Chaotic Analysis of Reservoir Inflow Series: A Case Study on Koyna Reservoir Inflow

Abstract

The significance of treating the reservoir inflow as a chaotic system instead of a stochastic system is gaining interest in the recent past. Out of various chaotic methods available to analyse time series data, correlation dimension method, the most commonly employed method in hydrology is used in the present study. Apart from identifying the behaviour of the series, correlation dimension method indicates the number of dimensions required to predict the future value in the time series. Correlation dimension of a time series is estimated using Heaviside step function through Grassberger–Procaccia algorithm. In order to prove the reliability of Grassberger–Procaccia algorithm, initially a deterministic series and two types of random number series are analyzed to identify their behaviour as well as to determine the correlation dimension. The daily reservoir inflow observed at Koyna reservoir for a period of 49 years (1961–2009) in Maharashtra, India, has been taken up to study its behaviour. From the detailed non-linear dynamic analysis using correlation dimension method it is found that the Koyna reservoir inflow is showing a low chaotic behaviour. The minimum correlation dimension for the daily Koyna reservoir inflow is around one and maximum correlation dimension is around four. It is also evident that only short term prediction is reasonable in this reservoir. This study proves the strength of Grassberger–Procaccia algorithm in classifying the behaviour of time series.