A Smoother-Predictor of 3D Hidden Gauss-Markov Random Fields for Weather Forecast

In this paper, we offer a solution to the stochastic realization problem for a Gaussian Markov field defined on a tridimensional lattice, which is a graph with nodes regularly positioned to form a discrete parallelepiped in the euclidean space and arcs connecting 'internal' nodes with five nearest neighbors along the three coordinate directions. Next we show how the stochastic realization can be used for weather forecasting via a Kalman predictor, relying on partial observations and just a purely statistic a-priori knowledge of the Markov field, similarly to a classic Hidden Markov Model (HMM). An application carried out on real climate data shows the effectiveness of the approach taken.