A renewal cluster model for the inter-arrival times of rainfall events
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Date
2000
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Massey University
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Abstract
A statistical model, based on a renewal cluster point process, is proposed and used to infer the
distributional properties of dry periods in a continuous-time record. The model incorporates a mixed
probability distribution in which inter-arrival times are classified into two distinct types, representing
cyclonic and anticyclonic weather. This results in rainfall events being clustered in time, and enables
objective probabilistic statements to be made about storm properties, e.g. the expected number of events
in a storm cluster. The model is fitted to data taken from a gauge near Wellington, New Zealand, by
maximising the likelihood function with respect to the parameters. The Akaike Information Criteria is
used to select the best fitting distributions from a range of candidates. The log-Normal distribution is
found to provide the best fit to the times between successive storm clusters, whilst the Weibull
distribution is found to provide the best fit to the times between successive events in the same storm
cluster. Harmonic curves are used to provide a parsimonious parameterisation, allowing for the seasonal
variation in precipitation. Under the fitted model, the interval series is transformed into a residual series,
which is assessed to determine overall goodness-of-fit.
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Keywords
Rainfall
Citation
Cowpertwait, P.S.P. (2000)A renewal cluster model for the inter-arrival times of rainfall events. Research Letters in the Information and Mathematical Sciences, 1, 119-127