Fractal Scaling Properties in Rainfall Time Series: A Case of Thiruvallur District, Tamil Nadu, India

Abstract

In the present study, the features of rainfall time series (1971–2016) in 9 meteorological regions of Thiruvallur, Tamil Nadu, India that comprises Thiruvallur, Korattur_Dam, Ponneri, Poondi, Red Hills, Sholingur, Thamaraipakkam, Thiruvottiyur and Vallur Anicut were studied. The evaluation of rainfall time series is one of the approaches for efficient hydrological structure design. Characterising and identifying patterns is one of the main objectives of time series analysis. Rainfall is a complex phenomenon, and the temporal variation of this natural phenomenon has been difficult to characterise and quantify due to its randomness. Such dynamical behaviours are present in multiple domains and it is therefore essential to have tools to model them. To solve this problem, fractal analysis based on Detrended Fluctuation Analysis (DFA) and Rescaled Range (R/S) analysis were employed. The fractal analysis produces estimates of the magnitude of detrended fluctuations at different scales (window sizes) of a time series and assesses the scaling relationship between estimates and time scales. The DFA and (R/S) gives an estimate known as Hurst exponent (H) that assumes self-similarity in the time series. The results of H exponent reveals typical behaviours shown by all the rainfall time series, Thiruvallur and Sholingur rainfall region have H exponent values within 0.5 < H < 1 which is an indication of persistent behaviour or long memory. In this case, a future data point is likely to be followed by a data point preceding it; Ponneri and Poondi have conflicting results based on the two methods, however, their H values are approximately 0.5 showing random walk behaviour in which there is no correlation between any part and a future. Thamaraipakkam, Thiruvottiyur, Vallur Anicut, Korattur Dam and Red Hills have H values less than 0.5 indicating a property called anti-persistent in which an increase will tend to be followed by a decrease or vice versa. Taking into consideration of such features in modelling, rainfall time series could be an exhaustive rainfall model. Finding appropriate models to estimate and predict future rainfalls is the core idea of this study for future research.