References

ACP

Atmospheric Chemistry and Physics

ACP

1680-7324

Copernicus GmbH

Göttingen, Germany

10.5194/acp-12-10015-2012

Technical Note: Spectral representation of spatial correlations in variational assimilation with grid point models and application to the Belgian Assimilation System for Chemical Observations (BASCOE)

Errera

¹ Ménard

Insitut d'Aéronomie Spatiale de Belgique, BIRA-IASB, Belgium

Air Quality Research Division, Environment Canada, Dorval (Qc), Canada

01 11 2012

12 21 10015 10031

This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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The formulation of the background error covariances represented in the spectral space is discussed in the context of univariate assimilation relying on a grid point model, leaving out all the aspects of balances between the different control variables needed in meteorological assimilation. The spectral transform operations are discussed in the case of a spherical harmonics basis and we stress that there is no need for an inverse spectral transform and of a Gaussian grid. The analysis increments are thus produced directly on the model grid. The practice of producing analysis increments on a horizontal Gaussian grid and then interpolating to an equally spaced grid is also shown to produce a degradation of the analysis. The method discussed in this paper allows the implementation of separable and non-separable spatial correlations. The separable formulation has been implemented in the Belgian Assimilation System for Chemical ObsErvations (BASCOE) and its impact on the assimilation of O<sub>3</sub> observed by the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) is shown. To promote the use of this method by other non-meteorological variational systems and in particular chemistry, the Fortran code developed is made available to the community.

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