Methods to Identify Changes in Background 

Water-Quality Conditions Using DissolvedSolids Concentrations and Loads as 

Indicators, Arkansas River and Fountain 

Creek, in the Vicinity of Pueblo, Colorado

By Roderick F. Ortiz

U.S. Department of the Interior

U.S. Geological Survey

Prepared in cooperation with the

SOUTHEASTERN COLORADO WATER ACTIVITY ENTERPRISE

Scientific Investigations Report 2004–5024
U.S. Department of the Interior

Gale A. Norton, Secretary

U.S. Geological Survey

Charles G. Groat, Director

U.S. Geological Survey, Reston, Virginia: 2004

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

Box 25286, Denver Federal Center

Denver, CO 80225

For more information about the USGS and its products:

Telephone: 1-888-ASK-USGS

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

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

endorsement by the U.S. Government.
Contents iii

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

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

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

Description of the Study Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Determination of Background Water-Quality Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Indicator Parameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Selection of Background Periods from Available Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Comparison of Background Periods to Historical Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Variability Within the Background Concentrations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Identification of Short-Term Changes in Water Quality Using Dissolved-Solids Concentrations 

and Loads. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Tolerance Limits for Dissolved-Solids Concentration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Tolerance Limits for Flow-Adjusted Dissolved-Solids Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Tolerance Limits for Estimated Dissolved-Solids Load. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Identification of Long-Term Changes in Water Quality Using Dissolved-Solids Load . . . . . . . . . . . . . . . . . . . . . . . . . 14

Comparison of Cumulative Load at Selected Sites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Comparison of Percent Contribution of Load from Selected Sites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Comparison of Unmeasured Load from Other Sites. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

References Cited. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Figures

1. Map showing location of study area and selected surface-water and water-quality sites. . . . . . . . . . .2

2. Bar graphs showing annual streamflow at Arkansas River near Avondale, Colorado, 

1975–2002 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

3. Boxplot showing comparison of instantaneous specific-conductance data at selected 

sites on the Arkansas River, 1975–1985 and 1986–2001, and at Fountain Creek at Pueblo, 

1982–1985 and 1986–2001. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7

4–11. Graphs showing:

4. Variability of estimated daily mean dissolved-solids concentrations during background 

period at selected sites on the Arkansas River and Fountain Creek. . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

5. Tolerance limits for estimated dissolved-solids concentrations at selected sites on the 

Arkansas River and Fountain Creek. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

6. Comparison of estimated daily dissolved-solids concentrations in 2002 with maximum 

concentrations during background periods and calculated tolerance limits at 

selected sites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

7. Tolerance limits on flow-adjusted dissolved-solids concentration data at selected 

sites on the Arkansas River and Fountain Creek with comparisons to flow-adjusted 

concentrations for 2002. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

8. Tolerance limits on dissolved-solids load at selected sites on the Arkansas River 

and Fountain Creek. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

9. Comparison of cumulative dissolved-solids loads at Arkansas River above Pueblo 

and Fountain Creek at Pueblo to cumulative dissolved-solids load at Arkansas River 

near Avondale, 1986–2001 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

10. Percent contribution of dissolved-solids loads from Arkansas River above Pueblo 

and Fountain Creek at Pueblo to dissolved-solids load at Arkansas River near 

Avondale, 1986–2001 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

11. Percent contribution of dissolved-solids load from unmeasured sources to 

dissolved-solids load at Arkansas River near Avondale, 1986–2001. . . . . . . . . . . . . . . . . . . . . . . . . . . 18
iv 

Tables

1. Period of record for daily specific conductance and streamflow, years used to 

define background and test period, and percentage of background data reported 

as missing at selected sites in the Arkansas River and Fountain Creek in the 

vicinity of Pueblo, Colorado . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3

2. Least-squares regression equations to estimate dissolved-solids concentration from 

specific conductance for selected sites in the lower Arkansas River Basin in the 

vicinity of Pueblo, Colorado . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5

3. Regression-model coefficients for estimation of daily specific conductance from 

streamflow at selected sites on the Arkansas River and Fountain Creek. . . . . . . . . . . . . . . . . . . . . . 13

CONVERSION FACTORS, VERTICAL DATUM, ABBREVIATIONS, AND ACRONYMS

Degree Celsius (°C) may be converted to degree Fahrenheit 

(°F) by using the following equation:

°F = 9/5 (°C) + 32

Vertical coordinate information is referenced to the National Geodetic Vertical Datum of 

1988 (NAVD 88). 

Horizontal coordinate information is referenced to the North American Datum of 1983 

(NAD 83).

Abbreviations and Acronyms Used in this Report:

mg/L milligrams per liter

PSOP Preferred Storage Options Plan

USGS U.S. Geological Survey

NWIS National Water Information System

LOWESS Local regression

Multiply By To obtain

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

cubic foot per second (ft3

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

acre-feet (acre-ft) 1,233.5 cubic meter (m3

)
Methods to Identify Changes in Background 

Water-Quality Conditions Using Dissolved-Solids 

Concentrations and Loads as Indicators, Arkansas River 

and Fountain Creek, in the Vicinity of Pueblo, Colorado

By Roderick F. Ortiz

Abstract

Effective management of existing water-storage capacity 

in the Arkansas River Basin is anticipated to help satisfy the 

need for water in southeastern Colorado. A strategy to meet 

these needs has been developed, but implementation could 

affect the water quality of the Arkansas River and Fountain 

Creek in the vicinity of Pueblo, Colorado. Because no known 

methods are available to determine what effects future changes 

in operations will have on water quality, the U.S. Geological 

Survey, in cooperation with the Southeastern Colorado Water 

Activity Enterprise, began a study in 2002 to develop methods 

that could identify if future water-quality conditions have 

changed significantly from background (preexisting) waterquality conditions. A method was developed to identify when 

significant departures from background (preexisting) waterquality conditions occur in the lower Arkansas River and Fountain Creek in the vicinity of Pueblo, Colorado. Additionally, the 

methods described in this report provide information that can be 

used by various water-resource agencies for an internet-based 

decision-support tool.

Estimated dissolved-solids concentrations at five sites in 

the study area were evaluated to designate historical background conditions and to calculate tolerance limits used to identify statistical departures from background conditions. This 

method provided a tool that could be applied with defined statistical probabilities associated with specific tolerance limits. 

Drought data from 2002 were used to test the method. 

Dissolved-solids concentrations exceeded the tolerance limits 

at all four sites on the Arkansas River at some point during 

2002. The number of exceedances was particularly evident 

when streamflow from Pueblo Reservoir was reduced, and 

return flows and ground-water influences to the river were more 

prevalent. No exceedances were observed at the site on Fountain Creek. These comparisons illustrated the need to adjust the 

concentration data to account for varying streamflow. As such, 

similar comparisons between flow-adjusted data were done. At 

the site Arkansas River near Avondale, nearly all the 2002 flowadjusted concentration data were less than the flow-adjusted 

tolerance limit which illustrated the effects of using flowadjusted concentrations. Numerous exceedances of the flowadjusted tolerance limits, however, were observed at the sites 

Arkansas River above Pueblo and Arkansas River at Pueblo. 

These results indicated that the method was able to identify a 

change in the ratio of source waters under drought conditions. 

Additionally, tolerance limits were calculated for daily 

dissolved-solids load and evaluated in a similar manner. 

Several other mass-load approaches were presented to help 

identify long-term changes in water quality. These included 

comparisons of cumulative mass load at selected sites and comparisons of mass load contributed at the Arkansas River near 

Avondale site by measured and unmeasured sources. 

Introduction

Effective management of existing water-storage capacity 

in the Arkansas River Basin is anticipated to help satisfy the 

need for water in southeastern Colorado. Additionally, the 

development of more water-storage capacity in the basin is 

anticipated as the population along the Arkansas River and 

Fountain Creek corridors increases over the next 40 years 

(fig. 1). An overall strategy to meet these needs has been developed by the Southeastern Colorado Water Activity Enterprise. 

The strategy is defined in the Preferred Storage Options Plan 

(PSOP) and sets a target of 122,100 acre-ft of new storage 

within the next 25 years (GEI Consultants, Inc., 2000). Elements of the PSOP include long-term contracts for water storage in excess capacity in Fryingpan-Arkansas Project space (by 

2004), enlargement of Pueblo Reservoir (by 2013), enlargement 

of Turquoise Reservoir (by 2025), and various ongoing waterconservation measures. 

Implementation of the PSOP could have an effect on the 

water quality of the Arkansas River and Fountain Creek in the 

vicinity of Pueblo, Colorado. A water-quality management program would be implemented if water quality was substantially 

degraded as a result of future changes in water operations. The 

management program would address these water-quality 
2 Methods to Identify Changes in Background Water-Quality Conditions Using Dissolved-Solids Concentrations and Loads 

as Indicators, Arkansas River and Fountain Creek, in the Vicinity of Pueblo, Colorado

Colorado

Springs

Turquoise

Reservoir

0 10 20 MILES

0 10 20 KILOMETERS

Fountain Creek 

at Pueblo

Arkansas River 

near Avondale

Pueblo Wastewater

Treatment Plant Arkansas River

Boone

Arkansas River 

at Pueblo

Avondale

Pueblo

Arkansas River 

at Portland

Arkansas River 

above Pueblo

Pueblo

Reservoir

Wild Horse Creek

Salt Creek

Florence Custer County

38 ̊15'

38 ̊30'

38 ̊45'

105 ̊15' 105 ̊ 104 ̊45' 104 ̊30' 104 ̊15' 104 ̊ Lincoln County

Pueblo

COLORADO

Arkansas River

Pueblo County

El Paso County

Fremont County

Teller County

Huerfano County

Pueblo County

Crowley County

EXPLANATION

Study site and site name

Otero County

38 ̊

Base modified by Denver Water Board, 1998

from U.S. Geological Survey Digital Line Graphics, 1:100,000, 1981-1983

Cities from Colorado Department of Transportation, 1:50,000, 1998

Albers Equal-Area projection

Standard parallels 37 ̊30' N and 40 ̊30' N

Central meridian 105 ̊30' W

Fountain

Creek

St. Charles River

Sixmile Creek

Figure 1. Location of study area and selected surface-water and water-quality sites.
Introduction 3

concerns by using best-management practices or other appropriate measures in a manner consistent with applicable watersupply needs and water-quality requirements (PSOP Implementation Committee, 2001). In 2002, a basic water-quality monitoring program was established in the basin to collect additional 

data needed to support the PSOP. Because no known methods 

are available to determine what effects future changes in operations will have on water quality, the U.S. Geological Survey 

(USGS), in cooperation with the Southeastern Colorado Water 

Activity Enterprise, began a study in 2002 to develop methods 

that could identify if future water-quality conditions have 

changed significantly from preexisting water-quality conditions 

(hereinafter referred to as “background conditions”).

Purpose and Scope

 This report presents the results of a study to develop 

methods to identify changes in background water-quality 

conditions using dissolved-solids concentrations and loads as 

indicators at selected sites in the Arkansas River and Fountain 

Creek in the vicinity of Pueblo, Colorado. Specifically, this 

report designates background conditions at selected sites 

in the study area with respect to estimated daily dissolved-solids 

concentration and load, establishes the use of tolerance limits to 

identify statistically significant future daily departures from a 

background condition, and presents other analysis techniques to 

help identify long-term changes in dissolved-solids load along 

selected reaches of the study area. Additionally, this report 

provides information that can be used by various waterresources agencies for an internet-based decision-support tool 

that can be used on a real-time basis to monitor dissolved-solids 

concentration and load as a surrogate for water-quality conditions in the study reaches and determine whether future waterquality conditions are significantly different from background 

conditions.

Five sites were selected for evaluation as part of this study 

(fig. 1 and table 1). The sites Arkansas River above Pueblo 

(07099400), Fountain Creek at Pueblo (07106500), and Arkansas River near Avondale (07109500) were of primary interest. 

The largest changes in water operations that could affect water 

quality are most likely to happen along the stream reaches represented by these three sites. Daily streamflow and specific conductance measurements have been collected for several years at 

all five study sites (table 1). Daily streamflow and specific conductance collected in 2002 were used to test the methodologies 

described in this report.

Table 1. Period of record for daily specific conductance and streamflow, years used to define background and test period, and 

percentage of background data reported as missing at selected sites in the Arkansas River and Fountain Creek in the vicinity of Pueblo, 

Colorado.

[P, primary site; S, secondary site]

Site name 

used in this report

(USGS station

identification 

number) 

Site 

designation

Period of record Calendar 

years used 

to define 

background 

period

Calendar 

year 

used as 

test 

period

Percentage of data 

missing during 

background period

Daily specific 

conductance Daily streamflow

Specific 

conductance

Streamflow

Arkansas River 

at Portland 

(07097000)

S Nov. 1982 to Sept. 2002 May 1939 to Sept. 1952;

Oct. 1974 to Sept. 2002

1983–2001 2002 6 0

Arkansas River 

above Pueblo

(07099400)

P Dec. 1985 to Sept. 2002 Oct. 1965 to Sept. 2002 1986–2001 2002 4 1

Arkansas River 

at Pueblo

(07099970)

S Oct. 1988 to Sept. 2002 Oct. 1988 to Sept. 2002 1989–2001 2002 11 0

Fountain Creek 

at Pueblo

(07106500)

P Dec. 1985 to Sept. 2002 Jan. 1922 to Sept. 1925;

Oct. 1940 to Sept. 1965;

Feb. 1971 to Sept. 2002

1986–2001 2002 6 0

Arkansas River near 

Avondale

(07109500)

P July 1979 to Sept. 1980;

Dec. 1985 to Sept. 2002

May 1939 to Sept. 1951;

Feb. 1965 to Sept. 2002

1986–2001 2002 6 0
4 Methods to Identify Changes in Background Water-Quality Conditions Using Dissolved-Solids Concentrations and Loads as 

Indicators, Arkansas River and Fountain Creek, in the Vicinity of Pueblo, Colorado

Description of the Study Area

The study area is located in the vicinity of Pueblo, Colorado, and extends about 32 mi from the site Arkansas River at 

Portland to the site Arkansas River near Avondale (fig. 1). River 

elevations along this reach range from 5,021 to 4,509 ft. The 

area is characterized by a semiarid climate with a mean annual 

precipitation of about 12 in. (Pielke and others, 2002). Mean 

annual humidity is relatively low at about 36 percent. The range 

in daily temperature averages about 18°C. Streamflow in the 

Arkansas River exhibits considerable seasonal variability with 

the majority of the total annual streamflow resulting from snowmelt runoff in the Rocky Mountains west of the study area. 

Streamflow from 1986 to 2001 averaged 732 ft3/s at the site 

Arkansas River above Pueblo and 999 ft3/s at the site Arkansas 

River near Avondale (U.S. Geological Survey, 1987–2002). 

The average streamflow at the site Fountain Creek at Pueblo 

was 166 ft3/s during 1986–2001 (U.S. Geological

Survey, 1987–2002).

Pueblo Reservoir is a multipurpose facility constructed by 

the Bureau of Reclamation (fig. 1). The primary uses of the reservoir are for the storage and regulation of native and transmountain water for the Fryingpan-Arkansas Project and for 

flood control of the Arkansas River east of Pueblo Reservoir. 

Native water originates within the Arkansas River Basin while 

transmountain water (nonnative) originates from outside the 

basin and is conveyed by ditches or tunnels to the Arkansas 

River Basin. Storage capacity in the reservoir reserved for 

Fryingpan-Arkansas Project water is 80,400 acre-ft. Storage of 

some nonproject water is granted under a limited number of 

storage contracts when reservoir space is available. The nonproject reservoir storage space may be used for the storage of 

exchangeable water which is water that is diverted at one 

location in the river system and subsequently replaced with a 

like amount of water at another location (Lewis, 1999). Storage 

and release operations at Pueblo Reservoir control streamflow 

in the lower Arkansas River Basin. About 55 percent of the 

annual inflow to the reservoir occurs during the snowmelt 

period from April through July. Reservoir storage decreases 

substantially by the end of the growing season because of 

decreased inflow and large downstream demands for irrigation 

water. Water is stored under the Winter-Water Storage Program 

from November 15 to March 15 of each year. The program 

allows downstream irrigation-canal companies to store their 

direct-flow water in the reservoir for release in the spring or late 

summer when streamflow in the river may not be sufficient for 

irrigation needs. Prioritized direct-flow water rights for the 

Arkansas River were established as long ago as 1859 and are 

based on the doctrine that the first in time to use the water is first 

in right to receive that water in subsequent years (Lewis and 

Brendle, 1998). Those entities with the oldest direct-flow water 

rights are said to have the senior water rights.

Fountain Creek is an important tributary to the Arkansas 

River and is used to convey transmountain return flows from 

Colorado Springs to the Arkansas River. The City of Colorado 

Springs exchanges sewered and nonsewered return flows to 

Fountain Creek, which originate from its importation and use of 

non-native water, for water in the Arkansas River. The city first 

executed the transmountain return-flow exchange in 1981 

(Lewis, 1999). Larger volumes of transmountain-return flow in 

Fountain Creek are likely as the City of Colorado Springs and 

other entities increase deliveries of transmountain water. Additionally, expected growth by the city could result in larger 

volumes of wastewater-treatment-plant effluent entering 

Fountain Creek and, ultimately, the Arkansas River.

Determination of Background WaterQuality Conditions

It is advantageous to know the background (preexisting) 

condition when conducting a scientific investigation. Specific 

knowledge of the background condition can be invaluable, particularly when changes to the system have happened or are 

likely to happen. The U.S. Environmental Protection Agency 

(1992) states that a background level is “the concentration of a 

hazardous substance that provides a defensible reference point 

that can be used to evaluate whether or not a release from the 

site has occurred.” Additionally, “background levels do not 

necessarily represent prerelease conditions, nor conditions in 

the absence of influence from source(s) at the site.” Although 

specific to hazardous-materials applications, the previous statements provide important criteria needed to define the background condition for each site in this study. As such, the 

rephrased definition states that the background condition is the 

concentration of a substance that provides a defensible reference point that can be used to evaluate whether or not a statistically significant change in water quality has occurred at a site. 

For the scope of this study, three questions needed to be 

addressed to determine the background condition at a site. What 

substance is an appropriate indicator of water quality? What 

timeframe (period of data) represents the background condition 

and provides a defensible reference point to assess future 

changes? Does the background condition allow evaluation so 

that a significant change can be identified? The following 

sections address these three questions.

Identification of significant changes requires a statement 

of the risk that is acceptable to the scientist, manager, or decision maker. This risk, or significance level, is the probability of 

incorrectly rejecting the null hypothesis when, in fact, it is true 

(Helsel and Hirsch, 1992). Whereas the risk does not depend on 

the data, the p-value provides information on the strength of the 

scientific evidence. The p-value is the probability of obtaining 

the computed test statistic, or one even less likely, when the null 

hypothesis is true (Helsel and Hirsch, 1992). The smaller the 

p-value the stronger the evidence for rejection of the null 

hypothesis.
Determination of Background Water-Quality Conditions 5

Indicator Parameter

Dissolved solids was chosen as the indicator parameter in 

this study for several reasons. First, dissolved-solids concentrations in the river have been a concern to local water managers, 

water suppliers, and farmers in the lower Arkansas River Basin 

for many years. Batie and Healy (1983) described the highsalinity issue in this area as the most pervasive problem associated with irrigated agriculture in the United States; the Colorado 

Department of Public Health and Environment (2001) refers to 

dissolved solids as salinity. Second, dissolved solids also 

are a good indicator of the general water quality in the study 

area and can be accurately estimated from available specificconductance data (Cain, 1987; Ortiz and others, 1998). Specific 

conductance is a measurement of the ability of a solution to 

conduct electrical current (measured at 25°C). The presence of 

charged ionic species in solution makes the solution conductive. 

The conductance of a solution increases as ion concentrations 

increase; therefore, the specific-conductance measurement 

provides an indication of ion or dissolved-solids concentration 

of the solution (Hem, 1985). Third, dissolved-solids concentrations (specific conductance) are sensitive to changes in streamflow, water operations, and source contributions. Lastly, the use 

of dissolved-solids concentration data combined with streamflow allows for analysis of mass loading as a parameter of 

interest. For the study, daily dissolved-solids concentrations at 

each site were calculated by developing a regression equation at 

each site from paired specific-conductance and dissolved-solids 

data dating from 1979 through 2001 (table 2), and applying the 

regression equation at each site to the mean daily specific 

conductance measured at each site to obtain an estimated or 

computed mean daily dissolved-solids concentration.

Selection of Background Periods from Available Data

Available daily specific-conductance data for the five 

study sites were retrieved from the USGS National Water Information System (NWIS). Daily values represent the average for 

a given day computed from as many as 96 measurements. These 

data are published annually in the USGS Water-Data Reports 

for Colorado (U.S. Geological Survey, 1984–2003). For the 

purposes of this study, the background period at each site was 

defined by the number of consecutive calendar years that continuous daily specific-conductance data were available for a site 

(table 1). These data were available for 16 calendar years at the 

three primary study sites (1986–2001), 19 calendar years at 

Arkansas River at Portland (1983–2001), and 13 calendar years 

at Arkansas River at Pueblo (1989–2001). Missing values were 

estimated by using linear interpolation given the particular 

streamflow conditions at that time; from 4 to 11 percent of the 

specific-conductance data were reported as missing values 

(table 1). Daily specific-conductance data for calendar year 

2002 also were retrieved but were not used to determine the 

background period, rather, these data were used to test the 

results of the methodology. 

Available instantaneous specific-conductance data for the 

five study sites were retrieved from NWIS; instantaneous data 

are single measurements in time. These data are published 

annually in the USGS Water-Data Reports for Colorado (U.S. 

Geological Survey, 1976–2003). Instantaneous specificconductance data dating back to January 1975 were retrieved 

for all study sites on the Arkansas River (U.S. Geological 

Survey, 1976–2001). Similarly, instantaneous specificconductance data dating back to January 1982 were retrieved 

for Fountain Creek at Pueblo (U.S. Geological Survey, 1983–

2001). These dates generally correspond with major changes in 

Table 2. Least-squares regression equations to estimate dissolved-solids concentration from specific conductance for selected 

sites in the lower Arkansas River Basin in the vicinity of Pueblo, Colorado.

[DS, dissolved-solids concentration, in milligrams per liter; SC, specific conductance, in microsiemens per centimeter; <, less than]

Site name 

(figure 1)

Number 

of paired 

measurements

(1979–

2001)

Regression equation Coefficient of 

determination

Standard 

error of 

the

estimate

p-value

Dissolved solids

Arkansas River at Portland 121 0.95 0.014 <0.001

Arkansas River above Pueblo 42 .94 .030 <.001

Arkansas River at Pueblo 26 .99 .019 <.001

Fountain Creek at Pueblo 26 .98 .024 <.001

Arkansas River near Avondale 39 .98 .020 <.001

DS = ( ) 0.664 × SC – 14.8

DS = ( ) 0.746 × SC – 51.8

DS = ( ) 0.831 × SC – 103.1

DS = ( ) 0.772 × SC – 100.6

DS = ( ) 0.820 × SC – 108.3
6 Methods to Identify Changes in Background Water-Quality Conditions Using Dissolved-Solids Concentrations and Loads as 

Indicators, Arkansas River and Fountain Creek, in the Vicinity of Pueblo, Colorado

water operations in the study area and, although earlier data 

may exist, define the historical extent of water-quality conditions that corresponds to current water operations in the study 

area. 

Daily-streamflow data were retrieved from NWIS for all 

continuous streamflow sites in the study area (U.S. Geological 

Survey, 1976–2003). These data were available for all sites on 

the Arkansas River after October 1974 with the exception of 

Arkansas River at Pueblo (table 1). Daily values were uninterrupted with less than 1 percent of the data at any site requiring 

estimation of missing values. Data prior to 1974 were available 

for some sites but were more intermittent and did not exhibit 

streamflow patterns associated with the operation of Pueblo 

Reservoir (Arkansas River sites) and transmountain-return 

flows (Fountain Creek at Pueblo). 

Comparison of Background Periods to Historical Data

Sixteen years of daily specific-conductance data were used 

to define the background period (1986–2001) for dissolvedsolids concentration at the three primary study sites (table 1). 

However, no daily specific-conductance data were available for 

the years prior to 1986 which included some of the driest years 

on record (fig. 2). To determine if the designated background 

period was representative of the longer period since the completion of Pueblo Reservoir (1975–2001), instantaneous specificconductance data from 1975 through 1985 were compared to 

instantaneous data from 1986 through 2001 (fig. 3). The two 

data sets were compared using a Wilcoxon rank-sum test to see 

if the means were significantly different (S-PLUS 2000 User’s 

Guide, 1999). A similar comparison was done for data from 

Fountain Creek at Pueblo dating back to January 1982. The test 

indicated that there was no significant difference in the means 

at a 95-percent confidence level (p < 0.05) for the test periods 

for the sites Arkansas River above Pueblo, Arkansas River near 

Avondale, and Fountain Creek at Pueblo. At the site Arkansas 

River at Portland, however, the statistical test indicated there 

was a significant difference in the means for the two periods. 

This result may be because a large number of samples were collected during the drought of 1977–1978, thus, biasing the data 

set, and because no data were collected prior to 1977. There was 

no significant difference in the mean values for the two periods 

when the data collected in 1977–1978 were removed and the 

test was run again. A comparison could not be made at the site 

Arkansas River at Pueblo because no data were collected prior 

to 1988. These results indicate that the background periods used 

for the primary study sites and, most likely, the secondary study 

sites generally are representative of the historical conditions 

since the last major changes in water operations in the Arkansas 

River downstream from Pueblo Reservoir and in Fountain 

Creek, except possibly during severe drought conditions.

1975197819811984198719901993199619992002

CALENDAR YEAR

0

500

1,000

1,500

ANNUAL STREAMFLOW, IN THOUSANDS OF 

ACRE-FEET PER YEAR

Daily specific-conductance data not available for 

 entire calendar year

Daily specific-conductance data available for 

 entire calendar year

Figure 2. Annual streamflow at Arkansas River near Avondale, Colorado, 

1975–2002.
Identification of Short-Term Changes in Water Quality Using Dissolved-Solids Concentrations and Loads 7

Variability Within the Background Concentrations

 The variability of the background data is important in 

determining how much change in dissolved-solids concentration is needed in order to identify a statistically significant 

change. Significant departures from a background condition 

can be determined for most data; however, to be of any real 

value the change must be reasonable within the context of ongoing processes in the system and what level of confidence is 

needed to identify any changes. For each study site, daily mean 

dissolved-solids concentrations were sorted by Julian date 

(JD1=Jan1, JD2=Jan2,..., JD365=Dec31) and plotted to evaluate the variability for any given day of the calendar year (fig. 4). 

The daily variability in concentration for any single Julian date 

shows relatively little change regardless of the season for the 

sites located on the Arkansas River. The average daily variability at the sites Arkansas River at Portland and Arkansas River 

above Pueblo was less than 170 mg/L per liter while the daily 

variability at the sites Arkansas River at Pueblo and Arkansas 

River near Avondale was less than 320 mg/L. Dissolved-solids 

concentrations at sites on the Arkansas River exhibited typical 

seasonal patterns associated with hydrologic events in the basin. 

That is, there is a relatively uniform base-flow concentration 

from about September to April followed by a decrease in concentration as snowmelt from the mountains occurs. In June and 

July, dissolved-solids concentrations are at a minimum due to 

dilution from the high streamflow conditions. Concentrations 

increase throughout the summer before reaching base-flow conditions again in September. Daily variability at the site Fountain 

Creek at Pueblo was more pronounced (fig. 4) during the summer period as dissolved-solids concentrations changed in 

response to depleted streamflow from irrigation and(or) 

ground-water pumping and storm runoff. The average daily 

variability at the site Fountain Creek at Pueblo from April 

through September was about 550 mg/L. The daily variability 

decreased to 308 mg/L from October through March. Nevertheless, the daily variability in the background conditions at all five 

sites was sufficiently small for application of a method to determine when statistically significant departures might occur.

Identification of Short-Term Changes in 

Water Quality Using Dissolved-Solids 

Concentrations and Loads

Tolerance intervals, confidence intervals, and prediction 

intervals are three commonly used tests to determine if new data 

are consistent with previous background data. Tolerance intervals were selected for this application because they provide an 

0

500

1,000

1,500

2,000

SPECIFIC CONDUCTANCE, IN MICROSIEMENS 

PER CENTIMETER

75th percentile

25th percentile

75th percentile plus 1.5

 times interquartile range

25th percentile minus 1.5

 times interquartile range

Median

Individual data value

EXPLANATION

ARKANSAS

RIVER ABOVE

PUEBLO

FOUNTAIN

CREEK AT

PUEBLO 

ARKANSAS

RIVER NEAR

AVONDALE

ARKANSAS

RIVER AT

PORTLAND

1975-1985

1982-1985

1986-2001

1977-1985

Figure 3. Comparison of instantaneous specific-conductance data at selected sites on 

the Arkansas River, 1975–1985 and 1986–2001, and at Fountain Creek at Pueblo, 1982–1985 

and 1986–2001.
8 Methods to Identify Changes in Background Water-Quality Conditions Using Dissolved-Solids Concentrations and Loads as 

Indicators, Arkansas River and Fountain Creek, in the Vicinity of Pueblo, Colorado

estimation of the range that should contain a certain percentage 

of each individual measurement in the population. Within the 

context of a one-tailed interval, an upper tolerance limit statistically defines what percentage of the population measurements 

will not exceed a defined upper limit. Confidence intervals, on 

the other hand, are limits within which we expect a given population parameter, such as the mean, to lie. Whereas tolerance 

limits and confidence intervals estimate characteristics of 

present populations, prediction intervals provide an estimation 

of what values will be in the future based on background data. 

For this study, an upper tolerance limit was calculated for each 

study site by using information about the means and the amount 

of variability in the background data. Future water-quality conditions (as daily dissolved-solids concentrations or loads) then 

can be compared to these limits to determine if there are any 

exceedances of the limits. A one-tailed upper tolerance limit can 

be calculated from the equations shown below (Natrella, 1963).

0

200

400

600

800

Arkansas River at Portland (1983-2001)

0

200

400

600

800

Arkansas River above Pueblo (1986-2001)

0

300

600

900

1,200

Arkansas River at Pueblo (1989-2001)

0

500

1,000

1,500

2,000

2,500

Fountain Creek at Pueblo (1986-2001)

0

300

600

900

1,200

1,500

Arkansas River near Avondale (1986-2001)

ESTIMATED DAILY DISSOLVED-SOLIDS CONCENTRATION, IN MILLIGRAMS PER LITER

JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC

Figure 4. Variability of estimated daily mean dissolved-solids concentrations during background period 

at selected sites on the Arkansas River and Fountain Creek.
Identification of Short-Term Changes in Water Quality Using Dissolved-Solids Concentrations and Loads 9

Tolerance limit = (1)

where 

is the mean value,

 s is the standard deviation,

 (2)

 k is , 

and

 a is , (3)

and

b is , (4)

where

is the critical value from the normal distribution 

that is exceeded with probability , 

is the critical value from the normal distribution 

that is exceeded with the probability , 

and N is the number of samples used to calculate k.

An upper tolerance limit was calculated for each Julian 

date for each site by using the equation shown above; for the 

remainder of this report, the term “tolerance limit” will imply 

the use of an upper tolerance limit. The mean is defined as the 

daily average dissolved-solids concentration for each Julian 

date for a background period. The variability term is the product 

of the k-value and the standard deviation. The k-value incorporates the probabilities and , which address two different characteristics of a tolerance limit. The first is the stated 

confidence in the test, that is, the probability that a value is 

greater than the computed tolerance limit. The second defines 

the fixed proportion of the population covered by the test, that 

is, the percent coverage. For instance, a k-value can be computed that uses a 99-percent confidence level and accounts for 

99.9 percent of the population. Care must be taken, however, to 

select appropriate probabilities for an application because 

k-values become increasingly large with increased confidence 

and coverage. For the purposes of the study, and in consultation 

with the Southeastern Colorado Water Activities Enterprise, a 

95-percent degree of confidence with a 97.5 percent population 

coverage was selected to determine the k-value for this report 

(Robert Hamilton, Southeastern Colorado Water Activities 

Enterprise, oral commun., November 2003). The number of 

samples (N) collected is required to calculate a k-value. For 

each site, the number of samples collected, for a particular 

Julian date, was set as the number of calendar years for which 

daily specific-conductance data were available (table 1). Tabled 

k-values for different sample numbers and various degrees of 

confidence and percentage of coverages can be found in 

Natrella (1963). 

One value for the standard deviation was used in the calculation of an individual tolerance limit at each site on the Arkansas River because the variance in the daily concentrations was 

relatively constant at each of these sites (fig. 4). Two values for 

the standard deviations, however, were used to compute tolerance limits at the site Fountain Creek at Pueblo because the 

daily variance showed substantial differences depending on the 

time of the year (fig. 4). One value was used for the period from 

late September (JD265) to early April (JD100) when the range 

in variance was relatively small. A second value was used for 

the intervening period when daily variances were larger. Computation of the standard deviation(s) for each site was completed in a four-step process. First, the daily variance for each 

Julian date at each site was calculated. Second, the variances 

were assessed for similarity and grouped by period or season, if 

needed. Third, the average variance was calculated for all Julian 

dates within a defined period or season. Lastly, the square root 

of the average variance was calculated, which resulted in the 

standard deviation used to calculate the tolerance limits 

(David Mueller, U.S. Geological Survey, written commun., 

May 2003).

Tolerance Limits for Dissolved-Solids Concentration

Tolerance limits for dissolved-solids concentrations 

at each site were calculated by converting daily specificconductance data to daily dissolved-solids concentrations using 

the regression equations shown in table 2 and then by using the 

methods described in the previous section. The resulting tolerance limit for each Julian date, at each site, was compared to 

selected summary statistics for the background period to ensure 

that results obtained by this methodology were reasonable 

(fig. 5). With relatively few exceptions, the 95th percentile 

value for a given Julian date did not exceed the defined tolerance limit. The 95th percentile was used in the comparison 

because it allowed for the exclusion of one potentially extreme 

outlier for a particular Julian date during the background period. 

It is worth restating that the tolerance limits shown in figure 5 

were based on a 95-percent confidence and a 97.5-percent population coverage. More or less rigid tolerance limits can be 

defined by increasing or decreasing either the confidence level 

or the percent population coverage.

The tolerance limits calculated for this study incorporated 

data through the year 2001. As such, the only comparison data 

available to test the methodology were the estimated dissolvedsolids concentrations for calendar year 2002. As it turned out, 

2002 proved to be one of the most severe drought years in 

Colorado since the drought of 1977 (Colorado Climate Center, 

2002). Streamflow and snowpack levels in much of Colorado 

were at record low levels, and agricultural and domestic water 

X s + ( ) × k

X

z( ) 1 – p z(1 – p)

2

+ – a b ×

a ---------------------------------------------------------

1

z(1 – γ )

2

2( ) N – 1 – --------------------

z(1 – p)

2 z(1 – γ )

2

N – ---------------

z( ) 1 – γ

1 – γ

z( ) 1 – p

1 – p

1 – γ 1 – p
10 Methods to Identify Changes in Background Water-Quality Conditions Using Dissolved-Solids Concentrations and Loads as 

Indicators, Arkansas River and Fountain Creek, in the Vicinity of Pueblo, Colorado

supplies were severely limited. In the study area, conditions 

were similar as only the most senior water rights were satisfied, 

and discharge from Pueblo Reservoir was reduced substantially 

or shut down for an extended period during the summer. 

Monthly mean streamflow at the site Arkansas River above 

Pueblo for August and September in 2002 were 16.5 and 

4.1 ft3/s, respectively, compared to the historical means of 2,716 

and 1,040 ft3

/s for the same two months (U.S. Geological Survey, 2003). As streamflow decreased in 2002, dissolvedsolids concentrations increased to record levels in the study 

area. Estimated dissolved-solids concentrations from about 

mid-June through December were either the highest or among 

the highest on record at the sites Arkansas River above Pueblo, 

Arkansas River at Pueblo, and Arkansas River near Avondale 

(fig. 6). A similar pattern was observed at the site Arkansas 

River at Portland, but it was not as pronounced. No record

0

200

400

600

800

0

200

400

600

800

0

300

600

900

1,200

0

500

1,000

1,500

2,000

2,500

0

300

600

900

1,200

1,500

ESTIMATED DAILY DISSOLVED-SOLIDS CONCENTRATION, IN MILLIGRAMS PER LITER

Tolerance limit (95th-percent confidence 

 level and 97.5th-percent population coverage)

95th percentile value of the 

 background concentration data

Mean value of the background concentration data

5th percentile value of the 

 background concentration data

EXPLANATION

Arkansas River at Portland (1983-2001)

Arkansas River above Pueblo (1986-2001)

Arkansas River at Pueblo (1989-2001)

Fountain Creek at Pueblo (1986-2001)

Arkansas River near Avondale (1986-2001)

JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC

Figure 5. Tolerance limits for estimated dissolved-solids concentrations at selected sites on the 

Arkansas River and Fountain Creek.
Identification of Short-Term Changes in Water Quality Using Dissolved-Solids Concentrations and Loads 11

maximum concentrations were observed at the site Fountain 

Creek at Pueblo during 2002 (fig. 6) because base flow from 

Colorado Springs maintained a near-normal streamflow.

In 2002, dissolved-solids concentrations exceeded the 

tolerance limit at some point during the summer at all four sites 

on the Arkansas River (fig. 6). These exceedances were particularly evident at the sites Arkansas River above Pueblo and 

Arkansas River at Pueblo, where for an extended period of time, 

concentrations were much higher than the tolerance limits. 

Streamflow from Pueblo Reservoir was reduced substantially 

during this period and ground water and return flows to the river 

had a marked effect on the river. Although streamflow was 

reduced, relatively few exceedances were observed at the site 

Arkansas River at Portland because the source of the water in 

0

200

400

600

800

Arkansas River at Portland (1983-2001)

Daily value in 2002 that exceeded

 maximum background value

Daily value in 2002 that did not 

 exceed maximum background value

Mean value for background period

Tolerance limit (95th-pecent confidence 

 level and 97.5th-percent 

 population coverage)

0

300

600

900

1,200

Arkansas River above Pueblo (1986-2001)

0

500

1,000

1,500

2,000

2,500

Arkansas River at Pueblo (1989-2001)

0

500

1,000

1,500

2,000

2,500

Fountain Creek at Pueblo (1986-2001)

EXPLANATION

0

400

800

1,200

1,600

Arkansas River near Avondale (1986-2001)

ESTIMATED DAILY DISSOLVED-SOLIDS CONCENTRATION, IN MILLIGRAMS PER LITER

JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC

Figure 6. Comparison of estimated daily dissolved-solids concentrations in 2002 with maximum 

concentrations during background periods and calculated tolerance limits at selected sites.
12 Methods to Identify Changes in Background Water-Quality Conditions Using Dissolved-Solids Concentrations and Loads as 

Indicators, Arkansas River and Fountain Creek, in the Vicinity of Pueblo, Colorado

the river did not change appreciably. Exceedances of the tolerance limit routinely occurred at the site Arkansas River near 

Avondale but not to the extent observed at the sites Arkansas 

River above Pueblo or Arkansas River at Pueblo. The high 

dissolved-solids concentrations in the Arkansas River likely 

were diluted by near-normal streamflow from Fountain Creek. 

No exceedances of the tolerance limit were observed at the site 

Fountain Creek at Pueblo. As discussed previously, two different values for the standard deviations were used to calculate the 

tolerance limit at this site because of the high daily variability 

observed during the summer period (fig. 4). 

The use of the 2002 data to test the utility of the method 

illustrated two important points. First, changes in concentration 

could be attributable to either a change in streamflow, a change 

in the predominant source water to the system, or a combination 

of both. Second, because dissolved-solids concentration is 

significantly related (inversely) to streamflow, it would be 

advantageous to adjust the concentration data to account for 

varying streamflow, thus diminishing the influence of streamflow on dissolved-solids concentrations. The following section 

describes the use of tolerance limits on flow-adjusted concentrations to help identify changes in water quality in the study 

area.

Tolerance Limits for Flow-Adjusted Dissolved-Solids 

Concentration

The concentrations of many constituents are affected by 

streamflow. Typically, adjustment of the concentration data to 

account for varying streamflow is needed before further analysis to evaluate differences in concentration is done. The effects 

of streamflow can pose a problem when evaluating changes in 

specific conductance and dissolved solids because of the inherent inverse relation between these variables and streamflow. 

The use of flow-adjusted concentrations by the residuals 

method provides a way to remove the source of much of the 

variance due to the influence of streamflow (Rickert, 1985). 

Residuals analysis regresses the measured value on some function of streamflow and uses the residuals from the regression 

(the observed measurement minus the predicted value) as flowadjusted values. The residual method works well if a functional 

form of the measured value to streamflow regression produces 

a reasonable fit. To estimate daily specific-conductance values 

from streamflow, instantaneous specific-conductance data and 

continuous daily streamflow data were input into a multiparameter regression model (Cohn and others, 1992). The 

regression equation is shown below: 

(5)

where

ln is natural logarithm function;

SC is instantaneous specific-conductance value, in microsiemens per centimeter at 25°C;

 are model coefficients;

Q is mean-daily streamflow, in cubic feet per second;

 is centered streamflow, in cubic feet per second;

sin is sine function; and

 is numerical constant approximated by the 

value 3.142857;

T is time measured in years to two decimal points;

cos is cosine function;

 is independent, random error.

The equation requires the estimation of five parameters: 

 is a constant; and describe the relation between concentration and streamflow; and describe the seasonal 

variability in the measured specific-conductance data. The 

error, denoted , is assumed to be independent and normally 

distributed with zero mean and variance. is a “centering” 

variable that simplifies the numerical work and has no effect on 

the estimates. Additional documentation for the regression 

equation can be found in Cohn (2002). The coefficients for the 

5-parameter regression model are listed in table 3. Those coefficients shown in bold type were determined to be significant in 

describing the concentration data. For consistency among the 

five study sites, all coefficients are shown in table 3 even if the 

coefficient was not significant (p-value>0.05) in describing the 

concentration data.

The specific conductance to streamflow regression equations in table 3 were used to predict daily specific-conductance 

values from measured daily streamflow at each study site for 

each Julian date of the background periods. Predicted daily 

specific-conductance values were converted to estimated dissolved-solids concentrations using the regression equations in 

table 2. This conversion was done in the same manner as was 

described in the section titled “Indictor Parameter” to estimate 

dissolved-solids concentrations from observed daily specific 

conductance. The predicted estimated dissolved-solids concentrations were subtracted from corresponding observed estimated daily dissolved-solids concentrations (computed from 

the observed specific-conductance values) resulting in residual 

dissolved-solids concentrations for each day. The residual concentrations were sorted by Julian date, and a tolerance limit was 

computed for each site by using techniques described in the section titled “Identification of Short-Term Changes in Water 

Quality Using Dissolved-Solids Concentrations and Loads.” 

Comparisons of the flow-adjusted tolerance limits to flowadjusted data for 2002 are shown in figure 7. For the 2002 data, 

nearly all flow-adjusted concentrations at the sites Arkansas 

River at Portland and Arkansas River near Avondale were less 

than the tolerance limits; previous comparisons to nonadjusted 

concentrations at these two sites (fig. 6) showed numerous 

exceedances. These results illustrate the effects of using flowadjusted concentrations to remove the variability associated

ln( ) SC β0 β1ln( ) Q Q⁄ β2[ ] ln( ) Q Q⁄

2

β3

( ) 2πT

sin

β4cos( ) 2πT ε

++ +

+ +

=

βn

Q

π

ε

β0 β1 β2

β3 β4

ε

Q
Identification of Short-Term Changes in Water Quality Using Dissolved-Solids Concentrations and Loads 13

with streamflow, particularly when the mixture of source waters 

did not change to a large extent such as was seen at the sites 

Arkansas River at Portland and Arkansas River near Avondale. 

The results of the two concentration analyses (nonadjusted and 

flow adjusted) illustrate an important point concerning the use 

of these methods to identify changes in water quality, that is, 

how many consecutive exceedances warrant eliciting changes in 

water management? Certainly a single exceedance would not 

warrant eliciting change in water management, but at what point 

are the number of exceedances considered to be excessive? For 

example, the board of the Southeastern Colorado Water Activities Enterprise, which represents various water-resource entities, decided that seven exceedances during any consecutive 10-

day period would constitute a change in water quality (Robert 

Hamilton, Southeastern Colorado Water Activities Enterprise, 

oral commun., November 2003). This change would warrant 

additional investigation by the board to determine the likely 

cause(s) of the exceedances and the appropriate response measures needed.

Numerous exceedances of the flow-adjusted tolerance 

limits were observed at the sites Arkansas River above Pueblo 

and Arkansas River at Pueblo during late summer and fall of 

2002 (fig. 7). Although much of the variability associated with 

streamflow was removed by flow adjusting the concentrations, 

the results were similar to those observed using nonadjusted 

concentration data. The results indicated that the method was 

able to identify a change in the ratio of source waters at these 

sites under streamflow conditions somewhat less than 50 ft3

/s; 

that is, the proportion of ground water or return flow increased 

substantially when reservoir releases ceased.

Although no exceedance of the flow-adjusted tolerance 

limit was observed at the site Fountain Creek at Pueblo, several 

intermittent values approached the limit. Most occurred when 

daily streamflow increased for a single day in response to localized storms. The timing of these occurrences could indicate that 

these data also represent a different mixture of source water 

than background conditions. 

Tolerance Limits for Estimated Dissolved-Solids Load

Comparisons to tolerance limits derived from dissolvedsolids concentration data, whether adjusted for flow or not, provide a way to help identify potential changes in water quality. 

The concept of dissolved-solids load, however, is not addressed 

by these approaches. Dissolved-solids loading is of great concern to many water users in the lower Arkansas River Basin particularly as it pertains to potential increases in soil salinity of 

irrigated lands. Daily load for the background period at each 

study site was estimated, and a tolerance limit was calculated as 

described in the section titled “Identification of Short-Term 

Changes in Water Quality Using Dissolved-Solids Concentrations and Loads.” Daily loads (tons per day) were calculated as 

the product of estimated daily dissolved-solids concentration 

(milligrams per liter), mean daily streamflow (cubic feet per 

second), and a conversion factor of 0.002697. Daily variability 

in dissolved-solids load from early-September to early-April 

(base-flow conditions) at all five study sites was relatively small 

in comparison to the much larger variability observed during 

the spring and summer (fig. 8). Daily variability in dissolvedsolids load increased in the spring and summer months as 

streamflow increased as a result of snowmelt runoff or thunderstorm activity. As such, the tolerance limit at each site was calculated by using two distinct standard deviations, which represented the variability between the low-flow period (September 

3–April 10) and the high-flow period (April 11–September 2).

Comparisons of daily loads for 2002 to tolerance limits did 

not show any exceedances because of the low streamflow 

observed in 2002. The daily load at the site Fountain Creek at 

Pueblo on July 6, 2002, however, did help illustrate the utility 

of using a tolerance limit on load. Streamflow on that day 

increased nearly 24 times from the previous day in response to 

Table 3. Regression-model coefficients for estimation of daily specific conductance from streamflow at selected sites on the 

Arkansas River and Fountain Creek.

[β0, constant; β1, coefficient of the regression parameter ln(Q/ ); β2, coefficient of the regression parameter [ln(Q/ )]2; β3, coefficient of the regression 

parameter sin(2 T); β4, coefficient of the regression parameter cos(2 T); Q, streamflow in cubic feet per second; T, time in decimal years; s, standard error 

of the regression; R2, fraction of variance explained by the regression; coefficient values shown in bold type indicate significance at a p-value <0.05]

Site name

β0

constant

β1

ln(Q/ )

β2

[ln(Q/ )]2

β3

sin(2 T)

β4

cos(2 T) s R2

Arkansas River at Portland 5.8374 –.4108 –.0111 –.0283 .0144 0.150 79.9

Arkansas River above Pueblo 6.1987 –.0752 –.0229 .1306 .0705 0.154 49.8

Arkansas River at Pueblo 6.4501 –.1295 .0010 .0870 .0341 0.143 63.8

Fountain Creek at Pueblo 7.1449 –.2107 –.0190 –.0072 .0864 0.086 85.4

Arkansas River near Avondale 6.5576 –.2419 .0483 .0529 .1204 0.118 81.7

Q Q

π π

Q Q π π
14 Methods to Identify Changes in Background Water-Quality Conditions Using Dissolved-Solids Concentrations and Loads as 

Indicators, Arkansas River and Fountain Creek, in the Vicinity of Pueblo, Colorado

a storm. Dissolved-solids concentration decreased as well, but 

to a lesser extent than would be expected for sustained summer 

streamflow at this level. The resulting load was nearly large 

enough to exceed the daily tolerance limit at the site Fountain 

Creek at Pueblo. This example showed that a load could 

approach the threshold if streamflow increased without a corresponding decrease in dissolved solids, again indicating waterquality changes occurred with respect to loading.

Identification of Long-Term Changes in 

Water Quality Using Dissolved-Solids Load

The use of dissolved-solids load to identify changes in 

water quality is not limited to comparisons using a tolerance 

limit. Other analysis techniques that use a mass-load approach 

could provide valuable information about long-term changes in 

-400

-200

0

200

400

-200

0

200

400

600

800

1,000

-400

0

400

800

1,200

1,600

-400

-200

0

200

400

600

800

-500

-250

0

250

500

FLOW-ADJUSTED DISSOLVED SOLIDS CONCENTRATION, IN MILLIGRAMS PER LITER

2002 flow-adjusted dissolved-solids concentration

Mean value of the background concentration data

Tolerance limit (95th-percent confidence level and 

 97.5th-percent population coverage)

EXPLANATION

Arkansas River at Portland (1983-2001)

Arkansas River above Pueblo (1986-2001)

Arkansas River at Pueblo (1989-2001)

Fountain Creek at Pueblo (1986-2001)

Arkansas River near Avondale (1986-2001)

JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC

Figure 7. Tolerance limits on flow-adjusted dissolved-solids concentration data at selected sites on the 

Arkansas River and Fountain Creek with comparisons to flow-adjusted concentrations for 2002.
Identification of Long-Term Changes in Water Quality Using Dissolved-Solids Load 15

the study area. The following sections of this report describe 

three other approaches that use estimates of dissolved-solids 

load to make long-term comparisons between sites in the study 

area. The focus of these approaches is on the primary sites— 

Arkansas River above Pueblo, Arkansas River near Avondale, 

and Fountain Creek at Pueblo (fig. 1). Dissolved-solids load at 

the site Arkansas River above Pueblo represents the mass in the 

main stem of the Arkansas River from Pueblo Reservoir downstream to the confluence with Fountain Creek. Dissolved-solids 

load at the site Fountain Creek at Pueblo represents the major 

tributary inflow to the Arkansas River in the study area. Load at 

the site Arkansas River near Avondale represents the approximate sum of these two upstream sites and any unmeasured 

mass. The majority of the unmeasured mass consists of several 

unmeasured inflows along the study reach. These analyses do 

not provide results for short-term decision making for implementing a water-quality management program but do provide 

an additional means of assessing long-term changes in water 

quality.

JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC

2002 estimated daily dissolved-solids load

Mean value of the background load data

Tolerance limit (95th-percent confidence 

 level and 97.5th-percent population coverage)

EXPLANATION

Arkansas River at Portland (1983-2001)

Arkansas River above Pueblo (1986-2001)

Arkansas River at Pueblo (1989-2001)

Fountain Creek at Pueblo (1986-2001)

Arkansas River near Avondale (1986-2001)

0

500

1,000

1,500

2,000

2,500

0

1,000

2,000

3,000

4,000

5,000

0

1,000

2,000

3,000

4,000

5,000

0

1,000

2,000

3,000

4,000

0

2,000

4,000

6,000

8,000

ESTIMATED DISSOLVED SOLIDS LOAD, IN TONS PER DAY

Figure 8. Tolerance limits on dissolved-solids load at selected sites on the Arkansas River and Fountain 

Creek.
16 Methods to Identify Changes in Background Water-Quality Conditions Using Dissolved-Solids Concentrations and Loads as 

Indicators, Arkansas River and Fountain Creek, in the Vicinity of Pueblo, Colorado

Comparison of Cumulative Load at Selected Sites

Daily dissolved-solids load was estimated for each primary site as described in the section “Tolerance Limits for Estimated Dissolved-Solids Load.” Daily loads at each site were 

summed to provide a cumulative load for each site starting January 1, 1986, when all the sites had continuous water-quality 

monitors in place to measure specific conductance. A doublemass plot (fig. 9) of the cumulative loads for the sites Arkansas 

River above Pueblo and Fountain Creek at Pueblo compared to 

the cumulative load at the site Arkansas River near Avondale 

shows that the contribution of mass at the site Arkansas River 

near Avondale from the site Arkansas River above Pueblo 

became proportionately less beginning about 1993. Conversely, 

the mass contributed by the site Fountain Creek at Pueblo 

became increasingly larger after 1993; transmountain returnflow exchanges in Fountain Creek began in 1981 (Lewis, 1999). 

Although these double-mass curves do not provide immediate 

feedback, a marked change in the relation among the sites over 

several years are a useful tool for identifying changes in the 

source areas for dissolved solids.

Comparison of Percent Contribution of Load from 

Selected Sites

Daily dissolved-solids loads at the sites Arkansas River 

above Pueblo and Fountain Creek at Pueblo were compared to 

the daily load at the downstream site, Arkansas River near 

Avondale. The percent contribution of load from each site with 

respect to the downstream site was calculated on a daily basis 

(fig. 10). Local regression (LOWESS) smoothing of the daily 

calculated values showed that there was a general increase in 

the percent contribution from Fountain Creek (Fountain Creek 

at Pueblo) and a decrease in contribution from the Arkansas 

River downstream from Pueblo Reservoir (Arkansas River 

above Pueblo) from 1986 to 1996. LOWESS smoothing is a 

nonparametric smoothing technique that uses a running mean to 

predict values at each point (S-PLUS 2000 User’s Guide, 1999). 

However, the percent contributions from the two sites have 

remained relatively unchanged since 1997 with an average of 

about 35 percent of the dissolved-solids load at the site Arkansas River near Avondale coming from each site.

Median seasonal loads for high-flow and low-flow periods 

for each calendar year also were computed (fig. 10). The highflow period included those data from April 11 through September 2 of each year whereas the low-flow period included those 

data from September 3 through April 10. A comparison of the 

LOWESS smoothing lines showed the differences in contribution from the sites Arkansas River above Pueblo and Fountain 

Creek at Pueblo during each of the two seasonal periods. During 

high flow, the contribution of load from the site Fountain Creek 

at Pueblo generally was less than 20 percent because of the 

much larger load typically observed in the Arkansas River at 

this time; seasonal contributions from the site Fountain Creek at 

Pueblo ranged from 8 to 38 percent. Overall, an increasing trend 

in the contribution from the site Fountain Creek at Pueblo was 

observed from 1986 to 2001. Typically, the contribution from 

the Arkansas River during high flow ranged from 48 to 

0

0 123 4 56 7

1

2

3

4

5

CUMMULATIVE DISSOLVED-SOLIDS LOAD,

IN MILLIONS OF TONS

CUMULATIVE DISSOLVED SOLIDS LOAD AT ARKANSAS

RIVER NEAR AVONDALE, IN MILLIONS OF TONS 1990 1995

1986-1993

1986-1993

1993-2001

1993-2001

Arkansas River above Pueblo

Fountain Creek at Pueblo

Trend line

2000

Figure 9. Comparison of cumulative dissolved-solids loads at Arkansas River 

above Pueblo and Fountain Creek at Pueblo to cumulative dissolved-solids load at 

Arkansas River near Avondale, 1986–2001.
Identification of Long-Term Changes in Water Quality Using Dissolved-Solids Load 17

73 percent. During low flow, the contributions from the 

two upstream sites were similar. The site Fountain Creek at 

Pueblo contributed from 22 to 45 percent of the load, and the 

Arkansas River contributed from 19 to 38 percent. These analyses showed that changes in the contributions from the 

upstream sites are helpful in identifying long-term changes in 

source areas associated with changes in water quality.

Comparison of Unmeasured Load from Other Sites

The analysis described in the previous section showed that, 

on average, about 70 percent of the dissolved-solids load at the 

downstream site Arkansas River near Avondale can be associated with the sites Arkansas River above Pueblo and Fountain 

Creek at Pueblo. As such, the contribution from the unmeasured 

sources was about 30 percent for the entire period (fig. 11). This 

percentage, however, is somewhat higher during low-flow periods (September–March) when smaller loads are present in the 

river and contribution from inputs such as wastewater-treatment 

effluent, tributary inflows, and ground-water inflow is more 

pronounced. The percent contribution from these unmeasured 

sources decreases during high-flow periods (April–August). 

The most important unmeasured sources of dissolved-solids 

load to the Arkansas River have been identified, but insufficient 

daily data existed to make reliable estimates of the daily contribution. Potential important sources in the study area (fig. 1) are 

Wild Horse Creek, Pueblo Wastewater Treatment Plant, Salt 

Percent contribution of load during 

 seasonal high-flow period

Percent contribution of load during 

 seasonal low-flow period

Percent contribution of daily load

Percent contribution of load during 

 high-flow period (LOWESS curve)

Percent contribution of load during 

 low-flow period (LOWESS curve)

EXPLANATION

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

0

20

40

60

80

100

0

20

40

60

80

100

DAILY AND SEASONAL DISSOLVED-SOLIDS LOAD, AS A PERCENTAGE 

OF DAILY AND SEASONAL DISSOLVED-SOLIDS LOAD 

AT ARKANSAS RIVER NEAR AVONDALE 

Percent contribution from Fountain Creek at Pueblo

Percent contribution from Arkansas River above Pueblo

Figure 10. Percent contribution of dissolved-solids loads from Arkansas River above 

Pueblo and Fountain Creek at Pueblo to dissolved-solids load at Arkansas River near 

Avondale, 1986–2001.
18 Methods to Identify Changes in Background Water-Quality Conditions Using Dissolved-Solids Concentrations and Loads as 

Indicators, Arkansas River and Fountain Creek, in the Vicinity of Pueblo, Colorado

Creek, St. Charles River, and ground-water inflow. Additional 

data-collection activities are needed to quantify these sources. 

This analysis identifies long-term changes in the overall percentage of unmeasured dissolved-solids load to the system.

Summary

Effective management of existing water-storage capacity 

in the Arkansas River Basin is anticipated to help satisfy the 

need for water in southeastern Colorado. A strategy to meet 

these needs has been developed, but implementation could 

affect the water quality of the Arkansas River and Fountain 

Creek in the vicinity of Pueblo. Because no known methods are 

available to determine what effects future changes in operations 

will have on water quality, the U.S. Geological Survey, in cooperation with the Southeastern Colorado Water Activity Enterprise, began a study in 2002 to develop methods that could identify if future water-quality conditions have changed 

significantly from background (preexisting) water-quality conditions. Specifically, this report: (1) designates daily background water-quality conditions at selected sites; (2) establishes 

the use of tolerance limits to identify statistically significant 

daily departures from these background conditions; and (3) presents other analysis techniques to help identify long-term 

changes in mass load. Additionally, these methods provide 

information that can be used by various water-resource agencies for an internet-based decision-support tool. 

The primary study sites were Arkansas River above 

Pueblo, Fountain Creek at Pueblo, and Arkansas River near 

Avondale. Additional sites included Arkansas River at Portland 

and Arkansas River at Moffat Street at Pueblo. Dissolved solids 

(salinity) was chosen as the indicator parameter in this study 

because it is a good indicator of the general water quality in the 

study area and can be accurately estimated from available specific-conductance data. For the study, daily dissolved-solids 

concentrations at each site were calculated by developing a 

regression equation at each site from paired instantaneous 

specific-conductance and dissolved-solids data collected from 

1979 through 2001, and applying the regression equation at 

each site to the mean daily specific conductance measured at 

each site to obtain an estimated or computed mean daily dissolved-solids concentration.

Daily and instantaneous specific-conductance data for the 

study sites were retrieved from the USGS NWIS database. The 

background periods included calendar years 1986–2001 for all 

three primary study sites, 1983–2001 for Arkansas River at 

Portland, and 1989–2001 for Arkansas River at Pueblo. In addition, daily streamflow data were retrieved for all sites.

Tolerance limits were computed by using background 

information about the means and the amount of variability in the 

data. A one-tailed tolerance limit (upper) was calculated. One 

value for the standard deviation was used in the calculation of 

an individual tolerance limit at each site on the Arkansas River 

0

20

40

60

80

100

DAILY AND SEASONAL DISSOLVED-SOLIDS 

LOAD, AS A PERCENTAGE OF 

DAILY AND SEASONAL

DISSOLVED-SOLIDS LOAD AT

ARKANSAS RIVER NEAR AVONDALE 

Percent contribution of load during seasonal 

 high-flow period

Percent contribution of load during seasonal 

 low-flow period

Percent contribution of daily load

Percent contribution of load during high-flow 

 period (LOWESS curve)

Percent contribution of load during low-flow 

 period (LOWESS curve)

EXPLANATION

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

19981999

2000

2001

Percent contribution from unmeasured sources

Figure 11. Percent contribution of dissolved-solids load from unmeasured sources to 

dissolved-solids load at Arkansas River near Avondale, 1986–2001.
References Cited 19

because the variance in the daily concentrations was relatively 

constant at each of these sites. Two values for the standard deviations were used to compute tolerance limits at the site Fountain 

Creek at Pueblo because the daily variance showed substantial 

differences depending on the time of the year. Tolerance limits 

for dissolved-solids concentrations were calculated and compared to selected summary statistics for the background period 

for each site to determine if the methodology was reasonable. 

The methodology provided a tool with defined statistical probabilities associated with the various tolerance limits.

Dissolved-solids concentrations exceeded the tolerance 

limits at all four sites on the Arkansas River during the summer 

of 2002. These exceedances were particularly evident when 

streamflow from Pueblo Reservoir was reduced and return 

flows and ground-water influences to the river were more prevalent. Downstream from Pueblo, dissolved-solids concentrations in the river were diluted by Fountain Creek, which 

resulted in routine exceedances of the tolerance limit but to a 

lesser extent. No exceedances were observed at Fountain at 

Pueblo. Comparisons to the 2002 data illustrated the utility of 

using concentration data in the analysis and the need to adjust 

the concentration data to account for varying streamflow.

Background concentrations were flow adjusted to remove 

much of the variability due to streamflow. Comparisons to 2002 

data showed that nearly all the flow-adjusted concentrations at 

the site Arkansas River near Avondale were less than the tolerance limit. The results illustrated the effects of using flowadjusted concentrations. However, numerous exceedances of 

the flow-adjusted tolerance limits were observed at the sites 

Arkansas River above Pueblo and Arkansas River at Pueblo. 

These results were similar to the results observed using nonadjusted concentration data, which indicated that the method 

was able to identify a change in the ratio of source waters at 

these sites under streamflow conditions somewhat less than 

50 ft3/s. 

Daily dissolved-solids loads at each study site were estimated, and tolerance limits were calculated. Comparisons of 

daily load for 2002 to tolerance limits at each site did not show 

any exceedances, which was expected because of the low 

streamflow observed in 2002. However, it was shown that the 

calculated loads could approach the thresholds if streamflow 

increased without a corresponding decrease in dissolved-solids 

concentration.

Other analysis techniques using a mass-balance approach 

also can provide valuable information about long-term changes 

in the study area. A marked change in the cumulative mass load 

at two sites could help identify a change in the source areas for 

dissolved solids. Changes in the percent contribution of dissolved-solids load at the sites Arkansas River above Pueblo and 

Fountain Creek at Pueblo with respect to the site Arkansas 

River near Avondale also can prove helpful in identifying longterm changes in source areas. Similarly, changes in the unmeasured proportion of the mass load equation could signify 

changes in the source areas to the river. Additional data-collection activities are needed to quantify the sources of unmeasured 

load to the river.

References Cited

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Cain, Doug, 1987, Relations of specific conductance to streamflow and selected water-quality characteristics of the Arkansas River Basin, Colorado: U.S. Geological Survey WaterResources Investigation Report 87–4041, 93 p.

Cohn, T.A., Caulder, D.L., Gilroy, E.J., Zynjuk, L.D., and Summers, R.M., 1992, The validity of a simple log-linear model 

for estimating fluvial constituent loads: An empirical study 

involving nutrient loads entering Chesapeake Bay: Water 

Resources Research, v. 28, no. 9, p. 2,353–2,364.

Cohn, T.A., 2002, ESTIMATOR 2002: A Beta release by Tim 

Cohn accessed December 12, 2002, at http://

www159.pair.com/cohns/TimCohn/ TAC_Software/

Estimator/e2002

Colorado Climate Center, 2002, Department of Atmospheric 

Science, Colorado State University, Fort Collins, 

Colorado, accessed May 24, 2003, at http://

climate.atmos.colostate.edu/droughtqanda.shtml

Colorado Department of Public Health and Environment, 2001, 

Water Quality Control Commission Regulation No. 31, The 

basic standards and methodologies for surface water, 

accessed March 23, 2002 at http://www.cdphe.state.co.us/op/

regs/waterregs/100231.pdf

GEI Consultants Inc., 2000, Southeastern Colorado Water and 

Storage Needs Assessment Enterprise: Preferred Storage 

Options Plan, Englewood, Colorado, 101 p.

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

Water Resources, Elsevier Science Publishing Company 

Inc., New York, New York.

Hem, J.D., 1985, Study and interpretation of the chemical characteristics of natural water: U.S. Geological Survey WaterSupply Paper 2254, 263 p.

Lewis, M.E., and Brendle, D.L., 1998, Relations of streamflow 

and specific conductance trends to the lower Arkansas River, 

Southeastern Colorado: U.S. Geological Survey WaterResources Investigations Report 97–4239, 48 p.

Lewis, M.E., 1999, Simulated effects of water exchanges on 

streamflow and specific conductance in the Arkansas River 

upstream from Avondale, Colorado: U.S. Geological Survey 

Water-Resources Investigations Report 98–4140, 34 p.

Natrella, M.G., 1963, Experimental Statistics, NBS Handbook 

91, National Bureau of Standards, Washington, D.C.

Ortiz, R.F., Lewis, M.E., and Radell, M.J., 1998, Water-quality 

assessment of the Arkansas River Basin, Southeastern Colorado, 1990–93: U.S. Geological Survey Water-Resources 

Investigations Report 97–4111, 69 p.
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Indicators, Arkansas River and Fountain Creek, in the Vicinity of Pueblo, Colorado

Pielke, Sr., R.A., Doesken, N., and Bliss, O., 2002, Climate of 

Colorado. Climatography Report #60, National Climatic 

Data Center, Asheville, NC. accessed June 4, 2003, at http://

ccc.atmos.colostate.edu/pdfs/climateofcoloradoNo.60.pdf

PSOP Implementation Committee, 2001, Final Draft PSOP 

Implementation Committee Report, Southeastern Colorado 

Water Activity Enterprise, Pueblo, Colorado, 29 p.

Rickert, D.A., 1985, Compensation for discharge in detecting 

trends in water-quality data: U.S. Geological Survey, Branch 

of Water Quality, Memorandum 85.17.

S-PLUS 2000 User’s Guide, 1999, Data Analysis Products 

Division, MathSoft, Seattle, Washington.

U.S. Environmental Protection Agency, 1992, Hazard Ranking 

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