Copula-based multivariate analysis of hydro-meteorological drought

Droughts have far-reaching detrimental impacts on the environment, society, and economy, ranging from regional to national levels. As the drought characteristics are interrelated, multivariate analysis of those is necessary to understand the actual drought situation in a region. However, such studies are limited. Hence, this study aimed to develop a framework to investigate the meteorological and hydrological droughts using a multivariate analysis of drought characteristics in the Pennar River basin (a semi-arid region) of India, dominated by agricultural activity. Long-term observations (1980-2015) of precipitation, temperature, and streamflow were used to calculate the Standardized Precipitation Evapotranspiration Index (SPEI) and Streamflow Drought Index (SDI) at a 3-month timescale. Based on these indices, drought duration, severity, and peak were abstracted using the Run Theory. The best-fit marginal distribution was determined for every drought characteristic to establish the bivariate joint probability distribution (the copula function). Based on the best-fit copula function, the joint probabilities and the joint return periods were estimated. Results revealed that, for meteorological drought, Frank Copula and Survival Clayton copula were the best-fit copula function for the joint risk of drought duration and severity and the combination of drought duration and peak as well as drought severity and peak, respectively. The joint return period of a drought event with characteristics above the 25(th) percentile of the same varies between 1 and 2 years, whereas it spans between 1 and 45 years for the 50(th) percentile. This analysis will provide vital information for water management and planning in a region to mitigate droughts.