U.S. Department of the Interior

U.S. Geological Survey

Estimating Concentrations of Road-Sal

Constituents in Highway-Runoff from 

Measurements of Specific Conductanc

By GREGORY E. GRANATO and KIRK P. SMITH

Water Resources Investigation Report 99-4077

Prepared in cooperation with the

MASSACHUSETTS HIGHWAY DEPARTMENT

Northborough, Massachusetts

1999 
U.S. DEPARTMENT OF THE INTERIOR

BRUCE BABBITT, Secretary 

U.S. GEOLOGICAL SURVEY

Charles G. Groat, Director 

The use of trade or product names in this report is for identification 

purposes only and does not constitute endorsement by the 

U.S. Geological Survey.

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

Chief, Massachusetts-Rhode Island District U.S. Geological Survey

U.S. Geological Survey Information Services

Water Resources Division Box 25286

10 Bearfoot Road Denver, CO 80225-0286

Northborough, MA 01532
Con

CONTENTS

Abstract .............................................................................................................................................................................

Introduction .......................................................................................................................................................................

Field and Laboratory Methods ..........................................................................................................................................

Highway-Runoff Monitoring Records ..............................................................................................................................

Theoretical and Empirical Analyses of Specific Conductance Data .................................................................................

Regression Analysis ................................................................................................................................................

Superposition...........................................................................................................................................................

Concentration Effects ....................................................................................................................................

Other Effects..................................................................................................................................................

Adjusted Superposition ...........................................................................................................................................

Estimation of Road-Salt Constituent Concentrations........................................................................................................

Conclusions .......................................................................................................................................................................

References .........................................................................................................................................................................

FIGURES

1. Map showing location of study area and test sites along State Route 25, southeastern Massachusetts ............

2–4. Graphs showing:

2. Highway-runoff data collected at monitoring station B619 along State Route 25 during 1994 ...............

3. Highway-runoff data collected at monitoring station B619 along State Route 25 during a

winter storm, February 1994 .....................................................................................................................

4. Highway-runoff data collected at monitoring station B619 along State Route 25 during an

antecedent dry period and two summer storms, August 1994...................................................................

5. Scatter-plot matrix showing relations between calcium, sodium, and chloride concentrations, and specific 

conductance in 233 highway-runoff samples collected from August 1988 through March 1995.....................

6–10. Graphs showing: 

6. Measured specific conductance, specific conductance calculated by superposition,

and percent error of calculated values for 233 highway-runoff samples collected from

August 1988 through March 1995 ............................................................................................................

7. Theoretical contribution of the hydrogen and hydroxyl ions and populations (n=15,000) of

pH measurements recorded at two highway-runoff monitoring stations (B619 and D492), 

State Route 25, during 1994......................................................................................................................

8. Attenuation of measured specific conductance by soluble organic compounds .......................................

9. Measured specific conductance, specific conductance calculated by adjusted superposition, and

percent error of calculated values for 233 highway-runoff samples collected from

August, 1988 through March, 1995 ..........................................................................................................

10. Comparison of the predictive ability of adjusted superposition and regression equations 

shown as percent error populations using 233 highway-runoff samples...................................................

TABLES

1. Regression statistics used to compute the line of organic correlation between

the log transformations of specific conductance, calcium, sodium, and chloride...............................................

2. Equivalent ionic conductance at infinite dilution and specific conductance calculated

by superposition from the concentrations of measured constituents in samples of precipitation 

and highway runoff, State Route 25, southeastern Massachusetts, during several storms from 1991 

through 1995 .......................................................................................................................................................
IV Contents

CONVERSION FACTORS AND WATER QUALITY UNITS

CONVERSION FACTORS 

WATER QUALITY UNITS

Chemical concentration is given in units of milligrams per liter (mg/L) or milliequivalents per liter

(meq/L). Milliequivalents per liter are units expressing the number of electron-moles of a solute per

unit volume (liter). A mole is the mass in grams numerically equal to the atomic mass of a given element. Milligrams per liter are units expressing the mass of the solute per unit volume (liter) of water.

Milligrams per liter is equivalent to “parts per million.”

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

Multiply By To obtain

centimeter (cm) 0.3937 inch

liter (L) 0.2642 gallon

kilogram (kg) 2.205 pound avoirdupois

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

°F=1.8°C+32
Ab

Estimating Concentrations of Road-Salt

Constituents in Highway-Runoff from

Measurements of Specific Conductance

By Gregory E. Granato and Kirk P. Smith

Abstract

Discrete or composite samples of highway 

runoff may not adequately represent in-storm 

water-quality fluctuations because continuous 

records of water stage, specific conductance, pH, 

and temperature of the runoff indicate that these 

properties fluctuate substantially during a storm. 

Continuous records of water-quality properties can 

be used to maximize the information obtained 

about the stormwater runoff system being studied 

and can provide the context needed to interpret 

analyses of water samples.

Concentrations of the road-salt constituents 

calcium, sodium, and chloride in highway runoff 

were estimated from theoretical and empirical 

relations between specific conductance and the 

concentrations of these ions. These relations were 

examined using the analysis of 233 highwayrunoff samples collected from August 1988 

through March 1995 at four highway-drainage 

monitoring stations along State Route 25 in southeastern Massachusetts.

Theoretically, the specific conductance of a 

water sample is the sum of the individual conductances attributed to each ionic species in solution—the product of the concentrations of each ion 

in milliequivalents per liter (meq/L) multiplied by 

the equivalent ionic conductance at infinite dilution—thereby establishing the principle of superposition. Superposition provides an estimate of 

actual specific conductance that is within measurement error throughout the conductance range of 

many natural waters, with errors of less than ±5 

percent below 1,000 microsiemens per centimeter 

(μS/cm) and ±10 percent between 1,000 and 

μS/cm if all major ionic constituents are acc

for.

A semi-empirical method (adjusted s

position) was used to adjust for concentratio

effects—superposition-method prediction e

high and low concentrations—and to relate 

sured specific conductance to that calculated 

superposition. The adjusted superposition m

which was developed to interpret the State R

25 highway-runoff records, accounts for co

tions of constituents other than calcium, sod

and chloride in dilute waters. The adjusted 

position method also accounts for the attenu

of each constituent's contribution to conduc

as ionic strength increases. Use of the adjus

superposition method generally reduced pre

error to within measurement error througho

range of specific conductance (from 37 to 5

μS/cm) in the highway runoff samples. The 

of pH, temperature, and organic constituent

the relation between concentrations of disso

constituents and measured specific conduct

were examined but these properties did not 

stantially affect interpretation of the Route 2

set.

Predictive abilities of the adjusted 

superposition method were similar to result

obtained by standard regression techniques

the adjusted superposition method has seve

advantages. Adjusted superposition can be a

using available published data about the 

constituents in precipitation, highway runof

the deicing chemicals applied to a highway
2 Estimating Concentrations of Road-Salt Constituents in Highway-Runoff from Measurements of Specific Conductance

semi-empirical method can be used as a predictive 

and diagnostic tool before a substantial number of 

samples are collected, but the power of the 

regression method is based upon a large number of 

water-quality analyses that may be affected by a 

bias in the data.

INTRODUCTION

Specific conductance is one of the most 

commonly measured and most useful properties of 

water (Miller and others, 1988), but applications of 

relations between the concentrations of chemical 

constituents and specific conductance are not well 

advanced, and many interpretations are qualitative 

(Smedley, 1980). Improved theoretical and empirical 

relations between measured constituent concentrations 

and specific conductance would improve 

interpretations in many hydrologic studies. 

Specific conductance is a physical property of 

aqueous solutions. The ability of pure water to conduct 

an electric current is very low (Hem, 1982). In aqueous 

solutions, electrical current is conducted by charged 

ions moving hydrodynamically through the relatively 

nonconductive solvent (Smedley, 1980; Hem, 1982; 

Miller and others, 1988). The principal factors that 

affect the measured specific conductance of solutions 

include concentrations of dissolved ions; temperature; 

physical and thermodynamic properties of individual 

ions, such as ionic radius, charge, and mobility; 

properties of the solvent, such as viscosity and 

dielectric constant; and ion-ion and ion-solvent 

interactions (Smedley, 1980; Hem, 1982; Miller and 

others, 1988; Greenberg and others 1992). These 

factors, the thermodynamic properties of natural 

waters, and interactions among water molecules and 

dissolved constituents vary as a function of temperature 

and concentration (Harned and Owen, 1958; Smedley, 

1980; Miller and others, 1988; Hughes and others, 

1994). Therefore, prediction of conductivity is 

complicated by variations in the physical and chemical 

properties of natural waters. 

A sound method for interpretation of specific 

conductance in continuous records is needed to 

accurately determine annual salt loads in highway 

runoff. In highway-drainage systems, lack of base 

flow, uncertainty in dates and times of expected 

precipitation, and the short time scale of runoff and the 

“first-flush” phenomenon often preclude a meaningful 

manual-sampling program. Also, flow data are 

for surface-water quality assessments because 

concentrations and resultant loads of many cons

are affected by changes in flow (Norris and othe

1990). 

At monitoring sites, continuous records o

measured water stage and specific conductance 

provide a useful component of water-quality 

monitoring programs if used carefully and calib

by periodic solute analyses. Continuous records 

stage—the measured water level used to calcula

flow—and specific conductance can minimize s

collection and analysis costs and maximize the 

and quantity of information obtained about a sy

(Gurnell and others, 1994). Concentrations and 

of individual ionic constituents may be estimate

continuous records of specific conductance, sta

other physical properties, because, in many hyd

systems, ionic composition remains nearly cons

although concentrations vary with dilution (Lin

1970). Estimates can be made using these conti

records and available water analysis data and(o

knowledge of common sources for ions such as 

salt or naturally occurring minerals. 

The theoretical and empirical methods dev

herein may have other potential uses for estima

loads and concentrations of water-quality const

from continuous records of stage and conductan

collected with automated surface- or ground-wa

monitoring systems. These interpretive method

also be used in a quality-assurance/quality-cont

(QA/QC) program to verify chemical analyses 

discrete water samples (Miller and others, 1988

Results of a laboratory analysis may be examin

calculating a conductance based upon the meas

analytes and comparing this value to the measu

conductance to detect differences that are larger 

expected measurement error. 

The purpose of this paper is to develop an

compare theoretical and empirical methods use

estimate concentrations of the road-salt constitu

calcium, sodium, and chloride on the basis of 

continuous records of specific conductance of h

runoff. Effects of high constituent concentratio

extreme pH (less than 5 or greater than 9 standa

units), fluctuations in temperature, or the presen

organic chemicals in solution on measured 

conductance are also explored to guide choices 

adjustments to the quantitative relations among 

properties and constituents. Use of theoretical a
Introd

42o

73o 72o 71o

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MASSACHUSETTS

41o30'

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50 KILOMETERS

50 MILES

41o47'

41o46'

41o45'

70o40' 70o39' 70o38' 70o37' 70o36' 70o35'

Base from U.S. Geological Survey digital data, 1:25,000, 1991

Massachusetts State Plane

Zone 4151

0 1 MILE

0 1 KILOMETER

empirical methods to estimate conductance from 

measured concentrations of major constituents is also 

discussed for interpretive use and analytical QA/QC. 

The data used in this report were collected in a 

study done by the U.S. Geological Survey (USGS), in 

cooperation with the Massachusetts Highway 

Department (MHD), to investigate the relative 

effectiveness of four highway drainage designs in 

preventing contamination of ground water by road salt 

(Church and others, 1996). For this study, highwayrunoff data were collected from 1987 through 1996. 

The study was conducted along State Route 25 

rural area of southeastern Massachusetts (fig. 1)

Route 25 is a six-lane, asphalt-surfaced highwa

an annual average daily traffic volume of about 

vehicles per day. The highway overlies a sand a

gravel aquifer that is a source of public and agri

water supplies. Continuous records of specific 

conductance and water stage measured in flume

emplaced in the highway drainage system were 

estimate the salt loads in runoff diverted by the 

highway-drainage systems (Church and others, 

Figure 1. Location of study area and test sites A, B, C, and D along State Route 25 in southeastern 

Massachusetts.
4 Estimating Concentrations of Road-Salt Constituents in Highway-Runoff from Measurements of Specific Conductance

FIELD AND LABORATORY METHODS

During the Route 25 study, highway runoff was 

monitored in a calibrated Palmer-Bowlus flume built 

within the trunkline drainage pipe of each system. 

Monitoring probes, including pH, water temperature, a 

low-range [0–10,000 microsiemens per centimeter 

(μS/cm)] and a high-range (0–100,000 μS/cm) 

conductance probe were mounted close to each other in 

a small backwater pool in the approach section of the 

flume. Probes were emplaced about 3 cm below the 

elevation of the flume throat to minimize spatial 

variation, probe fouling, and response time to runoff. 

The intake orifice of the water-sampling apparatus was 

placed immediately downstream of the throat section to 

take advantage of the mixing action of the flume throat.

The monitoring system was controlled by a 

battery-powered datalogger. Stage and water-quality 

probe readings were recorded hourly when there was 

no flow. An increase in measured stage activated the 

program to record stage and water-quality probe 

readings at a minimum frequency of 10 minutes and a 

maximum frequency of 1 minute in response to the rate 

of change in stage and specific conductance. The 

automated sampler was triggered by changes in 

specific conductance while the stage exceeded the 

minimum threshold. Each sample was recorded as a 

sequentially numbered event with collection time and 

probe readings.

Laboratory analyses for dissolved concentrations 

of calcium, sodium, and chloride, and for specific 

conductance were completed for 233 discrete highwayrunoff samples collected in the study area from August 

1988 through March 1995. Salt samples were 

collected from the local MHD maintenance facility and 

some highway-runoff samples were collected for 

analysis of major and trace constituents to characterize 

the road-salt runoff (Granato, 1996). The samples were 

analyzed according to standard methods (Fishman and 

Friedman, 1989) at the U.S. Geological Survey 

National Water-Quality Laboratory in Arvada, 

Colorado. 

The QA/QC program for this study included: 

(1) regular maintenance and calibration of the field 

probes; (2) participation in standard USGS QA/QC 

programs; (3) repetitive laboratory analysis of discrete 

samples; (4) calibration measurements using standard 

solutions; and (5) check measurements using 

independent field and laboratory probes. Analy

methods for determining ionic concentrations w

reported to be accurate to within the range of ±3 

percent for major ions, depending on the ionic 

concentration in solution and the analytical met

used (Fishman and Friedman, 1989). The accu

measurements by the conductance probes, as 

determined from calibration and check measure

was about ±5 to 10 percent for the period of rec

±2 to 5 percent during the period 1993–96.

HIGHWAY-RUNOFF MONITORING 

RECORDS

Stage, specific conductance, pH, water 

temperature, and air temperature were recorded 

continuously at four highway-runoff monitoring 

stations during this study. Changes in measured 

pH, and water temperature were used separate f

together with specific conductance to determine 

type of runoff event and hydrologic response. T

collected during 1994 at monitoring station B6

(fig. 2) were considered typical of highway run

during the study period (Church and others, 199

The hydraulic characteristics of the highw

drainage system were indicated by the record o

stage (fig. 2). The drainage area was a paved hi

surface with runoff contributions from grass sho

and a grass median strip. Therefore, there was 

flow. Runoff events—indicated by spikes on th

of water stage—were caused by either precipita

snowmelt. Runoff changed rapidly with variatio

precipitation (fig. 3).

During the study period, specific conduct

highway runoff ranged from 2.69 to 63,275 μS/

the continuous monitoring records and from 37 

51,500 μS/cm in the 233 discrete highway-runo

samples. By comparison, values of specific 

conductance reported in published materials we

to 3 μS/cm for deionized water (Greenberg and 

1992), 2 to 195 μS/cm for regional precipitation 

and Melching, 1995), 50 to 1,500 μS/cm for po

water (Greenberg and others, 1992), about 

50,000 μS/cm for seawater, and up to 225,000 μ

for brines (Hem, 1992). 
Highway-Runoff Monitoring Re

10

6

8

pH, IN STANDARD UNITS

40

-20

0

20

TEMPERATURE, IN 

DEGREES CELSIUS

J FM AM J J A S O N D

1994

1

100,000

10

100

1,000

10,000

SPECIFIC CONDUCTANCE, 

IN MICROSIEMENS PER CENTIMETER 

0.4

0.2

FLUME STAGE, IN METERS

0 

Water temperature

Mean air temperature

4

Figure 2. Highway-runoff data collected at monitoring station B619 during 1994 along State Route 25, 

southeastern Massachusetts.
6 Estimating Concentrations of Road-Salt Constituents in Highway-Runoff from Measurements of Specific Conductance

10

4

6

8

pH, IN STANDARD UNITS

6

0

2

4

WATER

TEMPERATURE, IN 

DEGREES CELSIUS

2400 0400 0800 1200 1600 2000 2400 0400

24 25

February 1994

20,000

0

10,000

SPECIFIC CONDUCTANCE, 

IN MICROSIEMENS PER 

CENTIMETER 

0.2

0.1

FLUME

STAGE, IN METERS

0 

Figure 3. Highway-runoff data collected at monitoring station B619 along State Route 25, southeastern 

Massachusetts, during a winter storm, February 1994.
Theoretical and Empirical Analyses of Specific Conduc

The chemical characteristics of highway-runoff 

were indicated by the specific-conductance record 

(fig. 2). Application of road salt to the highway before 

or during storms caused large increases of specific 

conductance in highway runoff, as was apparent during 

the last storm in February, 1994 (fig. 3). Measurements 

of runoff quality from many storms, such as the storms 

that began on August 13 and 15, 1994, indicated a first 

flush of water that had a higher specific conductance 

followed by more dilute water (fig. 4), a pattern 

characteristic of many highway drainage systems 

(Barrett and others, 1993). The gradual increase in 

specific conductance between storm events indicated 

evaporative concentration of waters in the small 

backwater pool above the flume throat (fig. 4). In July, 

1994, the flume was drained for maintenance; 

therefore, the probes were dry until the next storm. 

Records of measured pH indicated that runoff 

had substantial in-storm and between-storm variations 

(with measured pH ranging from about 5.1 to 8.0 

standard pH units) but was generally a nearly neutral 

solution (fig. 2). For example, a substantial drop in pH 

(from about 6.8 to 5.5 standard pH units) was recorded 

for the storm on August 13, 1994, but measured pH 

increased (from about 6.3 to 7.0 standard pH units) 

during the next storm (fig. 4). Although the pH record 

in the winter of 1994 for station B619 was incomplete, 

records from past years and other stations indicate that 

road salts did not cause substantial changes in pH of 

highway runoff in the drainage system.

Records of temperatures also were used in the 

interpretation of specific conductance (fig. 2). The 

temperatures of air and runoff-water indicated the type 

of event (rain, snow, or snowmelt), and were essential 

in applying corrections to conductance measurements; 

incorrect temperature compensation can be the greatest 

source of error in conductance measurements (Hem, 

1982). Measured air and runoff temperatures indicated 

a beneficial temperature buffering provided by a buried 

highway-drainage system. During runoff, the flumewater temperature reflected the mean daily outside air 

temperature but not the daily extremes (fig. 2).

THEORETICAL AND EMPIRICAL 

ANALYSES OF SPECIFIC 

CONDUCTANCE DATA

Regression Analysis

Regression analysis, which defines the 

mathematical relation between two (or more) va

is the most commonly used method to relate sp

conductance to concentrations of dissolved 

constituents. Regression results can provide 

reasonable estimates for individual water-qualit

variables in a given system (Hem, 1992). Data 

examined using standard regression techniques, 

misleading preconceptions (Helsel and Hirsch, 

An established regression equation may be used 

monitoring stations in an area, and may be usef

estimation at stations where complete data sets 

available (Cain, 1987). 

Constituents of road salt account for abou

percent of the chemical constituents in highway 

on an annual basis (Harned, 1988). Therefore, 

calcium, sodium, and chloride concentrations a

specific conductance have a high degree of cova

(fig. 5). The regression model known as the lin

organic correlation (Helsel and Hirsch, 1992) w

chosen for use here because it minimizes errors 

the x and y directions, producing a unique equat

can be used to predict either variable from the o

The line of organic correlation follows the form

, 

where

yi is the predicted variable,

y is the mean of the y population,

sign(r) is the sign of the linear correlation coeffi

Sy is the standard deviation of the y popula

Sx is the standard deviation of the x popula

xi is the predictor variable, and

x is the mean of the x population. 

High R-square values and residual plots indicat

excellent predictive abilities for equation variab

presented in table 1. 

yi ( ) – y sign r( )

Sy

Sx

---- xi = × × ( ) – x
8 Estimating Concentrations of Road-Salt Constituents in Highway-Runoff from Measurements of Specific Conductance

300

0

100

200

SPECIFIC CONDUCTANCE, 

IN MICROSIEMENS PER 

CENTIMETER 

0.2

0

0.1

FLUME

STAGE, IN METERS

10

4

6

8

pH, IN STANDARD UNITS

24

16

18

20

22

WATER

TEMPERATURE, IN 

DEGREES CELSIUS

10 11 12 13 14 15

August 1994

Figure 4. Highway-runoff data collected at monitoring station B619 along State Route 25, southeastern 

Massacusetts, during an antecedent dry period and two summer storms, August 1994.
Theoretical and Empirical Analyses of Specific Conduc

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

1 2 3 4 5 0 1 2 3 4 5 -1 0 1 2 3 4

-1

0

0

1

2

3

4

5

0

1

2

3

4

0

1

2

3

4

5 Chloride (mg/L)

S

o

d

i

u

m

(mg/L)

Sodium (mg/L)

C

a

l

c

i

u

m

(mg/L)

Calcium (mg/L)

S

p

e

c

i

f

i

c

C

o

d

a

e

(μS

Regression models also have disadvantages. The 

predictive ability of a regression model is a function of 

the number and distribution of available measurements 

from the population being studied. If used without an 

appreciation for relevant physical principles and a 

knowledge of the data set, regression may be 

misleading or may under-utilize the available data in 

the search for the best interpretation (Helsel and 

Hirsch, 1992). For example, multicollinearity—

the independent variables are correlated among 

themselves (Helsel and Hirsch, 1992)—among 

road-salt constituents calcium, sodium, and chl

would be a problem for interpretations based on 

multiple-linear regression equation that predicts 

specific conductance from measured values of a

constituents. 

Figure 5. Relations between calcium, sodium, and chloride concentrations, and specific conductance in 233 highwa

runoff samples collected from August 1988 through March 1995 along State Route 25, southeastern Massachusett
10 Estimating Concentrations of Road-Salt Constituents in Highway-Runoff from Measurements of Specific Conductance

Superposition

The principle of superposition, Kohlrausch's law, 

states that the specific conductance of dilute 

electrolytic solutions can be calculated as the sum of 

the equivalent ionic conductances of all anions and 

cations in solution (Harned and Owen, 1958; Hem 

1982). The equivalent ionic conductance at infinite 

dilution for each individual ion in solution was derived 

from observations that different combinations of ions 

in electrolytic solutions showed characteristic curves 

that approached asymptotic values with increasing 

dilution (Harned and Owen, 1958). Others also 

developed the principle of superposition using the 

Debye-Hückel model of electrolyte solutions by 

assuming that each ion is a hard sphere migrating in a 

dielectric continuum (Smedley, 1980).

To calculate the specific conductance of an 

aqueous solution by superposition, one simply sums 

the individual conductances attributed to all major 

ionic constituents in solution. The individual 

conductance of each ionic constituent in solution is the 

product of the concentration times the equivalent ionic 

conductance at infinite dilution for that ionic 

constituent. The equation is:

, (2)

where

cc is specific conductance calculated by

superposition, in microsiemens per

centimeter at 25 degrees Celsius;

n is the number of major ions in solution;

ci is the concentration of the ith major ionic

constituent, in milliequivalents per liter; and

eci is the equivalent ionic conductance at infinite

dilution for the ith ionic constituent, in

microsiemen-liters per centimetermilliequivalent at 25 degrees Celsius.

The equivalent ionic conductance at infin

dilution is readily obtainable from published m

for most major constituents in aqueous system

(Harned and Owen, 1958; Lind, 1970; Weast a

others, 1985). Equivalent ionic conductances a

infinite dilution for some major ions are presen

table 2. Although values for some trace elemen

not readily available from published materials, 

minor contribution of trace ions may be ignored 

1970).

Examination of calculated specific-condu

values from analyses of water samples indicate

estimates of measured specific conductance bel

1,000 μS/cm by superposition are accurate whe

complete major ion analysis is available (table 2

this conductance range, the difference between 

calculated and measured specific conductance is 

the error of ±5 percent expected for conductanc

probes (Hem, 1982) and is often close to the err

charge balance of the laboratory analysis. The 

difference between measured and calculated sp

conductance increases with increasing concentr

of dissolved constituents, but does not exceed 1

percent until specific conductance approaches 

4,000 μS/cm. Therefore, superposition provides 

approximation throughout the specific-conducta

range of most natural waters. The difference inc

however, from about 3 percent at a specific 

conductance of 757 μS/cm to about 12 percent 

4,730 μS/cm, and to about 26 percent at 10,190 

indicating that measured specific conductance d

increase linearly with increasing solute concent

(table 2). 

Concentration Effects

Superposition was applied to analyses of 

calcium, sodium, and chloride for 233 highway

samples collected from August 1988 through M

1995 (fig. 6). Plots of calculated specific condu

and the percent error of calculated values over t

range of measured specific conductance indicat

systematic error that varied with concentration. 

500 μS/cm an apparent “low-concentration effe

underestimation of specific conductance—was 

by the omission of major ions other than calciu

sodium, and chloride. Above 2,000 μS/cm, calc

values increasingly overestimated measured spe

conductance, an apparent “high-concentration e

These differences, however, could be explained 

theoretically.

cc ci eci ( ) ×

i = 1

n

= ∑

Table 1. Regression statistics used to compute the line of 

organic correlation between the log transformations of specific 

conductance, calcium, sodium, and chloride

[--, no data]

Constituent Mean Standard 

deviation Pearson’s r R2

Specific conductance 2.92 0.766 -- --

Calcium .755 .630 0.962 0.926

Sodium 2.16 .807 .999 .998

Chloride 2.35 .836 .998 .997
Theoretical and Empirical Analyses of Specific Conduct

Omission of many major constituents in most 

chemical analyses of water samples collected along 

Route 25 accounts for the apparent “low-concentration 

effect” in specific conductance estimates below 

500 μScm (fig. 6). Most chemical analyses included 

only calcium, sodium, and chloride as analytes in water 

samples collected for the Route 25 study. These analyses omitted other major constituents contributed by 

road salt, such as sulfate (Granato, 1996), and the other 

major constituents contributed by precipitation and the 

road surface. When measured specific conductance was 

less than 500 μS/cm, the relative contribution of the 

other major ions to specific conductance was substantial. Therefore, the estimate of total conductance made 

using the superposition method with available highway-runoff analyses of calcium, sodium, and chloride 

was too low, hence, the “low-concentration effect.”

The error was relatively low (±5 five percent) in 

the range of specific conductance from 500 μS/cm to 

2,000 μS/cm (fig. 6). In this conductance range, the 

constituents measured (calcium, sodium and chloride) 

dominate the measured conductance, and attenuating 

effects caused by high concentrations are not yet 

pronounced. 

The “high-concentration effect”—the inc

tendency of the superposition method to over es

measured conductance above 2,000 μS/cm—is 

by physical and chemical changes in solution 

properties with increasing concentrations of sol

this range. As concentrations increase, more ion

complexed, and ionic interference becomes sub

(Harned and Owen, 1958). Attenuation of ionic 

mobility occurs because ion activities decrease 

increases in concentrations (Hamer and DeWane

Smedley, 1980). High concentrations also affec

properties of the solvent, such as the viscosity a

dielectric constant, which also attenuate ionic m

(Harned and Owen, 1958; Smedley, 1980). All 

effects combine to reduce the capability of the i

solution to transport electricity. Therefore, the 

measured conductance will be lower than the 

calculated conductance estimated by superposit

(fig. 6). The “high-concentration effect” is impo

because substantial amounts of road salt are 

transported in highway runoff when the specific 

conductance is above 2,000 μS/cm.

Table 2. Equivalent ionic conductance at infinite dilution and specific conductance calculated by superposition from the 

concentrations of measured constituents in samples of precipitation and highway runoff, State Route 25, southeastern 

Massachusetts, during several storms from 1991 through 1995

[Equivalent ionic conductance at infinite dilution from Weast and others (1985). Two highway runoff samples were collected at different times duri

on February 28, 1995. μS/cm, microsiemens per centimeter at 25 degrees celsius; [(μS L)/(cm meq)], microsiemen-liter per centimeter-milliequiva

degrees celsius; --, no data]

Constituent

Equivalent ionic 

conductance at 

infinite dilution 

[(μS L)/(cm meq)]

Specific conductance calculated by superposition (μS/cm

Precipitation Highway runoff

3/07/91 1/07/95 3/24/93 2/28/95 2

Calcium ............................................... 59.47 0.77 8.03 11.0 148 

Magnesium.......................................... 53.00 1.38 3.18 4.24 19.2 

Sodium ................................................ 50.08 14.4 78.8 283 1,850 

Potassium ............................................ 73.48 .22 1.18 .955 10.2 

Bicarbonate ......................................... 44.50 1.3 -- 7.12 -- 

Hydrogen1 ...........................................

1Concentrations used for calculations were derived from pH.

349.65 .011 .055 .174 .11 

Sulfate ................................................. 80.00 2.9 11.2 15.8 55 

Chloride............................................... 76.31 23.7 123 452 3,230 7,

Fluoride ............................................... 55.40 -- -- .332 -- 

Iron, ferrous......................................... 54.00 -- .27 .108 .216 

Manganese .......................................... 53.5 .054 -- .054 -- 

Total specific conductance

Calculated2 .....................................................................

2Specific conductance is calculated using equation 2.

44.8 225 775 5,310 12,

Measured........................................................................ 44 229 757 4,730 10,

Percent difference

Specific conductance...................................................... 1.8 -1.71 2.41 12.4 

Charge balance............................................................... -6.8 .93 -2.89 -3.64 
12 Estimating Concentrations of Road-Salt Constituents in Highway-Runoff from Measurements of Specific Conductance SPECIFIC CONDUCTANCE CALCULATED USING SUPERPOSITION, IN MICROSIEMENS PER CENTIMETER AT 25 DEGREES CELSIUS

MEASURED SPECIFIC CONDUCTANCE, IN MICROSIEMENS 

PER CENTIMETER AT 25 DEGREES CELSIUS

1:1

Number of samples = 233

PERCENT ERROR OF SPECIFIC 

CONDUCTANCE CALCULATED

USING SUPERPOSITION

10

Residual

10

100,000

100

1,000

10,000

10 100,000 100 1,000 10,000

60

-60

-40

-20

0

20

40

Figure 6. Measured specific conductance, specific conductance calculated by superposition, and 

percent error of calculated values for 233 highway-runoff samples collected along State Route 25, 

southeastern Massachusetts, from August 1988 through March 1995.
Theoretical and Empirical Analyses of Specific Conduct

Other Effects

Concentration effects may not be the only cause 

for error in estimating specific conductances on the 

basis of water-quality data. Other factors include the 

effects of variations in pH and temperature, and the 

effect of organic chemicals on the measured 

conductance. These effects were examined for their 

application to the analysis of data from highway-runoff 

samples.

The effect of extreme pH on measured specific 

conductance can be important because the hydrogen 

ion is five to seven times more conductive than cations 

of comparable charge and size and because the 

hydroxide ion is two to three times more conductive 

than comparable anions (Johnsson and Lord, 1987). 

Mobility of these ions is hypothesized to be higher than 

ions of similar size and charge because proton transfer 

(similar to electron transfer in metals) augments 

hydrodynamic migration (Smedley, 1980). At very 

high salt concentrations (above 1 mol/kg), however, the 

reduced mole fraction of water inhibits this proton 

transfer (Smedley, 1980).

The theoretical contribution of the hydrogen and 

hydroxyl ions is shown in figure 7 with a population of 

about 15,000 pH measurements recorded at two 

highway-runoff monitoring stations along State Route 

25 during 1994. The median pH measured in these two 

drainage systems was slightly below a neutral value of 

7 standard pH units, and the range of pH for most of 

the population of measurements as indicated by the box 

and whisker plots in figure 7, was 6 to 8 standard pH 

units. The magnitude of the theoretical contribution of 

the hydrogen and hydroxyl ions to specific 

conductance in this pH range was less than 0.5 μS/cm 

(fig. 7). The pH effect was not substantial for highway 

runoff monitored along State Route 25, despite the fact 

that regional precipitation was acidic, with a median 

pH of 4.4 (Gay and Melching, 1995).

Temperature compensation can be the greatest 

source of error in the measurement and interpretation 

of specific-conductance data (Hem, 1982). Specific 

conductance increases by about 0.5 to 3 percent per 

degree above zero degrees Celsius because a 

comparable decrease in the viscosity and solvation of 

water increases the hydrodynamic mobility of ions in 

this temperature range (Smedley, 1980; Johnsson and 

Lord, 1987; Miller and others, 1988; Fishman a

Friedman, 1989; Talbot and others, 1990). The 

temperature effect on measured conductivity de

on ion-solvent interactions that vary with 

concentrations and characteristics of different io

solution, and with the temperature (Smedley, 19

These complications make temperature compen

very difficult.

Different methods are available to perform 

necessary temperature compensation. Probes ar

commonly temperature-compensated using the 

documented temperature response of standard 

potassium chloride solutions. These standard 

temperature-compensation methods, however, m

bias measured specific conductance in solutions 

mixed electrolytes (Hem, 1982). The most effec

way to minimize temperature compensation erro

determine a temperature relation for water samp

collected in the study area and to apply the resu

records of uncompensated conductance that are 

calibrated to specific conductance at 25 degrees 

Celsius. Temperature compensation was not a l

source of error in continuous records collected 

State Route 25 because the instruments were ca

routinely at different temperatures, and tempera

buffering by the buried highway-drainage syste

minimized the effect of temperature fluctuation

Organic constituents in solution also can 

substantial effect on measured specific conduct

Organic constituents can attenuate the measure

specific conductance of a solution by inhibiting 

dissociation of electrolytes in water (Harned an

Owen, 1958). Organics that do not dissociate c

current poorly (Greenberg and others, 1992), an

that do dissociate can reduce conductivity by 

complexing with inorganic constituents (Drever

Smedley, 1980).

The potential magnitude of the “organic 

constituent effect” was measured by laboratory 

Equivalent volumes of deionized water (used as 

control to measure the effect of dilution) and re

grade methanol and acetone were added to diffe

samples of 100-, 1,000-, and 10,000-μS/cm pot

chloride specific-conductance standards. After 

volume was added, the specific conductance of 

mixture was measured. The results show that sm
14 Estimating Concentrations of Road-Salt Constituents in Highway-Runoff from Measurements of Specific Conductance

D492

B619

HIGHWAY

STATION

0.01

10,000

0.02

0.05

0.1

0.2

0.5

1

2

5

10

20

50

100

200

500

1,000

2,000

5,000

SPECIFIC CONDUCTANCE, IN MICROSIEMENS PER CENTIMETER 

AT 25 DEGREES CELSIUS

THEORETICAL VALUES

Hydrogen-ion (H+) contribution

Hydroxide-ion (OH-) contribution

Sum of H+ and OH0 2 4 6 8 10 12 14

pH, IN STANDARD UNITS

10th 25th 50th 75th 90th

Percentiles

EXPLANATION

Figure 7. Theoretical contribution of the hydrogen and hydroxyl ions and populations (n=15,000) of pH 

measurements recorded at two highway-runoff monitoring stations (B619 and D492), State Route 25, 

southeastern Massachusetts, during 1994.
Theoretical and Empirical Analyses of Specific Conduct

percentages of these organic constituents in solution 

may substantially decrease measured conductance 

values (fig. 8). However, the magnitude of attenuation 

caused by each different organic constituent depends 

on its particular properties (Harned and Owen, 1958; 

Smedley, 1980). 

The attenuating effect of dissolved organic 

constituents on measured specific conductance was of 

concern because mean concentrations of total organic 

carbon in highway runoff vary from 2.4 to 7.7 percent 

of solution by mass (Barrett and others, 1993). 

Relations between chloride and specific conductance 

for 233 highway-runoff samples collected along State 

Route 25 were compared to relations for 33 samples of 

road-salt solutions created in the laboratory. The 

nonparametric rank sum test was applied to results of 

analysis from the 233 field samples and 33 laboratory 

samples in the specific conductance range from 20 to 

50,000 μS/cm. No significant differences were found 

between the sampled populations at a 95 percent 

confidence interval, indicating no substantial organic 

attenuation for this study site. Particulates bind greater 

than 90 percent of the total organics in highway runoff 

(Barrett and others, 1993), which could have reduced 

organic attenuation of specific conductance at this site. 

Adjusted Superposition

Adjusted superposition, a semiempirical method, 

can improve quantitative relations among estimated 

and measured specific conductance and constituent 

concentrations. Although the effects of pH, 

temperature, and organic constituents in highway 

runoff at the study site did not warrant adjustment, the 

concentration effects shown in figure 6 were 

problematic. A semiempirical method was used 

because the physical phenomena attenuating measured 

conductance could not be adequately quantified using 

purely theoretical approaches (Harned and Owen, 

1958; Smedley, 1980). 

Adjustment for the “low-concentration effect”—

omission of analysis for major constituents other than 

calcium, sodium, and chloride—on calculated specific 

conductance below 500 μS/cm (fig. 6) was 

accomplished by estimating the contribution of the 

other major constituents in precipitation to spec

conductance. The total specific conductance of 

precipitation samples collected along State Rou

ranged from 15 to 80 μS/cm, of which 6 to 21 μ

respectively, was estimated to derive from the o

major constituents. The contribution of the othe

constituents in precipitation collected near the s

area (Gay and Melching, 1995) was estimated t

from about 1.76 to about 68 μS/cm when total 

measured specific conductance ranged from 2 t

μS/cm, respectively. A value of 18.2 μS/cm was 

estimated from median values presented by Gay 

Melching (1995) as the contribution of major io

other than calcium, sodium, and chloride to me

specific conductance in precipitation. This med

chosen because precipitation-quality was simila

both studies and the data of Gay and Melching 

had many more analyses than the limited numb

available from the State Route 25 project data s

Adding this median non-salt contribution to the 

conductance estimated using superposition imp

the predictive capability of the equation betwee

and 500 μS/cm (fig. 9). 

Empirical relations were used to account 

high-concentration effects—attenuation of the 

contribution to conductance by each constituen

ionic strength increases—because quantitative 

information (including details about inter-ionic 

and water/solute interactions for the solution in 

question) is usually not available. Therefore, a 

regression analysis was used to relate measured 

estimated specific conductance values to the res

difference between measured and estimated val

This regression analysis provided the neccessar

information to formulate the equations for adju

superposition. Regression equations were deve

using the ordinary least squares method. It was 

appropriate to fix the intercept at zero because t

covered several orders of magnitude and the 

attenuation of each constituent's conductance at 

dilution approaches zero with decreasing ionic 

strength. The independent variable was transfor

the three-halves power to linearize the residuals 

improve homoscedasticity (Helsel and Hirsch, 
16 Estimating Concentrations of Road-Salt Constituents in Highway-Runoff from Measurements of Specific Conductance

0 0.05 0.10 0.15 0.20 0.25

FRACTION OF DEIONIZED WATER OR ORGANIC COMPOUND 

IN SOLUTION

0.50

1.05

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

FRACTION OF INITIAL SPECIFIC CONDUCTANCE

Deionized water--100 μS/cm

Deionized water--1,000 μS/cm

Deionized water--10,000 μS/cm

Acetone--100 μS/cm

Acetone--1,000 μS/cm

Acetone--10,000 μS/cm

Methanol--100 μS/cm

Methanol--1,000 μS/cm

Methanol--10,000 μS/cm

Figure 8. Attenuation of measured specific conductance by soluble organic compounds.
Theoretical and Empirical Analyses of Specific Conduct

10

100,000

100

1,000

10,000

SPECIFIC CONDUCTANCE CALCULATED USING

ADJUSTED SUPERPOSITION , IN MICROSIEMENS

PER CENTIMETER AT 25 DEGREES CELSIUS

10 100,000 100 1,000 10,000

MEASURED SPECIFIC CONDUCTANCE, IN MICROSIEMENS

 PER CENTIMETER AT 25 DEGREES CELSIUS

1:1

Number of samples = 233

-60

60

-40

-20

0

20

40

PERCENT ERROR OF SPECIFIC 

CONDUCTANCE CALCULATED 

USING ADJUSTED SUPERPOSITION

Residual

Figure 9. Measured specific conductance, specific conductance calculated by adjusted superposition, 

and percent error of calculated values for 233 highway-runoff samples collected along State Route 25, 

southeastern Massachusetts, from August 1988 through March 1995.
18 Estimating Concentrations of Road-Salt Constituents in Highway-Runoff from Measurements of Specific Conductance

The adjusted superposition equation developed 

by combining the empirical regression and the 

contributions from precipitation are:

, (3)

where

ce is the specific conductance calculated by

adjusted superposition, in 

microsiemens per centimeter at 25

degrees Celsius;

cc is specific conductance calculated by

superposition (equation 2), in 

microsiemens per centimeter at 

25 degrees Celsius;

co is the specific conductance from

constituents not analyzed; in this case,

18.2 microsiemens per centimeter at 

25 degrees Celsius.

Also, when the results of analysis are 

suspect, it would be desirable to check the 

analysis and(or) the measured specific 

conductance as a QA/QC measure. The 

equation:

, (4)

where

cm is the measured specific conductance, in

microsiemens per centimeter at 

25 degrees Celsius, 

may be used to relate the measured conductance 

to the theoretical specific conductance 

calculated by superposition.

Specific conductance may be estimated 

accurately from analysis of the major 

constituents of road salt (calcium, sodium, and 

chloride), if corrections are made for the major 

constituents omitted in the water analysis and 

for attenuating effects caused by increasing 

concentration. Estimates of specific 

conductance by adjusted superposition match 

closely the corresponding measured 

conductances (fig. 9). The adjustments improve 

the relation shown in figure 6, eliminating 

systematic error and generally reducing random 

ce cc 0.00097 cc

3/2 = – × + co

cc cm 0.00137 cm

3/2 = + × – co

error to within ±5 percent (the accuracy expected of fie

specific-conductance measurements). The error still ev

the estimated specific-conductance values below 100 μ

can be attributed to variations in precipitation chemistr

effect on specific conductance increases as the effect o

salt constituent concentrations decreases.

ESTIMATION OF ROAD-SALT CONSTITUE

CONCENTRATIONS 

Specific-conductance records were used to calcu

concentrations of calcium, sodium, and chloride to det

road-salt loads in highway runoff. First, adjusted 

superposition (equation 4) was used to convert the mea

specific conductance value (cm) to an equivalent calcu

conductance value (cc). Then, concentrations of each i

estimated from the calculated conductance value (cc). 

equation to determine constituent concentrations from 

calculated conductance value includes three unknowns 

(concentrations of calcium, sodium, and chloride). 

The equations used to estimate constituent 

concentrations from the calculated conductance can be 

with information about the chemical composition of th

water (in this case it was road salt in highway runoff). 

equations used to derive each constituent from the calc

conductance (eq. 4) are as follows:

, 

, 

and

where

cc is specific conductance calculated by

superposition, in microsiemens per

centimeter at 25 degrees Celsius;

Ca is the molar concentration of calcium;

Na is the molar concentration of sodium;

Cl is the molar concentration of chloride;

Rca is the molar ratio of calcium to chloride, which

varies with measured specific conductance;

Rna is the molar ratio of sodium to chloride, 

Ca Rca Cl = ×

Na Rna Cl = ×

Cl cc = ( ) ÷ [ ( ) Rna Cna × + + ( ) Rca Cca × ( 1 × C
Estimation of Road-Salt Constituent Concentra

(about 0.958); 

Cca is the equivalent conductance at infinite

dilution of calcium;

Cna is the equivalent conductance at infinite

dilution of sodium; and

Ccl is the equivalent conductance at infinite

dilution of chloride (equivalent conductances

at infinite dilution are reported in table 2).

The ratios of sodium to chloride and calcium to 

chloride in the highway-runoff samples were used to 

determine the concentration of each constituent in 

solution because the data were available. In the 

absence of an extensive data set, median ratios of 

calcium and sodium to chloride in samples of road salt 

(Granato, 1996) could be used to estimate 

concentrations of calcium, sodium, and chloride in 

highway runoff from measured specific-conductance 

records. 

The ratio of sodium to chloride in the highwayrunoff samples was relatively constant over the entire 

range of specific conductance (fig. 5). The median 

molar ratios for sodium to chloride in seawater (Hem, 

1992), regional precipitation (Gay and Melching, 

1995), road-salt samples (Granato, 1996), and the 

highway-runoff samples from the study area were 

0.852, 0.906, 0.958, and, 0.963, respectively. The ratio 

of sodium to chloride was relatively constant even in 

low-conductance highway runoff because precipitation 

at the study site was affected by the sodium chloride 

from seawater. Therefore, the median ratio of sodium 

to chloride either in the road-salt samples or in the 

highway-runoff samples could be used to estimate the 

relation between sodium and chloride in highway 

runoff. 

Calcium had greater variance and lower 

concentrations than was measured for sodium and 

chloride in highway runoff samples (fig. 5). In the 

study area, calcium chloride generally was applied to 

the highway surface in a premix of 80 percent sodium 

chloride and 20 percent calcium chloride by mass 

(Church, and others, 1996). During winter storms, 

sodium chloride, premix, or both may have been 

applied to the highway. The molar ratio of calcium to 

chloride was 0.0075 in sodium chloride and 0.097 in 

the premix used during the study (Granato, 1996). 

Calcium represented only about 2 percent by mass of 

the deicing-chemicals spread each year because 

infrequent use of the calcium chloride premix. 

median molar ratio of calcium to chloride in th

highway-runoff samples was 0.022, and about 

percent of the deicing chemicals measured. Th

ratio of calcium to chloride varied substantially 

coastal precipitation (between 0.009 and 0.06 f

Gay and Melching, 1995) but was generally hig

than in seawater (0.019 from Hem, 1992). Also

concrete drainage system may have been a sour

calcium in dilute waters. In highway-runoff sa

the molar ratio of calcium to chloride in the rang

to 200 μS/cm, 200 to 1,000 μS/cm, 1,000 to 6,0

cm, and greater than 6,000 μS/cm were 0.038, 0

0.020, and 0.0075, respectively. These ratios sh

transition from the median precipitation ratio o

0.048 at low specific-conductance values to the 

found in sodium-chloride road salt in the highe

conductance range. 

The relative precision and accuracy of 

calculations using adjusted superposition (eqs. 

and 7) were compared to the regression equatio

(eq. 1) graphically (fig. 10) and statistically usi

nonparametric Wilcoxon rank sum test. The est

of chloride concentrations by adjusted superpo

were significantly different and are slightly bett

estimates from regression at a 95-percent confi

interval. The differences in predictive capabilit

adjusted superposition and regression for speci

conductance and the constituents sodium and c

were not significantly different at a 95-percent 

confidence interval. 

Although the predictive abilities for regre

and adjusted superposition for this data set wer

generally equivalent, the predictive ability of a 

regression relation is a function of the number 

distribution of available measurements from the 

specific-conductance population studied. Adju

superposition, however, can provide reasonable 

estimates of expected specific-conductance valu

constituent concentrations from available inform

describing the composition of road salt, precipi

and natural waters reported in published materi
20 Estimating Concentrations of Road-Salt Constituents in Highway-Runoff from Measurements of Specific Conductance

CONCLUSIONS

Highway-runoff monitoring records indicate that 

in highway-drainage systems, the lack of base flow, 

uncertainty in dates and times of expected 

precipitation, the short time scale of runoff, and the 

first flush-phenomenon may preclude a meaningful 

manual sampling program. Runoff records show 

substantial fluctuations in measured stage, specific 

conductance, pH, and temperature throughout the 

course of each storm. Continuous records of these 

water-quality properties provide the context needed to 

interpret analyses of discrete samples. Therefore, 

results of manual- or automatic-sampling programs 

may be questionable without a supporting record of 

real-time measurements.

Concentrations of calcium, sodium, and 

chloride—dissolved constituents of road salt—can be 

estimated in real time for the interpretation of highwayrunoff monitoring records using theoretical and 

empirical relations between specific conductance and 

constituent concentrations. If used carefully an

calibrated by periodic solute analyses, continuo

records of stage and specific conductance can b

to maximize the information obtained about the 

hydrologic system being studied while minimiz

costs of sample collection and analysis.

If information is known about the major 

constituents in the source water, and about the s

of contaminants—either from published materi

from a sampling program—superposition can b

to provide an accurate estimate for relations bet

constituent concentrations and specific conduct

Briefly, the principle of superposition states tha

electrical conductance measured in a water sam

function of the sum of the conductances of all i

constituents in solution. Relations between mea

specific conductance and estimated constituent 

concentrations can be formulated using periodi

quality analyses, or by using information about 

composition of road-salt used in the study area 

sufficient water-quality analyses are not availab

SCl RCl SNa RNa SCa RCa SSpC RSpC

SAMPLES OF ESTIMATED CONCENTRATIONS

-50

80

-40

-20

0

20

40

60

ERROR OF ESTIMATE, IN PERCENT

EXPLANATION

10th percentile

25th percentile

Median

75th percentile

90th percentile

SCl

RCl

SNa

RNa

SCa

RCa

SSpC

RSpC

Chloride by adjusted 

superposition

Chloride by

regression

Sodium by adjusted

superposition

Sodium by

regression

Calcium by adjusted

superposition

Calcium by

regression

Specific conductance b

adjusted superpositio

Specific conductance b

regression

Figure 10. Comparison of the predictive ability of adjusted superposition and regression equations shown as percent 

error populations using 233 highway-runoff samples collected along State Route 25, southeastern Massachusetts.
Refere

Superposition can provide an estimate that is within 

measurement error throughout the specificconductance range of many natural waters (with errors 

of less than ±5 percent below 1,000 μS/cm and ±10 

percent below 4,000 μS/cm) if all major ionic 

constituents are measured. 

Adjusted superposition can be used when the 

sources of constituents are not fully characterized, or 

when solutions of high conductance (greater than 

4,000 μS/cm) are studied. For example, the median 

contribution of constituents other than calcium, 

sodium, and chloride from published values for 

regional precipitation (about 18.2 μS/cm) was used to 

estimate conductance in highway runoff, and this 

correction reduced error substantially when 

conductance values were below 500 μS/cm. Adjusted 

superposition can also be used to reduce error when 

measured specific conductances are large. In this 

study, adjusted superposition generally reduced the 

error of estimates from specific conductance to ±10 

percent or less for runoff with high ionic strengths. 

Other factors, including temperature, pH, and the 

presence of organic constituents in solution, may have 

a substantial effect on the relation between 

concentrations of dissolved constituents and measured 

specific conductance. These other factors did not seem 

to affect relations between concentrations of dissolved 

ions and specific conductance of highway runoff in this 

study.

Although the predictive abilities for regression 

analysis and adjusted superposition are generally 

equivalent, regression analysis requires an extensive 

data set that may be expensive and time-consuming to 

obtain. In addition, analytical errors may define the 

regression model, and omissions of important 

constituents cannot be detected by regression. The 

predictive ability of regression requires many waterquality analyses over the expected range of specific 

conductance, whereas superposition can provide a 

close approximation of relations between conductance 

and water-quality characteristics using the molar ratios 

of constituents and other information available in 

published materials. Measurements and estimates of 

specific conductance can be compared to check waterquality analyses as samples are obtained and analyzed. 

Superposition is not affected by analytical errors that 

may define a regression model. Values for estimated 

specific-conductance that are substantially lower than 

measured values may indicate that an important 

constituent (or constituents) has been omitted in 

water-quality analysis. 

REFERENCES

Barrett, M.E., Zuber, R.D., Collins, E.R., III., Malin

Jr., Charbeneau, R.J., and Ward, G.H., 1993, A 

and evaluation of literature pertaining to the qu

and control of pollution from highway runoff a

construction: Bureau of Engineering Research, 

University of Texas at Austin, Report CRWR-2

140 p.

Cain, D., 1987, Relations of specific conductance to 

streamflow and selected water-quality character

the Arkansas River Basin, Colorado: U.S. Geol

Survey, Water-Resources Investigations Report 

4041, 93 p. 

Church, P.E., Armstrong, D.S., Granato, G.E., Stone

Smith, K.P., and Provencher, P.L., 1996, Effect

of highway-drainage systems in preventing 

contamination of ground water by road salt, Ro

Southeastern Massachusetts–description of stud

data collection programs, and methodology: U.

Geological Survey Open-File Report 96-317, 7

Drever J.I., 1988, The geochemistry of natural water

ed.): Englewood Cliffs, N.J., Prentice Hall, 437 

Fishman, M.J. and Friedman, L.C., (eds.), 1989, Met

determination of inorganic substances in water 

fluvial sediments: U.S. Geological Survey Tech

of Water-Resources Investigations, book 5, cha

545 p.

Gay, F.B. and Melching, C.S., 1995, Relation of 

precipitation quality to storm type, and constitu

loads in Massachusetts, 1983-85: U.S. Geologi

Survey Water-Resource Investigations Report 9

82 p.

Granato, G.E., 1996, Deicing chemicals as a source 

constituents in highway runoff: Transportation 

Research Record 1533, p. 50–58.

Greenberg A.E., Clesceri L.S., Eaton A.D., and Fran

M.A.H. (eds.), 1992, Standard methods for the 

examination of water and wastewater (18th ed.

Washington, D.C., American Public Health Asso

American Water Works Association, Water 

Environment Federation, 1100 p.

Gurnell, A.M., Brown G.H., and Tranter, M., 1994, 

Sampling strategy to describe the temporal 

hydrochemical characteristics of an alpine prog

stream: Hydrological Processes, v. 8, p. 1–25.
22 Estimating Concentrations of Road-Salt Constituents in Highway-Runoff from Measurements of Specific Conductance

Hamer, W.J., and DeWane, H.J., 1970, Electrolytic 

conductance and the conductances of the halogen acids 

in water: National Standards Reference Data Service, 

National Bureau of Standards (U.S.) NSRDS-NBS-33, 

37 p.

Harned, D.A., 1988, Effects of highway runoff on 

streamflow and water quality in the Sevenmile Creek 

Basin, a rural area in the Piedmont Province of North 

Carolina, July 1981 to July 1982: U.S. Geological 

Survey Water-Supply Paper 2329, 105 p.

Harned, H.S., and Owen, B.B., 1958, The physical chemistry 

of electrolytic solutions (3rd ed.): New York, Reinhold 

Publishing Corporation, 803 p.

Helsel, D.R., and Hirsch, R.M., 1992, Statistical methods in 

water resources: New York, NY, Elsevier, 522 p. 

Hem, J.D., 1982, Conductance: a collective measure of 

dissolved ions: in R.A. Minear and L.A. Keith (eds.), 

Water Analysis, v. 1., part 1. Inorganic Species, New 

York, NY, Academic Press, p. 137–161.

Hem, J.D., 1992, Study and interpretation of the chemical 

characteristics of natural water (3rd ed): U.S. 

Geological Survey Water-Supply Paper 2254, 263 p.

Hughes, S.G., Taylor, E.L., Wentzell, P.D., McCurdy, R.F., 

and Boss, R.K., 1994, Models for conductance 

measurements in quality assurance of water analyses: 

Analytical Chemistry, v. 66, no. 6, p. 830–835.

Johnsson, P.A., and Lord, D.G., 1987, A computer p

for geochemical analysis of acid-rain and other 

ionic-strength, acidic waters: U.S. Geological S

Water-Resources Investigations Report 87-4095

Lind, C.J., 1970, Specific conductance as a means o

estimating ionic strength: U.S. Geological Surv

Professional Paper 700-D, p. D272-280. 

Miller, R.L., Bradford, W.L., and Peters, N.E., 1988, 

conductance: theoretical considerations and app

to analytical quality control: U.S. Geological S

Water-Supply Paper 2311, 16 p.

Norris, J.M., Hren, J., Myers, D., Chaney, T.H., and 

Childress, C.J.O., 1990, Water-quality data-col

activities in Colorado and Ohio—Phase III, Ev

of existing data for use in assessing regional 

water-quality conditions and trends: U.S. Geolo

Survey Open-File Report 89-391, 63 p.

Smedley, S.I., 1980, The interpretation of ionic cond

in liquids: New York, Plenum Press, 195 p.

Talbot, J.D.R., House, W.A., and Pethybridge, A.D., 

Prediction of the temperature dependence of el

conductance for river waters: Water Research, v

no. 10, p. 1295–1304.

Weast, R.C., Astle, M.J., and Beyer, W.H., 1985, CR

handbook of chemistry and physics: Bocca Rat

CRC Press, 2290 p.
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