U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 

Feasibility of Acoustic Doppler Velocity 

Meters for the Production of Discharge 

Records from U.S. Geological Survey 

Streamflow-Gaging Stations

By Scott E. Morlock, Hieu T. Nguyen, and Jerry H. Ross

Indianapolis, Indiana

2002

01–4157
U.S. DEPARTMENT OF THE INTERIOR

GALE A. NORTON, Secretary

U.S. GEOLOGICAL SURVEY

Charles G. Groat, Director

The use of firm, trade, and brand names in this report is for identification purposes only and does

not constitute endorsement by the U.S. Geological Survey.

For additional information write to: Copies of this report can be purchased

U.S. Geological Survey

Information Services

Box 25286

Federal Center

Denver, CO 80225

from:

District Chief

U.S. Geological Survey

5957 Lakeside Boulevard

Indianapolis, IN 46278–1996
CONTENTS III

CONTENTS

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

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

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

Physical Setting ........................................................................................................................................................... 3

Acoustic Doppler Velocity Meters......................................................................................................................................... 3

Principles of Operation ................................................................................................................................................ 3

Description of Models Used ........................................................................................................................................ 6

Installation Considerations .......................................................................................................................................... 8

Theory of Computation of River Discharge ................................................................................................................ 10

Study Methods....................................................................................................................................................................... 11

Installation of Acoustic Doppler Velocity Meters ................................................................................................................. 11

Rating Development .............................................................................................................................................................. 14

Stage-Area Ratings ...................................................................................................................................................... 14

Kankakee River at Davis.................................................................................................................................... 15

Fall Creek at Millersville ................................................................................................................................... 16

Iroquois River near Foresman............................................................................................................................ 17

Index Velocity Ratings................................................................................................................................................. 17

Kankakee River at Davis.................................................................................................................................... 20

Fall Creek at Millersville ................................................................................................................................... 24

Iroquois River near Foresman............................................................................................................................ 28

Ratings Applications and Limitations ......................................................................................................................... 31

Acoustic Doppler Velocity Meter Discharge Records........................................................................................................... 35

Computation of the Records ........................................................................................................................................ 35

Comparison of the Records ......................................................................................................................................... 38

Evaluation of the Records............................................................................................................................................ 42

Use of Acoustic Doppler Velocity Meters for the Production of Discharge Records ........................................................... 47

Ice-Affected Periods .................................................................................................................................................... 47

Multi-Cell Capabilities ................................................................................................................................................ 48

Velocity Shifts.............................................................................................................................................................. 48

Real-Time Discharge Data........................................................................................................................................... 48

Upland Rivers and Streams.......................................................................................................................................... 48

Rating of Acoustic Doppler Velocity Meter Discharge Records................................................................................. 49

Potential Future Studies......................................................................................................................................................... 49

Summary and Conclusions .................................................................................................................................................... 49

References.............................................................................................................................................................................. 51

Appendix................................................................................................................................................................................ 53

FIGURES

1. Map showing locations of acoustic Doppler velocity meter evaluation sites in Indiana .......................................... 4

2. Schematic of acoustic Doppler velocity meters ........................................................................................................ 5

3. Photographs of Argonaut-SL and EasyQ .................................................................................................................. 6

4. Sketch of acoustic Doppler velocity meter signal strength showing selection of ADVM sample-volume end 

based on a boundary-interference spike and instrument-noise level......................................................................... 9

5–7. Photographs and site sketch of acoustic Doppler velocity meter evaluation station:

5. Kankakee River at Davis, Ind............................................................................................................................ 11

6. Fall Creek at Millersville, Ind. .......................................................................................................................... 12

7. Iroquois River near Foresman, Ind.................................................................................................................... 13

8. Graph of acoustic Doppler velocity meter velocity unit values showing the effect of increasing the ADVM 

averaging interval from 1 to 10 minutes, from the Iroquois River near Foresman, Ind., ADVM evaluation 

station, June 25–27, 2000.......................................................................................................................................... 14
IV CONTENTS

9–11. Surveyed and standard cross sections at acoustic Doppler velocity meter evaluation station:

9. Kankakee River at Davis, Ind............................................................................................................................ 15

10. Fall Creek at Millersville, Ind. .......................................................................................................................... 16

11. Iroquois River near Foresman, Ind.................................................................................................................... 18

12–21. Graphs showing:

12. Mean velocity and acoustic Doppler velocity meter velocities from discharge measurements made at the

Kankakee River at Davis, Ind., ADVM evaluation station ............................................................................... 22

13. Index velocity ratings for cells 1 and 2 of an acoustic Doppler velocity meter at the ADVM evaluation 

station Fall Creek at Millersville, Ind. .............................................................................................................. 26

14. Index velocity rating for an acoustic Doppler velocity meter at the ADVM evaluation station Iroquois River 

near Foresman, Ind............................................................................................................................................ 30

15. Velocity profiles from the Kankakee River at Davis, Ind., acoustic Doppler velocity meter evaluation 

station, for profiles collected at high and low stages, and the Iroquois River near Foresman, Ind., and 

Kankakee River at Davis, Ind., ADVM evaluation station ............................................................................... 33

16. Acoustic Doppler velocity meter cell 1 and 2 velocity unit values and beam-amplitude unit values

from the ADVM evaluation site Fall Creek at Millersville, Ind., December 1, 2000–February 28, 2001........ 37

17. Comparison of mean-daily discharge hydrographs produced by conventional method and acoustic Doppler

velocity meter methods from the Kankakee River at Davis, Ind., ADVM evaluation station, 

June 1, 1999–February 28, 2001....................................................................................................................... 39

18. Comparison of mean-daily discharge hydrographs produced by conventional method and acoustic Doppler

velocity meter methods, using ADVM cell 1, from the Fall Creek at Millersville, Ind., ADVM evaluation 

station, March 23, 2000–February 28, 2001 ..................................................................................................... 40

19. Comparison of mean-daily discharge hydrographs produced by conventional method and acoustic Doppler

velocity meter methods, using ADVM cell 2, from the Fall Creek at Millersville, Ind., ADVM 

evaluation station, March 23, 2000–February 28, 2001.................................................................................... 41

20. Comparison of mean-daily discharge hydrographs produced by conventional method and acoustic Doppler

velocity meter methods from the Iroquois River near Foresman, Ind., ADVM evaluation station, 

October 1, 1999–February 28, 2001 ................................................................................................................. 43

21. Stage and acoustic Doppler velocity meter (ADVM) measured velocity unit values from the Iroquois River 

near Foresman, Ind., ADVM evaluation station, April 15–July 31, 2000......................................................... 44

22. Example of near real-time discharge hydrograph from Iroquois River near Foresman, Ind., served on the 

World Wide Web ...................................................................................................................................................... 46

23. Photographs of tow tank and tow cart and deep tank at the U.S. Geological Survey Hydraulics Laboratory,

Stennis Space Center, Mississippi............................................................................................................................. 56

TABLES

1. Selected specifications for the Argonaut-SL and EasyQ instruments installed at U.S. Geological Survey 

streamflow-gaging stations in Indiana .................................................................................................................... 7

2. Selected river characteristics at three acoustic Doppler velocity meter evaluation sites, Indiana .......................... 14

3. Stages and computed channel areas used to create a tabular stage-area rating for the Fall Creek at 

Millersville, Ind., acoustic Doppler velocity meter evaluation station ................................................................... 17

4. Stages and computed channel areas used to create a tabular stage-area rating in ADAPS for Iroquois River, Ind.,

ADVM evaluation station........................................................................................................................................ 19

5. Summary of discharge-measurement data from the Kankakee River at Davis, Ind., acoustic Doppler velocity 

meter evaluation station, June 30, 1999–February 27, 2001................................................................................... 21

6. Comparison of discharges computed using an acoustic Doppler velocity meter (ADVM) to measured 

discharges at the Kankakee River at Davis, Ind., ADVM evaluation station for June 30, 1999–

February 27, 2001 ................................................................................................................................................... 24

7. Summary of discharge-measurement data from the Fall Creek at Millersville, Ind., acoustic Doppler velocity 

meter station, March 30, 2000–August 23, 2000 .................................................................................................... 25

8. Comparison of discharges computed using an acoustic Doppler velocity meter to measured discharges from the 

Fall Creek at Millersville, Ind., ADVM evaluation station, March 30, 2000–January 24, 2001 ............................ 28
CONTENTS V

9. Summary of discharge-measurement data from the Iroquois River near Foresman, Ind., ADVM evaluation 

station, October 15, 1999–June 26, 2001................................................................................................................ 29

10. Comparison of discharges computed from acoustic Doppler velocity meter to measured discharges from the

Iroquois River near Foresman, Ind., ADVM evaluation station, October 15, 1999–February 12, 2001................ 31

CONVERSION FACTORS

Additional abbreviation:

MHz, megahertz

Multiply By To obtain

inch 2.54 centimeter

centimeter (cm) 0.3937 inch

foot (ft) 0.3048 meter

meter (m) 3.281 foot

mile (mi) 1.609 kilometer

square mile (mi2) 2.590 square kilometer 

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

pound, avoirdupois (lb) 0.4536 kilogram 

kilogram (kg) 2.205 pound, avoirdupois

foot per second (ft/s) 30.48 centimeters per second
Abstract 1

Feasibility of Acoustic Doppler Velocity Meters 

for the Production of Discharge Records from

U.S. Geological Survey Streamflow-Gaging Stations

By Scott E. Morlock, Hieu T. Nguyen, and Jerry H. Ross

Abstract

It is feasible to use acoustic Doppler 

velocity meters (ADVM’s) installed at 

U.S. Geological Survey (USGS) streamflowgaging stations to compute records of river 

discharge. ADVM’s are small acoustic current 

meters that use the Doppler principle to measure 

water velocities in a two-dimensional plane. 

Records of river discharge can be computed 

from stage and ADVM velocity data using the 

“index velocity” method. The ADVM-measured 

velocities are used as an estimator or “index” of 

the mean velocity in the channel.

In evaluations of ADVM’s for the computation of records of river discharge, the USGS 

installed ADVM’s at three streamflow-gaging 

stations in Indiana: Kankakee River at Davis, Fall 

Creek at Millersville, and Iroquois River near 

Foresman. The ADVM evaluation study period 

was from June 1999 to February 2001. Discharge 

records were computed, using ADVM data from 

each station. Discharge records also were 

computed using conventional stage-discharge 

methods of the USGS. The records produced from 

ADVM and conventional methods were compared 

with discharge record hydrographs and statistics. 

Overall, the records compared closely from the 

Kankakee River and Fall Creek stations. For the 

Iroquois River station, variable backwater was 

present and affected the comparison; because the 

ADVM record compensates for backwater, the 

ADVM record may be superior to the conventional record. For the three stations, the ADVM 

records were judged to be of a quality acceptable 

to USGS standards for publications and near realtime ADVM-computed discharges are served on 

USGS real-time data World Wide Web pages. 

INTRODUCTION

The U.S. Geological Survey (USGS) operates a 

network of more than 7,200 streamflow-gaging 

stations in the United States (Wahl and others, 1995) 

for the production of continuous records of stream and 

river discharge. The USGS annually publishes the 

record from each streamflow-gaging station as mean 

daily discharge values and provides real-time 

discharge data from more than 4,200 streamflowgaging stations (Wahl and others, 1995). The availability of near real-time discharge data has become 

increasingly important to government agencies and 

private companies who require detailed data quickly 

for optimal water-management strategies (Mason and 

Weiger, 1995).

Historically, the USGS has relied on conventional methods to produce discharge records from 

streamflow-gaging stations. Conventional methods 

include the measurement and recording of stage 

(“stage” as used here means the water level of the river 

or stream referenced to an established datum) by automated sensors and electronic data loggers; the periodic 

measurement of discharge, using mechanical or 

acoustic current meters for a range of stages; and the 

development of a relation called a “stage-discharge 

rating.” 

USGS personnel make periodic discharge 

measurements at streamflow-gaging stations by 

measuring water depths with a wading rod or sounding 
2 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

weight, measuring velocities with a propeller-type 

current meter in numerous subsections across a river 

or stream channel, and integrating the subsection 

discharges (Rantz and others, 1982, explains the 

method in detail). Another method of measuring 

discharge is to use a hydroacoustic device, called an 

acoustic Doppler current profiler (ADCP), attached to 

a moving boat (for purposes of this discussion, ADCP 

is used as a generic term and does not refer to any 

particular product or model). The ADCP simultaneously measures water velocities, depths, and 

traverse length to compute discharge as it is moved 

across the channel (see Morlock, 1994, for more 

detailed information about ADCP discharge measurements). 

For each measurement of discharge, a mean 

stage for the measurement period is computed. When 

enough discharge measurements have been made for a 

wide range of stages, a stage-discharge rating can be 

developed for a streamflow-gaging station. Discharges 

then can be computed from the stage data. Stages 

are recorded on an even interval (commonly 15 or 

60 minutes) called a stage “unit value”; each stage unit 

value yields a computed discharge unit value. The 

average of the discharge unit values over a 24-hour 

period is the mean daily discharge. A record of mean 

daily discharges is called discharge record.

Once a stage-discharge rating is developed, 

discharge measurements continue to be made to check 

the validity of the rating. Changes in the hydraulic 

characteristics of a stream can cause temporary or 

lasting changes in the stage-discharge rating. These 

changes are found when discharge measurements 

depart from the stage-discharge rating by more than 

a USGS-set percent tolerance that is based on the 

quality of the discharge measurement. It is standard 

USGS practice, when one or more measurements 

reveal a change in the rating, to apply a “stage shift” 

that temporarily adjusts the rating so that the measurement and rating-computed discharges are within tolerance. The USGS has procedures for determining shifts 

and correcting a rating (Rantz and others, 1982). 

Complex flow conditions at many potential 

streamflow-gaging stations may negate stable stagedischarge ratings and make the use of conventional 

methods impractical or impossible. These conditions 

include flow reversals, backwater effects, hysteresis 

effects (different stage-discharge relations for rising 

and falling stages), and channel-roughness changes 

(such as seasonal vegetation growth, ice cover, and 

changes in bed forms as in the case of dune migration).

For stations where conventional methods cannot 

be used, the USGS has installed velocity-measuring 

instruments, including electromagnetic and mechanical deflection-vane instruments. Instruments that use 

hydroacoustics (sound propagated in the water) have 

become prevalent for velocity measurements. The 

velocity data from these instruments, together with 

stage data, can be used to produce discharge records 

from data collected at streamflow-gaging stations. 

Acoustic velocity meters (AVM’s), instruments that 

use traveltimes of acoustic signals to measure water 

velocities, were the first hydroacoustic instruments 

used by the USGS at streamflow-gaging stations. 

These instruments continue to be used to produce 

discharge records at streamflow-gaging stations across 

the United States.

Recently, hydroacoustic instruments called 

acoustic Doppler velocity meters (ADVM’s), developed for river applications, have become available for 

use at streamflow-gaging stations. ADVM’s are small 

and easy to install and maintain. With the use of 

ADVM’s, it may be possible to produce discharge 

records from stations where conventional methods 

cannot be used. ADVM’s may not only assist in the 

production of discharge records from stations where 

conventional methods work, but they may do so with 

greater accuracy and efficiency. As of February 2001, 

an estimated 150 to 200 ADVM’s have been purchased 

by the USGS for installation at streamflow-gaging 

stations. 

Purpose and Scope

The purpose of this report is to describe the 

feasibility of using ADVM’s for the computation of 

discharge records from USGS streamflow-gaging 

stations. Two models of ADVM’s from two different 

manufacturers were used in this feasibility study: the 

SonTek Argonaut-SL and the Nortek EasyQ. It is not 

the intent of this study to compare the instruments or 

to recommend an instrument as the better one for the 

purpose of producing discharge records. It is not 

meant to imply that these are the only two instruments 

of this general type that could be used to produce 

discharge records. These two instruments were 

included in the study because both were designed 

specifically for producing discharge records.
ACOUSTIC DOPPLER VELOCITY METERS 3

The study was performed by installing ADVM’s 

at three USGS streamflow-gaging stations in Indiana. 

ADVM data were used to compute records of discharge from each of the streamflow-gaging stations. 

These records of discharge were compared to the 

records of discharge computed with conventional 

methods. The study period was from June 1, 1999, 

to February 28, 2000.

Physical Setting

ADVM’s were installed at three USGS streamflow-gaging stations in Indiana: Kankakee River at 

Davis, Fall Creek at Millersville, and Iroquois River 

near Foresman (fig. 1): 

• The Kankakee River at Davis (05515500) is in the 

Illinois River Basin. The USGS has operated this 

station since October 1924 (Stewart and others, 

1999). The drainage area upstream from the 

station is 537 mi2

.

• The Iroquois River near Foresman (05524500) is in 

the Illinois River Basin. The USGS has operated 

this station since December 1948 (Stewart and 

others, 1999). The drainage area upstream from 

the station is 449 mi2.

• Fall Creek at Millersville (03352500) is in the 

Wabash River Basin. The USGS has operated this 

station since October 1929 (Stewart and others, 

1999). The drainage area upstream from the 

station is 298 mi2

. The flow is regulated by an 

upstream water-supply reservoir.

The Kankakee River and Fall Creek stations 

were selected as ADVM evaluation stations because 

the quality of the discharge record produced by 

conventional USGS methods was judged to be good, 

which provided a basis for comparison of the 

discharge record produced with ADVM data. 

The Iroquois River station was selected for 

ADVM installation in an effort to improve the record 

of discharge. Historically, variable backwater has 

affected the quality of the record from this station; the 

cause of the backwater has not been determined. A 

stable stage-discharge rating can be determined only 

when rates of change in discharge are stable in relation 

to rates of change in stage. Backwater is a condition 

where stage increases are not accompanied by stable 

changes in discharge—in some cases, discharge may 

decrease as stage increases. Backwater can be caused 

by debris, ice jams, control structures, or the confluence of another river downstream from a streamflowgaging station. For the Iroquois River station, the 

cause of the backwater has never been determined. 

The backwater affecting this station is called variable 

backwater because it only occurs during some periods. 

Because ADVM-measured velocity data are a more 

direct measure of discharge than stage data, it was 

hoped that ADVM data could be used to produce accurate discharge records during variable-backwater 

periods. 

ACOUSTIC DOPPLER VELOCITY METERS

The term “acoustic Doppler velocity meter” is 

descriptive of how the instrument operates. An ADVM 

measures water by velocity using the Doppler principle applied to sound (acoustics) transmitted underwater. 

Principles of Operation

An ADVM uses a pair of monostatic acoustic 

transducers set at a known orientation to measure 

water velocities. “Monostatic” refers to the capability 

of each transducer to transmit and receive sound 

(SonTek Corporation, 2000). Each ADVM transducer 

transmits sound pulses (pings) of a known frequency 

along a narrow “acoustic beam” (fig. 2). As the pings 

travel along the acoustic beam, they strike particulate 

matter (scatterers) suspended in the water. When the 

pings strike scatterers, some of the sound is reflected 

along the acoustic beam to the transducer. The returned sound (echo) has a frequency (Doppler) shift 

proportional to the velocities of the scatterers and 

water they are traveling in along the acoustic beam. 

The two acoustic beams are set at a known angle 

(beam angle) in a two-dimensional plane that is 

parallel to the water surface (fig. 2) so if seen from 

above, they would be in a “V” configuration. From 

velocities measured along the individual acoustic 

beams, the ADVM uses trigonometry (because the 

beam angle is known) to compute velocity in a user-set 

part (sample volume) of the plane defined by the 

beams (fig. 2). An ADVM will compute and output a 

mean velocity for the sample volume; the velocity is 
4 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

LAKE MICHIGAN

Figure 1. Locations of acoustic Doppler velocity meter evaluation sites in Indiana.
ACOUSTIC DOPPLER VELOCITY METERS 5

Sample volume Beam angle

Pings

Echoes

Scatterers

Velocity measured along acoustic 

beam

Computed

samplevolume 

velocities

x-component 

y-component

Flow direction

ADVM with convex 

transducer head 

Sample volume 

divided into three 

evenly spaced 

cells

ADVM with 

concave transducer 

head

Cell 1

Cell 2

Cell 3

Shore

output in terms of an x-component and a y-component. 

In a typical installation where the ADVM is mounted 

on the side of the river, the x-component is the component of velocity parallel to the main flow direction 

of the river (“along flow”) and the y-component of 

velocity is perpendicular to the main flow direction 

of the river (“across flow”). The ADVM’s sample 

velocities over a period of time set by the user, the 

“averaging interval,” and report the x- and y-components of the mean velocity sampled during the 

averaging interval. 

An important ADVM parameter is signal 

strength, which is a measure of the strength of the 

echoes returned to the ADVM. Signal strength 

decreases with distance from the ADVM because of 

sound absorption and spread of the acoustic beams 

(SonTek Corporation, 2000). The maximum-measurement range of an ADVM is dependent upon the 

Figure 2. Acoustic Doppler velocity meters (ADVM’s).
6 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

distance at which the signal strength approaches the 

instrument-noise level. For this discussion, the instrument-noise level may be considered the signal strength 

of the ADVM measured while the ADVM is out of the 

water (SonTek Corporation, 2000). ADVM manufacturers sometimes use the terms “signal strength” and 

“beam amplitude” interchangeably. 

Description of Models Used

The Argonaut-SL and EasyQ (fig. 3) are similar 

in construction and features. Both consist of a transducer head attached to a canister-shaped housing that 

contains the instrument data-processing electronics. 

The Argonaut-SL has a convex transducer head, while 

the EasyQ has a concave transducer head (fig. 2). Both 

instruments have a watertight cable connector for the 

attachment of a communications/power cable. 

Selected specifications for the Argonaut-SL and 

EasyQ used in this study are given in table 1.

The EasyQ measures and outputs velocities 

from three separate, consecutive cells within the 

sample volume (fig. 2). Each cell’s size can range from 

0.4 to 2 m (the maximum distance to the beginning of 

the first cell is 6 to 8 m, giving a maximum range of 

16 m). The EasyQ was equipped with an upwardlooking transducer designed to measure stage acoustically. 

Argonaut-SL’s and EasyQ’s are available with 

features or options not present in instruments used for 

this study. For example, the Argonaut-SL is available 

in different form factors (shapes) and has an upwardlooking stage transducer and multi-cell (5 cells) capability, as well a 3.0-MHz-frequency unit intended for 

smaller rivers and streams. A long-range, 1-MHz 

EasyQ model is available with 4-m cells. The operating principles and application of instruments 

discussed in this report generally will be unaffected by 

these other features or options. 

The Argonaut-SL and EasyQ manufacturers 

provide software used to program their instruments. 

Programmable parameters include sample-volume size 

and velocity-sampling interval. The software also is 

used to perform data-quality and instrumentdiagnostic checks. 

Figure 3. Photographs of Argonaut-SL and EasyQ.
ACOUSTIC DOPPLER VELOCITY METERS 7

The Argonaut-SL and the EasyQ can be interfaced with electronic data loggers (EDL’s). The USGS 

uses EDL’s to collect and store parameters from 

sensors; the parameters then can be retrieved remotely 

from the EDL’s by using various telemetry methods 

for real-time-data applications. The ADVM can be 

interfaced with an EDL by using the SDI-12 (serialdigital interface at 1200 baud) communication 

protocol commonly used by the USGS. To use the 

SDI-12 protocol, a sensor is connected to a cable that 

consists of a data wire, power wire, and ground wire. 

Using the SDI-12 protocol, a number of sensors can be 

connected to the same EDL through a single communications port. An EDL using the SDI-12 protocol 

issues a measurement command to the ADVM. The 

ADVM returns a data string to the EDL that tells the 

EDL the length of time the ADVM will sample and the 

number of parameters that will be returned to the EDL 

after the sampling is complete. After the sampling is 

complete, the ADVM sends a data string to the EDL 

containing the sampled parameters.

The SDI-12 standard allows an EDL to collect 

up to nine parameters from the Argonaut-SL. The 

parameters relevant to using an Argonaut-SL for the 

production of river discharge include the following:

• Velocity x-component: the x-component of the 

mean velocity measured within the sampling 

cell (fig. 2).

• Velocity y-component: the y-component of the 

mean velocity measured within the sampling 

cell (fig. 2).

• Computed velocity vector: the resultant vector 

computed from the x- and y-velocity components, 

using the following formula:

V = (Vx2 + Vy2

)

1/2 (1)

where,

Vx is the velocity x-component, 

Vy is the velocity y-component, and

V is the computed velocity vector.

• Standard deviation: the mean standard deviation 

of the Argonaut-SL velocity measurement.

• Signal strength: the mean strength of the echoes 

returning to the Argonaut-SL.

• Temperature: the mean temperature measured 

by the Argonaut-SL.

The SDI-12 option allows an EDL to collect up 

to 18 parameters from an EasyQ. The parameters relevant to using an EasyQ for the production of river 

discharge include the following five:

Table 1. Selected specifications for the Argonaut-SL and EasyQ instruments installed at U.S. Geological Survey 

streamflow-gaging stations in Indiana 

[cm, centimeter; kg, kilogram; m, meter; MHz, megahertz]

Feature Argonaut-SL EasyQ

Length (cm) 18.0 58.9

Diameter (cm) 15.2 7.5

Weight in air (kg) 2.5 1.7

Transducer beam angle (degrees) 25 25

Sample volume minimum start distance (m) .5 .2

Sample volume maximum distance (range) (m) 22.0 16.0

Transducer frequency (MHz) 1.5 2.0

Number of cells within sample volume 1 3
8 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

• Velocity x-components for cells 1, 2, and 3: the 

x-components of the mean velocities measured 

within each of the three EasyQ cells (fig. 2).

• Velocity y-components for cells 1, 2, and 3: the 

y-components of the mean velocities measured 

within each of the three EasyQ cells (fig. 2).

• Amplitudes for cells 1, 2, and 3: the average echo 

strength within each of the three EasyQ cells.

• Stage: the stage output from the EasyQ upwardlooking transducer. 

• Pitch and roll: the pitch and roll of the EasyQ 

computed by the EasyQ on-board tilt sensor.

Installation Considerations

A primary ADVM-installation consideration is 

avoidance of acoustic-beam signal contamination 

caused by boundary reflections. Boundaries in a river 

can include the water surface, river bottom, structures 

such as bridge piers, and objects such as rocks and 

logs. The ADVM’s described in this report have 

narrow (about 2-degree) acoustic beams; the beams 

spread with range from the ADVM and, in a shallow 

river or stream, may strike the surface or bottom, 

causing beam contamination and biases in the ADVM 

velocity measurements. Boundary interference can be 

prevented with the use of aspect ratio, which provides 

an estimate of maximum ADVM range and is 

expressed as range/distance. “Range” is the maximum 

sample volume range, and “distance” is the distance to 

the closest boundary (an example using an aspect ratio 

of 4: an ADVM that is 1 m deep and 2 m from a river 

bottom should be programmed so that the maximum 

sample volume range is no greater than 4 m). The 

aspect ratio indicates that an ADVM will have less 

range in shallow than in deep rivers and streams. In 

most conditions, aspect ratios of 8 to 10 will work and, 

at many stations with high backscatter and smooth 

bottoms, aspect ratios could be greater than 15 (Craig 

Huhta, SonTek Corporation., written commun., May 

23, 2001).

ADVM signal strength can be used to check for 

boundary interference within the sample volume. If no 

boundary interference is present, the signal strength of 

each beam should peak at the transducer and then 

gradually decrease with distance from the transducer 

(fig. 4). Boundary interference will cause the signal 

strength to increase markedly or “spike” (fig. 4). 

A spike in the ADVM sample volume means that 

boundary interference may produce unreliable velocity 

data. The size of the sample volume would need to be 

selected so the spike remains outside the sample 

volume. ADVM manufacturers recommend the end of 

the sample volume be placed no closer than 10 percent 

of the total distance from the ADVM to the boundary 

(for example, if a boundary is discovered at 10 m, the 

end of the sample volume should be no farther than

9 m). The 10-percent recommendation is designed to 

minimize a phenomenon known as “sidelobe interference” (SonTek Corporation, 2000).

If no boundary interference is detected within 

the maximum range of the ADVM, selection of the 

sample-volume-end distance should be based on 

the instrument-noise level. The manufacturers recommend that the sample-volume end be programmed so 

that the beam-signal strengths at the sample-volume 

end are about five counts above the instrument-noise 

level (fig. 4). ADVM software will display the signal 

strengths in units of counts, where one count equals 

about 0.43 decibel. 

The end of the sample volume is selected to 

prevent boundary interference and to be above the 

instrument-noise level. The beginning of the sample 

volume should be selected to minimize turbulence 

from the structure on which the ADVM is mounted. 

If beam-signal strengths drop below the five 

counts above the instrument-noise level, the ArgonautSL has a feature that automatically will reduce the end 

of the sample volume. To ensure accuracy, the user 

should consider setting the end of the sample volume 

as specified above so the Argonaut-SL does not reduce 

the end of the sample volume; a reduction would 

change the sample-volume size and could change the 

index-velocity relation. 

Another programming consideration is the relation of velocity-measurement errors to the averaging 

interval. ADVM measurement errors will result from 

instrument and environmental sources; environmental 

errors likely will dominate instrument errors. There 

will be random instrument errors associated with the 

measurement of velocity using a single ping. Errors 

are reduced by averaging pings, which increases the 

averaging interval. Some environmental errors will be 
ACOUSTIC DOPPLER VELOCITY METERS 9

caused by turbulence, the size of turbulent eddies as 

dictated by channel geometry, and short-term flow 

pulsations. At stations where river turbulence is 

pronounced, a longer averaging interval may be 

needed to attain the level of accuracy a shorter interval 

would produce at stations with less turbulence. The 

averaging intervals used at the ADVM stations 

detailed in this report were arrived at by trial and error; 

they appear to minimize the measurement errors. In 

general, the averaging interval for each station will 

need to be considered individually and some experimentation may be needed to find an optimal interval. 

For ADVM installation, it is important to 

consider flow disturbances caused by structures on 

which an ADVM is mounted. It is often desirable to 

mount instruments on the downstream face of a bridge 

pier, which provides some protection from debris. 

Mounting to the downstream face of a pier, however, 

could cause the ADVM to sample within the vortices 

caused by flow separation from the upstream face of 

the pier (wake turbulence). The beginning of the 

sample volume would need to be beyond the waketurbulence zone. The following equation, derived from 

Hughes and Brighton (1991), can be used to estimate 

the extent of the wake-turbulence zone (David 

Mueller, U.S. Geological Survey, written commun., 

2001): 

b = c(dx)

0.5, (2)

where,

b is the lateral distance from the pier center line 

to the approximate edge of the wake-turbulence zone,

d is the width of the pier,

x is the distance to the upstream face of the pier, 

c is a factor accounting for pier shape: c is 0.62 

for circular or round-nosed piers; c is 0.81 

for rectangular piers.

For stations with long piers or narrow channels, 

it may not be practical to set the sample volume totally 

outside the wake-turbulence zone. If a part of the 

sample volume is within the zone, it may be necessary 

to use a longer averaging interval to compensate for 

the additional turbulence. If possible, the sample 

volume should be set to be outside the wake-turbulence zone. 

Some other installation considerations include 

the following:

• Protection—The ADVM should be protected from 

debris and vandalism. Its mount should be 

durable and rigid, and the instrument should be 

accessible for maintenance.

• Power—The longer the averaging interval, the 

greater the power consumption (ADVM manufacFive counts above i.n.l.

Spike caused by boundary

interference

Sample-volume end

RANGE FROM ADVM (METERS) 9 10

SIGNAL STRENGTH (COUNTS)

EXPLANATION

ADVM beam 1

ADVM beam 2

Instrument-noise level (i.n.l.)

Figure 4. Acoustic Doppler velocity meter (ADVM) signal strength showing selection of ADVM 

sample-volume end based on a boundary-interference spike and instrument-noise level.
10 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

turers can be consulted concerning computation 

of power consumption). 

• Cable lengths—The maximum recommended 

cable length for SDI-12 operation is 250 ft (for 

distances above 250 ft, it may be possible to 

provide SDI-12 communications using SDI-12 

radios). 

Theory of Computation of River Discharge

The following approach to the computation of 

river discharge is based on methods developed by the 

USGS to produce discharge records from instruments 

that measure water velocities. These methods were 

developed mainly for AVM’s and now can be applied 

to ADVM’s.

River discharge can be computed, as:

Q = VA, (3)

where,

Q is the discharge in cubic feet per second;

V is the mean velocity for a specified channel 

cross section (mean velocity) in feet per 

second; and, 

A is the channel area for a specified cross section 

in square feet.

Channel area for a river can be determined by 

surveying a river cross section. The channel area for 

a given stage then can be computed from the crosssection survey. Because a range of stage occurs 

in most rivers, it is necessary to develop a relation 

between stage and channel area, called a “stage-area 

rating.” 

The mean velocity for a river can be computed 

from the water velocity measured by an ADVM. To 

compute mean velocities from ADVM-measured 

velocities, the relation between mean channel and 

ADVM-measured velocities must be determined. 

The method used to relate mean velocity and 

ADVM-measured velocity is the index velocity 

method. The instrument measures velocity in a part of 

the stream and that velocity is used to estimate, or 

“index,” the mean channel velocity. The index 

velocity method includes the following steps:

1. An ADVM is installed at a streamflow-gaging 

station. The ADVM is connected to an EDL 

that begins logging data from the instrument. 

2. The channel is surveyed and a stage-area rating 

is developed. 

3. River-discharge measurements are made near the 

streamflow-gaging station while the ADVM is 

sampling velocity. Discharge measurements are 

made using a USGS mechanical current meter or 

an ADCP. 

4. Mean velocity is derived for each individual discharge measurement by dividing the measured 

discharge from the channel area computed from 

the stage-area rating. 

5. For each discharge measurement, ADVM velocities 

are averaged for the discharge-measurement 

period. For purposes of this discussion, “ADVM 

velocity” refers to the one ADVM velocity 

parameter to be used as the primary velocity 

parameter for the computation of discharge. For 

the Argonaut-SL, the velocity x-component or 

the computed velocity vector (eq. 1) could be the 

ADVM velocity. For the EasyQ, any of the 

velocity x-components from any of the three cells 

could be the ADVM velocity (alternately, the 

x-components from two or all three cells could be 

averaged into a single velocity that would 

become the ADVM velocity.

6. Each discharge measurement yields a computed 

mean channel velocity and an average ADVM 

velocity. These data then can be used to develop a 

relation to compute mean velocities from ADVM 

velocities. This relation is called an “index 

velocity rating.” Stage also may be a factor in 

the development of an index velocity rating. 

Various methods can be used to develop an 

index velocity rating. For example, an index velocity 

rating could be a single coefficient to relate ADVM 

to mean velocity, provided the range in stage at the 

station is negligible (the USGS Indiana District has 

used a single-coefficient index velocity rating to 

generate an accurate streamflow record from an AVMequipped, streamflow-gaging station in northwestern 

Indiana since 1991). Other ratings could be more 

complex, particularly at stations with bidirectional 

flow or a large range of stage. For example, the development and accuracy of complex index velocity 

ratings for an AVM-equipped USGS streamflowgaging station on a tide-affected river is described in 
STUDY METHODS 11

Railroad bridge

Acoustic beam

Highway bridge

Instrument 

shelter

Sample

volume

ADVM

Pier

Railroad bridge

Flow

Highway bridge, 

downstream face

Not to scale

Simpson and Bland (1999). For stations with a large 

range of stage, stage may be a factor in the computation of mean velocities from ADVM velocities. The 

index velocity rating must be developed individually 

for each station based on collected data. A detailed 

discussion of the rating construction for each of the 

ADVM stations described in this report is given in the 

section “Index Velocity Ratings.”

After a stage-area and index velocity rating are 

developed, discharges can be computed from a streamflow-gaging station equipped with an ADVM. A 

discharge can be computed from each ADVM velocity 

recorded by the station EDL. A measurement of stage 

also must be recorded with the ADVM so that channel 

area can be computed. Various USGS stage sensors are 

described in Rantz (1982).

STUDY METHODS

The same approach was used to produce records 

of streamflow for the three USGS streamflow-gaging 

stations used for this study, using the ADVM data 

from each of the stations. Each instrument was 

installed and interfaced with an EDL; data collection 

and transmission then began. A channel cross section 

was surveyed, from which a stage-area rating was 

produced. Discharge measurements were made, from 

which an index velocity rating was produced. Stageand ADVM-velocity data then were used to compute 

records of discharge. 

ADAPS (Automated Data Processing Software) 

is the USGS computer program used to compute 

records of discharge. All stage- and ADVM-parameter 

data logged by the station EDL’s were transmitted by 

telemetry to computers at the USGS Indiana District 

Office and placed in the ADAPS database. The stagearea and index velocity ratings were entered into 

ADAPS; the stored stage and velocity data were used 

to compute discharge. 

INSTALLATION OF ACOUSTIC DOPPLER 

VELOCITY METERS

An Argonaut-SL ADVM was installed at the 

Kankakee River at Davis streamflow-gaging station in 

June 1999 and at the Iroquois River near Foresman 

station in September 1999. An EasyQ was installed at 

the Fall Creek at Millersville station in March 2000. 

The range of expected flows at the Kankakee 

(fig. 5) and Iroquois River (fig. 7) stations would be 

contained by the main channel where the ADVM 

samples velocities. For the Fall Creek station (fig. 6), 

flows below about 1,600 ft3/s would be contained in 

the main channel, but higher flows would spread 

across a flood plain on both sides of the channel. 

Selected river characteristics for the three evaluation 

sites are given in table 2.

Figure 5. Photograph and site sketch of Kankakee 

River at Davis, Ind., acoustic Doppler velocity meter 

(ADVM) evaluation station.
12 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

Acoustic beam

Sample volume

cells

ADVM

Pier

Flow

Highway bridge

Instrument 1 2 3

shelter

Flood plain Main channel Flood plain

View looking upstream Highway bridge, downstream face

Not to scale

A custom mount for the ADVM was constructed 

and attached to a downstream highway-bridge pier at 

each of the three stations for protection from downstream-moving debris. ADVM’s were mounted at 

depths of about 1 m (at median flow) for the Kankakee 

and Iroquois River stations and about 0.5 m at the Fall 

Creek station. The mounts were built of galvanized 

steel and aluminum for strength and weather resistance. Each mount was designed so that the ADVM 

could be pulled up for maintenance. Each ADVM was 

connected by cable to an EDL in the station instrument 

shelter. The cable allowed the ADVM to be interfaced 

for programming and allowed the EDL and ADVM to 

communicate, using the SDI-12 communications 

protocol. 

Following installation, the ADVM software 

was used to examine signal strengths for spikes so 

the sample volume end could be programmed. At 

each station, the sample volume or cell size was 

programmed so that no known obstacles were in the 

sample volume or cell and so that the end of the 

sample volume was positioned in such a way that 

signal strengths were at least five counts above the 

instrument-noise level. The start and end distances for 

Figure 6. Photographs and site sketch of Fall Creek at Millersville, Ind., acoustic Doppler 

velocity meter (ADVM) evaluation station.
INSTALLATION OF ACOUSTIC DOPPLER VELOCITY METERS 13

Acoustic beam

Highway bridge

Instrument

shelter

Sample 

volume

ADVM Pier

Flow

View, looking upstream

Not to scale

the sample volume, as measured from the ADVM 

transducers, were 2 and 8 m, respectively, for the 

Kankakee River ADVM and 1 and 8 m, respectively, 

for the Iroquois River ADVM. For the Fall Creek 

ADVM (which has a sample volume composed of 

three cells) the start of the first cell was programmed at 

a distance of 0.5 m from the ADVM transducers. The 

cell size was programmed to be 0.75 m; thus the ends 

of cells 1, 2, and 3 were at 1.25, 2.0, and 2.75 m, 

respectively, from the ADVM transducers. The start of 

the sample volumes for the Kankakee and Iroquois 

River stations were beyond the estimated extent of the 

bridge-pier wake-turbulence zone (as computed, using 

eq. 2); for the Fall Creek station, cell 1 lies totally 

within the estimated extent of the bridge-pier waketurbulence zone. 

After installation, the velocity-averaging 

interval for the three AVDM’s was programmed at 

1 minute. For each of the stations, the EDL was 

programmed with a sampling interval of 15 

minutes—every 15 minutes, the EDL would command 

the ADVM to sample. Upon completion of the 

ADVM-averaging interval, the EDL was programmed 

to log ADVM parameters such as velocities, beam 

amplitudes, and quality indicators. Thus, an ADVM 

velocity unit value was the 1-minute average velocity 

measured by the ADVM logged every 15 minutes. 

The velocity-averaging interval was increased 

from 1 to 10 minutes for the Kankakee River ADVM 

on August 14, 2000, and for the Iroquois River ADVM 

on June 26, 2000. The Fall Creek ADVM velocityaveraging interval was increased from 1 to 13 minutes 

on April 17, 2000—the ADVM velocity unit values 

were logged on 15-minute intervals, but the velocityaveraging interval was increased to 10 or 13 minutes. 

This interval increased the time that velocities were 

being sampled from 7 to 67 percent for the Kankakee 

and Iroquois River stations and from 7 to 87 percent 

for the Fall Creek station. Increasing the sampling 

time lowered random ADVM velocity variations from 

sample to sample by as much as 100 percent (an 

example from the Iroquois River station is shown in 

fig. 8). Because velocity unit-value variations were 

reduced and velocities were being sampled a greater 

percentage of the time, velocity and discharge uncertainties from short-time scale fluctuations were 

reduced. 

The EDL’s also logged stage data from separate 

stage sensors with the ADVM data. The EDL’s at 

the Kankakee and Iroquois River stations were 

equipped with a satellite transmitter and were 

programmed to transmit stage, velocity, and signal 

strength to the USGS Indiana District Office for 

processing. The Fall Creek station EDL was equipped 

for land-line telephone telemetry for automated 

retrieval by the USGS Indiana District Office of all 

logged ADVM parameters. 

Figure 7. Photograph and site sketch of Iroquois River 

near Foresman, Ind., acoustic Doppler velocity meter 

(ADVM) evaluation station.
14 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

RATING DEVELOPMENT 

For each of the three study stations, stage-area 

and index velocity ratings were created. The stage-area 

ratings were created so channel area could be 

computed from stage data; the index velocity ratings 

were created so mean velocities could be computed 

from ADVM velocity data. 

Stage-Area Ratings

A stage-area rating was developed for each 

station. The same method was used to create ratings 

for the three study stations. First, the channel (and 

surrounding flood plain, if applicable) was surveyed 

and a surveyed cross section was derived. Next, a standard cross section was developed from the surveyed 

Table 2. Selected river characteristics at three acoustic Doppler velocity meter evaluation sites, Indiana

[ft3/s, discharge in cubic feet per second; ft, feet]

Characteristic

Acoustic Doppler velocity meter evaluation station

Kankakee River at 

Davis

Fall Creek at

Millersville

Iroquois River near 

Foresman

Mean dischargea (ft3/s) 527 298 410

Median dischargea (ft3

/s) 452 127 198

Maximum dischargea (ft3/s) 1,920 10,600 5,930

Discharge rangea (ft3

/s) 1,766 10,592 5,924

Peak stage (ft) 13.79 13.53 21.0

Stage rangeb

 (ft) 8.5 13.5 21.0

Channel widthc

 (ft) 51 45 78

Mean channel depthc (ft) 5.5 1.7 6.0

a

Applies to mean daily discharges for period of record.

b

Refers to instantaneous stages for the period of record; the stage range is approximate because of changes in streamflow-gage 

datum or channel geometry over time. c

At location of acoustic Doppler velocity meter measurement section, at median discharge.

Figure 8. Acoustic Doppler velocity meter (ADVM) velocity unit values showing the effect 

of increasing the ADVM averaging interval (a.i.) from 1 to 10 minutes, from the Iroquois 

River near Foresman, Ind., ADVM evaluation station, June 25–27, 2000.

2400 0800 1600 2400 0800 1600 2400 0800 1600 2400

25 26 27

June 2000

0.95

1.30

1.00

1.05

1.10

1.15

1.20

1.25

VELOCITY IN FEET PER SECOND

1 minute a.i. 10 minute a.i.
RATING DEVELOPMENT 15

cross section (the standard cross section approximates 

the surveyed cross section and has a simpler geometric 

shape to facilitate computation of channel area from 

stage). Elevations for the standard cross sections are in 

terms of stage referenced to the station datums. The 

creation of stage-area ratings is discussed below for 

each of the study stations. 

Kankakee River at Davis

The stage-area rating was developed by first 

surveying the channel at the upstream side of a railroad bridge that is about 100 ft downstream from the 

ADVM. This location was selected because the 

channel was uniform in depth and geometry. The 

channel was surveyed with an ADCP deployed from a 

boat to collect depth data as the boat traversed the 

channel. The channel was surveyed between the two 

railroad-bridge piers. The surveyed cross section had 

an irregular bottom and nearly vertical sides (fig. 9). 

The standard cross section for this station was rectangular, with a depth of 18 ft and width of 51 ft. Because 

the standard cross section had nearly vertical sides, a 

linear equation to relate stage and channel area could 

be developed. The slope of the equation (stage multiplier) is 50 and the y-intercept is –142. 

ADAPS allows stage-area ratings to be created 

using either equations or tables. The ADAPS equation 

for stage-area ratings is

OUTPUT = A + B(INPUT)C (4)

where,

OUTPUT is channel area in square feet, 

A is a constant,

B is a multiplier,

INPUT is the unit-value stage in feet, and

C is a power coefficient.

0 5 10 15 20 25 30 35 40 45 50 55

STATION, IN FEET

15

2

3

4

5

6

7

8

9

10

11

12

13

14

Surveyed cross section

Standard cross section

Left bank Right bank

STAGE, IN FEET ABOVE STATION DATUM

Figure 9. Surveyed and standard cross sections at Kankakee River at Davis, Ind., acoustic Doppler velocity meter 

evaluation station.
16 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

The ADAPS stage-area rating representing the 

linear stage-area rating for this station is

OUTPUT = –142 +50(INPUT)1

(Note: C = 1 because the rating is a linear 

equation)

For every stage-unit value, ADAPS outputs the 

computed-channel area to be used for computation of 

discharge. 

Fall Creek at Millersville

The stage-area rating was developed by first 

surveying the cross section at the downstream side of 

the bridge where the ADVM was attached. The cross 

section consisted of a main channel in which low to 

medium flows were contained; at higher stages and 

flows, the water would spread into flood-plain areas on 

either side of the main channel. The cross-section 

survey was completed by using a surveyor’s level gun 

to compute elevations and a tagline for distance 

measurement. The resulting surveyed cross section 

had an irregular bottom and sloping sides; from this 

surveyed cross section, the standard cross section was 

developed (fig. 10). 

Because the geometry of the standard cross 

section was more complex than a rectangular section, 

a single equation in ADAPS could not be used for a 

stage-area rating. Instead, the following procedure was 

used. The standard cross section was divided into rectangular and triangular subsections. For a given stage 

value, the area of the standard cross section then could 

be computed by first computing the areas of the appropriate subsections, then summing the subsection areas. 

This approach was used in a computer spreadsheet 

program to compute a table of areas from stages for a 

stage range from 0 to 17.5 ft (table 3). The table of 

0 50 100 150 200 250 300 350 400

STATION, IN FEET

22

0

2

4

6

8

10

12

14

16

18

20

Surveyed cross section

Standard cross section

Left bank Right bank

STAGE, IN FEET ABOVE STATION DATUM

Figure 10. Surveyed and standard cross sections at Fall Creek at Millersville, Ind., acoustic Doppler velocity meter 

evaluation station.
RATING DEVELOPMENT 17

stages and areas was entered into ADAPS, creating a 

tabular stage-area rating. For stage values between 

stages entered in the table, ADAPS performs a linear 

interpolation to compute channel area. Thus, for any 

stage value, ADAPS can compute the associated 

channel area. 

Iroquois River near Foresman

The stage-area rating was developed by first 

surveying the cross section at the downstream side of 

the bridge where the ADVM was attached. The cross 

section was a trapezoid in which all flows were 

contained. The cross-section survey was completed 

using a steel measurement tape referenced to the low 

chord of the bridge to measure elevations and a steel 

tape for distance measurement. The resulting surveyed 

cross section had an irregular bottom and sloping 

sides; from this surveyed cross section, the standard 

cross section was developed (fig. 11). Because the 

geometry of the standard cross section was more 

complex than a rectangular section, the same approach 

described for Fall Creek at Millersville was used to 

compute a table of areas developed from stages for a 

stage range of 2 to 24 ft (table 4). The table of stages 

and areas was entered into ADAPS, creating a tabular 

stage-area rating. For stage values between stages 

entered in the table, ADAPS performs a linear interpolation to compute channel area. Thus, for any stage 

value, ADAPS can compute the associated channel 

area. 

Index Velocity Ratings

An index velocity rating represents the relation 

between ADVM and mean velocity, so that mean 

velocities can be computed from the ADVM velocities 

recorded at a station. The mean velocities computed 

with the index velocity rating can be multiplied by 

channel area to compute discharge unit values. 

To develop index velocity ratings, concurrent 

ADVM and mean velocities needed to be collected. 

The data-collection process included the following 

steps:

1. Measurements of discharge were made using 

mechanical, rotating-cup current meters or 

ADCP’s. 

2. For each discharge measurement, the average stage 

during the measurement period was used to 

compute channel area at the ADVM standard 

cross section, using the stage-area rating. 

3. The mean velocity in the standard cross section was 

computed by dividing the measurement discharge 

by the channel area computed in step 2. 

4. ADVM velocity unit values were logged by the 

EDL during the discharge measurement. When 

referring to the construction of index velocity 

ratings, the ADVM velocity becomes the average 

of ADVM velocity unit values recorded during 

the discharge-measurement period. 

Every measurement of discharge yields a mean 

velocity and an ADVM velocity. The relation between 

ADVM velocity and mean velocity can be expected to 

vary with discharge and possibly also stage. Thus, 

Table 3. Stages and computed channel areas used to create a tabular stage-area rating for the Fall Creek at 

Millersville, Ind., acoustic Doppler velocity meter evaluation station

[ft, feet; ft2, square feet]

Stage

(ft)

Channel 

area

(ft2)

Stage

(ft)

Channel 

area

(ft2)

Stage

(ft)

Channel 

area

(ft2)

Stage

(ft)

Channel 

area

(ft2)

0.00 0 2.00 61.9 5.50 453 11.50 2,175

.50 7.8 2.50 85.4 6.00 558 12.50 2,493

.75 13.7 3.00 110 6.50 693 13.50 2,816

1.00 21.0 3.50 136 7.50 971 14.50 3,142

1.25 29.7 4.00 190 8.50 1,259 15.50 3,472

1.50 39.8 4.50 269 9.50 1,557 16.50 3,806

1.75 50.7 5.00 357 10.50 1,862 17.50 4,144
18 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

multiple measurements of discharge for a range of 

discharges and stages are required to develop an index 

velocity rating. 

Common practice in developing index velocity 

ratings for AVM’s is to plot the mean velocity and 

AVM-measured velocities from a series of measurements on an x-y plot, where the y-axis represents mean 

velocity and the x-axis represents AVM velocity. The 

plot is the start of the analysis of the relation between 

mean velocity and AVM velocity. The same approach 

can be used for ADVM’s. With the plot and a knowledge of the hydraulics at the station, an index velocity 

relation is developed. For some stations, the relation 

may be linear. For others, the relation may best be 

described as curvilinear or as a compound curve. 

The index velocity ratings for the three indexvelocity stations were represented by a linear relation. 

If the relation between mean velocity and ADVM 

velocity is linear, it can be defined by a linear equation

V = XVi

 + C (5)

where,

V is the computed mean channel velocity,

Vi is the index velocity measured by the ADVM,

X is the slope of the line defined in equation 5, 

commonly called a velocity coefficient, and

C is the y-intercept of the line defined in equation 5, and is commonly referred to as the 

“constant” of the line. 

If mean velocity is found to be equal or nearly 

equal to ADVM velocity under all flow conditions, 

equation 5 could be reduced to V = Vi

 (X=1 and C=0). 

This relation would be possible if the ADVM sample 

volume covered a large part of the horizontal distance 

across the channel and if the ADVM sample volume 

were located at a position in the vertical that represented the mean vertical velocity. This relation occurs 

at about 60 percent of the total depth of a channel in 

0 20 40 60 80 100 120 140 160 180

STATION, IN FEET

0

26

2

4

6

8

10

12

14

16

18

20

22

24

Surveyed cross section

Standard cross section

Left bank Right bank

STAGE, IN FEET ABOVE STATION DATUM

Figure 11. Surveyed and standard cross sections at Iroquois River near Foresman, Ind., acoustic Doppler velocity meter 

evaluation station.
RATING DEVELOPMENT 19

many streams and rivers. In most instances, including 

the installations described in this report, mean velocity 

would not equal ADVM velocity under all flow conditions because only a fraction of the horizontal channel 

distance usually is measured and because changing 

stage affects the relation of ADVM velocity to mean 

vertical velocity. 

If a plot of mean velocity and ADVM velocity 

indicates a linear relation, various tools are available to 

derive equation 5. One tool would be to draw a line 

“by eye” to fit the data points; two points from the line 

then can be used to compute equation 5. A second tool 

would be to perform a least-squares linear regression 

to fit the data. 

A linear regression is a method of producing a 

straight line that can be used to compute a quantity, 

called the dependent variable (“mean velocity” in this 

discussion) from a second known quantity, called the 

independent variable (ADVM velocity). The method 

takes all of the observations (mean velocity and 

ADVM velocity) into account and produces a line so 

that sum of the squares of the departure of mean 

velocity from the line will be as small as possible. This 

line is the best fit for the data because it gives 

computed values of mean velocity that come as near as 

possible to agreeing with all of the values of observed 

mean velocity (Ezekial and Fox, 1959). 

The linear regression method has advantages 

over drawing the line by eye. Drawing the line by eye 

introduces subjectivity in that different persons could 

have different line fits. The least-squares method of 

linear regression is a formal, computational method of 

fitting a line to data, and it eliminates the subjectivity 

of drawing a line by eye. A linear regression produces 

tools that can be used to assess how well the equation 

derived from the linear regression fits the data. 

Riggs (1968) gives four assumptions required 

for linear regressions:

1. The deviations of the dependent variable (mean 

velocity) about the regression line are normally 

distributed; 

2. Values of the independent variable (ADVM 

velocity) are known without error; 

3. Observed values of the dependent variable (mean 

velocity) are uncorrelated random events; and 

4. Individual variables are homogeneous (for example, 

all values of the independent variable are ADVM 

velocity, measured in the same way and in the 

same units). 

Assumption 2 cannot be met perfectly because 

ADVM measurements of velocity will have errors, 

including instrument errors and environmental errors. 

Any instrument that measures a physical quantity will 

have errors associated with the measurement. For the 

purposes of creating an index velocity rating, it is 

assumed that ADVM velocity is known with a level 

of accuracy sufficient to compute mean channel 

velocities. 

A linear-regression analysis provides three tools 

that can be used to assess the quality of the fit of the 

regression-derived equation: 

1. Coefficient of determination (r2

)—r2 indicates what 

proportion of the variance in the dependent variable can be explained by variation in the indepenTable 4. Stages and computed channel areas used to create a tabular stage-area 

rating in ADAPS for Iroquois River, Ind., ADVM evaluation station

[ft, feet; ft2, square feet, --, no data available]

Stage

(ft)

Channel 

area

(ft2)

Stage

(ft)

Channel 

area

(ft2)

Stage

(ft)

Channel 

area

(ft2)

2 43 10 587 18 1,490

3 91 11 680 19 1,628

4 145 12 779 20 1,772

5 205 13 884 21 1,921

6 270 14 994 22 2,076

7 341 15 1,109 23 2,237

8 417 16 1,231 24 2,403

9 499 17 1,358 -- --
20 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

dent variable. An r2 of 1 indicates that all of the 

variance in the dependent variable is explained 

by the variance of the independent variable. In 

the case of mean velocity and ADVM velocity, 

for example, an r2

 of 0.97 indicates that 

97 percent of the variation in mean velocity can 

be explained by the variation of ADVM velocity. 

Lower values of r2 may indicate that factors other 

than ADVM velocity (such as stage) may have a 

significant effect on the accurate prediction of 

mean velocity. 

2. Standard error of estimate—this parameter is a 

measure of how nearly the values of the dependent variable computed by the regression line 

agree with observed values (Ezekial and Fox, 

1959). The standard error is in the same units as 

the dependent variable and can be compared to 

values of the dependent variable.

3. Residual plots—a residual is the difference between 

an observed sample of the dependant variable 

and the value computed by the regression equation. In a residual plot, residuals are plotted on 

the y-axis with the independent variable on the 

x-axis. For a valid regression, the plot of residuals should be a random array of points with no 

discernible pattern. Residual plots can be used to 

help find regression errors such as nonlinearity, 

nonconstant variances, and outliers (a residual 

much larger than the others). 

The basic premises for applying equation 5 are 

(a) that mean velocity can be computed from ADVM 

velocity; (b) that the changes in mean velocity can be 

computed by changes in ADVM velocity as defined by 

the slope of the equation line; and (c) that ADVM 

velocity is the only parameter to consider when developing an index velocity rating. 

Patino and Ockerman (1997) and Patino, Hittle, 

and Zucker (2001) found that for some AVM stations, 

stage was a significant parameter in the prediction of 

mean velocity from AVM-measured velocity. Patino, 

Hittle, and Zucker give an equation relating both AVM 

velocity and stage to mean channel velocity that can 

also be applied to ADVM’s: 

V = Vi

(X + YH) + C, (6)

where,

V is the computed mean velocity,

Vi is the velocity measured by the ADVM,

X is the velocity coefficient,

Y is the stage coefficient,

H is stage, and

C is the constant. 

Equation 6 represents a situation where the 

slope or coefficient that relates ADVM to mean 

velocity varies with stage. Equation 6 can be arrived at 

by performing a multiple linear regression, where the 

dependent variable is mean velocity and the independent variables are Vi

 and the product of Vi X H. 

The tools of assessing the fit of an equation 

based upon a multiple linear regression are similar to 

those discussed for a single-parameter linear regression. In the case of a multiple linear regression, r2 is 

the coefficient of determination and indicates what 

proportion of the variance in the dependent variable 

can be explained by variations in the independent variables. The standard error for a multiple linear regression is a measure of the departure of computed values 

from the measured values of the independent variable. 

Two residual plots can be produced from a multiple 

linear regression, where the departure of computed 

values from measured values of the dependent variable 

are plotted separately against each of the independent 

variables. 

Equation 5, the equation for relating mean 

velocity to ADVM velocity only, may be seen as a 

form of equation 6: when the YH or stage term in 

equation 6 is zero (stage is not a significant factor in 

predicting mean velocity from ADVM velocity), equation 6 takes the form of equation 5. Thus, equation 6 

can be thought of as a general linear equation for 

developing an ADVM index velocity rating. 

Equation 6 was the basis of index velocityrating development for the three ADVM evaluation 

stations. Development of the ratings for each station is 

described in detail below for each station. 

Kankakee River at Davis

Twelve discharge measurements, 623 to 634, 

were made during the study period (June 1, 1999–

February 28, 2001) at the Kankakee River evaluation 

station (table 5). Eleven of the measurements could be 

used to construct an index velocity rating (the ADVM 

velocities were not recorded by the EDL during 

measurement 624). For the 11 measurements, the 

mean stages during the measurement periods (referred 

to as measurement stages hereinafter) ranged from 

6.18 to 11.77 ft, whereas measurement discharges 
RATING DEVELOPMENT 21

ranged from 301 to 1,410 ft3/s. Mean velocities 

computed from the measurements ranged from 1.71 

to 3.16 ft/s. 

The Argonaut-SL-computed velocity vector 

(eq. 1) was selected as the velocity parameter from 

which to compute discharge and became the ADVM 

velocity for which index velocity ratings were developed. 

Excluding 624, the first four measurements of 

the study period indicated that the index velocity 

rating within the range of stages (6.37 to 7.59 ft) and 

discharges (306 to 488 ft3

/s) of the measurements 

could be expressed by the equation V = 1.06Vi

. A 

subsequent measurement with a stage of 8.54 ft and 

discharge of 662 ft3

/s departed from this equation. The 

departure was attributed to a change in the relation of 

mean velocity to ADVM velocity caused by stage 

change. Further measurements throughout the study 

period, particularly the last measurement (634), 

confirmed this assumption; the stage for this measurement, 11.77 ft, was higher than the other measurement 

stages (the peak stage for the period of record is 

12.79 ft). 

Each discharge measurement had an associated 

quality rating of either “good,” “fair,” or “poor.” 

Discharge measurements made by the USGS are given 

a rating of excellent, good, fair, or poor by the 

personnel who made the measurements. A rating of 

“excellent” means that the measurement would depart 

no more than 2 percent from the true discharge (a 

measurement error not greater than 2 percent). A 

rating of “good” is judged to depart no more than 

5 percent from the true discharge; “fair,” by 8 percent: 

and “poor,” by more than 8 percent (Sauer and Meyer, 

1992). Criteria used to judge the quality of a measurement include measurement technique (for example, 

how many velocity samples were taken across the 

channel) and environmental characteristics (such as 

turbulence). When creating a rating, it is possible to 

give more importance (weight) to measurements rated 

“good,” followed by “fair,” then by “poor.” Plots of the 

data could indicate whether or not the weighting of 

measurements by quality was necessary for rating 

development. 

A plot of mean and ADVM velocity from the 

11 discharge measurements made during the study 

period (fig. 12) indicated that a line using ADVM 

velocity for an index velocity rating would not be a 

good fit of the data. A linear-regression analysis of 

mean and ADVM velocities from the 11 measurements yielded an r2

 of 0.87, indicating that 13 percent 

of the variation in mean channel velocities could not 

be explained by the variation in ADVM velocities. The 

standard error from the regression was 0.16 ft/s; which 

Table 5. Summary of discharge-measurement data from the Kankakee River at 

Davis, Ind., acoustic Doppler velocity meter evaluation station, June 30, 1999–

February 27, 2001

[ft, feet; ft3/s; cubic feet per second; ft/s, feet per second]

Discharge measurement 

Number Date Rated Stage

(ft)

Discharge

(ft3/s)

Mean velocity

(ft/s)

623 06/30/99 Poor 7.59 488 2.05

624 09/02/99 Fair 5.92 222 1.44

625 10/04/99 Fair 6.55 317 1.71

626 12/06/99 Good 7.22 404 1.84

627 02/07/00 Fair 6.37 306 1.73

628 02/29/00 Good 8.54 662 2.32

629 04/10/00 Fair 7.20 440 2.02

630 06/19/00 Poor 8.02 644 2.49

631 08/14/00 Fair 6.20 301 1.79

632 10/02/00 Poor 6.18 318 1.90

633 02/05/01 Fair 7.50 502 2.15

634 02/27/01 Good 11.77 1,410 3.16
22 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

is 7.5 percent of the average of the mean velocities 

(2.11 ft/s) computed from the 11 measurements used 

in the regression analysis. The data from all discharge 

measurements were weighted equally in the regression.

It was assumed that, in addition to ADVM 

velocity, stage was a factor in computing mean 

velocity. A multiple linear regression was performed 

with ADVM velocity and the product of stage and 

ADVM velocity as the independent variables. The data 

from all discharge measurements were weighted 

equally in the regression analysis. The regression 

yields the equation:

V = Vi

(0.521 + 0.073H) + 0.102 (7)

1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3

ADVM VELOCITY, IN FEET PER SECOND

1.6

3.2

1.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3.0

3.1

MEAN VELOCITY, IN FEET PER SECOND

623 Discharge-measurement number and value

626

627

628

629

634

632

633

623

631

630

625

Figure 12. Mean velocity and acoustic Doppler velocity meter (ADVM) velocities from discharge 

measurements made at the Kankakee River at Davis, Ind., ADVM evaluation station.
RATING DEVELOPMENT 23

The r2 for the regression was 0.97, and the standard error was 0.08 ft/s, which is 3.8 percent of the 

average of the mean velocities computed from the 

11 measurement used in the regression analysis. 

ADAPS has two rating types that can be used 

for index velocity ratings: the deflection/velocity 

rating and the stage-velocity factor rating. For either of 

these options, an equation can be entered that uses the 

same form as that discussed for the Kankakee River at 

Davis stage-area rating (eq. 4). In review, equation 4 is 

given as:

OUTPUT = A + B(INPUT)C.

The input unit value would be velocity for the 

deflection-velocity rating and stage for the stagevelocity factor rating. The output in both cases would 

be mean channel velocity. Equation 4 (V = XVi

 + C) 

can be entered as deflection/velocity rating, with the 

input as ADVM velocity, A as the constant (C), B as 

the velocity coefficient (X), and C as 1 because equation 4 is linear. 

An equation that computes mean velocity from a 

single parameter can be entered into ADAPS (equation 

7 cannot be entered because as of this writing, ADAPS 

does not support multiple-parameter equation ratings). 

It would be possible to compute the mean velocity 

from equation 7 outside ADAPS, then import the mean 

channel velocities to ADAPS for discharge computation. This computation would involve writing a custom 

program to operate on ADVM data outside of ADAPS. 

Alternatively, it is possible for some EDL’s to be 

programmed to compute mean velocity using equation 

7, then store and transmit the computed mean velocity. 

A criterion of this study was that ADAPS would 

be used to produce discharge records from ADVM 

data. Therefore, ratings were created to approximate 

equation 6. An approximation of equation 7 is given as

V = (0.521 + 0.073H)(Vi

 + 0.102). (8)

Equation 8 is not mathematically equivalent to 

equation 7—in equation 7, Vi

 is multiplied by the 

quantity (0.521 + 0.073H), then the constant 0.102 is 

added; in equation 8, 0.102 is first added to Vi

 then this 

quantity is multiplied by (0.521 + 0.073). Mean velocities computed from the ADVM velocities and stages 

associated with the 11 discharge measurements using 

equation 8 are within 0.6 percent of mean velocities 

computed using equation 7. One exception is measurement 634, where mean velocities departed by 1.2 

percent. Because mean velocities computed using 

equation 8 compare closely with mean velocities 

computed using equation 7, equation 8 can be represented by equation ratings in ADAPS.

Equation 8 is represented in ADAPS, using a 

deflection/velocity rating and a stage-velocity factor 

rating. The quantity (0.521 + 0.073H) is represented 

by a stage-factor correction rating:

OUTPUT = 0.521 + 0.073(INPUT)1 (9)

where,

INPUTis unit value stage.

The quantity (Vi

 + 0.102) is represented by the 

deflection/velocity rating 

OUTPUT = 0.102 + 1.0(INPUT)1 (10)

where,

INPUT is unit value ADVM velocity.

ADAPS multiplies the outputs of ratings (9) and 

(10) to compute mean velocity. For each unit value of 

stage and ADVM velocity, ADAPS computes and 

stores a computed mean velocity unit value that (when 

multiplied by channel area) yields a discharge unit 

value. 

The validity of the index velocity ratings (and 

stage-area rating) in the range of discharge measurements that produced the rating can be evaluated by 

comparing discharges computed from the ADVM 

data, using the ratings (ADVM discharges) to the 

measured discharges. A factor in the comparison is the 

quality of the discharge measurement as assessed by 

the person making the measurement. 

Comparison of measured to ADVM discharges 

for the 11 discharge measurements used to create the 

ratings is given in table 6. Departures of the measured 

discharges from ADVM discharges ranged from 0.1 to 

8.0 percent. The measured discharges for all measurements (with the exception of 626) were within tolerances, as defined by the quality ratings of each 

measurement (5, 8, or greater than 8 percent for 

ratings of “good,” “fair,” or “poor,” respectively), of 

the respective ADVM discharges. The measured 
24 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

discharge of measurement 626, (rated “good”) 

departed 5.8 percent from the ADVM discharge. 

It is standard USGS practice when using 

conventional stage-area methods to refine or make a 

temporary adjustment (shift) to a stage-area rating if a 

discharge measurement rated “good” or “fair” departs 

by more than 5 or 8 percent, respectively, from the 

rating discharge; the shift brings the measurement 

discharge within tolerance of the rating discharge. The 

departure of a single discharge measurement from the 

rating may indicate a shift period (Rantz, 1982). Rantz 

acknowledges that a person who analyzes a rating has 

the responsibility for explaining the hydraulics that 

caused the shift detected by a single measurement. 

Although measurement 626 departed by more 

than 5 percent from the ADVM discharge, adjustments 

to the ratings were not made for the following reasons: 

(1) the measurement was made prior to August 14, 

2000, when the ADVM averaging interval was 

changed from 1 to 10 minutes to reduce measuredvelocity uncertainties, and (2) no reason was found to 

change the rating—all ADVM parameters, including 

velocities and quality parameters, were acceptable 

during the measurement period, and measurement data 

did not reveal any obvious changes to the channel 

geometry near the measurement section. 

The measurements collectively did not reveal 

any biases (for example, if all measurement discharges 

were less than the respective rating-computed 

discharges). Because all of the measurements were 

within tolerance of the respective rating discharges 

(and there were justifications for not adjusting the 

ratings based on measurement 626), the ratings were 

judged to be adequate for the production of streamflow 

within the range of measurements and within the time 

period of the measurements. 

Fall Creek at Millersville

Nine discharge measurements, 1255 to 1263, 

were made during the study period (March 23, 2000–

February 28, 2001) at the Fall Creek evaluation 

station. Six of the measurements, 1255 to 1260, were 

used to develop an index velocity rating. For the six 

measurements, the measurement stages ranged from 

1.69 to 3.11 ft (table 7), whereas measurement 

discharges ranged from 45.8 to 263 ft3

/s. Mean velocities computed from the measurements ranged from 

0.95 to 2.27 ft/s. 

Table 6. Comparison of discharges computed using an acoustic Doppler velocity meter 

(ADVM) to measured discharges at the Kankakee River at Davis, Ind., ADVM evaluation 

station for June 30, 1999–February 27, 2001

[ft3/s; cubic feet per second; ADVM, acoustic Doppler velocity meter; --, no data available]

Discharge measurement ADVM-computed

Number Date Rated Discharge

(ft3/s)

Discharge

(ft3/s)

Discharge

departure from 

measurement 

discharge

(percent)

623 06/30/00 Poor 488 514 5.3

624 09/02/00 Fair 222 -- --

625 10/04/99 Fair 317 321 1.3

626 12/06/99 Good 404 427 5.8

627 02/07/00 Fair 306 303 –.9

628 02/29/00 Good 662 663 .1

629 04/10/00 Fair 440 436 –.9

630 06/19/00 Poor 644 631 –2.0

631 08/14/00 Fair 301 316 5.0

632 10/02/00 Poor 318 293 –8.0

633 02/05/01 Fair 502 503 .3

634 02/27/01 Good 1,410 1,431 1.5
RATING DEVELOPMENT 25

The EasyQ provided an x-velocity component 

from each of three cells that could potentially be used 

as ADVM velocities for computation of discharge. 

Analysis of the velocity unit values from the three 

cells indicated that cell 3 velocities appeared to be 

questionable for long periods. For example, many of 

the cell 3 velocities were negative when all velocity 

values from the other two cells always were positive 

(velocities should have always have been positive 

because the flow in this region always has been 

observed to be downstream). Because the channel is 

shallow, it is possible that periodic bending of the 

beams cause the beams to strike the bottom within cell 

3 or that sidelobe interference caused the questionable 

velocities. Because the velocities from cell 3 were 

questionable, separate index velocity ratings were 

developed that used the x-component velocities from 

cells 1 and 2 for discharge computation. 

Plotting ADVM cell 1 and 2 velocities with the 

mean channel velocities indicated that a well-defined 

linear relation between ADVM and channel velocities 

was present within the range of stages and discharges 

represented by measurements 1255 to 1260 (fig. 13). 

As a result, the relation between ADVM-measured 

velocities and mean velocities for both cells could be 

represented by best fitting a straight line to the data. 

A computer statistics program was used to 

perform two linear regressions, one for cell 1 and one 

for cell 2. For cell 1, the six mean channel velocities 

computed from the six discharge measurements were 

regressed against the corresponding cell velocities. All 

six measurements were weighted equally in the regression. The equation of the line developed for cell 1 is

V = 1.22 Vi

 + 0.39 (11)

The r2 for the regression was 0.99 and the 

standard error was 0.05 ft/s, which is 3.4 percent of 

the average of the mean channel velocities (1.45 ft/s) 

computed from the six measurements used in the 

regression analysis. The r2 of 0.99 indicated that 

99 percent of the variation in mean channel velocities 

was accounted for in variations of the ADVM velocities. Therefore, it was assumed that within the range of 

discharge measurements used to produce equation 11, 

stage was not a factor. The residual plot from the 

regression analysis did not indicate nonlinearity, nonconstant variances, or large outliers. Equation 11 was 

found to be an adequate fit of the measurement data 

and became the index velocity rating for cell 1. Equation 11 is represented in ADAPS as a deflection/ 

velocity rating:

OUTPUT = 0.39 + 1.22(INPUT)1 (12)

where,

INPUT is unit value ADVM velocity, cell 1.

The equation of the line developed for cell 2 is

V = 1.40Vi

 + 0.05. (13)

Table 7. Summary of discharge-measurement data from the Fall Creek at Millersville, Ind., 

acoustic Doppler velocity meter (ADVM) station, March 30, 2000–August 23, 2000

[ft, feet; ft3/s; cubic feet per second; ft/s, feet per second]

Discharge measurement 

Number Date Rated Stage

(ft)

Discharge

(ft3/s)

Mean velocity

(ft/s)

1255 03/30/00 Good 2.27 110 1.47

1256 04/19/00 Good 2.56 164 1.86

1257 06/15/00 Good 3.11 263 2.27

1258 07/27/00 Good 2.02 84.8 1.35

1259 08/22/00 Fair 1.69 45.8 .95

1260 08/23/00 Good 1.81 59.2 1.11
26 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

0 0.5 1.0 1.5 2.0 2.5 3.0

ADVM CELL 1 VELOCITY, IN FEET PER SECOND

0

3.0

0.5

1.0

1.5

2.0

2.5

MEAN VELOCITY, IN FEET PER SECOND

Index velocity rating from least-squares regression

0 0.5 1.0 1.5 2.0 2.5 3.0

ADVM CELL 2 VELOCITY, IN FEET PER SECOND

0

3.0

0.5

1.0

1.5

2.0

2.5

MEAN VELOCITY, IN FEET PER SECOND

1257

1256

1255

1258

1260

1259

Discharge-measurement number

1257

1256

1255

1258

1260

1259

1259

Index velocity rating from least-squares regression

1259 Discharge-measurement number

Figure 13. Index velocity ratings for cells 1 and 2 of an acoustic Doppler velocity meter 

(ADVM) at the ADVM evaluation station Fall Creek at Millersville, Ind.
RATING DEVELOPMENT 27

During measurement 1255, cell 2 velocities 

were erratic; the maximum and minimum velocities 

during the period varied by more than 25 percent (the 

variance was less than 8 percent for cell 1). As a result, 

this measurement departed below the regression line 

of equation 13. When the measured discharges and 

ADVM discharges computed with equation 13 were 

compared, all of the ADVM discharges were lower 

than the measured discharges. To eliminate this bias, a 

new regression analysis was performed with measurements 1256 to 1260. The resulting equation of the line 

from the analysis is

V = 1.42Vi

 + 0.07. (14)

Discharges computed with equation 15 did not 

indicate the negative bias produced by equation 13. 

The r2

 for the regression was 0.97; the standard error 

was 0.09 ft/s, which is 6.2 percent of the average of the 

mean channel velocities (1.45 ft/s) computed from the 

six measurements used in the regression analysis. The 

r

2 of 0.97 indicated that 97 percent of the variation in 

mean channel velocities was accounted for in variations of the ADVM velocities. It was assumed that, 

within the range of discharge measurements used to 

produce equation 14, stage was not a significant factor. 

The residual plot from the regression analysis did not 

indicate nonlinearity, nonconstant variances, or large 

outliers. Thus, equation 14 was found to be an 

adequate fit of the measurement data and became the 

index velocity rating for cell 2. Equation 14 is represented in ADAPS as a deflection/velocity rating:

OUTPUT = 0.07 + 1.42(INPUT)1 (15)

where, 

INPUT is unit value ADVM velocity, cell 2.

ADAPS uses ratings 12 and 15 to compute mean 

velocity for cells 1 and 2, respectively. Thus, for each 

stage unit value and ADVM cell 1 and 2 velocity, 

ADAPS computes and stores a computed mean 

velocity unit value that, when multiplied by channel 

area, yields a discharge unit value for each cell. The 

validity of the index velocity ratings (and stage-area 

rating) in the range of discharge measurements that 

produced the rating was evaluated by comparing 

computed discharges to measurement discharges. 

Comparison of computed to measured 

discharges for cells 1 and 2 for the six discharge 

measurements used to create the ratings is given in 

table 8. Also in table 8 are comparisons of computed 

to measured discharges for three discharge measurements (1261 to 1263) made after the ratings discussed 

previously were developed. 

For cell 1, departures of measured discharge 

from ADVM discharges for measurements 1255 to 

1260 ranged from less than 0.6 to 5.7 percent. 

Measurements 1255 to 1260 were used to create the 

rating, whereas measurements 1261 to 1263 were 

made after development of the rating. Except for 

numbers 1258 and 1263, the measured discharges for 

all measurements were within tolerances as defined by 

the quality ratings of each measurement (5, 8, or 

greater than 8 percent for ratings of “good,” “fair,” 

or “poor,” respectively) of the respective ADVM 

discharges. Measurement 1258, rated “good,” departed 

by 5.1 percent and measurement 1263, rated “good,” 

departed by 5.7 percent. 

Although measurement 1258 and 1263 departed 

by more than 5 percent from the ADVM discharges, 

adjustments to the ratings were not made for the 

following reasons. (1) These measurements were rated 

“good” by the person who made the measurement, but 

the particular measurement section used is rocky and 

turbulent and the rating of measurement quality is 

somewhat subjective—the measurements could have 

been rated “fair,” in which case they would have been 

within tolerance (8 percent) of the respective ADVM 

discharges. (2) No reason to change the rating was 

found—all ADVM parameters, including velocities 

and quality parameters, were acceptable during the 

measurement period, and the measurement did not 

reveal any obvious changes to the channel geometry 

near the measurement section. 

The measurements collectively did not reveal 

any biases (for example, if all measurement discharges 

were less than the respective rating-computed 

discharges). Because all measurements were within 

tolerance of the respective rating discharges and there 

were justifications for not adjusting the ratings based 

on measurements 1258 and 1263, the rating was 

judged to be adequate for the computation of streamflow records within the range of measurements and 

within the time period of the measurements. 

For cell 2, departures of the measured from 

ADVM discharges for measurements 1256 to 1263 

ranged from 0.0 to –32.9 percent. Excluding 1255 and 
28 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

with the exception of 1261 and 1263, the measured 

discharges were within tolerances of the respective 

ADVM discharges. Measurements 1261 and 1263 

were made after the creation of the index velocity 

rating for cell 2. The measurement 1261 discharge, 

rated “good,” departed by 8.2 percent from the ADVM 

discharge. Though measurement 1261 departed by 

more than 5 percent from the ADVM discharge, 

adjustments to the ratings were not made because no 

reason to change the rating was found. All ADVM 

parameters, including velocities and quality parameters appeared to be of good quality during the 

measurement period, and the measurement did not 

reveal any changes to the channel geometry near the 

measurement section. 

Measurement 1263, made on January 24, 2001, 

and rated “good,” departed by –32.9 percent from the 

ADVM discharge. The –32.9 percent departure of 

measurement 1263 was the result of a bias in cell 2 

velocities that occurred from December 18, 2000, to 

February 9, 2001. The bias likely was caused by an 

obstruction in cell 2; the bias and measures implemented to compensate for the bias are discussed in the 

section “Computation of the Records.” Because of the 

bias, the departure of measurement 1263 from the 

ADVM discharge is explainable and does not invalidate the rating. Because measurement 1261 was the 

only other measurement that departed outside the 

tolerance assigned by the measurement-quality rating 

and because measurement 1261 was made after 

creation of the rating, the rating was not adjusted. A 

continued trend in departures would justify a rating 

adjustment. Measurement 1262, made after 1261, was 

within tolerance of the rating. 

The offset from equation 11 (that became the 

cell 1 index velocity rating) is 0.39, compared to the 

offset from equation 14 (that became the cell 2 index 

velocity rating) of 0.07. The offset for cell 1 is large 

compared to that for cell 2 and implies that when the 

ADVM measures zero velocity, some flow still is 

present in the channel. This larger offset could be 

a result of the proximity of cell 1 to the bridge 

pier—friction from the pier would slow down the 

water velocity in the pier’s vicinity. Cell 2 is farther 

from the pier and therefore would not be affected to 

the extent of cell 1. 

Iroquois River near Foresman 

Eighteen discharge measurements, 521 to 544, 

were made during the study period (October 1, 2000–

February 28, 2001) at the Iroquois River evaluation 

station. Fourteen of the measurements, 521 to 536, 

Table 8. Comparison of discharges computed using an acoustic Doppler velocity meter (ADVM) to 

measured discharges from the Fall Creek at Millersville, Ind., ADVM evaluation station, March 30, 2000–

January 24, 2001

[ft3/s; cubic feet per second; ADVM, acoustic Doppler velocity meter]

Discharge measurement 

ADVM computed

 Discharge

(ft3/s)

Departure from 

measurement 

discharge

(percent)

Number Date Rated Discharge 

(ft3/s) Cell 1 Cell 2 Cell 1 Cell 2

1255 03/30/00 Good 110 114 125 3.7 13.9

1256 04/19/00 Good 164 168 161 2.3 –1.6

1257 06/15/00 Good 263 261 265 –.6 .7

1258 07/27/00 Good 84.8 80.4 86.5 –5.1 2.0

1259 08/22/00 Fair 45.8 47.0 45.8 2.7 0

1260 08/23/00 Good 59.2 59.8 59.0 1.1 –.3

1261 10/16/00 Good 134 137 123 2.2 –8.2

1262 12/13/00 Fair 356 354 342 –.6 –3.9

1263 01/24/01 Good 158 167 106 5.7 –32.9
RATING DEVELOPMENT 29

were used to construct an index velocity rating. 

Measurement 523 was not used to construct the rating 

because the river was ice covered when the measurement was made; measurement 527 was not used 

because pertinent measurement data were not available at the time the rating was created. For the 

14 measurements, stages ranged from 4.23 to 12.24 ft 

(table 9), whereas measurement discharges ranged 

from 25.3 to 988 ft3/s. Mean channel velocities 

computed from the measurements ranged from 0.27 to 

1.48 ft/s. The Argonaut-SL x-component of velocity 

was used for development of the index velocity rating. 

Plotting ADVM and mean velocities indicated 

that a well-defined linear relation between ADVMmeasured velocities and mean velocities is present 

within the range of stages and discharges represented 

by measurements 521 to 536 (fig. 14). As a result, the 

relation between ADVM-measured velocities and 

mean velocities could be represented by fitting a 

straight line to the data. 

A linear regression was performed in which the 

14 mean channel velocities computed from the 14 

discharge measurements were regressed against the 

corresponding cell velocities. All measurements were 

weighted equally in the analysis. The equation of the 

line is 

V= 0.97Vi

 – 0.10. (16)

The r2 for the regression was 0.98, and the standard error was 0.05 ft/s, which is 5.9 percent of the 

average of the mean velocities (0.85 ft/s) computed 

from the 14 measurements used in the regression analysis. The r2 of 0.98 indicated that 98 percent of the 

variation in mean velocities was accounted for in variations of the ADVM velocities. Therefore it was 

assumed that, within the range of discharge measurements used to produce equation 16, stage was not a 

factor. The residual plot from the regression analysis 

did not indicate nonlinearity, nonconstant variances, or 

large outliers. Equation 16 was found to be an 

adequate fit of the measurement data and became the 

index velocity rating for cell 1. Equation 16 is represented in ADAPS as a deflection/velocity rating:

OUTPUT = –0.10 + 0.97(INPUT)1 (17)

where,

 INPUT is unit value ADVM velocity.

Table 9. Summary of discharge-measurement data from the Iroquois River near Foresman, Ind., 

ADVM evaluation station, October 15, 1999–June 26, 2001

[ft, feet; ft3/s; cubic feet per second; ft/s, feet per second; --, no data available]

Discharge measurement 

Number Date Rated Stage

(ft)

Discharge 

(ft3/s)

Mean velocity 

(ft/s)

521 10/15/99 Fair 4.23 25.3 0.27

522 12/16/99 Poor 5.50 94.9 .51

523 02/02/00 Fair 4.84 39.5 --

524 03/01/00 Good 8.20 318 .88

525 04/06/00 Fair 5.75 112 .63

526 04/24/00 Good 10.71 566 .88

527 05/09/00 -- 6.96 203 --

528 05/10/00 Fair 10.76 717 1.31

529 05/10/00 Fair 10.92 742 1.25

530 05/11/00 Fair 11.02 698 1.15

531 05/11/00 Fair 11.00 720 1.14

532 05/11/00 Fair 10.93 645 1.10

533 05/11/00 Fair 10.87 644 1.09

534 06/07/00 Good 8.30 349 .94

535 06/21/00 Fair 11.52 988 1.48

536 06/26/00 Fair 12.24 773 1.10
30 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

The output of rating 17 is mean velocity. Thus, 

for each ADVM velocity unit value, ADAPS computes 

and stores a computed mean velocity unit value that, 

when multiplied by channel area, yields a discharge 

unit value. The validity of the index velocity rating 

(and stage-area rating) in the range of discharge 

measurements that produced the rating was evaluated 

by comparing measured discharges to ADVM 

discharges. 

Computed discharges and measured discharges 

for the 14 discharge measurements used to develop 

the ratings are compared in table 10. Also, measured 

discharges and ADVM discharges for four discharge 

measurements (537 to 540) made after the ratings 

discussed above were created are compared in 

table 10. Except for measurements 521, 525, and 526, 

all 18 discharge measurements were within tolerance 

of the ADVM discharges (table 10). 

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

ADVM VELOCITY, IN FEET PER SECOND

0

2.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.8

MEAN VELOCITY, IN FEET PER SECOND

521

522

524

525

526

528

529

530

531

532 and 536

533

535

534

Index velocity rating from least-squares regression

525 Discharge-measurement number

1.6

Figure 14. Index velocity rating for an acoustic Doppler velocity meter (ADVM) at the ADVM evaluation station Iroquois River near Foresman, Ind.
RATING DEVELOPMENT 31

Though measurements 521, 525, and 526 

departed by more than the tolerance from the ADVM 

discharges, adjustments to the ratings were not made 

for the following reasons: (1) the measurements were 

made prior to June 26, 2000, when the ADVM averaging interval was changed from 1 to 10 minutes to 

reduce measured-velocity uncertainties; (2) no reason 

to change the rating was found—all ADVM parameters, including velocities and quality parameters, were 

acceptable during the measurement period, and the 

measurement did not reveal any obvious changes to 

the channel geometry near the measurement section. 

The measurements collectively did not indicate 

any bias. Because all of the measurements (except 

521, 525, and 526) were within tolerance of the 

respective ADVM discharges, and there were justifications for not adjusting the rating based on the those 

three measurements, the rating was judged to be 

adequate for the computation of discharge records 

within the range of measurements and within the time 

period of the measurements. 

Ratings Applications and Limitations

Each of the ratings developed for these stations 

is based upon the linear relation described by equation 

6. The validity of using linear equations to define the 

ratings was confirmed by line-fit plots and other analysis tools. In addition to application of these tools, it is 

necessary to examine if an index velocity rating also 

reflects hydraulic conditions at the station. 

In the case of Kankakee River index velocity 

ratings, stage and ADVM velocity are parameters. 

Table 10. Comparison of discharges computed from acoustic Doppler velocity meter (ADVM) 

to measured discharges from the Iroquois River near Foresman, Ind., ADVM evaluation station, 

October 15, 1999–February 12, 2001

[ft3/s; cubic feet per second; ADVM, acoustic Doppler velocity meter; --, data not available]

 Discharge measurement ADVM computed 

Number Date Rated Value

(ft3/s)

Discharge

(ft3/s)

Discharge 

departure from 

measurement 

discharge

(percent)

521 10/15/99 Fair 25.3 23.0 –9.1

522 12/26/99 Poor 94.9 92.7 –2.3

523 02/02/00 Fair 39.5 -- --

524 03/01/00 Good 318 324 1.9

525 04/06/00 Fair 112 129 15.2

526 04/24/00 Good 566 494 –12.7

527 05/09/00 -- 203 -- --

528 05/10/00 Fair 717 768 7.1

529 05/10/00 Fair 742 749 .9

530 05/11/00 Fair 698 694 –.6

531 05/11/00 Fair 720 684 –5.0

532 05/11/00 Fair 645 648 .5

533 05/11/00 Fair 644 649 .8

534 06/07/00 Good 349 357 2.3

535 06/21/00 Fair 988 972 –1.6

536 06/26/00 Fair 773 774 .1

537 07/12/00 Fair 1,300 1,290 –.8

538 10/13/00 Fair 36.0 37.0 2.8

539 11/15/00 Fair 121 112 –7.4

540 02/12/01 Fair 2,090 2,090 –4.3
32 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

Stage is a parameter in the index velocity rating 

because the relation of mean to ADVM velocity 

changes with stage. Two velocity profiles were 

collected on different days within the ADVM sample 

volume, using an ADCP (fig. 15). The ADCP was held 

stationary and collected velocity data for about 

1 minute; the velocity data that form each profile were 

averaged over the 1-minute sampling period. One 

profile was collected at a stage of 6.20 ft, and the 

second was made at a stage of 11.77 ft. The ADVM is 

fixed at a stage of about 4 ft. The mean velocity for the 

lower stage profile occurs at a depth of about 3.5 ft and 

the higher stage profile occurs at a depth of about 

6.0 ft. This result illustrates that the ratio of ADVMmeasured velocity to mean velocity changes as stage 

changes; from discharge measurements made on the 

days the profiles were collected, the ratios of mean to 

ADVM-measured velocities were 0.96 and 1.42, 

respectively, for the lower and higher stage scenarios. 

Because the shapes of the lower and higher 

stage profiles are similar, the assumption that the 

effect of stage may be expressed as part of a linear 

equation is also reasonable. Within the range of 

discharge measurements used to develop the rating, 

the channel geometry for the Kankakee River station is 

constant—all flows are confined to the rectangular 

channel. A substantial change in channel geometry for 

certain flow conditions (such as when the flow spills 

over the channel into a flood plain) almost certainly 

causes a departure of the index velocity rating from a 

linear form. Because this change in channel geometry 

does not occur at the Kankakee River station, the 

assumption of linearity in the index velocity rating 

is supported further. 

In the case of Iroquois River index velocity 

rating, ADVM velocity is the only parameter. The 

assumption that stage is not a necessary parameter 

for the Iroquois River station within the range of 

discharge measurements used to create the rating also 

can be made by examining a velocity profile from the 

station. The previously discussed higher stage profile 

from the Kankakee River and a higher stage profile 

collected from the Iroquois River station are compared 

in figure 15. The Iroquois River profile has less curvature than the Kankakee River profile; the velocity 

varies by no more than 0.15 ft/s (the mean channel 

velocity is about 2.3 ft/s) from a stage of 13.99 to

5.79 ft. The reason is that the Kankakee River channel 

bottom is rougher (composed of rock and gravel) than 

the Iroquois River channel bottom (composed of silt). 

Increased channel roughness causes the curvature of 

the velocity profile to increase (Chow, 1959). Because 

of the smooth bottom, the lack of curvature of much of 

the velocity profile at the Iroquois River station can 

mean that the relation of mean velocity to ADVM 

velocity will remain relatively constant regardless of 

changing stage; this result supports the assumption 

that stage is not a factor in the creation of an index 

velocity rating. The assumption of the linear relation 

between mean velocity and ADVM velocity is 

supported by the fact that the channel geometry 

remains constant over the range of discharges used 

to create the index velocity rating. 

ADVM velocity is the only parameter for 

the Fall Creek at Millersville index velocity rating. 

Because of the shallow depth during discharge 

measurements, velocity profiles were not collected 

during the study period. Because the stream has a 

rocky bottom, however, velocity profiles likely would 

resemble those from the Kankakee River, indicating 

that stage also likely would be a factor. Stage is not 

a factor for the rating created from the range of 

discharge measurements because the total range of 

stage represented by the rating is 1.46 ft. This range 

means that the position change in the vertical of mean 

velocity to ADVM velocity is not great enough to alter 

the relation between mean and ADVM velocity. 

The linearity of the ratings represented in this 

study does not indicate that all index velocity ratings 

for all stations would be linear. For many stations, a 

curvilinear rating (or a rating represented by various 

curves) would be more appropriate. To produce accurate discharge records, a rating should represent the 

hydraulics at the station and be confirmable by 

comparisons of rating-computed discharges to 

measured discharges. Thus, ratings must be developed 

on a case-by-case basis. 

The range of measurement discharges and 

stages used to develop the index velocity ratings for 

each of the stations is less than the range of discharges 

and stages that historically have occurred at the 

stations. For example, the range of measured 

discharges for Kankakee River at Davis was 301 to 

1,410 ft3

/s, or 1,109 ft3/s (table 6). The range of mean 

daily discharges for the period of record is 1,766 ft3

/s; 

thus, the range of discharges from measurements 

used to construct the index velocity rating is about 

62 percent of the historical range of mean daily 

discharges at the station. For Fall Creek at Millersville 

and Iroquois River near Foresman, the range of 
RATING DEVELOPMENT 33

0.5 1.0 1.5 2.0 2.5 3.0 3.5

VELOCITY, IN FEET PER SECOND

2

10

3

4

5

6

7

8

9

STAGE, IN FEET ABOVE STATION DATUM

Velocity profile for high stage

Velocity profile for low stage

1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6

VELOCITY, IN FEET PER SECOND

2

16

4

6

8

10

12

14

STAGE, IN FEET ABOVE STATION DATUM

Velocity profile from Kankakee River

Velocity profile from Iroquois River

Approximate location, ADVM sample volume

Approximate location, mean velocity

A

B

Figure 15. Velocity profiles from (A) the Kankakee River at Davis, Ind., 

acoustic Doppler velocity meter (ADVM) evaluation station, for profiles 

collected at high and low stages, and (B) the Iroquois River near Foresman, 

Ind., and Kankakee River at Davis, Ind., ADVM evaluation station.
34 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

measurement discharges used to construct the index 

velocity ratings was 2 and 38 percent, respectively, of 

the historical range of mean daily discharges at the 

stations. This result means that the index velocity 

ratings described in this report will be used to compute 

discharge records for discharge values outside the 

range of each rating.

Based on analysis tools and comparison of 

measured discharge and rating discharges, the ratings 

for all three stations appear to be valid within the range 

of measurements made during the study period; this 

result does not mean the ratings will remain valid 

outside the range of stages and discharges of the 

measurements that were used to develop the ratings. 

For the ratings to remain valid, the relations defined 

by the ratings must remain stable. Each station must be 

examined for assumptions to be made about the 

validity of the ratings beyond the range of the 

measurements used to develop the ratings. 

For Kankakee River at Davis, the measurements 

appear valid for 62 percent of the historical flow range. 

Because the range of flows would be confined to the 

channel at the ADVM measurement section, it is 

reasonable to expect the ratings to remain valid outside 

the range of measurements. 

The Iroquois River rating may remain valid 

outside the measurements used to create it. The range 

of flows would be confined to the channel, so it is 

reasonable to assume that the change in mean channel 

velocity would remain linear with the change in 

ADVM-measured velocity. This assumption was 

tested by measurement 540, made after creation of the 

rating and with a greater discharge (2,090 ft3/s) than 

the maximum measurement used to create the rating 

(988 ft3/s). The measurement was within tolerance of 

the rating discharges. While it is reasonable to assume 

that the ratings for Kankakee River at Davis and 

Iroquois River near Foresman will remain stable 

outside the range of measurements used to create the 

rating, the only way to confirm this assumption is to 

continue to make discharge measurements outside the 

range of the ratings. 

For Fall Creek, the rating would not be expected 

to remain valid for all stage and discharge ranges. The 

ratings for cells 1 and 2 assume a linear relation 

between mean velocity and ADVM velocity; as previously discussed, these relations appear valid within the 

range of discharge measurements used to create the 

ratings. The linear relation between mean velocity and 

ADVM velocity may remain linear when most of the 

discharge is contained within the main channel—field 

experience indicates that most of the discharge is 

contained within the main channel below a stage of 

about 6 ft and discharge of about 1,600 ft3/s. Above

6 ft, flows will begin to occur in the flood plain (fig. 6) 

and the relation between mean velocity and ADVM 

velocity is likely to depart from the linear relation 

defined by the index velocity ratings described in this 

report. Flows in the flood plain mean that a small 

change in stage represents a larger change in area than 

an equivalent stage change with flow confined to the 

channel, equating to a larger change in channel area 

and a lower change in mean velocity. The ADVM still 

would be measuring in the main channel, so the relation of change in mean velocity to ADVM velocity 

likely would depart from the relation seen in the main 

channel. 

During the period of record, mean daily 

discharges from the Fall Creek station were below 

1,600 ft3

/s about 97 percent of the time; therefore, 

flows usually are confined to the channel (where the 

index velocity rating is valid). Peak discharges are 

important; it will be necessary to make discharge 

measurements at flows above 1,600 ft3/s to define the 

rating so that higher flows may be accurately 

computed. Because the rating shape likely would 

depart from a straight line above about 1,600 ft3/s, a 

rating to reflect the departure would be a compound 

rating consisting of the current linear relation for flows 

restricted to the channel and the relation(s) defined by 

measurements for higher flows. At present, such a 

rating cannot be entered into ADAPS, so the rating 

would be implemented as a table in ADAPS. The table 

would consist of inputs (ADVM velocities) and corresponding outputs (mean velocities). Table values 

would be computed outside ADAPS, using the appropriate relation for the flow condition. 

For a rating to continue to be valid at a station, 

factors that could invalidate the rating must not occur. 

Factors that could adversely affect the validity of an 

index velocity rating include (but are not limited to) 

the following:

1. Changes in the channel geometry at the ADVM 

standard cross-section location—could be caused 

by scouring and filling of the riverbed by floods 

or dredging.

2. Overbank or flood-plain flows, as discussed previously for Fall Creek—might invalidate a rating 
ACOUSTIC DOPPLER VELOCITY METER DISCHARGE RECORDS 35

for flows confined to the channel when overflow 

occurs. 

3. ADVM velocity-measurement errors—an object 

such as a submerged log within the ADVM 

sampling volume would tend to bias the ADVM 

velocity low. ADVM malfunctions, such as a 

temperature sensor failure, could result in 

velocity biases. 

4. Weed growth in the channel—would bias the 

ADVM velocities low if the weeds are in the 

sampling volume. 

5. Ice cover—could change the vertical velocity distribution and effective channel area. 

6. Density gradients in the water, such as temperature 

gradients—exist because of variations in physical 

constituents such as water temperature. The 

speed of sound in water is affected by gradients 

that have the effect of bending an acoustic beam 

as it travels through the water (Laenen, 1985). If 

an ADVM ray bends, the position of the sample 

volume could change and thus change the relation between ADVM velocity and mean velocity. 

In a worst-case scenario, one or both beams 

could be bent enough to touch the water surface 

or riverbed, biasing the measured velocities. 

Ultimately, it is only possible to confirm the 

continued validity of an index velocity rating by 

continuing to make measurements of discharge. Accurate discharge records depend upon the accuracy of the 

mean velocity produced from the index velocity rating. 

ACOUSTIC DOPPLER VELOCITY METER 

DISCHARGE RECORDS

Records for discharge were produced from each 

of the three ADVM evaluation stations. These records 

could be compared to conventional records and evaluated. 

Computation of the Records

The same records-computation procedures were 

used for the three evaluation stations. First, unit value 

stages and ADVM velocities were analyzed for 

obvious errors, called “spikes,” using plots of the unit 

values. Spikes occurred infrequently and were of short 

duration—usually there was no more than one spike 

on any day a spike occurred. In these instances a spike 

manually was edited so that the spike conformed to the 

values that preceded and followed. 

The quality of all unit value velocity data was 

examined by analyzing

• Beam amplitudes—for sudden, unexplained 

changes. Most of the time, beam amplitudes 

would increase with and decrease with discharge 

because suspended-sediment concentrations 

would increase and decrease with discharge 

(increasing suspended-sediment concentrations 

represent an increase in backscatter and therefore 

cause the return strength from the ADVM beams 

to increase). 

• Velocity standard deviation—collected from the 

Argonauts; in general, the standard deviation 

remained low and constant throughout the study 

period. 

• x- and y-velocity components—for accurate 

discharges to be computed from ADVM velocities, the mean river flow direction should not 

change significantly. Because an ADVM outputs 

both x- (downstream) and y- (across-stream) 

velocity components, flow-direction changes can 

be assessed. If the river flow direction remains 

constant, the y-components of velocity should 

remain small relative to the x-components of 

velocity (y-components were small in comparison 

to x-components at the three evaluation stations). 

• Velocity output from multiple cells—of the Fall 

Creek at Millersville ADVM were compared over 

time. Comparison of velocities from adjacent 

cells is a valuable diagnostic tool. 

There was only one period at one station of the 

three with a persistent data-quality problem. The 

problem affected the velocity and the computed 

discharge from cell 2 of the Fall Creek ADVM. 

Measurement 1263, made January 24, 2001, departed 

by –32.9 percent from the discharge computed from 

cell 2 (table 8). From December 18, 2000, to February 

9, 2001, cell 2 velocities departed from cell 1 velocities. On average, cell 2 and cell 1 velocities were 

within 0.03 ft/s; during the period in question, cell 2 

velocities were as much as 0.8 ft/s lower than cell 1 

velocities (fig. 16). This departure in velocities was 
36 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

accompanied by an increase in cell 2 beam amplitudes. 

Normally, cell 2 beam amplitudes are lower than cell 1 

(cell 2 is farther away from the ADVM than cell 1, and 

the beam amplitudes are less than those from cell 1); 

during the period in question, beam amplitudes were 

greater from cell 2 than from cell 1 (fig. 16). It is likely 

that an object or objects, such as tree branches, 

became stationary in cell 2. A stationary object in 

cell 2 would bias measured velocities low and increase 

beam amplitudes. The departures of cell 2 velocities 

from cell 1 velocities were about 0.35 ft/s, on average, 

through January 5; then these gradually began to 

increase to about 0.62 ft/s on February 2. The 

0.62-ft/s departure remained constant from February 2 

to February 9. On February 9, during a flow increase, 

velocities and beam amplitudes rapidly normalized. It 

is likely that debris in cell 2 caused the velocity departures, and that the area of cell 2 affected by debris 

grew in volume from January 5 through February 2 

and then remained constant. The flow rise on February 

9 then apparently moved the debris completely out of 

cell 2. 

The low-velocity bias that affected cell 2 velocities caused the discharges computed from cell 2 to 

depart from those from cell 1 by more than 60 percent, 

on average, from December 18, 2000, to February 9, 

2001. To compensate, a velocity shift was applied to 

the cell 2 velocities for this period. The concept of 

velocity shift is similar to that of a stage shift used to 

compute discharges, using conventional stagedischarge methods. The velocity shift was implemented in ADAPS in a manner similar to application 

of stage shift in ADAPS. The magnitude of the 

velocity shift was computed by adding to cell 2 the 

mean departures of cell 2 from cell 1: +0.35 held 

constant to January 5, then steadily increased 

(prorated) to +0.65 on February 2, and held at +0.65 

until February 9 when the shift was prorated to zero 

during the flow rise. After application of the shift, 

the discharges computed from cell 2 were within 

2 percent, on average, of those computed from cell 1. 

After the analysis of unit-value data was 

complete, and any necessary processing such as the 

editing of spikes and the velocity-shift application was 

completed, ADAPS was used to produce the discharge 

record. To compute the discharge record from unit 

values, ADAPS would

1. Compute channel-area unit values from stage-unit 

values, using the stage-area rating.

2. Compute mean velocity unit values from ADVM 

velocity unit values, using the index velocity 

rating(s) (for the cell 2 velocities from the Fall 

Creek ADVM during the velocity-shift period, 

ADAPS added the appropriate shift value to the 

unit-value velocity before computing mean 

velocity from the rating). 

3. Compute unit-value discharges, using equation 2 

(Q = VA) by multiplying unit-value mean velocities by channel areas.

4. Computing mean daily discharge by averaging the 

computed unit value discharges for a 24-hour 

period. 

The ADAPS discharge record was evaluated by 

a comparison to the conventional discharge record. 

Wahl, Thomas, and Hirsch (1995) outline the general 

process for producing discharge records using conventional methods.

Following a measurement, a preliminary evaluation is made of the degree to which the stage-discharge 

relation has changed on the basis of measurements 

made up to that time—provisional discharges are 

determined, assuming that the most recent measurements define the channel condition. This process is 

repeated following each measurement. With each 

measurement, however, more measurements are available to evaluate the stage-discharge relation. This 

process may lead to changes in the provisional 

discharges that had been computed for previous 

months. At the end of the year, all measurements are 

available for review. The entire set of measurements 

are used to reevaluate the rating conditions for the 

year. Final decisions are made about the stagedischarge relation that were in effect during the year, 

and the record is refined or recomputed as necessary. 

This record then is passed through a rigorous review 

process and, once approved, the data are considered 

final and are placed in the archives and published.

Relevant USGS standards and practices (Rantz, 

1982) were used to compute the conventional record. 

The conventional and ADVM records were computed 

independently of one another and by different 

personnel; the ADVM and conventional records then 

were compared. 
ACOUSTIC DOPPLER VELOCITY METER DISCHARGE RECORDS 37

5 10 15 20 25 31 5 10 15 20 25 31 5 10 15 20 

December January February

2000 2001

03

12

VELOCITY, IN FEET PER SECOND

EXPLANATION

ADVM CELL 1 UNIT VALUESADVM CELL 2 UNIT VALUES

5 10 15 20 25 31 5 10 15 20 25 31 5 10 15 20 

December January February

2000 2001

3080

40506070

BEAM AMPLITUDE, IN DECIBELS

Figure 16. Acoustic Doppler velocity meter (ADVM) cell 1 and 2 velocity unit values and beam-amplitude unit values from the ADVM evaluation site Fall Creek at Millersville, Ind., December 1, 2000–February 28, 2001 (Note: beam-amplitude scale is ap
38 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

Comparison of the Records

The ADVM and conventional records were 

compared qualitatively, using hydrographs. In the 

context of this discussion, a hydrograph is a time 

series of the mean daily discharges and is a valuable 

tool in the analysis of the discharge record. For 

instance, a hydrograph, in conjunction with weather 

data, can indicate whether an increase in discharge is 

legitimate (caused by rainfall) or is the result of a 

physical factor (such as a debris jam downstream from 

the gage; this would cause an increase in stage without 

a true increase in discharge). Hydrographs of the 

conventional and ADVM-produced records were 

compared for the three evaluation stations. The records 

for each evaluation station also were compared quantitatively; that is, the differences in mean daily 

discharges between conventional and ADVMproduced records were examined using statistics. 

When using conventional methods, it is sometimes necessary to estimate the record for certain 

periods. Equipment malfunctions can cause data loss 

or the storage of incorrect data; periods in which 

malfunctions occur must be estimated. Ice is another 

reason to estimate record. When ice partially or totally 

covers a river, the stage-discharge rating becomes 

invalid. The method of estimation during such a period 

is to graphically compare the hydrograph to one or 

more stations with similar characteristics (Rantz, 

1982, explains the procedure in detail). Periods in 

which the record was estimated are not included in the 

comparisons between ADVM and conventional 

records in order to eliminate the subjectivity associated with discharge estimates. 

The ADVM and conventional mean daily 

discharge hydrographs for the study period from 

Kankakee River at Davis are shown in figure 17. 

Within the period, 561 mean daily discharges (days in 

which discharges were not estimated) were available 

for comparison. Generally, the conventional hydrographs and ADVM hydrographs compare 

closely—high- and low-flow periods correspond, and 

larger peaks are supported by precipitation data. Some 

periods of noticeable departure can be seen in the 

hydrographs: in June and August of 1999, ADVM 

discharges were approximately 8 to 12 percent higher 

than the corresponding conventional discharges; from 

September through December 2000, conventional 

discharges were approximately 8 to 14 percent higher 

than the ADVM discharges. The reasons for these 

departures are not known. 

The conventional and ADVM records compare 

closely. For the 561 nonestimated data days within the 

study period, the average of mean daily discharges was 

426 and 427 ft3/s, for the conventional and ADVM 

records, respectively. The average difference between 

conventional and ADVM discharges was 

1.08 ft3/s and the standard deviation of the difference 

was 30.1 ft3/s. The maximum percent difference 

between conventional and ADVM discharges was 

21.1. Ninety-eight percent of the ADVM 

discharges were within 15 percent of the conventional 

discharges; 86 percent were within 10 percent of the 

conventional discharges; and 51 percent were within 

5 percent of the conventional discharges. 

The ADVM and conventional hydrographs for 

the study period from Fall Creek at Millersville 

ADVM cells 1 and 2 are shown in figures 18 and 19, 

respectively. Within the study period, 322 mean daily 

discharges (days in which discharges were not estimated) were available for comparison. Generally, the 

conventional and ADVM hydrographs compared 

closely for both cells—high- and low-flow periods 

correspond and larger peaks are supported by precipitation data. For cell 1, there were short periods of 

departure from the conventional discharges where 

ADVM discharges were 5 to 10 percent greater than 

the conventional discharges; generally, these departure 

periods occurred within the 70- to 200-ft3/s range and 

on the recession of flow peaks. During peak discharges 

in June and October, ADVM discharges were on 

average about 10 percent lower than conventional 

discharges. For cell 2, discharges compared closely on 

these same peaks. For this reason, it is speculated that 

bridge-pier turbulence may have affected cell 1 velocities during higher flows. Because cell 2 is farther away 

from the pier, the effect of turbulence would be lessened for cell 2. For the rest of the study period, cell 2 

discharges compared closely to conventional 

discharges; there were short periods of departure 

during the period November 2000 to January 2001. 

The conventional and ADVM cell 1 and 2 

records compare closely. For the 322 nonestimated 

data days within the study period, the average of mean 

daily discharges was 242 ft3/s for the conventional 

record and 242 ft3/s for the records from both cells. 

The average difference between conventional and 

ADVM discharges was 1.51 and 1.79 ft3/s for cells 1 

and 2, respectively, and the standard deviation of the 
A

COUSTICDOPPLERVELOCITYMETERDISCHARGERECORDS

39

J J A S O N D J F M A M J J A S O N 

1999 2000 

100

10,000

150

200250300400500600700800900

1,0001,5002,0002,5003,0004,0005,0006,0007,0008,0009,000

DISCHARGE, IN CUBIC FEET PER SECOND

Conventional-method discharge hydrograph

ADVM-method discharge hydrograph

Figure 17. Comparison of mean-daily discharge hydrographs produced by conventional method and acoustic Doppler velocity meter (A

the Kankakee River at Davis, Ind., ADVM evaluation station, June 1, 1999–February 28, 2001 (Note: breaks in graph represent period
40 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

Apr May June July Aug Sept Oct Nov Dec Ja

2000 

10

10,000

20

30405070

100200300400500700

1,0002,0003,0004,0005,0007,000

DISCHARGE, IN CUBIC FEET PER SECOND

Conventional-method discharge hydrograph

ADVM-method discharge hydrograph

Figure 18. Comparison of mean-daily discharge hydrographs produced by conventional method and acoustic Doppler velocity meter 

using ADVM cell 1, from the Fall Creek at Millersville, Ind., ADVM evaluation station, March 23, 2000–February 28, 2001 (Note: breaks periods of missing data).
ACOUSTIC DOPPLER VELOCITY METER DISCHARGE RECORDS 41 Apr May June July Aug Sept Oct Nov Dec Ja

2000 

10

10,000

20

30405070

100200300400500700

1,0002,0003,0004,0005,0007,000

DISCHARGE, IN CUBIC FEET PER SECOND

Conventional-method discharge hydrograph

ADVM-method discharge hydrograph

Figure 19. Comparison of mean-daily discharge hydrographs produced by conventional method and acoustic Doppler velocity meter (A

using ADVM cell 2, from the Fall Creek at Millersville, Ind., ADVM evaluation station, March 23, 2000–February 28, 2001 (Note: breaks sent periods of missing data).
42 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

difference was 35.4 and 29.8 ft3/s for cells 1 and 2, 

respectively. The maximum percent difference 

between conventional and ADVM discharges was 

19.8 and 25.6 for cells 1 and 2, respectively. For

cell 1, 97 percent of the ADVM discharges were 

within 15 percent of the conventional discharges; 

74 percent were within 10 percent of the conventional 

discharges; and 42 percent were within 5 percent of 

the conventional discharges. For cell 2, 94 percent of 

the ADVM discharges were within 15 percent of the 

conventional discharges; 82 percent were within 

10 percent of the conventional discharges; and 

57 percent were within 5 percent of the conventional 

discharges. 

The ADVM and conventional hydrographs for 

the study period from the Iroquois River near 

Foresman are shown in figure 20. Within the period, 

387 mean daily discharges (days in which discharges 

were not estimated) were available for comparison. 

There was more departure in the hydrographs for this 

station than in the other two study stations. Historically, variable backwater has been noted at this station. 

Variable backwater particularly is evident during some 

high-discharge periods, such as June 25–July 17, 

2000. The effect of backwater is illustrated in a graph 

of unit-value stages and ADVM velocities for April 15 

to July 31, 2000 (fig. 21). From April 15 to June 24, 

the relation between stage and ADVM velocity 

appears stable (thus, the relation between stage and 

discharge would remain stable); velocities increase 

with stage, and the patterns of peak velocity to stage 

are consistent. Starting with a secondary peak on 

June 25, a change is visible in the relation between 

stage and velocities. During the June 25 peak, velocities were lower than velocities during smaller peaks 

prior to June 25. For the two large peaks July 2 to 19, 

velocities are considerably lower than velocities that 

occurred on earlier peaks with lower stages. Analysis 

of unit-value stages and velocities for other periods 

reveal that some backwater likely is present at times 

during low-discharge periods as well. 

During the entire study period, the average of 

mean daily discharges compares closely: for the 387 

nonestimated days within the study period, the averages of mean daily discharges were 242 and 237 ft3

/s 

for the conventional and ADVM records, respectively. 

The average difference between conventional and 

ADVM discharges was 5.41 ft3/s, and the standard 

deviation of the difference was 51.8 ft3/s. Other statistics reflect departures in the conventional and ADVM 

discharges. The maximum percent difference between 

conventional and ADVM discharges was 49.0. Sixtynine percent of the ADVM discharges were within 

15 percent of the conventional discharges; 56 percent 

of the ADVM discharges were within 10 percent of the 

conventional discharges; and 34 percent were within 

5 percent of the conventional discharges. 

Evaluation of the Records

The USGS has the following accuracy ratings 

for discharge records: “excellent” means that about 

95 percent of the daily discharges are within 5 percent 

of their true values; “good,” within 10 percent; and 

“fair,” within 15 percent (Kennedy, 1983). Records 

that do not meet any of these criteria are rated “poor” 

(note that accuracy ratings for discharge measurements differ from accuracy ratings assigned to individual discharge measurements). Assuming that the 

discharge record produced by conventional methods 

represents the true discharge record, then the 

Kankakee River at Davis and Fall Creek at Millersville 

ADVM records (cell 1 and 2) could be called “fair” 

because about 95 percent of the ADVM discharges 

were within 15 percent of the conventional discharges 

for the study period. The conventional record, 

however, cannot be said to represent the true discharge 

record because of error sources in this method, 

including:

• Errors in the discharge measurements used to create 

the stage-discharge rating;

• Errors in the stage-discharge rating (such as regions 

that are not well defined by discharge measurements); and 

• Errors in the applications of stage shifts—whereas 

there are standard procedures of the application of 

shifts (Rantz, 1982, and Kennedy, 1983), there is 

subjectivity in shift application. The person 

producing the record must use personal judgment 

as to shift periods, magnitudes, and shapes (in this 

study, no shifts were needed for the Kankakee 

River conventional record as all discharge 

measurements were within tolerance of the stagedischarge rating; for Fall Creek at Millersville, 

four periods of shift application were required to 

bring the stage-discharge rating within tolerance 

of discharge measurements). 

Because the index velocity ratings were proven 

valid within the range of discharge measurements used 
A

COUSTICDOPPLERVELOCITYMETERDISCHARGERECORDS

43

O N D J F M A M J J A S O N 

1999 2000 

10

10,000

20

30405070

100200300400500700

1,0002,0003,0004,0005,0007,000

DISCHARGE, IN CUBIC FEET PER SECOND

Conventional-method discharge hydrographADVM-method discharge hydrograph

Figure 20. Comparison of mean-daily discharge hydrographs produced by conventional method and acoustic Doppler velocity met

from the Iroquois River near Foresman, Ind., ADVM evaluation station, October 1, 1999–February 28, 2001 (Note: breaks in graph missing data).
44 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

15 20 25 30 5 10 15 20 25 31 5 10 15 20 25 30 5 10 15 

April May June July

2

18

468

10121416

STAGE, IN FEET ABOVE STATION DATUM

STAGEVELOCITY

Figure 21. Stage and acoustic Doppler velocity meter (ADVM) measured velocity unit values from the Iroquois River near Foresmanstation, April 15–July 31, 2000.
ACOUSTIC DOPPLER VELOCITY METER DISCHARGE RECORDS 45

to create the ratings and because the quality of ADVM 

data was good, a rating of “good” was given to parts, if 

not all, of the record from the Kankakee and Fall 

Creek stations. 

For the Iroquois River near Foresman station, 

the conventional and ADVM records depart more than 

the other two stations do. This station has a history of 

variable backwater and discharge-record quality problems that have been documented by the hydrographers 

who analyzed the record. Historically, extensive shift 

periods had to be used to produce the conventional 

record; it is likely that the quality of the ADVM record 

exceeds that of the conventional record. The velocity 

that the ADVM record is based on will compensate for 

backwater effects because velocities are a more direct 

index of discharge than are stages where backwater is 

present. 

The ADVM record was compared to the 

conventional record to assess the ADVM record based 

on a record produced by long-standing USGS 

methods. The conventional and ADVM records from 

the Kankakee River and Fall Creek stations compare 

closely. Additionally, discharge measurements made 

through the study period confirm the validity of the 

stage-area and index velocity ratings. Thus the ADVM 

record from these stations for the study period can be 

rated “good.” For the Iroquois River station, the 

comparison between conventional and ADVM records 

was not as close as the other two stations; there is 

evidence to support the conclusion that the ADVM 

record may be more accurate than the conventional 

record. Also, discharge measurements during the study 

period confirm the validity of the rating. Thus the 

ADVM record from the Iroquois River near Foresman 

can be rated “good.”

The quality of the ADVM record meets USGS 

publication standards. The ADVM records for 

Kankakee River at Davis and Iroquois River near 

Foresman were published in Stewart and others 

(2000); the record from the three stations were 

published in 2001. Real-time unit value discharges 

computed from ADVM data are served on the Indiana 

District Real-Time Surface-Water-Data Retrieval 

World Wide Web pages for the three evaluation 

stations (fig. 22).

Instrument reliability is an important factor in 

the feasibility of using ADVM’s for the production of 

discharge records. For the stations and study periods 

documented in this report, no ADVM malfunctions 

caused lost or missing records and the ADVM’s 

required no special maintenance. Light coatings of silt 

and biological growth on the ADVM transducers did 

not appear to reduce the quality of the ADVM data. 

Little, if any, maintenance was required to keep the 

ADVM’s operational. 

The comparison of ADVM discharge records 

with conventional records for the study stations was 

one tool used to assess the quality of the ADVM 

record. At other stations, such a comparison may not 

be possible (for example, stations where a stagedischarge relation is not present, such as in estuarine 

rivers or bidirectional flow stations). If an ADVM is to 

be installed at a new USGS streamflow-gaging station, 

it would be important to produce discharge record 

from the ADVM as soon as possible and to avoid 

producing redundant conventional records. To make 

ADVM use practical, there must be ways of assessing 

the accuracy of the ADVM record. Ultimately, the 

accuracy of an ADVM discharge record produced by 

an ADVM will depend primarily on: 

1. Accuracy of the stage-area and index velocity 

ratings, 

2. Stability of the stage-area and index velocity 

ratings, 

3. Accuracy of stage measurements, and

4. Accuracy of ADVM velocity measurements.

The accuracy of the index velocity ratings is 

dependent upon the accuracy of the discharge 

measurements used to create the ratings and also upon 

whether the number of measurements made 

adequately defines the ratings. The accuracy of the 

stage-area curve should be acceptable if cross-section 

data were collected with care and if the stage-area 

relation remains stable, provided the channel geometry 

does not change significantly. If index velocity ratings 

can be represented by mathematical models such as 

linear equations, plots and various statistical tools can 

be used to gage the accuracy of the model. Ultimately, 

the only way to continue to assess the validity of the 

stage-area and index velocity ratings is by continued 

measurements of discharge.

USGS policy states that stage should be 

measured with an accuracy of 0.01 ft or 0.2 percent of 

the effective stage being measured, whichever is less 

restrictive (U.S. Geological Survey, 1992). This policy 

was designed to support computation of discharge 

from stage-discharge relations. For ADVM’s, stage 

accuracy is important because errors in stage will 

produce errors in computation of channel areas, 
46 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

producing discharge errors proportional to channelarea errors (Q = VA). For example, at median flow, a 

0.05-ft error in stage would cause a 0.6-, 1.0-, and 

3.3-percent error in channel area and discharge at the 

Kankakee River, Iroquois River, and Fall Creek evaluation stations, respectively. A greater discharge error 

would occur at Fall Creek because of channel geometry. Rivers or streams that are shallow and wide are 

more sensitive to area and discharge errors caused by 

stage errors. 

Stage sensors used at the Kankakee and Iroquois 

River stations were incremental shaft encoders in 

stilling wells that met USGS stage-accuracy requirements. For the Fall Creek station, an incremental shaft 

encoder was used as the primary stage sensor 

(“primary” refers to a stage sensor that produces the 

stage used in discharge-record computation) until 

September 30, 2000. From October 1, 2000, to 

February 28, 2001, the stage from the EasyQ upwardlooking transducer was used as the primary stage 

sensor. Throughout the study period, the EasyQ stage 

was within, on average, 0.01 ft of the encoder stage 

and was used as the primary stage sensor for the 

period. The stage from the EasyQ was used as the 

primary stage sensor for part of the study period, but 

the absolute accuracy has not been assessed formally 

by the USGS. The same is true of the upward-looking 

stage transducer available with newer models of the 

Argonaut-SL. 

Errors in discharge computation are directly 

proportional to velocity-measurement errors (Q = VA). 

The manufacturers of the Argonaut-SL and the EasyQ 

claim velocity accuracies of 1 percent of the measured 

velocity ±0.5 centimeters per second (0.016 ft/s). This 

accuracy has not been assessed formally by the USGS. 

Because the ADVM velocity data were used to 

Figure 22. Example of near real-time discharge hydrograph from Iroquois River near Foresman, Ind., served 

on the World Wide Web. 
USE OF ACOUSTIC DOPPLER VELOCITY METERS FOR THE PRODUCTION OF DISCHARGE RECORDS 47

produce acceptable records of discharge for the three 

study stations, it is assumed that the ADVM velocitymeasurement accuracy was sufficient for computation 

of mean daily discharges acceptable to the USGS. 

Mean channel velocities from the three study stations 

ranged from about 0.2 ft/s at the Iroquois River station 

to about 3.5 ft/s at the Kankakee River station. 

Velocity accuracies may not be sufficient to produce 

accurate discharge records under all conditions. At 

some stations, such as those in estuaries, mean velocities may be significantly lower than the range of mean 

velocities observed at the three study sites (velocity 

uncertainties would be a larger percentage of the mean 

velocities and, thus, discharges at low-velocity 

stations). 

Because factors 1 to 4 are station dependent and 

because all stations will have different characteristics, 

the best assessment of discharge-record accuracy will 

be the continued comparison of discharges computed 

from the ADVM data to discharges measured in the 

field. 

USE OF ACOUSTIC DOPPLER VELOCITY 

METERS FOR THE PRODUCTION OF 

DISCHARGE RECORDS

Whereas the scope of this study was limited to 

three streamflow-gaging stations located in Indiana, 

the study revealed some implications and issues that 

may have a wider application. 

Ice-Affected Periods

During ice-affected periods, a stage-discharge 

rating often is not reliable; the ice will cause stages to 

rise without a corresponding rise in discharge. During 

such periods, the discharge record must be estimated; 

the estimation is aided if one or more discharge 

measurements were made during the period. Otherwise, comparisons with the hydrographs of other 

stations in conjunction with weather data must be used 

to estimate the record. Estimated records during ice 

periods are subjective and usually are rated “poor.” 

ADVM’s may allow for less-subjective estimates of discharge during ice-affected periods. An 

ADVM discharge was computed during a discharge 

measurement (523) made at the Iroquois River station 

when the river was totally ice covered. The measurement yielded a discharge of 39.5 ft3

/s. The ADVMcomputed discharge during the measurement period 

was 51.0 ft3/s, a difference of 29 percent. Measurement notes indicated the average ice thickness was 

0.5 ft, and when holes were chopped in the ice to make 

the measurement, the water level came to the top of the 

ice. This result means that the river was under pressure 

and that the channel area used to compute ADVM 

discharge was based on a stage that was about 0.5 ft 

high. When the channel area was recomputed manually for a 0.5-ft lower stage, the ADVM discharge for 

the measurement period was recomputed at 42.6 ft3/s, 

7.8 percent higher than the measurement discharge. 

Because of the rough underside of the ice, the velocity 

profile usually is different than when the surface is 

free of ice. Rantz and others (1982) recommend that 

for velocities sampled at 60 percent of the distance 

from bottom of ice to streambed, a coefficient of 0.92 

be applied to estimate the mean velocity. Because the 

ADVM measured velocity at about 60 percent of the 

depth under the ice during the measurement period, 

the ADVM-computed velocity was adjusted by multiplication of 0.92. This yielded a recomputed ADVM 

discharge of 39.2 ft3/s, which is within 1 percent of the 

measured discharge. 

A more rigorous approach to estimates of 

discharge during ice-affected periods is explained by 

Wang (2000). Flow-distribution models for deriving 

station-specific equations are used to compute 

discharges from AVM velocities during periods of 

channel ice cover. In this approach, bed-roughness and 

ice-roughness parameters are estimated from velocity 

profiles collected at a station. A hydraulic parameter is 

determined from cross-section area and locations 

of the AVM transducers. A “beta” coefficient is 

computed from the roughness and hydraulic parameters. AVM velocity multiplied by the beta coefficient 

yields discharge for a particular stage. The beta coefficient can be expressed as a function of stage through a 

regression analysis. Thus, discharge becomes a function of stage and AVM velocity. Discharges computed 

from this method compared closely to discharge 

measurements made at AVM stations in Canada during 

ice periods (Wang, 2000). Discharges computed from 

Wang’s methods, although developed for AVM 

stations, can be applied directly to ADVM’s as well. 

Whether using a simple coefficient or Wang’s 

approach, the stage of the bottom of the ice needs to be 

known. One way to estimate the stage of the bottom of 

the ice is to use an ADVM equipped with an upward-
48 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

looking stage transducer. For the Iroquois River near 

Foresman, the thickness of the ice was estimated, 

using the discharge-measurement data and temperature records, for the ice-affected period. The Fall 

Creek at Millersville ADVM was equipped with an 

upward-looking transducer and measured the stage of 

the ice bottom during the ice-affected period 

December 18, 2000, to January 4, 2001, thus 

computing channel area and discharge based on this 

stage. No discharge measurements were made during 

this period to confirm the discharge. The records for 

the ice-affected periods from the three stations were 

rated “poor.” 

Multi-Cell Capabilities

The EasyQ three-cell feature provided a qualityassurance tool for comparison of velocity and amplitude data from the cells. Noticeable departures in 

velocities and beam amplitudes can identify problems 

in one cell, whereas periods with no departures can 

add confidence to the ADVM record. Each cell can be 

rated separately to produce discharge, and if one cell 

appears to produce a better record, it can be used as the 

“primary cell.” For Fall Creek at Millersville, for 

example, cell 2 may do better at high flows because it 

is farther from the bridge pier, and it may be less 

affected by bridge-pier turbulence. The multi-cell 

capability allowed the discovery of the velocity bias in 

cell 2 for a period at the Fall Creek at Millersville 

station and allowed the computation of velocity shifts 

to compensate for the errors caused by the velocity 

bias. The Argonaut-SL’s used at the study stations did 

not have the multi-cell feature. 

Multiple cells can have disadvantages: velocity 

instrument “noise” would be higher than for a single, 

larger cell, and there are more data parameters to log, 

store, and analyze. The multi-cell feature may not be 

applicable at all stations but can be considered as a 

valuable quality-assurance tool.

Velocity Shifts

If the stage-area and index velocity ratings 

remain stable and the velocity measurements remain 

unbiased, shifts should not need to be applied to 

produce ADVM discharge records. As demonstrated 

for cell 2 of the Fall Creek ADVM, it is possible to use 

velocity shifts to compensate for discharge-computation errors induced by velocity-measurement biases. It 

might be possible to compensate for changes in the 

stage-area rating caused by channel-geometry changes 

by using a stage shift. ADAPS will use the shifted 

stage to compute channel area. If the channel geometry changes, the index velocity rating also will likely 

become invalid because the station hydraulic characteristics will change. In this case, new stage-area and 

index velocity ratings likely will be required. It may be 

difficult to produce accurate ADVM discharge records 

if such changes are frequent. 

Real-Time Discharge Data

When supplying near real-time discharge data, 

as the USGS provides on the World Wide Web for 

many stations, ADVM—as opposed to conventionalmethod discharges—may be advantageous. If a station 

has stable channel and hydraulic characteristics and 

the ADVM ratings are reliable, the real-time discharge 

data should be accurate. For many stations measured 

with conventional methods, discharge measurements 

indicate that shifts need to be applied in periods for 

which real-time data were provided; the post-measurement computed discharges will be different than the 

real-time values. Periods of shifting were required to 

produce the discharge record, using conventional 

methods, for the Fall Creek and Iroquois River study 

stations; no shifts were required for the Fall Creek 

cell 1 and Iroquois River ADVM-produced discharge 

records during the study period. 

Upland Rivers and Streams

The USGS has used hydroacoustic instruments 

like AVM’s at streamflow stations where the relation 

between stage and discharge is unstable (Laenen, 

1985). ADVM’s can be valuable at new streamflowgaging stations under similar conditions. The 

Kankakee River and Fall Creek stations described in 

this report may be classified as small- to mediumsized upland rivers that do not appear to be subject to 

stage-discharge instabilities. Stage-discharge methods 

have produced accurate discharge records at such 

stations, so this method primarily has been used in the 

USGS. It may be advantageous for the USGS to install 

ADVM’s at such stations. ADVM’s can offer the 

advantages of more reliable real-time discharge and 
POTENTIAL FUTURE STUDIES 49

more accurate estimates of the discharge record during 

ice-affected periods. 

Rating of Acoustic Doppler Velocity Meter 

Discharge Records

In judging the accuracy of the record, various 

factors can be considered. The accuracy of the ADVM 

ratings can be determined with analysis tools such as 

those discussed in this report and by studying the 

departures of discharge measurements from ADVM 

discharges. Particular caution should be exercised for 

discharge records that are outside the range of 

discharge measurements used to define the index 

velocity rating(s). If the hydraulics at a station indicate 

that the rating likely will change at a certain stage 

and(or) discharge thresholds, then it would be prudent 

to reduce (downrate) records that exceed those thresholds. For example, the record from Fall Creek at Millersville might be rated as follows: “record good except 

for discharges above 1,600 ft3

/s, which are poor” 

(because at discharges above 1,600-ft3/s, flows in the 

flood plain will likely cause a departure from the linear 

index velocity rating). It is important to base ADVM 

ratings upon the knowledge of conditions at a station 

in order to make informed decisions concerning rating 

of the record. 

Questionable ADVM data, such as the velocity 

biases seen at the Fall Creek station, are cause to 

downrate the quality of a discharge record. It is important to continue to use all diagnostic tools available to 

assess the quality of the ADVM records. This includes 

study of recorded ADVM parameters and on-station 

checks. It would be prudent to perform a beam-amplitude check every time an ADVM station is visited and 

to note any unusual results. 

POTENTIAL FUTURE STUDIES

It would be beneficial to quantify accuracies of 

ADVM’s in a laboratory setting as well as in the field. 

Informal laboratory testing of the ADVM’s used in 

this study is described in the Appendix. As the ADVM 

models used in this study are upgraded with new 

features, it would be beneficial to test the new features 

in the laboratory and field. Testing of instruments from 

other manufacturers as they become available would 

be beneficial. 

Other beneficial potential future studies could 

include

• Ice-period studies—further studies could identify 

problems and suggest methods for evaluation of 

ADVM records during ice periods. Such studies 

might produce recommended methods (for 

example, the application of coefficients to the 

ADVM velocities). 

• Bidirectional flow studies—studies of ADVM 

stations with different flow regimes, such as very 

slow and(or) bidirectional flow, would be useful, 

particularly documentation concerning rating 

development and discharge-record quality. 

• Nonlinear rating-development studies—studies that 

document nonlinear rating development and 

assessment would be beneficial for those with 

ADVM stations that cannot be accurately 

modeled with linear ratings. 

SUMMARY AND CONCLUSIONS

The purpose of this study was to describe the 

feasibility of using velocity data collected by acoustic 

Doppler velocity meters (ADVM’s) for the computation of discharge records from three USGS streamflow-gaging stations. Two models of ADVM’s (the 

SonTek Argonaut-SL and Nortek EasyQ) from two 

different manufacturers were used.

ADVM’s were installed at three USGS streamflow-gaging stations in Indiana: the Kankakee River at 

Davis, Fall Creek at Millersville, and Iroquois River 

near Foresman. The Kankakee River and Fall Creek 

stations were selected for the installation because the 

quality of the discharge record produced by conventional USGS methods was judged to be “good,” thus 

providing a basis for comparison of the discharge 

record produced with ADVM data (the USGS has the 

following accuracy ratings for discharge records: 

“excellent” means that about 95 percent of the daily 

discharges are within 5 percent of their true values; 

“good,” within 10 percent; and “fair,” within 15 

percent—records that do not meet any of these criteria 

are rated “poor”). The Iroquois River station was 

selected for ADVM installation in an effort to improve 

the record of discharge; historically, variable backwater has affected the quality of the record from this 

station. 
50 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

Stage-area and index velocity ratings were 

created for each of the three study stations. The stagearea ratings were created so that channel area could be 

computed from stage data; the index velocity ratings 

were created so that mean velocities could be 

computed from ADVM velocity data. Stage-area 

ratings were created on the basis of surveyed channel 

cross sections: the Kankakee River cross section was 

rectangular; the Fall Creek cross section included a 

broad flood plain, and the Iroquois River cross section 

was trapezoidal. The Kankakee River stage-area rating 

was represented as a linear equation in ADAPS, 

whereas the Iroquois River and Fall Creek ratings 

were tabular ratings. 

Stage, mean velocity, and ADVM velocity data 

from discharge measurements were used to develop 

index velocity ratings for the three stations, based on 

linear models: the Kankakee River rating used stage 

and ADVM-measured velocities as significant parameters for computation of mean velocities, whereas the 

Fall Creek and Iroquois River ratings used ADVMmeasured velocities only for computation of mean 

velocity. The validity of the ratings was confirmed by 

analysis of coefficients of determination, standard 

errors, and residual plots from the linear regressions 

used to create the ratings and by comparisons of 

discharges computed from the ratings to measured 

discharges. Based on hydraulic features at the stations, 

Kankakee and Iroquois River ratings may remain valid 

outside the range of the discharge measurements used 

to create the ratings; the Fall Creek ratings likely will 

not remain valid above discharges where significant 

flows in the flood-plain area begins. 

Stage and water-velocity data from the ADVM’s 

were used to compute a continuous record of discharge 

from each of the streamflow-gaging stations. These 

records of discharge were compared to the records of 

discharge computed by using conventional USGS 

methods. ADVM records for the Kankakee River and 

Fall Creek at Millersville stations compared closely to 

the conventional records. 

For the Kankakee River, the average of mean 

daily discharges were 426 and 427 ft3/s for the 

conventional and ADVM records, respectively, during 

the study period. Ninety-eight percent of the ADVM 

discharges were within 15 percent of the conventional 

discharges; 86 percent were within 10 percent of the 

conventional discharges; and 51 percent were within 

5 percent of the conventional discharges. 

For Fall Creek at Millersville, the average of 

mean daily discharges was 242 ft3/s for the conventional record and 242 ft3

/s for the records from cells 1 

and 2. The maximum percent difference between 

conventional and ADVM discharges was 19.8 and 

25.6 for cells 1 and 2, respectively. For cell 

1, 97 percent of the ADVM discharges were within 

15 percent of the conventional discharges; 74 percent 

were within 10 percent of the conventional discharges; 

and 42 percent were within 5 percent of the conventional discharges. For cell 2, 94 percent of the ADVM 

discharges were within 15 percent of the conventional 

discharges; 82 percent were within 10 percent of the 

conventional discharges; and 57 percent were within 

5 percent of the conventional discharges.

For the Iroquois River near Foresman, the 

average of mean daily discharges were 242 and 

237 ft3/s for the conventional and ADVM records, 

respectively. Sixty-nine percent of the ADVM 

discharges were within 15 percent of the conventional 

discharges; 56 percent of the ADVM discharges were 

within 10 percent of the conventional discharges; and 

34 percent were within 5 percent of the conventional 

discharges. Because of the presence of variable backwater at the Iroquois River station and the ability of 

the ADVM data to compensate for this backwater, the 

discharge record from the ADVM is probably more 

accurate than the conventional discharge record. 

The scope of this study was limited to three 

streamflow-gaging stations in Indiana, but the study 

did reveal some issues that may have application 

beyond these stations. ADVM’s may be able to 

provide discharge estimations during ice-affected 

periods that are less subjective than estimations with 

conventional methods. The multiple-cell ADVM 

feature provides a valuable tool for data-quality 

assessment. ADVM-generated discharge data are valuable for real-time-data dissemination. ADVM installation on upland rivers could be useful even though 

conventional methods have been predominant for such 

rivers. When judging the quality of discharge records 

produced from ADVM data, factors to consider 

include the range of validity of index velocity ratings 

and the quality of stage and ADVM velocity data. 

In conclusion, this study has shown that it is 

feasible to use ADVM’s installed at streamflowgaging stations to produce records of discharge of 

acceptable quality for publication and distribution. 

This statement, however, does not imply that ADVM’s 

can be used at all stations. Rivers at some stations will 
REFERENCES 51

be too shallow or will have hydraulic and other physical characteristics that make ADVM use impractical. 

Conditions at candidate stations need to be assessed 

individually to see if ADVM use will be feasible. 

REFERENCES

Chow, Ven te, 1959, Open channel hydraulics: New York, 

McGraw-Hill, p. 25.

Ezekial, Mordecai, and Fox, Kenneth, 1959, Methods of 

correlation and regression analysis (3d ed.): New York, 

John Wiley and Sons, p. 188–198.

Gordon, R. Lee, 1999, Technical evaluation of the EasyQ 

river flow monitor, NortekUSA, San Diego, Calif., 

http://nortekusa.com/PDF/EZQ-Report.pdf

(accessed 11/15/01).

Hittle, Clinton, Patino, Eduardo, and Zucker, Mark, 2001, 

Freshwater flow from estuarine creeks into northeastern Florida bay: U.S. Geological Survey WaterResources Investigations Report 01–4164, 32 p.

Hughes, W.F., and Brighton, J.A., 1991, Theory and problems of fluid dynamics: Schaurns Outline Series, 

McGraw-Hill, 344 p. 

Kennedy, E.J., 1983, Computation of continuous records of 

streamflow: U.S. Geological Survey Techniques of 

Water-Resources Investigations, book 3, chap. A17, 

53 p.

Laenen, T.A., 1985, Acoustic velocity meter systems: 

U.S. Geological Survey Techniques of WaterResources Investigations, book 3, chap. A13, 38 p.

Mason, Jr., R.R., and Weiger, B.A., 1995, Stream gaging 

and flood forecasting: U.S. Geological Survey Fact 

Sheet FS–209–95, 3 p.

Morlock, S.E., 1994, Evaluation of acoustic Doppler current 

profiler measurements of river discharge: U.S. Geological Survey Water-Resources Investigations Report 95–

4218, 37 p.

Patino, Eduardo, and Ockerman, Darwin, 1997, Computation of mean velocity in open channels using acoustic 

velocity meters: U.S. Geological Survey Open-File 

Report 97–220, 12 p.

Rantz, S.E., and others, 1982, Measurement and computation of streamflow: U.S. Geological Survey WaterSupply Paper 2175, 2 v., 631 p.

Riggs, H.C., 1968, Some statistical tools in hydrology:

U.S. Geological Survey Techniques of WaterResources Investigations, book 4, chap. A 1, 39 p.

Sauer, V.B., and Meyer, R.W., 1992, Determination of error 

in individual discharge measurements: U.S. Geological 

Survey Open-File Report 92–144, 21 p.

Simpson, Michael, and Bland, Rodger, 1999, Techniques 

for accurate estimation of net discharge in a tidal 

channel: Proceedings of the Institute of Electrical and 

Electronics Engineers Sixth Working Conference on 

Current Measurement, Airlie, Va., p. 125–130.

SonTek Corporation, 2000, SonTek Argonaut-series instruments technical documentation: San Diego, Calif., 

77 p.

Stewart, J.A., Keeton, C.R., Hammil, L.E., Nguyen, H.T., 

and Majors, D.K., 2000, Water resources data, Indiana, 

Water Year 1999: Water-Data Report IN–99–1, 386 p.

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

Memorandum 93.07, Policy Statement on Stage Accuracy, December 4, 1992.

Wahl, K.L., Thomas, W.O., and Hirsch, R.M., 1995, 

Stream-gaging program of the U.S. Geological Survey: 

U.S. Geological Survey Circular 1123, 22 p.

Wang, Dapei, 2000, Discharge calculation of natural 

channel flows with AFM data: Proceedings of the 

American Society of Civil Engineers 2000 Joint Water 

Resources Conference, Minneapolis, Minn., 10 p.
APPENDIX
APPENDIX: LABORATORY EVALUATIONS 55

LABORATORY EVALUATIONS

Informal laboratory testing has been performed 

on both the EasyQ and Argonaut-SL at the USGS 

Office of Surface Water Hydraulics Laboratory, 

Stennis Space Center, Miss. To perform tests on 

ADVM velocity-measurement ability, a tow-tank 

facility was used. The tow tank is a concrete channel 

with a 12-ft by 12-ft cross section and a length of 450 

ft; an electric tow cart moves along tracks atop the tow 

tank (fig. 23) at a selectable speed from 0.05 to 16 ft/s. 

A data-acquisition system is used to monitor elapsed 

time and distance traveled to determine the cart speed. 

The ADVM’s were tested by attaching them to the tow 

cart so that they were suspended in the tow tank. The 

tow cart with the attached ADVM was run across the 

tow tank at known speeds. 

ADVM stage-measurement tests were performed using a large cylindrical holding tank (deep 

tank) measuring 33 ft in diameter and 37 ft deep 

(fig. 23). A catwalk across the tank allowed the 

ADVM’s to be lowered to different depths, and a steel 

tape attached to the mount holding the ADVM and 

marked in 0.01-ft intervals was used to measure instrument depth position. 

A test was performed on the EasyQ, July 26–29, 

1999. The EasyQ stage-measurement capability was 

tested in depths from about 1 to 12 ft. The stage uncertainty associated with the test was estimated to be 

0.02 ft; some of the uncertainty likely was because of 

observed movement of the EasyQ mount. Ideally, the 

top of an EasyQ stage transducer should be perfectly 

level so it is parallel with the water surface. From the 

tests, it appeared that angles of about 3 degrees offlevel could be tolerated. Forty-five tow-tank tests were 

performed for a range of speeds from about 0.1 to 

15 ft/s. The velocity-measurement uncertainty was 

estimated at 0.09 ft/s; much of the uncertainty was 

attributed to internal velocity waves in the tank that 

would affect low-speed runs. Had the low-speed runs 

been discounted in the data analysis, the velocity 

uncertainty would have been less. Gordon (1999) 

details the procedures and results of this test. A second 

test on the EasyQ stage-measurement capability was 

done in the deep tank on October 23 and November 

20, 2000. A data-quality parameter associated with 

EasyQ stage indicated that there was a problem with 

the quality of stage data collected both days, and the 

cause of the problem could not be determined; no 

conclusions could be drawn from the tests. 

A test was performed on the velocity-measurement capabilities of the Argonaut-SL August 21–25, 

2000. The Argonaut-SL was tested at various pitch, 

roll, and yaw angles and for speeds ranging from about 

0.05 to 2.2 ft/s (Craig Huhta, SonTek Corporation, 

written commun., August 25, 2000). Linear regressions of cart speed and ADVM-measured velocities 

were performed for the various tests, and the deviations of the slopes (from 1.0) and offsets (from 0.0) of 

the regression lines were used as estimators of velocity 

uncertainties. In summary, for test runs with the Argonaut in a normal orientation (pitch, roll, and yaw 

angles negligible), the velocity uncertainty was within 

about 1 percent of measured velocities for runs above 

0.10 ft/s. Runs below 0.10 ft/s were not included in the 

analysis because of internal velocity waves, as noted 

for the EasyQ tests. On one set of runs, with a roll 

angle of 10 degrees, and another set of runs, with a 

pitch angle of 15 degrees, the velocity uncertainties 

were about 3 percent of the measured velocities. The 

cause of the greater uncertainties for these runs was 

not discovered; the tests were repeated and did not 

show this bias. Tests of the Argonaut-SL stagemeasurement capabilities were performed in the deep 

tank on October 23 and November 20, 2000. Fifteen 

tests at Argonaut depths of about 5 to 32 ft were 

performed. The stage uncertainty from the tests was 

estimated to be within 0.03 ft. Six more tests were 

carried out at depths of about 2, 5, and 15 ft while 

waves were being generated in the deep tank. The 

stage uncertainty for these tests was estimated to be 

0.01 ft. 

The laboratory tests performed on the ADVM’s 

did not confirm or reject ADVM manufacturer accuracy specifications, but some conclusions could be 

drawn from the tests: (1) the tests indicate that the 

instruments have the potential to meet accuracy 

requirements for many discharge-computation applications; (2) although absolute stage accuracies were 

not established, the first EasyQ test produced estimated stage uncertainties of 0.02 ft, which agreed with 

estimated accuracies from the Fall Creek ADVM field 
56 Feasibility of Acoustic Doppler Velocity Meters for the Production of Discharge Records from U.S. Geological Survey 

Streamflow-Gaging Stations

Tow cart

Tow tank

Deep tank

Catwalk

evaluation (the laboratory tests indicated that Argonaut-SL stage uncertainties are similar); and (3) the 

laboratory tests were valuable in that they performed 

the function of providing base-line data and suggested 

new approaches for further testing. 

Further testing would be beneficial for two 

reasons. First, the velocity tests and subsequent analysis were not consistent. The EasyQ was tested over a 

range of velocities from about 0.1 to 15 ft/s, whereas 

the Argonaut-SL range was about 0.05 to 3 ft/s. The 

Argonaut was tested at various yaw, pitch, and roll 

angles, and the EasyQ was tested at a single orientation (yaw, pitch, and roll angles were zero). Because 

the tests were informal and took place at different 

times, consistency was not a goal. Second, in the test 

process, some problems were noted that could 

adversely affect the test results, such as the presence of 

tow-tank internal currents noted by Gordon (1999). 

Another problem with tow-tank testing is that at high 

speeds, the velocity-sampling interval is very short, 

which can increase measured velocity errors.

The laboratory ADVM-velocity tests suggest 

that future velocity testing might be conducted in a 

large flume in addition to tow-tank testing. The 

problem with internal tow-tank currents biasing lowvelocity tests would be eliminated, and a consistent 

averaging interval could be used for all velocity tests 

(velocity averaging is dependent on tow-cart speed in 

tow-tank testing). A problem with flume testing is in 

determining the reference velocity for comparison. For 

further stage tests, to reduce uncertainties related to 

the movements of catwalk-suspended mounts, it may 

be advisable to suspend the instruments from a frame 

that is independent of the catwalk structure. Figure 23. Photographs of tow tank and tow cart (top) and 

deep tank (bottom) at the U.S. Geological Survey Hydraulics 

Laboratory, Stennis Space Center, Mississippi.