Integrated Drought Index based on Vine Copula Modelling

Abstract

AbstractAs a natural hazard, drought is a complex multivariate phenomenon that does not depend on only one hydrometeorological variable, as well as, considering a particular kind of drought may not be effective for drought management. Considering this, many multivariate drought indices have been developed based on linearity assumptions or conventional copulas assuming symmetric relationships among univariate drought indices. In this study, D‐vine copula was applied to construct a four‐dimensional index, named as Integrated Drought Index (IDI), by combining four univariate drought indices (Standardized Precipitation Index [SPI], Reconnaissance Drought Index [RDI], Standardized Soil moisture Index [SSI] and Standardized stream flow Drought Index [SDI]) to better reflect many hydrometeorological variables (precipitation, evapotranspiration, soil moisture and stream flow) and different kinds of drought (meteorological, agricultural and hydrological) simultaneously. Vine copula was used to solve nonlinear and asymmetric relationships among drought indices due to its flexibility over the free selection of copula(s) in each step of hierarchical structure in high dimensional modelling. The IDI was constructed for 1‐ and 4‐month timescales for the upper Tapti basin of the central region in India. The performance of IDI was tested with dependence measures (Pearson's correlation coefficient, Mutual Information) and evaluated against the Terrestrial Water Storage Anomaly data derived from the Gravity Recovery and Climate Experiment (GRACE) mission. Spatial analysis of drought was carried out by fuzzy c‐means (FCM) clustering algorithm with IDI. IDI based on vine copula solved the nonlinear and asymmetric relationships among different variables associated with the occurrence of droughts effectively with a reduction of uncertainty as compared to the single drought indices for different kinds of droughts. Analysis revealed spatially different drought risks in the upper and lower river basins. In general, the vine copula addresses nonlinear and asymmetric relationships that exist between the variables associated with natural hazards like drought.