Set Membership Approach to Identification and Prediction of Lake Eutrophication

Generally, ecosystems modeling is obstructed by the problem of sparse and unreliable data, and lack of knowledge about processes dominating the system. Under these circumstances, set theoretic uncertainty models are an appropriate alternative to probabilistic models. The only requirement is that the uncertainty is pointwise bounded. A newly developed set membership identification procedure is presented and demonstrated by an application to the modeling of shallow lake eutrophication. First, a set of parameter vectors is identified. Analysis of the set reveals a dominant direction spanned by four algal growth and death parameters. Second, on the basis of additional fuzzy set theoretic assumptions, a formal min-max estimation is performed to obtain information about the model validity. If the model appears to be (partially) invalid, the degree of invalidity, affecting the model prediction uncertainty, can be represented by an estimate of the model structure error in addition to the uncertainty contained in the identified set of parameter vectors.