Regression Models for Estimating Salinity and Selenium 

Concentrations at Selected Sites in the Upper Colorado 

River Basin, Colorado, 2009–2012

Open-File Report 2014–1015

U.S. Department of the Interior

U.S. Geological Survey
Prepared in cooperation with the Bureau of Reclamation, the Colorado River Water 

Conservation District, and the Bureau of Land Management

Regression Models for Estimating Salinity and Selenium 

Concentrations at Selected Sites in the Upper Colorado 

River Basin, Colorado, 2009–2012

By Joshua I. Linard and Keelin R. Schaffrath

Open-File Report 2014–1015

U.S. Department of the Interior

U.S. Geological Survey
ii

U.S. Department of the Interior

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia 2014

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Suggested citation:

Linard, J.I., and Schaffrath, K.R., 2014, Regression models for estimating salinity and selenium concentrations at 

selected sites in the Upper Colorado River Basin, Colorado, 2009–2012: U.S. Geological Survey Open-File Report 

2014–1015, 28 p., http://dx.doi.org/10.3133/ofr20141015.

ISSN 2331-1258 (online)
iii

Contents

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

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

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

Study-Area Description .............................................................................................................................................. 3

Study-Site Selection and Data Compilation ............................................................................................................... 5

Model Development....................................................................................................................................................... 8

Regression Models To Estimate Salinity and Selenium Concentration ......................................................................... 9

Salinity Models..........................................................................................................................................................11

Selenium Models ......................................................................................................................................................16

Use of Continuous Data in the Application of Salt and Selenium Regression Models..................................................23

Summary ......................................................................................................................................................................26

References Cited..........................................................................................................................................................27
iv

Figures

Figure 1. The study area and study sites within the Upper Colorado River Basin, Colorado, also showing 

irrigated land and the Mancos Shale ............................................................................................................................. 4

Figure 2. Comparison of measured and estimated salinity concentrations at six sites using either specific 

conductance or streamflow as an explanatory variable. A, SCanyon. B, PiceanceRyan. C, PiceanceWhite. 

D, Yellow. E, DoloresAtBedrock. F, DoloresNrBedrock ............................................................................................... 11

Figure 3. Comparison of measured and estimated selenium concentrations at six sites using specific 

conductance, streamflow, and (or) seasonality explanatory variables. A, Stateline. B, GunnWhitewater. 

C, GunnDelta. D, NForkGunn. E, UncDelta. and F, UncColona .................................................................................. 17

Figure 4. Example of the use of continuous data with the regression models to estimate A, salinity 

concentration at PiceanceWhite and B, selenium concentration at GunnWhitewater using continuously 

measured specific conductance .................................................................................................................................. 24

Tables

Table 1. Summary statistics of salinity and selenium data used to develop regression models for selected study 

sites within the Upper Colorado River Basin, Colorado ................................................................................................. 6

Table 2. Model coefficients and evaluation statistics for salinity and selenium regression models developed for 

selected study sites within the Upper Colorado River Basin, Colorado ....................................................................... 10
v

Conversion Factors

Inch/Pound to SI

Multiply By To obtain

Area

square mile (mi2) 259.0 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2) 

Flow Rate

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

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

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

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

Water year, as used in this report, refers to the period that begins on October 1 of the previous year and ends the following 

September 30 and is designated by the year in which it ends.
1

Regression Models for Estimating Salinity and Selenium 

Concentrations at Selected Sites in the Upper Colorado 

River Basin, Colorado, 2009–2012

By Joshua I. Linard and Keelin R. Schaffrath

Abstract

Elevated concentrations of salinity and selenium in the tributaries and main-stem reaches of the 

Colorado River are a water-quality concern and have been the focus of remediation efforts for many years. 

Land-management practices with the objective of limiting the amount of salt and selenium that reaches the 

stream have focused on improving the methods by which irrigation water is conveyed and distributed.

Federal land managers implement improvements in accordance with the Colorado River Basin Salinity 

Control Act of 1974, which directs Federal land managers to enhance and protect the quality of water 

available in the Colorado River. In an effort to assist in evaluating and mitigating the detrimental effects of 

salinity and selenium, the U.S. Geological Survey, in cooperation with the Bureau of Reclamation, the 

Colorado River Water Conservation District, and the Bureau of Land Management, analyzed salinity and 

selenium data collected at sites to develop regression models. The study area and sites are on the Colorado 

River or in one of three small basins in Western Colorado: the White River Basin, the Lower Gunnison

River Basin, and the Dolores River Basin. By using data collected from water years 2009 through 2011, 

regression models able to estimate concentrations were developed for salinity at six sites and selenium at 

six sites. At a minimum, data from discrete measurement of salinity or selenium concentration, 

streamflow, and specific conductance at each of the sites were needed for model development. 

Comparison of the Adjusted R2 and standard error statistics of the two salinity models developed at each 

site indicated the models using specific conductance as the explanatory variable performed better than 

those using streamflow. The addition of multiple explanatory variables improved the ability to estimate 

selenium concentration at several sites compared with use of solely streamflow or specific conductance.

The error associated with the log-transformed salinity and selenium estimates is consistent in log space; 

however, when the estimates are transformed into non-log values, the error increases as the estimates 

decrease. Continuous streamflow and specific conductance data collected at study sites provide the means 

to examine temporal variability in constituent concentration and load. The regression models can estimate 

continuous concentrations or loads on the basis of continuous specific conductance or streamflow data. 

Similar estimates are available for other sites at the USGS National Real-Time Water Quality Web page 

(http://nrtwq.usgs.gov) and provide water-resource managers with a means of improving their general 

understanding of how constituent concentration or load can change annually, seasonally, or in real time.

Introduction

Elevated concentrations of salinity and selenium in the tributaries and main-stem reaches of the 

Colorado River are a water-quality concern and have been the focus of remediation efforts for many years. 

“Salinity” refers to mineral salts or solids dissolved in water, and selenium is a trace element that 

bioaccumulates in the food chain. Salt and selenium limit municipal uses of water, reduce agricultural 

productivity, and, in the case of selenium, can lead to mortality, abnormalities, and reproductive failure in 
2

waterfowl and fish (Butler and others, 1996; Presser and Luoma, 2006; Tuttle and Grauch, 2009; Leib and 

others, 2012). In 1985, the National Irrigation Water Quality Program, a multiagency program within the 

Department of the Interior, began investigating the effects of irrigation drainage on water quality and on 

fish and wildlife in the Western United States (Bureau of Reclamation, 2001). The investigations led to the 

discovery that irrigation drainage contributes a significant part of the nonpoint-source salinity and 

selenium to the Upper Colorado River Basin and the discovery that high concentrations of selenium are 

present in water, biota, and sediment (Wright and Butler, 1993; Butler, 1996; Butler and others, 1991,

1996; Butler and Leib, 2002). 

Selenium is paradoxical in that it is a nutritional requirement in small amounts but toxic in slightly 

greater amounts (Lemly, 1993). Various tributaries to the Gunnison and Colorado Rivers are on the State 

of Colorado’s 303(d) list as impaired for selenium (Colorado Department of Public Health and 

Environment, 2012). Selenium cycles through the aquatic environment and can quickly reach toxic levels 

as a result of bioconcentration in aquatic organisms (Lemly, 2002). Toxic levels of selenium can cause 

reproductive failure, deformities, and other adverse effects in birds and fish, including some threatened 

and endangered fish species (Ohlendorf and others, 1986; Presser and Ohlendorf, 1987; Hamilton, 1998; 

Lemly, 2002). The Colorado River and portions of the river’s tributaries are designated critical habitat for 

four fish species listed under the Endangered Species Act: the Colorado pikeminnow (Ptychocheilus 

lucius), razorback sucker (Xyrauchen texanus), bonytail (Gila elegans), and humpback chub (Gila cypha).

The geology, land cover, land use, and precipitation characteristics in the basin control streamflow 

and water chemistry (Kenney and others, 2009). Natural, nonpoint sources of salinity and selenium 

generally originate from the weathering and dissolution of geological formations that have high salt and 

selenium content (Presser and Ohlendorf, 1987; Prairie and others, 2005). Salts and trace elements are 

mobilized through dissolution, surface runoff, and percolation into the groundwater system, which 

discharges to the river system as base flow (Warner and others, 1985). The application of irrigation water 

to agricultural lands increases the percolation rate and, consequently, the dissolution and transport of 

salinity and selenium to streams (Prairie and others, 2005; Kenney and others, 2009). 

Land-management practices aimed at limiting the amount of salt and selenium that reaches the 

stream have focused on improving the methods by which irrigation water is conveyed and distributed. 

Federal land managers implement these practices in accordance with the Colorado River Basin Salinity 

Control Act of 1974, which directs Federal land managers to enhance and protect the quality of water 

available in the Colorado River. To provide the Bureau of Reclamation with information that assists in 

evaluating and planning salinity-control needs, Liebermann and others (1989) developed multiple linear 

regression models to estimate annual and monthly salinity concentrations. Streamflow and specific 

conductance (depending on data availability) were the explanatory variables used in the multiple linear 

regression models. Streamflow had a negative relation to the concentration of dissolved solids, termed 

“salinity” in this report, and specific conductance had a positive relation to salinity, which was consistent 

with patterns described by Hem (1985). To assist the Bureau of Reclamation with understanding salinity,

the salinity concentration estimates were converted to loads, which are defined as the weight of material 

flowing past the sampling site during a specific time interval. Since the publication of the study by 

Liebermann and others (1989), the U.S. Geological Survey has applied the models on a biennial basis to 

estimate salinity concentration and load at 20 of the sites analyzed by Liebermann and others (1989). The 

most recent updates to the models and their estimates were made publically available in a report produced 

by the Bureau of Reclamation (2011b, http://www.usbr.gov/uc/progact/salinity/pdfs/PR23.pdf). A more 

current study by Mayo and Leib (2012) produced multiple linear regression models capable of estimating 

selenium concentrations at two sites in the Gunnison and Colorado Rivers. These models used daily 

streamflow and time data, capturing a seasonal cycling of selenium, as their explanatory variables.

Increased interest in estimates of water quality at temporal resolutions greater than annual or 

monthly has led to the use of continuously monitored data in the application of multiple linear regression 
3

models. Specifically, the U.S. Geological Survey National Real-Time Water Quality Web page

(http://nrtwq.usgs.gov) computes water quality at numerous sites across the United States from real-time,

continuously measured data. Currently, there is an effort to use continuous data measured in the Upper

Colorado River Basin in the application of the regression models developed at 20 of the sites analyzed by 

Liebermann and others (1989). 

To enhance the understanding of salinity and selenium in the Upper Colorado River Basin, the 

network of sites measuring those types of data was expanded. Discrete and continuous data were collected 

at these additional sites. In an effort to assist in evaluating and mitigating the detrimental effects of salinity 

and selenium in the Upper Colorado River Basin, the U.S. Geological Survey, in cooperation with the 

Bureau of Reclamation, the Colorado River Water Conservation District, and the Bureau of Land 

Management, developed regression models from the discrete salinity and selenium data collected at the 

new sites. 

Purpose and Scope

This report documents regression models developed to assist land managers with evaluating and 

planning salinity and selenium control needs in the Upper Colorado River Basin. A description of the 

discrete data collected at 11 sites in the Upper Colorado River Basin from water years 2009 to 2011 is 

provided. Using those data, regression models for estimating concentrations were developed for salinity at 

six sites and selenium at six sites. Data from October through April of water year 20121 were used to 

verify the models. The models provide a general understanding of the temporal dynamics of constituent 

concentration or load on a seasonal or annual basis when applied to continuous data. Moreover, 

concentration and loads estimated at study sites in real time from continuous data, similar to that presented 

by the USGS (http://nrtwq.usgs.gov), provide water-resource managers with easy access to data for the 

system they manage.

Study-Area Description

The study area and sites are on the Colorado River or in one of three small basins in Western 

Colorado (fig. 1). From north to south, the basins are the White River Basin, the Lower Gunnison River 

Basin, and the Dolores River Basin. The majority of precipitation in the lower elevations, which are 

classified as a semiarid climate, falls as rain during the late summer and early fall (July through 

September). The headwaters of all of the basins originate in higher elevations that are considered 

subalpine zones. The majority of precipitation in the higher elevations falls as snow and accumulates in a 

seasonal snowpack. The spring snowmelt of the seasonal snowpack dominates the annual streamflow 

cycle. Streamflow begins to increase in March or April, peaks between May and June, and decreases in 

July and August. In the lower elevations, smaller increases in streamflow occur in July and August 

because of summer thunderstorms. Exceptions to the snowmelt hydrograph result from irrigation season 

return flows and controlled releases from reservoirs in the study area (Butler and others, 1991). Based on 

the National Land Cover Database in 2001 (Homer and others, 2004), the land cover in Western Colorado 

is generally classified as shrubs or forest. All of the basins included in the study area have areas of 

irrigated agriculture. In the entire study area, there were more than 3,650 square kilometers (1,409 square 

miles) of irrigated parcels in 2005 (Colorado Water Conservation Board, 2010). The Mancos Shale 

underlies the irrigated parcels in many areas, and studies indicate this formation is the most important 

contributor of salinity and selenium to the streams in the Gunnison River Basin (Liebermann and others, 

1989; Seiler and others, 2003).

 1 A water year begins on October 1 of the previous year and ends the following September 30 and is designated by the year in 

which it ends.
4

Figure 1. The study area and study sites within the Upper Colorado River Basin, Colorado, also showing irrigated 

land and the Mancos Shale. (Complete site names given in table 1.)
5

Study-Site Selection and Data Compilation

Sites chosen for this study were selected on the basis of data availability and cooperator interest. 

At a minimum, data from discrete measurement of salinity or selenium concentration, streamflow, and 

specific conductance at each of the sites were needed for model development. In this report, the sites are 

referred to by the short names listed in table 1. For each site, salinity and selenium concentrations, along 

with streamflow and specific conductance measured at the time of sampling, were retrieved from the 

USGS National Water Information System (NWIS) (U.S. Geological Survey, 1998). Discrete sample data 

generally were available for water years 2009 through 2011. Additional data from October through April

of water year 2012 were used to verify the models.
6

Table 1. Summary statistics of salinity and selenium data used to develop regression models for selected study sites within the Upper Colorado River 

Basin, Colorado.

[Streamflow, in cubic feet per second; specific conductance, in microsiemens per centimeter at 25 degrees Celsius; selenium concentration, in micrograms per liter; 

salinity concentration, in milligrams per liter]

U.S 

Geological 

Survey 

streamflowgaging 

station 

number

Site short name (in 

bold) and full name 

(in parentheses)

Number 

of 

samples

Date Streamflow Specific conductance Constituent concentration

Beginning Ending Minimum Median Maximum Minimum Median Maximum Minimum Median Maximum

Salinity

09085150 SCanyon (Colorado 

R Abv South 

Canyon Cr Nr 

Glenwood Spgs) 

18 11/07/08 08/31/11 1,210 2,045 11,500 300 980 1,320 166 547 751

09306200 PiceanceRyan

(Piceance Creek Bl 

Ryan Gulch, Nr Rio 

Blanco, CO)

12 11/13/08 08/23/11 3.0 22 122 892 1,425 2,020 595 967 1,420

09306222 PiceanceWhite

(Piceance Creek at 

White River, CO) 

12 11/12/08 08/24/11 4.4 30 135 999 1,830 3,320 681 1,242 2,160

09306255 Yellow (Yellow 

Creek Near White 

River, CO)

12 11/12/08 08/24/11 0.49 1.2 3.5 2,210 3,800 4,260 1,570 2,588 2,890

09169500 DoloresAtBedrock

(Dolores River at 

Bedrock, CO)

16 11/19/08 08/18/11 33 62 958 294 768 1,250 177 447 854

09171100 DoloresNrBedrock

(Dolores River Near 

Bedrock, CO)

15 11/18/08 08/18/11 38 64 1,000 320 1,870 3,770 192 1,065 2,450
7

Table 1. Summary statistics of salinity and selenium data used to develop regression models for selected study sites within the Upper Colorado River 

Basin, Colorado.—Continued

[Streamflow, in cubic feet per second; specific conductance, in microsiemens per centimeter at 25 degrees Celsius; selenium concentration, in micrograms per liter; 

salinity concentration, in milligrams per liter]

U.S 

Geological 

Survey 

streamflowgaging 

station 

number

Site short name (in 

bold) and full name 

(in parentheses)

Number 

of 

samples

Date Streamflow Specific conductance Constituent concentration

Beginning Ending Minimum Median Maximum Minimum Median Maximum Minimum Median Maximum

Selenium

09163500 Stateline (Colorado 

River Near 

Colorado-Utah State 

Line)

18 10/7/08 9/30/11 2,560 3,750 19,300 373 1,060 1,280 1.3 3.6 5.3

09152500 GunnWhitewater

(Gunnison River 

Near Grand 

Junction, CO) 

16 10/15/08 09/20/11 1,230 1,860 6,150 390 765 991 1.6 4.2 7.2

09144250 GunnDelta

(Gunnison River at 

Delta, CO) 

9 07/21/09 09/15/11 827 1,360 13,500 214 538 764 0.48 2.30 3.4

09136100 NForkGunn (North 

Fk Gunnison River 

Above Mouth Nr 

Lazear, CO) 

16 04/28/09 09/14/11 98 187 4,010 186 1,069 1,460 0.47 2.94 4.6

09149500 UncDelta

(Uncompahgre 

River at Delta, CO)

10 07/21/09 09/15/11 166 330 883 735 1,314 1,570 5.4 11.5 20.0

09147500 UncColona

(Uncompahgre 

River at Colona CO)

12 10/14/09 08/29/11 56 220 700 373 529 624 0.42 0.83 1.2
8

The number of discrete samples collected at the six salinity sites differed, and the range of values 

of each data type also differed between sites. Although the number of samples differed between the 

salinity sites, a data comparison between the sites gives a qualitative indication of the varied water quality 

in the Upper Colorado River Basin. The ranges also indicate the limits for which the regression models 

developed from the data are representative. The SCanyon (09085150) site had the largest streamflows

(minimum, 1,210 cubic feet per second (ft3/s); maximum, 11,500 ft3/s). The range of the specific 

conductance (minimum, 300 microsiemens per centimeter at 25 degrees Celsius (μS/cm); maximum,

1,320 μS/cm) was at the low end of the overall range for the salinity sites, and the salinity concentrations

(minimum, 166 milligrams per liter (mg/L); maximum, 751 mg/L) were the lowest measured at any of the 

salinity sites (table 1). In the White River Basin, 12 discrete water-quality samples were collected within 

water years 2009–11 from each the salinity sites. Based on the discrete data, the White River Basin sites—

PiceanceRyan (09306200), PiceanceWhite (09306222), and Yellow (09306255)—had the lowest 

streamflows (minimums less than or equal to 4.4 ft3/s; maximums less than or equal to 135 ft3/s) (table1).

The White River Basin sites also had minimum specific conductance greater than or equal to 892 μS/cm, 

which was greater than that measured at any of the salinity sites, and had the highest minimum 

concentrations of salinity (greater than or equal to 595 mg/L) of the salinity sites. In the Dolores River 

Basin—DoloresAtBedrock (09169500) and DoloresNrBedrock (09171100)—streamflow was about an 

order of magnitude greater than at the White River Basin sites, although the specific conductances were 

similar (table 1). DoloresNrBedrock is downstream from DoloresAtBedrock, and East and West Paradox 

Creeks enter the Dolores River between those two sites (fig. 1). East Paradox Creek flows through 

Paradox Valley, which is the most concentrated source of salt in the Colorado River Basin (Bureau of 

Reclamation, 2011a). Contrasting those data, discrete water-quality sample data collected in the Dolores 

River Basin indicated minimum salinity concentrations in the low range of the salinity sites (less than or 

equal to 192 mg/L).

Similar to the salinity sites, the number of discrete samples collected at the six selenium sites 

differed, and the range of values of each data type also differed between sites. Streamflows at Stateline 

(09163500) were the highest among the selenium sites (minimum, 2,560 ft3/s; maximum, 19,300 ft3/s),

and specific conductances were near the middle of the ranges of the other sites (table 1). The range of 

selenium concentrations at Stateline (minimum, 1.3 micrograms per liter (μg/L); maximum, 5.3 μg/L) 

were near the middle of the ranges of concentrations measured at the selenium sites (table 1). At the 

GunnWhitewater site (09152500), the minimum streamflow (1,230 ft3/s) and minimum specific 

conductance (390 μS/cm) were the second highest of the selenium sites (table 1). The selenium 

concentrations (minimum, 1.6 μg/L; maximum, 7.2 μg/L) at GunnWhitewater were the near highest 

measured at the selenium sites (table 1). The streamflows increased from NForkGunn (09136100, 

upstream) to GunnDelta (09144250, downstream), and the lowest minimum specific conductances (less 

than or equal to 214 μg/L) were measured at those sites (table 1). The selenium concentrations (minimums 

less than or equal to 0.48 μg/L and maximums less than or equal to 4.6 μg/L) were some of the lowest of 

the six selenium sites (table 1). The lowest selenium concentrations (minimum, 0.42 μg/L; maximum, 1.2 

μg/L) were measured at UncColona (09147500); UncDelta (09149500, downstream of UncColona) had 

the highest selenium concentrations (minimum, 5.4 μg/L; maximum, 20.0 μg/L) of the six selenium sites 

(table 1).

Model Development

Model development used water year 2009–11 data associated with the sampling that included the 

discrete measurements of constituent concentration (response variables), specific conductance (in 

microsiemens per centimeter at 25 degrees Celsius) and streamflow (in cubic feet per second). Consistent 

with the ordinary least squared regression procedure described by Liebermann and others (1989), the input 

values for constituent concentration, streamflow, and specific conductance were natural-log transformed.
9

Whereas the equations for estimating salinity concentration used either specific conductance or 

streamflow as the explanatory variable, the procedure to develop the models to estimate selenium was 

slightly different in that variables representing seasonality were included as potential explanatory 

variables. Sine and cosine terms were included to address seasonal differences and account for the 

possibility of two and (or) three annual cycles (in equation 1: k=1 or 2) (Helsel and Hirsch, 2002). Both 

variables (sine and cosine) are required to account for the amplitude, or magnitude, and the day of the 

peak (Helsel and Hirsch, 2002), where time, T, is the seasonality term representing the decimal portion of 

the year starting January 1. A generalized form of a regression equation using streamflow and seasonality 

to estimate selenium concentration is equation 1:

(ln ) sin( 2 ) cos( 2 ) ˆ lnC = bo + b1 Q + b2 k πT + b3 k πT . (1)

where, b0 is the regression equation intercept, bn is the coefficient of the nth explanatory variable, T is the 

seasonality term representing the decimal portion of the year starting January 1, and lnQ is streamflow in 

units of natural-log-transformed cubic feet per second.

Analysis of all the possible combinations of explanatory variables yielded the final model 

equations for selenium. The choice of the best model was based on values of the Prediction Error Sum of 

Squares (PRESS), standard error of the model (se), Adjusted R2

, and the collinearity of the model as 

determined by the variance inflation factor (VIF) statistic (Helsel and Hirsch, 2002). Low values of the 

first two statistics and the highest Adjusted R2 indicated the best model. Explanatory variables within a 

model were considered collinear when the VIF statistics were greater than 10 (Helsel and Hirsch, 2002). 

The explanatory variables in the final models were chosen such that instances of collinearity did not occur.

Model diagnostic plots, used in addition to the evaluation statistics for model selection, included a 

normal-probability plot of residuals and plots of the standardized residuals. Normality of model residuals 

was apparent when the normal-probability plot was approximately linear and the plots of the standardized 

residuals had no pattern and showed uniformity of scatter (homoscedasticity). The p-values of the model 

coefficients had to be marginally significant, or less than 0.05, to be included in the final model. This final 

criterion has one exception: only one of the model coefficients on the sine-cosine pair of the Fourier series 

had to be significant for the pair to be included in the model (Helsel and Hirsch, 2002). 

Evaluation of the performance of the final models consisted of comparing estimated salinity and 

selenium concentrations to water-quality sample data from October 2011 through April 2012. There were 

three water-quality samples at each salinity site available for verification of the salinity models. A total of

13 samples was available for verification of models developed at selenium sites, consisting of 2 samples 

each at NForkGunn and GunnDelta, 4 samples each at UncColona and GunnWhitewater, and 1 sample at 

UncDelta. The estimates of concentration from the regression models were the natural log of the estimated 

concentration, so they needed retransformation into appropriate units. A bias correction factor is required 

to address retransformation bias (Bradu and Mundlak, 1970), and this factor was calculated for each 

model by using the smearing method described by Duan (1983). Comparison of the retransformed 

estimates to the water-quality sample data indicated model performance.

Regression Models For Estimating Salinity and Selenium Concentrations

The regression models for estimating salinity and selenium concentration were developed through 

evaluating diagnostic statistics and plots. Through the model development process, it became apparent that 

models which included both specific conductance and streamflow tended to exhibit collinearity; evidence 

consisted of either VIF statistics exceeding a value of 10 and (or) a switch from the expected positive or 

negative relation with salinity or selenium. Consequently, the final models use either specific conductance 

or streamflow as an explanatory variable rather than both (table 2).
10

Table 2. Model coefficients and evaluation statistics for salinity and selenium regression models developed for selected study sites within the Upper 

Colorado River Basin, Colorado.

[Streamflow, in units of natural-log transformed cubic feet per second; SC, specific conductance, in units of natural-log transformed microsiemens per centimeter at 

25 degrees Celsius; --, variables not used in the regression; R2

, coefficient of determination; Standard error in units of natural-log transformed concentration; bold 

values indicate statistical significance (p less than 0.05)]

U.S. 

Geological 

Survey 

streamflowgaging 

station 

number

Site short name Y-axis 

intercept

Streamflow 

coefficient

SC 

coefficient Seasonal terms, k2πT Model p-value Adjusted R2 Standard 

error

Bias 

correction 

factor

k=1 k=2

Sine 

coefficient

Cosine 

coefficient

Sine 

coefficient

Cosine 

coefficient

Salinity regression models

09085150 SCanyon 11.2929 -0.6558 -- -- -- -- -- <0.0001 0.992 0.048 1.001

-0.671 -- 1.0133 -- -- -- -- <0.0001 0.998 0.023 1.000

09306200 PiceanceRyan 7.5371 -0.2226 -- -- -- -- -- <0.0001 0.938 0.049 1.001

-0.8999 -- 1.0709 -- -- -- -- <0.0001 0.982 0.027 1.000

09306222 PiceanceWhite 8.1063 -0.3043 -- -- -- -- -- <0.0001 0.922 0.082 1.003

-0.0539 -- 0.9541 -- -- -- -- <0.0001 0.990 0.029 1.000

09306255 Yellow 7.8445 -0.1743 -- -- -- -- -- <0.0001 0.342 0.130 1.007

0.3078 -- 0.9170 -- -- -- -- <0.0001 0.978 0.024 1.000

09169500 DoloresAtBedrock 7.0376 -0.2433 -- -- -- -- -- <0.0001 0.339 0.324 1.053

-0.7738 -- 1.0322 -- -- -- -- <0.0002 0.969 0.070 1.002

09171100 DoloresNrBedrock 9.5603 -0.6146 -- -- -- -- -- 0.0001 0.671 0.422 1.087

-0.5358 -- 0.9931 -- -- -- -- 0.0001 0.982 0.098 1.004

Selenium regression models

09163500 Stateline 5.8133 -0.5529 -- -0.2222 -0.0590 -- -- <0.0001 0.917 0.128 1.007

-6.0433 -- 1.0530 -0.0920 -0.1049 -- -- <0.0001 0.956 0.093 1.003

09152500 GunnWhitewater 5.8155 -0.5740 -- -0.2384 0.0897 -- -- <0.0001 0.879 0.152 1.009

-7.8680 -- 1.4053 0.0418 0.1408 -- -- <0.0001 0.909 0.132 1.006

09144250 GunnDelta 4.8568 -0.5813 -- -0.4201 -0.0979 -- -- <0.0001 0.974 0.102 1.003

-8.9887 -- 1.545 -- -- -- -- <0.0001 0.973 0.104 1.008

09136100 NForkGunn 4.4273 -0.6349 -- -- -- -- -- <0.0001 0.955 0.195 1.017

-6.387 -- 1.0764 -- -- -- -- <0.0001 0.986 0.108 1.005

09149500 UncDelta 5.5657 -0.5440 -- -0.2338 0.1313 0.0861 0.2009 <0.0001 0.993 0.037 1.000

-10.9850 -- 1.8861 0.2214 -0.0909 -- -- 0.0002 0.930 0.120 1.004

09147500 UncColona 0.8729 -0.2227 -- -- -- -- -- 0.0251 0.350 0.276 1.031

-9.5214 -- 1.4805 -- -- -- -- 0.0009 0.648 0.203 1.018
11

Salinity Models

Comparison of Adjusted R2 and standard error statistics of the two salinity models developed at 

each site showed that the models (p-value < 0.05) using specific conductance as the explanatory variable 

performed better than those using streamflow (table 2). A model performing perfectly would fit a 1:1 line 

exactly. The SCanyon models performed similarly, although the model using specific conductance as the 

explanatory variable more closely fit the 1:1 line than the model using streamflow (fig. 2A). In the White 

River Basin this relation was most evident when comparing measured and estimated salinity 

concentrations at Yellow; the measured concentration deviates from the estimated concentration more for 

the model using streamflow as the explanatory variable than for the model using specific conductance 

(fig. 2D). The utility of specific conductance as an explanatory variable for estimating salinity 

concentration was most evident in the Dolores River Basin. Models using streamflow as an explanatory 

variable did not perform as well (greater deviation from the 1:1 line) at lower streamflow, which 

corresponds to high concentration, than they did at higher streamflow, which corresponds to low 

concentration (fig. 2E, F).

Figure 2. Comparison of measured and estimated salinity concentrations at six sites using either specific 

conductance or streamflow as an explanatory variable. A, SCanyon. B, PiceanceRyan. C, PiceanceWhite.

D, Yellow. E, DoloresAtBedrock. F, DoloresNrBedrock.
12

Figure 2. Comparison of measured and estimated salinity concentrations at six sites using either specific 

conductance or streamflow as an explanatory variable. A, SCanyon. B, PiceanceRyan. C, PiceanceWhite.

D, Yellow. E, DoloresAtBedrock. F, DoloresNrBedrock.—Continued
13

Figure 2. Comparison of measured and estimated salinity concentrations at six sites using either specific 

conductance or streamflow as an explanatory variable. A, SCanyon. B, PiceanceRyan. C, PiceanceWhite.

D, Yellow. E, DoloresAtBedrock. F, DoloresNrBedrock.—Continued
14

Figure 2. Comparison of measured and estimated salinity concentrations at six sites using either specific 

conductance or streamflow as an explanatory variable. A, SCanyon. B, PiceanceRyan. C, PiceanceWhite.

D, Yellow. E, DoloresAtBedrock. F, DoloresNrBedrock.—Continued
15

Figure 2. Comparison of measured and estimated salinity concentrations at six sites using either specific 

conductance or streamflow as an explanatory variable. A, SCanyon. B, PiceanceRyan. C, PiceanceWhite.

D, Yellow. E, DoloresAtBedrock. F, DoloresNrBedrock.—Continued
16

Figure 2. Comparison of measured and estimated salinity concentrations at six sites using either specific 

conductance or streamflow as an explanatory variable. A, SCanyon. B, PiceanceRyan. C, PiceanceWhite.

D, Yellow. E, DoloresAtBedrock. F, DoloresNrBedrock.—Continued

Selenium Models

The addition of multiple explanatory variables improved the ability of the models to estimate 

selenium concentration at several selenium sites over using solely streamflow or specific conductance. 

The models developed at Stateline and GunnWhitewater included the seasonal explanatory variable

representing two annual cycles (k2πT, where k equals 1), and the evaluation statistics indicated that the

model using specific conductance performed better than the model using streamflow. The models for 

GunnDelta and UncDelta using streamflow included more seasonal explanatory variables than the models 

using specific conductance; GunnDelta used two annual cycles compared to none and UncDelta used two 

and three cycles compared to just two in the specific conductance model. In contrast to all the other 

models in this report, the evaluation statistics, the Adjusted R2 and standard error, indicated that models 

using streamflow at GunnDelta and UncDelta (p-value <0.05) performed better than those using specific 
17

conductance (table 2). The relation between selenium estimates and the 1:1 line illustrated in figure 3

indicates that models developed at GunnDelta and UncDelta (fig. 3C,E) perform better at higher 

streamflow (low concentration) than at lower streamflow. At sites like NForkGunn and UncColona, the 

Adjusted R2 and standard error indicated that models using a single explanatory variable performed better 

and that models using specific conductance as the explanatory variable, rather than streamflow, performed 

best. Regarding the visual comparison of measured concentrations to estimated concentrations, the 

benefits were less clear (fig. 3D). At NForkGunn, the estimates from both salinity models more closely 

resembled the measured concentrations at higher streamflows, which correspond to lower concentrations,

than at lower streamflows, which correspond to higher concentrations (fig. 3D). The amount of 

streamflow at UncColona did not seem to affect the ability of the model to estimate salinity concentration 

(fig. 3F).

Figure 3. Comparison of measured and estimated selenium concentrations at six sites using specific conductance, 

streamflow, and (or) seasonality explanatory variables. A, Stateline. B, GunnWhitewater. C, GunnDelta.

D, NForkGunn. E, UncDelta. and F, UncColona.
18

Figure 3. Comparison of measured and estimated selenium concentrations at six sites using specific conductance, 

streamflow, and (or) seasonality explanatory variables. A, Stateline. B, GunnWhitewater. C, GunnDelta.

D, NForkGunn. E, UncDelta. and F, UncColona.—Continued
19

Figure 3. Comparison of measured and estimated selenium concentrations at six sites using specific conductance, 

streamflow, and (or) seasonality explanatory variables. A, Stateline. B, GunnWhitewater. C, GunnDelta.

D, NForkGunn. E, UncDelta. and F, UncColona.—Continued
20

Figure 3. Comparison of measured and estimated selenium concentrations at six sites using specific conductance, 

streamflow, and (or) seasonality explanatory variables. A, Stateline. B, GunnWhitewater. C, GunnDelta.

D, NForkGunn. E, UncDelta. and F, UncColona.—Continued
21

Figure 3. Comparison of measured and estimated selenium concentrations at six sites using specific conductance, 

streamflow, and (or) seasonality explanatory variables. A, Stateline. B, GunnWhitewater. C, GunnDelta.

D, NForkGunn. E, UncDelta. and F, UncColona.—Continued
22

Figure 3. Comparison of measured and estimated selenium concentrations at six sites using specific conductance, 

streamflow, and (or) seasonality explanatory variables. A, Stateline. B, GunnWhitewater. C, GunnDelta.

D, NForkGunn. E, UncDelta. and F, UncColona.—Continued
23

Use of Continuous Data in the Application of Salt and Selenium Regression 

Models

Continuous streamflow and specific conductance data collected at study sites provide the means to 

examine temporal variability in constituent concentration and load. The regression models can estimate 

continuous concentrations or loads on the basis of continuous specific conductance or streamflow data. Instream load is computed by multiplying the estimated concentration by the streamflow (cubic feet per 

second) and a unit conversion constant. An example of concentrations estimated by using continuous 

specific conductance data is provided for PiceanceWhite and GunnWhitewater (fig. 4; data gaps in the 

continuous record appear as breaks in the figure). Similar plots are available for other sites at the USGS 

National Real-Time Water Quality Webpage (http://nrtwq.usgs.gov) and provide water-resource managers 

with a means of improving their general understanding of how constituent concentration or load can 

change annually, seasonally, or in real time. With respect to the models presented in this study, the amount 

of relative streamflow should be considered when interpreting estimated salinity or selenium concentration 

or loads. The error associated with the log-transformed salinity and selenium estimates is consistent in log 

space; however, when the estimates are transformed into non-log values, the error increases as the 

estimates decrease (Helsel and Hirsch, 2002).
24

Figure 4. Example of the use of continuous data with the regression models to estimate A, salinity concentration at 

PiceanceWhite and B, selenium concentration at GunnWhitewater using continuously measured specific 

conductance.
25

Figure 4. Example of the use of continuous data with the regression models to estimate A, salinity concentration at 

PiceanceWhite and B, selenium concentration at GunnWhitewater using continuously measured specific 

conductance.—Continued
26

Summary

Elevated concentrations of salinity and selenium in the tributaries and main-stem reaches of the 

Colorado River are a water-quality concern and have been the focus of remediation efforts for many years. 

“Salinity” refers to mineral salts or solids dissolved in water, and selenium is a trace element that 

bioaccumulates in the food chain. Salt and selenium limit municipal uses of water, reduce agricultural 

productivity, and, in the case of selenium, can lead to mortality, abnormalities, and reproductive failure in 

waterfowl and fish. Selenium is paradoxical in that it is a nutritional requirement in small amounts but 

toxic in slightly greater amounts. Toxic levels of selenium can cause reproductive failure, deformities, and 

other adverse effects in birds and fish, including some threatened and endangered fish species. Natural, 

nonpoint sources of salinity and selenium generally originate from the weathering and dissolution of 

geological formations that have high salt and selenium content. Land-management practices aimed at 

limiting the amount of salt and selenium that reaches the stream have focused on improving the methods 

by which irrigation water is conveyed and distributed. 

Federal land managers implement improvements in accordance with the Colorado River Basin 

Salinity Control Act of 1974, which directs Federal land managers to enhance and protect the quality of 

water available in the Colorado River. In 1989, multiple linear regression models to estimate annual and 

monthly salinity concentrations were developed for the Bureau of Reclamation to assist in evaluating and 

planning salinity-control needs. Streamflow and specific conductance (depending on data availability) 

were the explanatory variables used in the regression models. A 2012 study produced multiple linear 

regression models capable of estimating selenium concentrations at two sites in the Gunnison and 

Colorado Rivers. These models used daily streamflow and time data, capturing a seasonal cycling of 

selenium, as their explanatory variables. 

In an effort to assist in evaluating and mitigating the detrimental effects of salinity and selenium, 

the U.S. Geological Survey, in cooperation with the Bureau of Reclamation, the Colorado River Water 

Conservation District, and the Bureau of Land Management, analyzed discrete salinity and selenium data 

collected at new sites to develop regression models for those sites. The study area and sites are on the 

Colorado River or in one of three small basins in Western Colorado: the White River Basin, the Lower 

Gunnison River Basin, and the Dolores River Basin. At a minimum, data from discrete measurement of 

salinity or selenium concentrations, streamflow, and specific conductance at each of the sites were needed 

for model development. Using data collected from water years 2009 through 2011, regression models, 

able to estimate concentrations, were developed for salinity at six sites (PiceanceRyan, PiceanceWhite, 

Yellow, SCanyon, DoloresAtBedrock, and DoloresNrBedrock) and selenium at six sites (NForkGunn, 

UncColona, GunnWhitewater, GunnDelta, and UncDelta). Evaluation of the performance of the 

regression models consisted of comparing estimated salinity and selenium concentrations to water-quality 

sample data from October 2011 through April 2012.

The regression models for estimating salinity and selenium concentration were developed through 

evaluating diagnostic statistics and plots. Through the model development process, it became evident that 

models that included both specific conductance and streamflow tended to exhibit collinearity. 

Consequently, the final models use specific conductance or streamflow as an explanatory variable rather 

than both. Comparison of the Adjusted R2 and standard error statistics of the two salinity models 

developed at each site (p-value<0.05) indicated that the models using specific conductance as the 

explanatory variable performed better than those using streamflow. The addition of multiple explanatory 

variables improved the ability to estimate selenium concentration at several selenium sites over using 

solely streamflow or specific conductance. More seasonal explanatory variables were included in the 

models for GunnDelta and UncDelta using streamflow than the models using specific conductance. In 

contrast to all the other models in this report, the evaluation statistics indicated that models developed for 

GunnDelta and UncDelta using streamflow performed better than those using specific conductance. The 
27

error associated with the log-transformed salinity and selenium estimates is consistent in log space; 

however, when the estimates are transformed into non-log values the error increases as the estimates 

decrease.

Continuous streamflow and specific conductance data collected at study sites provide the means to 

examine temporal variability in constituent concentration and load. The regression models can estimate 

continuous concentrations or loads on the basis of continuous specific conductance or streamflow data. 

Similar estimates are available for other sites at the USGS National Real-Time Water Quality Webpage 

(http://nrtwq.usgs.gov) and provide water-resource managers with a means of improving their general 

understanding of how constituent concentration or load can change annually, seasonally, or in real time.

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