Thermodynamic Characterization of Wet and Dry Atmospheric States Using a Two-State Hidden Markov Model over the Middle Belt Region of Nigeria
I. O. Agada *
Department of Physics, Joseph Sarwuan Tarka University, Makurdi. Benue State, Nigeria.
V. Adah
Department of Statistics, Joseph Sarwuan Tarka University, Makurdi. Benue State, Nigeria.
O. Peter
Department of Statistics, Joseph Sarwuan Tarka University, Makurdi. Benue State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Tropical temperature and rainfall variability in Nigeria is driven by interactions between thermal energy, latent and sensible heat fluxes, and large-scale circulation. Hidden Markov Models (HMMs) can link observed meteorological data to underlying thermodynamic regimes, providing a probabilistic framework to understand wet and dry seasonal transitions beyond traditional statistical approaches. This study investigated the temporal and seasonal evolution of rainfall and temperature variability in the core Middle Belt states (Benue, Plateau, Niger, Kogi, Nasarawa, Kwara, and FCT) of Nigeria using a two-state Hidden Markov Model (HMM). The model identified two hidden thermodynamic regimes representing dry and wet atmospheric states based on 30 years (1991-2020) daily rainfall and temperature data obtained from National Aeronautic and Space Administration (NASA) meteorological center. The results shows that dry-state persistence was strongest in Plateau (0.979), Benue (0.956), and Kogi (0.918), while wet-state persistence was particularly high in Kogi (0.961), Benue (0.911), and Plateau (0.955) as revealed by the transition probabilities, indicating stable atmospheric conditions once a regime is established. State frequency analysis revealed spatial heterogeneity across the Middle Belt, with dry-state dominance in Kwara (80%), Niger (73%), Plateau (69%), and Benue (68%), while wet-state dominance occurred in Nasarawa (77%), the Federal Capital Territory (74%), and Kogi (69%). Seasonal analysis confirmed strong dry-state dominance during the dry season in Plateau (0.996), Niger (0.994), and Kwara (0.985), whereas Nasarawa (0.993) and FCT (0.991) maintained wet-state characteristics even during nominal dry periods, indicating sustained atmospheric moisture availability. The study concludes that there is dual climatic domination in the Middle Belt, with some states (Kwara, Niger, Benue and Plateau) having a dry climate and others (Kogi, Nasarawa, FCT) a wet climate. The two-state HMM effectively captures these hidden atmospheric regimes and provides a physically meaningful framework for understanding seasonal climate variability, agricultural planning, risk flood assessment and improving climate predictability in central Nigeria.
Keywords: Hidden Markov model, temperature, rainfall, dry thermodynamic state, wet thermodynamic state, middle belt Nigeria, transition probability