An empirical orthogonal function (EOF) model is proposed as a prediction method for data collected over space and time. EOF models are widely used in a number of disciplines, including Meteorology and Oceanography. The appealing feature of this model is the advantage of not requiring any assumption for the covariance matrix structure. However, there is a need to account for the errors associated with the spatial and temporal features of the data. This is accomplished by incorporating information from the sampling design, used to establish the network, into the model. The theoretical developments and numerical solutions are presented in the first section of the paper. An application of the model to real data and the results of validation analyses are also presented.