A Nonstationary Multisite Model for Rainfall

Estimation and prediction of the amount of rainfall in time and space is a problem of fundamental importance in many applications in agriculture, hydrology, and ecology. Stochastic simulation of rainfall data is also an important step in the development of stochastic downscaling methods where large-scale climate information is considered as an additional explanatory variable of rainfall behavior at the local scale. Simulated rainfall has also been used as input data for many agricultural, hydrological, and ecological models, especially when rainfall measurements are not available for locations of interest or when historical records are not of sufficient length to evaluate important rainfall characteristics as extreme values. Rainfall estimation and prediction were carried out for an agricultural region of Venezuela in the central plains state of Guárico, where rainfall for 10-day periods is available for 80 different locations. The measurement network is relatively sparse for some areas, and aggregated rainfall at time resolutions of days or less is of very poor quality or nonexistent. We consider a model for rainfall based on a truncated normal distribution that has been proposed in the literature. We assume that the data y_it, where i indexes location and t indexes time, correspond to normal random variates w_it that have been truncated and transformed. According to this model, the dry periods correspond to the (unobserved) negative values and the wet periods correspond to a transformation of the positive ones. The serial structure present in series of rainfall data can be modeled by considering a stochastic process for w_it. We use a dynamic linear model on w_t = (w_1t, …, w_Nt) that includes a Fourier representation to allow for the seasonality of the data that 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.