques for the Blackstone River at the 

Massachusetts-Rhode Island State Line, 

Water Years 2013–14

0

200

400

600

800

1,000

1,200

0.01

0.10

1.00

Total phosphorus concentration, in milligrams per liter

Flow, in cubic feet per second

14-day total P concentration

Discrete total P concentration

Estimated total P concentration

Flow

12/22/2013

12/23/2013

12/24/2013

12/25/2013

12/26/2013

12/27/2013

12/28/2013

12/29/2013

12/30/2013

12/31/2013

01/01/2014

01/02/2014

01/03/2014

EXPLANATION

Date

Scientific Investigations Report 2017–5094

U.S. Department of the Interior

U.S. Geological Survey
Cover. Monitoring station on the Blackstone River at Millville, Massachusetts, in winter 2014.

Banner photograph: Panoramic shot of the Blackstone River at Millville, Massachusetts, station (01111230). 

Graph: Figure 9 from this report. 

Back cover photograph: Blackstone River, looking downstream from the railroad bridge about 400 feet upstream from the 

Blackstone River at Millville, Massachusetts, station (01111230). Photographs by Jason Sorenson, U.S. Geological Survey.
Nutrient and Metal Loads Estimated 

by Using Discrete, Automated, and 

Continuous Water-Quality Monitoring 

Techniques for the Blackstone River at the 

Massachusetts-Rhode Island State Line, 

Water Years 2013–14

By Jason R. Sorenson, Gregory E. Granato, and Kirk P. Smith

Prepared in cooperation with the 

Massachusetts Department of Environmental Protection

Scientific Investigations Report 2017–5094

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

RYAN K. ZINKE, Secretary

U.S. Geological Survey

William H. Werkheiser, Deputy Director

 exercising the authority of the Director

U.S. Geological Survey, Reston, Virginia: 2018

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Suggested citation:

Sorenson, J.R., Granato, G.E., and Smith, K.P., 2018, Nutrient and metal loads estimated by using discrete, automated, 

and continuous water-quality monitoring techniques for the Blackstone River at the Massachusetts-Rhode Island 

State line, water years 2013–14: U.S. Geological Survey Scientific Investigations Report 2017–5094, 41 p., 

https://doi.org/10.3133/sir20175094.

ISSN 2328–031X (print)

ISSN 2328–0328 (online)

ISBN 978-1-4113-4181-4
iii

Acknowledgments

The authors express their deep gratitude to Richard Chase, Mark Mattson, M. Reardon, 

A. Mayor, and Kimberly Groff of the Massachusetts Department of Environmental Protection for 

their thoughtful colleague reviews.

The authors also extend their gratitude to several U.S. Geological Survey (USGS) personnel. 

Andrew Horton, Sandra Petrakis, Irina Gumennick, Gina Daniels, Kim Campo, Jennifer Savoie, 

and Joan Whitley assisted in the field and in the laboratory. The authors gratefully acknowledge 

the technical assistance of Leslie DeSimone and Gardner Bent. Special thanks to John Mullaney 

and Austin Baldwin for their thoughtful colleague reviews.

v

Contents

Acknowledgments........................................................................................................................................iii

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

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

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

Study Area..............................................................................................................................................4

Data Collection...............................................................................................................................................4

Streamflow.............................................................................................................................................4

Automated, Flow-Proportional Water-Quality Sampling................................................................5

Manual Water-Quality Sampling........................................................................................................6

Continuous Water-Quality Parameter Measurements...................................................................9

Quality-Control Sampling...................................................................................................................10

Blank Samples............................................................................................................................10

Capsule Filter Blank Samples ..................................................................................................10

Equal-Width-Increment and Point Sample Comparisons ...................................................13

Data Analysis................................................................................................................................................13

Load Calculation..................................................................................................................................14

Correlation Analysis ...........................................................................................................................14

Correlations Among Potential Explanatory Variables...................................................................15

Regression Model Development......................................................................................................15

Analytical Procedures for Regression Analysis............................................................................15

Continuous and Manual Water-Quality Data ..........................................................................................17

Continuous Water-Quality Data........................................................................................................17

Automated and Manually Collected Concentration Data ............................................................17

Suspended Sediment ................................................................................................................17

Nitrogen and Phosphorus ........................................................................................................18

Trace Metals...............................................................................................................................18

Constituent Loads in the Blackstone River Crossing the Massachusetts-Rhode Island 

State Line, Water Years 2013–2014..............................................................................................22

Nitrogen and Phosphorus .................................................................................................................22

Trace Metals........................................................................................................................................22

Correlation Among Variables.....................................................................................................................25

Nutrient-Concentration Correlations...............................................................................................25

Correlations Between Potential Explanatory Variables and 

Nutrient Concentrations..............................................................................................25

Correlations Among Nutrient Concentrations ......................................................................25

Trace Metal Concentration Correlations ........................................................................................29

Correlations Between Potential Explanatory Variables and 

Metal Concentrations..................................................................................................29

Correlations Among Metal Concentrations...........................................................................29

Development of Water-Quality Regression Equations .................................................................29

Application of Water-Quality Regression Equations.....................................................................32

Limitations of the Analysis.................................................................................................................35

Summary and Conclusions.........................................................................................................................37

References Cited..........................................................................................................................................38
vi

Figures

1. Map showing the Blackstone River Basin in Massachusetts and Rhode Island, 

U.S. Geological Survey streamflow monitoring stations, and wastewater treatment 

facilities ..........................................................................................................................................3

2. Graph showing linear regression of 11 concurrent measurements collected at 

the Blackstone River at Millville, Massachusetts (01111230), and the Blackstone 

River at Route 122, Uxbridge, Mass. (01111212), stations between water years 2006 

and 2008..........................................................................................................................................5

3. Graphs showing A, flow and B, turbidity duration curves, Blackstone River at 

Millville, Massachusetts, station (01111230), 2012 to 2014 ....................................................9

4. Boxplots showing A, total nitrogen, B, total phosphorus, and C, dissolved 

phosphorus concentrations collected from the upstream train bridge, the 

Millville station intake point, and the automated system from the Blackstone River 

at Millville, Massachusetts, station (01111230), water years 2013 and 2014 ....................19

5. Boxplots showing concentrations of dissolved trace metals A, cadmium, 

B, chromium, C, copper, D, lead, E, nickel, and F, zinc, and of G, total aluminum 

collected from the upstream train bridge, the Millville station intake point, and 

the automated system from the Blackstone River at Millville, Massachusetts, 

station (01111230), water years 2013 and 2014 ......................................................................20

6. Boxplots showing concentrations of total trace metals A, cadmium, B, chromium, 

C, copper, D, lead, E, nickel, and F, zinc, and of G, chloride collected from the 

upstream train bridge and the Millville station intake point from the Blackstone 

River at Millville, Massachusetts, station (01111230), water years 2013 and 2014..........21

7. Graphs showing monthly loads of A, total nitrogen and B, total and dissolved 

phosphorus based on 14-day composite samples from the Blackstone River at 

Millville, Massachusetts, station (01111230), water years 2013 and 2014.........................23

8. Graphs showing 4-day loads of A, dissolved cadmium, B, dissolved chromium, 

C, dissolved copper, D, dissolved lead, E, dissolved nickel, F, dissolved zinc, and 

G, total aluminum, based on composite samples collected by the automated system 

from the Blackstone River at Millville, Massachusetts, station (01111230), water 

years 2013 and 2014....................................................................................................................24

9. Graph showing estimated 15-minute total phosphorus concentrations from the 

Blackstone River at Millville, Massachusetts, station (01111230), December 22, 2013, 

to January 1, 2014 .......................................................................................................................35
vii

Tables

1. Constituents, U.S. Geological Survey parameter codes, analytical methods, and 

method detection limits for the sampling program at the Blackstone River at 

Millville, Massachusetts, station (01111230), water years 2013 to 2014..............................7

2. Concentrations of water-quality constituents in quality-assurance blank samples 

for nutrients and trace metals collected from sampling equipment from the 

Blackstone River at Millville, Massachusetts, station (01111230)......................................11

3. Test results from capsule filter experiments..........................................................................12

4. Concentrations of nutrients, trace metals, and suspended sediment in sample 

pairs collected from the upstream railroad bridge and from the point location at 

the Blackstone River at Millville, Massachusetts, station (01111230)...............................13

5. Concentrations of nutrients, total aluminum, and dissolved trace metals in 14-day 

nutrient composite samples and 4-day metal composite samples collected by the 

automated sampling system from the point location at the Blackstone River at 

Millville, Massachusetts, station (01111230) during water years 2013 and 2014 .............14

6. Concentrations of nutrients, trace metals, and suspended sediment in manually 

collected samples from the upstream railroad bridge and from the collection point 

at the Blackstone River at Millville, Massachusetts, station (01111230) during 

water years 2013 and 2014 ........................................................................................................17

7. Loads of nutrients based on 14-day nutrient composite samples, and loads of 

dissolved trace metals and total aluminum based on 4-day metal composite 

samples collected by the automated sampling system from the point location at 

the Blackstone River at Millville, Massachusetts, station (01111230) during water 

years 2013 and 2014....................................................................................................................22

8. Correlation coefficients among potential explanatory variables .......................................26

9. Correlation coefficients between potential explanatory variables and nutrient 

concentrations ............................................................................................................................27

10. Correlation coefficients among nutrient concentrations ....................................................28

11. Correlation coefficients between potential explanatory variables and metal 

concentrations ............................................................................................................................30

12. Correlation coefficients among metal concentrations ........................................................31

13. Coefficients of the regression equations, regression statistics for estimating 

selected water-quality constituent concentrations from continuous monitoring 

data at the Blackstone River at Millville, Massachusetts, station (01111230), and 

resulting regression equations.................................................................................................33

14. Values needed to determine 90-percent prediction intervals for selected regression 

equations for estimating selected water-quality constituent concentrations from 

continuous monitoring data at the Blackstone River at Millville, Massachusetts, 

station (01111230)........................................................................................................................34

15. Ranges of values, population statistics, and standardized beta coefficients for the 

variables used in each regression model...............................................................................36
viii

Conversion Factors

U.S. customary units to International System of Units

Multiply By To obtain

inch (in.) 2.54 centimeter (cm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

square mile (mi2) 2.590 square kilometer (km2)

acre-foot (acre-ft) 1,233 cubic meter (m3)

foot per second (ft/s) 0.3048 meter per second (m/s)

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

International System of Units to U.S. customary units

Multiply By To obtain

micrometer (μm) 0.00003937 inch (in.)

milliliter (mL) 0.03381 ounce, fluid (fl. oz)

liter (L) 0.2642 gallon (gal)

cubic meter per second (m3/s) 35.31 cubic foot per second (ft3/s)

kilogram (kg) 2.205 pound avoirdupois (lb)

kilogram per year (kg/yr) 2.205 pound per year (lb/yr)

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

°F = (1.8 × °C) + 32.

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

°C = (°F – 32) / 1.8.

Datum

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Supplemental Information

Specific conductance is given in microsiemens per centimeter at 25 degrees Celsius (μS/cm at 

25 °C).

Concentrations of chemical constituents in water are given in either milligrams per liter (mg/L) 

or micrograms per liter (μg/L).
ix

Abbreviations

ASEE average standard error of the estimate

ASEP average standard error of the prediction

DOC dissolved organic carbon

EPA U.S. Environmental Protection Agency

EWI equal-width increment

FNU formazin nephelometric unit

MassDEP Massachusetts Department of Environmental Protection

NWQL National Water Quality Laboratory

ppb parts per billion

PRESS prediction error sum of squares

R2 coefficient of determination

RIDEM Rhode Island Department of Environmental Management

RPD relative percent difference

TSS total suspended sediment

USGS U.S. Geological Survey

WY water year

VIF variance inflation factor

Nutrient and Metal Loads Estimated by Using Discrete, 

Automated, and Continuous Water-Quality Monitoring 

Techniques for the Blackstone River at the 

Massachusetts-Rhode Island State Line, 

Water Years 2013–14

By Jason R. Sorenson, Gregory E. Granato, and Kirk P. Smith

Abstract

Flow-proportional composite water samples were collected in water years 2013 and 2014 by the U.S. Geological 

Survey, in cooperation with the Massachusetts Department 

of Environmental Protection, from the Blackstone River at 

Millville, Massachusetts (U.S. Geological Survey station 

01111230), about 0.5 mile from the border with Rhode Island. 

Samples were collected in order to better understand the 

dynamics of selected nutrient and metal constituents, assist 

with planning, guide activities to meet water-quality goals, and 

provide real-time water-quality information to the public. An 

automated system collected the samples at 14-day intervals to 

determine total and dissolved nitrogen and phosphorus concentrations, to provide accurate monthly nutrient concentration 

data, and to calculate monthly load estimates. Concentrations 

of dissolved trace metals and total aluminum were determined 

from 4-day composite water samples that were collected 

twice monthly by the automated system. Results from 4-day 

composites provide stakeholders with information to evaluate 

trace metals on the basis of chronic 4-day exposure criteria for 

aquatic life, and the potential to use the biotic ligand model to 

evaluate copper concentrations. Nutrient, trace metal, suspended sediment, dissolved organic carbon, and chlorophyll 

a concentrations were determined from discrete samples 

collected at the Millville station and from across the stream 

transect at the upstream railroad bridge, and these concentrations served as a means to evaluate the representativeness of 

the Millville point location.

Analytical results from samples collected with the 

automated flow-proportional sampling system provided the 

means to calculate monthly and annual loading data. Total 

nitrogen and total phosphorus loads in water year (WY) 2013 

were about 447,000 and 36,000 kilograms (kg), respectively. 

In WY 2014, annual loads of total nitrogen and total phosphorus were about 342,000 and 21,000 kg, respectively. Total 

nitrogen and total phosphorus loads from WYs 2013 and 2014 

were about 56 and 65 percent lower than those reported for 

WYs 2008 and 2009. The higher loads in 2008 and 2009 may 

be explained by the higher than average flows in WY 2009 and 

by facility upgrades made by wastewater treatment facilities in 

the basin.

Median loads were determined from composite samples 

collected with the automated system between October 2012 

and October 2014. Median dissolved cadmium and chromium 

4-day loads were 0.55 and 0.84 kg, respectively. Dissolved 

copper and total lead median 4-day loads were 8.02 and 

1.42 kg, respectively. The dissolved nickel median 4-day load 

was 5.45 kg, and the dissolved zinc median 4-day load was 

36 kg. Median total aluminum 4-day loads were about 197 kg.

Spearman’s rank correlation analyses were used with 

discrete sample concentrations and continuous records of 

temperature, specific conductance, turbidity, and chlorophyll a

to identify correlations between variables that could be used to 

develop regression equations for estimating real-time concentrations of constituents. Correlation coefficients were generated for flow, precipitation, antecedent precipitation, physical 

parameters, and chemical constituents. A 95-percent confidence limit for each value of Spearman’s rho was calculated, 

and multiple linear regression analysis using ordinary least 

squares regression techniques was used to develop regression 

equations for concentrations of total phosphorus, total nitrogen, suspended sediment concentration, total copper, and total 

aluminum. Although the correlations are based on the limited 

amount of data collected as part of this study, the potential to 

monitor water-quality changes in real time may be of value to 

resource managers and decision makers.

Introduction

Located in central Massachusetts and Rhode Island, the 

475 square mile (mi2) Blackstone River Basin contains several 

urban centers and other major areas of development along the 
2 Nutrient and Metal Loads Estimated for the Blackstone River, Massachusetts and Rhode Island, Water Years 2013–14

48-mile course of the river, which discharges into Narragansett 

Bay (fig. 1). The Blackstone River was once referred to as “the 

hardest working river in America” (Massachusetts Executive 

Office of Energy and Environmental Affairs, 2013), and in recognition of being one of the birthplaces of the industrial revolution, the Blackstone River Valley National Heritage Corridor 

was established in December 2014. Detailed descriptions of 

the study area and industrial heritage are in earlier reports 

(Barbaro, 2007; Massachusetts Department of Environmental 

Protection [MassDEP], 2010; Zimmerman and others, 2015).

The Blackstone River and several of its tributaries are 

included on the State of Massachusetts’ list of impaired waters 

for recreational and aquatic uses (MassDEP, 2014). Impairment causes include flow and habitat alterations, pathogens, 

high phosphorus and nutrient concentrations, excess algal 

growth and eutrophication, lead (Pb), sedimentation, and 

several others (MassDEP, 2014). The Blackstone River is 

also listed as impaired on the State of Rhode Island’s list of 

impaired waters (Rhode Island Department of Environmental 

Management [RIDEM], 2015). Impairments reported by the 

State of Rhode Island include pathogens, high phosphorus 

and nutrient concentrations, excess algal and invasive macrophyte growth, and high lead and cadmium (Cd) concentrations 

(RIDEM, 2015). The State of Massachusetts has developed 

draft total maximum daily loads for pathogens and nutrients 

for the Blackstone River. The State of Rhode Island has established total maximum daily loads for pathogens, cadmium, 

copper, and lead for the Blackstone River (RIDEM, 2013).

Impaired waters from the Blackstone River drain into 

Narragansett Bay. High nitrogen levels have been identified 

as the trigger for algal blooms and dissolved oxygen deficits 

in the bay (RIDEM, 1998). Numerous infrastructure improvements have been carried out within the Blackstone River Basin 

by regulated dischargers, and data show a downward trend 

in nutrient concentrations (MassDEP, 2010; Massachusetts 

Executive Office of Energy and Environmental Affairs, 2015; 

Savoie and others, 2017). Durant and Raposa (2011) reported 

decreasing trends in concentrations of nitrogen species in Narragansett Bay; they also reported anoxic and hypoxic events 

still occuring during the time of their study (2008–9).

Excess phosphorus is linked to excess algal and rooted 

macrophyte growth in freshwater reaches (Carr and Chambers, 

1998). Elevated trace metal concentrations may have adverse 

effects on an organism’s life expectancy, activity, growth, 

metabolism, or reproduction (Wright and Welbourn, 2002). 

Accurate load estimates are needed to support the allocation of 

allowable nitrogen and phosphorus loads among sources in the 

basin and to develop strategies for reducing nutrient loading. 

Dissolved trace metals data allow the surface-water quality of 

the river to be evaluated on the basis of 4-day exposure criteria 

for aquatic life (U.S. Environmental Protection Agency [EPA], 

1994, 2009).

U.S. Geological Survey (USGS) has collected waterquality samples on the Blackstone River at the Millville, 

Massachusetts, station (USGS station 01111230, hereafter 

referred to as the Millville station) since 1971 (USGS, 2016). 

The Millville station is about 1.3 miles (mi) upstream from the 

Massachusetts-Rhode Island State line. Monitoring nutrient 

concentrations near the State line is part of a comprehensive 

effort to improve water quality in the Blackstone River and 

Narragansett Bay. The potential to use automated measurements to estimate nutrient concentrations in real time was 

investigated in this study; this use could provide real-time 

monitoring of concentrations and loads and possibly reduce 

analytical costs.

This study utilized similar sampling techniques to those 

used by Zimmerman and others (2015), except that composite 

samples were not separated into stormflow and base-flow components but, rather, collected as a single composite for each 

14-day and 4-day sampling period. Collecting samples in this 

manner provided accurate monthly nutrient concentration data 

and two 4-day concentrations per month for dissolved trace 

metals and total aluminum (Al). The chronic 4-day exposure 

criteria for aquatic life were applied by using the biotic ligand 

model to evaluate copper. The biotic ligand model is a predictive tool that can account for variations in metal toxicity by 

using information on the chemistry of ambient water (Di Toro 

and others, 2001; HydroQual, Inc., 2005). The model incorporates metal speciation and the protective effects of competing 

cations into predictions of metal bioavailability and toxicity 

(Di Toro and others, 2001; Santore and others, 2001).

In October 2012, the MassDEP and the USGS reestablished a cooperative study of nutrient, trace metal, and 

suspended sediment loads in the Blackstone River at the 

Massachusetts-Rhode Island State line. Continued monitoring of nutrient, trace metal, suspended sediment, and other 

constituent concentrations will improve the understanding of 

the dynamics of these constituents, assist with planning, guide 

activities to meet water-quality goals, and provide real-time 

water-quality information to the public (EPA, 2009; Upper 

Blackstone Water Pollution Abatement District, 2012, 2013; 

Massachusetts Executive Office of Energy and Environmental 

Affairs, 2015).

The primary objectives of this study were (1) to provide 

continuous, real-time (15-minute) water temperature, specific 

conductance, turbidity, and chlorophyll a data; (2) to continue 

data-collection activities sufficient to produce reliable estimates of nutrient and trace metal loads crossing the Massachusetts-Rhode Island State line; and (3) to use the data to develop 

regression models for estimating real-time concentrations and 

loads for nutrients and selected metals and to establish a basis 

for estimating constituent concentrations and loads and potentially displaying them on the USGS National Real-Time Water 

Quality website (USGS, 2010; https://nrtwq.usgs.gov/).

Purpose and Scope

This report presents the continuous and discrete measurements of physical parameters and the analytical results of 

water-quality samples, including quality-control samples, from 

manual and automated flow-proportional sample collection 
Introduction 3

Pawtucket

Attleboro

North

Attleboro

Plainville

Cumberland

Wrentham

Lincoln

North Smithfield

Woonsocket

Glocester

Providence

Burrillville

Douglas

Bellingham

Blackstone

Millville

Uxbridge

Mendon

Hopedale

Milford

Grafton

Upton

Northbridge

Sutton

Oxford

Millbury

Boylston

West Boylston

Worcester Shrewsbury

Leicester

Auburn

Paxton

Holden

Upper Blackstone Water 

Pollution Abatement District

Grafton WWTF

Northbridge WWTF

Uxbridge WWTF

Burrillville WWTF

Bucklin Point 

WWTF

01109730

01110500

01111230 Blackstone River Millville

01113895

Narragansett

Bay

01111212 Blackstone River Uxbridge

01111200

01112500 Blackstone River Woonsocket

01110000

01111300

01111500

Rice City Pond Dam

Tupperware Dam

West Hill Dam

01110000

CONNECTICUT

RHODE ISLAND

MASSACHUSETTS

0

0

2 4 6 8

2 4 6 8

10 MILES

10 KILOMETERS

EXPLANATION

Blackstone River Basin boundary

Wastewater treatment facility (WWTF)

Selected dams 

State boundary

USGS streamflow monitoring station

and identifier

73°

43°

42°

41°

72° 71° 70°

MASSACHUSETTS

RHODE ISLAND

Boston

Providence

Worcester

Base from U.S. Geological Survey and Massachusetts Office of Geographic Information digital data, 2014

Massachusetts State Plane Coordinate System, mainland zone

Fields Point WWTF

71°50' 71°40' 71°30' 71°20'

42°20'

42°10'

41°50'

42°

Figure 1. The Blackstone River Basin in Massachusetts and Rhode Island, U.S. Geological Survey (USGS) streamflow 

monitoring stations, and wastewater treatment facilities. Modified from Zimmerman and others (2015).
4 Nutrient and Metal Loads Estimated for the Blackstone River, Massachusetts and Rhode Island, Water Years 2013–14

at the Blackstone River near the Massachusetts-Rhode Island 

border in Millville, Mass., primarily during water years1

(WYs) 2013 and 2014.

Monthly and annual load estimates of nutrients, dissolved 

trace metals, and total aluminum are presented. Loads are 

based on 14-day and 4-day composite samples for nutrients 

and trace metals, respectively. The monthly loads are approximated as the sum of loads measured in the two consecutive 

14-day composite sampling periods during each month. Point 

and equal-width-increment (EWI) (Wilde and others, 2002) 

sample results for nutrients, trace metals, and suspended sediment are also described. 

The report includes a discussion of the approach used 

to develop regression equations that may be used to estimate 

near real-time (15-minute) concentrations and loads and 

describe the variability of selected constituents by using the 

continuously collected records of physical parameters. The 

uncertainty associated with this approach is also discussed. 

Regression models are intended to provide a means to estimate 

loads by using surrogate variables from automated data 

collection. The regression equations and discussion of them 

can be used for monitoring changes in concentrations and 

loads and for comparing concentrations and loads with waterquality standards.

Study Area

Water-quality samples were collected at the Millville 

station, about 1.3 mi upstream from the MassachusettsRhode Island border (fig. 1). The Millville station monitors 

continuous river stage and selected water-quality parameters 

representing flow from the upper portion of the basin, which 

drains about 263 mi2 of the total basin area upstream from 

the State border (264 mi2), and contains parts or all of over 

20 municipalities (fig. 1). The Blackstone River mainstem flow is joined by flows from three major tributaries 

(Quinsigamond, West, and Mumford Rivers), as well as by 

discharge from four wastewater treatment facilities, and 

travels over nine dams along its nearly 33-mi course toward 

the Millville station (fig. 1). Discharge from these various 

point and diffuse sources may cause water-quality conditions 

to change within hours.

Flow upstream and downstream from the Millville 

station is regulated by two dams. The Rice City Pond Dam 

in Uxbridge, Mass. (fig. 1, national identification number 

MA00935), is about 9 mi upstream from the Millville station and has a maximum height of 21 feet (ft). It has a 

maximum storage capacity of about 1,762 acre-feet (2.2 million cubic meters [m3

]). About 1 mi downstream from the 

Millville station in Blackstone, Mass., is the Tupperware 

Dam, also known as the Stone Diversion Dam (fig. 1, Federal Energy Regulatory Commission number 3023; national 

1

In this report years are given as water years. A water year is defined as the 

12-month period from October 1 through September 30 and is designated by 

the calendar year in which it ends.

identification number MA00096) and the Blackstone Dam 

(MA01164). The Tupperware Dam is about 20 ft high and 

has an installed capacity of about 2,000 kilowatts. It retains 

between 790 and 1,762 acre-feet (between 974,450 and 

2,173,392 m3). Stage and discharge at the Millville station are 

affected by backwater and regulation at the Tupperware Dam.

Data Collection

The water-quality monitoring station in Millville, reactivated in October 2012 after being shut down in 2009, was 

equipped to continuously collect stage, precipitation, air and 

water temperature, specific conductance, turbidity, and chlorophyll a measurements in 15-minute intervals. The stream discharge record from the upstream USGS station at Route 122 

near Uxbridge, Mass. (01111212, referred to as the Rt. 122 

station), was used to represent flow conditions at Millville. At 

the Millville station, an automated flow-proportional sampling 

system designed by the USGS was used to collect 14-day 

composite samples for nutrients and 4-day composite samples 

for total aluminum and dissolved trace metals. Samples were 

also collected manually at the Millville station to ensure that 

the automated point sampling location was representative of 

stream conditions of the Blackstone River.

Streamflow

Surface-water records from the Rt. 122 station were 

rated as fair (8-percent rating accuracy) for WYs 2013 and 

2014 (USGS, 2015b). Flows at this station are affected at all 

flow levels by discharges from upstream wastewater treatment facilities and by power generation and dam maintenance 

at the Tupperware Dam about 4.5 mi downstream. Flow at 

the Rt. 122 station also is affected at high flows (greater than 

5.66 cubic meters per second [m3/s] or 200 cubic feet per second [ft3

/s]) by regulation at the U.S. Army Corps of Engineers 

Flood-Prevention Dam (or West Hill Dam) on the West River 

near Uxbridge, Mass. (fig. 1), and at extremely high flows 

(greater than 113.3 m3/s or 4,000 ft3/s) by flood bypass inflows 

from the Kettle Brook Diversion Weir in Auburn, Mass. (Wandle, 1984). Discharge records from the Rt. 122 station higher 

than about 5.66 m3/s (200 ft3/s) are considered good (5-percent 

rating accuracy); however, discharge measured at median to 

low flows (less than 5.66 m3/s or 200 ft3/s) are less accurate 

because of dam regulation at upstream and downstream locations. Streamflow was not measured at the Millville station in 

WYs 2013 and 2014 but was estimated by using data from the 

Rt. 122 station, located about 3.5 mi upstream (fig. 1), to trigger the flow-proportional sampling. This was the same method 

used by the sampling program reported by Zimmerman and 

others (2015).

A 19-mi2 increase in drainage area between the Rt. 122 

(244 mi2) station and Millville (263 mi2) station required 

estimating streamflow at the Millville station on the basis of 
Data Collection 5

the continuous streamflow data at the Rt. 122 station before 

loads could be calculated for this study. A drainage-area correction resulted in about a 7.2-percent increase in flow on 

average. Linear regression of 11 concurrent measurements 

collected at both the Route 122 and Millville stations between 

WYs 2006 and 2008 (USGS, 2015b, c) showed differences in 

flow ranging between about −12.7 to 9.5 percent and an average increase in flow of 1.6 percent (fig. 2). The equations for 

estimating streamflow at the Millville station covered a range 

from 1.7 to 53.2 m3/s (59 to 1,880 ft3/s), and flows estimated 

during WYs 2013 and 2014 ranged from 1.4 to 193.6 m3/s 

(50 to 6,836 ft3/s). Although some estimated low flows were 

slightly outside the range of measured streamflow, and some 

high flows were well outside the range of streamflow measurements used to develop the regression equations, the equations 

were extrapolated to more accurately estimate the extreme 

high flows at the Millville station. The linear regression equation was used to adjust the Rt. 122 flow record for use at the 

Millville station in this report. Mean annual flow estimated 

for the Millville station was 13.4 m3/s (472 ft3/s) for WY 2013 

and 10.1 m3/s (356 ft3/s) for WY 2014. Mean annual flow in 

WY 2013 at the Millville station was 11 percent less than the 

8-water year (2007–14) annual mean discharge at the Rt. 122 

station (15.0 m3/s or 529 ft3/s). WY 2014 annual average flow 

at the Millville station was 33 percent less than the 8-year 

annual mean discharge at Route 122 and about 25 percent less 

than in WY 2013.

Automated, Flow-Proportional Water-Quality 

Sampling

Flow-proportional water-quality samples for chemical analysis were collected at the Millville station between 

October 2012 and October 2014. A modified automated 

sampling system based on a USGS design from a previous 

Blackstone River study was used (Zimmerman and others, 

2015). The flow-proportional sampling at the Millville station was triggered by using the upstream flow measurements 

at the Rt. 122 station that were downloaded by the Millville 

datalogger. Stainless steel intake lines brought water from the 

river to the Millville shelter. Platinum-cured, flexible silicon 

tubing connected to the steel lines and routed sample water to 

the automated system by using three peristaltic pumps. The 

original system is fully described in Zimmerman and others (2015). Discharge at the Millville station was affected by 

backwater and regulation, so samples were collected as single 

composite samples rather than partitioned into base-flow 

and storm-flow components. A typical station visit included 

retrieving the previous 14-day nutrient samples and 4-day 

metal composite samples, documenting any errors or discrepancies, cleaning the system using 0.1-percent non-phosphate 

detergent and 5-percent hydrochloric acid solutions followed 

by thorough rinsing with deionized water, and replacing used 

capsule filters. Precleaned sampling bottles were installed, 

and the system was reset. Lastly, each 14-day sampling period 

04/20/2006

05/17/2006

08/02/2006 07/26/2006

09/19/2006

05/15/2007

07/03/2007

08/21/2007

08/27/2007

09/24/2007

02/04/2008

y = 1.0053x + 0.1395

R2 = 0.999

10

100

1,000

10,000

10 100 1,000 10,000

Flow, in cubic feet per second,

Blackstone River at Millville, Massachusetts (01111230)

Flow, in cubic feet per second,

Blackstone River at Route 122, Uxbridge, Massachusetts (01111212)

Figure 2. Linear regression of 

11 concurrent measurements 

collected at the Blackstone 

River at Millville, Massachusetts 

(01111230), and the Blackstone 

River at Route 122, Uxbridge, Mass. 

(01111212), stations between water 

years 2006 and 2008.
6 Nutrient and Metal Loads Estimated for the Blackstone River, Massachusetts and Rhode Island, Water Years 2013–14

required a new flow-proportional threshold to be entered into 

the datalogger. Thresholds were initially based on the mean 

14-day flow multiplied by the number of seconds in 14 days 

and assuming a minimum number of 55 samples in the 14-day 

composite. This first-cut threshold value was then modified 

by field personnel on the basis of precipitation forecasts and 

expected changes in flow at the Millville station. The datalogger used the same first-cut threshold calculation on day 10 of 

the 14-day sampling period to establish a flow threshold for 

the 4-day metal sample composite. This flow threshold was 

based on a 12-sample metal composite. Field personnel could 

also adjust the threshold remotely if needed as a result of 

changes in flow or precipitation.

Samples for analysis of total and dissolved nitrogen 

and phosphorus were collected and composited throughout 

the year over periods of approximately 14 days. Samples for 

analysis of selected dissolved metals—cadmium, chromium 

(Cr), copper (Cu), lead, nickel (Ni), and zinc (Zn)—and total 

aluminum were collected and composited throughout the year 

over periods of approximately 4 days for comparison to 4-day 

exposure criteria for aquatic life. Table 1 lists all analytes 

investigated as part of this study.

Nutrient samples were composited in two precleaned, 

14-liter (L) polyethylene bottles, one for whole-water 

samples and the second for dissolved samples, which was 

equipped with a single, in-line large-capacity capsule filter 

of 0.45 micrometer (μm) pore size attached to the sample 

bottle cap. The sample was pushed through the capsule filter 

by the system pumps. Bottles for collecting nutrient samples 

were preacidified with 20 milliliters (mL) of 4.5 normal 

sulfuric acid (H2SO4), sufficient to preserve a minimum 

sample volume of 2,500 mL. Nutrient sample volumes 

typically exceeded 10 L after the 14-day sampling period. 

Additional H2SO4 was added to the final sample volume as 

part of the collection and processing procedures to obtain a 

sample pH value between 1.6 and 1.9. Four-day composite 

samples of trace metals were distributed between three 2-L 

polyethylene bottles and were always processed after the 

nutrient samples. Two bottles contained the whole-water 

samples, and the third bottle contained the dissolved sample. 

One of the whole-water bottles was acidified with nitric acid 

(HNO3

) in the USGS laboratory in Northborough, Mass., and 

churn split for chemical analysis, and the second whole-water 

bottle was used for measuring the specific conductance and 

turbidity of the 4-day metals composite. Samples of dissolved 

trace metals were collected by using the automated system 

to pump through 0.45-μm capsule filters. Six capsule filters 

were installed within the pumping enclosure. A maximum of 

three samples were pulled through a single filter according 

to sampling protocols (Wilde and others, 2002). The system 

then switched to the next filter in line for collection of the 

next three samples. Trace metal sample bottles were not 

preacidified as the nutrient bottles were. All sample bottles 

and the filter used for nutrient composite samples were kept at 

4 degrees Celsius (°C) ± 2° in a small refrigerator installed in 

the station shelter during the sampling period.

About every 14 days, water-quality samples were 

retrieved by USGS personnel, stored on ice, and transported 

to the laboratory in Northborough, Mass. In WY 2013, a total 

of 56 days had no sample collection because of frozen sample 

lines during the winter, datalogger programming issues, 

or delayed sample retrievals. Programming modifications 

reduced the total number of days without sample collection to 

12 days in WY 2014.

During routine station visits, sample bottles were 

retrieved and replaced with clean bottles, the automated 

sampling system was cleaned, and the 14- and 4-day sampling 

cycles were reactivated so that the 14-day nutrient sampling 

cycle would restart immediately and the 4-day metal sampling 

cycle would start on day 10. Composite nutrient samples were 

weighed, and the required amount of additional preservative 

acid was added to the sample containers. Trace metal samples 

were also weighed, and the necessary amount of preservative 

nitric acid (HNO3

) was added to one of the whole-water metal 

sample bottles. Acidified whole-water and dissolved samples 

were allowed to equilibrate within their respective sample 

containers for 24 to 48 hours before being processed. Specific 

conductance and turbidity measurements were collected 

from the second whole-water metal sample bottle. Filtered 

samples were processed first by decanting all water from the 

14-L nutrient jug into a dedicated 14-L polyethylene churn 

splitter for nutrients and using it to distribute sample water 

into the appropriate sample bottles for laboratory analyses. 

Then whole-water samples were processed in the same way. 

Dissolved (filtered) and whole-water metal samples were then 

processed in the same way by a dedicated 4-L polyethylene 

churn splitter for metal samples. After processing, nutrient 

and trace metal samples were shipped overnight to the 

USGS National Water Quality Laboratory (NWQL) in 

Denver, Colorado.

Manual Water-Quality Sampling

Isokinetic, equal-width-increment (EWI) samples 

were collected manually at the railroad bridge about 400 ft 

upstream from the Millville station over a wide range of 

flow and turbidity conditions (fig. 3) in accordance with 

USGS protocols (Wilde and others, 2002, 2004). The 

EWI samples were used to ensure that samples collected 

automatically at a single point were representative of the 

entire cross section of the river. Point samples were used 

to develop regression equations to estimate near real-time 

(15-minute) concentrations and loads of selected constituents. 

Point samples were collected at the intake for the automatic 

sampling system, the 15 EWI samples were collected 

concurrently, and samples were analyzed for all constituents to 

assess how the point samples compared to the EWI samples. 

Although EWI samples have been collected at this station 

for decades, only data from January 2012 to March 2015 

were used for this study. Typical stream velocities at the 

Millville station (and at the railroad bridge 400 ft upstream) 
Data Collection 7

Table 1. Constituents, U.S. Geological Survey (USGS) parameter codes, analytical methods, and method detection limits for the 

sampling program at the Blackstone River at Millville, Massachusetts, station (01111230), water years 2013 to 2014.

[USGS, U.S. Geological Survey; N, nitrogen; P, phosphorus; mg/L, milligram per liter; μg/L, microgram per liter; --, no data; ltmdl, long-term method detection 

limit; mdl, method detection limit; irl, interim reporting level; EPA, U.S. Environmental Protection Agency; Bridge, sample collected along bridge transect 

using equal-width-increment methods; Point, sample collected from Millville station intake point; Composite, sample collected using automated flow-proportional system at the Millville station intake point]

Constituent

USGS 

parameter 

code

Unit

Method 

reporting 

limit

Reporting 

limit type Reference Water-quality sample type

Total nitrogen, water, unfiltered p00600 mg/L -- -- Calculated Bridge; Point

Total nitrogen, water, filtered p00602 mg/L -- -- Calculated Bridge; Point

Organic nitrogen, water, unfiltered p00605 mg/L -- -- Calculated Bridge; Point

Organic nitrogen, water, filtered p00607 mg/L -- -- Calculated Bridge; Point

Ammonia, water, filtered, as N p00608 mg/L 0.01 ltmdl Zimmerman and others (1997) Bridge; Point

Nitrite, water, filtered, as N p00613 mg/L 0.001 mdl Fishman (1993) Bridge; Point

Nitrate, water, filtered, as N p00618 mg/L 0.001 mdl Fishman (1993) Bridge; Point

Ammonia plus organic nitrogen, water, 

filtered, as N

p00623 mg/L 0.07 ltmdl Patton and Truitt (2000) Bridge; Point

Ammonia plus organic nitrogen, water, 

unfiltered, as N

p00625 mg/L 0.07 ltmdl Patton and Truitt (2000) Bridge; Point

Nitrate plus nitrite, water, filtered, as N p00631 mg/L 0.04 ltmdl Patton and Kryskalla (2011) Bridge; Point

Particulate nitrogen, suspended in water p49570 mg/L 0.03 ltmdl Zimmerman and others (1997) Bridge; Point

Total nitrogen (nitrate + nitrite + ammonia 

+ organic N), water, filtered, analytically 

determined

p62854 mg/L 0.05 ltmdl Patton and Kryskalla (2003) Bridge; Point; 

Composite

Total nitrogen (nitrate + nitrite + ammonia + 

organic N), water, unfiltered, analytically 

determined

p62855 mg/L 0.05 ltmdl Patton and Kryskalla (2003) Bridge; Point; 

Composite

Phosphorus, water, unfiltered, as P p00665 mg/L 0.004 ltmdl EPA 365.1 (1993) Bridge; Point

Phosphorus, water, filtered, as P p00666 mg/L 0.003 ltmdl EPA 365.1 (1993) Bridge; Point

Orthophosphate, water, filtered, as P p00671 mg/L 0.004 ltmdl EPA 365.1 (1993) Bridge; Point

Organic carbon, water, filtered p00681 mg/L 0.23 ltmdl Brenton and Arnett (1993) Bridge; Point

Carbon (inorganic plus organic), suspended 

sediment, total

p00694 mg/L 0.05 ltmdl Zimmerman and others (1997) Bridge; Point

Hardness, water, as calcium carbonate p00900 mg/L Bridge; Point

Calcium, water, filtered p00915 mg/L 0.022 ltmdl Fishman (1993) Bridge; Point; 

Composite

Magnesium, water, filtered p00925 mg/L 0.011 ltmdl Fishman (1993) Bridge; Point; 

Composite

Sodium, water, filtered p00930 mg/L 0.06 ltmdl Fishman (1993) Bridge; Point

Potassium, water, filtered p00935 mg/L 0.03 ltmdl Clesceri and others (1998) Bridge; Point

Chloride, water, filtered p00940 mg/L 0.02 ltmdl Fishman and Friedman (1989) Bridge; Point

Sulfate, water, filtered p00945 mg/L 0.02 ltmdl Fishman and Friedman (1989) Bridge; Point

Cadmium, water, filtered p01025 μg/L 0.03 ltmdl Garbarino and others (2006) Bridge; Point; 

Composite

Cadmium, water, unfiltered p01027 μg/L 0.03 ltmdl Garbarino and Struzeski 

(1998)

Bridge; Point

Chromium, water, filtered p01030 μg/L 0.30 ltmdl Garbarino and others (2006) Bridge; Point; 

Composite
8 Nutrient and Metal Loads Estimated for the Blackstone River, Massachusetts and Rhode Island, Water Years 2013–14

Table 1. Constituents, U.S. Geological Survey (USGS) parameter codes, analytical methods, and method detection limits for the 

sampling program at the Blackstone River at Millville, Massachusetts, station (01111230), water years 2013 to 2014.—Continued

[USGS, U.S. Geological Survey; N, nitrogen; P, phosphorus; mg/L, milligram per liter; μg/L, microgram per liter; --, no data; ltmdl, long-term method detection 

limit; mdl, method detection limit; irl, interim reporting level; EPA, U.S. Environmental Protection Agency; Bridge, sample collected along bridge transect 

using equal-width-increment methods; Point, sample collected from Millville station intake point; Composite, sample collected using automated flow-proportional system at the Millville station intake point]

Constituent

USGS 

parameter 

code

Unit

Method 

reporting 

limit

Reporting 

limit type Reference Water-quality sample type

Chromium, water, unfiltered, recoverable p01034 μg/L 0.40 ltmdl Garbarino and others (2006) Bridge; Point

Copper, water, filtered p01040 μg/L 0.80 ltmdl Garbarino and others (2006) Bridge; Point; 

Composite

Copper, water, unfiltered, recoverable p01042 μg/L 0.80 ltmdl Garbarino and others (2006) Bridge; Point

Lead, water, filtered p01049 μg/L 0.04 ltmdl Garbarino and others (2006) Bridge; Point; 

Composite

Lead, water, unfiltered, recoverable p01051 μg/L 0.04 ltmdl Garbarino and Struzeski 

(1998)

Bridge; Point

Nickel, water, filtered p01065 μg/L 0.20 ltmdl Garbarino and others (2006) Bridge; Point; 

Composite

Nickel, water, unfiltered, recoverable p01067 μg/L 0.20 ltmdl Garbarino and others (2006) Bridge; Point

Zinc, water, filtered p01090 μg/L 2.00 ltmdl Garbarino and others (2006) Bridge; Point; 

Composite

Zinc, water, unfiltered, recoverable p01092 μg/L 1.90 ltmdl Garbarino and others (2006) Bridge; Point

Aluminum, water, unfiltered, recoverable p01105 μg/L 3.80 ltmdl Garbarino and Struzeski 

(1998)

Bridge; Point; 

Composite

Pheophytin a, phytoplankton p62360 μg/L 0.10 irl Arar and Collins (1997) Bridge; Point

Chlorophyll a, phytoplankton, 

chromatographic-fluorometric

p70953 μg/L 0.10 irl Arar and Collins (1997) Bridge; Point

Dissolved solids, water, filtered, sum of 

constituents

p70301 mg/L -- -- Calculated Bridge; Point
Data Collection 9

10

100

1,000

10,000

0 10 20 30 40 50 60 70 80 90 100

Daily flow, in cubic feet per second

Percent of days flow exceeded

A

B

0

1

10

100

1,000

0 10 20 30 40 50 60 70 80 90 100

Daily turbidity, in formazin nephelometric units

Percent of days turbidity exceeded

Figure 3. A, Flow and B, turbidity 

duration curves, Blackstone 

River at Millville, Massachusetts, 

station (01111230), 2012 to 2014. 

Manual sampling events are 

shown as red markers.

were less than the 1.5 feet per second (ft/s) minimum needed 

to use isokinetic techniques, so a weighted bottle sampler 

was the appropriate approach (Wilde and others, 2002). The 

EWI subsamples, collected from across the stream transect, 

were composited into a churn splitter and then processed 

and analyzed, as previously described for samples collected 

by the automated sampling system. Manual samples were 

submitted for analysis of total (whole-water) and dissolved 

(filtered) concentrations of total and dissolved nitrogen and 

phosphorus, orthophosphate phosphorus, ammonia nitrogen, 

nitrate nitrogen, and nitrite nitrogen, total and dissolved 

organic carbon (DOC), common ions (calcium, magnesium, 

sodium, chloride, potassium, and sulfate), dissolved and total 

trace metals (cadmium, chromium, copper, lead, nickel, and 

zinc), and total aluminum concentrations (table 1). Additional 

constituents included suspended sediment concentration and 

turbidity (table 1). Suspended sediment concentrations were 

measured by using standard gravimetric techniques (American 

Society for Testing and Materials, 2002). DOC was measured 

by ultraviolet light-promoted persulfate oxidation and infrared 

spectrometry (Brenton and Arnett, 1993). Nutrient, common 

ion, DOC, and trace metal samples were shipped overnight to 

the USGS NWQL in Denver, Colo., and suspended sediment 

samples were shipped to the USGS Kentucky Water Science 

Center Sediment Laboratory in Louisville, Kentucky.

Continuous Water-Quality Parameter 

Measurements

Continuous water temperature, specific conductance, 

turbidity, and chlorophyll a measurements were collected 

at 15-minute intervals by a Eureka Manta 2 multiparameter 

probe and posted online in real time. The period of record 

included WYs 2013 and 2014, and the accuracies of all data 

were evaluated and adjusted on the basis of sensor fouling and 
10 Nutrient and Metal Loads Estimated for the Blackstone River, Massachusetts and Rhode Island, Water Years 2013–14

calibration drift. Minor data gaps exist in the records as the 

result of programming issues or deletion of very poor quality 

periods of record (Wagner and others, 2006). An extended 

gap in the continuous record occurred from September 2 

to October 30, 2014, following a lightning strike at the 

station, requiring the damaged sensor to be returned to the 

manufacturer for repair. Continuous water-quality data are 

available through the National Water Information System at 

https://nwis.waterdata.usgs.gov/nwis.

All water temperature records at the station were rated 

excellent (less than ±0.2 degrees Celsius (°C) (Wagner and 

others, 2006). Specific conductance records were also rated 

excellent (less than ±3 percent), except for several daily 

values that were rated good (±3 to 10 percent; Wagner and 

others, 2006).

Optical sensors such as those used for turbidity and chlorophyll a are sensitive to fouling compared to temperature and 

specific conductance sensors, especially in a slow-moving section of the river such as at the Millville station. The turbidity 

and chlorophyll a sensors were equipped with wipers and were 

regularly maintained by personnel. Although the accuracy 

of turbidity records was generally good (±0.5 to 1.0 turbidity units), the precision of the measurements was rated fair to 

poor (Wagner and others, 2006). Records for chlorophyll a

were not rated; however, continuous chlorophyll a concentration data were two to five times greater than laboratory concentrations and ranged to nearly an order of magnitude beyond 

the high-end calibration point.

Quality-Control Sampling

Blank and replicate samples were collected to assure that 

manual and composite sampling equipment was not a source 

of contamination and that sampling and laboratory procedures 

resulted in reproducible samples of the Blackstone River at 

the Millville station. All blank and replicate samples were processed in the USGS laboratory in Northborough, Mass., and 

shipped to the USGS NWQL and the USGS Kentucky Water 

Science Center Sediment Laboratory for analysis.

Blank Samples

A total of six equipment blank samples were collected 

from the automated sampling system. Blank water produced 

by a Millipore Elix Advantage 10 water system in the Northborough laboratory was run through the newly constructed 

automated sampling system before being deployed. System 

components were thoroughly cleaned according to USGS 

guidelines for the preparation of sampling equipment (Wilde, 

2004). Initial results from equipment blank samples collected 

from the system before deployment in September 2012 had 

detectable concentrations of chromium, lead, and nickel that 

were attributed to the milling of plastic components (table 2). 

After additional cleaning, a second set of blank samples was 

submitted, and resulting concentrations had smaller detections 

of the same three analytes. The remaining three system blank 

samples were all at or below detection limits, except for a 

single detection of aluminum, which indicated a potential 

contamination bias. The blank sample was collected on 

October 15, 2014. The resulting total aluminum concentration 

(9.6 micrograms per liter [μg/L]) was about 10 times less than 

the average concentration in samples collected by the automated system (94.7 μg/L), about 25 times less than the average concentration in manually collected samples (241.0 μg/L), 

and about 6 times less than the average concentration in 

samples collected by the system in October 2014 (56.9 μg/L), 

indicating the potential contamination bias is small.

A total of five blank samples were submitted for nutrient analysis. All results were less than detection limits for 

total and dissolved nitrogen and phosphorus. Blank water was 

decanted into the manual sampling equipment used to collect 

EWI samples at the railroad bridge, about 400 ft upstream 

from the Millville station’s point location, and from the 

point location itself. After 15 minutes of exposure to sampling equipment, blank water was poured from the sampling 

equipment into churn splitters and then decanted into sample 

bottles for shipping and analysis. Analytical results from these 

samples were all at or below detection limits (table 2).

Capsule Filter Blank Samples

The disposable Pall GWV high capacity in-line capsule 

filters (0.45 μm) that were used to process filtered samples in 

this study were found to be a source of organic nitrogen contamination when used in the automated sampling system and 

possibly for the collection of manual samples as well. Lowlevels of dissolved organic nitrogen (less than [<] 0.1 milligram per liter [mg/L]) were detected in blank samples used 

to test the quality of the capsule filters by the USGS NWQL 

quality-assurance program for sampling supplies (USGS, 

2015a). Preconditioning the capsule filters by passing 2 L 

of water through the filter prior to use was shown to reduce 

the level of contamination to below reporting limits and is 

the currently (2016) recommended procedure (USGS, 2009, 

2012). However, when filters were preconditioned but not 

used immediately, such as occurred in the automated sampling 

system and possibly for some manually collected samples, the 

level of nitrogen contamination was substantially greater. 

Field blanks collected during the sampling period used 

for load calculations (WYs 2013–14) showed no detections of 

nitrogen in filtered or unfiltered samples. However, these field 

blanks did not represent the additional potential for contamination that could have resulted from keeping the filters installed 

in the automated sampling system housing prior to use. There 

was evidence of organic contamination from capsule filters 

in instances when measured concentrations of dissolved total 

nitrogen were found to be substantially greater than concentrations of unfiltered total nitrogen. This evidence was in manually collected samples and samples collected by the automated 

sampling system. Concentrations of dissolved nitrogen greater 

than total nitrogen could result from analytical uncertainty, 
Data Collection 11

Table 2. Concentrations of water-quality constituents in quality-assurance blank samples for nutrients and trace metals collected from sampling equipment from the Blackstone River at Millville, Massachusetts, station (01111230).[mg/L, milligram per liter; P, phosphorus; N, nitrogen; μg/L, microgram per liter; Composite, sample collected using automated flow-proportional system at the Millville station intake point; EWI, equal-width increment; Bridge, sample collected along bridge transect using EWI methods; Point, sample collected from Millville station intake point; --, no data; <, less than]

Sampling 

equipment blank 

sample 

collected 

from

Date Time

Calcium, 

water, 

filtered 

(mg/L)

Magnesium, 

water, 

filtered

(mg/L)

Phosphorus, 

water, 

filtered

(mg/L as P)

Phosphorus, 

water, 

unfiltered 

(mg/L as P)

Total nitrogen 

(nitrate + nitrite 

+ ammonia + 

organic N), 

water, filtered, 

analytically 

determined 

(mg/L) 

Total nitrogen 

(nitrate + nitrite 

+ ammonia + 

organic N), water, unfiltered, 

analytically 

determined 

(mg/L)

Aluminum, 

water, 

unfiltered, 

recoverable 

(μg/L)

Cadmium, 

water, 

filtered 

(μg/L)

 Chromium, 

water, 

filtered 

(μg/L)

Copper, 

water, 

filtered 

(μg/L)

Lead, 

water, 

filtered 

(μg/L)

Nickel, 

water, 

filtered

(μg/L)

Zinc, 

water, 

filtered 

(μg/L)

Suspended 

sediment

concentration 

(mg/L)

Composite 9/27/2012 14:00 0.022 <0.011 <0.01 <0.01 <0.05 <0.05 <3.8 <0.016 0.11 <0.8 1.35 0.26 <1.4 --Composite 10/31/2012 11:31 0.024 <0.011 -- -- -- -- <3.8 <0.016 0.13 <0.8 0.252 0.21 <1.4 --Composite 12/12/2012 9:55 -- -- <0.5 <0.01 -- -- -- -- -- -- -- -- -- --EWI; Bridge 3/6/2013 13:45 <0.022 <0.011 -- -- -- -- <3.8 <0.016 <0.07 <0.8 <0.025 <0.09 <1.4 --Point 3/6/2013 13:50 <0.022 <0.011 -- -- -- -- <3.8 <0.016 <0.07 <0.8 0.062 <0.09 <1.4 --Composite 10/30/2013 16:00 0.034 <0.011 <0.01 <0.01 <0.05 <0.05 <3.8 <0.03 <0.3 <0.8 <0.04 0.25 <2 --Composite 4/16/2014 10:00 <0.022 <0.011 <0.01 <0.01 <0.05 <0.05 <3.8 <0.03 <0.3 <0.8 <0.04 <0.2 <2 <0.5Composite 10/15/2014 15:15 <0.022 <0.011 <0.01 <0.01 <0.05 <0.05 9.6 <0.15 <1.5 <4 <0.2 <1 <10 --Capsule 

filters

7/21/2015 14:49 -- -- <0.004 <0.004 <0.05 <0.05 -- -- -- -- -- -- -- --

Capsule 

filters

7/23/2015 10:59 -- -- <0.004 <0.004 0.23 <0.05 -- -- -- -- -- -- -- --

Capsule 

filters

12/18/2015 14:00 -- -- <0.01 <0.01 0.101 <0.05 -- -- -- -- -- -- -- --
12 Nutrient and Metal Loads Estimated for the Blackstone River, Massachusetts and Rhode Island, Water Years 2013–14

from contamination in dissolved (filtered) samples, or from 

underestimation of total nitrogen in whole-water (unfiltered) 

samples. Historical evidence shows that total nitrogen in 

whole-water samples could be underestimated by the alkaline persulfate digestion method in samples with suspended 

sediment concentrations higher than 500 mg/L. However, 

concentrations of suspended sediment in all samples were less 

than 10 mg/L (most were less than 4 mg/L), making it unlikely 

that the unfiltered samples were biased low as a result of 

incomplete oxidation of all nitrogen species to nitrate (Patton 

and Kryskalla, 2003, 2011; Mohrman, 2009). Overacidification with preservative also could result in underestimation of 

nitrogen in whole-water samples (Patton and Kryskalla, 2003), 

but samples were not overacidified in the present study.

The automatic sampling system employed in the present 

study used an automatic filtration process; the capsule filters 

used in the automated sampling system were preconditioned 

before being deployed in the field. A single capsule filter was 

deployed to filter the composite sample aliquots collected over 

a 14-day period for nutrients. Thus, the remaining six filters 

installed in line for use to filter samples for trace metal composite sampling typically remained in the monitoring shelter 

for more than a week before use. During this time, the protective effects of preconditioning may have been lost. However, 

the contamination effects are substantially minimized for trace 

metal constituents. In cases where water samples are composited into a single filtered bottle, such as used in the 14-day 

automated sampling routine for nutrients, only small amounts 

of water (<200 mL) are typically passed through a preconditioned filter in the field for analysis. This may not have been 

sufficient to rinse any contamination from the filter that was 

generated in it after preconditioning. For manual sample collection, in most cases, capsule filters are preconditioned the 

day they are to be used; in some cases, preconditioned filters 

may have been held in refrigerated storage for more than 

24 hours before use, and this hold time, or even a shorter hold 

time (<24 hours), may have resulted in sample contamination.

In December 2015, nine filters were tested in an effort to 

characterize potential contamination of water samples from 

organic nitrogen associated with the capsule filters. In this test, 

filters were preconditioned by following USGS National Field 

Manual recommended procedures: 2 L of deionized water was 

passed through each filter at several different time periods 

before the filter was used to collect test samples (table 3). One 

filter was preconditioned about 4 weeks prior to collecting 

test samples and was stored in the laboratory refrigerator. Six 

filters also were preconditioned about 4 weeks prior to collecting test samples and were installed in the field as part of the 

automatic sampling system. To serve as a control, two filters 

from a different manufacturer’s lot were not preconditioned 

Table 3. Test results from capsule filter experiments.

[Unless noted otherwise, all filters were prerinsed (conditioned) by flushing with 2 liters (L) of deionized water (DIW) at a rate less than or equal to 1 L per minute before samples were collected. Disposable Pall GWV high-capacity in-line capsule filters (0.45 micrometer) were used. NWIS, National Water Information 

System; N, nitrogen; mg/L, milligram per liter; mL, milliliter; --, no data; <, less than]

Sample Sample identification Water sampled

NWIS 

capsule 

filter lot 

number

Ammonia + 

organic N 

(mg/L)

Alkaline 

persulfate N 

(mg/L)

1 Source water Direct from Millipore Elix Advantage 10 water system-- <0.07 <0.05

2 Filter 1 (installed about 4 weeks in the field before testing) First 125 mL passed through filter 10027 4.35 5.2

3 Filter 1 (installed about 4 weeks in the field before testing) 125 mL after 875 mL passed 

through filter

10027 <0.07 0.089

4 Filter 2 (installed about 4 weeks in the field before testing) First 125 mL passed through filter 10027 6.33 7

5 Filter 3 (installed about 4 weeks in the field before testing) First 125 mL passed through filter 10027 14.9 17.3

6 Filter 3 (installed about 4 weeks in the field before testing) 125 mL after 875 mL passed 

through filter

10027 0.184 0.241

7 Filter 4 (installed about 4 weeks in the field before testing) First 125 mL passed through filter 10027 9.08 11.9

8 Filter 5 (installed about 4 weeks in the field before testing) First 125 mL passed through filter 10027 6.11 9.3

9 Filter 5 (installed about 4 weeks in the field before testing) 125 mL after 875 mL passed 

through filter

10027 <0.07 0.09

10 Filter 6 (installed about 4 weeks in the field before testing) First 125 mL passed through filter 10027 7.93 10.3

11 Filter 7 (not prerinsed, not conditioned) First 125 mL passed through filter 10033 0.108 0.127

12 Filter 8 (not prerinsed, not conditioned) First 125 mL passed through filter 10033 0.245 0.282

13 Filter 9 (stored about 4 weeks in refrigerator before testing) First 125 mL passed through filter 10027 <0.07 <0.05
Data Analysis 13

at all. Source water was provided from the Millipore water 

system. Concentrations of all nitrogen species in the source 

water were below detection limits (table 3). The capsule filters, 

except for the control filters, were tested by collecting the first 

125 mL of water that passed through the filter after the holding 

period; the control filters were tested with no preconditioning or holding period. For three filters that were previously 

installed in the field, a second sample was collected representing the terminal part of 1 L of filter water; that is, about 

875 mL of source water was passed through the filter to the 

sink, and the final 125 mL of source water was collected in the 

sample bottle. All samples were analyzed for unacidified dissolved ammonia plus organic nitrogen and for total dissolved 

nitrogen (table 3).

Concentrations of dissolved ammonia plus organic 

nitrogen and total dissolved nitrogen in water collected from 

capsule filters that were preconditioned and stored at ambient 

temperatures for several weeks were high, ranging from 4 to 

15 mg/L and 5 to 17 mg/L, respectively (table 3). Nitrogen 

concentrations were lower (about 80 times lower on average) 

when flushed with less than a liter of deionized water. Nitrogen concentrations for the blank samples collected through the 

preconditioned filters stored in the refrigerator in the filter test 

were less than detection limits. However, concentrations of 

dissolved ammonia plus organic nitrogen and total dissolved 

nitrogen in a USGS field blank sample collected in July 2015 

were 0.195 and 0.23 mg/L, respectively (USGS, unpub. data). 

The time of filter conditioning and (or) storage duration for 

the filter used to prepare the July 2015 field blank was not 

recorded, but storage in the refrigerator after preconditioning 

could have been a factor in the detections of ammonia plus 

organic nitrogen and total dissolved nitrogen.

Results from the tests described in the present study, as 

well as results from recent, similar testing of capsule filters 

and holding times by the NWQL (unpub. data, USGS, Office 

of Water Quality Information Note 2017.03), indicate that 

the organic nitrogen originating as contamination within the 

capsule filter is rapidly flushed from the filters. However, the 

filters in the automated system sit for 10 to 13 days, and detections under the conditions seen in the automated system make 

all dissolved total nitrogen results in filtered samples questionable. For this reason, loading calculations for dissolved total 

nitrogen in filtered samples based on automatically collected 

composite samples are not included in this report.2

Equal-Width-Increment and Point Sample 

Comparisons

Fifteen EWI and point sample pairs were collected 

concurrently from the upstream railroad bridge and at the 

Millville station intake point to evaluate the representativeness 

2

Contamination of organic nitrogen from capsule filters may have affected 

concentrations of total dissolved nitrogen in samples collected with the automated system in the previous Blackstone River loads study, Zimmerman and 

others (2015), but the extent of that potential effect is undetermined.

of the station’s single intake point for the entire cross section of the river. The timing of sampling events was chosen 

to cover as wide a range of flow and turbidity conditions 

as possible (fig. 2). EWI samples were collected from 9 to 

12 locations across the river on the downstream side of the 

railroad bridge and emptied into a precleaned polyethylene 

churn as a single composite sample. At the point location at 

the Millville station, 12 point samples were collected on a 

timed program into a precleaned polyethylene churn with an 

ISCO 6700 automated sampler equipped with a peristaltic 

pump. Table 4 shows the relative percent differences (RPDs) 

between these samples. About 11 percent of all constituents 

had an incidence or incidences where RPDs were greater than 

the established performance criterion of 20 percent (quality 

assurance project plan, Robert F. Breault and Kim W. Campo, 

U.S. Geological Survey, written commun., 2007). Suspended 

sediment concentration and particulate nitrogen had the highest number of values greater than established performance 

criteria. Dissolved copper, total and dissolved zinc, and ammonia had fewer 20-percent exceedances, and total aluminum 

and some trace metals had the least number of performance 

criteria exceedances (table 4). Of the three samples associated 

with the most RPDs greater than the performance criteria, two 

were collected during two low-flow periods, and one was collected during the highest flow of all sampling events between 

WYs 2013 and 2014. Only one of these three sampling events 

was associated with substantial rainfall prior to sampling.

Table 4. Concentrations of nutrients, trace metals, and 

suspended sediment in sample pairs collected from the upstream 

railroad bridge and from the point location at the Blackstone River 

at Millville, Massachusetts, station (01111230).

[Table available for download at https://doi.org/10.3133/sir20175094]

Many constituents had no or few RPD values greater than 

the performance criterion. These include water temperature, 

specific conductance, pH, dissolved oxygen, and alkalinity, as 

well as all major ions and several trace metals (table 4). The 

primary components of the study, total nitrogen (and almost 

all nitrogen species) and total phosphorus, showed agreement 

between point and EWI samples (table 4). All water-quality 

parameters were measured in situ by using multiple vertical 

measurements for the EWI/bridge samples and a single point 

measurement of water-quality parameters at the Millville 

station intake point. Overall the point location is considered 

representative of the Blackstone River.

Data Analysis

Data collected by this project were analyzed in multiple 

ways. Loads of constituents were calculated by using the concentrations provided by laboratory analysis and the average 

flow of the river during each respective sampling period.
14 Nutrient and Metal Loads Estimated for the Blackstone River, Massachusetts and Rhode Island, Water Years 2013–14

Explanatory variables are defined as those that can be 

measured continuously at a station by using automated sensors. Correlation analysis showed which of the possible predictive relations had the most potential to be used to estimate 

selected constituent concentrations, versus the generally more 

expensive option of collecting representative samples and 

submitting them for laboratory analysis.

Selected explanatory variables are related to selected 

water-quality constituents by using ordinary least squares 

regression techniques. Regression models were developed by 

using multiple linear regression analysis and one or more of 

the explanatory variables from the near real-time record to 

estimate the concentration of selected water-quality constituents in near real-time.

Load Calculation

Loads were calculated by multiplying 14-day nutrient 

and 4-day metal composite sample concentrations, collected 

with the automated flow-proportional system, by the average 

flow of their respective time periods (table 5). When flow data 

were missing, the average flow was based on the available 

data for the time period of interest, including data from the 

following sampling period. Two sets of 14-day nutrient loads 

were summed to approximate monthly loads, and all 14-day 

composite loads were combined to provide annual load values. All 15-minute streamflow values at the Millville station 

were estimated with the linear regression equation, using the 

15-minute streamflow at the Rt. 122 station.

Table 5. Concentrations of nutrients, total aluminum, and 

dissolved trace metals in 14-day nutrient composite samples 

and 4-day metal composite samples collected by the automated 

sampling system from the point location at the Blackstone River 

at Millville, Massachusetts, station (01111230) during water years 

2013 and 2014.

[Table available for download at https://doi.org/10.3133/sir20175094]

Correlation Analysis

Correlation analysis is a method to quantify the type and 

strength of relations between two variables (Haan, 1977; Press 

and others, 1992; Helsel and Hirsch, 2002; Granato, 2013, 

2014). Correlation coefficients were calculated for all of the 

water-quality variables collected during the monitoring period, 

as well as for the estimated streamflow and the precipitation 

variables (precipitation during the sampling event and precipitation recorded during the preceding 24, 48, and 72 hours). 

Rank correlations were calculated by using Spearman’s rho 

(ρ) (Haan, 1977; Helsel and Hirsch, 2002), and censored data 

were treated by using one-half of the detection limit. These 

correlation coefficients are dimensionless and are scaled to 

be in the range of −1 to 1, inclusive. The strength of relations 

between pairs of variables is indicated by the values of the 

correlation coefficients. The relation between two variables 

ranges from random association (no relation) to monotonic 

covariance (perfect correlation) as the absolute value of the 

correlation coefficient increases from 0 to 1. The sign of the 

correlation coefficient indicates the type of relation. A positive 

sign indicates that one variable generally increases as the other 

increases; a negative sign indicates that one variable generally 

decreases as the other increases; and a value of 0 indicates that 

variations in the two variables are totally unrelated. The statistical significance of the correlation coefficient is a function of 

the absolute value of the coefficient and the sample size.

The correlation coefficient is not a measure of a causal 

relation between variables. Variation in one variable may 

cause changes in another. For example, antecedent precipitation may be one factor causing increases in streamflow; 

another factor would be the streamflow that occurred before 

the precipitation event, or prestorm flow (Granato, 2010). Both 

variables may be affected by a third. For example, a positive correlation between specific conductance and pH may be 

affected by the negative correlations between these constituents and increasing streamflow. In this case, the positive correlation between the water-quality variables may be attributed 

to dilution from precipitation as well as chemical processes 

that affect both pH and conductance. An apparent correlation 

also may occur purely by chance. Confidence intervals for correlation coefficients indicate the likelihood that the value of a 

calculated correlation coefficient is due to chance.

Correlation coefficients, the associated 95-percent confidence intervals, and statistical-significance probability values 

for the coefficients were calculated by use of standard methods 

(Fisher, 1924; Haan, 1977; Press and others, 1992; Caruso and 

Cliff, 1997; Helsel and Hirsch, 2002; Granato, 2013, 2014). 

Paired sample sizes of five or more values were used to estimate correlation coefficients because Abdel-Megeed (1984) 

determined that at least five data pairs were necessary to begin 

to quantify the correlation. To compute Spearman’s rho, the 

data for the two selected variables x and y are ranked independently, and the correlation of the ranks is computed (Haan, 

1977; Press and others, 1992; Helsel and Hirsch, 2002). To 

calculate the ranks, the data are sorted and ranked from 1 to 

the number of data points (N). Tied data values are assigned a 

midrank, which is the average of the preceding and following 

ranks. The confidence interval is calculated from the sample 

size and the value of rho by using the Fisher’s Z transformation method (Fisher, 1924; Haan, 1977; Caruso and Cliff, 

1997). If the 95-percent confidence interval does not include a 

correlation value of 0, then the calculated correlation value is 

statistically significant. Spearman’s rho was calculated on the 

basis of the approaches described by Press and others (1992). 

The 95-percent confidence limits of each value of Spearman’s 

rho were calculated to determine the range of likely values of 

the actual rank correlation coefficient and to determine if the 

calculated value is significantly different from 0.

The rank correlations on the arithmetic and logarithmic 

values were calculated to help inform the development of predictive equations among variables. Analysis of the correlation 
Data Analysis 15

coefficients indicates the potential for developing quantitative 

regression equations between variables or the potential for 

multicollinearity among predictor variables if multiple linear 

regression equations are developed (Helsel and Hirsch, 2002). 

Spearman’s rho is a robust estimator of a monotonic relation 

between two variables that is resistant to outliers; the rho value 

is not dependent on the linearity of the relation between variables (Haan, 1977; Press and others, 1992; Helsel and Hirsch, 

2002; Granato, 2014).

Correlations Among Potential Explanatory 

Variables

Analysis of correlations among potential explanatory 

variables indicates possible causal relations between selected 

variables, possible predictive relations between variables, and 

the potential for relations that may cause multicollinearity if 

used. Strong correlations between variables also may provide 

an opportunity to substitute an expensive or difficult measurement with a less expensive and (or) more robust alternative. In 

this study, potential explanatory variables are defined as those 

variables that can be measured automatically by sensors at 

field monitoring stations. These variables include streamflow, 

water temperature, specific conductance, dissolved oxygen, 

pH, chlorophyll a, turbidity, and current or antecedent precipitation volumes.

Multicollinearity is of concern because strong 

correlations among predictor variables could adversely 

affect the development and interpretation of multiple linear 

regression equations between these explanatory variables and 

the water-quality constituents that are of interest to waterresource managers (Helsel and Hirsch, 2002). The effect of 

multicollinearity is quantified by using the variance inflation 

factor (VIF). The VIF increases the width of the confidence 

interval for the regression coefficient compared to a perfectly 

independent set of explanatory variables. Helsel and Hirsch 

(2002, p. 306) indicate that “serious problems” may occur if 

the VIF for a given predictor is greater than 10. The VIF for a 

variable is equal to the reciprocal of one minus the coefficient 

of determination (R2) between predictors. Therefore, a VIF 

of 10 would equal a correlation coefficient (R) value of about 

0.9486. A VIF value of 5 is the boundary between moderately 

and highly correlated variables and is equivalent to an R value 

of about 0.894 (Minitab Inc., 2015).

Regression Model Development

Regression models were developed to provide the 

means for estimating near real-time values of concentrations 

and loads of water-quality constituents of interest, such 

as dissolved and total nitrogen and phosphorus, from the 

explanatory variables that, in theory, can be measured 

throughout the year by continuous monitoring stations. The 

correlation analyses were used to evaluate the potential for 

developing regression equations for use with available near 

real-time measurements. Regression equations were developed 

for concentrations but not for loads. Because loads are the 

product of concentration and streamflow, regression equations 

developed for loads with the highest predictive power will by 

necessity include streamflow as an explanatory variable. The 

use of streamflow in this way, however, causes problems in 

the development and interpretation of the resulting regression 

equations and adversely affects regression statistics that are 

used to estimate prediction intervals for the equations; these 

problems are described as spurious self-correlation (Kenney, 

1982; Vogel and others, 2007; Shivers and Moglen, 2008). 

The problems associated with spurious self-correlations 

are made worse if logarithmic transformations are used to 

develop the regression equations (Kenney, 1982). This is 

not to say, however, that measured flow is not an important 

variable for consideration in the development of regression 

equations for estimating concentrations. Equations that use 

streamflow to estimate concentration, known as water-quality 

transport curves, can be the best way to accurately estimate 

concentrations if the relations are strong and other near realtime measurements are not readily available (O’Connor, 1976; 

Glysson, 1987; Granato, 2006; Granato and others, 2009). 

Therefore, measured flows and estimated concentrations 

provide the best possible load estimates with meaningful 

prediction-interval estimates.

Analytical Procedures for Regression Analysis

Ordinary least squares regression techniques were used 

to relate the selected explanatory variables to the selected 

water-quality constituents. Multiple linear regression analysis 

was used to develop regression models that incorporated one 

or more automated measurements to represent the concentration of constituents of concern in the near real-time record. 

Multiple linear regression analysis using ordinary least squares 

techniques provides a systematic method for estimating the 

coefficients of a mathematical equation of the relation between 

a response variable and two or more explanatory variables 

(Haan, 1977; Tasker and Granato, 2000; Helsel and Hirsch, 

2002). In this regression analysis, concentration (the dependent variable) is statistically related to one or more automated 

hydrologic or water-quality variables recorded at the monitoring station (the independent variables). This results in 

equations that can be used to estimate the water quality when 

water-quality sample analyses are not available. The multiple 

linear regression equations commonly are developed in the 

following form:

Yp = β0 + β1X1 + β2X2 + ... ++ βnXn + ε, (1)

or, if equations are developed by using the logarithms of data,

log(Yp) = β0 + β1log(X1) + β2 log(X2) + ... ++ βnlog(Xn) + ε, (2)
16 Nutrient and Metal Loads Estimated for the Blackstone River, Massachusetts and Rhode Island, Water Years 2013–14

where

Yp is the predicted water-quality value,

β0 is the estimated value of the linear intercept,

n is the number of explanatory variables used in 

the equation, 

X1 to Xn are the values of each of the n explanatory 

variables, 

β1 to βn are the slopes associated with each of the n

explanatory variables, and 

ε is the random error component (scatter of 

measured points around the regression 

estimates).

The concentrations and the potential explanatory variables were transformed to their common (base 10) logarithms 

to develop the regression models. The precipitation variables, 

however, were not readily transformable to logarithms. The 

precipitation variables have many 0 values, and the logarithm of 0 is undefined; therefore, a value of 1 inch (half the 

minimum reporting limit of the precipitation gage) was added 

to all precipitation values to enable use of the logarithms of 

precipitation variables. The value of 1 was selected because 

the common logarithm of 1 is equal to 0. Transforming the 

variables to logarithms increased the linearity of relations and 

reduced heteroscedasticity (nonconstant variance of residuals). 

Once the coefficients are calculated, equation 2 is transformed 

to a power equation in arithmetic space because the estimated 

concentrations (rather than the logarithms of the estimated 

concentrations) are of interest and because the arithmetic 

values of the explanatory variables are more intuitive to use. 

Addition in log space is equivalent to multiplication in arithmetic space, and multiplication in log space is equivalent to 

exponentiation in arithmetic space. If retransformed from the 

common (base 10) logarithms, equation 2 becomes

Y X p n X X n = × 10 × × ×× ×10 0 1 2

1 2

β β β  β ε. (3)

In regression analysis, the mean of the errors (ε) should be 

0 in log space; when transformed, this term would equal 1. 

However, the mean of the errors in logarithmic space is the 

geometric mean of errors in arithmetic space. As a consequence, the best-fit line in logarithmic space tends to provide 

a biased estimate of the dependent variable in arithmetic 

space, and a bias correction factor is needed to compensate. 

The nonparametric smearing estimator (the average of the 

retransformed log-regression residuals) proposed by Duan 

(1983) was selected as a bias correction factor for the regression equations developed in this study because it performs 

reasonably well and is not sensitive to statistical assumptions 

regarding residual-population characteristics (Gilroy and others, 1990; Crawford, 1991; Hirsch and others, 1993; Tasker 

and Granato, 2000; Helsel and Hirsch, 2002; Granato, 2012). 

The Duan (1983) bias correction factor is called the smearing 

estimator because the method applies or “smears” the average retransformed error over all measurements. A generalized 

expression of the smearing estimator, applicable for any logbased transformation, is the following:

BCF

e

N

i

i

n

xy

= =

∑G( ) 1 , (4)

where

BCF is the bias correction factor,

G is the retransformation function,

ei is the residual error, which is calculated by 

subtracting the regression estimate from 

the data value for each data point (Yi), and

Nxy is the number of XY data pairs.

For the common logarithms, G is:

G ei

ei ( ) = 10 . (5)

A number of statistics are commonly used to assess the 

strength of a regression equation (Haan, 1977; Gilroy and 

Tasker, 1990; Tasker and Granato, 2000; Helsel and Hirsch, 

2002; Granato, 2012). The coefficient of determination, commonly known as the R-squared (R2

), indicates the fraction of 

the variance explained by explanatory variables in the model. 

The adjusted R2 also indicates the fraction of the variance 

explained by the explanatory variables in the model; however, 

in contrast to R2, the adjusted R2 is adjusted for the number of 

variables in the model and the size of the sample. In general, 

larger R2 values indicate a better fit to the available data; a 

perfect linear fit would have an R2 value of 1. The prediction error sum of squares (PRESS) statistic is the sum of the 

squared errors calculated for each value (i) by using a version 

of the regression equation developed with all the other Nxy−1 

values. In theory, the equation with the minimum PRESS value 

will produce the least error when making predictions with new 

data. The average standard error of the estimate (ASEE) is also 

known as the mean-square error and as the variance of the residuals (σ2

); it is the sum of squared residual errors divided by 

Nxy−2. In this case, it is a measure of the variation between the 

concentration estimates and the observed predictive variables. 

The square root of the ASEE is known as the root mean-square 

error or the standard deviation of residuals (σ). In general, 

regression models with small ASEE values will produce the 

least error among the available data. ASEE values are calculated within log space and are commonly converted to percent 

errors to facilitate model evaluation and comparison. The 

ASEE statistic is converted from a logarithm to a percent error 

by using the following equation:

ASEE e percent = × − 



 



 ( ) ×( ) ( ) 100 1

2 2 10

0 5

σ ln

.

. (6)

Theoretically, about two-thirds of the estimates obtained from 

the equations in the regression analysis will have errors less 
Continuous and Manual Water-Quality Data 17

than the calculated standard errors of estimate. The average 

standard error of the prediction (ASEP) is similar to the ASEE

but is a measure of the predictive ability of the regression 

model. The ASEP can be estimated by using the PRESS statistic (Gilroy and Tasker, 1990; Koltun and Whitehead, 2002; 

Granato, 2012), as described in the following equation:

ASEP PRESS

N est

xy

= . (7)

The ASEP can be converted from a logarithm to a percent 

error by using the method shown in equation 7. In theory, 

regression models with small ASEP values will produce the 

least error for predictions using new data. Theoretically, about 

two-thirds of the concentration estimates obtained from automated measurements will have errors less than the calculated 

standard errors of prediction.

Continuous and Manual Water-Quality 

Data

This section of the report examines the range and quality of continuous water-quality measurements and discusses 

analytical results from samples collected by the automated 

sampling system at the Millville station, as well as samples 

collected manually from the intake point at the station and 

from upstream bridge.

Continuous Water-Quality Data

Temperature generally followed seasonal patterns, 

except during runoff events, and was warmest during summer months and coldest in winter months over the period of 

record (WYs 2013 and 2014). The median water temperature recorded at the Millville station was about 11.5 °C over 

the period of record. The lowest temperature was 0.0 °C on 

December 15, 2013, and many other days in winter, and the 

highest was 29.3 °C on July 3, 2014.

Changes in specific conductance also followed a typical seasonal pattern. Specific conductance was highest in 

winter months, and large peaks in the record were associated 

with the runoff of winter deicing and maintenance materials from impervious surfaces. Runoff from meltwater and 

spring rains begin to clear impervious surfaces and decrease 

specific conductance. Late spring and early summer are typically associated with the lowest specific conductance values. 

Although runoff events during the summer and fall cause 

short-term decreases in specific conductance observed until 

winter road maintenance activities begin again, the specific 

conductance gradually increases during the summer and fall. 

Median conductance was 476 microsiemens per centimeter 

at 25 degrees Celsius (μS/cm at 25 °C). The lowest recorded 

specific conductance was 202 μS/cm in April 2014, and the 

highest was 1,550 μS/cm in January 2014.

The lowest turbidity was 0.4 formazin nephelometric units (FNUs), and the highest turbidity, which followed 

sediment-laden winter runoff events, was 67 FNUs. The 

median turbidity for the period of record was 2.5 FNUs.

Median chlorophyll a was 8.1 parts per billion (ppb). The 

lowest measured chlorophyll a was 0.07 ppb, and the highest 

was 268 ppb. Diurnal fluctuations of chlorophyll a were also 

observed throughout the record during peak growing months 

(June through September). Chlorophyll a values have been 

used as a measure of algal concentrations in lakes (Vollenweider and Kerekes, 1982; Kreakie and others, 2015). Oligotrophic conditions, or low algal concentrations, are associated 

with chlorophyll a concentrations less than 2.0 ppb, whereas 

hypereutrophic conditions, or very high algal concentrations, 

are considered to be those chlorophyll a concentrations greater 

than 35 ppb.

Automated and Manually Collected 

Concentration Data

Analytical results from samples collected by the automated flow-proportional sampling system and manual sampling techniques are listed in tables 5 and 6, respectively. At 

the Millville station, fifty 14-day composite samples were 

collected by the automated flow-proportional system for nutrients, and fifty-two 4-day composite samples were collected 

by the automated system for dissolved trace metals and total 

aluminum. Over 30 manually collected samples were collected either at the Millville station (as point samples) or at the 

upstream railroad bridge (with the EWI method). A subset of 

these EWI and point samples were collected as pairs to evaluate representativeness of the Millville station intake point, 

discussed in the section “Equal-Width-Increment and Point 

Sample Comparisons.”

Table 6. Concentrations of nutrients, trace metals, and 

suspended sediment in manually collected samples from the 

upstream railroad bridge and from the collection point at the 

Blackstone River at Millville, Massachusetts, station (01111230) 

during water years 2013 and 2014.

[Table available for download at https://doi.org/10.3133/sir20175094]

Suspended Sediment

Excessive suspended sediment concentration limits light 

penetration and covers habitat in sediment, which can have 

negative ecological effects on fish, invertebrates, and aquatic 

vegetation (EPA, 2003). Suspended sediment guidelines 

are not established for the Blackstone River. However, the 

highest maximum daily concentration of total suspended 

sediment (TSS) in 24-hour composite samples of treated 

effluent, as specified in the 2010 Upper Blackstone Pollution 
18 Nutrient and Metal Loads Estimated for the Blackstone River, Massachusetts and Rhode Island, Water Years 2013–14

Abatement District, National Pollutant Discharge Elimination 

System (NPDES) permit, is 55 mg/L TSS. Therefore, for 

this study, concentrations greater than 55 mg/L TSS may be 

informally considered representative of poor water quality in 

the Blackstone and other northeastern U.S. streams (Kimberly 

Groff, MassDEP, written commun., 2011). Samples collected 

by the automated system were not submitted for suspended 

sediment analysis. Suspended sediment concentration in 

manually collected samples ranged from 1.0 to 75 mg/L 

during WYs 2013–14 (table 6).

Nitrogen and Phosphorus

Total and dissolved nitrogen concentrations in composite 

samples collected with the automated system ranged from 

0.77 to 2.71 mg/L and 0.69 to 2.65 mg/L, respectively, during 

WYs 2013 and 2014 (table 5). It is unclear how much contamination from the 0.45-μm capsule filters may have affected 

dissolved nitrogen concentrations in composite samples collected by the automated system. However, manually sampled 

concentrations of total and dissolved nitrogen were similar, 

ranging from 0.88 to 2.83 mg/L and 0.78 to 2.80 mg/L, respectively (table 6). Concentrations for each method of sample 

collection are shown as boxplots in figure 4A.

Total and dissolved phosphorus concentrations are also 

shown in boxplot form (figs. 4B and C). Composite samples 

collected with the automated system ranged from 0.030 to 

0.200 mg/L for total phosphorus and 0.010 to 0.150 mg/L for 

dissolved phosphorus (table 5). Manually sampled concentrations of total and dissolved phosphorus ranged from 0.040 to 

0.356 mg/L and 0.015 to 0.124 mg/L, respectively (table 6). 

Trace Metals

Unlike manually collected samples, which were analyzed 

for both total and dissolved trace metals, samples collected by 

the automated system were submitted for analysis of dissolved 

trace metals and total aluminum. Boxplots of dissolved metal 

and total aluminum concentrations from all three sampling 

methods are shown in figure 5. All other total metal concentrations and chloride concentrations from only manual sampling 

methods are shown in figure 6.

Dissolved cadmium and chromium concentrations in 

samples collected by the automated system ranged from 

0.11 to 0.75 and 0.19 to 2.5 μg/L, respectively, during 

WYs 2013–14 (table 5 and figs. 5A and B). Manually sampled 

concentrations of dissolved cadmium and chromium ranged 

from 0.13 to 0.46 and 0.14 to 0.70 μg/L, respectively (table 6 

and figs. 5A and B). Dissolved copper concentrations in 

composite samples collected with the automated system 

ranged from 2.1 to 9.2 μg/L (table 5 and fig. 5C). Manually 

sampled concentrations of total and dissolved copper ranged 

from 3.0 to 25.4 and 2.0 to 10.4 μg/L, respectively (table 6 and 

fig. 5C). 

Dissolved lead and nickel concentrations in automated 

samples ranged from 0.19 to 5.9 and 1.4 to 3.6 μg/L, respectively (table 5 and figs. 5D and E). Dissolved lead concentrations in manual samples ranged from 0.3 to 20.6 μg/L (table 6 

and fig. 5D). Dissolved nickel concentrations in manual 

samples ranged from 1.3 to 4.4 μg/L (table 6 and fig. 5E). 

Dissolved zinc concentrations in the automated 4-day composite samples ranged from 6.9 to 19.7 μg/L, and dissolved zinc 

concentrations in samples collected manually ranged from 5.9 

to 37.8 μg/L (tables 5 and 6 and fig. 5F). 

Total aluminum concentrations in samples collected by 

the automated system ranged from 12.8 to 395 μg/L; concentrations ranged from 35.8 to 1,080 μg/L in samples collected 

manually (tables 5 and 6 and fig. 5G). Manual sampling 

captured samples with much higher concentrations of aluminum. Manually collected samples with the largest concentrations of aluminum appear to be associated with storm runoff, 

particularly during the winter and spring. Composite samples 

collected by the automated system over 4 days were less sensitive to maximum and minimum concentrations than manually 

collected samples were.

Total cadmium concentrations in manually collected 

samples ranged from 0.23 to 1.18 μg/L, and total chromium 

concentrations ranged from 0.43 to 12.4 μg/L (table 6 and 

figs. 6A and B). Manually sampled concentrations of total 

copper ranged from 3.0 to 25.4 μg/L (table 6 and fig. 6C). 

Total lead concentrations in manual samples ranged from 0.70 

to 49.4 μg/L (table 6 and fig. 6D). Total nickel concentrations in manual samples ranged from 1.3 to 4.8 μg/L (table 6 

and fig. 6E). Total zinc concentrations in manually collected 

samples ranged from 9.5 to 55.2 μg/L (table 6 and fig. 6F).

Samples collected by both automated and manual techniques were also analyzed for selected major ions (tables 5 

and 6). Samples collected with the automated system were 

only analyzed for calcium and magnesium; however, manually collected samples were analyzed for calcium, chloride, 

magnesium, sodium, potassium, and sulfate concentrations, 

and results can be seen in tables 5 and 6. Two major ions are 

of particular interest are chloride and magnesium. Concentrations of chloride from manual samples ranged from 52.3 

to 201 mg/L (table 6 and fig. 6G). These data support the 

identification of upward trends in chloride identified in the 

Blackstone River by Savoie and others (2017). Concentrations 

of magnesium from samples collected by both methods ranged 

from 1.5 to 13.4 mg/L (tables 5 and 6). Magnesium concentrations from samples collected manually during WY13 were 

about 2.45 mg/L on average and in WY14 were about two 

times greater at 4.78 mg/L (table 6).
Continuous and Manual Water-Quality Data 19

x

x

x

24 20 52

x o

o

29 23 52

xx x

x

o

29 23 52

0.0

0.05

0.10

0.15

0.20

0.0

0.10

0.20

0.30

0.40

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Concentration, in milligrams per liter

A. Total nitrogen

B. Total phosphorus

C. Dissolved phosphorus

EWI/Bridge Point Auto/Composite

Number of values

Upper adjacent

Lower detached

75th percentile

25th percentile

Median

20

EXPLANATION

x

o

Lower adjacent

Lower outside

Upper outside

o Upper detached

x

Sample type

Figure 4. A, Total nitrogen, B, total phosphorus, and C, dissolved phosphorus concentrations collected from the 

upstream train bridge (EWI/Bridge), the Millville station intake point (Point), and the automated system (Auto/

Composite) from the Blackstone River at Millville, Massachusetts, station (01111230), water years 2013 and 2014. 
20 Nutrient and Metal Loads Estimated for the Blackstone River, Massachusetts and Rhode Island, Water Years 2013–14

x

x x

o

o

20 23 52

x

x

x

x

o

20 23 52

x

o

20 23 52

o

x

x x

o

o

oo

23 52

x

x

o

x

x

x

20 23 52

o

x

20 23 52

x x

x

xx

x

o

o

17 23 52

2

4

6

8

10

12

1.0

1.5

2.0

2.5

3.0

0.0

0.2

0.6

0.8

1.0

Concentration, in micrograms per liter

A. Dissolved cadmium

B. Dissolved chromium 

C. Dissolved copper

EWI/Bridge Point Auto/Composite

EWI/Bridge Point Auto/Composite

F. Dissolved zinc

E. Dissolved nickel

0.4

0.5

0.0

0

1

2

3

4

5

6

30

20

10

40

0

50

1

2

3

4

5

D. Dissolved lead 7

20

20.6 μg/L

600

400

200

1,000

0

1,200

800

G. Total aluminum

Sample type

Sample type

Number of values

Upper adjacent

Lower detached

75th percentile

25th percentile

Median

20

x

o

Lower adjacent

Lower outside

Upper outside

o Upper detached

x

EXPLANATION

Figure 5. Concentrations of dissolved trace metals A, cadmium, B, chromium, C, copper, D, lead, E, nickel, and F, 

zinc, and of G, total aluminum collected from the upstream train bridge (EWI/Bridge), the Millville station intake point 

(Point), and the automated system (Auto/Composite) from the Blackstone River at Millville, Massachusetts, station 

(01111230), water years 2013 and 2014.
Continuous and Manual Water-Quality Data 21

A. Total cadmium

B. Total chromium

C. Total copper

F. Total zinc

E. Total nickel

D. Total lead

G. Chloride

x xx

17 22

x

xx

17 22

x

x

17 22

x

x

o

x

x

17 22

x

xx

17 22

x

x

o x

x

17 22

x

x

x

o

x

x

27 22

20

0

5

25

10

30

4

6

8

10

12

14

0.2

1.4

Concentration, in micrograms per liter

EWI/Bridge Point

0.4

2

0

70

10

20

3

4

5

6

200

150

100

250

50

60

0

30

40

50

1

EWI/Bridge Point

Concentration, in micrograms per liter Concentration, in milligrams per liter

2

1.2

1.0

0.8

0.6

15

20

0

30

40

50

60

10

Sample type

Sample type

Number of values

Upper adjacent

Lower detached

75th percentile

25th percentile

Median

20

x

o

Lower adjacent

Lower outside

Upper outside

o Upper detached

x

EXPLANATION

Figure 6. Concentrations of total trace metals A, cadmium, B, chromium, C, copper, D, lead, E, nickel, and F, zinc, and 

of G, chloride collected from the upstream train bridge (EWI/Bridge) and the Millville station intake point (Point) from the 

Blackstone River at Millville, Massachusetts, station (01111230), water years 2013 and 2014. 
22 Nutrient and Metal Loads Estimated for the Blackstone River, Massachusetts and Rhode Island, Water Years 2013–14

Constituent Loads in the Blackstone 

River Crossing the MassachusettsRhode Island State Line, Water Years 

2013–2014

Concentrations of nutrients from the 14-day composite 

samples and metals from the 4-day composite samples collected by the automated system were individually multiplied 

by the average flow of their respective time periods to calculate loads. To compensate for missed days of sampling, the 

load per day times the number of missed sampling days within 

its time period was added to the load without missing days. 

Monthly, seasonal, and annual loading values for nutrients and 

metals are discussed on the basis of these adjusted values and 

are compared to previously published loads for the Blackstone 

River for WYs 2008 and 2009.

Nitrogen and Phosphorus

Fourteen-day loads of total nitrogen and total and dissolved phosphorus are listed in table 7. The maximum and 

minimum total nitrogen loads of the fifty 14-day composites collected during WYs 2013 and 2014 were 46,170 and 

1,932 kg, respectively. The ranges of total and dissolved 

phosphorus loads based on the 14-day composites were 5,397 

to 120 kg and 1,799 to 15 kg, respectively.

Table 7. Loads of nutrients based on 14-day nutrient composite 

samples, and loads of dissolved trace metals and total aluminum 

based on 4-day metal composite samples collected by the 

automated sampling system from the point location at the 

Blackstone River at Millville, Massachusetts, station (01111230) 

during water years 2013 and 2014.

[Table available for download at https://doi.org/10.3133/sir20175094]

Two 14-day composite loads were summed to approximate monthly total nitrogen loads and total and dissolved 

phosphorus loads, as shown in figure 7. The largest 28-day 

loads of total nitrogen were in April of 2014, followed by 

March and June of 2013 (fig. 7A). The largest 28-day loads of 

total phosphorus were in June 2013, followed by April 2014 

(fig. 7B). However, the largest 28-day dissolved phosphorus 

loads were observed in October 2012, followed by June 2013 

and April 2014 (fig. 7B). Seasonally, the largest nitrogen loads 

appeared in the spring and winter during WYs 2013 and 2014, 

and the largest phosphorus loads were seen in the spring and 

summer and associated with major storm events.

The annual load of total nitrogen in WY 2013 was about 

447,000 kg. Estimated flows at Millville in WY 2014 were 

about 25 percent lower than in WY 2013, and the annual load 

of total nitrogen in WY 2014 was about 342,000 kg. The 

annual loads of total and dissolved phosphorus in WY 2013 

were about 35,900 and 12,000 kg, respectively. In WY 2014, 

the annual loads of total and dissolved phosphorus were about 

20,700 and 8,220 kg, respectively. The lower flows seen in 

WY14 are a possible explanation for the 42-percent decrease 

in total phosphorus loading. 

Zimmerman and others (2015) used a similar sampling 

system and reported the following estimated annual loads in 

the Blackstone River at Millville. The estimated annual load of 

total nitrogen was 936,000 kg in WY 2008 and 878,000 kg in 

WY 2009. The estimated annual load of total phosphorus was 

81,400 kg in WY 2008 and 80,900 kg in WY 2009. Total nitrogen and total phosphorus annual loads from WYs 2013 and 

2014 were about 56 and 65 percent lower than those reported 

for WYs 2008 and 2009. The higher loads in 2008 and 2009 

may be explained by the higher than average flows in WY 

2009 and by facility upgrades made by wastewater treatment 

facilities in the basin.

The estimated annual load of suspended sediment was 

4,940,000 kg in WY 2008 and 7,040,000 kg in WY 2009. As 

a point of comparison, the flows in WYs 2008 and 2009 were 

about 38 and 25 percent less, respectively, than the long-term 

(WYs 1929–2012) mean annual flow of 22.5 m3/s (793 ft3/s) 

at the Blackstone River at Woonsocket, Rhode Island, gage 

(USGS station 01112500). During WYs 2013 and 2014, flows 

were about 50 and 76 percent less, respectively, than the 

Woonsocket mean annual flow. Downward trends in nutrient 

concentrations in both the Blackstone River and Narragansett 

Bay have been reported (Savoie and others, 2017; Durant and 

Raposa, 2011).

Trace Metals

Four-day loads of magnesium, dissolved trace metals, 

and total aluminum, based on composite sample concentrations collected by the automated station multiplied by the 

average 4-day flows, are listed in table 7 and shown as a function of time in figure 8 (except magnesium).

Dissolved cadmium 4-day loads collected by the automated system during WYs 2013 and 2014 (fig. 8A) ranged 

from 0.16 to 12.2 kg, and dissolved chromium loads (fig. 8B) 

ranged from 0.21 to 56.7 kg, and the largest cadmium and 

chromium loads were associated with flows following a storm 

event on June 6, 2013. Dissolved copper loads (fig. 8C) ranged 

from 2.90 to 208.8 kg, and dissolved lead loads (fig. 8D) 

ranged from 0.19 to 134.1 kg. Dissolved nickel loads (fig. 8E) 

ranged from 1.59 to 49.9 kg, and dissolved zinc loads (fig. 8F) 

ranged from 6.67 to 419.8 kg. Individual total aluminum 4-day 

loads (fig. 8G) ranged from 10 to 7,015 kg, and the largest 

aluminum load was during the March 29, 2014, event. Median 

dissolved cadmium and chromium 4-day loads were 0.55 and 

0.84 kg, respectively, during WYs 2013 and 2014. Dissolved 

copper and lead median loads were 1.42 and 8.02 kg, respectively. The dissolved nickel median load was 5.45 kg, and the 

dissolved zinc median load was 36 kg. Median total aluminum 

4-day loads were about 197 kg.
Constituent Loads in the Blackstone River Crossing the Massachusetts-Rhode Island State Line, Water Years 2013–2014 23

0

200

400

600

800

1,000

1,200

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

90,000

Monthly load, in kilograms

Total N

Average monthly flow

Average monthly flow

Average monthly flow, in cubic feet per second Average monthly flow, in cubic feet per second

EXPLANATION

EXPLANATION

0

200

400

600

800

1,000

1,200

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

Monthly load, in kilograms

Dissolved P

Total P

October 2012

November 2012

December 2012

January 2013

February 2013

March 2013

April 2013

May 2013

June 2013

July 2013

August 2013

September 2013

October 2013

November 2013

December 2013

January 2014

February 2014

March 2014

April 2014

May 2014

June 2014

July 2014

August 2014

September 2014

October 2014

October 2012

November 2012

December 2012

January 2013

February 2013

March 2013

April 2013

May 2013

June 2013

July 2013

August 2013

September 2013

October 2013

November 2013

December 2013

January 2014

February 2014

March 2014

April 2014

May 2014

June 2014

July 2014

August 2014

September 2014

October 2014

A

B

Month

Figure 7. Monthly loads of A, total nitrogen (N) and B, total and dissolved phosphorus (P) based on 14-day 

composite samples from the Blackstone River at Millville, Massachusetts, station (01111230), water years 

2013 and 2014. Monthly loads are approximated as the sum of loads measured from the consecutive 14-day 

composite samples during the month indicated.
24 Nutrient and Metal Loads Estimated for the Blackstone River, Massachusetts and Rhode Island, Water Years 2013–14

EXPLANATION

Constituent 4-day load

Average 4-day flow

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

5,000

7,015.4 kg

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0

1

2

3

4

5

6

7

8

12.2 kg

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0

2

4

6

8

10

12

14

56.7 kg

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0

10

20

30

40

50

60

70

80

90

100

208.8 kg

10/13/201212/13/201202/13/201304/13/201306/13/201308/13/201310/13/201312/13/201302/13/201404/13/201406/13/2014

08/13/2014

10/13/2014

10/13/201212/13/201202/13/201304/13/201306/13/201308/13/201310/13/201312/13/201302/13/201404/13/201406/13/2014

08/13/2014

10/13/2014

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0

5

10

15

20

25

30

134.1 kg

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0

10

20

30

40

50

60

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0

50

100

150

200

250

300

350

400

450

4-day load, in kilograms

Average 4-day flow, in cubic feet per second

A. Dissolved cadmium

B. Dissolved chromium 

C. Dissolved copper

F. Dissolved zinc

E. Dissolved nickel

D. Dissolved lead

G. Total aluminum

Date

Date

Figure 8. 4-day loads of A, dissolved cadmium, B, dissolved chromium, C, dissolved copper, D, dissolved lead, E, dissolved nickel, 

F, dissolved zinc, and G, total aluminum, based on composite samples collected by the automated system from the Blackstone River at 

Millville, Massachusetts, station (01111230), water years 2013 and 2014. kg, kilogram.
Correlation Among Variables 25

Various peak loads exist in the individual records for 

metals, but in general two large loads can be seen in figure 8. 

These two extremes are associated with major storm events 

that occurred during the 4-day sampling periods or within 

72 hours of their start times. During the first of these two 

periods, which began on June 6, 2013, sampled flows included 

runoff from 0.54 inches (in.) of rain in the previous 72 hours. 

The second sampling period, which began on March 29, 

2014, followed a storm event with 3.78 in. of precipitation, as 

recorded by the Millville station.

Correlation Among Variables

Correlation coefficients among the potential explanatory 

variables taken from the discrete point samples and their associated water-quality parameter readings are shown in table 8. 

Many of these water-quality and hydrologic variables have 

statistically significant correlations with one another; however, 

only temperature and dissolved oxygen are highly correlated. 

This relationship is expected because the solubility of oxygen 

in water is a function of atmospheric pressure and temperature 

(Hem, 1992). Temperature sensors are less expensive, require 

less maintenance, are more robust, and are more reliable than 

dissolved oxygen sensors, which commonly need temperature 

compensation (Wagner and others, 2006). Thus, correlation 

analysis and monitoring logistics indicate that temperature is 

a good predictor for dissolved oxygen and may be selected as 

one of the explanatory variables for other constituents of interest, even if the correlation to temperature is slightly less than 

the correlation to dissolved oxygen (table 8).

The rank correlations among the precipitation variables 

are strong, but only the linear correlation between the 48- and 

72-hour precipitation totals is strong; logarithmic transformations for these variables are not applicable because logarithms 

are limited to nonzero, positive values. In table 8, the magnitudes and signs of the various correlation coefficients are, 

by and large, consistent with theoretical relations between 

measured variables (Hem, 1992).

Nutrient-Concentration Correlations

The use of automated measurements to estimate constituent concentrations can provide valuable information to 

help monitor abrupt changes in quality or short-term signals 

missed by fixed-frequency measurement. Analytical results 

from manually collected samples and water-quality parameter 

measurements were used in the following correlation analysis 

discussions.

Correlations Between Potential Explanatory 

Variables and Nutrient Concentrations

The values of correlations between selected explanatory variables and nutrient constituents of interest indicate the 

potential for developing quantitative, single or multiple linear 

regression equations to relate values of one or more automated 

measurements to concentrations of the constituents of interest 

(table 9). For this study, a rho ≥0.90 is considered strong, a rho 

≥0.80 to <0.90 is semistrong, a rho ≥0.75 to <0.80 is moderate, and a rho <0.75 is weak. The only semistrong correlations 

between the potential explanatory variables and nutrients 

are between discharge and dissolved nitrate (rho = −0.866), 

specific conductance and total nitrogen (rho = 0.844), specific 

conductance and dissolved nitrogen (rho = 0.806), turbidity 

and particulate carbon (rho = 0.864), and turbidity and particulate phosphorus (rho = 0.834). The remaining correlations 

are weak to moderate, indicating that two or more explanatory variables are needed to produce nutrient concentration 

estimates.

Correlations Among Nutrient Concentrations

Analysis of correlations among nutrient concentrations 

indicates possible causal relations between selected variables, possible predictive relations between variables, and the 

potential for substituting a constituent that is less expensive to 

collect, process, and analyze for a more expensive constituent. 

Identification of possible causal relations between selected 

variables may provide information that decision makers can 

use to identify potential sources of a nutrient and therefore the 

most effective mitigation measures. The ability to substitute 

a constituent that is less expensive to collect could result in 

greater efficiency in field operations by potentially reducing 

time spent in the field while simultaneously providing estimated data at a greater frequency. Cost savings from reduced 

work hours in the field could be shifted towards helping to 

increase the number of sampling events, and thereby increase 

the confidence in the representativeness of data.

Strong correlation coefficients for the nitrogen and 

phosphorus species indicate potential sources and transport 

mechanisms. Strong and semistrong correlation coefficients 

are shown as bold values in table 10. Correlation coefficients 

for the nitrogen species indicate that the total nitrogen and dissolved nitrogen are highly correlated (exceeding 0.96 for rho), 

and both are strongly correlated to nitrate (0.921 or greater); 

this indicates either that the sources and processes that contribute nitrogen to the river produce dissolved nitrogen or that 

the sources are predominantly nitrate. Furthermore, moderate 

to semistrong negative correlations between the explanatory variable of discharge and total nitrogen (rho = −0.662), 

dissolved nitrogen (rho = −0.759), and nitrate (rho = −0.866) 

indicate dilution with increasing flow (table 9). These negative 

correlations indicate that the primary source of nitrogen may 

be from groundwater discharge or a relatively constant point 

source (O’Connor, 1976; Albek, 2003; Granato, 2006; Granato 

and others, 2009). Total organic nitrogen, particulate nitrogen, 

and particulate carbon have semistrong to strong relations with 

each other (table 10). Although suspended sediment has a semistrong correlation with the explanatory variable of discharge 

(rho = 0.724), only the total organic nitrogen constituent has 
26 Nutrient and Metal Loads Estimated for the Blackstone River, Massachusetts and Rhode Island, Water Years 2013–14 Table 8. Correlation coefficients among potential explanatory variables. [Correlation coefficients that are statistically significant at the 95th percentile are shown as italic numbers. Correlation coefficients that are greater than 0.8 are shown as bold italic numbers. Water-quality parameters: p00010, temperature, water, degrees Celsius; p00060, discharge, cubic feet per second; p00095, specific conductance, water, unfiltered, microsiemens per centimeter at 25 degrees Celsius; p00300, dissolved oxygen, water, unfiltered, milligrams per liter; p00400, pH, water, unfiltered, field, standard units; p32209, chlorophyll a, fluorometric method, corrected, water, micrograms per liter; p63676, turbidity, water, unfiltered, broadband light source (400–680 nanometers), detectors at multiple angles including 90 ± 30 degrees, ratiometric correction, nephelometric turbidity ratio unit; p7977a, precipitation, total, in inches; p7977b, antecedent precipitation, total, (24-hour), in inches; p7977c, antecedent precipitation, total, (48-hour), in inches; p7977d, antecedent precipitation, total, (72-hour), in inches] Water-quality parameter Spearman’s rho Discharge (Q); p00060 Temperature (Tmp); p00010 Specific conductance (SC); p00095 Dissolved oxygen (DO); p00300 pH; p00400 Chlorophyll a (CA); p32209 Turbidity (Trb); p63676 Precipitation (P); p7977a 24-hour precipitation (24P); p7977b 48-hour precipitation (48P); p7977c 72-hour precipitation (72P); p7977d Discharge (Q) 1 Temperature (Tmp) -0.370 1 Specific conductance (SC) -0.436 0.032 1 Dissolved oxygen (DO) 0.027 -0.951 -0.217 1 pH -0.327 -0.091 0.063 0.184 1 Chlorophyll a (CA) -0.205 0.506 0.159 -0.789 -0.097 1 Turbidity (Trb) 0.491 -0.101 0.009 -0.379 -0.517 0.287 1 Precipitation (P) 0.111 -0.199 -0.075 0.000 0.000 -0.034 0.061 1 24-hour precipitation (24P) 0.484 -0.216 0.032 0.007 -0.619 0.171 0.395 0.441 1 48-hour precipitation (48P) 0.481 -0.154 0.004 -0.021 -0.570 0.192 0.497 0.456 0.933 1 72-hour precipitation (72P) 0.481 -0.135 0.000 -0.071 -0.584 0.200 0.495 0.425 0.990 0.993 1
Correlation Among Variables 27

Table 9. Correlation coefficients between potential explanatory variables and nutrient concentrations.[Correlation coefficients that are statistically significant at the 95th percentile are shown as italic numbers. Correlation coefficients that are greater than 0.8 are shown as bold italic numbers. Water-quality parameters for potential explanatory variables: temperature, water, degrees Celsius (p00010); discharge, cubic feet per second (p00060); specific conductance, water, unfiltered, microsiemens per centimeter at 25 degrees Celsius (p00095); dissolved oxygen, water, unfiltered, milligrams per liter (mg/L) (p00300); pH, water, unfiltered, field, standard units (p00400); chlorophyll a, fluorometric method, corrected, water, micrograms per liter (p32209); turbidity, water, unfiltered, broadband light source (400–680 nanometers), detectors at multiple angles including 90 ± 30 degrees, ratiometric correction, nephelometric turbidity ratio unit (p63676); precipitation, total, in inches (p7977a); antecedent precipitation, total, (24-hour), in inches (p7977b); antecedent precipitation, total, (48-hour), in inches (p7977c); antecedent precipitation, total, (72-hour), in inches (p7977d). Water-quality parameters for nutrient concentrations: p00600 tTN, total nitrogen, water, unfiltered, mg/L; p00602 fTN, total nitrogen, water, filtered, mg/L; p00605 tON, organic nitrogen (organic N), water, unfiltered, mg/L; p00607 fON, organic N, water, filtered, mg/L; p00608 fNH3, ammonia, water, filtered, mg/L as nitrogen (mg/L as N); p00613 fNO2, nitrite, water, filtered, mg/L as N; p00618 fNO3, nitrate, water, filtered, mg/L as N; p00665 tTP, phosphorus (P), water, unfiltered, mg/L; p00671 fOP, orthophosphate, water, filtered, mg/L as P; p00681 fOC, organic carbon, water, filtered, mg/L; p00694 pC, carbon (inorganic plus organic), suspended sediment, total, mg/L; p49570 pN, particulate nitrogen, suspended in water, mg/L; p62854 fSN, total nitrogen (nitrate + nitrite + ammonia + organic N), water, filtered, analytically determined, mg/L as N; p62855 tSN, total nitrogen (nitrate + nitrite + ammonia + organic N), water, unfiltered, analytically determined, mg/L as N]

Water-quality 

parameter

Spearman’s rho

Total 

nitrogen, 

water, 

unfiltered 

(mg/L); 

p00600 tTN

Total 

nitrogen, 

water, 

filtered 

(mg/L); 

p00602 fTN

Organic 

nitrogen, 

water, 

unfiltered 

(mg/L); 

p00605 tON

Organic 

nitrogen, 

water, 

filtered 

(mg/L); 

p00607 fON

Ammonia, 

water, 

filtered 

(mg/L as N); 

p00608 fNH3

Nitrite, 

water, 

filtered 

(mg/L as N); 

p00613 fNO2

Nitrate, 

water, 

filtered 

(mg/L as N); 

p00618 fNO3

Phosphorus, 

water, 

unfiltered 

(mg/L as P); 

p00665 tTP

Orthophosphate, 

water, 

filtered 

(mg/L as P); 

p00671 fOP

Organic 

carbon, 

water, 

filtered 

(mg/L); 

p00681 fOC

Carbon 

(inorganic 

plus organic), 

suspended 

sediment, 

total

(mg/L); 

p00694 pC

Particulate 

nitrogen, 

suspended 

in water

(mg/L); 

p49570 pN

Total nitrogen 

(nitrate + 

nitrite + 

ammonia + 

organic N), 

water, filtered, 

analytically 

determined 

(mg/L); 

p62854 fSN

Total nitrogen 

(nitrate + 

nitrite + 

ammonia + 

organic N), 

water, unfiltered, 

analytically 

determined 

(mg/L); 

p62855 tSN

Discharge (Q) -0.662 -0.759 0.528 0.323 0.483 0.287 -0.866 0.234 -0.507 0.074 0.336 0.2 -0.741 -0.619Temperature (Tmp) 0.212 0.221 -0.004 -0.313 -0.675 -0.097 0.261 0.438 0.495 0.195 -0.036 0.169 0.204 0.344Specific conductance 

(SC)

0.844 0.806 0.018 0.016 -0.112 0.144 0.71 0.169 0.318 0.054 -0.002 0.181 0.828 0.871

Dissolved oxygen 

(DO)

-0.27 -0.152 -0.436 -0.181 0.486 0 -0.156 -0.801 -0.457 -0.562 -0.409 -0.789 -0.13 -0.64

pH 0.112 0.252 -0.434 -0.497 -0.304 -0.084 0.28 -0.030 -0.106 -0.248 -0.310 -0.224 0.345 -0.248Chlorophyll a (CA) 0.310 0.322 0.135 -0.331 -0.243 -0.023 0.313 0.551 0.238 0.013 0.268 0.542 0.390 0.463Turbidity (Trb) 0.072 -0.046 0.783 0.323 0.314 0.229 -0.165 0.834 0.109 0.285 0.864 0.770 -0.045 0.171Precipitation (P) -0.102 -0.074 -0.063 0.046 0.071 0.036 -0.074 -0.112 -0.046 0.253 -0.021 -0.042 -0.126 -0.17024-hour precipitation 

(24P)

-0.263 -0.368 0.451 0.137 0.470 0.420 -0.444 0.324 -0.416 0.245 0.562 0.412 -0.464 -0.269

48-hour precipitation 

(48P)

-0.243 -0.345 0.531 0.135 0.374 0.413 -0.410 0.416 -0.275 0.308 0.631 0.461 -0.434 -0.218

72-hour precipitation 

(72P)

-0.247 -0.344 0.523 0.285 0.351 0.372 -0.405 0.426 -0.305 0.306 0.614 0.456 -0.437 -0.222
28 Nutrient and Metal Loads Estimated for the Blackstone River, Massachusetts and Rhode Island, Water Years 2013–14 Table 10. Correlation coefficients among nutrient concentrations. [Correlation coefficients that are statistically significant at the 95th percentile are shown as italic numbers. Correlation coefficients that are greater than or equal to 0.8 are shown as bold italic numbers. Water- quality parameters: p00600 tTN, total nitrogen, water, unfiltered, milligrams per liter (mg/L); p00602 fTN, total nitrogen, water, filtered, mg/L; p00605 tON, organic nitrogen (organic N), water, unfiltered, mg/L; p00607 fON, organic N, water, filtered, mg/L; p00608 fNH3, ammonia, water, filtered, mg/L as nitrogen (mg/L as N); p00613 fNO2, nitrite, water, filtered, mg/L as N; p00618 fNO3, nitrate, water, filtered, mg/L as N; p00665 tTP, phosphorus (P), water, unfiltered, mg/L; p00671 fOP, orthophosphate, water, filtered, mg/L as P; p00681 fOC, organic carbon, water, filtered, mg/L; p00694 pC, carbon (inorganic plus organic), suspended sediment, total, mg/L; p49570 pN, particulate nitrogen, suspended in water, mg/L; p62854 fSN, total nitrogen (nitrate + nitrite + ammonia + organic N), water, filtered, analytically determined, mg/L as N; p62855 tSN, total nitrogen (nitrate + nitrite + ammonia + organic N), water, unfiltered, analytically determined, milligrams per liter as N] Water-quality parameter Spearman’s rho Total nitrogen, water, unfiltered (mg/L); p00600 tTN Total nitrogen, water, filtered (mg/L); p00602 fTN Organic nitrogen, water, unfiltered (mg/L); p00605 tON Organic nitrogen, water, filtered (mg/L); p00607 fON Ammonia, water, filtered (mg/L as N); p00608 fNH3 Nitrite, water, filtered (mg/L as N); p00613 fNO2 Nitrate, water, filtered (mg/L as N); p00618 fNO3 Phosphorus, water, unfiltered (mg/L as P); p00665 tTP Ortho- phosphate, water, filtered (mg/L as P); p00671 fOP Organic carbon, water, filtered (mg/L); p00681 fOC Carbon (inorganic plus organic), suspended sediment, total (mg/L); p00694 pC Parti- culate nitrogen, suspended in water (mg/L); p49570 pN Total nitrogen (nitrate + nitrite + ammonia + organic N), water, filtered, analytically determined (mg/L); p62854 fSN Total nitrogen (nitrate + nitrite + ammonia + organic N), water, unfiltered, analytically determined (mg/L); p62855 tSN p00600 tTN 1 p00602 fTN 0.975 1 p00605 tON 0.052 -0.119 1 p00607 fON 0.109 0.018 0.685 1 p00608 fNH3 -0.204 -0.272 0.326 0.302 1 p00613 fNO2 -0.088 -0.171 0.284 0.120 0.415 1 p00618 fNO3 0.921 0.962 -0.24 -0.105 -0.435 -0.257 1 p00665 tTP 0.255 0.148 0.746 0.255 -0.050 0.028 0.045 1 p00671 fOP 0.549 0.556 0.047 0.138 -0.495 -0.091 0.539 0.345 1 p00681 fOC -0.001 -0.061 0.220 0.227 -0.129 0.284 -0.114 0.248 0.395 1 p00694 pC 0.052 -0.125 0.863 0.435 0.303 0.496 -0.211 0.845 0.228 0.414 1 p49570 pN 0.234 0.122 0.741 0.322 0.129 0.465 0.056 0.860 0.255 0.294 0.892 1 p62854 fSN 0.963 0.997 -0.081 -0.006 -0.312 -0.184 0.963 0.145 0.560 -0.147 -0.141 0.109 1 p62855 tSN 0.993 0.927 0.212 0.097 -0.247 -0.046 0.900 0.378 0.687 0.012 0.191 0.363 0.929 1
Correlation Among Variables 29

a statistically significant positive correlation to discharge 

(rho = 0.528; table 9). Total phosphorus has weak and statistically insignificant relations with total and dissolved nitrogen 

but has a moderate and statistically significant correlation to 

total organic nitrogen (rho = 0.746) and semistrong correlations with particulate nitrogen (rho = 0.860) and particulate 

carbon (rho = 0.845; table 10). Orthophosphate has a weak but 

statistically significant correlation with the total and dissolved 

nitrogen constituents, nitrate, and total phosphorus (table 10). 

Thus, correlations among nutrients are suggestive but not 

definitive (the correlations seem logical given a knowledge of 

sources, transport, and fate, but insufficient to form quantitative relations), probably indicating various sources, variable 

geochemical effects, and the effect of seasonality on discharge 

and sources of nutrients.

Trace Metal Concentration Correlations

Composite samples were collected from the Blackstone 

River in 4-day increments and provide data that support 

biotic ligand model analysis. Similar to the potential to use 

automated measurements to estimate nutrient concentrations, 

if real-time monitoring of metal concentrations and loads is 

feasible, it would support faster recognition of conditions toxic 

to aquatic organism health and could reduce analytical costs.

Correlations Between Potential Explanatory 

Variables and Metal Concentrations

The values of correlations between selected explanatory 

variables and concentrations of metal constituents of interest 

indicate potential sources and transport mechanisms and 

the potential for developing quantitative, single or multiple 

linear regression equations to relate values of one or more 

automated measurements to concentrations of the constituents 

of interest (table 11). The only semistrong correlations 

between the potential explanatory variables and metals are 

between turbidity and total Cd, total Cr, total Cu, total Pb, 

total Zn, and total Al. There also are semistrong correlations 

between dissolved oxygen and dissolved copper and between 

temperature and dissolved zinc. The remaining correlations 

are weak to moderate, indicating that two or more explanatory 

variables are needed to describe the variability in estimates 

of trace metal concentration. Several dissolved trace metals 

have negative correlations to discharge and (or) antecedent 

precipitation, which may indicate that the dissolved species 

are from point sources that are diluted by runoff (O’Connor, 

1976) or perhaps from groundwater discharge. Many of these 

correlations are weak, however, and many of the correlations 

to antecedent precipitation are not statistically significant 

at the 95-percent confidence limit. In comparison, with the 

exception of total nickel, correlations between discharge and 

total metals, and between antecedent precipitation totals and 

total metals, are positive and statistically significant at the 

95-percent confidence interval. These values indicate that 

rainfall-washoff processes may be a substantial contributor to 

total metal concentrations.

Correlations Among Metal Concentrations

Analysis of correlations among metal concentrations 

indicates possible causal relations between selected variables, 

possible predictive relations between variables, and the potential for using whole-water values to predict dissolved (filtered) 

concentrations. Identification of possible causal relations 

between selected variables may provide information that decision makers can use to identify potential sources of a metal 

and therefore the most effective mitigation measures. Correlations among the total metals are generally positive, statistically 

significant, and semistrong to strong, and these characteristics 

indicate common sources (table 12). Correlations between 

total and dissolved concentrations for Cu, Pb, and Ni are 

positive, statistically significant, and moderate to strong. Correlations between total and dissolved concentrations for Cd, 

Cr, and Zn are positive but are not statistically significant and 

are weak. Negative correlations between dissolved Cr and 

dissolved Zn, dissolved Ni and dissolved Zn, and dissolved Ni 

and total Al are statistically significant but weak.

There are a number of nondetect concentration values 

for each metal, and these nondetect values may affect correlations. For example, the correlation between total and dissolved 

copper (0.452) is more than twice that of total and dissolved 

chromium (0.18), and total and dissolved lead concentrations 

(0.711) are about four times total and dissolved chromium. 

Chromium correlations that are unusually low may result from 

ties caused by using one-half detection limits.

Development of Water-Quality Regression 

Equations

The objective of this analysis was to provide regression equations that can be used to estimate concentrations of 

water-quality constituents of interest from automated monitoring measurements and to estimate instantaneous loads 

by multiplying estimated concentration times discharge. A 

multiple stepwise regression was done in which independent 

variables were added one at a time to obtain the final equation. In stepwise regression, the automated selection program 

finds the explanatory variable with the highest correlation (R2) 

with the response variable; it then tries each of the remaining variables until it finds the two explanatory variables with 

the highest R2; then it tries all of them again until it finds the 

three variables with the highest R2, and so on. The goal of the 

stepwise procedure is to ensure that only statistically significant independent variables are added to an equation and to 

exclude the variables that account for a very small part of the 

variance in the dependent variable. Correlation matrices with 

Spearman’s rank correlation coefficients (rho) (tables 10 and 

12) were used to assess relations between explanatory variables and the selected constituents collected manually from the 
30 Nutrient and Metal Loads Estimated for the Blackstone River, Massachusetts and Rhode Island, Water Years 2013–14 Table 11. Correlation coefficients between potential explanatory variables and metal concentrations. [Correlation coefficients that are statistically significant at the 95th percentile are shown as italic numbers. Correlation coefficients that are greater than 0.8 are shown as bold italic numbers. Water-quality param- eters: Tmp, temperature, water, degrees Celsius (p00010); Q, discharge, cubic feet per second (p00060); SC, specific conductance, water, unfiltered, corrected, water, micrograms per liter (μg/L) (p32209); Trb, turbidity, water, unfiltered, broadband light source (400–680 nanometers), detectors at multiple angles including 90 ± 30 degrees, ratiometric correction, nephelometric turbidity ratio unit (p63676); P, precipita- tion, total, in inches (p7977a); DO, dissolved oxygen, water, unfiltered, milligrams per liter (mg/L) (p00300); pH, water, unfiltered, field, standard units (p00400); CA, chlorophyll a, fluorometric method; 24P, antecedent precipitation, total, (24-hour), in inches (p7977b); 48P, antecedent precipitation, total, (48-hour), in inches (p7977c); 72P, antecedent precipitation, total, (72-hour), in inches (p7977d). Metal concen- trations: p00925 fMg, magnesium, water, filtered, mg/L; p01025 fCd, cadmium, water, filtered, μg/L; p01027 tCd, cadmium, water, unfiltered, μg/L; p01030 fCr, chromium, water, filtered, μg/L; p01034 tCr, chromium, water, unfiltered, recoverable, μg/L; p01040 fCu, copper, water, filtered, μg/L; p01042 tCu, copper, water, unfiltered, recoverable, μg/L; p01049 fPb, lead, water, filtered, μg/L; p01051 tPb, lead, water, unfiltered, recoverable, μg/L; p01065 fNi, nickel, water, filtered, μg/L; p01067 tNi, nickel, water, unfiltered, recoverable, μg/L; p01090 fZn, zinc, water, filtered, μg/L; p01092 tZn, zinc, water, unfiltered, recover- able, μg/L; p01105 tAl, aluminum, water, unfiltered, recoverable, μg/L] Water-quality parameter Spearman’s rho Magnesium, water, filtered (mg/L); p00925 fMg Cadmium, water, filtered (μg/L); p01025 fCd Cadmium, water, unfiltered (μg/L); p01027 tCd Chromium, water, filtered (μg/L); p01030 fCr Chromium, water, unfiltered, recoverable (μg/L); p01034 tCr Copper, water, filtered (μg/L); p01040 fCu Copper, water, unfiltered, recoverable (μg/L); p01042 tCu Lead, water, filtered (μg/L); p01049 fPb Lead, water, unfiltered, recoverable (μg/L); p01051 tPb Nickel, water, filtered (μg/L); p01065 fNi Nickel, water, unfiltered, recoverable (μg/L); p01067 tNi Zinc, water, filtered (μg/L); p01090 fZn Zinc, water, unfiltered, recoverable (μg/L); p01092 tZn Aluminum, water, unfiltered, recoverable (μg/L); p01105 tAl Discharge (Q) -0.535 -0.224 0.503 -0.26 0.565 -0.3 0.49 0.38 0.567 -0.685 -0.11 0.219 0.696 0.811 Temperature (Tmp) 0.305 -0.208 0.125 0.53 0.087 0.523 0.267 0.257 0.092 0.301 0.333 -0.807 -0.258 -0.292 Specific conductance (SC) 0.783 0.591 0.13 0.05 -0.029 0.523 0.106 -0.025 -0.042 0.663 0.632 0.134 -0.064 -0.127 Dissolved oxygen (DO) -0.156 0.149 -0.489 -0.73 -0.475 -0.918 -0.613 -0.638 -0.383 -0.447 -0.691 0.468 -0.184 -0.121 pH -0.168 0.259 -0.126 -0.189 -0.524 -0.105 -0.346 -0.573 -0.49 -0.147 -0.199 0.161 -0.301 -0.42 Chlorophyll a (CA) 0.406 0.302 0.345 0.073 0.251 0.462 0.378 0.086 0.313 0.245 0.184 -0.203 0.125 0.141 Turbidity (Trb) 0.194 0.253 0.837 0.099 0.886 0.316 0.871 0.523 0.870 -0.081 0.376 0.170 0.829 0.828 Precipitation (P) -0.152 0.118 0.09 -0.145 0.064 -0.069 0.029 -0.034 0.037 -0.003 0.104 0.203 0.119 0.094 24-hour precipitation (24P) 0.005 -0.025 0.503 -0.365 0.581 -0.189 0.477 0.186 0.466 -0.211 0.235 0.142 0.531 0.495 48-hour precipitation (48P) 0.025 0.044 0.645 -0.177 0.7 -0.091 0.591 0.302 0.571 -0.191 0.284 0.011 0.651 0.604 72-hour precipitation (72P) 0.017 0.021 0.626 -0.16 0.689 -0.067 0.585 0.32 0.557 -0.189 0.273 0.014 0.638 0.594
Correlation Among Variables 31

Table 12. Correlation coefficients among metal concentrations.[Correlation coefficients that are statistically significant at the 95th percentile are shown as italic numbers. Correlation coefficients that are greater than or equal to 0.8 are shown as bold italic numbers. Waterquality parameters: p00925 fMg, magnesium, water, filtered, milligrams per liter (mg/L); p01025 fCd, cadmium, water, filtered, micrograms per liter (μg/L); p01027 tCd, cadmium, water, unfiltered, μg/L; p01030 fCr, chromium, water, filtered, μg/L; p01034 tCr, chromium, water, unfiltered, recoverable, μg/L; p01040 fCu, copper, water, filtered, μg/L; p01042 tCu, copper, water, unfiltered, recoverable, μg/L; p01049 fPb, lead, water, filtered, μg/L; p01051 tPb, lead, water, unfiltered, recoverable, μg/L; p01065 fNi, nickel, water, filtered, μg/L; p01067 tNi, nickel, water, unfiltered, recoverable, μg/L; p01090 fZn, zinc, water, filtered, μg/L; p01092 tZn, zinc, water, unfiltered, recoverable, μg/L; p01105 tAl, aluminum, water, unfiltered, recoverable, μg/L]

Water-quality 

parameter

Spearman’s rho

Magnesium, 

water, 

filtered 

(mg/L); 

p00925 fMg

Cadmium, 

water, 

filtered 

(μg/L); 

p01025 fCd

Cadmium, 

water, 

unfiltered 

(μg/L); 

p01027 tCd

Chromium, 

water, 

filtered 

(μg/L); 

p01030 fCr

Chromium, 

water, 

unfiltered, 

recoverable 

(μg/L); 

p01034 tCr

Copper, 

water, 

filtered 

(μg/L); 

p01040 fCu

Copper, 

water, 

unfiltered, 

recoverable 

(μg/L); 

p01042 tCu

Lead, 

water, 

filtered 

(μg/L); 

p01049 fPb

Lead, 

water, 

unfiltered, 

recoverable 

(μg/L); 

p01051 tPb

Nickel, 

water, 

filtered 

(μg/L); 

p01065 fNi

Nickel, 

water, 

unfiltered, 

recoverable 

(μg/L); 

p01067 tNi

Zinc, 

water, 

filtered 

(μg/L); 

p01090 fZn

Zinc, water, 

unfiltered, 

recoverable 

(μg/L); 

p01092 tZn

Aluminum, 

water, 

unfiltered, 

recoverable 

(μg/L); 

p01105 tAl

p00925 fMg 1p01025 fCd 0.531 1p01027 tCd 0.153 0.367 1p01030 fCr 0.202 0.239 0.18 1p01034 tCr 0.059 -0.014 0.842 0.093 1p01040 fCu 0.503 0.562 0.446 0.664 0.182 1p01042 tCu 0.124 0.149 0.932 0.209 0.905 0.452 1p01049 fPb -0.173 -0.01 0.569 0.435 0.631 0.48 0.686 1p01051 tPb -0.013 -0.02 0.816 0.065 0.918 0.245 0.908 0.711 1p01065 fNi 0.635 0.445 -0.077 0.289 -0.11 0.538 -0.096 0.03 -0.153 1p01067 tNi 0.514 0.392 0.495 0.181 0.465 0.527 0.484 0.303 0.35 0.69 1p01090 fZn -0.17 0.447 0.042 -0.344 -0.123 -0.097 -0.148 -0.121 -0.083 -0.109 -0.172 1p01092 tZn -0.129 0.159 0.855 -0.1 0.821 0.136 0.806 0.538 0.833 -0.309 0.261 0.304 1p01105 tAl -0.218 0.078 0.746 -0.084 0.818 0.022 0.767 0.552 0.871 -0.404 0.115 0.227 0.906 1
32 Nutrient and Metal Loads Estimated for the Blackstone River, Massachusetts and Rhode Island, Water Years 2013–14

upstream railroad bridge near the Millville station. This was 

done to guide variable selection and minimize use of highly 

correlated variables in the same regression model. Coefficients of the regression equations, regression statistics, and the 

resulting equations for estimating the constituent concentrations from automated monitoring measurements are shown 

in table 13. The regression equations and regression statistics 

were calculated by using Minitab software (version 15). For 

this study, only the strongest regressions based on the limited 

data available are presented: total nitrogen, total phosphorus, 

suspended sediment concentration, total copper, and total 

aluminum. With additional data, additional relationships could 

be developed. Plots of the equation values and residuals were 

made and examined to ensure that predicted values were 

reasonable and that residuals were unbiased and had constant 

variance. The following section contains a detailed example of 

the calculations needed to obtain estimated concentrations of 

total phosphorus.

Application of Water-Quality Regression 

Equations

Each regression equation produces a value of the concentration for a unique combination of the values of the explanatory variables, but there is uncertainty associated with each 

estimate (Driver and Tasker, 1990). Prediction-interval estimates commonly are used to define the degree of uncertainty 

for estimating the concentrations for any given set of explanatory variables. The prediction interval for equations developed 

in logarithmic space by transforming data to the common 

(base 10) logarithms can be calculated by 

1

T

C

BCF

C C

BCF

T i

i

i < < , (8)

where Ci is the prediction interval for true concentration. 

Because the regression equations were developed by using the 

common (base 10) logarithms of the input variables, the value 

of T is calculated as follows:

T

t V n p pi

= − ( ) 



 



 ( )×

10 2

0 5

α / ,

.

, (9)

where t(α/2,n–p) is the critical value of the Student’s t distribution 

for the selected confidence interval for n–p degrees of freedom with n data points in the regression analysis dataset and 

p parameters in the regression equation. In both cases, Vpi is 

the variance of prediction for concentration i and is calculated 

as follows:

Vpi = σ2×(1+xiUxi′), (10)

where σ is the standard error of the estimate for the 

selected regression equation,

U is the variance-covariance matrix for the 

regression equation, and 

xi and xi′ are the row and column vector of the predictor 

variables for concentration i, respectively. 

For example, the row vector (xi) for the logarithmic total 

phosphorus equation (TP p00665) in table 13 would be the 

following:

xi = [1, log(p00010), log(p00095), log(p63676), log(p7977c+1)], (11)

which includes the constant 1 and the terms p00010 (temperature), p00095 (specific conductance), p63676 (turbidity) and 

p7977c (48-hour antecedent precipitation). The column vector 

is made up of the same four values transposed. The variable U

in equation 10 is the variance-covariance matrix for the regression equation. For example, the arithmetic total phosphorus 

equation (TP p00665) in table 13 would be the following:

U =

− −

−

31 6928 0 107122 11 8779 0 616279 2 78013

0 107122 0 482042

. . . . .

. . 0 205842 0 056612 0 141424

11 8779 0 205842 4 5342 0 283495

. . .

. . . .

−

− − − 1 0218

0 616279 0 056612 0 283495 0 448842 0 753287

2 7801 0

.

. . . . .

.

− − −

− .141424 1. . 0218 −0 753287 2.64014

































. (12)

The values needed to calculate the 90-percent confidence 

interval, the model error variance, and the variance-covariance 

matrix for selected regression equations are shown in table 14.

The procedure to estimate the total phosphorus 

concentration is explained by an example computation 

following the method of Driver and Tasker (1990). On 

December 30, 2013, at noon, values of explanatory variables 

were as follows: temperature, 3.3 degrees Celsius; specific 

conductance, 783 μS/cm; turbidity, 52 FNUs; and 48-hour 

antecedent precipitation, 1.01 in. The estimated total 

phosphorus concentration is calculated from the TP p00665 

equation as follows:

TP p00665 = 0.003 × 3.30.18934 × 7830.3897 × 520.5115 ×

 (1.01 + 1)−0.2329 × 1.01 = 0.327, (13)

given the following:

n–p is 18 – 4 = 14 (degrees of freedom);

α is 0.1 (90-percent confidence interval);

t

(α/2,n–p) is 1.761 (from table 14, or a statistical text);

xi is [1, log(3.3), log(783), log(52), 

log(1.01 + 1)], vector of basin 

characteristics (equation 11); 

U is equivalent to equation 7 (provided for the 

other regression equations in table 13);

σ2 is 0.00375, the variance of the regression 

model (from table 14); and

BCF is 1.01 (from table 13)
Correlation Among Variables 33

Table 13. Coefficients of the regression equations, regression statistics for estimating selected water-quality constituent concentrations from continuous monitoring data at the Blackstone River at Millville, Massachusetts, station (01111230), and resulting regression equations.[Coefficients represent variables from equation 3. Point data and associated water-quality parameter measurement data were used to develop regressions. Water-quality parameters: Tmp, temperature, water, degrees Celsius (p00010); Q, discharge, cubic feet per second (p00060); SC, specific conductance, water, unfiltered, microsiemens per centimeter at 25 degrees Celsius (p00095); Trb, turbidity, water, unfiltered, broadband light source (400–680 nanometers), detectors at multiple angles including 90 ± 30 degrees, ratiometric correction, nephelometric turbidity ratio unit (p63676); 48P, antecedent precipitation, total, (48-hour), in inches (p7977c+1). BCF, bias correction factor; ASEE, average standard error of the estimate in percent; PRESS, prediction error sum of squares; ASEP, average standard error of the prediction; -- variable not used in the regression equation]

Regression equation Count Intercept Q; p00060 Tmp; p00010 SC; p00095 Trb; p63676 48P; p7977c +1 Adjusted R-squared (percent) BCF ASEE PRESS; log10 ASEP log10 Percent log10 Percent

Total phosphorus (p00665) 18 0.003 -- 0.189 0.390 0.512 -0.233 92.2 1.010 0.061 14.2 0.132 0.086 19.9

TP (p00665) = 0.003 × (Tmp, p00010)0.18934 × (SC, p00095)0.3897 × (Trb, p63676)0.5115 × (48P, p7977c+1)−0.2329 × 1.010

Total nitrogen (p62855) 17 0.017 -0.131 -- 0.855 -- -- 74.5 1.017 0.077 17.9 0.144 0.092 21.5

TN (p62855) = 0.017 × (Q, p00060)−0.131 × (SC, p00095)0.855 × 1.017

Suspended sediment concentration (p80154) 19 0.083 0.592 -- -- 0.749 -- 86.4 1.109 0.204 49.7 1.141 0.245 61.2

SSC (p80154) = 0.083 × (Q, p00060)0.592 × (Trb, p63676)0.749 × 1.109

Total copper (p01042) 21 3.134 -- -- -- 0.498 -- 84.1 1.024 0.094 22.0 0.230 0.102 23.9

TotCu (p01042) = 3.134 × (Trb, p63676)0.498 × 1.024

Total aluminum (p01105) 22 2.622 0.459 -- -- 0.709 -- 96.5 1.019 0.085 19.7 0.221 0.100 23.4

TotAl (p01105) = 2.622 × (Q, p00060)0.459 × (Trb, p63676)0.709 × 1.019
34 Nutrient and Metal Loads Estimated for the Blackstone River, Massachusetts and Rhode Island, Water Years 2013–14 Table 14. Values needed to determine 90-percent prediction intervals for selected regression equations for estimating selected water-quality constituent concentrations from continuous monitoring data at the Blackstone River at Millville, Massachusetts, station (01111230). [The degrees of freedom is the number of samples minus the number of predictor variables. Water-quality parameters: p00010, temperature, water, degrees Celsius; p00060, discharge, cubic feet per second; p00095, specific conductance, water, unfiltered, microsiemens per centimeter at 25 degrees Celsius; p63676, turbidity, water, unfiltered, broadband light source (400–680 nanometers), detectors at multiple angles including 90 ± 30 degrees, ratiometric correction, nephelometric turbidity ratio unit; p7977c, antecedent precipitation, total, (48-hour), in inches. CI, confidence interval] Regression equation Count Degrees of free- dom Critical Student’s t for 90-per- cent CI Model error variance Variance-covariance matrix Total phosphorus (p00665) 18 14 1.761 0.061 Constant log10(p00010) log10(p00095) log10(p63676) log10(p7977c+1) Constant 31.7 0.107 -11.9 0.616 -2.78 log10(p00010) 0.107 0.482 -0.206 -0.057 0.141 log10(p00095) -11.9 -0.206 4.53 -0.283 1.022 log10(p63676) 0.616 -0.057 -0.283 0.449 -0.753 log10(p7977c+1) -2.78 0.141 1.02 -0.753 2.64 Total nitrogen (p62855) 16 14 1.761 0.077 Constant log10(p00060) log10(p00095) Constant 55.1 -3.37 -17.2 log10(p00060) -3.37 0.425 0.829 log10(p00095) -17.2 0.829 5.581 Suspended sediment concentration (p80154) 19 17 1.740 0.204 Constant log10(p00060) log10(p63676) Constant 2.319 -0.900 0.215 log10(p00060) -0.900 0.375 -0.151 log10(p63676) 0.215 -0.151 0.262 Total copper (p01042) 22 20 1.725 0.094 Constant log10(p63676) Constant 0.148 -0.143 log10(p63676) -0.143 0.199 Total aluminum (p01105) 22 20 1.725 0.085 Constant log10(p00060) log10(p63676) Constant 2.26 -0.885 0.226 log10(p00060) -0.885 0.372 -0.154 log10(p63676) 0.226 -0.154 0.255
Correlation Among Variables 35

Determine the variance of the concentration estimate and 

prediction interval by calculating as follows:

Vpi = 0.0613 × (1 + xiUxi′) =

 0.0613 × (1 + 0.6719) =0.1025 [eq. 10];

T = 10[1.761(0.1025)0.5] = 3.66 [eq. 9]; and

1

3 66

0 327

1 01

0 327 1 044 0 327

3 66

0 088 0 327 1 18 .

.

. . . .. × < < × or . . < < . . [ ] eq 8

Thus, the estimated phosphorus concentration is 0.327 mg/L, 

with a 90-percent confidence interval from 0.088 to 1.18, 

as calculated from the TP p00665 equation (table 13). In 

comparison, the measured concentration in the water sample 

was 0.351 mg/L. Regression equations developed with the 

logarithms of data produce confidence intervals that are 

proportional to the predicted value (Driver and Tasker, 1990; 

Granato, 2012).

Figure 9 shows a comparison of concentrations from 

manual and automated samples and estimated concentrations 

calculated from the regression equation. The date range of 

figure 9 reflects the 14-day sampling period for the automated 

system beginning on December 23, 2013, and ending on 

January 7, 2014.

Limitations of the Analysis

The major limitation of this regression analysis is that it 

is based on the limited number of samples. A longer term of 

data collection would narrow prediction intervals of concentration estimates. The 4-day composite sampling approach 

provided accurate information relative to the chronic exposure 

guidelines and biotic ligand model analysis, but it also resulted 

in missing data for large portions of WYs 2013 and 2014. The 

explanatory variables in the regression models are mainly 

automated monitoring data; these hydrologic and water-quality 

measurements are limited in range and subject to errors in 

measurement and interpretation. Streamflow at the Millville 

station was estimated by using a relation with the upstream 

continuous streamgage at the Rt. 122 station and thus inherently has more error than if streamflow were measured at the 

Millville station. In addition, stream velocities were often less 

than 1.5 ft/s and too slow for the use of isokinetic sampling 

0

200

400

600

800

1,000

1,200

0.01

0.10

1.00

Total phosphorus concentration, in milligrams per liter

Flow, in cubic feet per second

14-day total P concentration

Discrete total P concentration

Estimated total P concentration

Flow

12/22/2013

12/23/2013

12/24/2013

12/25/2013

12/26/2013

12/27/2013

12/28/2013

12/29/2013

12/30/2013

12/31/2013

01/01/2014

01/02/2014

01/03/2014

EXPLANATION

Date

Figure 9. Estimated 15-minute total phosphorus (P) concentrations (dark green line) from the Blackstone River at Millville, 

Massachusetts, station (01111230), December 22, 2013, to January 1, 2014. The total phosphorus concentration from the 14-day 

composite sample collected by the automated system (light green line) and the discrete multiple vertical sample collected manually 

from the upstream railroad bridge (yellow diamond) are shown for comparison.
36 Nutrient and Metal Loads Estimated for the Blackstone River, Massachusetts and Rhode Island, Water Years 2013–14

techniques. Extrapolation of regression equations beyond the 

range of explanatory variables used to formulate the regression 

may result in faulty estimates, and the confidence and prediction intervals are not valid beyond these ranges (Helsel and 

Hirsch, 2002; Rasmussen and others, 2009). 

Potential effects of misspecification of explanatory 

variables were assessed by using standardized beta coefficients 

(Driver and Tasker, 1990; Granato, 2012). Sensitivity tests 

indicate the effects of measurement and interpretive errors 

on estimation of the response variables in regression models. Standardized beta coefficients for all the variables in the 

regression models are listed in table 15 to facilitate sensitivity 

testing. The standardized beta coefficient is the standard deviation of the response variable divided by the standard deviation of the explanatory variable. This coefficient (table 15) 

reflects the change in the mean response per unit change in 

the explanatory variable (in units of standard deviations of 

both variables) when all other explanatory variables are held 

constant. Therefore, misspecification of a variable with a high 

standardized beta coefficient is likely to introduce more error 

than an equivalent error in a variable with a smaller beta coefficient. Some explanatory variables have more natural variance than others. Spacing of the observations on the explanatory variables, which may be somewhat arbitrary, also affects 

the standardized beta coefficients (Driver and Tasker, 1990). 

These equations could be used as a reconnaissance-level 

monitoring tool until new data are added and their respective 

correlations made more robust. Collecting new data could also 

allow development of new relationships for other constituents 

of concern, such as dissolved nutrient and metal species.

Table 15. Ranges of values, population statistics, and standardized beta coefficients for the variables used in each regression model.

[Water-quality parameters: p00010, temperature, water, degrees Celsius; p00060, discharge, cubic feet per second; p00095, specific conductance, water, unfiltered, microsiemens per centimeter at 25 degrees Celsius; p63676, turbidity, water, unfiltered, broadband light source (400–680 nanometers), detectors at multiple angles including 90 ± 30 degrees, ratiometric correction, nephelometric turbidity ratio unit; p7977c+1, antecedent precipitation, total, (48-hour), in inches]

Equation Variable Minimum Maximum

Mean

Median

Standard deviation Standardized

beta

coefficient Arithmetic Geometric Arithmetic Logarithm

Total phosphorus 

(p00665)

p00665 0.040 0.356 0.128 0.107 0.110 0.090 0.259 1.00

p00010 2.24 25.3 11.9 8.93 9.85 8.2 0.359 1.39

p00095 274 783 438 466 445 134 0.121 0.468

p63676 1.00 52 9.91 5.38 6.33 12.5 0.502 1.94

p7977c +1 1.00 4.61 1.71 1.51 1.19 1.00 0.213 0.824

Total nitrogen 

(p62855)

p62855 0.890 2.83 1.56 1.46 1.48 0.619 0.168 1.00

p00060 90.6 2,262 807 533 666 640 0.455 2.71

p00095 274 783 486 467 442 138 0.126 0.746

Suspended sediment 

concentration 

(p80154)

p80154 1.00 67.0 23.3 11.5 22.0 22.6 0.604 1.00

p00060 90.6 2,262 747 494 583 628 0.439 0.727

p63676 1.00 52.0 10.3 5.42 7.95 12.5 0.525 0.869

Total copper 

(p01042)

p01042 3.20 23.5 8.55 7.15 6.80 5.57 0.262 1.00

p63676 1.00 52.0 9.49 5.24 5.15 11.8 0.490 1.87

Total aluminum 

(p01105)

p01105 35.8 1,020 256 150 164 252 0.486 1.00

p00060 90.6 2,262 693 460 583 601 0.429 0.883

p63676 1.00 52.0 9.92 5.48 6.33 11.8 0.499 1.03
Summary and Conclusions 37

Summary and Conclusions

The main-stem Blackstone River and several of its tributaries continue to be designated as impaired for recreational 

and aquatic uses. Nutrients (total and dissolved nitrogen and 

phosphorus), trace metals, and suspended sediment are some 

of the constituents of concern. Impaired water draining into 

Narragansett Bay from the Blackstone River contributes 

to decreased clarity, seasonal eutrophication, and degraded 

habitat seen in Narragansett Bay. However, downward trends 

in nutrient concentrations in both the Blackstone River and 

Narragansett Bay have been reported.

To continue to assess the water quality of the Blackstone 

River, which drains central Massachusetts before crossing 

the State line into Rhode Island, the U.S. Geological Survey 

(USGS), in cooperation with the Massachusetts Department 

of Environmental Protection, reactivated the automated 

monitoring station on the Blackstone River at Millville, 

Massachusetts, near the State line with Rhode Island 

(USGS station 01111230) in October 2012.

The Millville monitoring station was used to provide 

continuous water-quality monitoring, monthly and annual 

loading information for nutrients, and 4-day loadings of 

trace metals for water years 2013–14. These data were used 

to evaluate the potential to use surrogate measurements 

of physical parameters to estimate real-time (15-minute) 

constituent concentrations in the Blackstone River as it enters 

Rhode Island from Massachusetts.

The Millville station was equipped with an automated 

flow-proportional sampling system that collected fifty 

14-day composite samples for total and dissolved nitrogen 

and phosphorus and fifty-two 4-day composite samples for 

dissolved trace metals and total aluminum. Temperature, 

specific conductance, turbidity, and chlorophyll a were also 

measured every 15 minutes. The point sampling location used 

by the automated system was determined to be representative 

over a wide range of flow conditions. Concentrations from 

composite samples collected by the automated system 

provide the basis to determine monthly and annual loads. 

Concentrations from discrete point samples from the point 

location were used to evaluate the potential to develop 

regression models to estimate constituent concentrations and 

allow for real-time load estimation. 

The annual load of total nitrogen as collected by the 

automated system in water year (WY) 2013 was about 

447,000 kilograms per year (kg/yr). Flows in WY 2014 were 

about 25 percent lower than in the previous year, and the 

annual load of total nitrogen was about 342,000 kg/yr. The 

annual loads of total and dissolved phosphorus in WY 2013 

were about 35,900 and 12,000 kg/yr, respectively. In WY 

2014, the annual load of total phosphorus was 20,700 kg/yr, 

and dissolved P was about 8,220 kg/yr. The lower flows seen 

in WY 2014 are a possible explanation for the 42-percent 

decrease in total phosphorus loading.

Median dissolved cadmium and chromium 4-day loads 

were 0.55 and 0.84 kilograms (kg), respectively, during 

WYs 2013 and 2014. Dissolved copper and lead median loads 

were 8.02 and 1.42 kg, respectively. The dissolved nickel 

median load was 5.45 kg, and the dissolved zinc median load 

was 36 kg. Median total aluminum 4-days loads were about 

200 kg.

Correlation coefficients were generated among flow, 

precipitation, antecedent precipitation, physical parameters, 

and chemical constituents. Spearman’s rho rank correlations 

were calculated. A 95-percent confidence limit for each value 

of Spearman’s rho was also calculated. These data allowed 

for the development of quantitative regression equations for 

selected constituents and determined the likelihood of multicollinearity between predictor variables.

Multiple linear regression analysis using ordinary least 

squares regression techniques was used to develop regression 

equations for the strongest correlations (total nitrogen, total 

phosphorus, total suspended solids, total copper, and total aluminum) from samples collected manually from the Millville 

point location during WYs 2013 and 2014. The independent 

variables with the greatest explanatory power were isolated in 

a stepwise manner to develop equations for the five selected 

constituents of concern. Each regression equation yields a 

unique value of constituent concentration that can therefore 

be estimated at the sampling point at the Millville station. 

Although the uncertainty associated with each estimate is 

greater than the uncertainty associated with an actual sample 

result from an analytical lab, the ability to estimate reconnaissance-level concentrations every 15 minutes is useful to monitor changes in concentrations and loads that may not be easily 

captured by traditional sampling techniques.

Concentrations from manually collected water-quality 

samples are sensitive to temporal changes, and in a heavily 

industrialized and urbanized basin such as the Blackstone 

River, concentrations can vary greatly from hour to hour. Concentrations from the automated flow-proportional system are 

less sensitive to environmental extremes (such as high-flow 

and low-flow conditions) than those from manually collected 

samples. The automated flow-proportional sampling approach 

captures daily variations and provides the high resolution 

needed to develop accurate monthly and annual loading information. Near real-time (15-minute) concentrations estimated 

by regression equations provide the greatest temporal resolution but also the greatest uncertainty. Continued monitoring 

and collecting of constituent concentration data would reduce 

uncertainties in these regression equations over time and 

improve their predictive power. Maintenance of instruments 

needed to provide the data for calculating real-time constituent concentrations and yielding real-time load estimates in a 

heavily impacted basin is labor intensive, but even in challenging environments, the continuous concentration data can 

contribute to critical knowledge of extreme events and enable 

event-based sampling and management strategies. This combination of traditional manual sampling and flow-proportional 

automated sampling provides accurate loading information. 

Although the data used to develop regression equations were 

limited to those collected in this study, by using the real-time 
38 Nutrient and Metal Loads Estimated for the Blackstone River, Massachusetts and Rhode Island, Water Years 2013–14

load-estimation capabilities from these data, regulators 

and stakeholders would have the information necessary to 

make time-sensitive and cost-effective decisions to improve 

impaired water resources and provide tools for monitoring the 

effectiveness of implemented management strategies.

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For more information about this report, contact:

Director, New England Water Science Center

U.S. Geological Survey

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dc_nweng@usgs.gov

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Pembroke Publishing Service Center
Sorenson and others—Nutrient and Metal Loads Estimated for the Blackstone River, Massachusetts and Rhode Island, Water Years 2013–14—SIR 2017–5094

Printed on recycled paper

ISSN 2328-031X (print)

ISSN 2328-0328 (online)

https://doi.org/10.3133/sir20175094