Office of Water

EPA 820-R-15-106

March 2016

Draft Technical Support Document: 

Recommended Estimates for Missing 

Water Quality Parameters for 

Application in EPA’s Biotic Ligand Model
i

Disclaimer Page

This technical support document (herein referred to as the “Missing Parameters TSD”) summarizes 

data analysis approaches EPA used to develop recommendations for default values for water quality 

parameters used in the copper BLM when data are lacking. When published in final form, this 

document will provide information to states, tribes, and the regulated community interested in using

the Biotic Ligand Model to protect aquatic life from toxic effects of copper. Under the CWA, states and 

tribes are to establish water quality criteria to protect designated uses. State and tribal decision 

makers retain the discretion to adopt approaches on a case-by-case basis when appropriate. This 

document does not substitute for the CWA or EPA’s regulations; nor is it a regulation itself. Thus, it 

cannot impose legally binding requirements on EPA, states, tribes, or the regulated community, and 

might not apply to a particular situation based upon the specific circumstances. EPA may change this 

document in the future. This document has been approved for publication by the Office of Science and 

Technology, Office of Water, U.S. Environmental Protection Agency. 

Mention of trade names or commercial products does not constitute endorsement or recommendation 

for use. This document can be downloaded from: 

http://water.epa.gov/scitech/swguidance/standards/criteria/aqlife/copper/2007_index.cfm

Cover photo: Credit USEPA
ii

Acknowledgements

 

Luis A. Cruz

(Document Coordinator and Contributor)

United States Environmental Protection Agency

Health and Ecological Criteria Division

Washington, D.C. 20460

Reviewers

Elizabeth Southerland, Elizabeth Behl, Kathryn Gallagher

United States Environmental Protection Agency

Office of Science and Technology

Washington, D.C. 20460
iii

Acronyms or Abbreviations

Acronym/Abbreviation Definition

ACR Acute to Chronic Ratio

ASE Average Standard Error

BLM Biotic Ligand Model

BOD Biochemical Oxygen Demand

CCC Criterion Continuous Concentration

CMC Criterion Maximum Concentration

CWA Clean Water Act

df Degrees of Freedom

DOC Dissolved Organic Carbon

Ecoregion Areas in which ecosystems and the type, quality, and quantity of environmental 

resources are generally similar. In this document is represented by EPA Level III 

Ecoregions

EMAP Environmental Monitoring and Assessment Program

EPA United States Environmental Protection Agency

FSC Fixed Site Criteria

GI Geochemical Ions; ion parameters for the Biotic Ligand Model (Ca, Mg, Cl, Na, K, SO4, 

alkalinity)

GIS Geographic Information System

GLEC Great Lakes Environmental Center

HUC Hydrologic Unit Code (a two to eight digit code that identifies each hydrologic unit)

IQR Interquartile range

IWQC Instantaneous Water Quality Criteria

LCL Lower Confidence Limit

LDC Legacy Data Center (EPA historical STORET database, recently renamed)

LR Linear Regression

mg/L Milligrams per liter

NHD National Hydrography Dataset

NHD-Plus National Hydrography Dataset Plus

NOCD National Organic Carbon Database (combined organic carbon data from two 

databases: USGS WATSTORE and EPA STORET)

NRC National Research Council

NRSA National River and Stream Assessment

NWIS National Waters Information System 

PCS Permit Compliance System

RPDs Relative Percent Differences

PCA Principal Components Analysis

pH Negative logarithm of the hydrogen ion concentration (in moles per liter); scale range 

from 0 to 14

POC Particulate Organic Carbon

POTWs Publicly Owned Treatment Works

RMSE Root Mean Square Error
iv

Acronym/Abbreviation Definition

RSS Residual Sum of Squares

SPLOM Scatter Plot Matrices

SO Strahler Stream Order

STORET EPA STOrage and RETrieval Data Warehouse (recently renamed Legacy Data Center, 

LDC)

TDS Total Dissolved Solids

TSD Technical support document

TSS Total Suspended Solids

TOC Total Organic Carbon

UCL Upper Confidence Limit

U.S. United States

USGS United States Geological Survey

WATSTORE USGS National WATer Data STOrage and REtrieval System (predecessor of NWIS)

WSA Wadeable Stream Assessment

WQC Water Quality Criteria

μS/cm Microsiemens per centimeter

μg/L Micrograms per liter
v

Executive Summary

The United States (U.S.) Environmental Protection Agency (EPA) developed revised freshwater aquatic 

life criteria for copper using the Biotic Ligand Model (BLM) in 2007. The 2007 Freshwater Copper BLM 

predicts acute copper toxicity based on site-specific water quality parameters, and calculates aquatic 

life criteria based on the predicted copper toxicity. The current freshwater copper BLM requires 10

input parameters to calculate copper criteria: temperature, pH, dissolved organic carbon (DOC),

alkalinity, calcium, magnesium, sodium, potassium, sulfate, and chloride, the last seven of which are 

also referred to as geochemical ions (GI). Previously available hardness-based copper criteria

incorporated consideration only of the effects of hardness on bioavailability, while the BLM 

incorporates consideration of all of the water chemistry parameters that have a major influence on 

metal bioavailability. This allows the BLM-based criteria to be customized to the particular water body 

under consideration. However, given the broad geographical range over which the BLM is likely to be 

applied, and the limited availability of data for input parameters in many areas, a practical method to 

estimate missing water quality parameters was needed to successfully run the BLM. This technical 

support document (herein referred to as the “Missing Parameters TSD”) summarizes data analysis 

approaches EPA used to develop recommendations for default values for water quality parameters 

used in the Freshwater Copper BLM when data are lacking. These default values could also be used to 

fill in missing water quality input parameters in the application of other metal BLM models as well, 

when data are lacking. EPA used three approaches to develop these default value recommendations:

• Conducted geostatistics and conductivity analyses to predict GI parameters

• Applied stream order to refine prediction of GI parameters

• Mined the National Organic Carbon Database (NOCD) to estimate DOC

In brief, EPA found that an approach that used correlation (with conductivity and discharge as 

explanatory variables), combined with geostatistical techniques (kriging), and a consideration of 

stream order produced the best estimates for BLM GI parameters. Tables 8, 9, and 10 present 

estimated inputs for each GI and water hardness in each ecoregion categorized by stream order for 

low, medium, and high order streams, respectively. Recommended GI values are based on the 10th

percentile of ecoregional Level III values for the appropriate stream order (size) and are expected to 

yield appropriately protective criteria values when applied in the BLM model. In Table 20 of Section 4, 

EPA provides estimates for DOC by ecoregion based on an analysis of a compilation of national organic 

carbon databases. The 10th percentile of ecoregional Level III values are recommended for DOC. There 

was insufficient data to refine the DOC estimates by stream order. EPA recommends measurement of 

pH and temperature directly to use as an input in the BLM. Temperature is a commonly measured 

parameter, and should be easily obtainable for use in the BLM. The following paragraphs summarize 

the contents of each section in this report.

Section 1 provides an introduction to this study, including background on the BLM. In developing the 

approaches outlined in this study, EPA relied upon several previous studies that attempted to estimate 

values for BLM input water quality parameters; these studies are outlined briefly in Section 1 and are 

described in detail in Appendices A through D. This earlier work demonstrates that protective water 
vi

quality criteria (WQC) for copper generally corresponded to a low percentile of the distribution of 

instantaneous water quality criteria (IWQC) predicted by the BLM. 

Section 2 provides a discussion of the approach taken by EPA to estimate BLM GI parameter values 

using geostatistics, which are a suite of statistical methodologies that use spatial coordinates to 

formulate models used in estimation and prediction. Section 2 also describes how EPA supplemented 

the geostatistical approach with conductivity as an explanatory variable, because conductivity data are 

abundant and correlate well to the BLM GI parameters.

Section 3 provides an analysis and discussion of the EPA approach to estimation of BLM GI parameters 

incorporating stream order as a variable, with a goal of providing BLM users with tables of 

recommended GI parameter estimates based upon both ecoregion and stream order. For each Level III 

ecoregion, we recalculated the 10th percentiles of the distributions of all daily water quality parameters 

measured at all NWIS stations taking into account stream orders or ranges (groups) of stream orders 

within each ecoregion. Values of the BLM GI parameters generally increased with stream order. Based 

upon this trend, we grouped the estimates for each parameter by stream order: 1 through 3 

(headwater streams), 4 through 6 (mid-reaches), and 7 through 9 (rivers).

Section 4 discusses the estimation of DOC based on the NOCD and two other databases. The NOCD was

compiled from a number of sources, including EPA’s Storage and Retrieval Data Warehouse (STORET)

and the United States Geological Survey’s National Water Data Storage and Retrieval System 

(WATSTORE) (the predecessor of the National Waters Information System (NWIS)). The two other 

databases, the Wadeable Stream Assessment (WSA) and the National River and Stream Assessment 

(NRSA), were used to supplement and update the DOC analysis. Section 4 summarizes the data 

sources, analysis, and uncertainty associated with ecoregional statistics for the NOCD and outlines how 

tests for bias in the data influence selection of 10th percentile DOC concentrations from either the 

NOCD or the WSA or NRSA databases. The importance of field sampling for DOC is highlighted in 

Section 4 because of limitations of the NOCD and the importance of DOC in criteria calculation.

Section 5 provides a summary of the three approaches used to develop EPA’s recommendations. Taken 

together, the approaches presented in this TSD describe EPA’s recommendations for default input 

parameters in the BLM to derive protective freshwater aquatic life criteria when data are lacking. 

However, it should be noted that site-specific data are always preferable for developing criteria based 

on the BLM and should be used when possible. Users of the BLM are encouraged to sample their water 

body of interest, and to analyze the samples for the constituent (parameter) concentrations as a basis 

for determining BLM inputs where possible.
vii

Table of Contents

Disclaimer Page ....................................................................................................................................................................i

Acknowledgements.............................................................................................................................................................ii

Acronyms or Abbreviations................................................................................................................................................iii

Executive Summary .............................................................................................................................................................v

Table of Contents .............................................................................................................................................................. vii

List of Figures....................................................................................................................................................................... x

List of Tables..................................................................................................................................................................... xiii

1 INTRODUCTION..........................................................................................................................................................1

1.1 Background and Objective.............................................................................................................................................1

1.2 Input Data and the BLM ................................................................................................................................................1

1.3 Previous Studies.............................................................................................................................................................2

1.3.1 An Examination of Spatial Trends in Surface Water Chemistry in the Continental United States: Implications 

for the Use of Default Values as Inputs to the BLM for Prediction of Acute Metal Toxicity to Aquatic 

Organisms (Carlton, 2006)....................................................................................................................................2

1.3.2 Approaches for Estimating Missing BLM Input Parameters: Correlation Approaches to Estimate BLM Input 

Parameters Using Conductivity and Discharge as Explanatory Variables (USEPA, 2007).....................................2

1.3.3 Copper Biotic Ligand Model (BLM) Software and Supporting Documents Preparation: Development of Tools 

to Estimate BLM Parameters (USEPA, 2008)........................................................................................................3

1.3.4 Approaches for Estimating Missing BLM Input Parameters: Projections of Total Organic Carbon as a Function 

of Biochemical Oxygen Demand (USEPA, 2006a).................................................................................................4

1.4 Approaches to Estimate Water Quality Parameters for the BLM..................................................................................4

2 USING GEOSTATISTICS AND CONDUCTIVITY TO PREDICT GI PARAMETERS.................................................................5

2.1 Data Source and Processing ..........................................................................................................................................5

2.2 Geostatistical Analysis of National Data for Geochemical Ions.....................................................................................8

2.2.1 Kriging of Conductivity Data ................................................................................................................................9

2.2.2 Co-kriging of GI Data ..........................................................................................................................................10

2.2.3 Projection of Geostatistical Predictions onto Level III Ecoregions.....................................................................12

2.2.3.2 Averaging Methods ..................................................................................................................................17

2.2.3.3 Tabulations of Ecoregional Estimated BLM Water Quality Parameters...................................................17

2.2.3.4 Confirmation of Results............................................................................................................................21

2.2.3.5 Conclusions for Selection of Water Quality Parameters..........................................................................33

2.2.3.6 Guidance Regarding Selection of Water Quality Parameters: pH and DOC.............................................33

3 USING STREAM ORDER TO REFINE PREDICTION OF GI PARAMETERS .......................................................................34

3.1 Determining SO of NWIS Surface Water Sampling Locations......................................................................................34

3.2 Estimating BLM Parameters for Ecoregions and SO....................................................................................................35

3.3 Results .........................................................................................................................................................................35
viii

3.3.1 Dependence of Ecoregional Parameter Estimates on SO..................................................................................35

3.3.2 SO-Based Parameter Estimates .........................................................................................................................40

3.3.3 Comparison of Parameter Estimates to Results of Probability-Based Surface Water Sampling .......................50

3.4 Summary......................................................................................................................................................................56

4 DOC ESTIMATION USING THE NATIONAL ORGANIC CARBON DATABASE..................................................................58

4.1 Description of the NOCD..............................................................................................................................................58

4.2 Recalculation of Ecoregional DOC Percentiles for Rivers and Streams........................................................................59

4.3 Testing for Bias in the NOCD .......................................................................................................................................62

4.3.1 Previous Efforts Using EMAP Data.....................................................................................................................62

4.3.2 Testing for Bias Using Data from the WSA.........................................................................................................63

4.3.2.1 Selection of Statistical Test to Assess Potential Bias in DOC Data............................................................64

4.3.2.2 Rank-Sum Test Comparing WSA DOC Data to NOCD ...............................................................................64

4.3.3 Results and Implications of Bias Testing ............................................................................................................73

4.4 Comparing NOCD to WSA/NRSA DOC Data.................................................................................................................75

4.5 Conclusions..................................................................................................................................................................81

5 SUMMARY AND RECOMMENDATIONS.....................................................................................................................82

5.1 Recommendations for BLM inputs for geochemical ions where site-specific data are not available..........................82

5.2 Recommendations for BLM inputs for DOC where site-specific data are not available ..............................................83

5.3 Recommendations for BLM inputs for pH where site-specific data are not available.................................................83

5.4 Conclusions..................................................................................................................................................................83

REFERENCES ......................................................................................................................................................................84

Appendix A: An Examination of Spatial Trends in Surface Water Chemistry in the Continental United States: 

Implications for the Use of Default Values as Inputs to the Biotic Ligand Model for Prediction of Acute 

Metal Toxicity to Aquatic Organisms.........................................................................................................87

A.1 Abstract ..................................................................................................................................................................87

A.2 Background.............................................................................................................................................................87

A.3 Description of Data.................................................................................................................................................88

A.4 Data Analysis..........................................................................................................................................................89

A.5 Developing Regional Defaults.................................................................................................................................97

A.6 Discussion ...............................................................................................................................................................99

A.7 Conclusions.............................................................................................................................................................99

A.8 References...............................................................................................................................................................99

Appendix B: Approaches for Estimating Missing Biotic Ligand Model Input Parameters. Correlation approaches to 

estimate Biotic Ligand Model input parameters using conductivity and discharge as explanatory variables

................................................................................................................................................................100

B.1 Introduction ..........................................................................................................................................................100

B.2 Data ......................................................................................................................................................................103
ix

B.3 Results...................................................................................................................................................................103

B.4 Discussion .............................................................................................................................................................111

B.5 References.............................................................................................................................................................112

Appendix C: Development of Tools to Estimate Biotic Ligand Model Parameters........................................................114

C.1 Introduction...............................................................................................................................................................114

C.2 Regression Analysis ...................................................................................................................................................114

C.2.1 pH.....................................................................................................................................................................114

C.2.2 DOC ..................................................................................................................................................................115

C.2.3 Alkalinity ..........................................................................................................................................................115

C.2.4 Calcium.............................................................................................................................................................115

C.2.5 Magnesium ......................................................................................................................................................115

C.2.6 Sodium.............................................................................................................................................................116

C.2.7 Potassium.........................................................................................................................................................116

C.2.8 Sulfate ..............................................................................................................................................................116

C.2.9 Chloride............................................................................................................................................................116

C.3 Application of Conductivity Regressions....................................................................................................................116

C.3.1 Naugatuck River, Connecticut..........................................................................................................................117

C.3.2 San Joaquin River, California............................................................................................................................119

C.3.3 South Platte River, Colorado............................................................................................................................121

C.3.4 Halfmoon Creek, Colorado...............................................................................................................................122

C.3.5 Summary of Site-Specific Test Results.............................................................................................................124

C.4 Combining GI-Conductivity Regressions with Geostatistical Techniques ..................................................................127

C.5 References.................................................................................................................................................................131

Appendix D: Approaches for Estimating Missing Biotic Ligand Model Input Parameters: Projections of Total Organic 

Carbon as a Function of Biochemical Oxygen Demand.............................................................................132

D.1 Introduction ..........................................................................................................................................................132

D.2 Data ......................................................................................................................................................................132

D.3 Results...................................................................................................................................................................133

D.3.1 TOC and BOD at All Monitoring Locations.......................................................................................................133

D.3.2 TOC and BOD at Effluent Monitoring Locations ..............................................................................................135

D.3.3 TOC and DOC at CARP Effluent Monitoring Locations.....................................................................................140

D.4 Discussion .............................................................................................................................................................142

D.5 References.............................................................................................................................................................145
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List of Figures

Figure 1. NWIS sample collection locations in the continental U.S. (Carleton, 2006) .................................................................6

Figure 2. Kriged prediction surface for 10th percentile of conductivity in the continental U.S. (sample locations in 

blue)....................................................................................................................................................................................10

Figure 3. Co-kriged prediction surface for 10th percentile of calcium in the continental U.S....................................................11

Figure 4. Co-kriged prediction surface for 10th percentile of alkalinity in the continental U.S. ................................................12

Figure 5. Map of Level III ecoregions in the U.S.........................................................................................................................16

Figure 6. Scatter plot matrix of ecoregional average 10th percentiles of data for conductivity (COND_SAM) and GI 

parameters (calcium=CA_SAM, magnesium=MG_SAM, sodium=NA_SAM, potassium=K_SAM, 

alkalinity=ALK_SAM, chloride=CL_SAM, sulfate=SO4_SAM)..............................................................................................22

Figure 7. Scatter plot matrix of ecoregional average 10th percentiles of geostatistical predictions of conductivity 

(COND_KR) and BLM GI parameters (calcium=CA_CO, magnesium=MG_SCO, sodium=NA_CO, 

potassium=K_CO, alkalinity=ALK_CO, chloride=CL_CO, sulfate=SO4_CO).........................................................................23

Figure 8. Ecoregional averages of kriged 10th percentiles of conductivity versus data.............................................................25

Figure 9. Ecoregional averages of cokriged 10th percentiles of alkalinity versus data ..............................................................26

Figure 10. Ecoregional averages of cokriged 10th percentiles of calcium versus data...............................................................27

Figure 11. Ecoregional averages of cokriged 10th percentiles of magnesium versus data ........................................................28

Figure 12. Ecoregional averages of cokriged 10th percentiles of sodium versus data ...............................................................29

Figure 13. Ecoregional averages of cokriged 10th percentiles of potassium versus data...........................................................30

Figure 14. Ecoregional averages of cokriged 10th percentiles of sulfate versus data................................................................31

Figure 15. Ecoregional averages of cokriged 10th percentiles of chloride versus data..............................................................32

Figure 16. Distribution of NWIS surface water sampling locations by SO.................................................................................35

Figure 17. Box plot of estimated ecoregional conductivities as a function of SO .....................................................................36

Figure 18. Box plot of estimated ecoregional alkalinity concentrations as a function of SO ....................................................37

Figure 19. Box plot of estimated ecoregional calcium concentrations as a function of SO ......................................................37

Figure 20. Box plot of estimated ecoregional magnesium concentrations as a function of SO................................................38

Figure 21. Box plot of estimated ecoregional sodium concentrations as a function of SO.......................................................38

Figure 22. Box plot of estimated ecoregional potassium concentrations as a function of SO..................................................39

Figure 23. Box plot of estimated ecoregional sulfate concentrations as a function of SO........................................................39

Figure 24. Box plot of estimated ecoregional chloride concentrations as a function of SO......................................................40

Figure 25. BLM parameter estimates (10th percentile values) for each SO group in Ecoregion 46 (Northern Glaciated 

Plains) .................................................................................................................................................................................48

Figure 26. BLM parameter estimates for each SO group in Ecoregion 83 (Eastern Great Lakes Lowland) ...............................49
xi

Figure 27. BLM parameter estimates for each SO group in Ecoregion 54 (Central Corn Belt Plains)........................................50

Figure 28. Scatter plot of ecoregional 25th percentile conductivity for NWIS Data (SO Class 1-3) versus ecoregional 

25th percentile conductivity for Griffith data (mostly SO 1-4)............................................................................................51

Figure 29. Scatter plot of ecoregional 25th percentile calcium concentration for NWIS data (SO class 1-3) versus 

ecoregional 25th percentile calcium concentration for Griffith data (mostly SO 1-4) ........................................................52

Figure 30. BLM predictions of copper criteria made with GI water quality parameters based on ecoregional 25th

percentile from NWIS data (SO class 1-3) versus ecoregional 25th percentile calcium Concentration for Griffith 

data (mostly SO 1-4). ..........................................................................................................................................................56

Figure 31. Comparison of probability distributions of DOC concentrations in Ecoregion 23....................................................74

Figure 32. Comparison of probability distributions of DOC concentrations in Ecoregion 77....................................................74

Figure A-1. NWIS sample collection locations in the continental U.S........................................................................................88

Figure A-2. Intensity of sampling (number of separate sampling dates) at each NWIS site......................................................89

Figure A-3. Median measured alkalinity (mg/L as CaCO3) at NWIS locations...........................................................................90

Figure A-4. HUC-averaged mean median observed alkalinity in the continental U.S................................................................90

Figure A-5. Kriging prediction map of median alkalinity............................................................................................................92

Figure A-6. Kriging map of alkalinity, projected into vertical dimension...................................................................................92

Figure A-7. Kriging-based alkalinity predictions, averaged over 8-digit HUC polygons.............................................................93

Figure A-8. Kriging-predicted vs. calculated HUC-averaged alkalinity; r2=0.537 .......................................................................93

Figure A-9. Scatter plot matrix of median concentration kriged predictions, averaged over 8-digit HUCs regions 

covering the continental U.S. .............................................................................................................................................94

Figure A-10. Scatter plot matrix of median concentrations from 772 monitoring locations in the continental U.S.................95

Figure A-11. Variance plot from PCA of HUC-average kriging-predicted concentrations .........................................................96

Figure A-12. Variance plot from PCA of site-median measured concentrations.......................................................................96

Figure A-13. Kriging 25th percentile map of median alkalinity .................................................................................................98

Figure A-14. Comparison of observed site-minimum alkalinities with HUC-mean 25th percentile kriging-predicted 

values..................................................................................................................................................................................98

Figure B-1. Relation of conductivity to chloride, hardness and sulfate concentrations in the Gila River at Bylas, 

Arizona..............................................................................................................................................................................102

Figure B-2. Scatter plot matrix for first quartile of site-specific data for discharge (LNDISCH), conductivity (COND), 

and BLM water quality parameters..................................................................................................................................108

Figure B-3. Scatter plot matrix for fifth quantile of site-specific data for discharge (LNDISCH), conductivity (COND), 

and BLM water quality parameters..................................................................................................................................109

Figure B-4. Scatter plot matrix of BLM water quality parameter data from NWIS Station 384551107591901 

(Sunflower Drain at Highway 92, near Read, Delta County, Colorado)............................................................................110

Figure B-5. Time series plot of conductivity (diamond symbols) and discharge (open circles connected by dashed 

line) at Station 384551107591901 (Sunflower Drain at Highway 92, near Read, Delta County, Colorado) ....................111
xii

Figure C-1. Instantaneous Criteria (IC) predicted with the BLM using site-specific data and IC predicted using 

measured pH and organic carbon and projected values of the GI BLM input parameters..............................................125

Figure C-2. 10th percentile of the IC distributions using data and projected (predicted) values of the GI BLM 

parameters .......................................................................................................................................................................126

Figure C-3. Percentile of the IC corresponding to the FSC for each site as a function of the correlation coefficient 

between the copper concentrations and the IC when the FSC is calculated with Copper correlation and when 

FSC is calculated without Copper correlation...................................................................................................................127

Figure C-4. Kriged surface of the 10th percentile of conductivity at all stations in Colorado, Utah and Wyoming ................129

Figure C-5. Kriged surface of the 10th percentile of hardness at all stations in Colorado ......................................................129

Figure C-6. Comparison of the 10th percentile of hardness at all stations in Colorado with estimates based on (a) 

direct kriging of hardness data and (b) kriging of conductivity to station locations and projecting conductivity 

to hardness via regression (“kriging/regression”) ............................................................................................................130

Figure D-1. Scatter Plot of Average Monthly Data (all Monitoring Locations) ........................................................................134

Figure D-2. Scatter Plot of Maximum Monthly Data (all Monitoring Locations).....................................................................135

Figure D-3. Scatter Plot of Average Monthly Data (Effluent Monitoring Locations) ...............................................................137

Figure D-4. Scatter Plot of Maximum Monthly Data (Effluent Monitoring Locations)............................................................138

Figure D-5. Residuals of the linear model, TOCavg = a + b BODavg ........................................................................................139

Figure D-6. Scatter plot of TOC versus DOC in CARP effluent monitoring data.......................................................................141

Figure D-7. Scatter plot of TOC versus DOC in CARP effluent monitoring data (TOC <50 mg/L).............................................142
xiii

List of Tables

Table 1. Summary of water quality data retrieved from NWIS ...................................................................................................7

Table 2. Model selection and cross validation statistics for geostatistical fitting of 10th percentiles of BLM GI 

parameters ...........................................................................................................................................................................9

Table 3. Level III ecoregions of the U.S. organized according to broader Level I ecoregions....................................................13

Table 4. Predicted 10th percentile concentrations for conductivity (μS/cm), BLM GI water quality parameters (mg/L) 

and hardness in each Level III ecoregion in the continental U.S. .......................................................................................18

Table 5. Spearman rank correlation matrix for unbiased log means of 10th percentile concentrations measured in 

Level III ecoregions.............................................................................................................................................................24

Table 6. Spearman rank correlation matrix for unbiased log means of 10th percentile predicted (kriged/cokriged) 

concentrations in Level III ecoregions ................................................................................................................................24

Table 7. Correlation coefficients and linear regression (LR) statistics between ecoregional average 10th percentiles 

of data and geostatistical predictions ................................................................................................................................32

Table 8. Recommended 10th percentile conductivity, GIs, and hardness estimates for SO Group 1 through 3 

(number of stations shown in parentheses if n<10)...........................................................................................................41

Table 9. Recommended 10th percentile conductivity, GIs, and hardness estimates for SO group 4 through 6 

(number of stations shown in parentheses if n<10)...........................................................................................................43

Table 10. Recommended 10th percentile conductivity, GIs, and hardness estimates for SO group 7 through 9 

(number of stations shown in parentheses if n<10)...........................................................................................................45

Table 11. Characteristics of the conductivity data for Ecoregion 19 in the low SO group. .......................................................53

Table 12. Characteristics of the conductivity data for Ecoregion 37 in the low SO group. .......................................................53

Table 13. Characteristics of the conductivity data for Ecoregion 38 in the low SO group ........................................................54

Table 14. Characteristics of the calcium data for Ecoregion 75 in the low SO group................................................................54

Table 15. Characteristics of the conductivity data for Ecoregion 78 in the low SO group. .......................................................54

Table 16. Lower percentile values of DOC in U.S. streams and rivers by ecoregion, including 95% confidence limits 

for percentile concentrations if n>20. ................................................................................................................................60

Table 17. Results of rank-sum test comparing Level III ecoregional DOC data from WSA and NOCD ......................................66

Table 18. DOC concentrations (mg/L) in each Level III ecoregion based upon data from the NOCD and the 

combined WSA/NRSA data: number of data (n); 10th percentiles; and results of the Wilcoxon 2-sample test ...............76

Table 19. DOC concentrations (mg/L) in 24 ecoregions where no significant difference in DOC concentrations was 

found between national organic carbon database (NOCD) and the WSA/NRSA datasets: number of data (n); 

10th percentiles from combined NOCD & WSA/NRSA data................................................................................................78

Table 20. Recommended ecoregional DOC concentrations (mg/L) based upon combined data from the NOCD and 

the WSA/NRSA data in 83 Level III ecoregions: number of observations (n); 10th percentiles; and source of 

data for each ecoregion......................................................................................................................................................79

Table A-1. Matrices of correlation coefficients between constituent concentrations..............................................................95
xiv

Table A-2. Loadings onto original variables from PCA on HUC-averaged predictions and site-median concentrations...........97

Table B-1. Number of observations and sites reported in NWIS for streams and rivers in Colorado .....................................104

Table B-2. Results of Spearman rank tests for correlation (ρ) between median values of variables at each site...................105

Table B-3. Results of Spearman rank tests for correlation (ρ) between the first quartile of values at each site....................106

Table B-4. Results of Spearman rank tests for correlation (ρ) between the fifth quantile of values at each site...................106

Table C-1. Copper Fixed Site Criterion predictions for the Naugatuck River, Connecticut using various calculation 

methods............................................................................................................................................................................118

Table C-2. Copper Fixed Site Criterion predictions for the San Joaquín River, California using various calculation 

methods............................................................................................................................................................................120

Table C-3. Copper Fixed Site Criterion predictions for the South Platte River, Colorado using various calculation 

methods............................................................................................................................................................................121

Table C-4. Copper Fixed Site Criterion predictions for the Halfmoon Creek, Colorado using various calculation 

methods............................................................................................................................................................................123

Table D-1. Least squares regression of average monthly TOC and BOD data for all monitoring locations.............................133

Table D-2. Least squares regression of maximum monthly TOC and BOD data for all monitoring locations .........................134

Table D-3. Least squares regression of average monthly TOC and BOD data for effluent monitoring locations....................136

Table D-4. Least squares regression of maximum monthly TOC and BOD data for effluent monitoring locations ................138

Table D-5. CARP organic carbon and total suspended solids (TSS) monitoring data for New Jersey discharger ....................140

Table D-6. Summary statistics for POTW average monthly effluent TOC concentrations, categorized according to 

average monthly effluent BOD concentration .................................................................................................................144

Table D-7. Summary statistics for POTW maximum monthly effluent TOC concentrations, categorized according to 

maximum monthly effluent BOD concentration ..............................................................................................................144
1

1 INTRODUCTION

1.1 Background and Objective

The United States (U.S.) Environmental Protection Agency (EPA) has a congressional mandate to 

develop and publish criteria for water quality that reflects the effects of pollutants on aquatic life and 

human health under 304(a)(1) of the Clean Water Act (CWA). The CWA was intended to protect the 

chemical, physical, and biological integrity of the Nation’s waters. Section 304(a)(1) of the CWA, 33 

U.S.C. § 1314(a)(1), directs the Administrator of EPA to publish water quality criteria that accurately 

reflect the latest scientific knowledge on the kind and extent of all identifiable effects on health and 

welfare that might be expected from the presence of pollutants in any body of water, including ground 

water. Under this authority, EPA developed revised aquatic life criteria for copper that are based on 

the Biotic Ligand Model (BLM) in 2007. The BLM predicts metal toxicity based on site-specific water 

quality parameters, and derives acute and chronic criteria from the predicted toxicity. Derivation of 

water quality criteria using the BLM requires 10 input parameters (temperature, pH, dissolved organic 

carbon (DOC), alkalinity, calcium, magnesium, sodium, potassium, sulfate, and chloride). Data 

regarding these parameters may not be available for many receiving waters. Given that the BLM is 

likely to be applied over a broad geographical range, and that limited data are available for many areas, 

a practical method to estimate missing water quality parameters was needed to facilitate full use of 

the BLM in water quality standards across the U.S. This technical support document (herein referred to 

as the “Missing Parameters TSD”) summarizes data analysis approaches EPA used to develop 

recommendations for default values for water quality parameters that may be used in the BLM when 

data are lacking. The section of the CWA related to the development of the information presented in 

this technical support document is CWA Section 304(a)(2). CWA Section 304(a)(2) generally requires 

EPA to develop and publish information on the factors necessary to restore and maintain the chemical, 

physical, and biological integrity of navigable waters. Section 304(a)(2) also allows EPA to provide 

information on the conditions necessary for the protection and propagation of shellfish, fish, and 

wildlife in receiving waters and for allowing recreational activities in and on the water. 

The objective of this report is to summarize recommendations that BLM users can apply to estimate

values for missing input water quality parameters.

1.2 Input Data and the BLM

The BLM calculates metal toxicity to aquatic organisms as a function of the concentrations of certain 

chemical constituents of water, including, for example, ions that can complex with metals and limit 

biological availability, and ions that compete with metals for binding sites at the ion exchange tissues 

of aquatic organisms (e.g., at the fish gill). The BLM predicts the metal criteria concentrations, such as 

copper in freshwater, which will vary according to changes in the associated water quality parameters. 

An appropriately protective acute and chronic copper (or other metals) criteria must reflect the 

variability of water quality parameters at the site. In previous analyses, EPA found that protective 

water quality criteria for copper generally correspond to approximately the 2.5th percentile of the 
2

distribution of instantaneous water quality criteria (IWQC) predicted by the BLM1 (USEPA, 2002). Thus, 

predictions made for a site using the corresponding low percentile of the water quality parameter 

distributions are appropriately protective. Copper BLM predictions are most sensitive to the following 

five important parameters: DOC, pH, and calcium, magnesium, and sodium concentrations (taken 

together). Estimates are most sensitive to DOC, and vary in direct proportion to a change in value (i.e., 

they are 100% sensitive to DOC). Estimates are 50% sensitive to a change in pH, and 20% sensitive to 

the combined concentrations of calcium, magnesium, and sodium.

1.3 Previous Studies

EPA has conducted previous studies to develop tools to estimate BLM water quality parameters for 

sites where there may be few (or no) water quality data available. Brief summaries of these previous 

studies are provided below, and more detailed descriptions are provided in Appendices A through D.

1.3.1 An Examination of Spatial Trends in Surface Water Chemistry in the Continental United 

States: Implications for the Use of Default Values as Inputs to the BLM for Prediction of Acute 

Metal Toxicity to Aquatic Organisms (Carlton, 2006) 

A large database of surface water chemistry monitoring data was examined to look for spatial trends in 

five chemical constituents that are key inputs to a model for predicting metal toxicity to aquatic 

organisms: pH, dissolved organic carbon, alkalinity, calcium, and sodium. Continuous prediction maps 

of concentrations were generated using various kriging techniques to interpolate between site-median 

values measured at several thousand separate locations throughout the continental U.S. Continuous 

concentration surfaces were then averaged over 8-digit Hydrologic Unit (HUC) polygons to produce 

block-averaged mean estimates of site-median concentrations. Pairwise comparisons indicated distinct 

trends between various HUC-averaged predicted constituents. The same analyses performed on data 

from 772 locations where all five constituents had been measured revealed similar relationships 

between monitored constituents. Principal components analyses (PCA) performed on these data sets 

showed that 80 to 90 percent of the variance in both cases could be explained by a single component 

with loadings on three of the five constituents. The use of kriging to produce appropriate quantile 

maps for block-averaging is suggested as a possible approach for developing regional values to use as 

default model inputs, when site-specific monitoring data are lacking. Refer to Appendix A for more 

information.

1.3.2 Approaches for Estimating Missing BLM Input Parameters: Correlation Approaches to 

Estimate BLM Input Parameters Using Conductivity and Discharge as Explanatory Variables 

(USEPA, 2007) 

In this 2007 report, EPA developed regression models to project BLM water quality parameters from 

conductivity data. EPA assessed supplementing the geostatistical approach with classical estimation 

methods, such as regression and correlation by assessing the degree of correlation between 

conductivity and each of the BLM water quality parameters using National Water Information System 

 

1 This was the median for 17 sites; the range was 1 to 36%.
3

(NWIS) data from three states (Colorado, Utah, and Wyoming). These states were selected because of 

the large spatial and temporal variability observed.

EPA concluded that conductivity is significantly correlated with BLM water quality parameters between 

sites, especially for the low-end distribution statistics of interest for parameter estimation. Since 

conductivity data are abundant and correlate well with BLM water quality parameters, EPA determined 

it is reasonable to incorporate conductivity in spatial projections of BLM parameters. Correlation 

coefficients were lower for pH and DOC than for the geochemical ions (GIs) and alkalinity, but were 

also significant. Refer to Appendix B for more information.

1.3.3 Copper Biotic Ligand Model (BLM) Software and Supporting Documents Preparation: 

Development of Tools to Estimate BLM Parameters (USEPA, 2008) 

In order to predict parameters based on geographic location, this 2008 report investigated how to 

project BLM water quality parameters for a given site based on other site data using geostatistical 

methods. There are a number of ways in which the conductivity regressions can be used to project 

BLM water quality inputs. The regressions allow estimates of the BLM water quality inputs from either: 

(1) a limited number of conductivity measurements, or (2) a low-end conductivity value estimated by 

geostatistical methods. 

The first approach, projecting BLM water quality inputs from conductivity measurements, was 

demonstrated for a limited number of test sites. Regression models were developed to project 10th

percentiles of BLM water quality input parameters from the 10th percentile of measured conductivity 

distributions at sites in Colorado, Utah, and Wyoming. The 10th percentile is the value below which 10

percent of the observations may be found. The regression models were tested using data and copper 

BLM predictions for four sites, and produced highly consistent results. The regression models for pH 

and DOC, the most sensitive of the BLM water quality parameters, were not sufficiently accurate to 

make reliable BLM parameter predictions. However, regression models for the GI parameters (calcium, 

magnesium, sodium, potassium, chloride, sulfate, and alkalinity) were reasonably accurate, as judged 

by comparing model predictions made using projected values of the these BLM input parameters to 

model predictions made using measured input data. No estimate for site-specific pH was superior to 

the observed weak conductivity regression. To improve upon this estimate, it was necessary to use 

actual site-specific pH data. For DOC, the Level III ecoregion (referred to herein as simply “ecoregion”) 

and water body type-specific DOC concentration percentiles tabulated by EPA for the National 

Bioaccumulation Factors Technical Support Document (USEPA, 2003) appear to be far better estimates 

of lower-percentile DOC concentrations than the estimates made using the conductivity regression.

EPA also provided a proof of concept for the second approach, which was to see whether combining 

the kriged conductivities with the conductivity-hardness regression would project the 10th percentiles 

of hardness better than direct kriging of the hardness data. EPA found that both approaches produce 

estimates of hardness that correlate significantly with the measured data (correlation coefficient 

r=0.80 for direct kriging of hardness; r=0.95 for conductivity kriging + regression). However, the kriging

+ regression approach fits the hardness data substantially better than direct kriging. Refer to Appendix 

C for more information.
4

1.3.4 Approaches for Estimating Missing BLM Input Parameters: Projections of Total Organic 

Carbon as a Function of Biochemical Oxygen Demand (USEPA, 2006a) 

DOC concentrations downstream of an effluent discharge are necessary inputs for the BLM to predict 

toxicity associated with a wastewater discharge. Effluent DOC is monitored by very few publicly-owned 

treatment works (POTWs) according to data retrieved from EPA’s Permit Compliance System (PCS). 

Biochemical oxygen demand (BOD) is monitored by most POTWs. EPA developed regressions to project 

total organic carbon (TOC) concentrations from BOD values using effluent samples at all POTWs 

reporting data for both parameters in EPA’s PCS. EPA concluded that this regression gives reasonable 

estimates of TOC in POTWs effluents and are likely the best available estimates of effluent TOC to 

determine DOC concentrations for the BLM. Refer to Appendix D for more information.

1.4 Approaches to Estimate Water Quality Parameters for the BLM

Building upon the studies described above, this report uses three approaches to develop default 

estimates for parameters needed for the BLM when empirical data are lacking. The three approaches

are listed below and are detailed in the following sections:

 Section 2: Using Geostatistics and Conductivity to Predict GI Parameters

 Section 3: Using Stream Order to Refine Prediction of GI Parameters

 Section 4: Using the National Organic Carbon Database to estimate DOC

EPA recommends that temperature and pH be measured directly in the field.
5

2 USING GEOSTATISTICS AND CONDUCTIVITY TO PREDICT GI PARAMETERS

The following section describes studies that demonstrate how geostatistical techniques, coupled with 

conductivity correlations, can be used to predict BLM input parameters for GIs when site-specific data 

are unavailable. In a previous study (USEPA, 2008) EPA demonstrated that combining kriging with 

regressions to estimate inputs based on conductivity improves the accuracy of GI estimates. In this 

section EPA has expanded on this approach and developed national estimates at the Level III ecoregion 

in the continental U.S.

The current freshwater copper BLM requires 10 input parameters that reflect water chemistry in order 

to calculate copper criteria: temperature, pH, DOC, alkalinity, calcium, magnesium, sodium, potassium, 

sulfate, and chloride, the last seven of which are GIs. The concentrations of GIs vary in surface waters 

due to dissolution, weathering, ground water-surface water interactions, and other geologic processes 

in the watershed, in addition to dilution by snowmelt and precipitation. Consequently, the 

concentrations of GI parameters tend to vary according to the regional geology. For example, alkalinity

has noticeable geographic trends. Areas dominated by carbonate rocks, such as limestone as in the 

prairie states, tend toward high alkalinity. Areas dominated by igneous rocks, such as granite, such as 

parts of the northeast, tend toward low hardness and alkalinity. 

In this section we expand on the EPA 2008 proof of concept (in Appendix C) using geostatistics to 

develop default missing GI parameter values based on geography. Geostatistics are statistical 

methodologies that use spatial coordinates to help formulate models used in estimation and prediction 

(ESRI, 2003). Geostatistical techniques are attractive because they explain parameter variation arising 

from spatial correlations, which are not used in conventional statistics. We have supplemented the 

geostatistical approach by adding conductivity as an additional explanatory variable. Conductivity is 

one of the most widely monitored water quality indicators in the U.S. Because conductivity data are 

abundant and correlate well to the BLM GI parameters, we incorporated conductivity in spatial 

projections of BLM parameters. Based on the proof of concept described above (and in Appendix C), 

we expected that this approach, which can be implemented by co-kriging (i.e., an interpolation 

technique that allows for better estimates by the incorporation of well-sampled, correlated secondary 

data) in geostatistical software, would allow more robust spatial projections of BLM water quality 

parameters.

2.1 Data Source and Processing

Water quality data for conductivity and BLM GI water quality parameters were retrieved from the

United States Geological Survey (USGS) National Water Information System (NWIS). NWIS contains 

data from millions of sampling events at tens of thousands of individual sampling locations (stations) in 

the continental U.S. (Figure 1). Not all water quality parameters of relevance to the BLM were 

monitored at each location. The numbers of sampling events at individual locations also range widely, 

with a mean of 15, and a mode of one (i.e., most sites were only sampled once). Examination of the 

spatial distribution of numbers of sampling events per site reveals that the Midwestern and Western 

states tended to be sampled most intensively (Carleton, 2006). Because environmental sampling data 

tend to be lognormally distributed, disparities in numbers of samples may tend to produce higher 

mean and median values at locations that have been sampled more frequently. As spatial distributions 

of representative (e.g., median) concentrations are examined, it should be kept in mind that apparent 
6

geographic trends in concentration may be in part simply the result of uneven sampling intensity 

(Carleton, 2006).

Figure 1. NWIS sample collection locations in the continental U.S. (Carleton, 2006)

We focused our efforts on data collected from rivers and streams between 1984 and 2009. Data 

collected prior to 1984 were excluded because a number of the analytical methods used by USGS prior 

to that date have been replaced by methods with improved precision and lower detection limits. 

Furthermore, only sites with 40 or more samples were included in the analysis. With support from 

USGS staff, we obtained a complete download of national water quality data from NWIS, which totaled 

4,714,165 measurements from 959,946 samples, collected at 5,901 sites. These data included 

measurements for BLM water quality input parameters required to calculate copper criteria using the 

BLM: pH, DOC, alkalinity, calcium, magnesium, sodium, potassium, sulfate, and chloride. Data were 

also collected on filtered (dissolved) copper, and the spatial coordinates (latitude and longitude) of 

each sampling station were also retrieved. No data were collected on temperature. Only the GI data 

were included in the geostatistical analysis. A summary of the water quality data retrieved from NWIS 

is provided in Table 1. 
7 

Table 1. Summary of water quality data retrieved from NWIS

BLM Water Quality 

Parameter

NWIS Parameter 

Code Parameter Description Number of Observations

Conductivity1

00094

Specific conductance, water, 

unfiltered, field, microsiemens per 

centimeter at 25 degrees Celsius

553,700

00095

Specific conductance, water, 

unfiltered, laboratory, 

microsiemens per centimeter at 25 

degrees Celsius

799

pH

00400 pH, water, unfiltered, field, 

standard units 352,336

00403 pH, water, unfiltered, laboratory, 

standard units 151,161

Dissolver Organic 

Carbon

00681 Organic carbon, water, filtered, 

laboratory, milligrams per liter

30,008

Alkalinity

00410

Acid neutralizing capacity, water, 

unfiltered, fixed endpoint (pH 4.5) 

titration, field, milligrams per liter 

as calcium carbonate

35,232

00417

Acid neutralizing capacity, water, 

unfiltered, fixed endpoint (pH 4.5) 

titration, laboratory, milligrams per 

liter as calcium carbonate

15,264

00419

Acid neutralizing capacity, water, 

unfiltered, incremental titration, 

field, milligrams per liter as calcium 

carbonate

10,198

00418

Alkalinity, water, filtered, fixed 

endpoint (pH 4.5) titration, field, 

milligrams per liter as calcium 

carbonate

2,686

Calcium 00915 Calcium, water, filtered, 

laboratory, milligrams per liter 146,608

Magnesium 00925 Magnesium, water, filtered, 

laboratory, milligrams per liter 145,938

Sodium 00930 Sodium, water, filtered, laboratory, 

milligrams per liter 136,310

Potassium 00935 Potassium, water, filtered, 

laboratory, milligrams per liter 132,659

Sulfate 00945 Sulfate, water, filtered, laboratory, 

milligrams per liter 147,824

Chloride 00940 Chloride, water, filtered, 

laboratory, milligrams per liter 146,601

1 Conductivity is not a BLM parameter, but was used as an explanatory variable for the other water quality parameters.

The data were screened using established quality assurance procedures. All data were checked to 

confirm that they contained numerical values without null (missing) records and remark codes were 
8

identified and reviewed. Minimum and maximum values for each parameter were confirmed to be 

within expected ranges and frequency distributions were plotted and examined for each of the 

parameters to identify outliers. We also confirmed that the spatial coordinate data placed each 

sampling location within the continental U.S. Additional data processing included the following steps: 

 For the data at each station, the observations for each variable were averaged on a daily basis. 

This was done to reduce the influence of high frequency sampling at a few stations. 

 Data were edited by censoring parameter(s) with fewer than 10 to 20 daily values at a station. 

The 10th percentile for that parameter at that station was censored to improve the reliability of 

the lower-tail (i.e., 10th) percentile statistics. 

 Tenth (rank order/nonparametric) percentiles of the distributions of all water quality 

parameters measured at each station were calculated. 

It should be emphasized that all of the statistical and geostatistical analyses and predictions presented 

in this report are based on the 10th percentiles of the concentration distribution measured for each 

parameter at every station. The estimates of water quality parameter values for “missing” data are 

therefore also 10th percentile concentrations. We selected the 10th percentile of the site parameter 

distributions as a statistic that is a practical compromise between a lower-bound concentration and a 

percentile that can be reliably determined from small sample sizes. Initial testing with the BLM 

suggested that protective water quality criteria (WQC) for copper generally corresponded to 

approximately the 2.5th percentile of the distribution of instantaneous water quality criteria (IWQC) 

predicted by the BLM. Thus, BLM predictions made for a site using the corresponding low percentiles 

of the water quality parameter distributions should (logically) also be a conservative approximation of 

a protective criterion. As a more reliably determined statistic, the 10th percentile of water quality 

parameters will also derive reasonably protective criteria, especially for small sample sizes where there 

may be greater uncertainty at lower percentile estimates. The 10th percentile estimates presented in 

this document were initially developed to implement the copper BLM published by EPA in 2007 and 

will apply to other metals as well.

2.2 Geostatistical Analysis of National Data for Geochemical Ions

The ESRI ArcGIS Geostatistical Analyst tool was used to create statistically valid two-dimensional 

surface models for conductivity and for each of the BLM GI parameters. Using the 10th percentile daily 

average concentrations at each sampling location from the NWIS data, Geostatistical Analyst was used 

to create predictions for unmeasured locations throughout the continental U.S. For each parameter, 

the surface models were fit by minimizing the statistical error of the predicted surface. Surface fitting 

involved three steps: exploratory spatial data analysis, structural analysis (modeling the semivariogram 

to analyze surface properties of data from nearby locations), and surface prediction and assessment of 

the results. The semivariogram represents autocorrelation of measured data points spatially.

Modeling of the semivariogram was based on cross-validation, which calculates error statistics that 

serve as diagnostics to indicate whether the model is reasonable for map production. Cross-validation 

was used to select the models that provided the most accurate predictions. The following criteria were

used to evaluate goodness of fit for the semivariogram model:

 Mean Standardized Error: close to 0;

 Root Mean Square Error (RMSE): as small as possible;
9 

 Root-Mean-Square Standardized Error: close to 1; and,

 RMSE close to Average Standard Error ASE). 

The difference between the prediction and the measured data value is the prediction error. For a 

model that provides accurate predictions, the mean prediction error should be close to 0 if the 

predictions are unbiased. The root-mean-square standardized prediction error should be close to 1 if 

the standard errors are accurate, and RMSE should be small if the predictions are close to the 

measured values (ESRI, 2003). 

A tabulation of the geostatistical model selected for each water quality parameter, the number of data 

points interpolated, and the resulting error statistics are presented in Table 2. We used the optimal 

parameters for a spherical semivariogram as calculated by the Geostatistical Analyst. No 

transformations were applied to the data. Anisotropy (directional influence on the semivariogram) was 

not incorporated in the semivariogram models.

Table 2. Model selection and cross validation statistics for geostatistical fitting of 10th

percentiles of BLM GI parameters

Parameter Geostatistical 

model

Number of 

samples

Mean 

standardized 

error

Root mean 

square error

RMS 

standardized 

error

Average 

standard 

error

Conductivity Universal kriging 4833 -0.01038 1361 1.081 1259

Alkalinity Universal cokriging 

with conductivity

1372 -0.001115 36.62 1.09 33.23

Calcium Universal cokriging 

with conductivity 2590 0.0001694 26.81 1.186 22.02

Magnesium Universal cokriging 

with conductivity 2578 -0.002258 15.92 1.16 13.58

Sodium Universal cokriging 

with conductivity 2439 -0.002929 156.3 1.583 95.78

Potassium Universal cokriging 

with conductivity 2379 -0.001184 3.488 1.429 2.381

Sulfate Universal cokriging 

with conductivity

2650 -0.0000225 114.5 1.29 87.04

Chloride Universal cokriging 

with conductivity 2792 0.001653 375.2 1.51 247

2.2.1 Kriging of Conductivity Data

Universal kriging with a constant trend was used to map the surface of 10th percentile conductivity 

values. Kriging weights the surrounding measured values to derive a prediction for each location. The 

weights are based on the distances between the measured points and the prediction location, as well 

as the overall spatial arrangement among the measured points. The kriged prediction surface of 10th

percentiles of conductivity is mapped in Figure 2. As the kriging results show, conductivities are highest 

in the south-central and southwestern regions, as well as along the Gulf and southern Atlantic coasts. 

Regions of lower conductivity are found in a number of parts of the country.
10

Figure 2. Kriged prediction surface for 10th percentile of conductivity in the continental U.S. (sample 

locations in blue)

2.2.2 Co-kriging of GI Data 

Co-kriging was used to improve surface predictions of the BLM GI parameters by taking into account 

secondary variables, in this case conductivity. As demonstrated above, conductivity is significantly 

correlated to all of the BLM GIs. Universal co-kriging with conductivity, assuming a constant trend, was 

used to map the surface of 10th percentile BLM GIs concentrations. For each of these parameters, cokriging produced cross-validation errors that were superior in terms of the goodness-of-fit criteria to 

errors produced by universal kriging. Prediction surfaces for calcium and alkalinity are mapped in 

Figures 3 and 4. The spatial distribution of calcium (Figure 3) shares a number of similarities with the 

mapping of conductivity (Figure 2). The co-kriged alkalinity surface (Figure 4) is rather different, with 

high alkalinity values reflecting geographic features (such as the carbonate geology of the prairie 

states) and low alkalinity values that reflect the granitic geology of the northeast. Prediction surfaces 

for the other BLM GI’s are generally similar to those for conductivity and calcium.
11

Figure 3. Co-kriged prediction surface for 10th percentile of calcium in the continental U.S.
12

Figure 4. Co-kriged prediction surface for 10th percentile of alkalinity in the continental U.S.

2.2.3 Projection of Geostatistical Predictions onto Level III Ecoregions

Although maps of the geostatistical predictions are informative, a tabulation of the results is preferable 

for the purpose of providing guidance to BLM users. We chose to spatially average the geostatistical 

predictions of BLM water quality parameters according to the Level III ecoregions of the continental 

U.S. (Table 3), as these ecoregions provide a sound basis for spatial averaging of the water quality 

predictions. Ecoregions are designed to serve as a spatial framework for environmental resource 

management and denote areas within which ecosystems (and the type, quality, and quantity of 

environmental resources) are generally similar. They typically provide a logical and useful spatial 

(geographical) framework for organizing the results of environmental measurements (Omernik and 

Griffith, 2014). Ecoregions can be distinguished by landscape-level characteristics that cause ecosystem 

components to reflect different patterns in different regions (Omernik, 1987). “Level III Ecoregions of 

the Continental U.S.” map layer shows ecoregion delineation based on common patterns of geology, 

physiography, vegetation, climate, soils, land use, wildlife, water quality, and hydrology. The map layer 

in Figure 5 was compiled by EPA (USEPA, 2013a) 

(http://www.epa.gov/wed/pages/ecoregions/level_iii_iv.htm).
13

Table 3. Level III ecoregions of the U.S. organized according to broader Level I ecoregions

Level I Ecological Regions

Level III Ecoregion Name of Ecoregion

Marine West Coast Forest

1 Coast Range

2 Puget Lowland

3 Willamette Valley

111 Ahklun and Kilbuck Mountains

113 Alaska Peninsula Mountains

115 Cook Inlet

119 Pacific Coastal Mountains

120 Coastal Western Hemlock-Sitka Spruce Forests

Northwestern Forested Mountains

4 Cascades

5 Sierra Nevada

9 Eastern Cascades Slopes and Foothills

11 Blue Mountains

15 Northern Rockies

16 Idaho Batholith

17 Middle Rockies

19 Wasatch and Uinta Mountains

21 Southern Rockies

41 Canadian Rockies

77 North Cascades

78 Klamath Mountains

105 Interior Highlands

116 Alaska Range

117 Copper Plateau

118 Wrangell Mountains

Mediterranean California

6 Southern and Central California Chaparral and Oak Woodlands

7 Central California Valley

8 Southern California Mountains

North American Deserts

10 Columbia Plateau

12 Snake River Plain

13 Central Basin and Range

14 Mojave Basin and Range

18 Wyoming Basin

20 Colorado Plateaus

22 Arizona/New Mexico Plateau
14

Table 3. Level III ecoregions of the U.S. organized according to broader Level I ecoregions

Level I Ecological Regions

Level III Ecoregion Name of Ecoregion

24 Chihuahuan Deserts

80 Northern Basin and Range

81 Sonoran Basin and Range

Temperate Sierras

23 Arizona/New Mexico Mountains

Great Plains

25 Western High Plains

26 Southwestern Tablelands

27 Central Great Plains

28 Flint Hills

29 Central Oklahoma/Texas Plains

30 Edwards Plateau

31 Southern Texas Plains

34 Western Gulf Coastal Plain

40 Central Irregular Plains

42 Northwestern Glaciated Plains

43 Northwestern Great Plains

44 Nebraska Sand Hills

45 Piedmont

46 Northern Glaciated Plains

47 Western Corn Belt Plains

48 Lake Agassiz Plain

Eastern Temperate Forest

32 Texas Blackland Prairies

33 East Central Texas Plains

35 South Central Plains

36 Ouachita Mountains

37 Arkansas Valley

38 Boston Mountains

39 Ozark Highlands

51 North Central Hardwood Forests

52 Driftless Area

53 Southeastern Wisconsin Till Plains

54 Central Corn Belt Plains

55 Eastern Corn Belt Plains

56 Southern Michigan/Northern Indiana Drift Plains

57 Huron/Erie Lake Plains

59 Northeastern Coastal Zone

60 Northern Appalachian Plateau and Uplands
15

Table 3. Level III ecoregions of the U.S. organized according to broader Level I ecoregions

Level I Ecological Regions

Level III Ecoregion Name of Ecoregion

61 Erie Drift Plain

63 Middle Atlantic Coastal Plain

64 Northern Piedmont

65 Southeastern Plains

66 Blue Ridge

67 Ridge and Valley

68 Southwestern Appalachians

69 Central Appalachians

70 Western Allegheny Plateau

71 Interior Plateau

72 Interior River Valleys and Hills

73 Mississippi Alluvial Plain

74 Mississippi Valley Loess Plains

75 Southern Coastal Plain

82 Laurentian Plains and Hills

83 Eastern Great Lakes and Hudson Lowlands

84 Atlantic Coastal Pine Barrens

Northern Forests

49 Northern Minnesota Wetlands

50 Northern Lakes and Forests

58 Northeastern Highlands

62 North Central Appalachians

Tropical Wet Forests

76 Southern Florida Coastal Plain

Southern Semi-Arid Highlands

79 Madrean Archipelago

Taiga

101 Arctic Coastal Plain

102 Arctic Foothills

103 Brooks Range

104 Interior Forested Lowlands and Uplands

106 Interior Bottomlands

107 Yukon Flats

108 Ogilvie Mountains

Tundra

109 Subarctic Coastal Plains

110 Seward Peninsula

112 Bristol Bay-Nushagak Lowlands

114 Aleutian Islands
16

Figure 5. Map of Level III ecoregions in the U.S.

(Image taken from ftp://ftp.epa.gov/wed/ecoregions/us/Eco_Level_III_US.pdf)
17

Using the differences in land and water interactions, regional variations in attainable water quality, 

distinct biogeographical patterns (MacArthur, 1972), and similarities and differences in ecosystems to 

delineate ecoregions makes the application of ecoregions in environmental analyses a powerful tool 

with which to organize environmental information. The approach can take into account regional 

factors related to attainable water quality, and thus can be used to designate lakes for protection and 

to establish lake-restoration goals that are appropriate for each ecoregion (National Research Council 

(NRC), 1992). The NRC of the National Academy of Sciences has similarly endorsed the use of the 

concept in restoring and managing streams, rivers, and wetlands (NRC, 1992).

The theory of ecoregion delineation states that natural water quality characteristics of lakes and 

streams within a single ecoregion will be more similar than the characteristics between ecoregions 

(Perry and Vanderklein, 1996). Water quality characteristics exist in a landscape framework; neither 

normal nor impacted conditions of water resources can be separated from controlling influences of the 

surrounding landscape. The ecoregion concept has been applied and tested rather extensively in 

streams, rivers, and lakes. Testing and validation has been conducted in many diverse areas of the U.S., 

including several streams in Arkansas, Colorado, Kansas, Minnesota, Ohio, and Oregon, and in lakes of 

Michigan, Minnesota, Ohio, and Wisconsin (NRC, 1992).

Carleton (2006) used HUCs instead of ecoregions as the basis for averaging geostatistical results. HUCs 

are spatial delineations used for river basin management. Although a river basin may offer a logical 

framework for water supply management, for water quality management river basins are less 

applicable. The assumption that basins share similar properties is not always borne out, because river 

basins are often linked only by the water that flows through them. As Carleton (2006) noted, the use of 

HUCs for spatial averaging of surface water concentrations presents other conceptual difficulties. Only 

about 45% of HUCs are actual watersheds (Omernik, 2003); the rest receive drainage from additional 

upgradient areas. Concentrations measured in flowing waters reflect the soil, vegetation, and land use 

properties of the aggregate upstream drainage areas rather than of the sampling locations themselves 

(Smith et al., 1997). 

2.2.3.1 Averaging Methods

To average the geostatistical predictions, a uniform grid was laid over the predicted surfaces and the 

predictions were sampled at the grid points falling within the polygons representing each ecoregion. 

The grid spacing was sized so that at least 30 points were sampled within each ecoregion. Unbiased log

means were then calculated from the sampled concentration predictions in each ecoregion. The 

logarithmic transformation was applied because this normalized the concentration distributions in 

almost all of the ecoregions.

2.2.3.2 Tabulations of Ecoregional Estimated BLM Water Quality Parameters

The average predicted 10th percentile concentrations for conductivity and the GI parameters for each 

of the Level III ecoregions in the continental U.S. are presented in Table 4. For each of these 

parameters, there is considerable variation between the ecoregional averages nationally. Chloride 

concentrations exhibit the greatest variation, with ecoregional 10th percentile averages that range from 

0.7 to 573 milligrams per liter (mg/L). Alkalinity was the least variable, but the ecoregional 10th

percentile average concentrations still ranged from 12 to 163 mg/L. 
18

Table 4. Predicted 10th percentile concentrations for conductivity (μS/cm), BLM GI water 

quality parameters (mg/L) and hardness in each Level III ecoregion in the continental U.S.

Unbiased log 

mean of 10th

percentile 

concentrations

Level III 

Ecoregion

Ecoregion 

Name 

Conductivity Calcium Magnesium Sodium Potassium Alkalinity Chloride Sulfate Hardness1

1 Coast Range 102 8.4 3.2 4.1 0.64 33 3.2 4.8 34.12

2 Puget Lowland 80 7.1 1.9 2.8 0.64 22 2.3 5.6 25.54

3 Willamette Valley 91 8.2 2.9 4.4 0.90 30 4.7 3.8 32.39

4 Cascades 107 6.6 2.9 3.5 0.74 35 2.2 3.2 28.39

5 Sierra Nevada 195 8.3 4.7 8.8 1.3 58 5.8 11 40.02

6 

Southern and 

Central California 

Chaparral and Oak 

Woodlands

600 42 24 48 2.5 124 56 136 203.4

7 Central California 

Valley 378 21 16 25 1.7 91 21 58 118.1

8 Southern California 

Mountains 772 63 25 63 3.8 150 54 171 260

9 

Eastern Cascades 

Slopes and 

Foothills

212 8.2 3.8 6.0 1.0 44 3.2 5.0 36.08

10 Columbia Plateau 166 15 5.2 9.3 1.8 40 3.3 10 58.82

11 Blue Mountains 142 11 3.9 7.7 1.4 49 3.3 7.1 43.49

12 Snake River Plain 273 33 10 13 2.3 109 10 22 123.5

13 Central Basin and 

Range 426 43 16 45 3.6 120 45 83 173.1

14 Mojave Basin and 

Range 976 69 27 81 6.3 138 85 258 283.2

15 Northern Rockies 90 11 3.1 2.3 0.67 44 0.72 4.4 40.21

16 Idaho Batholith 91 13 3.8 3.6 0.88 62 1.9 5.9 48.08

17 Middle Rockies 300 30 10 14 1.9 105 7.6 55 116

18 Wyoming Basin 446 35 13 33 1.7 96 7.2 104 140.8

19 Wasatch and Uinta 

Mountains 426 61 27 61 3.3 155 55 155 263.2

20 Colorado Plateaus 639 65 26 57 2.6 117 28 197 269.1

21 Southern Rockies 259 26 8.0 12 1.4 55 3.8 56 97.8

22 Arizona/New 

Mexico Plateau 697 50 15 65 3.0 96 65 143 186.5

23 Arizona/New 

Mexico Mountains 879 66 18 85 3.4 102 100 189 238.8

24 Chihuahuan 

Deserts 2712 176 50 379 8.6 106 573 608 645

25 High Plains 1770 104 35 191 6.0 112 281 353 403.5

26 Southwestern 2147 114 34 316 4.9 94 512 374 424.4
19

Table 4. Predicted 10th percentile concentrations for conductivity (μS/cm), BLM GI water 

quality parameters (mg/L) and hardness in each Level III ecoregion in the continental U.S.

Unbiased log 

mean of 10th

percentile 

concentrations

Level III 

Ecoregion

Ecoregion 

Name 

Conductivity Calcium Magnesium Sodium Potassium Alkalinity Chloride Sulfate Hardness1

Tablelands

27 Central Great 

Plains 1228 84 24 176 6.9 121 245 204 308.4

28 Flint Hills 406 42 8.5 30 4.3 121 42 45 139.85

29

Central 

Oklahoma/Texas 

Plains

925 60 16 107 4.1 95 164 108 215.6

30 Edwards Plateau 596 48 14 38 2.7 98 62 52 177.4

31 Southern Texas 

Plains 798 56 14 58 3.8 129 73 91 197.4

32 Texas Blackland 

Prairies 364 39 5.8 21 3.2 92 26 33 121.28

33 East Central Texas 

Plains 367 36 6.3 23 3.8 98 29 29 115.83

34 Western Gulf 

Coastal Plain 565 43 10 62 3.9 87 86 78 148.5

35 South Central 

Plains 160 12 2.8 11 2.3 34 15 15 41.48

36 Ouachita 

Mountains 116 7.9 2.8 8.4 1.3 34 10 11 31.23

37 Arkansas Valley 192 16 4.7 15 1.8 51 20 16 59.27

38 Boston Mountains 152 18 3.3 4.3 1.3 53 6.7 8.2 58.53

39 Ozark Highlands 258 31 10 4.5 1.6 96 6.0 20 118.5

40 Central Irregular 

Plains 310 39 8.5 11 3.0 100 13 50 132.35

41 Canadian Rockies 164 22 8.7 15 0.57 80 1.7 38 90.67

42 Northwestern 

Glaciated Plains 545 37 20 61 5.9 163 8.1 147 174.5

43 Northwestern 

Great Plains 828 49 24 84 5.3 151 10 247 220.9

44 Nebraska Sand Hills 486 47 13 35 6.9 151 10 96 170.8

45 Piedmont 75 5.8 1.9 4.0 1.5 19 3.9 4.1 22.29

46 Northern Glaciated 

Plains 524 40 20 38 9.1 163 13 106 182

47 Western Corn Belt 

Plains 464 48 16 16 3.4 136 16 45 185.6

48 Lake Agassiz Plain 441 42 18 16 5.1 140 8.6 62 178.8

49 Northern 

Minnesota 

229 24 10 3.2 1.4 95 2.6 8.4 101
20

Table 4. Predicted 10th percentile concentrations for conductivity (μS/cm), BLM GI water 

quality parameters (mg/L) and hardness in each Level III ecoregion in the continental U.S.

Unbiased log 

mean of 10th

percentile 

concentrations

Level III 

Ecoregion

Ecoregion 

Name 

Conductivity Calcium Magnesium Sodium Potassium Alkalinity Chloride Sulfate Hardness1

Wetlands

50 Northern Lakes and 

Forests 166 19 6.5 2.5 0.78 83 3.4 6.1 74.15

51 North Central 

Hardwood Forests 295 31 12 5.6 1.7 115 8.9 15 126.7

52 Driftless Area 348 34 15 5.1 1.6 107 10 17 146.5

53

Southeastern 

Wisconsin Till 

Plains

510 39 20 16 2.1 112 31 25 179.5

54 Central Corn Belt 

Plains 546 53 24 14 1.7 124 30 46 230.9

55 Eastern Corn Belt 

Plains 463 49 15 11 2.0 116 23 32 184

56

Southern 

Michigan/Northern 

Indiana Drift Plains

463 52 15 14 1.9 134 28 29 191.5

57 Huron/Erie Lake 

Plains 467 52 15 13 2.2 125 27 32 191.5

58 Northeastern 

Highlands 97 11 1.9 5.7 0.69 24 10 7.4 35.29

59 Northeastern 

Coastal Zone 176 8.3 2.0 14 1.3 15 22 8.4 28.95

60

Northern 

Appalachian 

Plateau and 

Uplands

271 33 7.3 37 1.3 53 64 22 112.43

61 Erie Drift Plain 364 31 8.1 19 2.3 64 29 38 110.71

62 North Central 

Appalachians 184 13 3.9 7.1 1.0 41 11 15 48.49

63 Middle Atlantic 

Coastal Plain 793 6.7 2.3 6.8 1.8 15 83 22 26.18

64 Northern Piedmont 208 21 5.8 10 1.9 39 17 15 76.28

65 Southeastern 

Plains 121 7.4 2.2 5.5 1.5 19 15 7.2 27.52

66 Blue Ridge 121 11 3.2 3.0 1.3 23 3.4 6.0 40.62

67 Ridge and Valley 163 17 4.5 4.6 1.4 33 6.3 15 60.95

68 Southwestern 

Appalachians 151 13 3.2 2.5 1.3 42 3.2 11 45.62

69 Central 

Appalachians 193 16 5.6 4.6 1.3 34 4.5 33 62.96
21

Table 4. Predicted 10th percentile concentrations for conductivity (μS/cm), BLM GI water 

quality parameters (mg/L) and hardness in each Level III ecoregion in the continental U.S.

Unbiased log 

mean of 10th

percentile 

concentrations

Level III 

Ecoregion

Ecoregion 

Name 

Conductivity Calcium Magnesium Sodium Potassium Alkalinity Chloride Sulfate Hardness1

70 Western Allegheny 

Plateau 276 23 7.3 10 1.7 46 14 47 87.43

71 Interior Plateau 237 27 5.9 4.4 1.5 65 7.0 20 91.69

72 Interior River 

Valleys and Hills 326 34 12 11 2.4 87 17 46 134.2

73 Mississippi Alluvial 

Plain 255 14 5.5 17 2.6 44 22 13 57.55

74 Mississippi Valley 

Loess Plains 102 10 2.9 3.9 1.6 38 4.5 8.4 36.89

75 Southern Coastal 

Plain 726 18 5.0 20 2.0 41 390 38 65.5

76 Southern Florida 

Coastal Plain 682 49 6.6 25 2.4 103 43 15 149.56

77 North Cascades 93 6.5 2.3 2.3 0.64 27 1.2 4.9 25.68

78 Klamath Mountains 156 8.7 4.6 4.0 0.66 44 2.1 3.5 40.61

79 Madrean

Archipelago 625 42 11 45 2.8 92 39 78 150.1

80 Northern Basin and 

Range 298 26 8.2 20 2.7 89 15 24 98.62

81 Sonoran Basin and 

Range 991 64 24 115 4.4 121 131 192 258.4

82 Laurentian Plains 

and Hills 104 4.8 0.78 2.5 0.48 12 2.7 4.4 15.198

83

Eastern Great 

Lakes and Hudson 

Lowlands

294 34 6.8 21 1.3 61 40 26 112.88

84 Atlantic Coastal 

Pine Barrens 261 7.4 2.7 10 1.7 23 16 11 29.57

1 2+ 2+ Water Hardness calculated as equivalents CaCO3 = 2.5 (Ca ) + 4.1 (Mg )

2.2.3.3 Confirmation of Results 

To confirm the results of the geostatistical predictions, a number of comparisons were made between 

the ecoregional average predictions and averages based directly on the data. For each GI parameter, 

we compared the ecoregional average predictions against the corresponding averages calculated from 

the data for each ecoregion. 

Scatter plot matrices provide a visual presentation of the correlations between different parameters. 

Scatter plot matrices were developed for the ecoregional averages of conductivity and GI parameters. 

Figure 6 is the scatter plot matrix for ecoregional averages based on the data, and Figure 7 is the 

scatter plot matrix for ecoregional averages based on the geostatistical predictions. Comparison of 
22

these figures shows that the predicted averages capture the same trends in terms of distributions and 

parameter correlations as those that are found for the ecoregional data. The similarities in the 

distributions and correlation structures between the ecoregional averages in Figures 6 and 7 

demonstrate that the geostatistical ecoregion predictions are reasonable.

Figure 6. Scatter plot matrix of ecoregional average 10th percentiles of data for conductivity 

(COND_SAM) and GI parameters (calcium=CA_SAM, magnesium=MG_SAM, sodium=NA_SAM, 

potassium=K_SAM, alkalinity=ALK_SAM, chloride=CL_SAM, sulfate=SO4_SAM)

COND_SAM

COND_SAM

CA_SAM MG_SAM NA_SAM K_SAM ALK_SAM CL_SAM SO4_SAM

COND_SAM

CA_SAM

CA_SAM

MG_SAM

MG_SAM

NA_SAM

NA_SAM

K_SAM

K_SAM

ALK_SAM

ALK_SAM

CL_SAM

CL_SAM

COND_SAM

SO4_SAM

CA_SAM MG_SAM NA_SAM K_SAM ALK_SAM CL_SAM SO4_SAM

SO4_SAM
23

Figure 7. Scatter plot matrix of ecoregional average 10th percentiles of geostatistical predictions of 

conductivity (COND_KR) and BLM GI parameters (calcium=CA_CO, magnesium=MG_SCO, 

sodium=NA_CO, potassium=K_CO, alkalinity=ALK_CO, chloride=CL_CO, sulfate=SO4_CO)

In addition to scatter plots, correlation coefficient matrices between the parameters in each of the two 

data sets were generated. The Spearman (rank order) correlation coefficients for data-based 

ecoregional averages are presented in Table 5; correlation coefficients for ecoregional average 

geostatistical predictions are presented in Table 6. Although not identical, the correlation coefficients 

are similar between the two datasets, again demonstrating that the geostatistical predictions are 

reasonable.

COND_KR

COND_KR

CA_CO MG_CO NA_CO K_CO ALK_CO CL_CO SO4_CO

COND_KR

CA_CO

CA_CO

MG_CO

MG_CO

NA_CO

NA_CO

K_CO

K_CO

ALK_CO

ALK_CO

CL_CO

CL_CO

COND_KR

SO4_CO

CA_CO MG_CO NA_CO K_CO ALK_CO CL_CO SO4_CO

SO4_CO
24

Table 5. Spearman rank correlation matrix for unbiased log means of 10th percentile 

concentrations measured in Level III ecoregions

Conductivity Calcium Magnesium Sodium Potassium Alkalinity Chloride Sulfate

Conductivity 1 

Calcium 0.895 1 

Magnesium 0.877 0.927 1 

Sodium 0.865 0.819 0.813 1 

Potassium 0.823 0.758 0.73 0.859 1 

Alkalinity 0.769 0.881 0.898 0.698 0.679 1 

Chloride 0.815 0.774 0.702 0.855 0.788 0.595 1 

Sulfate 0.894 0.864 0.85 0.883 0.786 0.725 0.744 1 

Table 6. Spearman rank correlation matrix for unbiased log means of 10th percentile 

predicted (kriged/cokriged) concentrations in Level III ecoregions

Conductivity Calcium Magnesium Sodium Potassium Alkalinity Chloride Sulfate

Conductivity 1 

Calcium 0.872 1 

Magnesium 0.843 0.924 1 

Sodium 0.87 0.82 0.778 1 

Potassium 0.842 0.803 0.753 0.836 1 

Alkalinity 0.747 0.868 0.901 0.672 0.745 1 

Chloride 0.829 0.715 0.592 0.826 0.725 0.461 1 

Sulfate 0.889 0.873 0.875 0.893 0.831 0.751 0.715 1 

As a final test of the accuracy of the geostatistical predictions, we regressed the ecoregional averages 

based on the geostatistical predictions against the ecoregional averages based on the data. Scatter 

plots and fitted regression lines are shown for each of the parameters: conductivity (Figure 8), 

alkalinity (Figure 9), calcium (Figure 10), magnesium (Figure 11), sodium (Figure 12), potassium (Figure 

13), sulfate (Figure 14), and chloride (Figure 15). Statistics for the linear regressions are provided in 

Table 7. For each of the parameters, the predicted and data-based ecoregional averages are 

significantly correlated. In each case, the linear regression coefficient is nearly 1.0, with a highly 

significant P value. As with the previous comparisons, the linear regression results demonstrate that 

the accuracy of the geostatistical predictions is high. 
25

Figure 8. Ecoregional averages of kriged 10th percentiles of conductivity versus data

100 1000

conductivity (uS/cm)

500

1000

1500

2000

2500 3000

kriged conductivity (uS/cm)
26

Figure 9. Ecoregional averages of cokriged 10th percentiles of alkalinity versus data

50

100

150200250

alkalinity (mg CaCO3/L)

40

80

120

160

cokriged alkalinity (mg CaCO3/L)
27

Figure 10. Ecoregional averages of cokriged 10th percentiles of calcium versus data

1 10 100

calcium (mg/L)

40

80

120

160

200

cokriged calcium (mg/L)
28

Figure 11. Ecoregional averages of cokriged 10th percentiles of magnesium versus data

10

20 3040506070

magnesium (mg/L)

10

20

30

40

5060

cokriged magnesium (mg/L)
29

Figure 12. Ecoregional averages of cokriged 10th percentiles of sodium versus data

1.0 10.0 100.0

sodium (mg/L)

10

100

cokriged sodium (mg/L)
30

Figure 13. Ecoregional averages of cokriged 10th percentiles of potassium versus data

24 6 8

1012

potassium (mg/L)

2

4

6

8

10

cokriged potassium (mg/L)
31

Figure 14. Ecoregional averages of cokriged 10th percentiles of sulfate versus data

1.0 10.0 100.0

sulfate (mg/L)

10

100

cokriged sulfate (mg/L)
32

Figure 15. Ecoregional averages of cokriged 10th percentiles of chloride versus data

Table 7. Correlation coefficients and linear regression (LR) statistics between 

ecoregional average 10th percentiles of data and geostatistical predictions

Parameter Correlation 

coefficient, r LR coefficient P (2 Tail)

LR 

constant

P 

(2 Tail)

Conductivity 0.908 0.98 <0.001 -20.992 0.495

Alkalinity 0.915 1.209 <0.001 -12.161 0.028

Calcium 0.922 1.061 <0.001 -1.994 0.365

Magnesium 0.885 1.097 <0.001 -1.169 0.22

Sodium 0.93 1.101 <0.001 -4.78 0.169

Potassium 0.906 1.073 <0.001 -0.184 0.297

Sulfate 0.865 1.264 <0.001 -13.599 0.041

Chloride 0.839 1.039 <0.001 -7.271 0.386

0.1 1.0 10.0 100.0 1000.0

chloride (mg/L)

1.0

10.0

100.0

cokriged chloride (mg/L)
33

2.2.3.4 Conclusions for Selection of Water Quality Parameters

In this section we used geostatistics to estimate an intermediate step in generating missing GI 

parameter values based on geography. We supplemented the geostatistical approach by adding 

conductivity as an additional explanatory variable to generate a more robust spatial estimate of the GI 

water quality inputs for the BLM because conductivity is one of the most widely monitored water 

quality indicators in the U.S. and correlates well with GIs. In section 3, these estimates are further 

refined by stream order. We present here the average predicted 10th percentile concentrations for the 

BLM GI water quality parameters, as presented in Table 4 by ecoregions. Because they are based on 

the 10th percentiles of the daily average data from each USGS monitoring station, they are expected to 

yield copper criteria that are reasonably protective of aquatic life when applied as missing data for 

parameters in the BLM model. These data could also be used to fill in missing water chemistry 

parameters in the application of other metal BLM models. The most appropriate parameter selection 

however would include consideration of stream order in GIs estimates. Section 3 presents further 

refinements of estimates of the GI parameters by stream order and EPA’s recommendations for 

default GI parameters for the BLM when data are lacking.

As with any estimate or prediction, it is appropriate to seek alternative estimates for the purpose of 

comparison or confirmation. If conductivity data are available for the site, either site-specific 

measurement data or data of opportunity from a database such as the NWIS, the regressions in EPA 

(2008; Appendix C) can be used to make independent estimates of the missing BLM water quality 

parameters. If the regression projections differ from the geostatistical average predictions, the lower 

(more conservative) estimate is recommended for application to ensure protection of aquatic life. As 

always, users of the BLM should be also encouraged to sample the water body of interest and to 

analyze for the constituent (parameter) concentrations as a basis for determining reliable BLM inputs. 

2.2.3.5 Guidance Regarding Selection of Water Quality Parameters: pH and DOC

Although the geostatistical and regression-based approaches can be used to reliably estimate GI 

parameters used as BLM inputs, the same approaches do not produce accurate site-specific estimates 

for the two most important BLM inputs: pH and DOC. The BLM is less sensitive to the GI parameters 

than to pH and DOC predicting site-specific criteria for copper. Since our analysis indicates that there is 

little or no trend in relationships between conductivity and pH, and direct kriging produced similarly 

ambiguous predictions, site-specific data for pH must be used for BLM application at a site. 

For DOC, analysis of NWIS data indicated a weak relationship with conductivity, so the regression 

approach is not appropriate for this parameter. In 2008, EPA recommended use of the ecoregional 

DOC concentration percentiles tabulated by EPA for the Development of National Bioaccumulation 

Factors Technical Support Document (USEPA, 2003) because they appeared to offer reasonable 

estimates of lower percentile DOC concentrations, and were based on substantially more DOC data 

than were available in the NWIS. In Section 4 of this report we further tested these ecoregional DOC

concentrations for use in the BLM where site-specific data are not available.
34

3 USING STREAM ORDER TO REFINE PREDICTION OF GI PARAMETERS

The following section discusses how stream order was used to address anthropogenic impacts. The

goal is to provide BLM users with tables of appropriately protective estimates of GI parameters, 

building on the ecoregional work described in Section 2. 

Estimations of values for the GI parameters (alkalinity, calcium, magnesium, sodium, potassium, 

sulfate, and chloride) tend to vary regionally. As demonstrated in Section 2, the spatial variation of 

these factors is generally known or at least predictable, and therefore spatial or geographic analysis of 

data can be used to estimate GI input parameter values. However, these values also vary due to 

anthropogenic impact. In the case of conductivity and GI parameters, a positive correlation between 

ion concentrations and measures of human activity, such as population density, urban and agricultural 

land use, road density, point and nonpoint pollutant sources, among other activities, is expected and 

may confound the pattern of geographic variability both within and between ecoregions. 

One way to account for surface water quality variability within ecoregions is to distinguish water 

bodies according to the Strahler stream order (SO). The SO is used to define stream size based on a 

hierarchy of tributaries (Strahler, 1952; 1957) and may range from 1st order (a stream with no 

tributaries) to 12th order (the Amazon, at its mouth). First through 3rd order streams are called 

headwater streams (source waters of a stream). Over 80% of Earth's waterways are headwater streams

(Strahler, 1957). A stream that is 7th order or larger constitutes a river. For example, the Ohio River is 

8th order and the Mississippi River is 10th order. According to the River Continuum Concept, changes in 

water quality are commonly observed between the upper, middle, and lower reaches of a stream 

(FISRWG, 1998; Ward, 1992; USEPA, 2015). 

In this section we consider variability in GIs by determining the SO of each surface water sampling 

location in the USGS NWIS2 database, and explore methods of incorporating SO variation in the

parameter estimates. Tables are provided in this section showing tabulations of parameter estimates 

based upon both ecoregion and SO to maximize the accuracy of estimated input parameters.

3.1 Determining SO of NWIS Surface Water Sampling Locations 

GIS was used to determine the SO of each NWIS surface water sampling location. Flowlines and 

catchments with SO were obtained from the NHD-Plus V2 geospatial hydrologic framework (McKay et 

al., 2012).

3 The point locations corresponding to the latitude-longitude coordinates of the NWIS 

sampling stations were snapped to the NHD-Plus flowlines using ArcGIS. A spatial join was then 

performed between these shapefiles and the NHD-Plus flowlines to link stream order to the sampling 

locations. Some of the NHD-Plus flowlines did not have SO data associated with the record. When a 

sampling location occurred on a flowline that didn’t have a SO, the SO from the catchment was used. 

When the catchment also did not have a SO, the SO of the nearest stream was applied. SO was added 

as an attribute to the information for each station in the database.

 

2 http://waterdata.usgs.gov/nwis

3 http://www.horizon-systems.com/NHDPlus/NHDPlusV2_home.php
35

3.2 Estimating BLM Parameters for Ecoregions and SO

Estimated (10th percentile) BLM water quality parameters were presented in Section 2 for 84 Level III 

ecoregions of the continental U.S. In the work presented here, the parameter estimates were 

recalculated for individual SOs or ranges (groups) of SOs within each ecoregion. 

3.3 Results

The distribution of NWIS sampling locations by SO is presented in Figure 16. The largest proportion of 

sampled locations (78%) was found to be in SO 1 through 4. 

Figure 16. Distribution of NWIS surface water sampling locations by SO

3.3.1 Dependence of Ecoregional Parameter Estimates on SO

Box plots were constructed to examine how the GIs estimates varied with SO. Box plots of conductivity 

(Figure 17), alkalinity (Figure 18), calcium (Figure 19), magnesium (Figure 20), sodium (Figure 21), 

potassium (Figure 22), sulfate (Figure 23) and chloride (Figure 24) all show a general increase in the 

magnitude of the estimate with SO. This trend was most apparent and consistent when comparing 

medium stream orders (SO 4-6) to higher stream orders (SO ≥7). In addition, the upper quartile 

parameter estimates were generally higher in SOs 4 through 6 than in lower order streams (SO ≤3). 

Based upon these trends, we grouped the estimates for each parameter by SO: 1 through 3 (headwater 

0%

5%

10%

15%

20%

25%

1 2 3 4 5 6 7 8 9

Proportion of sites

Strahler stream order
36

streams), 4 through 6 (mid-reaches) and 7 through 9 (rivers). There were no data for rivers with SO>9. 

Grouping simplified the presentation of results and improved the robustness of the parameter 

estimates, without losing significance of the SO trends. Parameter estimates for these three SO groups 

are included in the box plots in Figures 18 through 24, labeled as “13,” “46,” and “79.” The classes 

depicted as 13, 46, and 79 reflect groupings according to SO (i.e., 1 through 3, 4 through 6, and 7 

through 9).

Figure 17. Box plot of estimated ecoregional conductivities as a function of SO

Note: Classifications depicted as 13, 46, and 79 reflect groupings according to stream order (i.e., 1 

through 3, 4 through 6, and 7 through 9) as described in the text. For box plots, the bottom and top of 

each “box” displays the 25th and 75th percentile concentrations defined as the interquartile range (IQR) 

(i.e., the box contains 50% of the data values), respectively. The median is displayed as the horizontal 

line within the box. The “whiskers” show the relative distribution of data points outside of the IQR and 

represent 1.5 times the IQR. Data not included between the whiskers are plotted as outliers with a 

star/asterisk.

1 13 2 3 4 46 5 6 7 79 8 9

Strahler stream order

10

100

1000

10000

Conductivity (uS/cm)
37

Figure 18. Box plot of estimated ecoregional alkalinity concentrations as a function of SO

(Refer to note in Figure 17.)

Figure 19. Box plot of estimated ecoregional calcium concentrations as a function of SO

(Refer to note in Figure 17.)

1 13 2 3 4 46 5 6 7 79 8 9

Strahler stream order

1

10

100

Alkalinity (mg/L as CaCO3)

1 13 2 3 4 46 5 6 7 79 8 9

Strahler stream order

0.1

1.0

10.0

100.0

Calcium concentration (mg/L)
38

Figure 20. Box plot of estimated ecoregional magnesium concentrations as a function of SO

(Refer to note in Figure 17.)

Figure 21. Box plot of estimated ecoregional sodium concentrations as a function of SO

(Refer to note in Figure 17.)

1 13 2 3 4 46 5 6 7 79 8 9

Strahler stream order

0.10

1.00

10.00

100.00

Magnesium concentration (mg/L)

1 13 2 3 4 46 5 6 7 79 8 9

Strahler stream order

1.0

10.0

100.0

1000.0

Sodium concentration (mg/L)
39

Figure 22. Box plot of estimated ecoregional potassium concentrations as a function of SO

(Refer to note in Figure 17.)

Figure 23. Box plot of estimated ecoregional sulfate concentrations as a function of SO

(Refer to note in Figure 17.)

1 13 2 3 4 46 5 6 7 79 8 9

Strahler stream order

0.1

1.0

10.0

Potassium concentration (mg/L)

1 13 2 3 4 46 5 6 7 79 8 9

Strahler stream order

0.10

1.00

10.00

100.00

1000.00

Sulfate concentration (mg/L)
40

Figure 24. Box plot of estimated ecoregional chloride concentrations as a function of SO

(Refer to note in Figure 17.)

The range of values across SOs overlap greatly due to the inclusion of data across ecoregions. Tenth 

percentile estimates of conductivity increase with SO group in 58% of ecoregions when comparing low 

to medium SO groups, and 84% of ecoregions when comparing medium to high SO groups. The same 

trend was evident for the GIs. For example, 10th percentiles of calcium increased with SO group in 68% 

of ecoregions for low versus medium SO and 83% of ecoregions for medium versus high SO. In general, 

parameter estimates (10th percentiles of conductivity and ion concentrations) increased with SO, and 

the increase was most apparent and consistent for higher SOs (SO ≥7).

3.3.2 SO-Based Parameter Estimates

Tenth percentile parameter estimates for conductivity, GIs and hardness are grouped by SO and Level 

III ecoregions in Tables 8 through10. Tenth percentile parameter estimates for SOs 1 through 3 are 

presented in Table 8, for SOs 4 through 6 are presented in Table 9, and SOs 7 through 9 are presented 

in Table 10. The tables include the sample size for instances in which parameter estimates are highly 

uncertain due to limited data, i.e., cases where sample size is <10. Water quality data were limited in 

four ecoregions (11, 16, 49, and 78) for SO group 1 through 3, in Ecoregion 76 for SO group 4 through 

6, and in 28 ecoregions for SO group 7 through 9. With the exception of the specific ecoregions and SO

classes where data are limited, the parameter estimates in Tables 8 through 10 are recommended as 

improved default values for use in the BLM when data are not available for a location in a specific Level 

III ecoregion and SO group. 

1 13 2 3 4 46 5 6 7 79 8 9

Strahler stream order

0.10

1.00

10.00

100.00

1000.00

10000.00

Chloride concentration (mg/L)
41

Table 8. Recommended 10th percentile conductivity, GIs, and hardness estimates for SO Group 1

through 3 (number of stations shown in parentheses if n<10)

Ecoregion Conductivity Calcium Magnesium Sodium Potassium Alkalinity Chloride Sulfate Hardness

1 58 6.0 0.8 1.3 0.1 44 0.6 1.1 18.28

2 74 8.8 2.8 3.9 0.5 2.8 3.3 33.48

3 68 9.9 3.8 5.6 1.5 2.3 1.5 40.33

4 16 1.0 0.2 1.8 0.2 0.5 0.2 3.32

5 28 0.6 0.1 0.3 0.1 38 0.1 0.1 1.91

6 279 3.6 8.2 8.4 0.9 73 8.9 7.2 42.62

7 164 19 6.0 14 1.8 120 8.6 6.6 72.1

8 157 29 4.3 10 1.5 70 (7) 2.6 0.4 90.13

9 55 4.4 (8) 0.9 (8) 2.3 (9) 0.4 (9) 35 (2) 0.2 0.2 14.69

10 137 24.0 9.4 10.2 1.4 127 4.6 11 98.54

11 88 8.6 (2) 3.2 (2) 169 (2) 34.62

12 133 13 2.0 6.1 0.8 35 1.4 3.7 40.7

13 109 9.4 1.6 2.7 0.6 45 0.5 3.7 30.06

14 967 15 2.8 6.0 3.0 90 (7) 2.7 6.3 48.98

15 24 3.1 0.8 0.9 0.4 9.0 0.2 1.3 11.03

16 21 

17 93 6.9 1.6 1.5 0.5 31 0.3 3.0 23.81

18 92 22 6.3 4.7 0.9 3.3 7.3 80.83

19 76 59 11 5.1 0.6 96 2.5 44 192.6

20 189 59 12 19 1.4 157 6.7 129 196.7

21 37 3.5 0.7 0.8 0.3 18 0.2 1.9 11.62

22 115 13 1.1 2.3 0.8 55 1.2 7.2 37.01

23 62 6.3 1.8 3.7 0.7 20 0.8 4.3 23.13

24 453 43 7.9 35 3.4 32 20 74 139.89

25 194 43 11 31 3.7 228 7.3 35 152.6

26 199 18 3.0 63 3.4 53 3.6 11 57.3

27 293 21 5.0 9.9 1.5 122 5.1 13 73

28 346 50 8.2 4.4 0.8 125 1.5 22 158.62

29 217 30 4.0 17 2.9 74 8.2 9.9 91.4

30 189 25 1.8 1.6 0.9 99 2.6 4.9 69.88

31 639 48 5.5 47 2.9 71 51 142.55

32 183 26 1.7 5.9 1.9 52 5.1 15 71.97

33 132 24 2.1 5.8 2.3 29 8.1 6.0 68.61

34 141 13 2.3 9.8 2.6 44 13 4.7 41.93

35 25 0.9 0.5 1.9 0.2 5.0 3.0 1.7 4.3

36 19 0.9 0.7 0.9 0.3 4.0 1.3 2.0 5.12

37 107 23 3.5 23 3.3 36 2.5 3.5 71.85

38 51 0.9 (7) 0.6 (7) 0.63 (7) 0.6 (7) 35 1.1 1.8 4.71

39 172 26 1.9 1.3 0.7 62 2.0 4.2 72.79
42

Ecoregion Conductivity Calcium Magnesium Sodium Potassium Alkalinity Chloride Sulfate Hardness

40 223 20 4.6 8.4 2.8 46 5.2 23 68.86

41 93 13 3.8 0.4 0.1 60 (9) 0.1 1.6 48.08

42 256 23 7.3 7.4 1.6 91 1.3 14 87.43

43 327 17 16 26 3.7 144 2.7 119 108.1

44 156 21 3.2 6.5 4.7 80 (2) 0.7 5.5 65.62

45 44 2.7 0.8 2.5 1.2 12 2.4 1.9 10.03

46 400 32 13 15 7.8 94 5.4 60 133.3

47 380 41 11 4.8 1.3 83 12 15 147.6

48 295 31 15 4.9 2.5 4.3 13 139

49 402 (4) 227 (1) 

50 69 5.1 1.0 1.2 0.3 32 0.4 1.2 16.85

51 137 28 11 2.0 0.9 53 (4) 3.3 4.5 115.1

52 432 42 12 2.9 0.7 75 4.8 12 154.2

53 502 27 8.0 11 2.0 42 25 22 100.3

54 574 51 22 8.4 1.2 202 28 44 217.7

55 420 40 11 7.8 1.5 130 19 16 145.1

56 219 28 7.4 3.6 0.9 79 6.3 16 100.34

57 446 35 10 6.8 2.3 84 19 33 128.5

58 25 1.2 0.4 0.3 0.2 1.5 0.4 4.2 4.64

59 69 3.6 1.1 6.2 0.9 3.0 10 5.8 13.51

60 61 4.7 1.2 1.5 0.4 17 1.5 6.6 16.67

61 131 13.0 2.5 8.0 1.1 33 7.8 8.3 42.75

62 32 1.8 0.7 0.8 0.3 2.0 0.8 4.4 7.37

63 108 1.1 0.8 2.8 0.8 5.0 5.5 3.2 6.03

64 134 12.0 4.6 7.0 1.3 19 10 11 48.86

65 25 0.7 0.5 1.5 0.3 3.0 2.6 0.7 3.8

66 12 0.5 0.3 0.7 0.3 3.0 0.7 1.1 2.48

67 81 4.7 2.0 2.0 0.7 3.0 1.8 7.1 19.95

68 32 1.9 1.2 1.3 0.7 3.0 1.4 3.6 9.67

69 36 2.8 0.8 0.4 0.4 4.0 1.0 8.1 10.28

70 125 5.6 4.0 2.7 1.4 12 2.4 16 30.4

71 179 10 1.8 1.1 0.7 54 2.2 2.8 32.38

72 180 17 5.3 5.2 1.7 69 3.5 21 64.23

73 102 6.9 2.7 3.4 2.0 31 2.0 2.9 28.32

74 52 3.2 1.4 2.5 1.5 9.3 2.6 3.9 13.74

75 75 6.6 1.5 4.5 0.5 9.0 9.0 1.5 22.65

76 430 41 1.8 7.8 0.3 116 30 0.1 109.88

77 14 1.6 0.4 0.4 0.2 7.0 0.2 0.7 5.64

78 19 2.1 

79 340 30 6.2 25 2.8 92 (2) 13 23 100.42

80 78 6.3 1.1 4.3 2.2 24 0.2 2.5 20.26

81 203 19 2.4 10 2.8 52 2.6 6.1 57.34
43

Ecoregion Conductivity Calcium Magnesium Sodium Potassium Alkalinity Chloride Sulfate Hardness

82 37 1.5 0.5 4.3 0.2 6.6 1.8 5.8

83 198 16 3.9 5.0 1.0 51 21 29 55.99

84 50 0.8 0.6 2.8 0.6 1.0 5.0 4.4 4.46

Table 9. Recommended 10th percentile conductivity, GIs, and hardness estimates for SO group 4 

through 6 (number of stations shown in parentheses if n<10)

Ecoregion Conductivity Calcium Magnesium Sodium Potassium Alkalinity Chloride Sulfate Hardness

1 52 3.6 1.0 2.0 0.2 15 1.6 2.2 13.1

2 49 5.3 1.2 1.3 0.1 16 0.8 1.8 18.17

3 62 7.1 2.5 4.3 0.8 29 4.6 2.8 28

4 35 3.5 1.0 2.8 0.4 16 0.8 0.8 12.85

5 18 0.9 0.1 0.6 0.2 5.0 0.4 0.4 2.66

6 316 9.1 4.8 5.4 1.0 32 2.3 4.1 42.43

7 67 6.5 2.5 2.9 0.9 33 1.7 3.2 26.5

8 93 9.0 1.5 8.4 1.0 17 3.2 6.0 28.65

9 52 5.5 0.8 2.4 0.5 22 0.9 2.2 17.03

10 83 8.6 3.2 4.0 0.9 33 1.4 3.1 34.62

11 52 3.7 0.8 1.6 0.7 16 0.3 0.7 12.53

12 95 13 2.5 4.9 1.2 40 2.2 3.8 42.75

13 124 12 3.4 9.6 1.8 68 3.9 8.1 43.94

14 688 58 13 86 7.9 225 55 86 198.3

15 34 3.5 1.1 0.9 0.4 16 0.2 1.2 13.26

16 22 2.4 0.4 1.3 0.4 10 0.2 0.6 7.64

17 123 10 2.5 1.4 0.6 44 0.5 2.2 35.25

18 145 15 4.0 7.1 0.9 57 1.4 16 53.9

19 135 34 9.1 6.7 1.3 7.3 9.5 122.31

20 260 38 9.6 16 1.5 107 4.0 55 134.36

21 74 6.5 1.3 1.9 0.6 18 0.4 3.2 21.58

22 215 25 4.3 9.5 1.3 62 2.4 18 80.13

23 289 31 9.5 5.6 1.1 101 3.5 2.4 116.45

24 240 24 5.1 18 1.5 80 7.0 21 80.91

25 220 14 3.4 8.7 1.6 84 4.1 29 48.94

26 367 39 9.1 29 2.8 79 11 56 134.81

27 351 39 7.1 11 5.1 79 5.6 16 126.61

28 298 68 14 9.6 2.1 150 7.4 39 227.4

29 351 39 6.8 20 2.7 80 20 19 125.38

30 377 44 12 6.5 0.8 140 10 13 159.2

31 447 54 9.4 10 1.8 142 12 29 173.54

32 311 35 2.8 12 2.8 94 12 22 98.98

33 334 33 5.0 16 2.1 45 23 28 103

34 125 10 3.5 13 2.7 40 12.2 3.1 39.35
44

Ecoregion Conductivity Calcium Magnesium Sodium Potassium Alkalinity Chloride Sulfate Hardness

35 67 4.2 1.1 6.5 1.5 10 3.5 5.0 15.01

36 24 1.0 0.8 1.1 0.5 4.0 1.5 2.0 5.78

37 55 3.8 2.3 5.2 1.3 9.6 2.0 2.0 18.93

38 41 8.4 1.0 1.2 0.8 13 1.5 3.2 25.1

39 160 19 1.8 1.6 0.9 73 2.3 3.6 54.88

40 258 33 5.7 6.8 2.7 64 6.7 20 105.87

41 133 19 4.5 0.7 0.2 0.1 1.9 65.95

42 285 22 9.2 12 2.3 141 2.3 34 92.72

43 342 28 8.5 13 2.7 145 2.2 45 104.85

44 232 27 3.8 9.4 7.0 184 (1) 2.5 2.7 83.08

45 44 3.0 1.2 3.0 1.3 13 2.9 2.9 12.42

46 480 32 17 30 8.6 153 9.1 89 149.7

47 390 43 10 7.0 1.7 109 8.5 19 148.5

48 422 40 18 8.5 4.1 170 7.0 32 173.8

49 75 7.9 2.4 2.3 0.7 25 2.3 4.5 29.59

50 78 7.9 2.4 1.2 0.4 37 0.9 2.7 29.59

51 125 19 6.5 2.3 0.9 102 3.0 3.6 74.15

52 221 15 6.3 4.2 1.5 50 6.4 10 63.33

53 389 36 19 9.1 2.2 138 18 20 167.9

54 520 49 22 7.4 1.0 148 22 37 212.7

55 413 43 12 5.6 1.9 162 19 22 156.7

56 389 44 14 10 1.5 133 18 21 167.4

57 489 56 15 10 2.6 108 22 31 201.5

58 38 4.9 0.9 2.9 0.5 5.0 4.3 6.1 15.94

59 81 5.1 1.4 7.8 1.1 10 11 7.3 18.49

60 101 12 2.5 5.3 1.0 20 3.9 8.4 40.25

61 178 20 4.7 8.4 1.8 47 61 11 69.27

62 50 3.9 0.9 4.0 0.6 5.0 2.6 6.1 13.44

63 65 3.6 0.9 3.9 1.2 8.0 6.6 3.2 12.69

64 175 13 4.7 9.9 1.2 48 15 13 51.77

65 43 2.8 0.9 2.2 0.8 6.0 3.4 1.7 10.69

66 14 1.0 0.3 0.8 0.5 4.0 0.4 1.1 3.73

67 89 7.9 2.0 2.9 1.0 14 3.4 8.8 27.95

68 42 4.0 0.9 1.0 0.8 16 1.4 4.4 13.69

69 115 6.8 1.5 1.7 0.6 9.0 1.8 8.8 23.15

70 108 11 3.1 4.2 1.2 11 4.5 22 40.21

71 145 18 2.6 1.4 1.0 53 2.8 3.7 55.66

72 251 25 7.7 8.2 2.1 61 10 30 94.07

73 99 6.4 2.4 3.9 2.2 34 3.0 5.0 25.84

74 46 2.3 1.0 2.2 1.1 11 2.0 1.0 9.85

75 57 2.2 1.0 3.8 0.5 1.0 6.1 1.7 9.6

76
45

Ecoregion Conductivity Calcium Magnesium Sodium Potassium Alkalinity Chloride Sulfate Hardness

77 44 4.7 1.5 1.1 0.2 34 (3) 0.1 0.9 17.9

78 92 7.9 3.2 4.0 0.6 36 2.1 2.4 32.87

79 371 33 7.1 25 2.0 89 6.5 18 111.61

80 204 15 5.7 4.1 0.8 54 2.0 9.3 60.87

81 146 30 5.7 11 2.0 54 4.5 25 98.37

82 29 3.5 0.7 2.1 0.4 9.2 2.3 5.4 11.62

83 97 11 1.9 3.2 0.7 54 22 25 35.29

84 41 0.8 0.5 2.4 0.7 1.0 4.4 4.5 4.05

Table 10. Recommended 10th percentile conductivity, GIs, and hardness estimates for SO group 7

through 9 (number of stations shown in parentheses if n<10)

Ecoregion Conductivity Calcium Magnesium Sodium Potassium Alkalinity Chloride Sulfate Hardness

1 111 12 3.4 4.3 0.8 56 2.3 6.3 43.94

2

3 58 5.0 1.6 3.4 0.6 20 2.7 2.3 19.06

4 118 13 3.6 3.7 0.9 52 1.7 6.9 47.26

5

6 101 9.0 4.5 4.9 0.9 1.7 3.1 40.95

7 122 10 5.0 6.2 1.0 56 3.5 4.8 45.5

8

9

10 71 5.7 1.5 2.0 0.7 16 0.8 4.2 20.4

11 72 8.5 1.5 3.3 0.7 32 0.8 5.0 27.4

12 310 37 10 13 2.5 122 11 30 133.5

13 430 38 10 32 5.6 175 15 27 136

14 810 64 23 69 3.2 121 55 181 254.3

15 51 5.2 1.5 1.4 0.5 20 0.4 3.1 19.15

16

17 189 20 5.6 3.7 1.1 69 1.3 13 72.96

18 342 35 11 14 1.3 119 2.5 45 132.6

19 608 55 20 44 2.2 145 13.1 149 219.5

20 373 39 12 25 1.7 102 9.7 85 146.7

21

22 279 28 4.9 15 1.9 80 4.5 37 90.09

23

24 554 60 11 76 4.3 107 49 145 195.1

25 830 64 20 60 4.6 127 16 184 242

26 876 56 20 61 3.5 128 24 187 222

27 648 61 16 43 6.2 96 25 112 218.1

28 395 41 8.9 15 6.4 119 10 36 138.99

29 1194 71 19 132 4.7 89 210 130 255.4
46

Ecoregion Conductivity Calcium Magnesium Sodium Potassium Alkalinity Chloride Sulfate Hardness

30

31 817 59 16 76 4.1 102 88 141 213.1

32 438 45 6.2 28 3.9 107 37 38 137.92

33 428 46 5.3 31 4.7 128 42 28 136.73

34 477 47 6.9 36 4.3 103 49 35 145.79

35 85 6.9 1.6 5.8 1.4 46 5.0 8.0 23.81

36 179 2.4 0.7 (3) 1.4 (3) 1.7 (3) 20 21 8.87

37 355 28 7.0 29 2.9 73 30 28 98.7

38

39 215 28 7.7 2.8 1.1 96 3.4 6.0 101.57

40 310 34 5.2 6.4 3.0 96 7.3 24 106.32

41

42 338 49 18 26 3.4 144 8.7 87 196.3

43 394 36 12 24 2.4 122 6.2 74 139.2

44

45 53 4.1 1.7 6.0 1.5 13 5.0 7.3 17.22

46 642 52 25 49 12 176 22 149 232.5

47 570 48 12 15 3.7 159 11 44 169.2

48 425 44 19 14 5.3 188 9.9 61 187.9

49

50

51 353 44 16 7.2 2.1 217 10 13 175.6

52 115 12 4.4 2.9 1.1 40 4.4 5.0 48.04

53 544 53 33 7.9 1.8 19 22 267.8

54 388 41 18 9.7 2.1 131 16 25 176.3

55 502 48 18 20 3.0 182 (4) 32 33 193.8

56

57 405 43 12 9.5 2.8 104 20 30 156.7

58

59 65 3.9 0.7 8.5 0.8 6.0 13 6.0 12.62

60

61

62

63 80 3.6 1.4 5.1 2.0 8.5 6.5 7.4 14.74

64 148 14 3.5 4.6 1.3 28 8.0 20 49.35

65 69 4.7 1.2 3.7 1.2 15 4.1 5.7 16.67

66

67 96 15 3.4 4.7 1.2 28 5.7 12 51.44

68 138 17 3.5 4.1 1.1 57 (8) 5.7 12 56.85

69

70 225 21 5.4 9.8 1.4 29 10 44 74.64

71 183 23 4.3 3.2 1.4 56 3.8 13 75.13
47

Ecoregion Conductivity Calcium Magnesium Sodium Potassium Alkalinity Chloride Sulfate Hardness

72 310 34 10 8.3 2.3 88 12 23 126

73 146 14 3.7 3.4 1.7 54 3.5 6.0 50.17

74

75 70 4.8 1.2 3.2 1.0 15 4.6 3.9 16.92

76

77

78

79

80 71 8.9 (3) 2.4 (3) 7.7 (3) 2.1 (3) 2.1 (3) 5.1 32.09

81 898 64 23 80 3.8 123 69 160 254.3

82 38 4.0 0.8 1.9 0.4 8.1 2.4 4.5 13.28

83 174 18 3.2 6.1 0.8 41 10 12 58.12

84

At the level of individual ecoregions, the trends in parameter estimates as a function of SO group often 

reflect the assessment presented in the previous section. In the majority of ecoregions, most of the 

parameter estimates increase with SO group, as illustrated in Figure 25 for Ecoregion 46, the Northern 

Glaciated Plains. However, other trends were observed as well. In Ecoregion 83 (Eastern Great Lakes 

Lowland), conductivity and cation concentrations were approximately equal in the low and high SO 

groups and lower in the medium SO group, as shown in Figure 26. Figure 27 illustrates the trends in

Ecoregion 54, the Central Corn Belt Plains. In this ecoregion (and several others), most of the 

parameter estimates decreased with SO group. The explanation for different trends within ecoregions, 

which may reflect different causes, is beyond the scope of this effort.
48

Figure 25. BLM parameter estimates (10th percentile values) for each SO group in Ecoregion 46 

(Northern Glaciated Plains)

Key: Stream order: 1-3 are headwater streams, 4-6 are mid-reaches, and 7-9 are rivers.

1

10

100

1000

Cond. Ca Mg Na K Alk. Cl SO4

Tenth Percentile

SO group 1-3

SO group 4-6

SO group 7-9
49

Figure 26. BLM parameter estimates for each SO group in Ecoregion 83 (Eastern Great Lakes 

Lowland)

0.1

1

10

100

1000

Cond. Ca Mg Na K Alk. Cl SO4

Tenth Percentile

SO group 1-3

SO group 4-6

SO group 7-9
50

Figure 27. BLM parameter estimates for each SO group in Ecoregion 54 (Central Corn Belt Plains)

3.3.3 Comparison of Parameter Estimates to Results of Probability-Based Surface Water Sampling

There have been relatively few efforts to estimate GI concentrations in surface water at the national 

scale. Carleton (2006) developed a prototype geostatistical approach to estimate BLM parameters 

averaged over 8-digit HUC polygons. Carleton examined data from the NWIS and noted several 

limitations of this dataset in terms of uneven spatial sampling intensity. Carleton’s prototype did not 

incorporate SO in the analysis, nor did it generate BLM parameter estimates. 

Griffith (2014) compiled data from probability-based surface water quality sampling surveys conducted 

by EPA between 1985 and 2009, mostly from wadeable streams (SO group 1 through 4). These surveys 

included the National Acid Precipitation Assessment Program surveys, EMAP and regional EMAP 

surveys, WSA, and NRSA. The probability-based sample designs ensured that the results of these 

surveys represented the character of streams across the continental U.S. The water quality parameters 

included the same GIs as discussed above, and the results were presented on the same Level III 

ecoregion-specific basis.

We compared current results to those of Griffith (2014) because the lack of a probability-based sample 

design is a potential source of bias in the NWIS dataset. Parameter estimates based on the NWIS data 

for SO group 1 through 3 were compared to the corresponding estimates calculated by Griffith (2014). 

While Griffith did not tabulate 10th percentiles, he did tabulate first quartile (i.e., 25th percentile) 

1

10

100

1000

Cond. Ca Mg Na K Alk. Cl SO4

Tenth Percentile

SO group 1-3

SO group 4-6

SO group 7-9
51

statistics for each ecoregion in supplemental material published with his article. Accordingly, we 

calculated 25th percentiles of the ecoregional NWIS data in SO class 1 through 3 (in addition to the 10th

percentiles) to facilitate this comparison. The 25th percentiles from the two datasets are compared for 

conductivity in Figure 28 and calcium in Figure 29. The scatter plots reveal significant log-linear 

relationships between 25th percentiles for the two datasets; the coefficient of determination (R2) was 

0.668 for conductivity and 0.551 for calcium. For conductivity, the 25th percentiles differed by more 

than a factor of 2 in 17% of the Level III ecoregions; for calcium, 26% of the ecoregional results differed 

by more than a factor of 2. 

Figure 28. Scatter plot of ecoregional 25th percentile conductivity for NWIS Data (SO Class 1-3) versus 

ecoregional 25th percentile conductivity for Griffith data (mostly SO 1-4)

Solid diagonal line represents 1:1 agreement.

1

10

100

1000

1 10 100 1000

Ecoregional conductivity (Griffith data)

Ecoregional conductivity (NWIS data)
52

Figure 29. Scatter plot of ecoregional 25th percentile calcium concentration for NWIS data (SO class 1-

3) versus ecoregional 25th percentile calcium concentration for Griffith data (mostly SO 1-4)

Solid diagonal line represents 1:1 agreement.

These results suggest reasonable overall consistency between datasets, as well as significant disparity 

in specific ecoregions. For example, agreement was especially poor in Ecoregions 19 (Wasatch and 

Uinta Mountains), 37 (Arkansas Valley), 38 (Boston Mountains), 39 (Ozark Highlands), 75 (Southern 

Coastal Plain), and 78 (Klamath Mountains). NWIS data were examined at the station-specific level to 

understand why these ecoregional 25th percentiles of conductivity and calcium in the low SO group 

were so inconsistent with corresponding percentiles presented by Griffith. Table 11 presents salient 

characteristics of the conductivity data for Ecoregion 19, including the number of stations, samples per 

station, 25th percentile conductivity, the lowest station-specific 25th percentile conductivity in the NWIS 

data, and other remarks. In that ecoregion, conductivity data were reported for 62 stations in the NWIS

database; the number of observations per station ranged from 1 to 189, with a median of 22 

observations per station. In comparison, the EPA data analyzed by Griffith reported conductivity data 

for 32 stations, with a single observation per station. The 25th percentile conductivity based on NWIS 

data was 240 versus 22.9 microsiemens per centimeter (μS/cm) based on Griffith’s analysis of EPA 

data. When recalculated for individual stations in Ecoregion 19 low SO group, the 25th percentile 

conductivities varied widely, from 18.25 to 1590 μS/cm. Griffith reported a median conductivity of 213 

0.1

1

10

100

0.1 1 10 100

Ecoregional calcium concentration, mg/L (Griffith data)

Ecoregional calcium concentration, mg/L (NWIS data)
53

μS/cm (nine times larger than the 25th percentile), indicating considerable variability in that data as 

well.

Table 11. Characteristics of the conductivity data for Ecoregion 19 in the low SO group.

NWIS data Griffith data

Number of stations 62 32

Samples per station 1 – 189 1 

Median samples per station 22 1 

25th percentile conductivity (μS/cm) 240 22.9

Range of station-specific 25th

percentile conductivity (μS/cm) 18.25-1590

Other remarks

25th percentiles of conductivity reported by 

Griffith were marginally higher than the 

minimum station-specific 25th percentiles 

calculated from the NWIS data

Median conductivity = 213 

μS/cm (19x the 25th percentile 

value) indicates high variability

The same information is tabulated for Ecoregions 37, 38, 75, and 78 in Tables 12 through 15. Although 

the details regarding the data vary in each of these ecoregions, a number of commonalities emerge 

from these examinations:

 In four ecoregions, the number of NWIS stations in SO group 1 through 3 was small relative to 

other ecoregions (the median number of ecoregional stations in SO group 1 through 3 was 68).

 In three ecoregions, 10th and 25th percentiles of conductivity and/or calcium decreased with SO 

group, contrary to the general trend. 

 In three ecoregions, 25th percentiles of conductivity reported by Griffith were marginally higher 

than the minimum station-specific 25th percentiles calculated from the NWIS data for the 

corresponding ecoregion and low SO group. 

Table 12. Characteristics of the conductivity data for Ecoregion 37 in the low SO group.

NWIS data Griffith data

Number of stations 34 45

Samples per station 1 – 129 1 

Median samples per station 2 1 

25th percentile conductivity (μS/cm) 350 32

Range of station-specific 25th

percentile conductivity (μS/cm) 29-846.5

Other remarks

10th and 25th conductivity percentiles decrease with SO 

group; 

Small number of NWIS stations;

25th percentiles of conductivity reported by Griffith were 

marginally higher than the minimum station-specific 25th

percentiles calculated from the NWIS data
54

Table 13. Characteristics of the conductivity data for Ecoregion 38 in the low SO group

NWIS data Griffith data

Number of stations 31 38

Samples per station 1 – 8 1 

Median samples per station 3 1 

25th percentile conductivity (μS/cm) 137 22.9

Range of station-specific 25th

percentile conductivity (μS/cm) 22-384

Other remarks

10th and 25th conductivity percentiles decrease with SO 

group; 

Small number of NWIS stations; 25th percentiles of 

conductivity reported by Griffith were marginally higher than 

the minimum station-specific 25th percentiles calculated 

from the NWIS data

Table 14. Characteristics of the calcium data for Ecoregion 75 in the low SO group.

NWIS data Griffith data

Number of stations 360 42

Samples per station 1 – 177 1 

Median samples per station 17 1 

25th percentile calcium (mg/L) 13 1.41

Range of station-specific 25th

percentile calcium (mg/L) 0.02-91

Other remarks 10th and 25th calcium percentiles decrease with SO group 

Table 15. Characteristics of the conductivity data for Ecoregion 78 in the low SO group.

NWIS data Griffith data

Number of stations 15 45

Samples per station 1 – 18 1 

Median samples per station 8 1 

25th percentile conductivity (μS/cm) 26 98.4

Range of station-specific 25th

percentile conductivity (μS/cm) 19-326.5

Other remarks Small number of NWIS stations; 6 of 15 stations were Ashland 

Creek (OR) or tributaries

It is possible that the disparities noted above arise in part from non-representative sampling in the 

NWIS data. For example, representativeness of NWIS data is questionable in Ecoregion 78 because 40% 

of the stations were sampled in a single water body. There was also a difference in the way data for 

repeated sampling at individual stations were processed, due to differences between the NWIS data 

and data compiled by Griffith. In the NWIS data, water quality was sampled repeatedly at a significant 
55

number of stations, and we included daily averages of all of these measurements in the calculation of 

10th percentile estimates. In the probabilistic EPA surveys analyzed by Griffith, individual stations were 

usually sampled once. In the case of repeated sampling at a station, Griffith used data from only the 

first sample reported for the station in the statistics he calculated. This difference implies that our 

estimates of BLM parameters incorporate temporal as well as spatial variability in water quality, while 

Griffith’s results do not. Thus, it would be unrealistic to expect complete agreement between these 

results. It should also be reiterated that sampling bias in SO is probably not a factor in these disparities 

because the estimates from the NWIS data were based on measurements from stream orders 1

through 3, which is generally consistent with the data compiled by Griffith (2014).

It is particularly of concern when percentiles based on NWIS data are higher than those calculated 

based on Griffith data because this suggests the parameter estimates may result in non-conservative 

BLM predictions of copper, or others metals, criteria. To evaluate this concern, we ran the BLM 

(version 2.1.2) using the 25th percentile GI estimates of Griffith and those from the current analysis for 

NWIS SO group 1 through 3 for each ecoregion in which parameters were available. If the 25th

percentile of a GI was not available, the value was projected from the 25th percentile of conductivity 

using regressions based on NWIS data. If the 25th percentile of conductivity was not available (this 

occurred in 24 ecoregions), no BLM prediction was made. The inputs for pH and DOC were ecoregional 

values. There were 60 ecoregions where BLM predictions of copper criteria using the 25th percentile GI 

estimates from NWIS and Griffith could be compared. The criteria estimated in these ecoregions using 

GI input parameters from the two sources agree very well, as shown in Figure 30. The R2 was 0.9897, 

and relative percent differences (RPDs) ranged from -21 to 39% with an average RPD of 3% and a 

median of 0.1%. 
56

Figure 30. BLM predictions of copper criteria made with GI water quality parameters based on 

ecoregional 25th percentile from NWIS data (SO class 1-3) versus ecoregional 25th percentile calcium 

Concentration for Griffith data (mostly SO 1-4).

R2 = 0.99. Solid diagonal line represents 1:1 agreement

While it is possible that the GI estimates presented here as recommended input values for use in the 

BLM for copper could be improved, it is not clear that such improvement would result in substantially 

better predictions of protective copper criteria based on the BLM. This is because BLM predictions for 

copper are much more sensitive to pH and DOC. 

3.4 Summary

In this section we have incorporated SO variation in the GI water quality parameter estimates to refine 

the default parameters estimates for use in the BLM when data are not available.

EPA found that values of the GI parameter estimates generally increased with SO. This trend was most 

apparent and consistent for higher order streams (SO≥7). Tenth percentile estimates of conductivity 

increase with stream order group in 58% of ecoregions (comparing low to medium SO groups) and 84% 

of ecoregions (comparing medium to high SO groups). The same trend was evident for the GIs that are 

input parameters to the BLM. 

0.1

1

10

100

1000

0.1 1 10 100 1000

Copper IWQC (μg/L) calculated using Griffith 25th percentile estimates

Copper IWQC (μg/L) calculated using NWIS 25th percentile estimates
57

We compared the parameter estimates for SO group 1 through 3 to those calculated by Griffith (2014). 

This comparison revealed significant log-linear relationships between 25th percentiles for the two 

datasets; the coefficient of determination (R2) was 0.668 for conductivity and 0.551 for calcium. For 

conductivity, the 25th percentiles differed by more than a factor of 2 in 17% of the Level III ecoregions; 

for calcium, 26% of ecoregional results differed by more than a factor of 2. There is also considerable 

variability in the relationship between ecoregional statistics based on NWIS versus Griffith’s data. 

Possible causes of these disparities may be due to sampling bias in the NWIS database, limited 

numbers of samples in some ecoregions, and differences in the degree and treatment of repeated 

sampling at individual locations.

NWIS percentiles higher than Griffith (2014) suggest that the recommended parameter estimates may 

result in non-conservative BLM predictions of copper criteria. The BLM was run to predict copper 

criteria for 60 ecoregions using 25th percentile GI estimates as parameter inputs from NWIS and 

Griffith’s data. The criteria predicted using the two sets of GI parameter inputs agreed favorably. The 

R2 was 0.990, and RPDs ranged from -21 to 39% with an average RPD of 3% and a median of 0.1%. 

These results demonstrated that the recommended default GI parameter estimates are reasonably 

conservative.

EPA incorporated SO variation in the parameter estimates to refine recommended input values for use 

in the BLM. EPA found the 10th percentile ecoregion, SO group specific estimates to be reasonably 

protective inputs and recommends their use where site-specific parameters are not readily available. 
58

4 DOC ESTIMATION USING THE NATIONAL ORGANIC CARBON DATABASE

The following section summarizes our investigation into whether ecoregion and water body-typespecific DOC concentration percentiles tabulated by EPA for the Development of National 

Bioaccumulation Factors Technical Support Document (hereafter referred to as the National Organic 

Carbon Database (NOCD)) (USEPA, 2003)) offer reasonable estimates of lower-percentile DOC 

concentrations. A summary of the NOCD’s data sources, analysis, and uncertainty associated with 

ecoregional statistics derived from the NOCD is provided below. This section also discusses how we 

recalculated ecoregional DOC percentiles for rivers and streams, and then tested for bias in the NOCD. 

Finally, we compared results based on the NOCD and data from the Wadeable Stream Assessment 

(WSA) (USEPA, 2006b)) and the National River and Stream Assessment (NRSA) (USEPA, 2013)). 

4.1 Description of the NOCD 

The NOCD is a compilation of pre-2003 organic carbon data derived from two sources: EPA’s Storage 

and Retrieval Data Warehouse (STORET), recently renamed the STORET Legacy Data Center (LDC), and 

USGS’s National Water Data Storage and Retrieval System (WATSTORE), the predecessor of NWIS. A 

complete background on the NOCD is available in USEPA 2003.

EPA’s LDC database contains water quality monitoring data collected by academia, volunteer groups, 

and tribes, as well as federal, state, and local agencies. Geographically, the LDC data represent all 50 

states and all U.S. territories and jurisdictions, along with portions of Canada and Mexico. The database 

queried for this investigation is often referred to as the “historical” or “old” STORET database because 

it contains water quality data dating back to the early part of the 20th century through the end of 1998. 

Data from 1999 to the present are stored in the “modernized” STORET Data Warehouse.4 The LDC 

contains raw biological, chemical, and physical data for both surface water and groundwater. Each 

sampling result is accompanied by: information on sample collection location (latitude, longitude, 

state, county, HUC, and a brief site description), date the sample was gathered, the medium sampled, 

and the name of the organization that sponsored the monitoring. 

We retrieved data from LDC and WATSTORE in January 2000. Approximately 800,000 records 

containing data on particulate organic carbon (POC), dissolved organic carbon (DOC), or total organic 

carbon (TOC) were obtained for the period beginning in 1970 through the latest year that data were 

available (1999 for WATSTORE and 1998 for LDC). This initial retrieval was limited to samples taken 

from ambient surface waters (i.e., samples from wells, springs, effluents, and other non-ambient 

sources were excluded). Additionally, this retrieval included multiple types of organic carbon 

measurements to ensure that the data would be sufficiently comprehensive. 

WATSTORE was established in 1972 to provide an effective and efficient means for processing and 

maintaining water data collected through USGS activities and to facilitate release of that data to the 

public. The WATSTORE database resides on the central computer facilities of the USGS and contains 

results of approximately two million analyses of both surface and groundwater that provide data on 

 

4 Refer to http://www.epa.gov/storet/dbtop.html for more information on the STORET Data Warehouse and the LDC.
59

chemical, physical, biological, and radiological characteristics. EPA queried WATSTORE, the Water 

Quality File, to retrieve DOC data. 

After retrieval, the data from LDC and WATSTORE were combined into a single database. The data 

were then processed and screened to ensure that only the most appropriate data would be retained. 

This screening process is outlined below:

 Values that were coded in such a way as to suggest uncertainty in the measurement were 

deleted from the database. 

 The database was restricted to the following water body types: estuaries, lakes, reservoirs, and 

streams (including rivers). 

 “Pseudo-ecoregions” were added for the five Great Lakes.

 The time period for the data was restricted to 1980 through 1999. 

 Some values for DOC were reported to be below analytical detection levels. In this situation, 

the value was assumed to be half of the reported detection level. Values with “high” detection 

levels (i.e., >1.0 mg/L for DOC) were deleted from the database because of the greater 

uncertainty involved in estimating definitive values of DOC in these situations.

 A small fraction of the DOC and POC concentrations obtained from the LDC database exceeded 

concentrations considered to represent upper limits of DOC concentrations reported in U.S. 

water bodies (i.e., 0.2% exceeded 60 mg/L for DOC). These extreme values were based on a 

review of organic carbon data by Thurman (1985), who reported extreme values of DOC 

concentrations as high as 50 mg/L in dystrophic lakes and 60 mg/L in tributaries draining 

wetland systems. Therefore, values for DOC above 60 mg/L were removed from the database. 

The NOCD that resulted from processing and screening data retrieved from the LDC and WATSTORE 

databases has some limitations, which are described below:

 The WATSTORE and LDC databases do not reflect a random sampling of U.S. surface waters.

They contain datasets with a diversity of sampling design and thus data may be biased towards 

locations and water bodies with known water quality impairments. 

 These data also reflect spatial bias due to unequal sampling efforts in different areas. For 

example, about half of the DOC and POC values in the databases were from samples collected 

in Maryland, New York, Ohio, Florida, and Delaware. Therefore some states are 

disproportionally represented, even when one considers the relative surface water area likely 

to be contained within each state.

 WATSTORE and LDC generally contain more data from sampling sites in larger river and stream 

systems, and areas subjected to proportionately greater human influence compared with 

random statistical sampling.

4.2 Recalculation of Ecoregional DOC Percentiles for Rivers and Streams

Lower percentile (1st, 5th, 10th, and 25th percentiles) DOC concentrations were calculated from all data 

for rivers and streams in each Level III ecoregion (Table 16). Nonparametric (i.e., rank) percentiles were 

calculated following the recommendations of Dierickx (2008) and Hyndman and Fan (1996). We also 

calculated confidence limits for the percentiles using the method presented in Berthouex and Brown 
60

(1994). Upper and lower 95% confidence limits (UCLs and LCLs) were calculated if 20 or more DOC 

concentrations were available for an ecoregion (Berthouex and Brown, 1994).

Table 16. Lower percentile values of DOC in U.S. streams and rivers by ecoregion, including 95% 

confidence limits for percentile concentrations if n>20. 

Level III 

Ecoregion Ecoregion Name n (count) 1% 1% (LCL)

1% 

(UCL) 5% 5% (LCL)

5% 

(UCL) 10% 10% (LCL)

10% 

(UCL) 25% 25% (LCL)

25% 

(UCL)

1 Coast Range 91 ≤0.2 ≤0.2 0.6 0.9 ≤0.2 1.1 1.12 0.78 1.4 1.8 1.4 2 

2 Puget Lowland 835 0.84 0.47 1 1.9 1.7 2 2.5 2.3 2.7 3.9 3.5 4.1

3 Willamette Valley 66 ≤0.5 ≤0.5 0.73 0.8 ≤0.5 1.08 1.07 0.68 1.2 1.48 1.2 2 

4 Cascades 101 0 ≤0 0.2 0.3 ≤0 0.44 0.5 0.3 0.5 0.7 0.5 0.9

5 Sierra Nevada 32 ≤1.9 ≤1.9 1.9 1.9 ≤1.9 2.3 2.09 ≤1.9 2.3 2.55 2.13 3.11

6 Southern and Central California 

Chaparral and Oak Woodlands 480 1.1 ≤0 1.5 1.8 1.7 1.9 2.1 1.9 2.2 3 2.67 3.2

7 Central California Valley 180 1.21 ≤0.8 1.8 2.11 1.66 2.48 2.71 2.3 3.5 5.3 4.4 6.26

8 Southern California Mountains 6 ≤4.4 ≤4.4 ≤4.4 5.45 

9 Eastern Cascades Slopes and 

Foothills 13 ≤1.3 ≤1.3 1.42 1.75 

10 Columbia Plateau 73 ≤0.7 ≤0.7 1.3 1.67 ≤0.7 2.03 2.04 1.29 2.34 2.9 2.3 3.2

11 Blue Mountains 26 ≤1 ≤1 1.05 1.07 ≤1 1.45 1.34 ≤1 1.81 1.9 1.28 2.61

12 Snake River Plain 50 ≤2 ≤2 2 2 ≤2 2.2 2.2 ≤2 2.43 3.08 2.27 3.68

13 Central Basin and Range 1553 0.8 0.69 0.9 1.2 1.2 1.3 1.5 1.4 1.6 2 2 2.1

14 Mojave Basin and Range 35 ≤2.5 ≤2.5 2.55 2.58 ≤2.5 3 2.84 ≤2.5 3.32 3.6 2.99 3.8

15 Northern Rockies 778 0.7 0.6 0.72 0.9 0.9 1 1 1 1.1 1.3 1.3 1.4

16 Idaho Batholith 29 ≤1.2 ≤1.2 1.2 1.2 ≤1.2 1.4 1.4 ≤1.2 1.8 1.9 1.39 2.31

17 Middle Rockies 87 ≤0 ≤0 0 0 ≤0 0.14 0.18 0 0.46 1.1 0.42 1.4

18 Wyoming Basin 150 2.05 ≤1.9 3.03 3.56 2.26 4.18 4.31 3.59 4.6 5.48 5.1 5.8

19 Wasatch and Uinta Mountains 46 ≤1.5 ≤1.5 1.5 1.57 ≤1.5 1.82 1.8 ≤1.5 2.51 2.88 1.9 3.6

20 Colorado Plateaus 798 1.5 0.36 1.6 2.4 2 2.6 3 2.7 3.25 4.3 4.1 4.6

21 Southern Rockies 1129 0.2 0.1 0.3 0.5 0.4 0.5 0.6 0.6 0.6 0.8 0.8 0.9

22 Arizona/New Mexico Plateau 281 1.65 ≤1.2 2.01 2.2 2.09 2.4 2.62 2.3 2.91 3.7 3.3 3.9

23 Arizona/New Mexico Mountains 37 ≤1.3 ≤1.3 1.41 1.48 ≤1.3 2.35 2.16 ≤1.3 2.64 2.8 2.33 3.57

24 Chihuahuan Deserts 116 0.5 ≤0.5 0.64 1 0.5 2.15 2.34 1 3 3.68 3 4.44

25 High Plains 439 0.3 ≤0.1 0.4 0.8 0.5 3 4.4 3.2 4.9 7 6.42 7.78

26 Southwestern Tablelands 167 1.94 ≤1.8 2.04 2.5 2 2.98 3.28 2.52 3.7 4.4 4 4.9

27 Central Great Plains 228 0.59 ≤0.4 2.01 3 1.8 3.2 3.8 3 4 5 4.8 5.71

28 Flint Hills 10 ≤4.9 ≤4.9 4.9 5.15 

29 Central Oklahoma/Texas Plains 289 1.9 ≤1 2.09 3 2.5 3.38 3.8 3 4 4.8 4.21 5 

30 Edwards Plateau 200 0.5 ≤0.5 0.5 0.5 0.5 0.82 1 0.5 1 1 1 1.6

31 Southern Texas Plains 58 ≤0.5 ≤0.5 0.5 0.5 ≤0.5 1 1 0.5 1.34 2 1 2 

32 Texas Blackland Prairies 829 0.5 0.5 0.5 1 1 1 2 2 2 3 3 3.99
61

Level III 

Ecoregion Ecoregion Name n (count) 1% 1% (LCL)

1% 

(UCL) 5% 5% (LCL)

5% 

(UCL) 10% 10% (LCL)

10% 

(UCL) 25% 25% (LCL)

25% 

(UCL)

33 East Central Texas Plains 268 1 ≤1 1.95 2.6 2 3 3 3 3 3.83 3.1 4

34 Western Gulf Coastal Plain 399 2.8 ≤1.7 3 3.7 3 4 4 4 4 5 5 5.9

35 South Central Plains 523 1.45 ≤0.4 2.07 3.92 3.2 4 4.6 4.1 4.98 5.7 5.4 6

36 Ouachita Mountains 198 0 ≤0 0.47 0.8 0.4 1.1 1.1 0.86 1.6 2.38 2.08 2.8

37 Arkansas Valley 184 0.49 ≤0.4 0.65 0.8 0.55 1.4 1.9 0.85 2.39 3.73 3 4.4

38 Boston Mountains 21 ≤0.4 ≤0.4 0.4 0.4 ≤0.4 0.5 0.42 ≤0.4 0.5 0.5 0.4 0.74

39 Ozark Highlands 233 1.67 ≤1.5 2 2 2 2.12 2.3 2 2.5 3 2.7 3.15

40 Central Irregular Plains 434 2.71 ≤1.4 3 3.5 3.1 3.6 4 3.6 4 4.9 4.6 5

41 Canadian Rockies 36 ≤0.3 ≤0.3 0.35 0.39 ≤0.3 0.6 0.57 ≤0.3 0.9 0.93 0.6 1.03

42 Northwestern Glaciated Plains 36 ≤3 ≤3 3.05 3.09 ≤3 6.63 5.05 ≤3 11.23 13.25 6.12 16.34

43 Northwestern Great Plains 679 2.22 0.72 3.19 4.4 3.8 5.2 6.2 5.6 6.73 9.9 9.19 10

44 Nebraska Sand Hills 4 ≤1.4 ≤1.4 ≤1.4 1.4

45 Piedmont 309 0.4 ≤0 0.5 0.7 0.6 0.9 1 0.8 1.1 1.7 1.4 2.1

46 Northern Glaciated Plains 142 4.03 ≤3.3 8.01 9.13 5.11 9.82 9.9 9.16 11 12 11 12.86

47 Western Corn Belt Plains 193 0.44 ≤0.2 2.43 2.77 2.28 2.96 3.14 2.8 3.5 3.9 3.6 4.3

48 Lake Agassiz Plain 261 3.1 ≤0.8 4.52 6.41 4.72 7.1 7.6 6.87 7.97 9 8.7 9.22

49 Northern Minnesota Wetlands 44 ≤7.8 ≤7.8 8.25 9.05 ≤7.8 11 11 ≤7.8 12 13 11 14.88

50 Northern Lakes and Forests 403 2 ≤0.1 2.2 2.72 2.36 3.08 3.7 3.06 4.5 5.8 5.5 6.2

51 North Central Hardwood Forests 153 0.54 ≤0 2.19 2.67 1.42 2.9 3.1 2.7 3.77 4.95 3.9 5.6

52 Driftless Area 49 ≤1.7 ≤1.7 2.31 2.4 ≤1.7 3.25 3.1 ≤1.7 4.31 4.5 3.4 5.8

53 Southeastern Wisconsin Till 

Plains 439 2 ≤0.25 2.1 3.4 2.7 4.3 5.3 4.3 5.6 6.8 6.5 7

54 Central Corn Belt Plains 202 1 ≤0.7 1.68 2.12 1.61 2.5 2.73 2.2 3 3.9 3.57 4.8

55 Eastern Corn Belt Plains 1398 0 0 0 0 0 0.2 3.8 3 4 5.2 5 5.3

56 S. Michigan/N. Indiana Drift 

Plains 287 1.4 ≤1.4 1.92 2.7 2.05 3.43 3.8 3.17 4.2 5.4 4.9 5.7

57 Huron/Erie Lake Plains 3825 0 0 0 3.9 3.7 4.07 4.7 4.52 4.8 5.8 5.7 5.9

58 Northeastern Highlands 14044 0.25 0.25 0.25 0.25 0.25 0.5 0.64 0.62 0.65 0.95 0.94 0.97

59 Northeastern Coastal Zone 102 0.05 ≤0 1.6 2.02 ≤0 2.6 2.63 1.74 2.92 3.28 3 3.63

60 Northern Appalachian Plateau 

and Uplands 354 0.6 ≤0.5 0.8 1 0.87 1.1 1.3 1.1 1.4 2 1.9 2.3

61 Erie Drift Plains 919 0 0 0 4.8 4.6 4.9 5.1 5 5.1 5.5 5.4 5.6

62 North Central Appalachians 106 0.41 ≤0.4 0.5 0.5 ≤0.4 0.7 0.7 0.5 0.78 0.98 0.8 1.2

63 Middle Atlantic Coastal Plain 16730 1.1 1.01 1.2 1.8 1.8 1.8 2.2 2.2 2.2 2.7 2.7 2.7

64 Northern Piedmont 1525 0.43 0.3 0.5 1 0.99 1 1.3 1.2 1.4 2.2 2.1 2.4

65 Southeastern Plains 3813 1 0.51 1.1 2 1.9 2.03 2.4 2.38 2.5 3.3 3.2 3.3

66 Blue Ridge 699 0 0 0 0.4 0.3 0.4 0.5 0.4 0.5 0.6 0.6 0.7

67 Ridge and Valley 733 0.1 0.1 0.1 0.4 0.3 0.5 0.6 0.5 0.7 1.05 1 1.1

68 Southwestern Appalachians 47 ≤0.5 ≤0.5 0.5 0.58 ≤0.5 0.9 0.9 ≤0.5 1 1 0.9 1.38

69 Central Appalachians 864 0.3 0.15 0.4 0.6 0.5 0.6 0.7 0.7 0.8 1.1 1.1 1.2

70 Western Allegheny Plateau 1795 0 0 0 0.78 0.2 1 1.6 1.4 1.7 2.7 2.5 2.9

71 Interior Plateau 559 0.1 ≤0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.3 0.2 0.3
62

Level III 

Ecoregion Ecoregion Name n (count) 1% 1% (LCL)

1% 

(UCL) 5% 5% (LCL)

5% 

(UCL) 10% 10% (LCL)

10% 

(UCL) 25% 25% (LCL)

25% 

(UCL)

72 Interior River Valleys and Hills 328 1.32 ≤0.15 1.8 2.1 1.9 2.4 2.69 2.4 3.05 4.2 3.6 4.6

73 Mississippi Alluvial Plain 503 1.7 ≤1 2.14 2.82 2.4 3.1 3.4 3.2 3.6 4.3 4.1 4.5

74 Mississippi Valley Loess Plains 21 ≤1.4 ≤1.4 1.41 1.41 ≤1.4 2.61 1.72 ≤1.4 2.7 2.7 1.46 4.72

75 Southern Coastal Plain 4223 0.9 0.9 1.09 5.3 4.7 6 8 7.6 8.3 12.1 11.9 12.3

76 Southern Florida Coastal Plain - - - - -

77 North Cascades 50 ≤0.2 ≤0.2 0.2 0.26 ≤0.2 0.4 0.4 ≤0.2 0.4 0.48 0.4 0.5

78 Klamath Mountains 8 ≤1.7 ≤1.7 ≤1.7 2.3

79 Madrean Archipelago 9 ≤2.6 ≤2.6 2.6 4.05

80 Northern Basin and Range 16 ≤1.6 ≤1.6 1.81 2.5

81 Sonoran Basin and Range 133 1.33 ≤1.3 1.7 1.8 1.38 2.1 2.2 1.8 2.6 3.85 2.94 4.4

82 Laurentian Plains and Hills 21 ≤4.6 ≤4.6 4.7 4.69 ≤4.6 5.68 5.52 ≤4.6 7.98 8.45 5.15 9.3

83 Eastern Great Lakes and Hudson 

Lowlands 1430 0 0 0 0 0 0.2 1.9 1 2 5.1 5 5.5

84 Atlantic Coastal Pine Barrens 243 1 ≤0.9 1.1 1.22 1.1 1.5 1.6 1.32 2 2.6 2.4 3

Lake Erie 9 ≤1.1 ≤1.1 1.18 1.4

Lake Michigan 5 ≤2.6 ≤2.6 ≤2.6 2.6

Lake Ontario 14 ≤0.4 ≤0.4 0.4 2.2

Lake Superior 7 ≤1.2 ≤1.2 ≤1.2 1.4

As was the case for the BLM GI input parameters, we consider low percentiles of the ecoregional DOC 

concentration distributions to be reasonably protective inputs to the BLM for sites where DOC 

measurements are not available. 

4.3 Testing for Bias in the NOCD 

EPA conducted an evaluation of bias in the NOCD (USEPA, 2003) using data from EPA’s Environmental 

Monitoring and Assessment Program’s (EMAP) 1997 to 1998, which sampled mid-Atlantic streams and 

rivers (USEPA, 2006b). This effort is described below in Section 4.3.1.

We also evaluated the bias in the NOCD using independent data from EPA’s Wadeable Streams 

Assessment (WSA), which included DOC measurements from a statistically based random sample of 

approximately 2,000 wadeable, perennial 1st through 5th order streams (USEPA, 2006c). In Section 

4.3.2, we compare the WSA data to the ecoregion-specific DOC concentration percentiles calculated 

from the NOCD. 

4.3.1 Previous Efforts Using EMAP Data

Ideally, the data used to generate the distribution of national organic carbon concentration values 

should originate from a random sampling of U.S. surface waters, and should be appropriately stratified 

and weighted by spatial and temporal factors that would be expected to influence organic carbon 

concentrations in aquatic ecosystems (e.g., water body type, hydrologic and watershed characteristics, 

ecoregion, season). However, these data are not available on a national scale. The strength of this 

analysis is that the data from USGS’s WATSTORE and EPA’s LDC databases include a large number of 
63

records (e.g., >110,000 DOC values), a representation of DOC values for all 50 states, and reasonably 

long period over which data were collected (1980 through 1999 for these analyses).

Data generated by EMAP are based on a stratified, random sampling strategy that was specifically 

designed to minimize the influence of sampling bias on the data and to enable statistically based 

extrapolations across geographic regions (Herlihy et al., 2000). At the time the NOCD was developed, 

the EMAP databases containing DOC measurements were limited to smaller geographic scales and 

specific water body types. 

Previously, to address the question of sampling bias and its impact on the representativeness of the 

NOCD values, EPA made quantitative comparisons that involved contrasting geographically distinct 

subsets of the WATSTORE/LDC databases with geographically similar subsets of data produced by 

EMAP. DOC data from EMAP’s 1997 to 1998 sampling of mid-Atlantic streams and rivers were 

compared with similar geographic subsets from the WATSTORE/LDC databases. The mid-Atlantic EMAP 

database was chosen because sufficient DOC data were available for rivers and streams to make 

meaningful comparisons at the state and ecoregion levels. Similar comparisons are made for four midAtlantic ecoregions (Piedmont, Ridge and Valley, Central Appalachians, Western Allegheny Plateau) 

which is well represented in the WATSTORE/LDC databases (USEPA, 2003). 

Based on both sets of comparisons, it is apparent that the agreement between the WATSTORE/LDC 

and EMAP data was best at the middle to lower tails of the distributions, and poorest at the higher end 

of the distributions. At the lower tails of the distributions (e.g., 10th, 25th percentiles) the 

WATSTORE/LDC DOC data are generally within 30% of the EMAP data (Ecoregion 70 being the only 

exception). The median DOC values of the WATSTORE/LDC data show a slightly higher bias compared 

with median values from the EMAP data, but are usually within a factor of 1.5 (Ecoregions 47 and 70 

are about a factor of 2 greater). This result is expected, given the greater focus of the WATSTORE/LDC 

sampling sites on larger river and stream systems, and on areas subjected to proportionately greater 

human influence compared with the EMAP sampling sites. Since EPA is interested in supporting the 

generation of BLM values that are protective of aquatic life, the lack of bias noted for the lower tails of 

the DOC concentration distributions is noteworthy.

4.3.2 Testing for Bias Using Data from the WSA

A more comprehensive evaluation of the effects of sampling bias on the NOCD can now be made using 

the results of national statistically-designed water quality sampling surveys. We assembled a database 

of organic carbon data from 1,313 randomly selected sites throughout the continental U.S. collected 

for the WSA. GIS procedures were used to associate each site with the Level III ecoregion 

corresponding to its location. 

The 1,392 sites sampled for the WSA were identified using a probability-based sample design, a 

technique in which every element in the population has a known probability of being selected for 

sampling (USEPA, 2006). This ensured that the results of the WSA reflect the full range of variation 

among wadeable streams across the U.S. The target population for the WSA was wadeable, perennial 

streams in the conterminous U.S. (lower 48 states). The WSA used the National Hydrography Dataset 

(NHD), a comprehensive set of digital spatial data on surface waters (USGS, 2012), to identify the 

location of wadeable perennial streams. Rules for site selection included weighting to provide balance 

in the number of stream sites from each of the 1st through 5th SO size classes (Strahler, 1952, 1957), 
64

and controlled spatial distribution to ensure that sample sites were distributed across the U.S.). The 

basic sampling design drew 50 sampling sites randomly distributed in each of the EPA Regions and WSA 

ecoregions. The unbiased site selection of the survey design ensures that assessment results represent 

the condition of the streams throughout the nation. 

4.3.2.1 Selection of Statistical Test to Assess Potential Bias in DOC Data

The most appropriate statistical test for determining bias in the NOCD is the comparison of WSA and 

organic carbon database DOC data within each ecoregion as independent groups of data to determine 

if one group tends to contain larger values (Helsel and Hirsch, 2002; USGS, 2002). The WSA and organic 

carbon database DOC data are independent because there is no natural structure in the order of 

observations across groups. A nonparametric statistical test is most appropriate since no assumptions 

regarding normality of the data are required. As noted by Helsel and Hirsch (2002), nonparametric 

tests are, in general, never worse than their parametric counterparts in their ability to detect 

departures from the null hypothesis, and may be better. These considerations led us to select the ranksum test, a nonparametric procedure for determining whether data are significantly different between 

two independent groups. This test is also known as the Wilcoxon Rank-Sum Test or, alternatively, the 

Mann-Whitney U-Test.

In its most general form, the rank-sum test is a test to determine whether one group tends to produce 

larger observations than another group. It has as its null hypothesis: 

H0: Prob [x > y] = 0.5

where x are data from one group and y are from another group (the probability of an x value being 

higher than any given y value is one-half). The test is typically used to determine whether two groups 

come from the same population (same median and other percentiles), or alternatively whether they 

differ only in location (central value or median). If both groups of data are from the same population, 

about half of the time an observation from either group could be expected to be higher than that from 

the other, so the above null hypothesis applies. If the groups belong to different populations the null 

hypothesis does not apply.

In practice, the rank-sum test takes several forms, depending upon the size of the smaller sample (n

observations) and the larger sample (m observations). Walpole and Myers (1978; Section 13.2) present 

the details of four alternative forms of the rank-sum test, depending on the sizes of n and m. The exact 

form of the rank-sum test is the only form appropriate for comparing groups of sample sizes of 10 or 

smaller per group. When both groups have samples sizes greater than 10 (n, m > 10), the large-sample 

approximation may be used. 

4.3.2.2 Rank-Sum Test Comparing WSA DOC Data to NOCD

Table 17 presents the results of the rank-sum test comparing Level III ecoregional DOC data from the 

WSA (USEPA, 2006b) and the NOCD. The left-hand columns present statistics (sample size, median, and 

Mann-Whitney Ux, and Uy) for the ecoregion-specific DOC data from the two datasets. The next six 

columns to the right present the test statistics for the appropriate form of the rank-sum test. The righthand column provides a summary interpretation of the test for each ecoregion indicating whether the 

null hypothesis (H0: DOC concentrations from both datasets are not different) should be rejected at the 

5% level of significance, in favor of the alternative hypothesis (H1: DOC concentrations are higher in the 
65

national organic carbon database). In other words, rejection of the null hypothesis implies that DOC 

concentrations from the National Organic Carbon Database are biased high in that ecoregion relative 

to the WSA data.
66

Table 17. Results of rank-sum test comparing Level III ecoregional DOC data from WSA and NOCD

Level III 

Ecoregion

Ecoregion 

Name 

WSA dataset NOC database M-W test (n1>10 

and n2>10)

One large sample 

(n2>20)

Exact test 

(n2<20)

Exact test 

(n2<9)

Interpretation of 

test

1-sided @ 0.05

n median 

DOC

Ux n median 

DOC

Uy Z P Z P critical U (0.05 

level of signif.)

P (H0: same mean 

of distributions)

1 Coast Range 38 1.41 2535.5 91 2.2 922.5 4.17 1.54E-05 reject H0

2 Puget Lowland 3 0.96 2289 835 6.6 216 -2.48 6.63E-03 reject H0

3 Willamette 

Valley 2 2.47 84 66 2.9 48 -0.65 2.57E-01 do not reject H0

4 Cascades 23 0.75 1673 100 1.4 627 3.39 3.46E-04 reject H0

5 Sierra Nevada 14 0.91 448 32 3.6 0 5.35 5.96E-08 reject H0

6 

Southern and 

Central 

California 

Chaparral and 

Oak Woodlands

32 2.5 12372 479 4.6 2957 5.82 0 reject H0

7 Central 

California Valley 2 4.2 302 180 13 58 -1.65 4.98E-02 reject H0 (P~5%)

8 

Southern 

California 

Mountains

41 1.66 245 6 8.9 1 -3.89 5.03E-05 reject H0

9 

Eastern 

Cascades Slopes 

and Foothills

19 0.97 209 13 2.3 38 3.28 5.18E-04 reject H0

10 Columbia 

Plateau 8 2.59 477 73 3.6 107 -2.93 1.70E-03 reject H0

11 Blue Mountains 77 1.59 1625 26 3.1 376.5 4.74 1.07E-06 reject H0

12 Snake River 

Plain no test
67

Level III 

Ecoregion

Ecoregion 

Name 

WSA dataset NOC database M-W test (n1>10 

and n2>10)

One large sample 

(n2>20)

Exact test 

(n2<20)

Exact test 

(n2<9)

Interpretation of 

test

1-sided @ 0.05

n median 

DOC

Ux n median 

DOC

Uy Z P Z P critical U (0.05 

level of signif.)

P (H0: same mean 

of distributions)

13 Central Basin 

and Range 42 1.93 47300 1553 3 17926 4.986 2.98E-07 reject H0

14 Mojave Basin 

and Range 2 2.65 67 35 5.6 3 -2.15 1.58E-02 reject H0 

(P~1.6%)

15 Northern 

Rockies 19 1.54 9149 778 1.8 5634 1.77 3.81E-02 reject H0 

(P~3.8%)

16 Idaho Batholith 19 1.21 495 29 2.4 56 4.63 1.85E-06 reject H0

17 Middle Rockies 70 1.43 3142 81 1.9 2529 1.14 0.126 do not reject H0

18 Wyoming Basin 29 2.29 4006 150 7.3 344 7.17 0 reject H0

19

Wasatch and 

Uinta 

Mountains

25 2.11 978 46 4.8 172 4.85 5.96E-07 reject H0

20 Colorado 

Plateaus 24 2.22 15697 798 6.3 3455 5.34 5.96E-08 reject H0

21 Southern 

Rockies 43 2.05 18637 1129 1.3 29911 -2.59 4.83E-03 reject H0

22 Arizona/New 

Mexico Plateau 7 1.83 1723 281 5.6 244 -3.40 3.40E-04 reject H0

23

Arizona/New 

Mexico 

Mountains

31 1.94 984 37 5.3 163 5.02 2.38E-07 reject H0

24 Chihuahuan 

Deserts 1 1.48 110 116 6 6 -1.54 6.18E-02 do not reject H0

25 High Plains 6 3.5 2450 439 11 184.5 -3.62 1.48E-04 reject H0

26 Southwestern 

Tablelands 17 4.21 2246 167 6.3 593 3.95 3.90E-05 reject H0

27 Central Great 

Plains 12 4.71 2189 228 7 547 3.50 2.31E-04 reject H0

28 Flint Hills 2 4.91 19 10 8.7 1 1 reject H0
68

Level III 

Ecoregion

Ecoregion 

Name 

WSA dataset NOC database M-W test (n1>10 

and n2>10)

One large sample 

(n2>20)

Exact test 

(n2<20)

Exact test 

(n2<9)

Interpretation of 

test

1-sided @ 0.05

n median 

DOC

Ux n median 

DOC

Uy Z P Z P critical U (0.05 

level of signif.)

P (H0: same mean 

of distributions)

29

Central 

Oklahoma/ 

Texas Plains

6 5.58 1098 289 6.7 636 -1.12 1.32E-01 do not reject H0

30 Edwards 

Plateau no test

31 Southern Texas 

Plains no test

32 Texas Blackland 

Prairies 2 7.37 880 829 6 778 -0.15 4.40E-01 do not reject H0

33 East Central 

Texas Plains 3 15.03 108.5 268 5 695.5 2.17 9.85E-01 do not reject H0

34 Western Gulf 

Coastal Plain 9 7.47 1860 399 7 1732 -0.183 0.427 do not reject H0

35 South Central 

Plains 24 7.7 6744 523 7.7 5808 0.62 2.68E-01 do not reject H0

36 Ouachita 

Mountains 6 2.2 963.5 196 3.7 212.5 -2.66 3.88E-03 reject H0

37 Arkansas Valley 3 4.61 327 184 7 225 -0.55 2.92E-01 do not reject H0

38 Boston 

Mountains 3 2.18 19 21 0.8 44 1.09 8.62E-01 do not reject H0

39 Ozark Highlands 10 1.8 2248 233 4.1 82 -4.98 3.26E-07 reject H0

40 Central Irregular 

Plains 8 6.7 1772 434 6.3 1700 -0.10 4.60E-01 do not reject H0

41 Canadian 

Rockies 5 0.8 127.5 36 1.1 52.5 -1.49 6.76E-02 do not reject H0

42 Northwestern 

Glaciated Plains 13 9.27 362 36 18 106 2.90 1.87E-03 reject H0

43 Northwestern 

Great Plains 81 7.45 43205 679 14 11794 8.41 0 reject H0
69

Level III 

Ecoregion

Ecoregion 

Name 

WSA dataset NOC database M-W test (n1>10 

and n2>10)

One large sample 

(n2>20)

Exact test 

(n2<20)

Exact test 

(n2<9)

Interpretation of 

test

1-sided @ 0.05

n median 

DOC

Ux n median 

DOC

Uy Z P Z P critical U (0.05 

level of signif.)

P (H0: same mean 

of distributions)

44 Nebraska Sand 

Hills 1 6.46 0 4 3.2 4 0.2 do not reject H0

45 Piedmont 28 2.11 5379 308 3.4 3245 2.17 1.51E-02 reject H0 

(P~1.5%)

46 Northern 

Glaciated Plains 17 14.62 1443 142 15 971 1.315 9.42E-02 do not reject H0

47 Western Corn 

Belt Plains 42 2.84 6200 193 5.1 1907 5.38 5.96E-08 reject H0

48 Lake Agassiz 

Plain 13 10.38 1962 261 10 1431 0.95 1.71E-01 reject H0 

(P~1.7%)

49

Northern 

Minnesota 

Wetlands

1 11.71 37 44 17 7 -1.15 1.24E-01 do not reject H0

50 Northern Lakes 

and Forests 20 12.28 3099 403 8.1 4961 -1.74 4.05E-02 reject H0 (P~4%)

51

North Central 

Hardwood 

Forests

7 8.08 573.5 152 9.2 490.5 -0.35 3.64E-01 do not reject H0

52 Driftless Area 11 2.4 509 49 7.6 30 4.58 2.38E-06 reject H0

53

Southeastern 

Wisconsin Till 

Plains

5 3 2067 439 8 128.5 -3.40 3.41E-04 reject H0

54 Central Corn 

Belt Plains 9 2.69 1498 202 6.1 320 -3.29 5.07E-04 reject H0

55 Eastern Corn 

Belt Plains 6 2.83 7199 1325 6.8 751 -3.43 3.00E-04 reject H0
70

Level III 

Ecoregion

Ecoregion 

Name 

WSA dataset NOC database M-W test (n1>10 

and n2>10)

One large sample 

(n2>20)

Exact test 

(n2<20)

Exact test 

(n2<9)

Interpretation of 

test

1-sided @ 0.05

n median 

DOC

Ux n median 

DOC

Uy Z P Z P critical U (0.05 

level of signif.)

P (H0: same mean 

of distributions)

56

Southern 

Michigan/North

ern Indiana Drift 

Plains

9 4.62 1967 287 7 616 -2.67 3.77E-03 reject H0

57 Huron/Erie Lake 

Plains 3 5.05 8246 3762 7.1 3040 -1.38 8.33E-02 do not reject H0

58 Northeastern 

Highlands 23 3.54 79049 14044 1.4854 2E+05 -4.24 1.13E-05 reject H0

59 Northeastern 

Coastal Zone 10 4.01 561 101 4.2 449 -0.58 2.82E-01 do not reject H0

60

Northern 

Appalachian 

Plateau and 

Uplands

5 3.74 831 354 3.2 939 0.23 5.93E-01 do not reject H0

61 Erie Drift Plain 9 2.99 7834 901 6.2 275.5 -4.82 7.32E-07 reject H0

62 North Central 

Appalachians 4 3.34 102 106 1.7 322 1.76 9.60E-01 do not reject H0

63 Middle Atlantic 

Coastal Plain 2 18.54 16060 16726 3.4 17392 0.10 5.39E-01 do not reject H0

64 Northern 

Piedmont 15 2.18 18010 1524 4 4850 3.84 6.11E-05 reject H0

65 Southeastern 

Plains 18 2.55 49987 3801 4.3 18432 3.38 3.61E-04 reject H0

66 Blue Ridge 16 1.09 4915 686 0.9 6061 0.71 2.37E-01 do not reject H0

67 Ridge and 

Valley 27 1.56 10612 733 1.7 9180 0.64 2.61E-01 do not reject H0

68 Southwestern 

Appalachians 9 1.91 212.5 47 1.7 210.5 -0.02 4.91E-01 do not reject H0
71

Level III 

Ecoregion

Ecoregion 

Name 

WSA dataset NOC database M-W test (n1>10 

and n2>10)

One large sample 

(n2>20)

Exact test 

(n2<20)

Exact test 

(n2<9)

Interpretation of 

test

1-sided @ 0.05

n median 

DOC

Ux n median 

DOC

Uy Z P Z P critical U (0.05 

level of signif.)

P (H0: same mean 

of distributions)

69 Central 

Appalachians 10 1.84 3651 864 1.6 4990 0.84 8.01E-01 do not reject H0

70

Western 

Allegheny 

Plateau

19 2.17 25890 1735 4 7075 4.28 9.18E-06 reject H0

71 Interior Plateau 14 2.24 2153 559 0.4 5674 -2.88 2.00E-03 reject H0

72 Interior River 

Valleys and Hills 14 3.86 3143 328 6.2 1449 2.34 9.70E-03 reject H0 

(P~0.97%)

73 Mississippi 

Alluvial Plain 10 8.31 1646 503 5.5 3384 1.87 9.69E-01 do not reject H0

74

Mississippi 

Valley Loess 

Plains

1 1.26 21 21 5.4 0 -1.66 4.90E-02 reject H0 

(P~4.9%)

75 Southern 

Coastal Plain 6 6.7 20141 4222 15.5 5191 -2.50 6.18E-03 reject H0

76

Southern 

Florida Coastal 

Plain

 no test

77 North Cascades 54 0.82 1169 50 0.7 1531 1.18 1.19E-01 do not reject H0

78 Klamath 

Mountains 43 0.77 343 8 2.6 1 -4.43 4.74E-06 reject H0

79 Madrean 

Archipelago 3 1 27 9 7.9 0 3 reject H0

80 Northern Basin 

and Range 26 1.51 372.5 16 3.2 43.5 4.26 1.02E-05 reject H0

81 Sonoran Basin 

and Range 3 1.72 364 133 5.1 35 -2.44 7.40E-03 reject H0

82 Laurentian 

Plains and Hills 5 5.68 94 21 9.9 11 -2.70 3.47E-03 reject H0
72

Level III 

Ecoregion

Ecoregion 

Name 

WSA dataset NOC database M-W test (n1>10 

and n2>10)

One large sample 

(n2>20)

Exact test 

(n2<20)

Exact test 

(n2<9)

Interpretation of 

test

1-sided @ 0.05

n median 

DOC

Ux n median 

DOC

Uy Z P Z P critical U (0.05 

level of signif.)

P (H0: same mean 

of distributions)

83

Eastern Great 

Lakes and 

Hudson 

Lowlands

12 6.72 8228 1346 7 7925 0.11 4.55E-01 do not reject H0

84 Atlantic Coastal 

Pine Barrens 2 12.62 150 243 5.7 336 0.93 8.24E-01 do not reject H0
73

4.3.3 Results and Implications of Bias Testing

The results of the rank-sum test indicate that DOC concentrations from the NOCD are biased high (i.e., 

the null hypothesis was not rejected) in 52 of 81 (64%) of Level III ecoregions in which comparable data 

were available (no comparison was possible in four ecoregions). For those ecoregions where the null 

hypothesis was not rejected, BLM users can be confident that the lower percentile DOC concentrations 

listed in Table 16 are representative for that ecoregion. 

For ecoregions where the null hypothesis was rejected, the result suggests that the DOC data from the 

national organic carbon database are from biased samples. Recall discussion of both database in 

Sections 4.3, 4.3.1, and 4.3.2 that WSA is a random design sampling that ensures unbiased site 

selection. Whereas the NOCD is more influenced by locations with known water quality impairments 

and reflect unequal sampling efforts potentially creating a bias. It is likely that the percentile DOC 

concentrations tabulated for those ecoregions in Table 16 also reflect this bias towards high 

concentrations. This was confirmed by comparing the probability distributions of DOC concentrations 

in the ecoregions where n and m were large (n, m > 30). 

In large-sample ecoregions where the null hypothesis was rejected by the rank-sum test (Ecoregions 1, 

6, 11, 13, 23, 43, and 47), the probability distributions also show that the DOC concentration 

percentiles are substantially different, with the NOCD showing higher values. An example of such a 

comparison of DOC probability distribution is shown in Figure 31. On the other hand, in such largesample ecoregions where the null hypothesis was not rejected (Ecoregions 17, 21, and 77), the 

probability distributions show that the DOC concentration percentiles are comparable. An example of 

such a probability distribution is shown in Figure 32. In all cases where it was possible to compare the 

DOC probability distributions, the results of the rank-sum test were confirmed.
74

Figure 31. Comparison of probability distributions of DOC concentrations in Ecoregion 23

Figure 32. Comparison of probability distributions of DOC concentrations in Ecoregion 77

1

10

100

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

DOC (mg/L)

z score

Cumulative Frequency Distributions for DOC in ecoregion 23

WSA ecoregional DOC data

EPA national organic carbon database

0.1

1

10

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

DOC (mg/L)

z score

Cumulative Frequency Distributions for DOC in ecoregion 77

WSA ecoregional DOC data

EPA national organic carbon database
75

Because using a DOC concentration that is biased high as input to the BLM may lead to a nonconservative (high) site-specific copper criterion, it would be inappropriate to use the 10th percentile 

DOC concentrations in Table 16 for ecoregions in which the data from the NOCD come from biased 

samples. 

We have not addressed the issue of whether the streams sampled for the WSA are representative in 

terms of DOC concentrations for all lotic (flowing) waters. It is possible that larger rivers may have DOC 

concentrations that are different from streams. For this reason, we recommend that the estimated 

ecoregional DOC values be compared to data from EPA’s NRSA (NRSA, USEPA, 2013b; EPA 841-D-13-

001). If necessary, adjustment of the estimated DOC values can be made at that time.

4.4 Comparing NOCD to WSA/NRSA DOC Data 

The representativeness of the DOC data in the NOCD was evaluated by statistically comparing the data, 

at the ecoregional level, with the combined DOC data from two smaller random statistical surveys of 

rivers and streams. The two smaller surveys were: 

(1) the 2004-05 WSA (1,313 sites), and 

(2) the 2008-09 NRSA (2,113 sites). 

The NRSA was the first nationally consistent survey assessing the ecological condition of the full range 

of flowing waters in the conterminous U.S. The target population includes the Great Rivers (such as the 

Mississippi and the Missouri), small perennial streams, and urban and non-urban rivers. Run-of-theriver ponds and pools are included, along with tidally influenced streams and rivers up to the leading 

edge of dilute sea water.

NRSA sampling locations were selected by random selection. The locations of perennial streams were 

identified using the EPA-USGS National Hydrography Dataset Plus (NHD-Plus), a comprehensive set of 

digital spatial data on surface waters at the 1:100,000 scale. Information about stream order was also 

obtained from the NHD-Plus. The 1,924 sites sampled for the NRSA were identified using a probabilitybased sample design. Details about the NRSA probabilistic sampling design are described in Section 1.1 

of the NRSA: Field Operations Manual (USEPA, 2007; EPA-841-B-07-009). Site selection rules included 

weighting to provide balance in the number of river and stream sites from each of the size classes. Site 

selection was also controlled for spatial distribution to make sure sample sites were distributed across 

the U.S. Among these randomly selected sample sites were 359 of the original 2004 WSA sites. These 

were revisited as part of the NRSA to examine whether conditions have changed. When sites were 

selected for sampling, research teams conducted office evaluations and field reconnaissance to 

determine if the sites were accessible or if a river or stream labeled as perennial in NHD-Plus was, in 

fact, flowing during the sampling season. If a river or stream was not flowing or was determined to be 

inaccessible, it was dropped from the sampling effort and replaced with a perennial river or stream 

from a list of replacement sites within the random design.

The DOC data from these two smaller datasets were combined and described, hereafter, as WSA/NRSA 

data. GIS was used to determine which sampling sites were in each Level III ecoregion. The statistical 

test used was the non-parametric Wilcoxon 2-sample test, with a null hypothesis that DOC 

concentrations in the two different DOC sample datasets were equal. The alternative hypothesis was 

that DOC concentrations in the NCOD were significantly greater than those in the WSA/NRSA data, 
76

indicating positive bias possibly due to over-representation of impacted sites. The test was applied for 

each of 84 Level III ecoregions at alpha=0.05.

Table 18 below includes the number of data (n) in each ecoregion, and the 10th percentiles of DOC 

based upon data from the EPA DOC database (NOCD) and the combined WSA/NRSA data. For each 

ecoregion, the table also provides the result of the Wilcoxon 2-sample test, in terms of whether the 

null hypothesis (the two samples are equal) should be accepted or rejected. The null hypothesis was 

rejected in 59 of 83 ecoregions, indicating bias in DOC concentrations higher in the national organic 

carbon dataset for the majority of ecoregions. In these 59 ecoregions, low-end percentiles based on 

DOC concentrations in the WSA/NRSA data were selected as reasonably protective estimates of 

ecoregional DOC concentrations. 

Table 18. DOC concentrations (mg/L) in each Level III ecoregion based upon data from the NOCD and 

the combined WSA/NRSA data: number of data (n); 10th percentiles; and results of the Wilcoxon 2-

sample test

Ecoregion NOC database WSA/NRSA database H0 (equal means) 

n 10% n 10%

1 91 1.1 60 0.7 reject

2 835 2.5 8 0.36 reject

3 66 1.1 12 0.4 reject

4 100 0.5 37 0.3 reject

5 32 2.1 21 0.5 reject

6 479 2.1 42 0.8 reject

7 180 2.7 7 1.1 reject

8 6 4.4 43 0.7 reject

9 13 1.4 25 0.5 reject

10 73 2.0 22 1.0 reject

11 26 1.3 91 0.8 reject

12 50 2.2 6 1.2 reject

13 1553 1.5 82 0.7 reject

14 35 2.8 8 0.8 reject

15 778 1.0 39 0.8 reject

16 29 1.4 34 0.8 reject

17 81 0.2 94 0.7 accept

18 150 4.3 52 1.1 reject

19 46 1.8 41 0.9 reject

20 798 3.0 61 1.2 reject

21 1129 0.6 76 0.8 accept

22 281 2.6 27 0.7 reject

23 37 2.2 48 0.7 reject

24 116 2.3 10 1.4 reject

25 439 4.4 29 1.3 reject
77

Ecoregion NOC database WSA/NRSA database H0 (equal means) 

n 10% n 10%

26 167 3.3 47 1.9 reject

27 228 3.8 92 2.2 reject

28 10 4.9 8 1.2 reject

29 289 3.8 30 1.7 reject

30 200 1.0 4 1.0 accept

31 58 1.0 4 0.3 accept

32 829 2.0 9 3.1 accept

33 268 3.0 5 5.6 accept

34 399 4.0 18 2.8 accept

35 523 4.6 66 3.3 reject

36 196 1.1 18 0.7 reject

37 184 1.9 18 1.4 reject

38 21 0.4 7 0.5 accept

39 233 2.3 39 0.8 reject

40 434 4.0 32 3.3 reject

41 36 0.6 7 0.6 reject

42 36 5.1 43 2.5 reject

43 679 6.2 234 2.3 reject

44 4 1.4 4 1.0 accept

45 308 1.0 93 1.1 reject

46 142 9.9 28 6.1 reject

47 193 3.1 103 1.7 reject

48 261 7.6 26 5.4 reject

49 44 11.0 9 6.0 accept

50 403 3.7 77 2.7 accept

51 152 3.1 44 3.2 reject

52 49 3.1 49 1.1 reject

53 439 5.3 12 1.9 reject

54 202 2.7 21 1.8 reject

55 1325 3.6 30 2.1 reject

56 287 3.8 38 2.9 reject

57 3762 4.7 14 1.5 accept

58 14044 0.6 92 1.2 accept

59 101 2.6 81 2.7 accept

60 354 1.3 29 1.4 reject

61 901 5.1 26 1.8 reject

62 106 0.7 22 0.9 accept

63 16726 2.2 45 1.7 accept

64 1524 1.3 47 1.0 reject

65 3801 2.4 108 1.4 reject

66 686 0.5 40 0.6 accept
78

Ecoregion NOC database WSA/NRSA database H0 (equal means) 

n 10% n 10%

67 733 0.6 88 0.9 accept

68 47 0.9 17 0.8 accept

69 864 0.7 31 1.1 accept

70 1735 1.5 67 1.5 reject

71 559 0.1 54 1.1 accept

72 328 2.7 65 2.2 reject

73 503 3.4 107 2.8 reject

74 21 1.7 18 1.2 accept

75 4222 8.0 41 3.6 reject

76 1 na 0 na na

77 50 0.4 61 0.4 accept

78 8 1.7 56 0.6 reject

79 9 2.6 9 0.8 reject

80 16 1.8 49 1.0 reject

81 133 2.2 13 1.0 reject

82 21 5.5 18 2.8 reject

83 1346 1.0 32 2.6 reject

84 243 1.6 4 3.3 accept

In the 24 ecoregions where the null hypothesis was not rejected (i.e., no significant difference in DOC 

concentrations was found between datasets), the data were combined and the percentiles of the 

combined dataset were recalculated (Table 19). In these 24 ecoregions, low-end percentiles based on 

DOC concentrations in the combined data (NOCD and WSA/NRSA) were selected as reasonably 

protective estimates of ecoregional DOC concentrations. 

Recommended DOC estimated values for 83 of the 84 ecoregions are summarized in Table 20. In the 

remaining ecoregion (76; Southern Florida Coastal Plain), there were insufficient data in either dataset 

(NOC database or WSA/NRSA) to calculate DOC concentration percentiles.

Table 19. DOC concentrations (mg/L) in 24 ecoregions where no significant difference in DOC 

concentrations was found between national organic carbon database (NOCD) and the WSA/NRSA 

datasets: number of data (n); 10th percentiles from combined NOCD & WSA/NRSA data

Ecoregion n 

DOC (mg/L)

10%

17 175 0.6

21 1205 0.6

30 204 1.0

31 62 1.0

32 838 2.0
79

Ecoregion n 

DOC (mg/L)

10%

33 273 3.0

34 417 4.0

38 28 0.5

44 8 1.0

49 53 10.4

50 480 3.5

57 3776 4.6

58 14136 0.6

59 182 2.7

62 128 0.7

63 16771 2.2

66 726 0.5

67 821 0.6

68 64 0.9

69 895 0.7

71 613 0.1

74 39 1.5

77 111 0.4

84 247 1.6

Table 20. Recommended ecoregional DOC concentrations (mg/L) based upon combined data from the 

NOCD and the WSA/NRSA data in 83 Level III ecoregions: number of observations (n); 10th 

percentiles; and source of data for each ecoregion

Ecoregion n 

DOC (mg/L)

10%

Data Source

1 60 0.7 WSA/NRSA

2 8 0.3 WSA/NRSA

3 12 0.4 WSA/NRSA

4 37 0.3 WSA/NRSA

5 21 0.5 WSA/NRSA

6 42 0.8 WSA/NRSA

7 7 1.1 WSA/NRSA

8 43 0.7 WSA/NRSA

9 25 0.5 WSA/NRSA

10 22 1.0 WSA/NRSA

11 91 0.8 WSA/NRSA

12 6 1.2 WSA/NRSA

13 82 0.7 WSA/NRSA

14 8 0.8 WSA/NRSA

15 39 0.8 WSA/NRSA
80

Ecoregion n 

DOC (mg/L)

10%

Data Source

16 34 0.8 WSA/NRSA

17 175 0.6 NOCD & WSA/NRSA

18 52 1.1 WSA/NRSA

19 41 0.9 WSA/NRSA

20 61 1.2 WSA/NRSA

21 1205 0.6 NOCD & WSA/NRSA

22 27 0.7 WSA/NRSA

23 48 0.7 WSA/NRSA

24 10 1.4 WSA/NRSA

25 29 1.3 WSA/NRSA

26 47 1.9 WSA/NRSA

27 92 2.2 WSA/NRSA

28 8 1.2 WSA/NRSA

29 30 1.7 WSA/NRSA

30 204 1.0 NOCD & WSA/NRSA

31 62 1.0 NOCD & WSA/NRSA

32 838 2.0 NOCD & WSA/NRSA

33 273 3.0 NOCD & WSA/NRSA

34 417 4.0 NOCD & WSA/NRSA

35 66 3.3 WSA/NRSA

36 18 0.7 WSA/NRSA

37 18 1.4 WSA/NRSA

38 28 0.5 NOCD & WSA/NRSA

39 39 0.8 WSA/NRSA

40 32 3.3 WSA/NRSA

41 7 0.6 WSA/NRSA

42 43 2.5 WSA/NRSA

43 234 2.3 WSA/NRSA

44 8 1.0 NOCD & WSA/NRSA

45 93 1.1 WSA/NRSA

46 28 6.1 WSA/NRSA

47 103 1.7 WSA/NRSA

48 26 5.4 WSA/NRSA

49 53 10.4 NOCD & WSA/NRSA

50 480 3.5 NOCD & WSA/NRSA

51 44 3.2 WSA/NRSA

52 49 1.1 WSA/NRSA

53 12 1.9 WSA/NRSA

54 21 1.8 WSA/NRSA

55 30 2.1 WSA/NRSA

56 38 2.9 WSA/NRSA

57 3776 4.6 NOCD & WSA/NRSA
81

Ecoregion n 

DOC (mg/L)

10%

Data Source

58 14136 0.6 NOCD & WSA/NRSA

59 182 2.7 NOCD & WSA/NRSA

60 29 1.4 WSA/NRSA

61 26 1.8 WSA/NRSA

62 128 0.7 NOCD & WSA/NRSA

63 16771 2.2 NOCD & WSA/NRSA

64 47 1.0 WSA/NRSA

65 108 1.4 WSA/NRSA

66 726 0.5 NOCD & WSA/NRSA

67 821 0.6 NOCD & WSA/NRSA

68 64 0.9 NOCD & WSA/NRSA

69 895 0.7 NOCD & WSA/NRSA

70 67 1.5 WSA/NRSA

71 613 0.1 NOCD & WSA/NRSA

72 65 2.2 WSA/NRSA

73 107 2.8 WSA/NRSA

74 39 1.5 NOCD & WSA/NRSA

75 41 3.6 WSA/NRSA

77 111 0.4 NOCD & WSA/NRSA

78 56 0.6 WSA/NRSA

79 9 0.8 WSA/NRSA

80 49 1.0 WSA/NRSA

81 13 1.0 WSA/NRSA

82 18 2.8 WSA/NRSA

83 32 2.6 WSA/NRSA

84 247 1.6 NOCD & WSA/NRSA

4.5 Conclusions

EPA tested the 10th percentiles of ecoregional DOC concentrations against data from the Southern 

Rocky Mountains (Level III Ecoregion 21) as input to the copper BLM. Broad ranges of errors (including 

some that were larger than an order-of magnitude) were observed in BLM predictions made with the 

DOC estimates, in comparison to predictions made with actual measured site data. Although the 

copper criteria values predicted using the parameter estimates for DOC were found to be protective in

90% of the cases, in many of these cases these predictions were overly-protective (e.g., IWQC lower by 

a factor of 4 to 5). For this reason, BLM users should be cautious when considering lower percentiles of 

the distribution of DOC as estimates for missing input parameters to the BLM. In general, it is 

preferable to use site-specific measurements of DOC as BLM input because: (1) copper toxicities (and 

BLM model predictions) are highly sensitive to DOC concentrations and (2) reasonably protective DOC 

concentrations can be difficult to estimate at the ecoregional level, when data are limited.

For many ecoregions, the EPA recommended percentiles in Table 20 are based upon a relatively small

number of DOC data, which can be a cause for concern in terms of the reliability of these values. For 
82

example, in 47 ecoregions the DOC percentiles were calculated from 50 or fewer concentration values, 

and in seven ecoregions the DOC percentiles were calculated from fewer than 10 values. In the former 

case (n≤50), the lower 95% confidence limit of the 10th percentile cannot be calculated (Berthouex and 

Brown, 1994), while in the latter (n<9) the 10th percentile itself is below the lowest concentration 

value. Because of these and other limitations on the DOC database and the importance of this 

parameter in criteria calculation, users are encouraged to sample for DOC as a basis for determining 

BLM input rather than using default parameters where possible.

5 SUMMARY AND RECOMMENDATIONS

The BLM predicts acute copper toxicity based on site-specific water quality parameters, and calculates 

aquatic life criteria based on the predicted copper toxicity. The BLM requires 10 input parameters to 

calculate copper criteria: temperature, pH, DOC, alkalinity, calcium, magnesium, sodium, potassium, 

sulfate, and chloride, the last seven of which are also referred to as GIs. Given the broad geographical 

range over which the BLM is likely to be applied, and the limited availability of data for input 

parameters in many areas, a practical method to estimate missing water quality parameters was 

developed to support the use of the copper BLM for copper aquatic life criteria.

In this report we described three approaches EPA used to estimate default input parameters for GI and 

DOC for BLM that could be used where site-specific data are not available. EPA’s goal was to provide 

estimates for these missing input parameters that are reasonably protective. EPA used geostatistics to 

predict ecoregional input parameters from national water quality databases, and developed 

correlations between GI parameters and conductivity. These estimates were further refined using 

stream order.

Our analysis of national data indicates that there is no relationship between conductivity and pH, and 

geostatistical methods were found to produce similarly ambiguous results. Because pH is one of the 

most important BLM inputs for predicting criteria for copper, we conclude that site-specific data for pH 

are needed for successful BLM application. Temperature is a commonly measured parameter and 

should be easy to obtain by users for input in the BLM.

5.1 Recommendations for BLM inputs for geochemical ions where site-specific data are not 

available

In Section 2 we used geostatistics to estimate missing GI parameter values based on geography. We 

supplemented the geostatistical approach by adding conductivity as an additional explanatory variable 

to generate a more robust spatial estimate of the GI water quality inputs for the BLM because 

conductivity is one of the most widely monitored water quality indicators in the U.S. and correlates 

well with GIs. We presented average predicted 10th percentile concentrations for the BLM GI water 

quality parameters Level III ecoregions. We further refined these estimates by considering the effect of 

stream order (size) in Section 3. We found that values of the GI estimates generally increased with 

stream order, a trend that was most apparent and consistent for higher order streams. Tables 8, 9, and 

10 present best estimates of GI input parameters for the BLM. Estimated inputs are provided for each 

GI in each ecoregion categorized by stream order for low, medium, and high order streams, 

respectively. EPA recommends these 10th percentile Level III ecoregion, stream order group-specific 

values be used in the BLM where site-specific data are not available. 
83

5.2 Recommendations for BLM inputs for DOC where site-specific data are not available

In Section 4 we determined that the geostatistical and regression-based approaches used to estimate 

GI input parameters for the BLM do not produce accurate site-specific estimates for DOC. Because 

previous analyses indicate that DOC is the most important BLM input for estimating criteria for copper, 

we further refined our approach in Section 4 based on analyses using the NOCD to estimate lowerpercentile DOC concentrations. Based on statistical comparisons to an independent probabilistic 

dataset, we found that DOC concentrations from the NOCD are reasonably protective estimates of DOC 

for use as input parameters for the BLM for some ecoregions. For other ecoregions, EPA recommends 

using estimates based on the WSA dataset. Recommended 10th percentile DOC estimated values for 83 

of the 84 ecoregions are summarized in Table 20. In the remaining ecoregion (76; Southern Florida 

Coastal Plain), there were insufficient data in either dataset (NOC database or WSA/NRSA) to calculate 

DOC concentration percentiles. Because limitations in the DOC database and the importance of this 

parameter in criteria calculation, users are encouraged to sample for DOC as a basis for determining 

BLM input rather than using default parameters wherever possible.

5.3 Recommendations for BLM inputs for pH where site-specific data are not available

In Section 2 we determined that geostatistical and regression-based approaches used to estimate GI 

input parameters for the BLM did not produce accurate site-specific estimates for pH. Our analysis of 

national data indicates that there is no relationship between conductivity and pH, and geostatistical 

methods were found to produce similarly ambiguous results. Because pH is one of the most important 

BLM inputs for predicting criteria for copper, we conclude that site-specific data for pH are needed for 

successful BLM application. Temperature along with pH is similarly recommended to acquire sitespecific data for BLM application with the advantage of both of these been easy parameters to 

measure.

5.4 Conclusions

The approaches described in this TSD can be used to provide reasonable default values for input 

parameters in the BLM to derive protective freshwater aquatic life criteria for copper when data are 

lacking. These data could also be used to provide reasonable default values to fill in missing water 

quality input parameters in the application of other metal BLM models as well when data are lacking. 

Default recommended values for GI parameters are 10th percentile ecoregional, stream-order specific 

values. Default recommended values for DOC are 10th percentile ecoregional values. Both pH and 

temperature should be measured values when using the BLM. It should be noted that site-specific data 

are always preferable for use in the BLM and should be used to develop copper criteria via the BLM 

when possible. Users of the BLM are encouraged to sample their water body of interest, and to analyze 

the samples for the constituent (parameter) concentrations as a basis for determining BLM inputs 

where possible.
84

REFERENCES

Berthouex, P.M. and L.C. Brown. 1994. Statistics for Environmental Engineers. Lewis Publishers. Boca 

Raton, FL. 335p.

Carleton, J.N. 2006. An Examination of Spatial Trends in Surface Water Chemistry in the Continental 

United States: Implications for the Use of Default Values as Inputs to the Biotic Ligand Model 

for Prediction of Acute Metal Toxicity to Aquatic Organisms U.S. Environmental Protection 

Agency, Office of Water, Office of Science & Technology. (Appendix A to this report).

Clements, W.H., Brooks, M.L., Kashian, D.R. and R.E. Zuellig. 2008. Changes in dissolved organic 

material determine exposure of stream benthic communities to UV-B radiation and heavy 

metals: Implications for climate change. Global Change Biology 14:2201-2214.

Clements, W.H., Carlisle, D.M., Lazorchak, J.M. and P.C. Johnson. 2000. Heavy metals structure 

benthic communities in Colorado mountain streams. Ecological Applications 10:626-638.

Dierickx, T. 2008. Computing percentiles – are your values correct? (http://www.data-forall.com/documents/computing-percentiles.pdf)

ESRI. 2003. Using ArcGIS Geostatistical Analyst (ArcGIS 9). Environmental Systems Research Institute, 

Inc. Redlands, California.

FISRWG. 1998. Stream Corridor Restoration: Principles, Processes, and Practices. By the Federal 

Interagency Stream Restoration Working Group (FISRWG)(15 Federal agencies of the US 

government). GPO Item No. 0120-A; SuDocs No. A 57.6/2:EN 3/PT.653. ISBN-0-934213-59-3.

Gibbs, R. J. 1970. Mechanisms controlling world water chemistry. Science 170:1088–1090.

Griffith, M.B. 2014. Natural variation and current reference for specific conductivity and major ions in 

wadeable streams of the conterminous USA. Freshwater Science. 33(1):1-17. 

Helsel, D.R. and R.M. Hirsch. 2002. Techniques of Water-Resources Investigations of the United States 

Geological Survey Book 4, Hydrologic Analysis and Interpretation. Section A3, Statistical 

Methods. U.S. Geological Survey. September 2002. Publication available at: 

http://pubs.usgs.gov/twri/twri4a3/ (last accessed February, 2016). 

Herlihy, A.T., D.P. Larsen, S.G. Paulsen, N.S. Urquhart, and B.J. Rosenbaum. 2000. Designing a spatially 

balanced randomized site selection process for regional stream surveys: the EMAP mid-Atlantic 

pilot study. Environmental Monitoring and Assessment 63:95–113.

HydroQual, Inc. 2001. BLM-Monte User’s Guide, Version 2.0. HydroQual, Mahwah, NJ. October, 2001.

Hyndman, R.J., and Y. Fan. 1996. Sample quantiles in statistical packages. American Statistician. 50(4): 

361-365. 

Linton, T.K., W.H. Clement, W.F. Dimond, G.M. DeGraeve, and G.W. Saalfeld. 2007. Development of a 

copper criteria adjustment procedure for Michigan Upper Peninsula waters. Proceedings of the 

80th Annual Water Environment Federation Technical Exhibition and Conference. San Diego, 

CA.

MacArthur, R.H. 1972. Geographical Ecology. New York: Harper & Row.
85

McKay, L., Bondelid, T., Dewald, T., Johnston, J., Moore, R., and Rea, A. 2012. “NHDPlus Version 2: User 

Guide” (http://nhd.usgs.gov/).

National Research Council. 1992. Restoration of Aquatic Ecosystems. Committee on Restoration of 

Aquatic Ecosystems: Science, Technology, and Public Policy. National Academy Press, 

Washington, DC.

Omernik, J.M. 1987. Ecoregions of the conterminous United States. Annals of the Association of 

American Geographers 77:118-125.

Omernik, J., 2003. The misuse of hydrologic unit maps for extrapolation, reporting, and ecosystem 

management. Journal of the American Water Resources Association 39(3):563-573.

Omernik, J.M., and G.E. Griffith. 2014. Ecoregions of the conterminous United States: evolution of a 

hierarchical spatial framework. Environmental Management. 

Perry, J. and E.L. Vanderklein. 1996. Water Quality: Management of a Natural Resource. WileyBlackwell. 656 p.

Smith, RA, Schwarz, GE, Alexander, RB. 1997. Regional Interpretation of Water-Quality Monitoring 

Data. Water Resources Research. (33):2781–2798.

Stephan, C.E., D.I. Mount, D.J. Hansen, J.H. Gentile, G.A. Chapman and W.A. Brungs. 1985. Guidelines 

for deriving numerical national water quality criteria for the protection of aquatic organisms 

and their uses. PB 85—227049. National Technical Information Service, Springfield, VA.

Strahler, A.N. (1952). Hypsometric (area-altitude) analysis of erosional topology. Geological Society of 

America Bulletin. 63(1):1117-1142.

Strahler, A.N. (1957). Quantitative analysis of watershed geomorphology. Transactions of the American 

geophysical Union. 38(6):913-920.

Thurman, E.M. 1985. Organic geochemistry of natural waters. Martinus Nijhoff / DR W. Junk 

Publishers. 489pp.

USEPA. 2002. Development of Methodologies for Incorporating the Copper Biotic Ligand Model into 

Aquatic Life Criteria: Application of BLM to Calculate Site-Specific Fixed Criteria. Prepared by 

Great Lakes Environmental Center (GLEC) for U.S. Environmental Protection Agency, Office of 

Science and Technology, Health and Ecological Criteria Division, Work Assignment 3-38, 

Contract No. 68-C-98-134. 63p plus figures.

USEPA. 2003. Methodology for Deriving Ambient Water Quality Criteria for the Protection of Human 

Health (2000), Technical Support Document Volume 2: Development of National 

Bioaccumulation Factors (EPA-822-R-03-030). December 2003. 

USEPA. 2006a. Approaches for Estimating Missing BLM Input Parameters: Projections of Total Organic 

Carbon as a Function of Biochemical Oxygen Demand. Prepared by Great Lakes Environmental 

Center (GLEC) for U.S. Environmental Protection Agency, Office of Science and Technology, 

Health and Ecological Criteria Division, Contract No. 68-C-04-006, Work Assignment 2-34, Task 

1, Subtask 1-7. Report: December 7, 2006. (Appendix B to this report).
86

USEPA. 2006b. Mid-Atlantic Integrated Assessment (MAIA). State of the Flowing Waters Report. United 

States Environmental Protection Agency, Office of Research and Development. Washington, DC 

20460. EPA/620/R-06/001. February 2006.

USEPA. 2006c. Wadeable Streams Assessment, A Collaborative Survey of the Nation’s Streams. United 

States Environmental Protection Agency, Office of Research and Development and Office of 

Water. Washington, DC 20460. EPA 841-B-06-002, December 2006. 

USEPA. 2007. Approaches for Estimating Missing BLM Input Parameters: Correlation approaches to 

estimate BLM input parameters using conductivity and discharge as explanatory variables. 

Prepared by Great Lakes Environmental Center (GLEC) for U.S. Environmental Protection 

Agency, Office of Science and Technology, Health and Ecological Criteria Division, Contract No. 

68-C-04-006, Work Assignment 2-34, Task 1, Subtask 1-7. (Appendix C to this report).

USEPA. 2007. National Rivers and Streams Assessment: Field Operations Manual. EPA-841-B-07-009. 

U.S. Environmental Protection Agency, Washington, DC.

USEPA. 2008. Copper Biotic Ligand Model (BLM) Software and Supporting Documents Preparation, 

Task 3c: Development of Tools to Estimate BLM Parameters. Prepared by Great Lakes 

Environmental Center (GLEC) for U.S. Environmental Protection Agency, Office of Science and 

Technology, Health and Ecological Criteria Division. Contract No. 68-C-04-006, Work 

Assignment 4-18, Task 3 Progress Report: May 22, 2008. (Appendix D to this report).

USEPA. 2013a. U.S. Environmental Protection Agency, 2013, Level III ecoregions of the continental 

United States: Corvallis, Oregon, U.S. EPA - National Health and Environmental Effects Research 

Laboratory, map scale 1:7,500,000. ftp://ftp.epa.gov/wed/ecoregions/us/Eco_Level_III_US.pdf

USEPA. 2013b. National Rivers and Streams Assessment 2008–2009. A Collaborative Survey (Draft). 

U.S. Environmental Protection Agency. Office of Wetlands, Oceans and Watersheds. Office of 

Research and Development. Washington, DC. 20460 (EPA/841/D-13/001). February 28, 2013.

USEPA. 2015. Connectivity of Streams and Wetlands to Downstream Waters: A Review and Synthesis of 

the Scientific Evidence (Final Report). U.S. Environmental Protection Agency, Washington, DC, 

EPA/600/R-14/475F.

USGS. 2012. National Hydrography Geodatabase: The National Map viewer available on the World 

Wide Web (http://viewer.nationalmap.gov/viewer/nhd.html?p=nhd), accessed, 2012.

Walpole, R.E. and R.M. Myers. 1978. Probability and Statistics for Engineers and Scientists. MacMillan 

Publishing Co., New York. 580 p.

Ward, J. V. 1992. A mountain river. Pages 793-510 in Calow, P., and G. E. Petts (Editors). The Rivers

Handbook. Blackwell, Oxford, U.K.
87

Appendix A: An Examination of Spatial Trends in Surface Water Chemistry in the 

Continental United States: Implications for the Use of Default Values as 

Inputs to the Biotic Ligand Model for Prediction of Acute Metal Toxicity 

to Aquatic Organisms

Internal EPA Report (2006)

James N. Carleton

EPA, Office of Water, Office of Science & Technology.

A.1 Abstract

A large database of surface water chemistry monitoring data was examined to look for spatial trends in 

five chemical constituents that are key inputs to a model for predicting metal toxicity to aquatic 

organisms. Continuous prediction maps of concentrations were generated using various kriging 

techniques to interpolate between site-median values measured at several thousand separate 

locations throughout the continental United States (U.S.). Continuous concentration surfaces were 

then averaged over 8-digit Hydrologic Unit Code (HUC) polygons to produce block-averaged mean 

estimates of site-median concentrations. Pairwise comparisons indicated distinct trends between 

various HUC-averaged predicted constituents. The same analyses performed on data from 772 

locations where all five constituents had been measured revealed similar relationships between 

monitored constituents. Principal components analyses performed on these data sets showed that 80 

to 90% of the variance in both cases could be explained by a single component with loadings on three 

of the five constituents. The use of kriging to produce appropriate quantile maps for block-averaging is 

suggested as a possible approach for developing regional values to use as default model inputs, when 

site-specific monitoring data are lacking.

A.2 Background

The U.S. Environmental Protection Agency is planning in the near future to release proposed water 

quality criteria for copper (Note: EPA’s BLM-based Freshwater Copper Aquatic Life Ambient Water 

Quality Criteria document was released in 2007, EPA-822-R-07-001). These criteria are unlike most 

water quality criteria in that acceptable (safe) concentrations for aquatic life support, rather than being 

defined as simple numerical values that apply everywhere, will be addressed through the use of a 

chemical speciation model – the Biotic Ligand Model (BLM) (EPA, 2003). The BLM calculates metal 

toxicity to aquatic organisms as a function of simultaneous concentrations of additional chemical 

constituents of water, for example other ions that can either complex with copper and render it 

biologically unavailable, or compete with copper for binding sites at the point of entry into a vulnerable 

organism (i.e. at the fish gill). While the BLM has the potential to improve the accuracy of metal 

ecotoxicity predictions, its use requires input concentrations of nine separate chemical constituents 

and water temperature. Of these nine chemical constituents (Alkalinity (alk), calcium (Ca), magnesium 

(Mg), sodium (Na), sulfate (SO42-), potassium (K), chloride (Cl), dissolved organic carbon (DOC), and 

pH), model-predicted toxicity is most sensitive to five: Ca, alk, pH, Na, and DOC. States or other entities 

wishing to use the BLM to assess compliance with the proposed criteria in specific waters, or to 

develop effluent permit limits, will therefore require monitoring information on a suite of chemical 
88

constituents – information that is not always available. One possible way to deal with such missing 

information is to develop reasonably protective default values for these various model inputs, 

especially the five to which the BLM is most sensitive. Given that ambient surface water chemistry 

reflects, among other things, the influences of local soil types and land uses, it may make sense that 

any such defaults be developed on some kind of regional or local basis.

The exercise described in this report comprises a geospatial examination of a large amount of water 

chemistry monitoring data collected in recent years by the U.S. Geological Survey, and recorded in 

their National Water Information System (NWIS) database. The data includes monitoring information 

from several thousand separate surface water sampling locations throughout the U.S. (Figure A-1). The 

latitudes and longitudes of each sampling location are part of the data record. The primary objective of 

this analysis is to look for any obvious spatial trends in typical concentrations of the five most sensitive 

constituents, and to suggest procedures for making use of these trends to define regional default 

values for use as inputs to the BLM. For purposes of expediency, the geographic extent of this analysis 

is limited to the continental U.S.

Figure A-1. NWIS sample collection locations in the continental U.S.

A.3 Description of Data

Although NWIS contained data from 207,153 sampling events at 13,824 individual sampling locations 

in the continental U.S. (Figure A-1), all 10 constituents of relevance to the BLM were not monitored at 

each location. For the five constituents of interest, the numbers of discrete sampling locations were as 

follows: alk, 5,900; Ca, 10,940; DOC, 3,726; Na, 10,424; pH, 11,780. Numbers of sampling events at 

individual locations ranged from 1 to 2,605, with a mean of 15, and a mode of one (i.e. most sites were 
89

only sampled once). Examination of the spatial distribution of numbers of sampling events per site 

reveals that the most intensive sampling tended to occur in Midwestern and western states (Figure A2). Because environmental sampling data tend to be lognormally distributed, disparities in numbers of 

samples may tend to produce higher mean and median values at more-frequently-sampled locations. 

As spatial distributions of representative (e.g., median) concentrations are examined, it should be kept 

in mind that apparent geographic trends in concentration may be in part simply the result of uneven 

sampling intensity.

Figure A-2. Intensity of sampling (number of separate sampling dates) at each NWIS site

A.4 Data Analysis

Because environmental data tend to be positively skewed, the median statistic was chosen as 

providing the best central-tendency representation of each location’s concentration. For the purpose 

of looking for general spatial trends in the five constituents, the first step involved simply mapping the 

sampling locations as points, color-graded by median concentration. Figure A-3, for example, shows 

some apparent trends in alkalinity across the country, with lower concentrations along the eastern 

seaboard, and higher concentrations in parts of the Midwest. Similar kinds of trends at the national 

scale were also seen with the other constituents.
90

Figure A-3. Median measured alkalinity (mg/L as CaCO3) at NWIS locations

The next step in data visualization involved the calculation of median concentrations averaged over 

each 8-digit HUC containing sampling locations. These display essentially the same information as the 

point displays (Figure A-3), but with a degree of smoothing and summarization provided by the spatial 

averaging process, to make visual interpretation of general trends easier (Figure A-4).

Figure A-4. HUC-averaged mean median observed alkalinity in the continental U.S.

The use of 8-digit HUCs as the areal units over which to calculate representative concentrations for 

default BLM inputs makes some physical sense: HUCs are areas that are defined by some degree of 
91

interconnection between associated surface water features. HUCs may be either watersheds in their 

own right or downstream sections of larger watersheds (Omernik, 2003). In either case, all flowing 

surface water that passes through a HUC eventually (in theory) passes through the same downstream 

“pour point”. One advantage of using HUCs is that they divide the land area into roughly equally sized 

areas at a level of resolution roughly consistent with gross variations in median concentration (Figure 

A-3). One problem with using HUCs for spatial aggregation is that not all HUCs contain NWIS sampling 

locations, as the blank areas in Figure A-4 make clear. The third step in this analysis therefore involved 

the use of kriging to create continuous surfaces of interpolated concentrations that cover the entire 

area of interest. Spatial averaging of the results over each HUC was then used to provide estimates of 

expected concentrations for all HUCs, including those lacking NWIS samples.

For each of the five key constituents, the Geostatistical Analyst extension in ArcGIS was used to explore 

the data, and to look for sets of kriging model options that provided the best fit to the data. The 

criteria used to evaluate goodness of fit were as follows:

1. Mean Standardized Error as small as possible

2. RMSE as small as possible

3. Root-Mean-Square Standardized Error close to 1.0

4. RMSE and Average Standard Error close together

Trial and error parameter selection was used to search for a set of model options that best attained 

each of these four goals simultaneously. For each constituent, 10 to 20 combinations were tried, until a 

best option for each emerged, as determined by judgment of the author. The results are as follows:

Alk: Universal kriging, log transformation, constant trend, 50% global, 50% local, spherical 

semivariogram, no anisotropy. 

Ca: Ordinary kriging, log transformation, constant trend, 50% global, 50% local, exponential 

semivariogram, anisotropy.

DOC: Universal kriging, log transformation, constant trend, 50% global, 50% local, hole-effect 

semivariogram, anisotropy.

Na: Universal kriging, log transformation, constant trend, 50% global, 50% local, hole-effect 

semivariogram, anisotropy.

pH: Ordinary kriging, no transformation, constant trend, 50% global, 50% local, spherical 

semivariogram, no anisotropy.

Prediction surface maps were generated for each constituent using the above sets of kriging options. 

Figure A-5, which displays the results for alkalinity, shows patterns that are generally consistent with 

those in the data (Figures A-3 and A-4). Figure A-6 shows the predicted alkalinities projected into three 

dimensions using ArcScene. 
92

Figure A-5. Kriging prediction map of median alkalinity

Figure A-6. Kriging map of alkalinity, projected into vertical dimension

This technique demonstrates broad geographic trends most dramatically, for example emphasizing the 

fact that the highest alkalinities are apparently found in northern North Dakota and Montana. Figure A7 shows the predicted values averaged over HUC polygons by using the Zonal Statistics function of 

ArcGIS Spatial Analyst.
93

Figure A-7. Kriging-based alkalinity predictions, averaged over 8-digit HUC polygons

For HUCs containing NWIS sampling locations, linear regression plots of predicted versus measured 

concentrations (Figure A-8) provided a check on the accuracy of the kriging predictions. R-squared 

values for the five constituents were: 0.537 (alk), 0.238 (Ca), 0.686 (DOC), 0.351 (Na), and 0.139 (pH). 

In most cases, a handful of outliers appeared to be responsible for smaller-than-expected correlation 

coefficients.

Figure A-8. Kriging-predicted vs. calculated HUC-averaged alkalinity; r2

=0.537

HUC-Averaged Median Alkalinity

0

500

1000

1500

2000

0 500 1000 1500 2000

Observed

Predicted (kriged)

data 1:1 line regression line
94

A scatter plot matrix of cross-constituent comparisons revealed some interesting, non-random 

relationships between HUC-averaged concentrations (Figure A-9). For comparative purposes, a subset 

of 772 sampling locations was also identified, at which sampling for all five of the constituents had 

taken place. Coincident concentrations of all constituents allowed a scatter plot matrix of this data 

(Figure A-10) to also be constructed. Similarities between the kinds of relationships in Figure A-9 and A10 suggest that the predicted HUC mean median values are reasonable.

Figure A-9. Scatter plot matrix of median concentration kriged predictions, averaged over 8-digit 

HUCs regions covering the continental U.S.
95

Figure A-10. Scatter plot matrix of median concentrations from 772 monitoring locations in the 

continental U.S.

In addition to scatter plots, correlation coefficient matrices between constituents in each of the two 

data sets (HUC-mean kriged median values and site median values for 772 locations) were generated 

(Table A-1). Although not identical, the coefficients were generally similar between the two datasets, 

again suggesting that the kriging predictions are reasonable.

Table A-1. Matrices of correlation coefficients between constituent concentrations

2096 HUC-averaged predicted median values

Alk DOC Na pH Ca

Alk 1 

DOC -0.01456 1 

Na 0.327599 -0.02661 1 

pH 0.761675 -0.27746 0.286512 1 

Ca 0.698379 -0.02585 0.531727 0.58514 1 

772 site-median values

Alk DOC Na pH Ca

Alk 1 

DOC 0.019145 1 

Na 0.327028 0.165445 1 

pH 0.453161 -0.24067 0.169238 1 

Ca 0.842484 -0.05097 0.387617 0.374592 1 
96

Principal components analyses (PCA) were also run on both the HUC-averaged predictions and the 772 

sets of monitored constituent concentrations to look for linear combinations of variables that might 

explain most of the observed variation. Figures A-11 and A-12 show the resulting plots of the variance 

explained by each component, and Table A-2 lists the loadings of the components onto the original 

variables. The first component comprised 80 and 88% of the variance in the HUC-based and site-based 

analyses, respectively. As Table A-2 indicates, this component loaded entirely onto alk, Na, and Ca in 

both cases. For the HUCs, component 1 was primarily loaded on Na, while for the sites, it primarily 

loaded on alk.

Figure A-11. Variance plot from PCA of HUC-average kriging-predicted concentrations

Figure A-12. Variance plot from PCA of site-median measured concentrations
97

Table A-2. Loadings onto original variables from PCA on HUC-averaged predictions and site-median 

concentrations

HUCs:

Comp.1 Comp.2 Comp.3 Comp.4 Comp.5

Alk 0.219 0.932 -0.289 

DOC 0.999 

Na 0.965 -0.25 

pH -0.999

Ca 0.142 0.263 0.954 

 

Sites:

Comp.1 Comp.2 Comp.3 Comp.4 Comp.5

Alk 0.952 0.162 0.259 

DOC -0.997 

Na 0.13 -0.982 0.133 

pH 0.999

Ca 0.277 -0.955 

A.5 Developing Regional Defaults

Besides prediction maps of best-estimate median concentrations, the Geostatistical Analyst can be 

used, with the same sets of kriging parameters listed previously, to generate quantile surface maps 

that represent reasonably protective inputs to the BLM than standard kriging predicted values. The five 

key inputs examined in this paper are all positively associated with BLM-predicted LC50s. Thus, lower 

values of all of them tend to result in lower (i.e., more protective) site-specific criteria. Lower quantile 

predictions can be used to produce protective regional default inputs. As an example, Figure A-13 

displays the 25th percentile prediction map for alkalinity. When these values are block-averaged over 

the HUC polygons, the resulting alkalinities are lower than 67% of the site-minimum alkalinities (Figure 

A-14) measured inside the same areas.
98

Figure A-13. Kriging 25th percentile map of median alkalinity

Figure A-14. Comparison of observed site-minimum alkalinities with HUC-mean 25th percentile 

kriging-predicted values

0

200

400

600

800

1000

0 50 100 150 200 250

Alk (mg/L as CaCO3)

measured and kriging-predicted 

HUC mean Alk

site minimum observed Linear (HUC-mean 25th percentile kriged conc.)
99

A.6 Discussion

The use of HUCs for spatial averaging of surface water concentrations is not without conceptual 

difficulties. First, only about 45% of HUCs are actual watersheds (Omernik, 2003); the rest receive 

drainage from additional upgradient areas. Concentrations measured in flowing waters reflect the soil, 

vegetation and land use properties of the aggregate upstream drainage areas, rather than of the 

sampling locations themselves (Smith et al., 1997). Assignment of measured concentrations to a HUC 

through block averaging may understate the spatial relevance of the samples for HUCs that are only 

parts of watersheds. One way to address this concern might be to use, as the aggregation polygons, 

only samples from watersheds that are entirely contained within single ecoregions (Omernik, 1987). 

However, this would have the unacceptable consequence of excluding large areas, and perhaps much 

of the data, from analysis. Another critical problem with this idea is that watershed boundaries for all 

of the NWIS sampling locations are not readily available, so there is currently no basis for deciding 

which points should be included or excluded. One advantage provided by the use of HUCs is that they 

divide the entire land mass of interest in this case into roughly equal sized polygons, at a level of 

resolution that appears to be roughly compatible with that of observed concentration trends. Block 

averaging using other sets of similarly sized polygons, such as counties, might serve equally well for 

empirically capturing broad spatial variability in concentrations. However the resulting concentrations 

would be less useful because they would lack even the incomplete degree of organization by 

connected hydrology that HUCs provide. 

A.7 Conclusions

Kriging-predicted median concentrations of five water quality constituents, averaged over 8-digit 

HUCs, showed similar inter-constituent relationships as median concentrations from 772 specific 

sampling locations. PCA analyses revealed that in both cases, most of the observed variability was 

related to variations in three of the five constituents: alk, Na, and Ca. Results suggest that block 

averaging of kriging predictions over irregularly spaced sampling points can provide estimates that 

preserve much of the interrelationships between different measured entities. The use of suitable lowquantile kriging predictions is suggested as a way to estimate reasonably protective concentrations to 

serve as regional default inputs to the BLM.

A.8 References

Omernik, J., 1987. Ecoregions of the conterminous United States. Annals of the Association of 

American Geographers 77:118-125.

Omernik, J., 2003. The misuse of hydrologic unit maps for extrapolation, reporting, and ecosystem 

management. Journal of the American Water Resources Association 39(3):563-573.

Smith, R.A., Schwartz, G.E., and R.B. Alexander, 1997. Regional interpretation of water-quality 

monitoring data. Water Resources Research 33912):2781-2798.

U.S. Environmental Protection Agency, 2003. The Biotic Ligand Model: Technical Support Document for 

its Application to the Evaluation of Water Quality Criteria for Copper, EPA 822-R-03-027.
100

Appendix B: Approaches for Estimating Missing Biotic Ligand Model Input 

Parameters. Correlation approaches to estimate Biotic Ligand Model

input parameters using conductivity and discharge as explanatory 

variables

B.1 Introduction

Derivation of water quality criteria for copper and other metals from predictions of bioavailability 

generated by the Biotic Ligand Model (BLM) introduces a number of issues. For example, obtaining the 

data needed to apply the BLM may be problematic for many dischargers and receiving waters. The 

BLM requires 10 input parameters to characterize water quality at a particular site; the most important 

ones for predicting copper bioavailability and toxicity include pH, dissolved organic carbon (DOC), 

calcium, magnesium, sodium, alkalinity, and temperature. In stream segments with only small 

dischargers, or possibly no dischargers at all, the data needed to apply the BLM may not be available. 

Water quality criteria that rely upon BLM predictions would be greatly facilitated by the development 

of practical approaches to estimate values for BLM water quality parameters, which could be applied 

when data for one or more of these parameters are missing at a site. 

Given the broad geographical range over which the BLM is likely to be applied, potentially over the 

entire Nation, and the limited information that is available for many areas, a practical method to 

estimate missing water quality parameters is needed. The geostatistical methods employed by the U.S.

Environmental Protection Agency (EPA) (Carleton, 2006) presented a viable system to estimate missing 

water quality parameters required by the BLM. The prototype work developed by Carleton applied 

kriging to predict average concentrations of alkalinity, DOC, sodium, pH and calcium over hydrologic 

units (8-digit Hydologgic Unit Codes [HUCs]), using the U.S. Geological Service (USGS) National Water 

Information Service (NWIS) as the source of spatial data. Comparison of measured concentrations with 

kriging predictions were encouraging for several of the BLM water quality parameters, although the 

errors and uncertainties associated with these predictions were not fully explored. 

The geostatistical approach utilizes knowledge of spatial correlation to project values of a water quality 

parameter at sites where it has not been measured. The accuracy of these projections depends upon 

the availability of sufficient and spatially-proximate data for the specific parameter of interest. In 

addition, the seasonal and annual temporal variation in water quality must also be addressed in order 

to apply the BLM at a site. Water quality parameters often experience large changes during periods of 

snowmelt or intense rainfall. In many rivers and streams, the chemical composition and physical 

properties of water are following trends associated with increased land use in watersheds, water 

diversion for irrigation, regulation of river flow by dams, and other anthropogenic disturbances.

The acute BLM predicts an instantaneous acute copper criterion (i.e., a maximum short-term, non-toxic 

concentration of copper), which will vary according to changes in the water quality parameters. An 

appropriately protective copper criterion must therefore reflect the variability of water quality 

parameters at the site. In previous analyses we found that protective water quality criteria for copper 
101

generally corresponded to approximately the 2.5th percentile of the distribution of instantaneous 

water quality criteria (IWQC) predicted by the BLM.

5 BLM criteria predictions made for a site using the 

corresponding percentiles (i.e., 2.5%) of the water quality parameter distributions will be a 

conservative approximation of this protective criterion. The sensitivity of criteria predictions to the 

most important BLM water quality inputs is proportional (sensitivity to DOC is ~100%6

, [H+] is ~50%, 

calcium, magnesium and sodium is ~20%). Relevant site-specific water quality parameters will be 

values from the lower “tail” of the measured or estimated distributions.

There may be great value in supplementing the geostatistical approach with classical estimation 

methods, such as regression and correlation. Examination of the NWIS data used to develop the 

geostatistical approach suggests that two variables, discharge (flow rate) and conductivity, may be 

useful for estimating BLM input water quality parameters. The USGS maintains the most 

comprehensive routine water flow and water quality data for streams and rivers in the Nation. 

Discharge may be a relevant explanatory variable because the USGS measures or estimates flow on a 

daily basis for a large number of stream and river segments. Among water quality parameters, the data 

for conductivity are the most complete and cover the longest time period (Wang and Yin, 1997). The 

literature also indicates that conductivity is one of the most widely monitored water quality indicators 

in the U.S. In part, this is because conductivity measurements are usually included in automated 

multiparameter systems for monitoring changes in the quality of surface waters (Allen and Mancy, 

1972). 

Conductivity is useful as a general measure of stream water quality. Each stream tends to have a 

relatively constant range of conductivity that, once established, can be used as a baseline for 

comparison with regular conductivity measurements (USEPA, 1997). Conductivity in streams and rivers 

is affected primarily by the geology of the area through which the water flows. Streams that run 

through areas with granite bedrock tend to have lower conductivity because granite is composed of 

more inert materials that do not ionize (dissolve into ionic components) when washed into the water. 

On the other hand, streams that run through areas with clay soils tend to have higher conductivity 

because of the presence of materials that ionize when washed into the water. Ground water inflows 

can have the same effects depending on the bedrock they flow through.

Conductivity reflects the strength of major ions in water and is a good estimator of total dissolved 

solids (TDS). Linear relationships between conductivity and TDS have been developed for many USGS 

monitoring sites. Conductivity is also linearly related to the sum of cations (McCutcheon et al., 1993). 

In addition, conductivity measurements provide information about the total concentration of ionic 

species in a water sample (Tyson, 1988). Figure B-1 illustrates how conductivity relates to hardness and 

anion concentrations in a river that has a rather saline base flow maintained by irrigation drainage and 

groundwater inflows. The chemical characteristics of the base flow are generally constant but they are 

subject to seasonal dilution by runoff. Relationships between conductivity and chloride and sulfate 

concentrations are well defined. A similarly good association with hardness (calcium+magnesium) is 

 

5 This was the median for 17 sites; the range was 1 to 36%.

6 100% sensitivity implies that a model prediction (in this case, the criteria predicted by the BLM) varies in direct proportion 

to the change in the value of a specified input parameter.
102

indicated. Lines drawn by eye through the points for chloride and sulfate show slight curvature, but the 

departure from linearity is insignificant. It seems evident that a record of conductivity at this station 

could be used to compute the other chemical characteristics of the water with a good level of accuracy 

for major ions, except at high flow when the relationships would not be as well defined (Hem, 1985).

Figure B-1. Relation of conductivity to chloride, hardness and sulfate concentrations in the Gila River 

at Bylas, Arizona

(reprinted from Hem, 1985)

Wang and Yin (1997) established conductivity as a general water quality indicator based on spatial 

data. The concentration of major base metal cations in water explained the positive correlation 

between conductivity and hardness. This also explained a rather weak correlation between 

conductivity and the pH value. Its relationship with other materials, however, most likely resulted from 

the dilution effect of stream flow. Conductivity was negatively correlated with discharge (ρ=-0.729), 

and the same was found for most water quality variables that were positively correlated with 

conductivity. With increasing stream flow, the concentration of the dissolved material decreased, as 

did the conductivity. Wang and Yin’s analysis suggests that conductivity could be used as a general 

indicator of water quality, which is positively related to dissolved materials and soluble metals. As it is 
103

widely monitored and has relatively long records, conductivity has the potential to be a very useful 

variable for estimating missing water quality input parameters for the BLM.

We explored this possibility by assessing the degree of correlation between conductivity and each of 

the BLM water quality parameters. We used NWIS data from three contiguous states in the Western 

U.S. (Colorado, Utah and Wyoming) for this analysis. These states were selected because of the large 

spatial and temporal variability observed in BLM water quality parameters, and because they provided 

us a tractable dataset for analysis.

Discharge was included as one of the parameters in this correlation analysis. However, discharge is 

most often used to explain water quality variation at a particular site (Hem, 1985). The concentration 

of dissolved solids in the water of a stream is related to many factors, but it seems obvious that one of 

the more direct and important factors is the volume of water from rainfall available for dilution and 

transport of weathering products. Presumably, therefore, the concentrations of dissolved solids should 

be an inverse function of the rate of discharge of water over all or at least most of the recorded range 

(Hem, 1985). Regressing water quality parameter measurements against discharge is a common 

practice in environmental engineering, and many references on this subject are available (McDiffett et 

al.,1989; Chanat and Hornberger, 2002; Christensen et al., 2005; Godsey and Kirchner, 2005). We 

should also point out that correlating the variation in water quality parameters to streamflow is also 

necessary for effluent dilution calculations associated with use of the BLM (for example, the 

probabilistic dilution framework incorporated in the BLM-Monte software [HydroQual, 2001]).

B.2 Data

Data for discharge, conductivity, and BLM water quality parameters (temperature, pH, DOC, alkalinity 

calcium, magnesium, sodium, potassium, sulfate, and chloride,) were retrieved from the USGS NWIS 

web interface (http://nwis.waterdata.usgs.gov/usa/nwis/qwdata). Data were selected for 790 stream 

and river stations in Colorado, Utah, and Wyoming reporting 100 or more water quality observations. 

This latter constraint was imposed to eliminate the large number of stations reporting very few (often 

one) water quality observations. Even when the analysis was restricted to sites with more than 100 

water quality observations, there were frequently a marginal number of data for the multiple 

parameters needed to measure between-parameter correlations. We also restricted the analysis to 

observations made since 1975 to avoid the possible influence of pre-Clean Water Act discharges on 

water quality. 

Natural logarithms of the discharge data were used in the analysis, because discharge was clearly 

lognormally distributed at the majority of sites. In cases where a parameter was measured 

simultaneously by more than one method (field pH versus laboratory pH, for example), the reported 

results were averaged for analysis. We did not consider other approaches for selecting data based on 

preference for a particular analytic method (Roberson et al., 1963).

B.3 Results

Table B-1 provides an inventory of the number of observations, and number of sites with data, for 

several of the parameters in the state of Colorado (these numbers reflect the full NWIS dataset, 

uncensored for minimum number of observations or date). From this table, it is apparent that a vast 

amount of conductivity data exists, both in terms of the total number of observations and the number 

of sites reporting this parameter in comparison to the BLM water quality parameters. For example, 
104

there are almost four times as many observations of conductivity as there are for calcium, and they are 

measured at more than twice the number of sites. Discharge data is similarly abundant. 

Table B-1. Number of observations and sites reported in NWIS for streams and rivers in Colorado

Parameter Number of Observations Number of Sites

pH 62,005 3668

alkalinity 8136 839

calcium 45,490 2708

conductivity 168,110 6101

discharge 127,275 3340

To quantify the relationship between conductivity levels and values of water quality parameters 

required by the BLM, we performed correlation analyses on the NWIS water quality data for the three

states. We estimated correlations for several statistics that summarized the distribution of conductivity 

and water quality values at each station. These included median levels, as well as the first quartile and 

fifth quantile. The last two statistics represent the lower end of the distribution of parameter values at 

a site, and are appropriate statistics for calculation of BLM instantaneous criteria. A non-parametric 

correlation (Spearman’s rank correlation) was employed to avoid the problems of unknown data 

distributions and possibly non-linear relationships. To determine the statistical significance of the rank 

correlation coefficient (ρ), the significance level (P) was also calculated. The Spearman’s rank 

correlation was also used to examine the relationship between stream discharge and the water quality 

variables to reveal the effect of dilution.

For the median site concentrations, we found that six BLM water quality parameters, two-thirds of the 

nine variables examined in this study, had non-zero rank correlation coefficients at the 0.001 

significance level (Table B-2). As expected, strong positive correlations between conductivity and salt 

concentrations were found. For example, the correlation coefficients between conductivity and the 

concentration of salt cations and anions (sodium, potassium, magnesium, calcium, sulfate and 

chloride) were all higher than 0.80. However, median site conductivity was not significantly correlated 

to several other important BLM parameters including pH, DOC, and alkalinity. In terms of the site 

medians, there appears to be limited correlation between conductivity and the BLM water quality 

parameters. Furthermore, for the median site concentrations neither conductivity nor any of the BLM 

water quality parameters were significantly correlated to discharge. 
105

Table B-2. Results of Spearman rank tests for correlation (ρ) between median values of variables at 

each site.

Probability values (P) are not exact due to the presence of ties in the data

Conductivity Discharge

Conductivity ρ: 0.012

P: 0.892

pH ρ: 0.175

P: 0.019

ρ: 0.441

P: 0.008

DOC ρ: 0.866

P: 0.333 

ρ: 

P: 

Ca ρ: 0.867

P: <0.001

ρ: -0.371

P: 0.068

Mg ρ: 0.882

P: <0.001

ρ: -0.516

P: 0.008

Na ρ: 0.921

P: <0.001

ρ: 0.139

P: 0.695

K ρ: 0.846

P: <0.001

ρ: -0.128

P: 0.551

SO4 ρ: 0.905

P: <0.001

ρ: -0.514

P: 0.010

Alkalinity ρ: -0.600

P: 0.350

ρ: 

P: 

Cl ρ: 0.827

P: <0.001

ρ: -0.866

P: 0.333

We then repeated the correlation analysis for the site first quartiles (Table B-3) and fifth quantiles 

(Table B-4). For both of these low-end distribution statistics, all of the BLM water quality parameters 

were significantly correlated to conductivity, having non-zero rank correlation coefficients at the 0.001 

significance level, as listed in Tables B-3 and B-4. The correlation coefficients are lower for pH and DOC 

than for the salts and alkalinity, but are nevertheless significant. Apparently, the correlation structure 

between conductivity and the BLM water quality parameters is much stronger at the lower end of the 

site distributions. Ambiguity in correlations between conductivity and BLM water quality parameters 

disappears when low-end distribution statistics are analyzed. As was the case for the median site 

concentrations; neither conductivity nor any of the BLM water quality parameters were correlated 

with discharge for the low-end distribution statistics.
106

Table B-3. Results of Spearman rank tests for correlation (ρ) between the first quartile of values at 

each site.

Probability values (P) are not exact due to the presence of ties in the data

Conductivity Discharge

Conductivity ρ: 0.057 

P: 0.144

pH ρ: 0.287 

P: <0.001 

ρ: 0.070

P: 0.168

DOC ρ: 0.618 

P: <0.001 

ρ: -0.149

P: 0.031

Ca ρ: 0.920 

P: <0.001

ρ: -0.060

P: 0.305

Mg ρ: 0.935 

P: <0.001 

ρ: -0.107

P: 0.066

Na ρ: 0.910

P: <0.001

ρ: -0.075

P: 0.129

K ρ: 0.773 

P: <0.001

ρ: -0.109

P: 0.075

SO4 ρ: 0.941 

P: <0.001

ρ: -0.068

P: 0.247

Alkalinity ρ: 0.829

P: <0.001 

ρ: 0.099

P: 0.381

Cl ρ: 0.752

P: <0.001

ρ: 0.004

P: 0.958

Table B-4. Results of Spearman rank tests for correlation (ρ) between the fifth quantile of values at 

each site.

Probability values (P) are not exact due to the presence of ties in the data

Conductivity Discharge

Conductivity ρ: 0.056 

P: 0.213 

pH ρ: 0.382

P: <0.001 

ρ: 0.032

P: 0.579

DOC ρ: 0.558

P: <0.001 

ρ: -0.107

P: 0.134

Ca ρ: 0.920

P: <0.001

ρ: 0.017

P: 0.791

Mg ρ: 0.929

P: <0.001 

ρ: -0.056

P: 0.383

Na ρ: 0.845

P: <0.001

ρ: -0.089

P: 0.078
107

K ρ: 0.694

P: <0.001

ρ: -0.065

P: 0.353

SO4 ρ: 0.908

P: <0.001

ρ: 0.017

P: 0.790

Alkalinity ρ: 0.784

P: <0.001 

ρ: 0.184

P: 0.102

Cl ρ: 0.706

P: <0.001

ρ: 0.034

P: 0.671

To further illustrate these correlations, scatter plot matrices (or SPLOMs) were prepared for the first 

quartiles (Figure B-2) and fifth quantiles (Figure B-3). SPLOMs show scatter plots for each combination 

of parameters, arrayed as a matrix, with parameters labeled along the borders of the plot. Histograms 

for each parameter are plotted on the main diagonal. The correlations between conductivity and each 

of the BLM water quality parameters are apparent by examining the second row (from the top) of 

scatter plots in Figures B-2 and B-3. Likewise, the lack of correlation between these parameters and 

discharge is apparent in the top row of the scatter plots in these same figures.
108

Figure B-2. Scatter plot matrix for first quartile of site-specific data for discharge (LNDISCH), 

conductivity (COND), and BLM water quality parameters

LNDISCH

LNDISCH

COND PH DOC CA MG NA K SO4 ALK CL

LNDISCH

COND

COND

PH

PH

DOC

DOC

CA

CA

MG

MG

NA

NA

K

K

SO4

SO4

ALK

ALK

LNDISCH

CL

COND PH DOC CA MG NA K SO4 ALK CL

CL
109

Figure B-3. Scatter plot matrix for fifth quantile of site-specific data for discharge (LNDISCH), 

conductivity (COND), and BLM water quality parameters

To understand why the correlations between conductivity and the other BLM water quality parameters 

are so much stronger for the low-end distribution statistics than for the medians, it is necessary to 

examine the site-specific data itself. Figure B-4 is a SPLOM of the conductivity, discharge, and BLM 

water quality parameter data for a representative USGS station in Colorado. The histograms for 

conductivity, salts, and alkalinity are remarkable in that the distribution of each is clearly bimodal (i.e., 

two separate peaks are evident in the histograms). This was observed for many of the sites in this 

dataset (not shown). In Figure B-5, the conductivity and discharge data for this site are plotted as a 

time series, which reveals why the water quality data are bimodal: high values of conductivity (> 5,000 

micromhos/cm) occur when streamflow discharge is low, and low values of conductivity (< 2,000 

micromhos/cm) occur when the discharge is high. At this station (and many others in this region), 

streamflow discharge is high in the May-June period coinciding with snowmelt at higher elevations. 

Feth and others (1964) reported conductivities of melted snow in the Western US ranging from about 2 

to 42 picomhos/cm. Thus, the low values of conductivity (as well as concentrations of the salts and 

alkalinity) are the result of annual dilution from snow melt. At most other times, conductivity and salt 

and alkalinity concentration values are much higher. Depending upon how the water quality samples 

LNDISCH

LNDISCH

COND PH DOC CA MG NA K SO4 ALK CL

LNDISCH

COND

COND

PH

PH

DOC

DOC

CA

CA

MG

MG

NA

NA

K

K

SO4

SO4

ALK

ALK

LNDISCH

CL

COND PH DOC CA MG NA K SO4 ALK CL

CL
110

are allocated at a site, the median concentration of these parameters may fall in either mode of the 

bimodal distribution, resulting in quite different values that appear almost random. Fortunately, the 

low-end distribution statistics avoid this seeming randomness because they consistently reflect 

sampling from the lower mode of the concentration distribution.

Figure B-4. Scatter plot matrix of BLM water quality parameter data from NWIS Station 

384551107591901 (Sunflower Drain at Highway 92, near Read, Delta County, Colorado)

TEMP

TEMP

LNDISCH COND PH DOC CA MG NA K SO4 ALK CL

TEMP

LNDISCH

LNDISCH

COND

COND

PH

PH

DOC

DOC

CA

CA

MG

MG

NA

NA

K

K

SO4

SO4

ALK

ALK

TEMP

CL

LNDISCH COND PH DOC CA MG NA K SO4 ALK CL

CL
111

Figure B-5. Time series plot of conductivity (diamond symbols) and discharge (open circles connected 

by dashed line) at Station 384551107591901 (Sunflower Drain at Highway 92, near Read, Delta 

County, Colorado)

Figure B-4 also illustrates that, in terms of explaining site-specific variability, discharge is a much better 

predictive variable for a number of the BLM water quality parameters than conductivity. Each of these 

parameters (alkalinity calcium, magnesium, sodium, potassium, sulfate, and chloride) is clearly 

correlated to discharge, but not to conductivity. Discharge correlations are observed at many locations, 

and are commonly used to project water quality for various applications (Hem, 1985).

B.4 Discussion

Incorporating classical water quality correlation approaches, using conductivity and discharge as 

explanatory variables, within the geostatistical approach prototyped by EPA, appears promising. 

Conductivity, but not discharge, is significantly correlated to BLM water quality parameters between 

sites, especially for the low-end distribution statistics of interest for criteria calculations. Since 

conductivity data is abundant and it correlates well to BLM water quality parameters, it is reasonable 

to incorporate conductivity in spatial projections of BLM parameters. This may simplify the 

geostatistical approach and allow more robust spatial extrapolation of BLM water quality parameters.

Conversely, discharge is correlated to concentrations of a number of BLM parameters (salts and 

alkalinity) within many sites. Streamflow is a good explanatory variable for a number of the BLM water 

quality parameters (the salts and alkalinity) because their variabilities largely reflect dilution at high 

flow rates. Discharge data are also plentiful, so we believe that incorporating classical methods of 

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Jan-91 Jan-92 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04

conductivity (micromhos/cm)

-20

0

20

40

60

80

100

120

discharge (cfs)
112

correlating concentration to discharge may be a useful means to address within-station variability for 

BLM water quality parameters.

It should also be recognized that geostatistical and/or correlation approaches appear to most often fail 

for those water quality parameters which are the most sensitive and important to the BLM, namely 

DOC and pH. Additional sampling effort will likely be required to address these deficiencies. In the case 

of pH, it is worth noting that many surface water sampling crews carry electronic multiparameter 

instruments which measure pH, conductivity, and temperature simultaneously in the field. Therefore, 

data collection strategies which incorporate these three measurements may be especially effective.

Measurement of DOC is considerably more difficult and expensive. It may be worthwhile to investigate 

whether ultraviolet (UV) absorption spectroscopy could be used as a surrogate measurement 

technique for DOC. The organic ligands that bind metals are humic and fulvic compounds (HydroQual, 

2005). At least some of these compounds can be measured by UV absorption spectroscopy or related 

methods (Kalbitz et al., 2000; Wang and Hsieh, 2001), which may be easier and less expensive than 

DOC analysis. 

B.5 References

Allen, H.E. and K.H. Mancy. 1972. Design of measurement systems for water analysis. In: Ciaccio, L.L., 

ed. Water and water pollution handbook. Marcel Dekker, Inc. New York, N.Y.

Carleton, J.N. 2006. An Examination of Spatial Trends in Surface Water Chemistry in the Continental 

United States: Implications for the Use of Default Values as Inputs to the Biotic Ligand Model 

for Prediction of Acute Metal Toxicity to Aquatic Organisms U.S. Environmental Protection 

Agency, Office of Water, Office of Science & Technology. 

Chanat, J.G., Rice, K.C. and G.M. Hornberger. 2002. Consistency of patterns in concentration-discharge 

plots. Water Resources Research, 38 (8): 22-1.

Christensen, V.G., Jain, X. and A.C. Ziegler. 2005. Regression Analysis and Real-Time Water-Quality 

Monitoring to Estimate Constituent Concentrations, Loads, and Yields in the Little Arkansas 

River, South-Central Kansas, 1995-99. U.S. Geological Survey, Water-Resources Investigations 

Report 00-4126

USEPA. 2002. Development of Methodologies for Incorporating the Copper Biotic Ligand Model (BLM) 

into Aquatic Life Criteria: Application of BLM to Calculate Site-Specific Fixed Criteria. Prepared 

by Great Lakes Environmental Center (GLEC) for U.S. Environmental Protection Agency, Office 

of Science and Technology, Health and Ecological Criteria Division, Contract No.68-C-980134 

Work Assignment 3-38. 63 pp.

Feth, J. H., Roberson, C. E., and W.L. Polzer. 1964. Sources of mineral constituents in water from 

granitic rocks, Sierra Nevada, California and Nevada: U.S. Geological Survey Water-Supply Paper 

1535-L 70 p.

Godsey, S.E. and J.W. Kirchner. 2005. Concentration-Discharge Relationships Across Temporal and 

Spatial Scales, Eos Trans. AGU, 86(52), Fall Meet. Suppl., Abstract H22B-04.

Hem, J.D. 1985. Study and Interpretation of the Chemical Characteristics of Natural Water. U.S. 

Geological Survey, Water Supply Paper 2254.
113

HydroQual, Inc. 2001. BLM-Monte User’s Guide, Version 2.0. HydroQual, Mahwah, NJ. October, 2001.

HydroQual, Inc. 2005. Biotic Ligand Model Windows Interface, Version 2.1.2, User’s Guide and 

Reference Manual. HydroQual, Mahwah, NJ. June, 2005.

Kalbitz, K., Geyer, S. and W. Geyer. 2000. A comparative characterization of dissolved organic matter 

by means of original aqueous samples and isolated humic substances. Chemosphere. 

40(12):1305-12, June 2000.

McCutcheon, S.C., Martin, J.L. and T.O. Barnwell, Jr. 1993. Water Quality, Section 11, Handbook of 

Hydrology, David Maidment, Ed., McGraw-Hill, New York. 

McDiffett, W.F., Beidler, A.W., Dominick, T.F. and K.D. McCrea. 1989. Nutrient concentration-stream 

discharge relationships during storm events in a first-order stream. Hydrobiologia. 179 (2) July, 

1989.

Roberson, C.E., Feth, J.H., Seaber, P.R., and P. Anderson. 1963. Differences between field and 

laboratory determinations of pH, alkalinity, and specific conductance of natural water. U.S. 

Geological Survey Professional Paper 475– C, p. C212–C215.

Tyson, J. 1988. Analysis: What analytical chemists do. London: The Royal Society of Chemistry.

USEPA. 1997. Volunteer Stream Monitoring: A Methods Manual. United States Environmental 

Protection Agency, Office of Water (4503F), EPA 841-B-97-003, November, 1997.

Wang, G.S. and S.T. Hsieh. 2001. Monitoring natural organic matter in water with scanning 

spectrophotometer. Environ. Int. 26(4):205-12.

Wang, X. and Z.Y. Yin. 1997. Using GIS to assess the relationship between land use and water quality at 

a watershed level. Environment International. 23(1): 103-114.
114

Appendix C: Development of Tools to Estimate Biotic Ligand Model Parameters

C.1 Introduction

The U.S. Environmental Protection Agency (EPA) explored using regression models that project BLM 

water quality parameters from conductivity data for sites where there may be few or no data available 

to characterize water. We demonstrated previously (USEPA, 2007) that conductivity (specific 

conductance) is significantly correlated to Biotic Ligand Model (BLM) water quality parameters 

between a large number of monitoring sites in three western states (Colorado, Utah, and Wyoming), 

especially for the low-end distribution statistics of interest for site-specific fixed water quality criteria 

calculations. Since conductivity data are also abundant, it is reasonable to incorporate conductivity in 

spatial projections of BLM parameters. 

C.2 Regression Analysis 

Water quality data were retrieved from the U.S. Geological Survey (USGS) National Water Information 

System (NWIS; http://waterdata.usgs.gov/nwis/qw). We focused our efforts on data collected from 

rivers and streams in the western states of Colorado, Utah, and Wyoming between 1984 and 2005. 

Data from these three states were selected because conductivity was known to vary substantially, and 

the legacy of past mining in the region made the contamination of waterbodies by trace metals a 

possibility. Data collected prior to 1984 was excluded because a number of the analytical methods 

used by USGS prior to that date have been replaced by methods with improved precision and lower 

detection limits. Furthermore, only sites with 40 or more samples were included in the analysis. Data 

were retrieved for all BLM water quality input parameters including pH, dissolved organic carbon (DOC) 

(or total organic carbon (TOC), if no DOC data were available) and the geochemical ions (GIs). We also 

retrieved discharge measurements and filtered (dissolved) copper concentration data, although these 

data were not included in the regression analysis.

In work described in Appendix B, we found that the correlation structure between conductivity and the 

BLM water quality parameters was much stronger at the lower end of the concentration distributions. 

For various low-end distribution statistics, all of the BLM water quality parameters were significantly 

correlated to conductivity, having non-zero rank correlation coefficients at the 0.001 significance level. 

The correlation coefficients for pH and DOC were lower than for the GIs, but were nevertheless 

significant. We exploited this feature of the data in our current work. For each site, we estimated the 

10th percentile (i.e., the value exceeded by 90% of the data) of conductivities and the 10th percentile of 

BLM water quality parameter values. We then fit regression models to project 10th percentiles of BLM 

parameter values as a function of 10th percentiles of conductivities. 

We also fit regression models to the full NWIS dataset (data for all rivers and streams sampled in 

Colorado, Utah, and Wyoming between 1984 and 2005). This was done out of concern that the lower 

percentile data might be skewed due to sampling bias, censoring, fewer sites, etc. The results of both 

approaches are presented below.

C.2.1 pH

The following regression model appeared to be optimum for projecting the 10th percentile of pH from 

the 10th percentile of conductivity at the sites for which appropriate data were available:

ln(pH) = 1.85 + 0.0352·ln(EC)
115

We did not fit a regression model to the full NWIS dataset, because no trend was evident between 

conductivity and pH.

C.2.2 DOC

The following regression model appeared to be optimum for projecting the 10th percentile of DOC 

concentrations from the 10th percentile of conductivity at the sites for which appropriate data were 

available:

ln(DOC) = 0.671·ln(EC) – 1.60

As with pH, we did not fit a regression model to the full NWIS dataset, since no trend was evident 

between conductivity and DOC.

C.2.3 Alkalinity

The following regression model appeared to be optimum for projecting the 10th percentile of alkalinity 

concentrations from the 10th percentile of conductivity at the sites for which appropriate data were 

available:

ln(alkalinity) = 1.14·ln(EC) – 4.68

For the full NWIS dataset, the following regression model was developed to project alkalinity 

concentrations from conductivity:

ln(alkalinity) = 0.652·ln(EC) + 0.530

C.2.4 Calcium

The following regression model appeared to be optimum for projecting the 10th percentile of calcium 

concentrations from the 10th percentile of conductivity at the sites for which appropriate data were 

available:

ln(Ca) = 1.14·ln(EC) – 4.35

For the full NWIS dataset, the following regression model was developed to project calcium 

concentrations from conductivity:

ln(Ca) = 0.866·ln(EC) - 1.51

C.2.5 Magnesium

The following regression model appeared to be optimum for projecting the 10th percentile of 

magnesium concentrations from the 10th percentile of conductivity at the sites for which appropriate 

data were available:

ln(Mg) = 1.27·ln(EC) – 4.81

For the full NWIS dataset, the following regression model was developed to project magnesium 

concentrations from conductivity:

ln(Mg) = 0.986·ln(EC) – 3.48
116

C.2.6 Sodium

The following regression model appeared to be optimum for projecting the 10th percentile of sodium 

concentrations from the 10th percentile of conductivity at the sites for which appropriate data were 

available:

ln(Na) = 0.578·ln(EC) – 2.62

For the full NWIS dataset, the following regression model was developed to project sodium 

concentrations from conductivity:

ln(Na) = 1.32·ln(EC) – 4.96

C.2.7 Potassium

The following regression model appeared to be optimum for projecting the 10th percentile of 

potassium concentrations from the 10th percentile of conductivity at the sites for which appropriate 

data were available:

ln(K) = 0.882·ln(EC) – 3.29

For the full NWIS dataset, the following regression model was developed to project potassium 

concentrations from conductivity:

ln(K) = 0.647·ln(EC) – 3.04

C.2.8 Sulfate

The following regression model appeared to be optimum for projecting the 10th percentile of sulfate 

concentrations from the 10th percentile of conductivity at the sites for which appropriate data were 

available:

ln(SO4) = 1.16·ln(EC) – 4.85

For the full NWIS dataset, the following regression model was developed to project sulfate 

concentrations from conductivity:

ln(SO4) = 1.43·ln(EC) – 4.47

C.2.9 Chloride

For the full NWIS dataset, the following regression model was developed to project chloride 

concentrations from conductivity:

ln(chloride) = 1.39·ln(EC) - 6.15

Unfortunately, there were an insufficient number of sites reporting chloride data for a regression 

model to be developed for the 10th percentile of chloride. 

C.3 Application of Conductivity Regressions

There are a number of ways in which the conductivity regressions could be used to project BLM water 

quality inputs. However, the most important situation may be when a fixed copper criteria value must 

be calculated for a site where there may be little data available to characterize water quality. In such 

cases, the regressions allow some or all of the BLM water quality inputs to be projected from either (1) 
117

a limited number of conductivity measurements or (2) a low-end conductivity value estimated by 

geostatistical or other methods. The first approach, projecting BLM water quality inputs from 

conductivity measurements, will be demonstrated in this section for a limited number of test sites. The 

second approach, projecting the BLM water quality inputs based on conductivities estimated by 

geostatistical methods, is demonstrated in the following section (Section C4). 

The regression models presented above for projecting BLM water quality inputs from conductivity 

were tested using data and BLM predictions from a number of sites. For each site, a fixed copper 

criteria value was calculated using the Monte Carlo method described in EPA 2002. The BLM version 

2.2.3 was used for all BLM calculations. Fixed copper criteria values were determined by the Monte 

Carlo method, utilizing site-specific data for parameter distributions and variance-covariance structure 

of all BLM water quality parameter inputs as well as filtered copper concentrations. The test sites 

(below) were selected on the basis of convenience, number of water quality observations, and 

geographic location.

The BLM water quality inputs projected from the conductivity regressions are low-end percentiles 

appropriate for predicting the instantaneous criterion (IC) predicted by the BLM to estimate the fixed 

site criteria (FSC) value. We suggested this approximation previously, based on the observation that 

protective FSC for copper generally corresponded to approximately the 2.5th percentile of the 

distribution of IC predicted by the BLM. BLM estimates made for a site using the corresponding 

percentiles of the water quality parameter distributions will be a conservative approximation of this 

protective criteria values. For the present work, we are using this approach to test the 10th percentile 

water quality parameter values projected from the conductivity regressions.

Previously we noted that filtered copper concentrations were correlated to BLM input water quality 

parameters at many sites. Furthermore, we found that the degree of correlation between copper 

concentrations and BLM input parameters appeared to be an important site-specific factor in 

determining the relationship between the FSC and the IC. Copper concentrations are not required to 

run the BLM in its toxicity prediction mode, but they are used in the Monte Carlo method to determine 

the FSC. Because of this, we calculated the FSC both with and without (neglecting) the correlation 

between copper concentrations and BLM input parameters at each test site.

C.3.1 Naugatuck River, Connecticut

The USGS has sampled the Naugatuck River near Waterville, Connecticut (Station 01208049) since 

1967. Ninety-one water samples collected since 1984 provided near-concurrent measurements of all 

BLM water quality inputs and filtered copper concentrations. The water is low in hardness and 

alkalinity, slightly acidic (mean pH = 7.32), and fairly low in conductivity (10th percentile = 134 μS/cm at 

25o C). Organic carbon concentrations are representative for rivers and streams in this region and 

nationwide (logmean TOC = 4.02 mg/L), and the filtered copper concentrations are low (logmean 

filtered copper = 3.62 μg/L). The FSC for copper at this site was calculated to be 11.4 μg/L when the 

correlation between copper concentrations and BLM parameters was considered, and 7.0 μg/L when 

this correlation was neglected. Test results at this site are show in Table C-1.
118

Table C-1. Copper Fixed Site Criterion predictions for the Naugatuck River, Connecticut using various 

calculation methods

Calculation Method DOC (mg/L) pH Geochemical Ions

Copper Fixed 

Site Criterion 

(μg/L)

Monte Carlo FSC with [copper] 

correlated to inputs (r =0.7) Data Data Data 11.4

Monte Carlo FSC with no 

[copper] correlation Data Data Data 7.0

IC calculated with 10th % of input 

data 2.8 (10th % of data) 7.1 (10th % of data) (10th % of data) 6.4

IC calculated with input from 

10th % of conductivity and 

correlations 

5.49 (projected 

from correlations)

7.55 (projected 

from 

correlations)

(projected from 

correlations) 21.5

IC calculated with input from 

10th % of conductivity and 

correlations except DOC

2.7 (10th % from L3 

ecoregion)

7.55 (projected 

from 

correlations)

(projected from 

correlations) 10.5

IC calculated with input from 

10th % of conductivity and 

correlations except pH & DOC

2.7 (10th % from L3 

ecoregion)

7.1 (10th % of 

data)

(projected from 

correlations) 5.7

IC calculated with input from 

10th % of conductivity and 

correlations except pH & DOC

2.8 (10th % of data) 7.1 (10th % of 

data)

(projected from 

correlations) 5.9

The BLM was then applied to predict IC for copper, using low-end percentiles of the measured BLM 

water quality inputs. Using the 10th percentile values of all measured input data, an IC of 6.4 μg/L was 

predicted. This IC is 43% smaller than the FSC calculated considering the copper correlation, but only 

21% smaller than the FSC neglecting this correlation. When the 10th percentiles of all of the BLM water 

quality inputs were instead projected from conductivity using the regression models, the predicted ICs 

were 21.7 μg/L (using the regressions based on 10th percentiles of the three-state data) and 21.5 μg/L 

(using the regressions based on all of the data). These results illustrate two important points. First, the 

BLM predictions based on water quality inputs all projected from conductivity correlations are quite 

different from BLM predictions based on site data; this will be further considered below. Secondly, 

however, the BLM predictions based on projected water quality inputs do not really depend on which 

correlations are used. 

Clearly, this result shows that the regression models are unable to accurately project all BLM water 

quality inputs at this site. However, this was almost entirely due to inaccuracy in the pH and organic 

carbon projections. To demonstrate this, we recalculated the IC several times, using better estimates 

of the organic carbon and/or pH data, but all other BLM water quality inputs projected from 

conductivity using the regression models. The first recalculation was made using the 10th percentile of 

DOC from rivers and streams in the Northeastern Coastal Zone, the Level III ecoregion where the 
119

Naugatuck River is located.

7 In this case the predicted IC was 10.5 μg/L, a value much closer to the FSCs 

as well as the IC calculated using the 10th percentile values of all the measured input data. A second 

recalculation was made using the 10th percentile of the pH data, together with the ecoregional 10th

percentile of DOC and all other BLM water quality inputs projected from conductivity using the 

regression models. Finally, a third recalculation was made in which the 10th percentiles of both pH and 

DOC data were input, with the remaining BLM water quality inputs projected from conductivity using 

the regression models. For both of these cases, the ICs were within about 10% of the prediction made 

using the 10th percentile values of all the measured input data. In summary, if BLM predictions are 

made for copper IC using measured values of pH and organic carbon, minimal error results from 

projecting the other BLM water quality inputs using conductivity and the regression models. As will be 

shown in the following sections, the same result was found for the other test sites.

The correlation between filtered copper concentrations and BLM parameters and output was quite 

strong at this location (r = 0.70 between filtered copper and IC predictions). As a result, the FSC 

corresponds to an elevated percentile (40%) of the IC predictions. If this correlation is neglected in the 

Monte Carlo method, the FSC corresponds to only the 14th percentile of the IC predictions. This 

suggests that the relationship between FSC and IC (in terms of the percentile of the IC distribution 

corresponding to the FSC) may be somewhat site-specific. Regardless of this complication, the 

conductivity regressions appear to project reliable low-end percentile estimates of the BLM water 

quality inputs other than pH and organic carbon. This was demonstrated by repeating the analysis 

described above using 5th, 2.5th, and 1st percentile input values and projections, each of which 

produced comparable results (not shown).

C.3.2 San Joaquin River, California

The USGS has sampled the San Joaquin River near Vernalis, California (Station 1130500) since 1950. 

Water samples collected since 1984 provided 283 near-concurrent measurements of all BLM water 

quality inputs and 77 filtered copper concentrations. The water has moderate values of hardness and 

alkalinity, neutral pH, and moderately high conductivity (10th percentile = 307 μS/cm at 25o C). DOC

concentrations are representative for rivers and streams in this region and nationwide (logmean DOC = 

5.35 mg/L), and the filtered copper concentrations are low (logmean filtered copper = 1.75 μg/L). The 

FSC for copper at this site was calculated to be 39.1 μg/L, and the correlation between copper 

concentrations and BLM parameters was strong (r = 0.624 between filtered copper and IC predictions). 

This FSC value corresponds to the 46th percentile of the distribution of IC. When the FSC for copper was 

recalculated assuming no correlation between copper concentrations and BLM parameters, the value 

decreased to 11.1 μg/L (corresponding to the 4.5th percentile of the IC distribution). Test results at this 

site are tabulated Table C-2.

 

7 Ecoregion and water body-type specific DOC concentration percentiles were tabulated for the Methodology for Deriving 

Ambient Water Quality Criteria for the Protection of Human Health (2000), Technical Support Document Volume 2: 

Development of National Bioaccumulation Factors (EPA-822-R-03-030).
120

Table C-2. Copper Fixed Site Criterion predictions for the San Joaquín River, California using various 

calculation methods

Calculation Method DOC (mg/L) pH Geochemical Ions

Fixed Site 

Criterion 

(μg/L)

Monte Carlo FSC with [copper] 

correlated to inputs (r =0.6) Data Data Data 39.1

Monte Carlo FSC with no 

[copper] correlation Data Data Data 11.1

IC calculated with 10th % of input 

data 2.7 (10th % of data) 7.5 (10th % of data) (10th % of data) 11.9

IC calculated with input from 

10th % of conductivity and 

correlations 

9.38 (projected 

from correlations)

7.77 (projected 

from 

correlations)

(projected from 

correlations) 54.0

IC calculated with input from 

10th % of conductivity and 

correlations except DOC

2.79 (10th % from L3 

ecoregion)

7.77 (projected 

from 

correlations)

(projected from 

correlations) 16.0

IC calculated with input from 

10th % of conductivity and 

correlations except pH & DOC

2.79 (10th % from L3 

ecoregion)

7.5 (10th % of 

data)

(projected from 

correlations) 11.6

IC calculated with input from 

10th % of conductivity and 

correlations except pH & DOC

2.7 (10th % of data) 7.5 (10th % of 

data)

(projected from 

correlations) 11.2

The BLM was then applied to predict IC for copper, using low-end percentiles of the BLM water quality 

inputs. Using the 10th percentile values of all measured input data, an IC of 11.9 μg/L was predicted, 

which is 70% smaller than the FSC calculated considering the copper concentration correlation but 7% 

higher than the FSC neglecting this correlation. When the 10th percentiles of all of the BLM water 

quality inputs were instead projected from conductivity using the regression models, the predicted IC 

were 50.0 μg/L (using the regressions based on 10th percentiles of the three-state data) and 54.0 μg/L 

(using the regressions based on all of the data). Again, the BLM predictions based on projected water 

quality inputs do not really depend on which correlations are used. And, as was the case at the 

Naugatuck River site, the regression models were unable to accurately project all BLM water quality 

inputs at this site, although the error is again almost entirely due to inaccuracy in the pH and organic 

carbon projections. As in the previous case, we demonstrated this by recalculating the IC several times, 

using better estimates of the organic carbon and/or pH data, but all other BLM water quality inputs 

projected from conductivity using the regression models. The first recalculation was made using the 

10th percentile of DOC from rivers and streams in the Central California Valley, the Level III ecoregion 

where the San Joaquin River is located. In this case the predicted IC was 16.0 μg/L, a value much closer 

to the uncorrelated FSCs as well as the IC calculated using the 10th percentile values of all the 

measured input data. A second recalculation was made using the 10th percentile of the pH data, 

together with the ecoregional 10th percentile of DOC and all other BLM water quality inputs projected 

from conductivity using the regression models. Finally, a third recalculation was made in which the 10th

percentiles of both pH and DOC data were input, with the remaining BLM water quality inputs 

projected from conductivity using the regression models. For both of these cases, the ICs were within 
121

about 5% of the prediction made using the 10th percentile values of all the measured input data. BLM 

predictions made for copper IC at this site using measured values of pH and organic carbon, but all 

other BLM water quality inputs projected using conductivity regressions, were found to be accurate in 

comparison to model predictions made using all measured input data.

C.3.3 South Platte River, Colorado

The South Platte River has been sampled by the USGS at Denver, Colorado (Station 06714000) since 

1972. Water samples collected since 1984 provided 93 near-concurrent measurements of all BLM 

water quality inputs and 10 filtered copper concentrations. The water is moderately high in hardness 

and alkalinity, neutral pH, and moderate conductivity (10th percentile = 229 μS/cm at 25° C). Organic 

carbon concentrations are representative for rivers and streams in this region (logmean DOC = 5.50 

mg/L), and the filtered copper concentrations are low (logmean filtered copper = 3.27 μg/L). The FSC 

for copper at this site was calculated to be 35.4 μg/L. This FSC value corresponds to the 32nd percentile 

of the distribution of IC. Moderate correlation between copper concentrations and BLM parameters 

was observed at this site (r = 0.50 between filtered copper and IC predictions). When the FSC for 

copper was recalculated assuming no correlation between copper concentrations and BLM 

parameters, the value decreased to 20 μg/L (corresponding to the 4.3rd percentile of the IC 

distribution). Test results at this site are shown in Table C-3. 

Table C-3. Copper Fixed Site Criterion predictions for the South Platte River, Colorado using various 

calculation methods

Calculation Method DOC (mg/L) pH Geochemical Ions

Copper Fixed 

Site Criterion 

(μg/L)

Monte Carlo FSC with [copper] 

correlated to inputs (r =0.5) Data Data Data 35.4

Monte Carlo FSC with no [copper] 

correlation Data Data Data 20.0

IC calculated with 10th % of input 

data 4.1 (10th % of data) 7.5 (10th % of data) (10th % of data) 17.3

IC calculated with input from 10th % 

of conductivity and correlations 

7.7 (projected from 

correlations)

7.7 (projected 

from 

correlations)

(projected from 

correlations) 37.5

IC calculated with input from 10th % 

of conductivity and correlations 

except DOC

4.5 (10th % from L3 

ecoregion)

7.7 (projected 

from 

correlations)

(projected from 

correlations) 21.6

IC calculated with input from 10th % 

of conductivity and correlations 

except pH & DOC

4.5 (10th % from L3 

ecoregion)

7.5 (10th % of 

data)

(projected from 

correlations) 17.3

IC calculated with input from 10th % 

of conductivity and correlations 

except pH & DOC

4.1 (10th % of data) 7.5 (10th % of 

data)

(projected from 

correlations) 15.9
122

The BLM was applied to predict IC for copper, using low-end percentiles of the BLM water quality 

inputs. Using the 10th percentile values of all measured input data, an IC of 17.3 μg/L was predicted, 

which is 51% smaller than the FSC calculated considering the copper concentration correlation but only 

14% smaller than the FSC neglecting this correlation. When the 10th percentiles of all of the BLM water 

quality inputs were instead projected from conductivity using the regression models, the predicted IC 

was 37.5 μg/L. As was the case at the previous sites, the regression models were again unable to 

accurately project pH and organic carbon concentrations for input to the BLM. We demonstrated this 

by recalculating the IC several times, using better estimates of the organic carbon and/or pH data, but 

all other BLM water quality inputs projected from conductivity using the regression models. The first 

recalculation was made using the 10th percentile of DOC from rivers and streams in the Western High 

Plains, the Level III ecoregion where the South Platte River is located. In this case the predicted IC was 

21.6 μg/L, a value much closer to the uncorrelated FSCs as well as the IC calculated using the 10th

percentile values of all the measured input data. A second recalculation was made using the 10th

percentile of the pH data, together with the ecoregional 10th percentile of DOC and all other BLM 

water quality inputs projected from conductivity using the regression models. Finally, a third 

recalculation was made in which the 10th percentiles of both pH and DOC data were input, with the 

remaining BLM water quality inputs projected from conductivity using the regression models. For both 

of these cases, the ICs were within 10% of the prediction made using the 10th percentile values of all 

the measured input data. As with the previous cases, the BLM predictions made for copper IC at this 

site using measured values of pH and organic carbon, but where all other BLM water quality inputs 

were projected using conductivity regressions, were found to be accurate in comparison to model 

predictions made using all measured input data.

C.3.4 Halfmoon Creek, Colorado

The USGS has sampled Halfmoon Creek near Malta, Colorado (Station 07083000) since 1959. Seventythree water samples collected since 1984 provided near-concurrent measurements of all BLM water 

quality inputs and 18 filtered copper concentrations. The water is very low in hardness and alkalinity, 

slightly acidic (mean pH = 7.76), and low in conductivity (10th percentile = 50.1 μS/cm at 25° C). Organic 

carbon concentrations are low (logmean DOC = 0.92 mg/L), as are the filtered copper concentrations 

(logmean filtered copper = 1.75 μg/L). The FSC for copper at this site was calculated to be 1.56 μg/L, 

corresponding to the 6th percentile of the distribution of IC. The correlation between copper 

concentrations and BLM parameters was negligible at this site, so the Monte Carlo FSC were not 

calculated twice (i.e., with and without the copper correlation) as was done at the other sites. Test 

results at this site are shown in Table C-4.
123

Table C-4. Copper Fixed Site Criterion predictions for the Halfmoon Creek, Colorado using various 

calculation methods

Calculation Method DOC (mg/L) pH Geochemical Ions

Copper Fixed 

Site Criterion 

(μg/L)

Monte Carlo FSC with [copper] 

correlated to inputs (r =0.01) Data Data Data 1.56

IC calculated with 10th % of input 

data 0.6 (10th % of data) 7.2 (10th % of data) (10th % of data) 1.42

IC calculated with input from 10th % 

of conductivity and correlations 

2.8 (projected from 

correlations)

7.3 (projected 

from 

correlations)

(projected from 

correlations) 7.43

IC calculated with input from 10th % 

of conductivity and correlations 

except DOC

0.6 (10th % from L3 

ecoregion)

7.3 (projected 

from 

correlations)

(projected from 

correlations) 1.58

IC calculated with input from 10th % 

of conductivity and correlations 

except pH & DOC

0.6 (10th % from L3 

ecoregion)

7.2 (10th % of 

data)

(projected from 

correlations) 1.39

IC calculated with input from 10th % 

of conductivity and correlations 

except pH & DOC

0.6 (10th % of data) 7.2 (10th % of 

data)

(projected from 

correlations) 1.39

The BLM was then applied to predict IC for copper, using low-end percentiles of the BLM water quality 

inputs. Using the 10th percentile values of all measured input data, an IC of 1.42 μg/L was predicted, 

only 9% smaller than the FSC. When the 10th percentiles of all of the BLM water quality inputs were 

instead projected from conductivity using the regression models, the predicted IC was 7.43 μg/L. Again, 

this result clearly shows that the regression models are unable to accurately project all BLM water 

quality inputs at this site. As in the previous examples, this was almost entirely due to inaccuracy in the 

pH and organic carbon projections. As in the previous cases, we demonstrated this by recalculating the 

IC several times, using better estimates of the organic carbon and/or pH data, but all other BLM water 

quality inputs projected from conductivity using the regression models. The first recalculation was 

made using the 10th percentile of DOC from rivers and streams in the Southern Rockies, the Level III 

ecoregion where Halfmoon Creek is located. In this case the predicted IC was 1.58 μg/L, a value within 

about 10% of the FSC as well as the IC calculated using the 10th percentile values of all the measured 

input data. A second recalculation was made using the 10th percentile of the pH data, together with the 

ecoregional 10th percentile of DOC and all other BLM water quality inputs projected from conductivity 

using the regression models. Finally, a third recalculation was made in which the 10th percentiles of 

both pH and DOC data were input, with the remaining BLM water quality inputs projected from 

conductivity using the regression models. For both of these cases, the ICs were within about 2% of the 

prediction made using the 10th percentile values of all the measured input data. As in the previous 

examples, if BLM predictions are made for copper IC using measured values of pH and organic carbon, 

minimal error results from projecting the other BLM water quality inputs using conductivity and the 

regression models.
124

C.3.5 Summary of Site-Specific Test Results

The results of this work can be summarized as follows:

Regression models were developed to project 10th percentiles of BLM water quality parameters from 

the 10th percentile of conductivity distributions at sites in Colorado, Utah, and Wyoming. The 

regression models were tested using data and copper BLM predictions for four sites, and produced 

highly consistent results. The regression models for pH and DOC, the most sensitive of BLM water 

quality parameters, were not sufficiently accurate to make reliable BLM predictions. However, 

regression models for the GI parameters (alkalinity, calcium, magnesium, sodium, potassium, sulfate, 

and chloride, ) were reasonably accurate, as judged by comparison of model predictions made using 

projected values of the GI BLM input parameters to model predictions made using all measured input 

data. The regression models used to project GI parameters from conductivity were calculated two 

different ways; however, the BLM predictions of IC were not sensitive to this difference.

We were unable to find an estimate for site-specific pH that was superior to the (admittedly poor) 

conductivity regression. To improve upon this estimate it was necessary to use actual site-specific pH 

data. This appears to be the general case for reliable site-specific BLM application.

For DOC, the ecoregion and water body-type specific DOC concentration percentiles tabulated by EPA 

for the National Bioaccumulation Factors Technical Support Document appear to be far better 

estimates of lower-percentile DOC concentrations than the projections made using the conductivity 

regression. These tabulations are based on an organic carbon database compiled prior to 2003 from a 

number of sources including EPA’s STOrage and RETrieval Data Warehouse (STORET) and the USGS 

NWIS. The utility of these tabulations could be improved by updating them to incorporate newer 

information. For example, EPA recently released data from the Wadeable Stream Assessment, which 

included DOC measurements from a statistically based random sample of ~2,000 streams. Other 

statistically-based national water quality surveys, including national assessments of lakes and large 

rivers, will also be providing additional data in future years.

The Monte Carlo method developed to calculate FSC for copper was applied at each of the four sites, 

both with and without the correlation between filtered copper concentrations and the BLM water 

quality parameters that were found to be significant at three of the sites. We also approximated the 

FSC using the 10th percentile of the distribution of IC predicted by the BLM at each site. When copper 

concentration correlations were considered in the FSC calculations, the 10th percentile of the IC 

distributions was found to be highly conservative approximations of the FSC, underestimating the FSC 

by 44 to 70%. This is illustrated in Figure C-1, which also shows the good agreement between IC 

predicted with the BLM using site-specific data and IC predicted using measured pH and organic carbon 

but projected values of the GI BLM input parameters. Ecoregion and water body-type specific DOC 

concentration percentiles (“L3-DOC” in the figure below) were also an improvement over the 

projections based on conductivity regressions.
125

Figure C-1. Instantaneous Criteria (IC) predicted with the BLM using site-specific data and IC 

predicted using measured pH and organic carbon and projected values of the GI BLM input 

parameters

When copper concentration correlations were neglected in the FSC calculations, the 10th percentile of 

the IC distributions did a much better job approximating the FSC. This is shown in Figure C-2. In this 

case, the 10th percentile of the IC distributions was within 15% of the FSC. This figure also shows the 

good agreement between IC predicted with data and projected values of the GI BLM input parameters.

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35 40 45

Copper FSC (ug/L) calculated with copper concentration correlation

Copper IC (ug/L)

IC (10th % of data) 

IC (10th % of conductivity & correlations) 

IC (10th % conduct/correl. except L3-DOC)

IC (10th % conduct/correl. except pH & DOC)

ISC = FSC
126

Figure C-2. 10th percentile of the IC distributions using data and projected (predicted) values of the GI 

BLM parameters

The degree of correlation between filtered copper concentrations and BLM input water quality 

parameters appears to be an important site-specific factor in determining the relationship between the 

FSC and the IC. Figure C-3 plots the percentile of the IC corresponding to the FSC for each site as a 

function of the correlation coefficient between the copper concentrations and the IC, for two cases: (1) 

FSC calculated by the Monte Carlo method including the observed correlations between 

concentrations of copper and BLM input water quality parameters, and (2) FSC calculated with no 

correlation between concentrations of copper and BLM input water quality parameters. In the first 

case (plotted with dark diamond symbols), the percentile of the IC corresponding to the FSC increases 

substantially (6th to 46th percentile) as the correlation coefficient between the copper concentrations 

and the IC increases. If the correlation between concentrations of copper and BLM input water quality 

parameters is neglected (the second case, plotted in lighter square symbols), the percentile of the IC 

corresponding to the FSC is considerably lower (4.3rd to 14th percentile). This suggests that correlations 

between copper concentrations and BLM input parameters should be given careful consideration when 

calculating FSC.

0

10

20

30

40

50

60

0 5 10 15 20 25

Copper FSC (ug/L) calculated with no copper concentration correlation

Copper IC (ug/L)

IC (10th % of data) 

IC (10th % of conductivity & correlations)

IC (10th % conduct/correl. except L3-DOC)

IC (10th % conduct/correl. except pH & DOC)

ISC = FSC
127

Figure C-3. Percentile of the IC corresponding to the FSC for each site as a function of the correlation 

coefficient between the copper concentrations and the IC when the FSC is calculated with Copper 

correlation and when FSC is calculated without Copper correlation

C.4 Combining GI-Conductivity Regressions with Geostatistical Techniques

Geostatistical techniques are attractive because they explain parameter variation arising from spatial 

correlations, which are otherwise ignored by (and may, in fact, violate the assumptions of) 

conventional statistics. BLM input water quality parameters (except for pH and DOC) are GIs, the 

concentrations of which vary in surface water due to dissolution, weathering, ground water-surface 

water interactions, and other geologic processes in the watershed. Consequently, the concentrations 

of GI parameters tend to vary according to the regional geology. For example, water hardness has 

noticeable geographic trends. Areas with limestone geology, such as in the prairie states, tend toward 

high hardness and alkalinity. Areas of with granite geology, such as parts of the Northeast, tend toward 

low hardness and alkalinity. The estimation of GI parameter values based on geography thus seems 

possible. EPA has provided a prototype of a geostatistical approach8 that demonstrated this potential. 

That work applied kriging to predict median concentrations of five of the BLM water quality input 

parameters (pH, DOC, alkalinity, sodium, and calcium) averaged over 8-digit HUCs, using the USGS 

NWIS as the source of spatial data. Comparison of measured concentrations with kriging predictions 

were encouraging, especially for DOC and alkalinity. Geostatistical techniques to project BLM GI input 

 

0

5

10

15

20

25

30

35

40

45

50

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Correlation coefficient btwn. IC and filtered copper concentrations 

Percentile of IC corresponding to FSC

FSC calculated with copper correlation

FSC calculated with no copper correlation
128

parameters might well be developed from the same nationwide monitoring data used to develop a 

correlation approach. By the same token, geostatistical techniques based on these data may suffer the 

same problems experienced when developing the correlation approach. Most significantly, the NWIS 

data are not randomly distributed in either time or space, and the measurements of the BLM GI 

parameters are generally uneven (considerable differences in terms of the number of observations for 

different parameters) and/or inconsistent (i.e., relatively few concurrent measurements of BLM GI 

parameters). 

There may be great value in supplementing the geostatistical approach with classical estimation 

methods, such as regression and correlation. Examination of the NWIS data suggests that conductivity 

may be useful for estimating BLM input water quality parameters in conjunction with geostatistics. The 

literature indicates that conductivity is one of the most widely monitored water quality indicators in 

the US. Among water quality parameters, the data for conductivity are the most complete and cover

the longest time period (Wang and Yin, 1997). In part, this is because conductivity measurements are 

usually included in automated multiparameter systems for monitoring changes in the quality of surface 

waters (Allen and Mancy, 1972). A vast amount of conductivity data exists, both in terms of the total 

number of observations and the number of sites reporting this parameter in comparison to the BLM GI 

quality parameters. For example, NWIS data for the state of Colorado have almost four times as many 

observations of conductivity as for calcium, and they are measured at more than twice the number of 

sites. There are 20 times as many observations of conductivity as for alkalinity, and they are measured 

at more than seven times the number of sites. Since conductivity data are abundant, and correlate well 

to the BLM GI parameters (GLEC, 2007), it is reasonable to incorporate conductivity in spatial 

projections of BLM parameters. This may simplify the geostatistical approach and allow more robust 

spatial projections of BLM water quality parameters.

Although combining GI-conductivity regressions with geostatistical techniques seems promising for the 

reasons mentioned above, this approach had never been demonstrated. We conducted a simple test 

using NWIS conductivity and hardness data from the state of Colorado. We used data from Colorado 

because many more stations were sampled in comparison to the surrounding states. 

The data were processed in a manner similar to the methods used to develop the regressions in 

Section C.2. For each station, we calculated the 10th percentiles of conductivity and hardness. A 

regression model was fit to the full dataset (data for all rivers and streams sampled in Colorado

between 1984 to 2005). The following regression model was developed to project hardness from 

conductivity:

ln(hardness) = 0.984·ln(EC) – 0.870

We also kriged the 10th percentiles of conductivity and hardness, using latitude and longitude 

coordinates reported by USGS for each sampling station. Figure C-4 shows the kriged surface of the 

10th percentile of conductivity at all stations in Colorado, Utah, and Wyoming. Data are far more 

abundant in Colorado, as shown by the density of the dots representing the locations of sampling 

stations. Figure C-5 shows the kriged surface of the 10th percentile of hardness at all stations in 

Colorado. Kriging was done using the Vertical Mapper program, version 3.1; no attempts were made to 

optimize the kriging of conductivity or hardness by parameter adjustment.
129

Figure C-4. Kriged surface of the 10th percentile of conductivity at all stations in Colorado, Utah and 

Wyoming

Dots represent sampling stations; notice that data are far more abundant in Colorado.

Figure C-5. Kriged surface of the 10th percentile of hardness at all stations in Colorado

Our goal was to see whether combining the kriged conductivities with the conductivity-hardness 

regression would project the 10th percentiles of hardness better than direct kriging of the hardness 
130

data. For the combined kriging/regression approach, we determined the kriged conductivity values at 

all of the sampling locations and then projected the 10th percentiles of hardness at these locations 

using the regression equation. We also determined the directly-kriged 10th percentiles of hardness at 

all of the sampling locations. 

The hardness estimates obtained by each approach were then compared to the 10th percentiles of 

hardness measured at each station. The results of this comparison are shown graphically in Figure C-6. 

Both approaches produce estimates of hardness that correlate significantly with the measured data 

(correlation coefficient r= 0.80 for direct kriging of hardness; r= 0.950 for conductivity kriging + 

regression projection). However, the kriging+regression approach fits the hardness data substantially 

better than direct kriging. To quantify this, we calculated the residual sum of squares (RSS), a 

composite measure of the discrepancy between the data and our alternative hardness estimates. The 

smaller this discrepancy is, the better the estimation will be. In natural log space, the RSS for the 

kriging+regression approach is 18.6 (135 degrees of freedom, or df) while the log-space RSS for the 

direct kriging approach is 73.4 (136 df). Thus, for this test case substantially better estimates of the 10th

percentile of hardness were made by the kriging/regression approach compared to direct kriging.

Figure C-6. Comparison of the 10th percentile of hardness at all stations in Colorado with estimates 

based on (a) direct kriging of hardness data and (b) kriging of conductivity to station locations and 

projecting conductivity to hardness via regression (“kriging/regression”)

As this test demonstrated, combining kriging with regressions to project BLM GI inputs from 

conductivity appears to improve the accuracy of estimates of parameters used as BLM inputs. Applying 

the conductivity kriging/regression projection approach on a broader scale should be considered as a 

1

100

10000

1 100 10000

10th percentile hardness (data)

10th percentile hardness (kriged or projected)

kriged 10th % of hardness

projected 10th % of hardness

1:1 line (perfect fit)
131

“next step” in developing tools to estimate BLM water quality parameters for sites where there may be 

few or no data available to characterize water quality. Since direct kriging of most BLM GI parameters 

has already been done using data from NWIS, it will also be worthwhile to continue comparing the 

alternative estimates to the observed data in order to obtain the best estimates.

We should also note that although the kriging/regression approach can be used to improve the 

accuracy of estimates of GI parameters used as BLM inputs, this approach cannot be expected to 

produce accurate site-specific estimates for the two most important BLM inputs: pH and DOC. As 

shown in Section C.3, accurate estimates of the GI parameters are less important than pH and DOC in 

terms of predicting appropriate site-specific IC and FSC. Since our analysis of NWIS data indicates there 

to be either little no trend between conductivity and pH, and direct kriging produced similarly 

ambiguous predictions, we must conclude that site-specific data for pH must either be available or be 

collected for BLM application at a site. This may not be a significant obstacle, since pH data can be 

cheaply and readily acquired. 

Lack of methods to accurately estimate DOC is a bigger problem, since measurements of this 

parameter are comparatively rare and DOC is a relatively expensive measurement to make. For DOC, 

analysis of NWIS data again indicates no trend with conductivity, so the kriging/regression approach is 

not appropriate for this parameter. However, other analyses conducted suggested that DOC could be 

kriged with some success. And, as was demonstrated for the test sites in Section C.3, the ecoregion and 

water body-type specific DOC concentration percentiles tabulated by EPA for the National 

Bioaccumulation Factors Technical Support Document appear to offer reasonable estimates of lowerpercentile DOC concentrations. Further development of these approaches for estimating site-specific 

DOC appears worthwhile, for example by incorporating new data from the Wadeable Stream 

Assessment and other statistically-based national water quality surveys.

C.5 References

Allen, H.E. and K.H. Mancy. 1972. Design of measurement systems for water analysis. In: Ciaccio, L.L., 

ed. Water and water pollution handbook. Marcel Dekker, Inc. New York, N.Y.

USEPA. 2002. Development of Methodologies for Incorporating the Copper Biotic Ligand Model into 

Aquatic Life Criteria: Application of BLM to Calculate Site-Specific Fixed Criteria. GLEC Work 

Assignment 3-38, Contract No. 68-C-98-134. 63p plus figures.

USEPA. 2007. Approaches for Estimating Missing BLM Input Parameters: Correlation approaches to 

estimate BLM input parameters using conductivity and discharge as explanatory variables. GLEC 

Work Assignment 2-34, Task 1, Subtask 1-7. Contract No. 68-C-04-006. 18 p.

Wang, X. and Z.Y. Yin. 1997. Using GIS to assess the relationship between land use and water quality at 

a watershed level. Environment International. 23(1): 103-114.
132

Appendix D: Approaches for Estimating Missing Biotic Ligand Model Input 

Parameters: Projections of Total Organic Carbon as a Function of 

Biochemical Oxygen Demand

D.1 Introduction

The 2007 Update of the Ambient Water Quality Criteria for Copper (EPA-822-R-07-001) employs the 

Biotic Ligand Model (BLM) to estimate bioavailability of this metal in toxicity tests used in Criterion 

Maximum Concentration derivation, which requires data on the 10 input parameters for the BLM, 

including dissolved organic carbon (DOC). Data for DOC concentrations, in both effluents and receiving 

waters, are extremely limited. The BLM is very sensitive to DOC concentrations (HydroQual, 2005), 

which means that to ensure accurate predictions of copper bioavailability and toxicity reliable data on 

DOC concentrations in the water are needed. Effluent DOC concentrations, which are necessary for 

application of the BLM to predict copper toxicity associated with a wastewater discharge, are 

monitored by very few publicly-owned treatment works (POTWs). 

Projections of DOC concentrations from biochemical oxygen demand (BOD) values may be a viable 

solution for surmounting the lack of data on DOC. Effluent BOD (most typically 5-day BOD) is 

monitored by most POTWs. We expect a positive correlation between BOD and DOC, because the two

parameters are conceptually related. While DOC quantifies the concentration of many organic 

compounds dissolved in water, BOD is a routine surrogate test for estimating the load of organic 

carbon into the environment. Ideally, one might expect an almost stoichiometric relationship between 

organic carbon (i.e., DOC) and the oxygen consumed during its metabolization (i.e., BOD). For instance, 

Fadini et al. (2004) evaluated the possible replacement of BOD for DOC measurements in a number of 

different wastewater categories. A statistical relationship between effluent BOD and DOC would 

provide estimates of DOC concentrations, needed for application of the BLM, from routine BOD 

monitoring data. The effluent contribution to in-stream DOC could then be estimated, for example, by 

using a dilution model for a site.

Evidence, from analyses of effluent monitoring data from the New York State Department of 

Environmental Conservation (NYSDEC) Contaminant Assessment and Reduction Project (CARP), 

suggests that most of the total organic carbon (TOC) in POTW effluent is in the form of DOC. Therefore, 

a regression between BOD and TOC could be used as a surrogate for the relationship between BOD and 

DOC. The advantage of using TOC is the greater availability of data. TOC is reported for a significant 

number of major POTW dischargers. 

D.2 Data

In 2006, monitoring data from all major POTWs reporting TOC and 5-day BOD in the United States 

were downloaded from the U.S. Environmental Protection Agency (EPA) Permit Compliance System

(PCS) web site http://www3.epa.gov/enviro/facts/pcs-icis/search.html. Nine POTWs had 30 or more 

synchronous records of TOC and BOD, while 23 POTWs had at least 10 synchronous records. These 

numbers include both monthly average and maximum monthly values. 

Review of the data indicated several extremely high (>1,000 milligrams per liter [mg/L]) effluent TOC 

values for discharger CA0079243. We assumed that they presented errors in the reported unit, and 

divided them by 1,000 to convert from units of microgram per liter (μg/L) to mg/L. TOC and BOD 
133

records were matched by POTW, location (e.g., upstream, downstream, influent or effluent), year and 

month. Thus, “synchronous” measurements do not necessarily correspond to samples collected on the 

same day and time. The resulting table had 341 records.

D.3 Results

D.3.1 TOC and BOD at All Monitoring Locations

The first statistical evaluation involved data for all monitoring locations at the eight POTWs reporting 

30 or more synchronous records of TOC and BOD. Table D-1 presents the results of least squares 

regression of the average monthly data: TOCavg = a + b BODavg. A scatter plot of this data is shown in 

Figure D-1. Table D-2 presents the results of least squares regression of the maximum monthly data: 

TOCmax = a + b BODmax. A scatter plot of this data is shown in Figure D-2. Bimodal distributions are 

observed for TOC and especially BOD in this data set. It should be noted that the BOD concentrations 

of 200 mg/L or higher were measured in samples of untreated (influent) wastewater; TOC 

concentrations were also quite high in these samples. Both scatter plots (Figures D-1 and D-2) show a 

fairly strong correlation between TOC and BOD in the combined data for all POTWs. The linear 

relationship between TOC and BOD is better defined in the average data (Figure D-1).

Table D-1. Least squares regression of average monthly TOC and BOD data for all monitoring 

locations

POTW Location Intercept (a) Slope (b) r

2 df

CA0054372 Effluent Gross Value 

CA0105295 Effluent Gross Value 7.551 -0.379 0.009 41

CA0105295 Raw Sew/Influent 19.935 0.142 0.104 59

CA8000326 Effluent Gross Value* 

CA8000383 Effluent Gross Value 4.952 0.725 0.344 31

CA8000383 Raw Sew/Influent 59.586 0.107 0.038 30

ID0020443 Upstream Monitoring* 

ID0020443 Downstream Monitoring 3.500 -0.400 0.190 2 

ID0023981 Effluent Gross Value 6.268 0.281 0.196 26

ID0023981 Upstream Monitoring 3.200 -0.300 0.127 3 

LA0073521 Effluent Gross Value* 

TN0023353 Effluent Gross Value 2.628 0.391 0.438 35

All POTWs All locations 4.828 0.237 0.873 243

*note: POTW/location without regression results indicates less than 2 synchronous data records
134

Figure D-1. Scatter Plot of Average Monthly Data (all Monitoring Locations)

Table D-2. Least squares regression of maximum monthly TOC and BOD data for all monitoring 

locations

POTW Location Intercept (a) Slope (b) r

2 df

CA0054372 Effluent Gross Value 9.420 0.499 0.154 29

CA0105295 Effluent Gross Value 8.567 -0.114 0.007 50

CA0105295 Raw Sew/Influent 56.439 0.062 0.046 59

CA8000326 Effluent Gross Value 7.307 0.006 0.000 28

CA8000383 Effluent Gross Value 6.674 0.507 0.235 31

CA8000383 Raw Sew/Influent 149.293 0.047 0.052 30

ID0020443 Upstream Monitoring 0.300 1.175 0.039 4 

ID0020443 Downstream Monitoring 3.500 -0.400 0.190 2 

ID0023981 Effluent Gross Value 6.210 0.208 0.202 28

ID0023981 Upstream Monitoring 3.200 -0.300 0.127 3 

LA0073521 Effluent Gross Value 12.989 -0.818 0.110 18

TN0023353 Effluent Gross Value* 

All POTWs All locations 11.183 0.196 0.700 302

TOCavg ~ BODavg (All Samples)

Biochemical Oxygen Demand (mg O2/L)

Total Organic Carbon (mg C/L)

0 100 200 300 400 500

0 50 100 150 200
135

Figure D-2. Scatter Plot of Maximum Monthly Data (all Monitoring Locations)

Results of regression analyses revealed large differences in slopes of the linear model TOC = a + b BOD 

among locations and POTWs. Slopes for individual regressions ranged from –0.40 to 0.73 for average, 

and from -0.82 to 0.50 for maximum BOD and TOC values. Coefficients of determination (r2) for the 

regressions were low; for most of them r2 < 0.2. Pooling the data from all POTWs and locations 

increased the r2 to 0.87 for average and 0.70 for maximum BOD and TOC values. 

Diagnosis of regression analyses revealed that variance in both the average and maximum TOC rose 

with increasing values of biochemical oxygen demand. Such patterns were also evident from a simple 

inspection of the plots cited above. Homogeneity of variance, though, is a core assumption of ordinary 

least squares regression, and its violation compromises the quality of results generated by the analysis. 

The solution was to perform quantile regression analysis because it does not assume that variance of 

the response is homogeneous along the range of the independent variable. The fitted model for the 

50th quantile (median) was:

TOCavg = 5.5647 + 0.2088 BODavg (243 df, R1 = 0.77)

D.3.2 TOC and BOD at Effluent Monitoring Locations 

Although the quantile regression model above provided a reasonable fit of the data at all monitoring 

locations, we were specifically interested in the relationship between TOC and BOD measured in POTW 

effluents. Therefore, we conducted a separate statistical analysis of effluent monitoring data from the 

17 POTWs with more than one synchronous record of TOC and BOD retrieved from PCS. TOC and BOD 

records were again matched by POTW, year, and month. The resulting data tabulation had 373 

records. 

TOCmax ~ BODmax (All Samples)

Biochemical Oxygen Demand (mg O2/L)

Total Organic Carbon (mg C/L)

0 500 1000 1500 2000

0 100 200 300 400
136

The results of least squares regression of the average monthly effluent data: TOCavg = a + b BODavg

are presented in Table D-3. A scatter plot of this data is shown in Figure D-3. Table D-4 presents the 

results of least squares regression of the effluent maximum monthly data: TOCmax = a + b BODmax. A 

scatter plot of this data is shown in Figure D-4.

Table D-3. Least squares regression of average monthly TOC and BOD data for effluent monitoring 

locations

POTW Intercept (a) Slope (b) r

2 df

CA0054372 

CA0077691 

CA0079103 

CA0079243 

CA0102822 

CA0105295 7.5512 -0.3789 0.009 41

CA0107492 

CA0109991 

CA8000073 

CA8000326 

CA8000383 4.9522 0.7254 0.344 31

ID0023981 6.2679 0.2808 0.196 26

LA0069868 

LA0073521 

TN0023353 2.6284 0.3909 0.438 35

TN0023531 37.6422 -1.1348 0.076 3 

TN0023574 7.4142 0.0882 0.016 25

All POTWs 5.8740 0.2859 0.245 174
137

Figure D-3. Scatter Plot of Average Monthly Data (Effluent Monitoring Locations)

TOCavg ~ BODavg (All Samples)

Biochemical Oxygen Demand (mg O2/L)

Total Organic Carbon (mg C/L)

0 10 20 30 40

0 5 10 15 20 25 30
138

Table D-4. Least squares regression of maximum monthly TOC and BOD data for effluent monitoring 

locations

POTW Intercept (a) Slope (b) r

2 df

CA0054372 9.4197 0.4993 0.154 29

CA0077691 4.2750 0.7008 0.422 6 

CA0079103 23.3517 -0.1278 0.035 16

CA0079243 5.7979 -0.0367 0.008 8 

CA0102822 6.3526 0.1780 0.195 28

CA0105295 8.5667 -0.1143 0.007 50

CA0107492 5.9043 1.0676 0.027 2 

CA0109991 3.0331 0.8458 0.167 11

CA8000073 9.0000 0.0000 0.000 8 

CA8000326 7.3073 0.0056 0.000 28

CA8000383 6.6743 0.5070 0.235 31

ID0023981 6.2101 0.2083 0.202 28

LA0069868 7.6475 0.1139 0.535 5 

LA0073521 12.9886 -0.8184 0.110 18

TN0023353 

TN0023531 

TN0023574 

All POTWs 6.6930 0.4311 0.276 299

Figure D-4. Scatter Plot of Maximum Monthly Data (Effluent Monitoring Locations)

TOCmax ~ BODmax (All Samples)

Biochemical Oxygen Demand (mg O2/L)

Total Organic Carbon (mg C/L)

0 20 40 60

0 20 40 60 80
139

Results of the effluent regression analyses revealed large differences in slopes of the linear model TOC 

= a + b BOD among POTWs. Slopes for individual regressions ranged from –1.13 to 0.73 for average, 

and from -0.82 to 1.07 for maximum BOD and TOC values. Coefficients of determination (r2

) for the 

regressions were low; all r2 < 0.55 and for most of them r2 < 0.24. Low coefficients of determination 

were also recorded for regressions of TOC on BOD values from all POTWs (r2 = 0.245 and 0.276, for 

average and maximum values, respectively). Further investigations of the effluent regression analyses 

were performed, because visual inspection of Figures D-3 and D-4 suggested the presence of outliers in 

the data.

We examined the fit of the linear model, TOCavg = a + b BODavg, by inspecting its residuals (Figure D5). Studentized residuals were plotted against projected (fitted) TOC values in the left pane, and 

against quantiles of the standard normal distribution in the right pane. Four suspiciously-low average 

TOC points in Figure D-4 are labeled ‘324’, ‘308’, plus the two points adjacent to the latter (left pane). 

This plot reveals that residuals for high-TOC points ‘489’ and ‘64’ are far larger in magnitude than 

residuals for the four suspiciously-low points. Residuals for these two points greatly deviate from the 

normal distribution (right pane). Furthermore, points ‘335’ and ‘336’ have much greater leverage than 

any other (leverages for ‘335’: 0.164, ‘336’: 0.127). Fitting the linear model without points ‘489’, ‘64’, 

‘335’, and ‘336’ results in the following parameter values:

TOCavg = 6.0388 + 0.2171 BODavg (r2 = 0.185, 170 df) (Equation 1)

Figure D-5. Residuals of the linear model, TOCavg = a + b BODavg

(Left: plot of Studentized residuals (studres) against projected (fitted) TOC values; Right: plot of studies 

against quantiles of the standard normal distribution).

It should be noted that this model (Equation 1) projects average TOC concentrations very similar to the 

regression based upon the uncensored data (i.e., within ± 2 mg/L), for the range of BOD concentrations 

of interest (less than 30 mg/L).

Diagnosis of the regression analysis, TOCmax = a + b BODmax, revealed an excessively high residue for 

the (19, 91) point and very high leverage for the (71, 31) point. The projected regression line without 

those two points was:

fitted(toc.lm)

studres(toc.lm)

6 8 10 12 14 16 18

-2

0

2

4

6

489

64

336

335

324 308

Quantiles of Standard Normal

studres(toc.lm)

-2 -1 0 1 2

-2

0

2

4

6
140

TOCmax = 6.6242 + 0.4095 BODmax (r2 = 0.352, 297 df) (Equation 2)

This model (Equation 2) fits a single slope for all data. Our results, though, revealed large differences in 

slopes of regression lines among POTWs (Table D-4). We tested the significance of such differences 

with an F-test, which required fitting two additional models, one with the same slope for all POTWs 

and the other with a distinct slope for each POTW. The F-test compares model fits while taking into 

account the loss in degrees of freedom associated with the computation of multiple slopes. The 

estimated F-value (F = 4.92, 13 df) was highly significant (P < 0.001), indicating that distinct slopes are 

necessary to accurately project maximum TOC from maximum BOD values.

D.3.3 TOC and DOC at CARP Effluent Monitoring Locations

Effluent discharge samples were collected from 11 New Jersey POTWs in 2000 and 2001 for the 

NYSDEC CARP project (www.dec.state.ny.us/website/dow/bwam/CARP). These samples were analyzed 

for DOC, particulate organic carbon (POC), and total suspended solids (TSS) by the U.S. Geological 

Survey. TOC was calculated by adding together DOC and POC concentrations. The results are shown in 

Table D-5. Effluent DOC concentrations are generally much higher than POC because most of the 

particulate organic matter is removed from wastewater during secondary treatment. A scatter plot of 

the TOC and DOC data, Figure D-6, shows the strong linear correlation between TOC and DOC that 

results from the predominance of DOC in effluent. These data are replotted in Figure D-7 for TOC 

concentrations less than 50 mg/L. 

Table D-5. CARP organic carbon and total suspended solids (TSS) monitoring data for New Jersey 

discharger

DATE SITE DOC (mg/L) POC (mg/L) TOC (mg/L) TSS (mg/L)

Oct. 2-4, 2000 PVSC 43.0 10.5 53.5 51.4

MCMUA 0.10 6.75 6.85 36.3

BCMUA 22.2 10.6 32.8 54.1

JMEU 8.51 8.29 16.8 19.2

RVMUA 12.2 3.81 16.0 22.1

LRMUA 8.76 4.71 13.5 9.3

Dec. 11-15, 2000 PVSC 50.3 5.35 55.7 25.9

MCMUA 260 9.22 269 62.6

BCMUA 20.0 2.73 22.8 14.4

JMEU 23.0 5.23 28.2 31.1

RVMUA 23.4 8.73 32.1 42.0

LRMUA 10.4 11.4 21.8 55.2

NHH 14.0 3.07 17.1 22.5

NBC 28.6 6.67 35.3 23.3

NBW 21.8 3.38 25.2 7.8

NHWNY 18.7 5.66 24.3 18.1

SMUA 15.8 2.89 18.6 6.6

May 21-23, 2001 PVSC 34.5 14.2 48.7 41.1

BCMUA 15.0 9.17 24.1 11.9
141

DATE SITE DOC (mg/L) POC (mg/L) TOC (mg/L) TSS (mg/L)

RVMUA 9.26 10.2 19.5 12.0

LRMUA 14.7 9.34 24.1 10.9

EMUA 0.25 0.15 0.40 19.9

August 6-9, 2001 PVSC 123 8.74 132 35.6

MCMUA 20.6 5.34 25.9 22.6

BCMUA 109 15.4 125 45.6

JMEU 131 8.58 140 18.1

RVMUA 8.78 3.39 12.2 6.7

LRMUA 7.33 5.01 12.3 17.9

NBC 191 8.39 199 17.4

NBW 23.4 9.82 33.3 13.5

EMUA 14.7 5.33 20.1 7.5

NHWNY 17.7 12.1 29.8 13.8

SMUA 10.7 2.67 13.4 3.8

Figure D-6. Scatter plot of TOC versus DOC in CARP effluent monitoring data

y = 0.9266x

R2

 = 0.9898

0

50

100

150

200

250

300

0 50 100 150 200 250 300

TOC (mg/L)

DOC (mg/L)
142

Figure D-7. Scatter plot of TOC versus DOC in CARP effluent monitoring data (TOC <50 mg/L)

Least squares regression of the CARP effluent data (Table D-5) produces the following model: 

DOC = 0.9266 TOC (r2 = 0.9898, 32 df)

This regression was forced through the origin by constraining the intercept to be zero. At the limit of 

removal efficiency (i.e., as effluent TOC approaches zero), any remaining TOC should be in the form of 

DOC, as mentioned above. This argument justifies forcing the regression through the origin. If only the 

data for which TOC falls in the expected range for effluent concentrations (TOC < 50 mg/L) are 

considered, the regression (again forced though the origin) is:

DOC = 0.7133 TOC (r2 = 0.8913, 25 df)

For either case, the CARP effluent data show the strong linear relationship between TOC and DOC. 

Because TOC and DOC are linearly related in POTW effluent, the relationships between BOD and TOC 

reported above (Sections D.1 and D.2) also apply to DOC.

D.4 Discussion

Initially, we attempted to correlate BOD and TOC concentration measurements using data for all 

monitoring locations retrieved from PCS for major POTWs. We produced significant linear regression 

models for both average (Figure D-1) and maximum monthly (Figure D-2) data. Coefficients of 

determination were 0.87 and 0.70, respectively, for these data when combined for all locations. 

However, these correlations were substantially influenced by very high (i.e., greater than 50 mg/L) 

concentrations of BOD and TOC measured in untreated wastewater. 

y = 0.7133x

R2

 = 0.8913

0

5

10

15

20

25

30

35

40

0 10 20 30 40 50 60

TOC (mg/L)

DOC (mg/L)
143

When we repeated the statistical analysis using effluent monitoring data, we found large differences in 

the slopes of the linear model TOC = a + b BOD among POTWs. Low coefficients of determination were 

also recorded for regressions of TOC on BOD values from all POTWs (r2 = 0.245 and 0.276, for average 

and maximum values, respectively). In part, this may reflect random errors in the measurements of 

BOD and TOC, since data quality issues including loss of precision tend to be more frequent and 

significant at lower concentrations. The greater scatter in the plots of effluent BOD and TOC (Figures D3 and D-4) may also reflect the limitations of working with the monthly average and maximum data 

reported by PCS.

Direct inspection of the TOC data in Figures D-3 and D-4 is nevertheless instructive. Aside from some 

extreme high and low values, the great majority of effluent TOC concentrations are in the range of 5 to 

10 mg/L, especially for effluents with BOD concentrations below 10 mg/L. This is true for both average 

and maximum monthly TOC values. Table D-6 presents summary statistics for average monthly effluent 

TOC, for all data as well as data categorized according to the following BOD ranges: ≤5 mg/L, 5 to 10 

mg/L, 10 to 20 mg/L and > 20 mg/L. As noted in Table D-6, four very low TOC values (≤ 0.5 mg/L) were 

judged to be anomalies and were therefore censored from the data for these statistics. The same 

summary statistics are presented for maximum monthly effluent TOC in Table D-7. In this context, the 

regressions of TOC on BOD values from effluent samples at all POTWs are quite reasonable, despite the 

low coefficients of determination. For average monthly effluent data, the regression of TOC on BOD is:

TOCavg = 5.8740 + 0.2859 BODavg (r2 = 0.245, 174 df)
144

Table D-6. Summary statistics for POTW average monthly effluent TOC concentrations, categorized 

according to average monthly effluent BOD concentration

TOCavg

BODavg level

≤5 mg/L >5-10 

mg/L

>10-20 

mg/L >20 mg/L All levels

Mean 6.75 8.45 9.83 13.32 7.98

Median 6.17 8.15 8.70 13.25 6.90

Standard Deviation 2.47 2.41 5.26 5.79 3.76

5th quantile 4.90 6.08 4.46 6.53 4.96

95th quantile 10.00 10.58 18.40 21.8 14.52

n 98* 32* 34* 8 172*

*Four suspiciously-low TOC values were censored from the data for these statistics

Table D-7. Summary statistics for POTW maximum monthly effluent TOC concentrations, categorized 

according to maximum monthly effluent BOD concentration 

TOCmax 

BODmax level

≤5 mg/L >5-10 

mg/L

>10-20 

mg/L

>20 

mg/L All levels 

Mean 7.95 7.88 14.73 20.57 10.08

Median 7.30 7.85 11.00 20.60 7.90

Standard Deviation 3.28 2.74 15.97 7.75 7.60

5

th quantile 5.50 3.00 2.00 11.00 5.4

95th quantile 10.94 12.00 25.55 35.3 23.6

n 164 72 30 35 301

Given the substantial limitations imposed by the data available from PCS, we believe that this 

regression gives reasonable estimates of TOC in POTW effluents. These are also probably the best 

available estimates of effluent TOC for dilution calculations to determine DOC concentrations for use in 

the BLM (for example, the probabilistic dilution framework incorporated in the BLM-Monte software 

[HydroQual, 2001]). As shown in Section D.3, effluent DOC concentrations can be reliably predicted 

from TOC values:

DOC = 0.7133 TOC (r2 = 0.8913, 25 df)

It should be noted that the regressions presented here should not be applied to project water quality 

in natural receiving waters unimpacted by POTW effluent, because they are based solely on POTW 

effluent monitoring data. The characteristics of the constituents DOC, TOC, and BOD, as well as the 

relationships between them, may be quite dissimilar between natural waters and effluents.
145

D.5 References

Fadini, S.F., Jardim, W.F., J.R. Guimarães. 2004 Evaluation of organic load measurement techniques in a 

sewage and waste stabilisation pond. Journal of the Brazilian Chemical Society. 15(1): 131-135 

(http://jbcs.sbq.org.br/jbcs/2004/vol15_n1/19-152-02.pdf).

HydroQual, Inc. 2001. BLM-Monte User’s Guide, Version 2.0. HydroQual, Mahwah, NJ. October, 2001.

HydroQual, Inc. 2005. Biotic Ligand Model Windows Interface, Version 2.1.2, User’s Guide and 

Reference Manual. HydroQual, Mahwah, NJ. June, 2005.