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, hydr ology, and ecology. Stochastic simulation of rainfall data is also an impor tant step in the development of stochastic downscaling: methods where large -scale climate information is considered as an additional explanatory varia ble of rainfall behavior at the local scale. Simulated rainfall has also be en used as input data for many agricultural, hydrological, and ecological m odels, especially when rainfall measurements are not available for location s of interest or when historical records are not of sufficient length to ev aluate important rainfall characteristics as extreme values. Rainfall estim ation and prediction were carried out for an agricultural region of Venezue la in the central plains state of Guarico, where rainfall for 10-day period s is available for 80 different locations. The measurement network is relat ively 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 f or 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 b een truncated and transformed. According to this model, the dry periods cor respond to the (unobserved) negative values and the wet periods correspond to a transformation of the positive ones. The serial structure present in s eries of rainfall data can be modeled by considering a stochastic process f or w(it) We use a dynamic linear model on w(t) = (w(1t),...,w(Nt)) that inc ludes a Fourier representation to allow for the seasonality of the data tha t is assumed to be the same for all sites, plus a linear combination of fun ctions of the location of each site. This approach captures year-to-year va riability and provides a tool for short-term forecasting. The model is fitt ed using a Markov chain Monte Carlo method that uses latent variables to ha ndle dry periods and missing values.