Copula function with Variational Bayesian Monte Carlo for unveiling uncertainty impacts on meteorological and agricultural drought propagation

Agricultural drought (AD) is disastrous to natural and socioeconomic systems, and the propagation of meteorological drought (MD) plays an essential role in the occurrence of AD. However, how uncertainty affects the mechanism of propagation from MD to AD remains unclear. In this study, a novel method called C-VBMC is developed through coupling copula function with Variational Bayesian Monte Carlo (VBMC). The developed C-VBMC is then applied to the Aral Sea Basin to demonstrate its feasibility and capability. Results indicate that the method could effectively quantify the drought propagation probability under the impact of uncertainty. Several findings can be summarized: (1) compared with the low elevation areas, the propagation time and relationship between MD and AD tend to be longer and weaker in spring and winter at mid-high elevation areas; (2) drought propagation characteristics are significantly affected by seasonality, altitude, potential evapotranspiration, precipitation and soil moisture; (3) the posterior distribution of copula parameter by VBMC is similar with Markov chain Monte Carlo (MCMC), and VBMC only takes about 50% and 5% of the computation time required by MCMC for univariate and bivariate copula functions, the results highlight the superiority and flexibility of VBMC for large datasets; (4) the probability of AD occurrence and the uncertainty range are easily affected by same and more severe level MD; (5) the propagation probabilities tend to be underestimated without uncertainty impact, and the uncertainty range is lower than 0.05 for most grids. This study is helpful for drought warning management and disaster prevention systems.