Principle of Index-Velocity Method and its Application
Randy Marsden
Teledyne RD Instruments
Summary
ā¢ Principles
ā¢ Example
ā¢ Practical Procedures
Part 1:
Index-Velocity Method: Principles
Why is an Index-Velocity method needed?
ā¢ Need: Continuous discharge measurement for open channels where simple methods like stage-discharge relationship do not give reliable results
ā¢ Examples:ā Tidal riversā Backwater conditionsā Canals or rivers with control structures
ā¢ Establish a relationship between channel mean velocity and an Index-Velocity
ā¢ Index-velocity is a velocity measured at a local area (sampling volume) on the cross-section.
What is Index-Velocity Method?
ā¢ Developed by USGS in 1972ā¢ Used in U.S., China, France, Great Britain,
Japan, Canada, Mexicoā¦ā¦.
ā¢ Instruments for Index-velocity Horizontal ADCP, i.e., ChannelMaster Acoustic travel time instruments
Index Velocity Method
In practice, three types of local velocity can be used as Index-velocity
ā¢ Horizontally averaged velocity at a depth
ā¢ Depth averaged velocity in a vertical
ā¢ Point velocity
Three Types of Index-Velocity
Point velocity
Depth averaged velocity
Horizontally averaged velocity
ā¢ H-ADCP (horizontally-looking) or travel time system. ā Example: ChannelMaster
ā¢ Bottom-mounted ADCP: looking-upā Example: ADFM
ā¢ Point current meter for point velocityā Example: Marsh Mcbirney EM meter
How to measure Index-velocity?
Fundamentals
Discharge equation:
Q = A Vmean
Q = Discharge
A = Cross-section area
Vmean = Channel mean velocity
Cross-section area is a function of stage
A = f (H)
H = stage
A site may already have a table or curve for the stage-area relationship
Index Velocity Method - Area
Mean Velocity
ā¢ Vmean = k * Vindex
ā¢ k may depend on depth
ā Usually not the case on irrigation canals since depth does not vary as much as natural streams
0
5
10
15
20
25
0 50 100 150 200 250 300 350 400
Station (feet)
Sta
ge
(fe
et)
Surveyed Standard
Channel needs to be surveyed for a selected āstandardā cross-section to compute channel areas for a range of stages: stage-area ratingMan-made channels may use known dimensions.
Determining Cross-section Area
Channel area is always calculated at the āStandardā Cross-section
ā¢ H-ADCP not necessarily mounted at the āStandardā Cross-section location but it should not be too far away
Which cross-section?
A gauging station
1 = standard cross-section2 = wading measurement section3 = bridge measurement section
ā¢ Q1 = Q2 = Q3ā¢ Area is always computed at location 1!
1 2 3
GageCM
Stage-Area Rating
In many cases, stage-area rating may be expressed as:
A = a1 + a2 H + a3 H2
a1, a2, a3 = coefficients H = Stage
Rating curve = regression equation
One parameter regression
V = f (Vi )
Two parameter regression
V = f (Vi , H)
Index-Velocity Rating
A general, two parameter (Index-velocity and stage) linear regression:
Vmean = b1 + (b2+b3 H) VIndex
VI = Index-velocity
b1, b2, b3 = regression coefficients
Need at least six measurements at different velocities and depths to
due full regression
Linear Regression
One parameter linear regression
If b3 = 0:
Vmean = b1 + b2 VIndex
That is, channel mean velocity is a linear function of
Index-velocity.
Need at least four measurements at different velocities
and depths
Simple Linear
ā¢ If have only one or two measurements
Vmean = b2 VIndex
ā¢ Found to work well in canals and many rivers
when there is downstream control
Rating Development
Step One: Field data
collection
ā¢ Use ChannelMaster to
measure index velocity
ā¢ Use Rio Grande or
StreamPro to measure Q
and A
Rating Development
Step 2: Regression analysis
ā¢ Data collection need to be
conducted over a range of stage
or discharge to obtain a series of
data for Index-velocity and
channel velocity. Regression
analysis using a least-square
method to obtain Index-velocity
rating curve or equation.
ā¢ Same for area.
X Variable 1 Line Fit Plot
0
0.5
1
1.5
2
2.5
0 0.5 1 1.5 2
CM VELX
ME
AN
CH
AN
NE
L V
EL
Y
Predicted Y
Rating Results
ā¢ Q = Vmean(Vindex, H) * A(H)
ā¢ Simplest Case: trapezoidal canal
ā¢ Q = k * Vindex * (a2H + a3H2)
ā¢ a2 is width of bottom of canal
ā¢ a3 is slope of canal banks
Accuracy
ā¢ Accuracy depends on quality of rating data.ā How accurate and reliable is measured index
velocity?ā How well does index velocity represent the
mean velocity ā how good is k?ā How accurate and reproducible is measured
discharge and area?
Canal 18
ā¢ Take data with ChannelMaster1200 kHz20 each 0.5 meter cells30 pings, 0.5 sec/ping
ā¢ Result for 35 minutes of dataVavg = 0.329 m/s Ā± 2.3%
Canal 18 Continued
ā¢ Rio Grande Discharge data
ā 17 discharge measurements
ā Vmean = 0.283 m/s Ā± 1.4%
ā Amean = 41.06 m2 Ā± 1.7%
ā Qmean = 11.63 m3/s Ā± 1.9%
Canal 18 Rating
ā¢ b2 = 0.86 Ā± 2.7%
ā¢ a2 = 8.01m Ā± 1%
ā¢ a3 = 2.87 Ā± 1%
ā¢ Q = (b2*VIndex)*(a2* H + a3 *H2) Ā± 3%
ā¢ This is for each 30 second discharge measurement.
Canal 18
ā¢ Since the discharge measurement noise is primarily random it could be reduced by doing more pings during the 30 seconds. By reducing the ping time to 0.1 seconds, and pinging for 20 out of 30 seconds, the noise of Vindex would be reduced to Ā± 1.3% and the uncertainty of the discharge to Ā± 2.0%.
How is this possible?
ā¢ The ChannelMaster and the Rio Grande both use BroadBand ADCP technology which gives:
ā¢ Low noise velocity measurement in short averaging times ā
ā¢ a narrowband ADCP needs 50 times as many pings to reach the same precision for the same cell size.
BroadBand ADCP cont.
ā¢ BroadBand ADCPs can use smaller cells to measure the water
ā¢ For the ChannelMaster this means that there are more velocity measurements across the canal and they are closer to each bank ā better accuracy for Vindex.
ā¢ For the Rio Grande this means more vertical depth cells with less estimated flow ā better accuracy for Vmean.
Other reasons for BroadBand
ā¢ Less pings = less powerSmaller batteriesSmaller solar panels
ā¢ Pick the best number of cells and cell size for each siteCover more of flowReduce uncertainty
Part 2:
Application Example
Index-Velocity Rating Development at Imperial Irrigation District, California,
December, 2003
Imperial Irrigation District CaliforniaTrifolium 13 Check structure
600 kHz CM H-ADCPmounted upstream the check structure
Acousti cBeams
Mean FlowDi rectionX
Y
Z
Y
Cel l 1 Cel l jH-ADCP
H-ADCP
H0
0
CanalBank Canal
Bank
Canal Bottom
Water Surface
Sketch for ChannelMaster H-ADCP set-up
StreamPro ADCP used for discharge measurement
H-ADCP Parameter settings:
Cell size: 0.5 meterNumber of cells: 20Blank distance: 0.5 meterAveraging Interval: 37.4 secondsSampling Interval: 37.4 seconds
Screenshot from WinRiver software when
playing back a StreamPro data file
Time series of range averaged Vx for Cells 1 through 4 and
water level at the sampling/averaging interval of 37.4 seconds
0
0.1
0.2
0.3
0.4
0.5
0.6
12:00:00 13:12:00 14:24:00 15:36:00 16:48:00
Time
Ve
loc
ity
(m
/s)
0
0.1
0.2
0.3
0.4
0.5
0.6
Wat
er L
evel
(m
)
Velocity Water Level
Organizing Data for Regression Analysis
i
ki
ki
j
jjxkI VV
4 4
1, )(
4
1
5
1
Index-Velocity: calculate average velocity from CM during the time of a StreamPro velocity measurement
k = 1, 2, 3
Stage: Directly from H-ADCP vertical beam
)(]67.0
[ ADCPbottomADCP ZHWZH
A
Imperial Irrigation District Westside Highline CanalBed Geometry
0
1
2
3
4
5
0 3 6 9
Canal Boundary
Channel Master
Water level
compute from shape of canal
Note: H=1.07m, W=3.0 so
A=1.5Z2ADCP+6.21ZADCP +4.93
Cross-section Area
A
QV measuredmean
Canal Mean Velocity:
Get Qmeasured from StreamPro, Rio Grande, or āconventionalā methods
Partial Data from StreamPro ADCP and ChannelMaster H-ADCP Organized for Index-Velocity Rating Development
StreamPro ADCP Measurement ChannelMaster H-ADCP Measurement
Transect Start Time
Measured Discharge (Qmeasured)
[m3/s]
Canal Mean
Velocity (Vmean)
[m/s]Sample
Start Time
Water Level (H)
[m]
Index-Velocity
(VI)
[m/s]
Cross-Section Area (A)
[m2]
12:44:56 2.482 0.304 12:44:56 0.470 0.351 8.175
12:49:03 2.264 0.280 12:49:18 0.460 0.336 8.098
12:57:01 1.914 0.239 12:57:24 0.453 0.274 8.041
13:01:31 1.391 0.172 13:01:46 0.455 0.199 8.060
13:11:05 0.954 0.120 13:11:07 0.435 0.146 7.909
13:14:41 0.783 0.099 13:14:51 0.425 0.127 7.834
13:21:01 0.574 0.074 13:21:05 0.413 0.088 7.740
13:24:57 0.474 0.061 13:24:49 0.405 0.069 7.684
13:36:20 0.256 0.034 13:36:03 0.385 0.045 7.536
13:40:36 0.247 0.033 13:40:24 0.388 0.045 7.555
Regression equation:
Vmean vs. VI
y = 0.8606x
R2 = 0.995
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.000 0.100 0.200 0.300 0.400 0.500
VI (m/s)
Vm
ean
(m
/s)
2 m range Linear (2 m range)
Imean VV 8606.0
A stage-discharge rating cannot be created at this site
0
0.5
1
1.5
2
2.5
3
3.5
0.300 0.350 0.400 0.450 0.500 0.550
Water Level (m)
Dis
char
ge
(m^
3/s)
Time series of rated discharges by applying the rating to the H-ADCP data and StreamPro ADCP measured
discharges on December 9, 2003
0
0.5
1
1.5
2
2.5
3
3.5
12:00:00 13:12:00 14:24:00 15:36:00 16:48:00
Time
Dis
ch
arg
e (
m3/s
)
SP Rated Q
Rating evaluation
Regression coefficient: R or R2
Standard Error
Used as indication of goodness of fit: closer to 1.00 is a better fit
Part 3
ā¢ Procedures and recommendationsā¢ Site selectionā¢ Mounting depthā¢ Pitch and rollā¢ Mountā¢ Cell sizeā¢ Selection of the good cells
Site Selection
ā¢ Choose site with best aspect ratio
ā¢ Aspect ratio is width/center depth
ā¢ Do not want beam hitting bottom sooner than necessary
Mounting depth
ā¢ Mount at 50-60% of mean low water elevation. This is near the average velocity point of the vertical profile.
ā¢ Provides widest range of operation
Pitch and Roll
ā¢ Mount with pitch and roll as close to zero as possibleā Maximizes useful rangeā Beams looking at same plane of the waterā Requires pitch/roll sensor
ā¢ Use the Mount ADCP screen in WinHADCP to assist setting up.
ā¢ After maintenance you can be sure that CM is pointed in the same direction to prevent a shift of the rating.
The Mount
ā¢ The mount should be:
ā Rigid: shaking can introduce unwanted noiseā Adjustable: to allow pitch and roll to be set
close to zeroā Retractable: to allow routine cleaningā Reset easily: to put ADCP back to original
orientation
Example mounts
Cell size
ā¢ Select a good cell size for the applicationā¢ Compromise between low noise and maximum
profiling rangeā¢ Large cells have low noise but may limit how close
you can get to the far bank ā small cells averaged together have same noise as one large cell of the same width.
ā¢ 20 cells is enough for most applicationsā¢ SDI-12: up to 27 cells for SDI-12 Version 1.2 and
twenty cells for Version 1.3
Selection of good cells
ā¢ Do not want to use cells contaminated by far bank.
ā¢ Look at intensity and correlation plots do determine maximum useful profiling range
ā¢ Intensity appears to show data ok to 8.8 meters
ā¢ But we see that that cell ālooks wrongā
Selection of good cells continued
Correlation data shows that cell at 8.8 meters has correlation contamination and should not be used
?Questions?
LinearCurvilinear Compound
One Parameter Rating Forms
One Parameter Curvilinear Ratings
x
y
Polynomial
y = b + c1x + c2x2 + c3x3...
x
y
Logarithmic
y =c1ln(x) + b
x
y
Exponential
y =c1ebx
Power law
y =c1xb
x
y
One Parameter Compound Ratings
A B
Vi
V A
BTransition
A = Linear
B = Linear