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In this paper, we present how we used neural networks (NNs) and a pyramidal approach to model the data obtained by a weather radar and to short-range forecast the rainfall behavior. Very short-range forecasting useful, for instance, for estimating the path attenuation in terrestrial point-to-point communications. Radial basis function NNs are used both to approximate the rain field and to forecast the parameters of this approximation in order to anticipate the movements and changes in geometric characteristics of significant meteorological structures. The procedure is validated by applying it to actual weather radar data and comparing the outcome with a linear forecasting method, the steady-state method, and the persistence method. The same approach is probably useful also for predicting the behavior of other meteorological phenomena like clusters of clouds observed from satellites.