•A non-stationary meteorological drought index is developed using large-scale climate indices.•A copula-based bivariate analysis of drought properties is carried out.•Reliability-Resilience-Vulnerability of the non-stationary drought index is evaluated. The most of the available drought indices do not incorporate the environmental changes in the present scenario of climate change. In an attempt to encompass the climate variability in the computation of meteorological drought, a non-stationary gamma distribution with climate indices in its location parameter as a covariate is proposed. The performance of the non-stationary drought is evaluated based on the statistical performance as compared to the stationary drought. Focusing on two Himalayan states in India, the meteorological drought events are described and assessed based on the stationary and non-stationary drought index. Moreover, the bivariate analysis of different drought properties is carried out and compared with the univariate analysis. The management indices such as reliability, resilience, and vulnerability are also computed based on the developed drought index. The results in the study indicate that in most of the cases the non-stationary drought index is capable of capturing the drought characteristics over the study areas. The variability in the probability density of different drought properties is observed under 12-month drought scale in most of the cases. During bivariate analysis, a compare difference is noticed between secondary and primary return periods. Moreover, higher reliability and resilience is noticed during 12-month scale drought period. The newly developed drought index and the copula-based analysis of drought properties provide a new concept for robust and effective management practices in the changing environment.