## 1. Introduction

[2] Quantifying the spatio-temporal variations of CO_{2} surface fluxes over continents has been a scientific target of primary importance since the end of the 1980s [*Keeling et al.*, 1989; *Tans et al.*, 1990]. Several bottom-up methods have been developed, based on local observations [e.g., *Baldocchi et al.*, 2001], on ecosystem modelling [e.g., *Krinner et al.*, 2005], or on a combination of both. Despite dramatic improvements, the uncertainty of each estimate is still too large for these estimates to be reliably used for detailed regional estimates of carbon fluxes. One alternative and complementary approach consists in inferring the fluxes from the atmospheric concentration measurements, knowing how the movement of air parcels link the former to the latter (the top-down approach implemented by, e.g., *Enting et al.* [1995], *Gurney et al.* [2002], and *Rödenbeck et al.* [2003]). The diffusive nature of atmospheric transport makes such an inversion problem mathematically ill-posed: the measurements have to be combined with some other information to regularize it, usually through the Bayes' formula. This essential extra information consists of what one knows about the CO_{2} surface fluxes prior to the examination of the concentration measurements. If one knew nothing, one should choose uniform prior distribution probabilities for the fluxes (i.e., any flux state is all equally likely). There actually exists some (limited) knowledge of the biogeochemical processes that govern the fluxes and which are gathered in numerical models of the terrestrial carbon cycle. In situ pointwise measurements of the ecosystem fluxes at flux towers, large scale inventories of fossil fuel emissions, of carbon stocks changes, and satellite-based observations of vegetation activity and disturbances also provide some prior information about the fluxes.

[3] Empiricism has dominated the assignment of prior flux errors in Bayesian inversions so far, which bears consequences on the reliability of the inferred fluxes. For convenience, errors are usually modelled by tuneable multivariate (space-time) normal (Gaussian) distributions. Two different strategies could improve on the current situation. The first one, called “marginalization”, consists in treating the unknown characteristics of the prior errors, like the standard deviations, as unknown variables in the Bayes' rule. *Michalak et al.* [2005] developed a simplified approach along this path. This method is still difficult to implement for large dimension problems. Another strategy, which is favoured here, consists in estimating the prior error characteristics based on actual flux observations.

[4] In this paper, surface flux measurements made by the eddy-covariance technique [*Aubinet et al.*, 2000; *Baldocchi et al.*, 2001] on a continuous basis are used to investigate the errors of prior fluxes of the terrestrial biosphere. Prior CO_{2} fluxes (i.e., fluxes prior to the analysis of any concentration observation) are provided here by a numerical carbon cycle model: the Organizing Carbon and Hydrology In Dynamic EcosystEms model (ORCHIDEE) described by *Krinner et al.* [2005]. The model and the observations are presented in the next section. Section 3 shows the results, which are discussed in the last section.