Scientific Investigations Report 2016–5063

U.S. Department of the Interior

U.S. Geological Survey

Changes in Phosphorus Concentrations and Loads in 

the Assabet River, Massachusetts, October 2008 

through April 2014

Changes in Phosphorus Concentrations and Loads in 

the Assabet River, Massachusetts, October 2008 

through April 2014

Prepared in cooperation with the 

Massachusetts Department of Environmental Protection
Cover. Inset photographs: Wastewater-treatment plants on the Assabet River in central Massachusetts. Photographs courtesy of the 

Westborough (top left), Marlborough-Westerly (middle), and Hudson (bottom right) wastewater-treatment plants.

Background photograph: Hudson impoundment on the Assabet River in central Massachusetts. Photograph courtesy of the 

Organization for the Assabet, Sudbury, and Concord Rivers (OARS). 
Changes in Phosphorus Concentrations and 

Loads in the Assabet River, Massachusetts, 

October 2008 through April 2014

By Jennifer G. Savoie, Leslie A. DeSimone, John R. Mullaney, 

Marc J. Zimmerman, and Marcus C. Waldron

Prepared in cooperation with the 

Massachusetts Department of Environmental Protection

Scientific Investigations Report 2016–5063

U.S. Department of the Interior

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

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Director

U.S. Geological Survey, Reston, Virginia: 2016

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as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner.

Suggested citation:

Savoie, J.G., DeSimone, L.A., Mullaney, J.R., Zimmerman, M.J., and Waldron, M.C., 2016, Changes in phosphorus 

concentrations and loads in the Assabet River, Massachusetts, October 2008 through April 2014: U.S. Geological 

Survey Scientific Investigations Report 2016–5063, 40 p., http://dx.doi.org/10.3133/sir20165063.

ISSN 2328-031X (print)

ISSN 2328-0328 (online)

ISBN 978-1-4113-4059-6
iii

Acknowledgments

This study benefitted greatly from the interest, support, and assistance of many colleagues and 

agencies. Brian Friedman, Dennis R. Dunn, Alice Rojko, Kimberly Groff, Mark Mattson, and the 

late Arthur J. Screpetis of the Massachusetts Department of Environmental Protection, Office 

of Watershed Management, were instrumental in guiding the work. Wastewater-treatmentplant managers Harry Butland of Marlborough’s Westerly plant, Christopher Pratt of Veolia’s 

Westborough plant, and Mark Concheri of the Hudson plant directly provided monitoring data of 

great importance for assessing loads in the Assabet River. American Veterans (AMVETS) Post 

208 in Hudson, Massachusetts, gave permission to construct a water-quality-monitoring shelter 

on its property. 

Robert M. Hirsch of the U.S. Geological Survey provided especially beneficial advice and 

reviews of the statistical analyses. The contributions of many more U.S. Geological Survey 

personnel (Gardner C. Bent, Jean P. Campbell, Kimberly W. Campo, Timothy R. Driskell, 

Gerald G. Girouard, Andrew J. Massey, Laura Medalie, Douglas L. Moyer, Stephen G. O’Brien, 

Roy S. Socolow, Jason R. Sorenson, Britt O. Stock, Andrew M. Waite, Joan S. Whitley, and 

Joseph F. Whitley) and cooperative-education and other student aides (Gina Daniels, Michael 

Gowins, Irena Gumennic, Lisa Lach, Marine Langreney, Sandra Petrakis, and Nita Vaidya) are 

acknowledged.

v

Contents

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

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

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

Methods Used to Monitor Changes in Phosphorus Concentrations and Loads.................................3

Streamflow Measurements ................................................................................................................4

Environmental Sample Collection ......................................................................................................5

Quality-Control Samples......................................................................................................................8

Load Calculations..................................................................................................................................8

Changes in Phosphorus Concentrations and Loads................................................................................9

Phosphorus Concentrations ...............................................................................................................9

Streamflow During the Study Period...............................................................................................16

Phosphorus Loads ..............................................................................................................................20

Seasonal Differences in Phosphorus Concentrations and Loads..............................................21

Effects of Impoundments on Instream Phosphorus Loads..........................................................25

Hudson Impoundment...............................................................................................................25

Ben Smith Impoundment ..........................................................................................................31

Statistical Analyses of Changes in Phosphorus Concentrations ...............................................34

Summary and Conclusions.........................................................................................................................38

References Cited..........................................................................................................................................39

Figures

1. Map showing locations of water-quality-monitoring stations, wastewatertreatment plants, and impoundment dams in the study area along the Assabet 

River Basin in central Massachusetts ......................................................................................2

2. Orthophotograph map identifying the locations of water-quality-monitoring 

stations Port Street and AMVETS, upstream and downstream from the Hudson 

impoundment on the Assabet River, Massachusetts .............................................................4

3. Orthophotograph map identifying the locations of water-quality-monitoring 

stations Stow and Maynard, upstream and downstream from the Ben Smith 

impoundment on the Assabet River, Massachusetts .............................................................5

4. Graphs showing streamflow and sample-collection rate, demonstrating the 

flow-proportional sampling method ..........................................................................................7

5. Graphs showing streamflow and total phosphorus concentrations at the A, Port 

Street and B, AMVETS water-quality-monitoring stations, and daily average total 

phosphorus concentration in effluent from Westborough and MarlboroughWesterly wastewater-treatment plants, in the Assabet River, Massachusetts, 

2008–2014 .....................................................................................................................................10

6. Graphs showing streamflow and total phosphorus concentrations at the 

A, Stow and B, Maynard water-quality-monitoring stations, and daily average 

total phosphorus concentration in effluent from Westborough, MarlboroughWesterly, and Hudson wastewater-treatment plants, in the Assabet River, 

Massachusetts, 2008–2014 .......................................................................................................11
vi

7. Graphs showing streamflow and orthophosphate concentrations at the A, Port 

Street and B, AMVETS water-quality-monitoring stations on the Assabet River, 

Massachusetts, 2008–2014 .......................................................................................................12

8. Graphs showing streamflow and orthophosphate concentrations at the A, Stow 

and B, Maynard water-quality-monitoring stations on the Assabet River, 

Massachusetts, 2008–2014 .......................................................................................................13

9. Boxplot showing annual distributions of estimated daily concentrations of total 

phosphorus in wastewater-treatment-plant effluent to the Assabet River, 

Massachusetts, 2009–2013 .......................................................................................................14

10. Boxplots showing annual distributions of estimated daily concentrations of A, total phosphorus and B, orthophosphate in weekly flow-proportional composite 

samples from four water-quality-monitoring stations on the Assabet River, 

Massachusetts, 2009–2013 .......................................................................................................15

11. Graphs showing relations between streamflow and instream concentrations of 

total phosphorus at four water-quality-monitoring stations on the Assabet River, 

Massachusetts, before and after wastewater-treatment-plant (WWTP) upgrades 

to reduce phosphorus in WWTP effluent...............................................................................18

12. Graph showing interquartile range of mean daily streamflow from 1942 to 2014 

at station 01097000 repeated for each calendar year and overlaid with daily mean 

streamflow during the study period, from October 1, 2008, to April 30, 2014, 

Assabet River, Maynard, Massachusetts...............................................................................19

13. Boxplot showing annual distributions of estimated daily total phosphorus loads in 

wastewater-treatment-plant effluent into the Assabet River, Massachusetts, 

2009–2013 .....................................................................................................................................21

14. Boxplots showing annual distributions of estimated A, total phosphorus and 

B, orthophosphate loads in weekly flow-proportional composite samples from four 

water-quality-monitoring stations on the Assabet River, Massachusetts, 2009–2013....22

15. Boxplots showing seasonal distributions of estimated daily total phosphorus 

concentrations in effluent from the wastewater-treatments plants in A, Westborough, 

B, Marlborough-Westerly, and C, Hudson, Massachusetts, during nongrowing and 

growing seasons, on the Assabet River, Massachusetts, 2009–2014................................23

16. Boxplots showing seasonal distributions of estimated daily total phosphorus 

loads in effluent from the wastewater-treatment plants in A, Westborough, 

B, Marlborough-Westerly, and C, Hudson, Massachusetts, during nongrowing and 

growing seasons, 2009–2014 ....................................................................................................24

17. Boxplots showing seasonal distributions of estimated daily total phosphorus 

concentrations in flow-proportional composite samples from water-qualitymonitoring stations A, Port Street, B, AMVETS, C, Stow, and D, Maynard during 

nongrowing and growing seasons, on the Assabet River, Massachusetts, from 

2009 to 2014..................................................................................................................................26

18. Boxplots showing seasonal distributions of estimated daily orthophosphate 

concentrations in flow-proportional composite samples from water-qualitymonitoring stations A, Port Street, B, AMVETS, C, Stow, and D, Maynard during 

nongrowing and growing seasons, on the Assabet River, Massachusetts, from 

2009 to 2014..................................................................................................................................27

19. Boxplots showing seasonal distributions of estimated daily total phosphorus 

loads in flow-proportional composite samples from water-quality-monitoring 

stations A, Port Street, B, AMVETS, C, Stow, and D, Maynard during nongrowing 

and growing seasons, on the Assabet River, Massachusetts, from 2009 to 2014 ...........28
vii

20. Boxplots showing seasonal distributions of estimated daily orthophosphate loads 

in flow-proportional composite samples from water-quality-monitoring stations 

A, Port Street, B, AMVETS, C, Stow, and D, Maynard during nongrowing and 

growing seasons, on the Assabet River, Massachusetts, from 2009 to 2014 ...................29

21. Bar graphs showing estimated annual loads of A, total phosphorus of discharges 

from wastewater-treatment plants at Westborough and Marlborough-Westerly 

and instream at the Port Street and AMVETS water-quality-monitoring stations 

and B, orthophosphate instream at the Port Street and AMVETS water-qualitymonitoring stations on the Assabet River, Massachusetts, 2009–2013.............................30

22. Graphs showing streamflow and differences between estimated weekly loads of 

A, total phosphorus and B, orthophosphate upstream and downstream from the 

Hudson impoundment on the Assabet River, Massachusetts, October 2008 

through April 2014.......................................................................................................................31

23. Bar graphs showing estimated annual loads of A, total phosphorus discharges 

from the wastewater-treatment plants at Westborough, Marlborough-Westerly, 

and Hudson and instream at the Stow and Maynard water-quality-monitoring 

stations and B, orthophosphate instream at the Stow and Maynard water-qualitymonitoring stations on the Assabet River, Massachusetts, from 2009 to 2013 ................32

24. Graphs showing streamflow and differences between estimated weekly loads of 

A, total phosphorus and B, orthophosphate upstream and downstream from the 

Ben Smith impoundment on the Assabet River, Massachusetts, October 2008 

through April 2014.......................................................................................................................33

25. Graphs showing relations between streamflow and total phosphorus concentrations, and total phosphorus concentrations predicted for before and after the 

wastewater-treatment-plant upgrades, based on linear regression modeling for 

data from October 2008 through April 2014 for water-quality-monitoring stations 

on the Assabet River in the towns of Hudson, Stow, and Maynard, Massachusetts.....37

Tables

1. Location coordinates, drainage-basin areas, and annual mean daily and annual 

total streamflow (calendar years 2008 to 2013) for water-quality-monitoring stations 

on the Assabet River in the towns of Hudson, Stow, and Maynard, Massachusetts.......6

2. Median and mean flow and total phosphorus concentrations and loads at wastewater-treatment plants in the towns of Westborough, Marlborough, and Hudson 

on the Assabet River, Massachusetts, 2009 through 2013...................................................16

3. Median and mean flow and total phosphorus and orthophosphate concentrations 

and loads at water-quality-monitoring stations on the Assabet River in the towns 

of Hudson, Stow, and Maynard, Massachusetts, 2009 through 2013 ................................17

4. Coefficients and other regression metrics for linear regression models used to 

describe the relations between the natural log of composite total phosphorus 

concentrations and mean streamflow, and periods before and after wastewatertreatment-plant upgrades, for data collected from October 2008 through April 2014 

at water-quality-monitoring stations on the Assabet River in the towns of Hudson, 

Stow, and Maynard, Massachusetts.......................................................................................35

5. Results of pairwise F-test comparison of linear regression models 1, 2, and 3 for 

four water-quality-monitoring stations on the Assabet River, Massachusetts................36
viii

Conversion Factors

U.S. customary units to International System of Units

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2) 2.590 square kilometer (km2)

Volume

ounce, fluid (fl. oz) 29.57 milliliter (mL)

gallon (gal) 3.785 liter (L)

Flow rate

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

cubic foot per year (ft3/yr) 0.02832 cubic meter per year (m3/yr)

million gallons per day (Mgal/d) 0.04381 cubic meter per second (m3/s)

Mass

pound, avoirdupois (lb) 0.4536 kilogram (kg)

pound per day (lb/d) 0.4536 kilogram per day (kg/d)

pound per year (lb/yr) 0.4356 kilogram per year (kg/yr)

Datum

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

Supplemental Information

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

phosphorus.
ix

Abbreviations

AMVETS American Veterans

EPA U.S. Environmental Protection Agency

EWI equal-width increment

IGS inside grab sample

MDL method detection limit

NWQL National Water Quality Laboratory

orthoP orthophosphate

R2 R-squared (the coefficient of determination)

RPD relative percent difference

TMDL total maximum daily load

TP total phosphorus

USGS U.S. Geological Survey

WWTP wastewater-treatment plant

Changes in Phosphorus Concentrations and Loads in the 

Assabet River, Massachusetts, October 2008 through 

April 2014

By Jennifer G. Savoie, Leslie A. DeSimone, John R. Mullaney, Marc J. Zimmerman, and Marcus C. Waldron

Abstract

Treated effluent discharged from municipal wastewatertreatment plants to the Assabet River in central Massachusetts 

includes phosphorus, which leads to increased growth of 

nuisance aquatic plants that decrease the river’s water quality 

and aesthetics in impounded reaches during the growing 

season. To improve the river’s water quality and aesthetics, 

the U.S. Environmental Protection Agency approved a total 

maximum daily load for phosphorus in 2004 that directed 

the wastewater-treatment plants to reduce the amount of total 

phosphorus discharged to the river by 2012. The permitted 

total phosphorus monthly average of 0.75 milligrams per 

liter during the aquatic plant growing season (April 1 through 

October 31) was reduced by the total maximum daily load to a 

target of 0.1 milligrams per liter by 2012, and the nongrowingseason limit was unchanged at 1.0 milligrams per liter.

From October 2008 through April 2014, the U.S. 

Geological Survey, in cooperation with the Massachusetts 

Department of Environmental Protection, measured streamflow and collected weekly flow-proportional, composite 

samples of water from the Assabet River for analysis of 

concentrations of total phosphorus and orthophosphate. 

Streamflow and concentration data were used to estimate 

total phosphorus and orthophosphate loads in the river. The 

purpose of this monitoring effort was to evaluate phosphorus 

concentrations and loads in the river before, during, and 

after the wastewater-treatment-plant upgrades and to assess 

the effects of seasonal differences in permitted discharges. 

The locations of water-quality-monitoring stations, with 

respect to the Hudson and Ben Smith impoundments, enabled 

examination of effects of phosphorus entering and leaving 

the impoundments.

Annual median concentrations of total phosphorus in 

wastewater-treatment plants were reduced by more than 

80 percent with the plant upgrades. Measured instream annual 

median concentrations of total phosphorus in the Assabet 

River decreased by about 38 to 50 percent at three of the four 

monitoring stations following the wastewater-treatment-plant 

upgrades. At the station farthest upstream, the median total 

phosphorus concentration remained unchanged throughout the 

study; this may be attributed to the site location and potential 

resuspension of particulate organic matter during periods 

of increased streamflow. Annual median loads from the 

wastewater-treatment plants were reduced by up to 91 percent 

following the upgrades, instream annual median total 

phosphorus loads at the three downstream stations decreased 

by 71 to 76 percent, and instream orthophosphate loads at the 

three downstream stations decreased by 79 to 87 percent. 

Seasonal fluctuations (growing versus nongrowing) of 

total phosphorus and orthophosphate were observed instream 

before the upgrades. However, after the upgrades, fluctuations 

in phosphorus released from the treatment plants were slight 

and seasonal changes were typically not observed instream. 

Annual loads entering and leaving the two impoundments 

were inconclusive in determining whether the impoundments 

were sources or sinks of total phosphorus during the study. 

Total phosphorus loads entering the Hudson impoundment 

were consistently greater than those leaving; however, 

there was uncertainty about the loads at the monitoring 

station upstream from this impoundment. At the Ben Smith 

impoundment, total phosphorus and orthophosphate loads 

downstream were slightly greater than those upstream from 

the impoundment, but the differences may reflect additions 

from tributaries and overland runoff. 

Estimated instream total phosphorus concentrations 

and loads indicated that the decreases in total phosphorus in 

wastewater-treatment-plant discharges were accompanied by 

reductions measured in the Assabet River. A statistical analysis 

which incorporates the effect of varying flow conditions 

demonstrated significant reductions in total phosphorus 

concentrations after the wastewater-treatment-plant upgrades 

at three of the four instream monitoring stations. No 

significant change was observed at the most upstream location, 

the Assabet River at Port Street at Hudson, Massachusetts 

(station number 01096835), which may have been affected by 

flow-related resuspension of particulate phosphorus. 

Introduction

The 33-mile Assabet River flows from its headwaters 

in Westborough, Massachusetts, to its confluence with the 

Sudbury River in Concord, Mass., where they form the 

Concord River (fig. 1; Sudbury and Concord Rivers are 
2 Changes in Phosphorus Concentrations and Loads in the Assabet River, Massachusetts, October 2008 through April 2014

71°36'

42°18'

42°24'

42°30'

71°24'

42°36'

EXPLANATION

Assabet

River

Assabet River

Basin boundary

Town boundary

Wastewater-treatment plant (WWTP)

Dam

Westborough WWTP

Marlborough-Westerly WWTP

Port Street−01096835

Stow−01096885

Maynard−01097000

From U.S. Geological Survey and Massachusetts Office of Geographic Information

data sources, Massachusetts State Plane Coordinate System, Mainland Zone 

Ben Smith impoundment dam

Hudson impoundment dam

AMVETS−01096840

Hudson WWTP

Water-quality-monitoring station

0 5

Assabet Reservoir (A1 Impoundment)

l E i a be

B r oo k

z th

MILES

0 5 KILOMETERS

Junction with Concord

and Sudbury Rivers

HUDSON BERLIN

NORTHBOROUGH

WESTBOROUGH

BOLTON

STOW

HARVARD

LITTLETON

CLINTON

SHREWSBURY

GRAFTON

MARLBOROUGH

MAYNARD

SUDBURY

CONCORD

ACTON

BOXBOROUGH

WESTFORD

CARLISLE

BOYLSTON

MASSACHUSETTS

Assabet basin

Concord-Sudbury basin

Figure 1. Locations of water-quality-monitoring stations, wastewater-treatment plants, and impoundment dams in the study 

area along the Assabet River Basin in central Massachusetts. See table 1 for full station names. Modified from Zimmerman and 

Sorenson (2005, fig. 1).
Methods Used to Monitor Changes in Phosphorus Concentrations and Loads 3

outside the study area and not shown on any figure). The 

Assabet River is impaired throughout much of its course 

by high concentrations of nutrients, especially phosphorus. 

Land use in the basin is primarily forested or open and 

residential, with smaller fractions of commercial, industrial, 

and agricultural land use. All or parts of 20 towns or small 

cities lie in the basin, with urban (or developed) areas 

clustered along the Assabet River. Sources of phosphorus 

in the basin include discharge from wastewater treatment 

plants and stormwater runoff (Massachusetts Department 

of Environmental Protection, 2004). In 2004, the U.S. 

Environmental Protection Agency (EPA) approved a total 

maximum daily load (TMDL) for the Assabet River, which 

allocates phosphorus loads to each of the sources and defines a 

set of actions to bring the river into compliance with waterquality standards (U.S. Environmental Protection Agency, 

2015a). The TMDL established wasteload allocations for 

the wastewater-treatment plants (WWTPs) in Westborough, 

Marlborough, Hudson, and Maynard, Mass., to reduce the 

amounts of total phosphorus (TP) discharged to the Assabet 

River in treated wastewater effluent by 2012 (Massachusetts 

Department of Environmental Protection, 2004). As stated in 

the TMDL, monthly mean concentrations of total phosphorus 

in effluent are not to exceed 0.1 milligrams per liter (mg/L) 

(previous limit of 0.75 mg/L) from April through October, the 

primary growing season for nuisance aquatic plants. During 

the nongrowing season (November through March), the 

WWTPs are allowed to continue with the previously allowed 

restriction of monthly mean concentrations of total phosphorus 

in effluent of no more than 1.0 mg/L. The WWTPs achieved 

compliance with their wasteload allocations at different times 

because of different construction schedules; the Hudson 

WWTP was the first to reduce TP concentrations in October 

2009, followed by the Marlborough-Westerly WWTP in 

January 2012 and the Westborough WWTP in March 2012. 

The Maynard WWTP, which was downstream from the study 

area, achieved compliance in 2011. A report published by 

the EPA (2015b) describes the individual WWTP upgrades, 

treatment methods for removing TP, and the costs involved.

The TMDL was designed to have a phased approach. The 

first step is to reduce concentrations of WWTP phosphorus 

discharge in the hope that by doing so, water-quality 

conditions would improve in the Assabet River with reduced 

aquatic biomass, decreased diurnal fluctuations of dissolved 

oxygen concentrations caused by the growth of the floating 

and rooted macrophytes, and decreased phosphorus flux to 

and from riverine sediments (Massachusetts Department 

of Environmental Protection, 2004). Through the adaptive 

management approach of the TMDL, the EPA can require 

further reductions in concentrations of total phosphorus in 

WWTP releases and consider sediment dredging and dam 

removal if the water-quality standards are not achieved 

through the WWTP reductions of TP.

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

the Massachusetts Department of Environmental Protection, 

conducted a study designed to document the water-quality 

changes downstream from the WWTPs in the Assabet River, 

before, during, and after implementation of the TP TMDL. 

The study objectives addressed in this report are to (1) document changes in phosphorus concentrations and loads in the 

Assabet River before, during, and after implementation of the 

TMDL; (2) determine the effects of seasonal differences in 

permitted phosphorus releases on instream concentrations and 

loads; and (3) examine the effects of two impounded reaches 

on phosphorus concentrations and loads. 

This report presents analysis of data on concentrations of 

total phosphorus and orthophosphate (orthoP) and streamflow 

that were collected at four water-quality-monitoring stations 

on the Assabet River from October 2008 through April 2014, 

a period that extends before, during, and after implementation 

of the TMDL phosphorus-reduction requirements at the 

WWTPs. The report describes how monitoring data were used 

to calculate daily phosphorus loads, aggregated to seasons 

and calendar years. The magnitudes of the concentration and 

load reductions achieved by the WWTPs and those observed 

at the instream monitoring stations are compared. The effects 

of two impoundments on phosphorus dynamics are assessed, 

and the results of an analysis of covariance used to compare 

TP reductions to streamflow are examined. Zimmerman 

and Savoie (2013) summarizes previous studies that were 

used to develop the TMDL and understand nutrient cycling 

and sediment phosphorus flux in relation to the biomass 

distribution in the impounded reaches of the Assabet River.

Methods Used to Monitor Changes in 

Phosphorus Concentrations and Loads

Instream nutrient concentrations in the Assabet River can 

change rapidly and continuously as a result of many factors, 

including storm runoff, groundwater discharge, interactions 

with streambed and streambank sediments, and normal 

operation of the WWTPs. High-frequency (hourly to weekly) 

changes in instream phosphorus concentrations are not 

captured by conventional, discrete water-quality sampling. To 

ensure that the variable phosphorus concentrations in the river 

were adequately measured in this study, flow-proportional 

water-quality sampling and streamflow monitoring were 

used to estimate TP and orthoP loads. Water-quality samples 

were composited over weeklong sample-collection periods 

throughout the 5-year study period. TP and orthoP loads were 

estimated by multiplying constituent concentrations measured 

in the composite samples by the streamflow (the volume of 

water moving past the sampling point per unit of time) during 

the sampling period. Continuous, flow-proportional sampling 

captures the short-term, rapid increases and decreases in 

concentration and flow that occur during storm events, which 

can substantially influence the total loads carried by the river. 

Water-quality samples and streamflow data were 

collected from October 2008 through April 2014 at four 

monitoring stations: station number 01096835, Assabet River 
4 Changes in Phosphorus Concentrations and Loads in the Assabet River, Massachusetts, October 2008 through April 2014

at Port Street at Hudson, Mass. (Port Street); 01096840, 

Assabet River 200 feet below State Route 85 at Hudson, 

Mass. (AMVETS); 01096885, Assabet River at Sudbury Road 

near Stow, Mass. (Stow); and 01097000, Assabet River at 

Maynard, Mass. (Maynard). The monitoring stations bracket 

two shallow impoundments created by old mill dams: Hudson 

impoundment (in Hudson) and Ben Smith impoundment 

(in Stow and Maynard) (figs. 2 and 3; table 1). The Hudson 

impoundment is downstream from the Westborough and 

Marlborough-Westerly WWTPs; the Ben Smith impoundment 

is downstream from the Westborough, Marlborough-Westerly, 

and Hudson WWTPs. Additional descriptions of the 

monitoring stations and of the sampling and analysis methods 

can be found in Zimmerman and Savoie (2013).

Streamflow Measurements

Streamflow, in cubic feet per second (ft3/s), was estimated from continuous measurements of stream stage and 

the development of a stage-discharge relation at each of the 

four water-quality-monitoring stations on the Assabet River. 

A submersible pressure transducer at each station monitored 

71°34'30" 71°34'

42°23'30"

42°23'

Base from Massachusetts Office of Geographic Information, Color Ortho Imagery 1:5,000

Massachusetts State Plane projection, NAD 83

0 0.1 0.2 MILE 

0 0.1 0.2 KILOMETER 

Port Street—01096835

AMVETS— 01096840

Hudson impoundment dam

Port Street—01096835

AMVETS— 01096840

Hudson impoundment dam

Figure 2. Orthophotograph map identifying the locations of water-quality-monitoring stations Port Street (01096835) and AMVETS 

(01096840), upstream and downstream from the Hudson impoundment on the Assabet River, Massachusetts. See table 1 for full station 

names. Modified from Zimmerman and Savoie (2013, fig. 2).
Methods Used to Monitor Changes in Phosphorus Concentrations and Loads 5

stream stage at 15-minute intervals. Manual measurements 

of streamflow, calculated as the product of measured stream 

velocity and stream cross-sectional area, were made every 6 to 

8 weeks to develop the site-specific stage-discharge relations 

(Rantz and others, 1982). 

Environmental Sample Collection

Composite, flow-proportional samples were collected 

with portable automatic samplers outfitted with four-bottle 

racks and controlled by dataloggers. The weekly composite 

target was 32 subsamples (the approximate number of 

100-milliliter [mL] samples that the sample bottle could hold). 

Every week, the average daily streamflow for the upcoming 

week was estimated; the estimate was used to calculate a 

threshold volume that would activate the automated sampler. 

Samples were collected more frequently on the days with 

greater streamflow volumes; this is what is meant by “flowproportional sampling” (fig. 4). 

When the streamflow threshold was exceeded, a signal 

was transmitted to the automated sampler, causing it to purge 

the suction line and collect two 100-mL aliquots of water. 

Ben Smith

impoundment dam

Stow—01096885

Maynard—01097000

Stow—01096885

Maynard—01097000

71°30' 71°29' 71°28' 71°27'

42°26'

42°25'

Base from Massachusetts Office of Geographic Information, Color Ortho Imagery 1:5,000

Massachusetts State Plane projection, NAD 83

0 0.5 1 MILE

0 0.5 1 KILOMETER

Figure 3. Orthophotograph map identifying the locations of water-quality-monitoring stations Stow (01096885) and Maynard 

(01097000), upstream and downstream from the Ben Smith impoundment on the Assabet River, Massachusetts. See table 1 for full 

station names. Modified from Zimmerman and Savoie (2013, fig. 3).
6 Changes in Phosphorus Concentrations and Loads in the Assabet River, Massachusetts, October 2008 through April 2014 Table 1. Location coordinates, drainage-basin areas, and annual mean daily and annual total streamflow (calendar years 2008 to 2013) for water-quality-monitoring stations on the Assabet River in the towns of Hudson, Stow, and Maynard, Massachusetts. [Locations of monitoring stations are shown in figures 1 to 3. Latitude and longitude are given in degrees (°), minutes (′), and seconds (′′) relative to the North American Datum of 1983 (NAD 83), except for station number 01097000, whose coordinates are relative to the North American Datum of 1927 (NAD 27); USGS, U.S. Geological Survey; mi2, square mile; ft3/s, cubic foot per second; ft3/yr, cubic foot per year; MA, Massachusetts; ft, foot; Rt, State Route; Rd, Road, --, no data] USGS station name Short name USGS station number Latitude Longitude Drainage basin area (mi2

)

Assabet River at Port Street at 

Hudson, MA

Port Street 01096835 42°23′07′′ 71°34′40′′ 60.5

Assabet River 200 ft below Rt 85 

at Hudson, MA

AMVETS 01096840 42°23′24′′ 71°34′11′′ 64.2

Assabet River at Sudbury Rd near 

Stow, MA

Stow 01096885 42°24′42′′ 71°30′29′′ 88.0

Assabet River at Maynard, MA Maynard 01097000 42°25′55′′ 71°27′01′′ 116

Annual streamflow, by calendar year

Short name

Mean 

daily

(ft3/s)

Total

(ft3/yr)

Mean 

daily

(ft3/s)

Total

(ft3/yr)

Mean 

daily

(ft3/s)

Total

(ft3/yr)

Mean 

daily

(ft3/s)

Total

(ft3/yr)

Mean 

daily

(ft3/s)

Total

(ft3/yr)

Mean 

daily

(ft3/s)

Total

(ft3/yr)

2008 2009 2010 2011 2012 2013

Port Street -- -- 150 54,829 137 49,945 167 60,776 81 29,715 96 34,862AMVETS -- -- 161 58,642 153 55,974 187 68,163 91 33,123 109 39,720Stow -- -- 194 70,795 196 71,524 252 92,030 114 41,888 142 51,758Maynard 311 113,704 246 89,761 247 90,037 306 111,651 148 54,087 174 63,381
Methods Used to Monitor Changes in Phosphorus Concentrations and Loads 7

0

600

700

Example

weekly composite

Streamflow

Automated sample collection

600

500

90

80

75

4/18/2012 4/23/2012

EXPLANATION

Streamflow, in cubic feet per second

500

400

300

200

100

85

70

400

300

200

Time Time

02:0006:0010:0014:0018:00

22:00

02:00

22:0002:0006:0010:0014:0018:0022:0002:00

4/7/2012

4/11/20124/15/20124/19/20124/23/2012

4/27/2012

5/1/20125/5/2012

Streamflow, in cubic feet per second

Figure 4. Streamflow and sample-collection rate, demonstrating the flow-proportional sampling method.
8 Changes in Phosphorus Concentrations and Loads in the Assabet River, Massachusetts, October 2008 through April 2014

The first aliquot, the TP sample, was pumped into a 3.8-liter 

(L) polyethylene bottle previously acidified with 10 mL of 

sulfuric acid. The second aliquot, the orthoP sample, was 

pumped into a second bottle, which was modified so that the 

water sample could be completely pumped into a refrigerator 

by a peristaltic pump. Inside the refrigerator, the tubing 

connected to an inline polysulfone capsule filter with a pore 

size of 0.45 micrometer, polyester reinforcement, and an 

effective filtration area of 20 square centimeters. After passing 

through the filter, the sample entered a 9-L polyethylene 

storage bottle.

In the event that the week’s streamflow was 

underestimated and more than 32 samples were automatically 

collected, a second 3.8-L acidified TP bottle collected any 

additional TP samples; the 9-L orthoP storage bottle had ample 

capacity for additional samples. If the total weekly streamflow 

was overestimated, fewer than 32 TP and orthoP samples were 

collected, but the sample numbers were nevertheless collected 

proportional to flow. 

The weekly composite samples were processed and 

shipped to the USGS National Water Quality Laboratory 

(NWQL) in Denver, Colorado, for analysis of TP and orthoP 

(Fishman, 1993; U.S. Environmental Protection Agency, 

1993). Additional information about the study design is 

described in Zimmerman and Savoie (2013).

Quality-Control Samples

Quality-control samples were collected throughout the 

study period to confirm that the automated sampling system 

collected representative samples. Equal-width increment 

(EWI) samples and weighted-bottle point samples from 

bridges were collected concurrently with inside grab samples 

(IGSs) collected by the automated sampler. Details about 

EWI sampling methods are described in the USGS “National 

Field Manual for the Collection of Water-Quality Data” (U.S. 

Geological Survey, 2006). The TP and orthoP concentrations 

in the EWI and weighted-bottle point samples were compared 

to concentrations in IGS collected by the automated 

sampler to verify that the automated sampler was collecting 

representative river-water samples. Other quality-control 

samples included source solution blank samples and replicate 

(split-composite) samples. Source solution blank samples were 

collected to ensure that the laboratory-grade deionized water 

used for the weekly rinsing of sample bottles and cleaning 

of the sample-collection bottles did not contain detectable 

concentrations of TP and orthoP, and sample replicates were 

collected to estimate variability in the sample processing 

(splitting and filtering) (Mueller and others, 2015). 

Source solution blank samples, replicate (splitcomposite) samples, and concurrent (1) IGSs and EWI 

samples and (2) IGSs and weighted-bottle point samples are 

shown in Savoie (2016). Total phosphorus and orthoP were 

not detected in any of the rinse-water blank samples, and the 

median relative percent differences (RPDs) for the replicate 

samples were about 2 percent or less at all four locations. 

Concurrent IGS-weighted-bottle point and IGS–EWI samples 

were collected during periods of low-, average-, and highstreamflow conditions. The IGSs had good agreement with 

the weighted-bottle point and EWI samples most of the time, 

with RPDs within 20 percent. Two exceptions were at the 

Maynard monitoring station on October 1, 2008, and at the 

Port Street monitoring station on April 1, 2014. The reason for 

the dissimilar concurrent samples at the Maynard monitoring 

station (RPD value of about 35 percent) at the beginning of the 

study is unknown; however, subsequent concurrent samples 

had better agreement (11.4 percent or less). The dissimilar 

concurrent samples at the Port Street monitoring station 

(RPD value of 186 percent) alerted us to potential sediment 

buildup at the intake of the automated sampler; because of the 

sediment buildup, total phosphorus data for the last month at 

the Port Street monitoring station were estimated by using data 

from the AMVETS monitoring station. Overall, the qualitycontrol-sampling results indicate that the automated samplers 

were collecting representative samples from these well-mixed 

sections of the river. 

Load Calculations

Loads represent the mass of substance (phosphorus in 

this case) that passes the sampling location in a given period 

of time and incorporate the variability of concentration and 

the hydrologic system during the period of sample collection. 

Weekly composite concentrations of TP and orthoP were 

used to estimate daily loads of TP and orthoP at each waterquality-monitoring station by multiplying the concentration 

(in milligrams per liter) by the daily streamflow (in cubic feet 

per second) for each day during the composited week and 

converting the resulting value to units of kilograms per day. 

At times during the 5-year study, composite samples 

were not available, and concentrations were estimated—for 

example, when the sample tubing froze or became clogged 

with sediment, when the stream level dropped below the 

sampler intake, or when human errors prevented the collection 

of a week’s composite sample. During the 290-week sampling 

period, concentrations were estimated for 20 weeks of TP 

and 18 weeks of orthoP at the Port Street monitoring station, 

for 11 weeks of TP and 19 weeks of orthoP at the AMVETS 

monitoring station, for 14 weeks of TP and 17 weeks of orthoP 

at the Stow monitoring station, and for 17 weeks of TP and 

19 weeks of orthoP at the Maynard monitoring station. In 

situations with missing data, composite-sample concentrations were estimated by using either values from before and 

after the missing-data event at the station or concentration data 

from nearby upstream or downstream stations. 

The USGS NWQL method detection limit (MDL) for TP 

and orthoP is 0.004 mg/L. In cases where the reported orthoP 

results were less than the MDL, the actual laboratory result 

was used as the best estimate of concentration if the value 

fell between 0.002 and 0.004 mg/L; if the laboratory value 
Changes in Phosphorus Concentrations and Loads 9

was less than 0.002 mg/L, then 0.002 mg/L was used as the 

best estimate. The cases when less than MDL orthoP values 

were estimated were only 1 percent at the Port Street monitoring station, 4 percent at the AMVETS monitoring station, 

8 percent at the Stow monitoring station, and 7 percent at the 

Maynard monitoring station. The orthoP values estimated to 

be less than the MDL are not reported; only “<0.004 mg/L” is 

given in the data tables in Savoie (2016). 

Changes in Phosphorus Concentrations 

and Loads

This section presents data on instream changes in TP 

and orthoP concentrations and loads following decreases 

in TP concentrations in effluent from three WWTPs in the 

Assabet River. Changes in TP and orthoP concentrations and 

loads and effects of seasonal variations were examined at four 

monitoring stations downstream from the WWTPs following 

the implementation of the TP TMDL. Concentrations of 

TP and orthoP in the Assabet River were measured in flowproportional composite samples and, consequently, represent 

flow-weighted average concentrations in the river during 

weeklong sampling periods. The monitoring stations were 

located upstream and downstream of two large impoundments, 

and the effects of impoundments on concentrations and loads 

also were investigated.

Phosphorus Concentrations

Reductions in TP concentrations were observed in the 

WWTP effluent and at the instream monitoring stations 

downstream from the WWTPs (Savoie, 2016). The USGS 

used TP concentration data from 24-hour composite samples 

and daily effluent volumes obtained from the three WWTPs to 

estimate daily TP loads in WWTP effluent; concentration data 

were typically from samples collected weekly or at times more 

frequently (written commun., Christopher Pratt, Westborough 

WWTP, and Mark Concheri, Hudson WWTP, May 12, 2014; 

and Harry Butland, Marlborough-Westerly WWTP, August 

20, 2014). The TP concentrations in WWTP effluent were 

disaggregated to daily TP concentrations and estimated 

when not measured. Concentrations were estimated on days 

when the WWTPs did not measure TP. When missing daily 

concentrations were estimated, time-adjacent concentrations 

were used; if the adjacent concentrations differed, they were 

averaged. TP loads in WWTP effluent were calculated by 

multiplying concentrations of TP (in milligrams per liter) by 

the effluent discharge volume (in million gallons per day) 

and converted to units of kilograms per day (Savoie, 2016). 

OrthoP loads in WWTP effluent were not calculated because 

of incomplete data for the period of record.

Patterns of instream concentrations of TP at the 

Port Street and AMVETS monitoring stations in weekly 

flow-proportional composite samples and the combined daily 

average concentrations in effluent from the two upstream 

WWTPs are shown for the entire study period in figure 5. 

Similar patterns were observed in concentrations in weekly 

flow-proportional composite samples from the Stow and 

Maynard monitoring stations, which were downstream from 

all three WWTPs (fig. 6). Concentrations were highly variable; 

however, decreases in both TP effluent from the WWTPs 

and TP concentrations measured at the AMVETS, Stow, and 

Maynard monitoring stations were observed in the data for 

the period following implementation of the TMDL-mandated 

WWTP upgrades in March 2012. OrthoP (the filtered sample, 

or dissolved form of phosphorus) concentrations at the 

instream monitoring stations also decreased following WWTP 

upgrades, though the changes were not as great as the changes 

in TP concentrations (figs. 7 and 8). In addition to the longterm patterns observed across the entire study, some large, 

rapid, short-term decreases in TP and orthoP concentrations 

were associated with periods of increased streamflow—for 

example, during March and April 2010, March and April 2011, 

and December 2011.

The annual distributions of estimated daily total phosphorus concentrations in both the WWTP discharge effluent 

(fig. 9) and instream at the monitoring stations (fig. 10) are 

best represented by annual box plots that show the median, 

10-percent, interquartile, and 90-percent concentrations. 

For this analysis, the median values were taken as the best 

overall indicators of year-to-year changes; the 10-percent, 

interquartile, and 90-percent concentrations are an indication 

of the variability in the data. Median and mean TP and orthoP 

concentrations and loads in both the WWTP discharge effluent 

and in the instream monitoring stations are summarized in 

tables 2 and 3.

Changes in annual median TP concentrations reported 

by the WWTPs align with the dates in which the plants were 

upgraded to comply with TMDL-mandated reductions (fig. 9 

and table 2). Although the individual WWTPs became compliant with the TMDL at different times, all of the WWTPs were 

compliant by the end of March 2012. The annual median TP 

concentration for the Hudson WWTP (compliant October 

2009) decreased from 0.74 milligrams per liter (mg/L) in 2009 

to 0.12 mg/L in 2010 and remained at or below 0.10 mg/L 

through 2013. The annual median TP concentration for the 

Marlborough-Westerly WWTP (compliant January 2012) 

decreased from 0.47 in 2009 to 0.42 to 0.40 mg/L in 2010 

and 2011, respectively, to 0.08 mg/L in 2012 and 2013. The 

annual median TP concentration for the Westborough WWTP 

(compliant March 2012) ranged from 0.47 to 0.59 mg/L in 

2009 to 2011, decreased to 0.09 mg/L in 2012, and further 

decreased to 0.06 mg/L in 2013. Reductions in annual median 

TP concentrations in discharge at all three WWTPs represent 

reductions of more than 80 percent relative to before-TMDL 

implementation concentrations. The Westborough WWTP is 

the largest of the three WWTPs, and the annual discharge from 

the Westborough plant contributed 30 to 65 percent of the total 

annual discharge for all three plants during the study period.
10 Changes in Phosphorus Concentrations and Loads in the Assabet River, Massachusetts, October 2008 through April 2014

Total phosphorus concentration at 

 Port Street (01096835) and AMVETS (01096840)—Flow-proportional

 average concentrations for weeklong composite samples. Value is plotted on 

 first day of composited week. Estimated and censored concentrations

 are not shown

Streamflow

Daily average concentration at Westborough and 

 Marlborough-Westerly WWTPs

EXPLANATION

Streamflow, in cubic feet per second

0.01

0.10

1.00

10.00

10/1/2008

2/1/2009

6/1/2009

10/1/2009

2/1/2010

6/1/2010

10/1/2010

2/1/2011

6/1/2011

10/1/2011

2/1/2012

6/1/2012

10/1/2012

2/1/2013

6/1/2013

10/1/2013

2/1/2014

6/1/2014

0.01

0.10

1.00

10.00

0

500

1,000

1,500

2,000

2,500

0

500

1,000

1,500

2,000

2,500

Total phosphorus concentration, in milligrams per liter

A. Port Street

B. AMVETS

Before upgrades After upgrades

Before upgrades After upgrades

Figure 5. Streamflow and total phosphorus concentrations at the A, Port Street (01096835) and B, AMVETS (01096840) 

water-quality-monitoring stations, and daily average total phosphorus concentration in effluent from Westborough and 

Marlborough-Westerly wastewater-treatment plants (WWTPs), in the Assabet River, Massachusetts, 2008–2014. See 

table 1 for full station names.
Changes in Phosphorus Concentrations and Loads 11

0.01

0.10

1.00

10.00

10/1/2008

2/1/2009

6/1/2009

10/1/2009

2/1/2010

6/1/2010

10/1/2010

2/1/2011

6/1/2011

10/1/2011

2/1/2012

6/1/2012

10/1/2012

2/1/2013

6/1/2013

10/1/2013

2/1/2014

6/1/2014

0.01

0.10

1.00

10.00

0

500

1,000

1,500

2,000

2,500

0

500

1,000

1,500

2,000

2,500

Streamflow, in cubic feet per second

Total phosphorus concentration at 

 Stow (01096885) and Maynard (01097000)—Flow-proportional

 average concentrations for weeklong composite samples. Value is plotted on 

 first day of composited week. Estimated and censored concentrations

 are not shown

Streamflow

Daily average concentration at Westborough, 

 Marlborough-Westerly, and Hudson WWTPs

EXPLANATION

A. Stow

B. Maynard

Before upgrades After upgrades

Before upgrades After upgrades

Total phosphorus concentration, in milligrams per liter

Figure 6. Streamflow and total phosphorus concentrations at the A, Stow (01096885) and B, Maynard (01097000) water-qualitymonitoring stations, and daily average total phosphorus concentration in effluent from Westborough, Marlborough-Westerly, and 

Hudson wastewater-treatment plants (WWTPs), in the Assabet River, Massachusetts, 2008–2014. See table 1 for full station names.
12 Changes in Phosphorus Concentrations and Loads in the Assabet River, Massachusetts, October 2008 through April 2014

0.00

0.02

0.04

0.06

0.08

0.10

10/1/2008

2/1/2009

6/1/2009

10/1/2009

2/1/2010

6/1/2010

10/1/2010

2/1/2011

6/1/2011

10/1/2011

2/1/2012

6/1/2012

10/1/2012

2/1/2013

6/1/2013

10/1/2013

2/1/2014

6/1/2014

0.00

0.02

0.04

0.06

0.08

0.10

0

500

1,000

1,500

2,000

2,500

 A. Port Street 

 B. AMVETS 

Orthophosphate concentration, in milligrams per liter as phosphorus

0

500

1,000

1,500

2,000

2,500

Before upgrades After upgrades

Before upgrades After upgrades

Orthophosphate concentration at 

 Port Street (01096835) and AMVETS (01096840)—Flow-proportional

 average concentrations for weeklong composite samples. Value is plotted on 

 first day of composited week 

Streamflow

EXPLANATION

Streamflow, in cubic feet per second

Figure 7. Streamflow and orthophosphate concentrations at the A, Port Street (01096835) and B, AMVETS (01096840) waterquality-monitoring stations on the Assabet River, Massachusetts, 2008–2014. See table 1 for full station names.
Changes in Phosphorus Concentrations and Loads 13

0.00

0.02

0.04

0.06

0.08

0.10

10/1/2008

2/1/2009

6/1/2009

10/1/2009

2/1/2010

6/1/2010

10/1/2010

2/1/2011

6/1/2011

10/1/2011

2/1/2012

6/1/2012

10/1/2012

2/1/2013

6/1/2013

10/1/2013

2/1/2014

6/1/2014

0.00

0.02

0.04

0.06

0.08

0.10

A. Stow

0

500

1,000

1,500

2,000

2,500

B. Maynard 

0

500

1,000

1,500

2,000

2,500

Orthophosphate concentration at 

 Stow (01096885) and Maynard (01097000)—Flow-proportional

 average concentrations for weeklong composite samples. Value is plotted on 

 first day of composited week. Estimated and censored concentrations

 are not shown

Streamflow

EXPLANATION

Before upgrades After upgrades

Before upgrades After upgrades

Orthophosphate concentration, in milligrams per liter as phosphorus

Streamflow, in cubic feet per second

Figure 8. Streamflow and orthophosphate concentrations at the A, Stow (01096885) and B, Maynard (01097000) water-qualitymonitoring stations on the Assabet River, Massachusetts, 2008–2014. See table 1 for full station names.
14 Changes in Phosphorus Concentrations and Loads in the Assabet River, Massachusetts, October 2008 through April 2014

EXPLANATION

90th percentile

75th percentile

25th percentile

10th percentile

Median

Westborough WWTP (upgraded March 2012)

Marlborough-Westerly WWTP (upgraded January 2012)

Hudson WWTP (upgraded October 2009)

2009 2010 2011

0.5

1.5

0.0

1.0

2.0

2012 2013

Total phosphorus concentration, in milligrams per liter

Figure 9. Annual distributions of estimated daily concentrations of total phosphorus in wastewater-treatmentplant (WWTP) effluent to the Assabet River, Massachusetts, 2009–2013.

Annual median TP and orthoP concentrations at three 

of the four instream monitoring stations generally decreased 

following complete implementation of the WWTP upgrades in 

2012 (fig. 10 and table 3). Annual median TP concentrations 

decreased by about 38 to 50 percent at the AMVETS, Stow, 

and Maynard monitoring stations during the study period. The 

annual median TP concentration at the AMVETS monitoring 

station ranged from 0.07 to 0.09 mg/L from 2009 to 2011 and 

decreased to 0.05 mg/L in 2012 and 2013. The annual median 

TP concentration at the Stow monitoring station ranged 

from 0.07 to 0.08 mg/L from 2009 to 2011 and decreased to 

0.04 mg/L in 2012 and 2013. The annual median TP concentration at the Maynard monitoring station ranged from 0.06 to 

0.07 mg/L from 2009 to 2011 and decreased to 0.05 mg/L in 

2012 and to 0.04 mg/L in 2013. Decreases in annual median 

orthoP concentrations were observed throughout the study 

period at the AMVETS, Stow, and Maynard monitoring stations, with annual median orthoP concentrations of about 

0.017 to 0.019 mg/L in 2009 that decreased to about 0.004 to 

0.007 mg/L in 2013.

In contrast to annual median TP concentrations at the 

other three instream monitoring stations, the concentration 

at the Port Street monitoring station did not decrease but 

remained at 0.10 to 0.13 mg/L during the entire study period 

(fig. 10A and table 3). This difference between TP concentrations at the Port Street monitoring station and the other 

stations may be related to the location of the station, which 

was in a slow-moving section of the river at the upstream end 

of the Hudson impoundment. The monitoring system at the 

Port Street monitoring station may have been in a position to 

record seasonal and (or) flow-related resuspension of particulate phosphorus that accumulated in the bed sediments. TP 

concentrations and the proportion of TP that was particulate 

(the difference between TP and orthoP) were typically higher 

at the Port Street monitoring station than at the other stations 

downstream, especially after 2010. Downstream from the 

Port Street monitoring station, particulate matter is likely to 

rapidly settle in the Hudson impoundment, and particulate 

phosphorus constituted consistently smaller fractions of TP 

at the AMVETS monitoring station than at the Port Street 
Changes in Phosphorus Concentrations and Loads 15

A

B

2009 2010 2011 2012 2013

2009 2010 2011 2012 2013

0.00

0.05

0.10

0.15

0.20

0.25

Total phosphorus concentration, in milligrams per liter

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

Orthophosphate concentration, in milligrams per liter as phosphorus

 Port Street (01096835)

 AMVETS (01096840)

 Stow (01096885)

 Maynard (01097000)

EXPLANATION

90th percentile

75th percentile

25th percentile

10th percentile

Median

Figure 10. Annual distributions of estimated daily concentrations of A, total phosphorus and B, orthophosphate in weekly flowproportional composite samples from four water-quality-monitoring stations on the Assabet River, Massachusetts, 2009–2013. 

See table 1 for full station names.
16 Changes in Phosphorus Concentrations and Loads in the Assabet River, Massachusetts, October 2008 through April 2014

Table 2. Median and mean flow and total phosphorus 

concentrations and loads at wastewater-treatment plants in the 

towns of Westborough, Marlborough, and Hudson on the Assabet 

River, Massachusetts, 2009 through 2013.

[Locations of wastewater-treatment plants (WWTPs) are shown in figure 1. 

Results are for calendar year. Concentration values are based on estimated 

daily concentrations used for loads calculations. Mgal/d, million gallons per 

day; mg/L, milligram per liter; kg/d, kilogram per day; --, data not included]

Year

Total phosphorus

Flow 

(Mgal/d)

Concentration 

(mg/L)

Load 

(kg/d)

Median Mean Median Mean Median Mean

Westborough WWTP

2009 6.2 6.4 0.57 0.62 13.9 14.9

2010 5.5 6.2 0.59 0.65 12.3 15.6

2011 6.1 6.4 0.47 0.48 11.9 11.5

2012 4.9 5.0 0.09 0.23 1.6 4.4

2013 5.1 5.5 0.06 0.17 1.3 3.7

Marlborough-Westerly WWTP

2009 2.5 2.6 0.47 0.66 4.5 6.7

2010 2.1 2.3 0.42 0.58 3.3 6.3

2011 2.7 2.8 0.40 0.42 3.6 4.5

2012 1.9 1.9 0.08 0.11 0.6 0.8

2013 1.8 1.9 0.08 0.15 0.6 1.2

Hudson WWTP

2009 2.4 2.4 0.74 0.86 6.9 8.0

2010 1.7 2.0 0.12 0.31 0.7 2.9

2011 2.1 2.2 0.10 0.18 0.7 1.6

2012 1.6 1.7 0.09 0.12 0.5 0.8

2013 1.6 1.7 0.10 0.12 0.6 0.8

Westborough and Marlborough WWTPs

2009 -- -- -- -- 18.4 21.7

2010 -- -- -- -- 15.6 21.8

2011 -- -- -- -- 15.5 16.0

2012 -- -- -- -- 2.2 5.2

2013 -- -- -- -- 1.9 4.9

Westborough, Marlborough, and Hudson WWTPs

2009 -- -- -- -- 25.3 29.7

2010 -- -- -- -- 16.4 24.7

2011 -- -- -- -- 16.2 17.6

2012 -- -- -- -- 2.7 5.9

2013 -- -- -- -- 2.5 5.7

monitoring station. Annual median orthoP concentrations 

at the Port Street monitoring station also remained similar during the entire study, at 0.011 to 0.015 mg/L, further 

suggesting that concentrations at the Port Street monitoring 

station were behaving differently than concentrations at the 

downstream stations.

Relations of concentration to streamflow are commonly 

used to characterize phosphorus in streams in terms of its 

origin from point sources such as WWTPs. Instream phosphorus predominantly from WWTPs is diluted by inflows of 

runoff and (or) groundwater discharge so that concentrations 

are inversely related to flow. In contrast, instream phosphorus 

predominantly from overland runoff, such as agricultural or 

stormwater runoff, increases during high flows, resulting in 

higher concentrations during high flows. The TP and orthoP 

concentration data collected during this study are not ideal for 

analysis of source contributions because the data represent 

average concentrations during the weeklong sampling periods. The composite concentration data are also flow-weighted 

averages, which means that for sampling periods when flow 

varied, the data are more representative of concentrations during the parts of the week with higher flow than the parts with 

lower flow. This use of flow-weighted averages makes the data 

well suited to the calculation of instream loads, because more 

of the load is carried by the river during times of higher flow 

than during times of lower flow, but the method makes the 

data less suited for analysis of relations between streamflow 

and concentration.

During most of these weeklong periods, flows changed in 

response to storms of short duration (hours or days). Consequently, relations between concentration and flow in the 

stream that might be apparent in discrete samples are likely to 

be obscured by the averaging that is inherent in the composite 

samples. Nevertheless, some relations are apparent between 

concentration and flow, where flow is the average of daily 

mean flows for the seven days of the sampling period. Inverse 

relations between TP concentration and flow are most clearly 

apparent at the AMVETS monitoring station both before 

(2008–11) and after (2012–14) WWTP upgrades and at the 

Port Street and Stow monitoring stations before the WWTP 

upgrades (fig. 11). Inverse relations are consistent with the 

previous findings of WWTP effluent as the primary source of 

instream phosphorus in the Assabet River except during highflow wet-weather events (ENSR International, 2001; Massachusetts Department of Environmental Protection, 2004). 

The Port Street, AMVETS, and Stow monitoring stations are 

closer to the WWTPs than the Maynard monitoring station, so 

inverse relations with flow are more apparent at these stations 

than at the Maynard monitoring station, which is downstream 

from a large tributary (Elizabeth Brook, also known as Assabet 

Brook; fig. 1) and downtown Maynard.

Streamflow During the Study Period

Streamflow during the study period (October 2008 

through April 2014) was higher than average, in terms of 

annual mean flow, during the initial years of the study and near 

or below average during the final years of the study, based on 

flow at the long-term gaging station at Maynard (01097000, 

period of record 1942 to present; fig. 12). Annual mean flows 

at the Maynard monitoring station in calendar years 2009, 
Changes in Phosphorus Concentrations and Loads 17

Table 3. Median and mean flow and total phosphorus and orthophosphate concentrations and loads at water-quality-monitoring 

stations on the Assabet River in the towns of Hudson, Stow, and Maynard, Massachusetts, 2009 through 2013.

[Locations of instream monitoring stations are shown in figures 1 to 3. Full station names and numbers are listed in table 1. Results are for calendar year. Concentration values include estimated concentrations for periods of missing data. ft3

/s, cubic foot per second; mg/L, milligram per liter; kg/d, kilogram per day]

Year

Flow 

(ft3

/s)

Total phosphorus Orthophosphate

Concentration 

(mg/L)

Load 

(kg/d)

Concentration 

(mg/L)

Load 

(kg/d)

Median Mean Median Mean Median Mean Median Mean Median Mean

Port Street

2009 131 150 0.100 0.107 32.9 37.3 0.012 0.014 4.2 4.9

2010 62 137 0.130 0.135 22.4 28.5 0.014 0.016 2.6 3.8

2011 141 167 0.116 0.129 35.8 45.2 0.014 0.015 4.5 5.8

2012 65 81 0.124 0.134 17.8 28.0 0.012 0.014 2.2 2.9

2013 63 96 0.107 0.119 13.9 28.1 0.009 0.011 1.4 2.8

AMVETS

2009 135 161 0.082 0.084 27.1 32.4 0.017 0.018 6.0 7.4

2010 66 153 0.092 0.102 14.9 24.7 0.018 0.018 2.8 5.0

2011 149 187 0.070 0.074 23.3 29.5 0.011 0.015 4.6 6.5

2012 69.5 91 0.051 0.057 9.7 12.5 0.010 0.010 1.7 2.4

2013 69 109 0.051 0.053 7.4 13.0 0.007 0.009 1.1 2.6

Stow

2009 170 194 0.084 0.095 38.1 44.4 0.019 0.022 8.7 10.4

2010 92 196 0.070 0.073 18.4 30.2 0.011 0.012 2.9 5.0

2011 209 252 0.070 0.071 30.8 39.8 0.010 0.012 5.5 7.2

2012 91.5 114 0.045 0.049 10.5 14.4 0.007 0.008 1.7 2.4

2013 95 142 0.040 0.040 9.4 14.3 0.004 0.005 1.1 2.0

Maynard

2009 227 246 0.070 0.079 37.7 46.4 0.019 0.020 9.1 11.2

2010 127 247 0.064 0.065 21.5 37.6 0.010 0.011 3.8 6.3

2011 276 306 0.062 0.066 37.3 45.0 0.010 0.012 6.5 8.3

2012 121.5 148 0.048 0.055 14.6 18.5 0.009 0.010 2.3 3.5

2013 107 174 0.041 0.046 11.3 20.0 0.007 0.009 1.9 4.4

2010, and 2011 were 25, 25, and 55 percent, respectively, 

higher than the long-term average at the station (197 ft3/s), 

and annual mean flows in 2012 and 2013 were about 24 and 

12 percent lower, respectively, than the long-term average. 

The interannual variation in streamflow reflects climatic 

conditions during the study period: annual total precipitation 

at the National Oceanic and Atmospheric Administration 

precipitation monitoring station in nearby Natick, Mass., was 

50 inches (in.) in 2009, 52 in. in 2010, 57 in. in 2011, 44 in. in 

2012, and 49 in. in 2013 (National Oceanic and Atmospheric 

Administration, 2015).

In 2009, above-normal flows (flows greater than the 

75th percentile of mean daily flows) were mainly in the midsummer months, whereas above-normal flows in 2010 were 

mainly in the early spring. Below-normal flows (flows less 

than the 25th percentile) were measured in midsummer 2010. 

In 2011, flows during the first half of the year were generally normal, but flows during the late summer and fall were 

considerably above normal (on average, more than twice the 

75th percentile). Flows during 2012 were within the normal 

range throughout much of the year; the low annual mean flow 

for 2012 reflects the low flows in the spring. Flows in 2013 

were primarily below normal in late spring and late fall. 

Streamflow is an integral component of loads computations because instream constituent loads are determined by 

both constituent concentrations and the volume of water in 

which the concentrations occur. Differences in instream loads 

can reflect differences in instream concentrations, differences 

in streamflow, or both. However, the effect of streamflow 

variations on instream loads depends on the constituent and 
18 Changes in Phosphorus Concentrations and Loads in the Assabet River, Massachusetts, October 2008 through April 2014

0.4

0.3

0.2

0.1

0.0

0.4

0.3

0.2

0.1

0.0

0.20

0.15

0.10

0.05

0.00

0.4

0.3

0.2

0.1

0.0

Mean daily streamflow during the sampling period, in cubic feet per second

Total phosphorus concentration, in milligrams per liter

Port Street AMVETS

Stow Maynard

200400600800

1,000

0

200400600800

1,0001,2001,4001,600

0

200400600800

1,0001,200

0

200400600800

1,0001,2001,4001,6001,800

0

Before WWTP upgrades, 2008−11

EXPLANATION

After WWTP upgrades, 2012−13

Figure 11. Relations between streamflow and instream concentrations of total phosphorus at four water-qualitymonitoring stations on the Assabet River, Massachusetts, before and after wastewater-treatment-plant (WWTP) 

upgrades to reduce phosphorus in WWTP effluent. Sampling periods were 1 week long. See table 1 for full station 

names and numbers.
Changes in Phosphorus Concentrations and Loads 19

1

10

100

1,000

10,000

Streamflow, in cubic feet per second

Streamflow at Maynard, Massachusetts (station 01097000)

EXPLANATION

Mean daily streamflow, 1942−2014

Daily mean streamflow during

 the study period, 10/1/2008 to 4/30/2014

Annual mean (median) streamflow

 during the calendar year indicated

2009 2010 2011 2012 2013

10/1/2008

2/1/20096/1/2009

10/1/2009

2/1/20106/1/2010

10/1/2010

2/1/20116/1/2011

10/1/2011

2/1/20126/1/2012

10/1/2012

2/1/20136/1/2013

10/1/2013

2/1/2014

Interquartile range—Top of the shaded area is 

the 75th percentile and bottom of the 

shaded area is the 25th percentile

246 (227) 247 (127) 306 (276) 148 (122) 174 (107)

246 (227)

Date

Figure 12. Interquartile range of mean daily streamflow from 1942 to 2014 at station 01097000 repeated for each calendar 

year and overlaid with daily mean streamflow during the study period, from October 1, 2008, to April 30, 2014, Assabet River, 

Maynard, Massachusetts. See table 1 for full station names.
20 Changes in Phosphorus Concentrations and Loads in the Assabet River, Massachusetts, October 2008 through April 2014

how it is delivered to the stream. For constituent loads from a 

WWTP, to the extent that the loads are independent of hydrologic conditions, variations in streamflow are less important 

than for constituent loads from sources distributed throughout a watershed that are delivered to the stream by overland 

runoff. If loads from WWTPs were completely independent 

of hydrologic conditions and were the only source of instream 

loads, then instream loads would not be affected by streamflow variation. This is because the same constituent mass 

delivered to a larger volume of stream water would result in 

lower instream concentrations but not a larger load than if it 

were delivered to a smaller volume of stream water. 

The variation in streamflow during the sample-collection 

period is important to the present study because not all of the 

phosphorus loads in the river came from the WWTPs, and the 

WWTP loads are not completely independent of hydrologic 

conditions. A study conducted by ENSR International (2001) 

indicates that nearly all of the phosphorus loads in the river 

during dry weather come from the WWTPs; however, overland runoff can contribute substantially to the total phosphorus loads during wet weather. Flows and TP loads from 

the WWTPs were higher during periods of high streamflow, 

perhaps because of infiltration and inflow during wet weather.

Daily streamflow at the Port Street, AMVETS, and Stow 

monitoring stations was highly correlated with daily streamflow at the Maynard monitoring station. Linear regression 

analyses of daily streamflow at the Port Street, AMVETS, 

and Stow monitoring stations yielded R-squared (R2

) values of 0.97, 0.97, and 0.99, respectively. Mean annual flow 

increased by about 12 percent between the Port Street and 

AMVETS monitoring stations, by about 30 percent between 

the AMVETS and Stow monitoring stations, and by about 

25 percent between the Stow and Maynard monitoring stations 

(table 1).

Phosphorus Loads

Total phosphorus loads for the three WWTPs were 

calculated from concentration and flow data reported by the 

WWTPs. Annual median TP loads decreased at the three 

WWTPs from 2009 to 2013 (fig. 13 and table 2), with the 

largest decrease following completion of all treatment-plant 

upgrades. The annual median TP load between 2009 and 2013 

decreased by 91 percent (13.9 to 1.3 kilograms per day [kg/d]) 

at the Westborough WWTP, 87 percent (4.5 to 0.6 kg/d) at 

the Marlborough-Westerly WWTP, and 91 percent (7.0 to 

0.6 kg/d) at the Hudson WWTP. Decreases in mean TP loads 

were slightly lower, at 75 percent for Westborough, 82 percent for Marlborough-Westerly, and 90 percent for Hudson 

(table 2). The years 2009 and 2013 are chosen for comparison 

here because (1) 2009 was the first full calendar year of the 

study and preceded the most changes in WWTP operations, 

and (2) 2013 was the last full calendar year of the study, postdated all changes in WWTP operations, and was a relatively 

normal flow year. 

The changes in TP loads at the WWTPs were due primarily to changes in TP concentration rather than changes in 

wastewater flow. Flows from the WWTPs were lower in 2013 

than in 2009, but by small percentages—total or annual mean 

flow was 14 percent lower at Westborough, 27 percent lower 

at Marlborough-Westerly, and 29 percent lower at Hudson in 

2013 than in 2009. In contrast, median (mean) concentrations 

at the WWTPs were 89 (73) percent lower at Westborough, 83 

(77) percent lower at Marlborough-Westerly, and 86 (86) percent lower at Hudson in 2013 than in 2009 (table 2). 

Instream TP and orthoP loads were calculated from 

concentrations and flows measured at four USGS monitoring 

stations. Annual median TP loads between 2009 and 2013 

(fig. 14 and table 3) decreased from 33 kg/d in 2009 to 14 kg/d 

in 2013 at the Port Street monitoring station (57 percent), from 

27 kg/d in 2009 to 7 kg/d in 2013 at the AMVETS monitoring 

station (74 percent), from 38 kg/d in 2009 to 9 kg/d in 2013 

at the Stow monitoring station (76 percent), and from 38 kg/d 

in 2009 to 11 kg/d in 2013 at the Maynard monitoring station 

(71 percent). Changes in annual mean TP loads were smaller: 

from 37 to 28 kg/d at the Port Street monitoring station 

(24 percent), from 32 to 13 kg/d at the AMVETS monitoring 

station (59 percent), from 44 to 14 kg/d at the Stow monitoring 

station (68 percent), and from 46 to 20 kg/d at the Maynard 

monitoring station (56 percent). Instream loads of orthoP also 

decreased between 2009 and 2013. Annual median orthoP 

loads between 2009 and 2013 decreased from 4.2 kg/d in 2009 

to 1.4 kg/d at the Port Street monitoring station (67 percent), 

from 6.0 kg/d in 2009 to 1.1 kg/d in 2013 at the AMVETS 

monitoring station (82 percent), from 8.7 kg/d in 2009 to 

1.1 kg/d in 2013 at the Stow monitoring station (87 percent), 

and from 9.1 kg/d in 2009 to 1.9 kg/d in 2013 at the Maynard 

monitoring station (79 percent).

The changes in total instream TP loads, although smaller 

in terms of percentages than the decreases in WWTP TP loads, 

are comparable in magnitude. The decrease in annual mean 

TP loads between 2009 and 2013 at the AMVETS monitoring 

station (19.4 kg/d) is comparable with the combined decreases 

in annual mean TP loads from the upstream WWTPs at 

Westborough and Marlborough-Westerly (16.8 kg/d). The 

decreases in annual mean TP loads between 2009 and 2013 

at the Stow monitoring station (30 kg/d) and at the Maynard 

monitoring station (26 kg/d) are comparable with combined 

decreases in annual mean TP loads from the three upstream 

WWTPs at Westborough, Marlborough-Westerly, and 

Hudson (24 kg/d). Thus, the reductions in mean TP instream 

loads between 2009 and 2013 differed by only 14, 22, and 

8 percent at the AMVETS, Stow, and Maynard monitoring 

stations, respectively. The observed decreases in instream 

loads are slightly larger than observed decreases in WWTP 

loads (tables 2 and 3). This is consistent with smaller loads 

of phosphorus from sources other than WWTPs being 

delivered to the river through overland runoff and groundwater 

discharge during the later years of the study, when streamflows 

were lower than in the earlier years. Sources of phosphorus 

to the river other than WWTPs, such as overland runoff or 
Changes in Phosphorus Concentrations and Loads 21

EXPLANATION

90th percentile

75th percentile

25th percentile

10th percentile

Median

5

15

25

0

10

20

30

Westborough WWTP (upgraded March 2012)

Marlborough-Westerly WWTP (upgraded January 2012)

Hudson WWTP (upgraded October 2009)

2009 2010 2011 2012 2013

Total phosphorus load, in kilograms per day 

Figure 13. Annual distributions of estimated daily total phosphorus loads in wastewater-treatment-plant 

(WWTP) effluent into the Assabet River, Massachusetts, 2009–2013.

internal loading from sediments, were not directly measured 

as part of the present study; the observed changes in instream 

phosphorus loads represent net changes that may have 

been affected by such sources in addition to reductions in 

WWTP discharges.

Seasonal Differences in Phosphorus 

Concentrations and Loads

Following completion of all WWTP upgrades in 

March 2012, TP concentrations in treated effluent ranged from 

0.05 to 0.08 mg/L during the growing season (April through 

October) and 0.11 to 0.34 mg/L during the nongrowing season 

(November through March) (Savoie, 2016). These releases 

were consistent with the TMDL-mandated limit of 0.1 mg/L 

for the growing season and were well below the limit of 

1.0 mg/L for the nongrowing season.

In each year of the study, total phosphorus concentrations 

and loads released in treated effluent typically were greater 

at all three WWTPs during the nongrowing season than 

during the growing season, both before and after the TMDLmandated upgrades (figs. 15 and 16). Median before-upgrade 

loads reported by the Westborough WWTP ranged from 10 

to 16 kg/d, with median nongrowing-season loads slightly 

larger than growing-season loads. Median after-upgrade loads 

in effluent from the Westborough WWTP were much smaller 

during all seasons (3.0 to 6.0 kg/d during the nongrowing 

season and 1 kg/d during the growing season) than median 

before-upgrade loads, but the difference between seasons 

was greater after the upgrade. At the Marlborough-Westerly 

WWTP in 2009, all nongrowing-season loads were marginally 

larger than growing-season loads both before and after the 

upgrades, aside from one large TP load (16 kg/d) in the 

2009 nongrowing season. The Hudson WWTP completed 
22 Changes in Phosphorus Concentrations and Loads in the Assabet River, Massachusetts, October 2008 through April 2014

A

B

0

25

50

75

100

0

5

10

15

20

25

2009 2010 2011 2012 2013

2009 2010 2011 2012 2013

Total phosphorus load, in kilograms per day Orthophosphate load, in kilograms per day as phosphorus

 Port Street (01096835)

 AMVETS (01096840)

 Stow (01096885)

 Maynard (01097000)

EXPLANATION

90th percentile

75th percentile

25th percentile

10th percentile

Median

Figure 14. Annual distributions of estimated A, total phosphorus and B, orthophosphate loads in weekly flowproportional composite samples from four water-quality-monitoring stations on the Assabet River, Massachusetts, 

2009–2013. See table 1 for full station names.
Changes in Phosphorus Concentrations and Loads 23

C. Hudson WWTP (upgraded October 2009)

B. Marlborough-Westerly WWTP (upgraded January 2012)

A. Westborough WWTP (upgraded March 2012)

90th percentile

75th percentile

25th percentile

10th percentile

Median

EXPLANATION

Total phosphorus concentration, in milligrams per liter

2009 2010 2011 2012 2013 2014

2009 2010 2011 2012 2013 2014

2009 2010 2011 2012 2013 2014

0.5

1.5

2.5

0.0

1.0

2.0

3.0

 Nongrowing

 Growing

0.5

1.5

2.5

0.0

1.0

2.0

3.0

 Nongrowing

 Growing

0.5

1.5

2.5

0.0

1.0

2.0

3.0

 Nongrowing

 Growing

Figure 15. Seasonal distributions of estimated daily total phosphorus concentrations in effluent from the wastewatertreatments plants (WWTPs) in A, Westborough, B, Marlborough-Westerly, and C, Hudson, Massachusetts, during nongrowing 

(November through March) and growing (April through October) seasons, on the Assabet River, Massachusetts, 2009–2014.
24 Changes in Phosphorus Concentrations and Loads in the Assabet River, Massachusetts, October 2008 through April 2014

90th percentile

75th percentile

25th percentile

10th percentile

Median

EXPLANATION

A. Westborough WWTP (upgraded March 2012)

B. Marlborough-Westerly WWTP (upgraded January 2012)

C. Hudson WWTP (upgraded October 2009)

2009 2010 2011 2012 2013 2014

2009 2010 2011 2012 2013 2014

2009 2010 2011 2012 2013 2014

Total phosphorus load, in kilograms per day

5

15

25

35

0

10

20

30

40

 Nongrowing

 Growing

10

30

0

20

40

 Nongrowing

 Growing

10

30

0

20

40

 Nongrowing

 Growing

Figure 16. Seasonal distributions of estimated daily total phosphorus loads in effluent from the wastewater-treatment 

plants (WWTPs) in A, Westborough, B, Marlborough-Westerly, and C, Hudson, Massachusetts, during nongrowing 

(November through March) and growing (April through October) seasons, 2009–2014.
Changes in Phosphorus Concentrations and Loads 25

its upgrades in October 2009; therefore, two seasons (one 

nongrowing and one growing) of before-upgrade data were 

available. Annual median TP loads at the Hudson WWTP 

were 7.0 to 8.0 kg/d, with little seasonal variation before 

the upgrade. After-upgrade loads decreased to 6.0 kg/d in 

the nongrowing 2010 season and decreased further to 0.5 to 

1.0 kg/d in growing and nongrowing seasons for the remainder 

of the study period (2010 to 2013) (fig. 16).

Seasonal variations in TP and orthoP concentrations 

also were observed instream at the Assabet River monitoring stations; however, unlike WWTP concentrations, most 

instream growing-season concentrations were greater than 

instream nongrowing-season concentrations (figs. 17 and 18). 

The growing-season months include the summer and early fall 

months of low streamflow, so higher concentrations during 

the growing season likely result partly from less dilution of 

WWTP loads during these months. 

Instream growing-season loads at the Assabet River 

monitoring stations were typically similar or slightly higher 

than nongrowing-season loads (figs. 19 and 20). Less seasonal variation in phosphorus loading was observed during 

the study period at the four instream monitoring stations 

than in the WWTP effluent. Differences in nongrowing and 

growing median TP and orthoP loads were greater before 

the WWTP upgrades than after the upgrades. Seasonal TP 

concentrations at the Port Street monitoring station were 

about the same before and after the WWTP upgrades (fig. 17), 

and loads decreased after the upgrades and after-upgrade 

loads were 11 to 16 kg/d with little seasonal variation. At the 

AMVETS monitoring station, after-upgrade median TP loads 

were 9 kg/d during the nongrowing season and 7 kg/d during the growing season. The after-upgrade median TP load at 

the Stow monitoring station ranged from 9 to 12 kg/d during 

the nongrowing season and 8 to 9 kg/d during the growing 

season. At the Maynard monitoring station, the after-upgrade 

median TP loads were 13 kg/d during the nongrowing season and 11 kg/d during the growing season (fig. 19). Similar 

decreases in orthoP loads during the growing seasons were 

observed (fig. 20). In general, growing seasons tend to have 

months with lower streamflow and nongrowing seasons tend 

to have months with higher streamflow. After the upgrades, 

even though concentrations tended to be higher in the growing 

seasons, the loads were about the same between growing and 

nongrowing seasons.

Effects of Impoundments on Instream 

Phosphorus Loads

The effects of run-of-the-river impoundments on phosphorus dynamics in the Assabet River system were examined 

by monitoring changes in phosphorus loads entering and 

leaving the two impoundments in the study area. The two 

impoundments, each of which is bracketed by water-qualitymonitoring stations, have different physical characteristics. 

The Hudson impoundment is smaller and has a larger ponded 

area than Ben Smith impoundment. The Assabet River meanders and has a more streamlike character upstream from the 

Ben Smith impoundment dam than upstream from the Hudson 

impoundment dam. Both impoundments have tributaries entering between the monitoring stations. Also, both downstream 

monitoring stations (AMVETS and Maynard) may be affected 

by storm runoff from the towns of Hudson and Maynard, 

respectively. These potential sources of phosphorus were not 

measured in this study and complicate the use of only the 

upstream and downstream monitoring stations in understanding the effects of the reservoirs on the phosphorus dynamics. For each impoundment, loads were compared in terms 

of estimated total annual loads released by the WWTPs and 

as measured at the monitoring stations upstream and downstream. Differences between upstream and downstream loads 

were also compared. 

Hudson Impoundment

Estimated total annual TP loads recorded at the Port 

Street monitoring station at the upstream end of the impoundment were greater than total annual TP loads at the downstream monitoring station at the AMVETS monitoring station 

in each year of the study (fig. 21A). Annual loads at both 

the upstream and downstream stations generally decreased 

throughout the study. Annual TP loads estimated at the Port 

Street monitoring station were 13 percent greater than loads at 

the AMVETS monitoring station in 2009 and 2010, 34 percent 

greater in 2011, and 55 percent greater in 2012 and 2013. Estimated total weekly loads entering the Hudson impoundment 

near the Port Street monitoring station frequently exceeded 

loads leaving the impoundment during the sampling period 

from 2008 to 2014. Subtracting the downstream loads from 

the upstream loads demonstrates that upstream loads exceeded 

downstream loads (fig. 22A). On several occasions before the 

WWTP upgrades, downstream loads exceeded upstream loads 

during short-lived streamflow peaks. After the upgrades, loads 

were rarely greater leaving the impoundment than entering it.

Before the WWTP upgrades, orthoP loads at the 

AMVETS monitoring station (the impoundment outlet) were 

greater than loads at the upstream end of the impoundment 

at the Port Street monitoring station, and after the WWTP 

upgrades, orthoP loads were slightly greater at the Port Street 

monitoring station than at the AMVETS monitoring station 

(figs. 21B and 22B). The consistent difference in TP loads 

upstream and downstream from Hudson impoundment, 

such that there always appeared to be more TP entering 

the impoundment than leaving, could suggest that the 

impoundment is a sink for TP. However, TP concentrations 

and loads at the Port Street monitoring station, especially 

towards the end of the study, may have been affected by 

resuspension or other instream processes, as discussed in 

the “Phosphorus Concentrations” section, and this could be 

why TP loads did not decrease at the Port Street monitoring 

station after WWTP upgrades. Also, unlike the annual loads 

at the AMVETS monitoring station, which decreased by 
26 Changes in Phosphorus Concentrations and Loads in the Assabet River, Massachusetts, October 2008 through April 2014

A. Port Street B. AMVETS

C. Stow D. Maynard

2009 2010 2011 2012 2013 2014 2009 2010 2011 2012 2013 2014

2009 2010 2011 2012 2013 2014

0.0

0.1

0.2

0.3

0.1

0.3

 Nongrowing

 Growing

0.0

0.2

 Nongrowing

 Growing

0.0

0.1

0.2

0.3

Total phosphorus concentration, in milligrams per liter

 Nongrowing

 Growing

0.0

0.1

0.2

0.3

 Nongrowing

 Growing

EXPLANATION

90th percentile

75th percentile

25th percentile

10th percentile

Median

2009 2010 2011 2012 2013 2014

Figure 17. Seasonal distributions of estimated daily total phosphorus concentrations in flow-proportional composite 

samples from water-quality-monitoring stations A, Port Street, B, AMVETS, C, Stow, and D, Maynard during nongrowing 

(November through March) and growing (April through October) seasons, on the Assabet River, Massachusetts, from 

2009 to 2014. See table 1 for full station names and numbers.
Changes in Phosphorus Concentrations and Loads 27

B. AMVETS

D. Maynard

2009 2010 2011 2012 2013 2014

2009 2010 2011 2012 2013 2014 2009 2010 2011 2012 2013 2014

2009 2010 2011 2012 2013 2014

0.00

0.01

0.02

0.03

0.04

 Nongrowing

 Growing

0.00

0.01

0.02

0.03

0.04

 Nongrowing

 Growing

0.00

0.01

0.02

0.03

0.04

Orthophosphate concentration, in milligrams per liter as phosphorus

 Nongrowing

 Growing

0.00

0.01

0.02

0.03

0.04

 Nongrowing

 Growing

A. Port Street

C. Stow

75th percentile

90th percentile

25th percentile

EXPLANATION

10th percentile

Median

Figure 18. Seasonal distributions of estimated daily orthophosphate concentrations in flow-proportional composite 

samples from water-quality-monitoring stations A, Port Street, B, AMVETS, C, Stow, and D, Maynard during nongrowing 

(November through March) and growing (April through October) seasons, on the Assabet River, Massachusetts, from 

2009 to 2014. See table 1 for full station names and numbers.
28 Changes in Phosphorus Concentrations and Loads in the Assabet River, Massachusetts, October 2008 through April 2014

EXPLANATION

90th percentile

75th percentile

25th percentile

10th percentile

Median

2009 2010 2011 2012 2013 2014

2009 2010 2011 2012 2013 2014 2009 2010 2011 2012 2013 2014

0

25

50

75

100

 Nongrowing

 Growing

0

25

50

75

100

 Nongrowing

 Growing

0

100

Total phosphorus load, in kilograms per day

A. Port Street B. AMVETS

C. Stow D. Maynard

 Nongrowing

 Growing

0

100

 Nongrowing

 Growing

(107)

25

50

75

25

50

75

(106) (127) (136)

2009 2010 2011 2012 2013 2014

Figure 19. Seasonal distributions of estimated daily total phosphorus loads in flow-proportional composite samples from 

water-quality-monitoring stations A, Port Street, B, AMVETS, C, Stow, and D, Maynard during nongrowing (November through 

March) and growing (April through October) seasons, on the Assabet River, Massachusetts, from 2009 to 2014. See table 1 for 

full station names and numbers.
Changes in Phosphorus Concentrations and Loads 29

B. AMVETS

D. Maynard

A. Port Street

C. Stow

EXPLANATION

90th percentile

75th percentile

25th percentile

10th percentile

Median

2009 2010 2011 2012 2013 2014 2009 2010 2011 2012 2013 2014

2009 2010 2011 2012 2013 2014 2009 2010 2011 2012 2013 2014

0

5

10

15

20

25

30

 Nongrowing

 Growing

0

5

10

15

20

25

30

 Nongrowing

 Growing

0

5

10

15

20

25

30

Orthophosphate load, in kilograms per day as phosphorus

 Nongrowing

 Growing

0

5

10

15

20

25

30

 Nongrowing

 Growing

Figure 20. Seasonal distributions of estimated daily orthophosphate loads in flow-proportional composite samples from 

water-quality-monitoring stations A, Port Street, B, AMVETS, C, Stow, and D, Maynard during nongrowing (November through 

March) and growing (April through October) seasons, on the Assabet River, Massachusetts, from 2009 to 2014. See table 1 for 

full station names and numbers.
30 Changes in Phosphorus Concentrations and Loads in the Assabet River, Massachusetts, October 2008 through April 2014

2009 2010 2011 2012 2013

0

5,000

10,000

15,000

20,000

Total phosphorus load, in kilograms per year

 Sum of wastewater-treatment plants (Westborough and Marlborough-Westerly)

 Port Street (01096835)

 AMVETS (01096840)

2009 2010 2011 2012 2013

0

1,000

2,000

3,000

4,000

5,000

Orthophosphate load, in kilograms per year as phosphorus

EXPLANATION

B

A

Figure 21. Estimated annual loads of A, total phosphorus of discharges from wastewater-treatment plants 

(WWTPs) at Westborough and Marlborough-Westerly and instream at the Port Street and AMVETS waterquality-monitoring stations and B, orthophosphate instream at the Port Street and AMVETS water-qualitymonitoring stations on the Assabet River, Massachusetts, 2009–2013. See table 1 for full station names.
Changes in Phosphorus Concentrations and Loads 31

-400

-200

0

200

400

600

10/1/2008

2/1/20096/1/2009

10/1/2009

2/1/20106/1/2010

10/1/2010

2/1/20116/1/2011

10/1/2011

2/1/2012

6/1/2012

10/1/2012

2/1/2013

6/1/2013

10/1/2013

2/1/20146/1/2014

-150

-100

-50

0

50

100

Total phosphorus load, 

in kilograms per week

0

500

1,000

1,500

2,000

2,500

Streamflow, in cubic feet per second

Orthophosphate load, 

in kilograms per week as phosphorus

0

500

1,000

1,500

2,000

2,500

Streamflow, in cubic feet per second

 Upstream load minus downstream load

 Streamflow

EXPLANATION

A

B

Before upgrades After upgrades

Before upgrades After upgrades

Figure 22. Streamflow and differences between estimated weekly loads of A, total phosphorus and B, orthophosphate upstream 

and downstream from the Hudson impoundment on the Assabet River, Massachusetts, October 2008 through April 2014. 

a magnitude comparable to that of the decrease in WWTP 

loads (with the exception of 2011, when there was greater 

precipitation), the decrease in annual loads during the study 

at the Port Street monitoring station was not as great as the 

decrease in upstream WWTP loads over the study period. 

Additional investigation would be needed to determine the 

extent to which these processes affected the calculated TP 

loads at the Port Street monitoring station. 

Results of the application of the Wilcoxon matched-pair 

signed-rank tests further support the interpretation that loads 

upstream and downstream from the Hudson impoundment 

were significantly different (p less than 0.001) for TP and 

orthoP before and after the WWTP upgrades. Upstream TP 

loads were most often larger than downstream loads before 

and after the WWTP upgrades, and downstream orthoP loads 

were often larger before the upgrades; after the upgrades, the 

pattern was reversed so that orthoP loads were slightly larger 

upstream than downstream.

Ben Smith Impoundment

Estimated total annual TP loads were consistently greater 

(up to 40 percent) at the downstream end of the Ben Smith 

impoundment, as observed at the Maynard monitoring station, 

than they were upstream at the Stow monitoring station 

(fig. 23A). The pattern of decreasing annual loads estimated 

entering and exiting the Ben Smith impoundment mimics 

the pattern reported by the WWTPs (with the exception of 

2011, when precipitation was greater than in other years), 

with a 32 percent decrease at the Stow monitoring station 
32 Changes in Phosphorus Concentrations and Loads in the Assabet River, Massachusetts, October 2008 through April 2014

A

B

0

5,000

10,000

15,000

20,000

Total phosphorus load, in kilograms per year

0

1,000

2,000

3,000

4,000

5,000

Orthophosphate load, in kilograms per year as phosphorus

 Sum of wastewater-treatment plants (Westborough, Marlborough-Westerly, and Hudson)

 Stow (01096885)

 Maynard (01097000)

2009 2010 2011 2012 2013

2009 2010 2011 2012 2013

EXPLANATION

Figure 23. Estimated annual loads of A, total phosphorus discharges from the wastewater-treatment plants (WWTPs) 

at Westborough, Marlborough-Westerly, and Hudson and instream at the Stow and Maynard water-quality-monitoring 

stations and B, orthophosphate instream at the Stow and Maynard water-quality-monitoring stations on the Assabet River, 

Massachusetts, from 2009 to 2013. See table 1 for full station names.
Changes in Phosphorus Concentrations and Loads 33

and 19 percent decrease at the Maynard monitoring station 

between 2009 and 2010; loads increased by the same 

magnitude from 2010 to 2011 and then decreased by about 

60 percent in 2012 and 2013. Estimated total weekly loads 

exiting the Ben Smith impoundment near the Maynard 

monitoring station frequently (with the exception of 2009) 

exceeded loads entering the impoundment during the sampling 

period from 2008 to 2014 (fig. 24A). 

Estimated annual orthoP loads also were consistently 

greater at the downstream end of Ben Smith impoundment 

than they were at the upstream end (figs. 23B and 24B). The 

differences in magnitudes of both phosphorus species were, 

however, small (except during storm events), and phosphorus 

loads measured at the Maynard gage may have been influenced by phosphorus inputs from overland runoff in the town 

of Maynard and from other tributaries such as Elizabeth 

(Assabet) Brook. Results of the application of the Wilcoxon 

matched-pair signed-rank tests indicate that the downstream 

loads at the Maynard monitoring station were significantly 

greater than those upstream (p less than 0.001 for TP and 

orthoP).

Thus, as with the Hudson impoundment, results are 

inconclusive as to whether the Ben Smith impoundment is 

a net sink of TP or orthoP. However, the results do suggest 

that the impoundments are not large sources of phosphorus to 

instream loads. 

 Upstream load minus downstream load

 Streamflow

EXPLANATION

A

B

Before upgrades After upgrades

Before upgrades After upgrades

-800

-600

-400

-200

0

200

-200

-100

0

100

0

500

1,000

1,500

2,000

2,500

Streamflow, in cubic feet per second

0

500

1,000

1,500

2,000

2,500

Streamflow, in cubic feet per second

10/1/2008

2/1/20096/1/2009

10/1/2009

2/1/20106/1/2010

10/1/2010

2/1/20116/1/2011

10/1/2011

2/1/2012

6/1/2012

10/1/2012

2/1/2013

6/1/2013

10/1/2013

2/1/20146/1/2014

Total phosphorus load, 

in kilograms per week

Orthophosphate load, 

in kilograms per week as phosphorus

Figure 24. Streamflow and differences between estimated weekly loads of A, total phosphorus and B, orthophosphate upstream and 

downstream from the Ben Smith impoundment on the Assabet River, Massachusetts, October 2008 through April 2014.
34 Changes in Phosphorus Concentrations and Loads in the Assabet River, Massachusetts, October 2008 through April 2014

Statistical Analyses of Changes in Phosphorus 

Concentrations

Total phosphorus concentrations and loads in the Assabet 

River during the study were affected both by the changes 

in TP inputs that resulted from the WWTP upgrades and by 

the changes in streamflow that occurred seasonally and from 

year to year during the study period. One way to investigate 

the simultaneous effects of WWTP upgrades and streamflow 

variability is with an analysis of covariance (Helsel and 

Hirsch, 2002). The analysis of covariance incorporates a 

binary indicator variable, which distinguishes the time periods 

before and after the WWTP upgrades, into a multiple linear 

regression-equation model that also includes streamflow. 

TP concentrations in weekly composite samples are related 

to streamflow and to the indicator variable, which is 0 for 

the samples collected before WWTP upgrades and 1 for 

the samples collected after the upgrades. Streamflow in the 

model is the average streamflow during the weeklong samplecollection period (thus, the data fit by the models are those 

shown in fig. 11). With this approach, the changes in TP 

concentrations before and after the WWTP upgrades can be 

quantified and their statistical significance investigated while 

the variation in streamflow during the study is accounted for.

The before and after time periods were defined by 

March 31, 2012, the date when all WWTP upgrades were 

completed. Concentration and flow data were log-transformed 

(natural log) for the analysis. Three regression models were 

used:

ln(TP) = B0 + B1 × ln(Q) (1)

ln(TP) = B0 + B1 × ln(Q) + B2 × Z (2)

ln(TP) = B0 + B1 × ln(Q) + B2 × Z + B3 × X (3)

where

TP is total phosphorus concentration in the 

weeklong instream composite sample, in 

milligrams per liter;

ln is the natural log; and

Z is a binary indicator variable, 0 for the period 

before the WWTP upgrade (October 1, 

2008 through March 31, 2012), and 1 

for the period after the WWTP upgrade 

(April 1, 2012 through April 28, 2014).

The interaction variable (X) used to describe the change in the 

relationship of concentration and streamflow before and after 

the WWTP upgrades is calculated by using X = Z × ln(Q). 

Models 2 and 3 are two different ways of describing the 

relation of TP concentration to streamflow and to the time 

period of WWTP upgrades. Model 2 would be appropriate 

when the slope of the relation between concentration and 

flow did not change before and after the time period of 

WWTP upgrades, whereas model 3 would be appropriate 

when the slope of the relation between flow and concentration 

changed after upgrades. The slope of the relation indicates 

by how much concentration changes for a given change in 

flow. A change in slope of the relation between flow and 

concentration might be expected in parts of the river where 

phosphorus from sources other than WWTPs is important 

because this phosphorus could vary with flow differently than 

does WWTP phosphorus. Model 1 describes the relation of 

TP concentration to flow only and is used in conjunction with 

model 3 to examine changes in the relation of concentration 

and flow before and after WWTP upgrades.

The three regression models were tested by using the 

data from each of the four water-quality-monitoring stations 

on the Assabet River (Savoie, 2016). Regression model 

response variable coefficients and their statistical significance 

are shown in table 4; a negative coefficient indicates an 

inverse relation between TP concentrations and the response 

variable, and a positive coefficient indicates a direct relation. 

Regression models were evaluated by using residual plots (fit 

versus response, fit versus residuals, quantile-quantile, and 

ln(Q) versus residuals), the significance of response variables, 

the adjusted R-squared, and other statistical measures. 

Nested F-tests (Helsel and Hirsch, 2002) were used to select 

the regression model that best describes how water quality 

changed before and after the WWTP upgrades (table 5).

Graphs of the relation between predicted TP concentration and streamflow based on the best-fit regression model at 

each station are shown in figure 25. The lines shown on these 

graphs, depicting the relation between concentration and flow 

before and after the WWTP upgrades, were calculated with the 

regression equation by setting the treatment indicator variable 

equal to 0 for the before line and equal to 1 for the after line, 

for the range of data available in the prediction dataset. The 

modeled data also are shown.

At the Maynard monitoring station, the farthest 

downstream station, both flow [ln(Q)] and the time period 

relative to WWTP upgrades (Treatment) were significantly 

related to TP concentrations [ln(TP)] (table 4). The coefficients 

for the flow and treatment variables were both negative, 

indicating that TP concentration was inversely related to 

flow and that TP concentrations were significantly lower 

after WWTP upgrades. The more complex regression model 

3 did not provide a better fit to the data than the simpler 

model 2; interaction variable Treatment × ln(Q) in model 

3 was not significant at p less than 0.01. Thus, the slope of 

the relation between flow and concentration did not change 

significantly at the Maynard monitoring station after the 

treatment-plant upgrades. The magnitude of the difference 

in TP concentrations before and after WWTP upgrades that 

is indicated by the model for a given streamflow can be 

calculated from the coefficient for the Treatment variable. 

The coefficient for the Treatment variable was −0.324, which 

corresponds to an arithmetic value of 0.723 after converting 

back from natural log space [exp(−0.324) = 0.723]. This 
Changes in Phosphorus Concentrations and Loads 35

Table 4. Coefficients and other regression metrics for linear regression models used to describe the relations between the natural 

log of composite total phosphorus concentrations and mean streamflow, and periods before and after wastewater-treatment-plant 

upgrades, for data collected from October 2008 through April 2014 at water-quality-monitoring stations on the Assabet River in the towns 

of Hudson, Stow, and Maynard, Massachusetts.

[Shading indicates model chosen and plotted in figure 25. Model equations are in the “Statistical Analyses of Changes in Phosphorus Concentrations” section of 

the report, in which the variable “Z” represents Treatment. Full U.S. Geological Survey (USGS) station names are in table 1. Treatment, a binary variable equal 

to 0 before April 1, 2012, and equal to 1 on or after April 1, 2012; ln, natural log; Q, mean flow for composite period, in cubic feet per second; Constant, regression intercept; --, not applicable]

Model variables and 

other regression metrics

Model

1 2 3

Port Street (USGS station number 01096835)

Model response variable coefficients

Treatment -- -0.039 *

-1.425

Standard error -- -0.058 -0.302

ln(Q) *

-0.169 *-0.175 *-0.266

Standard error -0.031 -0.032 -0.036

Treatment × ln(Q) -- -- *

0.320

Standard error -- -- -0.068

Constant *

-1.446 *-1.406 *-0.982

Standard error -0.141 -0.154 -0.173

Regression metrics

Observations 271 271 271

R2 0.101 0.102 0.17

Adjusted R2 0.098 0.096 0.161

Residual standard error 0.439 0.439 0.423

AMVETS (USGS station number 01096840)

Model response variable coefficients

Treatment -- *

-0.524 *-1.353

Standard error -- -0.042 -0.216

ln(Q) *

-0.148 *-0.213 *-0.274

Standard error -0.028 -0.023 -0.027

Treatment × ln(Q) -- -- *

0.185

Standard error -- -- -0.047

Constant *

-2.026 *-1.520 *-1.231

Standard error -0.131 -0.112 -0.132

Regression metrics

Observations 266 266 266

R2 0.096 0.433 0.464

Adjusted R2 0.092 0.429 0.458

Residual standard error 0.41 0.325 0.317

Model variables and 

other regression metrics

Model

1 2 3

Stow (USGS station number 01096885)

Model response variable coefficients

Treatment -- *

-0.570 *-0.836

Standard error -- -0.049 -0.287

ln(Q) 0.02 -0.033 -0.049

Standard error -0.032 -0.027 -0.032

Treatment × ln(Q) -- -- 0.056

Standard error -- -- -0.059

Constant *

-2.914 *-2.457 *-2.377

Standard error -0.16 -0.137 -0.161

Regression metrics

Observations 273 273 273

R2 0.001 0.335 0.337

Adjusted R2 -0.002 0.33 0.33

Residual standard error 0.463 0.379 0.379

Maynard (USGS station number 01097000)

Model response variable coefficients

Treatment -- *

-0.324 -0.608

Standard error -- -0.053 -0.319

ln(Q) -0.012 †

-0.080 †-0.104

Standard error -0.031 -0.031 -0.041

Treatment × ln(Q) -- -- 0.056

Standard error -- -- -0.062

Constant *

-2.814 *-2.340 *-2.209

Standard error -0.161 -0.169 -0.223

Regression metrics

Observations 261 261 261

R2 0.001 0.128 0.13

Adjusted R2 -0.003 0.121 0.12

Residual standard error 0.415 0.388 0.388

*

Value significant at less than 0.01.

†

Value significant at less than 0.05.
36 Changes in Phosphorus Concentrations and Loads in the Assabet River, Massachusetts, October 2008 through April 2014

Table 5. Results of pairwise F-test comparison of linear 

regression models 1, 2, and 3 for four water-quality-monitoring 

stations on the Assabet River, Massachusetts.

[See Helsel and Hirsch (2002) for information on nested F-tests. Model 1 

relates the natural log of total phosphorus concentration [ln(TP concentration)] to the natural log of flow [ln(flow)]. Model 2 relates ln(TP concentration) to ln(flow) and an indicator variable describing time period relative to 

wastewater-treatment-plant (WWTP) upgrades. Model 3 relates ln(TP concentration) to ln(flow), an indicator variable describing time period relative 

to WWTP upgrades, and an interaction variable of ln(flow) and time period. 

See the “Statistical Analyses of Changes in Phosphorus Concentrations” section of the report for model equations. See table 1 for full U.S. Geological 

Survey (USGS) station names. <, less than]

F-test results Models compared

2 versus 1 3 versus 1 3 versus 2

Port Street (USGS station number 01096835)

F statistic 0.4581 11.168 21.842

F probability 0.4991 <0.0001 <0.0001

Better-fit model 1 3 3

AMVETS (USGS station number 01096840)

F statistic 156.69 90.203 15.235

F probability <0.0001 <0.0001 0.0001

Better-fit model 2 3 3

Stow (USGS station number 01096885)

F statistic 135.47 68.152 0.8871

F probability <0.0001 <0.0001 0.3471

Better-fit model 2 3 2

Maynard (USGS station number 01097000)

F statistic 35.577 19.183 0.815

F probability <0.0001 <0.0001 0.3675

Better-fit model 2 3 2

means that TP concentrations after WWTP upgrades averaged 

72.3 percent of the concentrations before upgrades, which 

is a reduction of about 30 percent relative to before-upgrade 

concentrations (fig. 25D). Note that the adjusted R2 value of 

the model was low (0.121). Thus, although flow and time 

period relative to upgrades were significant predictors of 

concentration, the data were widely scattered, and other 

factors, not represented by equation variables, accounted for 

much of the variability in concentration. 

At the AMVETS monitoring station, as at the Maynard 

monitoring station, both flow [ln(Q)] and the time period 

relative to WWTP upgrades (Treatment) were significantly 

related to TP concentrations [ln(TP)], and the coefficients for 

both variables were negative (table 4). However, the relation 

between flow and concentration at the AMVETS monitoring 

station, in contrast to that at the Maynard monitoring station, 

changed after the upgrades, and the best-fit regression model 

to describe TP concentrations was model 3. The adjusted 

R2

 value for model 3 at the AMVETS monitoring station, 

0.458, was the highest adjusted R2

 value for any model at all 

four stations, indicating that the multiple linear regression 

model at this station was best at explaining the observed 

variation in TP concentrations. Because of the change in the 

slope of relation between streamflow and concentration, the 

difference in TP concentrations indicated by the model varied 

by streamflow; for example, TP concentrations declined about 

0.07 mg/L (about 45 percent of before-upgrade concentrations, 

a reduction of about 55 percent) for 20 ft3/s, but only about 

0.01 mg/L for streamflow near 370 ft3/s (about 77 percent 

of before-upgrade concentrations, a reduction of about 

23 percent; fig. 25B). 

At the Stow monitoring station, TP concentrations were 

significantly and inversely related to the Treatment variable, 

indicating that, as at the Maynard and AMVETS monitoring 

stations, TP concentrations were significantly lower after 

WWTP upgrades. However, there was no significant relation 

(table 4) between TP concentrations and flow [ln(Q)] at the 

Stow monitoring station. Thus, model 3 did not provide 

a better fit to the data at the Stow monitoring station, and 

model 2 was the best-fit model. The adjusted R2 value of 0.33 

for model 2 indicates that this regression model provides a 

better fit to the data at the Stow monitoring station than the 

best-fit model at the Maynard monitoring station, but not as 

good a fit as the best-fit model at the AMVETS monitoring 

station. The coefficient for the Treatment variable in model 

2 was −0.570, such that the model describes concentrations 

after WWTP upgrades as averaging 56.6 percent of the 

concentrations before upgrades, which is a reduction of about 

40 percent; fig. 25C; table 4, model 2).

At the Port Street monitoring station, although the flow 

variable [ln(Q)] and (or) the Treatment variable were significant in models 2 and 3, examination of model residuals 

(table 4) and the low adjusted R2

 values indicated that none of 

the regression models provided good fits to the data. Visual 

inspection of the plotted data suggest an inverse relation 

between TP concentration and flow before WWTP grades that 

was not apparent after WWTP upgrades (figs. 11 and 25A), but 

this may have been an artifact of high flows before upgrades 

and the effects of resuspension near the end of the study 

period. Overall, TP concentrations at the Port Street monitoring station behaved differently than those at the other stations 

after WWTP upgrades, as noted previously, and results at the 

Port Street monitoring station are difficult to interpret. 

The statistical analysis demonstrates significant 

reductions in TP concentrations before and after the WWTP 

upgrades at three of the four monitoring stations. The finding, 

that the Treatment indicator variable is a significant predictor 

of TP concentrations even when streamflow is included in 

the equation, can be interpreted to mean that, for any given 

streamflow measured at the AMVETS, Stow, or Maynard 

monitoring stations, TP concentrations after WWTP upgrades 

were significantly lower than concentrations at the same 

streamflow before upgrades (Robert Hirsch, U.S. Geological 

Survey, written commun., 2015). At the downstream stations, 
Changes in Phosphorus Concentrations and Loads 37

EXPLANATION

Total phosphorus, before WWTP upgrade

Total phosphorus, after WWTP upgrade

Total phosphorus predicted, before WWTP upgrade

Total phosphorus predicted, after WWTP upgrade

0.01

0.02

0.05

0.10

0.20

0.50

1.00

1 10 100 1,000 10,000

Port Street

0.01

0.02

0.05

0.10

0.20

0.50

1.00

1 10 100 1,000 10,000

AMVETS

0.01

0.02

0.05

0.10

0.20

0.50

1.00

1 10 100 1,000 10,000

Stow

Total phosphorus concentration, in milligrams per liter

Streamflow, in cubic feet per second

0.01

0.02

0.05

0.10

0.20

0.50

1.00

1 10 100 1,000 10,000

Maynard

Figure 25. Relations between streamflow and total phosphorus concentrations, and total phosphorus concentrations predicted for before 

and after the wastewater-treatment-plant (WWTP) upgrades, based on linear regression modeling for data from October 2008 through April 

2014 for water-quality-monitoring stations on the Assabet River in the towns of Hudson (two stations, Port Street and AMVETS), Stow, and 

Maynard, Massachusetts. Refer to table 4 for the regression model used in each plot. See table 1 for full station names and numbers.
38 Changes in Phosphorus Concentrations and Loads in the Assabet River, Massachusetts, October 2008 through April 2014

Stow and Maynard, reductions were such that, for any given 

streamflow before or after WWTP upgrades, TP concentrations 

after upgrades were about 60 to 70 percent of concentrations 

before upgrades, corresponding to reductions of 30 to 

40 percent. At the AMVETS monitoring station, further 

upstream, the magnitude of the reduction in concentration 

varied by streamflow; reductions were larger, as fractions of 

before-upgrade concentrations, at lower streamflows than at 

higher streamflows. A tighter inverse relation between TP 

concentration and flow at the AMVETS monitoring station 

than at the Stow or Maynard monitoring stations is reasonable 

because flows are lower at the AMVETS monitoring station, 

and the AMVETS monitoring station is closer to the large 

WWTP inputs than the Stow and Maynard monitoring stations 

are; thus, wastewater phosphorus changes are more readily 

apparent at the AMVETS monitoring station. These reductions 

in TP concentrations for given streamflows calculated at the 

AMVETS, Stow, and Maynard monitoring stations also apply 

to reductions in TP loads, because loads are calculated as the 

product of concentration times streamflow. 

Summary and Conclusions

The Assabet River in central Massachusetts, valued for its 

scenic beauty, biological diversity, and history, was listed by 

the Massachusetts Department of Environmental Protection as 

an “impaired river” in 2004 with respect to nutrients, organic 

enrichment, and low dissolved oxygen. Problematic aquatic 

plant growth and decay during summer months not only 

detracts from the aesthetics of the river but also decreases oxygen levels and threatens the habitat of many aquatic species. 

In 2004, a total maximum daily load (TMDL) was 

established by the U.S. Environmental Protection Agency 

for total phosphorus (TP) for the Assabet River. The TMDL 

required the wastewater-treatment plants (WWTPs) in the 

towns of Westborough, Marlborough, and Hudson, Massachusetts, to limit monthly average effluent TP concentrations to 

0.1 milligram per liter (mg/L) during April through October 

and 1.0 mg/L during November through March. All WWTP 

upgrades were completed and the TMDL-mandated limits 

were achieved in March 2012. 

From October 2008 through April 2014, the U.S. 

Geological Survey, in cooperation with the Massachusetts 

Department of Environmental Protection, measured 

streamflow and collected flow-proportional TP and 

orthophosphate (orthoP) samples composited for 1-week 

periods at four locations : station number 01096835, Assabet 

River at Port Street at Hudson, Mass. (Port Street); 01096840, 

Assabet River 200 feet below State Route 85 at Hudson, Mass. 

(AMVETS); 01096885, Assabet River at Sudbury Road near 

Stow, Mass. (Stow); and 01097000, Assabet River at Maynard, 

Mass. (Maynard). The goals of the study were to document 

changes in phosphorus concentrations and loads before, 

during, and after implementation of the TMDL, to assess 

the effects of seasonal differences in mandated effluent TP 

concentrations, and to examine the effects of two run-of-theriver reservoirs on the Assabet River phosphorus dynamics. 

The study period included almost 3 years of observations prior 

to the full WWTP upgrades and 2 years of observations after 

the upgrades. Wastewater-treatment-plant concentrations and 

loads were compared with concentrations and loads measured 

in the river, and seasonal WWTP variations in effluent TP 

concentrations and loads were compared with seasonal 

concentrations and loads measured in the river. The waterquality-monitoring stations were upstream and downstream 

from two impoundments, and the changes in TP and orthoP 

entering and leaving the impoundments on an annual basis 

were assessed. 

Following completion of the TMDL-mandated upgrades, 

three WWTPs reported reductions in effluent TP annual 

median concentrations of more than 80 percent relative to 

before-TMDL implementation concentrations. Annual median 

TP concentrations in the WWTP effluent for 2012 and 2013 

were all under the TMDL-required limit of 0.1 mg/L. Total 

phosphorus concentrations measured in weekly composite 

samples collected in proportion to flow were similar at three 

of the four instream monitoring stations, with reduction 

in the annual median TP concentrations of about 38 to 

50 percent. Reductions of TP concentrations measured 

instream were not as great as reductions at the WWTPs 

because instream phosphorus was diluted by inflows of runoff 

and (or) groundwater discharge. Concentrations at the fourth 

monitoring station, Port Street, were different than at the 

other downstream stations. Concentrations at the Port Street 

monitoring station showed large amounts of total phosphorus 

but not orthoP (the filtered sample, or dissolved form of 

phosphorus) in several high-flow samples, which suggests that 

particulates were high and that the difference may be related 

to seasonal and (or) flow-related resuspension of particulate 

phosphorus at the location of the station. 

The calculation of loads accounts for the variability of 

phosphorus concentrations and the hydrologic system during 

sample collection, and calculated loads represent the mass of 

phosphorus instream. Annual median TP loads released at the 

WWTPs were reduced by 87 to 91 percent following completion of the TMDL-mandated upgrades, and the reductions 

were reflected at three of the four the four instream monitoring 

stations, where annual median TP loads decreased by 71 to 

76 percent. In particular, the reductions in median TP instream 

loads between 2009 and 2013 were comparable to the reductions in WWTP loads and differed only by 13 percent at the 

AMVETS monitoring station, 20 percent at the Stow monitoring station, and 8 percent at the Maynard monitoring station. 

Streamflow varied during the study period and was higher 

during the initial years and near or below average during the 

final years. Consequently, changes in TP were investigated 

by using a statistical analysis (analysis of covariance) that 
References Cited 39

incorporates the effects of variable flow conditions. That 

analysis demonstrated that the observed reductions in TP 

concentrations after the WWTP upgrades were statistically 

significant at three of the four instream monitoring stations, 

regardless of differences in streamflow during the study 

period. At the downstream monitoring stations at Stow and 

Maynard, reductions were such that, for any given streamflow 

before or after WWTP upgrades, TP concentrations after 

upgrades were reduced by 30 to 40 percent relative to 

before-upgrade concentrations. At the AMVETS monitoring 

station, further upstream, the magnitude of the reduction in 

concentration varied by streamflow; reductions were larger, 

as fractions of before-upgrade concentrations, at lower 

streamflows than at higher streamflows. No significant change 

was observed at the most upstream location at the Port Street 

monitoring station, which may have been affected by flowrelated resuspension of particulate phosphorus. 

Increased effluent TP concentrations permitted under 

the TMDL requirements during the nongrowing season 

(November through March) did not result in major seasonal 

differences in concentrations or loads of TP or orthoP at the 

four instream monitoring stations. Despite a permitted TP 

effluent concentration of 1.0 mg/L in the nongrowing season, 

the median effluent concentrations after the WWTP upgrades 

ranged from about 0.06 to 0.1 mg/L, well below the limit 

of 1.0 mg/L. Loads monitored at the four instream stations 

showed less seasonal variability than those at the WWTPs.

Hudson impoundment, which occupies a shorter stretch 

of the Assabet River than Ben Smith impoundment, may have 

been a sink for particulate phosphorus on an annual basis, 

considering that loads of TP entering the impoundment were 

larger than those leaving during all 5 complete years of the 

study. However, there was uncertainty about the loads at the 

upstream monitoring station at this impoundment. TP and 

orthoP loads leaving Ben Smith impoundment were slightly 

greater than those that entered the impoundment during each 

complete year of the study. The differences are not large and 

may reflect additions from tributaries and overland runoff 

between the stations and in downtown Maynard. 

The use of automated weekly, flow-proportional sampling and continuous streamflow monitoring provided an 

accurate measure of changing phosphorus concentrations and 

loads in this highly variable river system that is dominated by 

WWTP effluent. High-frequency (weekly to hourly) changes 

in instream phosphorus concentrations would not have been 

evident if a monthly or weekly sampling schedule were used, 

even if an attempt was made to adequately sample all stations 

during storms. Continuous, flow-proportional sampling, however, produced a complete record of the year-to-year changes 

and permitted a direct comparison of the relative magnitudes 

of the phosphorus-load reductions at the WWTPs and the 

monitoring stations.

References Cited

ENSR International, 2001, SuAsCo watershed Assabet River 

TMDL study, phase one—Assessment final report: Westford, Mass., ENSR International, U.S. Army Corps of 

Engineers, and Massachusetts Department of Environmental 

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For more information concerning this report, contact:

Director, New England Water Science Center

U.S. Geological Survey 

10 Bearfoot Road 

Northborough, MA 01532

dc_nweng@usgs.gov

or visit our Web site at:

http://newengland.water.usgs.gov/

Publishing support by: 

The Pembroke Publishing Service Center
ISSN 2328-031X (print)

ISSN 2328-0328 (online)

http://dx.doi.org/10.3133/sir20165063

Savoie and others—Changes in Phosphorus Concentrations and Loads in the Assabet River, Massachusetts—Scientific Investigations Report 2016–5063

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