Smoothing of Spheri- cal Markov Fields: Application to Climatic Data Processing

The smoothing problem is here considered for Gauss-Markov random fields defined on a kind of spherical lattice. Various observation models are included in the setting of this paper, such as the case of Gaussian noisy (even correlated) observations available only on a subset of sites, as well as a variable number of process components being measured. An efficient optimal smoothing algorithm is derived, based on the sparse representation of the potential matrix of the random field and on gaussian elimination. In view of applications in weather forecasting, an example using real data is presented, showing the capability of the proposed setting in a task of reconstruction of temperature maps.