A stochastic model for tropical rainfall at a single location

Modelling data that correspond to rainfall accumulated over fixed periods of time presents the challenging problem of dealing with a random variable that has a point mass at zero which corresponds to dry periods that occur with positive probability. One way to overcome this difficulty is to assume that the data correspond to a normal variate w, that has been truncated and transformed. The dry periods correspond to the (unobserved) negative values and the wet periods correspond to some power of the positive ones. The serial structure that is present in rainfall can be modelled by imposing a serial structure to w. We use a dynamic linear model on w using a Fourier representation to allow for the seasonality of the data, which in the case of tropical rainfall is very marked. The model is fitted using a Markov chain Monte Carlo method that uses latent variables to handle both dry periods and missing values. We use the model to estimate and predict both the amount of rainfall and the probability of a dry period. The method is illustrated with data collected in the Venezuelan state of Guarico.