## 1. Introduction

[2] Statistical inference systems are vulnerable to any structure in their random variables that is not well accounted for. Systematic errors, or biases, are a prominent example of such structures and receive much attention. Error correlations are another expression of organized patterns in the inference systems. A proper inference system should link correlated information pieces and weight them properly. For instance, correlated errors in the prior information reduce the effective dimension of the inversion problem and therefore theoretically should induce more accurate solutions. Correlated observation errors have a similar beneficial effect when each observation corresponds to a different variable to estimate. However, for a series of observations of a single variable *x*, the final uncertainty on *x* is larger for positively-correlated than for uncorrelated errors (the effect is opposite for negative correlations). In practice, correlations are often ignored, both because there are difficult to detect and quantify, and because properly taking them into account slows down the inversion systems to a large extent. A prominent illustration is given by the numerical weather prediction systems, since most of them assume uncorrelated observation errors (but correlated prior errors). To attenuate the effects of such a rough simplification, these systems include two empirical adjustments [e.g., *Liu and Rabier*, 2003, and references therein]: the observation density is thinned (i.e., only a subset of all possible remotely-sensed weather data is assimilated) and the errors assigned to the assimilated ones are usually inflated. For the estimation of CO_{2} surface fluxes from measurements of atmospheric concentrations, diagonal error matrices have been empirically used until recently [e.g., *Gurney et al.*, 2002]. Prior error correlations have been introduced in some studies [e.g., *Rödenbeck et al.*, 2003], but observation errors are still assumed to be uncorrelated, even though all components of the observation errors can be affected by correlations. For instance, error correlations in remote sensing measurements are generated by misinterpreted features in the electromagnetic spectrum and by the ancillary data used in retrieval [see, e.g., *Chevallier et al.*, 2005, Figure 2]. Since the observations are interpreted in the inversion system with the help of an atmospheric transport model (that links the fluxes to the measurements), such models also contribute to the observation error budget and induce space-time correlations between observation errors [e.g., *Kaminski et al.*, 2001].

[3] Before the end of the decade, two groundbreaking CO_{2}-dedicated instruments will be launched to monitor CO_{2} concentrations from space: Orbiting Carbon Observatory (OCO) [*Crisp et al.*, 2004] and Greenhouse Gases Observing Satellite (GOSAT) [*Inoue et al.*, 2006]. Several articles [e.g., *Rayner and O'Brien*, 2001; *Pak and Prather*, 2001; *Houweling et al.*, 2004; *Chevallier et al.*, 2007] have highlighted the potential of such data to significantly reduce the uncertainties related to flux variations. These successive studies describe observing system simulation experiments (OSSEs) with increasing realism, but all of them made the assumption of null observation error correlations. At best, the observation density was preliminarily thinned.

[4] This paper aims at investigating the impact of correlated errors in inverse modelling. OCO serves as a case study, with hypothetical error correlations of +0.5 introduced for observations 280 km apart. Such correlation errors could be present in the remote sensing product itself or could be caused by the transport model used in the inversion system. Despite the large number of observations, an analytical form of the covariance matrix inverse is found, given the instrument measurement configuration. This form serves us as a rigorous reference to assess the impact of commonly-used simplified treatments of the correlations: neglecting, observation thinning and error inflating. The set-up of our OSSEs is described in the next section. Results are shown in section 3, followed by a conclusion in section 4.