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Techniques and Methods 3–A23

Computing Discharge Using the Index Velocity Method

By Victor A. Levesque and Kevin A. Oberg

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Application of the index velocity method for computing continuous records of discharge has become increasingly common, especially since the introduction of low-cost acoustic Doppler velocity meters (ADVMs) in 1997. Presently (2011), the index velocity method is being used to compute discharge records for approximately 470 gaging stations operated and maintained by the U.S. Geological Survey. The purpose of this report is to document and describe techniques for computing discharge records using the index velocity method.

Computing discharge using the index velocity method differs from the traditional stage-discharge method by separating velocity and area into two ratings—the index velocity rating and the stage-area rating. The outputs from each of these ratings, mean channel velocity (V) and cross-sectional area (A), are then multiplied together to compute a discharge. For the index velocity method, V is a function of such parameters as streamwise velocity, stage, cross-stream velocity, and velocity head, and A is a function of stage and cross-section shape. The index velocity method can be used at locations where stage-discharge methods are used, but it is especially appropriate when more than one specific discharge can be measured for a specific stage.

After the ADVM is selected, installed, and configured, the stage-area rating and the index velocity rating must be developed. A standard cross section is identified and surveyed in order to develop the stage-area rating. The standard cross section should be surveyed every year for the first 3 years of operation and thereafter at a lesser frequency, depending on the susceptibility of the cross section to change. Periodic measurements of discharge are used to calibrate and validate the index rating for the range of conditions experienced at the gaging station. Data from discharge measurements, ADVMs, and stage sensors are compiled for index-rating analysis. Index ratings are developed by means of regression techniques in which the mean cross-sectional velocity for the standard section is related to the measured index velocity. Most ratings are simple-linear regressions, but more complex ratings may be necessary in some cases. Once the rating is established, validation measurements should be made periodically. Over time, validation measurements may provide additional definition to the rating or result in the creation of a new rating.

The computation of discharge is the last step in the index velocity method, and in some ways it is the most straight-forward step. This step differs little from the steps used to compute discharge records for stage-discharge gaging stations. The ratings are entered into database software used for records computation, and continuous records of discharge are computed.

First posted April 12, 2012

For additional information contact:
Kevin A. Oberg
National Hydroacoustics Coordinator
U.S. Geological Survey
Office of Surface Water
1201 West University Avenue, Suite 100
Urbana, IL 61801
(217) 328–9739

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Suggested citation:

Levesque, V.A., and Oberg, K.A., 2012, Computing discharge using the index velocity method: U.S. Geological Survey Techniques and Methods 3–A23, 148 p. (Also available at





Introduction to the Index Velocity Method

Site and Instrument Selection

ADVM Installation and Configuration

Routine Field Techniques

Routine Office Techniques

Rating Development and Analysis

Discharge Measurement Calibration Data

Index Velocity Rating

Computation and Analysis of Discharge

Summary and Conclusions



Appendix 1.  Mounts for Acoustic Doppler Velocity Meters

Appendix 2.  Forms and Quick-Reference Guides

Appendix 3.  Analysis of Data for Selection of Measurement Volume

Appendix 4.  Quality Control of Index Velocity Data for SonTek™/YSI Argonauts™

Appendix 5.  Evaluating Changes in Stage-Area Ratings

Appendix 6.  Implementing the Stage-Area and Index Ratings in National Water Informaiton System (NWIS) Automated Data Processing System (ADAPS) version 4.10

Appendix 7.  Index Velocity Rating Shifts

Appendix 8.  Example of an Index Velocity Station Analysis

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