# Index-Velocity Rating Development (Calibration) for H-ADCP Real-Time Discharge Monitoring in Open Channels

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2 Figure 2 After calibration, a ChannelMaster H-ADCP will turn into a flow meter that can directly output Q, V, H data in a text format through a serial port. This allows an H-ADCP being easily integrated with a telemetry system. The Index-Velocity method is especially useful at a site where a stage-discharge rating does not exist. An advantage of the Index-velocity method is that it can be used for a channel with its width much greater than the H-ADCP profiling range. This technical note describes the Index-velocity method and rating development or calibration of the H-ADCP built-in Index-velocity rating model. The Appendix describes the site selection considerations. 2.0 Index-Velocity Method and the H-ADCP Built-in Index-Velocity Rating Model The principle of the Index-velocity method is to establish a relation between the channel mean velocity and the Index-velocity. The Index-velocity defined here is a time and range averaged velocity measured by a ChannelMaster H-ADCP. The channel discharge Q is the product of the wetted cross-section area and the channel mean velocity: Q AV (1) where A = wetted area of the standard cross-section, and V = mean velocity of the channel. It should be pointed out that the standard cross-section used in the Index-velocity method does not need to be the same cross-section where an H-ADCP is mounted at. The wetted cross-section area depends on the cross-section geometry and water level. For a specific site, the wetted cross-section area is a function of water level only: A f (H) (2) 2

3 where H = water surface level (stage) above the local datum. Equation (2) is a stage-area rating that can be developed from the depth survey data. This rating is usually available at a hydrology station. The channel mean velocity V may be a function of the Index-velocity and the water level H: V f ( V, H) (3) I where V I = Index-velocity. The Index-velocity rating model that is built in the ChannelMaster H-ADCP firmware is: V b b b H ) (4) 1 ( 2 3 V I where b B1B bb2b b B3B bb4b are coefficients to be determined from field calibration tests. However, the use of the two parameter rating model, Eq. (4), beyond the parameter calibration range must be with caution. In addition, the model requires multiple regression analysis. In most cases, the channel mean velocity may be a function of the Index-velocity only. Thus, Eq. (4) is reduced to: V b1 b2 V I (5) In some cases, the coefficient b 1 is small and may be neglected. Thus, Eq. (5) is reduced to a simple coefficient rating: V b2 V I (6) The user needs to make a judgment for forcing b B1=0 (i.e., forcing the rating through zero) or not during a regression analysis. The key in using the Index-velocity method is to calibrate the rating model at a site because the model coefficients are site specific. The calibration, also called rating development, involves two steps. The first step is to conduct field calibration test. The test involves collecting H-ADCP velocity data from which the Index-velocity is obtained, and concurrently conducting discharge measurement from which the channel mean velocity is obtained. The second step is to create a relation between the channel mean velocity and the Index-velocity by regression analysis of the data obtained from the field calibration test. It should be note that other rating models such as power law and second-order polynomial may be used. However, at the present time, only the above rating models, Eqs. (4), (5), and (6), are built in the ChannelMaster H-ADCP firmware. Therefore, other rating models are not described here. 3.0 Field Calibration Test While an H-ADCP is sampling velocities, the calibration discharge measurements are conducted concurrently using a moving boat ADCP or a conventional current meter. It is 3

4 important to note that the calibration test must cover a flow or water level range from low to high to obtain a set of data for channel mean velocity, water level (stage), and Index-velocity. This is because, like a stage-discharge rating, an index-velocity rating will have uncertainties outside the range of the calibration measurements particularly if channel conditions (flow in the floodplain) change with stage/flow. Some sites may require a year to complete the calibration to cover the whole stage/flow range. 3.1 H-ADCP installation and configuration Referring to Figure 3, an H-ADCP may be mounted on a bank at an elevation of Z adcp above the local datum. A mounting structure must be designed and constructed based on site conditions. The H-ADCP must be mounted with its two horizontal beams in the horizontal plane. Tilt, either pitch or roll, must be zero or close to zero. The mount must be stable without changing over time. Z 0 H-ADCP Cell 1 Water Surface Cell j Y H Canal Bottom Canal Bank Acoustic Beams Canal Bank 0 Y H-ADCP X Mean Flow Direction Figure 3 A sketch of H-ADCP setup The H-ADCP s orientation should be perpendicular to the mean flow direction. That is, its instrument coordinate X should be parallel to the mean flow direction and Y is to the crosssection direction. The up-direction is defined as Z coordinate. Z = 0 is the local datum used or defined by the user or a local authority. For a channel with a flat bottom, the bottom may be set as Z = 0. 4

8 Note again that the wetted cross-section area A is taken at the so-called Standard Crosssection that may not be the same as the cross-section where the H-ADCP is mounted at. 4.5 Example of organized data Table 1 shows an example of the organized data from a field calibration test at the irrigation canal in California. A 600 khz ChannelMaster H-ADCP was used for Index-velocity measurements. A StreamPro ADCP was used for the calibration discharge measurements. Table 1 Example of organized StreamPro ADCP and ChannelMaster H-ADCP data from the field calibration test at the California irrigation canal StreamPro ADCP Measurement ChannelMaster H-ADCP Measurement Canal Wetted Transect Start Time Measured Discharge (Q measured ) [m 3 /s] Mean Velocity (V) [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: :53: :50: :58: :58: :21: :20: :24: :24: :43: :43: :47: :47: :51: :51: :54: :54: :57: :57: :00: :00: :09: :08: :15: :15: :19: :18: :23: :23: :27: :27: :31: :31: :36: :36: :42: :42: :06: :06: :11: :11: :15: :15:

9 Vm (m/s) Note that the calibration discharge measurement time, i.e., the transect start time, and Index velocity measurement time, i.e., the sample start time, must match as close as possible if the flow changes rapidly with time as it was at this site. The next step is to plot the data for channel mean velocity V vs. Index-velocity V I. Figure 5 shows the plot of the data shown in Table Vm = Vi Vi (m/s) Figure 5 Plot of data for V and V I shown in Table Regression analysis to determine rating model coefficients First, select a rating model based on the observation of the V vs. V I plot. Apparently, the plot shown in Figure 3 indicates a leaner relation. Second, conduct regression analysis for the mean velocity and index velocity using Excel or a rating creation software such as IVR-Creator. Below is the rating result obtained from the regression analysis for the data shown in Table 1: V (10) mean V I with a correlation coefficient of Note that in this case, a judgment of forcing b B1=0 was made during the regression analysis. Although the Excel spread sheet may be used for regression analysis to determine the rating model coefficients, its use requires knowledge of Excel and it is time consuming. IVR- Creator, the software that is specially designed for Index-velocity rating development is recommended. IVR-Creator does linear and nonlinear regression analysis using the leastsquare method. It accepts field data for channel cross-section geometry, discharge, water level (stage), and Index-velocity. Figure 6 shows a screen shot of the IVR-Creator software. IVR-Creator is very easy to use and saves a lot of time. It is a useful tool for Index-velocity rating development. 9

10 4.7 Rating quality evaluation Figure 6 Screenshot of the IVR-Creator software The quality of a calibrated rating model needs to be evaluated. Below are the parameters for rating quality evaluation. Correlation coefficient The correlation coefficient (r 2 ) indicates what proportion of variation in the dependent variable (V) can be explained by the independent variable (V I ). An r 2 of 0.97 indicates that 97% of the variation in V is explained by variation in V I. Lower values of r 2 could indicate that other parameters (variables) may be significant and missing in the rating. Residual plot A residual plot shows the departures of observed samples from the regression line (i.e., the calibrated rating model). The residuals should have a random pattern, be distributed equally above and below zero line, and have reasonable magnitudes. Attention should be given for the residual plots that reveal non-linearity and outliers. Figure 7 shows three example residual plots. 10

11 Residual (Vm - Vr) (m/s) Figure 7 Examples of residual plots It can be seen from Figure 7 that, Plot A looks good, Plot B has an outlier, and Plot C has a pattern or non-linearity. The outlier may be due to an error in the calibration discharge measurement. The pattern or non-linearity may be an indication that another independent variable (e.g., the water level) may be missing in the rating. Figure 8 shows the residual plot for the California irrigation canal rating example. The red lines are the 95% confidence intervals. Note that the residuals are random and relative uniformly distributed between the 95% confidence intervals Vm = Vi Vrated (Vr) (m/s) Figure 8 Residual plot for the California irrigation canal rating example Residual distribution plot The residuals from a good rating should have a nearly Gaussian distribution. Figure 9 shows the residual distribution plot for the California irrigation canal rating example. 11

12 Distribution (%) Vm = Vi^ Residual Figure 9 Residual distribution plot for the California irrigation canal rating example Standard error Standard error of estimate (S e ) is a measure of how nearly values of the dependant variable (V) predicted from the regression line agree with observed values. The smaller it is, the better the rating. The standard error is particular useful when comparing several rating models. Percent difference between the rated Q and the measured Q Regardless of the rating model used, you need to check the calibration measurement data points against your rating. That is, first calculate the rated channel mean velocity using your rating model. Secondly, calculate the rated Q = VA, where the wetted area A is calculated from the water level data and the cross-section geometry data. Then calculate the residual Q and the percent difference between the rated Q and the measured Q: Q residual Q Q (11) measured rated Percent Q difference measured Q Q measured rated 100 (%) (12) Table 2 shows the percent difference between the rated Q and the measured Q for the irrigation canal rating example. Note that some percent differences are greater than 14% during low flow conditions. But most of the differences are less than 5%. Table 2 Percent difference between the rated Q and the measured Q for the California irrigation canal rating example No. Measured Q (m 3 /s) Rated Q (m 3 /s) Residual Q (m 3 /s) Percent difference (%)

13 In theory, at least 30 data sets are required to obtain a statistically sound calibration. However, field calibration tests are time consuming and costly. Therefore, less data sets, say, 10 may be fine, particularly for initial calibration. The calibration may be refined when more calibration data are available. 4.8 Rating verification It is important to note that the created rating (i.e., the calibrated rating model) for a site may change over time in the following conditions: Cross-section change due to sediments deposition or bottom erosion H-ADCP sampling volume change due to mounting settlement, tilt, or high solids concentration Therefore, periodically filed discharge measurements may be required to verify the rating. Recalibration may be needed if the rating has a significant change. 13

15 Figure A-1 Wake flow generated by a pier. If an H-ADCP has to be mounted on a pier, avoid the H-ADCP sampling volume in the wake flow. Figure A-2 Bi-directional flow. It may be difficult or impossible to gage bi-directional flow with horizontal systems such as an H-ADCP 15

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