For hydrological applications, such as urban flood modelling, it is often important to be able to simulate sub-daily rainfall time series from stochastic models. However, modelling rainfall at this resolution poses several challenges, including a complex temporal structure including long dry periods, seasonal variation in both the occurrence and intensity of rainfall, and extreme values. We illustrate how the hidden Markov framework can be adapted to construct a compelling model for sub-daily rainfall, which is capable of capturing all of these important characteristics well. These adaptations include clone states and non-stationarity in both the transition matrix and conditional models. Set in the Bayesian framework, a rich quantification of both parametric and predictive uncertainty is available, and thorough model checking is made possible through posterior predictive analyses. Results from the model are interpretable, allowing for meaningful examination of seasonal variation and medium to long term trends in rainfall occurrence and intensity. To demonstrate the effectiveness of our approach, both in terms of model fit and interpretability, we apply the model to an 8-year long time series of hourly observations.

中文翻译：

---

每小时降雨时间序列的高级隐马尔可夫模型

对于水文应用，例如城市洪水建模，能够从随机模型模拟次日降雨时间序列通常很重要。然而，以这种分辨率模拟降雨会带来一些挑战，包括复杂的时间结构，包括长干旱期、降雨发生和强度的季节性变化以及极值。我们说明了如何调整隐马尔可夫框架来构建一个引人注目的次日降雨模型，该模型能够很好地捕捉所有这些重要特征。这些适应包括转移矩阵和条件模型中的克隆状态和非平稳性。设置在贝叶斯框架中，可以对参数和预测不确定性进行丰富的量化，通过后验预测分析可以进行彻底的模型检查。该模型的结果是可解释的，允许对降雨发生和强度的季节性变化和中长期趋势进行有意义的检查。为了证明我们的方法在模型拟合和可解释性方面的有效性，我们将模型应用于长达 8 年的每小时观测时间序列。