New Research Report - River Restoration Program
October 18, 2001
A new report from the CRC River Restoration Program is now available from the Centre Office: 'The Calculation of Streamflow from Measurements of Stage' by John Fenton and Bob Keller (CRC Report 01/6)
The calculation of river flow from measurements of surface elevation (stage) is a fundamental problem in river engineering that has been surprisingly little investigated. Existing International and Australian Standards reflect this lack of knowledge. The usual way in which stage and flow at a station are shown as being related is via a rating curve. Yet, the concept of a unique rating curve at a station is theoretically flawed. The hydraulics of river flow show that slope as well as stage is a determinant of flow, and in principle it would be best also to measure the slope at a gauging station, and use this also to calculate discharge. In practice the slope often does not vary much over a range of flows and rates of changes of flow at a point; the reasonable and convenient assumption is implicitly made that flow and stage are connected by a unique relationship that can be represented by a rating curve. Unfortunately the accuracy of this approach is rarely examined in practice. This report considers a number of aspects of the problem of representing stage and discharge measurements and using them to calculate flow from subsequent stage measurements. A critique of existing Standards is presented. The hydraulics of flow in channels and at gauging stations is considered. Procedures are described which could be implemented if slope also were measured. As this is rarely done, a method is developed here which gives a correction to the flow calculated from a rating curve allowing for the variation of elevation (and slope) with time. This provides a correction to the well-known Jones method. Formulae are presented to estimate when these unsteady effects are significant. For most gauging stations they are small, and a unique rating curve is a good approximation. Nevertheless the unsteady corrections are simply implemented, and a number of practical details for that are presented here.
A theoretical model is developed for a river with a gauging station affected by a local control. This is used to give an expression for the rating curve for low flows. Another expression is given for higher flows when the local control washes out, and the channel itself provides the control. The theory for both these ranges shows that in many cases the stage will vary approximately like the square root of discharge. This can be used to calculate an approximate rating curve in the absence of other information, or preferably, together with one or two ratings, to calibrate such a model. It is suggested that in presenting and approximating rating curves, plotting the square root of discharge against the stage has some advantages. Many data points from gaugings should plot roughly as a straight line, which can help the determination of the cease-to-flow point, as well as the possible extrapolation of the curve at high flows. It is shown how global approximation of the rating data can be implemented via a robust
numerical method.
Copies of the report are available from the Centre Office for $27.50 (includes postage and GST within Australia).
Reports, videos and software, available from the CRC are listed in our Publications List. Copies of the Publications List are available on request from the Centre Office or can be downloaded from this CRC website at:
http://www.catchment.crc.org.au/publications
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