Dr Alex Schmidt, Instituto de Matematica - UFRJ, Brazil
Modelling multiple series of runoff:  The case of Rio Grande Basin (joint work with Romy R Ravines and Helio S Migon)

This paper proposes a joint model for the rainfall and multiple series of runoff at a basin, two of the most important hydrological processes.  The proposed model takes into account the different spatial units in which these variables are measured, and as a natural benefit its parameters have physical interpretations. Also, we propose to model runoff and rainfall in their original scales, making no use of any transformation to reach normality of the data. More specifically, our proposal follows Bayesian dynamic nonlinear models through the use of transfer function models.  The resultant posterior distribution has no analytical solution and stochastic simulation methods are needed to obtain samples from the target istribution.  In particular, as the parameters of the dynamic model are highly correlated, we make use of the Conjugate Updating Backward Sampling recently proposed by Ravines, Migon and Schmidt (2007), in order to efficiently explore the space of the parameters. We analyze a sample from a basin located in the Northeast of Brazil, the Rio Grande Basin. The data consist of monthly recorded series from January 1984 to September 2004, at three runoff stations and nine rainfall monitoring stations, irregularly located in an area of drainage of 37,500 sq km. Model assessment, spatial interpolation and temporal predictions are part of our analysis. Results show that our approach is a promising tool for the runoff-rainfall analysis.