We present an analysis of runoff and rainfall data from Rio Grande, a basin located in the northeast of Brazil. The main challenges we face here are: (i) to model runoff and rainfall jointly, taking into account their different spatial units, (ii) to use stochastic models where all the parameters have physical interpretations, and (iii) to model these processes in their original scale, without assuming any transformation to attain normality of these variables.The intrinsically uncertain nature of these hydrological processes makes Bayesian analysis natural in this field. Our approach is based on dynamic models. The effect of rainfall on runoff is modeled through a transfer function, whereas the amount of rainfall is obtained after fitting a spatio-temporal model and dealing with the change of support problem. Besides the computational effort to implement the proposed models, some methodological novelties are also implemented.The data consist of monthly series from January 1984 to September 2004, at a runoff station and nine rainfall stations irregularly located in a drainage area of 37522.48 km2. Model assessment, spatial interpolation and temporal predictions were part of our analysis. The results show that our approach is a promising tool for rainfall–runoff analysis.