An Advanced Hidden Markov Model for Hourly Rainfall Time Series

Abstract

The hidden Markov framework is adapted to construct a compelling model for simulation of sub-daily rainfall, capable of capturing important characteristics of sub-daily rainfall well, including: long dry periods or droughts; seasonal and temporal variation in occurrence and intensity; and propensity for extreme values. These adaptations include both clone states and temporally non-homogeneous state persistence probabilities. Set in the Bayesian framework, a rich quantification of parametric and predictive uncertainty is available, and thorough model checking is made possible through posterior predictive analyses. Results from the model are highly interpretable, allowing for meaningful examination of diurnal, seasonal and annual variation in sub-daily rainfall occurrence and intensity. To demonstrate the effectiveness of this approach, both in terms of model fit and interpretability, the model is applied to an 8-year long time series of hourly observations.