Computing Discharge Using the Index Velocity Method

Techniques and Methods 3–A23

U.S. Department of the Interior

U.S. Geological Survey
COVER DESIGN

Photographs:

Michael Hall, USGS South Carolina Water Science Center

BROAD RIVER NEAR SOUTH CAROLINA
Computing Discharge Using the Index Velocity Method 

By Victor A. Levesque and Kevin A. Oberg

Techniques and Methods 3–A23

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: 2012

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Suggested citation:

Levesque, V.A., and Oberg, K.A., 2012, Computing discharge using the index velocity method: U.S. Geological Survey 

Techniques and Methods 3–A23, 148 p.

(Available online at http://pubs.usgs.gov/tm/3a23/)

ISBN 978 1 4113 3285 0
iii

Acknowledgments

This report is a cooperative effort with contributions from many people. It reflects more 

than 20 years of experience and practice by personnel in the USGS. Many instructors and 

students have provided inspiration and information for this report. In particular, the authors 

acknowledge the following USGS employees for their contributions to the report and their 

thorough peer reviews: Jeff East, Liz Hittle, Marc Stewart, and Molly Wood. Appreciation is 

extended to Sonny Anderson, Hugh Darling, and Jon Yokomizo for providing data, photos, and 

other information used in preparing this report.

The authors also acknowledge assistance provided by Paul-Emile Bergeron, Jeanette 

Fooks, and Francois Rainville, Environment Canada. 

v

Contents

Acknowledgments........................................................................................................................................iii

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

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

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

Applications of the Index Velocity Method ......................................................................................2

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

Introduction to the Index Velocity Method................................................................................................3

Site and Instrument Selection .....................................................................................................................3

Site Selection.........................................................................................................................................3

Instrument Selection............................................................................................................................6

ADVM Installation and Configuration.........................................................................................................6

ADVM Installation.................................................................................................................................6

ADVM Configuration ..........................................................................................................................10

Selection of Measurement Volume for Sidelooker ADVMs ...............................................10

ADVM Frequency and Instrument Noise Level ...........................................................11

Boundary and Object Interference................................................................................12

Flow Disturbance and Velocity Distribution .................................................................13

Setting the Measurement Volume .................................................................................14

Selection of Measurement Volume for Uplooker ADVMs ..................................................16

Measurement Interval and Averaging Period.......................................................................18

Initial Exploratory Time-Series Measurements ...........................................................19

Routine Time-Series Measurements.............................................................................20

Discharge Calibration and Validation Measurements................................................20

Salinity and Coordinate Systems ............................................................................................22

Internally Stored and Transmitted Data.................................................................................22

Routine Field Techniques............................................................................................................................23

Beam Checks.......................................................................................................................................23

Download and Review Internal Data...............................................................................................26

Log File..................................................................................................................................................26

ADVM Clock Check.............................................................................................................................26

Temperature Check ............................................................................................................................26

ADVM Cleaning...................................................................................................................................26

ADVM Alignment.................................................................................................................................27

Reconfigure the ADVM......................................................................................................................27

Start Date and Start Time ..................................................................................................................27

Re-Deploy the ADVM .........................................................................................................................27

Routine Office Techniques .........................................................................................................................27

Velocity Data........................................................................................................................................27

ADVM Water Temperature................................................................................................................28

Cell End.................................................................................................................................................28

Signal-to-Noise Ratio.........................................................................................................................28

Rating Development and Analysis ............................................................................................................28

Stage-Area Rating ..............................................................................................................................29
vi

The Standard Cross Section ....................................................................................................29

Cross-Section Survey ...............................................................................................................29

Stage-Area Rating Development ............................................................................................30

Stage-Area Rating Validation ..................................................................................................34

Discharge Measurement Calibration Data..............................................................................................34

Index Velocity Rating...................................................................................................................................35

Data Compilation.................................................................................................................................35

Rating Development and Analysis ...................................................................................................38

Graphical Data Analysis ...........................................................................................................39

Simple-Linear Regression Rating............................................................................................42

Rating Development .........................................................................................................42

Example of a Simple-Linear Regression Rating...........................................................46

Compound-Linear Regression Rating.....................................................................................48

Rating Development .........................................................................................................49

Example of a Compound-Linear Rating.........................................................................49

Multiple-Linear Regression Rating .........................................................................................53

Rating Development .........................................................................................................54

Example of a Multiple-Linear Rating .............................................................................56

Rating Validation ........................................................................................................................60

Computation and Analysis of Discharge..................................................................................................61

Summary and Conclusions.........................................................................................................................63

References....................................................................................................................................................64

Glossary.........................................................................................................................................................67

Appendix 1 – Mounts for Acoustic Doppler Velocity Meters...............................................................69

Appendix 2 – Forms and Quick-Reference Guides ................................................................................77

Appendix 3 – Analysis of Data for Selection of Measurement Volume..............................................95

Appendix 4 – Quality Control of Index Velocity Data for SonTekTM/YSI ArgonautsTM.....................103

Appendix 5 – Evaluating Changes in Stage-Area Ratings ..................................................................117

Appendix 6 – Implementing the Stage-area and Index Ratings in National Water Information 

 System (NWIS) Automated Data Processing System (ADAPS) version 4.10.......121

Appendix 7 – Index Velocity Rating Shifts .............................................................................................137

Appendix 8 – Example of an Index Velocity Station Analysis.............................................................145

Figures

 1. Channel cross section looking downstream with a non-uniform channel shape and 

non-uniform velocity distribution from an ADCP reconnaissance measurement.............5

 2. Channel cross section looking downstream with a uniform channel shape and a 

uniform velocity distribution from an ADCP reconnaissance measurement .....................5

 3. Channel cross section looking downstream with a uniform channel shape and an 

unusual velocity distribution from an ADCP reconnaissance measurement.....................5

 4. Diagram of sidelooker ADVM measurement volume and main acoustic beam ................7

 5. Plan view schematic of a sidelooker ADVM properly aligned to measure 

downstream and cross-stream velocity and improperly aligned to measure 

downstream and cross-stream velocity ...................................................................................8
vii

 6. Graphs showing beam velocity data from a properly aligned sidelooker ADVM 

and an improperly aligned sidelooker ADVM..........................................................................9

 7. Photographs showing absence of biological fouling on an uplooker ADVM that 

has been treated with antifouling paint and presence of biological fouling on an 

untreated sidelooker ADVM .....................................................................................................10

 8. Diagram showing generalized measurement volumes for a sidelooker ADVM ..............11

 9. Graph showing an example of a signal amplitude (beam) check for a sidelooker 

ADVM with a water-level acoustic beam...............................................................................12

 10. Diagrams showing theoretical bridge pier-wake turbulence dimensions........................13

 11. Graphs showing beam checks for the same site with acceptable signal amplitudes 

to the end of the measurement volume in October 2009, and decreased signal 

amplitudes in January 2010.......................................................................................................15

 12. Graph showing changing range-averaged cell end over time ...........................................16

 13. Change in cell end from automatic beam check diagnostic in January 2010 ..................17

 14. Diagrams showing generalized measurement volume for a two-beam and a 

three-beam uplooker ADVM.....................................................................................................18

 15. Graph showing the effect of using different measurement intervals and

averaging periods.......................................................................................................................19

 16. Graphs showing results of beam checks showing data collected with objects in 

the measurement volume, side-lobe interference, failed transducers, and a school 

of minnows in the measurement volume................................................................................24

 17. Schematic showing location of standard cross section at an index velocity station.....29

 18. Graph showing example of a channel cross-section shape...............................................30

 19. Combined stage-area survey created from standard surveying techniques on 

shore and a vessel-mounted ADCP used to capture channel bathymetry along 

measured cross sections and cross section derived from combined shore survey

with ADCP channel bathymetry ...............................................................................................31

 20. Cross-section data shown in U.S. Geological Survey AreaComp software.....................33

 21. Stage-area rating output from AreaComp..............................................................................33

 22. Graph showing an example of an index rating ......................................................................35

 23. Flowchart illustrating steps for creating an index rating.....................................................40

 24. Graph showing multi-cell index velocity data with measured-mean velocity .................40

 25. Diagram showing a water column velocity profile and possible change in the 

location of the ADVM measurement volume with changing stage....................................41

 26. Scatter plots with the same coefficient of determination (R2) value .................................43

 27. Graphs showing residuals with no trend in index velocity and date; and residuals 

with a trend in index velocity and time ...................................................................................45

 28. Plots of range-averaged X velocity, stage, Y velocity, and multi-cell X velocity 

with measured-mean velocity for simple-linear rating example........................................47

 29. Plots of measured-mean velocity and predicted mean velocity and regression 

residuals with index velocity, and regression residuals with measurement date ..........48

 30. Graph showing an example of a compound-linear index rating.........................................49

 31. Plot of measured-mean velocity, stage, and Y velocity with index velocity for 

compound-linear rating example.............................................................................................50

 32. Plots of measured-mean velocity and index velocity, and regression residuals 

with index velocity for lower range of compound-linear rating example.........................52

 33. Plots of measured-mean velocity and index velocity, and regression residuals 

with index velocity for upper range of compound-linear rating example.........................52
viii

 34. Two linear segments and the points used to define the transition between each 

segment for the compound-linear rating example................................................................53

 35. Plot showing curvature in the relation between index velocity and measured-mean 

velocity .........................................................................................................................................53

 36. Graphs showing patterns in plots of Y velocity and stage with measured-mean 

channel velocity..........................................................................................................................54

 37. Graphs showing patterns in plots of residuals from simple-linear regression with 

downstream index velocity and stage ....................................................................................54

 38. Plot of measured-mean velocity, stage, and Y velocity with index velocity for 

multiple-linear rating example..................................................................................................56

 39. Plots of measured-mean velocity and predicted mean velocity and regression 

residuals from simple-linear regression with index velocity and measurement 

date for multiple-linear regression example..........................................................................58

 40. Plots of measured-mean velocity with computed mean velocity and residuals 

with stage multiplied by index velocity and index velocity for multiple-linear 

regression using index velocity and stage multiplied by index velocity as 

independent variables ...............................................................................................................58

 41. Scatter plot and residuals plot for validation measurements .............................................61

Tables

 1. Examples of acoustic Doppler velocity meter measurement intervals, averaging 

periods, and data transfer times for three common streamflow conditions ...................20

 2. Index velocity data used for example index velocity and discharge measurement 

data synchronization..................................................................................................................21

 3. Discharge measurements used for example index velocity and discharge 

measurement data synchronization ........................................................................................21

 4. Channel bank survey data.........................................................................................................31

 5. Simplified ADCP bathymetry data............................................................................................31

 6. Combined bank survey and ADCP data ..................................................................................32

 7. Assembled continuous 1-minute index velocity and acoustic stage data........................36

 8. Compiled discharge measurement dates, times, discharges, measurement quality, 

and measurement method ........................................................................................................37

 9. Synchronization and synthesis of index velocity and stage data with 

discharge data ............................................................................................................................38

 10. Data assembled into a table for rating analysis ....................................................................39

 11. Typical output from a commonly used regression analysis software program...............42

12. Typical residuals output from a linear regression analysis.................................................43

 13. Results of simple-linear regression.........................................................................................47

 14. Linear regression results for lower range of the compound-linear index rating.............51

 15. Linear regression results for the upper range of the compound-linear index rating......51

 16. Data points used for implementation of the example compound-linear index rating.....53

 17. Results of simple-linear regression for the multiple-linear rating example .....................57

 18. Multiple-linear regression results using index velocity and stage multiplied by index 

velocity as the independent variables for the multiple-linear rating example.................59

 19. Multiple-linear regression coefficients used for implementing the example of a 

multiple-parameter rating in ADAPS.......................................................................................59
ix

Conversion Factors

Inch/Pound to SI

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

Flow rate

foot per second (ft/s) 0.3048 meter per second (m/s)

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

Pressure

decibars (dbars) 10 kilopascals (kPa)

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

°F = (1.8 × °C) + 32

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

Abbreviations and Acronyms Used in this Report:

ADAPS Automated Data Processing System

ADCP acoustic Doppler current profiler

ADVM acoustic Doppler velocity meter

AVM acoustic velocity meter

CRP continuous records processing

dbars decibars

EDA electronic data archive

FlowTracker SonTekTM/YSI FlowTracker Handheld acoustic Doppler velocimeter

NIST National Institute of Standards and Technology

NWIS National Water Information System

OLS Ordinary Least Squares

OSW Office of Surface Water, U.S. Geological Survey 

ppt parts per thousand

R2 coefficient of determination

SDI-12 serial-digital interface 1200 baud

SNR signal-to-noise ratio

USGS U.S. Geological Survey

WSC Water Science Center

Abstract 

Application of the index velocity method for computing 

continuous records of discharge has become increasingly 

common, especially since the introduction of low-cost acoustic 

Doppler velocity meters (ADVMs) in 1997. Presently (2011), 

the index velocity method is being used to compute discharge 

records for approximately 470 gaging stations operated and 

maintained by the U.S. Geological Survey. The purpose of this 

report is to document and describe techniques for computing 

discharge records using the index velocity method. 

Computing discharge using the index velocity method 

differs from the traditional stage-discharge method by separating velocity and area into two ratings—the index velocity 

rating and the stage-area rating. The outputs from each of 

these ratings, mean channel velocity (V) and cross-sectional 

area (A), are then multiplied together to compute a discharge. 

For the index velocity method, V is a function of such parameters as streamwise velocity, stage, cross-stream velocity, and 

velocity head, and A is a function of stage and cross-section 

shape. The index velocity method can be used at locations 

where stage-discharge methods are used, but it is especially 

appropriate when more than one specific discharge can be 

measured for a specific stage. 

After the ADVM is selected, installed, and configured, 

the stage-area rating and the index velocity rating must be 

developed. A standard cross section is identified and surveyed 

in order to develop the stage-area rating. The standard cross 

section should be surveyed every year for the first 3 years 

of operation and thereafter at a lesser frequency, depending 

on the susceptibility of the cross section to change. Periodic 

measurements of discharge are used to calibrate and validate 

the index rating for the range of conditions experienced at the 

gaging station. Data from discharge measurements, ADVMs, 

and stage sensors are compiled for index-rating analysis. 

Index ratings are developed by means of regression techniques 

in which the mean cross-sectional velocity for the standard 

section is related to the measured index velocity. Most ratings 

are simple-linear regressions, but more complex ratings may 

be necessary in some cases. Once the rating is established, 

validation measurements should be made periodically. Over 

time, validation measurements may provide additional definition to the rating or result in the creation of a new rating.

The computation of discharge is the last step in the 

index velocity method, and in some ways it is the most 

straight-forward step. This step differs little from the steps 

used to compute discharge records for stage-discharge gaging 

stations. The ratings are entered into database software used 

for records computation, and continuous records of discharge 

are computed. 

Introduction

The U.S. Geological Survey (USGS) operates and maintains a network of approximately 7,400 streamflow monitoring 

stations throughout the United States for the determination of 

stream and river discharge (Blanchard, 2007). The stagedischarge method for computing continuous discharge (Rantz 

and others, 1982a, 1982b) is used at the majority of these 

stations, and at present (2011) the index velocity method for 

computing continuous discharge is used at approximately 

470 stations (U.S. Geological Survey, 2011). Many State, 

local, and international hydrometric agencies also operate 

index velocity streamflow-gaging stations. In the stagedischarge method, continuous records of stage are used to 

compute discharge records by means of a single-parameter rating developed from concurrent measurements of discharge and 

water-surface elevation (stage). In the index velocity method, 

continuous records of stage and velocity are used to compute 

discharge records by means of two ratings developed from 

concurrent measurements of stage, velocity, and discharge.

In this report, index velocity refers to continuous measurement of velocity in a portion of a canal, stream, or river 

that can be used as an index of the mean channel velocity. 

Stage data are used as an index of the channel cross-sectional 

area. The index velocity data are used with discharge measurements to develop a relation between the in situ index velocity 

and the measured-mean channel velocity, and the stage data 

are used with cross-sectional geometry data to develop a 

relation between the in situ stage and the cross-sectional 

area of the channel. These relations allow the computation 

of continuous mean velocity and cross-sectional area and are 

used to compute continuous records of discharge at a station.

Rantz (1982b, p. 429–470) describes how to develop 

discharge ratings using index velocity as a parameter and 

lists four instruments that have been used to provide an index 

Computing Discharge Using the Index Velocity Method

By Victor A. Levesque and Kevin A. Oberg
2 Computing Discharge Using the Index Velocity Method

of the mean velocity in a channel cross section. Over time, 

the acoustic velocity meter (AVM) and the acoustic Doppler 

velocity meter (ADVM) emerged as favored instruments for 

the measurement of index velocity. AVMs make use of the 

acoustic travel time technique (Laenen, 1985), and ADVMs 

use the Doppler technique for measuring velocities (Morlock 

and others, 2002). In 1968, the first USGS operational AVM 

was installed in a large natural channel (Smith and others, 

1971). From the late 1980s and continuing through the 

mid-1990s, AVMs were the primary tool for index velocity 

measurements; during this period, the approach to computing 

discharge records using the index velocity technique evolved 

from those outlined by Laenen (1985). The development 

of relatively low-cost ADVMs in 1997 (SonTekTM/YSI 

ArgonautTM-SL and ArgonautTM-XR) resulted in a large 

increase in their use as index velocity meters. ADVMs from 

other manufacturers, such as the Teledyne RD Instruments 

ChannelMaster, the Nortek EZ-Q, and its successor, the 

Ott SLD, also are available and are used by the USGS as 

index velocity meters. ADVMs are relatively robust and are 

relatively affordable to install and maintain, making it possible 

to compute discharge at many locations where continuous 

streamgaging was impractical or very costly, such as streams 

affected by tides, variable backwater, or highly unsteady flow. 

Today (2011), the majority of index velocity measurements 

are made using ADVMs, although some AVM systems are 

still being operated by the USGS. The increased use of 

ADVMs by the USGS and changes in methods for developing 

stage-velocity-discharge ratings (index velocity ratings) has 

necessitated an update to the techniques and methods to select, 

install, operate and maintain, and develop ratings for index 

velocity discharge stations. 

Purpose and Scope

The purpose of this report is to document and describe 

techniques for computing discharge using the index velocity 

method under open-channel flow conditions. Although this 

report focuses on ADVMs, the techniques described herein 

can be applied to almost any index velocity meter with 

consideration to instrument-specific characteristics in openchannel flow conditions. The techniques described include 

topics such as site selection, instrument selection, instrument 

configuration, stage-area and index velocity rating development and implementation, and the computation of discharge. 

Report appendixes provide standard forms for documentation 

purposes to assist hydrographers with instrument installation 

and servicing, recommended instrument-specific configurations, field procedure checklists, rating implementation and 

shifting procedures, and data quality assurance guidelines. 

Rating development techniques presented in this report can be 

applied to almost any type of index velocity instrument. The 

techniques presented in this report are limited to open-channel 

flow conditions; computation of flow in pipes and flow under 

ice are not included in the report.

Applications of the Index Velocity Method

At streamflow-gaging stations with variable backwater 

or unsteady flow conditions, the discharge cannot be defined 

by a rating that is based on a single parameter, such as stage 

(Rantz, 1982b). Examples of variable backwater or unsteady 

flow conditions include but are not limited to stream confluences, streams flowing into lakes or reservoirs, tide-affected 

streams, regulated streamflows (dams or control structures), 

or streams affected by meteorological forcing, such as strong 

prevailing winds. If sufficient slope exists on the stream and 

the acceleration head in the energy equation can be ignored, 

then slope may be used as an additional variable to define the 

discharge rating (Rantz, 1982b, p. 391). However, using slope 

as a parameter is not feasible at all stations where a simple 

stage-discharge relation cannot be developed. For example, 

on low-gradient streams, small changes in measured watersurface slope may result in large and unrealistic changes in 

computed discharge, especially at low flows. When the slope 

of a stream is very low and (or) the channel reach available for 

slope measurement is too short, it is often extremely difficult 

to measure the slope accurately enough to use slope as a 

parameter in the discharge rating. However, index velocity 

could be used as a replacement for slope in the discharge 

rating. At other sites, such as tidal streams or regulated 

streams, the acceleration head in the energy equation cannot 

be ignored, and it is often possible to apply the index velocity 

method (Rantz and others, 1982b). For these flow conditions, 

discharge may be computed using the index velocity method 

by properly choosing the site location, the ADVM, the ADVM 

configuration, and developing suitable stage-area and index 

ratings.

Previous Studies

A number of previous studies relate to the index velocity 

method. Rantz and others (1982b) discuss using index velocity 

as a parameter in discharge ratings, provide information on 

why index velocity might be required at a site, and present 

methods to compute discharge. They described the use of 

AVMs and point velocity meters such as the Marsh-McBirney 

meter. Laenen and Smith (1983) provide a short history of the 

development and application of AVMs and present a method 

for developing ratings for the computation of discharge using 

AVMs. Laenen (1985) documented the theory of operation 

for AVMs and discussed phenomena that limit their use, the 

AVMs then (1985) available, site selection, data analysis, 

AVM calibration, and operation and maintenance of AVMs. 

In Morlock and others (2002), records of discharge computed 

using the index velocity method and two ADVMs were 

compared to discharge records computed using conventional 

stage-discharge relations at three USGS streamgaging 

stations; although published 5 years after the introduction 

of the first ADVM, this report was the first attempt to assess 

and demonstrate the overall usefulness of such instruments 
Site and Instrument Selection 3

for systematic streamgaging in the USGS. Ruhl and Simpson 

(2005) described the application of the index velocity method 

for computing discharge in tidal environments and provided an 

approach for determining daily discharge by using a tidal filter.

Introduction to the Index Velocity 

Method 

The discharge in any channel section can be computed by 

the equation

QVA = × ,

where Q is the discharge, V is the mean velocity for the cross 

section, and A is the cross-sectional area of the channel, 

normal to the direction of flow. Cost-effective continuous 

measurements of mean channel velocity and cross-sectional 

area often cannot be made, so mean channel velocity and 

cross-sectional area must be estimated using calibrated relations with in situ velocity (index velocity) and stage measurements. These relations, describing statistical or hydraulic 

relations between two or more parameters (for example stage 

and discharge) are commonly called ratings. Computing discharge using the index velocity method differs from computing discharge using the stage-discharge method by separating 

velocity and area into two ratings—the index-to-mean velocity 

rating and the stage-to-area rating. Throughout this report, 

the index-to-mean velocity and the stage-to-area ratings will 

be referred to as the index rating and the stage-area rating, 

respectively. The outputs from each of these ratings (V and 

A) are then multiplied together to compute a discharge. The 

stage-discharge rating uses a unique relation between stage 

(the combined effects of velocity and area) and discharge to 

compute discharge. 

For the index velocity method, V is often a simple 

function of the streamwise component of the measured index 

velocity. However, there are many sites where V may be 

a function of index velocity and stage, and still other sites 

where V is a function of streamwise index velocity, stage, 

cross-stream index velocity, and the velocity head (streamwise 

index velocity squared). This functional relation (index 

velocity-to-mean velocity) is referred to as the index rating. 

The cross-sectional area (A) is always a function of stage 

and the channel cross-section shape and is referred to as the 

stage-area rating.

The index velocity method has six essential components 

required for accurate computation of discharge records. In the 

following sections, each of these six components are described 

along with the detailed procedures associated with each. Site 

and instrument selection are described first, then ADVM 

installation and configuration, followed by routine field techniques for collecting data (cross section, stage, index velocity, 

and discharge), routine office procedures, rating development 

and analysis (assembling and analyzing the data, choosing the 

best ratings), and finally, computation of discharge.

(1)

Site and Instrument Selection

Site and instrument selection are vital to the successful 

application of the index velocity method. An accurate instrument may be chosen and installed, but site conditions may 

be such that discharge records computed using this method 

may be inaccurate. Likewise, if the instrument selected is not 

optimal for the site, discharge records computed using the 

index velocity method at the site also may be inaccurate. In the 

following sections, these two interrelated topics are discussed 

in detail.

Site Selection

Site selection is perhaps the most critical element of 

establishing an accurate index velocity station. Site selection 

not only includes choosing a good location for flow measurements but also the location of the ADVM measurement 

volume in the channel cross section. Thorough site reconnaissance and selection results in higher data quality, thus 

providing the best chance for developing accurate ratings for 

computing discharge.

Before examining possible sites for selecting the location 

of the ADVM, an electronic directory should be created on the 

Water Science Center electronic data archive (EDA) for any 

index velocity station under consideration. The EDA includes 

electronic documents with descriptions, plots, and evaluations 

of cross sections and their corresponding shapes and velocity 

distributions and the reasoning for selecting an ADVM 

location and orientation. The documentation should contain 

a written description of the locations investigated, the advantages and disadvantages of each location, and rationale for the 

site selected. Documenting a site selection reconnaissance and 

the rationale for selecting a particular site provides helpful 

background information about the site and the establishment 

of the gage and should be stored with station records.

After a general location has been chosen for monitoring, 

the specific location for the site must be selected. Good site 

selection requires comprehensive reconnaissance of the stream 

channel, and proper site reconnaissance starts in the office. 

The general area for the gage site is examined on topographic, 

geologic, and other maps and on aerial or satellite imagery. 

Stream reaches that are potential locations for an index 

velocity gage should have the following characteristics noted 

prior to any field reconnaissance: the planform orientation 

of the stream (for example, how straight the reach is), material composing the stream channel (for example, exposed 

consolidated rock or alluvium), possibility of overbank flow, 

proximity of inflows upstream and downstream, and the 

possibility of flow in multiple channels. The more favorable 

sites will be given critical field examination and should be 

marked on a map with access roads identified to facilitate the 

field reconnaissance (Rantz and others, 1982a). 

When possible, the channel cross section should be 

measured and documented using acoustic Doppler current 

profiler (ADCP) measurements. ADCP measurements provide 
4 Computing Discharge Using the Index Velocity Method

valuable information and can be used to evaluate the horizontal and vertical flow distribution and channel bathymetry at a 

potential index velocity site. If possible, surveys in the channel 

reach upstream and downstream from the section under consideration should be made along the thalweg and in the region 

where the ADVM will measure velocity from 5 to 10 channel 

widths upstream and downstream from the potential ADVM 

location. The bathymetry data can be used to detect any 

abrupt depth changes that may result in undesirable velocity 

distribution or turbulence that may adversely affect index 

velocity measurements. Investigating a reach of the river may 

be necessary to survey channel cross sections upstream and 

downstream from the standard cross section so that changes 

in the channel shape may be identified more readily over time. 

Once a suitable channel and cross-section location have been 

identified, an ADVM should be temporarily installed at the 

site. Recorded velocity data from this temporary installation 

should be analyzed to provide information about temporal 

changes in velocity.

The criteria for good stage-discharge site selection by 

Rantz and others (1982a, p. 4–9) also are applicable for index 

velocity sites. The ideal index velocity gage site should meet 

the following criteria, which are adapted from Rantz and 

others (1982a):

1. The ADVM measurement volume is in a region of 

relatively parallel and uniform flow lines, and all 

acoustic beams are measuring approximately the 

same water velocity at all stages.

2. The ADVM measurement volume is in or near the 

region of maximum velocity and free from any 

boundary effects on flow (for example, pier wakes 

or flow reversals).

3. The general course of the stream is straight for the 

greater of about 300 feet (ft) or 5 to 10 channel 

widths upstream and downstream from the gage site.

4. The ADVM is located a minimum of 5 to 10 channel 

widths upstream or downstream from any tributary 

inflows or flow control structure.

5. The total flow is confined to one channel at all 

stages, and no flow bypasses the site as subsurface 

flow.

6. The streambed is not subject to scour and fill and is 

generally free of aquatic growth.

7. A satisfactory reach for measuring discharge at all 

stages is available within reasonable proximity of 

the gage site. Low and high flows do not have to be 

measured at the same stream cross section.

8. The site is easily accessible for installation and 

operation of the gaging station.

9. Flow at the site is free from excessive air entrainment in the water column, such as might occur 

immediately downstream from the spillway of a 

dam.

If some of the above site-selection criteria cannot be 

met, it may still be possible to use the index velocity method. 

Typically, all of these requirements cannot be met at any one 

site; however, when at all possible, uniform horizontal and 

vertical flow distributions, parallel flow lines, and a stable 

channel shape should take precedence when locating an index 

velocity station. 

Aspects of some of these site-selection criteria are 

illustrated in figures 1–3. The velocity distribution, measured 

by an ADCP, in a cross section at the proposed location of 

an index velocity gaging station is shown in figure 1. The 

channel shape is irregular with two deeper sections toward 

the right bank and a more uniform section toward the left 

side of the channel with maximum velocity near 1.8 feet 

per second (ft/s). The irregular cross-section shape, channel 

conditions upstream and downstream, and along-stream 

channel irregularities likely contribute to the development of 

the observed non-uniform velocity distribution. Based on this 

ADCP measurement, the highest velocity occurs closer to the 

left side of the channel (approximately 0 to 200 ft from the 

left bank), with lower velocity occurring near the right bank 

(approximately 450 to 500 ft from the left bank). The vertical 

velocity distribution is closer to a logarithmic profile toward 

the left side of the channel, with the highest velocity nearer 

the surface and decreasing toward the streambed. The vertical 

velocity distribution deviates noticeably from a logarithmic 

profile near the right bank, where the region of maximum 

velocity is located approximately 3 to 6 ft below the water 

surface. This cross section is less than ideal because of the 

non-uniform velocity distribution; therefore, another cross 

section should be located if possible. 

The velocity distribution, measured by an ADCP, in a 

cross section at another proposed location of an index velocity 

gaging station is shown in figure 2. The channel shape is 

relatively uniform and bowl-shaped, which is an ideal crosssection shape, with a relatively uniform velocity distribution 

and a maximum velocity near 6 ft/s. However, the velocity 

near the left bank (approximately 0 to 180 ft from the left 

bank) is lower than the velocity through the center of the section and may not be the best area in the cross section to locate 

an ADVM. If the velocity distribution is proportionally the 

same over the entire range of stage and discharge, however, 

it may be possible to locate the ADVM at any location in this 

cross section, but the most desirable location would be near 

the region of maximum velocity. 

Figure 3 shows the velocity distribution in a cross 

section, measured by an ADCP, at a third proposed location 

of an index velocity gaging station. The section is uniformly 

bowl-shaped with maximum velocity near 0.6 ft/s, but has an 

unusual velocity distribution in the vertical. This stream is 

an outlet from a lake, which may explain the unusual vertical 

velocity distribution. The location of this cross section is 

not ideal for an index velocity gaging station, based on the 

site-selection criteria. 

Often there is no site that meets all the criteria for the 

ideal gage. If this is the case, the site reconnaissance will 
Site and Instrument Selection 5

Figure 1. Channel cross section looking downstream with a non-uniform channel shape and non-uniform velocity distribution from an 

ADCP reconnaissance measurement.

Figure 2. Channel cross section looking downstream with a uniform channel shape and a uniform velocity distribution from an ADCP 

reconnaissance measurement.

Figure 3. Channel cross section looking downstream with a uniform channel shape and an unusual velocity distribution from an ADCP 

reconnaissance measurement.
6 Computing Discharge Using the Index Velocity Method

enable the hydrographer to decide what type of ADVM should 

be used in the cross section and where in the cross section the 

ADVM should be located to best measure an index velocity. 

After a satisfactory cross section is located, the orientation, 

frequency, and location of ADVM in the cross section must be 

chosen such that reliable and accurate index velocity measurements may be obtained for the site. 

Instrument Selection

The ADVM should be selected after reconnaissance 

measurements and observations are made and documented, 

based on such things as site flow conditions, exploratory 

velocity and discharge measurements, channel bathymetry 

(cross-section shape), and temporary index velocity measurements. The orientation of the ADVM (horizontal or vertical) 

and ADVM frequency are selected based on reconnaissance 

data. If water depths near the potential ADVM location are 

adequate to measure a representative section of the channel, 

the site often can be measured with a horizontally oriented 

ADVM. Horizontally oriented ADVMs, hereafter referred to 

as sidelooker ADVMs, require a relatively uniform horizontal 

flow distribution and a consistent velocity profile shape 

(sometimes referred to as vertical velocity profile) over all 

flow ranges. If water depths are too shallow to use a sidelooker 

ADVM, then a properly located vertically oriented ADVM 

(hereafter referred to as an uplooker ADVM) may be used 

to develop a satisfactory index rating. Additionally, if the 

velocity profile is known to change irregularly over time and 

the horizontal flow distribution is uniform across the channel, 

then an uplooker ADVM might be the best choice of meters. 

If a stream has a sandy bed with adequate velocity to transport 

bed material, an uplooker ADVM may not be a good choice 

of instruments due to potential obstruction of transducers. 

In most cases, the ADVM measurement volume should be 

located in or near the region of maximum channel velocity, 

regardless of the ADVM orientation.

After the meter orientation (horizontal or vertical) is 

decided, the ADVM acoustic frequency should be selected. 

The range of measurement conditions required at a site will 

usually determine the ADVM frequency to be selected. The 

ADVM measurement range is inversely proportional to 

the acoustic frequency of an ADVM. (For example, lower 

frequency has greater minimum and maximum range than 

does higher frequency.) The ADVM frequency should be 

selected based on the measurement range (measurement 

volume) that can be accurately and reliably measured at the 

site. The ADVM frequency should be optimized because, for 

a fixed measurement volume and averaging interval, a higher 

frequency ADVM will measure velocity with a lower standard 

deviation than a lower frequency ADVM. When deciding on 

an ADVM frequency and measurement volume, it is more 

important to measure in a region of representative flow than 

to maximize the measurement volume (SonTekTM/YSI, 2007). 

This may mean that even though the river is wide, the channel 

shape may limit the range that can be accurately measured 

with a sidelooker ADVM, and a shorter range ADVM (higher 

frequency) could be selected and properly located in the cross 

section near the region of maximum velocity. Additionally, 

the concentration and size of scatterers in the water will affect 

measurement volume and may vary seasonally. For example, 

the concentration of scatterers (sediment, organic matter, 

etc.) in the water may be substantially lower in the winter 

than in the summer. Low scatterer concentration may limit an 

ADVM’s maximum range by not providing a strong enough 

return signal. Therefore, an ADVM with a higher acoustic 

frequency might be the best selection even though the channel 

geometry and river size normally would indicate an ADVM 

with a lower acoustic frequency. High scatterer concentration 

also may limit the ADVM maximum range by absorbing or 

scattering the transmitted acoustic signal so that the return 

signal strength is decreased to levels that are not detectable by 

the ADVM.

The measurement control and communication protocol 

may be a consideration when choosing the ADVM. Determine 

if the ADVM required measurement control and data output 

are compatible with the data logger intended for use. USGS 

personnel commonly use data loggers and ADVMs equipped 

with the serial digital interface 1200 baud (SDI-12) measurement control and data communication protocol.

ADVM Installation and Configuration 

After a suitable site and instrument have been selected, 

the ADVM must be installed and configured. The following 

sections describe procedures to be followed when installing an 

ADVM and the configuration of the ADVM. Configuration of 

the ADVM involves the selection of an appropriate measurement volume for the index velocity measurements, selection of 

the measurement interval and averaging interval, and configuration of the ADVM to store internal quality-assurance (QA) 

data and transmit velocity and ancillary data via telemetry. 

ADVM Installation

Once the site and instrument have been selected, the 

ADVM must be installed and properly oriented. The ADVM 

and the mount on which it is installed should be rigid and 

should resist vibration or any kind of movement. The mount 

should allow for the adjustment of the ADVM pitch, roll, 

and heading, and should be designed so that the ADVM can 

always be returned to the same location and orientation after 

servicing or replacement. Whenever possible, the ADVM 

mount should facilitate servicing the instrument at all stages 

and conditions (during high flows as well as low flows, or 

when there is ice cover in the channel, for example). The 

mount for the sidelooker ADVM should be oriented such that 

the acoustic beams do not impinge on any structure or object. 

ADVM mounts should provide a permanent mark or indicator 
ADVM Installation and Configuration 7

that allows the ADVM orientation to be monitored over time 

to ensure that the ADVM has not moved. See appendix 1 for 

examples of mounts and suggested mount requirements, and 

see appendix 2 for a field form for ADVM installation. 

Ideally, a sidelooker ADVM should be positioned 

approximately equidistant above the streambed and below 

the water surface with zero pitch or roll (acoustic beams 

parallel to the water surface) in order to allow for the largest 

possible velocity measurement volume (fig. 4). An exception 

to this rule may be made if the streambed slopes downward 

very near the ADVM position, possibly allowing the ADVM 

to be placed nearer to the streambed without affecting the 

maximum measurement volume. Sidelooker ADVMs also can 

be oriented with a downward or upward angle to measure the 

velocity laterally (across the channel) and vertically (up or 

down in the water column). This orientation can be effective 

in measuring stratified flows, but care must be taken to ensure 

that the measurement volume is not adversely affected by 

boundary interference at any stage. Another problematic effect 

of angling the sidelooker downward or upward is that if the 

ADVM has a vertically oriented acoustic beam for water-level 

measurement, stage data obtained from that vertical beam will 

be unusable. 

Maximum and minimum expected stage should be 

considered when positioning the sidelooker ADVM in 

order to optimize the measurement volume. Placement of 

sidelooker ADVMs requires that the stage during low flows be 

considered to ensure that the sampling range of the ADVM is 

not adversely affected by surface boundary interference that 

may cause a bias in the velocity data and require a change 

to the measurement volume over time. In order to avoid this 

situation, during installation, the ADVM can be temporarily 

positioned below the water surface at a depth corresponding 

to low stage conditions, and the acoustic signal amplitudes 

can be checked for surface interference using signal amplitude 

data (beam checks) to verify that the measurement volume 

would not have to be changed during periods of low flow. It 

is important to remember that changes in the measurement 

volume over time may result in a change to the index rating.

Maximum stages should be considered when deciding 

on a mounting elevation for the sidelooker ADVM. The depth 

of the ADVM near maximum stage may be relatively close 

to the streambed; therefore, the measured velocity may not 

be representative of the mean velocity in the stream. The 

distribution of flow can change at or near maximum stages, 

such that index velocity may not be representative of the mean 

velocity in the stream. For example, undesirable changes in 

flow direction in the region being measured may only occur at 

high stages.

The ADVM typically is connected to a data logger using 

a cable for power and communication. The cable should 

be protected from abrasion, debris, ice, and exposure using 

rigid or flexible conduit, split rubber hose, or some similar 

shielding. The cable should be routed and secured in order to 

prevent debris from being caught on the cable, while retaining 

the ability to easily access the ADVM. 

Requirements for uplooker ADVM mounts are similar to 

sidelooker ADVMs, with some additional requirements. Some 

uplooker ADVM mounting methods may require the use of 

divers to service or replace the ADVM. Uplooker ADVMs 

may be installed using a combination of above-the-water/

below-the-water mounts. The uplooker ADVM mount should 

allow for adjustment in pitch, roll, and heading while allowing 

for relatively easy removal and replacement of the ADVM. It 

might be possible to install a bottom mount in such a way as to 

negate the need to adjust the pitch, roll, and heading; however, 

it is often difficult to install a bottom mount so that the ADVM 

is level and oriented to the proper compass heading so that the 

heading does not change over time. 

The uplooker ADVM should be positioned in the stream 

near, or slightly offset from, the region of maximum velocity. 

Placement of the ADVM in a region of less-than-maximum 

velocity is possible, as long as a stable relation between the 

index velocity and the mean channel velocity can be developed. Cable length and protection are considerations which 

may result in adjustments from the optimum ADVM location 

in the stream. For example, the optimal location of the ADVM 

might require an excessively long cable (greater than 300 ft) 

in an area where boats are known to anchor. Instead, locating 

the ADVM in a slightly less than optimal location would 

allow a shorter cable to be used, reducing the potential cable 

damage from boats that anchor nearby. It is recommended that 

the cable be sheathed (flexible conduit, split garden hose) and 

either buried or somehow attached to the streambed to prevent 

abrasion and reduce the chance that the cable will catch debris.

Uplooker ADVMs are more susceptible to debris or 

sediment accumulation blocking one or more acoustic beams. 

One or more blocked beams can result in biased velocity 

measurements, and sediment or debris accumulation must be 

considered by assessing streamflow conditions. For example, 

it may prove difficult to collect valid velocity data in a sandbed stream that has adequate velocity to transport the sand. If 

an uplooker must be used because of channel shape and water 

depths, consideration should be given to prevent the beams 

from being covered with sediment. A possible solution is to 

elevate the ADVM above the streambed on the chosen mount, 

and for some types of ADVMs (ArgonautTM-SW), reversing 

the orientation of the ADVM can help prevent sediment 

accumulation on the downstream transducer face.

Minimum and maximum stages must be considered when 

choosing the location of an uplooker ADVM at a proposed 

Figure 4. Diagram of sidelooker ADVM measurement volume 

and main acoustic beam.

Main beam
8 Computing Discharge Using the Index Velocity Method

index velocity streamflow-gaging station. At many sites, the 

minimum depth at the ADVM location should be deep enough 

to allow a valid index velocity measurement to compute 

discharge; however, site conditions at low stages may allow 

for the use of a stage-discharge relation that will not require an 

index velocity measurement. The maximum depth should be 

considered to ensure that the chosen ADVM can measure the 

same proportion of the water column as at lower stages. 

One assumption inherent to the use of the Doppler 

principle in measuring velocities, and therefore to ADVMs, 

is that the velocity field measured by each acoustic beam is 

homogenous. In other words, the velocity field measured 

by each beam is essentially the same. Figure 5A shows a 

plan view of a sidelooker ADVM with the acoustic beams 

properly oriented relative to the primary flow direction for the 

measurement of downstream and cross-stream velocity at an 

index velocity station. ADVMs measure only that component 

of velocity that is parallel to the acoustic beam, which is called 

radial or beam velocity. Usually the measured beam velocities 

are transformed into an arbitrary Cartesian coordinate system 

(X and Y) that is relative to the ADVM. Both acoustic beams 

should be aligned so that the beam velocities measured by 

each beam are approximately equal in magnitude and opposite 

in direction; otherwise, the velocity measurement may be 

biased. Figure 5B shows a plan view of an ADVM improperly 

aligned with the primary flow direction. The beam velocity 

measured by beam 1 (V1) is very close to zero because it is 

oriented almost perpendicular to the primary velocity direction. The beam velocity measured by beam 2 (V2

) is much 

greater than that measured by beam 1 (V1), but the sampling 

volume for this beam may not be in a region of the channel 

suitable for index velocity measurements.

The ADVM-measured beam velocities can be used 

to determine if a two-beam ADVM (a sidelooker or an 

ArgonautTM-SW uplooker) is optimally oriented and if 

both beams are measuring the same velocity field. When 

the ADVM is initially installed, continuous data should be 

collected, and the individual beam velocity data should be 

evaluated for equal magnitude and opposite direction. The 

beam velocity data can be viewed using the manufacturer’s 

software by selecting “beam” from the available velocity 

coordinate systems of the ADVM. If a two-beam ADVM 

is properly aligned with the flow in the stream, the beam 

velocity data will be approximately equal in magnitude and 

opposite in sign (a mirror image) as shown in figure 6A. 

Although some slight differences exist between the two 

beam velocities, perhaps because of site conditions, they are 

nevertheless similar. It is important to know that the two beam 

velocity magnitudes do not have to be exactly equal, but they 

should be similar in magnitude and shape. A slight instrument 

misalignment with minor beam velocity differences likely 

can be accounted for with calibration measurements. The 

beam velocity data shown in figure 6B are from a sidelooker 

ADVM that has not been properly aligned with the flow in the 

stream and corresponds approximately to the orientation of 

the ADVM shown in figure 5B. The beam 2 velocity is near 

zero because it is oriented almost perpendicular to flow, but 

the beam 1 velocity is much greater in magnitude and different 

in shape from the beam 2 velocity. When determining ADVM 

alignment at a site, remember that the velocity patterns may 

change substantially with changes in discharge or stage, and 

the hydrographer must be aware that velocity streamlines may 

vary in direction depending on the discharge when assessing 

the beam velocity data. 

 ADVMs also may be affected by biological growth, 

debris, or sediment settling on one or more of the acoustic 

transducers, and an ADVM may have to be cleaned or cleared 

of debris when necessary. In some cases, it may be necessary 

v2

v2

v1

v1

vx

vy

A

Beam 2

Beam 2

Beam 1

Beam 1

Flow

Flow

B

ADVM axis

ADVM axis

vx

vy

Velocity along Beam 1

Velocity along Beam 2

Velocity orthogonal to ADVM axis

Velocity parallel to ADVM axis

v2

v1

EXPLANATION

vx

vy

Figure 5. Plan view schematic of a sidelooker ADVM (A) properly 

aligned to measure downstream and cross-stream velocity and 

(B) improperly aligned to measure downstream and cross-stream 

velocity. [V1,Velocity along beam 1; V2, = Velocity along beam 2; 

Vx, = Velocity orthogonal to ADVM axis; Vy, = Velocity parallel to 

ADVM axis].
ADVM Installation and Configuration 9

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

–1.5

–1

–0.5

0

0.5

1

1.5

A

May June

January

Beam velocity, in feet per second

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 2 4 6 8 10 12 14 16 18 20 –4

–3

–2

–1

0

1

2

3

4

B

Beam 1 velocity

Beam 2 velocity

EXPLANATION

Beam 1 velocity

Beam 2 velocity

EXPLANATION

Figure 6. Beam velocity data from (A) a properly aligned sidelooker ADVM and (B) an improperly aligned sidelooker ADVM.
10 Computing Discharge Using the Index Velocity Method

to clean the ADVM at every site visit. The possibility of debris 

or sediment blocking the transducers is always a concern but is 

more likely during floods. The ability to access the instrument 

in order to clean aquatic growth and clear debris or accumulated sediment should be possible in all flow conditions. 

Biological growth, debris, or sediment can block the acoustic 

transducers, preventing them from accurately measuring 

velocity. Manufacturer recommendations for selecting and 

applying antifouling paint to the ADVM should be followed 

in order to reduce or eliminate biological growth on the 

transducers and reduce the possibility of galvanic corrosion 

(SonTekTM/YSI, 2007, p. 168–169). Figure 7 shows an ADVM 

that has been treated with antifouling paint and an ADVM 

that has not been treated with antifouling paint. Biological 

fouling is especially a problem in warm coastal waters but is 

sometimes an issue in inland rivers as well.

ADVM Configuration

After instrument selection and installation, the ADVM 

and the stage sensor must be appropriately configured to 

measure the flow characteristics at the site. Three important 

parameters need to be configured in the ADVM for index 

velocity measurements: 

1. the measurement volume, 

2. the measurement interval, and 

3. the averaging period. 

The measurement volume is the area of the cross section 

where velocity measurements are made. The ADVM velocity 

measurement volume should measure water velocity without 

interference from boundaries (water surface or channel bottom) or fixed objects in the cross section (vegetation, debris, 

or structures). The measurement volume should be configured 

so that the ADVM will not measure in regions that are affected 

by flow disturbances such as pier wakes, boundaries, surface 

turbulence, or eddies. The measurement interval is the time 

interval between the start of each index velocity measurement. 

The averaging period is that part of the measurement interval 

during which the velocity measurements are made and 

averaged together. The measurement interval and averaging 

period also must be appropriately chosen, depending on site 

flow characteristics, to accurately measure a representative 

velocity and stage. 

In the following sections, techniques for selecting and 

configuring the measurement volume are provided. Measurement interval and averaging period are discussed together 

because they are interrelated.

Selection of Measurement Volume 

for Sidelooker ADVMs

Sidelooker ADVMs measure velocity in a specified 

volume of water that is aligned with the acoustic beams 

(measurement volume). The measurement volume is 

controlled in the ADVM by using commands that set the 

beginning and ending distances of the measurement volume. 

The measurement volume is aligned with each beam, and the 

volume along the beams is defined by a beginning and ending 

distance measured from the transducer faces perpendicular to 

the axis of the ADVM (fig. 8). In some cases, a single large 

measurement volume, called the range-averaged measurement 

volume, can be measured and the beginning and ending 

distance (typically called cell begin and cell end) for this 

volume are specified during configuration. Also, it is possible 

Figure 7. (A) Absence of biological fouling on an uplooker 

ADVM that has been treated with antifouling paint 

and (B) presence of biological fouling on an untreated 

sidelooker ADVM. (Top photograph by Victor Levesque, 

USGS; bottom photograph by Lars Soderqvist, USGS.)
ADVM Installation and Configuration 11

to configure the ADVM to measure a series of smaller multiple 

measurement volumes, called cells, by specifying the number 

of cells and the cell size. 

Some sidelooker ADVMs, such as the SonTekTM/YSI 

ArgonautTM-SL, allow for the measurement of one relatively 

large measurement volume and the simultaneous measurement 

of multiple, relatively smaller measurement volumes (fig. 8). 

The ArgonautTM-SL has two angled transducers that are used 

to measure velocity and a smaller third transducer on the top 

of the ADVM body that can be used to measure water depth. 

Some ADVMs only measure multiple, relatively smaller 

measurement volumes (multi-cell) and may or may not allow 

the multi-cell velocity data to be averaged together in the 

ADVM and then recorded as one velocity. The Teledyne 

RD Instruments ChannelMaster allows the hydrographer to 

average selected multi-cell velocity data in the ADVM. The 

Nortek EasyQTM and Ott SLD do not allow the multi-cell 

velocity data to be averaged in the ADVM. 

The settings for the measurement volume of sidelooker 

ADVMs are affected by ADVM frequency, instrument noise 

level, boundaries and obstructions, velocity distribution in the 

cross section, flow disturbance, and the concentration and size 

of scatterers in the water. Each of these factors plays a role in 

setting an appropriate measurement volume for a sidelooker 

ADVM.

ADVM Frequency and Instrument Noise Level

ADVM frequency determines the theoretical minimum 

and maximum range of the measurement volume as discussed 

in the section on instrument selection. For the actual measurement volume at a site, the minimum range typically will be 

defined as that portion of the flow that is not disturbed by the 

instrument, the mount, or other nearby obstacles. Visually, this 

minimum range can be estimated by identifying the location 

of undisturbed surface velocity streamlines and verified using 

multiple-cell velocity data. The maximum range for the actual 

measurement volume will be determined by the ADVM 

frequency, acoustic interference from boundaries or fixed 

objects, the concentration and size of scatterers in the stream, 

the instrument noise level at the site, and undisturbed velocity 

streamlines. 

The strength of sound energy returned to the ADVM 

while velocity measurements are being made (hereafter 

referred to as signal amplitude) is affected by the concentration and size of scatterers in the water, nearby boundaries, 

and even obstacles within the stream. Sufficient scatterers are 

necessary to provide return signal amplitudes greater than 

the instrument noise level in order for valid ADVM velocity 

measurements to be made. Conversely, high concentrations of 

scatterers in the water also can decrease the signal amplitudes 

to levels near to or less than the instrument noise level by 

absorbing or scattering the transmitted acoustic energy and 

reducing the maximum range of the measurement volume. 

Signal amplitudes are evaluated by conducting beam 

checks, which are plots of signal amplitude and range using 

manufacturer-supplied software. An example of a beam check 

is shown in figure 9, and information about recording and 

reviewing beam checks is in appendix 3.

The instrument noise level, composed of the internal and 

external electrical and acoustic noise that is specific to each 

instrument and site, limits the range at which the instrument 

can accurately detect a returned acoustic signal for velocity 

Figure 8. Generalized measurement volumes for a sidelooker ADVM.

Range-averaged

Measurement Volume

Cell Begin

Cell End

ADVM Cell 1 Cell 2

Cell 3

Cell 4 Cell 5

Cell 6

Cell 7

Cell 8

Cell 9

Cell 10

Multiple Measurement Volumes

(Multi-cells)

Blanking

Distance

Beam 2

Beam 1

Cell Size

vx

vy

Flow
12 Computing Discharge Using the Index Velocity Method

measurement. The instrument noise level is affected by local 

conditions and the instrument electronics, so it is possible for 

one instrument to have different noise levels at different sites. 

If signal amplitudes are close to or less than the instrument 

noise level, ADVM velocity measurements may be biased, and 

the measurement volume may be reduced. Therefore, signal 

amplitudes typically should be a minimum of 10 to 20 counts 

greater than the instrument noise. The hydrographer should be 

aware that the signal amplitudes can change over time and that 

this change can be caused by changes in the concentration and 

size of scatterers, biofouling, electronics, or other factors. It is 

recommended that a beam check be recorded at each site with 

the ADVM out of the water (in the air) and used as a record of 

the instrument and site noise level. The in-air beam check may 

provide important information relating to the site.

Boundary and Object Interference

Boundary and object interference can adversely affect 

the velocity measurement volume and cause a bias in the 

velocity measurement; therefore, they must be considered 

when configuring an ADVM. Boundary interference refers to 

the effects caused by sound energy reflecting from the water 

surface, the streambed, or the opposite streambank. Boundary 

interference can occur at stages that are lower than when the 

meter was installed. Boundary interference can result from 

density gradients that cause the acoustic beams to curve 

toward the surface or streambed as well as changes in the 

channel cross section (sediment deposition for example). 

Object interference refers to the effect produced by 

objects in or near the ADVM measurement volume such as 

a boulder, submerged aquatic vegetation, or a tree that has 

fallen into the water. Object interference is caused by solid or 

relatively solid objects (rocks, pilings, debris, schooling fish, 

or vegetation) that move through or grow into the measurement volume. Object interference also can be caused by debris 

that moves into the measurement volume. If debris enters and 

remains in one or more acoustic beams between the ADVM 

and the end of the measurement volume, the reported velocity 

will be biased. The ADVM cannot be used to make velocity 

measurements beyond solid objects like vegetation or fish or 

structures, even if signal amplitudes appear to be normal. 

Beam 1

Beam 2

Vertical Beam

Theoretical decay

Range, in meters

Signal amplitude, in counts

EXPLANATION

2 4 6 8 10 12 14 16 18 20

0

50

100

150

200

Cell Begin Cell End

Water-level acoustic signal

Velocity measuring acoustic signal

Instrument noise level

Figure 9. An example of a signal amplitude (beam) check for a sidelooker ADVM with a water-level acoustic beam.
ADVM Installation and Configuration 13

The possibility of boundary or object interference can be 

determined using beam check data that are manually recorded 

and reviewed during site visits. Manually recorded beam 

checks should be assessed in the field, and if anomalies are 

identified, the hydrographer should determine the source of the 

adverse change and decide if an adjustment to the cell end or 

instrument position is necessary to avoid biases in the velocity 

data due to boundary or object effects. Automatic diagnostic 

beam checks, recorded at regular intervals in the ADVM, also 

can show potential boundary or object interference problems 

in the measurement volume during the time the velocity meter 

was measuring velocity. 

Flow Disturbance and Velocity Distribution

The ADVM should be configured such that the 

measurement volume is (1) located in a region of relatively 

undisturbed velocity free from excessive turbulence, pier 

wakes, objects, or submerged features within the channel and 

along the streambanks and (2) located in regions of maximum 

or near-maximum velocity. Flow disturbance and velocity 

distribution observed during the site reconnaissance should 

be used to help the hydrographer determine the region of the 

cross section sampled by the ADVM. Flow disturbances may 

be caused by channel edges, fixed objects in the channel, or 

submerged channel features. The velocity distribution in the 

cross section can vary with discharge and other factors and 

should also be considered. 

Visual examination of the water surface may provide a 

cursory means of determining regions of disturbed flow, but 

analysis of the multi-cell velocity data will provide a more 

robust and accurate method of determining regions of flow 

disturbances. Because flow disturbance and turbulence may 

not be evident in range-averaged cell velocity data, multi-cell 

velocity data should always be analyzed to verify that the 

measurement volume is appropriate. Flow disturbance and 

turbulence usually can be identified by increased velocity 

standard error, noticeable reductions in magnitude, or substantial changes in the velocity component magnitudes and (or) 

direction between cells. When comparing multi-cell velocity 

data, look for data that appear noisy or substantially different 

from other velocity multi-cell data. These differences can 

indicate disturbed flow that should not be measured, and the 

measurement volumes should be adjusted to prevent measuring these velocities.

The multi-cell velocity data also must be analyzed to 

verify that the measurement volume is only measuring in a 

region of undisturbed velocity. Near-field and far-field flow 

disturbances usually can be identified by using multi-cell 

velocity data and comparing each cell velocity with each other 

and looking for substantially decreased velocity magnitude 

or increased velocity variability (increase in standard error). 

Additional information on analyzing and interpreting multicell velocity data is available in appendix 3.

When a sidelooker ADVM is mounted to a bridge pier, 

downstream from a structure in the channel or any flow 

obstruction, an initial theoretical computation can be used to 

estimate the width of the wake caused by flow separation from 

the bridge pier or obstruction. This estimate of wake width 

can be used as an initial estimate for the beginning of the 

measurement volume (that is, the beginning of the region of 

flow that should be free from wake turbulence). The following 

equation derived from Hughes and Brighton (1991) can be 

used to estimate the distance from the center of a bridge pier 

to the edge of the pier-wake turbulence (David S. Mueller, 

U.S. Geological Survey, written commun., 2001), assuming 

zero skew (angle) to the flow:

0.5 bc dx =× × ( ),

where

b = lateral distance from pier centerline to edge of 

wake turbulence zone;

c = form factor for pier shape (dimensionless)

(0.62 – round-faced pier and

0.81 – rectangular-faced pier);

d = effective pier width; and

x = distance from ADVM to upstream face of pier.

The parameters for computing the width of a pier wake are 

illustrated in figure 10.

The length values used in the wake turbulence equation 

can be in meters or feet, but must be used consistently 

throughout the equation. ADVMs commonly measure 

between bridge piers, so the region of wake turbulence should 

be estimated for the pier opposite to the ADVM also. This 

information should be used to assist in setting the end of the 

measurement volume. A non-zero flow angle (relative to the 

pier or obstacle) may result in an effective pier width that 

is greater than the physical pier width. The estimated wake 

turbulence distance is only an estimate and is independent of 

(2)

Flow Flow

d x x x x

d

b b

Bridge pier Bridge pier

Turbulence Turbulence

Figure 10. Theoretical bridge pier-wake turbulence dimensions.
14 Computing Discharge Using the Index Velocity Method

velocity, and the actual wake turbulence zone or region can 

be less than or greater than estimates based on equation 2; 

therefore, the actual wake turbulence zone should be verified 

by reviewing multi-cell velocity data as previously described. 

Setting the Measurement Volume

The measurement volume is initially set after the ADVM 

is mounted and in position at the site. Manufacturer-supplied 

software should be used to measure and perform beam 

checks. The signal amplitude (beam) check shown in figure 9 

illustrates the desired features of a beam check for an ADVM. 

The main acoustic beams do not appear to be affected by 

reflections from the water surface or the streambed. The 

signal amplitudes for the maximum range of the measurement 

volume [12 meters (m)] are well above the instrument noise 

level (almost 30 counts higher than the noise level). The signal 

amplitudes are similar in magnitude for each beam within 

the range of the measurement volume. The theoretical decay 

curve shown is an indication of how the signal amplitudes 

should decrease with range. The decay curve is based on 

the system frequency, user-selected salinity, measured water 

temperature, and theoretical scatterer concentration. Generally, 

if the average measured signal-strength profiles differ from the 

theoretical decay curve by more than 20 counts over the full 

range of the system, a problem may be indicated, or this could 

be a natural variation in the scattering strength that may not 

affect system operation (SonTekTM/YSI, 2007).

The signal amplitudes for beam checks should not 

show an increase in magnitude or leveling out followed by a 

decrease as the range from the ADVM transducers increases. 

If side lobes from one or more of the acoustic beams are being 

reflected from a boundary, signal amplitudes may either level 

out or increase slightly and then be followed by a decrease in 

signal amplitude. Side lobes are secondary lobes of acoustic 

energy, which fall outside of the main beam at predictable 

angles and have much lower acoustic energy. The amount of 

acoustic energy reflected from scatterers along the main beams 

is very small compared to the energy transmitted. Reflections 

of side lobes from boundaries or objects such as the streambed 

or a submerged boulder may have a much stronger acoustic 

return than the reflections from scatterers in the water column. 

Reflections from fixed boundaries such as the streambed, if 

received by the ADVM, will bias velocity measurements low 

because they will have a zero velocity (that is, they are stationary). Additional examples and more detailed instructions for 

interpreting beam checks are provided in appendix 3.

The signal amplitudes can vary over time due to changes 

in the amount of scatterers in the water and usually vary from 

season to season; therefore, decreases in the signal amplitudes 

should be anticipated when choosing the cell end. An example 

of seasonal changes that can occur in signal amplitudes is 

shown in figure 11, where a beam check was recorded in 

October 2009 and again in January 2010. In this example, the 

signal amplitudes at the location of the cell end in October 

are more than 20 counts above the instrument noise level. In 

January, the signal amplitudes start to approach the instrument 

noise level almost 10 m before the location of the cell end. In 

SonTekTM ArgonautTM-SL velocity meters, the ADVM will 

automatically adjust the cell end of the range-averaged measurement volume if the signal amplitudes from the measurement volume are less than 5 counts from the instrument noise 

level (typical instrument noise level is anywhere from 20 to 

50 counts depending on the ADVM and site). Figure 12 shows 

an example of changes in the cell end for the range-averaged 

cell over time for an index velocity station. The change in 

the cell end occurs automatically over time with this ADVM, 

and the feature cannot be disabled. While this adjustment 

is useful to always allow the ADVM to measure unbiased 

velocity, this is an undesirable occurrence in a sidelooker 

ADVM used for computing discharge using the index velocity 

method. Depending on the magnitude of the automatic cell 

end change, the change to the cell end may change the relation 

between the ADVM measured velocity (index velocity) and 

the measured-mean channel velocity for sidelooker ADVMs. 

The automatic change in cell end usually becomes a problem 

when the ADVMs are measuring near their maximum ranges, 

but changes in cell end can occur at shorter ranges as well and 

can be caused by decreases or increases in scattering material. 

Generally, the cell end should be chosen so that the signal 

amplitudes near the cell end are greater than 10 to 20 counts 

above the instrument noise level, with consideration for signal 

strength changes over time.

Sufficient scatterers are required to measure the velocity 

of the water with an ADVM. Too few scatterers can cause 

the reflected acoustic energy to be too weak to be detected 

by the instrument electronics and will result in erroneous 

velocity measurements. Conversely, too many scatterers in 

the water can cause the transmitted and reflected acoustic 

energy to be absorbed and scattered to such a degree that the 

reflected acoustic energy is also too weak to be detected by the 

ADVM. Either case will result in a decrease in the size of the 

measurement volume for which velocity measurements can be 

obtained. Therefore, continually evaluating the return signal 

amplitudes is necessary to ensure that the levels are greater 

than the instrument noise level. Routine signal amplitude 

checks (manual beam checks) can help to evaluate whether 

there are too few or too many scatterers in the water and 

are limited by short observation periods during site visits. 

Therefore, the multi-cell signal strength or signal-to-noise 

ratio (SNR) time series can provide information concerning 

the amount of the scatterers in the channel. It is important to 

understand that range-averaged signal amplitude time-series 

data may not be an absolute indicator of signal amplitude 

levels that are less than the instrument noise level because 

those time-series values are an average over the entire 

measurement volume. In addition to manual diagnostic signal 

amplitude checks (beam checks), the SonTekTM ArgonautTM 

series of ADVMs provide an automatic beam check feature 

that records a signal amplitude check at a fixed interval 

(factory default is every 100 measurements) providing a series 

of diagnostic beam check “snap shots” that can be reviewed 
ADVM Installation and Configuration 15

A

Beam 1

Beam 2

Vertical Beam

Theoretical decay

20 40 60 80 100 120 0

50

100

150

200

250

Range, in meters

Signal amplitude, in counts

EXPLANATION

Cell Begin

Cell End

Instrument noise level

Figure 11. Beam checks for the same site with (A) acceptable signal amplitudes to the end of the 

measurement volume in October 2009, and (B) decreased signal amplitudes in January 2010.

B Beam 1

Beam 2

Vertical Beam

Theoretical decay

20 40 60 80 100 120 0

50

100

150

200

Range, in meters

Signal amplitude, in counts

EXPLANATION

Cell Begin Cell End

Instrument noise level
16 Computing Discharge Using the Index Velocity Method

using the manufacturer’s software. The automatic diagnostic 

beam check is viewed using the manufacturer’s software 

ViewArgonaut and is selected using the “Diag” button on the 

tool bar near the top of the ViewArgonaut processing window 

or from the View menu (fig. 13). The internally recorded 

ADVM multiple-volume signal amplitude time-series data 

also should be reviewed routinely to verify that signal amplitudes are sufficiently greater than the instrument noise and not 

affected by objects in the acoustic beams that may affect the 

measured velocity.

Selection of Measurement Volume 

for Uplooker ADVMs

Vertically oriented (uplooker) ADVMs also measure 

velocity in a specified volume of water that is aligned with 

the acoustic beams (measurement volume). The measurement 

volume is controlled in the ADVM using commands that set 

the beginning and ending distances of the measurement volume. The uplooker ADVM measurement volume location in 

the cross section is controlled by the instrument location. The 

ADVM physical location should be in or near the region of 

maximum velocity in the cross section and clear of disturbed 

flow regions in the channel. The measurement volume of the 

uplooker ADVM is typically configured to measure from as 

near to the ADVM to as close to the water surface as possible. 

Although the measurement volume is aligned with the acoustic 

beams, the measurement volume range is defined by beginning 

and ending distances measured from the transducer faces 

perpendicular to the top plane of the ADVM (fig. 14).

The measurement volume of uplooker ADVMs is 

determined by the ADVM configuration and is limited by the 

ADVM acoustic frequency as well as the concentration and 

size of scatterers in the water. Uplooker ADVM measurement 

range is inversely proportional to the system frequency, with a 

lower frequency system having a greater possible range than a 

higher frequency system. The scatterers in the water also can 

control the maximum range of a specific frequency ADVM; 

too few or too many scatterers can reduce the maximum 

profiling range. 

An uplooker ADVM measurement volume cell end 

should be set to average velocity for the maximum depth of 

the water column at any given time. This is different from a 

sidelooker ADVM where a change in measurement volume 

over time may invalidate an index rating. Even though the 

uplooker’s measurement volume can and likely will change 

over time, the ability to measure the same proportion of the 

water column with changing stage can result in a stable index 

20 25 1 5 10 15

150

200

250

300

350

400

Cell end, in feet

February March

Figure 12. Changing range-averaged cell end over time.
ADVM Installation and Configuration 17

rating as long as the cross-section location of the uplooker was 

properly chosen. 

The SonTekTM ArgonautTM-SW and the Argonaut-XRTM 

are two uplooker ADVMs that have the capability to rangeaverage the measured velocity from near the ADVM (cell 

begin) to near the water surface (cell end) and record one 

depth-averaged velocity and automatically adjust the cell end 

as the water depth changes (dynamic boundary adjustment). 

These ADVMs also can simultaneously measure up to 

10 smaller multi-cells (configured using blanking distance, 

cell size, and number of cells). The blanking distance is that 

distance from the transducer face within which no velocity 

measurements are made and that corresponds to electronics 

and transducer recovery time after a ping is transmitted.

The ArgonautTM-SW has two angled transducers used 

for water velocity measurement (two-beam velocity measurement) and a third transducer that is used for stage measurement. The ArgonautTM-SW is oriented with one angled beam 

facing upstream and one angled beam facing downstream, 

and it reports an upstream/downstream (streamwise) velocity 

component and a vertical velocity component. The ArgonautXRTM has three angled transducers and a compass/pitch/roll 

sensor that measure three-dimensional water velocity in a 

user-selected reference (X-Y-Z, E-N-U, or beam) and uses a 

non-vented pressure sensor that measures stage.

These two instruments use different methods to set the 

cell end when the dynamic boundary adjustment is enabled. 

The ArgonautTM-SW uses the acoustic vertical beam to set the 

cell end and the XR uses the non-vented pressure sensor to set 

the cell end. The use of the non-vented pressure sensor on the 

XR can cause the cell end to be above the water surface if the 

pressure sensor is not properly zeroed in air at the site prior to 

deployment to compensate for location-specific differences in 

atmospheric pressure (altitude). Prior to zeroing the pressure 

sensor, the velocity meter should be allowed to equilibrate 

with the water temperature in the stream.

Once the ADVM is allowed to equilibrate with stream 

temperature, the instrument should be partially submerged 

(approximately 0.5 ft or 15 centimeters) when calibrating the 

pressure sensor. When prompted to enter the depth, enter a 

zero even though the pressure sensor is not in air (zero m) 

because this will help prevent the dynamic cell end from being 

set above the water surface if atmospheric pressure changes 

substantially over time. Measure the depth of water over the 

Argonaut-XRTM and note both the measured depth (from the 

Argonaut-XRTM) and the concurrent stage. These data can 

be used to verify that the cell end is always below the water 

surface. If the pressure sensor on the XR malfunctions or 

fails, the resulting invalid depth measurements will result 

in erroneous cell end settings, which will lead to erroneous 

velocity data and a change in the index rating.

Uplooker ADVMs should always be configured to measure multiple velocity cells in addition to the depth-averaged 

velocity cell. The blanking distance should be set the same as 

the depth-averaged velocity cell begin, and the multi-cell size 

should be selected to allow for at least one valid depth cell 

at the lowest expected stage. The range of the multiple depth 

cells (cell size multiplied by number of cells) should equal or 

exceed the maximum stage expected over the velocity meter. 

A compromise may be necessary depending on the minimum 

and maximum depth. If shallow conditions require the index 

velocity to be used at a site, then more weight should be given 

to having at least one multi-cell velocity at these conditions 

(smaller cell size). If the index velocity is required only 

for maximum stages, then more weight should be given to 

measuring all the way to the water surface (larger cell sizes). 

Figure 13. Change in cell end from automatic beam check diagnostic in January 2010. (Data from 

same site used in figure 11.)
18 Computing Discharge Using the Index Velocity Method

Beam 2

Beam 1

Acoustic waterlevel beam

Set by acoustic waterlevel measurement

Cell 1

Cell 2

Cell 3

Cell 4

Cell 5

Cell 6

Cell 7

Cell 8

Cell 9

Cell 10

Blanking Distance

Cell Begin

Cell End

Range-averaged

cell distance

A

Beam 2

Beam 1

Set by pressure

measurement

Cell 1

Cell 2

Cell 3

Cell 4

Cell 5

Cell 6

Cell 7

Cell 8

Cell 9

Cell 10

Blanking Distance

Range-averaged

cell distance

Cell Begin

Cell End

Beam 3

B

Y X

Z Flow

Y

X

Flow

Figure 14. Generalized measurement volume for a (A) two-beam and (B) three-beam uplooker ADVM.

The cell size and number of cells will determine the maximum 

depth that the velocity meter can measure using multiple 

cells. The minimum cell size also is a function of the system 

frequency.

If the multiple cell data have to be used as the index 

velocity because the depth-averaged cell is invalid (for 

example, because of erroneous acoustic stage or pressure 

sensor measurements) the hydrographer can use the multi-cell 

data to estimate the dynamically set depth-averaged velocity 

discussed previously. The multi-cell velocity data will have to 

be manually averaged to compute a depth-averaged velocity 

that only uses the depth cells that are below the water surface. 

This is not a common practice but can be used if the dynamic 

depth-averaged cell end malfunctions.

Measurement Interval and Averaging Period

The procedure of choosing the proper measurement 

interval and averaging period is an optimization exercise. 

All aspects of the data collection and flow conditions need to 
ADVM Installation and Configuration 19

be assessed in order to determine the optimum measurement 

interval and averaging period. Three different measurement 

intervals and averaging periods are used at an index velocity 

gaging station:

1. Initial exploratory time-series measurements,

2. Routine time-series measurements, and

3. Discharge calibration and validation measurements.

Each of these measurement intervals and averaging periods are 

described in the following sections.

Initial Exploratory Time-Series Measurements

An optimized measurement interval and averaging period 

should be determined for each index velocity gaging station. 

Ideally, initial exploratory data collected at the site would 

be analyzed to determine optimum measurement interval 

and optimum averaging period. However, for historical 

reasons and practical considerations, the USGS often selects 

a measurement interval, such as 15 minutes. Use of satellite 

telemetry will limit the measurement interval and (or) the 

number of parameters that can be transmitted to USGS 

databases. When possible, the best practice is to initially 

configure the velocity meter and stage sensor to sample and 

record at a rapid measurement interval (5 minutes or less) with 

the maximum averaging period for the selected measurement 

interval that will not deplete the power available at the site 

and allows adequate time for data transfer to a data logger. For 

example, initially the ADVM would be configured to measure 

every 5 minutes and average for 4 minutes. If an independent 

stage sensor is available at the gaging station, it also should 

be configured to measure every 5 minutes. The index velocity 

averaging period should be maximized for any given measurement interval in order to reduce the standard deviation of the 

velocity measurements and to include velocity fluctuations in 

the average recorded velocity value. 

After a few weeks or months of measurements, including 

normal flow conditions and some storm events if possible, the 

initial exploratory measurement interval data should be evaluated. The measurement interval and averaging period then can 

be optimized to match the flow conditions. The data should 

be evaluated for rapidly changing patterns in the velocity 

time-series data. The exploratory measurement interval data 

are used to determine the proper measurement interval that is 

required to accurately represent the velocity signal of the river 

or stream and will be used as the measurement interval for the 

routine time-series measurements. 

The optimal measurement interval is known as the 

Nyquist sampling rate (Nyquist, 1928). The optimal measurement interval is one that is rapid enough that the index 

velocity data measured and reported (sampled) can accurately 

reproduce the actual velocity response of the stream. Using the 

concepts outlined in Nyquist (1928), the measurement interval 

should be a minimum of two times as rapid as the hydrograph 

response (signal) in order that the reported measurements 

(samples) reproduce the hydrograph without aliasing. In time 

series analysis, aliasing is the distortion or artifact that can 

result when a signal (time series) reconstructed from samples 

(reported index velocity values) is different from the original 

continuous signal (actual velocity time series). For index 

velocity measurements, aliasing is the result of sampling with 

a measurement interval that is too long, causing an erroneous 

representation of the hydrograph and subsequent errors in the 

computation of river discharge. For example, if analysis of 

data indicates that a stream takes 10 minutes to change from 

base flow to the maximum storm-flow peak in response to a 

local storm event, then the measurement interval should be set 

to 5 minutes (maximum) in order to accurately reproduce the 

shape of the hydrograph. Although practical considerations 

often dictate the selection of the measurement interval used in 

streamgaging, the hydrographer should be aware that for some 

sites, it may be important to do an analysis to determine the 

optimum measurement interval. 

A relatively short averaging period results in measurement-to-measurement variation (velocity measurement 

uncertainty) that is greater than if a longer averaging period 

were used. For the example in figure 15, data recorded using 

a 15-minute measurement interval would be aliased, and the 

actual peak velocity would not be recorded. A measurement 

interval of less than 15 minutes should be chosen for this site. 

After the proper measurement interval is determined for a 

site, the measurement interval should be set to this optimized 

value for routine time-series measurements with a maximized 

averaging period. Figure 15 also shows that the shape of 

the velocity hydrograph can be changed artificially when 

short-term fluctuations are measured using a short averaging 

period (1 minute) with relatively long measurement intervals 

(15 minutes). If necessary, the exploratory time-series data 

can be re-sampled and re-averaged to determine the optimized 

routine time-series measurement interval and averaging period 

so all data for the site in the database will be the same. An 

ideal way to evaluate streamflow response over time is to 

use the internally recorded 5-minute ADVM data. Analysis 

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

12:57 13:04 13:12 13:19 13:26 13:33 13:40

Time

Index velocity, in feet per second

1-Minute velocity data

15-Minute velocity data

EXPLANATION

Figure 15. Effect of using different measurement intervals and 

averaging periods. 
20 Computing Discharge Using the Index Velocity Method

of these data allows the hydrographer to experimentally 

vary measurement interval and averaging period to optimize 

the ADVM routine time-series measurement interval and 

averaging period. ADVM internal storage memory, instrument 

power requirements, and the site power supply always should 

be considered when configuring the measurement interval 

and averaging period in order to prevent filling the internal 

memory before the next site visit or depleting the power 

source. 

Once the optimum measurement interval is determined, 

then the optimum averaging period can be determined using 

the exploratory data. At most index velocity sites, the optimum 

routine time-series averaging period will be 15 to 60 seconds 

less than the measurement interval. Most flows are always 

changing from turbulent pulsations (with durations measured 

in seconds) to flood waves (with durations measured in hours 

to days). A longer averaging period includes short-term velocity fluctuations and reduces the velocity measurement standard 

deviation; however, there can be discrepancies between the 

recorded time stamp and the actual measured time that can be 

affected by the duration of the averaging period depending on 

the flow conditions. 

Routine Time-Series Measurements

The routine time-series measurement interval and 

averaging period will be determined by the characteristics of 

the flow in the channel (backwater, structure control, tidal) 

and will have been determined using the exploratory data time 

series. Rapidly changing flow conditions typically require 

shorter intervals between measurements, but a stream with a 

slower response or steady-flow conditions may be measured 

with a longer measurement interval. When measuring routine 

time series, for steady flow conditions, the ADVM should be 

configured to allow the maximum averaging time between 

measurements without depleting power resources or preventing communication with an external data logger. Variation in 

the measured velocity time series is a function of the streamflow and the ADVM configuration. The averaging period can 

be used, to a limited extent, to reduce the measurement-tomeasurement variation of the velocity data. Maximizing the 

averaging period for a given measurement interval will reduce 

the velocity measurement uncertainty; however, as discussed 

in the previous section, longer averaging periods will cause 

the velocity data to be shifted in time unless the hydrographer 

corrects for the time difference to the mid-time of the averaging period. This effect will be most severe 

during rapidly changing flow conditions.

Communication between the ADVM 

and the data logger requires a short amount of 

time for the data transfer to occur, and a 15- to 

60-second data transfer interval is usually 

more than adequate to allow for SDI-12 data 

communication. A shorter data transfer interval 

may be determined more accurately using the 

data logger, the ADVM signal output, and any 

other sensors located at a site and checking 

the time needed for the data logger to record all the sensor 

inputs. Some data loggers are capable of receiving RS232 

or RS422 input and might be capable of more advanced 

measurement control and processing than allowed with 

SDI-12 communication. Table 1 shows suggested ADVM 

measurement intervals, averaging periods, and data transfer 

intervals for three common streamflow conditions, assuming 

SDI-12 data communication. The table is only an example 

because sites may experience other streamflow conditions; the 

actual measurement interval and averaging period will be site 

dependent for routine index velocity measurements, with a 

preference for maximizing the averaging period when the data 

are to be used for computing discharge.

Discharge Calibration and Validation Measurements

Discharge measurements are used to calibrate and 

validate the index velocity to mean velocity rating. Discharge 

measurements are used to define the index rating over a range 

of flow conditions. These measurements are referred to as 

calibration measurements. Once a rating is established using 

calibration measurements, additional discharge measurements 

are made in order to validate the accuracy of the rating over 

time or to indicate when changes to the index rating must be 

made. Synchronizing and synthesizing index velocity data 

with discharge calibration and validation measurements is best 

achieved using a continuous and rapid measurement interval 

for the ADVM. Index velocity data that are collected continuously with a short measurement interval provide a reliable 

way to relate the ADVM-measured index velocity to the mean 

channel velocity obtained from discharge measurements. 

Accurate discharge and index velocity measurements and 

synchronized timing of the measurements are required in order 

to attain the most accurate index rating. The clocks for each 

measurement instrument (discharge, index velocity, and stage) 

must be synchronized to within 1 or 2 seconds of each other in 

order to prevent timing errors in the index rating. 

When making discharge measurements, it is recommended that the index velocity and stage data measurement 

interval and averaging period both be set to 1 minute. This 

may seem counterintuitive, because 1-minute data will have 

an increased standard deviation compared to longer averaging 

periods; however, averaging the 1-minute data over the duration of the discharge measurement will reduce the overall standard deviation and improve the synchronization of the index 

velocity and the discharge data. If stage data are measured 

Table 1. Examples of acoustic Doppler velocity meter measurement intervals, 

averaging periods, and data transfer times for three common streamflow 

conditions.

Streamflow conditions

Measurement 

interval 

(seconds)

Averaging 

period 

(seconds)

Available time 

for data transfer 

(seconds)

Rapidly changing flow 300 240 60

Slow changing/steady flow 900 780 120

Tidally affected flow 360–900 240–840 60–660
ADVM Installation and Configuration 21

using an independent sensor, the averaging period for the stage 

measurement might not be 1 minute, but the measurement 

interval should be the same as the ADVM. This continuous 

measurement of index velocity and stage allows more precise 

synchronization to the discharge measurement start and end 

times and provides a representative measure of the index 

velocity and stage changes for the duration of the discharge 

measurement. Figure 15 illustrates why continuous 1-minute 

velocity and stage data should be used to synchronize ADVM 

and discharge measurement data rather than interpolation 

between routine measurement interval data. If the discharge 

measurement began at 13:00:00 and ended at 13:11:33 the 

mid-time of the measurement would be 13:05:46. In this 

example, the index velocity value obtained by interpolating 

between 13:00 and 13:15 would be substantially less than 

the value computed using the 1-minute index velocity values 

averaged over the duration of the discharge measurement (12 

one-minute values). This difference will result in an error being 

introduced into the index rating, and therefore the interpolation 

method of computing index velocity during discharge measurements should not be used. The continuous measurement of 

index velocity and stage and subsequent averaging provides 

data that are representative of any fluctuations or changes that 

may occur during a discharge measurement. 

An example of 1-minute index velocity data averaged 

for the duration of a four-transect discharge measurement is 

shown in table 2. The 1-minute continuous data (1-minute 

measurement interval and 1-minute averaging period) were 

downloaded from the ADVM recorder at the end of the 

discharge measurement session. The 1-minute velocity data 

are synchronized to the start time of the discharge measurement, and then the index velocity data are averaged together 

(synthesized) for the duration of the discharge measurement 

so that any variation in index velocity during the discharge 

measurement is included in the averaged index velocity value. 

This is referred to as the duration method of synchronizing 

and synthesizing index velocity data. The duration method of 

synchronizing and synthesizing index velocity with discharge 

measurements has shown to be more accurate than using 

interpolation methods.

An example data table with index velocity measurement 

date and start times on the left with the corresponding X 

(downstream or Vx) and Y (cross-stream or Vy) rangeaveraged cell velocity is shown in table 2, and corresponding 

example ADCP discharge measurement start and end times 

and transect discharges are shown in table 3. In this example, 

the index velocity times shown are the start time of the 

measurement, and the end time is 1 minute after the start 

time. Four ADCP transects have been averaged together, and 

because the flow conditions at the site were steady, they are 

considered as a single discharge measurement with a value 

of 193,000 cubic feet per second (ft3/s). The start time of the 

discharge measurement is used to determine the first value 

of index velocity data to be averaged, and the discharge end 

time is used to determine the last index velocity value to 

be averaged (table 3). The discharge measurement starts at 

09:26:49, 11 seconds before 09:27:00, which is the start of 

the index velocity measurement nearest in time. Because the 

Table 2. Index velocity data used for example index velocity 

and discharge measurement data synchronization.

[Vx, velocity in the X direction (perpendicular to the instrument); 

Vy, velocity in the Y direction (parallel to the instrument); ft/s, feet per 

second; gray shading indicates the period for the discharge measurement 

shown in table 3]

Date Time Vx (ft/s) Vy (ft/s)

7/10/2009 9:25:00 4.42 –0.21

7/10/2009 9:26:00 4.44 –0.07

7/10/2009 9:27:00 4.38 –0.07

7/10/2009 9:28:00 4.68 –0.08

7/10/2009 9:29:00 4.65 –0.20

7/10/2009 9:30:00 4.34 –0.03

7/10/2009 9:31:00 4.60 –0.17

7/10/2009 9:32:00 4.34 –0.17

7/10/2009 9:33:00 4.54 –0.14

7/10/2009 9:34:00 4.27 –0.11

7/10/2009 9:35:00 4.51 –0.08

7/10/2009 9:36:00 4.37 –0.13

7/10/2009 9:37:00 4.72 –0.12

7/10/2009 9:38:00 4.32 –0.19

7/10/2009 9:39:00 4.34 –0.14

7/10/2009 9:40:00 4.26 –0.05

7/10/2009 9:41:00 4.55 –0.15

7/10/2009 9:42:00 4.47 –0.25

7/10/2009 9:43:00 4.12 –0.13

7/10/2009 9:44:00 4.25 –0.13

7/10/2009 9:45:00 4.38 –0.19

7/10/2009 9:46:00 3.97 –0.10

7/10/2009 9:47:00 4.37 –0.12

7/10/2009 9:48:00 4.07 –0.10

7/10/2009 9:49:00 4.13 –0.17

7/10/2009 9:50:00 3.96 –0.01

7/10/2009 9:51:00 4.18 –0.06

7/10/2009 9:52:00 4.08 –0.13

Mean for duration of discharge

measurement (9:27 to 9:50) 4.36 –0.12

Table 3. Discharge measurements used for example index 

velocity and discharge measurement data synchronization.

[ft3/s, cubic feet per second; green shading indicates the beginning of the 

averaging period; red shading indicates the end of the averaging period]

Transect name Start time End time

Measured 

discharge

(ft3/s)

STC07102009000 9:26:49a 9:32:22 193,000

STC07102009001 9:32:32 9:38:13 195,000

STC07102009002 9:38:23 9:45:22 195,000

STC07102009003 9:45:30 9:50:40b 190,000

Mean 193,000 a

 Beginning of the averging period.

b

 End of the averaging period.
22 Computing Discharge Using the Index Velocity Method

discharge measurement started more than 30 seconds after the 

start of the 09:26:00 index velocity measurement, it will not be 

used in the average. This example illustrates why times should 

be reported to the seconds because timing becomes even more 

critical under rapidly changing flow conditions. Therefore, 

the first index velocity value to be used in the average is 

the 09:27:00 value. The discharge measurement ended at 

09:50:40, so the last index velocity value to be used in the 

average will be the one that started at 09:50:00 because the 

measured index velocity value starts at 09:50:00 and ends at 

09:51:00. All of the Vx and Vy index velocity values are then 

averaged together from 09:27:00 to 09:50:00 inclusive (table 2 

– index velocity times are highlighted in gray) to compute 

average Vx and Vy index velocity values for the corresponding 

discharge measurement (4.358 and –0.125 ft/s, respectively). 

The mid-time of the discharge measurement (for this example, 

09:38:44) is used as the recorded time for the synchronized 

and synthesized index velocity and discharge measurement 

data. This procedure is repeated for every discharge measurement. The ADVM configuration for discharge measurements 

(continuous measurement with 1-minute measurement interval 

and 1-minute averaging period) typically requires that the 

ADVM internal recorder be used to control and store the 

velocity data during calibration and validation measurements. 

The interpolation method has sometimes been used for 

data synchronization, but it is not recommended. For the 

interpolation method, the measurement interval for the ADVM 

and the data logger is kept constant (not reset to 60 seconds), 

and the index velocity that corresponds to the time of the 

discharge measurement is obtained by interpolation. The 

interpolation method, while easy to use, can create biases 

between the index velocity and measured-mean velocity and 

adversely affect the index rating. 

For example, assume a measurement interval of 15 minutes, and a discharge measurement is made between 11:02:05 

and 11:12:11. The synthesized index velocity that corresponds 

to the mid-time (11:07:08) of the discharge measurement is 

obtained by interpolation between values at 11:00:00 and 

11:15:00. The differences between interpolation and duration 

averaging methods to synchronize and synthesize index 

velocity data with discharge measurements are illustrated in 

figure 15. Index velocity data collected using a 15-minute 

measurement interval and 10-minute averaging period and 

a 1-minute measurement interval and 1-minute averaging 

period are plotted in figure 15. In this example, the 15-minute 

index velocity values are biased low. The interpolated index 

velocity data differ from the duration averaged data by –0.05 

to +0.30 ft/s. These values may seem small in this example, 

but clearly show that interpolating the index velocity data can 

result in values that are substantially different from the duration averaged data collected using a 1-minute measurement 

interval and averaging period. These differences can create 

biases between the index velocity and measured-mean velocity 

and adversely affect the index rating. 

Just as the index velocity measurement interval and 

averaging period must be selected based on the flow conditions at a site, the discharge measurement duration must also 

be chosen based on the flow conditions at the site. Discharge 

measurement duration is an optimization exercise and is 

site dependent. Discharge durations may be as short as 3 to 

12 minutes in rapidly changing flow conditions (using an 

ADCP) and as long as 12 to 60 minutes in steady flow conditions. The discharge measurement duration must not be too 

short or errors may be introduced in the measured discharges 

because of measurement uncertainty. Similarly, discharge 

measurement duration must not be too long, or errors may be 

introduced in the measured discharge because of changes in 

flow over time, especially in rapidly changing flow conditions. 

Recommended ADCP discharge measurement procedures are 

described by Mueller and Wagner (2009), and recommended 

mechanical current meter discharge measurement procedures 

are described by Turnipseed and Sauer (2010) and Rantz and 

others (1982a).

Salinity and Coordinate Systems

Various other ADVM configuration parameters need 

to be considered, such as salinity and the coordinate system 

for velocity measurements. The salinity at the site needs 

to be determined and configured in the ADVM in order to 

more accurately compute the speed of sound in the water 

and measure water velocity. Although the salinity will 

often change over time (for example, in estuaries), ADVMs 

typically allow only one salinity value to be entered in the 

instrument. However, a change in salinity from 0 to 35 parts 

per thousand (ppt) results in approximately a 3-percent change 

in the speed of sound and in the water velocity. When salinity 

varies over time at an index velocity gaging station, the midpoint of the salinity range should be used to set the fixed value 

in the ADVM configuration to reduce the potential for bias in 

velocity measurements. For example, if prior measurements 

indicate that salinity regularly ranges from 2 to 20 ppt, the 

mid-point of the salinity range would be 11 ppt. All estuarine 

sites should have continuous recording conductance/salinity 

sensors installed with the ADVM in order to provide data that 

can be used if it is necessary to compute a speed of sound 

correction as the salinity changes over time. 

For index velocity applications, the ADVM coordinate 

system should typically be set to XYZ or instrument to prevent 

compass errors from being introduced into the index velocity 

data. In the unlikely event that it is necessary to report velocities in an earth coordinate system (east-west, north-south, and 

vertical), the internal ADVM compass should be calibrated 

and evaluated at the time of installation or replacement. Mount 

materials must be non-ferrous, and nearby structures should 

be considered as possible sources of magnetic interference 

that may affect the compass accuracy and may cause the 

east-west (E) and north-south (N) transformed velocity data to 

be erroneous.

Internally Stored and Transmitted Data

The data that are recorded in the ADVM internal memory 

should be downloaded, reviewed, and archived for every site 
Routine Field Techniques 23

visit. After the data are downloaded, open the data file(s) in the 

manufacturer’s software to ensure that the files are complete 

and are not corrupt. Rename the data file(s) to clearly identify 

the site and current date and in accordance with the Water 

Science Center (WSC)-specific data archival procedures. 

Verify that all data on the recorder have been downloaded and 

create a backup of the data file(s) in accordance with USGS 

data archival procedures. After these steps are completed, 

the internal recorder may be erased. While not required, it 

is a good practice to erase the internal recorder during every 

site visit in order to reduce possible confusion about whether 

previously collected data have been downloaded or not. The 

gage-house log should be annotated to indicate that the data 

files have been downloaded and the internal recorder has 

been erased. Prior to leaving the site, the hydrographer should 

verify that the ADVM has enough internal memory available 

to record all data until the next site visit. The internally 

recorded data should be reviewed in the field for obvious 

problems and reviewed in more detail upon return to the office 

because internally recorded data allow for more comprehensive quality control than near-real-time data (SDI-12). 

After returning to the office, the hydrographer must transfer 

internally recorded index velocity data to the office Electronic 

Data Archive (EDA) according to their WSC’s electronic data 

archival procedures. 

Near-real-time ADVM data can be telemetered on a 

regular basis, providing an initial means to assess index velocity data quality and allowing for the computation of near-realtime discharge. The following data, in priority order, should be 

transmitted for ADVM-equipped index velocity sites:

1. Upstream/downstream range-averaged velocity,

2. Water temperature from ADVM,

3. Cell end,

4. Cross-stream range-averaged velocity,

5. Vertical range-averaged velocity (if applicable), and

6. Mean SNR or signal amplitude.

Multi-cell velocity data should be transmitted, reviewed, 

and stored in the appropriate National Water Information 

System (NWIS) database (U.S. Geological Survey, 2003). If 

the ADVM communicates to a data logger via RS232, RS422, 

or RS485, almost all of the internally stored data are available 

for transmission and should be considered for real-time data 

review and final database storage. If data telemetry constraints 

prevent the transmission of the minimum data previously 

specified, provisions should be made to routinely transfer and 

store the internally recorded data into the database. Internally 

recorded data from all index velocity stations should be stored 

in the NWIS database to allow easy access to quality-control 

data. Multi-cell data not transmitted may be needed to 

compute discharge before a reliable and accurate measurement 

volume is established or in situations where velocity data from 

the measurement volume are found to have been adversely 

affected over time. These possibilities provide additional 

motivation for storing internally recorded ADVM data in the 

NWIS database. Appendix 4 provides guidelines and examples 

for reviewing ADVM data. 

Routine Field Techniques

Routine site visits should include checking all aspects of 

the ADVM and stage sensor to ensure that the instruments are 

functioning properly. Observations of site conditions should be 

made and documented, acoustic beam signal amplitudes (beam 

checks) should be recorded and evaluated for obstructions in 

the measured volume, data from the internal recorder should 

be downloaded and reviewed, and the ADVM configuration 

should be checked and verified to ensure the correct velocity 

data are being measured. The 12 steps listed below and 

described in subsequent sections should be followed during 

routine site visits.

1. Record and analyze a beam (signal amplitude) 

check. 

2. Download and review internal data.

3. Rename and backup the downloaded data files.

4. Erase the internal ADVM recorder.

5. Create and save a log file to record command key 

strokes and ADVM response, if needed.

6. Check and record the ADVM internal clock for time 

drift and reset if necessary.

7. Check and record ADVM temperature against a 

reference meter.

8. Clean ADVM of biofouling or sediment accumulation if necessary and record beam check (after 

cleaning).

9. Check instrument alignment.

10. Reconfigure measurement interval and averaging 

period if making discharge measurements.

11. Set ADVM start date and start time.

12. Re-deploy ADVM to record data.

A field form and detailed checklists for performing routine 

field techniques for operating and maintaining ADVMs are 

provided in appendix 2.

Beam Checks

The hydrographer should initiate, record, and evaluate the 

acoustic beam signal amplitudes (beam check) during every

site visit to (1) ensure that the acoustic beams are not striking 

a strong reflector (surface, bottom, tree branch, shopping 

cart, schools of fish) within or near the measurement volume, 

(2) assess the signal amplitudes to verify that there are sufficient scatterers, (3) determine if a transducer is failing, and 

(4) assess whether excessive biofouling is affecting the signal 

strengths. An example of beam check results for a site having 

no discernible problems can be seen in figure 9. Examples 

of beam check results illustrating instances of objects in the 

measurement volume, possible side-lobe interference, failed 

transducers, and a school of minnows in the measurement 

volume are shown in figure 16. 
24 Computing Discharge Using the Index Velocity Method

Range, in meters

Signal amplitude, in counts

2 4 6 8 10 12 14 16 18 20 0

50

100

150

200

A Beam 1

Beam 2

Vertical Beam

Theoretical decay

EXPLANATION

Cell Begin

Cell End

Instrument noise level

Objects in the

measurement volume

B Beam 1

Beam 2

Vertical Beam

Theoretical decay

EXPLANATION

20 40 60 80 100 120

0

50

100

150

200

Range, in meters

Signal amplitude, in counts

Cell Begin Cell End

Instrument noise level

Possible side-lobe interference

Figure 16. Results of beam checks showing data collected with (A) objects in the measurement volume, 

(B) side-lobe interference, (C) failed transducers, and (D) a school of minnows in the measurement volume.
Routine Field Techniques 25

C Beam 1

Beam 2

Vertical Beam

Theoretical decay

EXPLANATION

Signal amplitude, in counts

0

20

40

60

80

100

120

140

160

180

200

Range, in meters

2 4 6 8 10 12 14 16 18 20

Cell Begin

Cell End

Instrument noise level

D Beam 1

Beam 2

Vertical Beam

Theoretical decay

EXPLANATION

Signal amplitude, in counts

0

100

50

200

150

Range, in meters

2 4 6 8 10 12 14 16 18 20

Cell Begin

Cell End

Instrument noise level

School of minnows in

measurement volume

Figure 16—Continued. Results of beam checks showing data collected with (A) objects in the measurement 

volume, (B) side-lobe interference, (C) failed transducers, and (D) a school of minnows in the measurement 

volume.
26 Computing Discharge Using the Index Velocity Method

If an obstruction or unusually strong reflector is identified in the signal amplitude data within the measurement 

volume, every effort should be made to determine the cause 

and remove the reflector if possible or adjust the ADVM 

orientation or configuration if practical. Moving the ADVM 

likely will change the index rating, so any adjustments to the 

physical position and location or measurement volume of the 

ADVM should be completed prior to making any calibration 

discharge measurements. If some unforeseen change to the 

index velocity measurement volume occurs after discharge 

measurements have been made to calibrate the index rating 

and a change to the index velocity location or orientation is 

necessary, a new index rating likely will need to be developed. 

All observations and adjustments to the ADVM should 

be recorded on the field notes and described in the station 

analysis.

Not all abnormalities in the beam checks are obvious. A 

common problem occurs when the acoustic beam side lobes 

strike a strong reflector such as the water surface prior to 

the cell end. This can result in a leveling off or a very slight 

increase in signal strength with range. The velocity measured 

at and beyond the range where leveling off or a slight increase 

occurs can be adversely affected and should not be used as 

valid velocity data. An example of this abnormality and other 

problems are discussed in appendix 3. 

Download and Review Internal Data

All internally recorded index velocity data and associated 

quality-control data should be downloaded and reviewed for 

every site visit. After downloading the internal recorder data, 

the data files should be renamed in accordance with WSC policies. The hydrographer should examine all time-series velocity 

data (range-averaged, multi-cell, downstream, and cross 

stream), velocity standard error data (if applicable), signal 

amplitude, temperature, cell end (if applicable), and heading, 

pitch, and roll (if applicable) as a minimum field check on data 

quality. Many problems identified in the field may be corrected 

immediately, reducing periods of invalid or questionable 

data. Appendix 4 provides guidelines for reviewing internally 

recorded ADVM data.

Log File

An electronic capture file (referred to as a log file, 

typically having a filename that ends with .log or .txt) can be 

recorded after performing a beam check and downloading 

the internally recorded data in order to record all commands 

sent to the ADVM and all system responses. This practice is 

strongly encouraged when changing the ADVM configuration 

or troubleshooting ADVM problems. The electronic capture 

file may be useful in troubleshooting the ADVM and is often 

requested by the manufacturer when diagnosing problems to 

verify that appropriate commands were used and the ADVM 

responses to the commands.

ADVM Clock Check

The time synchronization of all instruments used at an 

index velocity site (velocity, stage, and discharge) is essential 

for the successful calibration and validation of the index 

rating. For rapidly changing flow conditions, it is absolutely 

critical that time synchronization for all instruments be 

performed prior to making any calibration measurements. 

Time synchronization errors of as little as 15 seconds can 

cause errors in the index rating and must be avoided. All 

electronic equipment clocks gain or lose time (drift) and 

therefore must be checked and corrected during every site 

visit. The ADVM internal clock should be checked for time 

drift using a watch that was recently synchronized to the 

U.S. Department of Commerce, National Institute of Standards 

and Technology, Time and Frequency Division (NIST) time 

(http://tf.nist.gov and http://www.time.gov). Any discrepancy 

between NIST-synchronized watch time and the ADVM and 

data logger internal clock times should be recorded on the 

index velocity site-visit field form (appendix 2) to document 

any time discrepancy and provide the necessary information 

to apply a time correction to the internally recorded data. After 

checking and recording the synchronized watch time and the 

instrument internal clock times, the internal clocks should be 

reset to the nearest second, and the time of the reset should be 

recorded on the site-visit field sheet.

Temperature Check

The ADVM temperature sensor should be checked with 

an independent reference temperature sensor, recording the 

temperature concurrently. The independent reference temperature sensor should be at approximately the same depth and 

near to the ADVM. The temperatures measured by the ADVM 

and the independent reference instrument should be recorded 

on the ADVM field sheet and compared. If the temperature 

measured by the ADVM temperature sensor differs consistently from an independent temperature measurement by 

2 degrees Celsius (°C) or more, or if the ADVM temperature 

sensor has failed, the ADVM should be replaced as soon as 

possible (U.S. Geologial Survey, 2010b).

ADVM Cleaning

The ADVM should be routinely inspected for biological 

growth (biofouling), debris, sediment accumulation, or ice 

formation. Beam checks will often indicate some reduction 

in signal strength related to biofouling, debris, sediment 

accumulation, or ice accumulation, so after review of the beam 

check(s), the hydrographer will often be aware of the potential 

need to clean the ADVM. If the ADVM is cleaned of biofouling, accumulated sediment, or debris, an “after-cleaning” 

beam check should be recorded and the cleaning should be 

documented on the field form. Routine cleaning and inspection 

of the ADVM also provide a way to check and verify that 

the mounting system is functional and not deteriorating and 
Routine Office Techniques 27

should be performed at least once per year. For some sites, the 

ADVM will need to be cleaned during every site visit.

ADVM Alignment

The alignment of the ADVM should be checked and 

documented during every site visit. If the ADVM is moved 

from the original orientation for any reason, such as cleaning 

or exchanging the ADVM, the alignment of the ADVM should 

be carefully checked to ensure that the ADVM is returned to 

the original orientation and location by using the permanent 

markings on the ADVM mount. Every ADVM should have a 

mounting mechanism that allows the ADVM to be returned to 

its original depth and orientation and secured in place. Errors 

in positioning the ADVM in the vertical or in aligning the 

ADVM can result in changes to the index rating.

Reconfigure the ADVM

The measurement interval and averaging period will only 

need to be changed if the hydrographer is preparing to make 

calibration or validation discharge measurements or is returning the measurement interval and averaging period back to the 

routine time-series settings after the discharge measurements 

or if a refinement is required in the measurement interval 

and (or) the averaging period for routine time-series data 

collection. The measurement volume should usually remain 

the same over time unless analysis of the routine beam checks, 

automatic beam checks, or multi-cell velocity data indicate 

that the measurement volume is being adversely affected. 

Uplooker ADVMs will typically have a changing measurement volume, and the measurement volume range should be 

consistent with changing stage.

Start Date and Start Time

If the velocity meter has been configured for continuous 

velocity measurements (60-second measurement interval and 

60-second averaging period) during calibration or validation 

discharge measurements, then the ADVM should be used to 

control and record the index velocity data, and the ADVM will 

need to be programmed to start measuring and recording at a 

specific date and time. Follow the manufacturer’s format for 

specifying the correct start date and start time for internally 

(autonomously) recorded data.

Re-Deploy the ADVM

 If the ADVM will be measuring velocity continuously 

during discharge measurements, then the ADVM will likely 

control the measurements independent of a data logger at the 

site, and the proper commands must be sent to the ADVM 

to begin measurements. If the ADVM will be measuring and 

recording routine time-series data (no discharge measurements), then the ADVM will likely be controlled by an 

external data logger, and the proper commands should be sent 

to the ADVM to properly configure the meter for external 

measurement control. For more information, see ADVM user 

manuals (Nortek AS, 2001; SonTekTM/YSI, 2007; Teledyne 

RD Instruments, 2008) and appendix 2. Any responses from 

the ADVM after commands are sent should be monitored, and 

the recorded log file will provide an electronic record of the 

system responses. The log file should be closed (stop recording) after disconnecting the ADVM from the field computer.

Routine Office Techniques

A key to the successful operation and maintenance of 

any ADVM is routine review of the data being transmitted 

via telemetry and those data stored in the internal ADVM 

recorder. With the adoption of real-time or near-real-time 

telemetry for almost all USGS streamgaging stations, reviewing transmitted data has become standard practice for almost 

every instrument used. However, routinely downloading, 

storing, and reviewing data from the ADVM internal recorder 

should still be done. As previously discussed, data not 

routinely transmitted via telemetry should be recorded on the 

ADVM and should be downloaded during every site visit. 

In addition, these data should be archived with other data 

for the station and loaded into the NWIS database. Routine 

review of the ADVM recorder data can help detect and explain 

problems with the ADVM or installation, can help with quality 

assurance of the index velocity data, and can help to refine 

ADVM configuration over time. In the following sections, 

some of the more important techniques for reviewing internal 

recorder data are presented and discussed. Additional information on reviewing SonTekTM/YSI ADVM data is available in 

appendix 4.

Velocity Data

Routine review of all ADVM velocity data can provide 

information on flow characteristics at the site to help with site 

servicing and the index rating development. The streamwise 

velocity (usually the X velocity) should be reviewed routinely 

for abnormal patterns and abrupt or subtle changes to the 

overall shape of the time-series data. Changes in the streamwise velocity data can indicate problems with the ADVM or 

changes at the site. The cross-stream velocity (usually the 

Y velocity) should be reviewed because it provides an indication of changes in velocity distribution or possible changes 

to the ADVM orientation (change in heading). Typically the 

cross-stream velocity data should be very near zero but may 

change slightly as flow changes. Changes to the cross-stream 

velocity as the flow changes provide information about the 

flow characteristics at the site and can be useful when developing the index rating to determine when changes in a rating 

occur based on velocity characteristics. Cross-stream velocity 

data that are always different from zero are an indication that 
28 Computing Discharge Using the Index Velocity Method

the velocity meter is not properly oriented in relation to the 

velocity streamlines at the site. 

If using an uplooker ADVM, the vertical velocity (Z, up, 

or vertical velocity) should be reviewed because the vertical 

velocity data also can indicate changes in velocity distribution 

or ADVM orientation. Two-beam uplooker systems measure 

the vertical velocity, and the manufacturer’s user manual 

should be reviewed to verify what data are being measured 

and reported for each variable. The vertical velocity data 

should be very near zero for all flow ranges, and substantial 

variation from zero could indicate that the ADVM is in a 

less-than-ideal location in the flow, is not level, or has changed 

orientation in heading, pitch, or roll, or that one or more 

acoustic beams may be blocked or malfunctioning. 

ADVM Water Temperature

ADVM water temperature should be reviewed routinely 

to verify that the time-series measured temperature is within 

a reasonable range for a site. Temperature sensor failure can 

be obvious (a sudden jump to an unreasonable value) or more 

subtle (temperature changes slowly over time to erroneous 

values). The temperature data are used with the manually 

entered salinity value to compute a speed-of-sound measurement in water, which affects the calculation of velocity and 

the manually entered location of the measurement volume for 

sidelooker ADVMs. In water, a temperature difference of 5 °C 

will result in a velocity measurement bias of approximately 

1 to 1.3 percent, depending on the ambient water temperature. 

If the temperature measured by the ADVM temperature sensor 

differs consistently from an independent temperature measurement by 2 °C or more, or if the ADVM temperature sensor has 

failed, the ADVM should be replaced. 

Cell End

The cell end data can be output from SonTekTM/YSI 

ArgonautTM ADVMs and can be useful to detect changes in 

the acoustic beam signal strength data. Changes to the cell end 

data can indicate that site conditions have changed (change in 

scatters or acoustic beams) or that the ADVM configuration 

has changed (changes to measurement volume, instrument 

malfunction, etc.). For sidelooker ADVMs, changes to the 

measurement volume are not desirable and may change the 

index rating. If the cell end data indicate changes over time, 

the ADVM should be checked to make sure it is operating 

properly, or the measurement volume should be changed to 

eliminate the undesirable cell end changes. 

For uplooker ArgonautTM ADVMs, a changing cell end 

is desirable and a normal response to changing water depths. 

Uplooker ArgonautTM ADVMs’ cell end data also should be 

compared to the ADVM measured water depth to ensure that 

the water depth is nearly equal or slightly greater than the cell 

end and typically within 0.3 ft of each other. The ArgonautTM 

cell end data are recorded in increments of approximately 

0.3 ft (SonTekTM/YSI, oral commun., April 27, 2011) and 

will appear as steps in the data as opposed to smooth changes 

over time. If the measured water depth is less than the cell 

end by approximately 0.3 ft or more, the velocity data in the 

depth-averaged measurement volume may be biased, and the 

configuration must be corrected as soon as possible.

Signal-to-Noise Ratio

The signal-to-noise ratio (SNR) can be used to assess the 

amplitude (strength) of the received acoustic energy used to 

measure velocity and should be reviewed in addition to the 

velocity data. For some of the more commonly used ADVMs 

(SonTekTM/YSI), the SNR is defined as follows:

SNR [Signal Amplitude Instrument Noise] = k ∗ −

where k is a conversion factor from counts to decibels. For 

SonTekTM/YSI ADVMs, signal amplitude and instrument 

noise are in log space and k equals 0.43. SNR data are similar 

to signal amplitude data except that SNR data account for 

instrument noise so that when SNR values are at or near 1, the 

ADVM cannot detect the return signals above the instrument 

noise, resulting in biased velocity data. The transmitted nearreal-time SNR data should be reviewed for changes over time. 

The SNR data are typically an average of all the ADVM’s 

individual beams over the entire range of measurement volume; SNR data can be misinterpreted as good when actually 

one or more beams are partially or completely blocked. This 

can occur when there are strong SNR values from one beam 

and a reduced value from the other beam, but the average 

value of all beams is a reasonable value. So even though the 

SNR values may seem reasonable, invalid SNR values can be 

included in part of the range-averaged measurement volume 

that cannot be detected using the averaged SNR data alone. 

For this reason, all available data should be used to assess the 

overall function of the ADVM.

Rating Development and Analysis

The preceding sections of the report have provided guidance for site and ADVM selection, ADVM installation, and 

ADVM configuration and operation. Soon after the ADVM is 

operating and collecting data, the rating development process 

begins. Two ratings must be developed and maintained—the 

stage-area and index ratings—and both ratings require the 

collection and analysis of calibration data. The stage-area 

rating is straightforward, but the index rating usually requires 

more analysis. In order to compute measured-mean velocity 

from calibration and validation discharge measurements, the 

index rating requires the stage-area rating, and both ratings are 

required to compute discharge. The development and analysis 

of these ratings are discussed in the subsequent sections of the 

report.

(3)
Rating Development and Analysis 29

Stage-Area Rating

The stage-area rating is always developed first because 

it is required for development of the index rating. Measured 

stage data are used with the stage-area rating to compute 

stream cross-sectional area. The computed stream crosssectional areas (A) from the stage-area rating are used (1) to 

compute a measured-mean channel velocity (V = Q/A) for 

use in the index rating calibration and validation and (2) to 

compute continuous discharge (Q = V × A) in conjunction 

with computed continuous mean velocity (from index rating). 

The stage-area rating requires a survey of the stream 

cross section near the ADVM at what is known as the standard 

cross section, as well as stage measurements at the index 

velocity station during the survey. A standard cross section is a 

cross section near to the ADVM that is chosen for the development of the stage-area rating and which can be re-surveyed 

at regular intervals. For any channel, a stage-area rating can 

be represented as a look-up table of stage and area with an 

adequately small stage increment to minimize errors in linear 

interpolation between data points. If preferred, the stage-area 

rating for natural channels often can be closely approximated 

with a second-order polynomial equation (Rantz and others, 

1982b). The development of the stage-area rating comprises 

the following steps:

1. Establish a standard cross section,

2. Survey the standard cross section,

3. Develop stage-area rating, and

4. Validate stage-area rating.

These steps in stage-area rating development are presented in 

detail in the subsequent sections.

The Standard Cross Section

A standard cross section must be established and 

surveyed at the index velocity station soon after the ADVM 

is installed and configured. The cross-sectional area of a 

stream is determined by the channel cross-section shape and 

the stage at any given time. The standard cross section should 

be located as close to the ADVM as possible and marked and 

documented so that subsequent surveys can be performed at 

the same location.

The standard cross section (fig. 17) should be located as 

close to the ADVM as possible so that changes in the stream 

cross section can be monitored over time. Changes in the 

horizontal velocity distribution can be caused by changes in 

cross-section geometry near the ADVM location or at locations upstream or downstream from the ADVM. 

If the cross section substantially changes shape, the 

stage-area relation also may change substantially, the velocity 

distribution may change, and the index rating also may 

change. If the change is substantial and permanent, then a new 

stage-area rating and a new index rating likely will be required 

to compute accurate discharge. Aquatic growth and decay 

and scour and fill can be problems which, if severe, can cause 

changing cross-sectional shapes over time and a changing 

index rating. If the cross-sectional shape continually changes, 

collection of enough data to accurately define the changes 

over time can be extremely labor intensive. Continually 

changing cross-section shape may result in the inability to 

accurately compute discharge using the index velocity method. 

The standard cross section should be clearly identified in the 

field and documented in the station description so that any 

hydrographer can locate and re-survey the same standard cross 

section that was initially chosen and surveyed.

Cross-Section Survey

The first step toward creating a stage-area rating is the 

measurement of the stream cross-sectional shape from the 

tops of the streambanks to the streambed. The standard cross 

section should be perpendicular to the primary flow direction 

and as close to the ADVM as practical. Standard surveying 

techniques can be used to define the channel cross section 

for the purposes of stage-area rating development involving 

tools such as a surveying level and stadia, depth soundings 

and a tagline, echo sounder and tagline, an ADCP, or some 

combination thereof. Typically the survey consists of the 

collection of a series of two values: the horizontal position 

Gage

ADVM

Standard Flow

cross section

Wading

measurement

section

Bridge

measurement

section

Figure 17. Schematic showing location of standard cross section at an index velocity station.
30 Computing Discharge Using the Index Velocity Method

from some arbitrary reference point (typically the top of one 

of the streambanks) and the elevation associated with that 

position. An example of a surveyed cross section is shown 

in figure 18. The survey method for measuring horizontal 

position should be chosen to accurately define the shape of the 

stream channel. Standard elevation surveying techniques using 

a level and stadia are commonly used to measure the portion 

of the stream channel that is out of water from the water 

surface to the highest elevation on the channel banks and also 

can be used for the entire cross section for wadeable streams. 

For deeper streams, it is common to combine level and stadia 

survey methods for the above-water portions (left and right 

streambanks) with a bottom tracking ADCP for the deep 

over-water portion. It is a relatively easy procedure to combine 

these two methods to produce a complete cross-section shape 

as illustrated in figure 19A. Regardless of the chosen method, 

the section location should be documented and marked so that 

it is relatively easy to find at a later date. 

Table 4 shows a compilation of data from a survey 

using level and stadia techniques to define the above-water 

portions of the cross section on the left and right banks. The 

above-water bank surveys initially have relative starting and 

ending locations, and these locations were then combined with 

a bathymetry survey of the portion of the cross section under 

water. The combined data result in a continuous cross-section 

survey from the top of the left bank down to the streambed and 

back up to the top of the right bank.

Table 5 shows a simplified channel bathymetry dataset 

obtained using an ADCP that includes edge distance measurements that were made at the time of the ADCP cross-section 

measurement. The number of data points from the survey 

was reduced for illustrative purposes. When an ADCP is used 

to measure the cross-section bathymetry, slightly different 

procedures than those for discharge measurements are required 

to accurately measure the cross-section bathymetry. The 

ADCP path across the channel section must be perpendicular 

to the primary flow direction and as straight as possible. This 

often requires a faster traverse and good vessel handling and 

navigation skills to accurately measure the cross section. If 

the channel is not too wide and vessel traffic is not a safety 

concern, then a tagline with little or no sag can be an ideal 

method for traversing the cross section in an approximately 

straight line, perpendicular to the primary flow direction. 

Because each segment of the cross-section survey (left 

and right banks and channel) will commonly have different 

start and end times, the stage and time for each water-surface 

measurement (left and right edge of water and channel 

measurement) must be documented in order that each survey 

segment can be corrected to the same vertical datum. The 

water surface is assumed to be at the same elevation from one 

channel bank to the other, and it is at the same elevation in 

many instances; however, the site conditions could cause a 

difference in elevation across the channel during the time of 

the channel bathymetry survey. 

Data from a combination of the left and right bank 

surveys with the ADCP bathymetry survey are listed in table 6. 

The top left bank should be selected as the origin or starting 

point (zero distance) so that the data will be ordered such 

that the cross-section shape (when plotted) will be viewed 

as looking downstream. Horizontal position data from the 

bank and submerged channel surveys must be reconciled to 

combine the three datasets into one continuous cross-section 

dataset. Once the data are combined, the data should be 

checked visually to ensure that no errors occurred when 

correcting the vertical elevations and that the cross-section 

shape looks reasonable for the site. Figure 19B shows a plot of 

the combined cross-section data (left and right channel banks 

and ADCP bathymetry data) that is used as a verification of the 

survey data.

Stage-Area Rating Development

After the channel cross section is surveyed and the 

above-water topography and the underwater bathymetry 

data are combined, the combined cross-section data must be 

synchronized to the stage during the time of the cross-section 

survey, and the channel cross-sectional area for any stage 

can then be created. The measured cross-section horizontal 

position and corresponding elevations can be used in conjunction with hydraulic analysis software to compute a stage-area 

rating for the site. The computer program, AreaComp, is commonly used in the USGS for this purpose, but other hydraulic 

analysis programs may also be used. AreaComp is available 

for download from the USGS Hydroacoustics Website (http://

hydroacoustics.usgs.gov/indexvelocity/software.shtml). 

Figure 18. Example of a channel cross-section shape.

–8

–6

–4

–2

0

2

4

6

8

10

12

0 100 200 300 400 500 600

Station location from left bank looking downstream, in feet

Elevation, in feet
Rating Development and Analysis 31

Table 5. Simplified ADCP bathymetry data.

Station 

(feet)

Elevation (feet 

above gage datum) Comment

141 0.00 Left edge of water (water surface)

163 –5.20

195 –5.73

208 –6.24

220 –7.13

230 –7.21

231 –7.17

236 –7.10

244 –7.13

254 –7.42

256 –7.46

266 –7.42

276 –7.25

286 –6.61

295 –6.20

306 –5.70

317 –5.40

327 –4.75

336 –4.35

346 –4.21

356 –4.25

366 –4.28

376 –4.21

388 –4.25

398 –4.31

409 –4.39

419 –4.39

429 –4.54

440 –4.57

450 –4.39

460 –4.39

470 –4.31

479 –3.98

509 0.00 Right edge of water (water surface)

Table 4. Channel bank survey data.

Station 

(feet)

Elevation (feet 

above gage datum) Comment

Left bank survey

0 0.00 Left edge of water (water surface)

4 0.20

10 1.06

14 1.71

17 8.70

19 9.33

36 8.88

85 8.21

141 8.33 End of left bank survey

Right bank survey

0 0.00 Right edge of water (water surface)

13 0.54

17 3.01

20 5.29

28 5.00 Land surface extends nearly 

horizontal into forested wetland 

as far as you can see.

Figure 19. Combined stage-area survey created 

from (A) standard surveying techniques on shore 

(table 4) and a vessel-mounted acoustic Doppler 

current profiler (ADCP) used to capture channel 

bathymetry along measured cross sections (table 5) 

and (B) cross section derived from combined shore 

survey with ADCP channel bathymetry (diagram 

modified from Ruhl and Simpson, 2005).

–8

–6

–4

–2

0

2

4

6

8

10

12

0 100 200 300 400 500 600

Elevation, in feet

Station location from left bank looking downstream, in feet

Left bank survey

ADCP bathymetry

Right bank survey

EXPLANATION

Flow

Standard

cross section

A

B
32 Computing Discharge Using the Index Velocity Method

Table 6. Combined bank survey and ADCP data.

Station 

(feet)

Elevation (feet 

above gage datum) Comments

0 8.33 Beginning of combined survey on 

left bank

56 8.21

105 8.88

122 9.33

124 8.70

127 1.71

131 1.06

137 0.20

141 0.00 Left edge of water (water surface)

163 –5.20

195 –5.73

208 –6.24

220 –7.13

230 –7.21

231 –7.17

236 –7.10

244 –7.13

254 –7.42

256 –7.46

266 –7.42

276 –7.25

286 –6.61

295 –6.20

306 –5.70

317 –5.40

327 –4.75

336 –4.35

346 –4.21

356 –4.25

366 –4.28

376 –4.21

388 –4.25

398 –4.31

409 –4.39

419 –4.39

429 –4.54

440 –4.57

450 –4.39

460 –4.39

470 –4.31

479 –3.98

509 0.00 Right edge of water (water surface)

522 0.54

526 3.01

529 5.29

537 5.00 End of combined survey on right 

bank

Figure 20 shows a screen capture of the AreaComp software 

with an imported example dataset.

The AreaComp software allows users to enter survey data 

in various ways. A typical sequence when combining ADCP 

data and level/stadia data is as follows. Create a compatible 

ASCII file of the ADCP station and depth data from vendorsupplied ADCP software and import these data into 

AreaComp. The ADCP cross-section data from vendorsupplied software can then be exported as a comma- or 

space-delimited (*.csv) file. If left and right bank survey data 

are available (collected separately, not with the ADCP), these 

data can be entered into the comma- or space-delimited file 

by means of a text editor or spreadsheet software. Left bank 

station locations (distances) usually are entered as negative 

numbers, and the right bank station locations (distances) are 

added to the last station location from the ADCP bathymetry 

data. The resulting cross-section shape should be verified 

by the hydrographer in AreaComp to ensure that the shape 

looks similar to the plots created by the hydrographer when 

assembling the cross-section survey data (fig. 20). After the 

complete cross section has been entered into AreaComp, 

a minimum and maximum stage, stage datum, and stage 

increment are entered into the fields provided in the software. 

The stage measured during the standard cross-section survey 

is used to compute a datum for the survey (in this example, 

0.00) and is entered into the datum field. If, for example, the 

survey occurred at a gage height of 2.00 ft, then –2.00 would 

be entered into the datum field to correct the survey data to the 

water surface. The stage increment is entered according to the 

desired resolution of stage-area rating (0.01 will output an area 

for each increment of 0.01 ft of gage height). The “Animate 

Cross Section” button (fig. 20) should be activated to verify 

that the input fields were properly entered. The animated cross 

section provides a look at the changes in cross section based 

on the cross-section survey data and the input fields. Clicking 

the “Create Stage Area Rating” button (fig. 20) opens another 

window with a graphical representation of the stage-area 

rating based on the cross-section shape, the selected increment, and the range of stage specified (fig. 21). The stage-area 

rating table can then be exported and saved as a datafile and 

(or) a graphic. The stage-area rating data will be entered to 

the NWIS Automated Data Processing System (ADAPS; 

U.S. Geological Survey, 2003) as described in the “Computation and Analysis of Discharge” section of this report. The 

stage-area rating worksheet should contain a table of the 

stage and cross-sectional area data computed with AreaComp. 

The worksheet also should include information such as stage 

datum, range of stage applicable for this rating, documentation 

on the location and file name of the cross-section survey data, 

the date and time of the survey, and how the stage-area rating 

was developed. The stage-area rating, the data used to create 

it, and any other related documentation or notes should be 

saved in the WSC electronic data archive and described in the 

station description.
Rating Development and Analysis 33

Figure 20. Cross-section data shown in U.S. Geological Survey AreaComp software.

Figure 21. Stage-area rating output from AreaComp.
34 Computing Discharge Using the Index Velocity Method

Stage-Area Rating Validation 

The standard cross section should be re-surveyed and 

documented annually for the first 3 years that a station is 

operated. If less than 1 year has elapsed since the previous 

survey and a change in the cross section is suspected, the 

standard cross section should be re-surveyed. After 3 years, 

the frequency of re-surveys can be reduced to that used 

for station levels (typically every 3 years) if the following 

conditions are met:

1. The standard cross section does not show a substantial change in shape, 

2. A comparison of the stage-area ratings created from 

the annual (or more frequent) surveys indicates no 

substantial change, and 

3. The index rating does not show divergence (for 

example, the calibration and validation discharge 

measurements do not plot outside the confidence 

intervals for the index rating).

The cross section should always be re-surveyed when the 

index rating indicates divergence or after a high-flow event 

large enough to change channel geometry, unless previous 

experience or evidence indicates that morphological changes 

in the channel are unlikely. The hydrographer must make a 

determination about the magnitude of change measured in 

a channel area that would require a change in the stage-area 

rating. Each time the standard cross section is re-surveyed, the 

percentage of change in area between the base survey and new 

survey should be computed over the range of stages measured 

during the period in question (a water year1 or other flow 

computation period). The hydrographer should compare the 

percentage of change in the stage-area rating with the estimated error in the methods used to survey the standard cross 

section and with the discharge measurements made during 

the water year to determine if a change in rating is warranted. 

A technique for performing this evaluation is documented 

in appendix 5. Decisions about whether or not to change the 

stage-area rating must be made in conjunction with analysis of 

the index rating and computed discharge records. If measured 

discharges do not deviate substantially from the computed 

discharges and there are no significant trends in the deviations 

from computed discharge, generally a change in the stage-area 

rating is not warranted. However, a trend in the deviations of 

measured discharges from computed discharges, even when 

the differences are not large, may indicate that changes have 

taken place in the standard cross section. 

Discharge Measurement Calibration Data

Discharge measurements collected over the full range 

of flows are necessary to calibrate and validate the index 

rating. Periodic discharge measurements must be collected 

throughout the operation of the station to ensure that the index 

rating is stable (Ruhl and Simpson, 2005). When measuring 

discharge, the ADVM should be configured for a measurement 

interval of 60 seconds and an averaging period of 60 seconds. 

The shorter measurement interval and continual averaging 

will provide index velocity data that are representative of 

the streamflow conditions during the measurements, allow 

more flexibility in the start and end times of each discharge 

measurement, and provide more accurate synchronization 

with the discharge measurements. Discharge measurements 

need to be made close to the ADVM at a location where all 

of the flow can be measured. The discharge measurement 

cross section does not need to be in the same location as the 

standard cross section; however, the discharge at the measurement section must equal the discharge at the ADVM location. 

In other words, no significant inflows or diversions should 

occur between the measurement section and the location of the 

ADVM. The discharge measurement cross section should be 

chosen such that ADVM measurement volume is not adversely 

affected by flow disturbance by the measurement vessel or by 

acoustic interference between the instruments (ADVM and 

ADCP, for example). Flow disturbance or acoustic interference 

can lead to biased index velocity data and an invalid or biased 

index rating. This means that the discharge measurement 

section should not be located in the same cross section as the 

ADVM. In order to avoid acoustic interference, be sure that 

the discharge measurement section is at least 5 channel depths 

away from the ADVM section. This is especially important 

when an ADCP is used to make discharge measurements and 

the acoustic frequency of the ADCP is relatively similar to 

the acoustic frequency of the ADVM or is an exact multiple 

thereof. See figure 17 for an illustration of the possible location of the discharge measurement sections and their locations 

relative to the ADVM and the standard cross section.

Accurate discharge measurements are essential to 

developing the best possible index rating. The proper techniques and methods for making discharge measurements using 

mechanical current meters, acoustic Doppler velocimeters, and 

other methods are described by Turnipseed and Sauer (2010) 

and Rantz and others (1982a). The proper techniques for 

making discharge measurements using ADCPs are described 

by Mueller and Wagner (2009) and in USGS Office of Surface 

Water Technical Memoranda (http://water.usgs.gov/osw/pubs/

memo.summaries.html#STREAMFLOW). 

Collecting discharge measurement data for accurate 

calibration and validation of an index velocity streamgaging 

station, in both steady and unsteady flow conditions, requires 

data with exact time synchronization between measurement 

devices, appropriate discharge measurement duration, 

appropriate ADVM configuration, and measurement of both 

short-term and seasonal discharge variability. Timing discrepancies of as little as 15 seconds between measurement devices 

(ADVM or data logger and ADCP internal clocks) can cause 

erroneous relations between index velocity and measuredmean channel velocity, which are difficult, if not impossible, 

to correct once the data have been obtained. Regardless 

1

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

by the year in which the period ends.
Rating Development and Analysis 35

of flow conditions (unsteady or steady), all measurement 

recording devices should be synchronized to the NIST official 

time (http://tf.nist.gov and http://www.time.gov). Affordable 

watches that automatically synchronize to NIST time are 

recommended equipment for all hydrographers. 

Steady and unsteady flow conditions require that the 

duration of the discharge measurements be short enough to 

reduce the uncertainty in the horizontal and vertical velocity 

distribution as the flow changes yet long enough to minimize 

the uncertainty in the discharge. For unsteady flow conditions, 

the maximum discharge measurement duration will depend on 

channel width, measurement method, and the rate of change 

in flow. Experimenting with discharge measurement duration 

is sometimes necessary to determine an optimal site-specific 

duration for index rating development. When making ADCP 

measurements, reciprocal transect pairs should be averaged 

together and treated as one measurement of discharge in 

order to reduce the possibility of directional bias whenever 

conditions permit (U.S. Geological Survey, 2002; Mueller and 

Wagner, 2009). 

Discharge measurements must define any short-term variability in flow (minutes to days in duration) and any seasonal 

variability (weeks to months) to ensure that a comprehensive 

calibration dataset is collected and used to develop the most 

accurate index rating. Short-term variability may be caused 

by small-basin rainfall runoff, flow structure control, seiche 

effects from larger rivers or bodies of water, or wind or tidal 

effects. Longer-term variability can be caused by rainfall, 

snow, or ice-melt runoff, or spring-neap tidal effects. For 

tidally affected sites, discharge measurements should be made 

so that they characterize the short- and long-term variations in 

flow. This can be accomplished by making discharge measurements continuously over at least one-fourth to one-half the 

duration of the short-term variation (7 to 13 hours for tidally 

affected sites) at least once per year, and making 10 to 

20 discharge measurements each time the site is measured 

during the rest of the year to characterize long-term variations 

in the flow. Each site will have unique flow characteristics that 

will need to be measured and assessed in order to develop the 

index rating.

For steady flow stations, once an index rating is 

developed for a site, measurements should be plotted on 

the index rating before leaving the site in accordance with 

standard procedure for stage-discharge gaging stations. The 

hydrographer should also compute the percentage difference 

from the index rating (for discharge) and record this and other 

pertinent information on the gage-house log sheet. If discharge 

measurements deviate more than expected from the index 

rating, a check-discharge measurement should be made. The 

criteria for the expected deviation should be specified as part 

of the WSC or site-specific quality-assurance plan. Just as with 

other streamflow-gaging stations, check-discharge measurements should take into account the accuracy of the discharge 

measurements as well as the accuracy of the index rating.

Index Velocity Rating

After an adequate range of flows has been measured at 

the index velocity station, the stage-area rating along with 

quality-assured stage, index velocity, and discharge measurement data are used to develop the index rating. Each part of 

the index rating development must be thoroughly documented 

to indicate to the user and reviewer what steps were taken 

and what logic was used to develop and choose a particular 

rating. Ratings need to be checked for accuracy over time, and 

any adjustments or changes to the rating must be documented 

and saved along with any previous ratings. A sample index 

rating is shown in figure 22. The subsequent sections of the 

report describe techniques for compiling data for the index 

rating analysis, rating analysis and development, and rating 

validation.

Data Compilation

When assembling an index rating, it is necessary to 

compile the data to be used for rating analysis and development. The following example of data compilation is provided 

in order to illustrate how this compilation might be done. For 

this report, a spreadsheet tool (Microsoft® Excel) is used for 

data compilation and rating development, but other spreadsheets, statistical software, and specialized analysis tools also 

may be used. 

Data to be used in the index rating development should 

be tabulated in an index rating workbook. The following data 

should be compiled, entered, and computed in this workbook 

in separate worksheets:

• Index velocity data collected concurrently with 

discharge measurements,

• Stage data collected concurrently with discharge 

measurements,

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Index velocity, in feet per second

Measured-mean velocity, in feet per second

V =c i 0.92V + 0.02

Figure 22. Example of an index rating. 
36 Computing Discharge Using the Index Velocity Method

• Discharge measurement data with synchronized and 

synthesized index velocity and stage data,

• Stage-area rating,

• Regression analysis results, and

• Rating analysis summary information. 

The contents of the first four worksheets are described below, 

and the worksheets for regression analysis and rating development summary are discussed in the “Rating Development and 

Analysis” section.

Each worksheet in the workbook should contain an 

appropriate description of the data in the worksheet, and 

each column of data must be appropriately labeled. If the 

spreadsheet software does not provide for written documentation with the data, describe each data file and the data in a text 

file with a descriptive filename (for example “read_me_first.

txt”). Data that are not directly used in the regression analysis 

process should not be copied or linked to this worksheet or 

file in order to minimize errors and to minimize inclusion 

of unnecessary data to the rating analysis. All original data 

should be retained so that if mistakes are found, they can be 

readily corrected and a reviewer can easily access the data and 

check all steps in assembling the data. 

Index velocity data that were collected concurrently 

with the discharge measurements should be assembled into 

a worksheet. The worksheet should include the dates and 

times (to the second) with the time zone identified and all 

of the available velocity data including all measurement 

volume velocity components (X, Y, Z or E, N, Up) and the 

multi-cell velocity components (X, Y, Z or E, N, Up) for each 

cell (table 7). The velocity data should have a measurement 

interval and averaging period of 1 minute. 

The stage data collected concurrently with the discharge 

measurements should be compiled into a separate worksheet 

as well because the stage data may or may not have the same 

measurement interval as the velocity data. The stage data 

will then be used with the data in the discharge measurement 

worksheet to synchronize and synthesize velocity and stage 

data for the duration of each discharge measurement. Many 

ADVMs are equipped with an acoustic (upward-looking) stage 

sensor and (or) pressure transducer. These acoustic stagesensor data will be available at 1-minute time steps (similar to 

the index velocity data). Although these acoustic stage sensors 

do not meet current (2011) USGS accuracy requirements, 

they are useful as backup stage sensors, and they provide an 

independent measurement that can be used for quality control. 

Therefore, at most USGS streamgaging stations, a separate 

Table 7. Assembled continuous 1-minute index velocity and acoustic stage data.

[Vx, velocity in the X direction (perpendicular to the instrument); Vy, velocity in the Y direction (parallel to the instrument); UTC, coordinated universal time; 

ft/s, feet per second]

Date Start time 

(UTC)

Range-averaged Stage 

(ft)

Cell 1 Cell 2 Cell 3

Vx (ft/s) Vy (ft/s) Vx (ft/s) Vy (ft/s) Vx (ft/s) Vy (ft/s) Vx (ft/s) Vy (ft/s)

6/26/2008 15:15:00 1.67 0.10 6.79 1.73 –0.05 1.57 0.05 1.73 0.23

6/26/2008 15:16:00 1.59 0.14 6.79 1.56 0.01 1.53 0.11 1.58 0.17

6/26/2008 15:17:00 1.62 0.16 6.79 1.50 0.03 1.64 0.06 1.57 0.22

6/26/2008 15:18:00 1.75 0.16 6.80 1.82 0.13 1.61 0.19 1.67 0.13

6/26/2008 15:19:00 1.71 0.19 6.79 1.53 0.21 1.88 0.15 1.61 0.18

6/26/2008 15:20:00 1.77 0.13 6.79 1.60 0.07 1.87 0.09 1.72 0.14

6/26/2008 15:21:00 1.72 0.18 6.79 1.63 0.04 1.53 0.16 1.82 0.18

6/26/2008 15:22:00 1.78 0.12 6.79 1.92 0.03 1.71 0.12 1.80 0.16

6/26/2008 15:23:00 1.62 0.12 6.79 1.59 0.08 1.54 0.18 1.61 0.07

6/26/2008 15:24:00 1.79 0.13 6.79 1.66 0.08 1.79 0.07 1.99 0.16

6/26/2008 15:25:00 1.73 0.14 6.80 1.61 0.14 1.69 0.08 1.66 0.20

6/26/2008 15:26:00 1.62 0.12 6.80 1.47 0.07 1.54 0.08 1.65 0.14

6/26/2008 15:27:00 1.67 0.12 6.79 1.88 0.09 1.59 0.13 1.58 0.05

6/26/2008 15:28:00 1.77 0.14 6.81 1.65 0.10 1.77 0.16 1.69 0.16

6/26/2008 15:29:00 1.69 0.11 6.80 1.46 0.14 1.76 0.05 1.60 0.08

6/26/2008 15:30:00 1.63 0.12 6.80 1.79 –0.01 1.62 0.10 1.78 0.17

6/26/2008 15:31:00 1.59 0.08 6.81 1.51 0.09 1.66 0.09 1.70 0.05

6/26/2008 15:32:00 1.62 0.07 6.82 1.50 0.01 1.68 0.07 1.59 0.08

6/26/2008 15:33:00 1.59 0.12 6.81 1.39 0.12 1.63 0.10 1.46 0.07

6/26/2008 15:34:00 1.69 0.17 6.82 1.42 0.15 1.75 0.13 1.76 0.14

6/26/2008 15:35:00 1.54 0.17 6.82 1.40 0.25 1.48 0.12 1.68 0.12

6/26/2008 15:36:00 1.66 0.15 6.81 1.55 0.07 1.45 0.14 1.68 0.18

6/26/2008 15:37:00 1.60 0.14 6.82 1.57 0.08 1.55 0.11 1.68 0.12
Rating Development and Analysis 37

Table 8. Compiled discharge measurement dates, times, discharges, measurement quality, and measurement method.

[UTC, coordinated universal time; ft3/s, cubic feet per second; ADCP, acoustic Doppler current profiler]

Measurement 

number Date Start time (UTC)

End time 

(UTC)

Mid-time 

(UTC)

Discharge 

(ft3/s)

Measurement 

quality

Discharge 

measurement 

method

1 June 26, 2008 15:20:40 15:33:16 15:26:58 515 Good ADCP

2 August 11, 2008 13:11:22 13:26:45 13:19:03 781 Fair ADCP

3 September 22, 2008 17:05:04 17:23:33 17:14:19 1,510 Good ADCP

4 October 10, 2008 11:44:22 11:54:16 11:49:19 446 Poor ADCP

5 November 15, 2008 18:48:53 19:01:24 18:55:08 272 Good ADCP

6 December 13, 2008 15:54:28 15:58:50 15:56:39 333 Fair ADCP

stage sensor (that meets USGS accuracy requirements) is 

installed and operated. The data from this “external” stage 

sensor often will be collected at a time step that is not a 

1-minute time step. 

The discharge measurement summary, such as that shown 

in table 8, should contain all discharge measurement dates, 

start and end times, and the measured discharge. Discharge 

measurements to be used in the rating analysis must have 

been properly processed and quality assured using techniques 

from Mueller and Wagner (2009) and Turnipseed and Sauer 

(2010). Some acoustic discharge measurement system 

software provides easy-to-use mechanisms for electronically 

copying and pasting the pertinent discharge measurement data 

into a separate worksheet in the index rating workbook. The 

time zone used should be noted, all times for the discharge 

measurements should include start and end times to the second 

(hour:minute:second), and times must have been synchronized 

to NIST time along with the ADVM and the data logger. The 

discharge measurement quality (excellent, good, fair, or poor) 

should be included in the data table. Discharge measurement 

durations (start and end times) will be used to compute 

time-averaged values of stage and velocity that will be used 

in the regression/rating analysis. It is extremely important that 

all data times and data are checked for accuracy; otherwise, 

erroneously synchronized data or poor quality data will result 

in a poor rating. 

The stage, index velocity, and measured-mean velocity 

(discharge) data must be synchronized and synthesized 

accurately in order to develop the most accurate index rating. 

The ADVM stage (if available) and index velocity data should 

be averaged over the duration of the discharge measurement. 

It is important for the hydrographer to understand the time 

conventions of the particular system they are using in order to 

properly synchronize and synthesize their data. For example, 

the time recorded for each index velocity value usually is the 

start time of the measurement, and the end time of the index 

velocity data is determined by the averaging period. For 

SonTekTM ArgonautTM ADVMs, if the index velocity data time 

is shown as 15:36:00 (hh:mm:ss) and the averaging period 

is 60 seconds, then the index velocity end time is 15:37:00. 

Synthesized data are the stage and index velocity data that 

have been averaged over the duration of the discharge measurement using the discharge measurement start and end times. 

When using 1-minute ADVM data, as recommended, 

good results can be achieved if the index velocity data is 

averaged as follows. If the index velocity data start time is less 

than or equal to 30 seconds from the discharge measurement 

start time, then that index velocity value is used in the index 

velocity average value. Likewise, if the end time of the index 

velocity measurement is greater than 30 seconds from the end 

time of the discharge measurement, then that index velocity 

measurement is not used in the index velocity average for that 

discharge measurement. An example of the index velocity and 

stage data synchronization and synthesis is shown in table 9. 

The first discharge measurement in table 9 started at 15:36:06 

and ended at 15:40:32, so the index velocity (both X and Y) 

and stage measurements used in the duration average are the 

values recorded at 15:36:00 (0.36, –0.12, and 6.31), 15:37:00, 

15:38:00, 15:39:00, and 15:40:00 (0.45, –0.13, and 6.28). 

All of the values from 15:36:00 to 15:40:00 are averaged 

together to compute the duration averaged index velocity 

and stage values (0.39, –0.11, and 6.30). The first stage and 

index velocity data to be included in the duration averages are 

shaded in green in table 9, and the last value included in the 

average is shaded in red. The synchronized and synthesized 

duration averaged data (X velocity, Y velocity, and stage, in 

this example) are indicated by yellow highlighting for each 

discharge measurement duration.

After all stage and index velocity values have been 

synchronized and synthesized for each discharge measurement 

and assembled into a table as shown in table 10, the duration 

averaged stage value for each discharge measurement (derived 

from the “external gage sensor”) is used to compute an area 

for the standard cross section using the stage-area rating. 

The resultant area is divided into the discharge to compute a 

measured-mean velocity for each discharge measurement. The 

measured-mean velocity, the range-averaged X and Y index 

velocity and multi-cell X and Y data (not shown in table), 

and the stage data will be used in the index rating analysis to 

develop the best index rating. 
38 Computing Discharge Using the Index Velocity Method

Rating Development and Analysis

Graphical and statistical analyses should be used 

to develop the most appropriate index rating. Results of 

statistical analyses can be misleading at times and should 

not be relied on as the sole means to develop and assess the 

rating. Rather, the accuracy of the rating should be based on 

plots of the data used in the analyses and on statistical results 

from regression analysis. Furthermore, a simple index rating 

may yield similar results (computed discharge) to a more 

complicated index rating that is slightly better from a purely 

statistical point of view. 

The following steps should be followed when developing 

index ratings. 

A. Graphical data analysis

1. Create plots of data available for rating analysis.

2. Review plots and look for patterns. 

B. Simple-linear regression rating

1. Perform linear regression analysis using index 

velocity (from ADVM) and mean channel 

velocity (from discharge measurements); create 

residual plots.

2. Evaluate regression statistics.

3. Examine residual plots and look for patterns. 

4. If patterns in residual plots are evident, proceed 

to step B-6, otherwise if the regression results 

and plots are acceptable, proceed to next step.

5. Implement the simple-linear rating. 

6. If patterns in residual plots are evident, do the 

scatter or residual plots created in step A-1 or 

B-3 indicate a nonlinear trend? If so, proceed to 

step D-1. If the scatter or residual plots indicate a 

compound linear rating, proceed to step C-1.

Table 9. Synchronization and synthesis of index velocity and stage data with discharge data.

[Vx, velocity in the X direction (perpendicular to the instrument); Vy, velocity in the Y direction (parallel to the instrument); ft/s, foot per second; ft, foot; 

ft3/s, cubic foot per second. Green shading indicates transect start times, red shading indicates transect end times, and yellow shading denotes ADVM readings to 

be averaged for a given transect]

Date Start time 

(UTC)

Range-averaged Stage 

(ft)

Duration averaged Discharge measurement data

Vx 

(ft/s)

Vy 

(ft/s)

Vx 

(ft/s)

Vy 

(ft/s)

Stage 

(ft) Date Start time (UTC)

End time 

(UTC)

Mid-time 

(UTC)

Discharge 

(ft3/s)

6/26/2008 15:35:00 0.37 –0.06 6.31

6/26/2008 15:36:00 0.36 –0.12 6.31 0.39 –0.11 6.30 6/26/2008 15:36:06 15:40:32 15:38:19 2,410

6/26/2008 15:37:00 0.41 –0.08 6.30

6/26/2008 15:38:00 0.45 –0.06 6.30

6/26/2008 15:39:00 0.34 –0.16 6.29

6/26/2008 15:40:00 0.45 –0.13 6.28

6/26/2008 15:41:00 0.64 –0.12 6.28

6/26/2008 15:42:00 0.55 –0.13 6.27

6/26/2008 15:43:00 0.58 –0.14 6.27 0.58 –0.10 6.26 6/26/2008 15:42:56 15:47:48 15:45:22 3,760

6/26/2008 15:44:00 0.59 –0.17 6.26

6/26/2008 15:45:00 0.56 –0.10 6.26

6/26/2008 15:46:00 0.63 –0.06 6.26

6/26/2008 15:47:00 0.56 –0.02 6.27

6/26/2008 15:48:00 0.53 –0.07 6.25

6/26/2008 15:49:00 0.61 –0.06 6.26

6/26/2008 15:50:00 0.56 –0.11 6.26 0.59 –0.13 6.25 6/26/2008 15:49:37 15:53:58 15:51:47 4,360

6/26/2008 15:51:00 0.60 –0.11 6.26

6/26/2008 15:52:00 0.58 –0.16 6.25

6/26/2008 15:53:00 0.61 –0.14 6.24

6/26/2008 15:54:00 0.58 –0.11 6.24 0.72 –0.15 6.23 6/26/2008 15:54:28 15:58:50 15:56:39 5,210

6/26/2008 15:55:00 0.68 –0.14 6.24

6/26/2008 15:56:00 0.72 –0.16 6.22

6/26/2008 15:57:00 0.85 –0.15 6.22

6/26/2008 15:58:00 0.79 –0.18 6.21

6/26/2008 15:59:00 0.82 –0.16 6.21
Rating Development and Analysis 39

Table 10. Data assembled into a table for rating analysis.

[Vx, velocity in the X direction (perpendicular to the instrument); Vy, velocity in the Y direction (parallel to the instrument); UTC, coordinated universal time; ft3

/s, cubic foot per second; ft/s, foot per second; ft, foot; ft2, square foot]

Discharge measurement data Duration averaged Standard 

cross section

Date Mid-time 

(UTC)

Discharge 

(ft3/s)

Mean velocity 

(ft/s)

Vx 

(ft/s)

Vy 

(ft/s)

Stage 

(ft)

Area 

(ft2)

6/26/2008 15:38:19 2,410 0.30 0.39 –0.11 6.30 7,970

6/26/2008 15:45:22 3,760 0.47 0.58 –0.10 6.26 7,940

6/26/2008 15:51:47 4,360 0.55 0.59 –0.13 6.25 7,940

6/26/2008 15:56:39 5,210 0.66 0.72 –0.15 6.23 7,920

C. Compound-linear regression rating

1. Group the data based on slope changes.

2. Perform linear regression analysis for each linear 

segment; create residual plots.

3. Evaluate regression statistics for each linear segment.

4. Examine residual plots and look for patterns for 

each linear segment. 

5. Create transition between slopes of line segments.

6. Implement the compound rating.

D. Multiple-linear regression rating

1. Choose other variables to include for multiplelinear regression.

2. Run multiple-linear regression analysis on 

selected variables; create residual plots.

3. Evaluate regression statistics.

4. Examine residual plots and look for patterns.

5. Compare multiple-linear regression statistical 

results and residuals plots with simple-linear 

regression results. If there is not a significant 

improvement in the standard error and in the 

distribution and spread of residuals, implement simple-linear regression rating and collect 

additional data. If the multiple-linear regression 

indicates a significant improvement in the standard error and in the distribution and spread of 

residuals, proceed to the next step.

6. Implement the multiple-linear regression.

These steps are illustrated in the flowchart shown in 

figure 23 and are described in the subsequent report sections 

dealing with simple-linear, compound-linear, and multiplelinear ratings. An example of the application of each of these 

rating types also is presented in the subsequent sections.

Graphical Data Analysis

The first step in developing an index rating should be to 

plot the data available for analysis. Data plots are one of the 

most useful tools available to the hydrographer when developing ratings. The synchronized and synthesized index velocity 

and measured-mean velocity data should be evaluated first by 

plotting the data and observing the shape and distribution of 

the data. The index velocity measured by the ADVM is the 

independent variable (x-axis), and the measured-mean velocity 

(measured discharge divided by the corresponding area 

obtained from the stage-area rating) is the dependent variable 

(y-axis). If site selection, instrument location and position, 

instrument configuration, and synchronization of the calibration/validation data were properly performed, a linear relation 

between the index velocity and the measured-mean velocity 

data usually will be evident. 

Scatter plots of the measured-mean velocity data and 

downstream (typically the X velocity) and cross-stream index 

velocity (typically the Y velocity for sidelooker ADVMs), 

stage, and possibly index velocity squared may reveal linear 

or nonlinear relations among the variables. These plots can 

provide information and understanding about the hydraulics 

of flow at the gaging station that may be useful in developing 

an index rating for the site. Scatter plots also graphically 

summarize the number and range of discharge measurements; 

a small number of measurements (fewer than 10), or measurements taken during a limited range of conditions will decrease 

the reliability of the rating. A plot of the measured-mean 

velocity data (y-axis) and the range-averaged velocity (x-axis) 

and each multi-cell velocity (x-axis) also should be used 

in evaluating the index rating. Analyze the plots and look 

for the best linear relation between different index velocity 

measurement volumes (range-averaged and multi-cell) and 

measured-mean velocity. It is possible that only a small 

section of the index velocity measurement volume will result 

in the best fit with the measured-mean velocity. For example, 

multi-cell velocity data from cells 2, 3, and 4 might indicate 

the best linear relation with measured-mean velocity. If so, the 
40 Computing Discharge Using the Index Velocity Method

hydrographer would therefore begin by using data from these 

three cells to develop the index rating. Plotting the multi-cell 

velocity with measured-mean velocity also can indicate when 

one or more cells deviate from the other multi-cell data. When 

this occurs, the multi-cell data that deviate from the other data 

should be excluded from the regression. This result also would 

indicate that the range-averaged volume beginning and ending 

distances should be reconfigured for the ADVM; otherwise, 

the accuracy of the rating may be adversely affected. An 

example showing velocity data from cell 1 deviating from the 

general pattern observed for velocity data from cells 2 and 3 

is shown in figure 24. This plot indicates that velocity data 

obtained for cell 1 may be in a region of disturbed velocity and 

should be excluded from the regression analysis. If an unusual 

or nonlinear relation exists between the index velocity and 

measured-mean velocity, first check all date and time synchronizations to be sure they are correct. Verify that the index 

velocity range-averaged cell or multi-cells that are selected are 

free of erroneous data and (or) that the measurement volume 

did not change over time (for range-averaged cell).

Multi-cell X velocity, in feet per second

Measured-mean velocity, in feet per second

0.0

0.4

0.8

1.2

1.6

2.0

0.0 0.4 0.8 1.2 2.0 1.6

Cell 1

Cell 2

Cell 3

EXPLANATION

Figure 24. Multi-cell index velocity data with measured-mean 

velocity. 

Figure 23. Steps for creating an index rating.

Figure 23. Steps for creating an index rating.

Graphical Data Analysis (A)

Create data plots

(A-1)

Review plots

(A-2)

Simple Linear Rating (B)

Simple linear regression

(B-1)

Evaluate statistics

(B-2)

Look for patterns in

residual plots

(B-3)

Regression/plots

acceptable?

(B-4)

Implement rating

(B-5)

Review data plots.

Non-linear trend?

(B-6)

Compound Linear Rating (C)

Group data

(C-1)

Simple linear regression

on each group

(C-2)

Evaluate statistics

(C-3)

Look for patterns in

residual plots

(C-4)

Create transition

between segments

(C-5)

Implement rating

(C-6)

Implement rating

(D-6)

Multiple-Linear Rating (D)

Choose variables

(D-1)

Multiple-linear regression

(D-2)

Evaluate statistics

(D-3)

Look for patterns in

residual plots

(D-4)

Compare to simple

linear regression

(D-5)

No

No

Yes

Yes

Use Multiple-Linear

Use Simple Linear

Improvement in results?

Yes, Implement multiple-

 linear rating

No, Implement simple 

 linear rating
Rating Development and Analysis 41

Plot the measured-mean velocity and the stage data. This 

plot will provide information about the range of stage and 

measured-mean velocity (discharge measurements). Gaps 

in the data provide information about where more data will 

be required to define the index rating. A discernable pattern 

between the two variables may indicate that stage and mean 

velocity are correlated and stage may need to be considered as 

a variable in the regression analysis. Stage is often related to 

mean velocity, and the relation may be nonlinear, indicating 

that a site is possibly affected by backwater or that the velocity 

distribution is affected by channel features (submerged 

shoals). For sidelooker ADVMs, stage is commonly related 

to mean velocity because the ADVM measures at a fixed 

elevation in the cross section, and substantial changes in stage 

will change the location where the index velocity is measured 

in the velocity profile, especially if the site’s water column 

velocity profile has a substantial gradient (fig. 25). 

After visually inspecting the velocity and stage plots, the 

hydrographer should choose the index velocity measurement 

volume data that best fit the measured-mean velocity for use 

in the regression analysis. The rationale for the data selected 

for regression analysis (including the selected measurement 

volume) should be documented in the rating analysis. The 

independent variables selected will be used for regression 

analysis with the dependent variable (measured-mean 

velocity).

0

2

4

6

8

10

12

14

16

18

0 100 200 300 400 500 600 700

Station location distance from left bank looking downstream (feet)

Elevation, in feet Elevation, in feet

0 100 200 300 400 500 600 700

Main beam Main beam

0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

Low Flow

0 0

2 2

4 4

6 6

8 8

10 10

12 12

14 14

High Flow

ADVM Depth = 0.6 x Depth ADVM Depth

0.6 x Depth

Index velocity, in feet per second

Figure 25. A water column velocity profile and possible change in the location of the ADVM measurement volume with changing 

stage.
42 Computing Discharge Using the Index Velocity Method

Simple-Linear Regression Rating

Ordinary least squares (OLS) linear regression is a 

method of mathematically fitting a straight line to a dataset. 

The fitted straight line can be represented by a mathematical 

equation that can be used to estimate or compute a variable 

(mean velocity) from another variable (index velocity). The 

simple-linear regression equation usually has the form

y mX b error = ++ ,

where

y = computed-mean velocity,

m = slope of the line (also named the X variable 

coefficient),

X = index velocity,

b = y intercept or intercept (defined where the 

regression line crosses the y-axis when 

x = 0), and

error = error around the regression line.

For practical reasons, when developing index ratings, the error 

term in equation 3 is ignored. The fitted straight line is calculated by minimizing the difference between all the observed 

data and the fitted line. Statistical tools for performing OLS 

linear regression analysis are common and are often included 

in spreadsheet software. 

The six assumptions regarding the data used in the 

regression analysis are from Helsel and Hirsch (2002, 

p. 224–225) and Riggs (1968, p. 7).

1. The dependent and independent variables are 

linearly related,

2. Variables used in the regression (index velocity, 

stage, etc.) are representative of the data of interest 

(mean velocity), 

(4)

3. Residuals are of equal variance (homoscedastic),

4. Observed values of the mean velocity are uncorrelated random events, 

5. The residuals are normally distributed, and

6. Independent variable(s) is (are) measured with 

reasonable error.

The need to satisfy these assumptions depends on the purpose of the linear regression. Helsel and Hirsch (2002) state 

that only assumptions 1 and 2 are required to correctly use 

linear regression to predict mean velocity (y) given an index 

velocity (x), but a more accurate rating will result as more of 

the above assumptions are met. The accurate measurement of 

index velocity and corresponding discharge measurements are 

extremely important to the overall reliability of the regression 

equation. 

Rating Development

The calibration data (measured-mean velocity and 

index velocity) are used as input to the regression analysis 

software to fit the straight line that will be the index rating. 

The measured-mean velocity data are input as the dependent 

variable (y input), and the index velocity data are input as the 

independent variable (x input). A common mistake when using 

spreadsheet software is inadvertently transposing the dependent and independent variables during regression analysis. 

Care should be taken to ensure that the variables (x and y 

inputs) are properly selected and identified in the regression 

analysis.

The regression results can sometimes be overwhelming, 

but only five outputs from the regression analysis will be used 

to evaluate the mathematically fitted line. The five outputs that 

need to be evaluated are the coefficient of determination (R2), 

Table 11. Typical output from a commonly used regression analysis software program.

[R, correlation coefficient; R-square, coefficient of determination (also R2); ANOVA, analysis of variance; df, degrees of freedom; SS, sum of squares; 

MS, mean square; F, F-test statistic; Vi, Index velocity; t Stat, t-test statistic; P-value, P statistic for significance of regression coefficient; Lower 95%, lower 

value for 95% confidence limit; Upper 95%, upper value for 95% confidence limit. Yellow shading indicates the parameters used to evaluate the mathematically fitted line (regression)]

Regression statistics

Multiple R 0.997162

R-square 0.994332

Adjusted R-square 0.994242

Standard error 0.048462

Observations 65

ANOVA

df SS MS F Significance F

Regression 1 25.95845 25.95845 11052.69 1.71E-72

Residual 63 0.147962 0.002349

Total 64 26.10641

Coefficients Standard error t Stat P-value Lower 95% Upper 95%

Intercept 0.01768 0.01072 1.649276 0.104069 –0.00374 0.039102

Vi 0.901298 0.008573 105.1318 1.71E-72 0.884166 0.918429
Rating Development and Analysis 43

Observation

Predicted 

velocity 

(feet per 

second)

Residuals

(feet per 

second)

1 0.60 0.02

2 0.60 0.06

3 0.49 –0.01

4 0.49 –0.03

5 0.52 0.00

6 0.52 0.10

7 0.62 0.00

8 1.24 0.01

9 1.22 0.00

10 3.98 0.01

11 1.14 0.06

12 0.47 –0.03

13 1.11 –0.11

14 0.59 0.00

15 0.49 0.02

16 0.57 –0.03

17 0.88 0.00

18 0.64 –0.02

19 0.47 0.13

20 0.53 –0.01

21 0.63 –0.03

22 1.03 0.09

Observation

Predicted 

velocity 

(feet per 

second)

Residuals

(feet per 

second)

23 1.11 0.02

24 1.13 0.02

25 1.13 –0.04

26 1.10 0.02

27 1.11 –0.01

28 1.12 0.01

29 1.11 –0.01

30 1.10 –0.01

31 1.12 –0.04

32 1.10 0.00

33 1.52 0.04

34 1.36 0.00

35 0.60 –0.12

36 0.49 0.01

37 0.48 –0.07

38 0.49 –0.10

39 0.47 –0.08

40 0.49 –0.01

41 0.81 –0.01

42 0.84 –0.02

43 0.41 –0.03

44 0.64 0.01

Observation

Predicted 

velocity 

(feet per 

second)

Residuals

(feet per 

second)

45 0.34 0.00

46 2.84 0.03

47 2.79 –0.08

48 2.45 –0.01

49 0.88 0.07

50 0.86 –0.05

51 0.83 0.06

52 0.87 0.04

53 0.74 –0.06

54 0.68 0.01

55 2.14 –0.05

56 0.86 0.05

57 0.88 0.06

58 0.93 0.07

59 0.93 0.03

60 0.78 0.03

61 0.86 0.02

62 0.82 0.03

63 0.87 0.04

64 0.53 –0.03

65 0.41 –0.04

the standard error of the estimate, the number of observations, 

the statistical significance (p-values) of the variables selected 

for use in the regression, and the residual plots. Each of 

these outputs are described below. Examples of results from 

regression analysis for a simple-linear regression are provided 

in tables 11 and 12. 

The coefficient of determination (R2) is a numerical 

value that represents the proportion of the variance in mean 

velocity that can be explained by knowing the index velocity. 

For example, if R2 equals 0.90 for a simple-linear regression between index velocity and mean velocity, it means 

that 90 percent of the variance in computed-mean velocity 

(from the index rating) is attributable to the variance in the 

measured-mean velocity and that 10 percent of the variance in 

the computed-mean velocity is not explained by the variance 

in the measured-mean velocity (or selected parameters). The 

range of values for R2 can be from near 0 to 1, with values 

closer to 1 typically being more desirable. 

While R2 is an important value it should not be used alone 

as an indication of how well the data fit the regression line. 

Figure 26 illustrates why R2 alone is not sufficient to explain the 

accuracy of the regression equation. Each of the datasets shown 

in figure 26 has an R2 of 0.7. Clustered data can result in high R2

values. If only two measurements were used to create an index 

rating, the regression would result in a perfect R2 value of 1. 

The R2 value is just one piece of information that needs to be 

used with all of the available regression analysis tools—scatter 

plots, residuals plots, and other regression statistics.

A

C

B

D

Figure 26. Scatter plots with the same coefficient of determination 

(R2) value (modified from Chambers and others, 1983).

Table 12. Typical residuals output from a linear regression analysis.
44 Computing Discharge Using the Index Velocity Method

The standard error (or standard error of the estimate) 

is a way to measure the reliability of a regression and is the 

standard deviation of the distribution of residuals about the 

regression line (Riggs, 1968). The standard error (table 11) 

has the same units as the dependent variable (mean velocity), 

and lower values are desirable. The standard error also can 

be evaluated visually using the residual plots. The standard 

error is useful for comparing two regression analyses, such as 

when comparing a simple-linear regression to a multiple-linear 

regression.

The number of observations is used to determine the relative reliability of the regression analysis. Ideally, a minimum 

of 10 to 20 observations for each independent variable used 

in the regression is needed to improve the reliability. If index 

velocity is the only independent variable, use at least 10 

measurements of discharge over the widest possible range of 

stream conditions. A limited amount of data may reduce the 

ability of the regression/rating to accurately compute mean 

velocity, especially if the rating data do not represent the entire 

range of conditions for the stream. Even with a limited amount 

of data, the regression analysis should be performed because 

the results may provide an initial indication of whether or not 

the ADVM is properly located.

The statistical significance of each variable in the 

regression analysis is reported in the output as a p-value. The 

p-value can be used to determine if the variable in the regression equation is statistically significant or meaningful in the 

regression. For simple-linear regression with one independent 

variable (index velocity), there will be a p-value for two 

variables—the index velocity coefficient (slope of the line 

or rating) and the y-axis intercept coefficient (intercept). The 

p-values typically should be less than 0.05 (or 5 percent). A 

p-value of 0.05 indicates that there is a 95 percent chance that 

the coefficient in the regression equation is related to mean 

channel velocity, indicating that the coefficient is likely to be 

meaningful in the rating. 

The p-value alone should not be used to reject a variable 

in the regression analysis, but should be considered with the 

analyses of scatter plots, residuals plots, and the number of 

observations. For example, the p-value for the y-axis intercept 

sometimes is greater than 0.05. In some of these cases, the 

value for the intercept is still meaningful to the rating. The 

y-axis intercept in an index velocity regression is often needed 

to correctly define the index rating and normally should not be 

forced through zero. There are many reasons for the computed 

mean velocity from an index rating to have a non-zero 

value when the index velocity value is zero. In almost all 

index velocity installations, the measurement volume is not 

configured to exactly measure the mean channel velocity, so 

when the index velocity is zero, there is likely some non-zero 

component of mean channel velocity. The following quotation 

from Helsel and Hirsch (2002, p. 238) is appropriate for index 

ratings. In the quotation, β1 and b0 refer to the regression 

coefficients.

Even when the intercept is not significantly different from zero, there is little benefit to forcing it to 

equal zero, and potentially great harm in doing so. 

Regression statistics such as R2 and the t-ratio for β1

lose their usual meaning when the intercept term is 

dropped (set equal to zero). Recognition of a physical reason why y must be zero when x is zero is not 

a sufficient argument for setting b0 = 0.

Residuals are the difference between the measured-mean 

velocity from the discharge measurements and the computedmean velocity that is determined by the regression/rating 

equation. Example residuals from a regression analysis are 

shown in table 12. The residuals are plotted on the y-axis, and 

index velocity, computed-mean velocity (from the regression 

equation), stage, and time should be plotted on the x-axis 

(separate plot for each variable on the x-axis). Residual data 

plots are valuable tools for assessing the validity of using 

linear regression. Residual plots should ideally indicate 

uniform distribution about zero when plotted against the 

above-mentioned parameters. No trends or patterns should 

be readily discernible, and ideally no large outliers should be 

present (fig. 27). 

The residual plots should show a random pattern equally 

distributed around zero throughout the range of the variable 

plotted on the x-axis. If the residuals appear to be randomly 

distributed in the plot with reasonable variance, this indicates 

that the index velocity is an appropriate estimator for the 

mean channel velocity. A pattern can mean that one or more 

other variables affect the relation to mean channel velocity 

(multiple-linear rating) or the data should be divided into 

segments (compound rating). A multiple-linear regression, 

therefore, may be needed to develop an accurate rating, or 

the rating might be separated into different segments that 

represent different flow conditions (compound rating; fig. 

27C and D). A pattern also may indicate poor site selection 

or inappropriate ADVM configuration settings. The residual 

plots also provide a reliable method of identifying outliers. 

If an outlier is observed in the residual plot, it should not be 

deleted immediately, but should first be investigated to ensure 

the index velocity and discharge data are not in error. In other 

words, the hydrographer should verify that the measured 

index velocity was not biased for any reason and should verify 

that the discharge measurement was properly collected and 

processed. Also the date and time for all data must be verified 

for accuracy and proper synchronization. If errors are found 

with the index velocity or the discharge measurement data, 

the outlier may be considered for deletion. Poor discharge 

measurement technique also can affect the rating development. 

Ruhl and Simpson (2005, appendix E, figs. E-4 and E-5, 

p. 29–31) show an example of how poor discharge measurement technique can adversely affect the quality of the rating 

developed. If instrument, collection, or processing errors 

are not evident, the data point cannot be rejected without 
Rating Development and Analysis 45

Residuals, in feet per second

–0.20 –0.20

–0.15 –0.15

–0.10 –0.10

0.00 0.00

0.10 0.10

0.15 0.15

0.20 0.20

0.0 1.0 2.0 3.0 4.0 5.0

Index velocity, in feet per second

A

–1.2

–0.8

–0.4

0.0

0.4

0.8

1.2

0.0 1.0 2.0 3.0 4.0 5.0

Index velocity, in feet per second

C

Dec. 23 May 7 Sept.19 Jan. 31 June 15 Oct. 28 Mar. 11

Date

B

–0.20

–0.10

0.00

0.10

0.20

15:20 15:45 16:10 16:35

Time

D

Figure 27. Residuals with no trend in (A) index velocity and (B) date; and residuals with a trend in (C) index velocity, and (D) time.
46 Computing Discharge Using the Index Velocity Method

further investigation. If further investigation is warranted, the 

hydrographer should examine conditions at the time of the 

measurement. For example, was the stage at an unusually high 

value, was there something different about the cross section, 

was the water conductance different from other measurements, 

or were other conditions unique to the outlier? If some different condition can be identified, then the outlier should not be 

rejected because it provides important information about flow 

at the site. 

Example of a Simple-Linear Regression Rating

This example of rating development illustrates how 

simple-linear regression is used to create an index rating 

using one independent variable—index velocity. The first 

two steps in the rating analysis are plotting the data available 

for analysis (step A-1) and reviewing the plots for patterns 

(step A-2; fig. 23). Plots of data available for analysis are 

shown in figure 28. In this example, the range-averaged X 

(downstream) velocity is used as the index velocity. The plot 

of index velocity and measured-mean velocity (fig. 28A) 

shows a distinct linear relation. Some velocity ranges have 

not been measured yet; however, in the future, a special 

effort could be made to obtain discharge measurements in 

these ranges. For this example, the dataset has 41 discharge 

measurements with a very good range in velocity for defining 

the rating. Measured-mean velocities ranged from 0.04 ft/s 

to 1.79 ft/s, with the corresponding index velocities ranging 

from 0.06 ft/s to 2.03 ft/s. The plot of stage and measuredmean velocity (fig. 28B) does not show a distinct linear 

relation. This indicates that for the stages observed to-date, a 

significant statistical relation between stage and mean velocity 

is unlikely; therefore, stage can be excluded as a variable 

in the regression analysis. The plot of the range-averaged 

cross-stream (Y) velocity and measured-mean velocity 

(fig. 28C) also shows no distinct linear relation, indicating that 

cross-stream velocity should be excluded from the regression 

analysis. In figure 28D, multi-cell velocity data (X velocity) 

all show essentially the same relation with measured-mean 

velocity. The data for cell 1 may indicate a slightly different 

slope and intercept than the data for cell 2, etc., which is to be 

expected because the velocity increases in magnitude as the 

distance from the ADVM increases.

Step B-1 (fig. 23) is to perform simple-linear regression 

with software available for this analysis using index velocity 

(independent variable) and measured-mean velocity (dependent variable). Regression results for this example dataset are 

shown in table 13. As previously stated, the important results 

of the regression are the coefficient of determination (R2), the 

standard error of the estimate (standard error), the number of 

observations (observations), and the p-values for the regression coefficients. 

In step B-2, the regression statistics are evaluated. From 

table 13, it can be seen that the R2 (R-square in table 13) is 

approximately 0.99, indicating that the index rating (computed-mean velocity) explains the variation in measured-mean 

velocity quite well. This result is not surprising because the 

graphical data analysis indicated an obvious relation between 

measured-mean velocity and index velocity (fig. 28A). The 

plots created in step A (fig. 23) help verify that the R2 value 

is not spurious. The standard error is approximately 0.04 ft/s. 

This is a reasonable value, relative to the magnitudes of 

measured velocities, and indicates that the linear fit of the 

data is relatively accurate. The number of observations (41) 

is good because for every independent variable selected for 

regression analysis, there should be at least 10 observations 

(discharge measurements) for analysis. The coefficients for the 

rating equation are given in table 13 for the y-axis intercept 

(Intercept) and index velocity (Vi). The slope of the regression 

line (Vi = 0.90) indicates that the index velocity tends to be 

greater than the mean velocity because the slope is less than 1. 

The y-axis intercept (Intercept = –0.039) is close to zero, yet 

the p-value for the y-axis intercept (0.00014) indicates that the 

probability that the coefficient is equal to zero is very small 

(0.014 percent). This result provides strong evidence that the 

intercept should not be assumed to be zero. The p-value for 

the index velocity slope (8.97E-44) also indicates that the 

probability that the coefficient is equal to zero is very small. 

The analysis of the regression statistics seem to indicate 

that simple-linear regression can be used with confidence to 

develop the index rating. Nevertheless, evaluation of regression plots is necessary to confirm this conclusion.

Plots of the regression analysis, including a residual 

plot or plots, are analyzed in step B-3 (fig. 23). The predicted 

(computed) mean velocity appears to be a good approximation 

of the measured-mean velocity (fig. 29A). Furthermore, no 

trends are apparent in the plot of residuals with index velocity 

(fig. 29B). A plot of residuals with the time of the discharge 

measurements (fig. 29C) shows no distinct trend over time. 

The residuals also should be plotted with stage and any other 

variable of interest to look for trends or patterns.

Based on the results of the initial data plots (step A, 

fig. 23), regression analysis (step B-2, fig. 23), and examination of residual and regression plots (step B-3, fig. 23), it 

is reasonable to conclude that simple-linear regression is 

appropriate for defining the index rating for this example. The 

index rating equation is expressed as:

mean velocity 0.90 index velocity 0.04. =∗ −

For this example application, equation 4 was established as 

rating number 1 and entered into ADAPS effective June 1, 

2008. The process for entering the rating into ADAPS is 

described in the “Computation and Analysis of Discharge” 

section and in appendix 6 (Implementing an Index Rating). 

Future discharge measurements will provide additional refinement to the rating or will verify the rating. 

(5)
Rating Development and Analysis 47

Table 13. Results of simple-linear regression. 

[R, correlation coefficient; R-square, coefficient of determination (also R2); ANOVA, analysis of variance; df, degrees of freedom; SS, sum of squares; 

MS, mean square; F, F-test statistic; Vi, Index velocity; t Stat, t-test statistic; P-value, Probability value for the regression coefficient; Lower 95%, lower value 

for 95-percent confidence limit; Upper 95%, upper value for 95-percent confidence limit]

Regression statistics

Multiple R 0.996548

R-square 0.993108

Adjusted R-square 0.992931

Standard error 0.036884

Observations 41

ANOVA

df SS MS F Significance F

Regression 1 7.645403 7.645403 5619.887626 8.96512E-44

Residual 39 0.053056 0.00136

Total 40 7.698459

Coefficients Standard error t Stat P-value Lower 95% Upper 95%

Intercept –0.038573 0.009134 –4.223092 0.000139749 –0.057048561 –0.020098

Vi 0.904296 0.012063 74.96591 8.96512E-44 0.879896838 0.928695

600.50 600.75 601.00 601.25 601.50 601.75 602.00

Stage, in feet

–0.20 –0.15 –0.10 –0.05 0.00 0.05 0.10 0.15 0.20

Y velocity, in feet per second

A B

C D

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50

Multi-cell X velocity, in feet per second

0.0

0.0

0.2

0.2

0.4

0.4

0.6

0.6

0.8

0.8

1.0

1.0

1.2

1.2

1.4

1.4

1.6

1.6

1.8

1.8

2.0

2.0

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50

X velocity, in feet per second

Measured-mean velocity, in feet per second

Cell 1 X-velocity

Cell 2 X-velocity

Cell 3 X-velocity

Cell 4 X-velocity

Cell 5 X-velocity

EXPLANATION

Figure 28. Plots of (A) range-averaged X velocity, (B) stage, (C) Y velocity, and (D) multi-cell X velocity with measured-mean 

velocity for simple-linear rating example.
48 Computing Discharge Using the Index Velocity Method

Compound-Linear Regression Rating

Some sites may require a compound-linear index rating 

(sometimes referred to as a bimodal rating) due to the characteristics of the flow at the site. Such ratings are analogous 

to compound stage-discharge ratings where the rating has at 

least two distinct sections having differing slopes and (or) 

shapes (Rantz and others, 1982b, p. 331, fig. 165) caused by a 

section control and channel control. Stream morphology may 

cause a nonlinear relation (for example, a compound rating). 

In a stream with overbank flow at high stages, the relation 

between measured-mean velocity and index velocity may be 

different for overbank flows than for inbank flows. It is also 

not uncommon to have compound-linear ratings for gaging 

stations used to measure tidally affected flow, particularly at 

stations where there is a complete reversal of flow (that is, 

both positive and negative flows). These are but two possible 

situations where a compound-linear index rating may be 

indicated. Although compound ratings are sometimes needed, 

they are less common than simple-linear ratings. 

It is important to remember that the compound-linear 

rating should be derived from the best fit of the field data, 

reflect the hydraulic conditions that exist at the site, and be 

expressible as one or more mathematical equations. The data 

plots should be used to guide the decision as to whether a 

compound-linear index rating is required. It often becomes 

evident that a compound-linear rating is required when plotting measured-mean velocity with index velocity; however, 

the different linear segments may not be obvious, and this 

option should not be discarded until thorough exploratory 

analysis is completed. The residuals plot with index velocity 

can often be used to help identify where the data should be 

separated. The data will appear to fall into two or more distinct 

linear segments having differing slopes, such as that shown in 

figure 30, and as will be seen in the example provided in the 

“Example of a Compound-Linear Rating” section. The rating 

illustrated in figure 30 was developed for a gaging station that 

experiences tidally affected flow with complete flow reversals. 

The data used to develop this rating fall into two distinct linear 

segments. The transition between the two linear segments 

is not shown in figure 30, but is needed for implementation 

in ADAPS. In this example, the transition occurs near to an 

index velocity of 0.0 ft/s. This is consistent with the hydraulics 

of flow at this site and is confirmed by observations at the site 

during the transition from negative to positive flow. The rating 

equation for the upper (positive) section of the compoundlinear rating illustrated in figure 30 is

y x = ∗+ 0.65 0.05,

where x is the index velocity, and y is the computed mean 

velocity. The rating equation for the lower (negative) section 

of the compound-linear rating illustrated in figure 30 is

Figure 29. Plots of (A) measured-mean velocity and (6)

predicted mean velocity and (B) regression residuals 

with index velocity, (C) and regression residuals with 

measurement date.

A

B

C

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Measured-mean velocity, in feet per second –0.10

–0.10

–0.08

–0.08

–0.06

–0.06

–0.04

–0.04

–0.02

–0.02

0.00

0.00

0.02

0.02

0.04

0.04

0.06

0.06

0.08

0.08

0.10

0.10

0 0.5 1.0 1.5 2.0 2.5

Index velocity, in feet per second

Residuals, in feet per second

J J A A S S O O N N D D J J F F M M A A M M J J

2008 2009 2010

Measured mean velocity

Predicted mean velocity

EXPLANATION
Rating Development and Analysis 49

should result in acceptable values of R2, standard errors, 

number of observations, and the coefficients. With step C-4 

completed, two separate linear index ratings will have been 

created. In step C-5, a transition between the two linear segments must be developed. The development of this transition 

should be done with care and should also reflect knowledge of 

site hydraulics. For example, sharp discontinuities are unlikely 

to exist in the resulting compound rating. The development 

of the transition for a compound-linear index rating is similar 

to the way a smooth transition is created between section and 

channel control conditions for a stage-discharge rating. Lastly, 

the compound rating should be implemented in ADAPS. A 

compound rating is easily implemented in the current version 

of ADAPS and is described in the section of appendix 6 titled 

“Compound-Linear Index Ratings in ADAPS.”

Example of a Compound-Linear Rating

As in the simple-linear regression rating example, data 

available for the regression analysis are plotted and examined 

for trends. The plot of index velocity and mean velocity 

(fig. 31A) shows two distinct linear relations, indicating 

that a compound-linear rating will be necessary for this 

y x = ∗+ 1.93 0.09.

The differences in the coefficients for these two portions of 

the compound-linear rating indicate that the distribution of 

flow in the cross section during predominantly negative flow 

is different from the distribution of flow during predominantly 

positive (downstream) flow. During periods of negative flow, 

the measured index velocities tend to be smaller than the measured index velocities during periods of positive flow. 

Rating Development

The development of a compound-linear index rating 

differs little from that of a simple-linear rating. Once it is 

determined that a compound-linear index rating is required, 

the first step (step C-1; fig. 23) is to group the data for the two 

or more distinct line segments. In the next step (C-2), simplelinear regression analysis is performed using data from each 

group (similar to steps B-1 to B-3), and regression/residual 

plots are created. The regression statistics are evaluated in 

step C-3. As with simple-linear regression, no patterns in the 

regression and residual plots for each group should be evident 

(step C-4). Similarly, evaluation of the regression statistics 

(7)

–0.6 –0.4 –0.2 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

–0.8

–0.6

–0.4

–0.2

0

0.2

0.4

0.6

0.8

1.0

y = 0.65 *x + 0.05

UPPER RATING:

Index velocity, in feet per second

Measured-mean velocity, in feet per second

LOWER RATING:

y = 1.93 *x + 0.09

Measurements

Regression curve

EXPLANATION

Figure 30. Example of a compound-linear index rating (from Ruhl and Simpson, 2005, p. 23).
50 Computing Discharge Using the Index Velocity Method

site. In this dataset, only 14 discharge measurements are 

available to develop the rating. Measured-mean velocities 

ranged from 0.02 to 1.08 ft/s, and the corresponding index 

velocities ranged from 0.02 to 1.30 ft/s. The plot of stage and 

measured-mean velocity (fig. 31B) does not show a distinct 

linear relation. This indicates that stage also can be excluded 

as a variable in the regression analysis at this time. The plot of 

the range-averaged cross-stream (Y) velocity and measuredmean velocity (fig. 31C) also does not show a distinct linear 

relation, indicating that cross-stream velocity is not linearly 

related to mean velocity and should be excluded from the 

regression analysis. A plot (not shown) of multi-cell velocity 

data (X velocity) and measured-mean velocity did not indicate 

any substantial difference between cells for all but the first two 

cells. The ADVM index velocity measurement volume was 

reconfigured to exclude the range of the first two cells after 

developing the index rating using the average of multi-cells 

3 through 8.

In the first step of the rating analysis (C-1; fig. 23) for a 

compound-linear index rating, the data are separated into two 

groups based on the index velocity. The group for the lower 

part of the rating (index velocity less than 0.8 ft/s) contains 

eight discharge measurements, and the measured-mean and 

index velocity ranged from 0.02 to 0.86 ft/s and from 0.02 

to 0.77 ft/s, respectively. The group for the upper part of the 

rating contains six discharge measurements, and the measuredmean and index velocity ranged from 0.92 to 1.08 ft/s and 

from 0.94 to 1.30 ft/s, respectively. The two groups were 

determined using the apparent change in slope and after 

reviewing ADCP discharge measurements that indicated a difference between vertical velocity profiles for the two groups.

Next, simple-linear regression was performed for each 

group with index velocity as the independent variable and 

measured-mean velocity as the dependent variable (step C-2). 

Regression results for this sample dataset are shown in 

tables 14 and 15. The regression statistics were evaluated as in 

step B-2 for simple-linear ratings. For the lower range of the 

rating (table 14), the R-square (R2) is 0.98, indicating that the 

index rating explains much of the variance in measured-mean 

velocity. The standard error for the simple-linear rating for 

the lower range is 0.05 ft/s, indicating a relatively accurate 

linear fit. The number of observations (8) is less than the 

recommended minimum of 10, but only these measurements 

are currently available for analysis. The slope of the regression line (1.09) indicates that the index velocity tends to be 

measured in a region of the channel that is near to but a little 

less than the mean velocity because the slope is greater than 1 

and the y-intercept (–0.06) is almost equal to zero (table 14). 

The p-value for the index velocity slope (4.45E-06) indicates 

that the slope coefficient is unlikely to equal zero. The p-value 

for the intercept is larger than 0.05 (0.21), however, indicating 

that the hypothesis that the coefficient is equal to zero cannot 

be rejected. In other words, there is a 21-percent probability 

that the intercept equals zero. The number of observations 

available for analysis (<10) likely contributes to this result. 

Nevertheless, for the reasons stated previously in the section 

Figure 31. Plot of (A) measured-mean velocity, (B) stage, 

and (C) Y velocity with index velocity for compound-linear 

rating example.

A

B

C

0.0

0.0

0.0

0.2

0.2

0.2

0.4

0.4

0.4

0.6

0.6

0.6

0.8

0.8

0.8

1.0

1.0

1.0

1.2

1.2

1.2

1.4

1.4

1.4

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Index velocity, in feet per second

Measured-mean velocity, in feet per second

305.0 310.0 315.0 320.0 325.0 330.0 335.0 340.0

Stage, in feet

–0.20 –0.15 –0.10 –0.05 0.00 0.05 0.10 0.15 0.20

Y velocity, in feet per second

Lower range

Upper range

EXPLANATION
Rating Development and Analysis 51

Table 14. Linear regression results for lower range of the compound-linear index rating. 

[R, correlation coefficient; R-square, coefficient of determination (also R2); ANOVA, analysis of variance; df, degrees of freedom; SS, sum of squares; 

MS, mean square; F, F-test statistic; Vi, Index velocity; t Stat, t-test statistic; P-value, Probability value for the regression coefficient; Lower 95%, lower value 

for 95% confidence limit; Upper 95%, upper value for 95% confidence limit]

Regression statistics

Multiple R 0.987846

R-square 0.975841

Adjusted R-square 0.971814

Standard error 0.051928

Observations 8

ANOVA

df SS MS F Significance F

Regression 1 0.6535 0.6535 242.3507 4.45E-06

Residual 6 0.016179 0.002697

Total 7 0.669679

Coefficients Standard error t Stat P-value Lower 95% Upper 95%

Intercept –0.05523 0.009134 –1.39867 0.21142 –0.15185 0.041392

Vi 1.089987 0.070016 15.56762 4.45E-06 0.918663 0.928695

Table 15. Linear regression results for the upper range of the compound-linear index rating. 

[R, correlation coefficient; R-square, coefficient of determination (also R2); ANOVA, analysis of variance; degrees of freedom; SS, sum of squares; MS, 

mean square; F, F-test statistic; Vi, Index velocity; t Stat, t-test statistic; P-value, Probability value for the regression coefficient; Lower 95%, lower value for 

95-percent confidence limit; Upper 95%, upper value for 95-percent confidence limit]

Regression statistics

Multiple R 0.906568

R-square 0.821865

Adjusted R-square 0.971814

Standard error 0.051928

Observations 6

ANOVA

df SS MS F Significance F

Regression 1 0.014382 0.014382 18.45486 0.012687

Residual 4 0.003117 0.000779

Total 5 0.017499

Coefficients Standard error t Stat P-value Lower 95% Upper 95%

Intercept 0.606467 0.095174 6.372214 0.003111 0.342222 0.870711

Vi 0.374471 0.087169 4.295912 0.012687 0.13245 0.616491

on simple-linear regression, the results of this analysis will 

be accepted, and the intercept will not be set to zero. 

For the upper part of the compound-linear rating, the 

R2 (R-square in table 15) is 0.82, and the standard error is 

0.05 ft/s (table 15), indicating a relatively accurate linear fit. 

The number of observations (6) for this group is less than 

the minimum recommended and contributes to the lower R2

value. The slope of the regression line (0.37) indicates that 

the index velocity tends to be much greater than the mean 

velocity, and the y-intercept is 0.61. The p-values for the 

index velocity slope (0.013) and the intercept (0.003) indicate 

that it is unlikely that either the slope or the intercept are equal 

to zero. Based on the analysis of the regression statistics, both 

sections of the rating can be used with reasonable confidence 

for the index rating even though the number of observations 

is less than recommended. Evaluation of regression plots is 

necessary to confirm this conclusion.

Regression analysis plots for the lower and upper sections 

of the compound-linear rating are shown in figures 32 and 

33, respectively. The predicted (computed) mean velocity for 
52 Computing Discharge Using the Index Velocity Method

A

B

EXPLANATION

–0.10

–0.08

–0.06

–0.04

–0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Index velocity, in feet per second

Residuals, in feet per second

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Measured-mean velocity, in feet per second

Measurements

Index rating

A

B

EXPLANATION

Index velocity, in feet per second

Residuals, in feet per second Measured-mean velocity, in feet per second

Measurements

Index rating

–0.05

–0.04

–0.03

–0.02

–0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.9

1.0

1.1

1.2

0.9 1.0 1.1 1.2 1.3 1.4

Figure 32. Plots of (A) measured-mean velocity and index 

velocity, and (B) regression residuals with index velocity 

for lower range of compound-linear rating example.

Figure 33. Plots of (A) measured-mean velocity and index 

velocity, and (B) regression residuals with index velocity for 

upper range of compound-linear rating example.

both segments appears to be a reasonable approximation of 

the measured-mean velocity (figs. 32A and 33A). Furthermore, 

although the plot of residuals with index velocity suggests 

that a trend is possible (figs. 32B and 33B), it is difficult to 

conclude that a trend exists because of the limited number 

of observations. Additional measurements are needed to 

determine whether or not a trend in the residuals exists. No 

trends in the residuals were evident in a plot (not shown) 

of residuals with the date/time of discharge measurements. 

The index rating equation for the lower range of velocities is 

expressed as:

mean velocity 1.09 index velocity 0.05. =∗ −

The index rating equation for the upper range of velocities is 

expressed as:

mean velocity 0.37 index velocity 0.61. =∗ +

(8)

(9)

Based on the results of the initial data plots (steps A-1 and 

A-2), regression analyses (steps C-2 and C-3), and examination of residual and regression plots (step C-4), it can be concluded that each of these ratings can be used for the applicable 

range of velocity for each rating. This conclusion is made 

while recognizing that additional measurements will lend confidence to the resulting ratings or perhaps change the ratings.

Two steps remain before the process of developing a 

compound-linear rating is complete: development of the 

transition between the two ratings (step C-5) and implementation of the compound-linear rating in ADAPS (step C-6). A 

transition between the two linear segments is created largely 

by trial and error while ensuring that the transition is smooth. 

The data for the two linear segments, their respective linear 

fits, and the data points used to establish the transition are 

shown in figure 34. Ideally, future measurements in this and 

other ranges of velocity will help provide better definition 

for the transition while confirming that the rating is indeed 

compound.
Rating Development and Analysis 53

Implementation of the compound-linear index rating is a 

little more complicated than implementation of a simple-linear 

index rating. A table was created (table 16) using data points 

from the two index ratings and data points that define the 

transition between the two rating segments. For this application, the rating was established as rating number 1 and entered 

into ADAPS. The process for entering the rating into ADAPS 

is described in the “Computation and Analysis of Discharge” 

section and in appendix 6 (Implementing an Index Rating).

Multiple-Linear Regression Rating

Sometimes graphical data analysis indicates that index 

velocity alone is not adequate to estimate a mean channel 

velocity at the site; therefore, a simple-linear regression index 

rating likely cannot be used to accurately predict mean channel 

velocity. For example, if site selection was less than ideal or 

some features of the river and flow distribution in the river 

were incompletely defined during the reconnaissance, then the 

index rating data may be nonlinear. An example of a nonlinear 

relation between index velocity and mean channel velocity is 

shown in figure 35, along with a simple-linear regression fit to 

these data for reference purposes. Nonlinearity between index 

and mean channel velocity often indicates that other independent variables should be included in the regression analysis. 

Nonlinearity also can be caused by improperly synchronized 

calibration data (Ruhl and Simpson, 2005, appendix E). In 

many cases, nonlinearity can be explained by the location of 

the index velocity measurement volume, a significantly large 

range in stage, upstream or downstream channel geometry, or 

a combination of these. 

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Index velocity, in feet per second

Measured mean velocity, in feet per second

EXPLANATION

Lower range

Transition range

Upper range

Figure 34. Two linear segments and the points used to define the 

transition between each segment for the compound-linear rating 

example.

Table 16. Data points used for implementation of the example compound-linear index rating. 

Input 

(Index velocity)

Output 

(Predicted 

mean velocity)

Comments

0 –0.05 Equation: Mean velocity = 1.09 * index velocity – 0.05 0.77 0.79

0.85 0.88 Transition point

0.88 0.91 Transition point

0.91 0.93 Transition point

0.92 0.94 Transition point

0.93 0.95 Equation: Mean velocity = 0.37 * index velocity + 0.61 1.40 1.13

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Index velocity, in feet per second

Measured-mean velocity, in feet per second

Measurements

Index rating

EXPLANATION

Figure 35. Plot showing curvature in the relation between 

index velocity and measured-mean velocity.
54 Computing Discharge Using the Index Velocity Method

The multiple-linear regression equation is of the form

1 2 , n y aX bX nX I error = + + ++

where

y = computed-mean velocity,

a,b,n = slope coefficients for each independent variable,

X1, X2, Xn = independent variables,

I = y intercept (defined where the regression line 

crosses the y-axis when all terms = 0), and

error = error around the regression line.

Again, for practical reasons, the error term in equation 9 is 

ignored when developing index ratings. 

Rating Development

The first step in using multiple-linear regression analysis 

is to plot the independent variables available for use in 

the regression equation with the measured-mean channel 

velocity and to analyze the plots (steps A-1 and A-2; fig. 23). 

Sometimes patterns in the plots of stage, cross-stream velocity, 

(10)

Vi2, and mean velocity will be evident. Examples of obvious 

patterns in plots of measured-mean velocity with stage and 

cross-stream velocity are shown in figure 36. Even when such 

patterns are evident (suggesting multiple-linear regression is 

required), simple-linear regression (steps B-1 to B-6) should 

be performed using measured-mean velocity data as the 

dependent variable (y input) and the index velocity data as the 

independent variable (x input). Performing the simple-linear 

regression allows for the comparison between residuals from 

the simple-linear regression and multiple-linear regression, 

which can indicate whether or not the use of the more complicated multiple-linear rating results in substantial improvement. 

Residual plots such as those shown in figure 37 can provide 

evidence of the need for multiple-linear regression and the 

independent variables that should be considered. 

The assumptions for multiple-linear regression are 

the same as with simple-linear regression, and the most 

important assumption is that the independent variables and the 

dependent variable or residuals are linearly related. Distinct 

curvature in the relation between any independent variable 

and the measured-mean velocity (fig. 36) can be addressed in 

Figure 36. Patterns in plots of (A) Y velocity and (B) stage with 

measured-mean channel velocity.

Figure 37. Patterns in plots of residuals from simple-linear 

regression with (A) downstream index velocity and (B) stage.

0

0.2

0.4

0.6

0.8

1.0

1.2

6.0 6.05 6.10 6.15 6.20 6.25 6.30 6.35 6.40

Stage, in feet

Measured-mean velocity, in feet per second

0

0.2

0.4

0.6

0.8

1.0

1.2

–0.25 –0.20 –0.15 –0.10 –0.05 0

Y velocity, in feet per second

A

B

–0.2

–0.2

–0.1

–0.1

0.0

0.0

0.1

0.1

0.2

0.2

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Index velocity, in feet per second

Residuals, in feet per second

6.0 6.05 6.10 6.15 6.20 6.25 6.30 6.35 6.40

Stage, in feet

A

B
Rating Development and Analysis 55

mean velocity index velocity

(index velocity stage) ,

a

b I

= ∗

+ ∗ ∗ +

where a and b are the slope coefficients for index velocity and 

index velocity multiplied by stage, respectively, and I is the y 

intercept. This form of an index rating (eq. 12) is also supported in the current (2011) version of ADAPS.

Based on the analysis of the scatter plots, the independent 

variables should be selected and the multiple-linear regression 

analysis performed. Then residual plots should be created 

(steps D-1 and D-2). The next step in the index rating flowchart (fig. 23) is to evaluate the regression statistics (step D-3). 

This step differs little from that for simple-linear regression 

analysis, except that additional independent variable(s) need 

to be evaluated and included in the plots. When the regression equation has the form of equation 12, sometimes the 

regression statistics (p-value especially) may indicate that the 

coefficient for the index velocity variable is not statistically 

significant. However, if the coefficient for the index velocity 

variable in the simple-linear regression equation is statistically 

significant, then the index velocity variable should be included 

in the multiple-linear regression. After the regression statistics 

are evaluated and residual plots created and examined 

(step D-4), the hydrographer should determine whether the 

multiple-linear regression index rating is significantly more 

accurate than the simple-linear regression rating (step D-5). 

The improvement in accuracy with multiple-linear regression 

can be evaluated by comparing the standard errors and 

residual plots from the multiple-linear and the simple-linear 

regression analyses. Comparison of the residuals may or may 

not confirm the standard error comparison. The comparison 

of the results from multiple-linear regression with the results 

from simple-linear regression is important because the results 

from multiple-linear regression may yield only marginal 

improvements in accuracy. If so, the hydrographer may choose 

to use the simple-linear regression index rating because the 

gain in accuracy achieved with multiple-linear regression may 

not be substantially better than the simple-linear rating results. 

If a multiple-linear regression has been identified as a possible rating but not used due to no apparent improvement in 

accuracy, the multiple-linear regression option should continue 

to be evaluated as a possible rating as more measurements 

are made. Once a decision is made about the type of rating to 

be used, the multiple-linear or simple-linear rating must be 

implemented in ADAPS or in an external script file.

(12)

a number of ways. One way is to try a transformation of the 

variables similar to a stage-discharge rating where plotting the 

logarithm of stage versus the logarithm of discharge changes 

the relation from nonlinear to linear. Suitable transformations 

appropriate for hydraulic conditions are discussed in Helsel 

and Hirsch (2002, p. 228–229) and Riggs (1968, p. 10–11). A 

discussion of all possible transformations is beyond the scope 

of this report, and experience to-date (2011) has shown that 

they are often unnecessary.

A common multiple-linear regression application at index 

velocity sites is one in which stage is a factor in addition to 

index velocity. The change in stage, in such instances, can 

be great enough to cause a change in the relation between 

the index velocity and the measured-mean channel velocity. 

This dependency on stage is most common with sidelooker 

ADVMs, but can also be important with uplooker ADVMs. 

For example, the channel geometry upstream from an ADVM 

may cause flow to be concentrated in an area of the ADVM 

cross section at lower stages, but at higher stages the upstream 

geometry has little or no discernable effect on the horizontal 

flow distribution. This effect may not be noticed by the 

hydrographer until sufficient discharge measurements are 

available to cover the full range of stage and velocities or until 

the hydrographer evaluates the rating using regression analysis 

with multiple independent variables. 

It is relatively common in index rating applications 

requiring multiple-linear regression that index velocity 

and stage are multiplied together and used as an additional 

independent variable along with index velocity. Statistical 

methods normally dictate that when performing multiplelinear regression analysis in which two independent variables 

are multiplied together, each of these independent variables 

should be included as separate variables in the regression 

analysis with the conjoined variable (stage multiplied by index 

velocity). Equation 10 provides a generalized form for such a 

regression equation, in which 

mean velocity index velocity stage

(index velocity stage) ,

a b

c I

= ∗ + ∗

+ ∗ ∗ +

and a,b, and c are the slope coefficients for each variable, and 

I is the y intercept. However, analysis of numerous data sets 

has shown that the stage variable alone (b*stage) typically 

is not statistically significant. Furthermore, the physics of 

the flow would indicate that when the index velocity equals 

zero, the mean velocity in the channel also should be equal 

to, or nearly equal to, zero. Therefore, the common form for 

an index rating developed using multiple-linear regression in 

which stage is a factor is 

(11)
56 Computing Discharge Using the Index Velocity Method

Example of a Multiple-Linear Rating

The development of a multiple-linear index rating is 

illustrated in the following example. Twenty-two discharge 

measurements were available for developing the rating. 

Measured-mean velocities ranged from 0.25 to 1.15 ft/s, 

and the corresponding index velocities ranged from 0.44 

to 1.24 ft/s. Plots of index velocity, stage, and cross-stream 

velocity with mean velocity are shown in figure 38. The plot 

of index velocity and measured-mean velocity (fig. 38A) 

shows a general linear relation between the two variables with 

some divergence at a mean velocity of about 0.8 ft/s, indicating that another variable may be related to mean velocity. A 

strong linear relation between mean velocity and stage can be 

seen in figure 38B, and figure 38C shows that mean velocity 

and cross-stream velocity do not appear to be linearly related. 

In this example, 22 discharge measurements were available 

for developing the rating. Plots of multi-cell velocity data 

(X velocity) and measured-mean velocity (not shown) did 

not indicate any substantial difference between multiple cell 

velocities and range-averaged velocity. 

Simple-linear regression was performed using index 

velocity as the only independent variable to provide a baseline 

for comparison with results of the multiple-linear regression 

(steps B-1 to B-6). The results of the simple-linear regression 

for this sample dataset are shown in table 17. The R2 is 0.89, 

indicating that the index rating explains 89 percent of the 

variance in mean velocity. This R2 is somewhat less than 

ideal, but is nevertheless acceptable. The standard error for the 

simple-linear rating is 0.08 ft/s, which is a little greater than 

desired, but is still acceptable, indicating a reasonable linear 

fit. The slope of the regression line (1.00) indicates a one-toone relation between index velocity and the mean velocity. 

The p-value for the index rating slope (4.92E-11) indicates 

that it is unlikely that the slope is equal to zero and the same is 

true for the intercept. 

A

B

C

0.0

0.0

0.0

0.2

0.2

0.2

0.4

0.4

0.4

0.6

0.6

0.6

0.8

0.8

0.8

1.0

1.0

1.0

1.2

1.2

1.2

1.4

1.4

1.4

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Index velocity, in feet per second

Measured-mean velocity, in feet per second

Stage, in feet

–0.15 –0.10 –0.05 0.00 0.05 0.10 0.15

Y velocity, in feet per second

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

Figure 38. Plot of (A) measured-mean velocity, (B) stage, 

and (C) Y velocity with index velocity for multiple-linear 

rating example.
Rating Development and Analysis 57

Table 17. Results of simple-linear regression for the multiple-linear rating example. 

[R, correlation coefficient; R-square, coefficient of determination (also R2); ANOVA, analysis of variance; df, degrees of freedom; SS, sum of squares; MS, mean 

square; F, F-test statistic; Vi, Index velocity; t Stat, t-test statistic; P-value, Probability value for the regression coefficient; Lower 95%, lower value for 95-percent 

confidence limit; Upper 95%, upper value for 95-percent confidence limit]

Regression statistics

Multiple R 0.94328

R-square 0.889777

Adjusted R-square 0.884266

Standard error 0.082824

Observations 22

ANOVA

df SS MS F Significance F

Regression 1 1.107527 1.107527 161.4498 4.92E-11

Residual 20 0.137198 0.00686

Total 21 1.244724

Coefficients Standard error t Stat P-value Lower 95% Upper 95%

Intercept –0.17277 0.075673 –2.28306 0.033502 –0.33062 –0.01492

Vi 0.996586 0.078433 12.70629 4.92E-11 0.832979 1.160194

Regression analysis plots for the simple-linear rating 

are shown in figure 39. Although the predicted (computed) 

mean velocity appears to be a reasonable approximation of 

the measured-mean velocity (fig. 39A), the variability of the 

mean velocity and index velocity is greater than desired over 

the measured range. Despite this, no trends are apparent in 

the plot of residuals with index velocity (fig. 39B) nor in the 

plot of residuals with date/time of measurement (fig. 39C). 

Figures 39A and B do indicate a lack of measurements in 

the range between 0 and 0.6 ft/s. The index rating equation 

developed using simple-linear regression is expressed as:

mean velocity 1.00 index velocity 0.17. =∗ −

Although the analysis up to this point has produced 

an apparently acceptable index rating, the graphical data 

analysis has already shown that a distinct correlation between 

mean velocity and stage exists (fig. 38B). For this reason, 

multiple-linear regression analysis was performed using 

index velocity and stage multiplied by index velocity as 

independent variables. The results of this subsequent analysis 

are summarized in table 18 and in figure 40. The adjusted R2

(adjusted R-square) and the standard error of the regression 

(for multiple-linear regression with index velocity and stage 

multiplied by index velocity) are noticeably improved over 

the values for simple-linear regression (table 17). The adjusted 

R2, 0.93, is greater than the R2 for the simple-linear regression. When evaluating statistical output for multiple-linear 

regression, the hydrographer should evaluate the adjusted R2

rather than R2, even though both variables are presented. R2

will always increase as more terms are added to the regression 

equation. The adjusted R2 accounts for the number of variables 

(13)

introduced to the regression and penalizes a regression for the 

addition of explanatory variables which do not add predictive 

value to the regression. As such, the adjusted R2 is a better 

evaluation tool because it increases only if the addition of the 

new term results in a statistically significant improvement. 

Furthermore, the standard error of the regression 

decreased slightly from 0.08 ft/s to 0.06 ft/s. The coefficients 

for the intercept, index velocity, and stage multiplied by index 

velocity are now 0.16, 0.82, and –0.15, respectively (table 18). 

The p-values for each of the coefficients (table 18), with the 

possible exception of the intercept, indicate that the values of 

the coefficients are reasonable estimates and are unlikely to 

be equal to zero. The p-value for the intercept is larger than 

desired (0.10), but for reasons stated earlier, the intercept value 

(0.16) should still be used in order to more accurately estimate 

mean velocity. The index rating equation is then expressed as:

mean velocity 0.82 index velocity

0.15(stage index velocity) 0.16.

= ∗

−∗ +

Some of the plots used to analyze the results of this 

multiple-linear regression are shown in figure 40. (For the 

present example, not all of the plots routinely created for 

evaluating regression results are shown, but they should be 

created and reviewed by the hydrographer.) A comparison of 

the multiple-linear regression results with the simple-linear 

regression results also is shown in figure 40C. The plot of 

computed mean velocity and measured-mean velocity, which 

includes the combined effect of using index velocity and stage 

multiplied by index velocity, is shown in figure 40A. The plot 

of residuals with stage multiplied by index velocity (fig. 40B) 

shows no trends. The variation in the residuals (fig. 40C) is 

(14)
58 Computing Discharge Using the Index Velocity Method

Figure 40. Plots of (A) measured-mean velocity with 

computed mean velocity and residuals with (B) stage 

multiplied by index velocity and (C) index velocity for 

multiple-linear regression using index velocity and stage 

multiplied by index velocity as independent variables. 

A

B

C

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Measured-mean velocity, in feet per second

EXPLANATION

–0.20

–0.15

–0.10

–0.05

0.00

0.05

0.10

0.15

0.20

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Index velocity, in feet per second

Residuals, in feet per second

Measurements

Rated velocity

Index rating

–0.20

–0.15

–0.10

–0.05

0.00

0.05

0.10

0.15

0.20

J J A A S S O O N N D D J J F F M M A A M M J J

2008 2009 2010

Figure 39. Plots of (A) measured-mean velocity and predicted 

mean velocity and regression residuals from simple-linear 

regression with (B) index velocity and (C) measurement date 

for multiple-linear regression example.

A

B

C

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Index velocity, in feet per second

Measured-mean velocity, in feet per second

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

EXPLANATION

Computed mean velocity, in feet per second

–0.20

–0.20

–0.15

–0.15

–0.10

–0.10

–0.05

–0.05

0.00

0.00

0.05

0.05

0.10

0.10

0.15

0.15

0.20

0.20

Residuals, in feet per second

Multiple-linear rating

Simple-linear rating

0 0.50 1.00 1.50 2.00 2.50

Index velocity multiplied by stage, in square feet per second

EXPLANATION

Measurements

Index velocity
Rating Development and Analysis 59

Table 18. Multiple-linear regression results using index velocity and stage multiplied by index velocity as the independent variables for

the multiple-linear rating example. 

[R, correlation coefficient; R-square, coefficient of determination (also R2); ANOVA, analysis of variance; df, degrees of freedom; SS, sum of squares; 

MS, mean square; F, F-test statistic; Vi, Index velocity; Velx*Stage, index velocity multiplied by stage; t Stat, t-test statistic; P-value, Probability value for the 

regression coefficient; Lower 95%, lower value for 95% confidence limit; Upper 95%, upper value for 95% confidence limit]

Regression statistics

Multiple R 0.967618

R-square 0.936284

Adjusted R-square 0.929577

Standard error 0.064607

Observations 22

ANOVA

df SS MS F Significance F

Regression 2 1.165416 0.582708 139.6 4.37E-12

Residual 19 0.079308 0.004174

Total 21 1.244724

Coefficients Standard error t Stat P-value Lower 95% Upper 95%

Intercept 0.164684 0.096255 1.710909 0.103376 –0.03678 0.366148

Vi 0.821397 0.071668 11.46108 5.61E-10 0.671393 0.971401

Vi*Stage –0.1519 0.034217 –4.4394 0.000281 –0.22352 –0.08029

slightly less when using multiple-linear regression, confirming the observed reduction in the standard error. Therefore, it can be concluded that the multiple-linear regression 

rating using index velocity and index velocity multiplied 

by stage as independent variables (equation 13) is a more 

accurate method for estimating mean velocity and computing discharge than equation 12. The multiple-linear regression results (table 18) should be used as the index rating for 

this example (step D-6). This conclusion is based on (1) the 

improved fit of the regression when using index velocity 

and stage multiplied by index velocity when compared to 

simple-linear regression (table 17) and (2) the observed 

correlation between mean velocity and stage. 

Implementation of this multiple-linear index rating in 

ADAPS is accomplished by means of the ADAPS discharge 

processor feature. Table 19 summarizes the regression coefficients, the ADAPS rating equation prompts, and user entries 

from ADAPS for implementing this sample rating. The 

process for entering the rating into ADAPS is described in 

the “Computation and Analysis of Discharge” section and in 

appendix 6 (Implementing an Index Rating). Appendix 6 also 

provides a sample Perl script that can be used as a template to 

implement complex ratings outside of ADAPS. The limitation 

of implementing a multiple-linear rating using either ADAPS 

or the external Perl script is that the history of changes to the 

ratings is lost unless the hydrographer creates a document that 

includes the index ratings that are used over time.

Table 19. Multiple-linear regression coefficients used for implementing the example of 

a multiple-parameter rating in ADAPS.

[Vi, Index velocity; Velx*Stage, index velocity multiplied by stage]

Regression 

parameter

Regression 

coefficients

ADAPS 

equation 

parameter1

Explanation of ADAPS 

equation parameter

User 

input2

EQ Use mean-velocity equation Yes

Intercept 0.16 XC Equation X coefficient 0.82

Vi 0.82 YC Equation Y coefficient –0.15

Velx*Stage –0.15 EC Equation constant 0.16

1

Prompts from the U.S. Geological Survey ADAPS database software for entering the multipleparameter rating.

2

User response to ADAPS prompts.
60 Computing Discharge Using the Index Velocity Method

Rating Validation

After the stage-area and index ratings have been 

determined and implemented for the continuous computation 

of discharge, the ratings need to be continually validated to 

document possible changes over time. If rating changes occur, 

validation data will be used to modify an existing rating or 

to create a new rating. It is not straightforward to determine 

when the calibration of the index rating ends and the validation begins. Once a rating is developed and implemented, 

any discharge measurements made after that time should 

first be used to check the rating. Then they should be added 

to the calibration data so that a new regression analysis can 

be performed to check for significant changes in the slope or 

intercept coefficients compared to the initial rating. 

After additional discharge measurements have been 

collected, the same rationale used to evaluate stage-discharge 

ratings generally applies when considering whether a new 

rating is warranted or not. Some quotations from Rantz 

and others (1982b, p. 553 and p. 344–345, respectively) 

concerning stage-discharge ratings are helpful when analyzing 

whether or not an index rating has changed. 

When discharge measurements depart from the rating curve by more than 5 percent, but the indicated 

change in rating is short-lived—less than a month or 

two—it is common practice not to establish a new 

rating curve, as such, for the short period. Instead, 

gage height shifts (adjustments) are applied either 

to the rating in use prior to the period of shifting 

control or to a new rating, if one is later needed, 

that is established for use starting with the period of 

shifting control.

If a specific change in the rating stabilizes to the 

extent of lasting for more than a month or two, a 

new rating curve is usually prepared for the period 

of time during which the new stage-discharge relation is effective.

Stage-discharge relations are usually subject to 

minor random fluctuations resulting from the 

dynamic force of moving water, and because it is 

virtually impossible to sort out those minor fluctuations, a rating curve that averages the measured discharges within close limits is considered adequate. 

Furthermore, it is recognized that discharge measurements are not error-free, and consequently an 

average curve drawn to fit a group of measurements 

is probably more accurate than any single measurement that is used to define the average curve. If a 

group of consecutive measurements subsequently 

plot to the right or left of the average rating curve, it 

is usually clearly evident that a shift in the rating has 

occurred.

With many index ratings, the hydrographer can also make 

use of the standard error regression statistic and residual plot 

to compare the original rating to a proposed new rating. If a 

new rating (from the addition of new measurements to the 

rating analysis) shows a substantial reduction in the standard 

error and an improvement in the scatter and distribution 

of residuals, a new rating may be indicated. However, the 

hydrographer should not rely on comparisons of standard 

error only, but should base the decision on sound hydraulic 

principles and other pertinent information. It is important to 

document the rationale used to arrive at a decision, especially 

when it is not clear that a substantial improvement will be 

made with the new rating. 

If a validation measurement is within a reasonable error 

range (usually no more than the standard error associated with 

the initial rating), then the validation measurement should 

not be used immediately to refine the rating. This allows the 

hydrographer to determine if the rating has changed over 

time. For example, if the first validation measurement after 

the implementation of an index rating plots slightly above the 

regression line and then a second measurement made at a later 

date also plots above the regression line, indications are that 

the rating has not been completely defined or a change has 

occurred in the stream. If both of the validation measurements 

plot above the regression line but are within the standard 

error of the rating, then the two measurement points may not 

provide enough evidence to indicate a change in the rating. 

This is similar to a standard stage-discharge rating where 

measurements are continually made and a decision is made to 

(1) leave the rating unchanged, (2) apply a temporary shift to 

the rating, or (3) create a new rating. Temporary shifts to the 

index rating can be difficult to apply, but may be implemented 

using techniques described in appendix 7. Shifts are not 

typically applied in tidally affected streams. When discharge 

measurements diverge from the index rating, the hydrographer 

should make every effort possible to identify and document 

the cause of the divergence. In some cases, the cause may not 

be readily apparent until additional measurements can be made 

and site conditions can be observed. 

The steps involved in validating the rating are similar 

to the steps required for the rating calibration. Checking the 

index rating requires the same procedure as used for calibration discharge measurements described previously. Discharge, 

index velocity, and stage data are collected, the data are 

synchronized and synthesized, and the measured-mean velocity (from the discharge measurements) and the index velocity 

are plotted with the original calibration data on the index 

plot. The validation residuals are computed by subtracting 

the computed-mean velocity (from the index rating) from the 

measured-mean velocity and adding the values to the rating 

residual plots. Ideally, the measured-mean velocity from the 

validation measurement will be very similar to the computed 

mean velocity and within the residuals of the index rating. 

Figure 41 shows the range of residuals from the original rating 

(dashed and dotted lines) about the rating (solid line), along 

with subsequent validation measurements. 

The scatter plot of the validation data in figure 41 indicates that the validation measurements are reasonable because 
Computation and Analysis of Discharge 61

they generally plot near the regression line. The residuals plot 

also indicates that the validation measurements have no readily discernible pattern and are within the existing error range 

of the calibration measurements because the residuals of the 

validation measurements are no greater than the residuals of 

the regression. Any time the measured-mean velocity deviates 

substantially from the existing index rating, the discharge and 

index data should be checked for errors. If no errors are found 

in the measured data, and several discharge measurements are 

indicating a possible rating change, then the stage-area rating 

should be verified. If it is determined that the validation data 

do deviate substantially from the existing index rating, then a 

temporary shift may be implemented as described in appendix 

7, and the process for developing a new index rating may be 

considered. It may be determined that the index rating shift is 

only temporary by evaluating subsequent measurements and 

observations of channel conditions. 

Computation and Analysis of Discharge

The final step in the index velocity method is the computation of discharge. Most of the effort to compute records of 

discharge using the index velocity method is spent on obtaining an accurate stage and velocity record and the development 

and maintenance of the stage-area and index ratings. Once the 

stage-area rating and the index rating have been developed, the 

ratings are used to compute continuous records of discharge. 

Most often these ratings must be entered into a computer 

program that can be used to compute a continuous time series 

of discharge. In the USGS, ADAPS is the most common 

program used to enter and maintain the ratings and other 

ancillary information and to compute discharge records. 

The steps for implementing a stage-area rating in ADAPS 

are as follows.

1. Enter the NWIS system and start ADAPS.

2. Select the station and discharge data descriptor for 

the rating to be implemented.

3. Select the stage-area rating option, and then enter 

the rating identification number.

4. Select the rating expansion type (linear, log, or 

expansion). Usually the rating expansion type will 

be linear. During this step, enter remarks about the 

rating.

5. Enter the points that define the stage-area rating. 

Usually these points are available as output from 

AreaComp or other software used to develop the 

stage-area rating.

6. Save the stage-area rating and enter the dates and 

times for which the rating is effective.

7. Retrieve the rating that was saved in step 6 and 

verify that there are no data entry errors and that 

the version of the rating stored in NWIS correctly 

represents the one that was developed for this site. 

8. Store a copy of the new rating in the station 

folder/database.

A detailed example of how to implement a stage-area rating in 

NWIS is provided in appendix 6. 

For an index rating, the steps for implementing the rating 

in the records computation software are as follows.

1. Enter the NWIS system and start ADAPS.

2. Select the station and discharge data descriptor for 

the rating to be implemented. 

3. Select the velocity rating option and enter the rating 

identification number.

4. For a simple-linear equation, select the equation 

option for the rating expansion type. Alternatively, 

the user may select the linear expansion option. This 

linear expansion option is more often used for index 

ratings that have more than one slope (such as with 

compound ratings).

Figure 41. Scatter plot and residuals plot for validation 

measurements.

A

B

EXPLANATION

Index velocity, in feet per second

Validation

 measurements

Rating

Lower

Upper

EXPLANATION

Validation

 measurements

Extent of regression

 residuals

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

dnoces r ept eef in , yti c lo ev nae -mder usae M

–0.10

–0.02

0

0.02

0.06

0.10

–0.04

–0.06

–0.08

0.04

0.08

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

yti c lo ev nae -mder usae M su in m y, ti c lo ev det ar

r ept eef in dnoces

Figure 41. Scatter plot and residuals plot for validation 

measurements.
62 Computing Discharge Using the Index Velocity Method

5. Enter the index rating equation slope and offset if 

the equation option was selected in step 4. If the 

linear expansion option was chosen instead, enter 

the points (minimum of two pairs of X and Y values 

for simple-linear rating) that define the index rating.

6. Enter the dates and times for which the rating is 

effective. 

7. Retrieve a copy of the rating entered, using the 

expanded rating table option, and verify that the 

rating stored in ADAPS correctly represents the 

index rating that was developed. When using 

compound-linear ratings (linear ratings with more 

than one slope), check the transition of the rating 

from one linear rating segment to the other linear 

rating segment.

8. Store a copy of the expanded rating table in the 

station folder/database.

Detailed examples of how to implement index ratings in 

NWIS are provided in appendix 6, including examples of a 

simple-linear rating, a compound-linear rating, and a 

multiple-linear rating that use index velocity and index velocity multiplied by stage. An alternative method of implementing a complex rating outside of ADAPS is by means of a Perl 

script run automatically. A sample Perl script and instructions 

for implementing the script are provided in appendix 6. The 

Perl script can be used with slight modifications to implement 

a rating that will compute mean velocity and store the output 

in NWIS.

Typically, the extent of the rating should reflect the 

range of flow conditions for which discharge measurements 

are available for defining the rating; however, discharge 

measurements may not be available for the range of index 

velocities measured in a given year. Of course, this usually 

is the case for the rating extremes (high or low velocities). It 

may be necessary to extend the index rating beyond the range 

of points available for defining the rating, but this should be 

done with care. For index ratings, the rating should not be 

extrapolated more than two times the maximum measured 

velocity provided that overbank flow does not occur. If 

overbank flow does occur, the slope of the index rating likely 

would change; therefore, a substantial error in computed 

discharge could result if that range of conditions is not defined 

by the rating. The slope of the index rating can change because 

the cross-sectional flow area (for example a flood plain) is now 

significantly different once flow is out of bank. This recommendation is similar to that for extending a stage-discharge 

rating (Rantz and others, 1982b, p. 334). 

When discharge measurements indicate a substantial 

difference from the rating discharge, it may be necessary at 

times to apply a shift to the index rating. The hydrographer 

must thoroughly analyze the discharge measurement and the 

rating itself to determine whether or not the measured velocity 

falls within the error bounds of the rating. Consideration 

also must be given to the overall accuracy of the discharge 

measurements. At present (2011) an objective technique for 

computing the uncertainty of ADCP discharge measurements 

has not been developed; however, techniques for computing 

the uncertainty of current meter and FlowtrackerTM discharge 

measurements are available. The uncertainty for discharge 

measurements made with these instruments should be used to 

guide the rating analysis. Although application of a shift to an 

index velocity record may be necessary, little or no shifting 

will be necessary for many sites. Usually shifting should only 

be done when there is a logical explanation for the temporary 

change in the rating based on observations at the station before 

or after the discharge measurement or when strong inferences 

are available in records. Low-flow discharge measurements 

may have a large uncertainty, and great care should be used 

when considering shifts for such flow conditions. Additional 

low-flow measurements or a trend in low-flow measurements 

will greatly aid decisions on shifts or rating changes at low 

flow. Appendix 7 contains discussion about the application of 

shifts in more detail. 

The computation of the discharge records follows most 

of the same (or at least similar) steps as those used for a 

stage-discharge gaging station (Rantz and others, 1982b, 

p. 544–599). For each water year or record computation 

period, a daily record of discharge, a time series of instantaneous values of discharge for the period of record computation 

(for example, 5 or 15 minutes), instantaneous values of peak 

discharge, and minimum flow are computed for the gaging 

station. A brief overview of the steps for computing and 

documenting discharge records follows. 

1. A station analysis should be prepared by the hydrographer before the actual computation of discharge 

has begun. The station analysis should provide 

at least a clear understanding of how the records 

were computed, information about adjustments that 

were made, information about the performance of 

the stage and index velocity sensors, methods used 

to estimate missing record, the range of stage and 

index velocity encountered during the period, and 

the range of stage and index velocity used for the 

index rating. An example of a station analysis is 

provided in appendix 8.

2. The stage record should be reviewed and stage and 

datum corrections applied as necessary. 

3. The stage-area and index rating should be reviewed 

for applicability to the current record computation 

period. For a new rating, this will involve a review 

of the ratings that have been implemented in 

ADAPS. For existing ratings, the rating verification 

(as described in a previous section) will already have 

been completed. The primary purpose of this step is 

to ensure that the rating is applicable to the range of 

conditions observed throughout the period.
Summary and Conclusions 63

4. In the unlikely event that a shift is required, the period 

for the application of the shift should be defined 

and the shift entered into NWIS. These are actually 

applied as data corrections to velocity in ADAPS.

5. NWIS should be used to convert instantaneous stage 

and index velocity data into instantaneous discharge 

values. The daily mean discharge is computed as a 

24-hour average of instantaneous values for non-tidal 

gaging stations. Discharge records for tidally affected 

sites should be computed following techniques 

outlined by the U.S. Geological Survey (2010c). The 

output from the computations, known as the primary 

computations, should be reviewed to ensure that the 

maximum, minimum, and mean stages, velocities, 

and discharges are correctly computed, that the 

stage and datum corrections and shift corrections are 

correctly applied, and that the daily mean discharges 

and discharge statistics are correct. 

6. Hydrographic comparison of the resulting discharge 

record should be made with suitable nearby gaging 

station records. Typically, daily mean discharges are 

plotted with records from nearby gaging stations, 

and the plot is examined for inconsistencies and 

anomalies. If possible, all anomalous periods should 

be estimated. Statistical methods for hydrographic 

comparison and estimation of discharge records also 

may be used. The instantaneous records of discharge 

(sometimes referred to as unit-value discharges) 

also should be reviewed. Particular attention should 

be paid to those periods where a change in rating 

occurs or where shifts (if any) are applied. When 

a compound index rating is used, examine the 

unit-value discharge records for those periods where 

the rating transition(s) occur.

7. The station analysis should be updated to reflect the 

final discharge computation process and any changes 

to the record that have been made, such as the 

results of hydrographic comparison.

8. The discharge records are prepared for publication 

on the Internet using guidelines established by the 

USGS. 

9. A file, electronic or otherwise, should be maintained 

containing all pertinent documentation for the record 

computation period. This file will contain such 

things as all field notes, inspection and discharge 

measurement notes, the current station description, 

the station analysis, a summary of discharge 

measurements, a stage-area and index rating, the 

primary computation sheet, and the final table of 

daily mean discharges for the record computation 

period. The file may also contain copies of plots of 

stage, velocity, and discharge records and any other 

data or information used to compute records of 

discharge. 

The USGS is in the process of implementing continuous 

records processing (CRP) in accordance with USGS, WRD 

Policy Numbered Memorandum No. 2010.02 (U.S. Geological 

Survey, 2010a). Index velocity stations are not exempt from 

CRP requirements. Each WSC is developing WSC-specific 

guidelines for the processing of index velocity records as a 

part of the CRP.

Summary and Conclusions 

Application of the index velocity method for computing 

continuous records of discharge has become increasingly 

popular, especially since the introduction of low-cost acoustic 

Doppler velocity meters (ADVMs) in 1997. Presently (2011), 

the index velocity method is being used to compute discharge 

records for approximately 470 gaging stations operated and 

maintained by the U.S. Geological Survey (USGS). Index 

velocity gaging stations are operated in order to compute 

records of discharge in tidal and estuarine environments, at 

locations where the flow changes rapidly, and where variable 

backwater conditions occur. In this report, the techniques for 

computing discharge records using the index velocity method 

are described. 

Computing discharge using the index velocity method 

differs from traditional stage-discharge methods by separating 

velocity and area into two ratings—the index rating and the 

stage-area rating. The outputs from each of these ratings 

(V and A) are then multiplied together to compute a discharge. 

For the index velocity method, V is a function of such parameters as streamwise velocity, stage, cross-stream velocity, and 

velocity head, and A is a function of stage and cross-section 

shape. The index velocity method can be used when more 

than one specific discharge can be measured for a specific 

stage. 

Choosing the location of the index velocity meter 

(ADVM) is perhaps the most important step in accurately 

implementing the index velocity method and includes 

thorough reconnaissance of flow conditions and velocity 

distributions. Once a suitable location has been selected using 

site reconnaissance techniques, an ADVM can be selected and 

installed. The ADVM must be located in an area of the channel 

cross section where section velocity can be measured reliably 

and a stable relation between the index velocity measured by 

the ADVM and the mean channel velocity can be obtained. 

Acoustic Doppler current profiler (ADCP) discharge and 

velocity reconnaissance measurements are useful in helping to 

find suitable locations. In some cases, when a suitable location 

is not readily apparent, it may be necessary to temporarily 

deploy an ADVM to obtain a short-term index velocity record 

and to analyze that record in conjunction with discharge and 

velocity measurements made in the cross section. 

Once a site has been chosen, the ADVM should be 

appropriately positioned and mounted, and the ADVM and 

stage sensor must be properly configured to measure the flow 
64 Computing Discharge Using the Index Velocity Method

characteristics of the river, stream, or canal. The ADVM 

should be mounted in such a way that it is easy to service, 

accurately measures the index velocity, is able to measure 

throughout a range of stages and velocities, is not subject 

to damage by debris or other factors, and is not subject to 

interference or flow disturbance. Considerations for uplooker 

ADVMs are somewhat different than for sidelooker ADVMs. 

For example, uplooker ADVMs tend to be more susceptible 

to damage to the cable connecting the ADVM to the data 

logger. In some cases, a diver is required for installation and 

maintenance. The orientation of the uplooker ADVM is crucial 

to obtaining accurate index velocity data.

The measurement interval and averaging period of the 

ADVM must be appropriately configured to measure the flow 

response (hydrograph). The stage sensor measurement interval 

and averaging period must also be configured to accurately 

measure the stage at the site during the time the ADVM is 

measuring velocity. Techniques for locating and configuring 

the ADVM include but are not limited to analysis of (1) historical records of streamflow if available, (2) velocity data from 

temporary deployments or ADCP measurements, (3) beam 

checks, and (4) initial velocity time-series data. Particular 

attention needs to be paid to the selection of the measurement 

interval and averaging period so that the resulting time 

series is not aliased. The hydrographer should determine the 

optimum sampling interval for the site in question. When 

possible, the ADVM should be configured to store data in its 

internal recorder, in addition to sending data to the data logger 

for real-time transmission and storage in the database.

Operation and maintenance of the ADVM and the 

stage measurement sensor are crucial to obtaining accurate 

index velocity records. Routine site visits should always 

include beam checks, an independent water temperature 

measurement (for comparison with the ADVM-measured 

water temperature), and an ADVM clock check. The ADVM 

should be raised and cleaned at appropriate intervals. Data 

from the internal recorder (if available) should be downloaded 

and reviewed during every site visit and then stored in the 

USGS Water Science Center’s data archives. Downloaded and 

telemetered index velocity data should also be reviewed in the 

office on a routine basis.

Two ratings are required to compute a continuous record 

of discharge: a stage-area rating and an index rating. Channel 

cross-section survey measurements are used with stage data 

to develop and verify a stage-area rating. A cross section, 

known as the standard cross section, near the gaging station 

is selected based on specific criteria. The stage-area rating is 

developed for that cross section using traditional land-survey 

methods, ADCPs, soundings, or some combination thereof, 

and software such as AreaComp. The standard cross section 

should be re-surveyed annually for the first 3 years. After 3 

years, the frequency of re-surveys can be reduced to that used 

for gaging station levels (typically 3 years) provided certain 

conditions are met.

Periodic measurements of discharge are required in order 

to calibrate and validate the index rating for the range of 

conditions at the gaging station. When measuring discharge, 

the ADVM and stage sensor should be configured for a 

measurement interval of 60 seconds and an averaging period 

of 60 seconds. Care needs to be taken to accurately synchronize discharge measurement times with the ADVM clock. This 

is especially important when measuring unsteady flows. 

Discharge measurements are used with concurrent 

stage data, the stage-area rating, and index velocity data to 

develop an index rating. After discharge measurements have 

been made, the data from these discharge measurements, the 

ADVM, and the stage sensor must be compiled. As a part of 

this compilation, the hydrographer must make sure that the 

times for each instrument and for the discharge measurements 

are synchronized. Ratings are developed by means of regression techniques in which the mean cross-sectional velocity 

(for the standard section) is related to the measured index 

velocity. Most ratings are simple-linear regressions; however, 

in some cases, compound-linear or multiple-linear regression 

techniques may be necessary. Once the rating is established, 

validation measurements should be periodically made according to a previously defined interval. Over time, these measurements may provide additional definition to the rating, resulting 

in a new rating or refinement of the original rating.

The last step in the index velocity method is the 

computation of discharge. In many ways, this is similar to 

record computation for stage-discharge gaging stations. Index 

velocity stations differ from stage-discharge stations in that 

two ratings must be developed and maintained. The ratings 

must be entered into the database software [(USGS National 

Water Information System (NWIS)] used for computing 

records of discharge. After entering the ratings and defining 

the time periods for which they are effective, the hydrographer 

is ready to compute continuous records of discharge. The 

discharge computation process involves not only the execution 

of primary computation in the NWIS software but also the 

development of documentation (station analysis, plots of data, 

summaries of measurements, etc.), computation of extremes 

for the period-of-record computation, and estimation of 

discharge for period of missing records if necessary. 

References

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Streamflow Information Program: U.S. Geological Survey 

Fact Sheet 2007–3080, 6 p. 

Callow, M.E., and Callow, J.E., 2002, Marine biofouling—A 

sticky problem: The Biologist, v. 49, no. 1, p. 10–14.
References 65

Chambers, J.M., Cleveland, W.S., Kleiner, B., and Tukey, 

P.A., 1983, Graphical methods for data analysis: New York, 

Chapman and Hall, 395 p.

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

water resources: U.S. Geological Survey Techniques of 

Water-Resources Investigations, book 4, chap. A3, 522 p., 

accessed July 25, 2010, at http://pubs.usgs.gov/twri/

twri4a3/pdf/twri4a3-new.pdf.

Hughes, W.F., and Brighton, J.A., 1991, Theory and problems 

of fluid dynamics: Schaurns Outline Series, McGraw-Hill, 

344 p.

Laenen, A., and Smith W., 1983, Acoustic systems for the 

measurement of streamflow: U.S. Geological Survey WaterSupply Paper 2213, 30 p.

Laenen, Antonius, 1985, Acoustic velocity meter systems: 

U.S. Geological Survey Techniques of Water-Resources 

Investigations, book 3, chap. A17, 38 p.

Morlock, S.E., Nguyen, H.T., and Ross, J.H., 2002, Feasibility 

of acoustic Doppler velocity meters for the production of 

discharge records from U.S. Geological Survey streamflowgaging stations: U.S. Geological Survey Water-Resources 

Investigations Report 01–4157, 56 p.

Mueller, D.S., and Wagner, C.R., 2009, Measuring discharge 

with acoustic Doppler current profilers from a moving boat: 

U.S. Geological Survey Techniques and Methods 3A–22, 

72 p.

Nortek AS, 2001, EASYQ river flow monitor user manual: 

Sandvika, Norway, Nortek AS, 56 p.

Nyquist, Harry, 1928, Certain topics in telegraph transmission 

theory: Transactions of the American Institute of Electrical 

Engineers, v. 47, p. 617–644.

Rantz, S.E., and others, 1982a, Measurement and computation 

of streamflow—Volume 1. Measurement of stage and discharge: U.S. Geological Survey Water-Supply Paper 2175, 

284 p.

Rantz, S.E., and others, 1982b, Measurement and computation of streamflow—Volume 2. Computation of discharge: 

U.S. Geological Survey Water-Supply Paper 2175, 284 p.

Riggs, H.C., 1968, Some statistical tools in hydrology: 

U.S. Geological Survey Techniques of Water-Resources 

Investigations, book 4, chap. A1, 39 p.

Ruhl, C.A., and Simpson, M.R., 2005, Computation of discharge using the index-velocity method in tidally affected 

areas: U.S. Geological Survey Scientific Investigations 

Report 2005–5004, 31 p.

Smith, Winchell, Hubbard, L.L., and Laenen, Antonius, 1971, 

The acoustic streamflow measuring system on the Columbia 

River at The Dalles, Oregon: U.S. Geological Survey OpenFile Report, 60 p.

SonTekTM/YSI, 2007, SonTekTM/YSI ArgonautTM acoustic 

Doppler current meter technical documentation: San Diego, 

Calif., SonTekTM/YSI Corporation, 234 p.

SonTekTM/YSI, 2009, ArgonautTM-SL System Manual Firmware Version 12.0, San Diego, CA, SonTekTM/YSI Corporation, 316 p.

Teledyne RD Instruments, 2008, ChannelMaster horizontal 

ADCP operation manual: San Diego, Calif., Teledyne RD 

Instruments, 156 p.

Turnipseed, D.P., and Sauer, V.B., 2010, Discharge measurements at gaging stations: U.S. Geological Survey Techniques and Methods book 3, chap. A8, 87 p. (Also available 

at http://pubs.usgs.gov/tm/tm3-a8/.) 

U.S. Geological Survey, 2002, Policy and technical guidance 

on discharge measurements using acoustic Doppler current 

profilers: U.S. Geological Survey, Office of Surface Water 

Technical Memorandum 2002.02, accessed July 24, 2010, at 

http://hydroacoustics.usgs.gov/memos/OSW2002-02.pdf.

U.S. Geological Survey, 2003, User's manual for the National 

Water Information System of the U.S. Geological Survey—

Automated Data Processing System (ADAPS): U.S. Geological Survey Open-File Report 03–123, 413 p.

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Memorandum No. 2010.02, accessed January 14, 2011, at 

http://water.usgs.gov/admin/memo/policy/wrdpolicy10.02.

html.

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U.S. Geological Survey, Office of Surface Water Technical 

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water.usgs.gov/admin/memo/SW/sw10.07.html.

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Glossary 67

Glossary

Acoustic beam A beam of acoustic energy with a specific beam width and typically having a 

fixed acoustic frequency.

ADCP Acoustic Doppler current profiler – an acoustic instrument used to measure water 

velocity profiles, water depth, and boat velocities using the Doppler principle.

ADVM Acoustic Doppler velocity meter – an electronic/acoustic instrument that measures 

water velocity using the principle of the Doppler shift.

Averaging period Length of time that velocity is measured and averaged to compute a single 

value for velocity.

AVM Acoustic velocity meter – an instrument that measures water velocity using the time-oftravel method.

Beam check A method of evaluating the return-signal strength of transmitted acoustic pulses.

Blanking distance The distance from the transducer face within which no velocity measurements are made and that corresponds to electronics and transducer recovery time after a ping is 

transmitted.

Boundary A surface or object that causes a strong return signal from transmitted acoustic 

pulses.

Coefficient of determination A statistic that will give some information about the goodness 

of fit of a model. In regression, the coefficient of determination is a statistical measure of how 

well the regression line approximates the observed or measured data points. The coefficient of 

determination ranges from 0 to 1. A value of 1.0 indicates that the regression line perfectly fits 

the data. 

Counts Raw signal amplitude values that have not been normalized. Values often range from 

0 to 255.

Decibars (dbars) The bar is a unit of pressure equal to 100 kilopascals (kPa). 1 decibar equals 

0.1 bar, which also equals 10 kPa.

Gage height The gage height of a stream or lake is the height of the water surface above an 

established datum plane. Gage height and stage are often used interchangeably; however, gage 

height is more appropriate when used to indicate a reading on a gage. Gage height is usually 

expressed in feet and hundredths of a foot, or in meters and hundredths or thousandths of a 

meter.

Hydrograph A graph showing changes in the discharge of a river over a period of time.

Index velocity Water velocity measured in some portion of a stream that is used as an index 

or predictor of the mean velocity in the channel.

Instrument noise level A combined value of environmental and electronic noise level near 

which a reflected or returned acoustic signal cannot be detected by the instrument electronics.

Main beam The primary beam of acoustic energy transmitted by a transducer. Transducers 

emit sidelobes of acoustic energy at various angles not coincident with the main beam.

Measurement interval The time between two successive velocity measurements, usually 

measured from the beginning of each measurement.

Measurement volume A region of flow along the main beams that is measured by an acoustic 

Doppler velocity meter.

Multi-cells or multiple measurement volumes Multiple, discrete volumes of water sampled 

with an acoustic Doppler velocity meter for the measurement of water velocity. Usually a 

subset of the measurement volume.
68 Computing Discharge Using the Index Velocity Method

Ping A term used to describe an acoustic pulse or individual measurement of velocity

p-value The p-value represents the probability that the observed value is invalid.

Range-averaged measurement volume A relatively large volume aligned with the acoustic beams that begins near the ADVM transducers and ends at some distance away from the 

ADVM. 

Rating A relation between two or more parameters that is used in the computation of 

discharge records.

Regression A technique used to discover a mathematical relation between two or more 

variables using a set of individual data points.

Relation In statistics, the association of ordered pairs of values (such as stage and area or 

index velocity and mean velocity).

Residuals A residual is the difference between a measured value and the predicted value 

obtained from a regression equation.

Scatterers Small particles, such as suspended sediment or organic matter, that reflect acoustic 

energy transmitted by hydroacoustic instruments such as an ADVM or ADCP.

Side lobe A beam of acoustic energy emitted by a transducer having lower power than the 

main beam and at an angle other than the main beam of transmitted energy.

Sidelooker A horizontally oriented acoustic Doppler velocity meter often used for the purpose 

of index velocity measurements. 

Signal amplitude The strength (amplitude) of sound energy returned to the acoustic Doppler 

velocity meter while velocity measurements are being made, with units of counts, set to range 

from 0 to 255.

Signal-to-noise ratio (SNR) Often defined as the strength of a returned acoustic signal divided 

by the ambient acoustic/electronic noise as measured by an acoustic Doppler velocity meter. 

For SonTekTM/YSI acoustic Doppler velocity meters, the SNR is defined as SNR = (Signal 

Amplitude – Instrument Noise) * k, where k is a conversion factor from counts to decibels. The 

SNR is used to assess the amplitude (strength) of the received acoustic energy used to measure 

velocity. 

Stage The stage of a stream or lake is the height of the water surface above an established 

datum plane. Stage and the term “gage height” are often used interchangeably. Stage is 

usually expressed in feet and hundredths of a foot, or in meters and hundredths or thousandths 

of a meter.

Standard cross section A standard cross section is a cross section near an ADVM which is 

chosen for the development of the stage-area rating and which can be re-surveyed at regular 

intervals. 

Standard error Measures the dispersion of the actual Y values about the regression line of a 

plot. It is reported in the same units as the dependent variable.

Standard deviation The square root of the variance of a statistical population, dataset, or 

probability distribution.

Streamwise Flow direction that is oriented to the direction of the stream channel.

Uplooker A vertically oriented acoustic Doppler velocity meter often used to measure index 

velocity.
Introduction

Mechanisms for mounting sidelooker and uplooker acoustic Doppler velocity meters (ADVMs) are an important component of collecting high-quality data. This appendix provides information on a selection of mounts for ADVMs.

The ADVM mount should be rigid and should resist vibration or any kind of movement due to flow or other causes. The 

mount should allow for the adjustment of the ADVM pitch, roll, and heading and should be designed so that the ADVM can 

always be returned to the same location and orientation after servicing or replacement. The mount should allow for the depth of 

the ADVM to be changed if it becomes necessary. When possible, the ADVM mount should facilitate servicing of the instrument 

at all stages and conditions (during high flows as well as low flows, or when ice cover is in the channel, for example). ADVM 

mounts should be constructed of materials that will not easily corrode. Aluminum pipe and slip-on fittings, such as Speed-RailTM

(http://www.hollaender.com/, accessed October 29, 2010), are commonly used for constructing ADVM mounts. In some 

environments, it may be necessary to coat the mount, mounting pipe, and ADVM with antifouling paint. 

Mounts for Sidelooker ADVMs

In addition to the general requirements listed above, mounts for sidelooker ADVMs need to be made so that the ADVM can 

be raised and lowered for servicing and so that the cable running from the ADVM to the data logger is protected. The ADVM 

mount should have some means of adjusting the pitch and roll without having to adjust the entire mounting assembly. The mount 

must allow for the ADVM to be returned to the same depth and orientation to the mean flow after being serviced. This often 

requires careful planning prior to installation. Examples of sidelooker ADVM mounts are shown in figures 1-1 to 1-6.

Appendix 1 – Mounts for Acoustic Doppler Velocity Meters

Mounts for Uplooker ADVMs

Requirements for vertically oriented (uplooker) ADVM 

mounts are similar to those for sidelooker ADVM mounts, 

with some additional requirements. Some uplooker ADVM 

mounting methods may require the use of divers to service or 

replace the ADVM. Uplooker ADVMs may also be installed 

using a combination of above-the-water/below-the-water 

mounts (figs. 1-7, 1-10, and 1-11). The uplooker ADVM 

mount should allow for adjustment in pitch, roll, and heading 

while allowing for relatively easy removal and replacement 

of the ADVM. It might be possible to install a bottom mount 

in such a way as to negate the need to adjust the pitch, roll, 

and heading; however, experience has shown that it is often 

very difficult to install a level bottom mount with the proper 

heading that does not change over time. The mount for 

uplooker ADVMs should also be designed to minimize the 

possibility of sediment or debris accumulating on the ADVM 

transducers. A possible solution is to elevate the ADVM above 

the streambed on the chosen mount, and in some instances 

(ArgonautTM-SW) reversing the orientation of the ADVM 

might help prevent sediment accumulation on the downstream 

transducer face. Examples of uplooker ADVM mounts are 

shown in figures 1-7 to 1-11. Figure 1-1. H-beam and Speed-RailTM mount for sidelooker ADVM. 

(Photographs by Keith Ging, Lower Colorado River Authority; used 

with permission.)
70 Computing Discharge Using the Index Velocity Method

DETAIL D

2" 0 Aluminum Pipe

2 1⁄2" 0 Aluminum Pipe

Run winch cable

down to clamp and

terminate securely

D1

D2

Continuation of

winch cable; use

proper fittings

for termination

ADVM

2" pipe terminated

just above bottom

1 1⁄2" 0 Aluminum pipe

driven 2' to 3' into bottom

For winch cable termination:

3/8" bolt/nut lock

Typical clamp for 2" pipe fence post (S.S.)

Drill 3/4" hole through assembly

once ADVM is set properly,

then pin in place and padlock

1⁄2" SS bolts through

railing or SS U-bolts

to attach top plate

1⁄2"x 2 1⁄2" SS lag bolts

to attach bottom plate

to walkway

Figure 1-2. Schematic showing 

pipe mount for sidelooker ADVM. 

(Adapted by Molly S. Wood, 

USGS, from South Florida Water 

Management District specifications.)
Appendix 1 – Mounts for Acoustic Doppler Velocity Meters 71

Figure 1-3. Schematic of ADVM mount on shear fence along a navigable waterway.

Figure 1-2—Continued. Schematic showing pipe mount for sidelooker ADVM. (Adapted by Molly S. Wood, USGS, from South 

Florida Water Management District specifications.)

DETAIL D1 DETAIL D2

2" 0 Aluminum Pipe

2 1⁄2" 0 Aluminum Pipe

1 0 1⁄2" Aluminum Pipe

Saddle Mount Bracket

with extension plates and

appropriate fittings

Bottom Saddle

Mount Bracket

with extension plates

and appropriate fittings

5"

3"

Use S.S. hardware throughout except where noted.

Adapted from SFWMD Specifications.

3/4" x 6" steel pin

with 7/16" hole for

#5 Master lock;

taper nose as shown
72 Computing Discharge Using the Index-Velocity Method

Figure 1-4. Track mount and assembly for a sidelooker ADVM made by Approtek International. 

(Photograph by Molly S. Wood, USGS.)

Figure 1-5. Speed-RailTM mount for sidelooker ADVM. (Left photograph by Marc Zucker, USGS; 

right photograph by Victor Levesque, USGS.).
Appendix 1 – Mounts for Acoustic Doppler Velocity Meters 73

Figure 1-6. ADVM mount for I-beam mounted to channel wall. (Photograph by Don James, USGS.)

Figure 1-7. Speed-RailTM mount with sidelooker and 

uplooker ADVMs mounted to it. (Photograph by Molly S. 

Wood, USGS.)

Figure 1-8. Diver securing uplooker ADVM and mount to 

streambed. (Photograph by Greg Clark, USGS.)
74 Computing Discharge Using the Index-Velocity Method

Figure 1-9. Mounting plates for uplooker ADVMs. (Left photograph by Molly S. Wood, USGS; right photograph by Marc Blouin, USGS.)

Figure 1-10. Uplooker ADVM mount with ADVM and SpeedRailTM coated with antifouling paint. (Photograph by Lars 

Soderqvist, USGS.)

Figure 1-11. ADVM mount with a winch assembly for raising and 

lowering the ADVM. (Photograph by Jeff Banner, Sarasota County, 

Florida, Used with permission.)
Appendix 1 – Mounts for Acoustic Doppler Velocity Meters 75

Preventing Biological Fouling

Biofouling or biological fouling is the undesirable accumulation of microorganisms, plants, algae, and (or) animals on 

wetted structures. Biofouling (Callow and Callow, 2002) is divided into microfouling (biofilm formation and bacterial adhesion) 

and macrofouling (attachment of larger organisms, such as barnacles, mussels, seaweed, etc.). Macrofouling is the main concern 

for ADVMs and other sensors because it can affect the performance of these instruments. Biofouling is especially prevalent 

in the marine environment (fig. 1-12), but the kind of fouling that occurs and the rate of development vary from location to 

location. Biofouling can also occur in upland rivers. Zebra mussels have become quite prevalent in many streams in the United 

States (fig. 1-13). The movement of the transducer induced by the electromagnetic pulse used to generate sound waves may 

inhibit growth on the transducers, at least for some species. When biofouling is a concern, the manufacturer’s recommendations 

regarding use of antifouling paint should be followed (fig. 1-14).

Reference

Callow, M.E., and Callow, J.E., 2002, Marine biofouling—A sticky problem: The Biologist, v. 49, no. 1, p. 10–14. 

Figure 1-12. Sidelooker ADVM with biofouling. 

(Photograph by Lars Soderqvist, USGS.)

Figure 1-14. Uplooker ADVM on the streambed with 

biofouling paint applied. (Photograph by Victor Levesque, 

USGS.)

Figure 1-13. Sidelooker ADVM coated with zebra mussels. 

(Photograph by Paul Baker, USGS.)

Appendix 2 – Forms and Quick-Reference Guides

ADVM Installation and Set-up Form

ADVM Mounted on Cable Length 

 LB / RB / Other (describe): ft / m

Initial Beam Check Filename Boundary Reflection Identified? 

at ft / m 

Water Temp ADVM Temp Salinity ADVM Sal. Deploy Sensor SDI-12 Address

SDI-12 or Auto.

ADVM Date ADVM Time Deployment Name Orientation correction 

Set @: Yes or No

Heading Pitch Roll MagVar Depth Press. Depth

Station No. Station Name

Date Installed Installed by

Mfgr/Model Acoustic Freq. Firmware Ver. Serial # HIF # USGS W #

U.S. GEOLOGICAL SURVEY

ADVM INSTALLATION AND SETUP FORM August 2011

Mid-transducer Face Depth 

Stage minus Depth to Transducers equals Transducer stage

- =

Elevation of ADVM above streambed: ft or m 

Comments:

SonTek ADVM Configuration

Note: White Molex connector (jumper) connected for RS-232 communications and unplugged for SDI-12 communications

Output Format Recorder Averaging Int. (AI) Sampling Int. (SI) PowerPing

sec. sec. On Off

Cell Begin (CB) Cell End (CE) Blank (BD) Cell Size (CS) # of Cells

Teledyne RD Instruments ChannelMaster Configuration

Blanking 

Distance

No. of Cells

(WN)

Cell Size

(WS)

Water Pings 

(WP) 

Measurement 

Interval

Time between 

pings (TP) 

Cells Used for 

Index

sec. 

Other Commands/Info 
78 Computing Discharge Using the Index Velocity Method

Site Sketch with Dimensions, Remarks, and Initial Beam Check Plots (Attached)
Appendix 2 – Forms and Quick-Reference Guides 79

ADVM Recorder Data

Retrieve Data Names of downloaded file(s) 

Yes or No

Station Number Station Name 

Party Date Watch Time Logger Date Logger Time Reset?

Y / N @

Battery voltage Weather (Air temp., Wind speed & direction, etc.)

Field Observations

Time (Zone) DCP/Logger ETG/TI OG RP to WS Velocity

U.S. GEOLOGICAL SURVEY

INDEX-VELOCITY GAGE INSPECTION FORM September 2011

Beam Check

Beam Check Acceptable? Beam Check Filename(s) 

OK or Not OK

Describe Results/

Corrective Measures

ADVM Observations / Configuration

Log File Name

ADVM Sensor Readings 

ADVM Date Watch Time ADVM Time Reset Clock?

Y / N @

Heading Pitch Roll ADVM Stage

SDI-12 or Autonomous

Water Temp ADVM Temp Meas. Salinity ADVM Salinity Deploy Sensor 

ADVM Recording Info

Start Date Start Time

Intervals Sampling Int. Averaging Int.

Save Setup!

Comments:
80 Computing Discharge Using the Index Velocity Method

Field Procedures and Configuration – SonTekTM/YSI ADVMs

The following tip sheet provides step-by-step procedures that should be followed when servicing SonTek/YSI ArgonautTM 

series ADVMs and when making discharge measurements. A detailed version and a short version of these procedures are provided, the latter in the form of a checklist. Even though these procedures are written for sidelooker ADVMs, they may also be 

adapted for uplooker ADVMs. 

Tip Sheet for Servicing SonTek/YSI ArgonautTM ADVMs at Index Velocity Stations 

In this tip sheet, computer program names are italicized text, buttons that are clicked are indicated by bold, italicized text, 

ADVM commands are indicated by “bold text enclosed in quotes,” and window names are indicated by underlined text.

Tip Sheet for Servicing ArgonautTM ADVMs at Index Velocity Stations – Detailed Version

Connecting to the ADVM

1. Plug 9-pin ADVM communication (RS-232) cable 

into laptop serial port or a USB to serial port adapter.

2. Connect the two white plugs on the ADVM cable.

3. Open SonUtils. Click the green button next to the 

appropriate COM port. 

4. Click the Break button. If the ADVM was in SDI-12 mode, 

you should get a response from the ADVM indicating that 

it is in SDI-12 mode. If the ADVM was self-deployed, 

you should get a response that the ADVM is initializing.

5. To exit SDI-12 and enter RS-232 mode, type “?EXIT!” If 

the ADVM was self-deployed, you do not need to do anything other than enter direct commands or click on command buttons.

6. Click Show System, and verify that firmware is up-to-date. 

Downloading Recorder Data

1. In SonUtils, click the Recorder button.

2. In the Recorder window, click Select All to download all files or click on an individual filename to download.

3. Click Browse to select the directory where the files will be stored on your laptop (recommend having unique directory 

for each site).

4. Reset download baud rate to 57600 for faster downloads, using tab above the Browse window.

5. Click Download.

6. When the file has downloaded, leave SonUtils open, and open ViewArgonaut. (The following steps are to verify that 

you retrieved the files from the SL’s internal recorder.)

7. On the ViewArgonaut window, click Processing.

8. Go to File, Open, and navigate to the file you just downloaded. When the Argonaut File window pops up, verify that 

the file start and end date and time are correct, then click OK.

9. Click on Argonaut Config and select User Setup. Verify that the ADVM configuration/set up is correct. Review the 

data plots and look for anomalous data. Close the Processing (ViewArgonaut) window.

10. Go back to SonUtils and note the memory used and memory available in the SonUtils Recorder window. 

 If the memory available is less than approximately 300 to 500 kilobytes (kB), you should consider if there is enough 

memory left to record data until the next station visit. 

If you are satisfied with the data you collected from the recorder, and there is less than 300 to 500 kB, click the 

Format button on the SonUtils Recorder window. 
Appendix 2 – Forms and Quick-Reference Guides 81

 Caution: Once the recorder has been formatted, the files cannot be recovered.

11. Close the Recorder window.

12. Compare the ADVM water temperature with an independently measured water temperature made at or near the 

ADVM with an appropriate field temperature meter. If the ADVM thermistor is not functioning properly, the ADVM 

will not correctly measure velocities. At the command line prompt in SonUtils, type 

 “sensor cont”

 The ADVM will respond once per second with the ADVM temperature (degrees Celsius), pressure (deciBars~meters), 

and battery voltage. Record the ADVM temperature and the independent field meter values on the field sheet. 

 Press the Enter key to stop the continuous sensor readings.

13. Open a log file to record commands and ADVM responses. Click on File from the top menu and select Open Log File

(Ctrl-L are the shortcut keys). A File-Save window will open. Navigate to the station directory where you downloaded 

the Argonaut internal recorder data and name the log file using the following format: station_id_YYYYMMDD. 

SonUtils will automatically assign the .log suffix to the filename. On the main SonUtils screen,

a. Click on the Show Configuration button on the left margin of the main window, review the ADVM configuration and verify that the response is appropriate and the data are correct. 

b. Click on the Show System key, review and verify that the ADVM response and the system settings are correct. Verify that the most recent USGS-approved CPU Firmware version is installed on the ADVM (currently 

version 12.0, December 2010).

c. Click on Show Setup, review and verify that the ADVM is properly set up to collect routine data.

d. At the SonUtils command line prompt, type the following command to document the ADVM SDI-12 address: 

“sdi12address”

e. At the SonUtils command line prompt, type 

“sensor cont”

Let the ADVM measure for 4 or 5 seconds then press the Enter key to stop the data readings. Verify that the 

values are reasonable, agree with independent measurements, and record appropriate values on the station 

field sheet (temperature, pressure, and battery voltage).

f. If the ADVM is equipped with a compass, at the SonUtils command line prompt, type 

“compass cont”

The ADVM will respond with the heading, pitch, and roll of the ADVM compass. Let the ADVM measure 

for 4 or 5 seconds, then press the Enter key to stop the measurements. Verify that the values are reasonable 

and have not changed from previous station visits, and record the values on the station field sheet (heading, 

pitch, and roll).

g. If the ADVM has an acoustic water-level transducer, check the distance from the water surface to the acoustic 

water-level transducer by typing 

“level cont” in the SonUtils command line. The ADVM will respond with the distance from the face of the 

acoustic water-level transducer to the water surface in millimeters. Press the Enter key to stop the readings.

14. Check the ADVM clock time by entering 

 “time”

 in the SonUtils command line and by pressing the Enter key at the appropriate time. Look at your NIST-timesynchronized watch time and record the watch time and the ADVM clock time on the ADVM field sheet.

 Reset the ADVM time using your NIST-time-synchronized watch by entering 

 “time hh:mm:ss”

 in the SonUtils command line and press Enter at the exact time you are synchronizing. Record the time on the field 

sheet. Verify that the ADVM date is correct in the SonUtils command line prompt, type 

 “date” and press Enter, recording the date on the ADVM field sheet.

15. Close the log file by selecting File, Close Log File from the top menu, or by pressing Crtl-L again.
82 Computing Discharge Using the Index Velocity Method

Recording and Reviewing a Beam Check

1. In SonUtils, click the Beam Check button.

2. In the Beam Check window, click the green Start button.

3. Click the Averaging button to average all of the pings together.

4. Click the Record button to save the beam check to your computer.

5. When prompted for a file name, navigate to the same directory where you downloaded the internally recorded Argonaut data file and name the beam check with the station number and date (station_id_YYYYMMDD). SonUtils will 

automatically assign the .bmc suffix to the file name.

6. Record a minimum of 50 pings. 

7. Look for spikes, increase in amplitude with range, or leveling out in the signal amplitudes for either beam (red and 

blue solid lines) within or touching the sampling volume, which is marked with vertical dashed lines (cell begin and 

cell end). The measured signal amplitudes and the theoretical decay line (curved gray solid line) should be relatively 

similar in shape and follow the same general trend. Also look at the beam signal amplitudes in relation to the theoretical decay curve and the instrument noise line (horizontal dashed line). The signal intensities anywhere in the measurement volume (designated by the cell begin and cell end vertical dashed lines) should be at least 10 to 20 counts greater 

than the instrument noise line (horizontal dashed line). Click the Stop button and close the Beam Check window when 

finished.

Recording Data During ADCP Measurements

1. When making an ADCP measurement, reset the sampling interval and averaging interval in the ADVM to collect 

data on a 60-second continuous basis to more accurately synchronize ADVM velocity data with the discharge 

measurement(s). To reduce possible confusion or errors, it is recommended to reset the sampling and averaging 

intervals in the ADVM instead of in the data logger, and have the ADVM record the data internally only. 

 Note: Data will not be sent to the data logger during calibration or validation discharge measurements. 

In SonUtils:

2. Change the averaging interval (ai), type “ai 60” <Enter> where 60 is the desired averaging interval duration, in 

seconds.

3. Change sampling interval (si), type “si 60” <Enter> where 60 is the desired sampling interval, in seconds.

4. Set the correct Start Date (sd), type “sd YYYYMMDD” <Enter> for today’s date.

5. Set the correct Start Time (st), type “st hh:mm:00” <Enter> (use a time that is a few minutes in the future).

6. Type “ssu” <Enter> to save your changes (ssu = savesetup).

7. Enter comments to further document the conditions and procedures.

8. Type “deploy” in the SonUtils command line and press <Enter>. Verify that the start time will begin at an appropriate 

time:

Example:

Checking Setup Parameters...

3801088 free bytes left in recorder. Free space is sufficient for 14.12 days of operation.

Data collection will start on: 2010/06/24 at 14:55:00

In 0 days, 0 hours, 1 minutes and 15 seconds from now.

Data will be recorded to file FTHAM004.

9. Caution: Disconnect the communication cable to the computer before touching any other keys or buttons on the 

computer. Leave white jumper plugged together! You are not storing ADVM data to the data logger during this period 

– it will be stored internally ONLY.

10. Close SonUtils.

11. When the discharge measurement(s) is(are) completed, reopen SonUtils. Click green button next to the appropriate 

COM port button to connect.
Appendix 2 – Forms and Quick-Reference Guides 83

12. Click the Break button. 

13. Click on the Recorder button and download the file from the ADVM. 

14. View the file in ViewArgonaut to be sure the file is complete.

15. Note the memory used and memory available in the SonUtils Recorder window. If the memory available is less than 

approximately 300 to 500 kB, you should consider whether or not there is enough memory left to record data until the 

next station visit. If the data collected from the recorder is satisfactory and less than 300 to 500 kB remain, click the 

Format button on the SonUtils Recorder window. 

Note: Once the recorder has been formatted, the files cannot be recovered. 

Redeploying the ADVM After Measurements

1. In the SonUtils command line, type 

 “si xxx” <Enter>

 where xxx is the routine data measurement sampling interval, in seconds. A copy of the latest set up should be in the 

equipment shelter, and the log file that was captured earlier can be used to verify the correct value. 

2. Type

 “ai xxx” <Enter>

 where xxx is the routine data measurement averaging interval, in seconds.

3. Click the Show Deploy button. 

4. Enter the correct start time (st) by typing 

 st hh:mm:00 <Enter>

 where hh and mm are the next nearest routine sample measurement time (ex: 12:15:00, 12:30:00, 12:45:00, 13:00:00, 

etc).

5. Click the Show Deploy button again to verify that changes were accepted.

6. To save all settings type 

 “ssu” <Enter>

7. If you have made any permanent changes to the ADVM configuration (sampling interval, averaging interval, measurement volume, etc.), record another log file to document the new configuration. 

Open a log file to record commands and ADVM responses. Click on File, and select Open Log File (Ctrl-L are 

the shortcut keys) from the top menu. A Save File window will open. Navigate to the station directory where you 

downloaded the Argonaut internal data file and name the log file station_id_YYYYMMDD_after_update. SonUtils

will automatically assign the .log suffix to the filename. 

On the main SonUtils screen,

a. Click on the Show Configuration button on the left margin of the main window, review the response, and 

verify that the response is appropriate and the data is correct. 

b. Click on the Show System key, review the ADVM response, and verify that it and the system settings are correct. Verify that the most recent USGS-approved CPU Firmware version is installed on the ADVM (currently 

version 12.0, December 2010).

c. Click on Show Setup, review the configuration, and verify that the ADVM is properly set up to collect routine data.

d. Type “show sdi12” in the SonUtils command line to document the ADVM SDI-12 address. Everything that 

shows up in the resulting screen will be written to the log file.

 NOTE: It is recommended that another beam check be recorded and reviewed after the discharge measurements are 

complete in order to verify that the ADVM acoustic beams are functioning properly prior to leaving the station.

8. Click on File, select Close Log File (Ctrl-L) from the top menu.

9. When you are finished with SonUtils (setup, beam checks, etc.) type 

 “sdi12 on” <Enter>
84 Computing Discharge Using the Index Velocity Method

 The instrument will return a message that the “SDI12 address is n” (n = SDI address assigned to the ADVM) and 

will show how many days of internal memory are remaining. Verify that there is enough memory left until your next 

station visit.

 Example:

>“sdi12 on”

Checking Setup Parameters...

3866624 free bytes left in recorder.

Free space is sufficient for 215.39 days of operation.

Switching to SDI-12 mode

SDI-12 address is: 3

OK

10. Verify that sufficient memory is left in the ADVM and the SDI-12 address is correct.

11. Disconnect the communication cable to the computer and the ADVM before touching any other keys or buttons on the 

computer.

12. Close SonUtils, and unplug the white jumper plug. 

13. Archive all files (recorder, beam check, log configuration files, etc.) on the USGS Water Science Center data archive 

server upon return to the office. It is recommended that the Argonaut internal data files be renamed because of the 

limited naming abilities in the ADVM.

 Example: downloaded file is FTHAM004.ARG. Site was visited on June 24, 2010.

Rename the Argonaut files to:

• station_id_20100624.arg for the routine data time series, and

• station_id_20100624_qmeas.arg for the 60-second data file collected during the discharge measurement if applicable.
Appendix 2 – Forms and Quick-Reference Guides 85

Step Done

A. Downloading Recorder Data

1. Download datalogger/DCP data (8210,9210, Satlink, etc).

2. Check datalogger/DCP time and watch time. Record on field sheet.

3. Plug together white jumper on ADVM.

4. Connect to ADVM using SonUtils.

5. Switch to RS-232 mode in SonUtils.

6. Download internal ADVM recorder data to laptop.

7. Check ADVM internal clock time and watch time. Record on field sheet.

8. Reset ADVM internal clock time (“time hh:mm:ss”).

9. View downloaded files in ViewArgonaut; look for problems.

10. Compare ADVM water temperature with independently measured water temperature.

11. Format/erase internal ADVM recorder.

B. Recording and Reviewing a Beam Check

1. Run beam check on ADVM. Look for problems.

2. Pull up and clean ADVM.

3. Re-deploy ADVM and secure the mount.

4. Re-establish communication with ADVM using SonUtils.

C. Recording Data During ADCP Measurements

1. If making ADCP measurement, change Sampling Interval (SI) to 60 sec. and Averaging Interval (AI) to 60 sec., else skip to step D-2.

2. Type in comments (“comments” <enter>) Three lines, 60 char. long, are available. 

3. Set Start Date (sd) to current day- “sd YYYY/MM/DD”.

4. Set Start Time (st) to time slightly in the future- “st hh:mm:00”.

5. Type “deploy” (command used to record ADVM data on internal recorder during streamflow 

measurement).

6. Check terminal window for appropriate display. Example:

Data collection will start in 0 days, 0 hours, and 4 minutes from now. 

There is sufficient space in the recorder for 19.72 days of data collection.

7. Disconnect the communication cable to the ADVM before touching any other keys.

8. Leave the white jumper connector connected.

9. Make discharge measurement(s).

10. After discharge measurement(s) is complete, reconnect to ADVM using SonUtils.

11. Download ADVM data recorded during discharge measurement.

12. Record a log file to document changes to the ADVM and any responses from the ADVM after 

entering commands. Click on the Show System, Show Config, Show Setup, and Show Deploy

buttons. Review the values to ensure they are correct.

D. Redeploying the ADVM After Measurements

1. Return SI (typically 300 to 900 sec.) and AI to routine data collection settings.

2. Set start time to nearest quarter hour (hh:15:00, hh:30:00, hh:45:00, hh:00:00).

3. Record an after-measurement beam check.

4. Put ADVM in SDI-12 mode “sdi12 on”.

5. Read ADVM response to ensure: (a) ADVM received the command, (b) responded appropriately, and (c) there are sufficient days available for data collection.

6. Disconnect communication cable to the ADVM before touching any computer keys.

7. Unplug ADVM white connector.

8. Verify that velocity data are being written to datalogger/DCP and that telemetry works.

Tip Sheet for Servicing ArgonautTM ADVMs at Index Velocity Stations – Short Version

Appendix 2 – Forms and Quick-Reference Guides 87

Field Procedures and Configuration – Teledyne RD Instruments ADVMs

The following tip sheet provides step-by-step procedures for servicing and configuring a Teledyne RD Instruments (TRDI) 

ChannelMaster ADVM. 

Tip Sheet for Servicing TRDI ChannelMaster ADVMs at Index Velocity Stations 

In this tip sheet, computer program names are italicized text, buttons that are clicked are indicated by bold, italicized text, 

ADVM commands are indicated by “bold text enclosed in quotes,” and window names are indicated by underlined text. References to the ChannelMaster are indicated by “CM” in the text.

A. Connecting to the ADVM

1. Plug 9-pin CM serial cable into laptop serial port or use USB to serial port adapter.

2. When communicating with the CM directly with a laptop, it is 

recommended that BBTalk be used rather than WinHADCP.

3. Open BBTalk. 

4. Choose “ChannelMaster” in the device menu of the Connect To

window and select appropriate COM port.

5. Select correct baud rate.

6. In the Options window, only “Send break on New Connection” 

option is required.

7. Click the button Finish.

8. Once connection is successfully established, you should see a response like that shown to the right, giving the firmware version and other information.

9. Check the CM time by issuing the TS? command and comparing results to watch time. Record results on field sheet.

10. If necessary, reset CM time using TS command. Record results on field sheet.
88 Computing Discharge Using the Index Velocity Method

B. Retrieving Loop Recorder Data, Recording 

Configuration and Temperature

1. Having established communication with the CM using BBTalk, download 

data from the loop recorder. Click on the File > Recover Loop-Recorder 

menu option. (The loop recorder in the CM should be enabled.)

2. Enter the path on the laptop where the loop recorder data 

will be saved to. 

3. Once OK is clicked, the download will begin. This may take as long as 15 minutes. If the checkbox Disable Window 

Output is checked, the download may be faster. This is a good time to lower the independent temperature sensor to the 

same depth as the CM and near the CM. After the download is complete, a comparison between the CM temperature 

and the independent temperature sensor can be made using the “PC2” command. 
Appendix 2 – Forms and Quick-Reference Guides 89

4. Next, verify the CM configuration. Open a log file (using F3), and name it in accordance with USGS Water Science 

Center (WSC) naming conventions. The format recommended is station_id_YYYYMMDD. Alternatively, a script file 

(located at the end of this appendix) may be used to log all of the CM setup information to a text file. To execute the 

script, click on the “File” menu and then click on “Send Script File.” A dialog window will open. Locate the script 

file (in this example, the script is named CM_CheckScript20071017.txt. Once located, click OK to run the script.

5. The script will prompt the hydrographer for a log file name. The format recommended is station_id_YYYYMMDD. 

Store these data in a file and a directory specified in the WSC electronic data archive plan. 
90 Computing Discharge Using the Index Velocity Method

6. After the script is complete, issue the “PC2” command and compare the ADVM thermistor readings to the independent temperature sensor and record them on the field sheet. 

7. Close and review the log file to ensure that the CM is appropriately configured.

C. Reviewing Loop Recorder Data

1. Open WinHADCP. The Setup Wizard will appear.

2. Click the button Data Playback/Processing.

3. Select the loop recorder file just downloaded. 
Appendix 2 – Forms and Quick-Reference Guides 91

4. In the Configure Processing window note 

the “Start Time Date” and “End Time 

Date.” Usually only about 2 days of the 

most recent data will be available for 

review due to CM memory limitations. 

Click on the Show User Setup button 

to see how the CM was configured and 

compare to previously specified configuration parameters for the station. 

5. If a green LED is not shown in the Configure 

Processing window (step 6), averaging should be set. 

Click on the Set Averaging button in the Configure 

Processing window (step 6) and when the Average 

Setup widow opens, click on the 1 button.

6. In Average 1 Setup window, enter the “Range Average 

Start” and the “Range Average End” values to include 

the cells that are used for the index velocity or the entire 

range of cells available. Click on the OK button and then 

on OK in the Average Setup window. Then click on the 

Start Playback button in the Configure Processing window 

(step 6). It is also important to view individual cells, 

because the average value for a number of cells can mask 

data that may be invalid.
92 Computing Discharge Using the Index Velocity Method

7. Review CM data, paying close attention to the intensity profile to see if any obstructions or unusual patterns are 

evident for either of the two beams. Examine velocity data for unusual data.

D. Recording Data During ADCP Measurements

1. When making an ADCP measurement, the sampling interval and averaging interval in the ADVM should be set to 

60 seconds. Because of current (2011) firmware and software limitations, however, the hydrographer should not reset 

the CM sampling time during discharge measurements. Given current limitations in CM firmware, it is recommended 

is to always collect 1-minute data with the CM and allow the data logger used for recording and transmission of realtime data to do any averaging desired. If 15-minute data are desired for database storage and records computation, the 

CM should be configured to collect 1-minute data and the data logger should be configured to average the 1-minute 

data prior to transmission.

2. With this in mind, two options are available to the hydrographer—either use the CM loop recorder data or configure 

the data logger to temporarily store the 1-minute data. Because many data loggers are available to hydrographers, it is 

recommended that the data logger manual be used to properly configure the data logger. Regardless of which option 

is used, the 1-minute measurement interval data should be used to synchronize and synthesize the index velocity data 

with the discharge measurement durations.

3. To use the CM loop recorder, start BBTalk and connect to the CM as before.

4. If, and only if the data have previously been downloaded for review, erase the CM loop recorder. At the command 

prompt, enter the command ME.

5. At the command prompt, type MN filename where filename is the filename for the discharge measurement data and is 

specified in accordance with the WSC electronic data guidelines.

6. Make the discharge measurement.

7. Recover the loop recorder using BBTalk (using guidelines shown above) and disconnect the CM serial cable from the 

laptop.

8. Enter the CS command at the command prompt to start the CM pinging.

9. Verify that the SDI-12 data collection is functioning properly before leaving the gaging station.
Appendix 2 – Forms and Quick-Reference Guides 93

E. BBTalk Script for Checking ChannelMaster Configuration

$L

$B

$D2

$p THIS SCRIPT CHECKS AND LOGS THE CURRENT CHANNEL MASTER PARAMETERS 

$D3

$p DISPLAYING CURRENT CM SETUP COMMANDS... 

mn? 

wf?

ws?

wn?

mr?

wp?

tp?

te?

es? 

ed?

ez? 

cf? 

cj?

ct?

cl?

vp?

#vr?

cb?

$D1

$p POSSIBLE BAUD RATES ARE... 

$p CB411=9600 

$p CB511=19200 

$p CB611=38400 

$p CB711=57600 (best all around baud rate) 

$p CB811=115200 

$D3

$p STARTING SYSTEM TESTS... 

$D1

PS0

$D3

PS4

$D3

PA

$D3

PC4
94 Computing Discharge Using the Index Velocity Method

$D3

$p SYSTEM TESTS COMPLETED. CHECK FOR FAILURES! 

$p

$p DISPLAYING REAL-TIME SENSOR DATA... 

$P Make sure Pitch and Roll are correct and 

$p unchanged from previous log file results 

$P Make sure the Ambient Temp is correct 

$p Press any key to continue 

$D2

PC2

$D2

$W62,10000

$D1

$p Type your initials now and press “Enter”

$D10

$p Current date and time is... 

TS?

$D2

$p Make sure laptop time is correct and set to local Standard Time NOT Daylight Savings Time

$P Now hold down “Ctrl” & “T” (Sets ADCP Time)

$p Now type “cs” to deploy

$P Press F3 to stop log file (REVIEW SAVED LOG FILE!) 
Introduction

Review of beam checks and other available data is essential to the selection and (or) modification of the measurement 

volume for index velocity measurements with ADVMs and the ongoing quality assurance of the index velocity data. A brief 

description of a beam check is provided below followed by descriptions of problems that can be identified by means of beam 

checks. Analysis of other time-series data, such as signal amplitude, noise level, signal-to-noise ratio, X velocity, Y velocity, and 

velocity standard error, can be used to quality assure index velocity records. 

Description of a Beam Check

Beam checks are useful tools for selecting the measurement volume to be used with the ADVM installed at a site and 

for trouble-shooting problems that may occur from time to time. A beam check is a plot of signal amplitude for each ADVM 

acoustic beam. In some cases, manufacturer-supplied software for performing beam checks plots the theoretical decay curve 

along with the measured signal amplitudes. The decay curve is based on the system frequency, user-selected salinity, measured 

water temperature, and an assumed concentration for scatterers in the water. The USGS requires that a beam check be performed 

during every site visit. The ADVM should be configured to perform automatic beam checks at routine intervals between site 

visits, provided that the firmware and software for the ADVM are capable of doing so. The Index Velocity Gage Inspection 

Form (appendix 2) should be completed during the site visit. This form contains fields for providing information about the beam 

check(s) completed. In addition to performing the beam check, the hydrographer should analyze the results while still at the site 

to verify that no apparent changes or problems are indicated.

The result of a beam check is shown in figure 3-1, illustrating the desired features of a beam check for an ADVM. For 

this beam check, the main acoustic beams and side lobes do not appear to be affected by reflections from the water surface, the 

streambed, or any object within or beyond the selected measurement volume. The signal amplitudes for the maximum range of 

Appendix 3 – Analysis of Data for Selection of Measurement Volume

Beam 1

Beam 2

Vertical Beam

Theoretical decay

Range, in meters

Signal amplitude, in counts

EXPLANATION

2 4 6 8 10 12 14 16 18 20 0

50

100

150

200

Cell Begin Cell End

Water-level acoustic signal

Velocity measuring acoustic signals

Instrument noise level Figure 3-1. Results of a sample 

beam (signal amplitude) check for 

a sidelooker ADVM with a waterlevel acoustic beam.
96 Computing Discharge Using the Index Velocity Method

the measurement volume (12 meters) are well above the instrument noise level (almost 30 counts higher than the noise level for 

this example). The signal amplitudes are similar in magnitude for each beam within the range of the measurement volume and 

the trend expected from the theoretical acoustic decay curve. Generally, if the average measured signal-amplitude profiles differ 

from the theoretical decay curve by more than 20 counts over the full range of the system, a problem may be indicated; however, 

this could be a natural variation in the scattering strength that may not affect system operation (SonTek/YSI, 2007).

Identifying Potential Problems in Selecting a Measurement Volume

Identifying potential problems in beam checks and using other data recorded by the ADVM is crucial to selection of the 

proper measurement volume. Because stream conditions change over time, beam checks should be made regularly and results 

should be accurately interpreted. In this appendix, potential problems are illustrated by means of a series of figures showing 

beam-check data and other data, along with accompanying text discussing the potential problem(s).

Figure 3-2 shows the subtle, yet important, signal-strength characteristic that can be caused by side-lobe reflections from 

a boundary occurring at about 60 meters from the ADVM. Typically the acoustic beam signal amplitudes should decrease with 

range, although there are some exceptions. If the signal amplitudes show a leveling out (signal strength stays relatively the same 

as range increases) for a short distance then continue to decrease with increasing range, side lobes from one or both beams may 

be striking a strong reflector (water surface or streambed) causing the signal strength to remain nearly constant as the distance 

from the transducers increases.

Signal amplitudes shown in beam checks should not increase substantially over the range where velocity is to be measured. 

An increase in signal amplitude with range (rapid or gradual) indicates that one or more acoustic main beams are reflecting 

from a fixed or large object, the streambed, or the water surface. There are some rare exceptions when return-signal amplitudes 

increase with range and do not adversely affect the velocity measurement volume. Figure 3-3 is a beam-check plot that shows 

the effect of frazzle ice on the return signal strengths. Water temperature was at or below freezing prior to and during this beam 

check. Previous beam checks did not indicate any boundary-like effects in the signal amplitudes. Small chunks of ice were on 

the water surface but were moving with the river flow. The data did not indicate any rapid increase or decrease in the velocity. 

Based on the velocity data time series and discussions with the manufacturer, the velocity data did not appear to be affected by 

these unusual return signal strengths.

Beam 1

Beam 2

Vertical Beam

Theoretical decay

20 40 60 80 100 120

0

50

100

150

200

250

Range, in meters

Signal amplitude, in counts

EXPLANATION

Cell Begin Cell End

Instrument noise level

Possible side-lobe interference

Figure 3-2. Beam-check 

data indicating possible 

side-lobe interference. 
Appendix 3 – Analysis of Data for Selection of Measurement Volume 97

As previously mentioned, signal amplitudes should decrease as the range increases. Based on signal amplitude alone, the 

end of the range-averaged velocity (cell end) and (or) the far edge of the last multiple velocity cell should be chosen to be a 

minimum of 10 percent of the distance to the location where the first increase in signal amplitudes is detected or typically onehalf the pulse length of the transmitted signal, whichever is greater (consult manufacturer’s specifications to determine ADVM 

pulse length). Figure 3-4 shows a beam check that has subtle changes in signal amplitudes because of possible side-lobe reflections from boundaries along the path of both beams. Signal amplitudes begin to level off just before a distance of 55 meters and 

remain nearly constant until about 70 meters. For this example, the end of the measurement volume should be configured to be 

approximately 45 meters. At this range, the signal amplitudes are greater than 100 counts for this beam check and should provide strong signal amplitudes even if backscattering conditions change over time. Similarly, for this example, the ADVM should 

be configured so that the cell begin is set to be free from near-field flow disturbances that are discussed later in the appendix. 

The beam-check data shown in figure 3-5 indicates that the signal amplitudes increase substantially between 10 and 

13 meters from the transducers. In this example, the spike in the beam check was caused by the acoustic signals from the main 

beams reflecting from the far bank. For this ADVM, the cell begin for the range averaged cell was set to 3 meters because of the 

possibility of flow disturbance from the ADVM mount and channel features upstream from the ADVM. A shorter, more conservative cell end was chosen for this site, even though the signal amplitudes do not show an increase until about 9 meters. The 

stage at this site during low flow is known to be substantially less than the stage during this beam check. For this reason, a cell 

end of 6 meters was selected to reduce the possibility that the acoustic beams would be affected by reflections from the water 

surface at lower stages.

Results from a beam check used to configure an ADVM cell begin and cell end and the overlapping multi-cell volumes are 

shown in figure 3-6. Based on this beam check, the cell begin and cell end selected by the hydrographer appear to be appropriate 

for the site. Figure 3-7 shows the X component of velocity (X velocity) for the range-averaged measurement volume along with 

the standard error of the X-velocity data for the same ADVM configured using beam check data shown in figure 3-6. X-velocity 

data are shown in the top plot, and the standard error of the X velocity is shown on the bottom plot. Based on the beam-check 

data, cell begin was set at 2 meters, and the cell end was set at 15 meters. The ADVM was configured to measure multi-cell 

velocity data. The range-averaged X-velocity data do not exhibit unusual values, and the standard errors are reasonable. The 

standard error data show a slight increase as the magnitude of the X velocity increases, indicating that turbulence in the channel 

increases when velocity increases as would be expected.

Beam 1

Beam 2

Vertical Beam

Theoretical decay

20 40 60 80 100 120

Range, in meters

Signal amplitude, in counts

EXPLANATION

0

20

40

60

80

100

120

140

160

180 Cell Begin

Cell End

Instrument noise level

Figure 3-3. Effects 

of frazzle ice on signal 

amplitudes in a beam 

check.
98 Computing Discharge Using the Index Velocity Method Counts

Range, in meters

0 25 50 75 100 125 150

60

90

120

150

180

Signal strength "leveling out"

EXPLANATION

Beam 1

Beam 2

Beam 1

Beam 2

Vertical Beam

Theoretical decay

Range, in meters

Signal amplitude, in counts

EXPLANATION

2 4 6 8 10 12 14 16 18 20 0

50

100

150

200

Cell 

Begin

Instrument noise level

Cell End

Figure 3-4. Signal strength check with subtle increases in return signal amplitudes 55 to 70 meters from the ADVM.

Figure 3-5. Beam 

check with substantial 

increases in return signal 

amplitudes 10 to 13 

meters from the ADVM.
Appendix 3 – Analysis of Data for Selection of Measurement Volume 99

Beam 1

Beam 2

Vertical Beam

Theoretical decay

Range, in meters

Signal amplitude, in counts

EXPLANATION

2 4 6 8 10 12 14 16 18 20 0

50

100

150

200

Cell Begin Cell End

Instrument noise level

–0.5

0

0.5

1

1.5

2

2.5

3

Velocity, in feet per second

X velocity, range-averaged cell

0

0.02

0.04

0.06

0.08

0.1

0.12

Standard error, in feet per second

X-velocity standard error, range-averaged cell

25 30 5 5 10 15 20 25 30

November December

2009

October

EXPLANATION

EXPLANATION

A

B

Increases in standard error

Figure 3-6. Data from 

a beam check with 

cell begin and cell end 

chosen based on the 

return signal amplitudes.

Figure 3-7. Time series of range-averaged (A) X velocity and (B) X-velocity standard error data.
100 Computing Discharge Using the Index Velocity Method

The multi-cell velocity data also may be used to verify that the cell end has been appropriately chosen. Velocities measured 

in the various cells by the ADVM should show similar patterns and magnitudes when compared to one another and to the rangeaveraged cell. In figure 3-8 the range-averaged X-velocity data and the cell 1 X-velocity data are shown on top, and the standard 

errors for the range-averaged X velocity and cell 1 X velocity are shown in the bottom plot. The cell begin and the blanking 

distance were both set to 2 meters, and the cell end was set to 15 meters. The size of the velocity cells was set to 1.3 meters, and 

10 multi-cells were measured and recorded; therefore, the range-averaged measurement volume and the multi-cell volume are 

measuring the same region in the channel from 2 meters to 15 meters (multi-cells 1 through 10). 

The magnitudes for cell 1 X velocity (measurement volume is located from 2 to 3.3 meters) are substantially less the 

range-averaged X velocity data (2–15 meters). At the same time, the standard error of the cell 1 X-velocity data is greater than 

the range-averaged X velocity, which is to be expected. The range-averaged velocity measurement volume is 13 meters long, 

and the multi-cell velocity measurement volume is 1.3 meters long. For ADVMs, larger cell sizes (larger measurement volumes) 

have lower standard error than smaller cell sizes, so it is not unusual to see greater standard error in smaller multi-cell measurement volumes compared to larger measurement volumes. Plots of velocity and velocity standard error in figure 3-8 indicate that 

cell 1 and the cell begin for the range-averaged measurement volume may be too close to the transducers (2 to 3.3 meters) and 

may be measuring in a region of velocity that is affected by the channel banks or the ADVM mount. 

Another set of time series plots (fig. 3-9) shows the same ADVM velocity and standard error data as before with the addition of cell 2 (3.3–4.6 meters) X velocity and standard error data. The cell 2 X-velocity magnitude is approximately two times 

the magnitude of cell 1 X velocity and approximately equal to the range-averaged velocity. The standard error of the cell 2 X 

velocity is also less than the cell 1 X-velocity standard error. This information confirms the preliminary analysis, namely that 

the cell begin and the blanking distance should be increased to measure only in a region of higher velocity (and correspondingly 

lower standard errors). In figure 3-10, cell 3 X-velocity data are added to the plots; data indicate that the velocity from 4.6 to 

5.9 meters is approximately one-third greater than cell 2 X velocity. The standard error of cell 3 X velocity is approximately the 

same and sometimes slightly less than cell 2 X-velocity standard error. Based on these observations and plots, the cell begin and 

the blanking distance should be increased to approximately 5 or 6 meters in order to measure in the region of flow that is near 

the maximum velocity (and lower standard error) while also avoiding the possible effects of flow disturbance. 

In figure 3-11, X-velocity data from the range-averaged cell from 2 to 15 meters (red), multiple cells 3, 7, and 8, with 

corresponding ranges of 4.6–5.9, 9.8–11.1, and 11.1–12.4 meters, respectively, are shown. The magnitudes of cell 7 and 8 X 

velocity are less than the other cell velocities, and the velocity standard error for cell 7 is greater than the velocity standard error 

for cell 3. In addition, the velocity standard error for cell 8 shows an apparent decrease compared to the other cells. The decrease 

in standard error for cell 8 is not as meaningful as the substantial increase in the variability of cell 8 X-velocity data. This plot 

illustrates how velocity and standard error data should be used together to assess the quality of the measured velocity and the 

end of the measurement volume. The multi-cell velocity data evaluation combined with the beam-check data indicate that the 

maximum range for this site and ADVM installation should be no greater than approximately 10 meters. 

–0.5

0

0.5

1

1.5

2

2.5

3

Velocity, in feet per second

X velocity, range-averaged cell

X velocity, cell 1

0

0.02

0.04

0.06

0.08

0.1

0.12

Standard error, in feet per second

X-velocity standard error, range-averaged cell

X-velocity standard error, cell 1

25 30 5 5 10 15 20 25 30

November December

2009

October

EXPLANATION

EXPLANATION

A

B

Figure 3-8. Time series of (A) rangeaveraged X velocity and cell 1 X velocity 

and (B) their corresponding standard 

errors.
Appendix 3 – Analysis of Data for Selection of Measurement Volume 101

–0.5

0

0.5

1

1.5

2

2.5

3

Velocity, in feet per second

0

0.02

0.04

0.06

0.08

0.1

0.12

Standard error, in feet per second

25 30 5 5 10 15 20 25 30

November December

2009

October

EXPLANATION

EXPLANATION

A

B

X velocity, range-averaged cell

X velocity, cell 1

X velocity, cell 2

X-velocity standard error, range-averaged cell

X-velocity standard error, cell 1

X-velocity standard error, cell 2

Velocity, in feet per second Standard error, in feet per second

–0.5

0

0.5

1

1.5

2

2.5

3

0

0.02

0.04

0.06

0.08

0.1

0.12

25 30 5 5 10 15 20 25 30

November December

2009

October

A

B

EXPLANATION

X velocity, range-averaged cell

X velocity, cell 1

X velocity, cell 2

X velocity, cell 3

EXPLANATION

X-velocity standard error, cell 3

X-velocity standard error, range-averaged cell

X-velocity standard error, cell 1

X-velocity standard error, cell 2

Figure 3-9. Time series of (A) rangeaveraged X velocity, cell 1 X velocity, 

cell 2 X velocity, and (B) corresponding 

X-velocity standard errors.

Figure 3-10. Time series of (A) range-averaged X velocity, cell 1 X velocity, cell 2 X velocity, cell 3 X velocity, and (B) the corresponding 

X-velocity standard errors.
102 Computing Discharge Using the Index Velocity Method

–0.5

0

0.5

1

1.5

2

2.5

3

Velocity, in feet per second

0

0.02

0.04

0.06

0.08

0.1

0.12

Standard error, in feet per second

25 30 5 5 10 15 20 25 30

November December

2009

October

EXPLANATION

EXPLANATION

A

B

X velocity, range-averaged cell

X velocity, cell 3

X velocity, cell 7

X velocity, cell 8

X-velocity standard error, range-averaged cell

X-velocity standard error, cell 3

X-velocity standard error, cell 7

X-velocity standard error, cell 8

Figure 3-11. (A) Range-averaged X velocity, cell 3 X velocity, cell 7 X velocity, cell 8 X velocity, 

and (B) the corresponding X-velocity standard errors.

Beam checks and velocity data plots are useful tools for configuring the measurement volume for ADVMs as well as evaluating changes that can occur over time at a site. USGS requires that a beam check be performed during each site visit and that, if 

possible, the ADVM be configured to perform periodic, automatic beam checks between sites visits.

Reference

SonTek/YSI, 2007, SonTek/YSI Argonaut acoustic Doppler current meter technical documentation: San Diego, Calif., 

SonTek/YSI Corporation, 234 p.
The ADVMs described in this report are most often used in conjunction with electronic data loggers, which are used to 

transmit data for storage, retrieval, and display in USGS databases. However, most data loggers in use can only transmit and 

store a limited amount of the available ADVM data. Routine review of the transmitted ADVM data is necessary to provide an 

initial method of quality assuring the velocity data and minimizing invalid or questionable data. Procedures for reviewing those 

data transmitted and stored in USGS databases were discussed earlier in this report. 

SonTekTM/YSI ADVMs can record all available data to a built-in internal recorder. The data stored in the ADVM internal memory are useful for quality control of index velocity data in part because additional data are available (but not usually 

transmitted). With this in mind, procedures for reviewing data for quality control of ADVM data, especially those data stored in 

ADVM internal memory, are documented in this appendix. Familiarity with the manufacturer documentation is recommended 

for the reviewer because it can provide useful tips to aid in reviewing ADVM data.

Internally recorded ADVM data should be retrieved from the ADVM and reviewed during every site visit. A more thorough 

review of the data should be performed in an office setting. Typically, the easiest and most efficient way to review the internally recorded data is by means of the manufacturer software package, ViewArgonaut, using the Processing option. Data can 

be selected for display in the software by using the View option on the top menu and by selecting the “Select Graph Variables” 

option. A smaller window will open that has a number of different available selections that correspond to all internally recorded 

data.

The internally recorded ADVM data may be useful in determining the quality of velocity data. Determining the velocity data quality may require review of other parameter data (multi-cell data, signal amplitude, temperature, etc.) and use of the 

combined information from each data time series. Knowledge about the available ADVM data and how the data may be used in 

analyzing quality of index velocity measurements and the ability to readily differentiate good quality (valid) from poor quality 

(invalid) data will increase the efficiency of the review. Training, practice, and consultation with an expert will help the hydrographer develop this knowledge and ability. Figures in this appendix were re-created using data exported from ViewArgonaut 

software in order to more effectively illustrate quality-control concepts.

Velocity

The first step is to plot the velocity components (typically X, Y, and sometimes Z) and look for anomalies, rapid or abrupt 

changes, and apparent increases in standard error (noisier data). Reviewing the velocity component data (range-averaged and 

multi-cell X and Y velocity) can provide a good indication of velocity data validity, although sometimes additional parameter 

data must be reviewed in order to determine data validity. The measured index velocity data may sometimes appear acceptable 

after a cursory review, while the velocity data may actually be biased or completely invalid and can only be truly quality assured 

after reviewing more of the internally recorded data. Velocity data time series can be range-averaged, multi-cell, or both depending on the ADVM configuration. 

•	 X-velocity (range-averaged).—Look for consistent X-velocity data and correlation with stage data and (or) specific 

conductance data. Velocity data will have a characteristic variability (uncertainty) for the site, which is not to be confused 

with the variation in velocity that occurs in response to hydrologic events. A change in the uncertainty can be an indication 

that the instrument may have been reconfigured or may be malfunctioning, or that the measurement volume has changed 

or is being adversely affected by debris in one or more of the acoustic beams. An example of a change in velocity variability is illustrated in figure 4-1. At this gaging station, the ADVM was reconfigured on April 19, with the averaging interval 

changed from 1 minute to 10 minutes. The result of this change is a reduction in the velocity variability.

•	 Y-velocity (range-averaged).—Y-velocity data are typically the cross-stream velocity component and should be very near 

to zero. A change in the magnitude of the Y-velocity may indicate that the orientation of the ADVM has changed or that 

some obstruction may be affecting the velocity distribution in the measured portion of the stream channel. The Y-velocity 

commonly changes during high velocity events or flow reversals; those changes indicate that the velocity field changes 

direction during these periods. Changes in the cross-stream velocity in response to flow events should be used as an indicator that the cross-stream velocity may be a significant variable that may improve the index rating and should be investigated 

as described in the rating analysis section of the report. For two-beam uplooker ADVMs (ArgonautTM-SW), the Y-velocity 

Appendix 4 – Quality Control of Index Velocity Data for SonTekTM/YSI ArgonautsTM
104 Computing Discharge Using the Index Velocity Method

is actually the vertical velocity (see Z-Velocity discussion, below), and it should also be very near to zero and should not 

change with time. 

•	 Z-velocity (if applicable).—For three- or four-beam uplooker ADVMs, the Z-velocity is the up-down (vertical) velocity. 

Vertical velocity data should be approximately equal to zero and should not show any substantial changes over time. Large 

vertical velocities (greater than 10–20 percent of the X-velocity) can be an indication of turbulent velocity conditions or an 

improperly leveled ADVM. Changes (abrupt or gradual) can indicate a change in ADVM orientation or possible debris in 

the stream channel that affects the velocity distribution in the measured water volume.

•	 Multi-cell velocity data.—As many velocity cells as possible should be transmitted, routinely reviewed, and archived in 

the NWIS database. Currently (2011), SonTekTM/YSI ADVMs are only capable of providing data via SDI-12 for the first 

five cells; however, data for up to 10 cells may be stored in the internal recorder. Examine each cell velocity time series for 

evidence of changes in the uncertainty of the velocity data compared to other velocity cells and the range-averaged velocity. A substantial change can be an indication that the measurement volume velocity is biased or being adversely affected by 

debris, side-lobe interference (for sidelookers), or flow disturbance in the stream cross section. Continuous review of highquality data will allow the hydrographer to readily identify periods when velocity data is questionable or invalid.

Range-averaged X- and Y-velocity data with a 900-second measurement interval and 240-second averaging period for 

10 days are shown in figure 4-2. The X-velocity data (downstream direction) have short-term and long-term variations that 

appear normal, with some short-term variations that are slightly greater in magnitude throughout the time series. The Y-velocity 

data (cross-stream direction) is relatively close to zero and a near constant value, which is desirable; however, there are some 

small variations at times of increasing and decreasing downstream velocity. These variations can be expected depending on the 

channel geometry upstream and downstream from the ADVM. 

For SonTekTM/YSI ADVMs, the hydrographer can select the velocity coordinate system for displaying the velocity data 

in the manufacturer’s software. Typically, the velocity coordinate systems consist of beam (velocity towards or away from the 

transducer faces), XYZ (velocity oriented to the body of the ADVM), or ENU (velocity oriented to magnetic or geographic 

North) if the ADVM is equipped with a compass. For two-beam sidelooker or uplooker ADVMs (ArgonautTM-SL and -SW), 

plotting the velocity data in beam coordinates can be a useful tool when aligning the ADVMs as described in the instrument 

installation section of the report. When a two-beam ADVM is properly aligned, the beam-coordinate velocity data should look 

like a mirror image. Misalignment of the ADVM, non-uniform velocity streamlines, or acoustic beam interference can usually 

be determined with beam-coordinate velocity plots. Index velocity, in feet per second

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

April

ADVM averaging

interval changed from

1 to 10 minutes

Figure 4-1. Effect of changing 

averaging interval on 15-minute index 

velocity data. 
Appendix 4 – Quality Control of Index Velocity Data for SonTekTM/YSI ArgonautsTM 105

The range-averaged beam velocity data for the same site and time period as in figure 4-2 are shown in figure 4-3. ADVMs 

measure velocity towards or away from the acoustic transducers and then use beam geometry (transducer angle and orientation) and (or) magnetic compass measurements to convert the beam velocity to another coordinate system. Beam 1 and beam 2 

velocity data show nearly equal magnitude and opposite sign (a mirror image), indicating that the ADVM is optimally aligned 

with the velocity streamlines. If the beam velocity data show substantial differences either in magnitude or shape, this indicates 

that the ADVM is not properly aligned and the acoustic beams are not measuring homogenous velocity streamlines or may be 

oriented closer to perpendicular to the velocity streamlines. As an acoustic beam is oriented closer to perpendicular to the velocity streamlines, that beam velocity data will be closer to zero magnitude and will bias the measured index velocity.

1 2 3 4 5 6 7 8 9 10 –1

0

1

2

3

4

5

6

December 2009

Velocity, in feet per second

X-velocity, range-averaged cell

Y-velocity, range-averaged cell

EXPLANATION

Figure 4-2. Range-averaged velocity 

time series plot of X velocity and Y 

velocity with ADVM sidelooker properly 

aligned with streamflow and normal 

velocity fluctuations. 

–3

–2

–1

0

1

2

3

Velocity, in feet per second

Beam 1 velocity

Beam 2 velocity

1 2 3 4 5 6 7 8 9 10

December 2009

EXPLANATION

Figure 4-3. Time series velocity plot 

of beam 1 velocity and beam 2 velocity 

with ADVM sidelooker properly aligned 

with streamflow and normal velocity 

fluctuations.
106 Computing Discharge Using the Index Velocity Method

The multi-cell X- and Y-velocity data for five cells for the same site and time period as figures 4-2 and 4-3 are shown in 

figure 4-4. Multi-cell data for cells 1, 3, 5, 7, and 9 indicate that all of the cells have the same response as the range-averaged 

cell (fig. 4-2), with cell 1 velocity data being 0.1 to 0.5 ft/s less than velocity data for cells 3, 5, 7, and 9 most of the time. However, the velocities are almost the same magnitude during the latter part of the time period that corresponds with a substantial 

decrease in velocity. Because cell 1 is likely closer to a bank or structure, the velocity measured in cell 1 is likely affected by the 

channel bank or the structure where the ADVM is mounted, and the range-averaged measurement volume should be adjusted 

to exclude the range corresponding to cell 1 (increase the blanking distance). The multi-cell velocity data are slightly noisier 

than the range-averaged data, but it is normal to have greater velocity variation for ADVMs when measuring with a smaller cell 

size. The Y-velocity multi-cell data are essentially the same as the range-averaged Y-velocity, which should be expected. If one 

or more of the multi-cell velocity values were different, that would be an indication that there may be changes in the velocity 

streamlines across the channel, and this should be carefully evaluated to ensure that the measurement of skewed velocity streamlines will not adversely affect the index rating.

–1

0

1

2

3

4

5

6

Velocity, in feet per second

Velocity, cell 1

Velocity, cell 3

Velocity, cell 5

Velocity, cell 7

Velocity, cell 9

1 2 3 4 5 6 7 8 9 10

December 2009

EXPLANATION

Velocity Standard Error

Velocity standard error is the standard deviation of the velocity measurements from each acoustic ping divided by the 

square root of the number of pings averaged together during the averaging period (SonTekTM/YSI, 2009). Plot the range-averaged measurement volume velocity standard error and the multi-cell standard error. Make sure all y-axis scales have the same 

range to enable easy identification of differences in magnitude. Velocity standard error should not vary substantially over time, 

but may increase slightly as velocity increases due to increased turbulence in the river or stream at higher velocity. The multicell velocity standard error time series are useful when viewed simultaneously with multi-cell velocity data. Again, increases 

in an individual measurement cell compared with other multi-cells can indicate the possibility that the multi-cell is located in 

a more turbulent region, may be affected by side-lobe interference, or could be measuring velocity affected by boundaries or 

structures.

Figure 4-5A shows the range-averaged velocity standard error for downstream velocity (X-velocity) and the cross-stream 

velocity (Y-velocity) for the same site and time period shown in figures 4-2 to 4-4. The data is relatively constant throughout the 

period shown with a few short periods where the standard error data spikes to between 0.02 and 0.04 ft/s. Those small changes 

alert the hydrographer that something is different during those periods. Overall, the standard error data for the range-averaged 

velocity looks relatively good for the 10-day period shown. 

Figure 4-4. Multi-cell X- and Y-velocity 

time series data for cells 1, 3, 5, 7, and 9.
Appendix 4 – Quality Control of Index Velocity Data for SonTekTM/YSI ArgonautsTM 107

SonTekTM/YSI ADVMs used for index velocity measurement should be configured to collect multi-cell data that overlap the range-averaged measurement volume. Review the multi-cell velocity standard error for each data period and look for 

indications that can further help determine the quality of the data during deployment periods. Although it is recommended that 

all multi-cell data be reviewed, for this example, only 5 of the 10 multi-cells are shown and discussed. Figure 4-5B shows the 

standard error for five of the velocity multi-cells (cell 1, 3, 5, 7, and 9) for the same site and 10-day period used in previous 

examples. The data indicate that the velocity standard error for cells 1, 3, 5, and 7 are relatively constant at about 0.02 ft/s, but 

the standard error for cell 9 is substantially greater than that for the other cells, ranging from 0.02 to 0.08 ft/s. Because the rangeaveraged cell and multi-cells 1 through 9 are measuring the same volume of water, and cell 9 shows increased standard error, 

the range-averaged cell velocity data are likely biased and of poorer quality than the range-averaged data alone would suggest. 

For this station, the index velocity range-averaged measurement volume should be configured to coincide spatially with cells 2 

through 7 (assuming that cell 8 had the same increases in standard error as cell 9).

Signal Amplitude, Instrument Noise Level, and Signal-to-Noise Ratio

The beam signal amplitudes and the instrument noise level provide information about the return signals from the acoustic 

pulses emitted by the ADVM, the internal instrument noise, and the relative noise in the water at the site. The signal amplitudes 

are recorded in counts (1 count = 0.43 decibels), with higher counts corresponding to stronger return acoustic signals. Plot and 

review all of the beam signal amplitudes (signal amplitudes) and instrument noise level (noise level) time-series data. Rescale 

the left and right y-axes so that they both have the same range. The signal amplitude data will likely show variations over time, 

and these variations may be normal for a stream, but also may indicate data-quality problems. Look for abrupt changes and low 

values (counts) in the signal amplitude data and try to understand the causes of variations in the data. Abrupt changes may be 

related to changes in the scatterers in the water or may be an indication of problems with the acoustic signal. Spikes or rapid 

increases can be normal, but may also indicate that one or more of the acoustic beams or side lobes are striking a surface or 

object and increasing the signal amplitudes. Signal amplitude increases should be investigated for correlation with other available data such as water level, temperature, or velocity. The signal amplitudes should be substantially greater than the noise level. 

While signal amplitudes will vary over time, depending on backscatter concentration, the noise-level data should remain relatively constant for each time period and vary by no more than two or three counts (SonTekTM/YSI, 2009). Changes in the noise 

level can be an indication that the acoustic signal is degraded, site characteristics have changed, ADVM electronics are degrading, or the communication/power cable is damaged or degrading. 

0

0.02

0.04

0.06

0.08

0.1

Standard error, in feet per second

0

0.02

0.04

0.06

0.08

0.1

Standard error, in feet per second

1 2 3 4 5 6 7 8 9 10

December 2009

X-velocity standard error,

range-averaged cell

Y-velocity standard error,

range-averaged cell

EXPLANATION

X-velocity standard error, cell 1

X-velocity standard error, cell 3

X-velocity standard error, cell 5

X-velocity standard error, cell 7

X-velocity standard error, cell 9

EXPLANATION

A

B

Figure 4-5. Time series of (A) range-averaged velocity standard error and (B) velocity standard error for multi-cell data.
108 Computing Discharge Using the Index Velocity Method

The individual signal amplitudes for each beam should have similar magnitudes and patterns. Signal amplitudes for a beam 

that are substantially different from other beam signal amplitude(s) or beam signal amplitudes having a different pattern than 

other beams, may indicate that a beam or beams (depending on the ADVM) are affected by debris in the measurement volume or 

faulty electronics. If beam signal amplitude anomalies are present in the data, it may indicate poor quality velocity data. Depending on the ADVM manufacturer and model, the signal amplitude data can be displayed differently. SonTekTM/YSI ArgonautTM 

ADVMs record the signal amplitude time series for the range-averaged measurement volume as the average of the signal 

amplitudes from the beginning to the end of the measurement volume, the average signal amplitude for each multi-cell, and the 

average beam instrument noise level. The averaged value for the measurement volume may appear to be reasonable even when 

a portion of the measured volume (multi-cell data) may have signal amplitudes that are at or near the ADVM instrument noise 

level. If the range-averaged signal amplitudes are reasonable values and the cell end is changing over time, then it is likely that 

the signal amplitudes are not of sufficient magnitude somewhere in the measurement volume. If the signal amplitudes are not of 

sufficient magnitude anywhere in the range-averaged measurement volume, the measurement volume cell end will be automatically reduced to maintain adequate signal amplitudes throughout the entire measurement volume. The change in cell end may 

adversely affect the index rating and possibly degrade the quality of computed discharge.

Reviewing signal-to-noise ratio (SNR) data is not really necessary if the beam signal amplitudes and the instrument noise 

level are reviewed. The SNR data are calculated by using the signal amplitude, subtracting the instrument noise data, and 

converting the resulting value to decibels. Reviewing the signal amplitudes and noise levels will provide more information than 

reviewing the SNR data.

Figure 4-6A shows signal amplitudes and instrument noise levels for a 90-day data period for a sidelooker ADVM. The 

signal amplitudes are relatively high, but are normal for this stream because it has relatively high suspended-sediment concentrations. The time series show increased amplitudes at the beginning and later in the time series, both of which correspond to 

increases in velocity (not shown). In addition to the larger increases, there are periodic fluctuations in the signal amplitudes for 

most of the data period. After reviewing other available data, the battery voltage time series correlates well with the periodic 

fluctuations that are seen in signal amplitude data, which is expected. Changes in available power for the ADVM, such as a solar 

panel powered battery that increases voltage during the day and decreases at night, can cause changes in the transmitted acoustic 

energy and therefore cause corresponding changes in the signal amplitude data. The instrument noise data is relatively unchanging except for a short period near the end of the time series that corresponds with constantly changing roll data, which could be 

an indication that the mount has loosened. Essentially, the data seem to be of good quality and do not provide any indication that 

the index velocity data quality is substantially affected, with the exception of the elevated noise-level data near the end of the 

record.

Figure 4-6B shows signal amplitude and instrument noise-level data for a different ADVM during a 27-day data period. 

The signal amplitude data indicate numerous abrupt changes in magnitude that do not seem reasonable. For some of the abrupt 

changes in signal amplitudes, there are substantial increases in instrument noise, which is further indication that something could 

be occurring that degrades the velocity data quality. Additional review of ADVM data revealed that substantial changes in the 

cell end correspond with the abrupt changes in signal amplitudes but not with the increases in instrument noise. The increases in 

the noise-level data might be related to ice break up and increased noise in the water because this site is subject to ice formation.

Range-Averaged Cell End

The ADVM range-averaged measurement volume is configured using the cell-begin and cell-end commands; however, 

the cell end can change automatically. This behavior is expected and necessary for up-looking ADVMs, but is undesirable for 

sidelooking ADVMs used for index velocity measurement. The range-averaged cell-end data should be plotted and reviewed 

for changes with time. If the system is an uplooker ADVM, the cell end should change over time as the water depth changes. If 

the system is a sidelooker ADVM, the cell end should not change. If the sidelooker ADVM cell end changes over time, this may 

alter the index rating and degrade the quality of computed discharge. If the sidelooker cell end does change over time, determine 

the cause for the change or changes. It may be necessary to reduce the cell end in order to maintain a constant cell-end value 

throughout every deployment.

An up-looking ADVM cell-end change is desired so that the ADVM always measures the same proportion of the water 

column as the water depth changes. Depending on the ArgonautTM model, SW or XR, the cell end is adjusted automatically 

by either the vertical acoustic level (SW) or the non-vented pressure sensor (XR). The vertical level or pressure measurements 

should be plotted and compared with the cell end to verify that both measurements are reasonable and responding to changes in 

streamflow depth.
Appendix 4 – Quality Control of Index Velocity Data for SonTekTM/YSI ArgonautsTM 109

30 5 5 10

14 16 18 20 22 24 26 28 30

25 15 20 25 30

November December

0

50

100

150

200

250

2009

2009

Signal amplitude/noise, in counts

January

2 4 6 8

February

0

50

100

150

200

250

Signal amplitude/noise, in counts

A

B

October

Signal amplitude, beam 1

Signal amplitude, beam 2

Noise level, beam 1

Noise level, beam 2

EXPLANATION

Signal amplitude, beam 1

Signal amplitude, beam 2

Noise level, beam 1

Noise level, beam 2

EXPLANATION

Figure 4-6. Time series data with (A) relatively high, yet normal, signal amplitude and noise 

level and (B) unusual signal amplitude and unusual noise level. 
110 Computing Discharge Using the Index Velocity Method

Figure 4-7A shows a sidelooker range-averaged measurement volume cell-end time series where the cell end remains constant (desirable). Figure 4-7B shows the range-averaged measurement volume cell end that is from the same 27-day time series 

shown in figure 4-6B. The cell end in figure 4-7B is constantly changing, which would ultimately result in an unstable index 

rating. The range-averaged measurement volume for this ADVM/site should be reduced such that the cell end does not change 

over time. Based on examination of this short time period, the cell end should be set to no greater than 200 feet. The multi-cell 

data should also be reviewed to make sure the measurement volume is optimized for the conditions at the site as described in the 

Configuration section of the report.

18 20 22 24 26 28 30 2 2 4 4 6 8 10 12 14 16 18 20 22 24 26 28 30

June July August

30

30.5

31

31.5

32

32.5

33

33.5

34

34.5

35

2010

Cell end, in feet

13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9

January February

100

150

200

250

300

350

400

450

500

2009

Cell end, in feet

A

B

Figure 4-7. Sidelooker ADVM 

range-averaged measurement volume 

time-series data with (A) no change in 

cell end and (B) substantial changes in 

cell end. 
Appendix 4 – Quality Control of Index Velocity Data for SonTekTM/YSI ArgonautsTM 111

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Cell end, in feet

Water depth, in feet

Water depth, in feet

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

6

7

8

9

10

11

12

Cell end, in feet

6

7

8

9

10

11

12

A

B

5 5 10 15 20 25 10 15 20

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3

30

April

April May

May

2010

2010

Cell end

Water depth

EXPLANATION

Cell end

Water depth

EXPLANATION

Figure 4-8A shows an ArgonautTM-SW uplooker ADVM cell end and acoustic water-depth time-series plot that is considered correct and normal. The left and right y-axes have been rescaled to the same range in order to easily compare the cell-end 

distance and the water depth. The plot shows that the cell end adequately follows the changes in water depth and therefore 

should not adversely affect the velocity data quality. The cell-end data has steps, and the water-depth data is a continuous line 

because the cell end data are recorded in increments of 0.1 meter (0.3 feet).

Figure 4-8. Uplooker rangeaveraged measurement volume 

and water-depth time-series 

data for (A) ArgonautTM-SW and 

for (B) ArgonautTM-XR.
112 Computing Discharge Using the Index Velocity Method

Figure 4-8B shows an ArgonautTM-XR uplooker ADVM range-averaged measurement volume (red) and non-vented pressure depth (blue) time series that is considered correct and normal. When using SI units of measurement, the pressure data is 

reported in decibars (dbars), which is approximately equal to meters in freshwater, thus making it easy to compare pressure 

data to the cell end, which is reported in meters. The pressure data depths are greater than the cell-end ranges, and the offset is 

desirable in order to prevent the cell end from extending past the water surface if there are substantial changes in atmospheric 

pressure which could bias the measured velocity data. 

Temperature

The ADVM temperature sensor is used to estimate the 

speed of sound, which is required to compute an accurate 

velocity and to accurately set the cell-end distance for sidelookers. Temperature time series should reflect natural daily 

and seasonal variations. Typically when the temperature sensor 

fails, the data values are obviously erroneous; however, on 

occasion, the errors may be less obvious. If the temperature 

time series does not change at all (flat line), it is a strong 

indication that the sensor has failed. Routine field comparisons 

between an independent temperature sensor and the ADVM 

temperature should reduce the possibility that velocity data 

will be biased due to errors in ADVM temperature sensor 

measurements.

Figure 4-9 shows an ADVM temperature time-series 

plot that appears normal for approximately one-half of the 

time series, but then abruptly changes to an unrealistic value 

(14 degrees Fahrenheit) for the remainder of the deployment. 

A malfunctioning temperature sensor will often change to an 

unrealistic value and then remain constant over time, although it may be possible for the temperature sensor to malfunction more 

subtly. Therefore, it is important to routinely verify that the ADVM temperature sensor is operating properly by means of independent water temperature measurements during every station visit per USGS policy (U.S. Geological Survey, 2010). The velocity data and the cell end for sidelookers will be affected by a malfunctioning or failed temperature sensor. When the temperature 

sensor malfunctions, the ADVM should be replaced as soon as possible. It may be possible to adjust the velocity data if an 

independent temperature sensor is at the site; however, the cell-end change caused by an erroneous speed of sound computation 

cannot be corrected. The quality of the velocity data is therefore affected, and the data may have to be identified as estimated or 

poor quality for the period of the temperature sensor failure.

Pressure 

If the ADVM has a pressure sensor, pressure data should be reviewed to ensure that the pressure data changes according 

to changes in the water level and that the pressure values are reasonable for the depth of the ADVM. This can be critical for 

ArgonautTM-XR ADVMs using the dynamic-range adjustment feature because the water-column cell end is set based on the 

pressure-sensor data. A malfunction of the pressure sensor or an erroneous pressure reading can result in invalid velocity data. 

The ADVMs currently available (2011) all use non-vented pressure sensors that require the hydrographer to “zero” the pressure sensor in the air prior to deployment in order to correct for changes in local atmospheric pressure (altitude). When using a 

non-vented pressure sensor to determine a water level, a nearby quality-controlled barometric pressure senor will be required to 

correct for changes in local atmospheric pressure. 

Most sidelooking ADVMs are equipped with a non-vented pressure sensor that is used to make a coarse depth measurement. This coarse depth measurement is used to identify a range for a valid acoustic water-level measurement. If the pressure 

sensor is not zeroed properly at the site, or if the pressure sensor malfunctions, there is an increased chance for invalid acoustic 

water-level measurements.

Figure 4-10 shows ADVM pressure-sensor time-series data for a period when the pressure sensor was working at the beginning of the deployment period, but failing soon after the hydrographer left the station. For a sidelooking ADVM, the acoustic 

water-level measurements might be erroneous during the time that the pressure sensor failed. For an up-looking ArgonautTM-XR, 

the cell-end data would be improperly set, resulting in biased velocity data that will have to be marked as estimated and may 

have to be deleted. 

May June July

0

10

20

30

40

50

60

70

80

90

100

2009

Temperature, in degrees Fahrenheit

Figure 4-9. ADVM temperature time-series data with periods of 

valid and invalid data. 
Appendix 4 – Quality Control of Index Velocity Data for SonTekTM/YSI ArgonautsTM 113

October November

–5

0

1 1 5 5 10 15 20 25 30

5

10

15

2008

Pressure, in pounds per square inch

Internal Diagnostic Beam Checks

The ArgonautTM series of ADVMs enables an additional quality-assurance test—an automatically recorded, averaged beam 

check. By default, the ArgonautTM ADVMs measure the signal amplitude profile data every 100 measurements. The diagnostic 

beam checks should be reviewed on a routine basis using the manufacturer’s software. The diagnostic beam checks are viewed 

by clicking on the “Diag” button on the tool bar at the top of the ViewArgonaut Processing window, selecting View from the 

menu across the top of the window, then moving the cursor over the “View Diagnostic Data” option, or by holding the Ctrl 

key and simultaneously pressing the “D” key. The automatic diagnostic beam checks look like an averaged beam check that is 

routinely recorded during every site visit, except the individual pings cannot be displayed; only the average of the pings and a 

profile plot of signal amplitudes over the entire range of the ADVM are displayed. The number of pings averaged together is a 

function of the averaging period. These automatic beam checks can indicate inadequate signal amplitude above the instrument 

noise that may adversely affect the measurement volume range (cell end) even though the signal amplitude time-series data values are greater than the noise-level values. As described previously, the signal amplitude or SNR time-series data are the average 

value for the entire measurement volume, which can be misleading because signal amplitudes at the farther ranges may be lower 

than desired, while the average amplitude for the entire measurement volume is within an acceptable range (greater than the 

noise level). The automatic diagnostic beam checks can reveal periods when the velocity data quality may be questionable and 

possibly provide information on how to identify and possibly prevent the decreases in quality.

Figure 4-11 shows a series of automatic diagnostic beam checks (diagnostic checks) during one deployment period. In the 

ViewArgonaut software, the display for each diagnostic check has two plots. The signal amplitudes and noise level are displayed 

in the top plot, and the lower plot shows the signal-to-noise ratio data. Because the signal amplitude provides more information 

when coupled with the noise-level data, only the upper plot for each diagnostic check will be discussed here. The diagnostic 

checks were re-created using data exported from ViewArgonaut software and only show the data from the upper plot. The first 

two diagnostic checks (figs. 4-11A and B) show normal responses for signal amplitudes with an increase in signal amplitudes 

at about 24 feet (possibly side-lobe interference) and a strong return signal return at about 30 feet (possibly the far bank or a 

strong reflector in the cross section). The signal amplitudes also show separation beginning at about 16 to 18 feet that may indicate side-lobe interference. The theoretical decay line is shown as a curved gray line and provides a guide as to how the signal 

amplitudes should decrease with range under certain conditions. The noise level is shown as a horizontal gray line and is about 

30 counts, which is typical for ArgonautTM ADVMs. The cell begin and cell end for the range-averaged measurement volume 

are shown as vertical dashed lines. In this example (fig. 4-11), the ADVM has been configured to begin the range-averaged 

measurement volume at approximately 6 feet and end the measurement volume at 16 feet. Figures 4-11C and D show two more 

diagnostic checks later in the same deployment. These plots clearly indicate that some type of obstruction has moved into the 

ADVM measurement volume that may adversely affect the velocity data quality. The information provided by the diagnostic 

checks alone may not be enough information to determine the quality of the velocity data. The velocity data for this period of 

unusual diagnostic checks may be valid, but must be verified using the other data available for review. Another diagnostic check 

made after the previous two checks shows that the obstruction in the measurement volume is no longer there and provides some 

evidence that the velocity data may be of better quality during this period (fig. 4-11E).

Figure 4-10. ADVM pressure-sensor time-series data with 

periods of valid and invalid data. 
114 Computing Discharge Using the Index Velocity Method

0

50

100

150

200

250

0

50

100

150

200

250

Signal amplitude, in counts

0 10 20 30 40 50 60

Range, in feet

0 10 20 30 40 50 60

0

50

100

150

200

250

Range, in feet

A

C

E

B

D

Beam 1

Beam 2

Theoretical decay

EXPLANATION

Figure 4-11. Sequential internal diagnostic beam checks that exhibit a normal response (A, B, E) and an abnormal response (C, D).
Appendix 4 – Quality Control of Index Velocity Data for SonTekTM/YSI ArgonautsTM 115

Figure 4-12 shows ADVM diagnostic checks for a different station and deployment period than shown in figure 4-11. 

Figure 4-12A shows the signal amplitudes diverging from the theoretical decay curve; however, the shape of the plotted signal amplitutde data is similar for both beams. Of some concern is that the signal amplitudes near the cell end (approximately 

340 feet) are very close to the instrument noise at that range and the signal amplitudes level out and diverge before the cell end. 

Figure 4-12B shows another diagnostic check for the same station at a later date during the deployment and indicates that the 

signal amplitudes have decreased even further, resulting in the cell end being automatically reduced to about 240 feet, which is 

a change of approximately 100 feet from the previous diagnostic check. With this observation, the hydrographer should plot and 

review the cell-end time-series data to determine the validity of the range-averaged velocity data during this period due to the 

changing size of the measurement volume.

0

20

40

60

80

100

120

140

160

180

200

Signal amplitude, in counts

0 50 100 150 200 250 300 350

0

20

40

60

80

100

120

140

160

180

200

Range, in feet

Signal amplitude, in counts

Beam 1

Beam 2

Theoretical Decay

A

B EXPLANATION

Beam 1

Beam 2

Theoretical Decay

EXPLANATION

Possible side-lobe interference

Figure 4-12. Changes in signal 

amplitude and cell end from 

ArgonautTM-SL internal diagnostic 

beam checks from the same 

deployment. 
116 Computing Discharge Using the Index Velocity Method

Pitch, Roll, and Heading 

Many ADVMs are equipped with an internal compass that can provide information concerning the ADVM orientation. 

Substantial changes over time in pitch, roll, or heading may indicate instrument movement. Pitch, roll, and heading should not 

change substantially (greater than 2 degrees) over time, and the values should be included in the station description for documentation purposes and should be checked during routine station visits. Sometimes changes can be caused by malfunctioning 

electronics, so further investigation of other data and a physical inspection of the ADVM may be required to determine if the 

ADVM has changed position or if the compass electronics have malfunctioned. The pitch and roll sensors in the ADVM are 

typically accurate to plus or minus 1 or 2 degrees, so the ADVM should be installed using a bubble level. The pitch and roll 

sensors should be sampled when the ADVM orientation can be verified with a bubble level, and the values should be recorded 

on the ADVM Installation and Set-up Form or the Site Visit Form and transferred to the station description. The ADVM should 

then be lowered and fastened into its desired location and position, and the heading, pitch, and roll sensors should be sampled 

again. Any differences between the readings at the surface and at the desired location should be noted and may indicate that the 

ADVM mounting structure is not level, thus requiring the ADVM orientation to be adjusted.

Figure 4-13 shows time series plots for pitch and roll and heading for an ADVM equipped with a compass. Figure 4-13A 

shows a normal time series with little or no change during the deployment period. The values for pitch and roll are about 

–1 degree, indicating that the ADVM is approximately level. These values (–1 degree) are within the accuracy of the commonly 

used pitch-roll sensors. The pitch and roll data should not show changes or drift over time. Figure 4-13B shows the heading data 

for the same ADVM and time period as shown in figure 4-13A. The heading data shows a slight increase over time of about 

2 degrees. This increase may or may not indicate that the ADVM is rotating, but the position of the ADVM should be checked to 

ensure that it has not moved or cannot move. This small change in heading (approximately 2 degrees) may also be related to the 

compass error or the presence of ferrous metals near the ADVM. Therefore, when evaluating the heading data, consider that the 

compass can be affected by ferrous objects or materials near or around the ADVM.

Summary

Routine review of the transmitted ADVM data is necessary to provide quality-assured velocity data and minimize invalid 

or questionable data. The data stored in the ADVM internal memory are useful for quality control of index velocity data, in part 

because additional data are available but not usually transmitted. Internally recorded ADVM data should be retrieved from the 

ADVM and reviewed during every site visit, and a more thorough review of the data should be performed in an office setting. 

Awareness of the available ADVM data, use of the data for analyzing index velocity measurement quality, and the ability to 

readily differentiate valid data from invalid data can increase the efficiency of the review.

–2

–1

0

1

2

Pitch/roll, in degrees

October November December

260

261

262

263

264

2008

Heading, in degrees

EXPLANATION

Pitch

Roll

A

B

Figure 4-13. (A) Pitch and roll and (B) heading data time series. 

References Cited

SonTekTM/YSI, 2009, 

ArgonautTM-SL System Manual 

Firmware Version 12.0, San 

Diego, CA, SonTekTM/YSI 

Corporation, 316 p.

U.S. Geological Survey, 2010, 

Independent water temperature 

measurement for hydroacoustic 

measurements: U.S. Geological Survey, Office of Surface 

Water Technical Memorandum 

2010.07, accessed April 18, 

2011, at http://water.usgs.gov/

admin/memo/SW/sw10.07.html.
Three hypothetical examples of stage-area comparisons are presented to provide guidance on how to compare cross-section 

surveys and determine when a change to the stage-area rating may or may not be required. Figure 5-1 shows the results of the 

initial standard cross-section survey at an index velocity station and results of three re-surveys of the standard cross section 

during the same water year as the initial survey. The initial survey data was used to create the standard cross section when the 

station was established. The above-water portions of the original survey and re-surveys were obtained using levels and stadia. 

The below-water portions of the original survey and re-surveys were obtained by means of an ADCP and motorboat. The quality of each survey and re-survey was noted as “good.” The channel survey data for each example were entered into the USGS 

AreaComp program to compute cross-sectional area and to create a stage-area rating for the range of stage measured during the 

water year. 

For the first example, a flood event occurred at the station, and a re-survey was performed at the standard cross section after 

the flood waters receded. The results of the re-survey are shown in figure 5-1B. Using these data (from figure 5-1B), a new stagearea rating was created, and the computed areas from cross-section B were compared to the computed areas from the original 

stage-area rating (fig. 5-1A). The data for computed areas from the two stage-area ratings for the minimum, maximum, and mean 

stage for a water year are shown in table 5-1 (Example B). The data indicate that substantial change occurred in the cross section for the range of stages measured during the year (6.1–30 percent change from the original standard cross-section survey). 

Furthermore, the percentage of change exceeded (1) the uncertainty in the surveys, which had an uncertainty of 5 percent based 

on the stated quality of the surveys (“good”) and (2), the discharge measurement quality ratings shown in table 5-2. According to 

Turnipseed and Sauer (2010), the qualitative discharge measurement quality ratings of good, fair, and poor correspond to accuracies of 5, 8, and greater than 8 percent respectively. Therefore, the changes that occurred in the cross section and the corresponding changes to the original stage-area rating require that a new stage-area rating be developed and used for the station. A new or 

revised stage-area rating also may necessitate the development of a new index rating. Validation discharge measurements can be 

used to determine if a new index rating will be required.

In the second example, a standard cross-section re-survey was performed 1 year after the original survey (fig. 5-1C). No 

droughts or floods occurred during the water year. The difference between computed areas from the two stage-area ratings 

for the minimum, maximum, and mean stage for a water year are shown in table 5-1 (Example C). Data indicate that (1) little 

change occurred in the computed areas based on the comparison of the original and the re-survey stage-area rating outputs for 

the range of stage measured at the station (less than 2 percent), and (2) the changes were within the uncertainties in the surveys 

(less than 5 percent) and the discharge measurement quality ratings (good to poor, 2 to 8 percent) shown in table 5-2. Therefore, 

no change in the stage-area rating is indicated.

In the third example, a standard cross-section re-survey was performed 1 year after the original survey (fig. 5-1D). No 

significant floods occurred during the water year. The differences between computed areas for the two stage-area ratings for the 

minimum, maximum, and mean stage for a water year are shown in table 5-1 (Example D). The comparison of this re-survey to 

the original rating indicates that changes occurred in the computed areas for the cross section; however, the changes may not be 

large enough to justify a change to the rating (–8.0 to –1.5 percent with a mean of –3.6 percent for the range of stage measured 

at the station). The re-survey had an estimated uncertainty of 5 percent (rated as “good”), and the discharge measurements made 

during the year were rated poor to fair at low stages and fair to good at higher stages (table 5-2). In order to determine whether 

or not a change in the stage-area rating should be made, the index rating for low stage measurements should be analyzed for any 

biases (divergence) between computed mean velocity and the mean velocity of the discharge measurements. If no bias or trend is 

evident, a change to the stage-area rating would most likely not be justified; however, if a trend or bias in the index rating at low 

stages is evident, then a change to the stage-area rating (and possibly the index rating) might be justified. In this example, it may 

be difficult to justify a change in the stage-area rating because of the high uncertainty associated with the discharge measurements at low stages when they are compared to the computed discharges. In other words, any bias or trend in the comparison of 

discharge measurements to the index rating may be smaller than the uncertainty associated with individual measurements. If the 

stage-area rating is revised, then the index rating also may need revision.

Appendix 5 – Evaluating Changes in Stage-Area Ratings
118 Computing Discharge Using the Index Velocity Method

10

15

20

25

30

35

40

10

15

20

25

30

35

40

0 200 400 600 800

Location across channel, in feet

Elevation, in feet above datum

0 200 400 600 800

A. Original standard cross-section shape

C. Standard cross-section shape after 1 year with no event

B. Standard cross-section shape after flood event

D. Standard cross-section shape after 1 year with no event

Left bank Left bank

Left bank Left bank

Right bank Right bank

Right bank Right bank

Figure 5-1. The initial standard cross-section shape and three re-surveys of the standard cross section.
Appendix 5 – Evaluating Changes in Stage-Area Ratings 119

Table 5-1. Differences in stage-area rating outputs between an original stage-area rating and stage-area ratings associated 

with three re-surveys.

[ft, foot; ft2, square foot]

Statistic Stage 

(ft)

Original 

stage-area 

rating A

Stage-area rating,a

Example B

Stage-area rating,b

Example C

Stage-area rating,b

Example D

Rated area 

(ft2)

Rated area 

(ft2)

Percent 

difference 

from (A)

Rated area 

(ft2)

Percent 

difference 

from (A)

Rated area 

(ft2)

Percent 

difference 

from (A)

Minimum 22.15 1,760 2,290 30 1,730 –1.7 1,620 –8.0

Maximum 31.98 8,640 9,170 6.1 8,610 –0.4 8,510 –1.5

Mean 25.42 3,830 4,360 14 3,790 –1.0 3,690 –3.6 a

After flood event

b

After 1 year and no flood events

Table 5-2. Discharge measurements made during a water year for the station featured in table 5-1.

[ft3/s, cubic foot per second; ft, foot; ft/s, foot per second]

Measurement 

no.

Discharge 

(ft3/s)

Measurement 

quality rating

Gage height 

(ft above datum)

Index velocity 

(ft/s)

1 14,400 Good 25.10 3.90

2 8,790 Good 24.67 2.43

3 4,490 Fair 23.58 1.29

4 639 Poor 23.81 0.16

5 4,000 Fair 23.67 1.36

6 2,530 Poor 22.45 0.85

7 14,000 Good 25.67 3.34

8 30,000 Fair 31.66 3.56

9 3,540 Fair 24.56 1.00

10 586 Poor 24.98 0.13

Implementing a Stage-Area Rating

All ratings associated with discharge are implemented under the discharge data descriptor (DD). In order to compute discharge using other variables (DDs), a processor must be configured under the “SU” option in ADAPS. The database administrator should be consulted to enable the discharge processor for a site. The stage-area and index ratings are entered under the DD 

for discharge (“STAR” and “VELO” options, respectively). 

Many streams have complex cross-sectional shapes where the stage-area relation can be closely approximated using 2nd- or 

3rd-order polynomial equations; however, these equations cannot be expressed in the current version of ADAPS. A close approximation of the stage-area relation also can be expressed as a series of short straight lines (linear rating in ADAPS) where the 

stage-area rating is a “linear” rating (look-up table) with input values of stage and corresponding output values of cross-sectional 

area with values in between computed using linear interpolation. The number of rows for the ADAPS rating has a maximum of 

999 input-output value pairs, and the interval between each stage value of the stage-area rating should be chosen to adequately 

reproduce the shape of the stage-area relation. 

The following steps should be followed when implementing a stage-area rating in ADAPS. Screen captures illustrating 

the ADAPS program input/output are shown where appropriate in order to aid in the explanation of the rating implementation 

process.

1. Start ADAPS.

2. Select the Primary Data Processing (PR) option.

Appendix 6 – Implementing the Stage-Area and Index Ratings in National 

Water Information System (NWIS) Automated Data Processing System (ADAPS) 

Version 4.10
122 Computing Discharge Using the Index Velocity Method

3. Select Update/Display Rating Tables (option 4).

4. Select the station and DD that need a new or 

updated rating.

5. Select STAR (option 4).

 Enter the new 4-digit rating ID number. It is 

recommended that a rating ID convention be specified in the USGS Water Science Center (WSC) 

Surface-Water Quality-Assurance Plan (SW QA 

Plan). 

6. Select Linear (option 1) under the Expansion 

Types menu for an input-output table rating 

(recommended).

 The display will provide an area for remarks. 

Enter text for remarks about the rating. (Example: 

Established rating, rating based on re-survey of 

cross section on March 28, 2010). More than 

one line of remarks can be entered for each 

rating. Each line is limited to 120 characters It is 

strongly recommended that information about the 

rating is provided in the remarks to assist in the 

quality-assurance review process and for historical 

documentation. Follow the on-screen directions to 

enter remarks.
Appendix 6 – Implementing the Stage-Area and Index Ratings in NWIS ADAPS Version 4.10 123

7. After entering remarks, the linear expansion rating entry table will be displayed.

 Follow the on-screen directions for entering the stage-area input and output values for the linear (table) rating. Values 

must be entered in ascending numerical order from lowest to highest. To add the input-output data value pairs, enter 

“A,” then type a stage value, a space, and the corresponding area value (Example: 1 20). 

8. Press the enter key and repeat the sequence for all the data value pairs required to adequately define the stage-area 

rating. 

9. Enter “X” to exit the Add mode. After verifying that the correct data value pairs have been entered, save the rating 

(“S”). After saving the rating, choices for entering the starting date of the rating will be presented.

 Each stage-area rating for the station requires a starting date and time for the rating to begin. The starting date and 

time is entered by using “Append a new rating date” (AP) for a new rating. For existing ratings the display also allows 

the choice of editing (ED) the starting date and time for an existing rating. Use the “Edit a rating date” (ED) option 

for an existing rating that requires revision of the starting or ending date. Select the appropriate option (AP or ED) and 

enter the date and time you want the rating to be implemented. For new stations, this date and time typically will be 

the date and time of the first valid data value. For a new rating, the starting date display will only allow the choice of 

appending a new rating. 
124 Computing Discharge Using the Index Velocity Method

10. Select append (AP) and enter the starting date and time for the rating and select the appropriate time datum (EST, CST, 

PST, or UTC). For a situation in which a rating has changed and another rating is required to represent the channel 

cross section, the date and time may be near the peak of a high-flow event, or near the date and time of a cross-section 

re-survey if a flow event cannot be verified.

If the rating you want to enter is not the first rating, but an updated rating (new cross-sectional area), then the preceding rating must be ended at a specified date and time. Enter the date and time that marks the beginning of the new 

rating, and the older rating will automatically have the ending date entered. The ending date-time of the old rating and 

the starting date-time of the new rating should not leave a gap between time periods when no rating is active. If the 

ending date and time are not correct, the values can be edited using the “ED” option. 

11. After entering the starting date and time of the stage-area rating, remarks about the timing of the rating or general 

remarks about the rating can be entered. The remarks for how the rating was developed appear at the top of the rating. 

Remarks are used to describe the rating, and the remarks entered at the time of the starting date are listed with the 

rating start time.

Implementing an Index Rating

Some steps for implementing an index rating are identical to the stage-area rating implementation. ADAPS currently 

(2011) supports three methods for implementing an index rating; (1) single-variable equation, (2) table lookup, and (3) a multiparameter, stage-factor rating. A fourth method requires that an external script be executed outside of ADAPS on the NWIS 

server and is used for the most complicated ratings. Descriptions of how to use these methods are provided below. An example 

simple-linear index rating is implemented using the equation method. An example compound-linear index rating is implemented 

using the table lookup capability. Then two example multiple-linear ratings are implemented using the multi-parameter, stagefactor rating capability and an external script.

Simple-Linear Index Ratings in ADAPS

Use the following steps for the first Equation type index rating.

1. Start ADAPS.

2. Select the Primary Data Processing (PR) option.
Appendix 6 – Implementing the Stage-Area and Index Ratings in NWIS ADAPS Version 4.10 125

3. Select Update/Display Rating Tables (option 4).

4. Select the station and DD that need a new or updated rating.
126 Computing Discharge Using the Index Velocity Method

5. Select VELO (option 2).

 Enter the new 4-digit rating ID number. A rating ID 

convention should be specified in the USGS Water 

Science Center (WSC) Surface-Water QualityAssurance Plan (SW QA Plan).

 The form for the Equation type of index rating is the 

simplest. It is a single straight line (fig. 6-1) that can 

be expressed using a simple-linear equation of the 

form

y mX b = + ,

where

y = computed-mean velocity,

m = slope of the line (also named the X variable coefficient),

X = index velocity, and

b = y intercept or intercept (defined where the regression line crosses the y-axis when x = 0).

(6-1)

Figure 6-1. Equation type of index rating.

6. To implement this type of rating in ADAPS, the Equation expansion type is selected (option 3). 

Vmean

Vindex 0
Appendix 6 – Implementing the Stage-Area and Index Ratings in NWIS ADAPS Version 4.10 127

 The form of the equation in ADAPS is slightly different from the form of the simple-linear regression equation 6-1 

above, and only two of the four variables (A and D) are used to implement a simple-linear index rating. “A” is the 

slope of the line (“m” in previous equation), and “D” is the y-intercept. Leave the variables “B” and “C” blank so they 

will have no effect on the computation of mean velocity. 

7. After entering the equation rating in ADAPS, verify that the values entered are correct and quit the equation screen. 

Then, the rating “starting date” prompt will be displayed.

 For a new rating, the starting date display will only allow the choice of appending a new rating. For existing ratings, 

the display will also allow the choice of editing the starting date and time for an existing rating (ED option). Select 

append (AP option), enter the starting date and time for the rating, and select the appropriate time datum (EST, CST, 

PST, or UTC). For a situation in which a rating has changed and another rating is required to represent changes to the 

index rating, the date and time of the start of the rating may be near the peak of a high-flow event, or near the date and 

time of a cross-section re-survey that revealed a substantial change in cross-section geometry if a flow event cannot be 

verified. This is all that is required for implementing an Equation type of index rating in ADAPS.

Compound-Linear Index Ratings in ADAPS

The second type of index rating that can be implemented in ADAPS is referred to as a compound-linear rating. Occasionally the rating can be defined as two or more lines having differing slopes with transition regions linking the lines. An example 

of such a rating is for a stream where out-of-bank flows occur, and two straight lines and a transition region are required to 

define the index rating: (1) a linear rating for in-channel flow and (2) another linear rating for out-of-bank flow. A simplified 

graph of this rating is shown in figure 6-2.

Figure 6-2. Compound-linear rating.

B

Vm A

Vi
128 Computing Discharge Using the Index Velocity Method

Segments A and B can be expressed mathematically as two straight lines with different slopes and intercepts and a region of 

transition that may or may not be curved that connects the two segments. If the index rating is of this form, it can be expressed 

using what is called a linear expansion rating in ADAPS. The linear expansion rating is a lookup table of data values with an 

input value (index velocity) and an output value (measured-mean velocity).

After determining the two straight line segments using linear regression analysis methods for each segment, the intercept of 

the two lines can be solved by setting the two equations equal to each other and solving for the index velocity value, then using 

that index velocity value in one of the original equations to determine the corresponding mean velocity value. The transition 

between the two segments likely will be curved and may require additional data points to adequately define the transition.

When implementing this rating in ADAPS, steps 1–5 (listed previously for the simple-linear index rating) are the same.

6. After computing the lowest and highest velocity values for each segment and the transition points between the two 

segments, the rating can be entered into ADAPS using the “linear” expansion type.

7. After selecting the “linear” expansion type of rating, the input (index velocity) and output (mean velocity) data values 

are entered into a table rating. The input and output values must be entered in ascending numerical order from lowest 

to highest. Enter text for remarks about the rating. (Example: Established rating, rating based on measurements 1–35, 

velocity range 0.2 to 5 ft/s, and gage heights less than 35 ft). More than one line of remarks can be entered for each 

rating. Each line is limited to 120 characters. The remarks should provide information about the rating to assist in the 

quality-assurance review process and for historical documentation. Follow the on-screen directions to enter remarks. 

After entering remarks about the rating, the linear expansion rating entry table will be displayed.

 Follow the on-screen directions for entering the index rating input and output values for the linear (table) rating. 

Values must be entered in ascending numerical order from lowest to highest. To add the input-output data value pairs, 

enter “A”, then type an index velocity value, a space, and the corresponding mean velocity value (Example: 0.01 0). 

Press the enter key and repeat the sequence for all the data value pairs required to adequately define the index rating. 

8. Enter “X” to exit the Add mode. After verifying that the correct data value pairs have been entered, save the rating (S 

option). After saving the rating, choices for entering the starting date of the rating will be displayed.
Appendix 6 – Implementing the Stage-Area and Index Ratings in NWIS ADAPS Version 4.10 129

9. Each index rating for the station requires a start date and time for the rating to begin. The starting date and time is 

entered using “Append a new rating date” (AP) for a new rating. Use “Edit a rating date” (ED) for an existing rating 

that requires a revision for the starting or ending date. (ED is only available when ratings already exist.) Select the 

appropriate option (AP or ED) and enter the date and time you want the rating to be implemented and select the 

appropriate time datum (EST, CST, PST, or UTC). For new stations, this date and time typically will be the date and 

time of the first valid data value. For a new rating, the starting date display will only allow the choice of appending 

a new rating. For a situation in which a rating has changed and another rating is required to represent the change in 

relation between index and mean velocity, often the date and time are selected such that they are near to the peak of 

a high-flow event, or the date and time may be that of the first measurement used in the new index rating if a specific 

time cannot be verified.

If the rating you want to enter is not the first rating, but an updated rating (new cross-sectional area), then the preceding rating must be ended at a specified date and time. Enter the date and time that marks the beginning of the new 

rating, and the older rating will automatically have the ending date entered. The ending date-time of the old rating and 

the starting date-time of the new rating should not leave a gap in the time period when no rating is active. If the ending 

date and time are not correct, the date and time values can be edited using the “ED” option. 

10. After entering the starting date and time of the index rating, additional remarks about the timing of the rating or other 

general remarks about the rating can be entered. The remarks for how the rating was developed appear at the top of the 

rating and are used to describe the rating. The remarks entered at the time of the starting date are listed with the rating 

start time.
130 Computing Discharge Using the Index Velocity Method

Multiple-Linear Index Velocity Rating

The third type of index rating that can be implemented in ADAPS is referred to as a multiple-linear rating. Occasionally, 

the index rating is not adequately defined using index velocity alone. The most common additional variable that is related to 

mean velocity is stage. If regression analysis indicates that index velocity and stage are significant variables and using both 

variables significantly improves the index rating, then this more complex rating can be implemented in ADAPS. A simplified 

example of a multiple-linear rating using stage and index velocity is shown in figure 6-3.

The equation that defines figure 6-3 is of the form

1 12 y aX b X X c =+ + ( ).

where,

a = slope coefficient for X1,

b = slope coefficient for X2, 

c = y intercept,

X1 = index velocity, and

X2 = stage.

The determination of the coefficients a, b, and c is made using regression analysis with index velocity (X1) and index 

velocity × stage (X1×X2) as the two independent variables, as described previously in the “Multiple-Linear Regression Rating” 

section of the report. Equation 6-3 is modified by factoring out the common term X1 (index velocity) to rearrange the equation to 

yield

1 2 y X a bX c =++ ( ).

(6-2)

(6-3)

Figure 6-3. A multiple-linear index rating.

0

2.5

3.0

2.0

1.5

1.0

0.5

0

1 2 3 4

Index velocity, in feet per second

GH = 12

GH = 10.22

GH = 8.44

GH = 6.66

GH = 4.88

Mean velocity, in feet per second

EXPLANATION
Appendix 6 – Implementing the Stage-Area and Index Ratings in NWIS ADAPS Version 4.10 131

This form of the equation is used to input the rating into ADAPS. However, the rating must be defined by using the Update 

Support Files/Record Flags (SU option) that typically has restricted access, rather than the Update/Display Rating Tables option. 

The SU option in ADAPS is only accessible by someone with ADAPS administrator rights. The following steps should be used.

1. Select the SU option.

2. Select Update Data Descriptor information (option 3). 

3. Select the station that requires the rating, then choose Edit a Data Descriptor (option ED).
132 Computing Discharge Using the Index Velocity Method

4. A list of data descriptors (DDs) will be displayed. Select the correct discharge DD, then select Display/Update DD 

Processing Information (option 2).

5. The following table will be displayed.

6. The highlighted entries (SD, IS, IV, EQ, XC, YC, and EC) must be correctly input in order for the rating to work. An 

example of a correctly entered index velocity-stage-discharge rating is shown below and represents the equation:

mean velocity 0.462 0.033( ) 0.099. =+ + X XX 1 1 2 (6-4)
Appendix 6 – Implementing the Stage-Area and Index Ratings in NWIS ADAPS Version 4.10 133

Before any values for the equation can be entered, “Use mean-velocity equation” must be set to “Yes” (option EQ), and the 

processor status must be set to “working.” Ensure that the correct DDs (IS and IV) have been selected for the rating. Also ensure 

that any old velocity ratings configured under the PR 4 option have been ended prior to the “Starts On” date in the discharge 

processor. A limitation of this method is that the rating history is not retained in ADAPS as is done with the stage-area rating 

(STAR) and index velocity rating (VELO) previously described. An electronic file of the discharge processor stage-coefficient 

index rating should be created and archived according to the WSC SW QA Plan. This could be a text file with a copy of the 

discharge processor input display and associated dates and notes that can be appended if changes to the rating are required over 

time.

Implementing a Complex Index Velocity Rating Outside of ADAPS

The fourth rating method requires the automatic execution of a script file outside of (independently from) ADAPS using a 

time-based job scheduler such as the Unix cron service. The purpose of this script is to use data from specified variables such 

as stage, index velocity, combinations of stage and index velocity, and other parameters to compute a mean velocity. In general, 

such scripts would perform the following tasks.

1. The scripts retrieve data for all variables necessary for computing a mean velocity (variables that have been found to 

be significantly related to measured-mean velocity). 

2. After the data have been retrieved, the script computes mean velocity using equations that relate mean velocity to any 

number of variables. Logical operators (if, then, else) can also be used. For example, some equations may apply only 

if a certain stage (or any other parameter) criteria is met.

3. The script automatically writes the results to a file for import into NWIS.

The external implementation of an index rating requires that a special DD be created in ADAPS for “Computed-mean 

velocity.” As with the stage-coefficient index rating, historical documentation is not automatically retained in ADAPS when 

using a script file to compute mean velocity. An electronic text file should be created, providing documentation of the equations 

used to compute mean velocity. An example of a Perl script used for a station in Florida is included below and can be modified 

for any station and any number of DDs (input variables).

Perl-Script Rating 

The following are some notes about implementing the script rating example below.

1. Header has information about the file and its workings and has documentation throughout the text. 

2. Documentation information has a “#” at the start of the line. 

3. Variable names in the script were originally chosen for a specific site. They can be changed if so desired. If variable 

names are changed, all instances of that variable name must be changed throughout the script, otherwise the script will 

not work.

4. The script can be run automatically by the job scheduler at whatever frequency desired. In one implementation of this 

script, a Unix cron job (job scheduler for Unix) executes the Perl script which creates an output file that is stored in the 

satin/rtin (realtime in) folder. 

5. After the job is run and the output file created, the data in the output file are decoded and entered into NWIS using the 

DECODES process. The location of the output file will be office specific and will need to be changed accordingly. 

6. The script may also be executed manually using the last number of days or a start time and end time (GMT). 
134 Computing Discharge Using the Index Velocity Method

#!/usr/bin/perl5

# crystal_ind.pl

# 02310747 Crystal River at Bagley Cove nr Crystal River, FL.

# June 15, 2005 began for WY2004 MRD Rating # 1.0 Computes mean velocity

# This program pulls the index velocity and gage heights from NWIS and computes a mean velocity

# Need to create a DD for computed-mean velocity so the computed-mean velocity can be stored in NWIS

# The Discharge processor will have to use the computed-mean velocity DD and the Equation rating will only need a “1” value

# for the A coefficient, effectively multiplying the computed mean velocity by one (1).

# Rating # 1.0 is a bimodal rating using 88 measurements.

# INPUT: None

# INPUT: (OR) $num_days (one ARG input from command line in days)

# INPUT: (OR) beginning date ending date (2 inputs last 2 in nwis2rdb date/time format)

# OUPUT: date and computed mean velocity corresponding to gh and index velocity at Crystal River.

#xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

# $num_days is the default time period that the program will go back to start a data retrieval and Q calculation. (INPUT: None)

#$num_days = .25;

$num_days = 5;

$site_cnt = 0; # Number of sites to be processed

$i = 0; #Counter for time comparison loop

$gh_dt = 0;

$path = “/usr/opt/www/httpd/htdocs/ttpage/springs”;

# set $path_out to springs to print in this directory or rtin to send to satin.

#$path_out = “/usr/opt/www/httpd/htdocs/ttpage/springs”;

$path_out = “/usr/opt/decodes/satin/rtin”;

use Fcntl;

use Time::localtime;

use Time::Local;

$time=time;

#------------------------------------------------------------------------------------------

#------------------------------ Allow 0, 1 or 2 command line arguments

# This is where the program uses the time period selected.

if ($cnt = @ARGV == 1) {

$num_days = $ARGV[0];

# print “I’m in the on loop\n”;

}

elsif ($cnt = @ARGV == 2) { 

$beg = $ARGV[0];

$end = $ARGV[1];

# print “I’m in the three loop\n”;

}

else { $tm = localtime($time); $timeout = sprintf (“%04d/%02d/%02d 

%2d:%02d”,$tm->year+1900,$tm->mon+1,$tm->mday+1,$tm->hour,$tm->min);

#else { $tm = localtime($time); $timeout = sprintf (“%04d/%02d/%02d 

%2d:%02d”,$tm->year+1900,$tm->mon+1,$tm-#>mday,$tm->hour,$tm->min);

}

#use this to test arguments input to program

#print “The infile is $filein\n”;

#if($num_days) {print “The number of days before the present = $num_days\n”;}

if($beg && $end){print “$beg $end\n”;}

#----------------------------------------------------------------------------------------

#---------------------------Do time stuff if interval bp is required

unless($beg && $end){ $time_int = $time - (60 * 60 * 24 * $num_days);

 $tm = localtime($time);

 $tm2 = localtime($time_int);
Appendix 6 – Implementing the Stage-Area and Index Ratings in NWIS ADAPS Version 4.10 135

 $end = sprintf (“%04d%02d%02d”,

 $tm->year+1900,$tm->mon+1,$tm->mday+1);

 #$tm->year+1900,$tm->mon+1,$tm->mday);

 $beg = sprintf (“%04d%02d%02d”,

 $tm2->year+1900,$tm2->mon+1,$tm2->mday);

#test the output of the user specified interval before present calculation

#print “Calculated begin time = $beg\n”;

#print “Calculated end time = $end\n”;

}

#-------------------------------------------------------------------------------------

#------------------------BEGIN PROCESSING OF EACH STATION

#------------------------ Extract the Gage Height and Index Velocity Data from ADAPS

@crystal_gh = ();

#

# variable name stationID “unit vales” “computed” “DDID” “begin time” “end time”

#

# -n02310747 is the station ID and -d1 indicates DDID#1 - gage height

push(@crystal_gh, `nwts2rdb -n02310747 -tuv -sC -d1 -b$beg -e$end -lGMT`); 

@crystal_ivel = ();

#-d4 indicates DDID#4 - index velocity

push(@crystal_ivel, `nwts2rdb -n02310747 -tuv -sC -d4 -b$beg -e$end -lGMT`); 

# You can add more statements that will retrieve other variables from NWIS. You will also have to add routines/statements

# below for each variable you want to retrieve in order to separate the variables from the date-time values.

# If you don’t like the existing variable names you can change them, just make sure you change them for all instances. 

#------------------------ Write UV analysis---------------------------

# take the Gage Height RDB data and separate the time and the gage height data into different arrays.

foreach $crystal_gh (@crystal_gh){

chomp($crystal_gh);

if($crystal_gh =~ /^[12]/){

($date,$HMS,undef,$crystal_gh_data,undef)=split /\t/,$crystal_gh, 4;

($y,$m,$d) = unpack(‘a4a2a2’,$date); 

($H,$M,$S) = unpack(‘a2a2a2’,$HMS); 

if($H == 24) { $H = 23; $M = 59; $S = 58;}

 $crystal_gh_et1=timelocal($S, $M, $H, $d, $m -1, $y - 1900);

# print “$crystal_gh_data”;

 push @GH, join(‘ ‘, $crystal_gh_et1,$crystal_gh_data);

}

}

#---------------------------------------------------------------

#

# This is the same as above except it is for the index velocity data

# note the variable names...ex: crystal_ivel_data and crystal_ivel_et1 (time data)

foreach $crystal_ivel (@crystal_ivel){

 chomp($crystal_ivel);

 if($crystal_ivel =~ /^[12]/){

 ($date,$HMS,undef,$crystal_ivel_data,undef)=split /\t/,$crystal_ivel, 4;

 ($y,$m,$d) = unpack(‘a4a2a2’,$date); 

 ($H,$M,$S) = unpack(‘a2a2a2’,$HMS); 

if($H == 24) { $H = 23; $M = 59; $S = 58;}

 $crystal_ivel_et1=timelocal($S, $M, $H, $d, $m -1, $y - 1900);

 push @IVEL, join(‘ ‘,$crystal_ivel_et1,$crystal_ivel_data); 

}

}
136 Computing Discharge Using the Index Velocity Method

sysopen(FILEOUT,”$path_out/crystal_q.dat”, O_WRONLY|O_TRUNC|O_CREAT) or die

“Can’t create the output file $path_out/crystal_q.dat $!\n”;

print FILEOUT “//SOURCE edltpa EDL\n”;

print FILEOUT “//STATION 02310747\n”;

print FILEOUT “//DEVICE FILE\n”;

foreach $ivel (@IVEL){

($ivel_dt,$ivel_dat)=split / /,$ivel, 3;

 

 while($gh_dt < $ivel_dt & $i <= $#GH){

($gh_dt,$gh_dat)=split / /,$GH[$i],3;

 

#####################################################################

# Multiple linear regression # 1.0

# inputs gage height and index velocity

##################################################################

#----------------------------------------------

# Next calculate the mean velocity using multiple linear regression on gh and index vel

# The index-to-mean velocity calculations start here.

#

##################################################################

if($ivel_dat >= 0) {$mvel = 1.37*$ivel_dat+0.13*$gh_dat-1.32};

if($ivel_dat < 0) {$mvel = 1.71*$ivel_dat+0.48*$ivel_dat*$ivel_dat+0.09}; 

#(this equation has index velocity squared as the second term)

#-----------------------------------------------

$tmx = localtime($gh_dt);

$tm_out = sprintf(“%02d/%02d/%02d %02d:%02d”,

$tmx->mon+1,$tmx->mday,$tmx->year-100,$tmx->hour,$tmx->min);

print FILEOUT “$tm_out $q\n”;

# print FILEOUT “$tm_out $gh_dat $ivel_dat $mvel \n”;

$i++;

}

}

close FILEOUT or die “COULD NOT CLOSE THE OUTPUT FILE!$!”;
Development and Application of Shifts for Index Ratings

Application of shifts for stage-discharge ratings is a common method used to temporarily account for changes in the stream 

conditions that affect the stage-discharge rating. In stage-discharge ratings, mean channel velocity and cross-sectional area 

(discharge) are represented by one variable—stage, allowing the hydrographer to apply shifts to stage over time to temporarily change the stage-discharge rating based on discharge measurements and field observations. Computing discharge using the 

index velocity method requires two ratings: (1) a stage-to-area (stage-area rating) and (2) an index-to-mean-velocity rating 

(index rating). As with stage shifts for stage-discharge ratings, applying shifts to index ratings to account for temporary changes 

in streamflow characteristics also must be carefully considered for an index velocity site. The techniques for applying shifts to 

index ratings presented in this appendix are only appropriate to simple-linear or compound ratings that use only index velocity 

as the independent variable.

Although changes in the channel cross section may be substantial enough to change the stage-area rating and also cause 

changes to the index rating, shifts typically are applied to the index rating. A substantial change in the standard cross-section 

shape will change the stage-area rating and, therefore, the index rating as a result of changes to flow magnitudes and (or) flow 

distribution. Two examples of temporary standard cross-section shape changes that affect the stage-area rating and possibly the 

index rating are seasonal vegetation growth and decay and temporary scour or fill of a channel from a flow event. Changes to 

the cross-section shape upstream or downstream of an index velocity site also may cause changes to velocity distributions and, 

therefore, the index rating. 

Substantial changes to the index rating also may occur independently from any change in the standard cross-sectional 

shape. Typical causes for independent changes to the index rating (such as when stage-area rating is not affected) are inadvertent index velocity sensor movement, accidental re-positioning (pitch, roll, or heading) of the ADVM, electronic failure in the 

ADVM, or interference in one or more acoustic beams.

When discharge measurements diverge from the index rating, the cause of the divergence must be identified and documented (cross-section shape change or index velocity independent change). Additionally, the magnitude of the divergence from 

the rating must be considered prior to applying a shift. The errors associated with the discharge measurement(s) and the index 

rating also must be considered prior to applying a shift to the rating. If the divergence of the measurement from the index rating 

is greater than the error of the measurement and the error of the rating, then a shift may be considered. The discharge measurement quality (excellent, good, fair, poor) should be used as a qualitative accuracy indicator and considered in the shift analysis, 

just as with stage-discharge ratings. Therefore, for a single variable (downstream velocity) rating, error can be evaluated using 

the rating plot and the index rating residuals plot.

The following is an example of the analysis and application of an index velocity shift. Stage-area and index ratings were 

developed for the gaging station in this example by using a cross-sectional survey and 11 discharge measurements. The index 

rating is shown in figure 7-1A and is defined as

mean velocity 0.92 index velocity 0.01. =∗ +

A subsequent discharge measurement (number 12) was made and plotted on the index rating (fig. 7-1A). Measurement 

12 diverges from the index rating and plots outside the range of the residuals from previous measurements (fig. 7-1B), which 

may or may not indicate that a shift is justified. Usually, basing a shift on a single discharge measurement is not recommended, 

but it is justified in some cases. First, check the validity of all the data (stage, index velocity, discharge, and measurement time 

synchronization). Once the data are checked, other reasons for the divergence should be investigated. Discharge measurement 

12 was rated as fair (5 to 8 percent accuracy) by the hydrographer. The residual for this measurement diverges from the rating 

by approximately 15 percent, and the residuals plot indicates that the measurement 12 residual is substantially greater than the 

range in the residuals for the calibration measurements. For this example, the combined uncertainty of the discharge measurement (8 percent) and the uncertainty of the index rating (estimated as approximately 5 percent based on the residual differences 

from the rating) is approximately 13 percent.

(7-1)

Appendix 7 – Index Velocity Rating Shifts
138 Computing Discharge Using the Index Velocity Method

222

1 2 1 Total error n

n = ++ ∑ error error error

The rating should not be shifted based on this single measurement because the combined uncertainty (13 percent) is very near 

the combined uncertainty of the discharge measurement and the index rating (15 percent). Because the data were verified, a 

check measurement and cross-section re-survey should be performed. However, if additional measurements show the same 

divergent trend, a shift may be considered as long as there is a plausible hydraulic basis for it. 

Subsequently, additional discharge measurements (numbers 13–15) were obtained and plotted on the index rating (fig. 7-2). 

Measurements 14 and 15 were made on the same day; measurement 15 is a check measurement that verifies measurement 14. 

A cross-section re-survey was performed on the same day that measurements 14 and 15 were made. The re-survey indicated a 

slight change in the cross-sectional area of approximately 3 to 5 percent. The results of measurements 12 through 15 combine to 

provide convincing evidence that the index rating has changed and that either a shift or a new rating should be developed. 

An additional measurement (16) was then obtained. The rating, the data used to develop the rating, and the results of measurement 12 through 16, are shown in figure 7-3A. Measurement 16 suggests that the index rating has returned to the original 

index rating. The analysis of these measurements indicates that a rating shift can be established for a period of time ranging 

from near to the time of measurement 12 to a time between measurements 15 and 16. A range of measurements (12 through 15) 

provides a way to develop a shift that can be applied to the index velocity in order to compute a corrected mean velocity. 

A shift could be computed for each measurement using the existing index rating (previously defined) and the measuredmean velocity for each measurement, solving for the index velocity. 

(7-2)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Index velocity, in feet per second

Mean velocity, in feet per second

EXPLANATION

EXPLANATION

Measurements 1–12, rating data

Measurement 12

Measurements 1–11, rating data

Measurement 12

–0.20

–0.15

–0.10

–0.05

0.00

0.05

0.10

0.15

0.20

Index rating residuals, in feet per second

A

B

Mean velocity = 0.92 * Index velocity + 0.01

Figure 7-1. (A) Index rating plot and (B) residual plot 

with a divergent discharge measurement.
Appendix 7 – Index Velocity Rating Shifts 139

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Index velocity, in feet per second

Mean velocity, in feet per second

EXPLANATION

Measurements 1–11, rating data

Measurement 12

Measurement 13

Measurement 14

Measurement 15

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Index velocity, in feet per second

Mean velocity, in feet per second

EXPLANATION

EXPLANATION

Original Rating:

Mean velocity = 0.9175 * Xvel + 0.0082

Measurements 1–11, rating data

Measurements 12–15

Measurement 16

Measurements 1–11, rating data

Measurements 12–15

Measurement 16

–0.20

–0.15

–0.10

–0.05

0.00

0.05

0.10

0.15

0.20

2009 2010

Index rating residuals, in feet per second

Sept. Oct. Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct.

A

B

Figure 7-2. Divergent discharge measurements 

and the index rating. 

Figure 7-3. (A) Rating plot and (B) residuals plot 

with original rating measurements, the index rating, 

and five validation measurements.
140 Computing Discharge Using the Index Velocity Method

measured mean velocity 0.01 shifted index velocity = 0.92

−

Shifting to each individual measurement may not be exactly valid, depending on the stream conditions, because of uncertainties 

in the discharge measurements and the index velocity. Computing a shift that is based on all the measurements diverging from 

the original index rating may be more accurate. In this example, the average value of the individual shifts (0.16) is subtracted 

from the index velocity values during the time that the rating required a shift. This shifted index velocity is then used to compute 

mean velocity in the computation of discharge. Figure 7-4 shows the results of shifting the index velocity values to match the 

measured-mean velocity from the discharge measurements.

Once the shift magnitude is determined, the beginning and ending times of the shift must be established. It may be possible to establish the time of the shifts using the stream hydrograph if the shift was due to changes in velocity distribution. If 

an electronics failure occurred, accurately defining the start and end times may be more difficult. The record quality during the 

time of the shift should be considered, unless adequate information and documentation can justify the shift based on hydraulic 

reasoning. A plot of the velocity residuals over time (fig. 7-3B) may help establish the beginning and ending times for the shift. 

In this example, the shift should be prorated over time at the start and at the end unless distinct changes in the stream or the data 

would indicate otherwise. As with stage-discharge ratings, the shift applied to an index rating is only applicable to the range of 

discharge, stage, and index velocity measured. Applying a shift to a range of conditions greater than those defined by measurements may result in an erroneous computation of discharge.

When a shift is applied, the justification for the shift must be documented in the station analysis. Evidence for the shift 

may be as simple as vegetation growing along the channel edges upstream of the index velocity sensor location that has been 

observed and documented (ideally with photographs). If visual observations of the channel conditions do not reveal a possible 

cause for the shift, then other field observations or measurements and data analysis should be made in an effort to explain the 

divergence of the measurements from the rating. Examples of additional useful field observations are verification of the index 

velocity sensor location and orientation, cross-section shape (standard cross section, upstream, and downstream cross sections), 

stage sensor malfunction, or change in offset. Examples of additional data analysis that can aid documentation and verification 

of shifts include verification of the ADVM configuration, time synchronization between in situ sensors and the discharge measurement, and quality-assurance review of internally recorded ADVM data.

When a divergence in the index rating is determined to be caused by an independent change in the index velocity sensor 

position, configuration, beam interference, or electronic failure, a shift analysis can be performed that uses regression analysis to 

determine the quantitative shift correction value. Remember that the applied shift may be limited to the range of flow conditions 

used to define the shift. In the case of an ADVM that has moved, calibration discharge measurements collected before and after 

the move are required to accurately assess the shift needed to correct the velocity data. 

A shift may not be valid for any period other than that of the discharge measurement. For example, a sidelooking ADVM 

could have been accidentally rotated so that one beam was aligned parallel to the channel flow and the other beam was aligned 

nearly perpendicular to the channel flow. A shift may be difficult to determine and apply for conditions different from those at 

the time of the measurement, especially if the index velocity data are too noisy or not representative of the mean channel velocity. In this example, the velocity data during the time of the misaligned sensor should be considered invalid. 

(7-3)

Figure 7-4. Shifted index velocity data and the index rating. 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Index velocity, in feet per second

Mean velocity, in feet per second

EXPLANATION

Measurements 1–11, rating data

Measurements 12–15 (shifted)

Measurement 16
Appendix 7 – Index Velocity Rating Shifts 141

All available information should be considered in order to apply an index rating shift, and the limitations of using velocity 

shifts should be understood. An index rating shift can be caused by a change in cross-sectional area, a change in flow distribution, seasonal changes in channels caused by vegetative growth, or electronic failures. Discharge measurements are required to 

assess and determine any shift. If the computed mean velocity is a function of index velocity only, then a shift can be applied 

temporarily to the index velocity values. Index rating shifts may only be applicable for the specific measured condition and not 

for the total range of velocity. Determining appropriate times for shift application may be more difficult for index ratings than 

stage-discharge ratings, especially if an electronics failure occurs gradually over time. Field observations and measurements, as 

well as time-series data quality reviews, are critical to appropriate shift application. The same kind of hydrologic reasoning used 

for stage-discharge shift application (such as the hydraulics of the site, changes in channel shape or roughness, etc.) should be 

used for index velocity shifts. 

Implementing a Shift for Index Ratings in National Water Information System (NWIS) Automated 

Data Processing System (ADAPS) version 4.10

1. Start ADAPS.

2. Select the Primary Data Processing (PR) option.

3. Select Update/Display Shifts (option 6).
142 Computing Discharge Using the Index Velocity Method

4. Select the station and set the DD to Discharge. 

5. Select the rating to be shifted.

 If no shift exists for the selected rating during the given water year, the following prompt will appear: RECORD NOT 

FOUND - WOULD YOU LIKE TO ADD IT [Y/N DEFAULT=Y]

Enter “Y” or press enter to bring up the edit screen to add shifts.

 If a shift exists for the given rating in the given water year, a “shift correction” menu will appear. 

Selecting AD will bring up the edit screen with the cursor at a new line below the existing shifts. Selecting ED will 

bring up the edit screen with the cursor on an existing shift line.

6. The shift input table will be displayed after the rating is selected. 

 The station number, station name, and water year are listed at the top of the table. Listed next, with the line heading 

PRV, is the last shift for that rating from a previous water year. 
Appendix 7 – Index Velocity Rating Shifts 143

The first shift for the selected water year (the 2011 water year in this example) is displayed with the line heading 

“1.” The start date and time (24-hour time) and time zone are listed on the first line, followed by the input points and 

corresponding shift values (the ± correction to index velocity). The first shift has three input points and corresponding 

shift values.

 If it is a one-point shift, the shift will be applied as a constant across the entire range of index velocities regardless of 

the index velocity entered. If it is a two- or three-point shift, the shift will be prorated between the input index velocities and will be carried as a flat shift for values less than or greater than the least and greatest specified input index 

velocities, respectively.

 On the next line, the end date and time are followed by any comments pertaining to this shift. This shift is applied to 

the period between the start time and the end time. If no end time is entered (as in this example), the shift is prorated to 

the next shift, or held constant if there is no next shift.

 The variable shift input form displays up to three shift values per page. To move the cursor from one shift value to 

another shift value, enter “M” to move to the next one or “U” to move to the previous one. To see the next page of 

shift values, enter “F.” As many as 333 pages of shift information can be entered for a water year. To move back to a 

previous page, enter “B,” which returns you to the page immediately preceding the current one. 

7. Add a new variable shift value to the end of the list by entering “A.” This automatically places the cursor at the end of 

the list after which the entry is then made.

 Enter the month, day, time, time zone, input value (index velocity), and corresponding shift values in the spaces 

provided. The time zone can be skipped by pressing enter after the time. The default time zone for that station at that 

date and time will be automatically entered, and the entry will skip to the first shift index velocity input point. Up to 

three pairs of index velocity shifts may be entered on a line after the time data. These three points are entered with the 

first point being the lowest index-velocity shift. After entry of the first line of shift information, press enter to get to the 

second line. On the second line, the date and time can be left blank, and the shift will prorate linearly through time to 

the next available shift. If a date and time is entered on the second line, the shift will be held constant through time and 

ended at the date and time specified. 
144 Computing Discharge Using the Index Velocity Method

 Note: When inputting shifts (whether inserting, adding, or changing), the input points and the corresponding shift are 

separated by spaces. The values will not be lined up perfectly under the headers as they are entered. After entering all 

data on a line, a carriage return will center the data in their respective columns. Any comments on the end date line 

should be lined up under the comment header. 

The comment line should be filled out for every shift entered. The comment should provide information about why the 

shift was applied and about the events or measurements upon which the shift is based. 

8. To discontinue entries and exit from the Add mode, enter “X.”

9. To save entries and exit, enter “S.” 

 Note: The record must be recomputed for the shift adjustments to be applied correctly.
A station analysis is a document that describes the complete analysis of the data collected, procedures used in processing 

the data, and the logic used in rating analysis and discharge computations (Rantz and others, 1982). This document should be 

prepared for each year of record (or more frequently for the Continuous Records Process) to provide a basis for review and to 

serve as a reference in the event that questions arise about the records at some future date. The station analysis should be written 

concisely and clearly and contain enough information that a hydrographer unfamiliar with the station will be able to reproduce 

the same discharge record. Two examples of a station analysis for an index velocity streamflow-gaging station are provided in 

this appendix: one for a non-tidal streamflow-gaging station and one for a tidally affected streamflow-gaging station.

Station Analysis for Non-Tidal Streamflow-Gaging Stations

Station Analysis View

02356000 FLINT RIVER AT BAINBRIDGE, GA

Responsible Office

U.S. Geological Survey

Albany - Field Office

314 Roosevelt Avenue

Albany, GA 31702

(229) 430-8420 

Most recent revision: 1/19/2011

Revised by: agotvald 

LOCATION.--Lat 30°54'41", long 84°34'48" referenced to North American Datum of 1927, Decatur County, GA, Hydrologic 

Unit 03130008, on downstream side of bridge on US 27 (Business Route), 0.2 mi downstream from Seaboard Coast Line 

Railroad bridge, and 29.2 mi upstream from Jim Woodruff Dam, 5.19 mi upstream from confluence with Fourmile Creek, 

2.37 mi downstream from confluence with Big Slough Creek, 0.6 mi northwest of Bainbridge, and at mile 29.0.

EQUIPMENT.-- Satellite telemetry data is provided by a Design Analysis H-522+ Data Collection Platform (DCP), which is 

interfaced with a Vaisala 436BD shaft encoder, a Design Analysis H340 raingage, and a 1.5 MHz SonTek Argonaut SL acoustic Doppler velocity meter (ADVM). The DCP is housed in an aluminum box shelter over a 24 inch spiral aluminum pipe 

stilling well that is attached to the downstream side of the right center bridge pier. The float indicator is used as the primary 

reference gage. A wire-weight gage on the downstream side of the bridge serves as the outside gage. The ADVM is attached to 

a sliding track that is attached to the well braces on the downstream side of the right center bridge pier. The ADVM transducers point toward the left bank.

GAGE HEIGHT RECORD.-- The primary recorder (DCP interfaced with 436BD shaft encoder) furnished a complete gageheight record of stage for the 2010 water year.

VELOCITY RECORD.--The DCP and Sontek ADVM produced a complete record of index velocity for the 2010 water year, 

except for January 26-29 and February 6-10, when communications between the DCP and the ADVM were lost. The ADVM 

performs an automated beam check of the transducers approximately every hundred measurements. The automated beam 

checks are stored in the data logger of the ADVM. Also, manual beam checks are performed during every site visit. Signal 

strength, y-velocity, and water temperature data measured by the ADVM are transmitted through satellite transmissions via 

the DCP for quality control/quality assurance (QA/QC) purposes. The beam checks and QA/QC parameters indicated that the 

ADVM furnished good data for the 2010 water year. An independent water temperature measurement is made during each site 

visit to ensure that the ADVM is measuring the water temperature accurately. The independent water temperature and ADVM 

water temperature measurements were within 1 degree Celsius for the 2010 water year. 

Appendix 8 – Example of an Index Velocity Station Analysis 
146 Computing Discharge Using the Index Velocity Method

GAGE HEIGHT CORRECTIONS.--The primary recorder readings were within limits of the float tape indicator (primary 

reference gage) for the 2010 water year. No gage-height corrections were applied for the 2010 water year.

DATUM CORRECTIONS.—Levels were last run on May 28, 2009. All gages were found reading within allowable limits so 

no datum corrections were applied for the 2010 water year. 

RATING.--The channel is fairly straight for several thousand feet upstream and has a sharp bend about 500 ft downstream. 

Prior to backwater from Jim Woodruff Reservoir (beginning April 1955) the right bank is subject to overflow at about a stage 

of 20 feet. The left bank overflows at a stage of approximately 30 feet. The discharge is affected by backwater from Jim 

Woodruff Reservoir below a stage of 25 feet. Backwater appears to be negligible above a stage of 25 feet. The discharge cannot be computed using a stage-discharge relation due to the backwater affects, so index velocity methods are used to compute 

the discharge.

Stage-Area Rating 2.0 was carried over from the previous water year. The standard cross-section used to develop Stage-Area 

Rating 2.0 is located at the downstream side of the bridge. The standard cross-section is re-surveyed every year or after major 

flood events to ensure that no substantial scour or fill occurred at the standard cross-section. The standard-cross section was 

surveyed on January 13, 2010. The measured area was within 5% of the rated channel area. Stage-Area Rating 2.0 was used 

for the entire 2010 water year.

Velocity Rating 3.0, which was constructed during the 2007 water year using measurements #364-370, was carried over from 

the 2009 water year and used for the entire 2010 water year. 

RATING SHIFTS.--Six discharge measurements, #377-382, were used in the 2010 shift analysis. The range in stage and 

mean channel velocity of the measurements and the recorded stage and computed mean channel velocity during the year are 

as follows: 

Range of stage Range of Range of measured Range of computed 

 of measurements recorded stage mean channel velocity mean channel velocity

 

 Max. 21.62 ft Max. 27.12 ft Max. 1.27 ft/sec Max. 3.21 ft/sec

 Min. 18.37 ft Min. 18.28 ft Min. 0.28 ft/sec Min. 0.17 ft/sec

Measurements #377-382 plotted within allowable limits of Velocity Rating 3.0 so no shifts were applied during the 2010 

water year. 

DISCHARGE RECORD.--Discharge was determined using the computed unit value gage-height and velocity data through 

computer applications of Stage-Area Rating 2.0 and Velocity Rating 3.0. A hydrologic comparison was made using the upstream station Flint River at Riverview Plantation, near Hopeful, GA (02355662). The hydrologic comparison is considered 

good and was used to estimate the daily discharge on January 26-29 and February 6-10, when the velocity data was missing. 

REMARKS (SANAL).--Discharge records good, except for days of estimated discharge, which are poor.
Appendix 8 – Example of an Index Velocity Station Analysis 147

Station Analysis for a Tidally Affected Streamflow-Gaging Station

Station Analysis View

021989773 SAVANNAH RIVER AT USACE DOCK, AT 

SAVANNAH, GA

Responsible Office

U.S. Geological Survey

Savannah - Field Office

190 Technology Circle Suite 125

Savannah, GA 31407

(912) 966-2689 

Most recent revision: 1/19/2011

Revised by: agotvald 

LOCATION.--Lat 32°04'51", long 81°04'53" referenced to North American Datum of 1927, Chatham County, GA, Hydrologic Unit 03060109, at the United States Army Corps of Engineers Dock on Hutchinson Island, GA.

EQUIPMENT.--Satellite telemetry data provided by a Design Analysis H-522+ Data Collection Platform (DCP) interfaced 

with a Design Analysis H-350/355 gas pressure system and a SonTek Argonaut SL acoustic Doppler velocity meter (ADVM). 

The DCP is housed in an aluminum shelter located on the left upstream corner of the U.S. Army Corps of Engineers’ dock. 

The sonde and attachment cable are encased by PVC pipe that is drilled to allow for the free flow of water at all stages. The 

ADVM is attached to a sliding track attached to the dock near the gage house. A staff gage is attached to the dock near the 

gage house. The staff gage serves as the primary reference gage.

GAGE HEIGHT RECORD.--The primary recorder (DCP and H350/H355 pressure system) furnished a complete gageheight record of stage for the 2010 water year.

VELOCITY RECORD.--The DCP and ADVM produced a complete record of index velocity for the 2010 water year, except 

for November 29 - December 2, March 29 - April 1, and July 27-30, when communications between the DCP and the Sontek 

SL were lost. 

The ADVM performs an automated beam check of the transducers approximately every hundred measurements. The automated beam checks are stored in the data logger of the ADVM. Also, manual beam checks are performed during every site visit. 

Signal strength, y-velocity, and water temperature data measured by the ADVM are transmitted through satellite transmissions via the DCP for quality control/quality assurance (QA/QC) purposes. The ADVM also logs multi-cell velocity data for 

10 cells that subdivide the sample volume. The multi-cell velocity data are used to compute discharge when obstructions are 

found within the larger sample volume. 

The beam checks and QA/QC parameters indicated that the ADVM furnished good data for the entire water year, except for 

the period of January 13 to March 29. There was considerable beam separation (more than 10 counts) observed in both the 

automated and manual beam checks during this period. The malfunctioning 1.5MHz unit was replaced with a 500 kHz unit on 

March 30, 2009. A lower frequency unit was used in order to increase the cell end of the sample volume. 

An independent water temperature measurement is made during each site visit to ensure that the ADVM is measuring the 

water temperature accurately. The independent water temperature and ADVM water temperature measurements were within 1 

degree Celsius for the entire water year. Lastly, the velocity is affected by tides, and the average salinity over the tide cycle is 

approximately 8 ppt. This value is entered in the SL configuration for speed of sound adjustment.

GAGE HEIGHT CORRECTIONS.--The primary recorder readings were within limits of the staff gage (primary reference 

gage) for the 2010 water year. No gage-height corrections were applied for the 2010 water year.

DATUM CORRECTIONS.--Levels were run on August 17, 2010. The gages were found reading within allowable limits so 

no datum corrections were applied for the 2010 water year.
148 Computing Discharge Using the Index Velocity Method

RATING.--The channel is fairly straight for several thousand feet upstream and has a slight bend about 950 ft downstream. 

Flow reversal occur on a daily basis due to the effects of tides.

Stage-Area Rating 1.0 was carried over from the previous water year. The standard cross-section used to develop Stage-Area 

Rating 1.0 is located 50 feet upstream of the gage. The standard cross-section is re-surveyed every year to ensure that no substantial scour or fill occurred at the standard cross-section. The standard-cross section was last surveyed on May 19, 2010. The 

measured area was within 5% of the rated channel area. Stage-Area Rating 1.0 was used for the entire 2010 water year.

Velocity Rating 1.0, which was developed during the 2007 water year using measurements #1-77 made over a tide cycle on 

May 30, 2007, was carried over from the 2009 water year and remained in effect until March 30, 2010, when the 1.5MHZ SL 

was replaced with a 500 kHz ADVM due to transducer malfunction. Velocity Rating 2.0 was developed using measurements 

#91-130 made over a tide cycle on April 1, 2010. Velocity Rating 2.0 was put into effect on March 30, 2010 when the 500 

MHz SL was installed. Velocity Rating 2.0 was used for the remainder of the 2010 water year.

RATING SHIFTS.--Forty-six discharge measurements, #86-132, were used in the 2010 shift analysis. The range in stage and 

mean channel velocity of the measurements and the recorded stage and computed mean channel velocity during the year are 

as follows:

Range of stage Range of Range of measured Range of computed 

of measurements recorded stage mean channel velocity mean channel velocity

Max. 5.29 ft Max. 6.09 ft Max. 2.96 ft/sec Max. 3.74 ft/sec

Min. -4.00 ft Min. -7.26 ft Min. -1.87 ft/sec Min. -3.38 ft/sec

Measurements #86-90, which were made on December 7, plotted within limits of Velocity Rating 1.0. Measurement #90, 

which was made on March 16, plotted -27.4 percent from Velocity Rating 1.0 and indicated that the index velocities were 

biased low due the beam separation observed from January 13 to March 29. The velocity data was deleted during this period 

thus no shifts were applied to Velocity Rating 1.0 for the 2010 water year. A 500KHz was installed on March 30 and measurements #91-130 were made over a tide cycle on April 1 in order to develop a rating for the new 500 kHz unit. Velocity Rating 

2.0 was constructed using measurements #91-130. Check measurements #131 made on August 17, 2010 and #132 made on 

November 19, 2010 plotted within allowable limits of Velocity Rating 2.0 so no shifts were applied to Velocity Rating 2.0 for 

the 2010 water year.

DISCHARGE RECORD.--Discharge was computed using stage and velocity unit-values along with Stage-Area Rating 1.0 

and Velocity Ratings 1.0 and 2.0. A hydrologic comparison was made with the upstream site Savannah River at Georgia Highway 25, at Port Wentworth, GA (02198920) and the downstream site Savannah River at Fort Pulaski, GA (02198980). The 

hydrologic comparisons are considered good.

REMARKS (SANAL).--Discharge records are fair.

Reference

Rantz, S.E., and others, 1982, Measurement and computation of streamflow—Volume 2. Computation of discharge: 

U.S. Geological Survey Water-Supply Paper 2175, 284 p.
Manuscript approved on May 27, 2011.

Prepared by the USGS Science Publishing Network,

Raleigh Publishing Service Center

Editorial review by Kimberly A. Waltenbaugh

Layout by Kay P. Naugle

For additional information contact

Victor A. Levesque

U.S. Geological Survey

1270 Atlantic Avenue

Conway, SC 29526

levesque@usgs.gov

This report is available online at http://pubs.usgs.gov/tm/3a23/
Levesque and Oberg—Computing Discharge Using the Index Velocity Method—Techniques and Methods 3–A23