Application of Acoustic Velocity Meters For

Gaging Discharge of Three Low-Velocity

Tidal Streams in the St. Johns River Basin,

Northeast Florida

By John V. Sloat and W. Scott Gain

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 95–4230

Prepared in cooperation with the

St. Johns River Water Management District

Tallahassee, Florida

1995
U.S. DEPARTMENT OF THE INTERIOR

BRUCE BABBITT, Secretary

U.S. GEOLOGICAL SURVEY

Gordon P. Eaton, Director

For additional information Copies of this report may be

write to: purchased from:

U.S. Geological Survey

District Chief Earth Science Information Center

U.S. Geological Survey, WRD Open-File Reports Section

Suite 3015 Box 25286, MS 517

227 North Bronough Street Denver Federal Center

Tallahassee, Florida 32301 Denver, Colorado 80225
Contents III

CONTENTS

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

Introduction ........................................................................................................................................................................... 2

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

Application of Acoustic Velocity Meters for Gaging Discharge of Low-Velocity Tidal Streams ........................................ 2

Principles of Acoustic Measurement of Fluid Velocity............................................................................................... 2

Equipment Installation................................................................................................................................................. 5

Acoustic Path Configurations and Computational Approaches .................................................................................. 5

Development of Curves of Relation ............................................................................................................................ 8

Description of Sites and Suitability of Sites for AVM Measurement.................................................................................... 8

Six Mile Creek............................................................................................................................................................. 9

Dunns Creek ................................................................................................................................................................ 9

St. Johns River at Buffalo Bluff .................................................................................................................................. 10

Instrumentation, Measurement, and Computation of Discharge at Three AVM Streamflow Sites....................................... 11

Equipment Installation................................................................................................................................................. 12

Discharge Measurements............................................................................................................................................. 12

Stage-Area Relation..................................................................................................................................................... 14

Mean-Velocity Rating.................................................................................................................................................. 14

Estimation of Error ...................................................................................................................................................... 18

Summary................................................................................................................................................................................ 24

Selected References............................................................................................................................................................... 26

FIGURES

1. Map showing acoustic velocity meter stream-gaging sites................................................................................... 3

2. Schematic diagram of velocity components and acoustic-path angle for a single-path acoustic velocity

meter site ............................................................................................................................................................... 4

3. Schematic diagram of device configuration for acoustic velocity meter stream-gaging site................................ 6

4. Sketch of path configurations and velocity rating methods for acoustic velocity meter gaging sites................... 7

5. Sketch of acoustic velocity meter configuration on Six Mile Creek..................................................................... 10

6. Oblique cross section of Six Mile Creek channel at the gaging station................................................................ 11

7. Sketch of new acoustic velocity meter redundant-path configuration on Six Mile Creek.................................... 12

8. Sketch of the acoustic velocity meter stream-gaging site on Dunns Creek .......................................................... 13

9. Oblique cross sections of Dunns Creek channel at the gaging site....................................................................... 14

10. Sketch of the acoustic velocity meter multi-sectional configuration on the St. Johns River at Buffalo Bluff...... 15

11. Oblique cross sections of St. Johns River at Buffalo Bluff channel at the gaging site ......................................... 16

12. Sketch of acoustic velocity meter multi-redundant configuration on the St. Johns River at Buffalo Bluff.......... 17

13–17. Graphs showing:

13. Relation between stage and cross-sectional area for acoustic velocity meter stream-gaging sites ............. 18

14. Relation of mean velocity in stream to acoustic velocity meter-measured index velocity for AVM

stream-gaging sites ...................................................................................................................................... 19

15. Residuals from regression of mean velocity to stage with and without stage as an independent

variable for Dunns Creek Path 2.................................................................................................................. 23

16. Relation of discharge error as a function of cross-sectional area for acoustic velocity meter streamgaging sites .................................................................................................................................................. 25

17. Instantaneous stage and discharge for a 7-day period at Dunns Creek ....................................................... 26
IV Application of Acoustic Velocity Meters for Gaging Discharge of Three Low-Velocity Tidal Streams in the St. Johns River Basin

TABLES

1. Site-identification numbers for acoustic velocity meter (AVM) stream-gaging sites............................................ 9

2. Regression equations for the estimation of mean velocity at acoustic velocity meter (AVM) stream-gaging

sites ......................................................................................................................................................................... 22

CONVERSION FACTORS, VERTICAL DATUM, ABBREVIATIONS, AND ACRONYMS

Multiply By To obtain

Length

inch (in.) 25.4 millimeter

foot (ft) 0.3048 meter

mile (mi) 1.609 kilometer

Area

square foot (ft2

) 0.0929 square meter

Flow

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

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

Sea level: In this report “sea level” refers to the National Geodetic Vertical Datum of 1929—a geodetic datum derived from a general

adjustment of the first-order level nets of the United States and Canada, formerly called Sea Level Datum of 1929.

Equations for temperature conversion between degrees Celsius ( ̊C) and degrees Fahrenheit ( ̊F):

  ̊C = 5/9 ( ̊F - 32)

  ̊F = 9/5 ( ̊C) + 32

Acronyms and abbreviations used in report

ACM Acoustic current meter

AVM Acoustic velocity meter

HIF Hydrologic Instrumentation Facility

min minute

SDI-12 Serial Device Interface 12

SJRWMD St. Johns River Water Management District

SEE Standard error of the estimate

USGS U.S. Geological Survey
Abstract 1

APPLICATION OF ACOUSTIC VELOCITY METERS

FOR GAGING DISCHARGE OF THREE LOW-VELOCITY

TIDAL STREAMS IN THE ST. JOHNS RIVER BASIN,

NORTHEAST FLORIDA

By John V. Sloat and W. Scott Gain

Abstract

Index-velocity data collected with acoustic

velocity meters, stage data, and cross-sectional

area data were used to calculate discharge at three

low-velocity, tidal streamflow stations in northeast Florida. Discharge at three streamflow stations was computed as the product of the channel

cross-sectional area and the mean velocity as

determined from an index velocity measured in

the stream using an acoustic velocity meter. The

tidal streamflow stations used in the study were:

Six Mile Creek near Picolata, Fla.; Dunns Creek

near Satsuma, Fla.; and the St. Johns River at Buffalo Bluff. Cross-sectional areas at the measurement sections ranged from about 3,000 square

feet at Six Mile Creek to about 18,500 square feet

at St. Johns River at Buffalo Bluff. Physical characteristics for all three streams were similar

except for drainage area. The topography primarily is low-relief, swampy terrain; stream velocities ranged from about -2 to 2 feet per second; and

the average change in stage was about 1 foot.

Instantaneous discharge was measured using

a portable acoustic current meter at each of the

three streams to develop a relation between the

mean velocity in the stream and the index velocity

measured by the acoustic velocity meter. Using

least-squares linear regression, a simple linear relation between mean velocity and index velocity was

determined. Index velocity was the only significant

linear predictor of mean velocity for Six Mile

Creek and St. Johns River at Buffalo Bluff. For

Dunns Creek, both index velocity and stage were

used to develop a multiple-linear predictor of mean

velocity. Stage-area curves for each stream were

developed from bathymetric data.

Instantaneous discharge was computed by

multiplying results of relations developed for

cross-sectional area and mean velocity. Principal

sources of error in the estimated discharge are

identified as: (1) instrument errors associated with

measurement of stage and index velocity, (2)

errors in the representation of mean daily stage

and index velocity due to natural variability over

time and space, and (3) errors in cross-sectional

area and mean-velocity ratings based on stage and

index velocity. Standard errors for instantaneous

discharge for the median cross-sectional area for

Six Mile Creek, Dunns Creek, and St. Johns River

at Buffalo Bluff were 94, 360, and 1,980 cubic

feet per second, respectively. Standard errors for

mean daily discharge for the median cross-sectional area for Six Mile Creek, Dunns Creek, and

St. Johns River at Buffalo Bluff were 25, 65, and

455 cubic feet per second, respectively. Mean

daily discharge at the three sites ranged from

about -500 to 1,500 cubic feet per second at Six

Mile Creek and Dunns Creek and from about -500

to 15,000 cubic feet per second on the St. Johns

River at Buffalo Bluff. For periods of high discharge, the AVM index-velocity method tended to

produce estimates accurate within 2 to 6 percent.

For periods of moderate discharge, errors in

discharge may increase to more than 50 percent.
2 Application of Acoustic Velocity Meters for Gaging Discharge of Three Low-Velocity Titdal Streams in the St. Johns River Basin

At low flows, errors as a percentage of discharge

increase toward infinity.

INTRODUCTION

Low-velocity tidal streams are common in the

low-relief coastal areas of northeast Florida (fig. 1).

Gaging of these streams is complicated by unsteady,

variable flow conditions. Low-velocity tidal streams

commonly have small hydraulic gradients and are susceptible to reverse flow and backwater.

The common stream-gaging practice on upland

streams is the development of a discharge rating which

relates discharge to gage height. This approach is

based on several assumptions: (1) a reasonably stable

channel and control, (2) little or no variable backwater

conditions, (3) consistent gradient (no reverse flow),

and (4) gravity as the principal driving force (rate of

change of momentum is not great). These assumptions

are not always met in the study area because of tide

and backwater conditions that exist in many streams.

Under these conditions, the commonly used stage-discharge relation can be very inaccurate.

An alternate approach to compute discharge is

to measure a velocity index, relate the index to mean

velocity, and multiply that mean velocity by cross-sectional area. An index velocity can be measured either

at a point or along a line. Velocity measured along a

line is likely to relate better to average stream velocity

and is, therefore, a better index of mean velocity than

is point velocity. The line velocity can be measured

with a relatively high degree of accuracy, regardless of

flow direction, by using an acoustic velocity meter

(AVM; Laenen and Curtis, 1989). Cross-sectional area

is easily determined from field measurements.

To improve the accuracy of discharge record for

three gaging sites in the St. Johns River Basin in

northeast Florida, the U.S. Geological Survey

(USGS), in cooperation with the St. Johns River Water

Management District (SJRWMD), instrumented three

sites with AVMs during the summer and fall of 1989.

Evaluation of historical records indicated that the use

of standard mechanical current meters (Price AA) and

simple (stage-only) discharge ratings (as described in

Rantz and others, 1982) were not applicable at these

three sites because of complex streamflow conditions.

The decision to instrument these sites with AVMs followed the examination of field and tow-tank data collected at the USGS Hydrologic Instrumentation

Facility (HIF; Laenen and Curtis, 1989) which indicated that AVMs could be used to develop accurate

and dependable discharge records at low-velocity,

tidally affected gaging sites. These sites are part of the

basic data-collection network of the USGS.

Purpose and Scope

This report describes the instrumentation and

methods applied in the use of AVMs to obtain records

of discharge at the three selected sites. Instrumentation

used to measure and store stream data are discussed.

Procedures used to determine a calculated discharge

are described. These include bathymetric surveys of

channel cross sections, continuous measurement of an

index velocity using an AVM, discharge measurements using a portable acoustic current meter (ACM),

development of stage-area curves, statistical estimation of the relation between mean velocity and AVMmeasured index velocity, computation of instantaneous discharge, and estimation of error associated

with instantaneous and daily mean discharge.

APPLICATION OF ACOUSTIC VELOCITY

METERS FOR GAGING DISCHARGE OF

LOW-VELOCITY TIDAL STREAMS

The application of AVMs for gaging discharge

in low-velocity tidal streams includes several topics

directly related to the use of an AVM. These are: (1)

principles of the acoustic measurement of a fluid, (2)

AVM equipment installation, (3) acoustic path configurations and mean-velocity ratings, and (4) computation of discharge. Each of these topics are discussed in

the following sections.

Principles of Acoustic Measurement of Fluid

Velocity

The principles of acoustic measurement of fluid

velocity were mathematically expressed by Smith and

others (1971), and discussed in detail by Laenen and

Smith (1983). Principally, an AVM measures an average stream velocity along an acoustic path diagonal to

the direction of streamflow. Velocity of the water

between two fixed acoustic transducers is determined

from the difference in the velocity of sound between

two signals propagated downstream and then
Application of Acoustic Velocity Meters for Gaging Discharge of Low-Velocity Tidal Streams 3

10

95

95

95

95

0 5 10 15 MILES

0 5 10 15 KILOMETERS

13

207

13

13

16

17

17

17

17

Hastings

Welaka

Riverdale

Picolata St. Augustine

GAGING STATION

AND SITE NUMBER

EXPLANATION

Green Cove Springs

Six Mile Ck.

Mandarin

Ponte Vedra

Beach

Orange Park

Jacksonville

Mayport

DUVAL COUNTY

DUVAL COUNTY

St. Johns River

St. Jo hns River

CLAY COUNTY

ST. JOHNS COUNTY

Palatka

Buffalo

Bluff

ST. JOHNS COUNTY

CLAY COUNTY

FLAGLER COUNTY

Crescent Lake

Dunns Ck.

Oklawaha River

PUTNAM COUNTY

MARION COUNTY

PUTNAM COUNTY

3

2

1

1

Location of

study area

30°00′

29°45′

29°30′

30°15′

81°45′ 30′ 15′ 81°00′

Figure 1. Acoustic velocity meter (AVM) stream-gaging sites.
4 Application of Acoustic Velocity Meters for Gaging Discharge of Three Low-Velocity Titdal Streams in the St. Johns River Basin

upstream. Velocity vectors and the acoustic path angle

typical of a site are shown in figure 2.

The stream-velocity component parallel to the

acoustic path when the signal is traveling from point A

to point B (fig. 2) is:

(1)

where Vpd is the downstream integrated water

velocity vector along the acoustic path

from point A to point B,

c is the propagation rate of sound in still

water,

D is the distance from point A to point B,

and

Vpd

D

t

AB

= ------- – c,

tAB is the traveltime of acoustic signal from

point A to point B.

Similarly, the stream velocity parallel to the

acoustic path when the signal is traveling upstream

from point B to point A is:

(2)

where Vpu is the upstream integrated water-velocity vector along the acoustic path from

point B to point A (upstream), and

tBA is the traveltime of acoustic signal from

point B to point A.

Equations 1 and 2 are based on the velocity of

sound in still water (c), which varies with the conductance and temperature of water. However, path

Vpu

c

D

t

BA

= – -------,

Path Angle

Right Bank

Left Bank

Stream velocity component

along acoustic path (Vp )

Line Velocity (VL )

Acoustic path

Transducer A Transducer B

Θ

Figure 2. Velocity components and acoustic-path angle for a single-path acoustic velocity meter

(AVM) site.
Application of Acoustic Velocity Meters for Gaging Discharge of Low-Velocity Tidal Streams 5

velocity is computed as the average of upstream and

downstream velocities, and c cancels when equations 1

and 2 are summed:

(3)

where Vp is the average path velocity along the

acoustic path.

Equation 3 defines the velocity parallel to the

acoustic path. To determine the vector component of

velocity in the direction of flow (index velocity), the

cosine of the angle between the acoustic path and the

direction of flow must be considered as:

(4)

where VL is the average stream velocity component across the acoustic path (index

velocity) in the direction of streamflow;

and

Θ is the acute angle between the acoustic

path and the direction of streamflow.

Equipment Installation

Typically, an AVM site is instrumented with

water velocity and stage-measuring devices and a data

recorder. An index velocity is measured using the

AVM, acoustic transducers, and cabling. Stage is measured using one of several standard USGS stage measurement sensors, such as a float and counterweight,

tape, and shaft-encoder. Output from the measuring

devices is recorded by either an electronic datalogger

or telemetered (by satellite or phone modem) to an offsite database. Power is supplied to all equipment by a

12-volt battery (fig. 3).

The AVM contains a software program to: (1)

activate acoustic transducers, (2) compute average

velocities from one or more acoustic paths, (3) report

speed of sound and signal gain for signal quality, and

(4) report possible errors within the system. Instrument

settings must be made for several parameters within

the program. Depending on the AVM model used,

these parameters usually include internal timing

delays, speed of sound in water, acoustic-path lengths,

and path angles. Discussion of each parameter in an

AVM software program is beyond the scope of this

report; however, documentation is usually provided by

the manufacturer.

Vp

D

2

--- 1

t

AB

------- 1

t

BA

– -------     = ,

VL Vp = () Θ ⁄ ( ( ) cos ,

The acoustic transducer serves two functions

which are: (1) convert an electrical pulse to a sonic

pulse (transmit), and (2) convert a sonic pulse to an

electrical pulse (receive). The acoustic transducer is

excited by an electrical pulse (sending pulse) transmitted by the AVM. The transducer converts the electrical

pulse into a sonic pulse which is propagated across the

stream. The sonic pulse is then received by another

acoustic transducer that converts the sonic pulse back

into an electrical pulse, which is then transmitted to

the AVM (receiving pulse). The elapsed time between

the sending and the receiving pulses is measured by

the AVM. This process is applied in succession for

both upstream and downstream directions of signal

propagation, and the index velocity is computed using

the method previously described in this report.

Typically, the AVM is installed using prefabricated transducer mounts, cables, and acoustic transducers. The AVM is mounted in the gage house and

electrically grounded. Prefabricated transducer mounts

are attached to pre-driven pilings in the stream and

cables are run from the AVM to transducers on each

piling. The two acoustic transducers, after being

wired, are lowered to predetermined depths, and

aligned with one-another across the stream (corresponding to the acoustic path).

Transducers are manually aligned in the field for

maximum signal strength. First, the transducer face is

vertically leveled (this is done above the water surface). Second, each transducer is lowered to a similar

depth, and third, the transducers are rotated left or

right until the signal strength is maximized. To avoid

misalignment, transducers should be aligned when

velocities are sufficient to overcome density gradients

that may cause signal bending in the stream during

periods of low-flow.

Lengths of cable located above the water surface should be protected by grounded-metal conduit

(as recommended by the USGS HIF). Cable lengths

below the water surface are weighted down by tying

short lengths of heavy chain to the cable at 15- to 20-ft

intervals. Care must be taken to avoid sharp bends in

the cable which can eventually weaken it and possibly

cause signal failure.

Acoustic Path Configurations and

Computational Approaches

The arrangement of acoustic paths at an AVM

gaging installation affects effort required to maintain
6 Application of Acoustic Velocity Meters for Gaging Discharge of Three Low-Velocity Titdal Streams in the St. Johns River Basin

AVM

Stage measurement

Power Datalogger

supply

Acoustic

transducers

Cables

Direction of

flow

Water-level

sensor

the installation, and the way in which ratings are constructed and applied. Acoustic path configurations fall

into four general types: (1) single paths, (2) multiple

paths with simple redundancy, (3) multiple paths with

cross orientation, and (4) multiple paths with incremental subsections. A general schematic of each of

these configurations is shown in figure 4. The single

path configuration is the simplest arrangement and

requires the least effort to maintain and to rate. However, single paths may be insufficient in length to span

the entire width of a stream, may poorly represent

mean velocities where the angles of flow in relation to

the acoustic path vary over time and space, and may

lack the corroboration of alternative velocity data from

other paths.

Multiple-path configurations with simple redundancy add reliability to the system but require more

work in the field and only marginally improve the representativeness of measured index velocities. Where

multiple paths are oriented at cross angles to one

another, index velocities can be averaged for the multiple paths to account for variations in flow angle. This

increases the representativeness of measured index

velocities, but requires that all paths operate correctly

at all times, adding a considerable level of difficulty to

station operations and computations.

The use of multiple paths in incremental subsections is an extension of single and cross path configurations and generally is limited to wide cross sections.

As with the cross-path configuration, the sectional

configuration requires that all paths be in operation to

compute discharge.

The rating procedure for an AVM streamflow

station depends on the path configuration and the

Figure 3. Device configuration for acoustic velocity meter (AVM) stream-gaging site.
Application of Acoustic Velocity Meters for Gaging Discharge of Low-Velocity Tidal Streams 7

Single acoustic path

Cross acoustic path Sectional acoustic path

Redundant acoustic path

Flow

Flow

Flow

Flow

Vm1 Vm2 Vm3

Vm

VI

Vm Vm

VI VI1

VI2

VI1 VI2 VI3

Single Redundant Cross Sectional

PATH CONFIGURATION

RATING METHOD

Vm1 related to VI1 + Vm2

V m related to VI1 + VI2 +...+ VIn.

Vm related to VI1,VI2, ...VIn.

Vm related to VI.

related to VI2 + ... + Vmn

related to VIn.

n

Figure 4. Path configurations and velocity rating methods for acoustic velocity meter (AVM) gaging sites.
8 Application of Acoustic Velocity Meters for Gaging Discharge of Three Low-Velocity Titdal Streams in the St. Johns River Basin

quality of the data from each path. The single path system requires a single rating of mean velocity against

index velocity. Discharge measurements to determine

mean channel velocity can be made along the acoustic

path or any other path traversing the entire stream and

corrected for the angularity of flow. It is not necessary

that the single acoustic path traverse the entire width

of the stream or be coincident with the measurement

cross section to provide a representative index of mean

channel velocities as long as variations in velocity in

the horizontal and vertical axis are consistent.

A multiple-path system with redundancy

requires that two or more ratings be developed, one for

each path relating mean velocities to index velocity.

To compute discharge, it is necessary to select one or

another path or to average the paths depending on the

quality of the records for each acoustic path. This process adds a level of complexity to the computational

process. Computation with a cross-path system further

requires that a rating be developed to relate mean

channel velocity to the mean of two or more index

velocities. And a sectional configuration requires that

ratings be developed for the flow components in each

subsection of the stream channel.

The choice of a rating method reflects not only

the acoustic path configuration but also the quality of

the ratings and the reliability of the velocity data.

Cross and sectional multiple-path configurations can

be rated for average and sectional velocities or

reduced to simple single or multiple-path redundant

ratings. For multiple path configurations, the rating

method applied should minimize the uncertainty in

computed velocities. Because of complexities in collecting continuous index velocity data on multiple

paths, single-path ratings have often proven to be the

most practical approach.

Development of Curves of Relation

Discharge of a stream is computed as the product of the mean velocity and the channel cross-sectional area:

Q = A VM, (5)

where Q is discharge, in cubic feet per second,

A is cross-sectional area, in square feet,

and

VM is mean velocity, in feet per second.

Under the complex streamflow conditions that

exist when tidal or backwater conditions are present, it

is necessary to develop simple relations for area and

mean velocity in terms of measurable variables. In

equation 5 the cross-sectional area of the stream can

be expressed as a function of stage, and the mean

velocity can be expressed in terms of specific stream

variables including stage, index velocity, and rate of

change of stage and index velocity. Statistical methods

can be used to determine which stream variables are

significant for estimating mean velocity.

Rating tables can be developed for relations

between stage and cross-sectional area. Least-squares

multiple linear regression, a useful technique for estimating the relation between a response variable and

multiple independent variables, can be used for deriving relations between mean velocity and measured

stream variables (stage and AVM-measured index

velocity and rate of change of stage and velocity).

Additionally, the residuals (unexplained error) from

the resulting regression equation can be evaluated to

determine if a significant relation exists between the

response (mean velocity) and independent variable(s)

and if the response variable is adequately estimated.

Least-squares multiple linear regression and the analysis of residuals are described by Draper and Smith

(1982).

DESCRIPTION OF SITES AND

SUITABILITY OF SITES FOR

AVM MEASUREMENT

Reconnaissance was done on three low-velocity

tidal streams to determine overall suitability for measurement using AVM equipment and to determine specific locations where measuring could best be

accomplished. Acoustic phenomena of reflection,

refraction, and attenuation (related to measurement

with AVM equipment, described by Laenen, 1985)

were taken into consideration in the selection process,

as well as the logistical constraints of access, construction, ownership, and safety. Site-identification numbers are listed in table 1 and locations are shown in

figure 1.

Physical characteristics for all three streams are

similar except for drainage area: the topography primarily is low-relief, swampy terrain; stream velocities

range from about -2 to 2 ft/s, and the average daily

change in stage is about 1 ft.
Description of Sites and Suitability of Sites for AVM Measurement 9

Table 1. Site-identification numbers for acoustic velocity meter (AVM) stream-gaging sites

Map Latitude Longitude

number Station name Station number (degrees, minutes, seconds)

1 Six Mile Creek near Picolata, Fla. 02245328 29 ̊57’04” 81 ̊32’37”

2 Dunns Creek near Satsuma, Fla. 02244440 29 ̊34’39” 81 ̊37’35”

3 St. Johns River at Buffalo Bluff near Satsuma, Fla. 02244040 29 ̊35’46” 81 ̊41’00”

The location, length, and depth below the water

surface of the acoustic path(s) were assigned for each

site to minimize spurious fluctuations in the acoustic

signal. Paths were located in channel cross sections

free of turbulent effects from flow obstructions that

could cause unpredictable fluctuations in horizontal

and vertical velocity profiles. Path depths and lengths

were assigned based on minimum clearance distances

(to water surface and streambed), and maximum

stream-density gradients (temperature and conductivity in vertical and horizontal profiles). Clearance distances were assigned so that acoustic signals reflected

from the water surface or streambed would not interfere with the direct path signal. Density gradients were

measured and path lengths determined to minimize

signal fluctuations caused by refraction (bending of

the acoustic signal). Locations, acoustic path configurations, and channel cross sections for the three AVM

sites are described in the following sections.

For each site, the AVMs were activated at 15-

min intervals. Once activated, the AVM measures

index velocity every 2 seconds for a duration of 40

seconds. The average velocity during the 40-second

period, corresponding system diagnostics, and stage

are then recorded by an electronic datalogger.

Six Mile Creek

Six Mile Creek is a tributary of the St. Johns

River in St. Johns County, Fla. The AVM stream-gaging site is 1.0 mi upstream from the mouth, just below

the County Road 13 bridge (fig. 1).

The site has a single acoustic path (fig. 5). A

cross section of the channel along the acoustic path

(fig. 6) shows the depth of the acoustic transducers relative to the lowest water-surface elevation measured

during the study.

The AVM produced reliable velocity data when

the flow was well mixed. Further, discharge measurements made at the site indicated that a single path was

adequate for the estimation of the mean stream velocity. However, occasionally steep thermal gradients

(greater than 1°C/meter depth) would occur in the top

5 to 6 ft of the stream during mid-morning to early

afternoon, caused by the combination of low velocities

in the stream and warm ambient air temperature. The

thermal gradients caused the acoustic signals propagated across the stream by the AVM to become erratic,

which resulted in erratic velocity measurements and

occasional signal loss for periods up to about 6 hours.

In an effort to minimize these effects on the acoustic

signal, a second (redundant) acoustic path with a

shorter path length (60 ft) was installed under a bridge

at a depth about 2 ft below the original acoustic path

(fig. 7). Velocity data collected from the shorter path

indicated that the acoustic path was not affected by the

thermal gradients.

Dunns Creek

Dunns Creek is a tributary of the St. Johns River

in Putnam County, Fla. The AVM stream-gaging site

is 0.8 mi upstream from the mouth, just below the U.S.

Highway 17 bridge (fig. 1).

The two acoustic paths at the site are at similar

depth (fig. 8). A cross section along each acoustic

path (fig. 9) shows the depth of the acoustic path relative to the lowest water-surface elevation measured

during the study.

The AVMs performed well because flow at the

site was always well mixed, reducing the possibility of

signal loss from density gradients in the stream. Data

losses at the site primarily were caused by equipment

failure—broken cables, loss of power, lightning

strikes, vandalism, and weak acoustic transducers.

Equipment failures were most common on acoustic

path 1, thus rating measurements collected from

acoustic path 2 were more numerous. By using path 2

data instead of the combined data for paths 1 and 2, a

more accurate mean-velocity rating was obtained for

the site.
10 Application of Acoustic Velocity Meters for Gaging Discharge of Three Low-Velocity Titdal Streams in the St. Johns River Basin

St. Johns River at Buffalo Bluff

The AVM stream-gaging site on the St. Johns

River at Buffalo Bluff is located 89 mi upstream from

its mouth at the Atlantic Ocean, just above a railroad

bridge crossing the river in Putnam County, Fla.

(fig. 1).

Originally, the site had three acoustic paths that

together crossed 80 percent of the river width (fig. 10).

Cross sections of the channel along each acoustic path

(fig. 11) show the depth of each acoustic path relative

to the lowest water-surface elevation measured during

the study.

When the AVMs were operating properly they

produced reliable velocity data. However, several

problems with the installation resulted in frequent

periods of missing record that made the computation

of discharge difficult and time consuming. The primary cause of missing record was equipment failure.

Equipment failures, similar in nature to those

described for Dunns Creek, occurred more frequently

at Buffalo Bluff. Two predominant causes of the high

rate of equipment failure were the location of the two

gage houses for the AVM equipment (mounted on the

piers of a railroad bridge) and the location of the

upstream transducer piling (used to mount acoustic

Direction of

flow

Acoustic path

(275 ft.)

Left

bank

Right

bank

Six Mile Creek Site

Not to scale

N

Transducer

Transducer

Gage

Shelter

A

A’

Θ

County Road 13

Figure 5. Acoustic velocity meter (AVM) configuration on Six Mile Creek.
Instrumentation, Measurement, and Computation of Discharge at the Three AVM Streamflow Sites 11

transducers) for paths 1 and 2 (fig. 10). Rail cars crossing the bridge several times a day caused considerable

vibration in the equipment which tended to loosen

AVM electrical connections and to bend metal electrical conduit that was installed to protect the AVM

transducer cables (causing cable breaks). The

upstream transducers for acoustic paths 1 and 2 were

mounted in the river on a piling close to the shipping

channel. On several occasions, large barges passing

the site collided with the transducer piling and caused

transducer misalignment. The collisions also damaged

the transducer mounts and caused cable breaks.

The sectional configuration of the initial installation of the AVMs at the site was based on the best

information available at the time and on the general

philosophy that acoustical paths should span as much

of the river as possible. This philosophy assumes that

the AVM can be used directly to measure discharge if

sufficient horizontal coverage and well-defined vertical-velocity profiles exist at the site (Smith, 1969).

When all the acoustic paths were functioning properly,

total discharge was computed by simple algebraic

summation of partial discharge computed through

each of the three acoustic path subsections. However,

when one or two of the acoustic paths were not functioning or were producing unreliable data, alternative

velocity ratings, based on a relation between acoustic

paths, were used to estimate flow for the missing subsection. Routine computation of discharge by algebraic summation frequently was not possible because

of the number of paths and the high frequency of AVM

failure on any of the paths.

In an effort to improve the reliability of data and

simplify the computation of discharge, the acoustic

path configuration at Buffalo Bluff was changed.

Acoustic paths 1 and 2 were removed and a shorter

acoustic path was installed under the railroad bridge

(fig. 12). The acoustic path is approximately 60 ft in

length at an elevation similar to acoustic path 3. A

redundant mean-velocity rating method has been

adopted; each acoustic path is rated to mean velocity

in the entire cross section; discharge is rated to each

individual path; and the multi-paths serve as redundant

data. Since the change in the acoustic path configuration, data losses have been reduced significantly and

accuracies of new index-velocity ratings are consistent

to previous velocity ratings.

INSTRUMENTATION, MEASUREMENT,

AND COMPUTATION OF DISCHARGE AT

THE THREE AVM STREAMFLOW SITES

Several successive steps were necessary to compute discharge record at the AVM streamflow sites.

The first step was the installation of the AVM equipment, a stage-measurement device, and a datacollection device. The second step was to obtain

0 100 200 300 400 500

Transducer Transducer

Streambed

DISTANCE ALONG ACOUSTIC PATH, IN FEET

Acoustic path

20

10

0

-10

-20

-30

ELEVATION, IN FEET ABOVE GAGE DATUM

A A’

30

Figure 6. Oblique cross section of Six Mile Creek channel at the gaging station.
12 Application of Acoustic Velocity Meters for Gaging Discharge of Three Low-Velocity Titdal Streams in the St. Johns River Basin

measurements of discharge and cross-sectional area.

The third step was to develop relations between stage

and area and between mean velocity and AVM index

velocity. These steps are described in the following

sections.

Equipment Installation

The AVM sites were instrumented with velocity

and stage measuring devices and a datalogger for

recording. Water velocity is measured using an Accusonic model 7300 AVM, acoustic transducers, and

cabling; stage is measured using a float and counterweight, tape, and a shaft encoder. A datalogger (using

Serial-Digital-Interface-12 (SDI-12) protocol) is used

to record output from the measuring devices and a 12-

volt battery is used to supply power to all equipment.

Discharge Measurements

Discharge was measured at each AVM site to

determine mean velocity using a portable Neil-Brown

acoustic current meter (ACM). The portable ACM is a

vector-averaging (current magnitude and direction)

Direction of

flow

Original acoustic path

(275 ft.)

Left

bank Right

bank

Six Mile Creek Site

Not to scale

N

Transducer

Transducer

County Road 13

Gage

Shelter

A

A’

New acoustic path (60 ft.)

Figure 7. New acoustic velocity meter (AVM) redundant-path configuration on Six Mile Creek.
Instrumentation, Measurement, and Computation of Discharge at the Three AVM Streamflow Sites 13

current meter that can measure point velocities as low

as 0.03 ft/s. It also contains an internal magnetometer

compass that provides a magnetic-heading reference

for the measured current data.

The ACM was used to measure discharge

because of the limitations of the more common

mechanical, low-velocity Price current meter (type

AA). The recommended minimum velocity of the

Price meter is 0.2 ft/s (Rantz and others, 1982, v. 1, p.

86). Also, the use of conventional mechanical current

meters such as the Price meter require that the operator

visually observe the direction of streamflow. However,

when the measurement depth increases and visibility

decreases, the meter is no longer visible and the operator cannot observe the meter and the direction of

streamflow. In tidal streams, where flow is bi-directional and velocities are low, accurate flow measurements with conventional mechanical meters are often

unobtainable.

Because of rapidly changing stage and velocity,

the duration of each discharge measurement had to be

decreased. This was done by reducing the number of

measurement sections from a USGS standard minimum of 25 to a minimum of 18 and by reducing the

averaging interval for each point velocity from a

USGS standard measurement of 40 seconds to 20 seconds. This procedure follows recommendations presented by Rantz and others, 1982, v. 1, p. 174.

During each discharge measurement, ancillary data

such as AVM-measured index velocity, system diagnostics, and stage were recorded at 5-min intervals

using an electronic datalogger. The AVM-measured velocity and stage were then averaged for

the duration of the discharge measurement.

Direction of

flow

VP1 VP2

VL1 VL2

Transducer

Transducer

Transducer Transducer

N

Not to scale

Acoustic path 1

(415 ft.)

Acoustic path 2

(402 ft.)

Right

bank

Left

bank

Dunns Creek Site

Θ Θ2 1

U.S. Highway 17

Gage

shelter

B

B’

C

C’

Figure 8. Acoustic velocity meter (AVM) stream-gaging site on Dunns Creek.
14 Application of Acoustic Velocity Meters for Gaging Discharge of Three Low-Velocity Titdal Streams in the St. Johns River Basin

Additionally, system diagnostics were checked to ensure

the integrity of the AVM-measured index-velocity data.

Stage-Area Relation

A stage-area relation was developed for each

study site (fig. 13). The cross-sectional area was computed as a function of stage using a bathymetric survey

of the channel (measured using a fathometer) and various values of stage (as measured on the outside staff

gage). Cross-sectional areas were computed for values

of stage ranging between minimum and maximum

values expected at the site. Rating tables were then

developed relating stage to area.

Mean-Velocity Rating

Regression equations were developed relating

mean velocity computed from discharge measurements to the corresponding AVM index velocity measured by the AVM. The mean velocity and AVM

index-velocity data used in the regression analysis

were collected during periods of seasonal high and

low flow and during several tidal cycles. The analysis

Acoustic Path

Acoustic Path

Transducer

Transducer

Transducer

Transducer

Left

bank Right

bank

Streambed

Streambed

Acoustic Path 1

Acoustic Path 2

DISTANCE ALONG ACOUSTIC PATH, IN FEET

Right

bank

Left

bank

ELEVATION, IN FEET ABOVE GAGE DATUM

0

0

100

100 200

200

300

300

400

400

500

500

30

30

20

20

10

10

-10

-10

-20

-20

-30

-30

0

0

B B’

C C’

Figure 9. Oblique cross sections of Dunns Creek channel at the gaging station.
Instrumentation, Measurement, and Computation of Discharge at the Three AVM Streamflow Sites 15

required several assumptions about errors calculated

from the regression: errors must be independent over

time (not serially correlated), normally distributed,

and of equal variance over the range of velocities.

Residual plots for each regression generally confirm

these assumptions.

Regression equations initially were developed

using several mathematical combinations of stage,

AVM index velocity, the product of stage and index

velocity, and the rate of change of stage and AVM

index velocity as independent variables. With the

exception of Dunns Creek (path 2), AVM index velocity was the only significant linear predictor of stream

velocity. The general form of the resulting regression

equation for mean velocity for each study site is:

(6)

where VM is mean velocity in feet per second,

VI is index velocity measured from the

AVM, in feet per second, and a,b are

constants.

VM a VI = × + b,

St. Johns River Site

Transducer

Transducer Transducer Transducer

Transducer

Transducer

Acoustic path 1 Acoustic path 2

Acoustic path 3

(387 ft.) (497 ft.)

(377 ft.)

(215 ft.)

Railroad bridge

N

Not to scale

Left

bank

Right

bank

VP2 VP1

VP3

VI1

VI2

VI3 Θ Θ

Θ

2 1

3

Gage

shelter

Section 4 Section 3 Section 2 Section 1

Path 4

Direction of

flow

Figure 10. Acoustic velocity meter (AVM) multi-sectional configuration on the St. Johns River at Buffalo Bluff.
16 Application of Acoustic Velocity Meters for Gaging Discharge of Three Low-Velocity Titdal Streams in the St. Johns River Basin

Acoustic path 1

Acoustic path 2

Acoustic path 3

0

0

0

0

10

10

10

20

20

20

30

30

30

-10

-10

-10

-20

-20

-20

-30

-30

-30

ELEVATION, IN FEET ABOVE GAGE DATUM

DISTANCE ALONG ACOUSTIC PATH, IN FEET

Transducer

Water surface

Streambed

Acoustic path

100 200 300 400 500

Streambed

Streambed

Acoustic path

Acoustic path

Water surface

Water surface

Transducer

Transducer

Transducer

Transducer

Transducer

Figure 11. Oblique cross sections of St. Johns River at Buffalo Bluff channel at the gaging station.
Instrumentation, Measurement, and Computation of Discharge at the Three AVM Streamflow Sites 17

The relation between mean velocity and AVMmeasured index velocity for each AVM stream-gaging

site is shown in figure 14. Mean velocities were computed by dividing measured discharges by the crosssectional area from the stage-area rating for the average stage during the discharge measurement. The data

indicate that measured mean velocity is a simple linear

function of AVM index velocity, even during periods

of negative (upstream) flow. Generally, the data are

evenly distributed about the regression equation

throughout the range of measured values.

The standard error estimate for the regressions

ranged from 0.040 to 0.068 ft/s and is fairly uniform

St. Johns River Site

Transducer

Transducer

Acoustic path 1

Acoustic path 2

Acoustic path 3

(377 ft.)

Railroad bridge

N

Not to scale

Left

bank Right

bank

Gage

shelter

Transducer

(removed)

(removed)

New acoustic path

(60 ft.)

Direction of

flow

Figure 12. Acoustic velocity meter (AVM) multi-redundant configuration on the St. Johns River at Buffalo Bluff.

over the range of velocities. Regression equations for

each study site, along with the standard errors, are

listed in table 2.

A plot of the residuals of the regression of mean

velocity and stage for the rating at Dunns Creek is

shown in figure 15. This was the only site for which

stage was also a significant predictive variable for

mean cross-sectional velocity. The first plot (A) in figure 15 shows the residuals (from the regression of

mean velocity to AVM-measured index velocity)

before stage was added to the regression equation. The

downward trend in residuals with stage indicates that

stage is a useful predictor of a portion of the total
18 Application of Acoustic Velocity Meters for Gaging Discharge of Three Low-Velocity Titdal Streams in the St. Johns River Basin

variation in observed velocities. The second plot (B)

in figure 15 shows the residuals after stage has been

added as an independent variable in the regression

equation. The same comparison for the other two

streams (not shown) indicated no significant trends in

the residuals with stage.

Estimation of Error

Uncertainty in estimates of instantaneous and

mean daily discharge is produced by random and systematic errors. Three principal sources of error in the

estimated discharge can be identified: (1) instrumental

errors associated with measurement of area and index

velocity, (2) biases in the representation of mean daily

stage and velocity due to natural variability in these

10,000

9,000

8,000

7,000

6,000

5,000

4,000

3,000

2,000

1,000

6 6 8 8 10 10 12 12 14 14 16 16

Dunns Creek

Six Mile Creek

St. Johns River

Path 3

Path 2

Path 1

Section 4

STAGE, IN FEET ABOVE GAGE DATUM

CROSS-SECTIONAL AREA, IN SQUARE FEET

Figure 13. Relation between stage and cross-sectional area for acoustic velocity meter (AVM) stream-gaging

sites.

over time and space, and (3) errors in cross-sectional

area and mean-velocity ratings based on stage and

index velocity. In practice, instrumental errors in stage

and velocity measurements tend to be small and

appear to be randomly distributed. Errors in sample

representation tend to be periodic and may induce bias

in discharge computations over short periods of time,

but increasing the number of observations and the

length of the computational period tend to improve

representation. The errors in cross-sectional area ratings generally are relatively small because stage and

cross-sectional area are relatively easy to measure and

verify on a consistent basis. The largest single source

of error remaining in discharge computations is uncertainty in the mean-velocity rating.
Instrumentation, Measurement, and Computation of Discharge at the Three AVM Streamflow Sites 19

Smith (1969) identified both random and systematic errors associated with discharge measurements and the velocity ratings developed from these

measurements. Although random error in an empirical

rating can be reduced by increasing the number of

velocity measurements used, the rating itself remains a

single estimate of the true velocity relation and thus its

uncertainty produces a systematic error in the discharge computation process which cannot be reduced

-1.0 1.5 -0.5 0 0.5 1.0 -0.8

1.4

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Acoustic Path 1

VM = 0.9819(VI) + 0.0012

-1.0 1.5 -0.5 0 0.5 1.0 -1.0

1.4

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Acoustic Path 2

-1.5 1.0 -1.0 -0.5 0 0.5 -1.0

0.8

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6 Six Mile Creek

Dunns Creek Dunns Creek

VM = 0.6978(VI) + 0.038

INDICATOR VELOCITY, IN FEET PER SECOND

MEAN VELOCITY, IN FEET PER SECOND

INDICATOR VELOCITY, IN FEET PER SECOND

MEAN VELOCITY, IN FEET PER SECOND

H = 11.50

VM = 0.906(VI ) - 0.042(H) + 0.470

Figure 14. Relation of mean velocity in steam to acoustic velocity meter (AVM)-measured index velocity for AVM

steam-gaging sites. (VI

, AVM-measured index velocity, in feet per second; H, stage, in feet above gage datum.)

unless a whole new experimental setup (rating) is

tested. Biases produced by systematic error are not

easily separated from random error. However, where

errors in area ratings are small, uncertainty in discharge computations can be estimated mathematically

as something less than the standard error of regression

for the mean velocity ratings.

Errors in instantaneous discharges as the result

of errors in the velocity rating can be estimated for
20 Application of Acoustic Velocity Meters for Gaging Discharge of Three Low-Velocity Titdal Streams in the St. Johns River Basin

 each site as the product of instantaneous cross-sectional area (fig. 13) and the standard error estimate

(SEE) from the mean-velocity regression (table 2).

Errors in discharge are not expressed here in percentages as is commonly done, but instead are shown in

units of velocity (ft/s) or discharge (ft3/s). The ratings

in figure 14 show that the variance of residuals around

the regression line are fairly uniform over the range of

index velocity (VI). Expressing the standard error of

discharge estimates as a percentage of the total discharge tends to overestimate the accuracy of discharge

-1.0 1.5 -0.5 0 0.5 1.0 -0.8

1.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

-1.6 0.2 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0 0.2 -1.6

0.2

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0

0.2

VM = 1.174(VI )- 0.009

Section 1

VM = 1.012(VI) + 0.0299

Section 2

-1.5 1.5 -1.0 -0.5 0 0.5 1.0 -2.0

1.5

-1.5

-1.0

-0.5

0

0.5

1.0

VM = 1.134(VI) + 0.0244

Section 3

-1.5 1.0 -1.0 -0.5 0 0.5 -1.0

0.8

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6 Section 4

VM = 0.87(VI) + 0.019

St. Johns River at Buffalo Bluff (multi-sectional method)

INDICATOR VELOCITY, IN FEET PER SECOND

MEAN VELOCITY, IN FEET PER SECOND

Figure 14. Relation of mean velocity in steam to acoustic velocity meter (AVM)-measured index velocity for AVM

steam-gaging sites. (VI

, AVM-measured index velocity, in feet per second; H, stage, in feet above gage datum.)—

Continued

estimates at low flows and underestimate accuracies at

high flows. For example, a daily mean discharge of 50

ft3

/s at Dunns Creek may be 100 percent in error,

whereas a daily mean discharge of 1,500 ft3

/s may be

only 3 percent in error.

Computed instantaneous discharge errors are

shown as a function of cross-sectional area for each

study site (fig. 16). Standard errors in discharge for the

median cross-sectional areas for Six Mile Creek,

Dunns Creek, and St. Johns River are 94, 360, and

1,980 ft3/s, respectively (fig. 16). Over the range of
Instrumentation, Measurement, and Computation of Discharge at the Three AVM Streamflow Sites 21

measured cross-sectional areas, errors for instantaneous discharges range from 66 to 115 ft3/s for Six

Mile Creek, 271 to 408 ft3

/s for Dunns Creek, and

1,820 to 2,300 ft3

/s for St. Johns River (fig. 16).

Errors in mean discharges may be somewhat

less than those in instantaneous discharges because

of the central tendency of the mean. In the absence

of substantial errors in area ratings, the standard

error of mean daily discharges can be estimated as

the product of the daily mean cross-sectional area

and the standard error of the estimated value from

the mean velocity-index velocity relation. This

also assumes that mean velocity is linearly related

to index velocity and that cross-sectional area is

not covariant with index velocity (which is generally true in Florida). The equation for the standard

error of an estimated value is expressed in the following equation:

(7)

-0.8

0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

MEAN VELOCITY, IN FEET PER SECOND

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0

INDEX VELOCITY, IN FEET PER SECOND

Acoustic path 3

VM = 0.700(VI) + 0.064

St. Johns River at Buffalo Bluff (multi-redundant method)

Figure 14. Relation of mean velocity in steam to acoustic velocity meter (AVM)-

measured index velocity for AVM steam-gaging sites. (VI

, AVM-measured index

velocity, in feet per second; H, stage, in feet above gage datum.)—Continued

where x is the independent variable used in

mean-velocity rating,

SE(y(x)) is the standard error estimate of

mean velocity from the regression

equation at any value of the variable

x,

n is the number of data points (discharge measurements),

x is the mean of x values in the discharge measurements,

sx is the standard deviation of x values

in the discharge measurements, and

SEE is the standard error estimate.

The estimated value of velocity from equation 6 represents a mean VM for a given VI. The

standard error of this estimated mean velocity is at

a minimum at the mean of the observations of

index velocity input to the regression analysis.

This error increases for index velocities above and

below the mean. SE y( ) ˆ ( ) x

1

n

-- ( ) x x –

sx -----------------     2

= + ( ) SEE ,
22 Application of Acoustic Velocity Meters for Gaging Discharge of Three Low-Velocity Titdal Streams in the St. Johns River Basin

Table 2.--Regression equations for the estimation of mean velocity at acoustic velocity meter (AVM) stream-gaging sites

[All equations are for mean velocity in the stream, in feet per second. R2, correlation coefficient; ft/s, feet per second; AP, acoustic path; VM, mean velocity,

in feet per second; VI, AVM-measured index velocity, in feet per second; --, no data]

Path

number

(shown in

figs. 5,

 8, and 10),

Number of

discharge

measurements

Mean

velocity

range

Mean

VM

Equation R2

Standard

error of

estimate

(ft/s)

Standard

error of

the mean

(ft/s)

Six Mile Creek (single path method)

 AP 1 14 -0.48 – 0.65 0.010 VM = 0.6978 VI + 0.0380 0.99 0.057 0.015

Dunns Creek (redundant path method)

AP 1 17 -.69 – -1.01 .447 VM=0.982VI + 0.001 .99 .047 .011

 AP 2 32 -.92 – 1.35 .358 VM = 0.906 VI - 0.042H + 0.47 .99 .063 .011

St. Johns River at Buffalo Bluff (sectional method)

Section 1

AP 1 27 -.60 – 1.34 .592 VM = 1.174 VI - 0.0090 .99 .055 .011

Section 2

AP 2 16 -1.49 – .11 -.753 VM = 1.012 VI + 0.0299 .99 .060 .015

Section 3

AP 3 20 -1.47 – 1.23 -.294 VM = 1.134 VI + 0.0244 .99 .068 .015

Section 4

AP 4 14 -.86 – .50 -.183 VM = 0.8701 VI + 0.0190 .99 .043 .011

St. Johns River at Buffalo Bluff (redundant method)

AP 3 29 -.71 – +.81 -0.076 VM = 0.700VI + 0.064 .99 .040 .007

AP 4 -- -- -- -- -- -- --

The standard error of mean daily velocities near

the mean of the input data set can be simplified from

equation 7 to:

. (8)

Standard errors at the mean value of VI were

computed for each site using equation 8 and are

included in table 2. These errors represent a minimum

uncertainty for computed mean velocities given the

random error incorporated into the determination of a

velocity rating. The actual standard error for a given

computed daily mean velocity is probably somewhat

greater than this but less than the standard error of

computed instantaneous velocities (standard error of

regression). As noted previously, random errors in

instrument readings and random variations in the representativeness of AVM path velocities within a

streamflow cross section can be reduced by averaging

SE y( ) ˆ ( ) x

SEE

n = ----------

multiple instrument readings into a single daily value.

No amount of sampling replication and averaging,

however, can reduce the systematic error in the rating.

This error remains a bias in all computed velocities

(and discharges) based on the rating.

The instrumental precision of the AVM can

exceed the accuracy of the index velocity rating and

give the appearance of greater accuracy in computed

discharges than is justified. For example, the data-plotted instantaneous discharges for Dunns Creek (fig. 17)

show sufficient continuity over time to discern

changes and patterns within a range of discharges well

below the indicated standard error of ±300 to 400 ft3

/s.

The absence of noticeable random scatter around the

cyclic pattern of discharges would seem to indicate a

high degree of precision. The scatter of observations

around the rating line for Dunns Creek (fig. 14) and

the standard error of regression for the rating,

however, indicate somewhat lesser conformity
Instrumentation, Measurement, and Computation of Discharge at the Three AVM Streamflow Sites 23

-0.25

0.20

-0.20

-0.15

-0.10

-0.05

0

0.05

0.10

0.15

9.5 10.0 10.5 11.0 11.5 12.0 12.5

-0.2

-0.1

0

0.1

0.2

STAGE, IN FEET ABOVE GAGE DATUM

RESIDUAL

VM = 0.911(VI ) + 0.0001

VM = 0.906(VI ) - 0.0424(H) + 0.4721

Plot A

9.5 10.0 10.5 11.0 11.5 12.0 12.5

Plot B

Figure 15. Residuals from regression of mean velocity to stage with and without stage as an independent

variable for Dunns Creek Path 2. (VI

, AVM-measured index velocity, in feet per second; H, stage, in feet

above gage datum.)

between measured and computed instantaneous velocities than is indicated between successive computed

discharge.

The high degree of continuity in computed instantaneous discharges suggests that errors are not random

over time. If errors in computed discharge are defined as

the difference between the computed and true discharge

time-series data (both of which appear to be smooth and

periodic within the limits of measurement), then the time

series of errors must also be smooth and periodic. From

this it follows that errors in computed discharge must be

correlated, and thus biased, within a given period of time

which can be represented as the average correlation

length of the error time series. The periodicity of tidal

flow reversals in this system would suggest a possible

error correlation length similar in duration to the tide. By

extension, the standard error of discharges for averaging

intervals of less than several tidal cycles (such as daily

averages), will tend to be greater than the minimum

calculated using equation 8, and may tend toward the

greater standard error of instantaneous observations

represented by the standard error of regression. Over
24 Application of Acoustic Velocity Meters for Gaging Discharge of Three Low-Velocity Titdal Streams in the St. Johns River Basin

averaging intervals of many correlation lengths (such as

months or years), the standard error of the mean may

approach that computed from equation 8.

Though the standard errors of estimated velocity

are small (between 0.01 and 0.015 ft/s), errors in mean

daily discharge can be large due to large cross-sectional areas. Examples of standard errors in computed

mean daily discharges (for mean daily values computed near the mean) of VI are shown as a function of

cross-sectional area for each study site in figure 16.

Errors in discharge for the median cross-sectional area

for Six Mile Creek, Dunns Creek, and St. Johns River

at Buffalo Bluff (sectional method) during the study

period are 25, 65, and 455 ft3/s, respectively (fig. 16).

Though the use of AVMs in tidally affected

streams can produce reliable estimates of high discharge, the accuracy of the method applied at low, net

daily flows can be very poor. Mean daily discharge at

the three AVM sites ranged from about -500 to

+1000 ft3

/s at Six Mile and Dunns Creeks and from

-500 to +15,000 ft3

/s on the St. Johns River at Buffalo

Bluff. For periods of high discharge, the AVM indexvelocity method tends to produce estimates accurate

within 2 to 6 percent. For periods of moderate discharge, errors in discharge estimates may increase to

more than 50 percent. At low flows, errors in percentage of discharge increase toward infinity.

SUMMARY

Three tidally affected streams in northeast Florida were selected for application of acoustic velocity

meters (AVMs). Gaging of low-velocity tidal streams

is complicated by unsteady, variable flow conditions.

Development of a simple relation between stage and

discharge is not possible because of tidal and backwater conditions in these streams. AVMs can be used

under these conditions to compute discharge by multiplying cross-sectional area by mean velocity, estimated using index velocity measured by the AVM.

Physical characteristics for all three low-velocity tidal streams are similar except for drainage area.

The topography for all three sites primarily is lowrelief, swampy terrain. During a typical tidal cycle,

stream velocities range from -2 to 2 feet per second

and the average variation in stage is about 1 foot. Two

of the gaging sites, Six Mile Creek and Dunns Creek,

are tributaries of the St. Johns River, each located

about 0.8 to 1.0 mile upstream from the mouth. The

third gaging site is located on the St. Johns River at

Buffalo Bluff about 89 miles upstream from its mouth

at the Atlantic Ocean. Cross-sectional areas at the

measurement section ranged from about 2,500 square

feet at Six Mile Creek to 18,500 square feet at St.

Johns River at Buffalo Bluff.

The three stream-gaging sites were instrumented to measure index velocity (using an AVM),

corresponding system diagnostics, and stage (using a

shaft encoder). Measurements were made at 15-minute

intervals and recorded using a datalogger. To determine mean velocity, discharge was measured at each

site using a portable acoustic current meter and standard U.S. Geological Survey stream-gaging techniques. The acoustic current meter was used rather

than the low-velocity Price type AA current meter

because it more accurately measures velocity magnitude and direction vectors.

Stage-area curves for each stream were developed using bathymetric data. Least-squares multiple

linear regression was used to estimate mean velocity

as a function of the AVM-measured index velocity.

Results of the regression analysis for Six Mile Creek

and the St. Johns River study site indicate that a simple linear relation exists between mean velocity and

AVM-measured index velocity. Results of the regression analysis for the Dunns Creek study site indicate

that a multiple-linear relation exists between mean

velocity and AVM-measured index velocity and stage.

Instantaneous discharge was computed by multiplying results of relations developed for cross-sectional area and mean velocity. Principal sources of

error in the estimated discharge are identified as:

(1) instrument errors associated with measurement

of stage and index velocity, (2) errors in the representation of mean daily stage and index velocity due

to natural variability over time and space, and (3)

errors in cross-sectional area and mean-velocity ratings based on stage and index velocity. Errors in discharge are not expressed in percentages as is

commonly done, but instead are shown in absolute

units of velocity and discharge. Standard errors for

instantaneous discharge for the median cross-sectional area for Six Mile Creek, Dunns Creek, and St.

Johns River at Buffalo Bluff were 94, 360, and 1,980

cubic feet per second, respectively. Standard errors

for mean daily discharge for the median cross-sectional area for Six Mile Creek, Dunns Creek, and St.

Johns River at Buffalo Bluff were 25, 65, and

455 cubic feet per second, respectively. Mean daily
Summary 25

discharge at the three sites ranged from about -500 to

1,500 cubic feet per second at Six Mile Creek and

Dunns Creek and from about -500 to 15,000 cubic feet

per second on the St. Johns River at Buffalo Bluff. For

periods of high discharge, the AVM index-velocity

1,000 2,500 1,500 2,000

0

120

20

40

60

80

100

DISCHARGE ERROR, IN CUBIC FEET PER SECOND

Daily Mean

Instantaneous

Median

Six Mile Creek

4,000 7,000 5,000 6,000

0

450

50

100

150

200

250

300

350

400

Median

Instantaneous

Daily Mean

Dunns Creek

14,000 22,000 16,000 18,000 20,000

CROSS-SECTIONAL AREA, IN SQUARE FEET

200

2,400

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

2,200

DISCHARGE ERROR, IN CUBIC FEET PER SECOND

Median

Instantaneous

Daily Mean

St. Johns River

CROSS-SECTIONAL AREA, IN SQUARE FEET

Figure 16. Relation of discharge error as a function of cross-sectional area for acoustic velocity meter (AVM)

stream-gaging sites.

method tended to produce estimates accurate within 2

to 6 percent. For periods of moderate discharge, errors

in discharge may increase to more than 50 percent. At

low flows, errors as a percentage of discharge increase

toward infinity.
26 Application of Acoustic Velocity Meters for Gaging Discharge of Three Low-Velocity Titdal Streams in the St. Johns River Basin

Selected References

Chow, V.T., 1959, Open channel hydraulics: New York,

McGraw-Hill, p. 523–535.

Draper, N.R., and Smith, Harry, 1982, Applied regression

analysis: New York, John Wiley & Sons, p. 141–210.

Laenen, Antonius, 1985, Acoustic velocity meter systems:

U.S. Geological Survey Techniques of WaterResources Investigations, book 3, chap. 17, 38 p.

Laenen, Antonius, and Curtis, Jr., R.E., 1989, Accuracy of

acoustic velocity metering systems for measurement of

low velocity in open channels: U.S. Geological Survey

Water-Resources Investigations Report 89–4090, p. 15.

Laenen, Antonius, and Smith, Winchell, 1983, Acoustic

systems for the measurement of streamflow: U.S.

Geological Survey Water-Supply Paper 2213, 26 p.

6,000

-8,000

-7,000

-6,000

-5,000

-4,000

-3,000

-2,000

-1,000

0

1,000

2,000

3,000

4,000

5,000

DISCHARGE, IN CUBIC FEET PER SECOND

8.0

9.8

8.2

8.4

8.6

8.8

9.0

9.2

9.4

9.6

9.8

STAGE, IN FEET ABOVE GAGE DATUM

2400 0800 1600 2400 0800 1600 2400 0800 1600 2400 0800 1600 2400 0800 1600 2400 0800 1600 2400 0800 1600 2400

1 2 3 4 5 6 7

JANUARY 1992

Stage

Discharge

Figure 17. Instantaneous stage and discharge for a 7-day period at Dunns Creek.

Rantz, S.E., and others, 1982, Measurement and computation of streamflow: v. 1: Measurement of stage and discharge, p. 174–5, and v. 2: Computation of discharge:

U.S. Geological Survey Water-Supply Paper 2175, 631

p.

Smith, Winchell, 1969, Feasibility study of the use of the

acoustic velocity meter for measurement of net outflow

from the Sacramento-San Joaquin Delta in California:

U.SW. Geological Survey Water-Supply Paper 1977,

54 p.

Smith, Winchell, Hubbard, L.L., and Laenen, Antonius,

1971, The acoustic streamflow measuring system on

the Columbia River at The Dalles, Oregon: U.S.

Geological Survey Open-File Report, 60 p.