IV-2-A Chaotic Analysis of Koyna Reservoir Catchment Rainfall Data.

Abstract

The significance of treating rainfall as a chaotic system instead of a stochastic system is gaining interest in recent past studies and helps to understand the dynamic behaviour of the processes in a better way. Out of various chaotic methods available to analyse time series data, correlation dimension method is employed in the present study. Correlation dimension method is reported as a better method compared to other methods, especially when the data set is large and noisy. The scaling region in the Heaviside step function has to be identified to find the correlation exponent. The slope of the scaling region gives the correlation exponent value for various embedding dimension (m). Based upon the relationship, the behaviour of the system can be classified as chaotic (increasing and then saturating correlation exponent), stochastic (increasing correlation exponent with increase in embedding dimension) or deterministic (constant correlation exponent). The average daily rainfall observed at Koyna reservoir catchment area for a period of 49 years (1961-2009) in Maharashtra, India, has been taken up as a case study. From the detailed non-linear dynamic analysis using correlation dimension method it is found that the Koyna Reservoir catchment rainfall is showing a chaotic behaviour. The nearest whole number value of the saturation value of the correlation exponent is one, indicating that the correlation dimension for the daily average rainfall is one. This also indicates that the behaviour is low chaotic and high deterministic in nature.