Complexity in hydroecological modelling: A comparison of stepwise selection and information theory

Understanding of the hydroecological relationship is vital to maintaining the health of the river and thus its ecosystem. Stepwise selection is widely used to develop numerical models which represent these processes. Increasingly, however, there are questions over the suitability of the approach, and coupled with the increasing complexity of hydroecological modelling, there is a real need to consider alternative approaches. In this study, stepwise selection and information theory are employed to develop models which represent two realizations of the system which recognizes increasing complexity. The two approaches are assessed in terms of model structure, modelling error, and model (statistical) uncertainty. The results appear initially inconclusive, with the information theory approach leading to a reduction in modelling error but greater uncertainty. A Monte Carlo approach, used to explore this uncertainty, revealed modelling errors to be only slightly more distributed for the information theory approach. Consideration of the philosophical underpinnings of the two approaches provides greater clarity. Statistical uncertainty, as measured by information theory, will always be greater due to its consideration of two sources, parameter and model selection. Consequently, by encompassing greater information, the measure of statistical uncertainty is more realistic, making an information theory approach more reflective of the complexity in real-world applications.