Methods to quantify and identify the sources of uncertainty for river basin water quality models

Worldwide, the application of river basin water quality models is increasing, often imposed by law. It is, thus, important to know the degree of uncertainty associated with these models and their application to a specific watershed. These uncertainties lead to errors that are revealed when model outputs are compared to observations. Such uncertainty is typically described by calculating the residuals. However, residuals should not be seen as an estimate of total uncertainty, since through the calibration process, the residuals may be reduced by over-adjustment to the data, which is typically the case for over-parameterised models. Over-adjustment during a calibration period can also lead to highly biased results when the model is applied to other periods or environmental conditions. The total model uncertainties are, therefore, assessed by four components: the sum of the squares of the residuals (SSQ), parameter uncertainties (that can be ignored when their error is much smaller than SSQ), input data uncertainties, and an additional predictive uncertainty that is expressed when the model appears to be biased when it is applied for data other than the data used for calibration. The sources are ranked according to a quantification criterion (magnitude) as well as an identification criterion that depends on the number of observations that are covered by the confidence region. This approach is illustrated with SWAT2003 simulations for flow and sediment of Honey Creek, a tributary of the Sandusky River basin (Ohio). The results show the dominance of the model uncertainty. The input data uncertainty is less important.