A GENERAL-METHOD TO DEFINE CONFIDENCE-LIMITS FOR MODEL PREDICTIONS BASED ON VALIDATIONS

An algorithm has been derived to calculate 95% confidence limits for v alues predicted by, e.g., ecosystem models. The approach uses a valida tion procedure involving: regression of values predicted by the model against independent empirical data, not uncertainty analysis using Mon te Carlo simulations. The algorithm is: CI/R = (3.17/(n - 2) + 0.52)( 1 - r(2))(0.5) , where CI is the 95% confidence interval for the predi cted 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 - minim um y)/maximum y], n is the number of independent validations (n must b e greater than or equal to 3) and r(2) is the coefficient of determina tion from these validations. The practical use of the algorithm is exe mplified by a simple lake model. The confidence interval for absolute (untransformed) data is CI = MoMax CI/R, where MoMax = the maximum va lue predicted by the model for a given model variable (e.g., the conta minant 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 like ly that analytical solutions to this problem exist, although it is bey ond the scope of this paper to address that issue. The algorithm may b e used for both dynamic and statistical models where modelled values a re compared to empirical data.