A Global Synthesis Inversion Analysis of Recent Variability in CO2 Fluxes Using GOSAT

The precise contribution of the two major sinks for anthropogenic CO2 emissions, terrestrial vegetation and the ocean, and their location and year-to-year variability are not well understood. Top-down estimates of the spatiotemporal variations in emissions and uptake of CO2 are expected to benefit from the increasing measurement density brought by recent in situ and remote CO2 observations. We uniquely apply a batch Bayesian synthesis inversion at relatively high resolution to in situ surface observations and bias-corrected GOSAT satellite column CO2 retrievals to deduce the global distributions of natural CO2 fluxes during 2009-2010. Our objectives include evaluating bottom-up prior flux estimates, assessing the value added by the satellite data, and examining the impacts of inversion technique and assumptions on posterior fluxes and uncertainties. The GOSAT inversion is generally better constrained than the in situ inversion, with smaller posterior regional flux uncertainties and correlations, because of greater spatial coverage, except over North America and high-latitude ocean. Complementarity of the in situ and GOSAT data enhances uncertainty reductions in a joint inversion; however, spatial and temporal gaps in sampling still limit the ability to accurately resolve fluxes down to the sub-continental scale. The GOSAT inversion produces a shift in the global CO2 sink from the tropics to the north and south relative to the prior, and an increased source in the tropics of ~2 Pg C y-1 relative to the in situ inversion, similar to what is seen in studies using other inversion approaches. This result may be driven by sampling and residual retrieval biases in the GOSAT data, as suggested by significant discrepancies between posterior CO2 distributions and surface in situ and HIPPO mission aircraft data. While the shift in the global sink appears to be a robust feature of the inversions, the partitioning of the sink between land and ocean in the inversions using either in situ or GOSAT data is found to be sensitive to prior uncertainties because of negative correlations in the flux errors. The GOSAT inversion indicates significantly less CO2 uptake in summer of 2010 than in 2009 across northern regions, consistent with the impact of observed severe heat waves and drought. However, observations from an in situ network in Siberia imply that the GOSAT inversion exaggerates the 2010-2009 difference in uptake in that region, while the prior CASA-GFED model of net ecosystem production and fire emissions reasonably estimates that quantity. The prior, in situ posterior, and GOSAT posterior all indicate greater uptake over North America in spring to early summer of 2010 than in 2009, consistent with wetter conditions. The GOSAT inversion does not show the expected impact on fluxes of a 2010 drought in the Amazon; evaluation of posterior mole fractions against local aircraft profiles suggests that time-varying GOSAT coverage can bias estimation of flux interannual variability in this region.


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Our method is based on that used in the TransCom 3 (TC3) CO 2 inversion burning gases is neglected. The total amount of CO 2 chemical production from fossil and 184 biospheric gases is estimated to be ~1 Pg C y -1 (for year 2006; Nassar et al., 2010). 185 A priori flux uncertainties are derived from those assumed in the TC3 studies (Table 1)   assigned larger uncertainties by our scheme (described below), and therefore have less weight in 215 the inversion. For the JMA data, we omit only the hourly data with flag = 0, meaning the 216 number of samples is below a certain level, the standard deviation is high, and there is a large 217 discrepancy with one or both adjacent hourly values. Although some of the observation sites 218 used in our inversion are located close to each other, there is never any exact overlap in grid box 219 (altitude and/or longitude-latitude) or in time. Thus, all of those sites are kept for the inversions, 220 with observations at each site and day treated as independent (i.e. neglecting error correlations). 221 We estimate the uncertainties for the flask-air observations as the root sum square (RSS) represents an attempt to account for instrument error as well as transport/representation error. In 235 addition, based on initial inversion results, we enlarged all in situ total observation uncertainties 236 by a factor of 2 to lower the normalized chi-squared (χ 2 ) value closer to 1 (the final value of 237 which is shown in Table 2).

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GOSAT measures reflected sunlight in a sun-synchronous orbit with a 3-day repeat cycle 239 and a 10.5 km diameter footprint when in nadir mode (Yokota et al., 2009). The spacing 240 between soundings is ~250 km along-track and ~160 km or ~260 km cross-track (for 5-point/3-

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The values assumed for the GOSAT uncertainties are based in part on the retrieval 256 uncertainties provided with the ACOS data set. Following guidance from the data providers,  Inversions are conducted using different combinations of data, including the in situ data 264 ("in situ-only"), the GOSAT data ("GOSAT-only"), and both ("in situ + GOSAT"). 265 We use several additional data sets for independent evaluation of the inversion results.   (Rienecker et al., 2011). For this analysis, PCTM was run at a resolution of 2° latitude 287 × 2.5° longitude and 56 hybrid terrain-following levels up to 0.4 hPa. A "pressure fixer" scheme 288 has been implemented to ensure tracer mass conservation, the lack of which can be a significant 289 problem with assimilated winds (Kawa et al., 2004). This version of PCTM was among the    Model columns are weighted using ACOS column averaging kernels applied to 309 deviations of model CO 2 profiles from ACOS a priori profiles (Connor et al., 2008).      below 2 km, while the reverse is true in only 11 cases above 2 km and 25 cases below 2 km), but 409 it also is more often better than the prior than worse above 2 km (16 vs. 13 cases). In contrast, 410 the in situ inversion is more often worse than the prior than better (e.g. 27 vs. 12 cases above 2 411 km). Overall statistics, computed separately for lower and higher altitudes, are shown in Fig. 4.

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The model-observation histograms indicate that agreement with the aircraft observations is again 413 better for the GOSAT inversion than the in situ inversion, with smaller or comparable mean 414 differences and standard deviations. There is a near complete lack of in situ sites in the inversion 415 that are sensitive to Amazon fluxes (as suggested by Fig. 1a), contrasting with the availability of 416 some GOSAT data over the region (Fig. 1b), meaning that regional flux adjustments in the in situ  Table 1.

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The global total flux (including fossil emissions) is substantially more positive for the GOSAT-513 24 only inversion relative to the in situ-only inversion, 6.5 ± 0.2 Pg C y -1 vs. 4.1 ± 0.5 Pg C y -1 , 514 while that for the in situ + GOSAT inversion lies in between at 5.7 ± 0.2 Pg C y -1 . Such a large 515 difference in the atmospheric CO 2 growth rate implied by the two distinct data sets is plausible  (Table 1).

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The GOSAT results appear to contradict global carbon cycle studies that favor a weaker 540 terrestrial net source in the tropics compensated by a weaker northern extratropical sink (e.g. Hemisphere. The GOSAT inversion overestimates mole fractions in parts of the tropics, 554 sometimes by more than 1σ (Fig. 9), suggesting an overestimated tropical source. Uncorrected agree well with the surface observations ( Fig. 9; also seen in the individual site time series in 561 Fig. 2), which is expected given that these are the observations that are used in the optimization.

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The prior mole fractions are generally too high, which is consistent with the fact that the CASA-563 GFED biosphere is near neutral while the actual terrestrial biosphere is thought to generally be a 564 net CO 2 sink. above. However, given that the prior model also gives substantially higher mixing ratios than 583 HIPPO at these latitudes (by up to 11 ppm), the discrepancy could be due in part to transport 584 error.

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In the upper troposphere to lower stratosphere, the GOSAT inversion more often than not 586 exhibits better agreement with the HIPPO observations than the in situ inversion does for both 587 Mission 2 and 3 (Fig. 10c, f). A likely explanation is that the GOSAT data provide constraints 588 throughout the atmospheric column, whereas the in situ measurements constrain only surface 589 CO 2 . Figure 10 shows that the high-altitude mole fractions from the in situ inversion are 590 consistently close to those of the prior, suggesting that the lack of high-altitude constraints 591 prevents major adjustments in mole fractions at these levels, unlike in the GOSAT inversion.

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Although GOSAT biases may affect these altitudes as well, it appears to be the case that the data 593 still provide better constraints than no observations above the surface at all. Furthermore, an air given that emissions from fires in that region likely amount to < 0.7 Pg C y -1 . (Note that our N.

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Uncertainty reductions in the in situ inversion range from 15% to 93% for land regions and 15% 624 to 56% for ocean regions (Table 1). In the GOSAT inversion, the uncertainty reductions range 625 from 43% to 89% for land and 19% to 56% for ocean. And in the inversion with combined in 626 situ and GOSAT data, the uncertainty reductions are larger than or equal to those in either the in 627 29 situ-only or the GOSAT-only inversion, ranging from 61% to 96% for land and 40% to 67% for 628 ocean.  (Fig. 1b). Interestingly, there is not a sizable correlation between N. Africa and Europe inversions-in situ-only, GOSAT-only, and in situ + GOSAT-as was mentioned above, but the 675 land-ocean split is different. Our posterior ocean flux is -4.0 ± 0.8 Pg C y -1 , -3.1 ± 0.5 Pg C y -1 , 676 and -3.9 ± 0.3 Pg C y -1 for the three inversions, while it is -1.6 ± 0.5 Pg C y -1 , -1.2 ± 0.6 Pg C y -1 , priors generally exhibit better agreement with independent observations, e.g. lower-altitude 698 HIPPO observations (Fig. 13), and surface observations in the case of the GOSAT inversion 699 (Fig. 14), indicating that the effects of sampling and retrieval biases are reduced with tighter 700 prior uncertainties. The better agreement also lends support to the smaller ocean sink estimates. split in inversions using either in situ or GOSAT data is strongly influenced by error correlations 720 and dependent on the prior uncertainties assumed.

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The shift in the global terrestrial sink from the tropics/south to the north when comparing 722 the GOSAT-only inversion with the in situ-only inversion and the prior is still seen when prior 723 uncertainties are decreased, as is a substantially larger global total budget in the GOSAT 724 inversion relative to the in situ (Fig. 12). The uncertainty reductions in the test inversions are 725 smaller than those in the baseline inversions (Table 1)  provides full posterior error covariances, which allows us to quantitatively evaluate the degree to 849 which regional fluxes are constrained independently of one another.

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The GOSAT inversion is generally better constrained than the in situ inversion, with 851 smaller posterior regional flux uncertainties and correlations, except in places like North

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This study has successfully applied the batch inversion method to satellite data at 911 relatively high resolution to generate a solution useful for comparison with other techniques.

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However, for inversions over longer periods, using larger volumes of data such as from OCO-2, 913 or at higher flux resolution, more computationally efficient methods are essential.