A novel multivariate vine-copula-based drought index with application to high-elevation catchments

Drought is a complex, slowly evolving hazard governed by multiple interacting hydro-climatic factors, making it difficult to monitor, characterize, and predict. Conventional single-variable indices fail to capture the nonlinear, asymmetric dependence between precipitation and temperature-a limitation that is particularly critical in data-scarce, high-mountain catchments, where incomplete drought characterization undermines the reliability of early-warning systems. To address this, we propose a novel vine-copula-based Multivariate Drought Index (VMDI) that integrates the Standardized Precipitation Index (SPI), the Standardized Precipitation Evapotranspiration Index (SPEI), and the Standardized Precipitation Temperature Index (SPTI) within a flexible, station-adaptive dependence-modeling framework. VMDI's key novelty lies in its station-adaptive canonical vine (C-vine) copula structure in which each index is first transformed into uniform pseudo-observations via rank-based empirical CDFs. Dependence is then decomposed into unconditional (Tree 1) and conditional (Tree 2) pair-copulas with SPTI as the root variable, capturing both direct interactions and joint behavior conditioned on SPTI. Copula families are selected locally via information criteria, and Kendall's $\tau$ values derived from the fitted vine structure yield physically consistent, station-specific index weights. Validated across six stations in the Upper Indus Basin (UIB), VMDI substantially outperforms benchmark indices for precipitation-driven drought signals, achieving agreement improvements of 15-30%, MAE reductions exceeding 50%, skill-score gains of 30-40%, F1-score improvements of 33-37%, and lower-tail dependence coefficients above 0.70, while maintaining low conditional entropy (CE $<0.99$ ). For evapotranspiration-related drought conditions, JSDI outperforms VMDI relative to SPEI by about 27-38%, with the greatest improvements observed at the glacier-influenced stations of Bunji and Gilgit. Overall, VMDI and JSDI offer a complementary and operationally robust framework for comprehensive drought monitoring across complex mountain catchments.