Atmospheric inversion of the surface CO 2 flux with 13 CO 2 constraint

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Introduction
Over the last few decades, much progress has been made in estimating the global carbon cycle using different methods (Houghton et al., 2007;Canadell et al., 2007;Le Quéré et al., 2009).In particular, atmospheric CO 2 data measured near the surface have been used to infer the carbon flux over land and ocean surfaces through atmo-Figures

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Full  Peters et al., 2007).However, the uncertainty in the inferred flux is still very large, mostly because of the insufficient number of observation stations and the error in modeling the atmospheric transport of CO 2 from the surface to the observation stations.
To reduce this uncertainty, it would be useful to introduce constraints to the inversion using other gas species that are associated the CO 2 flux.
Measurements of the atmospheric concentration of the stable isotope 13 CO 2 at a number of stations across the globe since 1994 have been compiled in a database (GLOBALVIEW-CO2C13, 2009), and the number increased to 76 by 2009.The mole fraction of 13 CO 2 to CO 2 in the atmosphere is about 1.1 %, and the CO 2 exchange between the surface and the atmosphere would inevitably involve 13 CO 2 exchange.However, the proportion of the 13 CO 2 flux relative to the CO 2 flux differs at different locations and different times due to different mechanisms that discriminate against the heavier 13 CO 2 molecules in the exchange processes, and therefore the 13 CO 2 concentration measured in the atmosphere contains additional information for the CO 2 flux.This information is useful for differentiating between terrestrial and oceanic CO 2 exchanges with the atmosphere because the terrestrial CO 2 flux experiences much greater discrimination against 13 CO 2 than does the oceanic CO 2 flux (Tans et al., 1990;Ciais et al., 1995b;Francey et al., 1995).The other potential use of 13 CO 2 data is to differentiate between photosynthetic and respiratory fluxes over land as these two fluxes have different rates of discrimination against 13 CO 2 (Fung et al., 1997;Randerson et al., 2002;Suits et al., 2005).The 13 CO 2 observations over the globe, albeit with a limited number of stations, could therefore be used to assist in quantifying the global carbon cycle.
In previous studies (Siegenthaler and Oeschger, 1987;Keeling et al., 1989a;Francey et al., 1995;Randerson et al., 2002), atmospheric 13 CO 2 observations have been used to separate ocean and land CO 2 fluxes through the use of a technique dubbed "double deconvolution", by which the CO 2 fluxes of land and ocean are separated (deconvolved) based on different discrimination rates against 13 CO 2 in the atmospheric CO 2 exchange with land and ocean surfaces.This double deconvolution necessarily assumes that the discrimination rates over land and ocean are uniform and constant.Figures Through forward atmospheric transport modeling, the ocean and land CO 2 fluxes were also separated based on the spatial gradients of the measured 13 CO 2 /CO 2 ratio either globally (Keeling et al., 1989b) or by latitudinal bands (Ciais et al., 1995a).The same 13 CO 2 data have also been used in inverse modeling of the surface CO 2 flux (Enting et al., 1995;Rayner et al., 1999Rayner et al., , 2008)).Enting et al. (1995) pioneered a methodology for inverting annual mean ocean and land CO 2 fluxes from both atmospheric CO 2 and 13 CO 2 concentration data for 12 ocean regions and 8 land ecosystems for the 1986-1987and 1989-1990periods. Rayner et al. (1999) ) developed a different methodology to invert monthly CO 2 fluxes for 12 ocean and 14 land regions for the period from 1980 to 1995 from CO 2 observations at 12 stations and 13 CO 2 and O 2 /N 2 observations at 1 station.Rayner et al. (2008) refined their methodology and applied it to the period from 1992 to 2005 using CO 2 at from 67 sites and 13 CO 2 at 10 sites.These studies showed the usefulness of the additional information from 13 CO 2 observations in improving the inversion of annual mean and seasonality of the CO 2 flux over land and ocean.In these inversion studies, the discrimination rate for land is either assumed to be a constant (Enting et al., 1995;Rayner et al., 1999) or allowed to vary with the areal fraction of C4 plant in a region (Rayner et al., 2008).These inversions based on the Bayesian principle were also constrained with only simple prior estimates of the terrestrial and oceanic CO 2 and 13 CO 2 fluxes.Since the data density (the numbers of CO 2 and 13 CO 2 observation sites) is low, the assumed discrimination constants and these prior estimates would have considerable influence on the inverted results, as this is clearly demonstrated in Enting et al. (1995).
The overall goal of this study is to explore the information content of 13 CO 2 measurements for global CO 2 flux estimation through developing a Bayesian synthesis inversion system that uses both CO 2 and 13 CO 2 observations.This system is used to address the following specific objectives: (1) to investigate the difference in the inverted CO 2 flux by including 13 CO 2 data in the inversion, (2) to evaluate the importance of considering the spatial distributions of the 13 CO 2 discrimination rate over land and ocean in Figures the inversion of the CO 2 flux, and (3) to assess the impacts of 13 CO 2 disequilibria over land and ocean on the CO 2 inversion results.To achieve these objectives, a terrestrial ecosystem model named the Boreal Ecosystem Productivity Simulator (BEPS) is further developed to simulate the spatial distributions of the 13 CO 2 discrimination and disequilibrium rates over land and used them in a global synthesis Bayesian inversion with 13 CO 2 constraint.BEPS is also used to produce CO 2 and 13 CO 2 fluxes globally as prior fluxes to regularize the inversion.

Inversion system
The nested inversion system with a focus on North America developed by Deng et al. (2007) is adopted in this study.In this system, two of the Transcom regions (Gurney et al., 2002) in North America are divided into 30 regions according to ecosystem type and administrative boundaries (Fig. 1), in order to reduce spatial aggregation errors in the inversion over North America and to investigate the inverted spatial distribution of the carbon flux against ecosystem model results.Also shown in Fig. 1 are the spatial distributions of 210 CO 2 and 73 13 CO 2 observation sites selected in this study from the NOAA GLOBALVIEW database.Most 13 CO 2 sites except 11 are collocated with CO 2 sites.

Synthesis Bayesian inversion with CO 2 observations
To estimate the CO 2 flux (f), we represent the relationship between CO 2 measurements and the flux from the surface by a linear model: Introduction

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Full where c m×1 is a given vector of m CO 2 concentration observations over space and time (m equals number of stations times number of months, and for CO 2 only inversion, it is 12600, i.e. 210 stations ×60 months); ε m×1 is a random error vector with a zero mean and a covariance matrix cov(ε) = R m×m ; G m×(n−1) is a matrix representing a transport (observation) operator, where n − 1 is the number of fluxes to be determined (equals 3000, i.e.50 regions × 60 months); A m×1 is a unity vector (filled with 1) related to the assumed initial well-mixed atmospheric CO 2 concentrations (c 0 ) before the first month; and f (n−1)×1 is an unknown vector of monthly carbon fluxes of all studied regions.
Combining matrixes G and A as M m×n = (G, A) and vectors f and c 0 as Eq. ( 1) can be expressed as The inverse problem of estimating s from c is often poorly constrained and a Bayesian approach is used to circumvent this problem.Pre-existing knowledge and models incorporating additional sources of information can be used to provide an initial estimate of s, known as the a priori, to constrain the inverse problem.This a priori is then updated when it is combined with information from c measurement to form posterior estimate of s, known as the a posteriori.In Bayesian synthesis inversion (Tarantola, 1987), the following objective function is employed in the place of the traditional least square objective function: where s p,n×1 is the a priori estimate of s; the covariance matrix Q n×n represents the uncertainty in the a priori estimate; and R m×m is the transport model-data mismatch error covariance.By minimizing this objective function expressed in Eq. (3), we obtain the posterior best estimate of s as (Enting, 2002):

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Full Meanwhile the posterior uncertainty matrix for the posterior flux can be deduced as follows: We employ the sum of squares of normalized residuals of optimized CO 2 and 13 CO 2 after the inversion relative to observations to perform a χ 2 test to the consistency of the fit to data and prior flux estimates simultaneously (Gurney et al., 2003).

Synthesis Bayesian inversion with both CO 2 and 13 CO 2 observations
We attempt to use 13 CO 2 observations to provide an additional constraint to the otherwise CO 2 -only inversion presented above.This additional constraint is possible on the grounds that air 13 CO 2 concentration is affected differently by carbon fluxes through the ocean and land surfaces.Since the 13 CO 2 gas is transported passively in the same way as CO 2 , the same transport matrix M applies to 13 CO 2 data to associate 13 CO 2 observations with the surface 13 CO 2 flux.In order to conduct an inversion using both CO 2 and 13 CO 2 observations, we simply append 13 CO 2 -related data to the c, R and M matrixes in Eq. ( 4), while the s matrix remains unchanged as the purpose of this joint inversion is only to improve the CO 2 flux.For c and R, 13 CO 2 observations and their variances are appended directly to the original matrixes for the CO 2 only case, as shown in Eq. ( 6).Similarly, the M matrix is also extended to consider 13 CO 2 transport, and the relevant elements for the 13 CO 2 observation stations are from the original M matrix.However these elements are multiplied by a ratio of the CO 2 to the 13 CO 2 flux for each station and each month in order to convert the 13 CO 2 flux into the CO 2 flux.The underlying assumption of this mathematical treatment is that the ratio of these two prior fluxes is not affected by the inversion process, i.e., the posterior ratio is the same as the prior ratio.The extended M is a combination of the corrected M matrix appended to the M matrix for CO 2 (see Figures

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Full where c i is the CO 2 concentration (i=1 to m) and 13 CO 2 concentration (i=m+1 to m+k) from the starting month (i=0); M ij is the transport operator between region j and station i; and in which R j is the ratio of the 13 CO 2 to the CO 2 flux for region j.
For ocean regions, R j is calculated with following formula (Ciais et al., 1995): where S o,j ( 13 C) is the ocean net 13 CO 2 net flux in region j, S o,j (CO 2 ) is the ocean net CO 2 flux, α ao,j is the atmosphere-to-ocean fractionation, R a is the 13 C/ 12 C ratio in the atmosphere (‰), F oa,j is the one way ocean-to-atmosphere CO 2 flux, and R oe,j = α oa,j / α ao,j * R o , where R o is the 13 C/ 12 C where c i is the CO 2 concentration (i = 1 to m) and 13 CO 2 concentration (i = m + 1 to m + k) from the starting month (i = 0); M ij is the transport operator between region j and station i; and W ij = R j M ij , in which R j is the ratio of the 13 CO 2 to the CO 2 flux for region j.
For ocean regions, R j is calculated with following formula (Ciais et al., 1995b): R j = R fo,j = S o,j ( 13 C)/S o,j (CO 2 ) = α ao,j R a + α ao,j F oa,j (R oe,j − R a )/S o,j (CO 2 ) (6) where S o,j ( 13 C) is the ocean net 13 CO 2 net flux in region j, S o,j (CO 2 ) is the ocean net CO 2 flux, α ao,j is the atmosphere-to-ocean fractionation, R a is the 13 C/ 12 C ratio in the atmosphere (% ), F oa,j is the one way ocean-to-atmosphere CO 2 flux, and R oe,j = (α oaj /α ao,j )R o , where R o is the 13 C/ 12 C ratio in the ocean (% ) and α oa,j is the ocean-toatmosphere fractionation calculated with sea surface temperature (Ciais et al., 1995b;Enting et al., 1993).Actually, (R oe,j − R a ) is the disequilibrium between the atmosphere and the ocean.In order to avoid excessively large values for the second term in Eq. ( 7) when S o,j (CO 2 ) is close to zero, we limit the second term to within the range of ±2 % R a , resulting in R fo,j in the range from 0.0111473 to 0.0111024.Figures

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Full For land regions, R j is calculated with a similar formula (Ciais et al., 1995b): R j = R fb,j = S b,j ( 13 C)/S b,j (CO 2 ) = −α ph,j R a + α ph,j S resp,j (R be,j − R a )/S b,j (CO 2 ) (7) where S b,j ( 13 C) is the biosphere net 13 CO 2 flux in region j; S b,j (CO 2 ) is the biosphere net CO 2 flux, and α ph,j is the photosynthesis fractionation, defined as α ph,j = 1 − (δ a − ∆ j ), where δ a is the isotopic composition of current atmosphere CO 2 (8 % ) and ∆ j is the photosynthesis discrimination; R a is the 13 C/ 12 C ratio in the atmosphere (% ); and (R be,j − R a ) is the disequilibrium between the atmosphere and the biosphere.∆ j , S resp,j and (R be,j − R a ) are simulated with the BEPS model to be described below.In the implementation of Eq. ( 8), we limit the second term within the range of ±2 % R a to avoid its extreme values when S b,j (CO 2 ) is close to zero.
In order to investigate the influences of the isotopic discrimination and disequilibrium over land and ocean on the inversion results, we conduct six sets of inversions for the following six cases: Case I: variable ratios are used for 11 ocean and 39 land regions as calculated with Eqs. ( 7) and ( 8) that consider the spatial variations of CO 2 and 13 CO 2 fluxes and the isotopic disequilibrium.This is the ideal case as a basis to investigate other cases; Case II: the ratio for ocean regions is variable (same as Case I), but the ratio over land is taken as a constant of 0.010934 (−27 % ), which is taken as the sum of average δ 13 C a (−8 % ) and average photosynthesis discrimination ∆ j (−19 % ).This is a case to ignore regional differences in isotopic discrimination and disequilibrium over land; Case III: the ratio for land regions is taken as a constant (same as Case II) and the ratio for ocean regions is also taken as a constant, being 0.011125 (−10 % ) taken as the sum of δ 13 C a (−8 % ) and average ocean discrimination (−2 % ).This is a case to ignore the regional differences in isotopic discrimination and disequilibrium over both land and ocean.Case IV: the ratios for ocean regions remain the same as Case I, but the ratios for land regions are determined by photosynthetic discrimination only, i.e. the first term in Eq. ( 8).This is a case to ignore the isotopic disequilibrium between photosynthesis and respiration over land; Case V: the ratios for land regions remain the same as Case I, but the ratios for ocean regions are determined by the first Introduction

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Full term in Eq. ( 7).This case ignores ocean disequilibrium; and Case VI: both land and ocean disequilibrium are ignored, but all others are same as Case I.The 13 CO 2 concentration time series (c m+1 , . . .c m+k ) in Eq. ( 6) is determined as follows: where 13 C obs,i is the concentration of 13 CO 2 at observation station i, calculated with the following equation: where 13 δ obs,i is the observed 13 CO 2 /CO 2 ratio in per mil (% ), R PDB is the standard 13 CO 2 /CO 2 , and C obs,i is observed CO 2 concentrations.The second term in the right side of Eq. ( 9), Σ 13 C k ,i , is the sum of 13 CO 2 concentration increments due to emissions from fossil fuel, ocean, biosphere and fire.The details for these data are given in the following sections (2.2, 2.3 and 2.4).The third term in the right side of Eq. ( 9), 13 C var,i , accounts for the small variation in the observed 13 CO 2 due to the temporal variation in CO 2 concentration.Its value at t time step is calculated from: where C a (t − 1) and C a (t) are the CO 2 concentrations at t − 1 and t, respectively, and R a is the average 13 CO 2 /CO 2 ratio of the atmosphere between t − 1 and t.

Covariance matrixes for the CO 2 flux and CO 2 and 13 CO 2 concentration measurements
In the joint inversion using both CO 2 and 13 CO 2 measurements, the covariance matrix (Q) for the CO 2 flux remains the same as that in the CO 2 only inversion (Eq. 3) but Introduction

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Full the error matrix (R) for concentration measurements is expanded to the dimension of 16980 × 16980 to include 60 months of 13 CO 2 observations at 73 stations.Following Deng and Chen (2011), we use an uncertainty of 2.0 Pg C yr −1 for the total global land surface CO 2 flux, and this total uncertainty is spatially distributed to the 39 regions according to the annual total NPP of these regions simulated by BEPS.For each region, the annual total uncertainty is further distributed to each month according to the simulated seasonal variation in NPP.The uncertainty for the total ocean flux is prescribed as 0.67 Pg C yr −1 (Deng and Chen, 2011).In this way, all the diagonal elements (Q ii ) in the uncertainty matrix Q are determined, while off-diagonal values are assigned to zero, i.e. no flux covariances between regions and months are assumed.The uncertainty of CO 2 measurements in the R matrix is the same as that described in Deng and Chen (2011), following the approach of Peters et al. (2005) andBakers et al. (2006).
In this approach, the uncertainty of a monthly CO 2 measurement at a site is estimated as R ii = σ 2 const + GVsd 2 , where constant portion σ const in ppm is assigned according to site location: Antarctic (0.15), oceanic (0.30), land and tower (1.25), mountain (0.90), and aircraft (0.75), while the site-specific variable portion GVsd is obtained from the GLOBALVIEW-CO2 2008 database.The 13 CO 2 measurement uncertainty in the unit of ppm is calculated in a similar way: the constant portion is taken as R a σ const , where R a is the ratio of 13 CO 2 to CO 2 in the air (∼ 0.0112372), while the variable portion is obtained from the GLOBALVIEW-13CO2 2008 database after converting the unit from permil (% ) to ppm. the net terrestrial CO 2 flux and its components including the gross primary productivity (GPP), net primary productivity (NPP), heterotrophic respiration (S resp ), and net ecosystem productivity (NEP).GPP is calculated using the Farquhar's leaf-level model (Farquhar et al, 1980) upscaled to the canopy level using a recently refined two-leaf approach (Chen et al., 2012).NPP is taken as 45 % of GPP (Ise et al., 2010) as global biomass data and its components (stem, foliage, root) are lacking for reliable computation of the autotrophic respiration.S resp is calculated as the sum of the decompositional CO 2 release from 9 soil carbon pools, namely coarse and dead wood detritus pool, surface structural pool, surface metabolic pool, surface microbial pool, fine-root structural litter pool, fine-root metabolic pool, soil microbial pool, slow carbon pool, and passive carbon pool.The sizes of these pools for each cover type in each 1 • grid are estimated using a model spin-up approach based on simulated NPP in 2000 to create a global land sink of 3.73 Pg C yr −1 .The total NPP for each 1

Prior CO
• grid is taken as a weighted sum of NPP of 7 aggregated land cover types, and the weights are proportional to the areal fractions of the cover types determined using the GLC2000 land cover map at 1 km resolution (Chen et al., 2012).Remotely sensed LAI (Deng et al., 2006) at 1 km resolution and a clumping index map at 6 km resolution (Chen et al., 2005) and a soil textural map (Webb et al., 1991) are aggregated to 1 • grids for each cover type based on GLC2000 land and used as input to BEPS driven by National Center of Environmental Prediction (NCEP) reanalyzed data (Kalnay et al., 1996;Kanamittsu et al., 2002) are main input to BEPS to simulated hourly carbon fluxes.

Ocean fluxes
The daily flux of CO 2 across the air-water interface used in this study is constructed based on the results of daily CO 2 fluxes simulated by the OPA-PISCES-T model (Buitenhuis et al., 2006).This model is a global ocean general circulation model (OPA) (Madec et al., 1998)  two phytoplankton, two zooplankton and three types of dead organic particles of different sinking rates.OPA-PISCES-T is forced by daily wind stress and heat and water fluxes from the NCEP reanalyzed data (Kalnay et al., 1996;Kanamittsu et al., 2002).
Hourly S o ( 13 C) is calculated with gridded optimum interpolation sea surface temperature of NOAA National Climate Data Center (Reynolds and Smith, 1994;Reynolds et al., 2002).

Fossil-fuel emissions
The fossil fuel emission field (2000)(2001)(2002)(2003)(2004) used in this study (http://carbontracker.noaa.gov) is constructed based on (1) the global, regional and national fossil-fuel CO 2 emission inventory from 1871 to 2006 (CDIAC) (Marland et al., 2009) and ( 2) the EDGAR 4 database for the global annual CO 2 emission on a 1 • grid (Olivier et al., 2005).The 13 CO 2 flux from fossil-fuel consumption is calculated from CO 2 emissions of different fuel types multiplied by their respective 13 C/ 12 C ratios with consideration of their latitudinal distributions based on Andres et al. (2000).

Fire emissions
CO 2 emissions due to vegetation fires are an important part of the carbon cycle (van der Werf et al., 2006).Each year, vegetation fires emitted around or more than 2 Pg C of CO 2 into the atmosphere, mostly in the tropics.The fire emission field used in this study is based on the Global Emissions Fire Database version 2 (GFEDv2) (Randerson et al., 2007;van der Werf et al., 2006)  stomates, messophyll and chloroplast initially proposed by Farquhar et al. (1984Farquhar et al. ( , 1989) ) and implemented globally by Suits et al. (2005), we developed a module in BEPS for computing the total photosynthetic fractionation and the resultant 13 CO 2 flux.Specifically, the photosynthetic discrimination for C3 plants (∆ PC3 ) is calculated from

13 CO
where ∆ b , ∆ s , ∆ diss , ∆ aq , and ∆ f are the rates of discrimination against 13 CO 2 through leaf boundary layer, stomates, dissolution in mesophyll water, transport in aqueous phase, and fixation in chloroplast, respectively, and are assigned values of 2.9 % , 4.4 % , 1.1 % , 0.7 % and 28.2 % , respectively (Suits et al., 2005).A is the photosynthetic rate in mol m −2 s −1 and p equals to 0.022624T a /(273.16P)with the dimension of m 3 mol −1 , where T a is air temperature in K and P is the standard air pressure at 1.013 bar.C a and C c are the CO 2 concentrations in mol mol −1 in the free air and leaf chloroplast, respectively.For C4 plants, the photosynthetic discrimination (∆ PC4 ) is taken as a constant of 4.4 % (Suits et al., 2005).
The leaf boundary-layer (g b ) is calculated with the following equation where α is the diffusivity of CO 2 in dry air in m 2 s −1 calculated as 10 −6 (0.129+0.007T a ) and T a is the air temperature in • C; l is the leaf characteristic dimension in m, taken as a constant of 0.1 m; and N is the Nusselt number equal to (u d l/υ) 0.5 , where u d is the wind speed in m s −1 at the vegetation displacement height (80 % of the average vegetation height) and υ is the kinematic viscosity of dry air in m 2 s −1 calculated as 10 −6 (0.133 + 0.007T a ).u d is derived from the wind speed above the canopy based on LAI and vegetation height assigned according to plant functional type (Table 1).Introduction

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Full As part of the GPP calculation, the stomatal conductance (g s ) computed separately for sunlit and shaded leaves using the Ball-Berry equation (Ball, 1988), where f w is a scaling factor depending on soil moisture and texture (Chen et al., 2012); h s is the air humidity at the leaf surface; C s is the CO 2 concentration at the leaf surface; p is the same as in Eq. ( 12); and m and b are the slope and intercept in this linear relationship, and they are assigned values according to plant function type (Table 1) (Chen et al., 2012).The mesophyll conductance g m is calculated based on the method of Harley (1992): where A is the photosynthetic CO 2 assimilation rate; C i is partial pressure of CO 2 in the air spaces inside leaves; R d is the respiration rate occurring during the day not related to photorespiration; A is the CO 2 compensation point in the absence of R d ; and J is the rate of photosynthetic electron transport.These parameters are the same as those used in computing the CO 2 flux.
Our methods of computing stomatal and mesophyll conductances differ from previous studies (Suits et al., 2005;Scholz et al., 2008;Rayner et al., 2008) in the following ways: (1) these conductances are calculated separately for sunlit and shaded leaves because BEPS is a two-leaf model, in which the total GPP of a canopy is taken as the sum of sunlit and shaded leaf GPP; and (2) the mesophyll conductance mechanistically depends on a set of parameters rather than being treated as a constant or a value proportional to the stomatal conductance.Since it has been demonstrated that sunlit and shaded leaf separation is essential for accurate modeling of canopy-level photosynthesis (Chen et al., 1999;Sprintsin et al., 2011), it is expected that this separation 26543 Introduction

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Full is also essential for 13 CO 2 flux estimation.We found that the use of Harley's method for computing the mesophyll conductance makes the calculation of the 13 C photosynthetic fractionation stable for its global application, while the simpler method of treating the mesophyll conductance in proportion with the stomatal conductance often incurs abnormally large or small values of 13 C photosynthetic fractionation.
The photosynthetic 13 CO 2 flux is in disequilibrium with the respiratory 13 CO 2 flux because of the change in atmospheric 13 CO 2 concentration since the preindustrial time (Ciais et al., 1995b;Fung et al., 1997).The heterotrophic respiratory flux from the decomposition of organic matter of different ages carries the memory of the past atmospheric 13 CO 2 concentration, while the photosynthetic 13 CO 2 flux is affected by the current atmospheric 13 CO 2 concentration.Since one objective of our study is to utilize 13 CO 2 data for differentiating terrestrial photosynthetic and respiration, much attention is given to this disequilibrium in this study.The isotopic composition of each of the 9 soil carbon pools (δ 13 C soil,i ) is estimated with following formula: where δ 13 C a is the isotopic composition of carbon in atmosphere CO 2 in the past as determined by the ice-cord record (Francey et al., 1999); ∆ is the annual mean of photosynthetic discrimination in 2003; τ i is the age of carbon pool i (Table 2) (Ju et al., 2005).The mean δ 13 C soil is taken as the flux-weighted δ 13 C soil,i for the 9 carbon pools.
The results of δ 13 C soil for the globe are shown in Fig. 5.

Transport modeling
A transport-only version of the atmospheric chemistry and transport model TM5 (Krol et al., 2003(Krol et al., , 2005) ) is used for CO 2 and for Medium Range Weather Forecast (ECMWF) model.All physical parameterizations in TM5 are kept the same as the ECMWF formulation to achieve compatibility between them.The four background fluxes from terrestrial ecosystems, oceans, fossil-fuel burning, and biomass burning are individually inputted to TM5 to calculate the contributions of these fluxes to the atmospheric CO 2 and 13 CO 2 concentrations.

CO 2 and 13 CO 2 datasets
Monthly CO 2 and 13 CO 2 concentration data from 2000 to 2004 are compiled from the GLOBALVIEW CO 2 and 13 CO 2 database.Though the GLOBALVIEW database consists of both extrapolated and interpolated data that were created based on the technique devised by Masarie and Tans [1995], we selected the synchronized and smoothed values of actual observations to compile our concentrations datasets.To minimize the nonlinear aggregation effects of the large regions (Pickett-Heaps, 2007), the contributions of the four background fluxes are subtracted from the above monthly concentrations.So the matrix c in Eqs. ( 3) and ( 4) is expressed as where c obs is the monthly CO 2 and 13 CO 2 concentrations obtained from GLOBALVIEW, and c ff , c bio , c ocn , and c fire are simulated contributions of CO 2 and 13 CO 2 concentrations from the terrestrial biosphere, ocean, fossil-fuel, and fire fluxes, respectively.constraints to the otherwise ill-posed inversion based CO 2 and 13 CO 2 concentration observations alone.Depending on the assigned relative magnitudes of the error matrixes of these concentration observations and these prior fluxes (i.e., R and Q in Eq. 3), these prior fluxes can have equal or even dominant importance to these concentration observations in the inversion results.We have therefore paid a great attention in modeling these prior fluxes, in order to minimize the total inversion errors.Figure 2a shows an example of the global terrestrial GPP distribution in 2003 modeled by BEPS.The total GPP in this year is 132±22 Pg C yr −1 (Chen et al., 2012).This value is larger than some of the recent estimates, such as 123 Pg C yr −1 by Beer et al. (2010), mostly because the LAI values used as input to BEPS are generally larger than those of the MODIS product (Garrigues et al., 2008).Our LAI values are larger because we used a global clumping index map derived from a multi-angle satellite sensor POLDER (Chen et al., 2005).Clumping increases shaded leaves which contributed about 35 % to the total GPP globally.Without considering this clumping effect, the shaded leaf area is underestimated, resulting in an underestimation of the global GPP by 9 % (Chen et al., 2012).As the spatial distribution of clumping is not uniform (boreal and tropical forests are most clumped and crops and grasses are least clumped), this refinement in the GPP spatial distribution would have some effects on the inversion results between regions.
The net ecosystem productivity (NEP), the difference between GPP and ecosystem respiration, modeled by BEPS, is shown in Fig. 2b  zero after the preindustrial period because of the changes in climate and atmospheric composition (CO 2 and nitrogen) as well as disturbance.In our regional modeling, both disturbance and non-disturbance effects are considered for Canada (Chen et al., 2003) and USA (Zhang et al., 2012) forests.However, in our global model spin-up from 1901 (taken as the end of preindustrial period) to 2000, only the non-disturbance effects are considered because of lack of spatially explicit disturbance data outside of North America, while carbon emission due to fire disturbance in the study period from 2000 to 2004 is considered separately using the GFED dataset (Randerson et al., 2007;van der Werf et al., 2006).The prior net CO 2 fluxes for the 50 regions for the years 2002-2004 are given in Table 3 with inversion results with and without the 13 C constraint.
The global distribution of the total photosynthetic discrimination (δ 13 C pt = δ 13 C a −∆) modeled by BEPS is shown in Fig. 3. Forests, such as those in North America, Russia, Europe, Amazon, central Africa, central China and southeast Asia, generally have high photosynthetic discrimination rates (> 16 % ), while grassland and cropland (in particular C4 grasses and crops) have low discrimination rates.Also shown in Fig. 3 is the ocean diffusive discrimination against 13 CO 2 .The discrimination over ocean is much smaller than that over land.This difference between land and ocean discrimination may be considered as the largest signal of 13 CO 2 observations on the global carbon cycle (Tans et al., 1990;Rayner et al., 2008) and is considered in our inversion using different 13 CO 2 /CO 2 flux ratios for ocean and land regions (see Eq. 6).
To estimate the disequilibrium between photosynthetic and respiratory discrimination against 13 CO 2 , the global distribution of the mean soil carbon age is computed after weighting the ages of the 9 soil carbon pools against their fluxes due to decomposition (Fig. 4).Forests at high latitudes have the soil carbon age of about 40-60 yr, while the tropical forests have much lower values in the range from 10 to 30 yr.This latitudinal distribution pattern is mostly determined by soil temperature.In low latitudes, high temperature induces fast turnovers of detritus and fast soil carbon pools, while at high latitudes, low temperature maintains relatively large fractions of slow and passive soil carbon pools.Cropland and grassland also have larger fractions of fast and Introduction

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Full detritus carbon pools than forest cover types and therefore have younger soil carbon on average.This spatial distribution of soil carbon age has a strong influence on the total respiratory discrimination against 13 C (δ 13 C r ) calculated by BEPS (Fig. 5).Respiration from older carbon at high latitudes carries the memory of the older atmosphere with less 13 CO 2 concentration and hence has lower discrimination rates (larger δ 13 C r ).
However, respiration would mostly depend on the photosynthetic discrimination rates.As a result, forested areas have higher respiratory discrimination rates (lower δ 13 C r ).
Most of the high values of δ 13 C r (smaller absolute values) in Fig. 5 are associated with large fractions of C4 plants in the grid, such as the corn belt in the USA, cropland in northeast China, southern border of Sahara desert, southeast South America.
The global distribution of the disequilibrium between photosynthetic and respiratory discrimination, taken as the difference between Fig. 3 and Fig. 5, is shown in Fig. 6.The disequilibrium is the largest at the high latitude boreal forests in North America and Eurasia because their soil carbon is the oldest, as shown in Fig. 4. The spatial distribution pattern of the disequilibrium is similar to those of Ciais et al. (1995b) and Fung et al. (1997) but the magnitude is larger because the date of our result in 2000 is more recent than these two previous studies.As the time lapses, the atmosphere is getting lighter in terms of the isotopic composition of CO 2 resulting from the increased air-borne CO 2 from fossil fuel consumption.Also shown in Fig. 6 is the disequilibrium over the ocean estimated using the method of Ciais et al. (1995b).This ocean disequilibrium has a large latitudinal gradient because of the gradients in sea surface temperature gradient and the fluxes of CO 2 and 13 CO 2 .The spatial distribution in the disequilibrium and the differences in disequilibrium between ocean and land may be considered to be the secondary signal of 13 CO 2 observations on the global carbon cycle.The effects of these disequilibria on the carbon flux are considered in our inversion through the use of region-specific 13 CO 2 /CO 2 flux ratios in Eq. ( 6), and the magnitudes of these effects are investigated through different treatments (cases) of this ratio as shown in the following section.Introduction

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Results with and without 13 CO 2 constraint
To investigate the usefulness of13 CO 2 observations in inverse modeling of the CO 2 flux, we conducted inversions with and without 13 CO 2 constraint as expressed in Eq. ( 6), i.e. with and without the 13 C-related expansions of the matrixes.Figures 7     and 8 show the result of a CO 2 -only inversion (i.e.without 13 CO 2 constraint) and the result of CO 2 + 13 CO 2 inversion (i.e. with 13 CO 2 constraint), respectively, as the net carbon flux over land and ocean averaged for the period of 2002-2004.These results with 13 CO 2 constraint are obtained as Case I where the ratios for CO 2 and 13 CO 2 for land and ocean are variable among regions according to the land and ocean models.
Although the inversions were made for the 2000-2004 period, the results of the first two years are not included in the analysis because they are affected by the assumption of uniform CO 2 and 13 CO 2 global distributions at the start of our transport modeling using TM5.An 18-24 month period is usually considered to be necessary for the simulated distributions to reach realistic states with reasonably accurate prior surface fluxes from ocean and land and atmospheric transport simulations (Rödenbeck et al., 2003;Deng and Chen, 2011).The general patterns of the inverted carbon flux are similar between these two inversions because these inversions depend primarily on the CO 2 concentration, the prior flux and the error matrixes of the prior flux and concentration observation.However, there are several notable differences: (1) the carbon source from the Amazon region is greatly reduced, and this reduction is compensated by an increased carbon source in the ocean region immediately west to Amazon and a decreased sink in the southeast Asian land region.These large changes brought by the inclusion of 13 CO 2 in the inversion are likely caused by the relatively large addition of information from 13 CO 2 in these tropical regions where CO 2 observations are sparse.The contrast in Introduction

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Full carbon source with 13 CO 2 constraint, and this is also likely caused by the fact that this region is in the vicinity of ocean and therefore most affected by the difference in the discrimination rate between ocean and land.There are also small changes for other smaller regions in North America (Fig. 9).Under the 13 CO 2 constraint, most regions in North America show a small increase in sink, and their overall sink increases from 0.67 to 0.71 Pg C yr −1 .
The inverted results for the 21 large land and ocean regions with and without the 13 CO 2 constraint are shown in Fig. 10.Most regions show small but noticeable changes in the inverted carbon sinks or sources except aforementioned regions 31 (Amazon), 37 (Southeast Asia) and 41 (ocean region west of Amazon).These large and small changes modified significantly the inverted overall land and ocean sinks (Fig. 11).The land sink increases from 3.4 ± 0.84 to 3.70 ± 0.81 Pg C yr −1 , while the ocean sink decreases from 1.48 ± 0.40 to 1.12 ± 0.38 Pg C yr −1 .These land sink estimates do not include the emission due to fire.The mean fire emission is 2.25 Pg C yr −1 over the 2002-2004 period, and the net land sink is the inverted land sink less this amount due to fire emission.While the information content of 13 CO 2 observations in terms of the difference in discrimination between land and ocean appears to have large impacts on the inversion results for several regions, the usefulness of these observations for refining the spatial distribution of the carbon flux over land is less certain.

Results with different treatments of the 13 CO 2 /CO 2 flux ratio
The inversion results with 13 CO 2 constraint shown in Fig. 8  Case II is designed to investigate the importance of using an accurate spatial distribution of the photosynthetic isotopic discrimination for inverting the CO 2 flux by forcing the 13 CO 2 /CO 2 flux ratio to be constant over land, while the ocean discrimination remains spatially variable.Figure 12a shows the spatial distribution of the difference in this ratio among 39 land regions between Case I and Case II.Regions with negative differences in the flux ratio are shown with negative differences in the inverted CO 2 flux, meaning larger sinks, and vice versa.This is because a smaller 13 CO 2 /CO 2 flux ratio means a larger CO 2 flux from the atmosphere to the surface (larger negative value) for the same 13 CO 2 flux under the condition that the prior flux is negative (sink).Under the same condition, a larger 13 CO 2 /CO 2 flux ratio induces a smaller sink (less negative).While regional differences between Case I and Case II can be quite large, e.g. up to 10 g C m −2 yr −1 or 25 % of the sink in the Amazon area (Region 31), changes of the global sink values from Case I to Case II are small (Table 3): from 3.70 ± 0.81 to 3.66 ± 0.81 Pg C yr −1 for land and from 1.12 ± 0.38 to 1.17 ± 0.39 Pg C yr −1 for ocean.
Case III shows the consequence in flux inversion if the spatial distribution of the 13 CO 2 /CO 2 flux ratio is ignored over both ocean and land regions, similar to the case of double deconvolution at the global scale using the global mean values of discrimination for land and ocean separately.In this case, the ratio over land is the same as that in Case II, but the ratio over ocean differs significantly from that in Case I (Fig. 12c) because of the large variations of this ratio among ocean regions.The difference in the inverted CO 2 flux between Case I and Case III (Fig. 12d) is similar that that between Case I and Case II (Fig. 12b).Noticeable differences between these two difference maps are: Fig. 12d shows a larger sink in Amazon, smaller sinks in Europe and Russia, and a smaller source in North Africa, indicating that ignoring the small spatial variation of the 13 CO 2 discrimination rate over ocean can have noticeable influence on the inverted sink over land.The total land sink decreases only slightly from 3.70±0.81Pg C yr −1 for Case I to 3.66±0.81Pg C yr −1 for Case III, and correspondingly the ocean sink increases also slight from 1.12 ± 0.38 Pg C yr −1 to 1.16 ± 0. 39 Pg C yr −1 (Table 3).These results indicate that the double deconvolution method using constant Introduction

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Full discrimination rates (or 13 CO 2 /CO 2 flux ratios) is reliable is in partitioning sinks between land and ocean, but the distribution of the sink over land can be significantly distorted (up to 25 % for some regions).
Case IV, Case V and Case VI are conducted to investigate the importance in considering the disequilibrium in the 13 CO 2 flux over land and ocean for the CO 2 flux inversion.
In Case IV, where the disequilibrium over land is ignored while other settings remain the same as Case I, the land sink increases by 0.010 Pg C yr −1 , while the ocean sink decreases by 0.010 Pg C yr −1 in comparison with Case I.When the disequilibrium over ocean is ignored (Case V), the land sink increases by 0.008 Pg C yr −1 , while the ocean sink decreases by 0.008 Pg C yr −1 , in comparison with Case I.When the disequilibria over both land and ocean are ignored, the land sink increases by 0.018 Pg C yr −1 , while the ocean sink decreases by 0.018 Pg C yr −1 , in comparison with Case I. Results from these case studies suggest that in the joint inversion using both CO 2 and 13 CO 2 measurements, the inverted CO 2 flux is not sensitive to the existence of 13 CO 2 disequilibra over land and ocean.This is because these disequilibria only modify slightly the 13 CO 2 /CO 2 flux ratio (R j ), i.e., in the formulation of Eq. ( 6) with W ij = R j M ij , the disequilibria only influence slightly the magnitude of R j and consequently the 13 CO 2 concentration.This insensitivity of the inversion results to disequilibria suggest that our joint inversion methodology is not prone to the errors in the estimation of the disequilibria over land and ocean, and therefore the main utility of 13 CO 2 measurement in the inversion is to provide a constraint on the partition between ocean and land sinks.This insensitivity also indicates that our inversion methodology has not fully utilized 13 CO 2 measurement for differentiation between photosynthetic and respiratory fluxes over land, and this differentiation remains a challenge yet to be overcome.A different joint inversion strategy may be needed for this purpose.Introduction

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Discussion
The overall effects of including 13 CO 2 data in the inversion are small to moderate in terms of the total sinks to land and ocean, the partition between them, and their uncertainty reduction.This is may be because the number of 13 CO 2 observation sites ( 73) is much smaller than that of CO 2 observation sites (210) and only 11 13 CO 2 observation sites are not collocated with CO 2 observations sites.The temporal and spatial samplings of 13 CO 2 are therefore mostly correlated with those of CO 2 , and as a result, the joint inversion is dominated by CO 2 measurements.However, because of the additional information of 13 CO 2 for partitioning between ocean and land carbon fluxes, the inclusion of 13 CO 2 data in the inversion is shown to induce some large and meaningful changes in the spatial distribution of the inverted carbon flux, as demonstrated in Case II and Case III relative to Case I.The reduction of the uncertainty in the inverted CO 2 flux when 13 CO 2 data are used is small (∼ 3 %) (Table 3).Since the relative error in 13 CO 2 measurement is similar to that in CO 2 measurement, this small reduction in uncertainty may be indicative of the small additional information content of 13 CO 2 measurements for CO 2 flux inversion.In the joint inversion, the uncertainty in the prior 13 CO 2 flux estimation is not required, and therefore the posterior uncertainty in inverted CO 2 flux does not directly take into account of the error in the prior 13 CO 2 flux estimation, although through the 13 CO 2 /CO 2 flux ratio used in the transport matrix (M) (Eq.6), the prior 13 CO 2 flux estimation has influence on the inversion results.Errors in modeling the spatial and temporal variations of the 13 CO 2 flux stem from many sources including errors in modeling the discrimination, which is affected by the fractionation of the 13 CO 2 flow through leaf boundary layer, stomata, mesophyll, etc., and the disequilibrium, which depends on the sizes of 9 soil carbon pools and their ages.Although the ocean 13 CO 2 discrimination is small, but its disequilibrium has a strong latitudinal gradient, which is approximately calculated using the mean monthly temperature.The error in the calculated disequilibrium is Figures

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Full estimated to be ±0.6 % for the monthly values at a given location and ±0.2 % for the global annual total.Because of these errors, we estimate that the relative uncertainty in the prior 13 CO 2 flux is similar to that of the prior CO 2 flux over both land and ocean.
For the 3 yr (2002)(2003)(2004) included in this study, existing estimates (Le Quéré et al., 2009) for both oceanic and land carbon sinks are about 2 Pg C yr −1 .This land sink estimate also excludes fire emission.Although the prior estimates of these sinks in our inversions are similar to these values, our CO 2 only inversion considerably increases the land sink and decreases the ocean sink.The addition of 13 CO 2 measurements in the inversion further increases the land sink and decreases the ocean sink, i.e. further away from the existing estimates.Although our inversion results may subject to considerable errors in atmospheric transport modeling and prior flux modeling, there seems to be a strong pull by the atmospheric signal towards a larger land sink and a smaller ocean sink than the existing estimates.This "unusual" behavior of atmospheric inversion may deserve further attention.

Conclusions
The usefulness of atmospheric 13 CO 2 measurements at 73 stations for global carbon cycle estimation is explored through their use as an additional constraint on an atmospheric inversion of the surface carbon flux using CO 2 observations.The following conclusions are drawn from this study: 2. The impact of 13 CO 2 data on the CO 2 inversion is mostly caused by the large difference in isotopic discrimination between ocean and land.The spatial distributions of the 13 CO 2 discrimination rate over both land and ocean have noticeable impacts on the spatial distribution of the CO 2 sink over land (up to 25 % in some regions), suggesting reliable models for simulating the spatial distributions of the 13 C discrimination rate over both land and ocean are needed for effective use of 13 CO 2 data for global carbon cycle inversion.
3. The joint inversion methodology using both CO 2 and 13 CO 2 measurements can effectively consider the difference in 13 CO 2 discrimination between land and ocean for partitioning the carbon sink but is not sensitive to the disequilibrium in the 13 CO 2 over both land and ocean.A different methodology is yet needed to make full use of the information content of isotopic disequilibrium for discriminating between photosynthetic and respiratory fluxes.Introduction

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Full  Full  Full  ) and without (CO 2 only) 13 C constraint using the 13 CO 2 /CO 2 flux ratio.The negative sign denotes the flux from the atmosphere to the surface (sink).Various treatments are made to this ratio represented by the following cases: Case I: variable ratios for land and ocean regions with full consideration of the regional differences in discrimination and disequilibrium; Case II: variable ratios for ocean regions, but the ratio for land is constant (0.010934).Case III: ratios for both ocean and land are constants at 0.011125 and 0.010934, respectively.

Region
Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | below) Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | A process-based terrestrial ecosystem model called the Boreal Ecosystem Productivity Simulator (BEPS)(Chen et al., 1999;Liu et al., 1997) is used in this study to estimate Figures Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | coupled to an ocean biogeochemistry model (PISCES-T)(Aumont et al., 2003;Buitenhuis et al., 2006).PISCES-T represents the full cycles of C, O 2 , P, Si, total alkalinity and a simplified Fe cycle.It also includes a representation of 26540 Discussion Paper | Discussion Paper | Discussion Paper | 2 flux Based on the initial work of Chen et al. (2006), BEPS is further developed to include a capacity to compute the global distribution of the terrestrial 13 CO 2 flux.Following the principle of multi-stage 13 C fractionation in the pathway through leaf boundary layer, Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 13 CO 2 transport modeling to produce a fully linear operator on these fluxes.Tracer transport (advection, vertical diffusion, cloud convection) in TM5 is driven by offline meteorological fields taken from the European Centre Figures Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Terrestrial ecosystem models integrate many sources of information, including vegetation structure, soil, and meteorology, to estimate carbon exchange of the land surface.Prior CO 2 and 13 CO 2 fluxes produced by a model can therefore provide indispensible Figures Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | for 2003.Even though GPP has a large uncertainty (globally 22 Pg C yr −1 by BEPS), the uncertainty in NEP is much smaller (globally 2 Pg C yr −1 by BEPS) because a model spin-up approach is used to estimate the soil carbon pool sizes based on a dynamic equilibrium assumption.Under this assumption, the annual heterotrophic respiration (S resp ) equals annual NPP during the preindustrial period, and the soil carbon pool sizes are derived from S resp by solving a set of differential equations describing the decomposition and interactions among the pools (Govind et al., 2011).In this way, S resp is forced to depend on NPP and the systematic biases in GPP are not carried into NEP estimation.NEP is non-Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | are from Case I with the best estimates of the 13 CO 2 /CO 2 flux ratio and therefore represent a baseline study to which other cases are compared for the purpose of investigating the importance of accurate consideration of the spatial distributions of isotopic discrimination and dise-Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | made significant changes to the inversion results of the CO 2 flux.These changes are the largest at tropical land and ocean areas where CO 2 observations are sparse, and therefore the additional signal from 13 CO 2 data becomes most important.For the inversion period of 2002-2004, this 13 CO 2 constraint increased the land sink from 3.397 ± 0.836 to 3.704 ± 0.809 Pg C yr −1 and decreases the total oceanic carbon sink from 1.482 ± 0.396 to 1.049 ± 0.385 Pg C yr −1 (Table 3).Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Scholze, M., Ciais, P., and Heimann, M.: Modeling terrestrial 13 C cycling: climate, land use and fire, Global Biogeochem.Cy., 22, GB1009, doi:10.1029/2006GB002899,2008.Siegenthaler, U. and Oeschger, H.:. Biospheric CO 2 emissions during the past 200 years reconstructed by deconvolution of ice core data, Tellus B, 39, 140-154, 1987.Sprintsin, M., Chen, J. M., and Czurylowicz, P.: Combining land surface temperature and short-Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Fig. 1 .
Fig. 1.A global nested inversion system with a focus in North America, in which oceans are divided into 11 regions and land areas are divided into 9 large and 30 small regions outside and within North America, respectively.Also shown are CO 2 and 13 CO 2 observation stations included in the GlobalView database and used in this study.

Fig. 2 .Figure 3 .
Fig. 2. (a) gross primary productivity (GPP) distribution in 2003 computed using remote sensing LAI and land cover maps and climate and soil data, and (b) net ecosystem productivity (NEP) distribution in 2003.Both are calculated using the BEPS model.Annual NEP maps from 2000 to 2004 are used to as the prior flux in the inversions.This GPP map is used to distribute the flux uncertainty among the 39 land regions.

Figure 6 .
Figure 6.Disequilibria between 13 C fluxes to and from the land or ocean surface in 2000.At the land surface, the disequilibrium is the difference between photosynthetic and respiratory discriminations against 13 C, and at the ocean surface, it is the difference in 13 C discrimination between the one-way diffusive downward and upward fluxes.

Fig. 6 .Figure 7 .
Fig.6.Disequilibria between 13 C fluxes to and from the land or ocean surface in 2000.At the land surface, the disequilibrium is the difference between photosynthetic and respiratory discriminations against13 C, and at the ocean surface, it is the difference in13 C discrimination between the one-way diffusive downward and upward fluxes.

Fig. 9 .Figure 11 .
Fig. 9.Comparison between inversion results with and without 13 CO 2 constraint for 30 regions in North America.

Fig. 11 .Fig. 12 .
Fig. 11.Summary of inversion results with and without 13 CO 2 constraint for ocean and land for the period of 2002-2004.

Table 1 .
Chen et al. (2012)ters are assigned by plant functional types in BEPS.References for the chosen values of these parameters are found inChen et al. (2012).

Table 2 .
Global average ages of soil carbon pools computed by BEPS with consideration of the influences of temperature and soil moisture on the decomposition rates of these pools.