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.

翻译：在天气生成器与气候影响研究中，模拟逼真的干湿期至关重要。尽管有限阶马尔可夫链是标准方法，但由于其固有的次指数衰减特性，常难以再现持续干旱条件。我们通过引入持续时间增强的二元马尔可夫链来模拟降雨发生事件。我们建立了该模型与交替更新链之间的联系，从而能够对干湿期持续时间分布进行灵活的参数化建模。基于广义帕累托分布的一般类别，我们采用两种适应不同状态的规格对持续时间建模，从而在不同气候条件下获得灵活的尾部行为。我们针对每种规格采用了相应的估计方法。该模型应用于南欧约200个覆盖地中海与大陆性气候的站点。我们将其与标准马尔可夫模型在持续性描述以及高分位数外推能力方面进行比较。该方法具有普适性，可自然扩展至多状态设定或环境统计中其他二元序列的应用场景。