Nonlinear Dynamics and Chaos with Applications to Hydrodynamics and Hydrological Modelling

The theory of nonlinear dynamics and chaos, and the extent to which recent improvements in the understanding of inherently nonlinear natural processes present challenges to the use of mathematical models in the analysis of water and environmental systems, are elaborated in this work.

A hydroinformatics system represents an electronic knowledge encapsulator that models part of the real world and can be used for the simulation and analysis of physical, chemical and biological processes in water systems, in order to achieve a better management of the aquatic environment.  Thus, modelling is at the heart of hydroinformatics.  The theory of nonlinear dynamics and chaos, and the extent to which recent improvements in the understanding of inherently nonlinear natural processes present challenges to the use of mathematical models in the analysis of water and environmental systems, are elaborated in this work.  In particular, it demonstrates that the deterministic chaos present in many nonlinear systems can impose fundamental limitations on our ability to predict behaviour, even when well-defined mathematical models exist.  On the other hand, methodologies and tools from the theory of nonlinear dynamics and chaos can provide means for a better accuracy of short-term predictions as demonstrated through the practical applications in this work.