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Fitting hidden semi-Markov models to breakpoint rainfall data

Part of: Inference from stochastic processes Geophysics Geophysics (general)

Published online by Cambridge University Press:  14 July 2016

John Sansom  and
Peter Thomson
John Sansom*
Affiliation:
National Institute of Water and Atmospheric Research, New Zealand
Peter Thomson*
Affiliation:
Statistics Research Associates Ltd
*
1Postal address: PO Box 14–901, National Institute of Water and Atmospheric Research, Wellington, New Zealand.
2Postal address: PO Box 12–649, Statistics Research Associates Ltd, Wellington, New Zealand. Email: [email protected]
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Abstract

The paper proposes a hidden semi-Markov model for breakpoint rainfall data that consist of both the times at which rain-rate changes and the steady rates between such changes. The model builds on and extends the seminal work of Ferguson (1980) on variable duration models for speech. For the rainfall data the observations are modelled as mixtures of log-normal distributions within unobserved states where the states evolve in time according to a semi-Markov process. For the latter, parametric forms need to be specified for the state transition probabilities and dwell-time distributions.

Recursions for constructing the likelihood are developed and the EM algorithm used to fit the parameters of the model. The choice of dwell-time distribution is discussed with a mixture of distributions over disjoint domains providing a flexible alternative. The methods are also extended to deal with censored data. An application of the model to a large-scale bivariate dataset of breakpoint rainfall measurements at Wellington, New Zealand, is discussed.

Keywords

Hidden semi-Markov modelshigh-resolution rainfall datadwell-time distributionsEM algorithm

MSC classification

Primary: 62M05: Markov processes
Secondary: 86A10: Meteorology and atmospheric physics
Type
Estimation problems
Information
Journal of Applied Probability , Volume 38 , Issue A: Probability, Statistics and Seismology , 2001 , pp. 142 - 157
Copyright
Copyright © Applied Probability Trust 2001 

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