On the mapping of multivariate geophysical fields: Error and variability subspace estimates

A basis is outlined for the first-guess spatial mapping of three-dimensiona l multivariate and multiscale geophysical fields and their dominant errors. The a priori error statistics are characterized by covariance matrices and the mapping obtained by solving a minimum-error-variance estimation proble m. The size of the problem is reduced efficiently by focusing on the error subspace, here the dominant eigendecomposition of the a priori error covari ance. The first estimate of this a priori error subspace is constructed in two parts. For the 'observed' portions of the subspace, the covariance of t he a priori missing variability is directly specified and eigendecomposed. For the 'non-observed' portions, an ensemble of adjustment dynamical integr ations is utilized, building the non-observed covariances in statistical ac cord with the observed ones. This error subspace construction is exemplifie d and studied in a Middle Atlantic Eight simulation and in the eastern Medi terranean. Its use allows an accurate, global, multiscale and multivariate, three-dimensional analysis of primitive-equation fields and their errors, in real time. The a posteriori error covariance is computed and indicates c omplex data-variability influences. The error and variability subspaces obt ained can also confirm or reveal the features of dominant variability, such as the Ierapetra Eddy in the Levantine basin.