Nonlinear dynamics and chaos in hydrologic systems: latest developments and a look forward

Abstract

During the last two decades or so, studies on the applications of the concepts of nonlinear dynamics and chaos to hydrologic systems and processes have been on the rise. Earlier studies on this topic focused mainly on the investigation and prediction of chaos in rainfall and river flow, and further advances were made during the subsequent years through applications of the concepts to other problems (e.g. data disaggregation, missing data estimation, and reconstruction of system equations) and other processes (e.g. rainfall-runoff and sediment transport). The outcomes of these studies are certainly encouraging, especially considering the exploratory stage of the concepts in hydrologic sciences. This paper discusses some of the latest developments on the applications of these concepts to hydrologic systems and the challenges that lie ahead on the way to further progress. As for their applications, studies in the important areas of scaling, groundwater contamination, parameter estimation and optimization, and catchment classification are reviewed and the inroads made thus far are reported. In regards to the challenges that lie ahead, particular focus is given to improving our understanding of these largely less-understood concepts and also finding ways to integrate these concepts with the others. With the recognition that none of the existing one-sided 'extremeview' modeling approaches is capable of solving the hydrologic problems that we are faced with, the need for finding a balanced 'middle-ground' approach that can integrate different methods is stressed. To this end, the viability of bringing together the stochastic concepts and the deterministic concepts as a starting point is also highlighted.

Advancing catchment hydrology to deal with predictions under change

“…Taking the perspective of systems theory, hydrology deals with an overwhelmingly complex, non-linear coupled system, with feedbacks that operate at multiple spatiotemporal scales (Kumar, 2007;Sivakumar, 2009). The fact that aspects of the hydrological system have been successfully dealt with in greatly simplified ways (through isolated treatment of sub-systems and linearized approximation of dynamics), while neglecting many of the feedbacks, is made possible mainly by the fact that long-term co-evolution * of the various system components (morphology, vegetation, river networks, etc.…”

Encoding hydrologic information via a fractal geometric approach and its extensions

“…Sivakumar et al 2007), which may lead to an increased understanding of hydrologic and climatic regimes and the interrelation between rainfall and other relevant climatic variables. Finally, as the analysis of derived distributions leads to the identification of 'chaotic' and also 'random' dynamics for suitable regions in the FMFP parameter space (Puente et al 2002) and as one may perhaps study the dynamics of rainfall via the successive FMFP parameters corresponding to successive sets, the present results also suggest that the general framework explained herein may indeed serve as a sensible 'middle-ground' approach to hydrologic modeling, especially in tandem with a chaotic dynamic framework [see also Sivakumar (2004Sivakumar ( , 2009) for some details], one not requiring stochastic partial differential equations but rather geometric trends.…”

Hydropsychology: the human side of water research

“…They have also found their applications both in water science (e.g. Sivakumar 2000Sivakumar , 2009) and in psychology (e.g. Vallacher and Nowak 1994, Abraham and Gilgen 1995, Heath 2000, Guastello et al 2009).…”