Corresponding author: K. Steinkamp, National Institute of Water and Atmospheric Research, Private Bag 14-901, Wellington 6021, New Zealand. (firstname.lastname@example.org)
 We have estimated global surface fluxes of carbon dioxide for the period 1992–1996 using an inverse approach that sequentially considers four constraints: (1) atmospheric CO2, (2) ocean interior DIC (dissolved inorganic carbon) interpreted through an ocean interior inversion and surface ocean pCO2 (partial pressure of CO2), (3) annual prior fluxes for selected land regions, and (4) atmospheric model selection based on vertical transport skill. Estimated fluxes are monthly resolved for each of the 22 Transcom regions over land and ocean. The ocean constraint is particularly valuable, as it does not only add prior information about air-sea fluxes to the inversion problem but also preserves the regional variance-covariance structure from the underlying ocean interior inversion. It allows to constrain annual oceanic uptake of 1.8 PgCyr−1 to within 0.2 PgCyr−1, which implies a net annual land uptake of 1.3 (±0.3) PgCyr−1. Furthermore, it leads to a pronounced asymmetry in the seasonal pattern of global land uptake, which was not seen in previous atmosphere-only inversions. Tropical land is consistently estimated to be a source of carbon, though the source magnitude is reduced as more constraints are applied. With all four constraints, the inversion suggests a net tropical source of 1.1 (±0.9) PgCyr−1, which is comparable to global estimates of deforestation rates in tropical forests and therefore implies an annually balanced tropical land biosphere flux. This balance is not found, however, at the regional level: For the Amazonian region and after accounting for deforestation, we find a biospheric source of 0.6 (±0.5) PgCyr−1. This is at the upper range of estimates from bottom-up methods, which tend to identify the region as a sink.
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 In the 1990s, about 64 PgC were emitted to the atmosphere through fossil fuel burning and cement manufacture [Boden et al., 2010]; 33 PgC remained in the atmosphere, corresponding to 52% of the emissions. This caused an increase in CO2 concentration from 353 to 367 ppm, calculated as the average of the data from Mauna Loa and South Pole [cf. Globalview-co2, 2009]. The remaining 31 PgC have been taken up by the ocean and the land biosphere. Their combined sink strength is known with a high degree of confidence, because of the high accuracy of both the fossil emissions estimate and the CO2 records. However, the magnitudes of the individual land and ocean sinks are less certain, and additional regional breakdown (for example, into continental-/basin-scale budgets) increases the uncertainties further.
 Several methods have been applied to separate the ocean from the land sink. Some of them use the fact that oceanic uptake of carbon does not fractionate the isotopes of carbon substantially (δ13C method) [Battle et al., 2000], or occurs independently of the exchange of other gases, such as oxygen (O2/N2 method) [e.g., Keeling et al., 1996; Manning and Keeling, 1996]. Those studies show that in the 1990s, the land must have taken up less carbon than the ocean, in particular, when a possible climate-induced net outgassing of oceanic oxygen is taken into account [Plattner et al., 2002; Bopp et al., 2002]. Another possibility is to use surface ocean pCO2 data to determine the air-sea carbon flux [e.g., Takahashi et al., 2009b]. The terrestrial sink can then be calculated as the residual of atmospheric growth rate and air-sea flux after outgassing of river carbon has been taken into account [Sarmiento and Sundquist, 1992]. These studies suggest a smaller ocean sink and therefore attribute most of the combined uptake to the land biosphere.
 Oceanic and terrestrial carbon sinks can also be estimated by interpreting gradients in atmospheric CO2 concentration through an atmospheric transport inversion. Such inferences have a long history [e.g., Keeling, 1960] and have led to the development of sophisticated inversion methods on various spatiotemporal scales [e.g., Bousquet et al., 1999; Gurney et al., 2002, 2004; Roedenbeck et al., 2003; Baker et al., 2006; Peters et al., 2007]. Every atmospheric inversion is composed of three main components: a set of atmospheric CO2 data, an atmospheric transport model, and a regional set of surface fluxes. The regional fluxes are chosen such that their propagation through the transport model most closely resembles the observed atmospheric CO2 data. In a similar manner, gradients in dissolved inorganic carbon (DIC) in the interior ocean can be interpreted with an ocean circulation model to estimate air-sea fluxes of CO2 for prescribed surface regions [e.g., Gloor et al., 2003; Mikaloff Fletcher et al., 2006, 2007; Gruber et al., 2009]. Results from ocean inversions usually suggest a larger ocean sink. Gruber et al.  found −1.7 PgCyr−1 for the 1990s (sign convention assigns negative fluxes as out of the atmosphere). When combined with the global growth estimate, this leaves −1.4 PgCyr−1as terrestrial sink. On the other hand, the atmospheric inversion of Gurney et al. , using data for the period 1992–1996, estimates a smaller ocean sink of −1.3 PgCyr−1, and therefore attributes −1.8 PgCyr−1to the terrestrial biosphere.
 This study is motivated by the discrepancy of previous results and aims to reconcile flux estimates by a joint inversion of atmospheric CO2 and ocean interior DIC data. Results represent the 1992–1996 mean monthly fluxes for 11 ocean and 11 land regions, corresponding to those of the cyclostationary Transcom experiment [Gurney et al., 2004]. Ocean inversion results represent long-term mean fluxes due to the long time scales of ocean circulation, as opposed to the rapid atmospheric circulation that makes atmospheric inversions capable of resolving fluxes on monthly time scales. We use additional information about seasonal variability from a recently updated global climatology of surface ocean pCO2 [Takahashi et al., 2009b] to form a monthly average flux distribution. This seasonal approach overcomes the potential misallocation of seasonal flux variability from some terrestrial regions to adjacent ocean regions, which shows up in seasonal atmosphere-only inversions [Gurney et al., 2004].
 Our method is based on the annual joint ocean-atmosphere inversion of Jacobson et al. [2007a] but improves on it by resolving the seasonal cycle. We achieve this by coupling the ocean inversion, augmented with seasonal flux information based on the surface pCO2 network, to a seasonal atmospheric inversion. The resulting regional fluxes are formally consistent with atmospheric CO2, ocean interior DIC and ocean surface pCO2 observations. This not only allows to get new insights into the seasonal carbon cycle over land but also avoids the need to make any assumptions about a rectifier effect due to the seasonal coupling between atmospheric circulation and carbon exchange with the land biosphere.
 In their annual mean joint inversion, Jacobson et al. [2007a, 2007b] found very strong, compensating fluxes in certain regions. Tropical land appeared as a huge source of more than 4 PgCyr−1, and Southern Hemisphere land as a large sink of almost −2.5 PgCyr−1. This dipole is largely a manifestation of posterior error correlations between the different regions and the authors emphasized that great care needs to be taken when interpreting the individual estimates, as only their sum is well constrained. Nevertheless, it is interesting to point out that the estimated tropical forest source exceeds the estimated deforestation, implying that the natural, unperturbed forests must be a source of CO2 to the atmosphere as well. On the other hand, bottom-up studies based on forest inventories and eddy covariance flux towers indicate undisturbed tropical forests to be a net carbon sink, or nearly neutral, over the year [e.g., Phillips et al., 1998, 2009; Chave et al., 2008; Lewis et al., 2009; Pan et al., 2011]. In this study we revisit this apparent inconsistency between the land-based tropical constraint and that from the ocean inversion and also review correlations between tropical and Southern Hemisphere regions.
 From the observed latitudinal gradient of atmospheric CO2, inverse models commonly infer a large sink of CO2 over temperate land areas in the Northern Hemisphere [e.g., Tans et al., 1990; Peters et al., 2007; Pacala et al., 2007], while tropical land regions are either nearly balanced or rather weak carbon sinks. [Stephens et al., 2007] challenged this view through an analysis of 12 atmospheric transport models that have been used for atmospheric inversions before (Transcom models) [see Gurney et al., 2002]. Their model skill analysis is based on the models' ability to reproduce observed vertical CO2 gradients, which is known to be important for surface flux estimation [Bousquet et al., 1999]. They conclude that those models with the most accurate annual mean vertical gradient are characterized by weak northern and strong tropical land carbon uptake, as opposed to the common view. As part of this study, we confine our transport models to the Stephens subset to see if their conclusions also hold in a joint ocean-atmosphere inversion.
 In this study various constraints on the carbon cycle are considered: ocean DIC and pCO2, atmospheric CO2, bottom-up estimates for large-scale land regions, and model selection according to Stephens et al. . Two aims are pursued: (1) to characterize the information content of each constraint and to identify areas of contradiction and (2) to combine them in a joint inversion to estimate a set of regional and seasonal fluxes that is formally consistent with all of them. This extends the joint inversion of Jacobson et al. [2007a] in two important aspects. First, it resolves the seasonal cycle; second, it incorporates in a sequential manner also the land surface flux information of Sarmiento et al. .
 The joint inversion methodology developed by Jacobson et al. [2007a, 2007b] interprets carbon observations from the atmosphere and ocean to estimate exchange fluxes of CO2 between the atmosphere and both the terrestrial biosphere and the surface ocean. To link observations and fluxes, transport models are used to simulate the distribution of atmospheric CO2 and ocean DIC or more accurately, the imprint of atmospheric CO2 on ocean DIC. The global surface is partitioned into 11 terrestrial and 11 oceanic regions, for each of which the distribution of CO2/DIC in response to a unit dye tracer flux from that region is simulated. These regional footprints, or Green's functions, are then combined in such a way that in a linear least squares sense, their weighted sum most closely matches the observations. We use a suite of 10 oceanic and 12 atmospheric transport models to express transport uncertainty and to assess its impact on the inverse results. In the following, the ingredients of the joint inversion framework are presented briefly, which are (1) the atmospheric inversion, (2) the constraint from ocean DIC and pCO2 observations, (3) additional terrestrial constraints, and (4) the construction of the joint flux estimate. For details, the reader is referred to the supporting information.
2.1 Unregularized Inversion of Atmospheric CO2
 The atmospheric inversion combines monthly atmospheric CO2 observations with information about transport from 12 different atmospheric transport models to estimate 1992–1996 mean monthly fluxes between the atmosphere and both land and ocean regions. Fluxes represent net CO2 exchange excluding emissions due to fossil fuel burning, cement manufacture, and gas flaring, which are prescribed in the inversion. The same transport models are used as in the Transcom 3 Level 2 (T3L2) study [Gurney et al., 2004]. Observations are from the NOAA Globalview CO2 data set [Globalview-co2, 2009].
 Choosing the T3L2 models and basic setup allows us to assess transport uncertainty and directly compare results to earlier studies, yet it also means our inversion does not resolve interannual variability and is restricted to a relatively short period (1992–96). It is also limited to large-scale regions, which could introduce aggregation errors [Kaminski et al., 2001]. We follow the data weighting scheme developed for T3L2 to reduce these errors, although we have to admit that we cannot fully quantify the success of this approach.
 The setup generally follows the T3L2 control inversion described by Gurney et al. , but with some important deviations. A major difference is that we do not use any regularization techniques, i.e., we do not augment the inverse problem with prior information about fluxes and uncertainty structure. Further differences relate to the preparation of the observational network, the assignment of observational errors, and the global fossil fuel emission estimates [Marland et al., 2008]. However, these differences (details in the supporting information) are of substantially lesser importance compared to the choice of using an unregularized inversion.
2.2 Adding Ocean Constraints
 We use a combination of surface ocean pCO2 and ocean interior DIC data to derive in each region the mean air-sea CO2 fluxes over the 1992–1996 period and their mean seasonal cycle. Namely, we use annual mean air-sea CO2 fluxes estimated from ocean interior DIC data through an ocean inversion and scaled to the 1992–1996 period as our mean flux. The inversion also yields regional covariances, which we preserve in the joint inversion. To those annual mean fluxes we added the seasonal flux anomalies extracted from the surface ocean pCO2 data based flux estimates.
 The ocean inversion uses the Green's function approach introduced by Gloor et al. , with the footprints simulated by a set of 10 different Ocean General Circulation Models (OGCMs) within the scope of the Ocean Inversion Project (OIP) [Mikaloff Fletcher et al., 2006, 2007]. It separately inverts data-based inventories of anthropogenic carbon and natural, preindustrial carbon. The anthropogenic portion is separated from the measured DIC using the ΔC∗ method of Gruber et al.  and the natural component is estimated following Gruber and Sarmiento .
 The final contemporary annual mean flux estimate is formed by summing the two flux components [Gruber et al., 2009]. Because the joint inversion is designed to estimate fluxes representing the 1992–1996 period, the anthropogenic component is referenced to the midpoint of this period before summing. The riverine carbon outgassing is accounted for as described by Jacobson et al. [2007a]. The final contemporary CO2 fluxes and covariances are post-aggregated from the original 30 regions to the 11 oceanic Transcom regions used in the atmosphere inversion.
 The seasonal flux component is extracted from the recent pCO2 climatology of Takahashi et al. [2009a] by removing in each region the annual mean flux. The resulting monthly anomalies are then added to the 1992–1996 mean flux estimates from the ocean inversion. Monthly uncertainties are computed explicitly and are based on the uncertain gas exchange rate and the spatiotemporal sampling density of measurements: We use the spread of the fluxes computed by applying eight different parameterizations for the gas transfer velocity as one component of the flux uncertainty. Another component accounts for measurement undersampling and is proportional to the monthly flux variability in a given region divided by the number of measurements for that region and month. The final uncertainty assigned to a regional/monthly flux is then calculated as root-mean-square of both uncertainty components and lies typically between 0.2 and 0.4 PgCyr−1. The same seasonal flux cycle is used for all OGCMs. Error correlations from the ocean inversion are duplicated for each month and then used in the joint inversion.
2.3 Adding Land Constraints
 So far, no a priori information about terrestrial fluxes has entered the inversion system, allowing us to isolate the information contained in the atmospheric and oceanic carbon data before such priors are introduced.
 We chose to use weak annual flux constraints for four selected large-scale land areas. No monthly land priors are applied. The constraints cover land areas in the tropics and the Northern Hemisphere and are based primarily on bottom-up studies involving inventory methods. Fluxes, uncertainties, and respective references are listed in the supporting information.
 Opposed to other inversion studies, such as T3L2, no assumptions are made with regard to the seasonal cycle of the terrestrial fluxes. For tropical regions, where only a small seasonal flux amplitude is expected, we added a smoothing constraint to limit month-to-month flux variations. The smoothing was implemented as Gaussian with zero mean and a standard deviation of 5 PgCyr−1 for month-to-month differences. As this tends to decrease monthly uncertainties (effectively limiting them to 5 PgCyr−1) and tends to introduce across-month correlations, uncertainties and correlations are always reported based on the nonsmoothed inversion.
2.4 Selecting Atmospheric Transport Models
 For the final mode of our joint inversion setup, we restricted the atmospheric transport models to those three that showed most skill in reproducing annual mean vertical gradients in tropospheric CO2 [Stephens et al., 2007]. These are the GISS, JMA-CDTM, and TM3 models (see Table 3 in the supporting information for a complete list of models and references). However, their success in reproducing annual mean vertical gradients does not imply that these models have superior transport skill in all respects compared to the other models. In fact, for both the boreal winter and summer seasons, these models show vertical CO2 gradients that are smaller than observed, and for each season at least two of the other models perform better than any of this subset [Stephens et al., 2007, supporting information]. Because of the opposing sign of vertical gradients in summer and winter, the effects of a too strong ventilation in summer and winter compensate for each other, which is the reason for those models to reproduce annual gradients accurately. We will discuss the implications of this choice below.
2.5 Joint Inversion
 The joint inversion is set up in four modes to sequentially take into account the four constraints:
 atmospheric CO2 concentration data,
 ocean interior DIC and surface pCO2 data,
 inventory-based land fluxes for large-scale areas, and
 atmospheric model selection.
 The joint inversion is generally performed iteratively to achieve a mean reduced χ2 value of 1. In each iteration step, the observational uncertainty is scaled with a global factor until χ2=1. This procedure is in accordance with that used for Transcom and ensures that data and priors are adjusted by the inversion within a reasonable range compared to their uncertainty [Gurney et al., 2003]. In the supporting information we show that this does not introduce a bias in the model-data mismatch distribution.
 We will use the mode 4 inversion as our control case, as this mode optimizes the fluxes based on all available constraints simultaneously. However, the term control inversion is not a synonym for “best” inversion, but rather for “most informed” inversion. If any of the constraints were incorrect, the joint inversion would produce incorrect results as it balances all constraints. In particular, given the limitations of the model selection scheme, mode 4 should not be viewed as being better than mode 3.
 The sequence of constraints can affect the results from the joint inversion. The ocean constraint plays a key role in our study and is therefore included first, but the ordering of the land and model constraints is arbitrary. To study the influence of the model constraint independent of the land constraint, we defined an additional mode 3b where this ordering is swapped.
 The joint flux vector and covariance matrix are constructed using a Bayesian approach and are represented by a multivariate normal distribution (xj,Cj) with elements for all regions (22) and months (12). The air-sea fluxes are also represented by a multivariate normal distribution (xo,Co) with elements for all oceanic regions (11) and months (12); they enter the joint inversion in the form of prior information (annual air-sea fluxes are additionally included on the data side, see below). The joint inversion seeks the minimum of the objective function J:
where Ma is the atmospheric transport matrix and the vector da contains the atmospheric CO2 observations, the uncertainties of which are included in the diagonal covariance matrix . The matrix H maps the joint estimates into the space of ocean inverse estimates, i.e., it picks the 11×12 air-sea fluxes from the 22×12 element vector xj. A more detailed mathematical description of the inversion is provided in the supporting information. Figure 1 illustrates the construction of the joint fluxes and covariances.
 As the inversion is designed to estimate monthly fluxes, the uncertainty of their annual mean is only indirectly constrained by the monthly flux average and the error correlation structure. In order to inform the joint inversion about the strong constraint provided by the annual mean fluxes stemming from the ocean inversion, these fluxes are formally incorporated as additional observations. That is, both the observational vector da and the observational covariance matrix are extended to accommodate 11 additional elements, representing annual flux and uncertainty estimates from the ocean inversion. The transport matrix Ma is extended accordingly by 11 rows, each forming the annual mean flux from the monthly elements in the flux vector xj. This allows to directly propagate the annual constraints from the ocean inversion into the joint inversion without affecting the monthly prior fluxes and covariances. Despite this formal difference, we use the terms ocean constraint and ocean prior interchangeably throughout the paper.
 Our Bayesian inversion is mathematically equivalent to that used by Jacobson et al. [2007a], despite their different notation as a Kalman filter. This is because both methods propagate the full error correlation structure in Co through the minimization process. We refer to the supporting information for the necessary calculations and the detailed comparison of the Kalman filter with the Bayesian method in this particular case.
 The land constraint introduces only information about annual mean fluxes and uncertainties and does not provide monthly prior information. Unlike the monthly ocean prior, they are not incorporated into the inversion system as an additional prior term. Instead, they enter the inversion formally as additional observations, similar to the annual component of the ocean constraint. The observational vector is expanded by the four annual mean flux estimates and the observational covariance matrix is extended by four rows carrying the squared annual mean uncertainties on their main diagonal. The transport matrix is extended accordingly.
 To assess the performance of the joint inversion in modeling the atmospheric CO2 data, the model-data mismatch was analyzed for all stations and months and also compared to the assigned observational uncertainty. While observational uncertainties increase as more constraints are added to achieve χ2=1 for each mode (overall increase is 32% from mode 1 to 4), the joint inversion produces very similar mismatch distributions for all modes. Mismatch distributions show only very small biases in all modes (more details in the supporting information).
 The joint inversion is performed for each of the 10 oceanic transport models in combination with each of the 12 atmospheric transport models. For all of these 120 model pairs, a joint flux vector is obtained. For the control case (and mode 3b), the number of atmospheric transport models is reduced to three (the Stephens subset), which leaves joint results for 30 model pairs. From these the mean flux vector is calculated, representing the control result. To estimate the uncertainty, two contributions are considered: (1) the mean covariance matrix from all model pairs and (2) the covariance of the mean fluxes among the model pairs. The latter reflects the spread of flux results among models and serves as estimator for transport uncertainty. Despite the different nature of these two contributions, they are combined as a squared sum for simplicity. The resulting “total” uncertainty is what is reported throughout this paper.
3 Results and Discussion
 When presenting and discussing our results, we focus on those from our control inversion and compare them to flux estimates from the annual mean joint inversion of Jacobson et al. [2007a, 2007b] and to the Transcom 3 Level 2 inversion of Gurney et al. . The former (Ja07) differs from ours by being annual-mean only, the latter (T3L2) differs by being a purely atmospheric inversion, and by them applying explicit monthly prior fluxes to all land regions. Both studies cover the same 1992–1996 period, making our results directly comparable to theirs. For the land regions, we put particular emphasis on the evolution of flux estimates as additional constraints enter the inversion.
 Annual mean flux estimates for all modes are listed in Table 1.
Table 1. Annual Posterior Fluxes for All 22 Regions in the Inversion as Well as Some Additional Large-Scale Regionsa
Results from all inversion modes are compared to the inversions of Gurney et al.  (T3L2) and Jacobson et al. [2007b] (Ja07) as well as the bottom-up study of Pan et al.  (Pan11). Pan11 consider forested areas and use slightly different region definitions. Bold numbers indicate 90% statistical significance for the flux sign.
Boreal N America
0.30 ± 0.59
0.25 ± 0.55
0.29 ± 0.59
0.27 ± 0.34
0.20 ± 0.33
−0.13 ± 0.64
−0.23 ± 0.96
−0.46 ± 0.65
−0.65 ± 0.68
−0.36 ± 0.56
0.04 ± 0.72
Temp N America
−1.60 ± 1.25
−0.93 ± 0.76
−0.55 ± 0.61
−0.61 ± 0.55
−0.55 ± 0.49
−1.17 ± 1.76
−0.28 ± 1.13
0.18 ± 0.74
0.34 ± 0.61
−0.41 ± 0.81
−0.81 ± 1.20
2.13 ± 3.74
2.50 ± 2.18
0.74 ± 1.06
5.05 ± 5.13
−0.16 ± 2.92
0.09 ± 1.84
−0.05 ± 1.22
0.79 ± 1.01
1.62 ± 2.95
0.06 ± 4.14
0.51 ± 2.33
0.15 ± 1.63
−0.78 ± 0.69
0.27 ± 1.04
−0.50 ± 2.19
−4.51 ± 4.38
−0.32 ± 1.89
0.29 ± 1.35
−0.37 ± 0.73
−0.24 ± 0.88
−0.84 ± 1.72
1.35 ± 4.51
−1.07 ± 2.88
−0.81 ± 1.61
−0.22 ± 1.00
−0.51 ± 0.83
−1.74 ± 2.57
−0.25 ± 0.31
0.08 ± 0.23
0.05 ± 0.24
0.01 ± 0.19
−0.10 ± 0.21
0.15 ± 0.35
−0.17 ± 0.38
−0.16 ± 0.56
−0.31 ± 0.31
0.08 ± 0.75
−0.29 ± 0.34
−0.64 ± 0.67
−0.20 ± 0.31
0.45 ± 0.89
−0.10 ± 0.24
Trop Indian Ocean
−0.88 ± 0.71
−0.33 ± 0.32
0.66 ± 0.92
0.51 ± 0.57
1.92 ± 1.56
−0.05 ± 0.25
S Indian Ocean
−0.67 ± 0.53
−0.47 ± 0.57
2.86 ± 3.16
1.60 ± 1.50
1.80 ± 1.83
0.36 ± 3.23
0.24 ± 1.43
−0.83 ± 0.79
1.06 ± 1.50
1.12 ± n/a
−3.41 ± 4.08
−1.31 ± 1.87
−0.47 ± 0.89
−0.58 ± 0.63
−0.85 ± 1.17
−2.43 ± 2.02
3.84 ± 3.03
1.55 ± 1.60
1.13 ± 0.95
0.52 ± 0.43
0.95 ± 1.33
0.07 ± 0.78
−0.24 ± 1.04
0.03 ± 0.55
Ocean in South
1.44 ± 2.02
−0.49 ± 0.64
−0.42 ± 2.16
−2.72 ± 2.18
3.1 Sea-to-Air Fluxes
 Annual sea-to-air fluxes are well constrained in our study as was the case for Ja07, due to the small flux uncertainties associated with the ocean inversion (Figure 2). The weighted model mean global annual sea-to-air flux is estimated to be −1.78 (±0.24) PgCyr−1by the ocean inversion. Subtracting this number from the global sink estimate for the Earth surface leaves −1.25 (±0.29) PgCyr−1as annual mean global land-to-air flux, in agreement with the T3L2 estimate of −1.47(±0.97) PgCyr−1, but with a major uncertainty reduction of 70%. Ja07 estimated a slightly smaller terrestrial sink of −1.12(±0.23) PgCyr−1, mainly driven by their smaller estimate for global uptake.
 Annual posterior sea-to-air fluxes are consistent with Ja07 (Table 1) due to their using a similar constraint. Estimates are not equal, because Ja07 used a different set of ocean transport models; they used 10 models of which 5 correspond to the PRINCE model setups also used by us (see table in the supporting information). The similarity is mainly due to the overdetermined character of the ocean inversion as it is constrained by large amounts of data that reduce the impact of varying ocean transport models.
 Considerable differences exist in the T3L2 study, in particular, for the tropical and Southern Hemisphere oceans. T3L2 estimated global tropical oceans to be nearly neutral and Southern Hemisphere oceans to be a weak carbon sink of −0.49 (±0.64) PgCyr−1, while our control inversion estimates a tropical outgassing of 0.58 (±0.10) PgCyr−1 and a strong carbon sink of −1.41 (±0.15) PgCyr−1for Southern Hemisphere oceans, consistent with direct observations [Gruber et al., 2009; Takahashi et al., 2009b].
 The small flux uncertainties associated with the ocean inversion are a consequence of the large amount of ocean interior DIC data and the resulting negligible internal uncertainty. Remaining uncertainties are due to transport uncertainty. As discussed by Mikaloff Fletcher et al. , another possible error source is a bias in the carbon data sets underlying the ocean inversion. Matsumoto and Gruber  pointed out that the applied ΔC∗ method to separate anthropogenic CO2 from observed DIC may overestimate (by about 10%) anthropogenic CO2 in the upper ocean and slightly underestimate it in the deep ocean, leading to a global overestimation by about 7%. In order to investigate what effect such a bias would have on the estimated CO2 fluxes, we applied a correction factor to the anthropogenic CO2 as a function of water density and inverted the corrected data. In agreement with Mikaloff Fletcher et al. , the estimated flux of anthropogenic CO2 scales approximately linearly with the correction factor. The preindustrial flux estimates show almost no change, resulting in an 8% global reduction of the total (anthropogenic plus preindustrial) CO2 flux. We conducted a joint inversion with this corrected ocean prior to investigate the sensitivity of the land fluxes to the ocean data bias. It turns out that the estimated land fluxes show only little changes in all regions. Owing to the global flux constraint, the global land flux is increased by 8%, but this increase is distributed homogeneously over the land regions and leads nowhere to a significant change. We conclude from these analyses that a potential bias in anthropogenic CO2 would only slightly affect the joint flux estimates for both oceanic and land regions.
 In the joint inversion, the seasonal variability of air-sea prior fluxes is less constrained than the annual mean, as it is not based on the ocean inversion, but on the pCO2 climatology of Takahashi et al. [2009b]. As a result, the addition of the land and transport constraints has an effect on monthly air-sea flux estimates. However, this effect remains small in most regions. Exceptions are the northern oceans that are found to be more seasonally variable than suggested by the pCO2 prior, and the Southern Ocean, whose seasonal amplitude is increased by the joint inversion. The control inversion estimates a Southern Ocean outgassing of 0.3 PgC accumulated over the months July to October. By contrast, T3L2 found the Southern Ocean to be a constant sink throughout the year with much smaller seasonal amplitude, which is inconsistent with the pCO2-based estimates. Another issue with the weak ocean prior used by T3L2 is that it allows the inversion to erroneously allocate seasonal flux variability to ocean regions, which might in fact be caused by seasonal flux variability over adjacent land areas [Gurney et al., 2004].
3.2 Northern Extratropical Land
 Of all land fluxes, those for the Northern Hemisphere extratropical land (boreal and temperate) are generally best constrained by atmospheric CO2 concentrations, mainly due to the better observational coverage. Nevertheless, the inclusion of the ocean constraint in mode 2 of our joint inversion reduces the annual northern extratropical sink significantly (Figures 3 and 4). It also drives the total uncertainty below 2 PgCyr−1. The main effect of the further inclusion of land and model constraints in modes 3 and 4 is a continued uncertainty reduction until the control estimate of −1.8 (±0.4) PgCyr−1is obtained. The effect of the model subsetting does not depend on whether the land prior is applied or not, i.e., the difference between modes 3b and 2 is very similar (details in the supporting information) to that between modes 4 and 3. Thus, our method is able to isolate the effect of model subsetting from the effect of constraining land fluxes so that the ordering of constraints does not compromise the conclusions drawn from interpreting flux changes between modes 3 and 4. This is the case not only for northern extratropical land but for all land regions.
 This Northern Hemisphere extratropical land sink is much weaker than estimated by T3L2 and Ja07, yet still larger than estimated by a recent bottom-up study of Pan et al.  (henceforth Pan11), who find −1.1 (±0.1) PgCyr−1. This comparison needs to be applied with caution, however, as their study is based on forest inventory data and long-term ecosystem carbon studies and therefore accounts for forested areas only. In addition, their estimates represent the 1990-1999 period and their region definitions differ from ours. We accounted for the latter by aggregating their regions as closely as possible to the Transcom set of regions, but slight differences remain.
 Annual control results for the boreal regions in America and Asia are in very good agreement with the studies of T3L2 and Ja07 (Figure 3 and Table 1). They are not sensitive as to which constraints are included: already the atmosphere-only inversion (mode 1) is very similar to the control mode. Seasonal variability is also very consistent between T3L2 and all modes of the joint inversion. Uncertainties decrease only slightly when more constraints are added. Thus, fluxes from those regions are robust and can be determined by the inversion of atmospheric CO2 observations alone. Boreal regions take up −0.31 (±0.36) PgCyr−1, which is in very good agreement with Pan11, who estimated −0.29 (±0.06) PgCyr−1(our “Europe” region contains both Pan11's “European boreal” and “Europian Russia boreal” regions, which were aggregated accordingly).
 Annual uptake by northern temperate land is estimated to −1.5 PgCyr−1, smaller than the estimates of T3L2 and Ja07 (−2.3 PgCyr−1and −2.8 PgCyr−1, respectively) and closer to the estimated forest sink of −0.8 PgCyr−1of Pan11. The main reason is that the control inversion suggests a weak source of carbon in temperate Asia, while both Ja07 and T3L2 suggest a considerable sink. The switch from sink to source is caused by the inclusion of the land constraint in the inversion (see difference in annual mean flux between modes 2 and 3 in Figure 3). In mode 3, the Eurasian land region (boreal and temperate) was constrained to −0.5 (±0.4) PgCyr−1. Because the boreal Asian region and Europe are well-constrained by atmospheric CO2, the joint inversion preferably adjusts the flux from temperate Asia to match the constraint.
 Over temperate Asia, CO2 uptake during the growing season is greatly reduced compared to T3L2. Not only the total uptake is reduced but also the length of the growing season. It covers the months May to July, whereas it extends until September in the T3L2 study. This reduction is a consequence of the ocean constraint, which alters the seasonal cycle of the region despite the fact it constrains only ocean regions directly and is relatively weak at the seasonal scale. Further inclusion of the land and transport constraints does not have much impact. It is interesting to note that the reduced growing season uptake is not due to a simple reallocation of flux from adjacent ocean regions. For example, T3L2's strong seasonal signal in the tropical Indian ocean is not directly propagated to temperate Asia, as this would result in enhanced CO2 uptake there during the growing season. The same is true for the other two adjacent ocean regions, i.e., the north and west tropical Pacific. Hence, the reduced growing season uptake is a result of the application of the whole ocean constraint, and not only of a few selected regions.
3.3 Tropical Land
 We estimate a net annual pantropical land source of 1.1 (±0.9) PgCyr−1in our control inversion. Assuming a global tropical deforestation rate of 1.3 (±0.8) PgCyr−1[Houghton, 2003; Sarmiento et al., 2010] implies a near-neutral flux of 0.2 (±1.2) PgCyr−1for tropical regions unaffected by deforestation. Our joint inversion locates the net source solely in the tropical American region, which consists mainly of the Amazonian tropical rainforest. A more detailed discussion about implications for Amazonia follows later, while we focus here more on our results for the tropics in general and their sensitivity to the inclusion of additional constraints.
 Tropical land regions are often negatively correlated with Southern Hemisphere extratropical land regions, making regional flux uncertainties dependent on each other. This is discussed in more detail below.
 The control inversion finds the northern African region to be annually balanced with little seasonal variability (Figure 5). If the inversion is constrained by atmospheric CO2 alone (Figure 3), a huge source of 5.1 PgCyr−1is diagnosed there, together with an uncertainty of the same magnitude and an unrealistically strong seasonal variability. The inclusion of the ocean constraint completely changes the picture: northern Africa is now estimated to be annually balanced with a 42% reduction in uncertainty. The seasonal variability is reduced substantially and reflects already clearly the control case. Additional inclusion of land and model constraints does not alter the mean flux much, apart from a further reduction in uncertainty. The seasonal pattern is in general agreement with T3L2, although they found a more pronounced Northern Hemisphere type cycle with summer sink and winter source. While the estimate by T3L2 is strongly driven by the use of monthly land priors, ours is mainly a result of the strong ocean constraint, demonstrating the power of the ocean constraint for determining land fluxes.
 Tropical Asia is found to be an annual CO2 sink of −0.8 (±0.7) PgCyr−1, significant at an 87% level, compared to the insignificant source/sink attribution of T3L2 and Ja07. In modes 1 to 3, the annual mean flux is close to zero or weakly positive, before the inclusion of the transport model constraint drives it toward that sink. It is also in mode 4 that the uncertainty is reduced significantly by more than 50%, indicating that estimates for this region are very sensitive to the choice of transport models and highlighting similar transport characteristics in the tropics among the Stephens model subset.
 The constraint for the annual pantropical land flux was −0.1 (±1.1) PgCyr−1 [Sarmiento et al., 2010]. The posterior estimate of 1.1 (±0.9) PgCyr−1deviates clearly from that, owing to the constraints from both atmosphere and ocean (Figure 3). Hence, for tropical land areas, and in particular for tropical America, the information from land inventories and from ocean and atmosphere inversions continue to disagree (Figure 4). The ocean constraint drives the tropical American region toward a strong source of carbon, while the tropical regions in Asia and Africa are estimated to be sinks and neutral, respectively. To see whether it is the oceanic or rather the atmospheric constraint that implies the source, we conducted an inversion (not shown) where we replaced the standard twofold ocean constraint by a monthly oceanic CO2 flux prior based on pCO2 measurements alone. This prior had the same seasonal flux pattern as the original one, but with much larger uncertainty for annual fluxes (due to the lack of strong annual constraints from the ocean inversion). As a result, the tropical American source was halved and the pantropical source decreased to 0.2 PgCyr−1. Thus, it is the strength of the annual ocean flux constraint, combined with the information about the error structure of regional ocean fluxes, that implies the sizeable tropical land source, and not so much the a priori seasonal information.
3.4 Tropical Land Source and Northern Land Sink
 The balance between the tropical source and the Northern Hemisphere extratropical land sink is highly sensitive to the selection of models, confirming the results of Sarmiento et al. . Going from mode 3 to mode 4, the tropical source is reduced by nearly 0.6 PgCyr−1along with a reduction in Northern Hemisphere uptake. Figure 4 illustrates this correlation for all four inversion modes: The reduction of the tropical source appears to be mirrored by that of the northern sink.
 The reason why the Stephens model subset reduces this flux dipole is their tendency to have very strong atmospheric ventilation in both boreal winter and summer. In an atmospheric model with strong ventilation in boreal winter, the respired CO2 over or downwind from Northern Hemisphere continental areas is removed faster from the boundary layer. In the context of an inversion, this requires a stronger carbon source to match the elevated CO2 signal at boundary layer observing sites during winter. Similarly, in summer a strong ventilation makes a larger carbon sink necessary over northern land. This correlation between flux strength and ventilation rate is very strong for winter and rather weak for summer (probably due to opposing effects of fossil emissions and terrestrial carbon uptake during summer, cf. Stephens et al. ) and leads to a larger seasonal amplitude of northern land CO2 fluxes. When averaged over a year, the net effect of elevated ventilation is to reduce the annual mean carbon sink over Northern Hemisphere land. These two features of enhanced seasonal amplitude and reduced annual sink can be identified in our results for, e.g., Europe and temperate North America (Figure 3), where all-model mean (mode 3) results are compared with control (mode 4) results. Annual uptake of aggregated Northern Hemisphere land is reduced by more than 0.6 PgCyr−1(Figure 3).
 The tropical source reduction is not distributed homogeneously among the continents of Africa, Asia, and America. On the one hand, northern Africa remains neutral and tropical Asia is estimated to be a sink. Over tropical America, on the other hand, CO2 release increases by almost 0.6 PgCyr−1to 1.9 (±0.8) PgCyr−1from modes 3 to 4. For both the tropical Asian and American regions, the modeled uncertainties are greatly reduced, because the model subset agrees better on the flux estimates than all models. The model mean Bayesian error (within-model uncertainty) becomes comparable to the across-model spread for the tropical American region and even dominant for tropical Asia. For these two regions, this effectively attenuates transport error, making the uncertainty due to the lack of observations more apparent in tropical land areas. The tropical American control source exceeds 1 PgCyr−1with a probability of 88%.
3.5 Tropical and Southern Land Covariance
 As is often the case in atmospheric inversion studies [Gurney et al., 2004; Jacobson et al., 2007a; Gurney et al., 2002], the posterior error structure exhibits a strong negative correlation between tropical and Southern Hemisphere land areas, allowing the sum of both to be constrained much better than each individually. This follows from the ill-posed character of the inversion problem owing to the sparse and heterogeneously distributed observational data, while the global scale constraints are strong. As a result, the aggregated flux from tropical and Southern Hemisphere land (henceforth TSL) can be estimated with higher certainty than the individual fluxes (Figure 6).
 Figure 1 shows the 68% confidence ellipses for the tropical-Southern Hemisphere land combination based on the posterior covariance matrix. The strong error correlation between the two regions manifests itself in the narrowness of the ellipses and the tilt of their major axes toward the line with slope −1. For the model-mean ellipses, the 1σposterior total uncertainties for the individual regions are shown as well. By adding more constraints, the individual uncertainties as well as the area of the error ellipses are reduced significantly. The correlation (the off-diagonal element of the 2×2 correlation matrix) remains similar; it changes slightly from −0.8 to −0.9 when the ocean constraint is added and goes back to −0.8 after adding the land constraint.In general, in most regions and region aggregates, the additional constraints have a much smaller impact on posterior correlations than on fluxes and uncertainties; the posterior error structure remains largely determined by the atmospheric part of the inversion (see the supporting information for more details on region-region correlations). Exceptions are ocean-land region pairs, for which the ocean constraint often reduces posterior error correlations. This is because it constrains oceanic fluxes separately and increases their independence from land regions, which enables the joint inversion to better discriminate between ocean and land regions.
 Our control inversion finds a TSL source of 0.5 (±0.4) PgCyr−1, much smaller than the 1.8 (±1.1) PgCyr−1 estimate of Ja07 and also the 1.0 (±1.3) PgCyr−1estimate of T3L2. The main reason for this smaller source is the relatively small outgassing from tropical land, as discussed previously. The main portion of the uncertainty reduction is due to the inclusion of the ocean and the model constraints. Our TSL source is still larger than estimated by Pan11's forest inventory study, who find the region nearly neutral (0.1 (±0.8) PgCyr−1). It is encouraging that most of the convergence of both TSL estimates does not come from the inclusion of the bottom-up land constraint in mode 3, but from the ocean and model constraints.
 The TSL seasonal cycle is characterized by strong CO2 release in austral winter/spring, and uptake during summer/fall. The seasonal amplitude is much larger than estimated by T3L2, which results from the combined effect of increased southern land seasonal amplitude and a nearly anti-phased tropical seasonal cycle. The more pronounced seasonal cycle over TSL, in concert with the increased (boreal) winter respiration over northern land, leads to significant changes in the seasonal cycle of the global land area (Figure 3, overall land). Global seasonal amplitude is increased and the seasonal pattern markedly asymmetric compared to the T3L2 results. The asymmetry results from large release rates in September–December, together with small uptake rates in January–April.
3.6 Implications for the Carbon Balance of Amazonia and of Tropical America
 To obtain a flux estimate for Amazonia we map the tropical American source back on the prescribed within-region flux pattern used to create the model footprints and re-integrate over Amazonia. For easy comparison with other studies we follow Malhi et al.  and define Amazonia as the Legal Amazon in Brazil and the Amazon River watershed and Guyanas region outside of Brazil, summing up to 5 million km2. This results in a net annual mean Amazonian source of 1.1 (±0.5) PgCyr−1during 1992–1996.
 Estimates for carbon release in Amazonia due to deforestation lie between 0.3 and 1.1 PgCyr−1 for the 1990s [Malhi et al., 2008; Ramankutty et al., 2007; Houghton, 2003; DeFries et al., 2002] with a central estimate around 0.5 PgCyr−1[Malhi et al., 2008]. When using this estimate, our results imply a biospheric source of 0.6 (±0.5) PgCyr−1 in areas of pristine forests. A source of this size disagrees with most bottom-up studies, which usually find pristine tropical forests to be sinks for carbon. Baker et al.  and Phillips et al.  conducted studies based on observed changes in local biomass inventories and suggested that intact forests (plot results upscaled to 5 million km2) are a sink of up to −0.6 PgCyr−1. Upscaled estimates from eddy covariance measurements span the range from −0.5 to −3.0 PgCyr−1 sink strength in old-growth Amazonian forest [Ometto et al., 2005], where the spread reflects the heterogeneity within tropical forest ecosystems and the associated difficult upscaling process. The study of Saleska et al.  was also based on eddy flux observations, but for the first time identified a carbon source of 0.65 PgCyr−1in undisturbed forest areas. As opposed to other flux tower studies, they applied a correction to their measured nocturnal fluxes, in order to compensate for the effect of lateral carbon exchange that may not be detected by the instruments during calm nights without turbulence, resulting in an underestimation of nocturnal carbon release. They pointed out that without this correction, they would have found a sink instead of a source, like most other flux tower studies.
 Thus, the possibility of a positive carbon net flux from Amazonia cannot be excluded by bottom-up studies. Our finding of an annual mean source of 0.6 PgCyr−1(±0.5) is unexpected, though consistent with the study of Saleska et al. . We may ask the question if the selection of transport models according to Stephens et al.  is justified, as we find a considerably smaller source when averaging over all 120 model pairs (mode 3). Generally, as described above, these models predict a smaller tropical land source in conjunction with a weaker Northern Hemisphere land sink. But this reduction is not distributed evenly and is a result of the combination of partly offsetting effects: a significant carbon sink in tropical Asia and a substantial increase in tropical American CO2 release, while northern Africa remains neutral. Due to the large uncertainties the latter is statistically not significant, but both the tropical Asian sink and the tropical American source are well constrained, mainly due to a substantial enhancement of model agreement in the subset compared to all model pairs. The posterior error structure does not reveal any significant correlations between the two regions, suggesting that both are constrained individually. The driving constraints for the annual tropical Asian flux are the model selection and the ocean prior, while for the tropical American region, they resemble a tug of war between the land constraint and the ocean and model constraints.
 To see the influence of the ocean constraint on the tropical American flux, it is useful to look at Ja07's annual joint inversion, as they constrained the ocean with similar (annual) flux information. They found an even stronger source of 3.1 (±2.4) PgCyr−1 across tropical America and a 4.2 PgCyr−1 pantropical source resulting from an additional 1.6 PgCyr−1northern African source, whereas we find northern Africa to be neutral. Therefore, the ocean constraint generally drives a joint inversion (whether annual or seasonal) toward a large source in the tropics that is predominantly located on the American continent.
 The seasonal cycle over tropical America (Figure 5) suggests the region to be nearly neutral during months January to July, with an average carbon release of only 0.2 (±1.1) PgCyr−1. However, for the remainder of the year (months August to December), a very strong release of 4.2 (±1.3) PgCyr−1is estimated. The August to December outgassing is a robust feature across all modes of our joint inversion (Figure 3): It is already apparent in the atmosphere-only inversion, but becomes statistically significant only in mode 4. The transition from a neutral balance to a strong CO2 source happens rapidly between July and August, roughly coinciding with the onset of the Amazon mean wet season. The outgassing continues throughout the wet season with only little decline, before the region switches back to its neutral state in January. As Amazonia represents the main part of the tropical American region, we might conclude from these results that large parts of the rainforest release CO2 during the Amazon mean wet season. While this is consistent with other studies [e.g., Phillips et al., 2009], the uncertainties associated with our monthly flux estimates are too large to support strong statements about the underlying process. However, despite the large monthly uncertainty, we can state that the mean August to December CO2 source exceeds 2 PgCyr−1with a probability of 95%.
3.7 Southern Extratropical Land
 For Southern Hemisphere extratropical land, the control inversion estimates a sink of −0.6 (±0.6) PgCyr−1, in good agreement with the T3L2 flux of −0.9 (±1.2) PgCyr−1, although the uncertainties are so large that little process information can be deduced. Ja07 estimated an even larger uptake of −2.4 (±2.0) PgCyr−1. They assigned a significant uptake also to southern extratropical America, which is only a weak sink in both the T3L2 and our studies. Estimates for the Southern Hemisphere land flux are generally accompanied by large uncertainty due to the very limited availability of CO2 observations from Southern Hemisphere continental sites, which makes the various flux estimates formally consistent with each other, despite their large differences.
 Figure 3 reveals that for southern Africa the ocean constraint plays a key role in determining the annual mean flux as well as the seasonal variability. An explicit monthly land prior (as applied by T3L2) is therefore not needed to constrain fluxes much better than by atmospheric CO2 observations alone.
 The same is true in southern extratropical America, where the ocean constraint strongly adjusts the annual mode 1 sink of 4.5 PgCyr−1to a nearly balanced flux, which is subsequently changed only marginally by the land and model constraints. The seasonal cycle is also determined to a large extend already by the ocean constraint. In modes 2–4 the annual mean flux is consistent with T3L2. The seasonal flux amplitude is also consistent among modes 2–4, but is greatly enhanced compared to T3L2. This is partly due to the monthly land prior used by them, but the main reason is a change in how we detrended the transport model response fields during the computation of the cyclostationary response compared to T3L2 (see supporting information for more details). While this affects all regions in principle, it is negligible in all but the southern extratropical American region. We reproduced the T3L2 results and found that, if Gurney et al.  had used the same detrending in their T3L2 inversion, they would have detected a larger seasonal amplitude as well.
4 Summary and Conclusions
 The power of each constraint in the joint inversion is substantial: Omitting one constraint leads to substantial changes in the estimated fluxes and their associated uncertainties. While the uncertainty is reduced significantly by each constraint, the sign significance of the flux estimates does not necessarily increase (Figure 4). Posterior error correlations are largely determined by the atmospheric part of the inversion with the exception of ocean-land region pairs, where the ocean constraint often reduces them.
 For some regions, such as Northern Hemisphere land, all constraints drive the results in the same direction. However, in other regions two or more constraints point into opposite directions, for example, in tropical America, where the ocean prior and selected models imply a strong source, while the inventory-based annual land constraint suggests a neutral balance. This inconsistency between constraints may be real, e.g., data from inventories tell a different story than ocean data, or may be caused by data scarcity over tropical land or systematic deficiencies in the transport models.
 Inclusion of the ocean constraint has a major influence on flux estimates from underconstrained regions with only little available CO2 measurements, located in the tropics and Southern Hemisphere. In particular, it is the key constraint for regions in Africa and South America. Here the inclusion of further constraints does not lead to major changes in the seasonal flux cycle, nor in the annual mean flux, yet continues to decrease the uncertainty.
 The seasonal cycle in temperate Asia is mainly shaped by the inclusion of the ocean constraint as well, despite the better coverage of atmospheric CO2 sites there. We find the growing season to last only from May to July, in contrast to estimates from our atmosphere-only inversion and the T3L2 results of Gurney et al. , which extend it until September. When averaged over a year, the region is estimated to be neutral or a weak source.
 Fluxes from Northern Hemisphere land are already well-constrained by atmospheric CO2 alone, so that our results are in good agreement with previous atmosphere-only inversions. We estimate, however, an enhanced seasonal amplitude, driven by stronger winter respiration. This is mainly a result of the transport model constraint in mode 4, because selected models are characterized by enhanced ventilation over Northern Hemisphere land. Due to the seasonal coupling of atmospheric transport and CO2 fluxes, those models require stronger CO2 fluxes, in particular during winter when this coupling is strongest.
 Pantropical land is estimated to be a source of carbon, significant at the 90% level. This source is located solely in tropical America. It is partially offset by a sink in tropical Asia. Transport model subsetting has a strong influence on tropical fluxes, with different effects on the American and African/Asian continents. The aggregated African and Asian tropical flux is decreased, in fact turns from a source into a sink. By contrast, the tropical American source increases, despite the fact that the sink over temperate North America is reduced. This suggests that over the American continent the northern-tropical coupling does not play a key role, as opposed to the rest of the globe. Instead, it seems that those models show a stronger coupling between the tropics and the Southern Hemisphere, as the South American flux is decreased (i.e., turns from a source into a sink) by the model constraint.
 For the Amazonian region we find an annual mean biospheric source of 0.6 PgCyr−1after downscaling and subtracting a deforestation rate of 0.5 PgCyr−1. This disagrees with most bottom-up studies, which typically assign tropical American rainforests a sink of carbon. However, Saleska et al.  pointed out that analyses based on eddy covariance towers could be biased without proper correction of nocturnal fluxes during calm nights. After them applying such a correction, they obtained a source of 0.65 PgCyr−1for the Amazonian rainforest, in very good agreement with our result.
 For aggregated northern land and TSL regions, our results compare much better to the recent forest inventory study of Pan et al.  than those of other atmosphere or atmosphere-ocean inversions. Encouragingly, the reason for us to find a consistent weakening of the northern land sink and the TSL source is predominantly a result of the ocean and model constraints and not so much of the land constraint. Hence, it is possible to reconcile bottom-up with top-down fluxes without the need of a strong land prior.
 To conclude, well-constrained air-sea CO2 fluxes can substantially reduce flux uncertainties of large-scale land regions. These ocean fluxes permit to reconcile top-down estimated land fluxes with bottom-up estimates in many regions, though with notable exceptions such as tropical America. Further reductions in uncertainties require, however, more and better distributed observations and/or the inclusion of more powerful land constraints, such as process information or monthly priors. Finally, atmospheric transport errors need to be better understood and improved upon.
 We acknowledge the financial support of the EU through the collaborative CARBONES project under the 7th Framework Program (contract 242316). This work was further supported by funding from the Swiss State Secretariat for Education and Research (project C07.0077) as a contribution toward COST action 735. We thank Andy Jacobson and two anonymous reviewers for detailed and insightful comments that helped to improve the manuscript.