We are interested in the large-scale environmental phenomenon of West African monsoon. It is the major atmospheric phenomenon which drives the rainfall regime in Western Africa. The causes of spatio-temporal variability in monsoon rainfall have not yet been determined in an unequivocal manner. However, there is a considerable body of evidence suggesting that spatio-temporal changes in sea surface temperatures in the Gulf of Guinea (SST) and changes in the Saharan and sub-Saharan albedo are major factors. To simulate the rainfall, a regional atmospheric model (MAR) is used. An important point in this study is that the numerical storage and processing of model outputs, as far as the statistical description of the data, requires considerable computation resources. Hence an important preliminary step is the construction of a stochastic spatio-temporal metamodel approximating the MAR. In this work, we focus on the impact of SST on precipitation. We rst present the functional modeling for both SST and precipitation. Then we perform a regularized regression of the precipitation on the sea surface temperatures