Bruno Sansoand Lelys Guenni
We consider a model for rainfall based on truncated student distributions. We asume that the data, which are indexed in space and time, correspond to student variates that have been truncated. According to this model, the dry periods correspond to the (unobserved) negative values and the wet periods correspond to the positive ones.
The serial structure that is present in series of rainfall data can be modelled by imposing a serial structure on the latent variables. We use a dynamic linear model with a Fourier representation to allow for the seasonality of the data, which is assumed to be the same for all sites, plus a linear combination of functions of the location of each site. This approach captures year to year variability and provides a tool for short term forecasting.
The model is fitted using a Markov Chain Monte Carlo method that uses latent variables to handle 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 rainfall accumulated over periods of ten days collected in 80 different locations in the Venezuelan state of Guárico. The manuscript is available in PostScript format.