A general method to define confidence limits for model predictions based on validations

An algorithm has been derived to calculate 95% confidence limits for values predicted by, e.g., ecosystem models. The approach uses a validation procedure involving regression of values predicted by the model against independent empirical data, not uncertainty analysis using Monte Carlo simulations. The algorithm is: CIR = (3.17(n − 2) + 0.52)∗(1 − r2)0.5, where CI is the 95% confidence interval for the predicted y, expressed as a fraction of the maximum y-value, transformed as necessary to yield the most normal frequency distributions for the y- and x-data, R is the range of the relative values [(maximum y − minimum y)maximum y], n is the number of independent validations (n must be ≥ 3) and r2 is the coefficient of determination from these validations. The practical use of the algorithm is exemplified by a simple lake model. The confidence interval for absolute (untransformed) data is CI = MoMax∗CIR, where MoMax = the maximum value predicted by the model for a given model variable (e.g., the contaminant body burden of a species of fish) in a given ecosystem (e.g., a lake). The approach is meant to be generally valid, and it seems likely that analytical solutions to this problem exist, although it is beyond the scope of this paper to address that issue. The algorithm may be used for both dynamic and statistical models where modelled values are compared to empirical data.