Inverse Model


Various inverse modeling techniques (Enting, 2002) are currently available for estimating regional carbon fluxes using atmospheric CO2 concentration observations. However, the number of currently available observation stations is still sparse relative to the size of the global surface, and this essentially limits the number of regions that can be reliably inverted globally without using additional information as constraints to the inversion. In our study, An inverse modeling system has been developed based on the Bayesian principle for estimating the carbon fluxes over a nested framework of 48 regions globally and with a relatively fine grid of 28 regions over North America in monthly steps using CO2 concentration measurements of 2003 at 90 atmospheric stations. Preliminary inversion results of global carbon flux and a carbon flux field over North America have been obtained.


Inversion: We use the Bayesian synthesis method (Enting, 2002), solving for 37 land regions and 11 ocean regions (Fig. 1).

Model: NIES (Maksyutov, 2000), with horizontal resolution of 2.5 by 2.5 degree and 15 sigma vertical level, is used to perform forward simulation for 3 years to determine the transport matrix and the effects of distributed prior flux on baseline station CO2 concentration.

Data: The atmospheric CO2 concentration data used in this inversion are taken from GLOBALVIEW- CO2 (2004 ) for 2003 data. 90 sites are selected as presented is Fig. 1.

Model Data Mismatch Covariance: The diagonal matrix with diagonal variance is used (Transcom3, Level 2).

Pre-subtracted Fluxes: (i) the four background fluxes consisted of a 1995 fossil fuel emission field (Brenkert et al., 1998), (ii) an additional fossil fuel emission field in 2002 based on increases in the fossil fuel emission inventories of all countries from 1995 to 2002 (Marland and Boden, 2005), (iii) seasonal biosphere exchange based on the Biome-BGC model (Running et al., 1988, 1993), and (iv) air-sea gas exchange (Takahashi et al., 1999).

Prior Flux Covariance: We use an a priori flux covariance matrix with each element as a function of regional area and the a priori flux magnitude.

RESULTS - Annual Flux Estimation

Fig. 2 The inverted annual carbon flux distributions. (a) Annual total flux to the atmosphere, including fossil fuel emission, seasonal biosphere exchange, air-sea exchange, and others. a.2 is the zooming result of North America. (b) Annual total flux excluding fossil-fuel emission. b.2 is the zooming result of North America. ( PgC/Year).

Fig. 3 A comparison of TransCom3 annual results of NIES model and the model mean of TransCom3 Seasonal estimation with those results from this inversion. Region NA represents the combination of regions 1 to 28 in this inversion, which is the same as Boreal NA and Temperate NA of TransCom3. Pink line represents TransCom 3 results (Gurney et. Al., 2003). Green line represents the model mean results of TransCom 3 seasonal estimation (Gurney et al., 2004). Blue line is the results of this inversion.

RESULTS - Seasonal Variation of Estimated Flux

Figure 4 Seasonal patterns of the a priori flux (pink) and the inverted flux (blue) from ecosystems and their uncertainty in selected regions.


  1. Comparing to the previous TransCom3 inversions, the global lands and oceans have been a relative steady sink, i.e., the total flux from the atmosphere excluding fossil fuel emissions but including emissions associated with land use changes. The total sink is 2.93 PgC/year from this inversion, 2.81 PgC/year from the NIES model in TransCom3 annual inversion (Gurney et al. 2003), and 2.81 PgC/year from the mean of models used in TransCom3 monthly inversion (Gurney et al. 2004). However the proportion of the contribution from land and ocean have been changed, with 65.6% attributed to oceans in this inversion, 57.3% and 47.7% in the aforementioned two TransCom3 inversions, respectively.
  2. As in TransCom3 inversions, northern lands are the largest sinks. North America contributes a sink of 0.83PgC/year, with a weak sink of 0.063 PgC/year in Canada. Most of south lands, however, have changed into sources. The only exception occurred in Africa, where we are on the opposite end of TransCom 3 inversions.
  3. All of the four tropical ocean regions release carbon to atmosphere annually, and uptakes occurred in all other ocean regions, in agreement with Takahashi et al. (1999) while in Transcom3 inversions, only one of the four is a source.
  4. Most of the inversion results show that deviations from the a priori flux occurred in winter and summer seasons.

Future Work: As all of the inversion results are based on Global-View 2003 CO2 dataset, we will do this inversion for more years to investigate the long-term changes. Another ecosystem model BEPS (Liu et al, 1999) will be used to produce an different a carbon flux field based on remote sensing to see how sensitive of the inversion is to the a priori flux field.


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  • Gurney, K. R., et al. (2003), Transcom 3 CO2 Inversion Intercomparison: 1. Annual mean control results and sensitivity to transport and prior flux information, Tellus, Ser. B, 55, 555ĘC 579
  • Gurney, K. R., et al. (2004), Transcom 3 inversion intercomparison: Model mean results for the estimation of seasonal carbon sources and sinks, GLOBAL BIOGEOCHEMICAL CYCLES, VOL. 18, GB1010
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  • Takahashi, T., et al. (1999). Net sea-air CO2 flux over the global oceans: An improved estimate based on the sea ĘCair pCO2 difference, paper presented at 2nd CO2 in Oceans Symposium, Cent. for Global Environ. Res. Natl. Inst. for Environ. Stud., Tsukuba, Japan.
  • Liu, J., J. M. Chen, J. Cihlar, W. Chen (1999), Net primary productivity distribution in BOREAS region from a process model using satellite and surface data, J. Geophy. Res., 104, 27735-27754.

© Revised: Feb., 2006