## 1. Introduction

[2] Carbon dioxide (CO_{2}) is the primary greenhouse gas contributing to global climate change, and numerous studies have focused on developing a thorough understanding of the regional, continental, and global budgets of CO_{2}. Although significant progress has been made in understanding the processes controlling the sources and sinks of CO_{2}, important questions still remain regarding their magnitude, timing and geographic distribution.

[3] Increasingly, inverse modeling approaches are employed to improve estimates of carbon flux at a variety of spatial and temporal scales. These top-down approaches couple observations of CO_{2} with atmospheric transport models to trace concentration fluctuations back to surface fluxes at specific locations and over prescribed time periods [e.g., *Rayner et al.*, 1999; *Enting*, 2002]. However, the nature of atmospheric transport (e.g., mixing, diffusion, influence of weather patterns) and its associated uncertainties reduce the information content of available observations. As a result, atmospheric inversions are generally ill-posed, with substantially different flux distributions yielding similar modeled mixing ratios at observational network sites [*Enting*, 2002]. In this case, uncertainties in observational data and transport models can lead to high uncertainties on estimated fluxes [*Enting and Newsam*, 1990; *Brown*, 1993; *Hein et al.*, 1997].

[4] In order to circumvent this ill-posedness, additional information on CO_{2} sources and sinks is typically introduced into inversions in the form of explicit prior estimates of surface flux. This approach, commonly referred to as synthesis Bayesian inversion, typically obtains these a priori flux estimates from process-based models and/or inventories [e.g., *Kaminski et al.*, 1999; *Rödenbeck et al.*, 2003; *Gurney et al.*, 2004; *Baker et al.*, 2006]. Process-based, or biospheric models typically apply knowledge of small-scale causal mechanisms to predict carbon exchange at larger scales (e.g., Carnegie-Ames-Stanford Approach (CASA) model [*Randerson et al.*, 1997] and Lund-Potsdam Jena (LPJ) Dynamic Global Vegetation Model [*Sitch et al.*, 2000]).

[5] However, because the current global CO_{2} monitoring network is sparse, some regions of the world remain poorly constrained even after the introduction of a priori assumptions about flux distributions. Therefore, to avoid an underdetermined problem, synthesis Bayesian inversions often estimate fluxes for a small number of prespecified regions loosely based on continental boundaries [e.g., *Gurney et al.*, 2003, 2004; *Law et al.*, 2003; *Baker et al.*, 2006], or, more recently, based on biomes or land cover types [*Peters et al.*, 2007], while keeping the flux patterns within regions fixed. This approach can lead to aggregation errors [*Kaminski et al.*, 2001], where the inferred net estimate from a region can be biased by any inaccuracies in the flux patterns assumed within a particular region. In a few cases, sources and sinks have been estimated at finer scales to reduce such errors, by including a covariance matrix that describes the assumed spatial autocorrelation between fluxes [e.g., *Rödenbeck et al.*, 2003; *Rödenbeck*, 2005].

[6] Overall, flux estimates and uncertainties derived from atmospheric inversions are sensitive to a priori assumptions, such as the selection of observations, the transport model, prior information, prescribed flux patterns, and error covariance parameters. These differences lead to the observed inconsistencies between reported flux estimates from various inversion studies. There is a growing awareness of the strong influence of these assumptions, especially in regards to the use of explicit prior flux estimates from bottom-up models to define the magnitude and spatial distribution of fluxes [e.g., *Michalak et al.*, 2004; *Rödenbeck*, 2005]. This influence not only contributes to aggregation errors, but can also cause a posteriori estimates to revert to prior assumptions in underconstrained regions. As such, estimates from synthesis Bayesian inversions cannot be used directly to reconcile process-based understanding of flux behavior with the information content of atmospheric observations. The sensitivity of estimates to other assumptions has also been recognized, with researchers attempting to systematically quantify the magnitude and impact of model-data mismatch and a priori flux uncertainties [e.g., *Engelen et al.*, 2002; *Engelen*, 2006; *Krakauer et al.*, 2004; *Michalak et al.*, 2005].

[7] Owing to the strong influence of inverse modeling assumptions on estimated sources and sinks, there is a need for an inverse modeling approach for CO_{2} flux estimation that can more directly reflect the information content of available atmospheric measurements. Such an approach, based on a geostatistical inverse modeling framework, was proposed by *Michalak et al.* [2004]. This method aims to reduce the influence of modeling assumptions by (1) avoiding the use of bottom-up flux estimates for defining the magnitude and spatial patterns of fluxes, (2) estimating sources and sinks at resolutions that minimize the risk of aggregation errors, and (3) using a rigorous statistical framework for quantifying model-data mismatch and the degree of spatial autocorrelation in the flux distribution. In this manner, the approach yields CO_{2} flux estimates that are more strongly representative of the spatial and temporal variability of CO_{2} fluxes as seen through the atmospheric measurement network.

[8] This paper presents the first application of the geostatistical inverse modeling approach for estimating CO_{2} fluxes using atmospheric observations. The objectives of this work are to (1) explore the ability of the approach to constrain global fluxes with a level of uncertainty comparable to synthesis Bayesian inversions, (2) identify the information content of available observations with regard to the global CO_{2} flux distribution and its variability at various spatial and temporal scales, and (3) elucidate the impact of prior assumptions used in synthesis Bayesian inversions on flux estimates from previous studies.

[9] Monthly averaged CO_{2} fluxes are estimated at the resolution of the implemented atmospheric transport model, 3.75° latitude by 5° longitude, for 1997–2001, using observations from a subset of the NOAA-ESRL cooperative air sampling network. To further avoid the use of a priori assumptions, fossil fuel fluxes are not assumed known, contrary to past inverse modeling studies. Instead, this paper estimates total flux, including terrestrial, oceanic, and anthropogenic contributions, which avoids the possibility of aliasing the uncertainties and seasonality of fossil fuel emissions [*Gurney et al.*, 2005] onto the estimated biospheric flux signal. Estimated fluxes are compared at various spatial and temporal scales to bottom-up estimates of biospheric [*Randerson et al.*, 1997], oceanic [*Takahashi et al.*, 2002], and fossil fuel [*Brenkert*, 1998] fluxes, as well as estimates from the synthesis Bayesian inversion estimates of the TransCom3 Level 3 intercomparison [*Baker et al.*, 2006] and the *Rödenbeck et al.* [2003] study. A companion paper [*Gourdji et al.*, 2008] explores the ability of auxiliary environmental variables (e.g., surface air temperature, leaf area index) to further constrain flux distributions within the geostatistical inverse modeling framework, especially at fine spatial resolutions.

[10] The remainder of the paper is organized as follows. Section 2 presents the components of the geostatistical inverse modeling approach and the corresponding system of equations. This section also outlines the approach used to optimize the model-data mismatch and spatiotemporal covariance parameters. Section 3 presents and discusses the optimized covariance parameters and inversion results at the grid and continental scales, along with a comparison to previously published flux estimates. Finally, section 4 summarizes the conclusions of the paper and presents suggestions for future research.