U.S. Department of the Interior

U.S. Geological Survey

Open-File Report 2014–1148

Prepared in cooperation with the Bureau of Reclamation

Updated Estimates of Long-Term Average Dissolved-Solids 

Loading in Streams and Rivers of the Upper Colorado River 

Basin

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San Juan R.

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FRONT COVER

Map of the Upper Colorado River Basin showing sites with estimated long-term mean annual dissolved-solids loading.
Updated Estimates of Long-Term Average 

Dissolved-Solids Loading in Streams and 

Rivers of the Upper Colorado River Basin

By Fred D Tillman and David W. Anning

Prepared in cooperation with the Bureau of Reclamation

Open-File Report 2014–1148

U.S. Department of the Interior

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

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2014

For more information on the USGS—the Federal source for science about the Earth,

its natural and living resources, natural hazards, and the environment:

World Wide Web: http://www.usgs.gov or call 1-888-ASK-USGS

For an overview of USGS information products, including maps, imagery, and publications, visit

http://www.usgs.gov/pubprod

To order this and other USGS products, visit http://store.usgs.gov

Suggested citation:

Tillman, F.D, and Anning, D.W., 2014, Updated estimates of long-term average dissolved-solids loading in streams and 

rivers of the Upper Colorado River Basin: U.S. Geological Survey Open-File Report 2014-1148, 11 p., 

http://dx.doi.org/10.3133/ofr20141148.

ISSN 2331-1258 (online)

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

endorsement by the U.S. Government.

Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials 

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

Contents

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

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

Purpose and Scope .......................................................................................................................................2

Description of Study Area ............................................................................................................................2

Methods...........................................................................................................................................................2

Data.....................................................................................................................................................2

Development and Evaluation of Dissolved-Solids Models........................................................2

Dissolved-Solids Concentration Models and Estimated Loading..........................................................6

Summary and Conclusions.........................................................................................................................10

References Cited..........................................................................................................................................10

[Appendixes available online only at http://pubs.usgs.gov/ofr/20141148/]

Appendix 1—Water-Quality Data for Final Dissolved-Solids Regression Models, Weighted 

Observed/Estimated Statistics, and Model Coefficients for 323 Monitoring Sites in the 

Upper Colorado River Basin

Appendix 2—Estimated Long-Term Mean Annual Dissolved-Solids Loading, Flow-Weighted 

Concentration, and Yield for 323 Monitoring Sites in the Upper Colorado River 

Basin

Acknowledgments

Estimation of dissolved-solids loads in Upper Colorado River Basin streams and rivers 

was supported by the Bureau of Reclamation.

Figures

1. Maps showing (A) Upper Colorado River Basin study area, (B) major streams and rivers, 

 (C) average annual precipitation, and (D) major land-cover classifications ......................3

2. Graphical depiction of an example detrended series......................................................................5

3. Graph showing model term and dissolved-solids parameter for models used in estimating 

long-term dissolved-solids loads at selected sites in the Upper Colorado River Basin...7

4. Graphs showing comparison of estimated dissolved-solids mean annual flow-adjusted 

 concentrations (A) and mean annual loads (B) with values reported in Anning and 

Flynn (2014), Upper Colorado River Basin.................................................................................8

5. Map showing sites with log of estimated long-term mean annual dissolved-solids loading 

 in the Upper Colorado River Basin.............................................................................................9
iv 

Tables

1. Dissolved-solids regression models ...................................................................................................5

2. Daily streamflow model.........................................................................................................................5

3. Summary percentiles for estimated dissolved-solids concentration, long-term mean 

 annual load, and mean annual yield for 323 sites in the Upper Colorado River Basin......7
 v

Conversion Factors

Inch/Pound to SI

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

acre 4,047 square meter (m2

)

acre 0.4047 hectare (ha)

acre 0.4047 square hectometer (hm2

) 

acre 0.004047 square kilometer (km2

)

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)

Mass

ton per year (ton/yr) 0.9072 metric ton per year

Energy

kilowatt hour (kWh) 3,600,000 joule (J)

Horizontal coordinate information is referenced to the North American Datum of 

1983 (NAD 83).

Altitude, as used in this report, refers to distance above the vertical datum.

Concentrations of chemical constituents in water are given either in milligrams 

per liter (mg/L) or micrograms per liter (μg/L).

Updated Estimates of Long-Term Average Dissolved-Solids 

Loading in Streams and Rivers of the Upper Colorado River 

Basin

By Fred D Tillman and David W. Anning

Abstract

The Colorado River and its tributaries supply water to 

more than 35 million people in the United States and 3 million 

people in Mexico, irrigating over 4.5 million acres of farmland, and annually generating about 12 billion kilowatt hours 

of hydroelectric power. The Upper Colorado River Basin, part 

of the Colorado River Basin, encompasses more than 110,000 

mi2 and is the source of much of more than 9 million tons of 

dissolved solids that annually flows past the Hoover Dam. High 

dissolved-solids concentrations in the river are the cause of 

substantial economic damages to users, primarily in reduced 

agricultural crop yields and corrosion, with damages estimated 

to be greater than 300 million dollars annually. In 1974, the 

Colorado River Basin Salinity Control Act created the Colorado River Basin Salinity Control Program to investigate and 

implement a broad range of salinity control measures. A 2009 

study by the U.S. Geological Survey, supported by the Salinity 

Control Program, used the Spatially Referenced Regressions on 

Watershed Attributes surface-water quality model to examine 

dissolved-solids supply and transport within the Upper Colorado River Basin. Dissolved-solids loads developed for 218 

monitoring sites were used to calibrate the 2009 Upper Colorado River Basin Spatially Referenced Regressions on Watershed Attributes dissolved-solids model. This study updates and 

develops new dissolved-solids loading estimates for 323 Upper 

Colorado River Basin monitoring sites using streamflow and 

dissolved-solids concentration data through 2012, to support a 

planned Spatially Referenced Regressions on Watershed Attributes modeling effort that will investigate the contributions to 

dissolved-solids loads from irrigation and rangeland practices.

Introduction

More than 3 million people in Mexico and 35 million 

people in the United States depend on the Colorado River to 

supply their domestic and industrial water needs (Bureau of 

Reclamation, 2011; Colorado River Basin Salinity Control 

Forum, 2013). The Colorado River also supplies irrigation 

water for over 4.5 million acres of land in the United States and 

Mexico and hydroelectric power along the river and its tributaries generates about 12 billion kilowatt hours annually (Colorado 

River Basin Salinity Control Forum, 2011). From headwaters 

in the Rocky Mountains through seven states and Mexico, the 

Colorado River traverses more than 1,400 mi to discharge into 

the Gulf of California (fig. 1A). Dissolved-solids concentrations 

in the river increase from about 50 mg/L at the river headwaters 

to about 500 mg/L at Lees Ferry, Arizona to about 850 mg/L 

where it crosses the United States border with Mexico (Anning 

and others, 2007). More than 9 million tons of dissolved solids 

annually flow past Hoover Dam (Anning and others, 2007). The 

origin of Colorado River salinity is primarily geologic material that was deposited from ancient inland seas and waterways 

(Colorado River Basin Salinity Control Forum, 2013), and 

55–60 percent of the salinity in the river system is from natural 

sources—primarily saline spring discharge and erosion of saline 

geologic formations (Kenney and others, 2009). Dissolvedsolids concentrations also can increase through human activities 

that increase loading (primarily irrigation, but also municipal 

and industrial development, as well as mining and drilling 

operations) and through accumulation (evaporation from reservoir operations). The Bureau of Reclamation estimates that high 

salinity Colorado River water causes damages of more than 300 

million dollars per year to users in the United States (Colorado 

River Basin Salinity Control Forum, 2013), primarily owing 

to reduced agricultural crop yields, corrosion, and plugging of 

pipes and water fixtures in housing and industry (Bureau of 

Reclamation, 2011).

In 2009, a U.S. Geological Survey (USGS) investigation of 

Upper Colorado River Basin (UCRB) dissolved-solids sources 

and transport used the Spatially Referenced Regressions on 

Watershed Attributes (SPARROW) surface-water quality model 

to relate dissolved-solids loads to upland catchment attributes 

(Kenney and others, 2009). The 2009 UCRB SPARROW model 

focused on geologic and agricultural sources of dissolved solids 

in the basin and was calibrated to dissolved-solids loads from 

218 water-quality monitoring sites estimated by Anning and 

others (2007). A new UCRB SPARROW model is planned that 

will further investigate dissolved-solids sources and transport 

in the basin by incorporating geospatial information on irrigation practices and contributions from rangelands, among other 

improvements. Updated dissolved-solids loadings for UCRB 
2 Updated Estimates of Long-Term Average Dissolved-Solids Loading in Streams and Rivers of the Upper Colorado River 

 Basin

monitoring sites were developed to provide the revised SPARROW model with updated calibration data.

Purpose and Scope

This report documents the data and methods used to 

estimate long-term mean annual dissolved-solids loading at 

water-quality sites on UCRB streams and rivers. Existing 

streamflow and dissolved-solids concentration data from the 

USGS National Water Information System (NWIS) were 

used in the development of these estimates. Where sufficient 

data were available as described in this report, dissolvedsolids load estimates were detrended to water year 2010. The 

UCRB boundary used in this study is the watershed delineated by USGS hydrologic unit code 14 (HUC14), established as part of the USGS hydrologic unit system (Seaber 

and others, 1987). 

Description of Study Area

The Colorado River Basin drains parts of Wyoming, 

Utah, Colorado, New Mexico, Arizona, Nevada, California, 

and Mexico, and is divided into upper and lower basins at the 

compact point of Lee Ferry, Arizona, a location 1 mi downstream of the mouth of the Paria River (fig. 1A, 1B; Anderson, 

2004). The UCRB is defined for this study as the 113,406 mi2

drainage area (HUC14) upstream of USGS streamflow-gaging 

station 09380000, Colorado River at Lees Ferry, Arizona (fig. 

1B). Major tributaries to the Colorado River in the Upper Basin 

include the Dolores, Green, Gunnison, San Juan, White, and 

Yampa Rivers (fig. 1B). Average annual precipitation ranges 

from less than 10 in. in low elevation areas to more than 39 in. 

in high elevation areas in the Southern Rocky Mountains (fig. 

1C, PRISM Climate Group, Oregon State University, 2012). 

UCRB land cover is predominately shrub/scrub and evergreen 

forest (Fry and others, 2011), with few high-density population centers (fig. 1D). Major dissolved constituents in UCRB 

streams and rivers are the cations calcium, magnesium, sodium, 

and potassium; and the anions sulfate, chloride, and bicarbonate; and neutral silica (Liebermann and others, 1989). Important 

geologic sources of dissolved solids in the UCRB include the 

Upper Cretaceous Mancos Shale, the Paradox Member of the 

Pennsylvanian Hermosa Formation, and the Eocene Green 

River Formation (Liebermann and others, 1989). Factors that 

are related to the transport of salinity to UCRB streams and rivers include the amount of precipitation, soil type and thickness, 

and land-surface elevation (Kenney and others, 2009). 

Methods

Models of dissolved-solids concentrations were calibrated 

with streamflow and water-quality data by the Fluxmaster 

program that uses batch-processing methods in the SAS®

statistical software to estimate flow and water-quality models 

across multiple stations (Schwarz and others, 2006). For each 

of three dissolved-solids parameters (described in section, 

“Data”), six models were considered for each site that included 

varying combinations of flow, time (trend), and seasonality. 

The best option was selected from the six models for each 

dissolved-solids parameter at each site, followed by selection of 

the best dissolved-solids model from the three dissolved-solids 

parameters. Concentration and load results were compared with 

published estimates from Anning and Flynn (2014).

Data

Dissolved-solids concentration and daily streamflow data 

from NWIS (http://waterdata.usgs.gov/nwis) for UCRB study 

area sites were used to calibrate the dissolved-solids models. 

Data for different measures of dissolved solids, including 

specific conductance (SC; p00095), residue on evaporation at 

180 °C (ROE; p70300), and sum of the dissolved constituents 

(SUM; p70301), were compiled from NWIS. Dissolved-solids 

concentration data for more than 210,000 observations from 

710 sites in the UCRB constituted the base water-quality dataset 

for the study. The period of record for data used in calibrating dissolved-solids flux estimates was from October 1, 1984 

to September 30, 2012. The selected period of record was a 

balance of the necessity of having sufficient data with which 

to calibrate models with the desire to represent recent conditions in the study area. A search for outliers and quality issues 

in the dissolved-solids data was performed first by visually 

inspecting plots of data for all sites. Data that appeared to have 

quality issues (for example, a decimal place error), were low 

or high values relative to nearby points, or were few in number 

and distant in time (most more than 7 years) from other data 

were removed from the dataset. A second investigation of the 

dissolved-solids data was performed by computing ratios of the 

different dissolved-solids parameters (p70300/p00095, p70301/

p00095, and p70301/p70300) for times when multiple parameter data were available and removing observations that caused 

anomalously high or low ratios. The outlier search identified 

49 observations that were removed from the nearly 80,000 

available for the period of interest. 

Development and Evaluation of DissolvedSolids Models

The Fluxmaster program (Schwarz and others, 2006) was 

used to estimate mean annual loads of dissolved solids at UCRB 

sites. Fluxmaster estimates log-transformed dissolved-solids 

concentrations from log-transformed mean daily streamflow and 

other explanatory variables (described in this section) using a 

bias-corrected, log-linear regression model with ordinary least 

squares estimation (Cohn, 2005). Mean annual loads are predicted using adjusted maximum likelihood with retransformation bias correction developed by Cohn (2005). Criteria for data 
Methods 3

Water and wetlands

Developed

Barren

Forest

Shrubland

Grassland

Cultivated

Average Annual 

Precipitation (in)

61.6

4.8

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40°0'0"N

35°0'0"N

30°0'0"N

Lees Ferry

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Moab

Durango

Kayenta

Montrose

Shiprock

Telluride

Farmington

Rock Springs

Grand Junction

Glenwood Springs

Steamboat Springs

Page

USGS Streamgage 09380000 

Colorado River at Lees Ferry, AZ

Green River

Colorado River

San Juan River

Yampa River

Gunnison River

White River

Dolores River

0 65 130 260 MILES

0 105 210 420 KILOMETERS

Utah

Colorado

Nevada

Calif.

Wyoming

New Mexico

Southern 

Rocky 

Mountains

Arizona

MEXICO

Upper Colorado 

River Basin

Lower Colorado 

River Basin

Paria 

River Colorado River

A B

D C

Figure 1. Maps showing (A) Upper Colorado River Basin study area, (B) major streams and rivers, (C) average annual precipitation 

(PRISM Climate Group, Oregon State University, 2012), and (D) major land-cover classifications (Fry and others, 2011).
4 Updated Estimates of Long-Term Average Dissolved-Solids Loading in Streams and Rivers of the Upper Colorado River 

 Basin

used in Fluxmaster to estimate loads at UCRB sites include only 

water-quality and streamflow observations between October 1, 

1984 and September 30, 2012; a minimum of 20 observations 

must be available for the dissolved-solids parameter; and data 

must span a minimum of 5 years.

Six different dissolved-solids regression models were 

estimated for each UCRB site where sufficient data were 

available (see table 1):

where

DS is the modeled dissolved-solids parameter 

(SC, ROE, and SUM), 

	 flow is mean daily streamflow (ft3/s), 

T is decimal time, and 

bn are regression coefficients determined by 

Fluxmaster. 

Explanatory variables of sine and cosine of decimal time 

account for seasonal patterns in dissolved-solids concentrations with either first or second-order harmonics (linear or 

squared function). The long-term trend in dissolved-solids 

concentration is represented by T and T2.

A daily streamflow model is estimated by Fluxmaster for 

UCRB sites for use in computing dissolved-solids loads. This 

streamflow model is calibrated using maximum likelihood 

estimation and relates the logarithm of daily streamflow to the 

following variables (see table 2):

where 

AR3 is a 3-day autoregression term in the residuals 

to account for serial correlation in the 

daily values, and all other variables are 

previously defined.

Information from the streamflow model (model 7) is 

used to develop a series of daily streamflow values that are 

subsequently used in the dissolved-solids model (models 1–6) 

to estimate daily dissolved-solids concentrations. Fluxmaster 

generates daily loads from the product of daily streamflow 

and dissolved-solids concentrations, and these daily loads 

are summed on a water-year basis for an estimate of mean 

annual load. The long-term mean annual load is determined 

as the average of the available mean annual loads. A base 

year of 2010 was selected to detrend Fluxmaster load estimates. Detrending gives an estimate of the load that would 

have occurred if the dynamic factors causing trend were held 

constant throughout the entire period (equal to the values on 

the base date). This allows for comparison of loads for sites 

at different locations that were estimated for different periods (fig. 2; Schwarz and others, 2006). To ensure that load 

estimates were not extrapolated too distant in time to the 2010 

base year, dissolved-solids and streamflow data were required 

to be available within a “recent” period, relative to 2010, for 

detrending to be performed. Recent was defined as no more 

than 20 percent of the length of record for a site before 2010. 

For example, if a site had 10 years of streamflow data, then the 

streamflow record must end no more than 2 years (20 percent 

of 10 years) before 2010 for detrending of streamflow from 

that site. Because results from the dissolved-solids concentration and streamflow models potentially may be detrended, 

daily dissolved-solids loads are estimated by Fluxmaster in 

one of four ways. 

1. If recent (as defined previously) measured data are 

available for both streamflow and dissolved-solids 

concentration at a site, then a daily series of streamflow 

values detrended to base year 2010 is estimated using the 

measured daily streamflow data with the trend component 

removed, based on the estimated streamflow model coefficients b5

 and b6 from model 7 (fig. 2). These detrended 

daily flow values are then input to the dissolved-solids 

concentration model to simulate a series of daily concentration estimates without introducing a concentration 

trend owing to a trend in flow. In addition, the concentration prediction methods account for non-flow related trend 

components described by regression coefficients for T and 

T2 in models 1–3 and 5, resulting in a daily dissolved-solids concentration series detrended to the 2010 base year. A 

daily series of dissolved-solids loads, detrended to 2010, 

is then generated by multiplying the detrended daily flow 

values by the detrended daily concentration estimates.

2. If recent data are available for flow but are not available 

for dissolved-solids concentrations, then a daily series of 

streamflow values detrended to base year 2010 is estimated using the measured daily streamflow data with the 

trend component removed; these detrended daily flow 

values are then input to the dissolved-solids concentration 

model as previously mentioned. No detrending of nonflow components, however, is performed on the dissolvedsolids concentration model. In this case, the daily series 

of dissolved-solids loads, partially detrended to 2010, is 

generated by multiplying the detrended daily flow values 

by the partially detrended daily concentration estimates. 

3. If recent data are not available for both streamflow and 

dissolved-solids concentration at a site, then detrending of 

flow is not performed and measured daily streamflow data 

are used directly in the concentration model. The dissolved-solids concentration model and the resulting daily 

concentration estimates also are not detrended. In this 

case, the daily series of dissolved-solids loads is generated 

by multiplying the non-detrended daily flow data by the 

non-detrended daily concentration estimates. 

4. The fourth case in which there are recent dissolved-solids 

concentration data but no recent streamflow data does 

not occur in the dataset for this study and is not discussed 

here.

The final dissolved-solids model used to estimate longterm daily and annual loads at each UCRB site was selected 

by a three-step process: (1) eliminating models that achieve 

a poor fit—determined using an observed/estimated ratio, (2) 

selecting models for each site for each dissolved-solids parameter with the lowest Akaike information criterion corrected 

for finite sample sizes (AICc), and (3) selecting the model 

from the three parameters at each site with the lowest adjusted 
Methods 5

Table 1. Dissolved-solids regression models 

Model No. Model specifications

1 loge

(DS) = intercept + b1loge(flow) + b2loge(flow)2 + b3sin(2πT) + b4cos(2πT) + b5sin(2πT)2 + b6cos(2πT)2 + b7T + b8T2

2 loge

(DS) = intercept + b1loge(flow) + b2loge(flow)2 + b3sin(2πT) + b4cos(2πT) + b5sin(2πT)2 + b6cos(2πT)2 + b7T

3 loge

(DS) = intercept + b1loge(flow) + b2sin(2πT) + b3cos(2πT) + b4sin(2πT)2 + b5cos(2πT)2 + b6T

4 loge

(DS) = intercept + b1loge(flow) + b2sin(2πT) + b3cos(2πT) + b4sin(2πT)2 + b5cos(2πT)2

5 loge

(DS) = intercept + b1loge(flow) + b2T

6 loge

(DS) = intercept + b1loge(flow)

Table 2. Daily streamflow model

Model No. Model specifications

7 loge

(flow) = intercept + b1sin(2πT) + b2cos(2πT) + b3sin(2πT)2 + b4cos(2πT)2 + b5T + b6T2 + AR3

Figure 2. Graphical depiction of an example detrended series. Adapted from Schwarz and others (2006).

Time

Dissolved-solids load

Original Series

Detrended Series

Base date
6 Updated Estimates of Long-Term Average Dissolved-Solids Loading in Streams and Rivers of the Upper Colorado River 

 Basin

percent error for the load estimate. For each model estimated 

by Fluxmaster, a weighted average ratio of the observed daily 

load divided by a weighted predicted daily load for monitored 

days is computed. This observed-to-estimated ratio will be 

greater than 1 if the dissolved-solids load is underpredicted 

and less than 1 if load is overpredicted. For this study, models 

were eliminated from further consideration if the estimated 

loads differed from observed loads by more than ±15 percent, 

resulting in observed-to-estimated ratios less than 0.87 or 

greater than 1.18. To select one of the six models for each site, 

the AICc statistic was compared for all models for each of 

the dissolved-solids parameters. AICc incorporates a measure 

of model error with a penalty for additional model variables 

(Helsel and Hirsch, 2002). The model with the lowest AICc 

statistic was selected for each site for each parameter. For stations and parameters with multiple models with the same AICc 

value, the simplest of the models (highest of model numbers in 

table 1) was selected. 

Finally, to select among the three dissolved-solids 

parameters for the final model at each site, an adjusted 

percentage error of the long-term annual load estimates for 

each model was computed by combining the error from the 

load estimate with the error from converting loads to common units. First, the percentage error of the estimated load 

was calculated for each parameter at each site as the standard 

error of the average flux divided by the average flux. Next, 

ratios of SUM to SC values and SUM to ROE values were 

calculated for all times where both dissolved-solids parameters were measured, and an average ratio for each site was 

computed. The percentage error for these conversion ratios 

also was calculated as the standard error of the ratio divided 

by the mean of the ratio. For sites without available data to 

compute the ratios, the overall average of all UCRB sites 

was used to compute the percentage error. To combine the 

variance associated with the load estimation and the parameter ratio used to convert SC and ROE loads to SUM loads, 

an adjusted percentage error for the load at each site was 

computed as:

adjusted % error =

The model with the lowest adjusted percentage error 

was selected to estimate the long-term average load at each 

site. The average load at each site estimated by the final 

model was converted to SUM units (if the model was not 

already a SUM model) using the site-specific ratios or UCRB 

average ratio as previously described.

Dissolved-Solids Concentration 

Models and Estimated Loading

Sufficient data were available to calibrate 2,916 dissolved-solids models (model numbers 1–6) from 326 UCRB 

sites in the NWIS dataset. Removing dissolved-solids models 

in which estimated loads differed from observed loads by 

more than ±15 percent resulted in eliminating 59 models, 

and an average observed-to-estimated ratio of 0.994 for 

the remaining models. A model for each dissolved-solids 

parameter at each UCRB site was selected from the lowest 

AICc value among the remaining models. The lowest AICc 

selection resulted in 482 dissolved-solids models from 323 

UCRB sites. The mean ratio of SUM concentrations to SC 

concentrations for all UCRB sites was 0.668, comparable to 

the value of 0.645 reported by Anning and others (2007) for 

sites in the southwestern United States and the ratio of 0.616 

reported by Anning and Flynn (2014) for sites throughout 

the United States. The mean ratio of SUM to ROE concentrations for UCRB sites was 0.953, comparable to the 0.931 

ratio for United States sites reported in Anning and Flynn 

(2014). Final models for estimating long-term dissolved-solids loads at UCRB sites were selected by the lowest adjusted 

percentage error of the load for models at each site as previously described and are presented in appendix 1. One-third 

of the final models selected for estimating loads were of the 

form described by model 2, with nearly two-thirds of the 

models as described by model 2 or 4 (fig. 3, appendix 1). The 

dissolved-solids parameter most often represented in the final 

models for UCRB sites was specific conductance, accounting 

for 85 percent of the models (fig. 3, appendix 1).

Long-term mean annual and daily dissolved-solids 

loads were estimated for UCRB sites using the concentration model selected for each site, with the loads detrended 

to 2010 for sites with recent data. Approximately one-third 

of the sites (100) had recent data for both streamflow and 

dissolved-solids concentrations that permitted full detrending to 2010 of dissolved-solids loads; another approximately 

one-third of the sites (110) had recent data only for streamflow, resulting in detrending of only the flow-component of 

trend in dissolved-solids loads; and a final approximately 

one-third of the sites (113) had insufficient streamflow and 

dissolved-solids concentration data to permit any detrending 

of the dissolved-solids loads (appendix 2). For sites with dissolved-solids models with parameters other than SUM, loads 

were adjusted to SUM units by multiplying by the site-specific SUM-to-parameter ratio, or by the overall UCRB ratio 

if site-specific data were not available. Appendix 2 presents 

long-term mean annual dissolved-solids load, adjusted load, 

and yield information for UCRB sites, and indicates whether 

the load values were adjusted using a site-specific ratio or a 

UCRB-wide ratio. Estimated dissolved-solids flow-weighted 

concentrations (long-term mean annual dissolved-solids load 

divided by long-term daily flow) had a median value of 113 

mg/L for UCRB sites (table 3). For 170 comparable sites, 

the estimated mean annual flow-weighted concentrations 

in this study are generally lower than estimates reported in 

Anning and Flynn (2014) that were detrended to 2000 (fig. 

4A)—likely a result of decreasing trends in dissolved-solids 

concentration at many sites in the Anning and Flynn (2014) 

study. The SUM-adjusted, long-term mean annual loads for 

√ (% error of load)2 + (% error of SUM conversion ratio)2
Dissolved-Solids Concentration Models and Estimated Loading 7

0

20

40

60

80

100

120

Number of Sites

Sum of Constituents Residue on Evaporation Specific Conductance

42

107

21

94

6

53

intercept

Model term

flow

flow2

trend

trend2

seasonality

seasonality2

Model

1

Model

2

Model

3

Model

4

Model

5

Model

6

X X X X X X

X X X X X X

X X

X X X X

X X X X

X X X X

X

Figure 3. Graph showing model term and dissolved-solids parameter for models used in estimating long-term dissolved-solids loads at 

selected sites in the Upper Colorado River Basin.

Table 3. Summary percentiles for estimated dissolved-solids concentration, long-term mean annual load, and mean annual yield for 

323 sites in the Upper Colorado River Basin.

[mg/L = milligrams per liter; tons/yr = tons per year; (tons/yr)/mi2 = tons per year per square mile; SUM = sum of constituents; SC = specific conductance; ROE

= residue on evaporation]

Percentile

Minimum 10th 25th Median 75th 90th Maximum

Flow-weighted concentration (mg/L) 4 22 50 113 247 627 2,763

Long-term mean annual1

 load (tons/yr) 23 426 1,569 9,643 47,800 174,379 6,017,846

Mean annual yield2

 [(tons/yr)/mi2] 4 21 36 62 118 208 3663

1

Load adjusted to SUM units for regression models using SC or ROE dissolved-solids parameters.

2

Five sites had no drainage area information, so yield percentiles are based on 318 sites.

3

Yield not estimated for Reed wash near Mack, Colorado (gaging station 09153290) because flow is suspected to contain water from adjacent agricultural 

areas that are not strictly part of the site’s drainage area.
8 Updated Estimates of Long-Term Average Dissolved-Solids Loading in Streams and Rivers of the Upper Colorado River 

 Basin

Figure 4. Graphs showing comparison of estimated dissolved-solids mean annual flow-adjusted concentrations (A) and mean annual 

loads (B) with values reported in Anning and Flynn (2014), Upper Colorado River Basin. Concentrations and loads were detrended to 

base year 2000 (Anning and others, 2014) or base year 2010 (this report) if dissolved-solids concentration and flow data sufficiently 

recent to the base year were available.

100

1,000

10,000

100,000

1,000,000

10,000,000

100 1,000 10,000 100,000 1,000,000 10,000,000

(Anning and Flynn, 2014)

Mean annual load (tons/yr)

(this report)

Mean annual load (tons/yr)

1

10

100

1,000

10,000

1 10 100 1,000 10,000

Mean annual flow-adjusted concentration (mg/L)

(Anning and Flynn, 2014)

(this report)

Mean annual flow-adjusted concentration (mg/L)

A

B
Dissolved-Solids Concentration Models and Estimated Loading 9

EXPLANATION

 SUM-adjusted long-term mean 

dissolved-solids load (tons/yr)

!( 20.4 to 100

!( >100 to 1,000

!( >1,000 to 10,000

!( >10,000 to 100,000

!( >100,000 to 1,000,000

!( >1,000,000 to 5,460,000

Green R.

Colorado R.

San Juan R.

Yampa R.

White R.

Dolores R.

Gunnison R.

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Figure 5. Map showing sites with log of estimated long-term mean annual dissolved-solids loading in the Upper Colorado River Basin. 

Information on site names, locations, and dissolved-solids concentrations, loads, and yields are listed in appendixes 1 and 2.

UCRB sites were as high as 6 million tons/yr at Colorado 

River at Lees Ferry (streamflow-gaging station 09380000; 

table 3, appendix 2). Load estimates from this study are generally in line with estimates from Anning and Flynn (2014; 

fig. 4B). The distribution of mean-annual-yield estimates 

from UCRB sites were generally close to the median value of 

62 (tons/yr)/mi2 (table 3, appendix 2). 

The spatial distribution of stations with adequate data 

and dissolved-solids models for estimating dissolved-solids 

loading in UCRB streams and rivers indicates a majority of 

the 323 sites are in the eastern part of the study area 

(fig. 5). The highest dissolved-solids loads are at sites along 

the main stems of the Colorado, Green, Gunnison, San 

Juan, and Yampa Rivers that accumulate loads from feeder 
10 Updated Estimates of Long-Term Average Dissolved-Solids Loading in Streams and Rivers of the Upper Colorado River 

 Basin

streams, and lowest dissolved-solids loads are at sites in 

headwaters in the eastern and western parts of the UCRB 

(fig. 5; Appendix 2). 

Summary and Conclusions

Estimates of dissolved-solids loading for water-quality 

sites on Upper Colorado River Basin streams and rivers were 

developed using multiple linear regression to model observed 

dissolved-solids concentrations. Data for different dissolvedsolids parameters including specific conductance, residue on 

evaporation at 180 °C, and sum of the dissolved constituents 

were compiled from the U.S. Geological Survey National 

Water Information System database. The Fluxmaster program 

was used to estimate log-transformed, dissolved-solids concentration data from log-transformed mean daily streamflow, 

seasonal trend, and long-term trend explanatory variables. The 

best model for each site was determined through examination 

of the AICc statistic and the adjusted percentage error for all 

models at each site. Dissolved-solids models were developed 

for 323 Upper Colorado River Basin sites. Daily and mean 

annual dissolved-solids loads were predicted at the 323 sites 

for a base year of 2010 when recent data were available; otherwise, predicted loads were not detrended. 

References Cited

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html.
Menlo Park Publishing Service Center, California

Manuscript approved for publication

Edited by John Buursma

Design and layout by Cory Hurd
Tillman and Anning—Updated Estimates of Long-Term Average Dissolved-Solids Loading in Streams and Rivers of the Upper Colorado River Basin

ISSN 2014-1248 (online)

http://dx.doi.org/10.3133/ofr20141148