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

Lermusiaux, P.F.J., D.G.M. Anderson and C.J. Lozano, 2000. On the mapping of multivariate geophysical fields: error and variability subspace estimates. The Quarterly Journal of the Royal Meteorological Society, April B, 1387-1430.

A basis is outlined for the first-guess spatial mapping of three-dimensional 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 problem. The size of the problem is reduced efficiently by focusing on the error subspace, here the dominant eigendecomposition of the a priori error covariance. The first estimate of this a priori error subspace is constructed in two parts. For the “observed” portions of the subspace, the covariance of the a priori missing variability is directly specified and eigendecomposed. For the “non-observed” portions, an ensemble of adjustment dynamical integrations is utilized, building the nonobserved covariances in statistical accord with the observed ones. This error subspace construction is exemplified and studied in a Middle Atlantic Bight simulation and in the eastern Mediterranean. 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 complex data-variability influences. The error and variability subspaces obtained can also confirm or reveal the features of dominant variability, such as the Ierapetra Eddy in the Levantine basin.