We construct a data-driven model for solar irradiation based on satellite observations. The model yields probabilistic estimates of the irradiation field every thirty minutes starting from two consecutive satellite measurements. The probabilistic nature of the model captures prediction uncertainties and can therefore be used by solar energy producers to quantify the operation risks. The model is simple to implement and can make predictions in realtime with minimal computational resources. To deal with the high-dimensionality of the satellite data, we construct a reduced representation using factor analysis. Then, we model the dynamics of the reduced representation as a discrete (30-minute interval) dynamical system. In order to convey information about the movement of the irradiation field, the dynamical system has a two-step delay. The dynamics are represented in a nonlinear, nonparametric way by a recursive Gaussian process. The predictions of the model are compared with observed satellite data as well as with a similar model that uses only ground observations at the prediction site. We conclude that using satellite data in an area including the prediction site significantly improves the prediction compared with models using only ground observation site data.