Stage measurement uncertainty

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Typical quantitative results of discharge uncertainty studies: Stage Uncertainty.

This table originated from McMillan et al. (2012) but is now open to the community to add to and use as a resource.

SD = standard deviation

Uncertainty Type Estimation Method Magnitude Location Reference
Stage uncertainty Comparison with neighbouring stations SD of 25 mm Netherlands gauging network Van der Made (1982)
Effect of unstable bed Expert knowledge; uncertainty for individual measurement ±10 % Estimate for locations with shifting sand or moving dunes Sauer & Meyer (1992)
Instrument precision Review of previous studies; uncertainty for individual measurement ±3-10.8 mm or ±0.1-2 % Quoted in Harmel et al. (2006)
Instrument precision Expert knowledge Range ±10 mm; local oscillations of water surface can add additional uncertainty of ±20 mm Typical example of natural rivers Dottori et al. (2009)
Instrument precision: Float in stilling well 6 mm Quoted in Herschy (1998): Ackers et al. (1978)
Instrument precision: Pressure transducer 1.4-40 mm Herschy (1998)
Stage uncertainty Expert knowledge of typical uncertainties 4 mm (high accuracy) to 15 mm (low accuracy) Norwegian Water Resources & Energy Directorate Petersen-Øverleir & Reitan (2005)
Stage uncertainty Observed fluctuation 2-5 mm Rowden Experimental Research Platform (1 ha fields), Devon, UK. 250 x 37 cm weir box, stainless steel 45° V-Notch, float (Model 6541, Unidata), stilling well, ave. annual precipitation 1055 mm. Krueger et al. (2010)
Instrument precision Manufacturer cited random uncertainty 2.5 mm (Trutrack, Model PLUT-HR Water level recorder) Hillslope (172 m2), WS10 catchment, HJA Experimental Forest, Oregon, USA Graham et al. (2010)
0.3 mm (Model 2 Stevens Instruments Position Analog Transmitter) WS10 catchment (10.2 ha), HJA Experimental Forest, Oregon, USA. Mediterranean climate, rainfall 2200 mm yr-1, slopes 30-45 °.
Stage uncertainty Nominal uncertainty 3 mm Hamilton & Moore (2012)


Ackers, P., 1978. Weirs and flumes for flow measurement. Wiley, Chichester.

Dottori, F., Martina, M.L.V., Todini, E., 2009. A dynamic rating curve approach to indirect discharge measurement. Hydrology and Earth System Sciences, 13(6): 847-863.

Graham, C.B., van Verseveld, W., Barnard, H.R., McDonnell, J.J., 2010. Estimating the deep seepage component of the hillslope and catchment water balance within a measurement uncertainty framework. Hydrological Processes, 24(25): 3878–3893.

Hamilton, A.S., Moore, R.D., 2012. Quantifying Uncertainty in Streamflow Records. Canadian Water Resources Journal, 37(1): 3-21.

Harmel, R.D., Cooper, R.J., Slade, R.M., Haney, R.L., Arnold, J.G., 2006. Cumulative uncertainty in measured streamflow and water quality data for small watersheds. Transactions of the ASABE, 49(3): 689-701.

Herschy, R.W., 1998. Hydrometry : Principles and practices. Wiley, Chichester.

Krueger, T., Freer, J., Quinton, J.N., Macleod, C.J.A., Bilotta, G.S., Brazier, R.E., Butler, P., Haygarth, P.M., 2010. Ensemble evaluation of hydrological model hypotheses. Water Resources Research, 46: W07516.

McMillan, H., Krueger, T., Freer, J., 2012. Benchmarking observational uncertainties for hydrology: Rainfall, river discharge and water quality. Hydrological Processes 26(26): 4078–4111

Petersen-Øverleir, A., Reitan, T., 2005. Uncertainty in flood discharges from urban and small rural catchments due to inaccurate head measurement. Nordic Hydrology, 36(3): 245-257.

Sauer, V.B., Meyer, R.W., 1992. Determination of error in individual discharge measurements, U.S. Geological Survey Open-File Report 92–144.

van der Made, J.E., 1982. Determination of the accuracy of water level observations, Proceedings of the Exeter Symposium. IAHS Publications 134, pp. 172-184.