The use of fuzzy rules for the description of elements of the hydrological cycle

Abstract Fuzzy rules form the basis of fuzzy control systems, which have been and are being used in many practical applications, especially in industrial ones in Japan and Europe. However, fuzzy control systems include feedback which can help the adjustment process, in contrast the open-loop modeling that we are presenting here. In this paper a fuzzy rule-based methodology for the description of infiltration, surface runoff and unsaturated flow is described. Fuzzy rules are derived according to the expert-specified structure using synthetical data sets. Hierarchical rule systems are derived under consideration of space-time inhomogeneities. Compared to traditional modeling fuzzy systems provide a robust tool which can handle non-linearities, without requiring a prescribed functional structure. The simple rule structure makes the models very transparent. Rule-based models are less accurate than PDE-based mathematical modeling. In the case of heterogeneous real-life problems a purely analytical modeling can often only give a false impression of accuracy. The gain in simplicity, computational speed and flexibility may compensate for the possible loss in accuracy. Furthermore the fuzzy rule-based models can easily be coupled; for example, a model for flow in porous media may be coupled with a bacteriological growth model. They are capable of combining physical laws, expert knowledge and measurement data.