Modeling rainfalls using a seasonal hidden markov model

TL;DR

This paper introduces a seasonal hidden Markov model with exponential mixture emissions for daily rainfall simulation, effectively capturing seasonality, rainfall patterns, and dry/rainy spells, validated on German weather data.

Contribution

It presents a novel seasonal hidden Markov model with exponential mixtures for rainfall modeling, including a proof of strong consistency of the maximum likelihood estimator.

Findings

Model reproduces observed rainfall seasonality and distribution

Generates arbitrarily long realistic rainfall sequences

States have interpretable physical meanings

Abstract

In order to reach the supply/demand balance, electricity providers need to predict the demand and production of electricity at different time scales. This implies the need of modeling weather variables such as temperature, wind speed, solar radiation and precipitation. This work is dedicated to a new daily rainfall generator at a single site. It is based on a seasonal hidden Markov model with mixtures of exponential distributions as emission laws. The parameters of the exponential distributions include a periodic component in order to account for the seasonal behaviour of rainfall. We show that under mild assumptions , the maximum likelihood estimator is strongly consistent, which is a new result for such models. The model is able to produce arbitrarily long daily rainfall simulations that reproduce closely different features of observed time series, including seasonality, rainfall occurrence , daily distributions of rainfall, dry and rainy spells. The model was fitted and validated on data from several weather stations across Germany. We show that it is possible to give a physical interpretation to the estimated states.