U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2011–5136

Prepared in cooperation with the Massachusetts Department of Environmental Protection

Determination of Dilution Factors for Discharge 

of Aluminum-Containing Wastes by Public Water-Supply 

Treatment Facilities into Lakes and Reservoirs 

in Massachusetts
A

B

C

D

Cover.A, B, Flowing and drying sludge lagoons receiving filter backwash effluent, Northampton 

Mountain Street Water Treatment Plant, Northampton, Massachusetts (photos by Andrew J. 

Massey); C, Sampling site at mouth of diversion pipe from Perley Brook at discharge to Crystal 

Lake in Gardner, Massachusetts (photo by Melissa J. Weil); D, Sampling site at unnamed tributary 

to Haggetts Pond in Andover, Massachusetts at the northwest shore of the pond (photo by 

Andrew J. Massey).
Determination of Dilution Factors for 

Discharge of Aluminum-Containing 

Wastes by Public Water-Supply Treatment 

Facilities into Lakes and Reservoirs 

in Massachusetts

By John A. Colman, Andrew J. Massey, and Sara B. Levin

Prepared in cooperation with the 

Massachusetts Department of Environmental Protection

Scientific Investigations Report 2011–5136

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2011

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Colman, J.A., Massey, A.J., and Levin, S.B., 2011, Determination of dilution factors for discharge of aluminum-containing wastes by public water-supply treatment facilities into lakes and reservoirs in Massachusetts: U.S. Geological 

Survey Scientific Investigations Report 2011–5136, 36 p.

ISBN 978 1 4113 3238 6
iii

Contents

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

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

Purpose and Scope ..............................................................................................................................3

Previous Investigations.................................................................................................................................3

The Dilution-Factor Method.........................................................................................................................3

Calculating Dilution...............................................................................................................................3

Calculating the Settling Velocity ........................................................................................................4

Dilution at Low Flow .............................................................................................................................4

Data Requirements...............................................................................................................................4

Flows and Reservoir Volumes....................................................................................................5

Filter-Backwash Effluent Flows.................................................................................................5

Water Quality................................................................................................................................5

Application of the Dilution-Factor Method to Reservoirs .......................................................................5

Reservoirs Studied................................................................................................................................5

Flow, Area, and Volume Calculations ................................................................................................5

Water-Sample Collection, Processing, and Chemical Analysis ...................................................6

Quality Assurance of the Water-Quality Data..................................................................................7

Water-Quality Results and Associations ..........................................................................................7

Aluminum Mixing in Reservoirs..........................................................................................................8

Settling-Velocity Results....................................................................................................................11

Aluminum Simulation Results ...........................................................................................................14

Dilution-Factor Results.......................................................................................................................16

Low-Flow Dilution ......................................................................................................................16

Finding the Maximum Permissible Aluminum Discharge ...................................................16

Discussion of Method Applications..........................................................................................................23

Permitted Discharges.........................................................................................................................23

Limits to the Applicability of the Method ........................................................................................23

Environmental Consequences of Aluminum Discharges.............................................................23

Summary........................................................................................................................................................23

References Cited..........................................................................................................................................24

Appendix 1. Method for solving for aluminum concentrations in reservoirs using 

the MatLab differential equation solver.....................................................................................26

Appendix 2. Massachusetts water-supply reservoirs not included in the application 

of dilution factors............................................................................................................................29

Appendix 3. Bathymetry- and flow-data sources for 13 Massachusetts drinking-water 

supply reservoirs............................................................................................................................30

Appendix 4. Water-quality data from 13 Massachusetts reservoirs, influent streams, 

filter-backwash effluents containing aluminum, and streams sampled during 

August–November 2009 ................................................................................................................32
iv

Figures

1. Photograph showing Lily Pond, Cohasset, Massachusetts, showing riparian wetland 

button bush and brown water characteristic of dissolved organic carbon 

compounds ....................................................................................................................................8

2. Graph showing data and least squares linear regression line for concentrations 

of total aluminum and dissolved organic carbon in samples from 13 Massachusetts 

reservoirs and streams, collected from August through November 2009 ..........................9

3. Graph showing solubility of aluminum as a function of pH for two solid phases 

of aluminum, gibbsite and amorphous aluminum hydroxide, determined from the 

chemical speciation program PHREEQC ..................................................................................9

4. Graph showing absence of a relation between total aluminum concentration and pH 

in samples from 13 Massachusetts reservoirs and streams, measured from August 

through November 2009.............................................................................................................10

5. Graph showing aluminum concentration and temperature with depth in two 

Massachusetts reservoirs, sampled on August 20 and September 17, 2009 ...................10

6. Graph showing measured and simulated aluminum concentrations for an example 

reservoir, Haggetts Pond, for three trial settling velocities of aluminum..........................12

7. Graph showing relation between aluminum settling velocity and average 

concentrations of dissolved organic carbon .........................................................................13

8. Graph showing simulated aluminum concentrations for an example reservoir, 

Quittacas Pond in New Bedford, from October 1960 to September 2004, with the 

chronic standard for aluminum toxicity indicated ................................................................14

9. Graphs showing measured versus simulated aluminum concentrations and 

equivalence line for fall 2009 ....................................................................................................15

10. Graph showing aluminum-dilution factors and the 7DF10 for filter-backwash 

effluent for an example reservoir, Quittacas Pond in New Bedford, with an effluent 

concentration of 438 μg/L, measured during fall 2009..........................................................16

11. Graph showing annual lowest 7-day-average dilution factors based on simulation 

data for Quittacas Pond, New Bedford, and the level of the 7DF10...................................17

12. Graph showing fit of lowest annual 7-day-average dilution data to log Pearson 

type III distribution for Quittacas Pond, New Bedford.........................................................17

13. Graph showing annual lowest 7-day-average dilution factors based on simulation 

data for Quittacas Pond, New Bedford...................................................................................18

14. Graph showing fit of lowest annual 7-day dilution data to log Pearson type III 

distribution for Quittacas Pond, New Bedford.......................................................................19

15. Graph showing 7DF10 values as a function of aluminum concentration in filterbackwash effluent for Quittacas Pond, New Bedford..........................................................19

16. Graph showing the relation between filter-backwash-effluent concentration 

of aluminum and the reservoir concentration at the 7DF10 for Quittacas Pond, 

New Bedford ...............................................................................................................................20

17. Graph showing simulated aluminum concentrations in Quittacas Pond, 

New Bedford ...............................................................................................................................20
v

Tables

1. Massachusetts town surface-water supplies and reservoirs investigated for

aluminum-discharge permitting .................................................................................................6

2. Results of quality-assurance evaluation of sampling for aluminum and dissolved

organic carbon..............................................................................................................................7

3. Data collected to assess aluminum-settling velocities in five reservoirs 

in Massachusetts .......................................................................................................................11

4. Highest 7DF10 values, filter-backwash effluent concentrations, and fluxes that

meet standards for aluminum discharge in 13 reservoirs of Massachusetts town 

water supplies.............................................................................................................................21
vi

Conversion Factors

Inch/Pound to SI

Multiply By To obtain

Length

inch (in) 2.54 centimeter (cm)

Area

acre 4,047 square meter (m2)

Volume

gallon (gal) 3.785 liter (L) 

million gallons (Mgal) 3,785 cubic meter (m3)

Flow rate

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

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

Mass

pound, avoirdupois (lb) 0.4536 kilogram (kg) 
Determination of Dilution Factors for Discharge 

of Aluminum-Containing Wastes by Public Water-Supply 

Treatment Facilities into Lakes and Reservoirs 

in Massachusetts

By John A. Colman, Andrew J. Massey, and Sara B. Levin

Abstract

Dilution of aluminum discharged to reservoirs in filterbackwash effluents at water-treatment facilities in Massachusetts was investigated by a field study and computer simulation. Determination of dilution is needed so that permits for 

discharge ensure compliance with water-quality standards 

for aquatic life. The U.S. Environmental Protection Agency 

chronic standard for aluminum, 87 micrograms per liter 

(μg/L), rather than the acute standard, 750 μg/L, was used in 

this investigation because the time scales of chronic exposure 

(days) more nearly match rates of change in reservoir concentrations than do the time scales of acute exposure (hours). 

Whereas dilution factors are routinely computed for 

effluents discharged to streams solely on the basis of flow of 

the effluent and flow of the receiving stream, dilution determination for effluents discharged to reservoirs is more complex 

because (1), compared to streams, additional water is available for dilution in reservoirs during low flows as a result of 

reservoir flushing and storage during higher flows, and (2) 

aluminum removal in reservoirs occurs by aluminum sedimentation during the residence time of water in the reservoir. Possible resuspension of settled aluminum was not considered in 

this investigation. An additional concern for setting discharge 

standards is the substantial concentration of aluminum that 

can be naturally present in ambient surface waters, usually in 

association with dissolved organic carbon (DOC), which can 

bind aluminum and keep it in solution.

A method for dilution determination was developed 

using a mass-balance equation for aluminum and considering 

sources of aluminum from groundwater, surface water, and 

filter-backwash effluents and losses caused by sedimentation, 

water withdrawal, and spill discharge from the reservoir. The 

method was applied to 13 reservoirs. Data on aluminum and 

DOC concentrations in reservoirs and influent water were collected during the fall of 2009. Complete reservoir volume was 

determined to be available for mixing on the basis of vertical and horizontal aluminum-concentration profiling. Losses 

caused by settling of aluminum were assumed to be proportional to aluminum concentration and reservoir area. The constant of proportionality, as a function of DOC concentration, 

was established by simulations in each of five reservoirs that 

differed in DOC concentration. 

In addition to computing dilution factors, the project 

determined dilution factors that would be protective with the 

same statistical basis (frequency of exceedence of the chronic 

standard) as dilutions computed for streams at the 7-day-average 10-year-recurrence annual low flow (the 7Q10). Low-flow 

dilutions are used for permitting so that receiving waters are 

protected even at the worst-case flow levels. The low-flow 

dilution factors that give the same statistical protection are the 

lowest annual 7-day-average dilution factors with a recurrence 

of 10 years, termed 7DF10s. Determination of 7DF10 values 

for reservoirs required that long periods of record be simulated so that dilution statistics could be determined. Dilution 

statistics were simulated for 13 reservoirs from 1960 to 2004 

using U.S. Geological Survey Firm-Yield Estimator software 

to model reservoir inputs and outputs and present-day values 

of filter-effluent discharge and aluminum concentration.

Computed settling velocities ranged from 0 centimeters 

per day (cm/d) at DOC concentrations of 15.5 milligrams per 

liter (mg/L) to 21.5 cm/d at DOC concentrations of 2.7 mg/L. 

The 7DF10 values were a function of aluminum effluent discharged. At current (2009) effluent discharge rates, the 7DF10 

values varied from 1.8 to 115 among the 13 reservoirs. In most 

cases, the present-day (2009) discharge resulted in receiving water concentrations that did not exceed the standard at 

the 7DF10. Exceptions were one reservoir with a very small 

area and three reservoirs with high concentrations of DOC. 

Maximum permissible discharges were determined for watertreatment plants by adjusting discharges upward in simulations 

until the 7DF10 resulted in reservoir concentrations that just 

met the standard. In terms of aluminum flux, these discharges 

ranged from 0 to 28 kilograms of aluminum per day.
2 Dilution Factors for Discharge of Aluminum-Containing Wastes into Lakes and Reservoirs in Massachusetts

Introduction

Treatment of water supplies by aluminum sulfate (alum) 

coagulation, settling, and filtration prior to distribution has 

been a common practice in the United States (Gruninger 

and Westerhoff, 1974) and is currently used in many watertreatment plants in Massachusetts (Mass.). The effect of this 

treatment is settling and removal of aluminum hydroxide flock 

with associated coprecipitated contaminants. 

Typically, alum is applied in dry form or as a concentrated liquid to the supply water. The aluminum combines with 

hydroxide from the water and forms an aluminum hydroxide 

precipitate. Contaminants such as dissolved natural organic 

matter, colloidal inorganic or organic particles, and dissolved 

ions such as phosphate and heavy metals can be removed. 

The precipitate is removed from the supply in gravity settling 

basins and by filtration, often through sand filters. Waste solids 

from the alum-coagulation process can derive from both the 

coagulation-sedimentation-basin wastewater and from filter 

backwash. In this report the wastes are referred to as filterbackwash effluent. The filter-backwash effluent is typically 

discharged from the treatment plant to a settling basin, with 

overflow to a surface-water body—a stream, lake, or reservoir. 

This report is concerned with establishing permit requirements 

for discharge of aluminum-containing filter-backwash effluent from public water supply (PWS) treatment facilities to 

lakes or reservoirs. In Massachusetts, permits for discharge are 

regulated by the Massachusetts Department of Environmental 

Protection (MassDEP) under the National Pollution Discharge 

Elimination System (NPDES).

Many of the discharged filter-backwash effluents from 

PWS treatment facilities contain aluminum concentrations that 

are above ambient water-quality standards but that may be 

acceptable for discharge if sufficiently diluted by the receiving waters. Typically, discharge permits account for dilution 

by use of dilution factors. A dilution factor (DF) is the ratio of 

concentration in the effluent to concentration in the receiving 

water after mixing in the receiving water.

DFs are routinely computed for effluents discharged to 

streams (without significant instream ambient contaminant 

concentrations) as the ratio of flow in the stream to flow in the 

effluent (U.S. Environmental Protection Agency, 2008):

DF = (Qp + Qe)/Qe (1)

where 

Qp is the flow in the stream, and

Qe is the flow of the effluent.

In order to ensure that DFs are protective of aquatic life 

at the range of flows that might occur, permits for discharge of 

metals to streams are based on low-flow conditions, when little 

stream water is available for dilution. Permitting for metals 

discharge in Massachusetts defines low-flow conditions as the 

7-day-average 10-year-recurrence annual low flow (7Q10) and 

sets discharge limits based on the DF at that flow value.

Filter-backwash discharges from PWS can be as high 

as one million gallons per day or 1.55 cubic feet per second 

(ft3/s), and diluting stream flow discharges can be as small as 

a few cubic feet per second at low flow. Thus, if DFs for reservoirs were estimated as they are for streams, low DF values 

(less than 10) could result during low flow, and many current 

discharges would exceed the standard. However, additional 

processes that would likely increase the minimum DF values 

are involved for dilution of effluents entering reservoirs, as 

compared to effluents entering streams. These are (1) that 

additional water is available for dilution in reservoirs during 

low flow because of reservoir flushing and storage during 

higher flows and (2) that aluminum removal occurs in reservoirs because of aluminum sedimentation during the residence 

time of water in the reservoir. 

Another factor to consider when estimating the DF is 

the ambient concentration of aluminum from natural sources 

in the diluting stream or reservoir water. Aluminum concentration data from the U.S. Geological Survey (USGS) 

water-quality database (QWDATA) indicates that dissolved 

(0.45-μm filtrate) aluminum concentrations in Massachusetts 

surface-water samples collected during 1991–2009 ranged 

from undetected to 383 micrograms per liter (μg/L), with a 

median concentration value of 14.5 μg/L (n equals 261) and 

that total concentrations ranged from undetected to 519 μg/L, 

with a median concentration value of 100 μg/L (n equals 65). 

The chronic and acute toxicity water-quality standards for aluminum are 87 and 750 μg/L, respectively, as total aluminum 

(U.S. Environmental Protection Agency, 2010). Therefore, 

there may be some filter-backwash effluent disposal sites with 

aluminum concentrations in the receiving waters that would 

already exceed the U.S. Environmental Protection Agency 

chronic standard.

Whereas accounting for all the processes affecting aluminum concentration could result in accurate DFs for aluminum 

discharge into reservoirs, the use of DFs in permitting may be 

more complex than the use of DFs for streams, which is based 

only on the ratio of receiving water flow to effluent flow. The 

flow-ratio DF for streams, defined at low flow (7Q10), is a 

unique value and can be applied to any effluent concentration 

to determine concentration in the receiving water after dilution. In particular, the effluent concentration can be computed 

that would result, after dilution, in a receiving water concentration that just meets the standard, and this can be used as an 

upper-limit effluent concentration for permitting discharge.

When the DF also depends on processes like aluminum 

sedimentation in the reservoir, the DF is not independent 

of the concentration in the effluent discharge. Typically, the 

DF for reservoirs increases as the concentration discharged 

increases. Under these circumstances, statistical analysis of the 

concentrations in the receiving water resulting from a given 
The Dilution-Factor Method 3

discharge and associated daily DFs must be used to choose a 

discharge concentration-dilution combination that will protect 

the reservoir. The discharge concentration-dilution combination that is selected should afford the receiving water the same 

protection on the basis of frequency of standard exceedence 

as that resulting for discharge to streams when the flow-ratio 

dilution factor, based on the 7Q10 discharge, is used. 

Purpose and Scope

A method is described here that uses numerical solutions to a mass-balance equation to determine DF values for 

discharge of filter-backwash effluent that contains aluminum 

to reservoirs and lakes in Massachusetts. The method includes 

the effects of reservoir storage, aluminum sedimentation, and 

ambient concentration of aluminum in the receiving water. 

Possible resuspension of aluminum from the sediment is not 

considered. A method is described to use the resulting DFs 

to determine concentrations in filter-backwash effluent that 

would result in the same statistically equivalent protection 

against exceeding a standard for reservoirs that is currently 

provided for streams. Sufficient details are given so that the 

methods can be applied by report users with access to numerical-solution and statistical-analysis computer software. The 

method was applied to 13 reservoirs in Massachusetts where 

aluminum-containing filter backwash is discharged. Chemical 

and discharge data required to apply the method to a reservoir 

are described. The report includes data collected for those 

reservoirs for which DF values were computed. 

Previous Investigations

Although there have been no formal investigations of 

DFs for aluminum in reservoirs before this study, aspects of 

the question, including techniques for metals sampling and 

solute modeling in reservoirs, have been investigated. Sampling methods for trace metals, such as aluminum, are well 

documented (Wilde, 2004, 2006). Although no reservoir simulations of aluminum concentration are known to the authors, 

reservoir simulations of phosphorus concentration, another 

nonconservative element, have been conducted (Vollenweider, 

1979). In the current study, the same approach is used for aluminum as Vollenweider (1979) has used for phosphorus, simulating the reservoir as a mixed reactor with solute removal by 

sedimentation as well as by outflow from the reservoir. 

The aquatic chemistry of aluminum is well known. 

Chemical processes may enhance the removal of aluminum by 

precipitation (see, for example, Parkhurst and Appelo, 1999) 

or retain aluminum in solution, for example, by binding with 

dissolved organic carbon (DOC) (see, for example, Breault 

and others, 1996). Aluminum may also be deposited as sediment after incorporation on, and settling by, phytoplankton.

The Dilution-Factor Method

There are two parts to developing a method for computation of DF values for aluminum discharge to reservoirs. The 

first is developing the method for computing dilution at any 

given time for a given reservoir and discharge. This requires 

knowledge of mass-balance inputs and outputs of aluminum to 

and from the reservoir and numerical solution of an ordinary 

differential equation for concentration in the reservoir. The 

second part is developing a method for applying the reservoir 

DFs to permit writing that results in protection of the receiving water that is statistically comparable to the protection 

afforded by DFs determined at low flow (7Q10) for discharge 

to streams. 

Calculating Dilution

As discussed in the Introduction section, more factors 

are involved in dilution of aluminum-containing effluents that 

discharge to reservoirs than in discharge to streams. The additional factors are (1) dilution by water stored in the reservoir 

after flushing at high flow, (2) in-reservoir losses of aluminum 

through sedimentation, and (3) occasional natural occurrence 

of aluminum at high concentration in input streams. High 

natural aluminum concentrations, usually associated with high 

concentrations of aluminum-stabilizing DOC, render receiving waters less effective at diluting aluminum discharged from 

treatment plants.

The method for computing DF values that includes these 

three factors requires the numerical integration of the reservoir 

mass-balance equation for aluminum-concentration change. 

The mass-balance equation is:

 dC

dt

= + ( ) Q Ce e Q Cs s + + Q Cg g Q Cw v − AS C V/ (2)

where

C is the total aluminum concentration in the 

reservoir water,

Qe is the discharge of the filter-backwash 

effluent,

Ce is the total aluminum concentration in the 

filter-backwash effluent,

Qs is the discharge of the streams that are 

influent to the reservoir,

Cs is the total aluminum concentration in the 

stream,

Qg is the discharge of groundwater that is 

influent to the reservoir,

Cg is the total aluminum concentration in the 

groundwater,

Qw is the sum of water withdrawal for water 

supply and the downstream discharge from 

the reservoir,
4 Dilution Factors for Discharge of Aluminum-Containing Wastes into Lakes and Reservoirs in Massachusetts

A is the area of the reservoir,

Sv is the apparent settling velocity of total 

aluminum in the reservoir,

V is the volume of the reservoir subject to 

mixing, and

t is time.

The numerical integration of the mass-balance equation results in C, the aluminum concentration in the reservoir 

at any time t, and requires the specification of the variables 

shown in on the right side of equation 2. The DF value at any 

time t is then 

DF = Ce / C. (3)

Equation 2 was solved numerically in this study using 

the MatLab differential equation solver named “ode45” 

(Shampine and Gordon, 1975; Dormand and Prince, 1980), as 

described in appendix 1.

Calculating the Settling Velocity

The settling velocity, used to compute the loss of aluminum due to settling to the bottom sediment, can be determined 

from successive solutions of equation 2, using trial settling 

velocities, initial conditions determined from field data, which 

would likely increase the minimum DF values, and the additional data requirements used to solve equation 2 previously 

described. Simulated aluminum concentrations are compared 

to measured concentrations after each simulation run, and the 

settling velocity is adjusted (increased if simulated concentration was greater than measured, or vice versa) until the best 

agreement of predicted and measured plots is obtained, as 

determined by visual inspection. Because sampling four times 

at monthly intervals generated too few data points, more formal statistical curve fitting was not possible.

Dilution at Low Flow

The second part of developing discharge permits appropriate for reservoirs requires statistical analysis of the DF daily 

values to determine the relation between the concentration 

in the effluent and the frequency of the aluminum discharge 

exceeding the standard after dilution in the receiving water. 

For this study, the aluminum standard is taken as the chronic 

standard of 87 μg/L. The chronic, rather than the acute, standard (750 μg/L) was selected in consultation with the MassDEP, because concentrations in reservoirs change relatively 

slowly—on the order of days. All exposures to aluminum in 

reservoirs, therefore, are likely to be chronic exposures. For 

permitted limits, the frequency of standard exceedence for 

the reservoir should be at the same rate as for discharge to a 

stream regulated by a flow-ratio DF at low flow (7Q10). 

Permits based on DF at the 7Q10 flow for discharge 

to streams set limits that would result in the highest annual 

7-day-average concentration in the stream exceeding the 

standard, on average, once every 10 years. By analogy for 

discharge to reservoirs, permitting should result in the highest 

annual 7-day-average concentration in the reservoir exceeding 

the standard, on average, once in every 10 years. Because DFs 

for discharge to reservoirs are proportional to the reciprocal of 

reservoir concentration (equation 3), the highest annual 7-dayaverage reservoir concentration with a recurrence of 10 years 

would correspond to the lowest annual 7-day-average DF with 

a recurrence of 10 years. By analogy with flow, this is termed 

the 7DF10. 

Unlike 7DF10 values for discharge to streams, the 7DF10 

value for discharge to reservoirs is a function of effluent discharge concentration (Ce

). That is because the settling and the 

reservoir-discharge terms for aluminum in equation 2 depend 

on the aluminum concentration in the reservoir, which in turn 

is affected by the concentration in the effluent discharge. For 

every Ce value, there is a corresponding 7DF10. But there is 

only one 7DF10 and Ce pair that results in a reservoir concentration that just meets the chronic water-quality standard. 

Determination of this pair may necessitate computation of several 7DF10–Ce

 pairs that result in reservoir concentrations that 

bracket the standard, followed by interpolation to the values 

that result in the chronic standard being met in the reservoir.

In practice, the long DF records required to determine 

the 7DF10 are obtained by solving equation 2 for C each day. 

The daily concentrations are used to compute daily DFs from 

equation 3 and analyzed for a 7-day running average. The lowest 7-day average is selected for each year. The yearly data are 

fitted to a known distribution; a log Pearson type III distribution gave the best fit in this investigation. Finally, the DF at 

the 10th percentile is selected from the fitted distribution. The 

software SWSTAT is available to compute the 7-day averages, 

to select annual values, and to fit the frequency distribution 

(U.S. Geological Survey, 2002).

Data Requirements

Long records of hydrologic data are required to determine 

accurate 7DF10 values. This project determined 7DF10 values 

from daily DF values computed from 1960 to 2004. The reservoir input- and output-flow data used in the DF calculations 

represented hydrologic conditions over this period, but the 

effluent discharge and effluent concentration data were based 

on present-day practices for the water-treatment facilities. 

Therefore, the study results are for present practices for aluminum discharge and hydrologic variation that is representative 

of the 1960–2004 period. The implied assumption in application of the results is that future hydrologic variation will be 

similar to past variation.
Application of the Dilution-Factor Method to Reservoirs 5

Flows and Reservoir Volumes

Past investigations of reservoir flow and capacities in 

Massachusetts have produced hydrologic- analysis software 

for computing flows and volumes. For streamflow, the Massachusetts Sustainable Yield Estimator can be used (Archfield 

and others, 2010). Groundwater input and volume changes 

in reservoirs can be determined from the Firm-Yield Estimator1

 (Waldron and Archfield, 2006; Archfield and Carlson, 

2006; Levin and others, 2011). Reservoir bathymetry, which 

is necessary for the volume change estimates, is available 

from the water suppliers or may be obtained by bathymetricsurvey techniques.

Filter-Backwash Effluent Flows

Values of filter-backwash effluent flows are available 

from records kept by the PWS operators. Monthly average 

values and maxima are reported on Discharge Monitoring 

Requirement forms (K. Keohane, Massachusetts Department 

of Environmental Protection, written commun., 2010). More 

detailed records are also usually kept by suppliers and may be 

available on request.

Water Quality

Aluminum-concentration estimates are needed for influent streams and groundwater and for filter-backwash effluent discharge. In addition, aluminum concentrations in the 

reservoirs are needed for initial concentrations in the settlingvelocity trial simulations and to determine if simulated results 

match measured results. DOC concentrations in the reservoirs 

are also needed for simulations, because settling velocity 

depends on DOC.

Application of the Dilution-Factor 

Method to Reservoirs

Application of the dilution-factor method to discharges 

of reservoirs requires that daily reservoir input flows and aluminum concentrations be computed so that daily in-reservoir 

aluminum concentrations can be computed by solution of 

equation 2 and daily dilution factors computed from equation 3. Then the 7-day annual mean lowest dilution factor with 

a 10-year recurrence (7DF10) is computed and used with the 

discharge aluminum concentration in equation 3 to determine 

the reservoir concentration that would apply at that low level 

of dilution. 

If the computed reservoir aluminum concentration that 

results happens to be at the chronic standard, then the discharge concentration used would be the amount permitted for 

discharge. If the reservoir aluminum concentration is below 

the chronic standard, then a higher discharge concentration 

(double, for example) is chosen and then analysis begins again 

at number 2.

Determination of a 7DF10 and Ce pair that results in a 

reservoir concentration that just meets the chronic water-quality standard may necessitate computation of several 7DF10–Ce

pairs that result in reservoir concentrations that bracket the 

chronic standard. Interpolation can then determine the values 

that result in the chronic standard being met in the reservoir.

Reservoirs Studied

The dilution-factor method was applied to 13 reservoirs 

in this investigation to assess the discharge concentration that 

would meet the chronic aluminum standard (table 1). Of these, 

five were chosen for more intensive sampling used for determining settling velocities of aluminum in the reservoirs.

During discussion between the USGS and MassDEP 

before the project was initiated, 21 candidate reservoirs were 

identified for the study of aluminum dilution. For reasons of 

unavailability of data, special discharge circumstances, or 

determination that no aluminum was being discharged to a 

reservoir, 8 of the original 21 were not further investigated for 

dilution factors (appendix 2). 

Flow, Area, and Volume Calculations

Daily streamflow inputs to reservoirs (Qs) were simulated 

using the Massachusetts Sustainable-Yield Estimator (Archfield and others, 2010) for the period October 1960 through 

September 2004. At the five reservoir sites chosen for settlingvelocity determinations, the flow estimates were extended 

through December 2009, so that simulation data could be 

appropriately compared to measured data collected in fall 

2009. Daily groundwater input and output flows (Qg), daily 

reservoir volumes (V), and reservoir outflows, a component of 

Qw , were estimated with the Firm-Yield Estimator (Waldron 

and Archfield, 2006; Archfield and Carlson, 2006; Levin and 

others, 2011), which was modified to run on a daily time step. 

Daily water use, a component of Qw , was estimated by disaggregating average reported monthly withdrawal volumes from 

2005 to 2009. Discharge flows of the filter-backwash effluent 

(Qe) were determined variously from reporting from the suppliers to MassDEP or from more detailed descriptions made by 

the suppliers to USGS (appendix 3).

Regulation of reservoirs constituted additional inputs and 

withdrawals not dependent on the hydrologic cycle, and data 

on these were provided with a variable amount of detail from 

suppliers (appendix 3). Bathymetric surveys, needed for determining reservoir volume and surface area at different depths, 

were completed by boat survey or obtained from previous 

studies of the reservoirs (appendix 3).

1

 Firm yield is the maximum volume of water that can be withdrawn from a 

reservoir without causing the reservoir to fail during drought conditions.
6 Dilution Factors for Discharge of Aluminum-Containing Wastes into Lakes and Reservoirs in Massachusetts

Water-Sample Collection, Processing, and 

Chemical Analysis

Required water-quality samples include those used for 

aluminum input and output calculation, as well as those used 

for ancillary water-quality assessment. Thus, in addition to 

aluminum-concentration samples, samples were collected for 

determination of DOC concentrations used to assess effects 

on aluminum-settling velocity; and for measurements of pH, 

temperature, dissolved oxygen concentrations and conductance, all of which were used to assess aluminum solubility 

and mixing in the reservoirs.

Samples for aluminum analysis were collected using 

clean-sampling techniques (Wilde, 2004, 2006) and preserved 

on return to the Northborough, Mass., laboratory with 0.5 

milliliter (mL) of concentrated HNO3 per 125-mL polyethylene bottle. The acid-preserved samples were sent to the 

USGS National Water Quality Laboratory in Denver, Colorado 

(Colo.), for aluminum analysis after inbottle acid digestion 

(Hoffman and others, 1996). The analytical method was 

inductively coupled plasma-mass spectrometry (Garbarino and 

Struzeski, 1998). The reporting level was 5 μg/L. 

Many aluminum devices, including boats, which may be 

in proximity to samples, make special care necessary during 

collection and processing of these samples to prevent sample 

contamination. Sampling equipment and bottles were contained in plastic bags and not exposed to boat surfaces. 

Samples for DOC were filtered in the field with Aquaprep, 0.45-μm inline filters, and stored in prebaked, brownglass, 125-mL bottles. Samples were acidified on return to 

the laboratory in Northborough, Mass., with 1.0 mL of 4.5 N 

H2SO4. The acid-preserved samples were sent to the USGS 

National Water Quality Laboratory in Denver, Colo., for DOC 

analysis by ultraviolet-promoted persulfate oxidation and 

infrared spectrometry (Garbarino and Struzeski, 1998). The 

reporting level was 0.15 mg/L.

The field parameters pH, temperature, dissolved oxygen, 

and conductance were determined using a Eureka Manta multiprobe. Values can be read with the instrument lowered to the 

required depth in the reservoir or from samples poured into the 

multiprobe cup at the surface. 

Depth-profile samples, collected for aluminum in two 

reservoirs, were obtained by pumping at the surface with a 

peristaltic pump on plastic tubing lowered to sampling depths. 

A Eureka multiprobe, lowered to sampling depths, measured 

pH, temperatures, conductances, and concentrations of dissolved oxygen of samples. The probe was calibrated for pH, 

conductance, and dissolved oxygen on a daily basis.

Samples for aluminum analysis for most reservoirs 

were collected during one reservoir visit in the fall of 2009. 

Samples were collected to determine aluminum concentrations 

in backwash discharge (Ce), input streams (Cs), and three-sample reservoir-surface composites (C). Samples from reservoirs 

selected for settling-velocity calculations were collected durTable 1. Massachusetts town surface-water supplies and reservoirs investigated for aluminum-discharge permitting.

[USGS, U.S. Geological Survey; *, reservoir was used to determine settling velocities of aluminum; WTP, water-treatment plant; WTF, water-treatment 

facility; permit number, the National Pollutant Discharge Elimination System (NPDES) permit number]

Facility Permit 

number Receiving water

Latitude 

(decimal 

degree)

Longitude 

(decimal 

degree)

USGS station 

number for 

reservoir

*Andover WTP MAG640058 Haggetts Pond 42.646 -71.199 423844071115501

*Ashburnham/Winchendon WTP MAG640045 Upper Naukeag Lake 42.655 -71.923 423919071552401

*Cambridge WTP MAG640040 Fresh Pond Reservoir 42.385 -71.149 422305071090001

Clinton WTP MAG640047 Unnamed small pond 42.412 -71.701 422443071420301

*Cohasset WTP MAG640070 Lily Pond 42.224 -70.816 421326070485801

*Gardner WTF MAG640041 Crystal Lake 42.584 -71.993 423501071593501

Manchester-by-the-Sea and Hamilton WTP MAG640003 Gravelly Pond 42.599 -70.81 423555070483701

New Bedford WTP MAG640069 Little Quittacas Pond 41.793 -70.921 414734070551401

Northampton WTP MAG640034 Mountain Street Reservoir 42.401 -72.671 422404072401501

Salem and Beverly Water Supply Board MAG640059 Wenham Lake Reservoir 42.59 -70.891 423523070532801

Weymouth WTP MAG640031 Great Pond 42.156 -70.971 420920070581501

Winchester WTP MAG640037 South Reservoir 42.444 71.116 422639071065601

Worcester WTP MAG640052 Holden Reservoir #2 42.297 -71.867 421748071520001
Application of the Dilution-Factor Method to Reservoirs 7

ing the late summer and fall 2009 (generally in four samplings 

spanning 3 months).

Groundwater aluminum concentrations (Cg) were determined from data retrieved from the USGS water-quality database QWDATA. The retrieval was from all groundwater sites 

in Massachusetts after 1991, when clean-sampling techniques 

were implemented for metals. Dissolved (filtered-sample) 

concentrations were used, the assumption being that most 

aluminum transport in the aquifer is in the dissolved state. The 

median concentration value of 10 μg/L (n equals 452) was 

used. This value, 10 μg/L, was the method detection limit for 

many of the analyses. Use of the data median for the concentration of aluminum in groundwater, rather than a measured 

value for each reservoir, likely added little uncertainty to our 

model because groundwater fluxes (from the Firm-Yield Estimator described in the previous section) were small or zero for 

the reservoirs.

Quality Assurance of the Water-Quality Data

During the investigation, 27 quality-assurance (QA) 

samples were collected to assess error in aluminum and DOC 

measurements, including sample-bottle and acid blanks, standard reference samples, duplicate samples, and sample splits 

(table 2). QA results of the blank samples showed that possible 

contamination during sampling or sample handling or from 

sampling materials (the bottles and preservation acid) was 

insubstantial or did not occur. All concentrations measured 

for the four sampling-bottle blanks collected during the study 

were below detection for the respective analytes (table 2). Two 

samples of USGS standard reference solution (USGS T–195) 

submitted to the National Water Quality Laboratory as blind 

samples were within 4 percent of the known values (table 2). 

Concentrations of both aluminum and DOC in duplicate 

samples varied by about 1 percent. The good agreement for 

duplicates and standards and lack of contamination in blanks 

indicated that the clean-sampling techniques applied during 

sampling collection and processing were adequate.

Water-Quality Results and Associations

Aluminum measured in the reservoirs ranged from a 

low of less than 6 μg/L (below detection limit) to a high of 

414 μg/L (appendix 4). Concentrations of DOC in the reservoirs ranged from 1.5 to 15.5 mg/L, with a median value 

of 3.4 mg/L. The higher concentrations of DOC were likely 

dominated by humic compounds, which leach into water from 

wetland soils (fig. 1) (Aitkenhead-Peterson and others, 2003).

Aluminum can bind chemically with DOC so that highDOC systems typically have high natural aluminum concentrations (as determined in Massachusetts by Breault and others, 1996). The binding of aluminum by DOC keeps aluminum 

in solution in the water column, whereas unbound aluminum 

would precipitate from solution once the solubility product for 

the precipitate, aluminum hydroxide, was exceeded. Iron and 

aluminum form complexes with DOC or colloidal oxyhydroxides mixed with DOC, which keep the metals from settling 

from the water column (Berner and Berner, 1996). Sampling 

of reservoirs and streams for this study shows an association 

between DOC and aluminum (fig. 2). 

In the absence of DOC, the solubility of aluminum in 

water is low. Depending on what solid phase forms, solubility of aluminum could range to lower than 1 μg/L for the pH 

range 4.7 to 7.0. The lower concentrations in equilibrium with 

gibbsite are energetically favored, but equilibrium with this 

phase is established more slowly than with the more soluble 

amorphous form of Al(OH)3 (fig. 3). The low solubility of 

aluminum indicates that much of the aluminum discharged to 

reservoirs would likely settle to the bed sediments and remain 

there. Removal of aluminum by settling of the precipitate 

likely contributes substantially to the settling-velocity term of 

equation 2.

Table 2. Results of quality-assurance evaluation of sampling for aluminum and dissolved organic carbon.

[Al, aluminum; DOC, dissolved organic carbon; μg/L, micrograms per liter; mg/L, milligrams per liter; USGS, U.S. Geological Survey; %, percent]

Quality assurance measure Details Number of samples Result

Bottle blanks Sample bottles were filled in the field 

with blank water, and were preserved 

with acid.

5 Al and 2 DOC All concentrations less than the method 

detection limit—6 μg/L for Al and 

0.4 mg/L for DOC.

Standard reference sample USGS standard reference water sample, 

number T–195.

2 Al Mean relative error was 4%.

Duplicates at one time Samples taken sequentially on one sampling occasion.13 Al and 13 DOC Mean relative error was 2.1% for Al 

and 1.2% for DOC.
8 Dilution Factors for Discharge of Aluminum-Containing Wastes into Lakes and Reservoirs in Massachusetts

High DOC is also associated with lower pH, because 

many of the DOC compounds are acids—particularly 

humic acids and fulvic acids (McKnight and others, 2003). 

A correlation between DOC and aluminum could conceivably be an effect of pH, rather than of DOC. The aluminum 

concentration data for reservoirs and streams plotted against 

pH (fig. 4) shows little correlation, however, indicating that 

pH is probably not the primary factor that controls aluminum concentration.

Aluminum Mixing in Reservoirs

Dilution factors depend on the mixing volume in the 

receiving water that is available for dilution. In streams, 

the whole streamflow is used as the dilution volume, 

even though complete dilution across the stream channel 

likely happens some distance downstream from the point 

of effluent discharge, usually from a pipe or channel. For 

reservoirs, the entire reservoir volume should be available 

for dilution if mixing is rapid with respect to the rate of effluent discharge.

Mixing for reservoirs was investigated with vertical- and 

horizontal- profile sampling. Vertical profiles of two reservoirs 

show that, although temperature stratification occurs, typically 

with a thermocline at 6-m depth, aluminum concentrations are 

relatively constant above the thermocline and decrease somewhat below the thermocline (fig. 5). The absence of substantial 

vertical stratification of aluminum concentrations above the 

thermocline and the fact that only a small percentage of the 

total volume of the reservoirs was below the thermocline support an assumption of full reservoir availability for modeling 

of aluminum dilution.

Horizontal mixing was assessed by collecting separate samples from three widely separated surface points in 

Fresh Pond Reservoir on August 19, 2009 (appendix 4). The 

aluminum concentrations were identical (7 μg/L). Despite 

this evidence of horizontal mixing, reservoir concentrations 

were assessed in composites of samples from three surface locations. 

Figure 1. Lily Pond, Cohasset, Massachusetts, showing riparian wetland button bush and brown water (here visible in the 

boat’s wake) characteristic of dissolved organic carbon compounds.
Application of the Dilution-Factor Method to Reservoirs 9

Figure 3. Solubility of 

aluminum as a function 

of pH for two solid 

phases of aluminum, 

gibbsite and amorphous 

aluminum hydroxide

(Al(OH)3), determined 

from the chemical 

speciation program 

PHREEQC (Parkhurst and 

Appelo, 1999).

Figure 2. Data and least 

squares linear regression 

line for concentrations 

of total aluminum and 

dissolved organic carbon 

in samples from 13 

Massachusetts reservoirs 

and streams, collected 

from August through 

November 2009.

0 5 10 15 20 25 30

Dissolved organic carbon concentrations, in milligrams per liter

0

100

200

300

500

400

Aluminum concentrations, in micrograms per liter

3

EXPLANATION

Aluminum concentrations, in micrograms per liter

10 −1

10 0

10 1

10 2

10 3

10 4

10 5

Al(OH) 

Gibbsite

4 5 6 7 8 9

pH
10 Dilution Factors for Discharge of Aluminum-Containing Wastes into Lakes and Reservoirs in Massachusetts

Figure 4. Absence of 

a relation between total 

aluminum concentration 

and pH in samples from 13 

Massachusetts reservoirs 

and streams, measured 

from August through 

November 2009.

Figure 5. Aluminum 

concentration and 

temperature with depth 

in two Massachusetts 

reservoirs, sampled 

on August 20 (Crystal 

Lake, Gardner) 

and September 17

(South Reservoir, 

Winchester), 2009.

4 5 6 7 8

pH

0

100

200

300

400

500

Aluminum concentrations, in micrograms per liter

0 5 10 15 20 25 30

0

2

4

6

8

10

12

Aluminum concentrations, in micrograms per liter, and temperature, in degrees Celsius

Depth, in meters

Aluminum concentrations, South Reservoir

Aluminum concentrations, Crystal Lake

Temperature, South Reservoir

Temperature, Crystal Lake

EXPLANATION
Application of the Dilution-Factor Method to Reservoirs 11

Settling-Velocity Results

Aluminum settling velocity was estimated in five 

reservoirs selected to represent a range of DOC concentrations (table 3). The terms of equation 2 necessary to solve the 

equation with successive trial settling velocities were obtained 

as follows. Firm-yield estimates were used for reservoir water 

withdrawals (Qw) for the period 1960–2004 (appendix 3). 

Actual withdrawal patterns (provided by the water supplier) 

were applied for the period 2005–2009. For other terms of 

equation 2, the Sustainable-Yield Estimator and Firm-Yield 

Estimator software were modified to run through the fall of 

2009. Averages by reservoir of the three to four measured 

values for aluminum concentrations of input surface water 

(Cs) and filter-backwash effluent (Ce) were used in the simulations. The aluminum concentration used for groundwater (Cg

) 

was 10 μg/L (see section “Water-Sample Collection, Processing, and Chemical Analysis”) determined from the USGS 

QWDATA database.

Input data for one of the settling-velocity reservoirs 

(Upper Naukeag) could not be obtained because none of the 

streams were flowing. Also, the aluminum concentrations in 

the effluent discharge were highly variable, ranging from 183 

to 3,390 μg/L. Without better control on the concentrations 

of aluminum discharged, solution of equation 2 for settling 

velocity was not possible; therefore, Upper Naukeag Lake was 

excluded from the analysis for settling velocity.

Simulations of reservoir concentrations of aluminum (by 

solution of equation 2, see section “Calculating Dilution”) 

for each reservoir were run forward in time from the initial 

conditions, with differing settling velocities in successive trials 

for each reservoir. Trials were continued until approximate 

agreement was reached between measured and simulated 

concentrations (fig. 6). Initial conditions for each trial used the 

aluminum concentration measured in the first sampling.

Results from the four reservoirs used indicated that settling velocity does vary as a function of DOC, but that the 

relation was overly dependent on one of the reservoirs, Lily 

Pond (red line, fig. 7). Three of the four average DOC concentrations ranged from 2.7 to 4.5 mg/L, and corresponding best 

visual-fit settling velocities ranged from 18 to 15 centimeters 

per day (cm/d). The average DOC concentration in the fourth 

reservoir, Lily Pond, was 15 mg/L, and the best visual-fit 

settling velocity was zero. The zero settling velocity indicates 

that aluminum passage through the reservoir was completely 

conservative, the DOC apparently maintaining this otherwise 

insoluble element in solution. 

The possibility that settling velocity may also be zero for 

DOC concentrations lower than 15 mg/L cannot be evaluated 

using data from the four reservoirs alone because none of the 

reservoirs selected for settling-velocity determination had 

intermediate DOC values. However, sampling results from 

the method-application reservoirs indicated that the DOC 

concentration in Great Pond, Weymouth, was intermediate 

(7.8 mg/L). Settling velocity was estimated for Great Pond by 

extending the streamflow analysis for this pond through 2009. 

Successive trials were run forward from 1960, and the best-fit 

settling velocity determined using the aluminum value for the 

one sampling date available was 1.5 cm/d. The low settling 

velocity for this reservoir indicates that most of the aluminum 

was stabilized by DOC, but a small fraction was subject to 

settling. Linear least-square fit excluding Lily Pond but including Great Pond is shown by the gray and red line (fig. 7). 

Assuming that the x-axis intercept of this second regression 

line indicates the point at which all the aluminum is stabilized, 

the DOC-settling velocity relation between the x intercept and 

Lily Pond would coincide with the x axis (gray line, fig. 7). 

DOC concentrations for all of the remaining methodapplication reservoirs were less than that of Great Pond, 

Weymouth, so that the second regression line Sv equals -3.9 

* DOC + 32 can be used to estimate settling velocities for 

these reservoirs.

Although the analysis of the conditions in the reservoirs 

to compute settling velocity required substantial effort, the 

Table 3. Data collected to assess aluminum-settling velocities in five reservoirs in Massachusetts.

[Al, aluminum; DOC, dissolved organic carbon; Mgal/d, million gallons per day; μg/L, micrograms per liter; mg/L, milligrams per liter; cm/d, centimeters per 

day; dates in form YYYYMMDD (year, month, day); --, settling velocity could not be calculated]

Reservoir Period of water-quality 

record

Average 

effluent discharge (Qe

)

(Mgal/d)

Average 

discharge concentration (Ce

)

(μg/L)

Groundwater 

Al concentration 

(Cg)

(μg/L)

Average 

surface-water 

concentration (Cs)

(μg/L)

Average 

DOC 

(mg/L)

Final 

settling 

velocity 

(cm/d)

Lily Pond 20090924 to 20091119 0.11 804 10 206 15 0

Fresh Pond 20090819 to 20091118 0.44 1,450 10 17 3.6 20

Crystal Lake 20090820 to 20091110 0.59 1,900 10 74 2.7 25

Haggetts Pond 20090818 to 20091118 0.63 3,810 10 72 4.5 17

Upper Naukeag Lake1 20090826 to 20091110 0.12 1,280 10 17 2.3 --

1

 Because discharge concentrations were highly variable and no surface-water samples were collected, the average surface-water concentration was set to 

equal the value for Fresh Pond, and a final settling velocity could not be calculated.
12 Dilution Factors for Discharge of Aluminum-Containing Wastes into Lakes and Reservoirs in Massachusetts

Figure 6. Measured and simulated aluminum concentrations for an example reservoir, Haggetts Pond, for three trial settling 

velocities of aluminum.

08/13/09 8/23/09 9/2/2009 9/12/09 9/22/09 10/2/09 10/12/09 10/22/09 11/1/09 11/11/09 11/21/09

0

5

10

15

20

25

30

35

Date

Aluminum concentrations, in micrograms per liter

Settling velocity 10 

centimeters per day

Settling velocity 15

centimeters per day

Settling velocity 20

centimeters per day

Measured concentration

Simulated concentration

EXPLANATION
Application of the Dilution-Factor Method to Reservoirs 13

Figure 7. Relation between aluminum settling velocity and average concentrations of dissolved organic carbon. All results were 

from fitting simulation results to four sample measurements, except for the results for Great Pond, which were fit to one sample 

measurement. Equations are linear least-square fits of data.

0 2 4 6 8 10 12 14 16

0

5

10

15

20

25

Average concentrations of dissolved organic carbon, in milligrams per liter

Aluminum settling velocity, in centimeters per day

y = − 3.9*x + 32 y = − 1.6*x + 24

Great Pond,Weymouth

Lily Pond,

Cohasset

Crystal Lake, Gardner

Haggetts Pond, Andover

Fresh Pond, Cambridge

Original linear fit

With Great Pond

EXPLANATION
14 Dilution Factors for Discharge of Aluminum-Containing Wastes into Lakes and Reservoirs in Massachusetts

number of reservoirs and amount of data were not sufficient 

to define the DOC-settling velocity relation with certainty. 

Uninvestigated are any seasonal effects that may apply. The 

relation was used tentatively in this study and its appropriateness considered in the comparison of predicted versus measured results for all the reservoirs.

Aluminum Simulation Results

Simulations of aluminum concentrations in reservoir 

water columns are integral to determining the dilution factors, 

which are simply the ratios of aluminum concentration in the 

filter-backwash effluent to that of the reservoir. As an example, 

reservoir concentrations were calculated for Quittacas Pond, 

New Bedford, by solving equation 2, with the settling velocity 

determined as in the previous section. Daily values for aluminum concentration were computed for the period of record, 

October 1960 through September 2004. The simulation results 

typically show the aluminum concentration varying substantially with time because of differing input flows to the reservoir and include concentrations above the chronic standard of 

87 μg/L (fig. 8).

The settling velocity was calibrated using data from 5 of 

the 13 reservoirs, so the modeling approach can be verified 

to a degree by comparing predicted and measured aluminum 

concentrations for the remaining 8 application reservoirs. 

Because the Massachusetts Sustainable Yield Estimator data 

extended only through 2004, and our measurements were made 

in the fall of 2009, a time translation was necessary to make the 

comparison. Flows were relatively low in August and September of both 2004 and 2009, so that similar dilution by flow 

might apply. To make the comparisons, averaged simulated data 

from August and September 2004 were compared to the one 

measured data point in fall of 2009 for each reservoir (fig. 9). 

Values below 150 μg/L corresponded well, as indicated by the 

high R-squared value.

There was one outlier site, the unnamed pond at Clinton, 

Mass., which had a measured aluminum value of 221 μg/L 

and simulated aluminum value of 1,000 μg/L. This site also 

had uncertain inflow. The effluent discharge was to a small 

water body immediately below the large dam of the Wachusett 

Reservoir. Substantial flow by leakage from the upper reservoir 

likely occurred that was not accounted for in the Massachusetts 

Sustainable Yield Estimator analysis. The leakage flow could 

have diluted the aluminum concentration that was measured.

Figure 8. Simulated aluminum concentrations for an example reservoir, Quittacas Pond in New Bedford, from 

October 1960 to September 2004, with the chronic standard for aluminum toxicity (87 μg/L) indicated.

0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000

0

50

100

150

Time, in days since October 1, 1960

Aluminum concentrations, in micrograms per liter

Simulation result

Chronic aluminum standard

EXPLANATION
Application of the Dilution-Factor Method to Reservoirs 15

Figure 9. Measured versus simulated aluminum concentrations and equivalence line for fall 2009. Red symbols are for 

reservoirs used to determine settling velocity. Blue symbols are for application reservoirs. Equation represents linear leastsquares fit of data for the aluminum-concentration range of 0–150 micrograms per liter.

0 50 100 150 200 250 300 350 400

0

100

200

300

400

500

600

700

800

900

1,000

Measured aluminum concentrations, in micrograms per liter

Simulated aluminum concentrations, in micrograms per liter

0 50 100 150

0

50

100

150

Measured aluminum concentrations, in micrograms per liter

Simulated aluminum concentrations, 

in micrograms per liter

y = 0.983x + 1.7

R = 0.923

Unnamed pond, Clinton , MA

2

EXPLANATION

Reservoirs used to determine settling velocity 

Application reservoirs
16 Dilution Factors for Discharge of Aluminum-Containing Wastes into Lakes and Reservoirs in Massachusetts

Dilution-Factor Results

As computed by the ratio of discharge concentration to 

reservoir concentration (equation 3), DF values are variable 

and can range over several orders of magnitude (fig. 10). 

Low-Flow Dilution

As explained in the section named “Investigative 

Design,” DF values that represent the least amount of dilution 

are of interest for the purpose of setting discharge permits that 

are protective of the resource. In determining the 7DF10, the 

lowest 7-day average for each year is selected (fig. 11). Next, 

the annual minimum 7-day-average dilution factors are fit to 

a known distribution, so that the value with a 10-year recurrence interval (7DF10) can be selected (fig. 12). The 10-year 

recurrence interval corresponds to an annual nonexceedence 

probability of 10 percent. For simulation data from Quittacas 

Pond, the 7DF10 is 4.80 (fig. 12).

Finding the Maximum Permissible Aluminum 

Discharge

The goal of permitting is to protect water supplies from 

concentrations of aluminum toxic to aquatic life. To achieve 

that, it is important to know the maximum permitted discharge 

that would result, after low-flow dilution, in a reservoir concentration that just meets the standard. Because the DF is the 

ratio of concentrations of aluminum in the effluent to concentrations of aluminum in the reservoir water, the reservoir 

aluminum concentration at the 7DF10 can be computed. That 

concentration for Quittacas Pond is 438/4.80 equals 91.3 μg/L. 

The chronic criterion concentration for aluminum is 87 μg/L; 

therefore, this water supply system is just over the standard 

(by 4.3 μg/L). 

With discharges to streams, equation 3 can be used with 

the 7DF10 to determine the highest allowable aluminum 

discharge, which would be the value of Ce when C is 87 μg/L, 

the chronic limit. Determining how much decrease or increase 

Figure 10. Aluminum-dilution factors and the 7DF10 for filter-backwash effluent for an example reservoir, Quittacas 

Pond in New Bedford, with an effluent concentration of 438 μg/L, measured during fall 2009.

0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000

0

5

10

15

20

25

30

35

40

45

50

Time, in days since October 1, 1960

Dilution factor

7DF10
Application of the Dilution-Factor Method to Reservoirs 17

Figure 11. Annual lowest 

7-day-average dilution 

factors based on simulation 

data for Quittacas Pond, 

New Bedford, and the level 

of the 7DF10 (4.80, from 

fig. 12).

Figure 12. Fit of lowest 

annual 7-day-average 

dilution data to log Pearson 

type III distribution for 

Quittacas Pond, New 

Bedford. The lowest annual 

7-day-average dilution factor 

with a 10-year recurrence 

interval, which is the 7DF10 

value, corresponds to the 

annual nonexceedence 

probability of 10 percent, as 

indicated by the dashed line, 

and is equal to 4.80.

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

0

5

10

15

20

Annual lowest 7-day-average dilution factor

7DF10

Year

Lowest annual 7-day-average dilution factor

Lowest annual 7-day dilution factor

Log-Pearson Type III distribution

7DF10

Annual nonexceedence probability, in percent

100 95 90 80 70 50 30 20 10 5 2

1

10

100

EXPLANATION
18 Dilution Factors for Discharge of Aluminum-Containing Wastes into Lakes and Reservoirs in Massachusetts

is possible for reservoirs is complex, however, because the 

7DF10 may change when the discharge is changed.

For example, when Ce of Quittacus Pond is changed from 

438 to 200 μg/L, the 7-day-average values decrease (fig. 13). 

When fit to the log Pearson type III distribution, the 7DF10 

value is less also (fig. 14). The new 7DF10 is 2.27, which 

corresponds to a reservoir concentration of 200/2.27 equals 

88 μg/L, approximately equal to the chronic standard.

By comparison with the range of reservoir DOC concentrations measured in this study (1.5 to 15.5 mg/L, with a 

3.4 mg/L median), Quittacas Pond has a relatively high DOC 

concentration, 6.9 mg/L and thus high aluminum concentrations and low DFs, and it therefore requires a lower aluminum discharge than currently used to meet the standard. For 

other reservoirs and surface-water supplies with lower DOC 

concentrations, effluent concentrations after low-flow dilution would be expected to result in reservoir concentrations 

that were lower than the chronic standard. For example, the 

7DF10 under the present effluent discharge for South Reservoir is 105, and the associated aluminum concentration in the 

reservoir is 12.5 μg/L. This water supplier could increase the 

aluminum discharge and still be in compliance.

Generally, as concentration of effluent discharged to a 

reservoir is increased, the 7DF10 increases also. However, the 

7DF10 eventually converges on one value in successive model 

runs (fig. 15).

Multiple 7DF10-Ce pairs are thus required to find the one 

that corresponds to the reservoir concentration that is at the 

chronic standard. This computationally demanding requirement is lessened for ranges of Ce

 for which the variation of 

7DF10 with Ce is approximately linear. In those ranges, the 

plot of C versus Ce will also be linear, and the value of Ce that 

will correspond to the chronic standard being met in the reservoir can be determined by interpolation within these linearresponse zones (fig. 16).

Comparison of aluminum concentrations at a permitted discharge with Ce

 equals 200 μg/L and the current discharge with Ce

 equals 436 μg/L are shown for Quittacas Pond 

(fig. 17). At Ce equals 200 μg/L, the simulated concentrations 

are slightly less than at Ce equals 436 μg/L and extend above 

the 87 μg/L limit five times, close to the number that would 

be expected for a 10-year recurrence interval in a 44-year 

record (four).

Once the maximum concentration in effluent that meets 

the water-quality standard in the reservoir has been determined, the value can be converted to a maximum aluminum 

load by multiplying by effluent discharge (table 4).

The key factors that influence the amount of aluminum that can be discharged are summarized in table 4. They 

include the current concentrations of aluminum and DOC 

measured in the reservoir, estimated settling velocity of 

aluminum, current effluent discharge volume, the 7DF10 

that applies to current effluent discharge and the aluminum 

concentration in the effluent, and the 7DF10 and the effluent 

concentration that would apply if the effluent concentration 

were increased to the highest value that still allows the reservoir standard of 87 μg/L to be met. The ratio of the highest 

permissible effluent concentration and the original effluent 

concentration indicates the factor by which the concentration could be increased and still meet the standard (for ratios 

greater than 1) or the factor by which concentration must be 

decreased to meet the standard (for ratios less than 1). Aluminum flux in the discharge is the calculated amount that is permissible for the reservoir standard to be met. The calculated 

permissible aluminum fluxes ranged from 0 to 28 kilograms of 

aluminum per day.

Figure 13. Annual lowest 

7-day-average dilution 

factors based on simulation 

data for Quittacas Pond, 

New Bedford. Blue 

represents filter-backwasheffluent aluminum 

concentration of 200 μg/L 

and black filter-backwasheffluent aluminum 

concentration of 438 μg/L.

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Annual lowest 7-day-average dilution factor

7DF10

7DF10

Year

16

14

12

10

8

6

4

2

0

EXPLANATION

Annual lowest 7-day-average dilution 

factor for effluent concentrations of 

200 micrograms per liter

438 micrograms per liter
Application of the Dilution-Factor Method to Reservoirs 19

Figure 14. Fit of lowest 

annual 7-day dilution 

data to log Pearson 

type III distribution for 

Quittacas Pond, New 

Bedford, for two levels of 

filter-backwash-effluent 

aluminum concentration 438 

and 200 μg/L. The values 

for the 10-year recurrence 

interval, which are the 

7DF10 values, are 4.80 and 

2.27, respectively. 

Figure 15. 7DF10 values 

as a function of aluminum 

concentration in filterbackwash effluent for 

Quittacas Pond, New 

Bedford. Two nearly linear 

regions of the relation 

are identified.

Dilution factor

Annual nonexceedence probability, in percent

100 95 90 80 70 50 30 20 10 5 2

1

10

100

EXPLANATION

Log-Pearson Type III distribution

7DF10 values

Annual 7-day low dilution factor, effluent concentration = 438 μg/L

Annual 7-day low dilution factor, effluent concentration = 200 μg/L

0 2,000 4,000 6,000 8,000 10,000

0

5

10

15

20

25

Aluminum concentrations in effluent, in micrograms per liter

7DF10 dilution factor
20 Dilution Factors for Discharge of Aluminum-Containing Wastes into Lakes and Reservoirs in Massachusetts

Figure 16. Relation 

between filter-backwasheffluent concentration of 

aluminum and the reservoir 

concentration at the 7DF10 

for Quittacas Pond, New 

Bedford. The short dashed 

horizontal red line indicates 

the chronic standard of 

87 μg/L in the reservoir, and 

the dashed vertical red line 

shows the result of 200 μg/L 

for the effluent (Ce) at 

the 7DF10.

Figure 17. Simulated 

aluminum concentrations 

in Quittacas Pond, 

New Bedford, with 

concentrations of aluminum 

in the discharge of 436 

μg/L (red) and 200 μg/L 

(black). The horizontal line 

is the standard for chronic 

aluminum toxicity, 87 μg/L.

0 200 2,000 4,000 6,000 8,000 10,000

50

100

150

200

250

300

350

400

450

500

Aluminum concentrations in reservoir, in micrograms per liter

Aluminum concentrations in effluent, in micrograms per liter

87

0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000

0

50

100

150

Time, in days since October 1, 1960

Aluminum concentrations, in micrograms per liter

Chronic aluminum standard 87 μg/L

Simulated aluminum concentrations 

with 436-μg/L effluent

Simulated aluminum concentrations 

with 200-μg/L effluent

EXPLANATION
Application of the Dilution-Factor Method to Reservoirs 21

Table 4. Highest 7DF10 values, filter-backwash effluent concentrations, and fluxes that meet standards for aluminum discharge in 13 reservoirs of Massachusetts town water supplies.—Continued[m2, square meters; Mgal, million gallons; Mgal/d, million gallons per day; Al, aluminum; μg/L, micrograms per liter; DOC, dissolved organic carbon; mg/L, milligrams per liter; cm/d, centimeters per day; 7DF10, lowest annual 7-day average dilution factor with a recurrence interval of 10 years; Ce, total aluminum concentration in the filter-backwash effluent; kg, kilograms; WTP, water-treatment plant; WTF, water-treatment facility; --, no data; ≤, less than or equal to]

Facility and receiving water

Area (A, in m2) 

and volume 

(V, in Mgal)

Average stream 

discharge (Qs, 

in Mgal/d) and 

Al concentration 

(Cs, in μg/L)

Reservoir 

averages–

DOC (mg/L) 

and Al (μg/L)

Settling 

velocity

(cm/d)

Current 

effluent 

discharge 

(Mgal/d)

7DF10 and associated C

e

 value 

at the current 

discharge

Highest 

7DF10 and 

C

e

 that meet 

standard

C

e

 ratio–

new:old1

Permissible 

aluminum 

flux 

(kg per day)

Andover WTP

Haggetts Pond

A = 916,000 Qs = 6.12 DOC = 4.5 14.5 0.63 81 135 3.1 28

V = 856 C

s

 = 72 Al = 23 3,810 11,700

Ashburnham/Winchendon WTP

Upper Naukeag Lake

A = 1,270,000 Qs = 2.45 DOC = 2.3 23 0.12 62 624 16 24.6V = 1,572 Cs = 72 Al = 25.5 3,390 54,300

Cambridge WTP 

Fresh Pond Reservoir

A = 645,000 Qs = 15.9 DOC = 3.6 18 0.44 66 87 5.2 13V = 1,500 Cs = 17 Al = 17 1,450 7,500

Clinton WTP 

Unnamed pond

A = 16,400 Qs = 0.608 DOC = 1.8 25 0.33 3.7 3.2 0.076 0.34V = 4.58 C

s

 = 13 Al = 221 3,610 276

Clinton WTP run #2 

with increased groundwater flow

15.4 14.4 0.35 1.57

3,610 1,250

Cohasset WTP

Lily Pond

A = 206,000 Qs = 3.07 DOC = 15 0 0.11 2.2 -- Above standard even 

when C

e

 = 0

--

V = 73.5 C

s

 = 206 Al = 351 804

Gardner WTF

Crystal Lake

A = 616,000 Qs = 1.79 DOC = 2.7 21.5 0.59 49 90 4 17V = 746 C

s

 = 74 Al = 13.8 1,900 7,500

Manchester-by-the-Sea and Hamilton WTP 

Gravelly Pond

A = 203,000 Qs = 0.24 DOC = 3 20.3 0.02 51 139 113 0.94V = 327 C

s

 = 10 Al ≤ 6 107 12,200
22 Dilution Factors for Discharge of Aluminum-Containing Wastes into Lakes and Reservoirs in Massachusetts Table 4. Highest 7DF10 values, filter-backwash effluent concentrations, and fluxes that meet standards for aluminum discharge in 13 reservoirs of Massachusetts town water supplies.—Continued [m2, square meters; Mgal, million gallons; Mgal/d, million gallons per day; Al, aluminum; μg/L, micrograms per liter; DOC, dissolved organic carbon; mg/L, milligrams per liter; cm/d, centimeters per day; 7DF10, lowest annual 7-day average dilution factor with a recurrence interval of 10 years; 

Ce, total aluminum concentration in the filter-backwash effluent; kg, kilograms; WTP, water-treatment plant; WTF, 

water-treatment facility; --, no data; ≤, less than or equal to]

Facility and receiving water

Area (A, in m2) 

and volume 

(V, in Mgal)

Average stream 

discharge (

Qs, 

in Mgal/d) and 

Al concentration 

(Cs, in μg/L)

Reservoir 

averages–

DOC (mg/L) 

and Al (μg/L)

Settling 

velocity

(cm/d)

Current 

effluent 

discharge 

(Mgal/d)

7DF10 and associated 

Ce value 

at the current 

discharge

Highest 

7DF10 and 

Ce that meet 

standard

Ce ratio–

new:old1

Permissible 

aluminum 

flux 

(kg per day)

New Bedford

Little Quittacas Pond

A = 1,230,000

Qs = 1.97 DOC = 6.9 5.1 0.32 4.8 52 0.45 0.24

V = 606

Cs = 147 Al = 35 438 200

Northampton WTP

Mountain Street Reservoir

A = 283,000

Qs = 1.07 DOC = 1.7 25.4 0.27 10.7 11 4.3 1.97

V = 327

Cs = 190 Al ≤ 5 233 966

Salem and Beverly Water Supply Board 

Wenham Lake Reservoir

A = 1,030,000

Qs = 8.21 DOC = 4.6 14.1 0.41 17 45 5.8 6.14

V = 1,930

Cs = 83 Al = 12 672 3,900

Weymouth WTP 

Great Pond

A = 2,080,000

Qs = 4.24 DOC = 7.8 1.6 0.15 1.8 -- Above standard even 

when 

Ce = 0

--

V = 1,160

Cs = 286 Al = 102 442

Winchester WTP 

South Reservoir

A = 323,000

Qs = 0.545 DOC = 2.3 23 0.12 115 128 8.5

V = 669

Cs = 10 Al = 12 1,320 11,200 5.07

Worcester WTP

Holden Reservoir #2

A = 214,000

Qs = 1.08 DOC = 1.5 26.2 1 14.5 14.5 1.7 4.8

V = 244

Cs = 21 Al = 32 748 1,260

1 “New” means the 

Ce value that ensures just meeting the standard.
Summary 23

Discussion of Method Applications

Permitted Discharges

Results from the reservoirs simulated indicate that most 

suppliers could be discharging more aluminum in filter backwash than they are now and still meet the chronic standard 

for aluminum. Four reservoirs, however, are at or over the 

standard at the present rate of aluminum discharge. Three 

of these are reservoirs with high DOC concentrations in the 

water column and in tributaries (table 4, appendix 4). Several 

tributaries with high DOC concentrations had aluminum concentrations that were over the chronic standard for aluminum. 

Concentrations of aluminum in reservoirs receiving discharge 

from these tributaries would be greater than the chronic standard even without additional aluminum added from backwash discharges.

The high-aluminum, low-DOC reservoir exception was a 

small pond at the Clinton WTP, not part of the reservoir supply, which received a large aluminum discharge. In this case, 

removal by settling probably occurs, but is overwhelmed by 

the amount of aluminum discharged compared to the small 

area of the pond in which settling could occur. There is further 

discussion of this reservoir below.

Limits to the Applicability of the Method

The model did not apply well to the small pond receiving 

aluminum discharge at Clinton, Mass., the reservoir that plots 

well off the verification curve (fig. 9). The Firm Yield Estimator model likely was not suited for estimating the inflow 

to this reservoir because of substantial groundwater flow. 

Located just below the Wachusett Reservoir Dam, this pond 

likely also received substantial dilution water from leakage 

through the dam that was not accounted for by the Firm Yield 

Estimator model. Increasing the flow through the pond from 

groundwater (run # 2, table 4) by 4.5 million gallons per day 

(Mgal/d) brought the simulated concentration to the level of 

the measured concentration of 221 μg/L. With the extra flow, 

a greater amount of aluminum could be discharged than was 

the case in the original simulation. The second permissible 

aluminum-concentration result is still less than the value currently discharged, however. The increased flow used in the 

second run has not been verified, and thus accurate regulation 

at this site would require more flow investigation.

Environmental Consequences of Aluminum 

Discharges

Potential violations of aluminum concentration standards are primarily associated with reservoirs that have high 

concentrations of DOC. Although the aluminum concentrations in these reservoirs may be above standards, the binding 

with DOC may keep the aluminum from becoming toxic to 

aquatic life (Gundersen and others, 1994). Assessment of toxicity would require site-specific investigations of the effect of 

the water matrix on availability of aluminum to aquatic life.

Summary

A method was developed to assess dilution of the 

aluminum found in filter-backwash effluent discharged to 

reservoirs from water-treatment plants. The method was 

needed to facilitate discharge- permit writing by the Massachusetts Department of Environmental Protection to ensure 

compliance with water-quality standards for aquatic life. The 

method uses a mass-balance equation for aluminum in reservoirs that considers sources of aluminum from groundwater, 

surface water, and filter-backwash effluents and losses due 

to sedimentation, water withdrawal, and spill discharge from 

the reservoir. The method was applied to 13 water-supply 

reservoirs in Massachusetts.

A main result of this investigation was the determination 

that dilution for aluminum discharged to reservoirs depends 

on the concentration discharged, unlike the case generally 

assumed for discharge to streams. This means that a dilution 

factor (DF) value determined for low-flow conditions at one 

effluent concentration cannot be used to determine the effluent concentration that would just meet the standard. A series 

of determinations of dilution at multiple effluent concentrations can lead to a dilution-factor/discharge-concentration 

pair that will meet the standard. Although DF evaluation for 

reservoirs was different from that for streams, the method 

developed here results in protection from concentration 

exceedences above the chronic standard for reservoirs 

equivalent to that for discharge permitting for streams.

Aluminum loss from reservoirs by settling was found to 

be a function of the dissolved organic carbon (DOC) concentration in the reservoir. DOC binds aluminum chemically, 

thereby stabilizing it in the water column. Without stabilization by DOC, aluminum forms a hydroxide precipitate and 

settles out of the water column.

Simulations of aluminum dilution in the 13 reservoirs 

studied indicated that most of the aluminum discharges 

at present meet the chronic standard for aluminum, and 

discharge concentrations in 7 of the reservoirs could be 

increased and still meet the standard. Of the 4 reservoirs 

that do not meet the standard at the present discharge rate, 

2 would not meet the standard even if no aluminum were 

discharged. These were reservoirs with the highest aluminum and DOC concentrations in the water column and 

input streams.
24 Dilution Factors for Discharge of Aluminum-Containing Wastes into Lakes and Reservoirs in Massachusetts

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Appendixes 1–4
26 Dilution Factors for Discharge of Aluminum-Containing Wastes into Lakes and Reservoirs in Massachusetts

Appendix 1. Method for solving for aluminum concentrations in reservoirs 

using the MatLab differential equation solver

Three MatLab files were used: 

1. A file (data_entry2.m) to load data, which reads an Excel file of data and also requires input of the constants of 

equation 2, as described in the documentation after the % symbols;

2. A file (dsol_all2.m) that calls the differential equation, uses the loaded data to solve the equation with the solver, 

and plots the results; and 

3. A file (alode2.m) that defines the differential equation. 

One Excel data-input file is used with a .csv extension. 

The contents of these files are given below. Documentation is provided in the comment statements that are provided after 

the % symbols. 

Implementation involves putting all the files in the same directory and opening the MatLab software in that directory. Enter 

first data_entry2 at the prompt and then dsol_all2. The concentration and dilution results will be graphed and copied into a text 

file called “filea” in the directory that is being used.

MatLab file data_entry2.m [from lily pond]

B = importdata(‘Lily_DailyData_01_05_2010new.csv’,’,’,1);

%data for the time series inputs are loaded from the file named in single

%quotes

for k=1:2:1 %the statement that reads in the data for column 1 in the .csv file above

 B.data(:,k);

end

days=[ans]’; %data is assigned a name of days

for k=3:2:3 %reads in data from the third column

 B.data(:,k);

end

Vo=[ans]’; % data is assigned a name of Vo (for volume each day) 

for k=5:2:5 %fifth column

 B.data(:,k);

end

A=[ans]’; % this is area each day in meters squared

for k=12:2:12 % 12th column

 B.data(:,k);

end

Qsr=[ans]’; % assigned Qsr (daily flow in mgd from upstream reservoir).

Qsr = Qsr.*3.785*1000000; %Qsr is converted to liters per day

for k=14:2:14 % 14 column in liters per day

 B.data(:,k);

end

Qw=[ans]’;%Q Withdawal (Usage)

for k=7:2:7 %7th column in liters per day

 B.data(:,k);

end

Qsp=[ans]’;% reservoir spill discharge

for k=11:2:11 % 11th column in liters per day

 B.data(:,k);

end

Qs=[ans]’;%Q from streams inflowing

for k=9:2:9 % 9th column in liters per day

 B.data(:,k);
Appendix 1. Method for solving for aluminum concentrations in reservoirs using the MatLab differential equation solver 27

end

Qg=[ans]’;%Q of groundwater in

for k=15:2:15 %15th column in liters per day

 B.data(:,k);

end

Qe=[ans]’; %Q effluent--the volume of filter backwash water per day

Cs = 206; %concentration, in micrograms per liter, of aluminum in stream inputs

Cg = 10; %concentration, in micrograms per liter, of aluminum in groundwater inputs

Ce = 804; %concentration, in micrograms per liter, of aluminum in the filter backwash

Csr = 10; %concentration, in micrograms per liter, of aluminum in upstream reservoir 

%water input

vs = 0; % settling velocity in decimeters per day

QsrCsr= Qsr.*Csr; %product of Qet aluminum fluxsr and Csr

QsCs = Qs.*Cs; %product of Qs and Cs

QgCg = Qg.*Cg; %product of Qg and Cg

QeCe = Qe.*Ce; %product of Qe and Ce

Qsv = A.*vs.*100; %product of A, vs, and 100

QCin = QgCg+QsCs+QsrCsr+QeCe; %combined terms of aluminum flux in

Qout = Qw+Qsp+Qsv; %combined terms of flow out (to be multiplied by 

%concentration of aluminum in the reservoir to get aluminum flux)

MatLab file dsol_all2.m [from haggetts]

Vot = linspace(1,17973, 17973);%create Vot days for 1 to 17973--the 

%number from October 1 1960 to December 15, 2009

QCint = linspace(1,17973, 17973); %creates same days as above for QCint

Qoutt = linspace(1,17973, 17973);%creates same days as above for Qoutt

Tspan = [1 17973]; % establishes solving period from t=1 to t=17973

IC = 15; % c(t=0) = 15 micrograms per liter 

sol = ode45(@(t,c) alode2(t,c,days,QCint,QCin,Qoutt,Qout,Vot,Vo),Tspan,IC); 

%sol is the solution of aluminum concentratin in the reservoir over time 

%determined by the MatLab ordinary differential equation solver ode45

x = linspace(1,17973,17973); % makes again the number of that days 

%1990 to 2009

y = deval(sol,x,1); %computes a value of sol (Al concentration) at each day

dil = Ce./y; %computes the dilutions for each day

l_dil = log10(dil); %computes log of the dilution factors

figure %starts a new figure

plot(x,y); %plots aluminum concentration versus day number in the figure

xlabel(‘TIME, IN DAYS SINCE OCTOBER 1, 1960’);

ylabel(‘ALUMINUM, IN MICROGRAMS PER LITER’);

figure %starts a new figure

plot(x,dil) %plots the dilution factor versus the day number

xlabel(‘TIME, IN DAYS SINCE OCTOBER 1, 1960’);

ylabel(‘DILUTION FACTOR’);

a = [x; y; dil; l_dil]’; %creates a, which contains columns of day, 

%aluminum concentration, dilution factor, and log dilution factor

save filea a -ASCII; %saves a in a file called filea

x = linspace(17854,17946,17946); %creates x with values (days) between 

%17854 and 17946, which is when the settling velocity sampling took place

y1 = deval(sol,x,1); %%computes a value of sol (Al concentration) at each day

figure % starts figure 3

plot(x,y1); % plots aluminum concentration in a line for the period 17854 through 17946

xlabel(‘TIME, IN DAYS SINCE OCTOBER 1, 1960’); 

ylabel(‘ALUMINUM, IN MICROGRAMS PER LITER’);

hold on %saves the last figure for the next plotting 

plot(17854,24,’o’,17890,22,’o’,17918,21,’o’,17946,26,’o’); %plots 

%the aluminum concentrations for the sampling
28 Dilution Factors for Discharge of Aluminum-Containing Wastes into Lakes and Reservoirs in Massachusetts

MatLab file alode2.m

function dcdt = alode2(t,c,days,QCint,QCin,Qoutt,Qout,Vot,Vo)

QCin = interp1(days,QCin,t); % Interpolate the data set (days,Qw) at time t

Qout = interp1(days,Qout,t);

Vo = interp1(Vot,Vo,t);

dcdt = (-Qout.*c + QCin)/Vo;% this is the differential equation 

%that is being solved

Sample data from Lily Pond.

day Volume(MG) Volume(L) Area(Mi2) Area(m2) SpillVol(mgd) SpillVol(Lpd) Q(g)(mgd)

 Q(g) 

(Lpd) Q(s)(cfs) Qin(Lpd) SeriesResIn(mgd) Usage)(mgd) Usage(Lpd) Q(e)(Lpd)

1 73.47139 2.78E+08 0.079589 206136 0.295208 1117363 0 0 1.32044 3230556 0 0.406885 1540060 102195

2 73.45528 2.78E+08 0.079589 206136 0 0 0 0 0.830617 2032168 0 0.406885 1540060 102195

3 73.20601 2.77E+08 0.079576 206101 0 0 0 0 0.457888 1120257 0 0.406885 1540060 102195

4 72.92744 2.76E+08 0.079372 205571 0 0 0 0 0.410693 1004792 0 0.406885 1540060 102195

5 72.61159 2.75E+08 0.079143 204979 0 0 0 0 0.375953 919797.2 0 0.406885 1540060 102195

6 72.31863 2.74E+08 0.078884 204308 0 0 0 0 0.375797 919415.6 0 0.406885 1540060 102195

7 72.11263 2.73E+08 0.078643 203685 0 0 0 0 0.457628 1119621 0 0.406885 1540060 102195

8 71.85259 2.72E+08 0.078474 203247 0 0 0 0 0.457368 1118985 0 0.406885 1540060 102195

9 71.55886 2.71E+08 0.078261 202695 0 0 0 0 0.410523 1004375 0 0.406885 1540060 102195

10 71.2386 2.7E+08 0.07802 202070 0 0 0 0 0.3463 847248.8 0 0.406885 1540060 102195

11 70.89884 2.68E+08 0.077757 201389 0 0 0 0 0.346156 846897.3 0 0.406885 1540060 102195

12 70.59151 2.67E+08 0.077478 200667 0 0 0 0 0.346013 846546 0 0.406885 1540060 102195

13 70.27896 2.66E+08 0.077226 200014 0 0 0 0 0.345869 846194.8 0 0.406885 1540060 102195

14 69.9494 2.65E+08 0.076969 199350 0 0 0 0 0.345726 845843.8 0 0.406885 1540060 102195

15 69.61901 2.64E+08 0.076699 198649 0 0 0 0 0.372537 911438.8 0 0.406885 1540060 102195

16 69.47684 2.63E+08 0.076428 197947 0 0 0 0 0.410353 1003959 0 0.406885 1540060 102195

17 69.32189 2.62E+08 0.076311 197644 0 0 0 0 0.457108 1118350 0 0.406885 1540060 102195

18 69.09199 2.62E+08 0.076184 197315 0 0 0 0 0.456849 1117716 0 0.406885 1540060 102195

19 68.93124 2.61E+08 0.075995 196826 0 0 0 0 0.569427 1393147 0 0.406885 1540060 102195

20 72.64468 2.75E+08 0.075863 196485 0 0 0 0 3.983369 9745614 0 0.406885 1540060 102195

21 73.47139 2.78E+08 0.078911 204378 2.854871 10805687 0 0 6.536171 15991235 0 0.406885 1540060 102195

22 73.47139 2.78E+08 0.079589 206136 2.099165 7945341 0 0 4.142661 10135334 0 0.406885 1540060 102195

23 73.47139 2.78E+08 0.079589 206136 1.131916 4284302 0 0 2.604379 6371810 0 0.406885 1540060 102195

24 73.47139 2.78E+08 0.079589 206136 2.14382 8114360 0 0 3.301716 8077898 0 0.406885 1540060 102195

25 73.47139 2.78E+08 0.079589 206136 3.636054 13762464 0 0 4.434658 10849726 0 0.406885 1540060 102195

26 73.47139 2.78E+08 0.079589 206136 1.577989 5972687 0 0 3.301127 8076455 0 0.406885 1540060 102195

(Continues through day 17973)
Appendix 2. Massachusetts water-supply reservoirs not included in the application of dilution factors 29

Appendix 2. Massachusetts water-supply reservoirs not included in the application of dilution factors.

[WFP, water-filtration plant; WTP, water-treatment plant; Permit number, the National Pollutant Discharge Elimination System (NPDES) permit number]

Facility Permit number Receiving water

Latitude 

(decimal 

degree)

Longitude 

(decimal 

degree)

Reason for disqualification from 

dilution-factor investigation

Fitchburg Regional WFP MAG640039 Wyman Pond 42.533 -71.884 Not sampled: Discharge is to a stream 

leading to Wyman Pond, not to Wyman 

Pond directly.

Littleton Spectacle Pond WTP MAG640002 Spectacle Pond 42.564 -71.516 Not sampled: No use of aluminum in 

treatment process.

Peabody Coolidge Avenue WTP MAG64006 Lower Spring Pond 42.506 -70.945 Not sampled: Plant under construction, no 

access or data given.

Peabody Winona Pond MAG640028 Winona Pond 42.535 -71.009 Not sampled: Plant under construction, no 

access or data given.

Randolph WTP MAG640032 Great Pond 42.198 -71.047 Unknown discharge from Braintree and 

not enough Randolph discharge information to model.

Rockport WTP MAG640021 Cape Pond 42.640 -70.629 Not sampled: Discharge is to a wetland 

so that the reservoir simulations would 

not apply.

Rutland WTP MAG640033 Muschopauge Pond 42.383 -71.921 Not sampled: Effluent is discharged to 

an infiltration basin rather than to the 

reservoir.

Westborough WTP MAG640007 Hocomonco Pond 42.272 -71.650 Not sampled: No use of aluminum in 

treatment process.
30 Dilution Factors for Discharge of Aluminum-Containing Wastes into Lakes and Reservoirs in Massachusetts Appendix 3. Bathymetry- and flow-data sources for 13 Massachusetts drinking-water supply reservoirs.—Continued [Data were collected August–November 2009; WTP, water-treatment plant; Mgal/d, million gallons per day; DMR, discharge monitoring report; MassDEP, Massachusetts Department of Environmental Pro- tection; USGS, U.S. Geological Survey; SYE, Massachusetts Sustainable Yield Estimator; WTF, water-treatment facility; %, percent; ~, approximately] Facility Inflows data source/quality notes Effluent flow data source Bathymetry source Andover WTP Haggetts Pond—Receives inflow from Merrimack River diversion and Fish Brook Reservoir. These inflow volumes were obtained from the supplier for the years 2004–2009. Daily data reflect reservoir levels when withdrawals were at the system firm yield of 4.582 Mgal/d until January 2004; after this date, actual monthly diversion and withdrawal were used, until December 2009. Withdrawals after 2004 represent finished flow totals. Based on supplier-provided monthly summary difference for withdrawal and delivery for 2004–2009. Bathymetry provided by supplier. Ashburnham/Winchendon WTP Naukeag Lake—This is a stand-alone reservoir with no water imports from other reservoirs or diversions; there are no groundwater interactions for this reservoir. No information was available regarding the usable capacity for this lake or the intake elevation, so a firm yield could not be determined. Peak-usage factors and one month of daily data from September 2009 were available. The average September finished-withdrawals volume along with the peak-usage factors were used to get average monthly finished withdrawals (considerably lower than actual withdrawals for this lake), and these were used for the entire simulation. Based on DMR sheets to MassDEP. Bathymetry collected by USGS. Cambridge WTP Fresh Pond—Gets water from Stony Brook Reservoir. Several years of daily flow data were available from Stony Brook into Fresh Pond. Simulation was done with withdrawals at the estimated firm yield of 10.879 Mgal/d until January 1, 1991, when actual monthly usage was available from the supplier. Monthly averages were disaggregated into constant daily flow values. From supplier-provided representative (October 2009) backwash average. Bathymetry provided by supplier. Clinton WTP Discharge to unnamed pond—This pond has no withdrawals from it, so the program was run with zero usage. Methodology may not be good for this pond. Anecdotally, this is primarily a groundwater-fed pond with very little inflowing surface water. The firm yield uses a very simplistic groundwater calculation based on change in storage, but since there are no withdrawals, there will be very little change in storage, and therefore, very little groundwater inflow. A full transient groundwater model may be needed for better estimates for this pond. From supplier-supplied pumping rates January 2006 through September 2009. Bathymetry collected by USGS. Cohasset Lily Pond WTP Lily Pond—This reservoir receives water imported from Aaron River Reservoir, but no data on the volume of water that is imported was available. SYE database is incomplete for this reservoir as well, so the simulation was run as a stand-alone reservoir without any imports. Simulation was done using withdrawals equal to the firm yield of 0.432 Mgal/d. Winter and summer estimates of water supplier were less than state value, so used state value. Average from MassDEP DMRs. (Average for January 2009 from supplier: 0.01). Bathymetry collected by USGS. Gardner Crystal Lake WTF Crystal Lake—Receives water pumped from Perley Brook Reservoir. No pumping volumes were available from supplier for Perley Brook. Annual average pumping volumes from SYE wateruse database were used and disaggregated using peak-usage factors for Crystal Lake. Model was run with annual withdrawals set at the firm yield of 1.042 Mgal/d until January 1, 2005. Daily withdrawals from supplier for January 1, 2005–August 31, 2008 were used, and after August 2008, average daily flow values from the supplier were used. Daily difference for supplier provided withdrawal and delivery from 2005 to August 2009, then repeated for 2008 through December 15, 2009. Before 2005, used average of record. Bathymetry provided by supplier. Manchester-by-the-Sea WTP Gravelly Pond—No diversions or water imports. Daily data reflect reservoir levels when withdrawals were at the reservoir firm yield of 0.201 Mgal/d. Effluent volumes came from monthly data for 11 months 

in 2009 from the supplier.

Bathymetry collected 

by USGS.

New Bedford Quittacas WTP Little Quittacas—Spillway elevation estimated from topographic maps. This reservoir receives 

water from Great Quittacas Pond, but no pumping volumes were available for this, so it was run as a stand-alone reservoir, without any water imports. Withdrawals were set at the firm yield of 1.421 Mgal/d.

Daily values for effluent 

volume for 2005–2006 from the supplier.

Bathymetry provided 

by supplier.
Appendix 3. Bathymetry- and flow-data sources for 13 Massachusetts drinking-water supply reservoirs 31

Appendix 3. Bathymetry- and flow-data sources for 13 Massachusetts drinking-water supply reservoirs.—Continued[Data were collected August–November 2009; WTP, water-treatment plant; Mgal/d, million gallons per day; DMR, discharge monitoring report; MassDEP, Massachusetts Department of Environmental Protection; USGS, U.S. Geological Survey; SYE, Massachusetts Sustainable Yield Estimator; WTF, water-treatment facility; %, percent; ~, approximately]

Facility Inflows data source/quality notes Effluent flow data source Bathymetry source

Northampton WTP Mountain Street Reservoir—Does not receive any water from other reservoirs or diversions. 

No value of transmissivity was available for this reservoir, but because only a small portion of the reservoir is in contact with sand and gravel, the model was not very sensitive to this parameter for this reservoir. Simulations for this reservoir were run twice, once with a very low transmissivity and once with a relatively high transmissivity. Reservoir volumes and groundwater volumes were nearly identical for both runs. The final simulation was done with a medium transmissivity of 1,350 ft2/day and withdrawals at the firm yield level of 

0.588 Mgal/d.

Daily values for effluent volume 

for 2008 from the supplier.

Bathymetry provided 

by supplier.

Salem and Beverly Water Supply 

Board

Wenham—Receives water diversions from Longham Reservoir, Putnamville Reservoir, and 

the Ipswich River. Monthly data for these diversion volumes from 2004 to 2008 from supplier and from 1989–1995 from an Ipswich River basin model (Zarriello and Ries, 2000) were averaged for each month. This reservoir is in contact with sand and gravel, but no transmissivity values were available in the hydrologic atlases. MassGIS has a GIS layer of medium- and high-yield aquifers, which intersect part of Wenham Lake. For the rest of the lake, a low-transmissivity area was assumed (less than 1,350), and a rough weighted average was taken. A second run with high transmissivity of 4,000 was completed, which increased the groundwater fluxes by about 50%, but groundwater fluxes are very small compared to other fluxes in the system, so groundwater is not very substantial. Withdrawals were set at 7.992 Mgal/d, which is the firm yield calculated by this model. Note that this is considerably lower than the firm yield calculated by an Ipswich River basin model (Zarriello and Ries, 2000) and also much lower than current water usage (~14 Mgal/d). If the model is run using current usage, it goes dry in the 1960s drought and never recovers. There are multiple reasons why these simulations will be inaccurate for reservoirs like this. The diversions in this system operate under some complex rules which we are not simulating with the firm yield. This will be the case for other reservoir systems such as Holden and Quittacas as well.

One year 2008–2009 of daily 

flow data from the supplier.

Bathymetry collected 

by USGS.

Weymouth Great Pond WTP Great Pond (Weymouth)—This pond receives water pumped from South Cove Reservoir, 

which we are not modeling. The town has 10 years of monthly pumping volumes from South Cove (figure 5 in their firm yield report), but they didn’t give us the numbers. Annual pumping volumes from 2000 to 2004 from the SYE water-use database were used and disaggregated using the peak-usage factors for Weymouth Pond and then further disaggregated from monthly volumes into daily. Reservoir simulation was done with withdrawals set at the system firm-yield level of 3.061 Mgal/d.

One year 2008–2009 of daily 

flow data from the supplier.

Collected for previous 

firm-yield study (Waldron and Archfield, 2006).

Winchester WTP South Reservoir—Run in series with North and Middle Reservoirs. South Reservoir is the 

terminal reservoir. Water from North Reservoir is pumped into Middle Reservoir and then flows by gravity into South Reservoir. The firm yield from each upstream river was used instead of taking the system firm yield entirely from South Reservoir (this is the way the Firm-Yield Estimator tool runs reservoirs in series; this may not be correct for this system).

One year of monthly average 

discharges from the supplier.

Collected for previous 

firm-yield study (Waldron and Archfield, 2006).

Worcester WTP Holden—This reservoir gets a small amount of backwash water from the treatment plant and 

also releases some water back into Holden #1. It can also get water gravity fed from Holden #1, but there’s no volume data for this. Apparently, Worcester Department of Public Works mostly try to keep this reservoir at full pool. Withdrawals are taken out of Holden #1, not Holden #2, so the Firm-Yield Estimator tool was run with 0 water withdrawals from Holden Reservoir #2.

One value of effluent discharge 

(1 Mgal/d) from a diagram from the supplier.

Bathymetry collected 

by USGS.
32 Dilution Factors for Discharge of Aluminum-Containing Wastes into Lakes and Reservoirs in Massachusetts Appendix 4. Water-quality data from 13 Massachusetts reservoirs, influent streams, filter-backwash effluents containing aluminum, and streams sampled during August– November 2009.—Continued [mg/L, milligrams per liter; μS/cm, microsiemens per centimeter; μg/L, micrograms per liter; WTP, water-treatment plant; WTF, water-treatment facility; <, less than; --, no data] Station name Station number Latitude (decimal degrees) Longitude (decimal degrees) Date Time Dissolved oxygen (mg/L) pH, water, unfiltered field (stan- dard units) Specific conductance, water, unfiltered (μS/cm at 25 degrees Celsius) Temperature, water (degrees Celsius) Sampling depth (meters) Aluminum, water, unfiltered recoverable (μg/L) Organic carbon, water, filtered (mg/L) Andover WTP Andover WTF Backwash Effluent 423841071114801 42.645 -71.197 20090818 1330 -- -- -- -- -- 2,190 -- Andover WTF Backwash Effluent 423841071114801 42.645 -71.197 20090923 1330 10.7 6.9 388 -- -- 4,040 -- Andover WTF Backwash Effluent 423841071114801 42.645 -71.197 20091006 1200 7.9 6.7 380 -- -- 4,780 -- Andover WTF Backwash Effluent 423841071114801 42.645 -71.197 20091116 1200 7.9 6.5 370 -- -- 4,220 -- Haggetts Pond Deep Hole 423844071115501 42.646 -71.199 20090818 1200 8.4 7.8 372 -- -- 24 4.7 Haggetts Pond Deep Hole 423844071115501 42.646 -71.199 20090923 1320 9.6 6.9 353 -- -- 22 4.5 Haggetts Pond Deep Hole 423844071115501 42.646 -71.199 20091021 1400 9.8 6.8 347 -- -- 21 4.4 Haggetts Pond Deep Hole 423844071115501 42.646 -71.199 20091118 1330 9.9 7 339 -- -- 26 4.3 Unnamed Tributary at Haggetts Pond 423905071121301 42.651 -71.204 20090818 1100 1.3 6.3 321 -- -- 41 8.7 Unnamed Tributary at Haggetts Pond 423905071121301 42.651 -71.204 20090923 1300 1.1 6.1 409 -- -- 30 6 Unnamed Tributary at Haggetts Pond 423905071121301 42.651 -71.204 20091021 1350 5.3 6.6 471 -- -- 21 4.8 Unnamed Tributary at Haggetts Pond 423905071121301 42.651 -71.204 20091118 1230 5.2 6.6 336 -- -- 77 7.1 Ashburnham/Winchendon WTP Upper Naukeag Lake Deep Hole 423919071552401 42.655 -71.923 20090826 1510 7.8 6.5 49 -- -- 37 2.6 Upper Naukeag Lake Deep Hole 423919071552401 42.655 -71.923 20090922 1210 8.7 6.8 49 -- -- 21 2.3 Upper Naukeag Lake Deep Hole 423919071552401 42.655 -71.923 20091020 1250 11 7 49 -- -- 21 2.2 Upper Naukeag Lake Deep Hole 423919071552401 42.655 -71.923 20091110 1300 11.1 6.1 48 -- -- 23 2.2 Upper Naukeag Lake Treatment Facility Back- wash Effluent 423943071560601 42.662 -71.935 20090826 1400 7.1 6.9 71 -- -- 264 -- Upper Naukeag Lake Treatment Facility Back- wash Effluent 423943071560601 42.662 -71.935 20090922 1240 8.8 7.3 68 -- -- 3,390 -- Upper Naukeag Lake Treatment Facility Back- wash Effluent 423943071560601 42.662 -71.935 20091020 1230 10.4 7.7 62 -- -- 183 -- Cambridge WTP

Stony Brook Diversion Outlet 422248071085701 42.380 -71.149 20090819 1130 6.7 7.2 520 -- -- 24 5Stony Brook Diversion Outlet 422248071085701 42.380 -71.149 20090923 1030 8.3 7.2 621 -- -- 8 4.1Stony Brook Diversion Outlet 422248071085701 42.380 -71.149 20091021 1120 10.4 7.4 611 -- -- 9 3.8Stony Brook Diversion Outlet 422248071085701 42.380 -71.149 20091118 1030 9.4 7.7 458 -- -- 26 5.3
Appendix 4. Water-quality from 13 Massachusetts reservoirs, influent streams, filter-backwash effluents, and streams 33

Appendix 4. Water-quality data from 13 Massachusetts reservoirs, influent streams, filter-backwash effluents containing aluminum, and streams sampled during August–November 2009.—Continued[mg/L, milligrams per liter; μS/cm, microsiemens per centimeter; μg/L, micrograms per liter; WTP, water-treatment plant; WTF, water-treatment facility; <, less than; --, no data]

Station name Station number

Latitude 

(decimal 

degrees)

Longitude 

(decimal 

degrees)

Date Time

Dissolved 

oxygen 

(mg/L)

pH, water, 

unfiltered 

field (standard units)

Specific 

conductance, 

water, 

unfiltered 

(μS/cm at 

25 degrees 

Celsius)

Temperature, 

water 

(degrees 

Celsius)

Sampling 

depth 

(meters)

Aluminum, 

water, 

unfiltered 

recoverable 

(μg/L)

Organic 

carbon, 

water, 

filtered 

(mg/L)

Cambridge WTP—Continued

Cambridge WTF Backwash Effluent 422301071084101 42.384 -71.145 20090819 1240 -- -- -- -- -- 1,080 --Cambridge WTF Backwash Effluent 422301071084101 42.384 -71.145 20090929 0830 -- 6.8 550 -- -- 1,260 --Cambridge WTF Backwash Effluent 422301071084101 42.384 -71.145 20091019 0850 10.2 7.5 574 -- -- 2,440 --Cambridge WTF Backwash Effluent 422301071084101 42.384 -71.145 20091118 1100 10.4 7 564 -- -- 1,030 --Fresh Pond Site Brook at Cambridge, Mass. 422300071091001 42.383 -71.152 20090819 1200 6.6 7.2 519 -- -- 17 --Fresh Pond Site F4 at Cambridge, Mass. 422310071085901 42.386 -71.149 20090819 1215 7 7.2 518 -- -- 17 --Fresh Pond, Deep Hole at Cambridge, Mass. 422305071090001 42.385 -71.149 20090819 1100 7.1 7.2 510 -- -- 17 4.1Fresh Pond, Deep Hole at Cambridge, Mass. 422305071090001 42.385 -71.149 20090923 1020 9.3 7.3 535 -- -- 11 3.5Fresh Pond, Deep Hole at Cambridge, Mass. 422305071090001 42.385 -71.149 20091021 1030 9.7 7.6 556 -- -- 19 3.5Fresh Pond, Deep Hole at Cambridge, Mass. 422305071090001 42.385 -71.149 20091118 1020 9.8 7.6 548 -- -- 21 3.3

Clinton WTP

Clinton WTP Backwash Effluent 422438071420401 42.411 -71.701 20090909 1520 7.7 7.8 166 -- -- 3,610 --Upper Pond Tributary 422442071420001 42.412 -71.700 20090909 1400 8.4 6.7 184 -- -- 13 1.2Small Pond Deep Hole 422443071420301 42.412 -71.701 20090909 1430 7.2 6.7 170 -- -- 221 1.8

Cohasset WTP

Aaron River above Lily Pond 421257070490201 42.216 -70.817 20090924 1140 6.5 6.1 117 -- -- 204 15.2Aaron River above Lily Pond 421257070490201 42.216 -70.817 20091022 1150 8.4 6.2 117 -- -- 202 15.1Aaron River above Lily Pond 421257070490201 42.216 -70.817 20091119 1300 8.6 6.8 115 -- -- 214 14.4Lily Pond Deep Hole 421326070485801 42.224 -70.816 20090924 1130 9.5 7.5 128 -- -- 284 15.5Lily Pond Deep Hole 421326070485801 42.224 -70.816 20091022 1140 10.1 6.5 121 -- -- 357 15.1Lily Pond Deep Hole 421326070485801 42.224 -70.816 20091119 1230 9.0 6.4 119 -- -- 414 14.4Cohasset WTP Backwash Effluent 421334070490601 42.226 -70.818 20090924 1100 5.8 7.1 323 -- -- 827 --Cohasset WTP Backwash Effluent 421334070490601 42.226 -70.818 20091022 1110 9.9 7.9 283 -- -- 781 --Cohasset WTP Backwash Effluent 421334070490601 42.226 -70.818 20091119 1200 10.7 7.8 258 -- -- 380 --
34 Dilution Factors for Discharge of Aluminum-Containing Wastes into Lakes and Reservoirs in Massachusetts Appendix 4. Water-quality data from 13 Massachusetts reservoirs, influent streams, filter-backwash effluents containing aluminum, and streams sampled during August– November 2009.—Continued [mg/L, milligrams per liter; μS/cm, microsiemens per centimeter; μg/L, micrograms per liter; WTP, water-treatment plant; WTF, water-treatment facility; <, less than; --, no data] Station name Station number Latitude (decimal degrees) Longitude (decimal degrees) Date Time Dissolved oxygen (mg/L) pH, water, unfiltered field (stan- dard units) Specific conductance, water, unfiltered (μS/cm at 25 degrees Celsius) Temperature, water (degrees Celsius) Sampling depth (meters) Aluminum, water, unfiltered recoverable (μg/L) Organic carbon, water, filtered (mg/L) Gardner WTF Crystal Lake WTF Backwash Effluent 423459071592101 42.583 -71.989 20090820 1415 7.3 7.2 252 -- -- 1,970 -- Crystal Lake WTF Backwash Effluent 423459071592101 42.583 -71.989 20090922 1100 8.7 7.3 253 -- -- 1,670 -- Crystal Lake WTF Backwash Effluent 423459071592101 42.583 -71.989 20091020 1100 10 8 248 -- -- 2,290 -- Crystal Lake WTF Backwash Effluent 423459071592101 42.583 -71.989 20091110 1030 11.4 7.8 242 -- -- 1,650 -- Crystal Lake Deep Hole 423501071593501 42.584 -71.993 20090820 1300 6.5 7.3 249 27.3 0 21 3 Crystal Lake Deep Hole 423501071593501 42.584 -71.993 20090820 1320 6.8 7.3 249 27.3 1 17 -- Crystal Lake Deep Hole 423501071593501 42.584 -71.993 20090820 1325 6.4 7.2 248 26.4 2 18 -- Crystal Lake Deep Hole 423501071593501 42.584 -71.993 20090820 1330 6.8 7.1 247 25.1 3 13 -- Crystal Lake Deep Hole 423501071593501 42.584 -71.993 20090820 1335 5.8 7 248 24.1 4 12 -- Crystal Lake Deep Hole 423501071593501 42.584 -71.993 20090820 1340 5 6.8 248 23.3 5 10 -- Crystal Lake Deep Hole 423501071593501 42.584 -71.993 20090820 1345 4.8 6.7 248 22.1 6 10 -- Crystal Lake Deep Hole 423501071593501 42.584 -71.993 20090820 1350 4.8 6.5 254 18.2 7 8 -- Crystal Lake Deep Hole 423501071593501 42.584 -71.993 20090820 1355 3.6 6.4 259 14.2 8 9 -- Crystal Lake Deep Hole 423501071593501 42.584 -71.993 20090820 1400 2 6.3 261 11.5 9 10 -- Crystal Lake Deep Hole 423501071593501 42.584 -71.993 20090820 1405 0.2 6.4 269 10 10 10 -- Crystal Lake Deep Hole 423501071593501 42.584 -71.993 20090922 1010 8.5 7.2 244 -- -- 10 2.7 Crystal Lake Deep Hole 423501071593501 42.584 -71.993 20091020 1020 9.8 6.9 243 -- -- 12 2.8 Crystal Lake Deep Hole 423501071593501 42.584 -71.993 20091110 1000 11 7.5 238 -- -- 12 2.7 Perley Brook Diversion Outlet 423525071594401 42.590 -71.996 20090820 1220 2.5 5.8 174 -- -- 132 6.7 Perley Brook Diversion Outlet 423525071594401 42.590 -71.996 20090922 950 7.5 6.6 179 -- -- 81 5.9 Perley Brook Diversion Outlet 423525071594401 42.590 -71.996 20091020 1000 9.5 6.5 194 -- -- 85 5.4 Perley Brook Diversion Outlet 423525071594401 42.590 -71.996 20091110 930 9.8 7.6 190 -- -- 91 6 Tributary 1 Mouth 423527071592301 42.591 -71.990 20090820 1140 7.5 7.1 502 -- -- 43 8.1 Tributary 1 Mouth 423527071592301 42.591 -71.990 20090922 930 9.7 7.5 488 -- -- 18 5.7

Tributary 1 Mouth 423527071592301 42.591 -71.990 20091020 950 12.4 7.7 439 -- -- 52 5.2Tributary 1 Mouth 423527071592301 42.591 -71.990 20091110 900 11.4 7.5 405 -- -- 92 6.5
Appendix 4. Water-quality from 13 Massachusetts reservoirs, influent streams, filter-backwash effluents, and streams 35

Appendix 4. Water-quality data from 13 Massachusetts reservoirs, influent streams, filter-backwash effluents containing aluminum, and streams sampled during August–November 2009.—Continued[mg/L, milligrams per liter; μS/cm, microsiemens per centimeter; μg/L, micrograms per liter; WTP, water-treatment plant; WTF, water-treatment facility; <, less than; --, no data]

Station name Station number

Latitude 

(decimal 

degrees)

Longitude 

(decimal 

degrees)

Date Time

Dissolved 

oxygen 

(mg/L)

pH, water, 

unfiltered 

field (standard units)

Specific 

conductance, 

water, 

unfiltered 

(μS/cm at 

25 degrees 

Celsius)

Temperature, 

water 

(degrees 

Celsius)

Sampling 

depth 

(meters)

Aluminum, 

water, 

unfiltered 

recoverable 

(μg/L)

Organic 

carbon, 

water, 

filtered 

(mg/L)

Manchester by the Sea WTP

Manchester WTP Effluent 423548070482201 42.597 -70.806 20090915 1210 7.5 7.2 177 -- -- 107 --Gravelly Pond Site 1 423552070483501 42.598 -70.810 20090915 1310 8 7.3 159 -- -- <6 2.9Gravelly Pond Deep Hole 423555070483701 42.599 -70.810 20090915 1400 7.8 7.6 160 -- -- <6 3Gravelly Pond Site 2 423601070484001 42.600 -70.811 20090915 1320 7.7 7.4 160 -- -- <6 3.1Fish Brook above Fish Brook Pumping Station 424113071132301 42.687 -71.223 20090819 900 -- -- 175 -- -- 23 10Fish Brook above Fish Brook Pumping Station 424113071132301 42.687 -71.223 20090916 1200 -- 7.7 400 -- -- 71 6.1Fish Brook above Fish Brook Pumping Station 424113071132301 42.687 -71.223 20091014 1200 7 6.8 276 -- -- 44 5Fish Brook above Fish Brook Pumping Station 424113071132301 42.687 -71.223 20091111 1200 6.6 7 513 -- -- 221 8.7Merrimack River at Fish Brook Pumping Station 424113071132601 42.687 -71.224 20090819 910 -- -- 275 -- -- 121 4.1

New Bedford WTP

New Bedford Quittacas WTP Effluent 414703070545401 41.784 -70.915 20090916 1200 8.4 6.1 107 -- -- 438 --Unnamed Diversion Tributary at Mouth 414711070550601 41.786 -70.918 20090916 1400 1.3 5.1 109 -- -- 287 23Little Quittacas Reservoir Raw Water at Tap 414714070545201 41.787 -70.914 20090916 1430 6.5 7 86 -- -- 39 6.7Great Quittacas Tributary 414731070542501 41.792 -70.907 20090916 1240 7.9 6.8 86 -- -- 47 7.1Little Quittacas Reservoir Site 1 414734070551401 41.793 -70.921 20090916 1340 8.3 7.1 84 -- -- 35 6.9Spring Brook Tributary above Culvert 414808070552401 41.802 -70.923 20090916 1310 9.5 6.3 137 -- -- 107 5.6

Northampton WTP

Mountain Street Reservoir Deep Hole 422404072401501 42.401 -72.671 20090910 1200 7 7.2 75 -- -- <5 1.7Northhampton WTP Effluent 422421072401801 42.406 -72.672 20090910 1140 8.2 6.8 57 -- -- 233 --Unnamed Tributary 1 at Mouth 422441072400501 42.411 -72.668 20090910 1300 9.3 7.7 89 -- -- 190 0.9

Randolph WTP

Great Pond Deep Hole 421154071025001 42.198 -71.047 20091006 1510 10.6 7.5 346 -- -- 63 3.8

Salem/Beverly Supply Board

Salem/Beverly WTP Backwash Effluent 423458070532901 42.583 -70.891 20091027 1030 10.1 7.7 379 -- -- 672 --Wenham Lake Deep Hole 423523070532801 42.590 -70.891 20091027 1330 8.5 7.4 328 -- -- 12 4.6Unnamed Tributary 2 423534070540501 42.593 -70.901 20091027 1130 7.2 7.4 392 -- -- 31 8.3North Diversion Inflow 423601070535001 42.600 -70.897 20091027 1100 10 7.5 265 -- -- 12 5.7
36 Dilution Factors for Discharge of Aluminum-Containing Wastes into Lakes and Reservoirs in Massachusetts Appendix 4. Water-quality data from 13 Massachusetts reservoirs, influent streams, filter-backwash effluents containing aluminum, and streams sampled during August– November 2009.—Continued [mg/L, milligrams per liter; μS/cm, microsiemens per centimeter; μg/L, micrograms per liter; WTP, water-treatment plant; WTF, water-treatment facility; <, less than; --, no data] Station name Station number Latitude (decimal degrees) Longitude (decimal degrees) Date Time Dissolved oxygen (mg/L) pH, water, unfiltered field (stan- dard units) Specific conductance, water, unfiltered (μS/cm at 25 degrees Celsius) Temperature, water (degrees Celsius) Sampling depth (meters) Aluminum, water, unfiltered recoverable (μg/L) Organic carbon, water, filtered (mg/L) Weymouth WTP Unnamed Tributary 1 at Mouth 420910070575602 42.153 -70.965 20091022 1440 1.6 4.6 115 -- -- 286 25.9 Weymouth Great Pond Deep Hole 420920070581501 42.156 -70.971 20091022 1400 10.7 7.3 124 -- -- 102 7.8 Weymouth Drinking WTP Effluent 420959070580401 42.166 -70.968 20091022 1310 8 7.2 150 -- -- 442 -- Winchester WTP Winchester WTP Effluent 422627071071401 42.441 -71.121 20090917 1000 9.6 7.3 141 -- -- 1,320 -- Winchester South Reservoir Deep Hole 422639071065601 42.444 -71.116 20090917 1210 7.6 7.2 135 20.5 0 12 2.3 Winchester South Reservoir Deep Hole 422639071065601 42.444 -71.116 20090917 1215 7.7 7 135 20.5 1 10 -- Winchester South Reservoir Deep Hole 422639071065601 42.444 -71.116 20090917 1220 7.6 7 135 20.5 2 10 -- Winchester South Reservoir Deep Hole 422639071065601 42.444 -71.116 20090917 1225 7.5 7 135 20.5 3 10 -- Winchester South Reservoir Deep Hole 422639071065601 42.444 -71.116 20090917 1230 7.3 7 135 20.5 4 10 -- Winchester South Reservoir Deep Hole 422639071065601 42.444 -71.116 20090917 1235 7.4 7 135 20.4 5 11 -- Winchester South Reservoir Deep Hole 422639071065601 42.444 -71.116 20090917 1240 7.3 7.1 134 20.4 6 11 -- Winchester South Reservoir Deep Hole 422639071065601 42.444 -71.116 20090917 1245 5.2 6.5 116 18.2 7 14 -- Winchester South Reservoir Deep Hole 422639071065601 42.444 -71.116 20090917 1250 3.4 6.3 112 13.7 8 10 -- Winchester South Reservoir Deep Hole 422639071065601 42.444 -71.116 20090917 1255 1.9 6.3 114 11.5 9 9 -- Winchester South Reservoir Deep Hole 422639071065601 42.444 -71.116 20090917 1300 0.4 6.4 118 10.2 10 6 -- Winchester South Reservoir Deep Hole 422639071065601 42.444 -71.116 20090917 1305 0.3 6.6 146 9.4 11 <6 -- Winchester Middle Reservoir Outlet 422702071065701 42.451 -71.116 20090917 1140 9.1 7.5 255 -- -- 10 2.7 Worcester WTP Holden 2 Reservoir Deep Hole 421748071520001 42.297 -71.867 20090902 1200 7.4 7.3 100 -- -- 32 1.5 Unnamed Tributary 1 at Holden Reservoir 2 421753071520701 42.298 -71.869 20090902 1140 9.9 7.7 114 -- -- 21 1 Holden 2 WTP Backwash Effluent 421808071520601 42.302 -71.868 20090827 1200 -- 6.9 132 -- -- 748 --
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For more information concerning this report, contact:

Director

U.S. Geological Survey

Massachusetts-Rhode Island Water Science Center

10 Bearfoot Road

Northborough, MA 01532

dc_ma@usgs.gov

or visit our Web site at:

http://ma.water.usgs.gov/
Colman and others—Dilution Factors for Discharge of Aluminum-Containing Wastes into Lakes and Reservoirs in Massachusetts—Scientific Investigations Report 2011–5136

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