Study of the fractal nature of evapotranspiration time series from agricultural regions of Northern Karnataka

Abstract

Multifractal detrended fluctuation analysis (MFDFA) renders valuable insights pertaining to the randomness, inner regularity and long range correlations in the time series data. We applied this technique to assess the fractal behaviour and inherent correlations of the potential and reference crop evapotranspiration data collected from two regions of Karnataka, viz., Belgaum and Raichur. The annual periodic nature of the evapotranspiration data series was removed using seasonal trend decomposition method and it was seen that all the decomposed series consisted of long-term persistence. The multifractal behaviour in the evapotranspiration series at the two stations were seen owing to the strong dependency of generalised Hurst exponent H(q) on the values of q. We also tested for the reduction in the dependence of h(q) on q by shuffling the evapotranspiration time series and it is indicative of the fact that the multifractality is responsible for the correlation characteristics and also the probability density function of the evapotranspiration data series. The two regions, Belgaum and Raichur vary considerably in climatic and geomorphic conditions and this difference is evident in their corresponding evapotranspiration data as fractal properties. This is depicted by the values of the generalised Hurst exponent H(q) obtained using MFDFA technique.