A marked Poisson process model of summer rainfall in southern Ontario

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Abstract
A mathematical description of summer rainfall occurrences in southern Ontario is developed in this paper. The theory of Poisson point processes with specific application to rainfall modelling is presented with a critical review of previous literature on Poisson rainfall models. A marked Poisson process model of summer storms is formulated, using the marks to represent the random duration and intensity of the events. Model parameters are estimated for four locations in southern Ontario using a total of 48 seasons of hourly rainfall data. The model is applied to calculate the seasonal return period of extreme storms and the probability distribution of total seasonal rainfall volume. These two examples demonstrate the accuracy and usefulness of the model. Key words: rainfall, storm duration, storm intensity, temporal storm pattern, probabilistic model, Poisson process, exponential distribution, gamma distribution, Weibull distribution.

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