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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Volume 21, issue 1
Hydrol. Earth Syst. Sci., 21, 571–588, 2017
https://doi.org/10.5194/hess-21-571-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Hydrol. Earth Syst. Sci., 21, 571–588, 2017
https://doi.org/10.5194/hess-21-571-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 27 Jan 2017

Research article | 27 Jan 2017

Quantifying uncertainty on sediment loads using bootstrap confidence intervals

Johanna I. F. Slaets1, Hans-Peter Piepho2, Petra Schmitter3, Thomas Hilger1, and Georg Cadisch1 Johanna I. F. Slaets et al.
  • 1Institute of Plant Production and Agroecology in the Tropics and Subtropics, University of Hohenheim, Garbenstrasse 13, 70599 Stuttgart, Germany
  • 2Biostatistics Unit, Institute of Crop Science, University of Hohenheim, Fruwirthstrasse 23, 70599 Stuttgart, Germany
  • 3The International Water Management Institute, Nile Basin and East Africa Office, Addis Ababa, Ethiopia

Abstract. Load estimates are more informative than constituent concentrations alone, as they allow quantification of on- and off-site impacts of environmental processes concerning pollutants, nutrients and sediment, such as soil fertility loss, reservoir sedimentation and irrigation channel siltation. While statistical models used to predict constituent concentrations have been developed considerably over the last few years, measures of uncertainty on constituent loads are rarely reported. Loads are the product of two predictions, constituent concentration and discharge, integrated over a time period, which does not make it straightforward to produce a standard error or a confidence interval. In this paper, a linear mixed model is used to estimate sediment concentrations. A bootstrap method is then developed that accounts for the uncertainty in the concentration and discharge predictions, allowing temporal correlation in the constituent data, and can be used when data transformations are required. The method was tested for a small watershed in Northwest Vietnam for the period 2010–2011. The results showed that confidence intervals were asymmetric, with the highest uncertainty in the upper limit, and that a load of 6262 Mg year−1 had a 95 % confidence interval of (4331, 12 267) in 2010 and a load of 5543 Mg an interval of (3593, 8975) in 2011. Additionally, the approach demonstrated that direct estimates from the data were biased downwards compared to bootstrap median estimates. These results imply that constituent loads predicted from regression-type water quality models could frequently be underestimating sediment yields and their environmental impact.

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Determining measures of uncertainty on loads is not trivial, as a load is a product of concentration and discharge per time point, summed up over time. A bootstrap approach enables the calculation of confidence intervals on constituent loads. Ignoring the uncertainty on the discharge will typically underestimate the width of 95 % confidence intervals by around 10 %. Furthermore, confidence intervals are asymmetric, with the largest uncertainty on the upper limit.
Determining measures of uncertainty on loads is not trivial, as a load is a product of...
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