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Markov modulated Poisson process models incorporating covariates for rainfall intensity.

R Thayakaran¹, N I Ramesh

¹School of Computing and Mathematical Sciences, University of Greenwich, Old Royal Naval College, Park Row, Greenwich, London SE10 9LS, United Kingdom. R.Thayakaran@gre.ac.uk

Water Science and Technology : a Journal of the International Association on Water Pollution Research

|April 13, 2013

Summary

This study models rainfall patterns using a generalized Poisson process, incorporating weather data like temperature and pressure. Including these covariates improves statistical understanding of rainfall arrival times.

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Area of Science:

Environmental science
Statistical modeling
Meteorology

Background:

Rainfall arrival times are often complex and not easily modeled by simple Poisson processes.
Markov Modulated Poisson Processes (MMPP) offer a more flexible framework for time series data.
Understanding the influence of meteorological covariates on rainfall is crucial for accurate forecasting.

Purpose of the Study:

To investigate the impact of covariates on the statistical properties of MMPP models for rainfall.
To assess how temperature, sea level pressure, and relative humidity affect rainfall arrival processes.
To enhance the statistical inference of accumulated rainfall using covariate-informed models.

Main Methods:

Modeling rainfall time series using Markov Modulated Poisson Processes (MMPP).
Incorporating time-varying covariates: temperature, sea level pressure, and relative humidity.
Utilizing Maximum Likelihood Estimation (MLE) for parameter estimation and Likelihood Ratio Tests (LRT) for model comparison.

Main Results:

The inclusion of covariates significantly impacts the statistical properties of the MMPP rainfall model.
Covariate information refines the estimation of rainfall arrival rates and accumulated rainfall.
Simulated data analysis provides insights into the variability of daily rainfall rates.

Conclusions:

Markov Modulated Poisson Processes with covariates provide a robust framework for modeling rainfall time series.
Meteorological covariates are important factors influencing rainfall arrival processes.
The enhanced model improves statistical inference for rainfall prediction and analysis.