A Study on Detrended Fluctuation Analysis and Lyapunov Exponent of Northeast Rainfall of Tamil Nadu

In this paper, fractal dimensional analysis is used to investigate the Tamil Nadu rainfall dynamics. Here, the time series data of Tamil Nadu rainfall (annual, south west and northeast) has been analyzed using Detrended fluctuation analysis (DFA). For estimating the 110 years rainfall data, the scaling exponent analysis is used. The result shows a varying degree of persistence over shorter and longer time scales corresponding to distinct values of the DFA. Our studies suggest that DFA of the annual rainfall of Tamil Nadu is β=1 which indicates the 1/f noise, typical of systems in a self organized criticality (SOC), the southwest rainfall β=0.725 i.e., the time series is long-range correlated and for the northeast rainfall β=0.5 the time series corresponds to Gaussian white noise. Further, the Lyapunov exponent for the northeast rainfall of Tamil Nadu is analyzed. This paper estimates the various parameters like lyapunov exponent, maximum lyapunov characteristic exponent, lyapunov time for the northeast rainfall of Tamil Nadu. It is found that, the lyapunov exponent λ is positive, which implies that the orbit is unstable and chaotic, the maximum value of lyapunov exponent is 4.09 and this result verifies the DFA calculation. Therefore, no trend in amplitude can be discerned from the time series and hence, the northeast monsoon rainfall is unpredictable and chaotic.