Multifractal characterization of meteorological drought in India using detrended fluctuation analysis

Abstract

This study presents Multifractal Detrended Fluctuation Analysis (MF‐DFA) to describe the multifractality of Standardized Precipitation Index (SPI) series from 30 meteorological subdivisions of India estimated at different aggregation time scales (3, 6 and 12 months) based on long term monthly rainfall datasets of 1871‐2016 period. The plots of fluctuation function and generalized Hurst exponents confirmed that multifractality is evident in most of the SPI series, however it is found that its strength and persistency differ with time scale and space. The Hurst exponents of long term (SPI‐12) and medium term (SPI‐6) drought series of all subdivisions showed long term persistence irrespective of the climatic conditions of the region, while the short‐term droughts (SPI‐3) of six subdivisions displayed short term persistence. Further, the analysis by partitioning the data to four time spells: 1871‐1905, 1906‐40, 1941‐75 and 1976‐2016 showed that the persistency of long and medium term drought is rather permanent. The analysis on changes in multifractal properties with respect to the climatic shift of 1976/77 period showed that there is a clear increase in multifractal properties of all types of drought series in the recent past (post 1976 period). This study also finds that the Hurst exponents and degree of multifractality of all types of droughts increases with increase in aggregation time scales. The multifractality of all the long‐term drought series (SPI‐12) and most of the SPI‐6 series are found to be due to correlation properties, while that of SPI‐3 is because of joint effect of correlation properties and the broadness of probability distribution.