# An Advanced Hidden Markov Model for Hourly Rainfall Time Series

## TL;DR

This paper introduces an advanced hidden Markov model tailored for hourly rainfall data, effectively capturing complex temporal patterns, seasonality, and extremes, with Bayesian uncertainty quantification and interpretability demonstrated on 8 years of data.

## Contribution

It presents a novel adaptation of the hidden Markov model for sub-daily rainfall, incorporating clone states and non-stationarity, within a Bayesian framework for improved modeling and uncertainty analysis.

## Key findings

- Model accurately captures rainfall patterns and extremes.
- Provides interpretable insights into seasonal and long-term trends.
- Demonstrates effective application on 8-year hourly rainfall data.

## Abstract

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.