Modern Nonlinear Time Series Methods

Advances in computational power, scientific concepts, and data measurements have led to the development of numerous nonlinear methods to study complex systems normally encountered in various scientific fields. These nonlinear methods often have very different conceptual bases and levels of sophistication and have been found suitable for studying many different types of systems and associated problems. Their relevance to hydrologic systems and ability to model and predict the salient characteristics of hydrologic systems have led to their extensive applications in hydrology over the past three decades or so. This chapter presents an overview of some of the very popular nonlinear methods that have found widespread applications in hydrology. The methods include: nonlinear stochastic methods, data-based mechanistic models, artificial neural networks, support vector machines, wavelets, evolutionary computing, fuzzy logic, entropy-based techniques, and chaos theory. For each method, the presentation includes a description of the conceptual basis and examples of applications in hydrology.