Abstract:
Conventionally the process of rainfall is considered as a stochastic process and the last century witnessed many developments, however recently many rainfall series are proved to be a chaotic series. Out of various chaotic methods available to analyse time series data, the most commonly employed method, correlation dimension method is used in the present study to carry out the behavioral study of catchment rainfall process. The daily average rainfall observed over a period of 49 years (1961-2009) from the catchment area of Koyna reservoir in Maharashtra, India, has been taken up to study its behaviour. Daily rainfall from nine rain gage stations is averaged in order to obtain the above mentioned daily average rainfall. From the detailed non-linear dynamic analysis using correlation dimension method, it is found that the average rainfall of Koyna region is showing a chaotic behaviour. The effect of radius 'r' and its steps in the Heaviside function for plotting log r versus log Cr graph, the effect of scaling region in determining correlation exponent from the above plot and the effect of longer length of zeros in time series are analyzed in the present study. In addition to this, the chaotic behaviour of rainfall for various time steps (daily, weekly, monthly and seasonal) is also analyzed. It is found that the selection of radius 'r' and its steps is important in Heaviside function as there will be initial disturbances for smaller 'r' which is difficult to account while determining the correlation exponent whereas higher 'r' leads to the log Cr values close to zero making it impossible to estimate the slope of log r versus log Cr graph for determining correlation exponent. Nevertheless, the selection of scaling region is very crucial in determining the correlation exponent which subsequently determines the behaviour of the system as chaotic or not. Wrong selection of scaling region results in misinterpretation of results. In the present study, the correlation exponent value is saturating in case of daily full year rainfall, weekly rainfall and 10 daily rainfall indicating its chaotic behaviour whereas the correlation exponent value go on increasing with embedding dimension but not as in case of a stochastic series for daily monsoon rainfall, monthly rainfall and seasonal rainfall. The saturated value of correlation exponent is in between zero and one indicating correlation dimension of the three series (daily full year, weekly and 10 daily) as one.