Observations of

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., 2013). In particular,
atmospheric CO

Measurements of the atmospheric concentration of the stable isotope

In previous studies (Siegenthaler and Oeschger, 1987; Keeling et al.,
1989a; Francey et al., 1995; Randerson et al., 2002), atmospheric

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

Atmospheric CO

The overall goal of this study is to explore the information content of

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 types 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. This nested region serves the purpose of evaluating
the influence of the spatial distribution of isotopic discrimination on the
inverted carbon flux at a relatively high resolution. Also shown in Fig. 1
are the spatial distributions of 210 CO

To estimate the CO

Combining matrixes

The inverse problem of estimating

We attempt to use

In order to calculate

In order to reduce the errors of our inversion system (Eq. 6) that assumes
linear relationships between fluxes and concentrations, the contributions of
all fluxes, including prior biospheric and ocean fluxes, to the CO

Equation (8) is the theoretical basis for our joint

For land regions, BEPS is used to calculate all land variables in Eq. (8),
including

The

In Eq. (10),

The uncertainty of

The inversion system defined by Eq. (6) can be implemented in three ways
using (1) CO

In order to investigate the influences of the isotopic discrimination and
disequilibrium over land and ocean on the inversion results, we conduct five
sets of inversions for the following cases:

The spatial variations of all isotopic compositions and the discrimination and disequilibrium fluxes in Eq. (8) are considered for both land and ocean. This is the ideal case as the basis to investigate other cases.

The photosynthetic discrimination
(

All isotopic variables are the same as case I, but the land disequilibrium term
in Eq. (8) is ignored. This is a case to investigate the influence of the
land isotopic disequilibrium on the CO

All isotopic variables are the same as case I, but the ocean disequilibrium
term in Eq. (8) is ignored. This is a case to investigate the influence of
the ocean isotopic disequilibrium on the CO

Both land and ocean disequilibrium terms are ignored, but all
other isotopic variables in Eq. (8) are same as case I. This is a case to
investigate the importance of the total disequilibrium flux in CO

In the joint inversion using both CO

A process-based terrestrial ecosystem model called the BEPS (Chen et al., 1999; Liu et al., 1997) is used
in this study to estimate the net terrestrial CO

The daily flux of CO

The fossil-fuel emission field (2000–2004) used in this study
(

CO

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

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

The leaf boundary layer (

As part of the GPP calculation, the stomatal conductance (

The mesophyll conductance

Our methods of computing stomatal and mesophyll conductances differ from
previous studies (Suits et al., 2005; Scholze 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 to be proportional to the stomatal
conductance. Since it has been demonstrated that sunlit and shaded leaf
separation is essential for accurate modelling of canopy-level photosynthesis
(Chen et al., 1999; Sprintsin et al., 2011), it is expected that this
separation is also essential for

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.

The photosynthetic

The accuracy of the BEPS model in simulating atmospheric

A transport-only version of the atmospheric chemistry and transport model TM5
(Krol et al., 2003, 2005) is used for CO

Monthly CO

To minimize the non-linear 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

Terrestrial ecosystem models integrate many sources of information, including
vegetation structure, soil and meteorology, to estimate carbon exchange of
the land surface with the atmosphere. Prior CO

Inverted fluxes (Pg C year

The annual mean of the total photosynthetic

The NEP, which is the difference between GPP and
ecosystem respiration modelled by BEPS, is shown in Fig. 2b for 2003. Even
though GPP has a large uncertainty (globally 22 Pg C year

The global distribution of the total photosynthetic discrimination
(

Global distribution of the flux-weighted mean age of soil carbon pools (Eq. 8).

Global

Disequilibria between

To estimate the disequilibrium between photosynthetic and respiratory
discrimination against

Comparison of land and ocean disequilibrium coefficients and disequilibrium fluxes calculated in this study with those in previous studies.

Although the inversions were made for the 2000–2004 period, the results of
the first 2 years are not included in the analysis because they are
affected by the assumption of uniform global distributions of CO

Global isotopic mass budgets averaged for the 2002–2004 period for
the prior, double deconvolution, CO

To investigate the usefulness of

The impacts of

Comparison of land and ocean carbon sinks derived from inversions
with and without the

but the influences of the uncertainties in these fluxes on the inversion results are analyzed in Sect. 3.2.4.

Existing estimates for the ocean sink for anthropogenic CO

The

It is of particular importance to note that the

Global distribution of inverted CO

Difference of the inverted CO

The joint inversion results shown in Figs. 9–11 are from case I with the
best estimates of the

Comparison between inversion results with and without

Comparison between inversion results with and without

The average disequilibrium coefficients and fluxes for land and ocean derived
in this study are comparable to published results (Table 4), although the
estimates of the disequilibrium flux over ocean in previous studies vary in a
large range. The uncertainty in the estimated land and ocean disequilibrium
fluxes mainly arises from two sources: the estimated disequilibrium
coefficient and one-way CO

Case III, case IV and case V are conducted to investigate the relative
importance of the disequilibrium fluxes over land and ocean (Table 3) in the
CO

Inverted fluxes (Pg C year

The impacts of these disequilibrium fluxes on the inverted CO

According to the difference of the inverted flux between case III to case I,
the uncertainty of 8.0 Pg C year

Left panel: comparison of CO

After the CO

In order to provide a comprehensive evaluation, the posterior CO

CO

After adding

Comparison of prior

The usefulness of atmospheric

This

The
spatial distribution of the

The joint inversion is sensitive to the

The codes for the joint inversion system and the BEPS
model, the prior CO

The authors declare that they have no conflict of interest.

We greatly appreciate the GLOBALVIEW data set that is
available from the NOAA Climate Monitoring and Diagnostics Laboratory.
NCEP/DOE 2 Reanalysis data are provided by the NOAA/OAR/ESRL PSD, Boulder,
Colorado, USA, from their website at