Stream flowing over rocks through a forest.

The Measurement of Measurement Uncertainty

How much confidence should you have in your measurements?

For a discharge measurement result of 50.0 m3s-1, is the true value is between 49.95 and 50.05, as inferred by the trailing zero?  Maybe the true value is anywhere between 47.5 and 52.5 (+/- 5%), a range commonly used to determine ‘goodness of fit’ to a rating curve. Perhaps the measurement wasn’t made under ‘ideal conditions’, which is a qualifier usually associated with the assumption that the true discharge is within 5% of measured discharge. Our ability to make a measurement that provides a result that is very close to the ‘true’ value is a function of many factors including: training and experience; evaluation of conditions; verification of assumptions; selection of method; selection of equipment; quality and condition of measurement equipment; calibration of measurement equipment with reference to trusted reference standards; compliance with standards and protocols; sampling adequacy (spacing, extent, support); and detection and correction of errors. Our ability to distinguish between measurements that are very close to the ‘true’ value and measurements that are not close is a critical factor in deriving discharge from stage time-series. Our understanding of the uncertainty in a given rating measurement can make the difference in whether a shift is applied to a rating curve, or not. If the deviation between a measurement and a curve is greater than the ‘true’ uncertainty of the measurement then a shift is justified but how do we know what the ‘true’ uncertainty is? If a shift is applied based a measurement that is in error then the random error of the measurement is transformed into a systematic bias in the derived discharge time-series for the duration of the shift event. The preferred method of justifying shift corrections is to always conduct a check measurement – before leaving the gauging location – to verify the deviation from the base curve. The check measurement should, preferably, be done using different sample spacing and equipment from the original measurement. If the two measurements are in agreement then the deviation from the curve can be considered as a valid basis for a shift correction. However, there are often pragmatic reasons for not conducting a check measurement. Pelletier (1988) found a variety of error models for estimating the uncertainty in the measurement of discharge. One frequently referenced standard is ISO (1979). This standard is based on studies on streams in the United Kingdom using horizontal axis meters, conditions which don’t reflect the majority of use-cases in North America. Pelletier reported that all of the uncertainty values he found in the literature were developed in conditions that are seldom encountered in practice for North American stream gauging. Tim Cohn and Julie Kiang developed an error model based on interpolation of variance. The Interpolation Variance Estimator (IVE) method is not based on an assumption of ideal conditions. In principle, this method should be far superior to any of the previously published error models. A preliminary attempt to validate this method, with reference to the ISO 1979 standard, using ‘discovered’ data harvested from existing databases  (Kiang et al., 2011). However, a more rigorous approach is needed to advance the acceptance of this error model. The North American Stream Hydrographers (NASH) is planning a field campaign to be conducted in conjunction with the 2012 NASH symposium. The symposium will be held during the joint CWRA/CGU conference in Banff, Alberta. On Monday, June 5, 2012 TransAlta will provide up to four, specified, steady flow, releases into the Kananaskis River for the experiment. During each one of the release events, replicate measurements will be conducted on each of two sections, one providing tranquil flow conditions and the other providing turbulent flow conditions. Hydrographers from around the world are invited to come to participate in this event and evaluate their technique against other and against the TransAlta rated discharge. Further information will soon be available on the NASH website as plans for this flow regatta progress.


J.E. Kiang, T.A. Cohn, and R.R. Mason, Jr. 2011. Quantifying Uncertainty in Discharge Measurements: A New Approach Poster presented at the Canadian Water Resources Association 64th annual conference. St John’s, Newfoundland. ISO. 1979. Liquid Flow measurements in open channels – velocity area methods. International Organization for Standardization, Geneva, Switzerland. Technical Report 748. Pelletier, P.M. 1988. Uncertainties in the single determination of river discharge: a literature review. Can. J. Civ. Eng. 15, 834-850.

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