AbstractMost models of environmental systems can be expected to suffer, to a varying extent, from a lack of identifiability. Overparameterization seems both intrinsic and an intractable problem. As a result, interpretation of past observed behaviour through a model is ambiguous, and this will have obvious implications for any predictions of future behaviour. There has been much study of this issue of uncertainty in environmental modelling, yet very limited investigation of its consequences in the use of larger‐scale models. The paper examines some of these consequences for a model of the carbon and phosphorus cycles in Lake Ontario having 24 state variables and thirteen parameters. Filtering theory is used to provide both the conceptual framework for the analysis and a specific, recursive algorithm for the propagation of a variance‐covariance matrix of state prediction errors. Special attention is given to examining the ambiguities that may arise in the making of predictions, and the possibility of generating contradictory statements about future behaviour is introduced. It is found that with this relatively large model the propagation of prediction error variances is insensitive to the degree of correlation among the parameter‐estimation errors and to changes of the nominal estimated values of small subsets of param