Integrating Hidden Markov and Multinomial Models for Hydrological Drought Prediction under nonstationarity.

The prediction of hydrological droughts in a non-stationary context poses major challenges. Understanding the drivers of drought fluctuations is crucial for developing effective adaptation and management strategies. This study addresses this issue by developing a two-step modelling approach using a multivariate Hidden Markov Model (HMM) and a Multinomial Linear Regression model (MLR), with a bootstrap approach to assess uncertainty. Using HMM, we classify the low water level time series into Dry, Normal, and Wet years and assess the frequency of each class in the historical data. Dry years can be identified as hydrological droughts. To predict low-water level class transitions in a non-stationary context, we propose an MLR framework. With this, we estimate probabilities of low-water level class transitions by inputting 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 the 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. Simulations allowed estimates of probabilities of those persistent hydrological conditions at 21% and 4% probability, respectively. 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. Different precipitation thresholds were estimated conditioned on the current water levels: 1,040 mm for initiating a hydrological drought during a normal year and 1,180 mm to transition from a hydrological drought to normal conditions. The research advances non-stationary extreme event analysis by proposing an efficient new approach for non-stationary extreme event analysis. The approach is effective in estimating inhomogeneity in hydrological drought occurrence; identifying long persistence of hydrological drought episodes and their associated probabilities; defining precipitation thresholds that trigger drought occurrence conditioned on the current basin state; and revealing the importance of coupled drivers of low water level shifts.