• meteorological drought;
  • SPI;
  • trend detection;
  • copula;
  • frequency analysis


This article presents evaluation of trends and multivariate frequency analysis of droughts in three meteorological subdivisions of western India, namely, western Rajasthan, Saurashtra and Kutch and Marathwada regions. These regions are frequently affected by droughts and there is an urgent need for effective planning and management of droughts. Meteorological drought is modelled using Standardized Precipitation Index (SPI) at a time scale of 6 months over 110 years during 1896–2005. Trends in SPI time series are investigated by using nonparametric Mann–Kendall trend test for different time windows: entire study period of 1896–2005 and then splitting into three time windows of 1896–1931, 1932–1966 and 1967–2005. For total study period, the long-term trend in SPI time series is found to be in an upward direction for the three regions. However, statistically significant downward trend is observed during 1932–1966 for western Rajasthan region, and Saurashtra and Kutch region in the month of June, indicating increase in number of drought occurrences during this period. Further, drought is a multivariate natural calamity characterizing severity, duration and peak; hence, probabilistic assessment of drought characteristics is investigated using copula method. The joint distribution of drought properties is modelled using three fully nested forms of Archimedean copulas: Clayton, Gumbel–Hougaard and Frank and one elliptical class of Student's t copula. On performing various statistical tests as well as upper tail dependence test it is found that Student's t copula better represents trivariate drought properties when compared with other copula families. The joint distribution obtained from the copula is utilized for computation of conditional probabilities and joint return periods. The importance of trivariate frequency analysis of drought is elucidated over univariate and bivariate frequency analysis. Overall, the results of the study could provide valuable insight towards regional drought risk management under changing climate.