  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.
