Principle of Index-Velocity Method and its Application Randy Marsden Teledyne RD Instruments

Summary Principles Example Practical Procedures

Part 1: Index-Velocity Method: Principles

Why is an Index-Velocity method needed? Need: Continuous discharge measurement for open channels where simple methods like stage-discharge relationship do not give reliable results Examples: –Tidal rivers –Backwater conditions –Canals or rivers with control structures

Establish a relationship between channel mean velocity and an Index-Velocity Index-velocity is a velocity measured at a local area (sampling volume) on the cross-section. What is Index-Velocity Method?

Developed by USGS in 1972 Used in U.S., China, France, Great Britain, Japan, Canada, Mexico……. 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 Horizontally averaged velocity at a depth Depth averaged velocity in a vertical Point velocity Three Types of Index-Velocity

Point velocity Depth averaged velocity Horizontally averaged velocity

H-ADCP (horizontally-looking) or travel time system. –Example: ChannelMaster Bottom-mounted ADCP: looking-up –Example: ADFM Point current meter for point velocity –Example: Marsh Mcbirney EM meter How to measure Index-velocity?

Fundamentals Discharge equation: Q = A V mean Q = Discharge A = Cross-section area V mean = 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 V mean = k * V index k may depend on depth –Usually not the case on irrigation canals since depth does not vary as much as natural streams

Channel needs to be surveyed for a selected “standard” cross-section to compute channel areas for a range of stages: stage-area rating Man-made channels may use known dimensions. Determining Cross-section Area

Channel area is always calculated at the “Standard” Cross-section H-ADCP not necessarily mounted at the “Standard” Cross-section location but it should not be too far away Which cross-section?

A gauging station 1 = standard cross-section 2 = wading measurement section 3 = bridge measurement section Q1 = Q2 = Q3 Area is always computed at location 1! 1 23 Gage CM

Stage-Area Rating In many cases, stage-area rating may be expressed as: A = a1 + a2 H + a3 H 2 a1, a2, a3 = coefficients H = Stage

Rating curve = regression equation One parameter regression V = f (V i ) Two parameter regression V = f (V i, H) Index-Velocity Rating

A general, two parameter (Index-velocity and stage) linear regression: V mean = b 1 + (b 2 +b 3 H) V Index V I = Index-velocity b 1, b 2, b 3 = regression coefficients Need at least six measurements at different velocities and depths to due full regression Linear Regression

One parameter linear regression If b 3 = 0: V mean = b 1 + b 2 V Index That is, channel mean velocity is a linear function of Index-velocity. Need at least four measurements at different velocities and depths

Simple Linear If have only one or two measurements V mean = b 2 V Index Found to work well in canals and many rivers when there is downstream control

Rating Development Step One: Field data collection Use ChannelMaster to measure index velocity Use Rio Grande or StreamPro to measure Q and A

Rating Development Step 2: Regression analysis 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. Same for area.

Rating Results Q = V mean (V index, H) * A(H) Simplest Case: trapezoidal canal Q = k * V index * (a 2 H + a 3 H 2 ) a 2 is width of bottom of canal a 3 is slope of canal banks

Accuracy Accuracy depends on quality of rating data. –How accurate and reliable is measured index velocity? –How well does index velocity represent the mean velocity – how good is k? –How accurate and reproducible is measured discharge and area?

Canal 18 Take data with ChannelMaster  1200 kHz  20 each 0.5 meter cells  30 pings, 0.5 sec/ping Result for 35 minutes of data  Vavg = m/s ± 2.3%

Canal 18 Continued Rio Grande Discharge data –17 discharge measurements –V mean = m/s ± 1.4% –A mean = m2 ± 1.7% –Q mean = m3/s ± 1.9%

Canal 18 Rating b 2 = 0.86 ± 2.7% a 2 = 8.01m ± 1% a 3 = 2.87 ± 1% Q = (b2*V Index )*(a 2 * H + a 3 *H 2 ) ± 3% This is for each 30 second discharge measurement.

Canal 18 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 V index would be reduced to ± 1.3% and the uncertainty of the discharge to ± 2.0%.

How is this possible? The ChannelMaster and the Rio Grande both use BroadBand ADCP technology which gives: Low noise velocity measurement in short averaging times – a narrowband ADCP needs 50 times as many pings to reach the same precision for the same cell size.

BroadBand ADCP cont. BroadBand ADCPs can use smaller cells to measure the water For the ChannelMaster this means that there are more velocity measurements across the canal and they are closer to each bank – better accuracy for V index. For the Rio Grande this means more vertical depth cells with less estimated flow – better accuracy for V mean.

Other reasons for BroadBand Less pings = less power  Smaller batteries  Smaller solar panels Pick the best number of cells and cell size for each site  Cover more of flow  Reduce uncertainty

Part 2: Application Example

Index-Velocity Rating Development at Imperial Irrigation District, California, December, 2003

Imperial Irrigation District California Trifolium 13 Check structure 600 kHz CM H-ADCP mounted upstream the check structure

Sketch for ChannelMaster H-ADCP set-up

StreamPro ADCP used for discharge measurement

H-ADCP Parameter settings: Cell size:0.5 meter Number of cells: 20 Blank distance:0.5 meter Averaging Interval:37.4 seconds Sampling 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

Organizing Data for Regression Analysis 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 compute from shape of canal Note: H=1.07m, W=3.0 so A=1.5Z 2 ADCP +6.21Z ADCP Cross-section Area

Canal Mean Velocity: Get Q measured from StreamPro, Rio Grande, or ‘conventional” methods

Partial Data from StreamPro ADCP and ChannelMaster H-ADCP Organized for Index-Velocity Rating Development StreamPro ADCP MeasurementChannelMaster H-ADCP Measurement Transect Start Time Measured Discharge (Q measured ) [m 3 /s] Canal Mean Velocity (V mean ) [m/s] Sample Start Time Water Level (H) [m] Index- Velocity (V I ) [m/s] Cross- Section Area (A) [m 2 ] 12:44: :44: :49: :49: :57: :57: :01: :01: :11: :11: :14: :14: :21: :21: :24: :24: :36: :36: :40: :40:

Regression equation:

A stage-discharge rating cannot be created at this site

Time series of rated discharges by applying the rating to the H-ADCP data and StreamPro ADCP measured discharges on December 9, 2003

Rating evaluation Regression coefficient: R or R 2 Standard Error Used as indication of goodness of fit: closer to 1.00 is a better fit

Part 3 Procedures and recommendations Site selection Mounting depth Pitch and roll Mount Cell size Selection of the good cells

Site Selection Choose site with best aspect ratio Aspect ratio is width/center depth Do not want beam hitting bottom sooner than necessary

Mounting depth Mount at 50-60% of mean low water elevation. This is near the average velocity point of the vertical profile. Provides widest range of operation

Pitch and Roll Mount with pitch and roll as close to zero as possible –Maximizes useful range –Beams looking at same plane of the water –Requires pitch/roll sensor Use the Mount ADCP screen in WinHADCP to assist setting up. After maintenance you can be sure that CM is pointed in the same direction to prevent a shift of the rating.

The Mount The mount should be: –Rigid: shaking can introduce unwanted noise –Adjustable: to allow pitch and roll to be set close to zero –Retractable: to allow routine cleaning –Reset easily: to put ADCP back to original orientation

Example mounts

Cell size Select a good cell size for the application Compromise between low noise and maximum profiling range Large cells have low noise but may limit how close you can get to the far bank – small cells averaged together have same noise as one large cell of the same width. 20 cells is enough for most applications SDI-12: up to 27 cells for SDI-12 Version 1.2 and twenty cells for Version 1.3

Selection of good cells Do not want to use cells contaminated by far bank. Look at intensity and correlation plots do determine maximum useful profiling range Intensity appears to show data ok to 8.8 meters But we see that that cell ‘looks wrong’

Selection of good cells continued Correlation data shows that cell at 8.8 meters has correlation contamination and should not be used

Questions?

Linear Curvilinea r Compoun d One Parameter Rating Forms

One Parameter Curvilinear Ratings x y Polynomial y = b + c 1 x + c 2 x 2 + c 3 x 3... x y Logarithmic y =c 1 ln(x) + b x y Exponential y =c 1 e bx Power law y =c 1 x b x y

One Parameter Compound Ratings A B ViVi V A B Transition A = Linear B = Linear