Evaluation of a Spatial/Spectral Covariance Localization Approach for Atmospheric Data Assimilation

Mark Buehner Meteorological Research Division, Environment Canada, Dorval, Quebec, Canada

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Abstract

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).

Corresponding author address: Mark Buehner, Meteorological Research Division, Environment Canada, 2121 TransCanada Hwy., Dorval QC H9P 1J3, Canada. E-mail: mark.buehner@ec.gc.ca

Abstract

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).

Corresponding author address: Mark Buehner, Meteorological Research Division, Environment Canada, 2121 TransCanada Hwy., Dorval QC H9P 1J3, Canada. E-mail: mark.buehner@ec.gc.ca
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