A duration-augmented binary Markov chain for rainfall occurrence with long dry spells

2026-05-19

AI Summary

Traditional finite-order Markov chains struggle to capture persistent drought events in climate due to their sub-exponential decay characteristics. This work proposes a duration-augmented binary Markov chain model that integrates alternating renewal process theory and employs state-adapted extended generalized Pareto distributions to flexibly parameterize dry and wet spell durations, effectively capturing tail behavior across diverse climates. The framework naturally extends to multi-state or other binary sequences and demonstrates marked superiority over standard Markov models in validation across approximately 200 sites in southern Europe, particularly excelling in modeling precipitation persistence and high-quantile extrapolation.

Abstract

Simulating realistic wet and dry spells is central in weather generators and climate-impact studies. While finite-order Markov chains are standard, they often fail to reproduce persistent dry conditions due to their inherent subexponential decay. We model rainfall occurrence by introducing a duration-augmented binary Markov chain. We establish a link with alternating renewal chains, enabling flexible parametric modelling of wet and dry spell duration distribution. We model those using two regime-adapted specifications from the general class of extended Generalized Pareto Distributions, yielding flexible tail behaviour across various climates. We use estimation methods adapted to each specification. Our model is applied to around 200 stations in the South of Europe spanning diverse Mediterranean and continental climates. We compare this framework to standard Markov models in characterising persistence and high-quantile extrapolation. The approach is generic, extending naturally to multi-state settings or other binary sequence applications in environmental statistics.

Problem

• rainfall occurrence
• dry spells
• Markov chain
• persistence
• weather generators

Innovation

• duration-augmented Markov chain
• alternating renewal process
• extended Generalized Pareto Distribution
• dry spell persistence
• weather generator