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.