Construction of non-diagonal background error covariance matrices for global chemical data assimilation

Abstract

Abstract. Chemical data assimilation attempts to optimally use noisy observations along with imperfect model predictions to produce a better estimate of the chemical state of the atmosphere. It is widely accepted that a key ingredient for successful data assimilation is a realistic estimation of the background error distribution. Particularly important is the specification of the background error covariance matrix, which contains information about the magnitude of the background errors and about their correlations. As models evolve toward finer resolutions, the use of diagonal background covariance matrices is increasingly inaccurate, as they captures less of the spatial error correlations. This paper discusses an efficient computational procedure for constructing nondiagonal background error covariance matrices which account for the spatial correlations of errors. The correlation length scales are specified by the user; a correct choice of correlation lengths is important for a good performance of the data assimilation system. The benefits of using the nondiagonal covariance matrices for variational data assimilation with chemical transport models are illustrated.

Simultaneous assimilation of satellite NO<sub>2</sub>, O<sub>3</sub>, CO, and HNO<sub>3</sub> data for the analysis of tropospheric chemical composition and emissions

“…In complex chemical data assimilation systems, a realistic estimation of the background error distribution is very important, given the noisy observations along with imperfect model predictions, as suggested by Singh et al (2011).…”

“…EnKF approaches always have a spurious long distance correlation problem because of imperfect sampling of the probability distribution due to limited ensembles (Houtekamer and Mitchell, 2001). In complex chemical data assimilation systems, a realistic estimation of the background error distribution is very important (Singh et al, 2011;Massart et al, 2012). Boynard et al (2011) too large correlation of fields distant from the location of the observation.…”

Regional data assimilation of multi-spectral MOPITT observations of CO over North America

“…Figure 1 The inversion analyses here are carried out using the GEOS-Chem four-dimensional variational (4D-Var) data assimilation system, which was first described by Henze et al (2007) and has been widely used in the chemical assimilation of CO and other tracer gases (e.g. Kopacz et al, 2009Kopacz et al, , 2010Singh et al, 2011;Wells et al, 2014;Deng et al, 2014). Previous GEOS-Chem CO inversion analyses were conducted with the global version of the model.…”

A low-order coupled chemistry meteorology model for testing online and offline data assimilation schemes: L95-GRS (v1.0)

“…Hakami et al, 2007;Henze et al, 2007) and this has led to the implementation of easier approximate adjoints (Bocquet, 2005(Bocquet, , 2012Koohkan and Bocquet, 2012;Singh and Sandu, 2012). Attention has been paid to the construction of the background error covariance matrix (Elbern et al, 2007;Singh et al, 2011).…”