Chaos based analytical techniques for daily extreme hydrological observations

The existence of outliers in data sets affects the decision-making process related to design, operation, and management of water resources. Insufficient information on outliers limits our understanding and predictive ability of such extreme hydrologic phenomena. Hydrologic systems are complex and dynamic in nature where current state and future evolutions depend on numerous physical variables and their interactions. Such systems can be represented in a simplified form through chaotic approach. Chaotic approach can determine the tevel, of complexity of a system that provides the required information and parameters for subsequent predictive analyses. This research focuses on the application of chaotic analytical techniques to daily hydrologic series comprising of outliers. Different techniques and concepts of chaotic theory are adopted to enhance our understanding of the phenomena of outliers. Employing the streamflow data of the Saugeen River in Ontario, Canada, this paper illustrates the use of the autocorrelation functions, mutual information, power spectrum analysis, phase space reconstruction, correlation dimension, surrogate tests, and Hurst coefficients for the analysis of chaotic systems. Based on the results of analyses, one can arrive at the following conclusions: (1) The analyzed series exhibited random-like fluctuations. However, by rejecting the hypothesis of a random process, the analyzed series were found to be non-random. (2) The existence of outliers was found to increase the complexity of the analyzed series. High embedding dimensionalities obtained from the correlation analysis of the analyzed series support our conclusion. (3) The differentiation of a highly complex system from a random process, and the impact of outliers on the complexity of a system were quantitatively as well as visually presented from a chaotic perspective. (c) 2007 Elsevier B.V. All rights reserved.