Integrating Hidden Markov and Multinomial models for hydrological drought prediction under nonstationarity

Understanding the drivers of drought variability is crucial for developing effective adaptation and management strategies. This study develops a two-step modelling approach to characterize and predict hydrological droughts in a nonstationary context. First, a multivariate Hidden Markov Model (HMM) is used to classify low-water level time series into Dry, Normal, and Wet years, identifying Dry years as hydrological droughts. Second, a Multinomial Logistic Regression model (MLR) is proposed to predict low-water level class transitions, incorporating external variables into the transition matrix estimates. Precipitation thresholds for annual minima are also derived, with uncertainties and sensitivities assessed via bootstrap resampling. Our framework was successfully applied to the Paraguay River basin (PRB), where long-term changes in hydrological variables are frequent. The HMM transition matrix reveals a long persistence of years in each water level class and an inhomogeneity between two periods (1901–1960 and 1961–2024). The second period exhibits more extended runs of wet, dry, and non-dry years, suggesting a change in the driving dynamics. A multi-annual hydrological drought lasting for 13 years (1961–1973) was identified, followed by a stretch of 46 years (1974–2019) with no droughts in the study area. Our simulations indicate that the 46-year period with no drought had only a 4 % probability of occurrence. Precipitation is the primary predictor of regime shifts, but the class transition probabilities and precipitation thresholds are non-homogeneous and conditional on the current low-water level regime. We identify precipitation thresholds for initiating transitions between Dry, Wet and Normal years, conditioned on the current water levels: in a normal year, precipitation below 1040 mm triggers a hydrological drought, while in a drought year, precipitation above 1180 mm triggers a return to normal conditions. The research advances nonstationary extreme event analysis by proposing an efficient new approach to estimate inhomogeneity in hydrological drought occurrence; identify long persistence of hydrological drought episodes and their associated probabilities; define precipitation thresholds; and reveal the importance of coupled drivers of low water level shifts.