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Several drought indices have been developed based on various processes (e.g., precipitation, soil moisture, vegetation health) that respond differently to modes of climate variability, shadowing their relatability to teleconnections, which in turn, limits drought forecasting. In this study, we advanced the multivariate analysis of droughts by using long-term Terrestrial Water Storage estimates, soil moisture and precipitation data along with normalized difference vegetation index. To this end, we employed a Vine copula approach using Archimedean and Elliptical copula families to generate two novel multivariate drought indices called Combined Standardized Drought Index (CSDI), based on agricultural, meteorological, hydrological and ecological univariate indices (i.e., the Eco-meteo-hydrologic index and the Agro-meteo-hydrologic index) for 33 major river basins across the globe between 1982 and 2015. To overcome the challenges associated with vine copula building blocks, we exhausted the possible choices of vine trees and selected the superior model based on a variety of performance metrics. CSDIs showed an integrated representation of univariate drought indices and revealed a more comprehensive and improved picture of intensity, duration and frequency of droughts. Our composite analysis showed that El Niño and La Niña have a significant impact on the regional drought occurrences across the globe, with highest impacts observed for fall. Results also showed that CSDIs can extract more conclusive anomalies in response to ENSO signals than univariate indices, as they better represent the ecosystem response to teleconnections.