Bellie Sivakumar is a Professor in the Department of Civil Engineering, Indian Institute of Technology Bombay, India. He received his Ph. D. degree (Civil Engineering) from the National University of Singapore in 1999. Sivakumar has 25 years of experience in research, teaching, and professional services in the water-climate domain. He is internationally recognized for his contributions to research on nonlinear dynamic, chaos, fractal, and complex network theories in the water-climate domain. He has published three books and over 270 journal articles/book chapters. He has been an Editor-in-Chief/Associate Editor/Editorial Board Member of 16 international journals, Guest Editor of 12 journal special issues, and reviewer for over 50 journals and funding agencies. Sivakumar is a recipient of many international research fellowships, including from the United States, Australia, Japan, and South Korea. He is a Fellow of AOGS and has also been recognized as one of the Top 2% of Scientists in the World.
Hydrologic systems are complex nonlinear dynamically evolving systems. They are often made up of large number of interconnected components that change both in space and in time. Unraveling the nature and degree of complexity and connectivity in hydrologic systems across different spatial and temporal scales has always been a fundamental challenge. Many scientific theories have been proposed and successfully applied to numerous hydrologic systems, processes, and problems. Among such, some recent developments in the field of complex systems science show great promise for studying the complexity, connectivity, and scale properties of hydrologic systems. Specifically, chaos theory, complex network theory, and fractal theory offer unique avenues. This Lecture provides an overview of the progress made in studying the complexity, connectivity, and scale properties of hydrologic systems using these complex systems science theories, with a look toward the future. First, the vital roles of complexity, connectivity, and scale in hydrologic systems are highlighted. Second, key concepts of chaos theory, complex network theory, and fractal theory and their relevance for studying the inherent properties of hydrologic systems are described. Third, examples of applications of these theories to different hydrologic systems, processes, and problems are presented. Fourth, some major issues related to methodology and data in the applications of these theories to real hydrologic systems and interpretations of results are discussed. Finally, potential directions for future research on complexity, connectivity, and scale properties of hydrologic systems and for their reliable modeling and forecasting are offered, with particular focus on integration of the theories for large-scale hydrologic problems.