A fuzzy-based integrated drought index (FIDI) for multivariate hydroclimatic drought assessment

Abstract Drought arises from complex interactions between meteorological forcing and hydrological response, making the integrated assessment of hydroclimatic processes challenging. This study develops a fuzzy-based integrated drought index (FIDI) using a Mamdani-type fuzzy inference system to provide a diagnostic representation of multivariate hydroclimatic drought dynamics. The framework integrates streamflow with precipitation or climatic water balance and is evaluated in two contrasting Turkish river basins (Seyhan and Çoruh), representing distinct hydroclimatic regimes. FIDI is benchmarked against the copula-based Multivariate Standardized Drought Index (MSDI) and its univariate components, the Standardized Precipitation Evapotranspiration Index (SPEI) and the Standardized Streamflow Index (SSFI). Results show that FIDI closely reproduces the temporal evolution of integrated drought conditions with strong agreement ( r > 0.90, R 2 > 0.80), accurately capturing drought onset, persistence, and recovery phases across both basins. Unlike probabilistic multivariate approaches that rely on parametric dependence modeling and extensive data records, the proposed framework provides a distribution-free, interpretable, and computationally efficient alternative. The results demonstrate that FIDI can effectively represent the joint behavior of meteorological and hydrological droughts and offer a practical tool for multivariate drought diagnostics, particularly in data-scarce environments.