In this study, several approaches for estimating background-error covariances from an ensemble of error realizations are examined, including a new spatial/spectral localization approach. The new approach shares aspects of both the spatial localization and wavelet-diagonal approaches. This approach also enables the use of different spatial localization functions for the covariances associated with each of a set of overlapping horizontal wavenumber bands. The use of such scale-dependent spatial localization (more severe localization for small horizontal scales) is shown to reduce the error in spatial correlation estimates. A comparison of spatial localization, spatial/spectral localization, and wavelet-diagonal approaches shows that the approach resulting in the lowest estimation error depends on the ensemble size. For a relatively large ensemble (48 members), the spatial/spectral localization approach produces the lowest error. When using a much smaller ensemble (12 members), the wavelet-diagonal approach results in the lowest error. Qualitatively, the horizontal correlation functions resulting from spatial/spectral localization appear smoother and less noisy than those from spatial localization, but preserve more of the heterogeneous and anisotropic nature of the raw sample correlations than the wavelet-diagonal approach. The new spatial/spectral localization approach is compared with spatial localization in a set of 1-month three-dimensional variational data assimilation (3D-Var) experiments using a full set of real atmospheric observations. Preliminary results show that spatial/spectral localization provides a nearly similar forecast quality, and in some regions improved forecast quality, as spatial localization while using an ensemble of half the size (48 vs 96 members).
On the role of non-diagonal system–environment interactions in bridge-mediated electron transfer
