Abstract
Abstract. 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 O3 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.
Highlights
One of the critical aspects of any assimilation system is the formulation of the background spatial error covariances matrix, denoted the B matrix
It is based on the fact that a homogeneous and isotropic horizontal correlation matrix can be represented by a diagonal matrix in the spectral space
These concepts were extended to the sphere and applied successfully to large-scale atmospheric dynamics and analyses by Boer (1983) and Boer and Shepherd (1983) using spherical harmonics as the orthogonal basis
Summary
One of the critical aspects of any assimilation system is the formulation of the background spatial error covariances matrix, denoted the B matrix. The second approach for variational systems is based on a diffusion operator which uses the model’s diffusion to generate the effect of a Gaussian correlation function This method was introduced by Derber and Rosati (1989) and further developed by Weaver and Courtier (2001). Menard: Spectral representation of background error covariances is useful when the domain has complex boundaries (e.g. ocean data assimilation) where it is difficult to define positive definite correlations This method is well suited for models that have non uniform grid on a sphere (e.g. icosahedral grids) because it avoids the interpolation of analysis increments onto that grid (Elbern et al, 2010; Schwinger and Elbern, 2010).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
