Statistical Evaluation of Mechanistic Water-Quality Models

Current practice for the verification of water-quality simulation models is to use a combination of modeler judgment and graphical analysis to assess the adequacy of a model. Statistical testing of goodness-of-fit is sometimes undertaken, but usually with a null hypothesis that does not allow distinction between acceptable fit and highly variable data. In this paper, statistical methods are proposed to augment, but not replace, this conventional approach with a quantitative expression of goodness-of-fit. Model verification is expressed as a problem in hypothesis testing that may be conducted using a variety of statistical methods. Guidance is provided on the appropriate structure of the null hypothesis so that good model fit is not confounded with highly variable predictions and observations. In addition, consequences and corrective measures associated with assumption violations are examined. The t-test, the Wilcoxon test, regression analysis, and the Kolmogorov-Smirnov test are extensively discussed, and applications of each are presented for the verification of a mechanistic water-quality model.