U.S. Department of the Interior

U.S. Geological Survey

Prepared in cooperation with the U.S. Environmental Protection Agency Chesapeake Bay

Program and the Virginia Department of Environmental Quality

A Comparison of Turbidity-Based and Streamflow-Based 

Estimates of Suspended-Sediment Concentrations 

in Three Chesapeake Bay Tributaries

Scientific Investigations Report 2009–5165
Front Cover. The James River at Cartersville, Virginia, during stormflow conditions (photograph by John Jastram, U.S. Geological Survey).

Inset—U.S. Geological Survey personnel sampling the Rappahannock River near Fredericksburg, Virginia, from a 

cableway during stormflow conditions (photograph by Douglas Moyer, U.S. Geological Survey).

Back Cover. The shadow created by U.S. Geological Survey personnel sampling the Rappahannock River near Fredericksburg, 

Virginia, from a cableway during stormflow conditions (photograph by Douglas Moyer, U.S. Geological Survey).
A Comparison of Turbidity-Based 

and Streamflow-Based Estimates of 

Suspended-Sediment Concentrations in 

Three Chesapeake Bay Tributaries

By John D. Jastram, Douglas L. Moyer, and Kenneth E. Hyer

Prepared in cooperation with the U.S. Environmental Protection Agency Chesapeake 

Bay Program and the Virginia Department of Environmental Quality

Scientific Investigations Report 2009–5165

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2009

For more information on the USGS—the Federal source for science about the Earth, its natural and living resources, 

natural hazards, and the environment, visit http://www.usgs.gov or call 1-888-ASK-USGS

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

visit http://www.usgs.gov/pubprod

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

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

U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.

Suggested citation:

Jastram, J.D., Moyer, D.L., and Hyer, K.E., 2009, A comparison of turbidity-based and streamflow-based estimates 

of suspended-sediment concentrations in three Chesapeake Bay tributaries: U.S. Geological Survey Scientific 

Investigations Report 2009–5165, 37 p.

978 1 4113 2605 7
iii

Contents

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

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

Background............................................................................................................................................2

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

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

Description of Study Area ...................................................................................................................5

Approach and Methods................................................................................................................................5

Continuous Monitoring of Water Quality ..........................................................................................5

Collection of Discrete Water-Quality Samples ................................................................................7

Generation of Turbidity-Based Regression Models........................................................................7

Streamflow-Based Regression Models............................................................................................9

Comparison of Turbidity-Based and Streamflow-Based Estimates 

of Suspended-Sediment Concentrations ..........................................................................10

Water-Quality Monitoring Data .................................................................................................................10

Turbidity-Based Models..............................................................................................................................12

James River at Cartersville, Virginia................................................................................................12

Rappahannock River near Fredericksburg, Virginia.....................................................................15

North Fork Shenandoah River near Strasburg, Virginia...............................................................17

Streamflow-Based Models ........................................................................................................................19

Comparison of Turbidity-Based and Streamflow-Based Suspended-Sediment 

Concentration Estimates...............................................................................................................19

Comparison of Turbidity-Based and Streamflow-Based Nutrient Concentration Estimates..........22

Limitations and Challenges of the Turbidity-Based Method.................................................................32

Potential Applications of Turbidity-Based Estimation Models.............................................................33

Summary and Conclusions.........................................................................................................................34

Acknowledgments.......................................................................................................................................36

References....................................................................................................................................................36

Figures

1. Map showing the Chesapeake Bay watershed and the James River near 

Cartersville, Virginia, Rappahannock River near Fredericksburg, Virginia, 

and North Fork Shenandoah River near Strasburg, Virginia, basins ...................................4

2. Photograph of a typical bridge-mounted deployment of a continuous 

water-quality monitoring station................................................................................................6

3. Photograph of the monitoring buoy deployed in the Rappahannock River ........................7

4–15. Graphs showing—

4. Cumulative distribution frequency plot of continuous turbidity and streamflow 

measurements with sampled points at James River at Cartersville, Virginia, 

Rappahannock River near Fredericksburg, Virginia, and North Fork 

Shenandoah River near Strasburg, Virginia..................................................................11

5. Partial residual plots for turbidity-based suspended-sediment concentration 

estimation models using square-root and natural-logarithm transformations 

for the James River at Cartersville, Virginia..................................................................14

6. Partial residual plots for turbidity-based suspended-sediment concentration 

estimation models using square-root and natural-logarithm transformations 

for the Rappahannock River near Fredericksburg, Virginia .......................................16
iv

7. Partial residual plots for turbidity-based suspended-sediment 

concentration estimation model for the North Fork Shenandoah River 

near Strasburg, Virginia....................................................................................................18

8. Observed suspended-sediment concentration and estimated suspendedsediment concentration for the turbidity-based model and two streamflowbased models for James River at Cartersville, Virginia, Rappahannock River 

near Fredericksburg, Virginia, and North Fork Shenandoah River near 

Strasburg, Virginia.............................................................................................................21

9. Percentage of exceedance plots of the absolute value of residuals from the 

turbidity-based suspended-sediment concentration model and the two 

streamflow-based suspended-sediment concentration models for James 

River at Cartersville, Virginia, Rappahannock River near Fredericksburg, 

Virginia, and North Fork Shenandoah River near Strasburg, Virginia ......................23

10. Observed total phosphorus and estimated total phosphorus for the turbiditybased model and two streamflow-based models for James River at 

Cartersville, Virginia, and Rappahannock River near Fredericksburg, Virginia......26

11. Total phosphorus concentrations and percent particulate phosphorus for 

the James River at Cartersville, Virginia, and Rappahannock River near 

Fredericksburg, Virginia ...................................................................................................28

12. Observed total nitrogen and estimated total nitrogen for the turbidity-based 

model and two streamflow-based models for James River at Cartersville, 

Virginia, and Rappahannock River near Fredericksburg, Virginia ............................29

13. The absolute value of residuals from the turbidity-based total nitrogen 

estimation model and absolute value of residuals from the two streamflowbased total nitrogen estimation models for James River at Cartersville, 

Virginia, and Rappahannock River near Fredericksburg, Virginia ............................30

14. Total nitrogen concentration and percent particulate nitrogen for the 

James River at Cartersville, Virginia, and Rappahannock River near 

Fredericksburg, Virginia ...................................................................................................32

15. Monthly and annual suspended-sediment load estimations for the 2007 water 

year at the James River at Cartersville, Virginia, estimated using turbiditybased and streamflow-based methods .........................................................................34

Tables

1. Summary of continuous water-quality monitoring data at the monitoring stations 

at the James River near Cartersville, Rappahannock River near Fredericksburg, 

and North Fork Shenandoah River near Strasburg, Virginia...............................................10

2. Results of best-subsets regression for turbidity-based suspended-sediment 

concentration estimation models for the monitoring station at the James River 

at Cartersville, Virginia...............................................................................................................12

3. Details of top-ranked turbidity-based suspended-sediment concentration estimation 

models for the monitoring station at the James River at Cartersville, Virginia................13

4. Sum of squared errors, mean squared error, and mean absolute error for 

turbidity-based suspended-sediment concentration and instantaneous 

suspended-sediment load estimations using the natural-logarithm transformation 

model and the square-root transformation model for the monitoring station at the 

James River at Cartersville, Virginia .......................................................................................13

5. Results of best-subsets regression for turbidity-based suspended-sediment 

concentration estimation models for the monitoring station at the Rappahannock 

River near Fredericksburg, Virginia.........................................................................................15
v

6. Details of top-ranked turbidity-based suspended-sediment concentration 

estimation model for the monitoring station at the Rappahannock River 

near Fredericksburg, Virginia ...................................................................................................15

7. Results of best-subsets regression for turbidity-based suspended-sediment 

concentration estimation models for the monitoring station at the North Fork 

Shenandoah River near Strasburg, Virginia...........................................................................17

8. Details of turbidity-based suspended-sediment concentration estimation 

model for the monitoring station at the North Fork Shenandoah River 

near Strasburg, Virginia.............................................................................................................18

9. Coefficients for streamflow-based suspended-sediment concentration estimation 

models generated for the monitoring stations at the James River near Cartersville, 

Rappahannock River near Fredericksburg, and North Fork Shenandoah River near 

Strasburg, Virginia......................................................................................................................19

10. P-values for one-way squared-ranks tests on the variance of estimates 

and residuals comparing turbidity-based models to two streamflow-based 

models for the monitoring stations at the James River near Cartersville, 

Rappahannock River near Fredericksburg, and North Fork Shenandoah River 

near Strasburg, Virginia ............................................................................................................20

11. Error statistics for turbidity-based and streamflow-based estimates of suspendedsediment concentrations and instantaneous suspended-sediment load for the 

monitoring stations at the James River near Cartersville, Rappahannock River 

near Fredericksburg, and North Fork Shenandoah River near Strasburg, Virginia ........20

12. Details of turbidity-based estimation models for total phosphorus for the 

monitoring stations at the James River at Cartersville and Rappahannock River 

near Fredericksburg, Virginia ...................................................................................................24

13. Details of turbidity-based estimation models for total nitrogen for the monitoring 

stations at the James River at Cartersville and Rappahannock River near 

Fredericksburg, Virginia ............................................................................................................24

14. Coefficients for streamflow-based total phosphorus estimation models for the 

monitoring stations at the James River at Cartersville and Rappahannock River 

near Fredericksburg, Virginia ...................................................................................................25

15. Error statistics for turbidity-based and streamflow-based estimates of total 

phosphorus concentration and instantaneous load for the monitoring stations 

at the James River at Cartersville and Rappahannock River near 

Fredericksburg, Virginia ............................................................................................................27

16. P-values for one-way squared-ranks tests on the variance of estimates 

and residuals for turbidity-based and streamflow-based total phosphorus 

estimation models for the monitoring stations at the James River at Cartersville 

and Rappahannock River near Fredericksburg, Virginia .....................................................27

17. Coefficients for streamflow-based total nitrogen estimation models for the 

monitoring stations at the James River at Cartersville and Rappahannock River 

near Fredericksburg, Virginia ...................................................................................................28

18. Error statistics for turbidity-based and streamflow-based estimates of total 

nitrogen concentration and instantaneous load for monitoring stations at the 

James River at Cartersville and Rappahannock River near Fredericksburg, Virginia....31

19. P-values for one-way squared-ranks tests on the variance of estimates and 

residuals for turbidity-based and streamflow-based total nitrogen estimation 

models for the monitoring stations at the James River at Cartersville and 

Rappahannock River near Fredericksburg, Virginia.............................................................31
vi

Conversion Factors

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

Area

square mile (mi2) 259.0 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2) 

Flow rate

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

Mass

ton, short (2,000 lb) 0.9072 megagram (Mg) 

kilogram (kg) 2.205 pound avoirdupois (lb)

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

°F = (1.8 × °C) + 32

Specific conductance is given in microsiemens per centimeter at 25 degrees Celsius 

(μS/cm at 25 °C).

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

Abbreviations and Acronyms

AMLE adjusted maximum likelihood estimator

BMP best management practice

CBP Chesapeake Bay Program

CDF cumulative distribution frequency

CV	 	 coefficient of variation

FNU formazin nephelometric units

GOES Geostationary Operational Environmental Satellites

MAE mean absolute error

MSE mean squared error

NWISWeb National Water Information System Web site

RIM River Input Monitoring Program

SSC suspended-sediment concentration

SSE sum of squared errors

SSL suspended-sediment load

TMDL total maximum daily load

TN total nitrogen

TP total phosphorus

TTS turbidity threshold sampling

US EPA U.S. Environmental Protection Agency

USGS U.S. Geological Survey

VA DEQ Virginia Department of Environmental Quality

VA WSC Virginia Water Science Center

VIF	 	 variance inflation factor
Abstract 

Fluvial transport of sediment into the Chesapeake Bay 

estuary is a persistent water-quality issue with major implications for the overall health of the bay ecosystem. Accurately 

and precisely estimating the suspended-sediment concentrations (SSC) and loads that are delivered to the bay, however, 

remains challenging. Although manual sampling of SSC 

produces an accurate series of point-in-time measurements, 

robust extrapolation to unmeasured periods (especially highflow periods) has proven to be difficult. Sediment concentrations typically have been estimated using regression relations 

between individual SSC values and associated streamflow 

values; however, suspended-sediment transport during storm 

events is extremely variable, and it is often difficult to relate 

a unique SSC to a given streamflow. With this limitation for 

estimating SSC, innovative approaches for generating detailed 

records of suspended-sediment transport are needed. 

One effective method for improved suspended-sediment 

determination involves the continuous monitoring of 

turbidity as a surrogate for SSC. Turbidity measurements 

are theoretically well correlated to SSC because turbidity 

represents a measure of water clarity that is directly influenced 

by suspended sediments; thus, turbidity-based estimation 

models typically are effective tools for generating SSC 

data. The U.S. Geological Survey, in cooperation with the 

U.S. Environmental Protection Agency Chesapeake Bay 

Program and Virginia Department of Environmental Quality, 

initiated continuous turbidity monitoring on three major 

tributaries of the bay—the James, Rappahannock, and North 

Fork Shenandoah Rivers—to evaluate the use of turbidity 

as a sediment surrogate in rivers that deliver sediment to the 

bay. Results of this surrogate approach were compared to the 

traditionally applied streamflow-based approach for estimating 

SSC. Additionally, evaluation and comparison of these two 

approaches were conducted for nutrient estimations.

Results demonstrate that the application of turbiditybased estimation models provides an improved method 

for generating a continuous record of SSC, relative to the 

classical approach that uses streamflow as a surrogate for SSC. 

Turbidity-based estimates of SSC were found to be more 

accurate and precise than SSC estimates from streamflowbased approaches. The turbidity-based SSC estimation models 

explained 92 to 98 percent of the variability in SSC, while 

streamflow-based models explained 74 to 88 percent of the 

variability in SSC. Furthermore, the mean absolute error of 

turbidity-based SSC estimates was 50 to 87 percent less than 

the corresponding values from the streamflow-based models. 

Statistically significant differences were detected between 

the distributions of residual errors and estimates from the two 

approaches, indicating that the turbidity-based approach yields 

estimates of SSC with greater precision than the streamflowbased approach. 

Similar improvements were identified for turbidity-based 

estimates of total phosphorus, which is strongly related to 

turbidity because total phosphorus occurs predominantly in 

particulate form. Total nitrogen estimation models based on 

turbidity and streamflow generated estimates of similar quality, with the turbidity-based models providing slight improvements in the quality of estimations. This result is attributed 

to the understanding that nitrogen transport is dominated by 

dissolved forms that relate less directly to streamflow and 

turbidity. Improvements in concentration estimation resulted 

in improved estimates of load. Turbidity-based suspendedsediment loads estimated for the James River at Cartersville, 

VA, monitoring station exhibited tighter confidence 

interval bounds and a coefficient of variation of 12 percent, 

compared with a coefficient of variation of 38 percent for the 

streamflow-based load.

Introduction

Elevated suspended-sediment concentrations (SSC) 

are major water-pollution concerns in the Chesapeake Bay 

watershed, as they are in many sensitive ecosystems throughout the world. Nationwide, siltation ranked second on the 

U.S. Environmental Protection Agency’s (USEPA) 305b list 

of stressors causing stream impairments (U.S. Environmental 

Protection Agency, 2002). The Chesapeake Bay (hereafter 

A Comparison of Turbidity-Based and Streamflow-Based 

Estimates of Suspended-Sediment Concentrations in 

Three Chesapeake Bay Tributaries

By John D. Jastram, Douglas L. Moyer, and Kenneth E. Hyer
2 Turbidity-Based and Streamflow-Based Estimates of Suspended Sediment in Three Chesapeake Bay Tributaries

referred to as the bay), the Nation’s largest estuary, has been 

degraded through declines in water-quality conditions and 

loss of habitat. Excess sediment has an adverse effect on 

the living resources and associated habitat of the bay and its 

watershed. The bay was listed as an impaired water body in 

1998 under the Clean Water Act because of excess nutrient 

and sediment levels (Chesapeake Bay Program, 2008). The 

USEPA Chesapeake Bay Program (CBP) needs information 

with which to evaluate current conditions and assess progress 

toward meeting sediment-reduction goals.

Background

The detrimental effects of sediment transport are apparent 

in the terrestrial environments that serve as sediment sources 

and in the aquatic environments to which the sediments are 

delivered. Terrestrial effects of soil erosion (the source of 

most fluvial sediments) include the erosion of surficial soil, 

loss of soil nutrients, degradation of soil structure, reduction 

of tillable land, and the ultimate reduction of agricultural 

productivity (Walling and Collins, 2000). The effects of 

excessive sedimentation to the aquatic systems receiving 

the eroded sediments range from ecological degradation 

to economic expenses. Ecologically, suspended sediments 

harm aquatic ecosystems by decreasing light penetration 

into the water column (reducing photosynthesis), smothering 

benthic habitats, delivering excess nutrients, and potentially 

delivering soil-bound contaminants, such as phosphorus and 

bacteria (Christensen, 2001; Davies-Colley and Smith, 2001). 

Furthermore, toxic materials, including pesticides, metals, and 

radionuclides, may adsorb strongly to sediment particles; thus, 

introduction of excessive amounts of sediment to a water body 

from source areas where such materials are present may lead 

to toxic conditions for the biota that use the resource (Meade 

and Parker, 1984).

Economically, accelerated transport of suspended 

sediments increases the costs of water treatment for human use 

and may decrease profits from waterways used for recreational 

purposes because people typically perceive sediment-laden or 

turbid water as less desirable for recreation than clearer waters 

(Davies-Colley and Smith, 2001). Also, sediment accumulation within channels increases streambed elevation, leading to 

more damaging and life-threatening floods as the stormflow 

carrying capacity of the channel is decreased (Meade and 

Parker, 1984). Yet another economic cost related to sediment 

is the increased maintenance needs of structures within 

waterways carrying elevated sediment concentrations; most 

reservoirs in the United States trap at least half of the sediment 

transported by the impounded river, with larger dams trapping 

virtually the entire sediment load carried by the river (Meade 

and Parker, 1984). The reduction of reservoir capacity as sediment accumulates introduces multiple expenses: an aggrading 

reservoir may no longer serve the intended purpose, and the 

costs of maintenance may be compounded by contaminated 

sediments, preventing removal or making sediment removal 

extremely costly. The cost of sediment-transport related damages is estimated to range from $20 to $50 billion annually in 

North America (Pimentel and others, 1995; Osterkamp and 

others, 1998, 2004). Globally, erosion of soils and sediment 

transport are major issues, most notably in developing nations 

where the demands on marginal farmland and water resources 

are greatest (Walling and Collins, 2000).

Previous Studies

Given the consequences of elevated SSC and the need for 

accurate and precise data to aid management strategies aiming 

to reduce the problems associated with accelerated erosion 

and sediment transport, the scientific community has sought 

to understand and characterize the fluvial transport of sediment. Understanding and managing movement of suspended 

sediment has been challenging, however, because sediment 

transport is highly variable in time, across landscapes, and 

within stream channels. In order to quantify suspendedsediment transport within a stream channel at a given point 

in time, personnel must be onsite sampling with specialized 

equipment and proper methods during the sediment transport 

event. This effort can be especially difficult because most 

sediment transport is triggered and sustained by stormflow 

events (Wolman and Miller, 1960). Previous studies have demonstrated that as much as 98 percent of a river’s sediment load 

can be transported during just 10 percent of the time of record, 

and as much as 60 percent of the load can be discharged in 

only 1 percent of the time of record (Meade and others, 1990). 

Thus, monitoring programs must quantify sediment transport 

during stormflow events, which generally is the time when the 

fewest data are collected. 

Although manual sampling of SSC can produce an 

accurate series of point-in-time measurements, robust extrapolation to the many unmeasured periods (especially high-flow 

periods) has proven difficult because of the inherently 

complex nature of suspended-sediment transport. A fundamental link exists between streamflow and sediment transport 

because the runoff responsible for increasing streamflow is 

typically responsible for a large portion of the soil erosion 

that contributes to sediment transport. This relation has been 

used in traditional methods for calculating sediment transport; 

however, suspended-sediment transport during stormflow 

events is extremely variable, and relating a unique concentration to a given streamflow is difficult. As a result of the 

variability in sediment transport, using streamflow as the sole 

predictor of suspended-sediment concentration may provide 

results with large error terms when applied without regard 

for the complex nature of the relation and the underlying 

fundamental concepts (Walling, 1977). For example, Horowitz 

(2003) found that for multiple watersheds in the United States 

and Europe ranging from less than 385 square miles (mi2) to 

greater than 385,000 mi2, high sediment concentrations are 

often underpredicted and low sediment concentrations are 

often overpredicted, partly as a result of the differing relation 
Introduction 3

between SSC and streamflow on the rising and falling limbs 

of the stormflow hydrograph (often referred to as hysteresis). 

Although short-duration studies applying the rating curve 

method are subject to the largest errors, longer-duration studies calculating annual suspended-sediment loads (SSL) have 

been reported to have errors as high as 280 percent (Walling, 

1977). In addition to the potential for large error terms 

associated with transport estimates generated in this fashion, 

some studies have documented the inability to detect statistically significant correlations between streamflow and SSC. 

For example, Christensen and others (2002) identified that 

only four of their eight study stations actually had significant 

correlations between suspended sediment and streamflow.

Furthermore, studies that use discrete water-quality 

samples will generally suffer from several challenges that are 

inherent to discrete sampling, including:

• A relatively limited number of samples are used to 

develop interpretations.

• The delay between sample collection and reporting 

laboratory results, especially when the objective is to 

detect violations of a water-quality standard and(or) to 

protect public health, may expose the public to unnecessary risks.

• Detailed understanding of in-stream variability (diurnal 

patterns, for example) is difficult to develop.

• The time and cost associated with collecting representative water-quality samples can be considerable.

• Sampling designs for loading studies, which usually 

require targeted storm-runoff sampling, conflict with 

sampling designs for trend analyses, which typically 

require fixed-frequency sampling.

With the current limitations of discrete water-quality sampling 

and the challenges associated with predicting suspendedsediment levels solely from streamflow, innovative approaches 

for generating detailed records of SSC are needed. 

A potentially more effective technology for improved 

suspended-sediment determination involves the continuous 

monitoring of turbidity as a surrogate for SSC. Turbidity 

measurements are well correlated to SSC because turbidity 

is an optical measure of water clarity, and the presence of 

suspended particles directly influences this measurement. 

Using turbidity values as a surrogate for estimating SSC is 

not new, but until recently, technological limitations have 

made this approach largely unreasonable. As early as 1977, 

Walling described this surrogate approach using turbidity and 

demonstrated a sharp reduction in suspended-sediment prediction error using a turbidity-sediment relation relative to a 

streamflow-sediment approach. In the earlier-mentioned study 

by Christensen and others (2002), which demonstrated poor 

correlation between suspended-sediment concentrations and 

streamflow, all of their research stations demonstrated significant correlations between SSC and turbidity measurements. 

The development of continuous turbidity records to estimate 

SSC is now inherently more feasible because of technical 

improvements to in situ water-quality sensors and data 

telemetry. Continuous turbidity measurement has become a 

common field approach because it provides more detailed 

and more precise information on sediment transport than 

was previously possible (Christensen and others, 2000; 

Christensen, 2001).

Purpose and Scope

Efforts by CBP and the U.S. Geological Survey (USGS) 

to quantify sediment transport to the bay from major tributaries have traditionally relied on streamflow-based regression 

methods, such as the seven-parameter ESTIMATOR model 

introduced by Cohn and others (1992). This streamflow-based 

model incorporates variables to explain flow dependence, 

seasonal variability, and trends over time. In recognition of 

previous successful use of continuous turbidity monitoring 

and surrogate approaches to estimating concentrations of 

suspended sediment, the USGS, in cooperation with the 

CBP and the Virginia Department of Environmental Quality 

(VA DEQ), began an evaluation of the use of a turbidity-based 

approach to estimate sediment transport to the bay. The 

purpose of this report is to present a comparison of turbiditybased and streamflow-based estimates of suspended-sediment 

concentrations in three major tributaries to the bay: the James, 

Rappahannock, and North Fork Shenandoah Rivers. Specifically, the objectives of this investigation were to:

1. Evaluate the use of turbidity as a surrogate for estimating SSC in the James, Rappahannock, and North 

Fork Shenandoah Rivers, each of which drain into 

the Chesapeake Bay; and

2. Compare two methods of estimating SSC: turbiditybased and streamflow-based regression models.

These study objectives were expanded to include the 

evaluation of turbidity-based models to estimate nutrient 

concentrations, specifically total nitrogen (TN) and total 

phosphorous (TP).

Study sites for this project were identified primarily on 

the basis of existing water-quality data that indicated which 

of the major rivers in Virginia had the greatest suspendedsediment transport to the bay. Based on the available 

long-term data, the James, Rappahannock, and North Fork 

Shenandoah Rivers were selected for this study (Langland and 

others, 2004). To enhance the efficiency of this data collection, 

continuous water-quality monitors were collocated with an 

existing water-quality sampling and streamgaging station on 

each river—the James River at Cartersville, VA (USGS station 

number 02035000), Rappahannock River near Fredericksburg, 

VA (USGS station number 01668000), and North Fork 

Shenandoah River near Strasburg, VA (USGS station number 

01634000; fig. 1).
4 Turbidity-Based and Streamflow-Based Estimates of Suspended Sediment in Three Chesapeake Bay Tributaries

Figure 1. Chesapeake Bay watershed and the James River near Cartersville, Virginia, Rappahannock River near 

Fredericksburg, Virginia, and North Fork Shenandoah River near Strasburg, Virginia, basins.

75° 77°

79°

43°

41°

39°

NEW YORK

PENNSYLVANIA

MARYLAND

DELAWARE

WEST VIRGINIA

VIRGINIA

EXPLANATION

North Fork Shenandoah

Rappahannock

James

USGS monitoring station and site number 01634000

01634000

01668000

02035000

0 25 50 MILES

0 25 50 KILOMETERS

BAY

ATLANTIC

OCEAN

Potomac

Rappahanno

River

ck

R.

River

River

River

James

James

York North Fork

Shenandoah River 

Chesapeake Bay watershed boundary

MONITORING STATION BASINS

State boundaries from U.S. Geological Survey Digital Line Graph;

 1:2,000,000, 1987

Hydrography from Brakebill and others, 2001

Monitoring basins from Hayes and Wiegand, 1:24,000, 2006

Chesapeake Bay basin boundary from Chesapeake Bay Program, 2000

Figure 1. Chesapeake Bay watershed and the James River near Cartersville, Virginia, Rappahannock River near

Fredericksburg, Virginia, and North Fork Shenandoah River near Strasburg, Virginia basins.

CHESAPEAKE
Approach and Methods 5

In late 2003 and early 2004, the USGS initiated a 

continuous water-quality monitoring effort on the James and 

Rappahannock Rivers with the intent of generating a timeseries dataset for use in the estimation of SSC and nutrient 

concentrations. The network was expanded to a third river, 

the North Fork Shenandoah River, in 2006. This effort was 

augmented by ongoing discrete sample collection in support 

of the USGS Chesapeake Bay River Input Monitoring 

(RIM) Program.

Multivariate regression models to estimate SSC and 

nutrients were constructed using the datasets generated 

by the continuous water-quality monitoring and discrete 

sample-collection activities. Additionally, streamflow-based 

estimation models were generated using the ESTIMATOR 

program, which is the approach currently used for estimating 

nutrient and sediment concentrations and loads transported 

to the bay from its major tributaries. These two approaches 

for generating estimates of SSC and nutrients were compared 

using graphical, statistical, and hypothesis testing methods to 

determine if either provides greater accuracy or precision.

Description of Study Area

The James River watershed encompasses 10,200 mi2, 

making it the third-largest tributary basin in the bay watershed. 

Originating in the Appalachian Mountains near the West 

Virginia–Virginia border, the James River flows through 

the Valley and Ridge, Blue Ridge, Piedmont, and Coastal 

Plain Physiographic Provinces before flowing into the bay in 

southeastern Virginia. The drainage area of the James River at 

Cartersville monitoring station encompasses over 60 percent 

(6,252 mi2 ; Hayes and Wiegand, 2006) of the James River 

basin, has a long-term annual mean streamflow of 7,082 cubic 

feet per second (ft3/s), and a median annual suspended-solids 

yield of approximately 9.1 x 104 kilograms per square mile 

(kg/mi2; U.S. Geological Survey, 2007). Dominant 

land uses in the drainage area for this monitoring station are 

forest (80 percent) and agriculture (16 percent; Belval and 

Sprague, 1999). 

The Rappahannock River is the fourth largest tributary in 

the bay watershed, draining an area of 2,800 mi2. Originating 

in the Blue Ridge Physiographic Province, the Rappahannock 

River flows through the Piedmont and Coastal Plain Physiographic Provinces before entering the bay. The drainage area 

of the Rappahannock River near Fredericksburg monitoring 

station encompasses 57 percent (1,595 mi2) of the Rappahannock River basin (Hayes and Wiegand, 2006) and has a 

long-term annual mean streamflow of 1,686 ft3/s and a 

median annual suspended-solids yield of approximately 

1.4 x 105 kg/mi2 (U.S. Geological Survey, 2007). Dominant 

land uses in the drainage area for this monitoring station are 

forest (61 percent) and agriculture (36 percent; Belval and 

Sprague, 1999).

The North Fork Shenandoah River, a branch of the 

Shenandoah River, drains 1,034 mi2 of the 3,058 mi2

Shenandoah River watershed (Hayes and Wiegand, 2006). 

The Shenandoah River flows through the Valley and Ridge 

Physiographic Province and into the Potomac River near 

Harpers Ferry, WV. The drainage area of the North Fork 

Shenandoah River near Strasburg monitoring station encompasses 74 percent (770 mi2

) of the North Fork Shenandoah 

River Basin (Hayes and Wiegand, 2006) and has a long-term 

annual mean streamflow of 608 ft3/s and a median annual 

suspended-solids yield of approximately 4.2 x 104 kg/mi2 

(U.S. Geological Survey, 2007). Dominant land uses in the 

drainage area for this monitoring station are forest (59 percent) 

and agriculture (38 percent; Johnson and Belval, 1998).

Approach and Methods

The study approach relied on continuous water-quality 

data collected by an in-situ water-quality monitoring device, 

discrete water-quality data collected using manual samplecollection methods, and statistical analyses performed using 

various computing platforms for generation and evaluation of 

estimation models. 

Continuous Monitoring of Water Quality 

YSI 6920 multiparameter water-quality monitoring 

sondes (manufactured by YSI, Inc.) were selected for field 

deployment. These particular instruments were selected 

because the equipment seemed sufficiently rugged for the task 

and because YSI water-quality monitors were already being 

used for the collection of field data in several ongoing studies. 

Using the YSI 6920, the field parameters of water temperature, 

specific conductance, pH, and turbidity were measured at 

15-minute intervals. The YSI 6136 turbidity sensor was used 

for turbidity measurements. This turbidity sensor uses nearinfrared wavelengths with 90-degree detector geometry and 

is calibrated using formazin-based standards; therefore, 

data are expressed in formazin nephelometric units (FNUs; 

Anderson, 2005).

The water-quality monitors were deployed in such a way 

that the data recorded by the instruments would be representative of the stream cross section being monitored and not just 

the single point where the monitor was deployed. Because of 

specific site conditions, different deployment approaches were 

required for each of the study sites. At the James River and 

North Fork Shenandoah River monitoring stations, bridges 

were used as monitoring platforms. A water-quality monitor 

was suspended from the bridge and configured to make waterquality measurements approximately 1–2 feet below the water 

surface. Weights were added to the bottom of the water-quality 

monitor to ensure that the monitor remained underwater 

during high-velocity stormflow events. A 2-foot-long section 

of schedule 80 polyvinyl chloride piping with 1-inch holes 

drilled into the lower section of the pipe was used to shield the 

monitor from debris during flood events while still permitting 
6 Turbidity-Based and Streamflow-Based Estimates of Suspended Sediment in Three Chesapeake Bay Tributaries

a flow-through environment and good contact between the 

monitor and the river water. A braided steel cable was used 

to connect the water-quality monitor to the bridge, and all 

the supporting electronics were installed in a weather-proof 

box that was attached to the topside of the bridge. Using this 

approach, the water-quality monitor was securely deployed 

into a portion of the river that responded uniformly to various 

flow conditions; an example of this type of deployment is 

presented in figure 2.

At the Rappahannock River monitoring station, no bridge 

was available to use as a monitoring platform. Various bankmounted deployment systems were considered; however, none 

of these were used because of the concern that water-quality 

conditions at the edge of the river might not be representative 

of the average water-quality conditions throughout the cross 

section of the river. Consequently, a buoy-mounted system 

was developed to permit measurements from the approximate 

center of the streamflow. An estuarine monitoring buoy from 

Apprise Technology, Inc., was modified with minor welding 

work to allow the monitoring equipment to be deployed on the 

outside of the buoy (fig. 3). The buoy was moored in the river 

to a portion of exposed bedrock. Using this setup, the waterquality monitor was deployed approximately 1.5 feet below 

the water surface, under all flow conditions. The particular 

monitoring buoy used had a hollow internal cylinder that held 

all the necessary electronics for data logging. During a highflow event, the buoy was damaged beyond repair. In June 2007 

the water-quality monitor was relocated, and a new approach 

of directly attaching the monitor to a large, stable boulder was 

employed. Data from the old 

monitor location were compared 

with data from the new monitor 

location, and data were found to 

be similar. 

The water-quality monitors 

were programmed to make 

measurements of water temperature, specific conductance, pH, 

and turbidity every 15 minutes. 

These data were then stored in 

a Campbell Scientific CR10 

data logger and transferred by 

telephone modem every 3 hours 

to the USGS Virginia Water 

Science Center (VA WSC), or 

the data were stored on a Sutron 

Satlink II and transferred hourly 

to the VA WSC by Geostationary 

Operational Environmental 

Satellites (GOES). Upon arrival 

at the USGS office, the data were 

processed by a quality-control 

data-review program to screen 

possible problems with the data, 

and then data were made available to the public on the National 

Water Information System Web 

site (NWISWeb; http://waterdata.

usgs.gov/nwis/rt).

Approximately every 

4 weeks, the water-quality monitors were serviced in the field 

to clean the sensors, evaluate 

the quality of the data collected, 

and recalibrate the instrument 

(if necessary). This monitor servicing was performed in 

accordance with the USGS guidelines for the operation and 

maintenance of continuous water-quality monitors (Wagner 

and others, 2000). Because these guidelines were followed, 

only a summary of the maintenance steps are presented 

here. In all cases, parameters were measured before and 

after the instrument was cleaned of any silt, debris, algae, or 

bio-film that may have accumulated. The differences before 

and after this cleaning were used to determine the need for, 

and the magnitude of, corrections for instrument fouling. 

Following this fouling check, calibrations of the pH, specific 

Figure 2. A typical bridge-mounted deployment of a continuous water-quality monitoring station.

SUBMERGED WATER-QUALITY MONITOR

SUPPORT AND COMMUNICATIONS CABLES

ON-BRIDGE EQUIPMENT ENCLOSURE

Figure 2. A typical bridge-mounted deployment of a continuous water-quality monitoring station.
Approach and Methods 7

conductance, and turbidity sensors were checked using known 

standards. Discrepancies between the known values of the 

check standards and the readings from the sonde were used to 

determine whether the data needed to be corrected for a drift in 

instrument calibration. Following the fouling and calibration 

checks, any sensor out of tolerance was recalibrated (Wagner 

and others, 2000). After the maintenance visit, any necessary 

data corrections were made, the database was updated with the 

corrected data, and the original values were archived.

In addition to the monthly monitor maintenance, the 

entire water-quality record for each parameter was reviewed 

and finalized at the end of each water year1. This annual 

review involved evaluation of all the fouling and calibration 

drift checks, screening the data for anomalous values, and 

rating the quality of the record as excellent, good, fair, or poor. 

These ratings were determined on the basis of the corrections 

that had been applied to the record, and the criteria used for 

the ratings were those provided by Wagner and others (2000). 

Collection of Discrete Water-Quality Samples

In addition to the continuous water-quality monitoring 

at each sampling site, discrete water-quality samples were 

collected at these sites. These discrete water-quality samples 

were collected as part of a joint effort by USGS, VA DEQ, 

and the CBP to understand sediment and nutrient inputs to the 

bay from major tributaries in Virginia. These discrete samples 

were collected during a broad range of environmental conditions through scheduled monthly sampling and targeted storm 

sampling. 

1

 Water year is the period October 1 through September 30 and is identified 

by the year in which the period ends.

The discrete water-quality samples were collected using 

standard USGS sampling protocols for the collection of 

representative water-quality samples (U.S. Geological Survey, 

1998). These protocols for representative sampling involve 

the collection of depth- and width-integrated water-quality 

samples, and the use of isokinetic samplers when required by 

the water depth or velocity. Water-quality samples were sent 

to the USGS Kentucky Sediment Laboratory for analysis of 

SSC using analytical methods from Sholar and Shreve (1998). 

Nutrient analyses were performed by the Virginia Division 

of Consolidated Laboratory Services. All results from these 

two laboratories were reviewed and quality assured by USGS 

VA WSC staff before the data were entered into the USGS 

database (http://va.water.usgs.gov/chesbay/RIMP/index.html).

Generation of Turbidity-Based 

Regression Models

Using data from the continuous water-quality monitors 

and from laboratory analysis of the discrete samples, multivariate turbidity-based SSC estimation models were generated 

such that the general form of the model was:

1

0 1

ˆ ˆ ˆ ˆ [ ( ) ( )... ( ) ] j j k k SSC f f turbidity f x f x      − = + + + , (1)

where

SSC is suspended-sediment concentration, in 

milligrams per liter; 1 f −

is the inverse of the transformation selected 

for the response variable (SSC); ˆ

i are coefficients estimated by ordinary least 

squares;

0

ˆ

 is a constant;

f is the transformation function selected for 

the explanatory variables (such as natural 

logarithm or square root);

1

ˆ

 describes the relation between SSC and 

turbidity; ... j k x x are additional site-specific explanatory 

variables (such as streamflow, water 

temperature, and specific conductance) 

evaluated for inclusion using best-subsets 

regression; ˆ ˆ ...   j k describe the relations between concentration 

and ... j k x x ; and

 is residual error, assumed to be normally 

distributed with zero mean and variance 2  .

Figure 3. The monitoring buoy deployed in the 

Rappahannock River.

MODIFICATION FOR 

SONDE ATTACHMENT

Figure 3. The monitoring buoy deployed in the Rappahannock River.
8 Turbidity-Based and Streamflow-Based Estimates of Suspended Sediment in Three Chesapeake Bay Tributaries

Turbidity-based estimation models were developed and 

compared using SAS (version 9.1.3) for Windows and JMP 

7.0 software (SAS Institute, Cary, NC). Multivariate models 

were generated using best-subsets regression, which ranks all 

2k possible regressions (where k is the number of explanatory 

variables evaluated) according to user-specified statistics; Mallows’ Cp was used in this study. Selecting a model with the 

smallest Mallows’ Cp value provides a compromise between 

explaining the most variance possible in the response through 

incorporation of all relevant regressors and minimizing the 

variance of the estimates by minimizing the number of regressors (Helsel and Hirsch, 2002). Additionally, the adjusted R2

was used to evaluate the proportion of variability explained 

by the models selected by the best-subsets procedure. R2, 

or coefficient of determination, is a measure of the fraction 

of the variability in the response variable explained by the 

model, and the adjusted R2 is a similar measure corrected for 

the number of explanatory variables in the model (Helsel and 

Hirsch, 2002). This adjustment is necessary to determine an 

accurate measure of explained variability in multiple regression because R2 will increase with each additional explanatory 

variable, regardless of explanatory power (Helsel and Hirsch, 

2002). The additional explanatory variables evaluated for 

inclusion in the turbidity-based model include streamflow 

and water-quality parameters (water temperature and specific 

conductance) that were measured at the same temporal scale 

as turbidity and have the potential to explain variance induced 

by processes related to sediment transport. Variables selected 

by the best-subsets regression procedure were evaluated for 

multicollinearity and to ensure that sound reasoning existed 

for inclusion of the variables. Multicollinearity occurs 

when one explanatory variable is closely related to one or 

more other explanatory variables and results in errors in the 

estimation of model coefficients (Helsel and Hirsch, 2002; 

Montgomery and others, 2006). Each variable was tested for 

multicollinearity using the variance inflation factor (VIF; 

Marquardt, 1970), calculated as:

2

1

(1 ) j

j

VIF

R = −

where

VIFj is the variance inflation factor for the j

th

variable, and 2 Rj is the coefficient of determination ( 2 R ) of a 

regression of the j

th variable on all other 

explanatory variables.

Ideally, VIF ≅ 1 for all explanatory variables, indicating the 

absence of multicollinearity ( 2 Rj = 0), but 10 VIFj > ( 2 Rj > 0.9) 

indicates serious problems with multicollinearity (Helsel and 

Hirsch, 2002; Montgomery and others, 2006). This threshold 

value ( 10 VIFj > ) is used in this study because the purpose of 

the models is to generate estimates of concentration; multicollinearity is of lesser concern when the model is used only for 

estimations, and interpretations of the model coefficients are 

not made (Helsel and Hirsch, 2002; Montgomery and others, 2006). Furthermore, the concern over multicollinearity is 

reduced when estimates are generated from the same range 

of explanatory variables as is used in the specification of the 

model, as is the case in this study (Helsel and Hirsch, 2002; 

Montgomery and others, 2006).

Transformations of the explanatory and response variables were required to generate normally distributed residual 

errors (residuals = observed concentration – estimated concentration) with approximately constant variance (homoscedasticity) because these are assumptions inherent in linear regression 

(Helsel and Hirsch, 2002). Logarithmic (natural log) and 

square-root transformations were investigated; logarithmic 

transformations are commonly applied for turbidity-based 

estimations of SSC (Christensen and others, 2000; Rasmussen 

and others, 2005, 2008; Miller and others, 2007), and the 

square-root transformation is another commonly applied 

transformation for right-skewed hydrologic data (Helsel and 

Hirsch, 2002). The natural logarithm was used in this study 

instead of the base-10 logarithm because the natural logarithm 

is used by the ESTIMATOR and LOADEST applications. 

A transformation-bias-correction procedure was applied 

to the re-transformed estimates of SSC. In the case of the 

logarithmic transform, re-transforming estimates into original 

units produces estimates of the geometric mean concentration 

(which approximates the median concentration), rather than 

estimates of the mean concentration. This bias typically results 

in underestimating the mean concentration, which must be 

corrected using a bias-correcting procedure. The Duan (1983) 

smearing factor, which “smears” the average estimation error 

over all estimates, was used to correct transformation bias in 

the turbidity-based models in this study. The Duan smearing 

factor, as presented by Helsel and Hirsch (2002), is the mean 

of the re-transformed residuals when a log-based transformation is used; thus, bias-corrected concentration estimates are 

computed from natural-logarithm-transformed data as:

1

exp[ ]

ˆ ˆ exp[ ]

n

i

i

D

e

c y

n

= = •

∑

where ˆDc is the smeared, or bias-corrected, estimation 

of concentration;

exp is the inverse of the natural-logarithm 

function;

yˆ is the re-transformed estimate of 

concentration from the turbidity-based 

model;

i e are the residual errors; and 

n is the number of observations in the turbiditybased estimation model.

The same factor is applied to all values to be corrected.

In the case of non-logarithmic transformations, such as 

the square-root transformation used in this study, application of the Duan smearing correction requires the use of 

, (2)

, (3)
Approach and Methods 9

spreadsheet software or scripting programs when a large 

number of observations are used to specify models because 

the correction for a single value is calculated using all of the 

residuals from the model specification dataset. For example, 

the smearing correction for the square-root transformation is 

calculated as:

2

1

( ) ˆ

ˆ

n

i

i

D

y e

c

n

=

+

=

∑

where ˆDc is the smeared, or bias-corrected, estimation 

of concentration;

yˆ is the re-transformed estimate of 

concentration from the turbidity-based 

model;

i e are the residual errors; and 

n is the number of observations in the turbiditybased estimation model.

The Duan approach corrects only the transformation 

bias. Potential bias in the coefficient estimations resulting 

from sample error was expected to be negligible (sample error 

goes to zero with large samples), and final estimations were 

graphically evaluated for the presence of bias. 

The determination of which transformation to apply at 

each site was made through assessment of the distribution 

of residual errors, relation between the residuals and each 

explanatory variable in the model, and the relation between 

the residuals and the estimated values. When both transformations provided equally acceptable residuals, the analysis was 

expanded to directly compare the error in the estimates of 

SSC, and consequently instantaneous SSL, provided by each 

transform. This comparison was accomplished using the sum 

of squared errors (SSE), mean squared error (MSE), and mean 

absolute error (MAE) for the re-transformed and biascorrected estimates. The SSE, MSE, and MAE are expressions 

of the error of the estimates in concentration units (milligrams 

per liter), calculated as:

2

1

n

i

i

SSE e == ∑

2

1

1 n

i

i

MSE e

n =

= ∑

1

1 n

i

i

MAE e

n =

= ∑

where

n is the number of observations used in the 

regression,

i e is the residual error of the i

th estimate, and

i e is the absolute value of the i

th residual (e). 

Evaluating these statistics for instantaneous SSL provides 

error measures that give greater weight to concentration errors 

at high streamflow. Concentration errors during high streamflow are the critical errors to minimize because the majority of 

the SSL is transported during periods of elevated streamflow. 

Instantaneous SSL was computed using the equation presented 

by Porterfield (1972):

inst w s SSL Q C k = × ×

where

inst SSL is the instantaneous suspended-sediment load, 

in tons per day;

Qw is the instantaneous streamflow, in cubic feet 

per second;

Cs is the concentration of suspended sediment, in 

milligrams per liter; and

k is a coefficient based on the unit of 

measurement of water discharge, which 

equals 0.0027 in this instance. 

Streamflow-Based Regression Models

The seven-parameter log-linear ESTIMATOR model 

developed by Cohn and others (1992) is used by the RIM 

Program to estimate loads of sediment at multiple sites on 

tributaries of the bay, including the three sites used in this 

study. The ESTIMATOR model is a streamflow-based model 

that estimates the natural logarithm of sediment concentration 

using the model:

2

0 1 2

2

3 4 5

6

ˆ ˆ ˆ ln( ) ln( / ) [ln( / )]

ˆ ˆ ˆ ( ) ( ) sin(2 )

ˆ cos(2 ) ,

c c

c c

c q q q q

t t t t t

t

  

   

  

= + +

+ − + − +

+ +

where

ln is the natural-logarithm function;

c is measured SSC, in milligrams per liter;

q is measured daily-mean streamflow, in cubic 

feet per second;

t is time, in decimal years;

qc,t

c are centering variables for streamflow and 

time, respectively; ˆ

i are coefficients estimated by ordinary least 

squares;

0

ˆ

 is a constant;

1

ˆ

 , 2

ˆ

 describe the relation between concentration 

and streamflow;

3

ˆ

 , 4

ˆ

 describe the relation between concentration 

and time, independent of flow;

5

ˆ

 , 6

ˆ

 describe seasonal variation in concentration 

data; and

 is residual error, assumed to be normally 

distributed with zero mean and variance 2  .

, (4)

, (7)

, and (6)

, (5)

, (8)

(9)
10 Turbidity-Based and Streamflow-Based Estimates of Suspended Sediment in Three Chesapeake Bay Tributaries

The adjusted maximum likelihood estimator (AMLE) 

is used to assign a concentration value to those samples with 

observed concentration values below the detection limit to 

eliminate sample bias in the estimation of model coefficients 

(Cohn, 1988). This model estimates the natural logarithm of 

concentration; thus, the estimated concentrations are subject 

to re-transformation bias when transformed back into original 

units. This bias is corrected using the Bradu and Mundlak 

(1970) minimum variance unbiased estimator as described by 

Gilroy and others (1990). 

For the purpose of estimating nutrient and suspendedsediment loadings to the bay, the ESTIMATOR model is 

typically run on a 9-year moving window of data, as described 

by Yochum (2000). This 9-year period of data was used to 

generate the streamflow-based concentration estimates for the 

James, Rappahannock, and North Fork Shenandoah Rivers for 

the comparison in this study. For this study, streamflow-based 

models also were generated using the same data period that 

was used to generate the turbidity-based estimation models. 

Comparison of Turbidity-Based and 

Streamflow-Based Estimates of SuspendedSediment Concentrations

The turbidity-based approach was compared with two 

iterations of the streamflow-based approach: one model 

generated from the 9-year dataset used by the CBP and a 

second model generated from a dataset containing only the 

data collected during the period of the dataset used to generate 

the turbidity-based model. Using the 9-year dataset allowed a 

comparison of overall approaches, and using the two models 

built using the same period of data allowed a direct comparison of the models.

Comparison of the accuracy of estimates from the 

streamflow-based and turbidity-based estimation models 

was achieved through measures of the difference between 

estimated and observed concentrations for those observations 

included in each of the three estimation models. Multiple plots 

of the residuals of the re-transformed bias-corrected estimates 

from both approaches were evaluated, and SSE, MSE, and 

MAE values were compared. Comparison of the precision of 

the two approaches was achieved using a squared-ranks test 

for equal variance (Conover, 1980) on the estimates and the 

residuals of the re-transformed bias-corrected estimates of 

SSC; estimates and residuals with lesser variance are more 

precise than those with greater variance. The squared-ranks 

test for equal variance is a non-parametric test in which the 

variance of two populations is compared using the absolute 

deviations from the means of the populations (Conover, 1980). 

These deviations are then ranked, and the ranks are squared 

for calculation of the test statistic. This test can be constructed 

as a two-tailed test of the null hypothesis that the variances of 

the two populations are the same, or as a one-tailed test of the 

null hypothesis that the variance of one population is greater 

than the variance of the other population. The one-tailed test is 

used in this study to test the null hypothesis that the variances 

of the streamflow-based estimates and errors are greater than 

those from the turbidity-based model.

Water-Quality Monitoring Data

Continuous water-quality monitoring was initiated on different dates for each site depending on instrument deployment 

requirements (table 1). Although there were no long-term gaps 

in monitoring, short periods of data are missing as a result 

of instrument malfunction, ice, or fouling. These periods of 

missing data typically span less than 1 week and cause the 

records to be less than 100 percent complete. 

Table 1. Summary of continuous water-quality monitoring data at the monitoring stations at the James River near 

Cartersville, Rappahannock River near Fredericksburg, and North Fork Shenandoah River near Strasburg, Virginia.

[°C, degrees Celsius; FNU, formazin nephelometric units; μS/cm, microsiemens per centimeter]

Period of 

record Parameter Percentage of record complete Minimum Maximum Median

James River at Cartersville, VA

12/11/2003

to

9/30/2007

Water temperature (°C) 96 0.0 34.8 16.6

Turbidity (FNU) 92 0.0 720 5.7

Specific conductance (μS/cm) 96 43 412 139

Rappahannock River near Fredericksburg, VA

3/4/2004

to

9/30/2007

Water temperature (°C) 93 0.0 34.4 17.0

Turbidity (FNU) 79 0.0 1,316 5.6

Specific conductance (μS/cm) 88 42 146 87

North Fork Shenandoah River near Strasburg, VA

2/3/2006

to

2/3/2008

Water temperature (°C) 96 0.0 31.4 16.9

Turbidity (FNU) 88 0.0 660 1

Specific conductance (μS/cm) 94 119 467 363
Water-Quality Monitoring Data 11

Width- and depth-integrated samples of SSC were 

collected at each monitoring station to represent the range 

of hydrologic conditions observed during the monitoring 

period. The observed range of turbidity and streamflow was 

adequately sampled, as demonstrated by the distribution of 

sampled points on the cumulative distribution frequency 

(CDF) plots of the continuous turbidity and streamflow data 

(fig. 4). 

Figure 4. Cumulative distribution frequency plot of continuous turbidity and streamflow measurements with sampled 

points at (A) James River at Cartersville, Virginia, (B) Rappahannock River near Fredericksburg, Virginia, and (C) North 

Fork Shenandoah River near Strasburg, Virginia.

0

20

40

60

80

100

0

20

40

60

80

100

PERCENTAGE OF TIME CONDITION EQUALED OR LESS THAN

0

20

40

60

80

100

0.1 1 10 100 1,000 10,000 100,000

TURBIDITY, IN FORMAZIN NEPHELOMETRIC UNITS, AND STREAMFLOW, IN CUBIC FEET PER SECOND

Streamflow

Turbidity

Streamflow

Turbidity

Figure 4. Cumulative distribution frequency plot of continuous turbidity and streamflow measurements with sampled points at

(A) James River at Cartersville, Virginia, (B) Rappahannock River near Fredericksburg, Virginia, and (C) North Fork Shenandoah

River near Strasburg, Virginia.

(B)

(C)

(A)

Streamflow

Turbidity
12 Turbidity-Based and Streamflow-Based Estimates of Suspended Sediment in Three Chesapeake Bay Tributaries

Turbidity-Based Models

Site-specific turbidity-based SSC estimation models were 

developed for each site using the aforementioned procedures 

and datasets. Model specification is site-specific because the 

distribution of observed SSC and water-quality parameter data 

varies in response to watershed characteristics and hydrologic 

regime during the period of study. 

James River at Cartersville, Virginia

The best-subsets regression procedure was used to rank 

potential formulations of the turbidity-based estimation model 

for the James River at Cartersville (table 2). Only models 

with a smaller Mallows’ Cp than the single-variable (turbidity 

only) model are presented, and a single-variable model using 

streamflow as the explanatory variable did not outperform 

the single-variable turbidity model. The top-ranked model 

(according to Mallows’ Cp) for both the natural-logarithm and 

square-root transformations included transformed turbidity, 

streamflow, and water temperature. All coefficients were 

significant at the 0.05 α-level with attained significance levels 

(p-values) less than 0.05 (table 3). There were no problems 

with multicollinearity according to the specified criteria 

(table 3; fig. 4). Partial residual plots reveal that each transformation provides a model with residuals having approximately 

constant variance (fig. 5), as is required to meet the assumption of normally distributed residuals in linear regression 

(Helsel and Hirsch, 2002). 

These two models (natural-logarithm and square-root 

transformations) were evaluated to determine which transformation provided estimates of SSC and SSL with the least 

amount of error. The values of SSE, MSE, and MAE (table 4) 

were calculated using the residuals of the re-transformed 

bias-corrected estimates for each model, and these calculations 

were compared. The magnitude of errors is greater for the 

natural-logarithm transformed model than for the square-root 

transformed model, as indicated by the error statistics. With 

greater error in the estimates from the natural-logarithm 

model, the square-root model was selected as the best possible 

estimation model for this dataset. 

Table 2. Results of best-subsets regression for turbidity-based suspended-sediment concentration 

estimation models for the monitoring station at the James River at Cartersville, Virginia.

[ln, natural logarithm; Q, streamflow; WT, water temperature; SC, specific conductance; √, square root]

Explanatory variables Mallows’ Cp1 Adjusted coefficient of 

determination

Natural-logarithm transformation models

ln(Turbidity) ln(Q) ln(WT) 3.00 0.925

ln(Turbidity) ln(SC) ln(Q) ln(WT) 5.00 0.924

ln(Turbidity) ln(Q) 8.23 0.918

ln(Turbidity) ln(SC) ln(Q) 9.98 0.917

ln(Turbidity) ln(SC) ln(WT) 33.82 0.889

ln(Turbidity) ln(SC) 34.94 0.888

ln(Turbidity) 37.08 0.885

ln(Q) 63.88 0.854

Square-root transformation models

√(Turbidity) √(Q) √(WT) 3.55 0.971

√(Turbidity) √(SC) √(Q) √(WT) 5.00 0.971

√(Turbidity) √(SC) √(Q) 7.56 0.970

√(Turbidity) √(Q) 8.28 0.969

√(Turbidity) 43.39 0.953

√(Q) 164.14 0.901

1

Mallows’ Cp values are only comparable for models using the same transformation.
Turbidity-Based Models 13

Table 3. Details of top-ranked turbidity-based suspended-sediment concentration estimation 

models for the monitoring station at the James River at Cartersville, Virginia.

[<, less than; N/A, not applicable; ln, natural logarithm; Q, streamflow; WT, water temperature; √, square root]

Variable Model 

coefficient (β) p-value

Variance 

inflation 

factor

Number of 

observations

Adjusted 

coefficient of 

determination

Natural-logarithm model

Intercept –6.125 <0.0001 N/A

69 0.925

ln(Turbidity) 0.545 <0.0001 5.21

ln(Q) 0.799 <0.0001 5.44

ln(WT) 0.199 0.0086 1.10

Square-root model

Intercept –3.514 <0.0001 N/A

69 0.971

√(Turbidity) 0.825 <0.0001 7.52

√(Q) 0.044 <0.0001 7.91

√(WT) 0.336 0.0114 1.18

Table 4. Sum of squared errors (SSE), mean squared error 

(MSE), and mean absolute error (MAE) for turbidity-based 

suspended-sediment concentration (SSC) and instantaneous 

suspended-sediment load (in parentheses) estimations using 

the natural-logarithm transformation model and the squareroot transformation model for the monitoring station at the 

James River at Cartersville, Virginia.

Statistic Natural-logarithm 

model

Square-root 

model

SSE 220,492 (6.5 x 109) 66,265 (1.2 x 109)

MSE 3,196 (9.5 x 107) 960 (1.8 x 107)

MAE 23.2 (2.8 x 103) 14.3 (1.4 x 103)
14 Turbidity-Based and Streamflow-Based Estimates of Suspended Sediment in Three Chesapeake Bay Tributaries

Figure 5. Partial residual plots for turbidity-based suspended-sediment concentration estimation models using square-root and naturallogarithm transformations for the James River at Cartersville, Virginia.

RESIDUAL ERROR

Figure 5. Partial residual plots for turbidity-based suspended-sediment concentration estimation models using

square-root and natural-logarithm transformations for the James River at Cartersville, Virginia.

–2 –1 0 1 2 3 4 5 6 7

NATURAL-LOGARITHM TURBIDITY

5

4

3

2

1

0

–1

–2

–3

–4

–5

2.5

2.0

1.5

1.0

0.5

0

–0.5

–1.0

–1.5

2.5

2.0

1.5

1.0

0.5

0

–0.5

–1.0

–1.5

2.5

2.0

1.5

1.0

0.5

0

–0.5

–1.0

–1.5

2.5

2.0

1.5

1.0

0.5

0

–0.5

–1.0

–1.5

5

4

3

2

1

0

–1

–2

–3

–4

–5

5

4

3

2

1

0

–1

–2

–3

–4

–5

5

4

3

2

1

0

–1

–2

–3

–4

–5

0 2 4 6 8 10 12 14 16 18 20

SQUARE-ROOT TURBIDITY

6 7 8 9 10 11 12

NATURAL-LOGARITHM STREAMFLOW

–2 –1 0 1 2 3 4 5 6 7 8

ESTIMATED NATURAL-LOGARITHM SUSPENDEDSEDIMENT CONCENTRATION

–2 –1 0 1 2 3 4

NATURAL-LOGARITHM WATER TEMPERATURE

0 50 100 150 200 250 300

SQUARE-ROOT STREAMFLOW

0 1 2 3 4 5 6

SQUARE-ROOT WATER TEMPERATURE

0 5 10 15 20 25 30

ESTIMATED SQUARE-ROOT SUSPENDEDSEDIMENT CONCENTRATION
Turbidity-Based Models 15

Rappahannock River near 

Fredericksburg, Virginia

The results of the best-subsets regression procedure were 

used to rank potential formulations of the estimation model 

for the Rappahannock River near Fredericksburg monitoring 

station (table 5). Only models with a smaller Mallows’ Cp 

than the single-variable (turbidity only) model are listed in 

table 5, and a single-variable model using streamflow as the 

explanatory variable did not outperform the single-variable 

turbidity model. 

Evaluation of partial residual plots for the models 

containing the natural-logarithm transformed variables 

revealed undesirable patterns in the residuals, indicating 

non-constant variance (fig. 6); therefore, only the models 

containing square-root transformed variables were considered 

for use. Two of the top-ranked square-root transformed models 

included water temperature; however, this variable was not 

statistically significant (for α = 0.05) in either case, so these 

models were deemed unacceptable. The details about the 

highest-ranked model with acceptable variables in terms of 

significance, multicollinearity, and residual distributions are 

given in table 6 and figure 6. 

Table 5. Results of best-subsets regression for turbidity-based suspended-sediment concentration estimation models for the 

monitoring station at the Rappahannock River near Fredericksburg, Virginia.

[ln, natural logarithm; Q, streamflow; WT, water temperature; SC, specific conductance; √, square root]

Explanatory variables Mallows’ Cp1 Adjusted coefficient of 

determination

Natural-logarithm transformation models

ln(Turbidity) ln(Q) ln(WT) 4.97 0.863

ln(Turbidity) ln(SC) ln(Q) ln(WT) 5.00 0.866

ln(Turbidity) ln(Q) 8.97 0.848

ln(Turbidity) ln(SC) ln(Q) 9.67 0.849

ln(Turbidity) 14.57 0.830

ln(Q) 56.09 0.711

Square-root transformation models

√(Turbidity) √(SC) √(Q) √(WT) 5.00 0.929

√(Turbidity) √(SC) √(Q) 6.28 0.925

√(Turbidity) √(Q) √(WT) 9.97 0.920

√(Turbidity) √(Q) 11.47 0.916

√(Turbidity) 25.64 0.893

√(Q) 47.74 0.859

1

Mallows’ Cp values are only comparable for models using the same transformation.

Table 6. Details of top-ranked turbidity-based suspended-sediment concentration estimation model for the 

monitoring station at the Rappahannock River near Fredericksburg, Virginia.

[N/A, not applicable; √, square root; <, less than; SC, specific conductance; Q, streamflow]

Variable Model 

coefficient (β) p-value Variance inflation factor

Number of 

observations

Adjusted coefficient 

of determination

Square-root model

Intercept –15.807 0.005 N/A

50 0.925

√(Turbidity) 0.774 <0.0001 6.22

√(SC) 1.426 <0.0001 1.61

√(Q) 0.105 0.0121 6.96
16 Turbidity-Based and Streamflow-Based Estimates of Suspended Sediment in Three Chesapeake Bay Tributaries

Figure 6. Partial residual plots for turbidity-based suspended-sediment concentration estimation models using square-root and naturallogarithm transformations for the Rappahannock River near Fredericksburg, Virginia.

0 10 20 30 40 50

0 5 10 15 20 25 30 35

–2 –1 0 1 2 3 4 5 6 7 8

–3 –2 –1 0 1 2 3 4

–1 0 1 2 3 4 5 6 7

0 5 10 15 20 25

RESIDUAL ERROR

Figure 6. Partial residual plots for turbidity-based suspended-sediment concentration estimation models using

square-root and natural-logarithm transformations for the Rappahannock River near Fredericksburg, Virginia.

–8

–6

–4

–2

0

2

4

6

–8

–6

–4

–2

0

2

4

6

SQUARE-ROOT TURBIDITY

ESTIMATED NATURAL-LOGARITHM SUSPENDEDSEDIMENT CONCENTRATION

SQUARE-ROOT SPECIFIC CONDUCTANCE

0 20 40 60 80 100 120 140 160 180 4 5 6 7 8 9 10 11 12 –8

–6

–4

–2

0

2

4

6

SQUARE-ROOT STREAMFLOW NATURAL-LOGARITHM STREAMFLOW

NATURAL-LOGARITHM WATER TEMPERATURE

NATURAL-LOGARITHM TURBIDITY

ESTIMATED SQUARE-ROOT SUSPENDEDSEDIMENT CONCENTRATION

6

4

2

0

–2

–4

–6

–8

2.0

1.5

1.0

0.5

0

–0.5

–1.0

–1.5

2.0

1.5

1.0

0.5

0

–0.5

–1.0

–1.5

2.0

1.5

1.0

0.5

0

–0.5

–1.0

–1.5

2.0

1.5

1.0

0.5

0

–0.5

–1.0

–1.5
Streamflow-Based Models 17

North Fork Shenandoah River near 

Strasburg, Virginia

The best-subsets regression procedure was used to 

rank potential formulations of the estimation model for the 

North Fork Shenandoah River near Strasburg monitoring 

station (table 7). Only models that ranked higher than the 

single-variable (turbidity only) model are listed in table 7, 

and in the case of the square-root transformation, the singlevariable model using streamflow as the explanatory variable 

did not outperform the single-variable turbidity model. In the 

best-subsets results for the natural-logarithm transformation, 

however, the single-variable model using streamflow as the 

only explanatory variable ranked above the single-variable 

model using turbidity as the only explanatory variable.

The natural-logarithm transformation did not produce 

any satisfactory estimation models because all possible 

formulations had problems with significance of variables and 

non-constant variance in the residuals. Each of the multivariate 

models using the square-root transformation were unsatisfactory because of multicollinearity, non-significant variables, 

or non-constant variance in the residuals. These results likely 

can be attributed to the small sample size used to specify the 

model because the variance of parameter estimates increases 

with decreased sample size, leading to elevated VIF values 

and issues with detecting significance (O’Brien, 2007). The 

single-variable (turbidity only) model using the square-root 

transformation was determined to be an acceptable model and 

was used as the estimation model for this site; the coefficients 

and summary statistics for this model are given in table 8, with 

the partial residual plots shown in figure 7.

Streamflow-Based Models

Two versions of the streamflow-based model were 

generated for each station. One used the data period used for 

generation of the turbidity-based model, and a second version 

of the model was generated using data from the 9-year period 

(water years 1999 through 2007), as is used by the CBP 

for estimates at the RIM Program stations. The parameter 

coefficients (βs) and coefficient of determination (R2) for each 

model formulation are given in table 9. The streamflow-based 

ESTIMATOR model is applied consistently by the RIM 

Program at all monitoring stations in the bay watershed using 

all seven explanatory variables regardless of their statistical 

significance. The estimation model therefore may include 

explanatory variables that do not explain a significant amount 

of the variability in SSC. An evaluation of the goodness of the 

fit of these models is presented later in this report.

Table 7. Results of best-subsets regression for turbidity-based suspended-sediment concentration estimation 

models for the monitoring station at the North Fork Shenandoah River near Strasburg, Virginia.

[ln, natural logarithm; SC, specific conductance; Q, streamflow; WT, water temperature; √, square root]

Explanatory variables Mallows’ Cp1 Adjusted coefficient of 

determination

Natural-logarithm transformation models

ln(Turbidity) ln(SC) ln(Q) 3.70 0.921

ln(Turbidity) ln(SC) ln(Q) ln(WT) 5.00 0.919

ln(Turbidity) ln(Q) 5.72 0.909

ln(Turbidity) ln(Q) ln(WT) 7.38 0.906

ln(Turbidity) ln(WT) 18.86 0.858

ln(Q) 19.29 0.856

ln(Turbidity) 20.25 0.852

Square-root transformation models

√(Turbidity) √(SC) √(Q) √(WT) 5.00 0.993

√(Turbidity) √(SC) √(Q) 5.71 0.992

√(Turbidity) √(SC) √(WT) 23.77 0.985

√(Turbidity) √(SC) 23.85 0.985

√(Turbidity) √(Q) 28.80 0.984

√(Turbidity) √(Q) √(WT) 30.76 0.983

√(Turbidity) √(WT) 32.33 0.982

√(Turbidity) 32.37 0.982

√(Q) 183.67 0.931

1

Mallows’ Cp values are only comparable for models using the same transformation.
18 Turbidity-Based and Streamflow-Based Estimates of Suspended Sediment in Three Chesapeake Bay Tributaries

Table 8. Details of turbidity-based suspended-sediment concentration estimation model for 

the monitoring station at the North Fork Shenandoah River near Strasburg, Virginia.

[√, square root; N/A, not applicable]

Variable

Model 

coefficient 

(β)

p-value Variance 

inflation factor

Number of 

observations

Adjusted 

coefficient of 

determination

Square-root model

Intercept 0.510 0.0294 N/A

27 0.982 √(Turbidity) 1.159 <0.0001 N/A

Figure 7. Partial residual plots for turbidity-based suspended-sediment concentration estimation model for the 

North Fork Shenandoah River near Strasburg, Virginia.

0 5 10 15 20 25

ESTIMATED SQUARE-ROOT SUSPENDED-SEDIMENT CONCENTRATION

RESIDUAL ERROR

–2

–1

0

1

2

3

4

–2

–1

0

1

2

3

4

0 5 10 15 20 25

SQUARE-ROOT TURBIDITY
Comparison of Turbidity-Based and Streamflow-Based Suspended-Sediment Concentration Estimates 19

Comparison of Turbidity-Based 

and Streamflow-Based SuspendedSediment Concentration Estimates

Comparison of the two methods for estimating SSC 

focused on the precision and accuracy of the estimates by 

testing for differences in the variance of the estimates and 

associated residual errors and comparing the estimated values 

to the observed values. One-way squared-ranks tests for 

homogeneity of variance were used to test the null hypothesis 

that the variance of the estimates and residuals from the 

streamflow-based models was greater than the variance of 

the values generated by the turbidity-based models. The 

squared-ranks tests revealed significantly greater variance 

(less precision) in the estimates generated with the 

streamflow-based model for all comparisons (p-values < 0.01; 

table 10). All squared-ranks tests on the residuals revealed 

significantly greater variance (less precision) in the residuals 

from the streamflow-based models than from the turbiditybased models, except for the study-period streamflow-based 

model at the North Fork Shenandoah River. The lack of 

significance for the test on residuals when a significant result 

was obtained on the test of the estimates may be attributed to 

the smaller dataset used for this comparison.

Three measures of uncertainty were calculated to 

describe the accuracy of each of the models, SSE, MSE, and 

MAE, with these values given in table 11. To allow comparison, these values were calculated using the re-transformed 

bias-corrected estimates of SSC associated with those 

observations that were included in all three models. In every 

instance, the accuracy of the turbidity-based SSC and SSL 

estimations is greater than the accuracy of the corresponding 

streamflow-based estimations, with the exception of the SSL 

estimations at the North Fork Shenandoah River. The error 

statistics for SSL for the turbidity-based and study-period 

streamflow-based models at the North Fork Shenandoah River 

are nearly identical (MSE of the turbidity-based estimation is 

slightly higher than the streamflow-based MSE), but error in 

the estimates of SSL from the 9-year streamflow-based model 

are greater than the error terms for the estimations from the 

other two models.

In addition to the aforementioned statistics, graphical 

evaluations of the data were performed to compare the 

accuracy of each approach. Plots of observed SSC and 

estimated SSC (fig. 8) were generated to depict how accurately 

the models replicate the observed concentrations. A perfect 

estimation model would generate estimates along the 1:1 line; 

departures from this line indicate error in the estimations. 

At each of the three sites, the turbidity-based estimates have 

a greater degree of accuracy than the streamflow-based 

estimates, exhibited by a generally tighter fit along the 1:1 line 

than the streamflow-based estimates. This result becomes 

more apparent as SSC values increase, where departures of 

the streamflow-based estimates from the 1:1 line increase 

Table 9. Coefficients for streamflow-based suspended-sediment concentration estimation models generated for the monitoring 

stations at the James River near Cartersville, Rappahannock River near Fredericksburg, and North Fork Shenandoah River near 

Strasburg, Virginia.

[ln, natural logarithm; q, streamflow in cubic feet per second; qc, centered streamflow (streamflow – mean streamflow); t, decimal time; tc, centered decimal 

time (decimal time – mean decimal time); sin, sine function; cos, cosine function; π, pi]

Dataset

Coefficient (p-value) Number of 

observations

Adjusted 

coefficient of 

determination Intercept ln (q / qc

) [ln (q / qc)]2 (t – t

c

) (t – t

c

)

2 sin(2πt) cos(2πt)

James River near Cartersville, VA

9-year 

window

2.776 

(<0.01)

1.583 

(<0.01)

0.077 

(0.03)

–0.022 

(0.38)

0.012 

(0.33)

–0.015 

(0.85)

–0.0422 

(<0.01) 195 0.851

Study 

period

3.125

(<0.01)

1.624 

(<0.01)

0.078 

(0.17)

0.039 

(0.54)

–0.002 

(0.98)

–0.206 

(0.05)

–0.504 

(<0.01) 80 0.883

Rappahannock River near Fredericksburg, VA

9-year 

window

2.480

(<0.01)

1.182 

(<0.01)

0.170 

(<0.01)

–0.063 

(0.06)

0.009 

(0.65)

–0.019 

(0.85)

–0.530 

(<0.01) 174 0.781

Study 

period

2.555

(<0.01)

1.165 

(<0.01)

0.232 

(0.17)

–0.115 

(0.26)

–0.098 

(0.37)

0.132

(0.40)

–0.484 

(<0.01) 72 0.791

North Fork Shenandoah River near Strasburg, VA

9-year 

window

1.518

(<0.01)

1.258

(<0.01)

0.430

(<0.01)

–0.106

(<0.01)

0.006

(0.70)

0.152

(0.22)

–0.346

(<0.01) 124 0.742

Study 

period

2.091

(<0.01)

1.572

(<0.01)

0.218

(0.03)

0.249

(0.39)

–0.117

(0.88)

0.020

(0.92)

–0.687 

(<0.01) 31 0.878
20 Turbidity-Based and Streamflow-Based Estimates of Suspended Sediment in Three Chesapeake Bay Tributaries

Table 10. P-values for one-way squared-ranks tests on the variance of estimates 

and residuals comparing turbidity-based models to two streamflow-based models 

for the monitoring stations at the James River near Cartersville, Rappahannock River 

near Fredericksburg, and North Fork Shenandoah River near Strasburg, Virginia.

Streamflow-based p-values

 (using 9-year dataset)

Streamflow-based p-values 

(using study-period dataset)

James River near Cartersville 

Estimates <0.01 <0.01

Residuals <0.01 <0.01

Rappahannock River near Fredericksburg

Estimates <0.01 <0.01

Residual <0.01 <0.01

North Fork Shenandoah River near Strasburg

Estimates <0.01 <0.01

Residual <0.01 0.645

Table 11. Error statistics for turbidity-based and streamflow-based estimates of suspendedsediment concentrations and instantaneous suspended-sediment load (in parentheses) 

for the monitoring stations at the James River near Cartersville, Rappahannock River near 

Fredericksburg, and North Fork Shenandoah River near Strasburg, Virginia.

[n, number of observations/estimations used to compute statistics; SSE, sum of squared errors; MSE, mean 

squared error; MAE, mean absolute error]

Turbidity-based 

error statistics

Streamflow-based 

error statistics 

(using 9-year dataset)

Streamflow-based 

error statistics 

(using study-period dataset)

James River near Cartersville (n = 67)

SSE 57,551 (9.5 x 108) 377,496 (6.6 x 109) 566,794 (1.3 x 1010)

MSE 846 (1.4 x 107) 5,634 (9.9 x 107) 8,460 (2.0 x 108)

MAE 13 (1.2 x 103) 36 (3.6 x 103) 38 (4.1 x 103)

Rappahannock River near Fredericksburg (n = 49 )

SSE 115,565 (2.5 x 108) 1,077,044 (4.0 x 109) 836,820 (2.8 x 109)

MSE 2,358 (5.1 x 106) 21,980 (8.1 x 107) 17,078 (5.8 x 107)

MAE 25 (6.2 x 102) 56 (2.1 x 103) 50 (1.8 x 103)

North Fork Shenandoah River near Strasburg (n = 27)

SSE 9,241 (3.9 x 108) 1,017,429 (1.6 x 109) 134,158 (3.9 x 108)

MSE 342 (1.5 x 107) 37,683 (5.8 x 107) 4,969 (1.4 x 107)

MAE 9 (1.4 x 103) 68 (2.7 x 103) 30 (1.4 x 103)

greatly. Additionally, the departures from the 1:1 line for the 

streamflow-based models at the Rappahannock River indicate 

bias resulting in increased underestimation as SSC concentrations increase. Large errors in the estimation of SSC at these 

higher values are of great concern because the majority of the 

sediment load is transported during the short periods of time 

when concentrations are in this upper range; thus, accurately 

characterizing these periods is critical.
Comparison of Turbidity-Based and Streamflow-Based Suspended-Sediment Concentration Estimates 21

Figure 8. Observed suspended-sediment concentration and estimated suspended-sediment concentration for the turbiditybased model and two streamflow-based models for (A) James River at Cartersville, Virginia, (B) Rappahannock River near 

Fredericksburg, Virginia, and (C) North Fork Shenandoah River near Strasburg, Virginia.

Exceedance-probability plots of the absolute value of the 

residuals for each model show that divergence in the distribution of residuals from the turbidity- and streamflow-based 

models generally occurs between the 20- and 30-percent 

exceedance levels (fig. 9). At the 10-percent exceedance 

level, the residual error in the streamflow-based estimates is 

1.5 to more than 10 times the residual error in the turbiditybased estimates.

0

200

400

600

800

1,000

1,200

0 200 400 600 800 1,000 1,200

0

200

400

600

800

1,000

1,200

0 100 200 300 400 500 600

OBSERVED SUSPENDED-SEDIMENT CONCENTRATION, IN MILLIGRAMS PER LITER 

ESTIMATED SUSPENDED-SEDIMENT CONCENTRATION, IN MILLIGRAMS PER LITER 

0

200

400

600

800

1,000

1,200

0 200 400 600 800 1,000 1,200

Figure 8. Observed suspended-sediment concentration and estimated suspended-sediment concentration

 for the turbidity-based model and two streamflow-based models for (A) James River at Cartersville, Virginia, 

 (B) Rappahannock River near Fredericksburg, Virginia, and (C) North Fork Shenandoah River

 near Strasburg, Virginia.

(A)

(B)

(C)

Turbidity-based model

Streamflow-based model (9 year)

Streamflow-based model (study period)

1:1 Line

Turbidity-based model

Streamflow-based model (9 year)

Streamflow-based model (study period)

1:1 Line

Turbidity-based model

Streamflow-based model (9 year)

Streamflow-based model (study period)

1:1 Line
22 Turbidity-Based and Streamflow-Based Estimates of Suspended Sediment in Three Chesapeake Bay Tributaries

Figure 9. Percentage of exceedance 

plots of the absolute value of residuals 

from the turbidity-based suspendedsediment concentration model and the 

two streamflow-based suspendedsediment concentration models for 

(A) James River at Cartersville, 

Virginia, (B) Rappahannock River 

near Fredericksburg, Virginia, and 

(C) North Fork Shenandoah River near 

Strasburg, Virginia.

–100 0 100 200 300 400 500 600

100

90

80

70

60

50

40

30

20

10

0

100

90

80

70

60

50

40

30

20

10

0

100

90

80

70

60

50

40

30

20

10

0

–100 0 100 200 300 400 500 600 700 800

PERCENTAGE EXCEEDANCE

–100 0 100 200 300 400 500 600 700 800 900

SUSPENDED-SEDIMENT CONCENTRATION RESIDUALS, IN MILLIGRAMS PER LITER

Turbidity-based model

Streamflow-based model (9 year)

Streamflow-based model (study period)

Turbidity-based model

Streamflow-based model (9 year)

Streamflow-based model (study period)

Turbidity-based model

Streamflow-based model (9 year)

Streamflow-based model (study period)

(B)

(C)

(A)
Comparison of Turbidity-Based and Streamflow-Based Nutrient Concentration Estimates 23

Comparison of Turbidity-Based 

and Streamflow-Based Nutrient 

Concentration Estimates

After the main objectives of this study were completed, 

additional analysis of the data indicated that the methods 

developed for SSC estimation also applied well to estimation 

of nutrients. Other investigators have successfully generated 

estimation models for nutrients and other chemical constituents using continuous water-quality data (Christensen and 

others, 2000, 2002; Rasmussen and others, 2005, 2008; Miller 

and others, 2007). The objective of this additional analysis 

was to demonstrate the applicability of this approach in major 

tributaries of the bay and to compare this approach with the 

streamflow-based estimation approach typically used for 

estimation of nutrient transport in these tributaries.

The approach for data collection and analysis used at 

monitoring stations at the James and Rappahannock Rivers 

was the same as the approach used for generation of the SSC 

estimation models. The approach was not attempted at the 

North Fork Shenandoah River station because of the smaller 

nutrient dataset available for this station. Nutrient samples 

were collected concurrently with the SSC samples; thus, the 

nutrient dataset is representative of conditions observed during 

the period of study (fig. 4). Nutrient analyses were conducted 

by the Virginia Department of Consolidated Laboratory 

Services in Richmond, VA; this effort focused on the total 

phosphorus (TP) and total nitrogen (TN) analyses. The same 

continuous water-quality and streamflow datasets were used 

for generation of the nutrient estimation models as were used 

in the SSC estimation models. 

The TP and TN estimation models were selected 

from the best-subsets regression procedure and subsequent 

residual evaluation for the two monitoring stations (tables 12 

and 13). These estimation models were the highest ranked 

(lowest Mallows’ CP) models with acceptable residuals and 

summary statistics. The nutrient estimation models explain 

83–94 percent of the variability in the nutrient concentrations, 

depending on the site and nutrient species, as indicated by the 

adjusted R2 values.

The variance explained by the streamflow-based TP 

estimation models ranged from approximately 57–85 percent, 

according to the adjusted R2 values (table 14). For the two 

monitoring stations investigated, the model using the study 

period dataset explained a greater portion of the variability in 

TP than the model generated using the 9-year window dataset, 

presumably because these smaller datasets contained less 

variability in the TP concentrations.

Table 12. Details of turbidity-based estimation models for total phosphorus for the monitoring 

stations at the James River at Cartersville and Rappahannock River near Fredericksburg, Virginia.

[N/A, not applicable; √, square root]

Variable Model 

coefficient (β) p-value

Variance 

inflation 

factor

Number of 

observations

Adjusted 

coefficient of 

determination

James River at Cartersville 

Intercept –0.5883 0.042 N/A

61 0.942

√Turbidity 0.0268 <0.001 7.94

√Streamflow 0.0007 0.006 7.43

√Water temperature 0.0149 0.003 1.35

√pH 0.2217 0.035 2.03

Rappahannock River near Fredericksburg

Intercept –0.5473 0.026 N/A

42 0.851

√Turbidity 0.0197 0.004 8.59

√Streamflow 0.0031 0.006 9.08

√Specific conductance 0.0631 0.012 1.83
24 Turbidity-Based and Streamflow-Based Estimates of Suspended Sediment in Three Chesapeake Bay Tributaries

Table 13. Details of turbidity-based estimation models for total nitrogen for the monitoring stations at 

the James River at Cartersville and Rappahannock River near Fredericksburg, Virginia.

[N/A, not applicable; √, square root]

Variable Model 

coefficient (β) p-value

Variance 

inflation 

factor

Number of 

observations

Adjusted 

coefficient of 

determination

James River at Cartersville

Intercept 0.5481 <0.001 N/A

61 0.847

√Turbidity 0.0419 <0.001 1

Rappahannock River near Fredericksburg

Intercept 0.0421 0.906 N/A

42 0.834

√Turbidity 0.0510 <0.001 1.72

√Water temperature –0.074 <0.001 1.08

√Specific conductance 0.0961 0.014 1.79

Table 14. Coefficients for streamflow-based total phosphorus estimation models for the monitoring stations at the James River at 

Cartersville and Rappahannock River near Fredericksburg, Virginia.

[ln, natural logarithm; q, streamflow in cubic feet per second; qc, centered streamflow (streamflow – mean streamflow); t, decimal time, t

c

, centered decimal 

time (decimal time – mean decimal time); sin, sine function; cos, cosine function; π, pi]

Dataset

Coefficient (p-value) Number of 

observations

Adjusted 

coefficient of 

determination Intercept ln (q / qc

) [ln (q / qc)]2 (t – t

c

) (t – t

c

)

2 sin(2πt) cos(2πt)

James River at Cartersville

9-year 

window

–2.623

(<0.01)

0.412 

(<0.01)

0.234 

(<0.01)

–0.072 

(<0.01)

–0.019

(<0.01)

–0.065 

(0.20)

–0.107 

(0.04) 224 0.575

Study 

period

–2.768

(<0.01)

0.766 

(<0.01)

0.224 

(<0.01)

–0.004 

(0.91)

–0.091 

(0.02)

–0.172 

<0.01)

–0.299

(<0.01) 73 0.849

Rappahannock River near Fredericksburg

9-year 

window

–3.276

(<0.01)

0.635 

(<0.01)

0.105 

(<0.01)

–0.032 

(0.04)

0.009 

(0.13)

–0.176 

(<0.01)

–0.254

(<0.01) 196 0.759

Study 

period

–3.047

(<0.01)

0.690 

(<0.01)

0.199

(<0.01)

0.054

(0.36)

–0.154 

(0.01)

0.030 

(0.74)

–0.282

(<0.01) 65 0.837

Comparison of TP estimations from the streamflow-based 

models and the turbidity-based models revealed that greater 

accuracy was achieved using the turbidity-based model at 

each of the two monitoring stations, as indicated by the fit of 

the estimates around the 1:1 line in figure 10. Additionally, 

the streamflow-based models tend to underestimate TP, but 

there is no indication of bias in the turbidity-based estimates 

of TP. Error statistics, MSE, SSE, and MAE, calculated from 

the re-transformed and bias-corrected estimates of TP and 

instantaneous TP load further exemplify the greater accuracy 

of the turbidity-based approach (table 15). Also, a significant 

difference in the variance of the estimates and residuals 

from the turbidity-based and streamflow-based models, as 

demonstrated by the squared-ranks test (table 16), indicates 

that the turbidity-based model provides estimates of TP with 

greater precision than the streamflow-based model. 

Overall, these results demonstrate that the turbidity-based 

approach generates estimates of TP that are more accurate 

and precise than those estimated using the streamflow-based 

approach. This result is likely attributable to the characteristics 

of phosphorous transport because the majority of phosphorous 

transported in these rivers is in particulate form (fig. 11) and 

turbidity is a better estimator of particulate material than 

streamflow, as demonstrated by the results presented for 

SSC estimation.
Comparison of Turbidity-Based and Streamflow-Based Nutrient Concentration Estimates 25

Figure 10. Observed total phosphorus and estimated total phosphorus for the turbidity-based model and 

two streamflow-based models for (A) James River at Cartersville, Virginia, and (B) Rappahannock River near 

Fredericksburg, Virginia.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

OBSERVED TOTAL PHOSPHORUS, IN MILLIGRAMS PER LITER

ESTIMATED TOTAL PHOSPHORUS, IN MILLIGRAMS PER LITER

(A)

(B)

Figure 10. Observed total phosphorus and estimated total phosphorus for the turbidity-based model

 and two streamflow-based models for (A) James River at Cartersville, Virginia, and (B) Rappahannock

 River near Fredericksburg, Virginia.

Turbidity-based model

Streamflow-based model (9 year)

Streamflow-based model (study period)

1:1 Line

Turbidity-based model

Streamflow-based model (9 year)

Streamflow-based model (study period)

1:1 Line
26 Turbidity-Based and Streamflow-Based Estimates of Suspended Sediment in Three Chesapeake Bay Tributaries

Table 15. Error statistics for turbidity-based and streamflow-based estimates of 

total phosphorus concentration and instantaneous load (in parentheses) for the 

monitoring stations at the James River at Cartersville and Rappahannock River near 

Fredericksburg, Virginia.

[n, number of observations/estimations used to compute statistics; SSE, sum of squared errors; 

MSE, mean squared error; MAE, mean absolute error]

Turbidity-based 

error statistics

Streamflow-based 

error statistics 

(using 9-year dataset)

Streamflow-based 

error statistics 

(using study-period dataset)

James River at Cartersville (n = 61)

SSE 0.055 (626.3) 0.370 (4,568.6) 0.164 (1,868.7)

MSE 0.001 (10.3) 0.006 (74.9) 0.003 (30.6)

MAE 0.019 (1.2) 0.044 (3.6) 0.030 (2.4)

Rappahannock River near Fredericksburg (n = 42)

SSE 0.191 (124.4) 0.376 (1,135.7) 0.276 (718.7)

MSE 0.005 (3.0) 0.009 (27.0) 0.007 (17.1)

MAE 0.035 (0.6) 0.046 (1.3) 0.039 (1.1)

Table 16. P-values for one-way squared-ranks tests on the variance of estimates 

and residuals for turbidity-based and streamflow-based total phosphorus 

estimation models for the monitoring stations at the James River at Cartersville 

and Rappahannock River near Fredericksburg, Virginia.

[<, less than]

Streamflow-based p-values 

(using 9-year dataset)

Streamflow-based p-values 

(using study-period dataset)

James River at Cartersville

Estimates <0.01 <0.01

Residuals <0.01 0.119

Rappahannock River near Fredericksburg

Estimates 0.02 <0.01

Residuals <0.01 <0.01
Comparison of Turbidity-Based and Streamflow-Based Nutrient Concentration Estimates 27

Figure 11. Total phosphorus concentrations and percent particulate phosphorus for the James River at Cartersville, 

Virginia, and Rappahannock River near Fredericksburg, Virginia.

0

10

20

30

40

50

60

70

80

90

100

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

TOTAL PHOSPHORUS, IN MILLIGRAMS PER LITER

PERCENT PARTICULATE 

Rappahannock

James

Figure 11. Total phosphorus concentrations and percent particulate phosphorus for the James River at Cartersville, Virginia,

and Rappahannock River near Fredericksburg, Virginia.

The streamflow-based TN estimation models were not as 

efficient at explaining variability as the streamflow-based TP 

estimation models; the TN estimation models explained only 

about 60–68 percent of the variability in TN (table 17). As 

with the TP estimation models, the streamflow-based model 

generated using the study-period dataset explained a greater 

portion of the variance in TN than did the model specified 

using the 9-year window dataset, likely because the shorter 

dataset contains less variability in the TN concentrations.

Results of the comparison of TN estimates from the 

streamflow-based model and from the turbidity-based model 

indicate that both methods provide similar results, with the 

turbidity-based approach providing only slightly improved 

accuracy (fig. 12). Although the fit of the streamflow-based 

TN estimates at the James River at Cartersville monitoring 

station is comparable to the fit of the turbidity-based estimates, 

a slightly better fit is observed in the turbidity-based estimates 

at the Rappahannock River monitoring station. 

Comparison of the magnitude (absolute value) of the 

residuals at each site is shown in figure 13, where points 

plotting above the 1:1 indicate greater error in the streamflowbased estimates and points below the 1:1 line indicate greater 

error in the turbidity-based estimates. Although not as apparent in figure 12, the magnitude of residuals at the James River 

monitoring station tends to be less for the turbidity-based 

estimates, and the magnitude of residuals at the Rappahannock River monitoring station tends to be greater for the 

streamflow-based estimates. These findings are supported 

Table 17. Coefficients for streamflow-based total nitrogen estimation models for the monitoring stations at the James River at 

Cartersville and Rappahannock River near Fredericksburg, Virginia.

[ln, natural logarithm; q, streamflow in cubic feet per second; qc, centered streamflow (streamflow – mean streamflow); t, decimal time; t

c

, centered decimal 

time (decimal time – mean decimal time); sin, sine function; cos, cosine function; π, pi]

Dataset

Coefficient (p-value) Number of 

observations

Adjusted 

coefficient of 

Intercept ln (q / qc) [ln (q / qc)] determination 2 (t – t

c

) (t – t

c

)

2 sin(2πt) cos(2πt)

James River at Cartersville

9-year 

window

–0.670

(<0.01)

0.404

(<0.01)

0.084

(<0.01)

–0.014

(0.15)

–0.001

(0.75)

–0.061

(0.09)

–0.078

(0.03) 222 0.618

Study 

period

–0.622

(<0.01)

0.407

(<0.01)

0.101

(<0.01)

–0.017

(0.61)

–0.035

(0.30)

–0.107

(0.05)

–0.119

(0.03) 77 0.677

Rappahannock River near Fredericksburg

9-year 

window

–0.328

(<0.01)

0.360

(<0.01)

0.031

(<0.01)

–0.018

(0.18)

–0.003

(0.65)

–0.002

(0.97)

0.024

(0.64) 194 0.596

Study 

period

–0.292

(<0.01)

0.330

(<0.01)

0.036

(0.08)

–0.005

(0.91)

0.013

(0.80)

0.009

(0.90)

0.107

(0.20) 74 0.627
28 Turbidity-Based and Streamflow-Based Estimates of Suspended Sediment in Three Chesapeake Bay Tributaries

Figure 12. Observed total nitrogen and estimated total nitrogen for the turbidity-based model and two 

streamflow-based models for (A) James River at Cartersville, Virginia, and (B) Rappahannock River near 

Fredericksburg, Virginia.

(A)

(B)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

OBSERVED TOTAL NITROGEN, IN MILLIGRAMS PER LITER

ESTIMATED TOTAL NITROGEN, IN MILLIGRAMS PER LITER

Figure 12. Observed total nitrogen and estimated total nitrogen for the turbidity-based model and two

streamflow-based models for (A) James River at Cartersville, Virginia, and (B) Rappahannock River

near Fredericksburg, Virginia.

Turbidity-based model

Streamflow-based model (9 year)

Streamflow-based model (study period)

1:1 Line

Turbidity-based model

Streamflow-based model (9 year)

Streamflow-based model (study period)

1:1 Line
Comparison of Turbidity-Based and Streamflow-Based Nutrient Concentration Estimates 29

Figure 13. The absolute value of residuals from the turbidity-based total nitrogen estimation model and 

absolute value of residuals from the two streamflow-based total nitrogen estimation models for (A) James 

River at Cartersville, Virginia, and (B) Rappahannock River near Fredericksburg, Virginia.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.200

0.000

0.400

0.600

0.800

1.000

1.200

1.400

1.600

0.000 0.200 0.400 0.600 0.800 1.000 1.200 1.400 1.600

(A)

(B)

ABSOLUTE VALUE OF TURBIDITY-BASED MODEL RESIDUAL ERROR

ABSOLUTE VALUE OF STREAMFLOW-BASED MODEL RESIDUAL ERROR

Figure 13. The absolute value of residuals from the turbidity-based total nitrogen estimation model and absolute

value of residuals from the two streamflow-based total nitrogen estimation models for (A) James River at

Cartersville, Virginia, and (B) Rappahannock River near Fredericksburg, Virginia.

Streamflow-based model (9 year)

Streamflow-based model (study period)

1:1 Line

Streamflow-based model (9 year)

Streamflow-based model (study period)

1:1 Line
30 Turbidity-Based and Streamflow-Based Estimates of Suspended Sediment in Three Chesapeake Bay Tributaries

Table 18. Error statistics for turbidity-based and streamflow-based estimates of total nitrogen 

concentration and instantaneous load (in parentheses) for monitoring stations at the James 

River at Cartersville and Rappahannock River near Fredericksburg, Virginia.

[n, number of observations/estimations used to compute statistics; SSE, sum of squared errors; MSE, mean 

squared error; MAE, mean absolute error]

Turbidity-based 

error statistics

Streamflow-based 

error statistics 

(using 9-year dataset)

Streamflow-based 

error statistics 

(using study-period dataset)

James River at Cartersville (n = 61)

SSE 1.28 (7,105.4) 2.30 (1,5606.0) 2.21(13,699.6)

MSE 0.021 (116.5) 0.038 (255.8) 0.036 (224.6)

MAE 0.106 (4.8) 0.146 (7.5) 0.143 (7.4)

Rappahannock River near Fredericksburg (n = 42)

SSE 2.04 (1,691.3) 6.52 (8,008.4) 7.06 (10,899.3)

MSE 0.049 (40.3) 0.155 (190.7) 0.168 (259.5)

MAE 0.177 (2.5) 0.276 (4.7) 0.27 (5.0)

Table 19. P-values for one-way squared-ranks tests on the variance of 

estimates and residuals for turbidity-based and streamflow-based total 

nitrogen estimation models for the monitoring stations at the James River 

at Cartersville and Rappahannock River near Fredericksburg, Virginia.

Streamflow-based 

p-values (using 

9-year dataset)

Streamflow-based 

p-values (using 

study-period dataset)

James River at Cartersville

Estimates 0.789 0.063

Residuals 0.035 0.022

Rappahannock River near Fredericksburg

Estimates 0.766 0.250

Residuals 0.078 0.095

by the error statistics for the models at each site, which also 

demonstrate less error (greater accuracy) in the turbidity-based 

estimates compared to the streamflow-based estimates of TN 

and instantaneous TN load (table 18). 

The squared-ranks test performed on the TN estimates 

and residuals at each site yielded mixed results, with most 

outcomes failing to detect significant differences in the 

precision of the two estimation approaches (table 19). The 

exception to this lack of significance is that the variance of the 

residuals from the turbidity-based TN estimation at the James 

River monitoring station is significantly less than that of the 

streamflow-based estimation models. The results of the test of 

residuals at the Rappahannock River monitoring station are 

not significant using the significance level established for this 

study (α-level = 0.05).

The finding that there is generally no major difference 

in the accuracy and precision of TN estimates from turbiditybased and streamflow-based approaches is reasonable because 

nitrogen transport is dominated by dissolved species. This 

results in generally low percent-particulate values, which are 

not well represented by these methods (fig. 14). 
Limitations and Challenges of the Turbidity-Based Method 31

Limitations and Challenges of the 

Turbidity-Based Method

Although the turbidity-based approach of estimating 

suspended-sediment and nutrient concentrations provides 

greater accuracy and precision than the traditional streamflowbased approach, the method is not without limitations. These 

limitations range from data collection challenges to limitations 

in the tools available for data analysis.

Collection of continuous water-quality data, such as 

turbidity, presents challenges similar to those associated 

with operating continuous-record streamgages, as well as 

challenges unique to continuous water-quality sensors. As 

with streamgages, consideration must be given to site-specific 

conditions to ensure the water-quality monitor and associated 

components are adequately protected from high water, high 

velocities, and any associated debris, while maintaining 

acceptable in-stream performance. Unlike streamgages, 

sensors on continuous water-quality monitors (particularly 

optical turbidity sensors) are susceptible to fouling by biological growth, siltation, and entangled debris. These effects 

may be minimized through careful sensor placement and 

other creative solutions, but ultimately, successful operation 

of continuous water-quality monitors requires flexibility in 

staffing to perform unscheduled site maintenance when such 

fouling occurs. These episodes of sensor fouling create a 

data-analysis challenge because discarded data from fouled 

sensors result in data gaps that must be addressed prior to 

data analysis. Resolving data gaps requires consideration of 

study objectives and effects on end products (such as loads 

and yields). In some circumstances, filling in missing periods 

of data using the existing data as a guide may be acceptable; 

in other cases, using an alternative method to make inferences 

about conditions during gaps in the continuous water-quality 

monitor data may be necessary.

Application of methods using continuous water-quality 

data for the estimation of constituent loadings has one 

apparent major limitation—methods and tools for estimating 

loads and associated variance require further development. 

Currently available tools, such as ESTIMATOR, LOADEST 

(Runkel and others, 2004), and the turbidity threshold sampling (TTS) software developed by Lewis and Eads (2008), do 

not contain the functionality required to calculate the variance 

of loads estimated from concentration-estimation models 

using transformations of the response variable other than the 

natural-logarithm. This is a major limitation; this study has 

demonstrated that estimation models using natural-logarithm 

transformations may not produce the best possible concentration estimates, and in some circumstances, models using the 

natural-logarithm transformation do not meet the assumptions 

of linear regression. This limitation is a result of the lack of 

development of statistical methods for estimating the variance 

of loads generated from models using non-logarithm transformations (C.G. Crawford, D.L. Lorenz, and G.E. Schwarz, 

U.S. Geological Survey, oral commun., 2008). Derivation of 

the statistical methods and development of a tool for application of such procedures would require a concerted effort. 

The statistical methods for calculation of the variance of load 

estimates using natural-logarithm transformations developed 

by Gilroy and others (1990) require calculation of the variance 

and covariance of all variables, which is a computationally 

intensive process available in software packages designed for 

load estimation. A similar effort would be required to develop 

these procedures for use with non-logarithm transformations. 

A further limitation of LOADEST for use with continuous 

water-quality data is that the finest temporal resolution achievable is hourly; with continuous water-quality data typically 

Figure 14. Total nitrogen concentration and percent particulate nitrogen for the James River at Cartersville, Virginia, 

and Rappahannock River near Fredericksburg, Virginia.

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

0

10

20

30

40

50

60

70

80

90

100

PERCENT PARTICULATE 

Rappahannock

James

TOTAL NITROGEN, IN MILLIGRAMS PER LITER

Figure 14. Total nitrogen concentration and percent particulate nitrogen for the James River at Cartersville, Virginia, and

Rappahannock River near Fredericksburg, Virginia.
32 Turbidity-Based and Streamflow-Based Estimates of Suspended Sediment in Three Chesapeake Bay Tributaries

collected at 15-minute intervals, software capable of using 

data at this resolution is needed. The TTS software package 

was developed by investigators working in flashy headwater 

streams and was designed for use with data collected at 

10-minute intervals (Lewis and Eads, 2008).

Potential Applications of TurbidityBased Estimation Models

Continuous turbidity data and estimations of constituent 

concentrations based on continuous turbidity data represent 

an accurate and temporally dense dataset that can provide 

a valuable tool for resource managers, policy makers, 

academics, and others to apply to a wide range of waterresource problems. As demonstrated by this investigation, 

these data can be used to effectively estimate sediment and 

nutrient concentrations; in addition, effective turbidity-based 

estimation models may be generated for other particulate 

or particulate-associated constituents such as bacteria and 

sediment-bound contaminants. These estimation models 

may provide the foundational data needed for process-level 

transport studies, watershed modeling, time-series analysis, 

trend analysis, total maximum daily load (TMDL) studies, 

public health investigations and warning systems, and many 

additional applications at scales ranging from individual best 

management practice (BMP) structures to large rivers.

One possibility for applying turbidity-based estimation 

models in public health matters is the development of realtime beach-closure programs. Currently, most beach-closure 

programs operate on a lag, typically 24 hours, because of the 

incubation time required for bacteria analysis (Francy and 

Darner, 2002; Francy and others, 2006). Coupling realtime 

turbidity measurements with turbidity-based bacteria estimation models can provide a means for basing beach-closure 

decisions on current conditions, rather than on conditions from 

the previous day (Francy and Darner, 2002; Francy and others, 

2006). This approach could greatly reduce beachgoers risk of 

exposure to pathogens and potentially reduce the economic 

impact of beach closures in resort areas as periods of risk 

would be more accurately defined.

Another possible application of turbidity-based estimation models, when coupled with real-time data collection, 

is for the detection of changing or impaired water-quality 

conditions. Real-time water-quality alone may be used to 

detect changes in, or impairments from, those measured 

parameters. Furthermore, estimation models may be coupled 

with those data to detect changes in, or impairments from, 

constituents that can be effectively estimated. In addition 

to these methods for instantaneous detections, frequency 

distributions of measured parameters or estimated constituents 

may be used to detect impairments when impairment criteria 

are based on exceeding a given value for a given period of 

time, or to detect change over time. Such changes over time 

may be in the form of declining water quality in response to 

detrimental near-stream or landscape-level activities, or in 

the form of improving water-quality conditions in response to 

BMP implementation or stream-restoration activities.

Many investigations seek to quantify the total mass of 

a constituent transported by a river of interest in order to 

determine the loading to receiving waters (such as the bay) 

or to assist in the development of TMDLs for regulatory 

purposes. Using concentration estimates generated from 

regression models on continuous water-quality data to estimate 

constituent loading is an obvious application of the data. 

This study has demonstrated that these models are capable of 

estimating constituent concentrations and instantaneous loads 

with greater precision and accuracy than streamflow-based 

approaches, and summed load estimates based on these 

concentration estimates will also have greater accuracy and 

precision than those based on streamflow. 

Total monthly and annual suspended-sediment loads 

for water year 2007 have been estimated for the James River 

at Cartersville monitoring station using streamflow- and 

turbidity-based concentration estimation models presented 

earlier in this report. These estimations were generated to 

demonstrate the load estimation application and the improvement over the streamflow-based approach. Current software 

packages do not permit the use of transformations other 

than natural logarithm for the response variable; thus, the 

turbidity-based estimation model using the natural-logarithm 

transformation (table 3) was used in the LOADEST program 

to estimate turbidity-based loads. Although the naturallogarithm model was determined to provide estimates of SSC 

with greater error than the square-root transformed model, 

the natural-logarithm model was found to be an acceptable 

model because the assumptions of linear regression were not 

violated. Hourly turbidity, water temperature, and streamflow 

values were extracted from the 15-minute-interval datasets for 

use in LOADEST. Short periods (approximately 8 hours or 

less) of missing values for all parameters were estimated as the 

average of nearest neighbors. The turbidity dataset contained 

two periods of missing data that were longer in duration, 

occurring as a result of biological fouling during extended 

periods of low streamflow and turbidity. Because no storm 

event occurred during these periods, resulting in negligible 

sediment transport, these periods were assigned estimated 

turbidity values equal to the 25th percentile of the observed 

turbidity dataset; graphical analysis of the resulting dataset 

indicated that this was a reasonable approximation. Finally, 

all turbidity values equal to zero were assigned a value of 0.1 

to permit the use of the natural-logarithm transform. These 

modifications to the dataset are not expected to adversely 

alter the load estimates. The streamflow-based estimates of 

SSL were calculated using the 9-year-window model in the 

ESTIMATOR program. 

Results of the load estimation procedures demonstrate 

that although the streamflow- and turbidity-based methods 

typically generate similar estimates of SSL, the turbidity-based 

approach provides estimates of load with reduced uncertainty 

(fig. 15), which is expected given the results of the comparison 
Summary and Conclusions 33

of concentration models and instantaneous SSL. This reduced 

uncertainty is quantified by the mean monthly coefficient of 

variation (CV), or standard error of prediction as a percentage 

of the load. The CV is 38 percent for the streamflow-based 

load estimates and 12 percent for the turbidity-based load 

estimates. These results are consistent with those presented 

by Miller and others (2007) for a similar analysis on the 

Anacostia River in Maryland. The improved precision in the 

turbidity-based loads is a direct effect of the improved precision in the turbidity-based concentration estimates. With the 

square-root transformed model generating SSC estimates with 

even less uncertainty than the natural-logarithm transformed 

model, uncertainty in load estimations is expected to be further 

reduced if a tool could be developed for use with such models. 

The reduction of uncertainty in load estimates has numerous practical implications. Primarily, reduced uncertainty in 

the load estimates will facilitate change or trend detection, as 

smaller changes in load will be necessary to detect statistically 

significant differences. This may lead to more accurate and 

timely detection of trends resulting from management practices on the landscape, which ultimately leads to an improved 

understanding of processes affecting sediment and nutrient 

transport from the terrestrial environment to, and through, 

fluvial systems.

Summary and Conclusions 

Elevated suspended-sediment concentrations (SSC) and 

nutrient concentrations are major water-quality concerns in 

the Chesapeake Bay, the Nation’s largest estuary. Excess 

sediment is having an adverse effect on the living resources 

and associated habitat of the bay and its watershed. Because 

of excess nutrient and sediment levels, the bay was listed as an 

impaired water body in 1998 under the Clean Water Act. The 

USEPA Chesapeake Bay Program (CBP) needs information 

with which to evaluate current conditions and assess progress 

toward meeting sediment-reduction goals.

Implementation of recent technological and methodological advances in continuous water-quality monitoring and 

surrogate approaches has helped to generate estimates of SSC 

and suspended-sediment loads (SSL) with improved precision 

as compared with traditional approaches. The U.S. Geological 

Survey, in cooperation with the Chesapeake Bay Program and 

the Virginia Department of Environmental Quality, evaluated this approach in three major tributaries to the bay and 

compared the results with the conventionally applied approach 

using streamflow as the primary regressor for SSC estimation. 

Specifically, the objectives of this investigation were to

Figure 15. Monthly and annual suspended-sediment load estimations for the 2007 water year at the 

James River at Cartersville, Virginia, estimated using turbidity-based and streamflow-based methods.

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

TOTAL

10,000

100,000

1,000,000

10,000,000

100,000,000

1,000,000,000

SUSPENDED-SEDIMENT LOAD, IN KILOGRAMS

WATER YEAR 2007

Figure 15. Monthly and annual suspended-sediment load estimations for the 2007 water year at the James

River at Cartersville, Virginia, estimated using turbidity-based and streamflow-based methods.

Streamflow based Turbdity based

Upper 95-percent

confidence interval

Lower 95-percent

confidence interval

Upper 95-percent

confidence interval

Lower 95-percent

confidence interval
34 Turbidity-Based and Streamflow-Based Estimates of Suspended Sediment in Three Chesapeake Bay Tributaries

1. Evaluate the use of turbidity as a surrogate for estimating SSC in the James, Rappahannock, and North 

Fork Shenandoah Rivers, each of which drain into 

the Chesapeake Bay; and

2. Compare two methods of estimating SSC: turbiditybased and streamflow-based regression models.

These study objectives were expanded to include the 

evaluation of turbidity-based models to estimate nutrient 

concentrations, specifically total nitrogen (TN) and total 

phosphorous (TP).

Multivariate turbidity-based estimation models were 

generated using best-subsets regression procedures, with 

potential explanatory variables including continuously 

measured water-quality and streamflow parameters. Naturallogarithm and square-root transformations of the explanatory 

and response variables were evaluated, and in all instances, 

the square-root transformation provided estimates of constituent concentration with the least uncertainty. Turbidity-based 

models using the square-root transform explained 92–98 percent of the variability in SSC, 85–94 percent of the variability 

in TP, and 83–85 percent of the variability in TN. With one 

exception, a single-variable model using turbidity 

as the explanatory variable outperformed a single-variable 

model using streamflow as the explanatory variable. Furthermore, the use of a square-root transformation was shown to 

produce the most statistically acceptable models. In the case 

of similar levels of acceptability between the square-root and 

log-based transformations, the square-root transformation was 

shown to produce estimates of SSC and SSL with the least 

unexplained variance.

Two iterations of the streamflow-based estimation models 

were generated using the ESTIMATOR program. One was 

generated using a 9-year window of data because this is the 

dataset used by the CBP to estimate nutrient and sediment 

loadings to the bay. The second model was generated using 

the data from the same time period that was used to generate 

the turbidity-based models. These two models were generated 

so that comparisons of both the streamflow-based model 

and the approach used by the CBP could be compared with 

the turbidity-based models. Each of the streamflow-based 

estimation models explained a large portion of the variance 

in the estimated constituent, describing 74–88 percent of the 

variability in SSC, 58–85 percent of the variability in TP, and 

60–68 percent of the variability in TN. The streamflow-based 

estimation models specified using the study-period dataset 

consistently described a greater portion of the variance than 

the model generated from the 9-year window; this result is 

attributed to the shorter datasets having less variability in the 

constituent concentrations. 

Comparison of the streamflow-based and turbidity-based 

methods focused on the accuracy and precision of the two 

methods. Accuracy was evaluated through graphical and 

statistical comparison of the error in the re-transformed biascorrected concentration estimates. Precision was compared 

using a squared-ranks test of equal variance on the estimates 

and the residual errors in those estimates. Using these multiple 

lines of evidence, results of this study indicate that the 

turbidity-based modeling approach is capable of generating 

estimates of the concentration of particulate constituents with 

greater precision and accuracy than the streamflow-based 

modeling approach. Interpretation of the accuracy of the 

turbidity-based approach using graphical analysis of the 

model fit and residual error distributions is supported by the 

summary statistics calculated from the re-transformed and 

bias-corrected estimates of SSC, where the mean absolute 

error (MAE) of the turbidity-based estimates is found to be 

50–87 percent less than the corresponding value from the 

streamflow-based approach. The magnitude of error for the 

turbidity-based estimates of TP also was generally smaller, 

with MAE values 10–57 percent less than those from the 

streamflow-based estimates. Improvements in precision over 

the streamflow-based approach are typically evident through 

significant results from the squared-ranks test on the distribution of SSC estimates and associated residual errors. While the 

turbidity-based approach yields estimates of SSC and TP with 

greater accuracy and precision, the streamflow-based approach 

remains practicable.

The accuracy and precision of estimates of particulate 

concentrations using turbidity as an explanatory variable are 

improved because of the strong relation between turbidity 

and particulate material, and the lesser relation between 

streamflow and particulate concentrations. Turbidity is a 

measure of the optical properties of water, and those optical 

properties are directly influenced by suspended particulate 

matter. Therefore, the relation between turbidity and suspended matter stays the same, regardless of flow conditions. 

In contrast, streamflow influences suspension and transport 

of particulate material, so a relation exists between the two, 

but many confounding factors (such as variable source 

area contribution, variations in runoff intensity, and other 

non-constant variables) degrade the strength of the relation 

between streamflow and particulate concentrations. 

Results from the estimation of TN, a primarily dissolved 

constituent, did not indicate that either approach provided 

a definite advantage for estimating concentrations. Both 

approaches were found to provide acceptable estimates of 

TN. The turbidity-based model generated slightly more 

accurate concentration estimates, and precision tests gave 

mixed results about the significance of differences in variance 

of the estimates and residuals. Although the results were not 

typically statistically separable, the turbidity-based approach 

appears to provide more desirable results than the streamflowbased approach. The finding that neither approach yielded 

appreciably better estimates of TN follows the understanding 

that TN occurs mostly as nitrogen in the dissolved form; thus, 

neither turbidity nor streamflow are measures of TN that may 

be influenced by either predictor.

Improvements in the concentration estimates were shown 

to translate into similar improvements in load estimates. 

Monthly and annual suspended-sediment loads estimated for 

the James River at Cartersville monitoring station were shown 
References 35

to be more precise when estimated using the turbidity-based 

approach, with an average monthly coefficient of variation of 

12 percent compared with the average monthly coefficient of 

variation of 38 percent for the streamflow-based approach. The 

demonstrated improvements reveal the desirable characteristics of turbidity-based estimations; however, the streamflowbased approach remains a viable practical methodology.

Results of this effort demonstrate that use of continuous 

water-quality data and turbidity-based regression models to 

estimate SSC and nutrients is viable for use in tributaries to 

the bay. Furthermore, this investigation identified advantages 

of using the turbidity-based methodology relative to the 

currently applied streamflow-based approach. The advantages 

are that

1. The use of continuously monitored water-quality 

data coupled with turbidity-based regression models 

permits generation of a dense time-series dataset of 

accurate SSC and nutrient estimations, and

2. The precision of turbidity-based SSC and nutrient 

estimates, and consequently loads calculated from 

those estimates, is often significantly greater than 

the precision of those values estimated using the 

streamflow-based approach.

Although the turbidity-based approach has been shown 

to provide a more effective means for estimating constituent 

concentrations and loads, the approach requires further 

development to take full advantage of the improved precision 

in load estimates. Currently available statistical methods and 

load-calculation tools do not permit the use of response variable transformations other than natural logarithm because the 

tools to calculate estimates of the variance of the load have not 

been developed for other transformations. With the development of such statistical procedures and software to apply these 

procedures, reductions in the uncertainty of load estimations 

are expected to be greater than the reductions observed in 

this investigation. 

In conclusion, the model based on continuous turbidity 

data has been found to be capable of providing more precise 

estimates of sediment and nutrient concentrations and loads 

for the Chesapeake Bay tributaries than a model based on 

continuous streamflow data. These findings are important to 

many groups, including scientists, resource managers, policy 

makers, and the general public because application of this new 

methodology could promote an enhanced understanding of 

trends and transport processes. 

Acknowledgments

The authors thank U.S. Geological Survey (USGS) 

Hydrologic Technicians Amy Jensen, Brian Hasty, and Cathy 

Wright for their dedication to the success of the continuous 

water-quality monitoring and sampling efforts. Karen Ryberg 

and Greg Schwarz, of the USGS, and Gary Shenk, of the 

U.S. Environmental Protection Agency Chesapeake Bay 

Program, provided technical reviews of this report that 

resulted in multiple improvements, and the authors thank 

them for their efforts. This study was supported by Grant 

DW1494421701 from the Chesapeake Bay Program Office of 

the U.S. Environmental Protection Agency.

References

Anderson, C.W., 2005, Turbidity (version 2.1): U.S. Geological Survey Techniques of Water-Resources Investigations, 

book 9, chap. A6, section 6.7, accessed July 17, 2008, 

at http://water.usgs.gov/owq/FieldManual/Chapter6/

Section6.7_v2.1.pdf.

Belval, D.L., and Sprague, L.A., 1999, Monitoring nutrients in 

the major rivers draining to Chesapeake Bay: U.S. Geological Survey Water-Resources Investigations Report 99–4238, 

8 p.

Bradu, Dan, and Mundlak, Yair, 1970, Estimation in lognormal linear models: Journal of the American Statistical 

Association, v. 65, no. 329, p. 198–211.

Brakebill, J.W., Preston, S.D., and Martucci, S.K., 2001, 

Digital data used to relate nutrient inputs to water quality 

in the Chesapeake Bay watershed, version 2.0: U.S. Geological Survey Open-File Report 01–251, 17 p. 

Chesapeake Bay Program, 2000, Chesapeake Bay watershed boundary, accessed November 19, 2008, at 

ftp://ftp.chesapeakebay.net/pub/Geographic/MidAtlantic/

Watersheds/Chesapeake Bay/chesbay.zip.

Chesapeake Bay Program, 2008, Chesapeake Bay TMDL, 

accessed April 2, 2009, at http://archive.chesapeakebay.net/

pressrelease/TMDL_2008.pdf.

Christensen, V.G., 2001, Characterization of surface-water 

quality based on real-time monitoring and regression analysis, Quivira National Wildlife Refuge, south-central Kansas, 

December 1998 through June 2001: U.S. Geological Survey 

Water-Resources Investigations Report 01–4248, 28 p. 

Christensen, V.G., Jian, Xiaodong, and Ziegler, A.C., 2000, 

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, 36 p.

Christensen, V.G., Rasmussen, P.P., and Ziegler, A.C., 2002, 

Comparison of estimated sediment loads using continuous 

turbidity measurements and regression analysis [abs.], in

Proceedings of Turbidity and Other Sediment Surrogates 

Workshop, April 30–May 2, 2002, Reno, NV. 
36 Turbidity-Based and Streamflow-Based Estimates of Suspended Sediment in Three Chesapeake Bay Tributaries

Cohn, T.A., 1988, Adjusted maximum likelihood estimation of 

the moments of lognormal populations from type I censored 

samples: U.S. Geological Survey Open-File Report 88–350, 

34 p.

Cohn, T.A., Caulder, D.L., Gilroy, E.J., Zynjuk, L.D., and 

Summers, R.M., 1992, The validity of a simple statistical 

model for estimating fluvial constituent loads—An empirical study involving nutrient loads entering Chesapeake Bay: 

Water Resources Research, v. 28, no. 9, p. 2353–2363.

Conover, W.L., 1980, Practical nonparametric statistics 

(2d ed.): New York, John Wiley and Sons, 493 p.

Davies-Colley, R.J., and Smith, D.G., 2001, Turbidity, 

suspended sediment, and water clarity—A review: Journal 

of the American Water Resources Association, v. 37, no. 5, 

p. 1085–1101.

Duan, Naihua, 1983, Smearing estimate—A nonparametric 

retransformation method: Journal of the American Statistical Association, v. 78, p. 605–610.

Francy, D.S., and Darner, R.A., 2002, Forecasting bacteria 

levels at bathing beaches in Ohio: U.S. Geological Survey 

Fact Sheet FS–132–02, 4 p.

Francy, D.S., Darner, R.A., and Bertke, E.E., 2006, Models 

for predicting recreational water quality at Lake Erie 

beaches: U.S. Geological Survey Scientific Investigations 

Report 2006–5192, 13 p.

Gilroy, E.J., Hirsch, R.M., and Cohn, T.A., 1990, Mean square 

error of regression-based constituent transport estimates: 

Water Resources Research, v. 26, no. 9, p. 2069–2077.

Hayes, D.C., and Wiegand, Ute, 2006, Drainage areas of 

selected streams in Virginia: U.S. Geological Survey OpenFile Report 2006–1308, 51 p.

Helsel, D.R., and Hirsch, R.M., 2002, Statistical methods in 

water resources: U.S. Geological Survey Techniques of 

Water-Resources Investigations, book 4, chap. A3, 523 p. 

Horowitz, A.J., 2003, An evaluation of sediment rating curves 

for estimating suspended sediment concentrations for 

subsequent flux calculations: Hydrological Processes, v. 17, 

no. 17, p. 3387–3409.

Johnson, H.M., and Belval, D.L., 1998, Nutrient and suspended solids loads, yields, and trends in the non-tidal 

part of five major river basins in Virginia, 1985–96: 

U.S. Geological Survey Water-Resources Investigations 

Report 98–4025, 36 p.

Langland, M.J., Phillips, S.W., Raffensperger, J.P., and Moyer, 

D.L., 2004, Changes in streamflow and water quality 

in selected nontidal sites in the Chesapeake Bay basin, 

1985–2003: U.S. Geological Survey Scientific Investigations Report 2004–5259, 50 p.

Lewis, Jack, and Eads, Rand, 2008, Implementation guide 

for turbidity threshold sampling—Principles, procedures, 

and analysis: Albany, CA, U.S. Department of Agriculture, 

Forest Service, Pacific Southwest Research Station, General 

Technical Report PSW–GTR–212, 86 p.

Marquardt, D.W., 1970, Generalized inverses, ridge regression, biased linear estimation, and nonlinear estimation: 

Technometrics, v. 12, no. 3, p. 591–612.

Meade, R.H., and Parker, R.S., 1984, Sediment in rivers of the 

United States, in U.S. Geological Survey, National water 

summary 1984—Hydrologic events, selected water-quality 

trends, and ground-water resources: U.S. Geological Survey 

Water-Supply Paper 2275, p. 49–60.

Meade, R.H., Yuzyk, R.T., and Day, T.J., 1990, Movement 

and storage of sediment in rivers of the United States and 

Canada, in Wolman, M.G., and Riggs, H.C., eds., The geology of North America, v. 0–1: Boulder, Colorado, Geological Society of America, p. 255–280.

Miller, C.V., Gutiérrez-Magness, A.L., Feit Majedi, B.L., 

and Foster, G.D., 2007, Water quality in the upper 

Anacostia River, Maryland—Continuous and discrete 

monitoring with simulations to estimate concentrations 

and yields, 2003–05: U.S. Geological Survey Scientific 

Investigations Report 2007–5142, 43 p.

Montgomery, D.C., Peck, E.A., and Vining, G.G., 2006, Introduction to linear regression analysis (4th ed.): Hoboken, NJ, 

John Wiley & Sons, Inc., 612 p.

O’Brien, R.M., 2007, A caution regarding rules of thumb for 

variance inflation factors: Quality & Quantity, v. 41, 

p. 673–690. 

Osterkamp, W.R., Heilman, Phillip, and Gray, J.R., 2004, An 

invitation to participate in a North American sedimentmonitoring network: Eos Transactions American Geophysical Union, v. 84, no. 40, p. 386.3

Osterkamp, W.R., Heilman, Phillip, and Lane, L.J., 1998, Economic consideration of a continental sediment-monitoring 

program: International Journal of Sediment Research, v. 13, 

p. 12–24.

Pimentel, D., Harvey, C., Resosudarmo, P., Sinclair, K., 

Kurz, D., McNair, M., Crist, S., Shpritz, L., Fitton, L., 

Saffouri, R., and Blair, R., 1995, Environmental and 

economic costs of soil erosion and conservation benefits: 

Science, v. 267, p. 1117–1123.

Porterfield, George, 1972, Computation of fluvial-sediment 

discharge: U.S. Geological Survey Techniques of WaterResources Investigations, book 3, chap. C3, 66 p.
References 37

Rasmussen, T.J., Lee, C.J., and Ziegler, A.C., 2008, Estimation 

of constituent concentrations, loads, and yields in streams of 

Johnson County, northeast Kansas, using continuous waterquality monitoring and regression models, October 2002 

through December 2006: U.S. Geological Survey Scientific 

Investigations Report 2008–5014, 103 p.

Rasmussen, T.J., Ziegler, A.C., and Rasmussen, P.P., 2005, 

Estimation of constituent concentrations, densities, loads, 

and yields in lower Kansas River, northeast Kansas, using 

regression models and continuous water-quality monitoring, January 2000 through December 2003: U.S. Geological 

Survey Scientific Investigations Report 2005–5165, 117 p.

Runkel, R.L., Crawford, C.G., and Cohn, T.A., 2004, Load 

estimator (LOADEST)—A FORTRAN program for estimating constituent loads in streams and rivers: U.S. Geological Survey Techniques and Methods, book 4, chap. A5, 

69 p.

Sholar, C.J., and Shreve, E.A., 1998, Quality-assurance plan 

for the analysis of fluvial sediment by the Northeastern 

Region, Kentucky District Sediment Laboratory: U.S. Geological Survey Open-File Report 98–384, 20 p.

U.S. Environmental Protection Agency, 2002, National water 

quality inventory—2000 report: U.S. Environmental Protection Agency EPA–841–R–02–001, 207 p.

U.S. Geological Survey, 1998, National field manual for the 

collection of water-quality data: U.S. Geological Survey 

Techniques of Water-Resources Investigations, book 9 

[variously paged].

U.S. Geological Survey, 2007, Chesapeake Bay, River Input 

Monitoring Program—Retrieve loads, accessed March 25, 

1999, at http://va.water.usgs.gov/chesbay/RIMP/loads.html.

Wagner, R.J., Mattraw, H.C., Ritz, G.F., and Smith, B.A., 

2000, Guidelines and standard procedures for continuous 

water-quality monitors—Site selection, field operation, calibration, record computation, and reporting: U.S. Geological 

Survey Water-Resources Investigations Report 00–4252, 

53 p.

Walling, D.E., 1977, Assessing the accuracy of suspended 

sediment rating curves for a small basin: Water Resources 

Research, v. 13, no. 3, p. 531–538.

Walling, D.E., and Collins, A.L., 2000, Integrated assessment of catchment sediment budgets—A technical manual: 

United Kingdom, University of Exeter, 168 p.

Wolman, M.G., and Miller, J.P., 1960, Magnitude and frequency of forces in the geomorphic processes: Journal of 

Geology, v. 68, p. 54–74.

Yochum, S.E., 2000, A revised load estimation procedure for 

the Susquehanna, Potomac, Patuxent, and Choptank Rivers: 

U.S. Geological Survey Water-Resources Investigations 

Report 00–4156, 49 p.

Prepared by:

USGS Enterprise Publishing Network

Raleigh Publishing Service Center

3916 Sunset Ridge Road

Raleigh, NC 27607

For additional information regarding this publication, contact:

Director

USGS Virginia Water Science Center

1730 East Parham Road

Richmond, VA 23228

phone: 804–261–2600

email: dc_va@usgs.gov

Or visit the Virginia Water Science Center Web site at:

http://va.water.usgs.gov

This publication is available online at http://pubs.usgs.gov/sir/2009/5165/.
Printed on recycled paper

Jastram and others—Turbidity- and Streamflow-Based Estimates of Suspended-Sediment Concentrations in Three Chesapeake Bay Tributaries—Scientific Investigations Report 2009–5165