Quantifying uncertainty on sediment loads using bootstrap confidence intervals

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.