U.S. Department of the Interior

U.S. Geological Survey

Techniques and Methods 3–C4

Guidelines and Procedures for Computing Time-Series 

Suspended-Sediment Concentrations and Loads from 

In-Stream Turbidity-Sensor and Streamflow Data

Chapter 4 of

Book 3, Applications of Hydraulics

Section C, Sediment and Erosion Techniques
Front cover. Background photograph shows Little Arkansas River near Sedgwick, Kansas. Inset photograph shows waterquality monitors suspended from bridge and lowered by USGS personnel into the Little Arkansas River near Sedgwick, Kansas (all 

photographs taken by Patrick Rasmussen, USGS) (http://nrtwq.usgs.gov/).

Back cover. Inset is screen capture from USGS Real Time Computed Water Quality for Kansas, Little Arkansas River near Sedgwick 

site (http://nrtwq.usgs.gov/).
Guidelines and Procedures for Computing 

Time-Series Suspended-Sediment 

Concentrations and Loads from In-Stream 

Turbidity-Sensor and Streamflow Data

By Patrick P. Rasmussen, John R. Gray, G. Douglas Glysson, and 

Andrew C. Ziegler

Chapter 4 of

Book 3, Applications of Hydraulics

Section C, Sediment and Erosion Techniques

Techniques and Methods 3–C4

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

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

Revised: 2011

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Rasmussen, P.P., Gray, J.R., Glysson, G.D., and Ziegler, A.C., 2009, Guidelines and procedures for computing timeseries suspended-sediment concentrations and loads from in-stream turbidity-sensor and streamflow data: 

U.S. Geological Survey Techniques and Methods, book 3, chap. C4, 52 p.

ISBN 978-1–4113–2410–7
iii

Contents

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

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

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

Related Guidelines................................................................................................................................3

Types of Turbidity Sensors ...........................................................................................................................4

Nephelometry........................................................................................................................................5

Optical Backscatter..............................................................................................................................6

Relation of Turbidity to Suspended-Sediment Concentration................................................................6

Model-Calibration Data Set ................................................................................................................6

Evaluation of Fixed-Location and Cross-Section Turbidity...................................................8

Determination of Turbidity and Streamflow Associated with Suspended-Sediment 

Concentrations ...............................................................................................................8

Identification of Outliers ...........................................................................................................10

Adequacy of Model-Calibration Data Set..............................................................................10

Update of Station Analysis.......................................................................................................12

Regression Model Development......................................................................................................12

Correlation...................................................................................................................................13

Simple Linear Regression for Computation of Suspended-Sediment Concentrations ..13

Transformation of Data .............................................................................................................15

Model Residual Analysis ..........................................................................................................16

Simple Linear Regression Model and Bias Correction Factor...........................................17

Prediction Intervals ...................................................................................................................18

Multiple Linear Regression ......................................................................................................19

Regression Model Summary....................................................................................................19

Computation of Suspended-Sediment Concentration and Load Time-Series Record.....................20

Estimates for Periods of Missing Data............................................................................................20

Computation of Suspended-Sediment Load Time-Series Records ............................................22

Model Validation and Maintainenance of a Long-Term Suspended-Sediment 

Concentration Record .................................................................................................22

Validation of Suspended-Sediment Concentration Model .................................................23

Sampling Plan......................................................................................................................................23

Changes to Turbidity Sensor Model or Type ..................................................................................24

Factors Affecting Relation Between Turbidity and Suspended-Sediment 

Concentration ...............................................................................................................25

Summary........................................................................................................................................................25

Acknowledgments.......................................................................................................................................25

Selected References...................................................................................................................................25

Appendix 1. Examples of Suspended-Sediment Concentration Models from Kansas, 

Oregon, Florida, and California ....................................................................................................32

Example 1. Complete Review Package for Little Arkansas River near Sedgwick, Kansas....33

Example 2. Turbidity Computed Suspended-Sediment Concentrations from Oregon.............39

Example 3. Turbidity Computed Suspended-Sediment Concentrations from Florida..............44

Example 4. Turbidity Computed Suspended-Sediment Concentrations Using 

Nonparametric Regression, California ..............................................................................46
iv

Appendix 2. Computation, Storage, and Real-Time Display of Time-Series SuspendedSediment Concentrations and Loads in National Water Information System .....................48

Appendix 3. Comparison of Computed Suspended-Sediment Concentrations with WaterQuality Criteria ................................................................................................................................51

Figures

1. Photographs showing three self-cleaning nephelometric turbidity sensors—A, YSI 

Incorporated (Yellow Springs, Ohio) model 6136 turbidity sensor, B, Hydrolab 

(Loveland, Colorado) self-cleaning turbidity sensor, and C, Forrest Technology 

Systems (Blaine, Washington) model DTS-12 turbidity sensor ............................................5

2. Photographs showing optical backscatter sensors (A) OBS 3+ (Campbell Scientific, 

Inc., Logan, Utah) and (B) Hach (Loveland, Colorado) Solitax ..............................................6

3. Check list for development, verification, and approval of a regression model to 

compute suspended-sediment concentration and load time-series data..........................7

4–18. Graphs showing—

4. Comparison of fixed-location and median cross-section turbidity measurements 

for U.S. Geological Survey streamgage on Little Arkansas River near Sedgwick, 

Kansas, November 1998–June 2005 ..........................................................................................8

5. A, Time-series turbidity and streamflow data, August 14–18, 2002, and B, duration 

of cross-section turbidity and suspended-sediment sample collection, 

August 15, 2002, at U.S. Geological Survey streamgage on Little Arkansas River 

near Sedgwick, Kansas ...............................................................................................................9

6. Comparison of turbidity to suspended-sediment concentration in water from 

U.S. Geological Survey streamgage on Little Arkansas near Sedgwick, Kansas, 

August 2000–June 2005 .............................................................................................................10

7. Duration curves for A, turbidity and B, streamflow and corresponding values 

associated with suspended-sediment concentration samples collected at 

U.S. Geological Survey streamgage on Little Arkansas River near Sedgwick, 

Kansas, 1999–2005......................................................................................................................11

8. Relations between A, turbidity and suspended-sediment concentration, 

B, streamflow and suspended-sediment concentration in linear space,

C, turbidity and suspended-sediment concentration, and D, streamflow and 

suspended-sediment concentration in log10 space for U.S. Geological Survey 

streamgage on Little Arkansas River near Sedgwick, Kansas, 1999–2005.......................14

9. Comparison of turbidity and streamflow at the time of sample collection in 

A, linear space and in B, log10 space for U.S. Geological Survey streamgage 

on Little Arkansas River near Sedgwick, Kansas, 1999–2005 .............................................15

10. Results of simple linear regression analysis for A, turbidity and suspendedsediment concentration data, and a comparison of B, estimated suspendedsediment concentrations and regression residuals, and C, probability plot of 

residuals for U.S. Geological Survey streamgage on Little Arkansas River near 

Sedgwick, Kansas, 1999–2005 ..................................................................................................16

11. Results of simple linear regression analysis using log-transformed data for 

A, turbidity and suspended-sediment concentration data, and comparison of 

B, computed log10 suspended-sediment concentration and regression residuals, 

and C, probability plot of residuals for U.S. Geological Survey streamgage on Little 

Arkansas River near Sedgwick, Kansas, 1999–2005.............................................................16
v

12. Comparison of turbidity and suspended-sediment concentration model-calibration 

data and uncorrected and bias-corrected simple linear regression lines for 

U.S. Geological Survey streamgage on Little Arkansas River near Sedgwick, 

Kansas, 1999–2005......................................................................................................................18

13. Comparison of measured and model-estimated suspended-sediment concentrations 

for U.S. Geological Survey streamgage on Little Arkansas River near Sedgwick, 

Kansas, 1999–2005......................................................................................................................18

14. Comparison of streamflow in A, linear space and in B, log10 space to residuals 

from a simple linear regression analysis of turbidity and suspended-sediment 

concentrations for U.S. Geological Survey streamgage on Little Arkansas River 

near Sedgwick, Kansas, 1999–2005.........................................................................................19

15. Comparison of measured and estimated suspended-sediment concentration and 

residuals in log space from A, simple and B, multiple linear regression models for 

U.S. Geological Survey streamgage on Little Arkansas River near Sedgwick, 

Kansas ..........................................................................................................................................21

16. Model-calibration data set (water years 1999–2005) and new (water year 2006) 

turbidity and suspended-sediment concentration data for U.S. Geological Survey 

streamgage on Little Arkansas River near Sedgwick, Kansas ...........................................23

17. Comparison of turbidity measurements from YSI turbidity models 6026 and 6136 in 

various solutions.........................................................................................................................24

18. Relation between YSI 6026 and YSI 6136 turbidity sensor values, U.S. Geological 

Survey streamgage on Little Arkansas River near Sedgwick, Kansas, July 14, 2004, 

to August 26, 2005 .......................................................................................................................24

Tables

1. Selected specifications for selected turbidity instruments...................................................4

2. Statistical summary of model-calibration data set for U.S. Geological Survey 

streamgage on Little Arkansas River near Sedgwick, Kansas, January 1999–

December 2005............................................................................................................................12

3. Diagnostic statistics of linear regression for evaluation and comparison of 

regression models ......................................................................................................................15

4. Expressions of simple linear regression and multiple linear regression models 

for U.S. Geological Survey streamgage on Little Arkansas River near Sedgwick, 

Kansas ..........................................................................................................................................20
vi

Conversion Factors

Multiply By To obtain

Length

micrometer (μm) 3.937 x 10-5 inch (in.)

nanometer (nm) 3.937 x 10-5 inch (in.)

Area

square mile (mi2) 2.590 square kilometer (km2) 

Rate

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

ton per day (ton/d) 0.9072 metric ton per day

ton per second (ton/s) 0.9072 megagram per second (Mg/s)

Water-Quality Units

Chemical concentration is given in units of milligrams per liter (mg/L). Milligrams per 

liter are units expressing the mass of solute per unit volume (liter) of water. Milligrams per liter 

are equivalent to parts per million.

Acronymns and Abbreviations

< less than or equal to

> greater than

ADAPS Automated Data Processing System (U.S. Geological Survey)

ANCOVA analysis of covariance

ASTM American Society for Testing and Materials

AU attenuation units

BCF bias correction factor

BU backscatter units

Cp Mallow’s Cp

DD data descriptor

DECODES Device Conversion and Delivery System (U.S. Geological Survey)

DV daily value

ei residual error

FAU formazin attenuation units

FBU formazin backscatter units

FNMU formazin nephelometric multibeam units

FNRU formazin nephelometric ratio units

FNU formazin nephelometric units

GCLAS Graphical Constituent Loading Analysis System (U.S. Geological Survey)

ISO International Organization for Standardization

log10 base-10 logarithm 

MLR multiple linear regression

MSPE model standard percentage error
vii

Acronymns and Abbreviations—Continued

MVUE minimum variance unbiased estimator

NTMU nephelometric turbidity multibeam units

NTRU nephelometric turbidity ratio units

NTU nephelometric turbidity units

NWIS National Water Information System (U.S. Geological Survey)

OBS optical backscatter

OLS ordinary least squares

PPCC probability plot correlation coefficient

PRESS prediction error sum of squares

QWDATA U.S. Geological Survey water-quality database

r correlation coefficient

R2 coefficient of determination

R2

a adjusted coefficient of determination

RDB relational database

RMSE root-mean-squared error

SLR simple linear regression

SSC suspended-sediment concentration

SSL suspended-sediment load

TSS total suspended solids

USEPA U.S. Environmental Protection Agency

USGS U.S. Geological Survey

UV unit value

VIF variance inflation factor

WSC Water Science Center (U.S. Geological Survey)

YSI YSI Inc. (Yellow Springs, Ohio)

Abstract

In-stream continuous turbidity and streamflow data, calibrated with measured suspended-sediment concentration data, 

can be used to compute a time series of suspended-sediment 

concentration and load at a stream site. Development of a simple linear (ordinary least squares) regression model for computing suspended-sediment concentrations from instantaneous 

turbidity data is the first step in the computation process. If 

the model standard percentage error (MSPE) of the simple 

linear regression model meets a minimum criterion, this model

should be used to compute a time series of suspended-sediment concentrations. Otherwise, a multiple linear regression 

model using paired instantaneous turbidity and streamflow 

data is developed and compared to the simple regression 

model. If the inclusion of the streamflow variable proves to 

be statistically significant and the uncertainty associated with 

the multiple regression model results in an improvement over 

that for the simple linear model, the turbidity-streamflow 

multiple linear regression model should be used to compute a 

suspended-sediment concentration time series. The computed 

concentration time series is subsequently used with its paired 

streamflow time series to compute suspended-sediment loads 

by standard U.S. Geological Survey techniques. 

Once an acceptable regression model is developed, it 

can be used to compute suspended-sediment concentration 

beyond the period of record used in model development with 

proper ongoing collection and analysis of calibration samples. 

Regression models to compute suspended-sediment concentrations are generally site specific and should never be considered 

static, but they represent a set period in a continually dynamic 

system in which additional data will help verify any change in 

sediment load, type, and source.

Introduction

Collection, computation, storage, and publication of 

suspended-sediment concentrations (SSCs), suspend-sediment 

loads (SSLs), and related environmental data can be important 

parts of investigations to evaluate the effects of fluvial sediment on a water resource (Glysson, 1989a). Suspended sediment can adversely affect water supply, recreation, aquatic 

life, flood control, transportation, fisheries, reclamation, and 

navigation (Angino and O’Brien, 1968). The U.S. Environmental Protection Agency (2008) lists sediment and other 

solid-phase constituents to be the most prevalent source of 

impairment of the Nation’s surface water.

Traditionally, SSC data have been derived from analytical 

results from physical samples collected by methods described 

by Edwards and Glysson (1999), Nolan and others (2005), and 

Gray and others (2008). SSL data have been computed from 

SSC and streamflow data by methods described by Porterfield 

(1972) and Koltun and others (1994, 2006). The traditional 

U.S. Geological Survey (USGS) computation technique presented by Porterfield (1972) is predicated on the availability of 

more frequent than daily (continuous) streamflow time-series 

data and a concurrent trace of SSC interpolated from physical 

samples, and where necessary, SSC estimates. Interpolated and 

estimated parts of a SSC trace for a stream site can include 

periods during which a substantial cumulative fraction of the 

annual SSL occurs. Hence, considerable hydrologic judgment 

often is required to compute sediment records by Porterfield’s 

(1972) method.

Turbidity is an expression of the optical properties of 

a sample that causes light rays to be scattered and absorbed 

rather than transmitted in straight lines through the sample 

(Anderson, 2005; ASTM International, 2007). Turbid water 

results from the presence of suspended and dissolved matter such as clay, silt, finely divided organic matter, plankton, 

other microscopic organisms, organic acids, and dyes (ASTM 

International, 2007). 

The magnitude of turbidity in streams, lakes, and 

estuaries is often proportional to SSC. When proportional, 

the turbidity-SSC relation can be quantified through linear 

regression analysis (Walling, 1977; Gilvear and Petts, 1985; 

Buchanan and Schoellhamer, 1995; Lewis, 1996; Christensen 

and others, 2000; Uhrich and Bragg, 2003; Lietz and Debiak, 

2005; Rasmussen and others, 2005; Lee and others 2009). 

The turbidity-SSC regression model, in turn, can be used to 

compute SSC values from turbidity data within the turbidity 

Guidelines and Procedures for Computing Time-Series 

Suspended-Sediment Concentrations and Loads from 

In-Stream Turbidity-Sensor and Streamflow Data

By Patrick Rasmussen, John R. Gray, G. Douglas Glysson, and Andrew C. Ziegler
2 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data

meter’s measurement range. Continuously monitored turbidity 

data enable computation of a SSC time series that can be used 

with its paired streamflow time series to compute continuous 

SSL without the routine need for interpolation or estimation. 

When the turbidity-SSC model is deemed adequate, 

regression-computed SSC can provide a more reliable and 

reproducible SSC time series with smaller uncertainty values 

than either a sediment-transport curve using streamflow as the 

sole independent variable for computations of SSC (Rasmussen and other, 2005; Lee and others, 2008) or arguably with 

SSC data produced by Porterfield’s (1972) computational 

method (for which there is no quantitative method for deriving 

uncertainty). When the turbidity-SSC model is deemed inadequate, the addition of streamflow as a second model variable 

may result in an acceptable time series of SSC. The turbidity- or turbidity-and-streamflow-based computational scheme 

to produce SSC data has a number of advantages over that of 

Porterfield’s (1972) method, as follows: 

1. No subjective interpolation or estimation is required; 

2. The computational procedure is precisely reproducible;

3. The scheme takes full advantage of the available database 

and computational resources; hence, it can substantially 

reduce the time and effort needed to compute SSL records; 

and

4. Estimates of uncertainty can be computed for the 

SSC time series.

The turbidity- or turbidity-and-streamflow-based computational scheme also has advantages over the traditional 

sediment-transport curve method (Glysson, 1987). The reliability of SSL computed from a transport curve depends on a 

number of factors, including the range of streamflow and SSC

over which the data were collected to define the curve, the 

number and reliability of the concentration-discharge relations 

used to define the curve, and whether the data are representative of water and sediment loads for the computational period 

(Gray and Simões, 2008). Walling (1977) found that annual 

SSL computed using a sediment-transport curve could result 

in errors of as much as 280 percent, whereas errors in monthly 

SSL could range between +900 percent and -90 percent. 

Glysson and others (2001) compared SSL computed by the 

Porterfield (1972) method and a transport curve for 34 years 

of streamflow and suspended-sediment records at the USGS 

streamgage on the Rio Grande at Otowi Bridge, New Mexico. 

Daily SSL computed by these two techniques differed by as 

much as 4,000 percent, whereas the maximum difference in 

annual SSL computations was 526 percent. SSL for the 34-year 

period of record differed by 38 percent. Lee and others (2008) 

compared the uncertainty of annual SSL computed using a 

sediment-transport curve and a turbidity-SSC model at three 

sites near John Redmond reservoir, Kansas. The uncertainties 

associated with the annual SSL derived from sediment-transport curves ranged from 16–20 percent, whereas those derived 

from the turbidity-SSC model ranged from 1.1–3.2 percent. 

Glysson and others (2001) observed that estimates of 

SSLs that are based on sediment-transport curves are subject to 

significant errors, in part because of the large range in SSC that 

can occur at any given water discharge. They concluded that, 

although a well-defined, carefully constructed and judiciously 

applied sediment-transport curve can be a useful tool for 

estimating SSL, SSL estimates derived from sediment-transport 

curves should not be considered a substitute for daily-sediment records computed by Porterfield’s (1972) method. Lewis 

(1996) indicated that regression models using turbidity instead 

of streamflow improved the root-mean-squared errors of sediment rating curve estimates by 7 to 15 percent.

Hence, the use of a linear regression model to compute 

SSC from turbidity time-series data, and in some cases, turbidity and streamflow time-series data measured at a fixed location in a stream provide statistical estimates of uncertainty of 

SSC (Christensen and others, 2000). The use of a linear regression model, depending on the characteristics of the sediment 

in suspension, is likely a more accurate method for estimating 

a SSC time series than either the Porterfield (1972) method or 

traditional transport-curve method (Walling, 1977; Horowitz 

and others, 2003; Putnam and Pope, 2003). 

SSC computed from regression models can be used for 

a variety of purposes, including use to describe variability 

in suspended-sediment conditions, to evaluate SSC relative 

to water-quality criteria and water-resource management 

goals, and to compare the SSC and SSL characteristics among 

watersheds. Computed SSC and streamflow data in riverine 

applications can be used to compute SSL to reservoirs, which 

in turn can be used to infer loss of reservoir capacity. Computed SSC and SSL also can be used in the study of channel 

morphology and basic process analysis of sediment sources. 

Also, by relating the continuous, time-series turbidity data to 

the sampled SSC, it may be possible to identify the sources 

and timing of sediment transport more accurately than on the 

basis of periodic sample collection. Subsequently, computed 

daily, monthly, seasonal, and annual SSL can be used to assess 

differences in fluvial-sediment characteristics between basins 

as a function of hydrologic conditions, contributing drainage 

area, land use, sediment sources, and (or) human activity. Turbidity time-series data also can be used to compute a variety 

of constituent concentrations—for example, total nitrogen and 

total phosphorus (Rasmussen and others, 2005) and indicator bacteria (Rasmussen and Ziegler, 2003) that correlate 

well with SSC, which in turn can be used to compute loads of 

those constituents.

Historically, most State agencies have collected samples 

for analyses of total suspended solids (TSS) in lieu of SSC

samples (Pruitt, 2003). This is largely a consequence of the 

fact that the U.S. Environmental Protection Agency presently 

only recognizes the TSS analytical method (American Public 

Health Association, American Water Works Association, and 

Water Pollution Control Federation, 2005). TSS data tend to be 

biased low, particularly when sand constitutes more than about 

20 percent of the mass of the water-sediment mixture (Gray 

and others, 2000; and Glysson and others, 2000, 2001). For 
Introduction 3

systems that convey primarily silt- and clay-sized sediment in 

suspension, Christensen and others (2000) and Rasmussen and 

others (2008) have used turbidity-TSS models to compute TSS

values with acceptable uncertainties. However, TSS data are 

acceptable alternatives to SSC data only after being conclusively documented in a published report that the TSS data 

can adequately represent SSC data over the range of expected 

flows at a site (U.S. Geological Survey, 2000).

Purpose and Scope

This report provides guidelines and procedures for computing time series of SSC and SSL from time series of turbidity 

and streamflow data using a generally site-specific, simple or 

multiple regression model relating SSC from periodically collected in-stream water samples to in-stream turbidity measurements. Included is the requisite knowledge to:

1. Develop and evaluate an empirical statistical relation 

between turbidity and SSC measurements; 

2. Compute time series of SSC and SSL from turbidity and 

streamflow time-series data; and 

3. Maintain a long-term SSC record. 

Examples of applications of the analytical and computational methods described herein are provided using data 

from USGS streamgages in California, Florida, Kansas, and 

Oregon. Although this guidance is for application in a riverine environment, selected aspects of the guidelines may be 

adapted for use in lacustrine or estuarine applications. 

References to principles of sediment transport, sampling 

techniques, and related field procedures, along with qualitycontrol procedures, are presented because an understanding of these principles and procedures is fundamental to the 

computation of time-series suspended-sediment records. 

Concepts, statistical procedures, and techniques are presented 

for computing SSC and SSL time series. Material in this report 

includes procedures and techniques to maintain a multiyear 

SSC time series and to prepare suspended-sediment data for 

public dissemination. Selected duplication of material contained in other publications and guidelines is necessary and 

intentional to provide guidance for computing SSC and SSL

from turbidity and streamflow data. Specific USGS guidance 

on methods for computing and storing computed suspendedsediment data in the USGS National Water Information System (NWIS) database is presented.

Related Guidelines

Porterfield (1972) describes two basic types of sediment 

records—daily and periodic—calculated from sampled SSC

and using gage height and (or) streamflow data to synthesize the SSC trace for unsampled periods. Daily records are 

prepared for sites where sufficient determinations of SSC and 

streamflow are obtained to enable computation of daily SSL

(Porterfield, 1972). The end product is a tabulation of daily 

time-weighted mean SSC, SSL, and, in many cases, periodic 

determinations of particle-size distributions of suspended 

sediment and bed material. These are combined with other 

hydrologic data and released, usually by water year (October 1 

through following September 30), by the USGS in stream-site 

data sheets for specific States or in the Open-File or Scientific 

Investigation Report series. Periodic records are prepared 

for sites where frequency of determination of SSC and (or) 

streamflow are insufficient to justify computation of daily SSL

or where only miscellaneous samples are collected infrequently. In addition to publication of the records, the data and 

supporting documentation on computations are maintained on 

file in the USGS Water Science Centers and are available for 

examination or for use in interpretative reports and research.

Wagner and others (2006) provide basic guidelines and 

procedures used by USGS personnel for operating water-quality monitors, including site selection, field procedures, calibration of continuous water-quality monitors, record computation 

and review, and data reporting. In addition, Wagner and others 

(2006) present methods for servicing fixed-location waterquality monitors (including turbidity sensors) in freshwater 

environments and estuaries. Alternative methods for servicing 

monitors also are included. These basic guidelines are minimal 

requirements that may be modified to meet local environmental conditions or specific study objectives. Knowledge of 

monitoring-equipment operation and first-hand knowledge 

of the salient aspects of the watershed form the core of the 

data-evaluation process. Record-computation procedures 

presented in Wagner and others (2006) provide a uniform 

set of minimum requirements for computing water-quality 

records. Examples of the application of scientific judgment in 

the evaluation of data records are presented and are, by necessity, site specific. Other specific examples also are included to 

demonstrate the range of environmental conditions that affect 

the evaluation process. 

Equipment and procedures for collection and measurement of fluvial sediment are described by Edwards and 

Glysson (1999), which contains two major sections regarding suspended-sediment equipment and techniques that are 

germane to developing turbidity/suspended-sediment relations. The “Sediment-Sampling Equipment” section includes 

information on the characteristics and limitations of various 

models of Federal Interagency Sedimentation Project (2008) 

isokinetic, depth- and point-integrating samplers (Davis, 

2005), non-isokinetic single-stage samplers, automatic pumping samplers, and selected support equipment. The “SedimentSampling Techniques” section in Edwards and Glysson (1999) 

includes information on sediment-discharge measurements, 

including collection of representative samples, characteristics of sampling sites, equipment selection relative to the 

sampling conditions and needs, depth- and point-integration 

sampling techniques, surface and dip sampling, determination 

of sampler transit rates, sampling programs, and cold-weather 

sampling. The sediment-sampling equipment and techniques 

sections in Edwards and Glysson (1999), the subject matter of 
4 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data

which is also the focus of Nolan and others (2005) and Gray 

and others (2008), provide the fundamental information for 

collecting representative water-sediment samples. The derived 

SSC data, in turn, are used in correlations to turbidity. A more 

detailed description of suspended-sediment data-collection 

techniques is beyond the scope of this report.

Although streamflow computations can be accomplished 

by several techniques depending on site and equipment 

characteristics, they usually entail collection of stage records 

along with periodic streamflow measurements. Stage records 

are obtained from a water-stage recorder. Streamflow measurements usually are made with a current meter (Rantz and 

others, 1982; Kennedy, 1984) or acoustic Doppler current 

profiler (Lipscomb, 1995; U.S. Geological Survey, 2002). The 

methods are consistent with the American Society for Testing and Materials (ASTM) standards and generally follow the 

standards of the International Organization for Standardization 

(ISO). A more detailed description of streamflow time-series 

computation is beyond the scope of this report.

Helsel and Hirsch (2002) provide a stand-alone text 

of applied statistical methods for hydrology. Their chapters “Simple Linear Regression” and “Multiple Linear 

Regression” are cited throughout this guide and are essential 

for understanding and performing the statistical procedures 

presented. 

Types of Turbidity Sensors

There are many methods for quantifying water clarity, including Secchi and black disks, laser diffraction (Gray 

and others, 2003; Gray and Gartner, 2009; Gray and Gartner, 

in press), digital-optic techniques (Gray and others, 2003; 

Gooding, in press) and optical light scattering and absorption 

techniques (table 1; Gray and others, 2003; Rasmussen and 

others, in press). The techniques in this report are predicated 

on use of either of two types of turbidity sensors that are based 

on nephelometric or optical-backscatter (OBS) principles 

and are commonly used to measure turbidity for the purposes 

of computing SSC (Gray and Gartner, 2006). These sensors 

are designed for extended in-situ deployment, are relatively 

inexpensive, and are either self recording or produce signals 

compatible with a data logger. 

Table 1. Selected specifications for selected turbidity instruments (Anderson, 2005).

Light source Multiple or single 

light sources Detection angle Single or multiple detectors Designated units

White or broadband 

(400–680 nanometers) 

Single 90-degree detection angle Single NTU (nephelometric 

turbidity unit)

White or broadband 

(400–680 nanometers) 

Single 90-degree detection angle Multiple detectors, 

ratio compensation

NTRU (nephelometric 

turbidity ratio unit)

White or broadband 

(400–680 nanometers) 

Single 30- (plus or minus 15) degree 

detection angle (backscatter)

Single BU (backscatter unit)

White or broadband 

(400–680 nanometers) 

Single 180-degree detection angle 

(attenuation)

Single AU ( attenuation unit)

White or broadband 

(400–680 nanometers) 

Multiple Detectors at 90 degrees and possibly other angles to each beamMultiple NTMU (nephelometric 

turbidity multibeam unit)

Near infrared 

(780–900 nanometers) 

or monochrome 

Single 90-degree detection angle Single FNU (formazin 

nephelometric unit)

Near infrared 

(780–900 nanometers) 

or monochrome. 

Single 90-degree detection angle Multiple detectors, 

ratio compensation

FNRU (formazin 

nephelometric ratio unit)

Near infrared 

(780–900 nanometers) 

or monochrome

Single 30- (plus or minus 15) degree 

detection angle (backscatter)

Single FBU (formazin backscatter 

unit)

Near infrared or 

monochrome 

Single 180-degree detection angle 

(attenuation)

Single FAU (formazin attenuation 

unit)

Near infrared 

(780–900 nanometers) or monochrome 

(including Great Lakes 

Instruments, Inc., 

1992—Method 2) 

Multiple Detectors at 90 degrees and possibly other angles to each beamMultiple FNMU (formazin 

nephelometric multibeam 

unit)
Types of Turbidity Sensors 5

Unlike absolute measurements of selected physical properties of water, such as specific conductance, pH, temperature, 

or dissolved oxygen, turbidity is a relative index of scattering 

and absorption of light in water. Turbidity is not a direct measure of suspended particles in water but instead is a measure of 

the scattering and absorbing effect such particles have on light 

(Sadar, 1998). Anderson (2005) provides a review of available 

turbidity sensor technologies with a decision tree to select a 

suitable instrument for a specific site or application and guidelines for calibration, operation, quality-assurance procedures, 

and reporting of data. Several characteristics of the water and 

suspended-sediment mixture, such as particle size, shape, 

and color, can affect the optical measurement (Sadar, 1998; 

Davies-Colley and Smith, 2001; Ziegler, 2002a,b; Anderson, 

2005; Downing, 2005, 2006). The effects of these characteristics are discussed in the section on “Factors Affecting Relation 

Between Turbidity and Suspended-Sediment Concentration.” 

Nephelometry

Nephelometry is the measurement of light scattering using a light detector 90 degrees from the incident light 

(U.S. Environmental Protection Agency, 1999). Nephelometric 

measurements reflect the collective optical properties of solution that cause light to be scattered or attenuated rather than 

transmitted in straight lines through the solution; the larger the 

amount of scatter or attenuation of light, the larger the value 

measured by the nephelometric turbidity meter. Nephelometric measurements typically are expressed in turbidity units 

defined by the light source, detection angle, and whether the 

sensor has single or multiple detectors (table 1). Approved 

methods (in 2008) for the measurement of turbidity include 

those that conform to at least three protocols. These are stated 

in: (1) U.S. Environmental Protection Agency (USEPA) 

Method 180.1 (U.S. Environmental Protection Agency, 1979), 

(2) ISO Method 7027 (International Organization for Standardization, 1999), and (3) standard methods recommended by 

the American Water Works Association and the Water Environment Federation (Clesceri and others, 1998). 

Wagner and others (2006) describe methods for measuring turbidity with submersible-type (fig. 1) and nonsubmersible nephelometric sensors. The nephelometric measurements 

shown in the examples in this report were made with either 

an YSI 6026 or YSI 6136 turbidity probe (YSI Incorporated, 

2003). These YSI sensors conform to the ISO Method 7027 

and ASTM D-7315 measurement standards. Each has a light 

A B

C

Figure 1. Three self-cleaning nephelometric turbidity 

sensors—A, YSI Incorporated (Yellow Springs, Ohio) 

model 6136 turbidity sensor, B, Hydrolab (Loveland, 

Colorado) self-cleaning turbidity sensor, and C, Forest 

Technology Systems (Blaine, Washington) model 

DTS-12 turbidity sensor.
6 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data

source of 860 ± 30 nanometers (nm) with a single detector 

oriented at 90 degrees from the incident light path. Nephelometric readings from the YSI 6026, YSI 6136, and other 

turbidity sensors can be different and not directly equivalent 

(Sadar, 1998; Davies-Colley and Smith, 2001; Landers, 

2003; YSI Incorporated, 2003; Ziegler, 2003a; Rasmussen 

and others, 2005). Different turbidity values, therefore, can 

be measured for an individual sample by different turbidity sensors conforming to the same standard method. See 

the “Changes to Turbidity Sensor Model or Type” section of 

this report for a discussion of data processing from different 

turbidity sensors.

Optical Backscatter

OBS sensors measure the same properties as nephelometric sensors, but the angle between the light source and the 

detector is less than 90 degrees. An OBS sensor is typically 

a cylinder utilizing an optical window from which light is 

both emitted and received (fig. 2; Downing and others, 1981; 

Downing, 1983). A pulse of either white or near-infrared light 

is transmitted through the optical window and is scattered or 

reflected by particles in front of the window in a 165-degree 

conical zone within some distance. Some of this scattered 

or reflected light is returned to the optical window where a 

receiver converts the backscattered light to a proportional 

voltage output. The relation of OBS sensor voltage output to 

SSC varies depending on the size, shape, and optical properties of the suspended sediment (Levesque and Schoellhamer, 

1995). Downing (2006) provides a thorough discussion of the 

history and use of OBS measurements to compute SSC. Typically, OBS sensors are used at locations where the nephelometric sensor maximum reporting level, ranging from 1,000 to 

2,000 formazin nephelometric units (FNUs) or SSC values 

larger than 1,000 milligrams per liter (mg/L), are exceeded 

frequently. 

Relation of Turbidity to SuspendedSediment Concentration

A constituent concentration may be computed as a function of another measurement by means of linear regression 

models (Helsel and Hirsch, 2002). SSC, for example, can 

be computed from turbidity and (or) streamflow measurements by means of linear regression. The regression methods 

used in this guide are described in Helsel and Hirsch (2002) 

and are similar to those applied by Gilvear and Petts (1985), 

Lewis (1996), Christensen and others (2000), Uhrich and 

Bragg (2003), Lietz and Debiak (2005), and Rasmussen and 

others (2005). 

To illustrate the techniques and methods discussed in 

these guidelines, turbidity, streamflow, and SSC data from 

USGS streamgage 07144100, Little Arkansas River near 

Sedgwick, Kansas, are used. A riverine example is presented 

because it is the most likely and common application of this 

method. Some of the methods discussed are not applicable to 

lacustrine or estuarine applications. Data sets and regression 

model examples of other riverine and estuarine data sets are 

provided in Appendix 1.

Steps in the procedure for computing time-series records 

of SSC and SSL are given in the checklist shown in figure 3. 

There are three major steps to completing the computation:

1. Compilation of a model-calibration data set of concurrent 

turbidity, streamflow, and SSC values;

2. Development of a linear regression model to compute 

instantaneous values of SSC; and

3. Computation and storage of instantaneous values of SSC

and daily values of SSL.

Compilation, development, and computation methods are 

described in detail in the following sections.

Model-Calibration Data Set

Compilation of the model-calibration data set is the first 

step in the development of a linear regression model. The 

model-calibration data set consists of concurrent instantaneous 

in-stream measurements of turbidity and streamflow, and 

sampled SSC values that correspond to the paired turbiditystreamflow measurements. Appendix 2 discusses retrieval of 

these data types from the USGS National Water Information 

Figure 2. Optical backscatter sensors—A, OBS 3+ (Campbell 

Scientific Inc., Logan, Utah) and B, Hach (Loveland, Colorado) 

Solitax.

B

A
Relation of Turbidity to Suspended-Sediment Concentration 7

[NWIS, U.S. Geological Survey National Water Information System; ADAPS, U.S. Geological Survey Automated Data Processing

System; QWDATA, U.S. Geological Survey water-quality database; SSC, suspended-sediment concentration; SSL, suspendedsediment load, R2

, coefficient of determination; RMSE, root-mean-squared error; MSPE, model standard percentage error; PRESS,

prediction error sum of squares; VIF, variance inflation factor; R2

a, adjusted coefficient of determination ; MVUE, minimum-variance

unbiased estimator; ANCOVA, analysis of covariance]

Checklist for time-series suspended-sediment records

Worked Reviewed Approved

1) Compile model calibration data set 

a) Retrieve data from NWIS _________ ________ _________

i) Approved time-series data: turbidity and streamflow (from ADAPS) _________ ________ _________

ii) Discrete sample data: SSC, sand-silt percentage (from QWDATA) _________ ________ _________

b) Assign turbidity and streamflow values to be used in regression _________ ________ _________

c) Plot raw data to identify potential outliers (turb against SSC) _________ ________ _________

d) Plot samples on turbidity and streamflow duration curves _________ ________ _________

e) Compile statistical summary of model calibration data set _________ ________ _________

f) Write model-calibration data-set summary in station analysis _________ ________ _________

2) Development of a regression model

a) Correlations and scatter plots of all data _________ ________ _________

b) Simple linear regression turbidity/SSC, untransformed and log10

transformed and regression diagnostics

(R2

, R2 , RMSE, PRESS, MSPE) _________ ________ _________

c) Determine proper transformation _________ ________ _________

d) Model residual plots _________ ________ _________

g) Bias correction factor (Duan or MVUE)

_________ ________ _________

h) 90-percent prediction interval

_________ ________ _________

e) Plot model residual against streamflow, Julian day

_________ ________ _________

f) Evaluate simple and multiple linear regression models

(residual plots, VIF, partial F-test, R2

a

, PRESS, MSPE)

_________ ________ _________

i) Regression model summary in station analysis _________ ________ _________

3) Computation and storage of time-series suspended-sediment

concentration and load record in NWIS

a) Set up data descriptors in ADAPS _________ ________ _________

b) Enter bias adjusted equation _________ ________ _________

c) Select period of suspended-sediment record for application of model _________ ________ _________

d) Compute SSC unit value and SSL daily values _________ ________ _________

e) Estimate missing SSC or SSL data _________ ________ _________

f) Evaluate period of record graphs _________ ________ _________

g) Update station analysis _________ ________ _________

4) Annual model validation

a) Plot calibration data set and recent annual data _________ ________ _________

b) Compare original model to model with additional data (ANCOVA) _________ ________ _________

c) Update model in ADAPS _________ ________ _________

d) Determine start date and time of new model _________ ________ _________

\\Sps1dkslwr\home\pubs\report_figs\13_0162_c_rasmussen\figures\fig_03.ai

a

Figure 3. Checklist for development, verification, and approval of a regression model to compute suspendedsediment concentration and load time-series data. 
8 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data

System (NWIS) database. The sampled SSC must be representative of the mean cross-sectional SSC value at the time of 

collection. The rationale for examination and quality assurance of the data are presented in the following paragraphs. 

The computation of turbidity and streamflow time-series data 

are assumed to have been completed by means of established 

USGS guidelines and procedures (Wagner and others, 2006; 

U.S. Geological Survey, variously dated). The guidance that 

follows is intended only to supplement procedures presented 

in Wagner and others (2006).

Evaluation of Fixed-Location and Cross-Section 

Turbidity

Comparisons of fixed-location and cross-section instream turbidity measurements should be part of the turbidity 

record analysis (Wagner and others, 2006). Fixed-location, 

in-stream (hereinafter referred to as “fixed-location”) turbidity 

measurements collected concomitant with cross-section turbidity measurements should be retrieved from the “approved” 

time-series data set (U.S. Geological Survey, 2006, p. 20, 

188–195). The turbidity cross-section measurements should 

be made with a properly cleaned and calibrated field turbidity sensor of the same make and model as the fixed-location 

turbidity sensor. Cross-section turbidity measurements are 

collected at several points across the stream routinely near the 

surface and periodically at different depths (Anderson, 2005). 

Those points at suspended-sediment sampling verticals are 

used for either the equal-width increment or equal-discharge 

increment methods (Edwards and Glysson, 1999; Nolan and 

others, 2005; Gray and others, 2008). These measurements 

are averaged and used in evaluations of the representativeness of data produced from fixed-location turbidity time-series 

measurements (fig. 4). 

Large turbidity values warrant special evaluation. 

Although the values may be valid, spurious data can occur, 

including those recorded when turbidity exceeds the sensor’s 

maximum recording level. Sensor-measurement truncation 

produces constant-value artifacts when in-stream turbidity levels exceed the maximum recording level of the sensor (1,000–2,000 mg/L for most nephelometric sensors and 

4,000–50,000 mg/L for most OBS). The maximum recording 

level is unique for each turbidity sensor and should be routinely quantified and documented for each sensor (Anderson, 

2005). Because the maximum recording level of the sensor 

is reported for all turbidity values equal to or larger than the 

maximum recording level, truncation is manifested as a horizontal line or plateau in the temporal turbidity trace of plotted 

data (fig. 5). Routine calibration of the turbidity sensor can 

change the maximum recording level; therefore, turbidity measurements within about 10 percent of the maximum 

recording level should be evaluated to determine if those 

values are artifacts of truncation. Generally, these values 

should not be used as part of the model-calibration data set. 

Exceptions should be clearly noted and fully explained as 

part of the summary in the station analysis (Appendix 1 at the 

back of this report). The use of turbidity sensors to compute 

SSC at a site subject to frequent turbidity truncation may 

not be appropriate. OBS sensors should be used for streams 

where a significant percentage of SSL occurs at SSC values 

exceeding about 2,000 mg/L. However, currently (2009) most 

OBS sensors are not self cleaning and require more frequent 

routine maintenance. 

Determination of Turbidity and Streamflow 

Associated with Suspended-Sediment 

Concentrations

Turbidity and streamflow corresponding to each SSC

sample should be determined from the time-series data 

sets–preferably, time-weighted averages of turbidity and 

streamflow values recorded immediately before, immediately after, and during the SSC sample collection (fig. 5). The 

hydrographer should ensure that the turbidity and streamflow 

time-series data retrieved from the USGS time-series database, ADAPS, have a data-aging status of “approved” (U.S. 

Geological Survey, 2006, p. 20 and 188–195). Once turbidity 

and streamflow values have been determined for each SSC

value, the hydrographer should compile a data set for statistical analyses. 

TURBIDITY FROM FIXED-LOCATION IN-STREAM SENSOR, IN FORMAZIN

NEPHELOMETRIC UNITS (YSI 6026 TURBIDITY SENSOR)

MEDIAN TURBIDITY IN CROSS SECTION, IN FORMAZIN

NEPHELOMETRIC UNITS (YSI 6026 TURBIDITY SENSOR)

0

400

200

600

800

1,000

1,200

1,400

0 200 400 600 600 1,000 1,200 1,400

\\Sps1dkslwr\home\pubs\report_figs\13_0162_c_rasmussen\figures\fig_04.ai

Number of observations = 68

y = 0.94x + 2.07

Coefficient of determination (R2

) = 0.96

1 : 1 line

Figure 4. Comparison of fixed-location and median cross-section 

turbidity measurements for U.S. Geological Survey streamgage 

on Little Arkansas River near Sedgwick, Kansas, November 1998–

June 2005.
Relation of Turbidity to Suspended-Sediment Concentration 9

Figure 5. A, Time-series turbidity and streamflow data, August 14–18, 2002, and B, duration of cross-section turbidity and suspendedsediment sample collection, August 15, 2002, at U.S. Geological Survey streamgage on Little Arkansas River near Sedgwick, Kansas.

Sample collection Cross-section

measurement

Median cross-section

turbidity value

Hourly streamflow value

Mean streamflow value for sample

Mean turbidity value for sample

Hourly turbidity value

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

14 15 16 17 18

AUGUST 14−18, 2002

AUGUST 15, 2002

Truncated hourly turbidity values

Time of sample collection

Streamflow

Turbidity

TURBIDITY READING FROM FIXED-LOCATION, IN-STREAM SENSOR, IN FORMAZIN NEPHELOMETRIC

UNITS (YSI 6026 TURBIDITY SENSOR) AND STREAMFLOW, IN CUBIC FEET PER SECOND

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

8:00AM 9:00AM 10:00AM 11:00AM 12:00PM 1:00PM

A

B
10 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data

Loose bottle lid

Abnormally large

percentage of sand

Database entry errors

for SSC values

Database entry errors

for SSC values

TURBIDITY READING FROM FIXED-LOCATION, IN-STREAM SENSOR, IN

FORMAZIN NEPHELOMETRIC UNITS (YSI 6026 TURBIDITY SENSOR)

SUSPENDED-SEDIMENT CONCENTRATION (SSC),

IN MILLIGRAMS PER LITER

1

10

100

1,000

10,000

1 10 100 1,000 10,000

Figure 6. Comparison of turbidity to suspended-sediment 

concentration in water from U.S. Geological Survey streamgage 

on Little Arkansas near Sedgwick, Kansas, August 2000–

June 2005.

Identification of Outliers

The development of a SSC regression model should be 

preceded by evaluation of a scatterplot of the turbidity and 

SSC calibration data. The hydrographer can sometimes discern 

outliers on the basis of the scatter of the data. Helsel and 

Hirsch (2002, p. 11, 31–34, 246–248) provide additional guidance on the identification and treatment of outliers. 

Once an outlier is identified, the hydrographer should 

use all technically supportable analytical tools and methods to 

attempt to discredit the value in question. This includes:

1. Confirmation that the correct value was entered into the 

database;

2. Evaluation of laboratory analytical results; and 

3. Review of the field notes to ensure that proper collection 

techniques were used or to otherwise identify factors that 

might lend credit to or that might refute the outlier. 

Remove outliers from the analysis that can be discredited with 

a high degree of confidence. Conversely, if an outlier cannot be discredited, the hydrographer must determine the type 

of adjustment and document the attempts to verify the value 

in the station analysis summary (Appendix 1). Outliers that 

cannot be discredited may affect the analysis and may help 

the hydrographer better understand the relations among site 

turbidity, SSC, and streamflow. Numerous outliers may be 

indicative of problems with the measuring apparatus and (or) 

monitoring site that may in turn warrant corrective measures.

In the comparison of Little Arkansas River fixed-location 

turbidity measurements to SSC (fig. 6), five data points plotted outside the scatter and pattern of the other 68 data points. 

Inspection of field and laboratory notes and results of particlesize analyses indicated that these outliers should be either 

corrected or removed. One of the five outliers was derived 

from a sample that arrived at the laboratory with a loose bottle 

lid and an abnormally small sample volume. On the basis of 

this information, it was surmised that some sample water had 

leaked while most if not all of the sediment remained at the 

container’s bottom, resulting in a spuriously large SSC. The 

discredited outlier was removed from the data set. 

Values for two SSC samples that plot as outliers on 

opposite sides of the data scatter (identified as “Database 

entry errors for SSC values” in figure 6) were evaluated. The 

field forms for these samples confirmed that turbidity values 

in the database matched the turbidity measurements made 

concomitant with SSC sample collection. However, a review 

of the analytical summaries for the SSC samples indicated that 

data-entry errors comprising misplaced decimal points resulted 

in one value appearing as 10-fold its true value and the other 

one-tenth of its true value. The two sample results were duly 

corrected in the database and replaced the erroneous values in 

the model-calibration data set. 

Evaluation of the particle-size analyses performed on 

the suspended-sediment samples collected at relatively low 

streamflows indicated an abnormally large percentage of sand 

(particle sizes exceeding 63 micrometers [μm]) for two other 

outliers. Typically, sand in samples collected at this site during 

similar low streamflow conditions constitutes no more than 

2 percent of the sediment mass. Sand in these two samples 

constituted 10 and 30 percent of the dry sediment mass. 

Transport of sand at these low streamflows is unsupported by 

sedimentological theory and samples collected previously at 

this site. The outliers were deemed to be artifacts attributable 

to sampling error (inadvertently scooping sand-size bed material into the suspended-sediment sampler) and were removed 

from the data set. 

A revised scatterplot identified no other data points that 

deviated sufficiently from the rest to justify further scrutiny. 

Adequacy of Model-Calibration Data Set

An adequate model-calibration data set consists of an 

appropriate number of instantaneous, manual SSC samples 

and concurrent turbidity and streamflow measurements collected throughout the observed range of hydrologic conditions for the period of record (Glysson, 1989b; Rasmussen 

and others, 2002). The number of samples is often cited as 

the primary criterion for determining if a data set is adequate 

for computational purposes. Initially, approximately monthly 

samples collected over a 2- to 3-year period for the range of 

hydrologic conditions may be needed. Although the sample 

total is relevant, the distribution of the data over the range of 

observed turbidity, SSC, and streamflow values for the site is 
Relation of Turbidity to Suspended-Sediment Concentration 11

of paramount importance. A regression model developed from 

15 samples more or less evenly distributed throughout the 

seasons and range of turbidity and streamflow at a site might 

result in a more representative model than one developed 

using a 50-sample data set where distribution of values defines 

only a limited time or range of the sedimentological conditions 

over which the model will be applied. Defining turbiditySSC relations during medium and high streamflow periods 

normally takes precedence over more equal spacing of data 

collection throughout the year, particularly if the purpose is to 

compute SSL. For example, where the number of site visits to 

collect manual samples is limited, sample collection should be 

skewed toward medium and higher flows. Regardless of the 

range of data values, the data points representing the extremes 

will have the greatest effect in determining the slope of the 

relation. For instance, erroneously large turbidity values during low streamflow and low SSC conditions can artificially 

increase the slope of the regression line. 

Another factor to be considered when determining the 

adequacy of a data set is the amount of variability in the relation between turbidity and SSC. The larger the variability in 

the relation between turbidity and SSC at a site, the greater 

the need is to collect more samples. Often, the hydrographer’s 

challenge is to adequately characterize this variability with the 

fewest number of samples.

Serial correlation (also called autocorrelation) occurs 

when data are collected close enough in time that the regression assumption of data independence is violated. For instance, 

multiple samples may be collected during the rising and falling 

limb of a single runoff period. The serial correlation between 

the multiple data points can cause underestimation of the 

regression uncertainty. Helsel and Hirsch (2002, p. 250–251) 

present methods for identifying the presence of serial correlation. If serial correlation is detected, the solution is to randomly 

select a single data point from each group of correlated data. 

The single point should be used in the model-calibration data 

set. Alternately, Glysson (1987) describes a procedure by which 

mean SSC values are computed for each of several contiguous, 

discrete SSC intervals for the data set. These mean values are 

used to develop the regression equation. 

Duration curves represent another tool to evaluate the distribution of SSC data and adapt subsequent sample-collection 

strategies. Ideally, turbidity and streamflow associated with the 

SSC samples should span the ranges of the time-series turbidity and streamflow values for the site (Rasmussen and others, 

2002). For example, turbidity and streamflow values associated with discrete SSC sample data are plotted on duration 

curves of turbidity and streamflow (fig. 7A and B). The turbidity duration curve in figure 7A was developed from hourly 

recorded turbidity measurements by the fixed-location sensor 

for the study period. The turbidity values associated with the 

SSC samples were plotted along the duration curve. Sample 

collection can be determined by closely monitoring the realtime turbidity and streamflow time-series data and optimizing sample-collection times to coincide with duration-curve 

segments undefined by sample values. As new SSC samples 

are collected, the hydrographer should add the corresponding 

turbidity and streamflow values to the duration-curve plots so 

that overall temporal distribution of samples can be assessed. 

Routine use of this tool will maximize the potential that the 

model-calibration data set optimally represents the range of 

turbidity and streamflow conditions.

Turbidity values for one or more years are sorted (or 

ranked) from smallest to largest to construct a turbidity duration curve from a turbidity time series. Then, exceedance 

probabilities are calculated for each turbidity value using Cunnane’s plotting position (Cunnane, 1978; Helsel and Hirsch, 

2002). The minimum turbidity-value duration percentage is 

100 percent (all values within the data set are larger than or 

equal to this value). The maximum turbidity-value duration 

percentage is 0 percent (no values within the data set exceed 

this value). All the turbidity values within the data set are plotted according to calculated probabilities forming the turbidity 

duration curve. Symbols are plotted on the curve at the probability computed for turbidity values associated with each SSC

sample. A streamflow duration curve can be constructed in a 

similar manner by substituting a streamflow time series for the 

turbidity time series. Streamflow duration curves representing 

the study period and, if different, the entire period of record 

provide study period and long-term comparisons. 

A

1

10

100

1,000

10,000

100,000

FREQUENCY OF EXCEEDANCE, IN PERCENT

TURBIDITY READING FROM FIXED-LOCATION,

IN-STREAM SENSOR, IN FORMAZIN

NEPHELOMETRIC UNITS (YSI 6026

TURBIDITY SENSOR)

STREAMFLOW, IN CUBIC FEET PER SECOND

0 10 20 30 40 50 60 70 80 90 100

Sample

Range of turbidity sensor,

maximum recording levels

B

1

10

100

1,000

10,000

100,000

Sample

Figure 7. Duration curves for A, turbidity and B, streamflow 

and corresponding values associated with suspended-sediment 

concentration samples collected at U.S. Geological Survey 

streamgage on Little Arkansas River near Sedgwick, Kansas, 

1999–2005.
12 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data

Update of Station Analysis

The station analysis for a stream site should be updated to 

summarize the data analyses performed. This summary should 

include the rationale behind: 

1. Determination of turbidity and streamflow values associated with each SSC value;

2. Acceptance or exclusion of turbidity values near the 

sensor-dependent turbidity maximum recording level; 

3. Identification of outliers of turbidity, streamflow, and (or) 

SSC values; and

4. Determination of the adequacy of the model-calibration 

data set using turbidity and streamflow duration curves. 

Other information necessary to complete the station 

analysis includes a table of summary statistics of the modelcalibration data set. General statistics of the model-calibration 

data set and the time-series data set indicate the representativeness of the model-calibration data set (table 2). The minimum 

and maximum turbidity values for the model-calibration data 

set define the ideal limits for which the resulting regression 

model should be used to compute SSC values. An understanding of suspended-sediment transport processes and sound 

hydrologic judgment—ideally drawn from years of experience—is required when deciding if values outside these limits 

are appropriate. 

The hydrographer should review data plots, duration 

curves, and data statistics to evaluate the sufficiency of the 

model-calibration data set for developing a reliable regression 

model. If any of these categories are insufficient, the hydrographer may opt to suspend the model analysis and focus on 

additional sample collection so that the model-calibration data 

set may better represent the range of the time-series data set. 

As new sample results are added to the model-calibration data 

set, these same steps can be used to evaluate how the new data 

enhance or otherwise alter the model. 

Regression Model Development

The key elements for computing SSC time-series data 

from periodic instantaneous SSC, turbidity, and streamflow 

data are the type and goodness-of-fit of the regression model 

used in the computation. A number of quantifiable variables 

can be used to compute SSC in streams, including turbidity; 

hydrologic characteristics, including streamflow, stream stage, 

streamflow rise or fall, and rates of rise and fall; precipitation rate and intensity; and seasonality, sediment sources, and 

land use. The explanatory variables turbidity and streamflow 

generally are the most important in SSC regression analysis. Thus, these guidelines focus on turbidity and, to a lesser 

extent, streamflow as explanatory variables of SSC. A SLR 

model relating turbidity to SSC is often sufficient for reliable 

computations of SSC. Criteria are provided for determining 

the sufficiency of a SLR model and for determining when a 

multiple linear regression (MLR) model relating both turbidity and streamflow to SSC results in a significant improvement 

over the SLR model that is based on turbidity alone. Typically, 

addition of a streamflow variable is more likely to improve 

the turbidity-SSC regression as the percentage of the SSC that 

is sand-size or larger material (coarser than 63 μm) increases. 

Concepts for development and use of a SLR model to compute SSC and, when appropriate, a MLR model as a function 

of turbidity and streamflow to compute SSC, are explained in 

the following sections. The following regression analysis is 

site-specific and applies to a single model-calibration data set. 

A comparison between sites and model-calibration data sets 

is beyond the scope of this report. Specifically excluded from 

these guidelines is use of a SLR model for routine computation of SSC solely from streamflow due to varying degrees of 

hysteresis common in the SSC-streamflow relation. Currently 

(2009), ADAPS is limited to only SLR models using turbidity for computing a more frequent than daily SSC time series 

(U.S. Geological Survey, 2003). For example, ADAPS cannot 

compute more frequent than daily SSC using streamflow or 

more than one explanatory variable.

There are a variety of approaches to building an appropriate model, including SLR and MRL (Helsel and Hirsch, 

2002) and Kendell-Theil robust line (Granato, 2006). The 

following sections provide some general guidance on develop 

a linear regression model using turbidity and streamflow as 

explanatory (x) variables and SSC as the response (y) variable. Linear regression is not only used to derive a final model 

to compute SSC but also is used in the intermediate steps to 

determine the final model form. The hydrographer may need 

to evaluate the performance of more than one intermediate 

regression model before determining the optimal model for 

computing SSC. Regression results are an effective means for 

Table 2. Statistical summary of model-calibration data set for 

U.S. Geological Survey streamgage on Little Arkansas River near 

Sedgwick, Kansas, November 1998–June 2005. 

[mg/L, milligrams per liter; FNU, formazin nephelometric units; ft3/s, cubic 

feet per second]

Summary 

statistic

Calibration data set 

(68 samples)

Time-series data 

set (61,200 hourly 

values)

Suspendedsediment 

concentration 

(mg/L)

Turbidity 

(FNU)

Streamflow 

(ft3/s)

Turbidity 

(FNU)

Streamflow 

(ft3/s)

Minimum 4 4 8 1 3

Maximum 1,250 1,300 12,000 2,000 15,000

Mean 350 370 1,500 140 380

Median 240 240 210 41 60

Standard 

deviation

350 380 2,500 260 1,200
Relation of Turbidity to Suspended-Sediment Concentration 13

evaluating whether or not variables should be transformed and 

which variables are necessary to best estimate the variability 

in SSC. The following sections describe methods by Helsel 

and Hirsch (2002) for deriving the optimal regression model 

for computing SSC. A detailed summary of SLR development for turbidity-SSC and evaluation of MLR for turbidity 

and streamflow-SSC is presented in example 1 of Appendix 1. 

Complete and detailed presentations of these regression 

methods are not presented in these guidelines and procedures 

but can be found in Helsel and Hirsch (2002, p. 221–263 and 

295–321). S-Plus (Insightful Corporation, 2001) is the USGSsupported statistics software package for performing SLR and 

MLR analyses. Microsoft® Excel®can be used, but results from 

Excel should always be verified with S-Plus derived results. 

Results from both software packages are provided in example 1 of Appendix 1. 

Correlation

Correlation coefficients measure the strength of association between two variables (Helsel and Hirsch, 2002). The 

most commonly used measure of correlation is Pearson’s r. 

This correlation also is called the linear correlation coefficient 

because r measures the linear association between two variables (Helsel and Hirsch, 2002, p. 218). Measures of correlation have the characteristic of being dimensionless and scaled 

to lie in the range -1 ≤ r ≤ 1. When there is no correlation 

between two variables, r = 0. When the increase or decrease in 

the variables is synchronous, r is positive. When the variables 

vary in opposite directions, r is negative. When one variable 

is a measure of time or location, correlation becomes a test for 

temporal or spatial trend, respectively. 

Whenever a correlation coefficient is calculated, it 

should be presented with a scatter plot of the data. No single 

numerical measure can substitute for insights that can be 

gained from visual examination of such a plot. Scatter plots 

and correlations of turbidity, streamflow, and SSC values 

are simple and convenient ways of identifying which of the 

variables are statistically related and whether transformation 

of the data might improve the relation between the explanatory and response variables (fig. 8). The hydrographer can get 

a better idea from a simple analysis of which or both of two 

variables—turbidity and streamflow—are superior for computing SSC. Generally, the closer the correlation coefficient is 

to 1 (perfect positive correlation), the stronger the association 

between variables.

For MLR, multicollinearity—a case of MLR in which 

the explanatory variables are themselves highly correlated—

can result in undesirable consequences for model results. 

Helsel and Hirsch (2002, p. 305) suggest computing a variance inflation factor (VIF) for measuring multicollinearity. 

The VIF for turbidity and streamflow is readily computed by 

using the coefficient of determination (R2)from the regression of turbidity on streamflow (equation 11.6 in Helsel and 

Hirsch, 2002, p. 305). A VIF larger than 10 (or a Pearson’s r

larger than 0.95 between turbidity and streamflow) indicates 

multicollinearity between turbidity and streamflow, and suggests that the use of either variable would explain about the 

same amount of variability and that the two variables should 

not be used together as explanatory variables in a MLR (Helsel and Hirsch, 2002, p. 305–6). The scatter plot and VIF of 

data from the Little Arkansas River near Sedgwick, Kansas 

(fig. 9), suggest that turbidity and streamflow are not strongly 

multicollinear and could be used as explanatory variables in a 

MLR model to compute SSC.

Simple Linear Regression for Computation of 

Suspended-Sediment Concentrations

Values of a response variable can be expressed in terms 

of a single explanatory variable or many explanatory variables 

using linear regression models (Helsel and Hirsch, 2002). An 

explanatory variable such as turbidity can be used in a regression model to compute the response variable SSC. The most 

common estimation technique is SLR, as presented in chapter 9 of Helsel and Hirsch (2002). SLR models can be computed using many statistical software packages. SLR analysis 

of the Little Arkansas River model-calibration data set yields 

the plots shown in figure 10 using untransformed data and in 

figure 11 using log10-transformed data.

A list of diagnostics for linear regression can be used to 

evaluate various steps in the model- building process (Helsel 

and Hirsch, 2002, p. 226–7). The coefficient of determination 

adjusted (R2

a

) for the number of explanatory variables (or, 

equivalently, the degrees of freedom) in the model indicates 

the fraction of variability in the response variable that is 

explained by the model. The root-mean-squared error (RMSE) 

is a measure of the variance between regression-computed 

and observed values. The RMSE is approximately equal 

to one standard deviation (σ) or the 67-percent prediction 

interval and is expressed in the same units as the response 

variable. RMSE expressed in log units is not directly comparable with RMSE expressed in milligrams per liter. RMSE can 

be expressed as a percentage (Hardison, 1969), hereinafter 

referred to as the model standard percentage error (MSPE). 

MSPE can be used to compare any regression model. For 

RMSE expressed in log10 units, the MSPE interval is:

 (1)

For RMSE expressed in milligrams per liter, the MSPE interval 

is:

MSPE = ± x ,

RMSE

y

100 (2)

where

 is the mean of the response variable.

Upper

Lower

 MSPE=

 MSPE=

10 1 100

1 10 100

RMSE

RMSE

( )

–

–

( ) -

x , and

x .

y
14 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data

C D

A B

\\Sps1dkslwr\home\pubs\report_figs\13_0162_c_rasmussen\figures\fig_08.ai SUSPENDED-SEDIMENT CONCENTRATION IN MILLIGRAMS PER LITER

200

400

600

800

1,000

1,200

1,400

TURBIDITY READING FROM FIXED-LOCATION, IN-STREAM SENSOR, IN

FORMAZIN NEPHELOMETRIC UNITS (YSI 6026 TURBIDITY SENSOR)

0

0 500 1,000 1,500

Correlation coefficient (r) = 0.96

STREAMFLOW, IN CUBIC FEET PER SECOND

0 5,000 10,000 15,000 

Correlation coefficient (r) = 0.54

Correlation coefficient (r) = 0.99

TURBIDITY READING FROM FIXED-LOCATION, IN-STREAM SENSOR, IN

FORMAZIN NEPHELOMETRIC UNITS (YSI 6026 TURBIDITY SENSOR)

SUSPENDED-SEDIMENT CONCENTRATION

IN MILLIGRAMS PER LITER

10,000

1,000

100

10

1

1 10 100 1,000 10,000

STREAMFLOW, IN CUBIC FEET PER SECOND

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

Correlation coefficient (r) = 0.85

Figure 8. Relations between A, turbidity and suspended-sediment concentration, B, streamflow and suspended-sediment 

concentration in linear space, C, turbidity and suspended-sediment concentration, and D, streamflow and suspended-sediment 

concentration in log10 space for U.S. Geological Survey streamgage on Little Arkansas River near Sedgwick, Kansas, 1999–2005.
Relation of Turbidity to Suspended-Sediment Concentration 15

The lowest MSPE corresponds to the model with the least 

uncertainty associated with regression-computed values. The 

PRESS (prediction error sum of squares) statistic is one of 

the best measures of the quality of a regression model and 

also can be computed using RMSE (Helsel and Hirsch, 2002, 

p. 247). Table 3 presents when and how a diagnostic statistic 

can be used for comparison among regression models. Note 

that none of these diagnostic statistics can be used to compare 

regression with different response variables units. 

Transformation of Data

The purposes for transformation of data prior to an 

analysis are to make the residuals more symmetric, linear, 

and homoscedastic (associated with a constant variance). 

Helsel and Hirsch (2002, p. 252–4) describe the rationale for 

and the results of data-set transformations. Serious problems 

can occur when regression models are developed and residuals do not possess the assumed characteristics of symmetry, 

linearity, and homoscedasticity. Comparisons of transformed 

and untransformed data and regression results are presented 

throughout this section so that the hydrographer can better 

understand how data transformation improves the computation of SSCs. 

Base-10 logarithmic transformation is one of several 

mathematical functions that sometimes can be used to transform data sets so that the assumptions for linear regression 

analysis are met. Helsel and Hirsch (2002, p. 12–14) discuss 

other transformation options and characteristics. Logarithmic 

base-10 transformation has been shown to be effective in 

normalizing residuals of turbidity-SSC regressions. Hydrographers should start with base-10 logarithm transformation 

but are encouraged to experiment with other transformation 

options to determine if a different transformation of the dataset results in a model that better satisfies the assumed residual 

characteristics for regression analysis. Other considerations 

should include the ease of retransforming the results from the 

model, the bias associated with the retransformation, and rationale for complex transformations. As Helsel and Hirsch (2002) 

point out, it is better to choose a single transformation for data 

from several sites than it is to have custom transformations for 

every data set. The examples presented here use a logarithmic 

base-10 transformation of both the response and explanatory 

variables, which is equivalent to the power function regression performed on untransformed variables and used for many 

streamflow-SSC transport curves (Glysson, 1987; Curtis and 

others, 2006). From Helsel and Hirsch (2002), page 315.

“Should y (SSC) be transformed? To decide whether 

to transform the y variable, plot residuals against predicted 

values for the untransformed data. Compare this to a residuals 

plot for the best-transformed model, looking for three things:

Figure 9. Comparison of turbidity and streamflow at the time 

of sample collection in A, linear space and in B, log10 space for 

U.S. Geological Survey streamgage on Little Arkansas River near 

Sedgwick, Kansas, 1999–2005.

A

0

2,000

4,000

8,000

6,000

10,000

12,000

14,000

STREAMFLOW, IN CUBIC FEET PER SECOND

1 100 1,000 10,000

B

1

10

100

1,000

10,000

100,000

10

0 200 400 600 800 1,000 1,200 1,400

TURBIDITY READING FROM FIXED-LOCATION, IN-STREAM SENSOR, IN FORMAZIN

NEPHELOMETRIC UNITS (YSI 6026 TURBIDITY SENSOR)

Correlation coefficient (r) = 0.55

Variance inflation factor (VIF) = 1.43

Correlation coefficient (r) = 0.84

Variance inflation factor (VIF) = 3.4

Sample

Sample

Table 3. Diagnostic statistics of linear regression for evaluation and comparison of regression models (Helsel and Hirsch, 2002). 

[R2, coefficient of determination; R2

a

, adjusted coefficient of determination; RMSE, root-mean-squared error; MSPE, model standard percentage error; ↑, 

maximize; ↓, minimize]

Type of models being compared R2 R2

a RMSE PRESS MSPE

Same response variable (y) units ↑ ↑ ↓ ↓ ↓

Differing response variable (y) units ↓

Same y and same number of x variables ↑ ↑ ↓ ↓ ↓

Same y and varying number of x variables ↑ ↓ ↓ ↓

Should y be transformed? ↓

Should x ('s) be transformed? ↑ ↑ ↓ ↓ ↓
16 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data

1. Constant variance across the range of the y (SSC);

2. Normality of residuals; and

3. A linear pattern, not curvature, centered vertically around 

the zero residual line.

The statistics R2, R2

a

, RMSE, and PRESS are not appropriate 

for comparison among models having different units of y.

Should x (or several x’s) be transformed? The decision 

about whether to transform an x variable should be made using 

partial-residual plots. Check for the same three patterns of 

constant variance, normality, and linearity. Considerable help 

can be obtained from statistics such as R2

a

 (maximize it), or 

RMSE or PRESS (minimize it). Many transformations can be 

rapidly checked with such statistics, but a residuals plot should 

always be produced and inspected prior to accepting or rejecting a transformation scheme.”

Model Residual Analysis

Regression models are evaluated by examining the model 

residuals. Ordinary residuals are defined as the difference 

between the observed values and the model estimates (the 

term “model estimate” is used here because the values are 

estimates of actual samples or observed values). The residual 

error (ei) for the computed SSC values should be random 

and, in theory, should be normally distributed with a mean of 

zero and a constant variance (Helsel and Hirsch, 2002). The 

residuals from a regression of SSC on turbidity indicate how 

Figure 10. Results of simple linear regression analysis for A, turbidity and suspended-sediment concentration data, and a comparison 

of B, computed suspended-sediment concentrations and regression residuals, and C, probability plot of residuals for U.S. Geological 

Survey streamgage on Little Arkansas River near Sedgwick, Kansas, 1999–2005.

B

0

100

200

300

400

500

-100

-200

-300

-400

-500 0 500 1,000 1,500

RESIDUALS

ESTIMATED SUSPENDED-SEDIMENT CONCENTRATION,

IN MILLIGRAMS PER LITER

General trend of variation

General trend of variation

1,400

1,200

1,000

800

600

400

200

0 500 1,000 1,500

A

SUSPENDED-SEDIMENT CONCENTRATION (SSC),

IN MILLIGRAMS PER LITER (mg/L)

TURBIDITY (Turb) FROM FIXED-LOCATION, IN-STREAM

SENSOR, IN FORMAZIN NEPHELOMETRIC UNITS

(YSI 6026 TURBIDITY SENSOR)

SSC = 0.91(Turb) + 17.0

Adjusted coefficient of determination (R2

a) = 0.96

Root-mean-square error (RMSE) = 90

Model standard percentage error (MSPE) = ± 25 percent

Measured SSC (mg/L)

Predicted SSC (mg/L)

0

0

100

200

300

400

500

-100

-200

-300

-400

-500

RESIDUALS

-3

Probability plot correlation coefficient (PPCC) = 0.92

C

-2 -1 0 1 2 3

NORMAL QUANTILES

B

0

0.1

0.2

0.3

0.4

-0.1

-0.2

-0.3

-0.4

0.1

0.2

0.3

0.4

-0.1

-0.2

-0.3

-0.4 0 500 1,000 1,500

RESIDUALS

ESTIMATED SUSPENDED-SEDIMENT CONCENTRATION,

IN MILLIGRAMS PER LITER

10,000

10

100

1,000

1 10 100 1,000 10,000

A

SUSPENDED-SEDIMENT CONCENTRATION (SSC),

IN MILLIGRAMS PER LITER (mg/L)

TURBIDITY (Turb) FROM FIXED-LOCATION, IN-STREAM

SENSOR, IN FORMAZIN NEPHELOMETRIC UNITS

(YSI 6026 TURBIDITY SENSOR)

Measured SSC (mg/L)

Predicted SSC (mg/L)

1

0

RESIDUALS

-3

Probability plot correlation coefficient (PPCC) = 0.98

C

-2 -1 0 1 2 3

NORMAL QUANTILES

General trend of variation

log(SSC) = 0.943*log(Turb) + 0.130 General trend of variation

Adjusted coefficient of determination (R2

a) = 0.98

Root-mean-square error (RMSE) = 0.10

Model standard percentage error (MSPE) = + 25 percent

- 21 percent

Figure 11. Results of simple linear regression analysis using log-transformed data for A, turbidity and suspended-sediment 

concentration data, and comparison of B, estimated log10 suspended-sediment concentration and regression residuals, and 

C, probability plot of residuals for U.S. Geological Survey streamgage on Little Arkansas River near Sedgwick, Kansas, 1999–2005.
Relation of Turbidity to Suspended-Sediment Concentration 17

the model-estimated SSC varies from the observed SSC. A 

residual value of 0 indicates that the model-estimated SSC is 

equal to the observed value. A positive residual indicates that 

the observed value was larger than the estimated value, and 

a negative residual indicates that the observed value was less 

than the estimated value.

The variance of the residuals can be evaluated by plotting 

them against the model estimated SSC (figs. 10B and 11B). 

The residuals plotted in figure 10B indicate a heteroscedastic pattern (nonconstant variance; as indicated by the dashed 

lines) where the variability of the residuals increases as estimated SSC values increase, which suggests the need for some 

sort of variance stabilizing transformation of the response variable. The residuals plot for the log10-transformed regression 

(fig. 11B) indicates a homoscedastic pattern (constant variance) and a more normal distribution. Normality of residuals 

can be evaluated by plotting residuals on a normal-probability 

plot (figs. 10C and 11C) and computing the probability plot 

correlation coefficient (PPCC; Helsel and Hirsch, 2002, 

p. 253). Non-normally distributed residuals will not be linear 

or equally distributed on a normal-probability plot and have a 

smaller PPCC. The probability plot for the log10-transformed 

regression provides a more linear, even distribution of residuals and a slightly larger PPCC than the residuals from the 

regression with untransformed variables (figs. 10C and 11C). 

The plots in figures 10B and 11B confirm that log10 transformation provides more homoscedastic, normally distributed 

residuals.

Simple Linear Regression Model and Bias 

Correction Factor 

The SLR model for the Little Arkansas River near Sedgwick, Kansas, for data collected from November 1998 to June 

2005 is shown below with basic model information, regression 

coefficients, model diagnostics, and Duan’s bias correction 

factor (Duan, 1983):

log10(SSC) = 0.943log10(Turb) + 0.130, (3)

where

SSC is suspended-sediment concentration, in 

milligrams per liter, and

Turb is turbidity, in formazin nephelometric units, 

measured with YSI model 6026. 

Model information:

Number of measurements = 68,

root-mean-squared error (RMSE) = 0.10,

model standard percentage error (MSPE) = + 25.9 and 

-20.6 percent,

90-percent prediction interval = + 41 percent,

adjusted coefficient of determination (R2

a

) = 0.98,

PRESS = 0.663.

Duan’s bias correction factor = 1.03.

Coefficients:

Value Standard 

error

t-statistic p-value

Intercept 0.130 0.041 3.02 0.0035

log10(turbidity) 0.943 0.018 50.9 1.13E-54

Correlation matrix of coefficients:

Intercept log10(Turb)

Intercept 1

log10(Turb) -0.9588 1

Some of the regression statistics are useful in evaluating 

this regression model. For example, the RMSE (even though 

it is expressed in log units), the MSPE, and the 90-percent 

prediction interval indicate the range in uncertainty associated 

with each regression-computed SSC value. R2

a

 indicates that 

the regression model explains 97 percent of the variability in 

sampled SSC. The PRESS is only relevant for comparisons 

to other regression models with the same response variable 

units. The t-statistics for the y intercept and coefficient (slope) 

of log10 (turbidity) are larger than 2, and the p-values are less 

than 0.05, indicating that both are significant and should be 

included in the final model form. Helsel and Hirsch (2002, 

p. 239) discuss the option of omitting the y intercept (thus 

forcing the y intercept to equal zero). There are several tests 

the hydrographer can perform to help aid in the decision, but 

generally, omitting the y intercept is discouraged. Hydrographers are encouraged to develop a regression model by forcing the y intercept to equal zero as an iterative step in better 

understanding the data set and the effect of certain data points, 

specifically the smaller turbidity-SSC values. 

Transformation of the response variable (SSC) has a 

consequence that must be considered when computing SSC: 

The regression estimates must be retransformed to the original units, a step that introduces a bias (usually negative) in 

computed SSC values (Miller, 1951; Koch and Smillie, 1986) 

unless the data are perfectly and positively correlated [as 

the R2

a

 approaches 1.0, the bias correction factor (BCF) also 

approaches 1.0]. The bias arises because regression estimates 

are the mean of y given x in log units, and retransformation 

of these estimates is not equal to the mean of y given x in 

linear space. To correct for this retransformation bias, Duan 

(1983) introduced a nonparametric BCF called the “smearing” 

estimator (Helsel and Hirsch, 2002, p. 256). The equation to 

compute the smearing BCF for base-10 logarithmic transformation is:

 (4)

where

n is the number of samples, and

BCF =

10

1

e

i

n i

n

= .

∑
18 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data

ei is the residual or the difference between each 

measured and estimated concentration, in 

log units. 

Regression-computed SSC values for Little Arkansas River 

near Sedgwick, Kansas, are corrected for bias by multiplying 

the retransformed SSC value by the BCF. 

Model-calibration data plotted concomitant with the biascorrected model line may not always result in what appears 

to be the best fit of the data. For BCFs larger than 1.0, model 

values will plot on the high side (more data points are below 

the curve than above it; fig. 12); that is, when the results of the 

simple linear-regression line are multiplied by the BCF and 

plotted, the curve is shifted upward from the original position. 

This same effect of BCFs with sediment-transport equations 

has been shown to fit data on the high side in other sedimenttransport studies (Bent, 2000). There also is an exact, minimum-variance unbiased estimator (MVUE; Cohn and others, 

1989), but MVUE assumes a normal distribution of the residuals, which frequently is not the case. 

A comparison of measured and model-estimated SSC

indicates the accuracy of the regression model (fig. 13). The 

closer that points plot to the 1:1 line the more accurate the 

model predictions are. 

Once the turbidity-SSC model is determined, the 

hydrographer needs to consider the potential benefits of adding streamflow as an explanatory variable. SLR analysis is 

preferred for sites where turbidity is the measure most strongly 

correlated with SSC or where MSPE is less than 20 percent. 

Sites with a homogeneous source of suspended sediment and 

more than about 80 percent of the suspended material finer 

than 63 μm are the best candidates for SSC computations using 

the SLR model. When turbidity is less correlated with SSC

or when the MPSE is larger than 20 percent or sand (particle 

size coarser than 63 μm) constitutes an increasing percentage 

of the sediment in suspension as SSC increases, streamflow in 

addition to turbidity may better describe the variability in SSC. 

MLR model building is similar to SLR but should not precede 

SLR model development. Methods for building MLR models 

are discussed in a later section of this report titled “Multiple 

Linear Regression.”

Prediction Intervals

Prediction intervals can be used to evaluate the uncertainty of SSC regression-computed values (Helsel and 

Hirsch, 2002). Prediction intervals define a range of values 

for the regression estimate associated with a known level 

of certainty. For a given turbidity value (explanatory variable), the 90-percent prediction interval represents a range 

of values within which there is a 90-percent certainty that 

the true SSC value occurs. The larger the 90-percent prediction interval, the more uncertainty there is associated with 

computed SSC. The prediction interval for a single response yi

is approximately:

 (5)

Figure 13. Comparison of measured and model-estimated 

suspended-sediment concentrations for U.S. Geological Survey 

streamgage on Little Arkansas River near Sedgwick, Kansas, 

1999–2005. MODEL-ESTIMATED SUSPENDED-SEDIMENT CONCENTRATION, IN MILLIGRAMS PER LITER

1

10

100

1,000

10,000

1

MEASURED SUSPENDED-SEDIMENT CONCENTRATION,

IN MILLIGRAMS PER LITER

10 100 1,000 10,000

1 : 1 line

Figure 12. Comparison of turbidity and suspended-sediment 

concentration model-calibration data and uncorrected and 

bias-corrected simple linear regression lines for U.S. Geological 

Survey streamgage on Little Arkansas River near Sedgwick, 

Kansas, 1999–2005. 

TURBIDITY READING FROM FIXED-LOCATION, IN-STREAM SENSOR, IN

FORMAZIN NEPHELOMETRIC UNITS (YSI 6026 TURBIDITY SENSOR)

SUSPENDED-SEDIMENT CONCENTRATION,

IN MILLIGRAMS PER LITER

0

400

200

600

800

1,000

1,200

1,400

0 200 400 600 600 1,000 1,200 1,400

Bias correction factor corrected

Simple linear

regression line

Bias correction factor = 1.03

E y t s i ( ) ± × ,
Relation of Turbidity to Suspended-Sediment Concentration 19

where

E(yi) is the regression-estimated value, at xi;

t is the value of the student’s t distribution 

having n-2 degrees of freedom (n is 

the number of observations) with the 

exceedance probability of α/2 (alpha value 

obtained from t tables in the appendix of 

most statistics textbooks) for 90-percent 

prediction interval α = 0.10; and

s is the standard error of regression or the 

RMSE.

Multiple Linear Regression

As previously stated, MLR represents an alternate tool 

for computing SSCs when the SLR MSPE is larger than 

20 percent. However, MLR should only be considered for use 

when the p-value (probability value) of the partial F statistic 

(Helsel and Hirsch, 2002, p. 298) for streamflow is less than 

0.025. Comparison plots of the residuals from the turbiditySSC SLR to streamflow can indicate when an MLR model 

may decrease the amount of variability explained. The residual 

plots for the Little Arkansas River near Sedgwick, Kansas, 

indicate that there is little or no change in variability with 

streamflow (fig. 14A and B). Neither of these plots supports 

the addition of streamflow to the SSC model.

Other methods for evaluating which explanatory variables to include in the regression model are part of MLR 

model-building method described in Helsel and Hirsch (2002, 

p. 312–315). The possible explanatory variables in this case 

include turbidity and streamflow. Turbidity and streamflow are 

typically log10 transformed for a better regression model, but 

any combination of transformed or untransformed explanatory 

variables can be evaluated. 

The MSPE for the SLR model of the Little Arkansas 

River near Sedgwick, Kansas, is larger than 20 percent, 

indicating that a MLR model with streamflow and turbidity should be considered. The streamflow variable is deemed 

significant in the regression model if the p-value of the partial 

F statistic is less than a predetermined alpha value (α) of 

0.025. As shown in table 4, the p-value is larger than 0.025 for 

streamflow in the MLR model for the Little Arkansas River 

near Sedgwick, Kansas, indicating that the SLR model–and 

not a MLR model–should be used for computing SSC. The R2

a

should never be the sole criterion used to assess the appropriateness of a regression model because a large R2

a

 can occur 

even though the linear fit is poor (see Helsel and Hirsch, 2002, 

p. 18 and 228, and Glysson, 1987, p. 39–43). The regression 

diagnostics are reported in the default regression model output 

from Microsoft Excel or the “Regression Subset Selection” 

option of the USGS library for S-Plus for Windows (Slack and 

others, 2003). 

Comparison plots of measured and model-estimated 

SSC for the SLR and MLR models can indicate the regression 

model with the most accuracy (fig. 15A and B). The closer the 

points plot to the 1:1 line, the more accurate the model predictions are. The variance of the MLR residuals should be evaluated and compared to the SLR residuals (fig. 15A and B). The 

measured/estimated SSC and residual plots are nearly identical 

for the SLR and MLR models, suggesting that the models 

produce similar results. 

Regression Model Summary

The regression model selected to compute SSC timeseries values for the Little Arkansas River near Sedgwick, 

Kansas, is the turbidity-SSC SLR model. Comparisons with 

the MLR model indicate that the addition of the streamflow 

variable slightly improved the SSC prediction but not sufficiently so as to justify its inclusion. In general, the simplicity of a SLR model is preferred over a MLR model that 

imparts modest improvement in accuracy to the computational 

process. Currently (2009), ADAPS (U.S. Geological Survey, 2003) can compute SSC using a SLR model. The use of 

ADAPS for computing SSC is desired because of the documentation of the regression model and when it was used. Had 

the MLR model been chosen, SSC values would have to be 

Figure 14. Comparison of streamflow in A, linear space and 

in B, log10 space to residuals from a simple linear regression 

analysis of turbidity and suspended-sediment concentrations for 

U.S. Geological Survey streamgage on Little Arkansas River near 

Sedgwick, Kansas, 1999–2005.

A

-0.4

-0.2

0

0.2

0.4

RESIDUAL LOG SUSPENDED-SEDIMENT CONCENTRATION

1 100 1,000 10,000 100,000

B

-0.4

-0.2

0

0.2

0.4

10

0 2,000 4,000 6,000 8,000 10,000 12,000 14,000

STREAMFLOW, IN CUBIC FEET PER SECOND

Sample

Sample
20 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data

computed outside of ADAPS and then loaded to ADAPS (see 

Appendix 2).

A summary of regression information and expressions 

should be recorded in the station analysis for “Suspended 

Sediment” (example 1 of Appendix 1). The summary contains 

information specific to the development of the regression 

model. The hydrographer should summarize the reasoning for 

selection of the model, the final regression model and associated statistics, and the dates for which the model was used to 

compute SSC and SSL. A senior hydrographer should review 

the summary to determine its adequacy. 

Computation of Suspended-Sediment 

Concentration and Load Time-Series 

Record

SSC time series should be computed at the same time step 

as the measured in-stream turbidity and streamflow time series 

by means of an appropriate regression model. Depending on 

the model form and which explanatory variables are used, the 

regression model can be implemented as a turbidity-SSC rating 

in NWIS to calculate a SSC time series. Details for developing 

a SSC time series within NWIS are presented in Appendix 2. 

Log10-transformed SLR models can be expressed as a 

power function and used to compute instantaneous values of 

SSC in ADAPS. The “equation rating” in ADAPS computes 

instantaneous values for the output data description (DD) 

and SSC on the basis of instantaneous values of the input DD 

(turbidity; U.S. Geological Survey, 2003). Retransformation 

of the log10-transformed SLR model (equation 6) is shown in 

equation 7. 

The log10-transformed SLR model follows:

 (6)

where

SSC is suspended-sediment concentration, in 

milligrams per liter;

b1 is the slope; 

Turb is turbidity; and

b0 is the y intercept.

The log10-transformed SLR model (equation 6) can be 

retransformed and corrected for bias with a BCF resulting in 

equation 7:

 (7)

For the Little Arkansas River near Sedgwick, Kansas, the 

model, log10SSC = 0.943log10Turb + 0.130, and BCF, 1.03, can 

be retransformed to SSC = 100.130Turb0.943 × 1.03, or 

SSC = 1.39Turb0.943. (8)

The hydrographer also should consider and perhaps limit 

computed values extrapolated beyond the range of explanatory variable values (minima and maxima of the explanatory 

variables). The veracity of extrapolated model values must be 

evaluated. Typically, the number of extrapolated values can be 

minimized if: (1) the range of the model-calibration data set is 

maximized by collecting samples at both extremes, and (2) the 

make and model of the fixed-location turbidity sensor are 

identical to the manually deployed field-turbidity sensor with 

similar maximum recording levels. Computed values that are 

substantially beyond the range of the calibration data should 

be withheld from public display until those values can be verified by new SSC data. If a replacement or supplemented sensor 

has a maximum recording level that is more than 10 percent 

larger than the maximum value of the calibration data set, 

the computed SSC values greater than the calibration data set 

maximum should be withheld from display until those values 

can be verified with samples collected in the range between 

the new sensor maximum recording level and the upper limit 

of the regression model. 

Estimates for Periods of Missing Data

USGS policy (2009) precludes storage of estimated 

instantaneous values of turbidity in the NWIS database (Office 

of Water Quality Technical Memorandum 2005.03; U.S. Geological Survey, 2005). However, data collected from sources 

other than the fixed-location turbidity sensor can be used to 

supplement discrete periods of missing turbidity time-series 

record, which includes periods for which measured turbidity 

values are considered unreliable, such as from turbidity sensor 

Table 4. Expressions for determining use of simple linear regression (SLR) or multiple linear regression (MLR) models for U.S. 

Geological Survey streamgage on Little Arkansas River near Sedgwick, Kansas. 

[n, number of samples; R2

a

, adjusted coefficient of determination; RMSE, root-mean-squared error in log units; MSPE, model standard percentage error; n/a, 

not applicable]

Explanatory 

variables n R2

a RMSE MSPE p-value for 

streamflow

t-statistic for 

streamflow

Turbidity 68 0.975 0.101 +25.9, -20.6 n/a n/a

Turbidity and streamflow 68 0.977 0.098 +25.3, -20.2 0.043314 2.06

log ( ) log ( ) , 10 10 0 SSC = + b Turb b 1

SSC Turb BCF b b 10 0 1 = × .
Computation of Suspended-Sediment Concentration and Load Time-Series Record 21

Figure 15. Comparison of measured and estimated suspended-sediment concentrations and residuals in log space from A, simple and 

B, multiple linear regression models for U.S. Geological Survey streamgage on Little Arkansas River near Sedgwick, Kansas.

B

A

10,000

1,000

100

10

1

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

MODEL-ESTIMATED SUSPENDED-SEDIMENT CONCENTRATION,

IN MILLIGRAMS PER LITER

1

10

100

1,000

10,000

1:1 line

1:1 line

RESIDUAL LOG SSC-0.4

-0.3

-0.2

-0.1

0.1

0.2

0.3

0.4

0

MEASURED SUSPENDED-SEDIMENT CONCENTRATION,

IN MILLIGRAMS PER LITER

MODEL-ESTIMATED SUSPENDED-SEDIMENT CONCENTRATION,

IN MILLIGRAMS PER LITER

-0.4

-0.3

-0.2

-0.1

0.1

0.2

0.3

0.4

0
22 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data

truncation at large SSC values. For example, onsite measurements made using a cleaned and calibrated field sensor while 

the fixed-location sensor is being cleaned and calibrated can 

be used to fill in a part of the missing turbidity time-series 

record during the site visit.

The appropriateness of estimating mean daily turbidity 

values is governed by a number of factors, the most effectual 

of which are the duration of the missing record, availability of 

flow data for the missing-record period, and the availability of 

data describing historical relations among turbidity, streamflow, and SSC. Daily statistics for periods containing missing 

data should be calculated with an appropriate level of scrutiny 

and in accordance with Wagner and others (2006). Mean daily 

turbidity values should not be calculated solely for the purpose 

of calculating mean daily SSC values. Daily SSC values should 

be estimated by methods described by Porterfield (1972) or 

Koltun and others (2006). The hydrographer should note in 

the station analysis that the uncertainties associated with SSC

estimates derived from estimated turbidity data are unknown. 

Rasmussen and Ziegler (2003), Bragg and others (2007), and 

Lee and others (2009) demonstrate different techniques for 

estimating missing or truncated instantaneous values of turbidity and SSC. 

Estimation of missing or truncated instantaneous SSC

values (without estimating turbidity values) in some instances 

can be performed outside of ADAPS to meet study objectives. 

The method(s) used in those instances to develop estimates 

should be well documented and peer reviewed. 

Computation of Suspended-Sediment Load 

Time-Series Record

A time series of SSL is calculated from SSC and streamflow for the same site. Instantaneous SSL is calculated using 

the following equation:

 (9)

where

SSLi is the computed suspended-sediment load, in 

tons per second, or pounds per second;

SSCi is the computed suspended-sediment 

concentration for the ith value, in 

milligrams per liter;

Qi is the streamflow for the ith value, in cubic 

feet per second; and

c is a constant, 3.121 × 10-8, for converting the 

units to tons per second, or 6.242 × 10-5 for 

pounds per second.

The instantaneous SSC and streamflow values also can 

be used to compute daily, monthly, or annual SSLs using the 

following equation:

 (10)

where

SSLn is the computed suspended-sediment load for 

the desired time period, in tons;

Ci is the suspended-sediment concentration for 

the ith time, in milligrams per liter;

Ci-1 is the suspended-sediment concentration for 

the ith minus 1 time, in milligrams per 

liter;

Qi is the streamflow for the ith value after 

midnight, in cubic feet per second;

Qi-1 is the streamflow for the ith minus 1 value 

after midnight, in cubic feet per second;

t

i is the time for the ith value after midnight;

t

i-1 is the time for the (ith-1) value after midnight; 

c is a constant, 0.0027, for converting the units 

to tons per day; and

n is the number of instantaneous values within 

the desired period (day, month, year).

The hydrographer should identify any periods of missing 

record and determine how to provide the best estimate of SSL

for periods when computed SSC data, streamflow data, or both 

are missing. The options to estimate SSL include: (1) interpolate the missing values between known values, taking into 

consideration other available data, (2) estimate SSL on the 

basis of some other data, such as streamflow (a sedimenttransport curve for the site) or SSL derived from a streamgage 

with similar sediment characteristics using appropriate scaling factors, or (3) another technically supportable method. 

Regardless of the method or combination of methods used 

to estimate missing SSL data, the rationale should be fully 

explained in the station analysis or associated report. 

Uncertainty estimates of long-term suspended-sediment 

load computed by summing retransformed SSC from SLR 

or MLR models with transformed response variables can be 

computed. Estimates of the mean squares errors are discussed 

in Gilroy and others (1990). 

Model Validation and Maintenance of a LongTerm Suspended-Sediment Concentration 

Record

Once an acceptable regression model is developed, it can 

be used to compute SSC beyond the period of record used in 

model development with proper sample collection and analysis. Maintenance of a long-term SSC record requires ongoing 

collection of turbidity and streamflow time-series data and 

sample collection for reanalysis and verification of the current 

SSC regression model. The method for validating the regression model is affected by the frequency of calibration-sample 

collection and the purpose of the study. Regression models can 

be validated annually (or at some other frequency as needed 

on the basis of the nature of the monitored hydrologic system 

and its watershed, and the needs and constraints of the monitoring program) after sufficient applicable new data have been 

collected or on the basis of other valid criteria. A fundamental 

SSL SSC Q c i i i = × × ,

SSL

C C Q Q t t c n

i i i i i

i

n

= ( ) ( ) ( ) - - -

=

1 1 1 1

1 4 ∑ , + + × × × –
Computation of Suspended-Sediment Concentration and Load Time-Series Record 23

characteristic of hydrology is variability, with periods of 

floods and periods of droughts. Additionally, watershed conditions can change seasonally or from other factors such as 

through changes in land use, implementation of best management practices, or by wildfire. Therefore, regression models 

to compute SSC at a site should never be considered static 

but rather considered to represent a set period in a continually 

dynamic system in which additional data will help verify any 

change in SSL, type, and source. 

Validation of Suspended-Sediment 

Concentration Model

One approach to updating the regression model is to plot 

new observations with the original model-calibration data 

set and recompute the regression coefficient(s) and y-intercept. Typically, at least 4 to 10 SSC samples and associated 

turbidity and streamflow values representing a wide range 

of streamflows are collected annually, depending on the site 

and monitoring program, to validate the existing regression 

model. More such data may be needed. The additional data 

plotted along with the model-calibration data set for comparison should indicate any significant change in the turbiditySSC relation that would signal the need for a completely 

revised regression model or additional and more frequent 

sample collection. A review of the scatter plot for the Little 

Arkansas River near Sedgwick, Kansas, suggests that there 

has been no significant change in the turbidity-SSC relation 

(fig. 16). 

A regression model developed from new measurements 

not used in previous model development should be compared 

to the existing regression model. Analysis of covariance 

(ANCOVA; see Helsel and Hirsch, 2002, p. 316) can be used 

to test (1) the regression model on the basis of the original 

model data and additional data, (2) the original regression 

model, and (3) the regression model solely on the basis of 

the additional data. ANCOVA will determine if the slope or 

y intercept of any of these models is significantly different, 

indicating a fundamental shift in the turbidity-SSC relation and 

the possible need to develop a new model. If a shift occurred, 

the hydrographer also will need to determine when it occurred 

and when to cease use of the existing model and begin use 

of a new model. A fundamental shift such as this should be 

accounted for by a major change in sediment source or transport processes in the watershed, such as those resulting from 

a substantial change in land use or land cover, construction or 

removal of an impoundment, wildfire, landslide, or a major 

flood. A more likely scenario is a gradual change over years 

that can be detected only by continued sample collection and 

analysis.

New data that do not significantly change the original 

regression should be added to the model-calibration data set 

to refine the regression model. The slope, y intercept, and the 

computed SSC values from the new model will not be significantly different from the old model, but the improved estimate 

of RMSE may reduce the prediction interval. The hydrographer has to determine when the refined model will take effect. 

If sample collection and analysis are considered on an annual 

basis, the new model should start at the beginning of the 

ensuing water year. An approved computed SSC time series 

should not be recomputed unless there is strong evidence that 

the turbidity-SSC relation changed during the approved period. 

The hydrographer in this case has determined that the revised 

model (fig. 16) will take effect at the beginning of water 

year 2006.

Sampling Plan

A sampling plan to obtain the requisite turbidity, streamflow, and SSC data should be devised to periodically validate 

and refine the existing regression model. Conditions or events 

that may cause variability in the turbidity-SSC relation also 

should be considered when devising a sampling plan for 

maintaining long-term SSC record. Sample values from the 

model-calibration data set may indicate periodic, seasonal, or 

other fluctuations that may induce variability in the current 

model. These fluctuations should be considered when collecting representative samples to facilitate adequate validation 

of an existing regression model. A prudent and affordable 

annual sampling plan for the Little Arkansas River near 

Sedgwick, Kansas, includes two to four spring stormwater 

runoff sample sets, two to four summer stormwater runoff or 

Figure 16. Model-calibration data set (water years 1999–2005) 

and new (water year 2006) turbidity and suspended-sediment 

concentration data for U.S. Geological Survey streamgage on 

Little Arkansas River near Sedgwick, Kansas.

SSC = 1.39Turb0.943

Model standard percentage error (MSPE)= +25.9 and -20.6

Adjusted coefficient of determination (R2

a

) = 0.98

TURBIDITY (Turb) FROM FIXED-LOCATION, IN-STREAM SENSOR, IN FORMAZIN

NEPHELOMETRIC UNITS (YSI 6026 TURBIDITY SENSOR)

SUSPENDED-SEDIMENT CONCENTRATION (SSC),

IN MILLIGRAMS PER LITER

1

10

100

1,000

10,000

1 10 100 1,000 10,000

New data

Model calibration data set
24 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data

base streamflow sample sets, and one to two winter base-flow 

sample sets. 

Changes to Turbidity Sensor Model or Type

Different sensors can provide different turbidity readings 

for the same environmental sample (Landers, 2003). Manufacturers have made improvements and design changes to turbidity sensors over time. A change of sensor model or type most 

likely will require an adjustment to the historical values so that 

the equivalency of turbidity-sensor-response characteristics of 

historical and newly collected data is maximized. The hydrographer should compare turbidity measurements between 

differing sensors in a range of environmental samples. The 

difference between sensors cannot be identified in formazin 

standards (Hach; Loveland, Colo.) and may be reversed in 

polystyrene bead standards (APS Analytical Standards Inc.; 

Redwood City, Calif.; fig. 17). 

Typically, turbidity data collected with an old sensor can 

be adjusted to an approximately equivalent reading for a new 

sensor by means of a conversion factor. The conversion factor 

is computed from a data set consisting of concurrent turbidity 

measurements collected by the old and new sensors arrayed 

adjacent to each other in the stream. Care should be taken to 

ensure that the range of the concurrent measurements spans 

the known range of turbidity values at the site. One way of 

achieving this is to operate both sensors in-stream, side-byside, over a wide range of turbidity conditions. The resulting 

data set will provide a robust conversion factor for the monitoring site.

The site-specific turbidity conversion factor can be 

calculated several ways, such as from the mean or median 

of the instantaneous conversion factors or by means of an 

ordinary least squares (OLS) regression (if the relation is 

linear; fig. 18). The median conversion factor computed as the 

ratio, new sensor value/old sensor value, is the least likely to 

be affected by outliers and was selected for use. YSI Incorporated (2003) suggests a conversion factor of 0.65 for converting turbidity measurements made with sensor model 6026 to 

comparable measurements made with sensor model 6136. The 

conversion factor for the Little Arkansas River near Sedgwick, 

Kansas, was 0.64, which was obtained by taking the median 

of the instantaneous conversion factors from several months 

of concurrent in-stream turbidity measurements with both sensors (fig. 18). 

The model-calibration data set can be adjusted using the 

conversion factor, and new regression model coefficients can 

be computed for the historical turbidity data. Each historical 

turbidity value in the model-calibration data set is multiplied 

by an empirically derived (or, lacking that, manufacturerspecified) conversion factor. Thus, the converted historical 

data are normalized with respect to the non-model data so that 

either sensor would provide the same value under identical 

environmental conditions. The adjusted model-calibration data 

then are used to recompute the regression model for computing SSC following the same steps used to develop the original 

model. The revised regression model then can be used to compute SSC on the basis of measurements from the new turbidity 

sensor. Historical SSC and turbidity time-series data with the 

ADAPS aging status of “approved” should not be recalculated 

or deleted. The hydrographer should plot the time series of 

historical SSC values that overlap with the time series from 

the new SSC regression model to ensure that the new and old 

equations are comparable. 

Polystyrene standard

(APS, Analytical Standards Inc.,

Redwood City, California)

approximately 0.3 μm

Formazin standard

(Hach, Loveland, Colorado)

approximately 1.3 μm

Environmental sample

2–4 μm

0

20

40

60

80

100

120

140

TURBIDITY, IN FOMAZIN NEPHELOMETRIC UNITS

TURBIDITY MEASUREMENT

YSI model 6026

YSI model 6136

Figure 17. Comparison of turbidity measurements from YSI 

turbidity models 6026 and 6136 (YSI Incorporated, Yellow Springs, 

Ohio) in various solutions. 

Number of data points = 8045

Median of YSI 6136/YSI 6026 ratios = 0.64

Mean of YSI 6136/YSI 6026 ratios = 0.63

YSI 6136 = 0.625*(YSI 6026)

Coefficient of determination (R2

) = 0.9825

TURBIDITY READING FROM FIXED-LOCATION, IN-STREAM SENSOR,

IN FORMAZIN NEPHELOMETRIC UNITS (YSI MODEL 6136 SENSOR)

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

TURBIDITY READING FROM FIXED-LOCATION, IN-STREAM SENSOR,

IN FORMAZIN NEPHELOMETRIC UNITS (YSI MODEL 6026 SENSOR)

0 200 400 600 800 1,000 1,200 1,400 1,600 1,800 2,000

Figure 18. Relation between YSI 6026 and YSI 6136 turbidity 

sensor values, U.S. Geological Survey streamgage on Little 

Arkansas River near Sedgwick, Kansas, July 14, 2004, to 

August 26, 2005.
Selected References 25

Factors Affecting Relation Between Turbidity 

and Suspended-Sediment Concentration

The hydrographer should be mindful of factors other 

than SSC that can affect turbidity measurements. Particle 

size, shape, and color all affect the amount of light scattered, 

the important parameter for turbidity (Sutherland and others, 2000). Light is absorbed and scattered as it travels from 

a light source, to suspended particles, and is reflected back to 

a detector. When particle sizes larger than about 90 μm (very 

fine sand) are in suspension, the turbidity-SSC relation will be 

negatively biased, and that bias will increase as particle size 

increases (Anderson, 2005). Particle shape affects the scatter intensity. Darker or more black-colored (Munsell Color 

Co., 2000) particles also have been shown to substantially 

affect turbidity measurements by imparting a negative bias in 

measurements (Sutherland and others, 2000). Insights as to 

the potential effects of these and other factors might be gained 

from having particle-size and color analyses performed on 

selected water-sediment samples. Other factors affecting the 

turbidity-SSC relation are measurement error (including SSC

sample collection and analysis) and natural variability caused 

by processes not evaluated in the regression model. Turbidity 

resulting from the presence of suspended microorganisms–

principally phytoplankton–can result in increased uncertainty 

in the SSC determination. Hence, caution should be used when 

inferring SSC from turbidity or turbidity and streamflow values in water with substantial microbiological activity. 

Summary

Collection, computation, and publication of suspendedsediment and related environmental data are a necessary part 

of investigations to evaluate effects of fluvial sediment and 

sediment-associated constituents on water resources. In-stream 

continuous turbidity data, or continuous turbidity and streamflow data, calibrated with measured suspended-sediment 

concentration (SSC) data, can be used to compute a time series 

of SSC and suspended-sediment load (SSL). Development of a 

simple linear regression model between turbidity and measured SSC data is the first step in computing a SSC time series. 

If the model standard percentage error (MSPE) simple linear 

regression model meets an established minimum criterion, this 

model can be used to compute a time series of SSC. If the simple regression model does not meet the acceptability criterion, 

a multiple linear regression model using paired instantaneous 

turbidity and streamflow data is developed. If the addition 

of streamflow is statistically significant and the uncertainty 

associated with the multiple regression model results in an 

improvement over that for the simple linear model and is ultimately acceptable, it is used as the basis for computing a time 

series of SSC. The computed SSC time series is subsequently 

used with its paired streamflow time series to compute a time 

series of SSL by standard U.S. Geological Survey techniques. 

Time-series SSC and SSL data can be used to better describe 

variability in suspended-sediment conditions, to evaluate SSC

relative to numerical water-quality criteria and management 

goals, and to make watershed comparisons.

 Once an acceptable regression model is developed, it can 

be used to compute SSC beyond the period of record used in 

model development with proper sample collection and analysis. Maintenance of a long-term SSC record requires ongoing 

collection of turbidity and streamflow time-series data and 

calibration-sample collection for reanalysis and verification of 

the current SSC regression model. The method for validating 

the regression model is affected by the frequency of sample 

collection and the purpose of the study. Regression models can 

be validated annually (or at some other frequency as needed 

on the basis of the nature of the monitored hydrologic system 

and its watershed, and the needs and constraints of the monitoring program) after sufficient new data have been collected 

or on the basis of other valid criteria. Regression models to 

compute SSC are generally site specific and should never be 

considered static but rather considered to represent a set period 

in a continually dynamic system in which additional data will 

help verify any change in SSL, type, and source. 

Acknowledgments

This report was prepared by the USGS Kansas Water 

Science Center (WSC), Lawrence, Kansas, and the Offices 

of Surface Water and Water Quality, Reston, Virginia. USGS 

personnel in the California, Kansas, Oregon, and Pennsylvania 

WSCs provided astute technical advice and assistance. Information, discussion, comments, and suggestions from Teresa J. 

Rasmussen (Kansas WSC) and USGS colleague reviewers 

Paul A. Buchanan (California WSC), Elizabeth A. Hittle 

(Pennsylvania WSC), Gregory F. Koltun (Ohio WSC), David 

K. Mueller (Central Region), and Mark A. Uhrich (Oregon 

WSC) resulted in substantial improvements to this document. 

Trudy Bennett was responsible for oversight and data collection at the Little Arkansas River near Sedgwick, KS site.

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Cunnane, C., 1978, Unbiased plotting positions—A review: 

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Davies-Colley, R.J., and Smith, D.G., 2001, Turbidity, suspended sediment, and water clarity—A review: Journal 

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Appendixes
32 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data

Appendix 1. Examples of Suspended-Sediment Concentration Models from 

Kansas, Oregon, Florida, and California 

Turbidity and SSC data and models from rivers in four States are presented to illustrate turbidity-SSC applications at a 

variety of geographic locations, drainage areas, and freshwater/saltwater conditions. Examples are courtesy of Heather Bragg 

and Mark Uhrich of the Oregon WSC (2007), Paul Buchanan of the California WSC (2004), A.C. Lietz (retired), and Elizabeth 

Hittle of the Pennsylvania WSC (2005).

U.S. Geological streamgages used for examples of turbidity and suspended-sediment concentration (SSC) data and regression 

models.

Example Station 

number Station name

Turbidity 

instrument make 

and model

Fresh- or 

saltwater

Drainage area 

(square miles)

1 07144100 Little Arkansas River near Sedgwick, Kansas YSI model 6026 Freshwater 1,239

2 14178000 North Santiam River below Boulder Creek, Oregon YSI model 6026 Freshwater 216

3 02279000 C-51 Canal, Palm Beach County, Florida YSI model 6026 Freshwater Not applicable

4 11458370 Mare Island Causeway, San Pablo Bay, California D and A OBS Saltwater Not applicable
Appendixes 33

Example 1. Complete Review Package for Little Arkansas River near Sedgwick, Kansas

WATER-QUALITY MONITOR STATION ANALYSIS

2005 WATER YEAR

SUSPENDED-SEDIMENT RECORD

07144100

Little Arkansas River near Sedgwick, Kansas

MODEL-CALIBRATION DATA SET—All data were collected using USGS protocols and are stored in USGS NWIS 

databases. The regression model is based on 68 concurrent measurements of turbidity and streamflow and SSC samples collected from November 1998 through June 2005. Samples were collected throughout the range of continuously observed hydrologic and turbidity conditions. Turbidity and streamflow values are time-averaged approved unit values corresponding with the 

duration of sample collection. A comparison of cross-section mean and corresponding time-series monitor readings is provided. 

Water-quality data were collected using an YSI 6600 monitor with a 6026 turbidity sensor (FNU). Selected data values used to 

develop the regression models were removed on the basis of sample evaluation. Five SSC values were removed from the data set 

because of transcription errors, sampling errors, and a sample compromised during shipping. Three data values were affected by 

sensor limitations (within 10 percent of the sensor maxima) and, therefore, were removed from the data set. Summary statistics 

and the complete model-calibration data set are provided. 

MODEL DEVELOPMENT—Initially, data plots of the response variable (SSC) and possible explanatory variables turbidity and streamflow indicate both are correlated to SSC. Regression analysis was done using S-Plus software, and the final output 

is provided. Turbidity and streamflow were examined together as explanatory variables for estimating SSC, but the p-values for 

streamflow were larger than 0.025. Different combinations of untransformed and log10-transformed data were evaluated. Log10-

transformed turbidity and SSC were selected as the best model on the basis of residual plots, MSPE, and p-value for streamflow. 

Residual plots for evaluating variance, normality, homoscedasticity, and curvature are provided. For log10-transformed models, 

estimated values were multiplied by a calculated retransformation bias correction factor (Duan, 1983). Ninety-percent prediction intervals are provided for evaluating uncertainty of the estimates. 

MODEL SUMMARY—Summary of final regression analysis for suspended-sediment concentration at Little Arkansas 

River near Sedgwick, Kansas.

log10(SSC) = 0.943 log10(Turb) + 0.130,

where

SSC = Suspended-sediment concentration, in milligrams per liter; and 

Turb = Turbidity (YSI 6026), in formazin nephelometric units.

Model information:

Number of measurements = 68,

root-mean-squared error (RMSE) = 0.10,

model standard percentage error (MSPE) = +25.9 and -20.6 percent

90-percent prediction intervals = + 41 percent,

adjusted coefficient of determination (R2

a

) = 0.98,

PRESS = 0.663.

Duan’s bias correction factor = 1.03.

Coefficients:

Coefficient Standard 

error

t-statistic p-value

Intercept 0.130 0.041 3.02 0.0035

log10(Turb) 0.943 0.018 50.9 1.13E-54
34 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data

Correlation matrix of coefficients:

Intercept log10(Turb)

Intercept 1

log10(Turb) -0.9588 1

SSC RECORD—The record is computed using a regression model and ADAPS software. Data are computed at 15-minute 

intervals. The record is complete for the year except as noted. The turbidity monitor was removed for a short period in December-February to avoid ice damage. 

Daily values for partial days were updated where data existed during the expected time for the occurrence of the maximum 

or minimum, if at least 12 hours of values were available for the day, and if values were present adjacent to the extreme for the 

day. 

312 days of record out of 365 days (85 percent) will be published.

REMARKS— 

• A new turbidity sensor, YSI model 6136, was installed to collected concurrent turbidity measurements. These measurements will be used to convert YSI model 6136 values to the YSI model 6026 to compute SSC with the new 6136 sensor.

• T.B. Bennett collected field data. 

• Cross-section survey results can be retrieved from NWIS, database 02. 

• The Excel® “Field Measurement Summary” spreadsheet for this site and water year summarizes the number of site visits, 

calibration results, and calculations of the magnitude of fouling and calibration drift.

Computed: P.P. Rasmussen, November 1, 2005 

Checked: C.J. Lee, November 22, 2005 

Reviewed: T.J. Rasmussen, November 26, 2005
Appendixes 35

Model-calibration data set for Little Arkansas River near Sedgwick, Kansas, November 1998–June 2005.

Date

Turbidity from fixed-location 

sensor, in formazin 

nephelometric units 

(YSI 6026 turbidity sensor)

Streamflow, 

in cubic feet per second

Suspended-sediment 

concentration, 

in milligrams per liter

Percentage of suspended 

sediment finer than 

62 micrometers

November 5, 1998 390 7,800 381 92

December 4, 1998 100 219 78 99

February 1, 1999 977 4,460 1,180 95

February 19, 1999 20 111 19 89

April 7, 1999 912 1,500 791 98

April 16, 1999 924 5,410 896 93

May 24, 1999 1,233 1,610 931 99

June 18, 1999 457 396 323 100

June 21, 1999 452 2,080 549 97

August 3, 1999 1,115 4,170 1,040 97

September 28, 1999 1,164 1,920 897 99

February 9, 2000 19 84 28 86

March 7, 2000 448 1,120 520 98

May 19, 2000 74 87 90 99

May 31, 2000 326 175 263 100

June 28, 2000 856 1,100 835 99

July 20, 2000 107 134 129 99

August 16, 2000 37 24 35 97

September 8, 2000 36 20 36 96

September 25, 2000 21 21 14 78

October 26, 2000 582 5,400 499 78

November 8, 2000 112 83 84 97

December 4, 2000 6 46 8 81

April 13, 2001 947 400 791 100

April 26, 2001 36 97 49 85

May 8, 2001 217 152 232 100

June 4, 2001 808 1,040 873 99

June 6, 2001 870 8,690 678 92

June 23, 2001 525 4,260 560 94

July 11, 2001 51 67 55 97

August 2, 2001 69 25 61 98

August 28, 2001 44 28 47 97

August 28, 2001 46 28 53 95

September 20, 2001 989 4,170 877 98

October 31, 2001 13 28 18 89
36 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data

Model-calibration data set for Little Arkansas River near Sedgwick, Kansas, November 1998–June 2005.—Continued

Date

Turbidity from fixed-location 

sensor, in formazin 

nephelometric units 

(YSI 6026 turbidity sensor)

Streamflow, 

in cubic feet per second

Suspended-sediment 

concentration, 

in milligrams per liter

Percentage of suspended 

sediment finer than 

62 micrometers

January 10, 2002 4 37 6 96

February 21, 2002 15 42 35 97

April 9, 2002 66 96 61 99

May 13, 2002 340 412 274 100

May 22, 2002 310 140 201 100

June 6, 2002 466 245 286 100

June 13, 2002 743 5,630 651 100

July 9, 2002 43 30 48 98

August 15, 2002 555 823 927 100

September 19, 2002 68 14 53 100

December 18, 2002 16 41 20 100

March 20, 2003 820 6,320 886 91

April 23, 2003 196 292 254 100

May 29, 2003 218 195 218 100

June 11, 2003 73 97 77 100

June 24, 2003 54 56 63 99

July 30, 2003 43 8 44 100

September 3, 2003 327 567 333 99

October 14, 2003 523 1,100 431 97

December 11, 2003 7 46 4 95

March 9, 2004 929 1,800 948 98

March 30, 2004 130 294 172 99

May 26, 2004 43 49 47 100

June 16, 2004 88 54 102 99

June 22, 2004 410 1,040 303 93

July 27, 2004 320 5,850 384 99

January 27, 2005 135 170 122 99

March 23, 2005 435 5,840 506 89

March 31, 2005 71 150 79 --

May 10, 2005 259 186 314 --

May 27, 2005 1,290 700 1,250 --

June 6, 2005 425 1,940 449 98

June 9, 2005 840 12,200 649 99
Appendixes 37

Summary statistics of model-calibration data set for Little Arkansas River near Sedgwick, Kansas, November 1998–June 2005.

[FNU, formazin nephelometric unit; mg/L, milligrams per liter; ft3/s, cubic feet per second; >, greater than; --, not applicable]

Statistical summary of data sets

Summary statistic Turbidity, 

FNU

Calibrated data set 

(68 samples)

Time-series data set 

(61,368 hourly values)

Suspendedsediment 

concentration, 

mg/L

Streamflow, 

ft3/s

Turbidity, 

FNU

Streamflow, 

ft3/s

Minimum 4 4 8 65 55

Maximum 1,300 1,200 12,000 >2,000 16,000

Mean 370 350 1,500 140 380

Median 250 240 210 41 60

Standard deviation 370 350 2,500 260 1,200

Missing turbidity values -- -- -- 1,264 643

Turbidity values greater than maximum sensor limit -- -- -- 254 --
38 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data

S-Plus Output of Regression Model Development of Turbidity and SSC for Little Arkansas River near 

Sedgwick, Kansas

*** Linear Model ***

Call: lm(formula = SSC ~ Turb, data = SDF5, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

 -0.2943 -0.06414 0.009471 0.06104 0.3053

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.1298 0.0429 3.0256 0.0035 

 Turb 0.9430 0.0185 50.8736 0.0000 

Residual standard error: 0.1007 on 66 degrees of freedom

Multiple R-Squared: 0.9751 

F-statistic: 2588 on 1 and 66 degrees of freedom, the p-value is 0 

Correlation of Coefficients:

 (Intercept) 

Turb -0.9586 

Analysis of Variance Table

Response: SSC

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 Turb 1 26.23809 26.23809 2588.118 0

Residuals 66 0.66910 0.01014 
Appendixes 39

Example 2. Turbidity Computed Suspended-Sediment Concentrations from Oregon

From Bragg, H.M., Sobieszczyk, Steven, Uhrich, M.A., and Piatt, D.R., 2007, Suspended-sediment loads and yields in the 

North Santiam River Basin, Oregon, water years 1999–2004: U.S. Geological Survey Scientific Investigations Report 2007–

5187, 26 p., available on Web, accessed March 2008, at http://pubs.usgs.gov/sir/2007/5187/.

Samples collected every 15 minutes during a single period of runoff. (Photograph by Heather Bragg, U.S. Geological Survey, 

October 20–22, 2003.)
40 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data

Model-calibration data set for North Santiam River below Boulder Creek, Oregon, October 1998–August 2004.—Continued

[Q, streamflow; ft3/s, cubic feet per second; FNU, formazin nephelometric units; SSC, suspended-sediment concentration; mg/L, milligrams per liter]

Date and time Q

(ft3/s)

Turbidity 

(FNU)

SSC

(mg/L)

10/16/98 12:05 468 1 2

11/16/98 14:30 791 3 3

11/21/98 13:00 4,210 22 44

11/25/98 14:05 3,205 7 17

12/2/98 16:10 5,377 33 97

12/28/98 15:13 7,625 79 219

1/13/99 14:30 1,050 4 4

1/21/99 13:30 2,690 4 13

1/26/99 13:13 1,350 2 2

2/4/99 9:30 1,050 1 1

2/11/99 17:25 1,022 1 2

2/18/99 13:10 1,227 3 7

2/24/99 8:40 2,237 6 14

3/3/99 12:05 2,040 2 7

3/17/99 9:15 1,020 1 2

3/22/99 16:55 1,420 1 2

4/14/99 15:45 943 1 1

4/23/99 16:30 1,510 1 1

4/30/99 11:07 1,340 1 1

5/3/99 17:05 1,770 1 1

5/12/99 16:05 1,392 1 1

5/18/99 10:55 2,420 4 9

5/18/99 18:25 2,558 4 10

6/17/99 16:55 2,162 3 3

7/1/99 15:33 1,459 1 2

8/10/99 10:20 767 1 3

9/1/99 16:45 644 1 1

9/15/99 15:20 576 1 1

10/13/99 13:20 514 1 1

11/5/99 10:45 525 1 2

11/15/99 16:45 580 1 2

11/25/99 12:32 5,679 285 366

11/26/99 13:55 8,778 190 331

12/2/99 10:06 2,404 14 30

12/7/99 14:35 1,580 4 6

12/13/99 14:20 1,730 3 5

12/13/99 14:38 1,727 3 5

12/13/99 14:58 1,721 3 4

12/16/99 14:05 3,397 26 65

12/16/99 22:05 3,680 15 64

12/17/99 11:15 3,155 6 30

1/7/00 9:22 978 1 2

1/21/00 10:25 1,040 1 2
Appendixes 41

Model-calibration data set for North Santiam River below Boulder Creek, Oregon, October 1998–August 2004.—Continued

[Q, streamflow; ft3/s, cubic feet per second; FNU, formazin nephelometric units; SSC, suspended-sediment concentration; mg/L, milligrams per liter]

Date and time Q

(ft3/s)

Turbidity 

(FNU)

SSC

(mg/L)

2/1/00 12:40 2,273 14 35

2/1/00 14:00 2,430 16 41

2/1/00 17:10 2,777 16 49

2/2/00 7:40 2,983 8 26

2/22/00 12:04 1,281 2 2

2/22/00 13:22 1,315 3 3

3/2/00 15:48 1,460 1 2

3/17/00 9:30 1,400 1 1

4/6/00 12:10 1,577 1 1

5/4/00 15:45 1,410 1 2

5/31/00 10:40 1,127 1 4

6/12/00 19:20 1,990 4 7

6/13/00 18:30 1,570 2 1

6/14/00 12:45 1,430 2 2

6/21/00 10:40 931 1 1

9/20/00 11:40 447 1 2

10/2/00 15:50 458 21 13

10/20/00 22:00 798 16 22

11/9/00 12:20 543 2 2

11/27/00 13:30 599 3 4

11/30/00 13:37 580 2 4

12/28/00 11:17 726 1 2

1/10/01 11:24 644 1 1

2/5/01 14:28 853 1 3

3/19/01 13:54 1,230 10 14

3/19/01 14:23 1,230 10 18

3/28/01 10:55 1,592 6 12

3/28/01 10:57 1,591 6 12

4/30/01 15:50 1,723 13 22

4/30/01 16:15 1,815 15 29

4/30/01 20:54 2,316 36 50

5/1/01 15:08 1,727 4 9

5/16/01 11:23 2,232 6 16

5/16/01 11:32 2,228 6 12

7/24/01 12:16 366 1 2

8/16/01 8:48 344 4 3

8/16/01 9:18 342 3 2

9/25/01 15:50 318 2 3

9/26/01 8:35 332 4 5

10/11/01 13:00 480 12 13

10/23/01 17:05 548 3 6

10/31/01 16:01 883 7 14

11/14/01 13:34 783 7 5
42 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data

Model-calibration data set for North Santiam River below Boulder Creek, Oregon, October 1998–August 2004.—Continued

[Q, streamflow; ft3/s, cubic feet per second; FNU, formazin nephelometric units; SSC, suspended-sediment concentration; mg/L, milligrams per liter]

Date and time Q

(ft3/s)

Turbidity 

(FNU)

SSC

(mg/L)

11/22/01 15:30 3,280 64 147

11/23/01 12:56 2,111 7 14

11/23/01 13:16 2,089 7 15

11/29/01 10:10 2,033 5 15

12/7/01 9:00 1,890 3 5

12/14/01 11:40 3,427 13 28

12/16/01 15:26 3,450 11 34

12/16/01 15:45 3,440 11 38

1/8/02 11:17 5,209 43 134

2/21/02 14:02 907 1 2

3/12/02 11:33 2,969 8 23

4/14/02 13:36 7,350 87 225

7/18/02 7:27 650 11 9

12/11/02 16:00 644 7 7

12/16/02 10:48 1,440 8 16

12/16/02 11:22 1,440 7 13

12/27/02 16:24 1,428 8 15

1/3/03 14:40 2,670 8 37

1/30/03 15:24 6,216 63 213

3/22/03 12:01 4,903 34 157

8/18/03 15:10 395 5 3

8/21/03 7:40 385 4 3

9/12/03 13:30 395 17 11

9/12/03 14:45 392 14 9

10/21/03 12:31 395 569 415

10/21/03 15:16 390 216 173

10/23/03 13:55 385 19 18

10/29/03 11:31 375 39 26

11/19/03 13:45 799 4 9

12/13/03 17:00 6,080 118 418

1/29/04 9:04 4,031 16 70

6/25/04 16:02 719 10 11

7/21/04 9:43 502 3 4

8/25/04 11:24 655 14 18

8/25/04 15:32 791 23 29
Appendixes 43

1

\\Sps1dkslwr\home\pubs\report_figs\13_0162_c_rasmussen\figures\fig_22.ai

10,000

1,000

100

10

1 10 100 1,000

A B

SUSPENDED-SEDIMENT CONCENTRATION (SSC),

IN MILLIGRAMS PER LITER (mg/L)

SSC = 1.54(Turb)

1.04

Root-mean-square error (RMSE) = 0.89

0.2

0.4

0.6

0

-0.2

-0.4

-0.6

1 10 100 1,000

SUSPENDED-SEDIMENT CONCENTRATION, IN MILLIGRAMS PER LITER

0

0.2

0.4

0.6

0.8

-0.2

-0.4

-0.6

-0.8

-3

C

-2 -1 0 1 2 3

NORMAL QUANTILES

LOGRESIDUALS

LOG RESIDUALS

TURBIDITY (Turb),IN FORMAZIN NEPHELOMETRIC UNITS

Samples

Results for simple linear regression analysis for A, turbidity and suspended-sediment concentration data, and comparison of 

B, computed suspended-sediment concentrations and regression residuals, and C, probability plot of residuals for 

U.S. Geological Survey streamgage on North Santiam River below Boulder Creek, Oregon, 1998–2004.
44 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data

Model-calibration data set for C-51 Canal, Palm Beach County, 

Florida, November 2003–December 2004.

[SSC, suspended-sediment concentration, in milligrams per liter; Turb, 

turbidity, in formazin nephelometric units; Q, streamflow, in cubic feet per 

second; mm, millimeters; --, not determined]

Date

(month/

day/year)

SSC Turb Q

Percentage 

finer than 

0.063 mm

11/13/03 6 4.2 408 89 

11/17/03 6 6.5 871 98 

02/10/04 16 13.4 857 97

02/26/04 15 15.8 955 97

03/15/04 9 10.4 246 94

04/12/04 8 4.6 1,010 36 

07/27/04 5 2.9 735 53 

08/02/04 7 4.6 226 77

08/04/04 6 6.2 678 89

08/06/04 6 4.8 0 82 

08/13/04 7 6.5 718 94 

08/14/04 8 6.2 696 84 

08/27/04 5 4.1 481 83 

09/07/04 25 18.1 2,690 96

09/08/04 16 7.8 2,180 97

09/22/04 17 24.2 1,920 98 

09/27/04 30 23.1 4,060 94

10/13/04 20 14.0 1,499 97

10/27/04 -- -- 869 95

11/09/04 14 24.0 267 93

12/15/04 54 78.0 584 95

Example 3. Turbidity Computed Suspended-Sediment Concentrations from Florida

From Lietz, A.C., and Debiak, E.A., 2005, Development of rating curve estimators for suspended-sediment concentration 

and transport in the C-51 canal based on surrogate technology, Palm Beach County, Florida, 2004–05: U.S. Geological Survey 

Open-File Report 2005–1394, 19 p., available on Web, accessed March 2008, at http://pubs.usgs.gov/of/2005/1394/.
Appendixes 45

0

\\Sps1dkslwr\home\pubs\report_figs\13_0162_c_rasmussen\figures\fig_23.ai

1,400

1,200

1,200

1,000

800

600

400

200

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

A B

0.1

0.2

0.3

0

-0.1

-0.2

0.6 0.8 1 1.2 1.4 1.6 1.8

ESTIMATED LOG SUSPENDED-SEDIMENT CONCENTRATION

AT CROSS SECTION, IN MILLIGRAMS PER LITER

LOG SUSPENDED-SEDIMENT CONCENTRATION (SSC)

AT CROSS SECTION, IN MILLIGRAMS PER LITER

ESTIMATED LOG SUSPENDED-SEDIMENT CONCENTRATION

(SSC) AT CROSS SECTION, IN MILLIGRAMS PER LITER

0

100

300

500

-200

-400

-500

-2

C

-1 0 1 2

NORMAL QUANTILES

RRESIDUALS, IN MILLIGRAMS PER LITER

RRESIDUALS, IN MILLIGRAMS PER LITER

Log10 SSC (at cross section) = 0.30 + 0.75 log10 turbidity

r

2

 = 0.85

Results for simple linear regression analysis for A, turbidity and suspended-sediment concentration data, and comparison of 

B, computed suspended-sediment concentrations and regression residuals, and C, probability plot of residuals for 

U.S. Geological Survey streamgage on C-51 canal, Palm Beach County, Florida, 2003–4.
46 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data

Example 4. Turbidity (Optical Backscatter) Computed Suspended-Sediment Concentrations Using 

Nonparametric Regression, California

From Buchanan, P.A., and Ganju, N.K., 2004, Summary of suspended-sediment concentration data, San Francisco Bay, California, water year 2002: U.S. Geological Survey Open-File Report 2004–1219, 45 p., available on Web, accessed March 2008, at 

http://pubs.usgs.gov/of/2004/1219/.

Model-calibration data set for Mare Island Causeway, San Pablo 

Bay, California, water years 2001–04.

[OBS, optical backscatter; SSC, suspended-sediment concentration; mg/L, 

milligrams per liter]

OBS sensor output 

(milliVolts)

SSC

(mg/L)

22.3 11

45.9 31

100 74

94.7 55

166 88

138.6 77

283 186

272.5 161

77.9 36

77.5 26

254 156

49 17

110.55 61

203 118

220 141

144 76

135 91

60.4 20

71.6 28

37.8 18

47.7 24
Appendixes 47

Calibration of mid-depth optical backscatter sensor at Mare Island 

Causeway, San Pablo Bay, California, water year 2004 (from 

Buchanan and Ganju, 2004).

\\Sps1dkslwr\home\pubs\report_figs\13_0162_c_rasmussen\figures\fig_24.ai

Number of water samples = 21

Calibration equation: y = 0.65* x - 10.9

Non-parametric prediction interval: +12 to -8

95 percent confidence bound on equation slope (0.65): 0.583 to 0.701

SUSPENDED-SEDIMENT CONCENTRATIONS, IN MILLIGRAMS PER LITER

20

0

40

60

80

100

120

140

160

180

200

SENSOR OUTPUT, IN MILLIVOLTS

0 50 100 150 200 250 300

Non-parametric prediction interval

Water sample
Appendix 2. Computation, Storage, and Real-Time Display of Time-Series 

Suspended-Sediment Concentration and Load in National Water Information 

System

In some cases, ADAPS, a subsystem of NWIS, can compute SSC unit values (UVs) and SSL daily values (DVs). SSC UVs 

can only be computed in NWIS if turbidity is the sole explanatory variable in the regression model. Currently (2009), NWIS 

cannot compute SSC values if:

1. The model includes computed UVs, such as streamflow, for an explanatory variable, or 

2. The model is a MLR model. 

For SSC models that NWIS cannot compute, the hydrographer should refer to the Graphical Constituent Loading Analysis 

System (GCLAS; Koltun and others, 2006) or a spreadsheet application. The time series of computed SSC unit values then can 

be loaded to ADAPS using Device Conversion and Delivery System (DECODES) (U.S. Geological Survey, 2003). 

SSL DVs are computed using mean daily SSC and streamflow. The resulting SSL DV is correct only if the SSC and streamflow are correlated in time. Typically, this is not the case and results in erroneous SSL DVs. Hydrographers should instead use 

GCLAS or a spreadsheet application to compute SSL UVs and DVs. The time series of computed SSL unit values then can be 

loaded to ADAPS using DECODES (U.S. Geological Survey, 2003). 

The following presents the general methods for computation, storage, and real-time display of SSC unit values and SSL

daily values using NWIS. For complete instructions, refer to U.S. Geological Survey (2003), http://pubs.usgs.gov/of/2003/

ofr03123/. NOTE: The user must have a user class of “adba” or “syst” to have access to perform several of the following steps 

(U.S. Geological Survey, 2003).

In ADAPS, the site must have a data descriptor (DD) for computed:

• SSC unit values (NWIS parameter code 99409—suspended-sediment concentration, water, unfiltered, estimated by 

regression equation, milligrams per liter) and 

• SSL unit values (NWIS parameter code 80295—sediment suspended sediment load, water, unfiltered, estimated by 

regression equation, pounds per second, 80296–sediment suspended sediment load, water, unfiltered, estimated by 

regression equation, tons per second, 80297–suspended sediment load, water, unfiltered, computed, the product of regression-computed suspended sediment concentration and streamflow, tons per day, or 80298–suspended sediment load, 

water, unfiltered, regression computed, turbidity and streamflow as regressors, tons per day).

The DD setup for SSC and SSL should include:

1. Adding a DD optional description (30 characters maximum). 

SSC—Add the SLR model (example, “SSC = 1.39Turb^0.943”)

SSL—example, “by regression using turbidity DD##,” where DD## is the turbidity data descriptor number. 

2. The processor for the SSC DD needs to be identified as a “standard rating computation” and have the turbidity DD identified 

as the input DD. 

3. The rating values of measured turbidity and estimated SSC should be calculated outside of ADAPS using the SLR model 

and the BCF and entered as a “dependent, parameter” rating. The proper “rating expansion type” for Little Arkansas River 

near Sedgwick, Kansas example is “equation.”

• The rating “Remarks” (99 characters maximum) should include the SLR model, the BCF, and the turbidity sensor’s 

manufacturer and model number and (or) the parameter and method codes. (example, SSC = 1.39Turb^0.943, turb = YSI 

6026 = DD##, parameter 63680, method TS086). 

• The SSC values for Little Arkansas River near Sedgwick, Kansas, are computed using equation 7, where the BCF is 

incorporated into the model.

• When SSC model coefficients change due to addition of samples, the rating, rating remarks, and start and end dates need 

to be updated. 

48 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data
Appendixes 49

4. Primary computation must be performed on the SSC DD to compute the SSC UVs. 

• In ADAPS, select menu options:

“PR—Primary Data Processing,”

“7—Primary Computations,”

select the desired site number, DD, and dates,

<Enter>

select the desired options, and 

<Enter> .

• Enter Hydra to compare SSC UVs with turbidity UVs;

select “PR—Primary Data Processing,”

select “2—Edit Time-Series Data using Hydra,”

select “3. COMPUTED UNIT VALUES,” 

select the desired site number, DD, and dates, and

add a reference curve for the turbidity DD.

• View the plot of the two curves and verify that the data look correct. For instance, for the Little Arkansas River near 

Sedgwick, Kansas, the SSC and turbidity are nearly identical at values less than 400. For SSC values larger than 400, the 

difference increases as SSC increases so that turbidity is larger than SSC. 
5. Currently (2009), ADAPS computes mean daily SSL from mean daily SSC and streamflow and the appropriate conversion 

factor. The resulting SSL DV is only correct if SSC and streamflow are highly correlated (r > 0.95). In most cases, they 

are not highly correlated, and therefore, ADAPS should not be used to compute SSL. The hydrographer should use either 

GCLAS or a spreadsheet application for the computation of SSL UVs or DVs. If the hydrographer can verify that the SSC

and streamflow for their site is highly correlated (r > 0.95), then the following instructions can be used to compute SSL DVs 

in ADAPS.

Primary computations must be performed on the SSL DD to compute SSL DVs.

• Compute SSL DVs using DV_MANIP in ADAPS. From the ADAPS prompt:

type DV_MANIP (or “PR 9”),

select “A” to write the DVs to ADAPS,

select the desired site number, dates, and the SSL DD,

<Enter>,

select option (8) compute load from streamflow and concentration,

select “A,”

select the desired site number, dates, and the streamflow DD,

<Enter>,

select “A,”

select the desired site number, dates, and the SSC DD,

select “e” (edited or estimated) to set the DV remark code, and 

select “s” to store the data in ADAPS.

6. Plot to SSL DVs, SSC UVs, and streamflow UVs in either Hydra or Tkg2 for comparison.

7. NWISWeb can be configured to display up to 60 days of SSC unit values, all available daily values, daily, monthly, and 

annual statistics for turbidity, streamflow, SSC, and SSL and SSC values from discrete sample collection. 

50 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data
Appendixes 51

Appendix 3. Comparison of Computed Suspended-Sediment Concentrations 

with Water-Quality Criteria

Currently (2009), there are no State criteria for SSC. Five States (Hawaii, Nevada, New Jersey, South Dakota, and Utah) 

have numeric criteria for total suspended solids (TSS), which range from a minimum concentration of 35 milligrams per liter 

(mg/L) in Utah to a maximum of 158 mg/L in South Dakota (U.S. Environmental Protection Agency, 2001). The differences 

between values of SSC and TSS as metrics for the suspended solid-phase content of surface waters are discussed in Gray and 

others (2000). SSC remains one of the most cited water-quality impairments in the United States even with the lack of State criteria. The SSC values computed using SLR methods have a quantifiable uncertainty that allows for several methods of comparison with criteria. In the following examples, 100 mg/L is an assumed SSC water-quality criterion for comparison. 

Continuous SSC can be used, for example, to construct cumulative frequency distribution (duration) curves to determine 

percentage of time that computed concentrations exceed water-quality criteria. Computed concentration duration curves can be 

used to evaluate current water-quality conditions and to estimate the duration and magnitude of potential water-quality degradation. Without SSC water-quality criteria, water-resource managers can use duration curves to assess how frequent a potential 

water-quality criterion may be exceeded. When OLS regression is used to generate estimates for which probability statements 

are made, such as with duration curves and probability of exceeding criteria, values at the upper end likely are underestimated, 

and values at the lower end may be overestimated (Helsel and Hirsch, 2002).

In the example below, 28 percent of the hourly computed SSC values exceeded 100 mg/L for the period October 1999 

through September 2005. The 90-percent prediction interval indicates that 100 mg/L could be exceeded 22 to 36 percent of the 

time. Simple linear regression (SLR) was used to compute the values plotted in figure 20 after SLR was determined to be the 

most appropriate regression technique. Like all regression techniques, the true relation of the response and explanatory variables 

is unknown, and the regression model is only an estimate of this relation. Other regression techniques might yield different models and, therefore, different duration curves. The differences between regression techniques typically are within the 90-percent 

prediction interval of the SLR regression.

FREQUENCY OF EXCEEDANCE, IN PERCENT

HOURLY SUSPENDED-SEDIMENT CONCENTRATION,

IN MILLIGRAMS PER LITER

1

10

100

1,000

10,000

1 20 40 60 80 100

Prediction intervals

 Upper 90 precent

 Lower 90 percent

Sample

Duration curve and 90-percent prediction intervals for computed hourly suspended-sediment concentrations in Little Arkansas River 

near Sedgwick, Kansas, October 1999–September 2005.
Although prediction intervals are approximate indicators of uncertainty, a range of values is not very useful for comparing 

the water quality of a stream to water-quality criteria. Probability of exceedance provides water managers with a single hourly 

value for decisionmaking. Probabilities of exceeding designated water-quality criteria or other values of interest for a log10 transformed model can be determined as follows:

 

where

Pr is the probability that the criterion has been exceeded (0 < Pr < 1),

D is the cumulative distribution function for the standard normal curve—values for it are obtained from tables in 

statistics textbooks or equations that approximate the exact values, 

SC is the BCF-corrected, regression-computed SSC value;

Criterion assumed 100 mg/L [if RMSE is in log10 space, then criterion is log10(100)]; and

RMSE is root-mean-squared error, or standard error of the regression, or standard deviation of the residuals.

The probability of hourly SSC also can be displayed as probability curves. Each curve represents an SSC and is plotted 

using frequency of exceedance (x axis) and the probability that the actual SSC is equal to the given threshold (y axis). The 

figures can be used to estimate the frequency of exceedance for 5 values of SSC. For instance, 20 percent of all hourly values 

of SSC for Little Arkansas River at Sedgwick have a 99-percent chance of exceeding 100 mg/L. Two percent of all hourly SSC

values have a 50-percent chance of exceeding 1,000 mg/L for Little Arkansas River at Sedgwick.

52 Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data

Cumulative frequency curves showing probability of exceedance 

of suspended-sediment concentration thresholds of 10, 30, 100, 

300, and 1,000 milligrams per liter, Little Arkansas River near 

Sedgwick, Kansas, 1999–2005.

0

10

20

30

40

50

60

70

80

90

100

PROBABILITY OF EXCEEDING VARIOUS

THRESHOLDS, IN PERCENT

EXPLANATION

10 mg/L

30 mg/L

100 mg/L

300 mg/L

1,000 mg/L

Suspended-sediment concentration

 thresholds, in milligrams per

 liter (mg/L)

0 20 40 60 80 100

FREQUENCY OF EXCEEDANCE, IN PERCENT

P r

log log SSC Criterion DSSC Criterion

RMSE ( ) ≤ ( ) ( ) 1 10 10

= [ [ – –
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4821 Quail Crest Place

Lawrence, KS 66049

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Rasmussen and others—Computing Time-Series Suspended-Sediment Concentrations and Loads from Turbidity-Sensor and Streamflow Data—Techniques and Methods 3–C4

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