Reduced rank covariances for the analysis of environmental data

In this work we propose a Monte Carlo estimator for non stationary covariances of large incomplete lattice or irregularly distributed data. In particular, we propose a method called “reduced rank covariance” (RRC), based on the multiresolution approach for reducing the dimensionality of the spatial covariances. The basic idea is to estimate the covariance on a lower resolution grid starting from a stationary model (such as the Mathérn covariance) and use the multiresolution property of wavelet basis for evaluating the covariance on the full grid. Since this method doesn’t need to compute the wavelet coefficients, it is very fast in estimating covariances in large data sets. The spatial forecasting performances of the method has been described through a simulation study. Finally, the method has been applied to two environmental data sets: the aerosol optical thickness (AOT) satellite data observed in Northern Italy and the ozone concentrations in the eastern United States.