Abstract. We present a method in which the optimal interpolation of multi-scale processes can be expanded into a succession of simpler interpolations. First, we prove how the optimal analysis of a superposition of two processes can be obtained by different mathematical formulations involving iterations and analysis focusing on a single process. From the different mathematical equivalent formulations, we then select the most efficient ones by analyzing the behavior of the different possibilities in a simple and well-controlled test case. The clear guidelines deduced from this experiment are then applied to a real situation in which we combine large-scale analysis of hourly Spinning Enhanced Visible and Infrared Imager (SEVIRI) satellite images using data interpolating empirical orthogonal functions (DINEOF) with a local optimal interpolation using a Gaussian covariance. It is shown that the optimal combination indeed provides the best reconstruction and can therefore be exploited to extract the maximum amount of useful information from the original data.