Data-based mechanistic modelling, generalised sensitivity and dominant mode analysis

Since the inherent uncertainty associated with most environmental and climatic systems is often acknowledged, it is surprising that most mathematical models of such systems are large, complex and completely deterministic in nature. In this situation, it seems sensible to consider alternative modelling methodologies which overtly acknowledge the often poorly defined nature of such systems and attempt to find simpler, stochastic descriptions which are more appropriate to the often limited data and information base. This paper considers one such approach, Data-based Mechanistic (DBM) modelling, and demonstrates how it can be useful not only for the modelling of environmental and other systems directly from time series data, but also as an approach to the evaluation and simplification of large deterministic simulation models. To achieve these objectives, the DBM approach exploits various methodological tools, including advanced methods of statistical identification and estimation; a particular form of Generalised Sensitivity Analysis based on Monte Carlo Simulation; and Dominant Mode Analysis, the latter involving a new statistical approach to combined model linearisation and order reduction. These various techniques are outlined in the paper and they are applied to the stochastic modelling of water pollution in rivers and the evaluation of nonlinear global carbon cycle models.