On the ability of a global atmospheric inversion to constrain variations of CO 2 fluxes over Amazonia

The exchanges of carbon, water and energy between the atmosphere and the Amazon basin have global implications for the current and future climate. Here, the global atmospheric inversion system of the Monitoring of Atmospheric Composition and Climate (MACC) service is used to study the seasonal and interannual variations of biogenic CO2 fluxes in Amazonia during the period 2002–2010. The system assimilated surface measurements of atmospheric CO2 mole fractions made at more than 100 sites over the globe into an atmospheric transport model. The present study adds measurements from four surface stations located in tropical South America, a region poorly covered by CO2 observations. The estimates of net ecosystem exchange (NEE) optimized by the inversion are compared to an independent estimate of NEE upscaled from eddy-covariance flux measurements in Amazonia. They are also qualitatively evaluated against reports on the seasonal and interannual variations of the land sink in South America from the scientific literature. We attempt at assessing the impact on NEE of the strong droughts in 2005 and 2010 (due to severe and longer-thanusual dry seasons) and the extreme rainfall conditions registered in 2009. The spatial variations of the seasonal and interannual variability of optimized NEE are also investigated. While the inversion supports the assumption of strong spatial heterogeneity of these variations, the results reveal critical limitations of the coarse-resolution transport model, the surface observation network in South America during the recent years and the present knowledge of modelling uncertainties in South America that prevent our inversion from capturing the seasonal patterns of fluxes across Amazonia. However, some patterns from the inversion seem consistent with the anomaly of moisture conditions in 2009.

Q.1.3) At a minimum, do the simulated observations from INVSAm capture the assimilated observations within 95% of their confidence intervals? A) Table A1 below (provided as supplementary material) compares the standard deviations of the prior and posterior misfits between the simulations and the observation, and the ~95% confidence interval (two standard deviations) of the configuration of the observation errors (for hourly observations) in the inversion system (following section 2.1). The prior misfits are much larger than our observation errors at ABP, MAX, and GUY which makes the prior simulation lie outside the 95% confidence interval of the observation error except at SAN (where prior misfits are still slightly larger than the observation error). Misfits between MACCv10.1 and the observations are similar to the prior misfits at SAN and GUY and much smaller than the prior misfits at the coastal sites ABP and MAX, which could be related to a very large scale improvement of the fluxes in the Southern Hemisphere. The corrections from MACCv10.1 thus make the posterior simulation fall within the 95% confidence interval of the observation error at all the sites but GUY. When assimilating the data from the South American sites, misfits are decreased compared to both the prior and MACCv10.1 at all sites. The INVSAm posterior simulation still lies in the 95% level interval of the observation error at ABP, MAX, and SAN and nearly reaches the threshold at GUY. It is close to the 68% confidence interval at MAX and within this interval at SAN, while it was not the case for MACCv10.1. This and the high increments (in terms of relative difference to the prior fluxes) applied to the fluxes in South America both in MACCv10.1 and when adding South American stations lead us to consider that the corrections from the inversion are significant, even though we do not have the means for deriving the actual statistical significance. We discuss this in Sect. 3.1 of the revised manuscript. "The significance of the reduction of the misfits between the mole fractions observed and simulated from the inversion is seen from the comparison between the standard deviations of these misfits and the estimate of the standard deviation of the observation errors (i.e. of the transport model errors) for hourly values in the configuration of the R matrix (Table A1, in supplementary material).According to this comparison, the prior misfits are much larger than the observation errors at ABP, MAX, and GUY, but are slightly smaller than these at SAN. Misfits between MACCv10.1 and the observations are similar to the prior misfits at SAN and GUY and are much smaller than the prior misfits (and smaller than the 95% confidence interval of the observations) at the coastal ABP and MAX sites. Misfits are further decreased when assimilating the data from the South American sites: they are about the standard deviation of the observation errors at all sites but GUY (where they are twice as large)." Q.1.4) Error bounds will also allow better judging the performance in Figures 6 and 9. Hence, I would strongly encourage the authors to reconsider their decision to skip the calculation of these posterior uncertainties.
A) As explained above, deriving theoretical uncertainties for the mean seasonal cycle and the inter-annual anomalies is not affordable in the framework of this study (see our answer to General Comment Q.1.1 from Referee #2). Furthermore, as detailed in the answer to the reviewer's General Comment Q.1.2, such theoretical numbers are not critical for judging the performance of the system. Even though we prefer not to launch such computations of the theoretical uncertainties, we discuss better this topic in the revised manuscript, based on our answers to the reviewer. Q.
2) The lack of discussion on uncertainties is also related to choices that have been made about the prior covariance. Why did the authors persist with using correlations in B that are based on data from towers in the Northern Hemisphere? Are there alternatives to the Chevallier et al. [2006] approach that the authors could have used to determine a more suitable B for the study region? Even though this study solves for global fluxes, the use of correlations that are appropriate for the Amazon basin seems necessary. Can the authors comment on their choice?
A) The reviewer is right about the fact that some lack of confidence in the configuration of the prior and observation error covariance for the limited and specific area, on which this study focuses, is an important explanation why we think that the computation of theoretical uncertainties would not be useful while highly expensive. We believe that the use of eddy covariance measurements is presently the best way to assess the statistics of the prior uncertainties at the time and space scales for which the B matrices need to be setup. Some computations of the standard deviation of misfits between ORCHIDEE and eddy covariance measurements in South America indicated that the configuration of the standard deviation of the prior uncertainty at the weekly scale was robust for this continent as well as for others. However, the small number of eddy covariance measurement sites in South America prevented us from deriving spatial correlations specifically for this continent. This explains why we used in South America the scales derived using the global eddy covariance dataset, which is strongly biased by the higher number of sites in the Northern hemisphere. Furthermore, the method used to model the observation error in CH2010 and in our study has been developed and evaluated based on analysis of model data comparisons using mainly atmospheric data from the mid latitudes in the Northern Hemisphere ( Q.3) How likely is it that the dipole issue (Figure 8, also Page 1932, Lines 5-12) is related to the spatial correlations that have been pre-specified in B? In fact in Lines 10-12, the authors seem to question their own choice of B. In order to completely investigate this dipole issue, the authors may need to look at the ocean fluxes. As the focus of this study is on the land component, I agree with the decision of the authors to skip any discussion on the ocean fluxes (Page 1924, Line 4). But in light of the dipole issue as well as the negative results, it may be worthwhile to add as supplementary material a discussion on the ocean fluxes; for example, even a spatially-aggregated evaluation with respect to the MACCv10.1 (or CH2010) product may provide some insights on the performance of the inversion system.
A) The answer to General Comment Q.2 from the reviewer gives more details about the lack of confidence in B over Amazonia. However, regarding the dipole, it seems to be mainly driven by a large-scale behaviour of the inversion connected to the atmospheric transport rather than by the B matrix, as demonstrated by the increments to the ocean fluxes. We comment this in the revised manuscript. Our original discussion on the dipole could have been misleading regarding the role of B in the dipole and has been reformulated in the new section 3.2. Previous Fig. 8 has been updated (new Fig. 6 . S1), which is in line with the fact that this site is located more inland than the others. Such high control of the data in the TSA region (even when checking the SAN and MAX, or the MAX, ABP and GUY datasets only) over the zonal patterns of flux corrections also highlights the very large-extent impact of these data, and of the data in the southern hemisphere in general, despite the relatively small spatial correlation length scales in the B matrix, and the limited area in which the station footprints are very high. The inversion also generates patterns of corrections of smaller spatial scale close to the measurement sites in the TSA region when these sites are used by the inversion. This raises hope that the NEE over the whole TSA region is strongly constrained by the observations, but can also raise questions regarding the spatial variations of the corrections applied by the inversion to the NEE within the TSA region, at least when considering areas at more than 500 km from the measurement sites. However, various pieces of evidence ( Fig. 5 and 6, the analysis of the decrease in misfits to the observations from the inversion in section 3.1, and the previous analysis of the high increments to the monthly mean and annual mean NEE over the entire TSA region) indicate that the corrections from the inversion are significant."

C) A new section, "3.2 Characterization of the monthly to annual mean inversion increments to the prior fluxes" has been included in the manuscript. In this section we
Q.4) Page 1934, Lines 18-20: The authors state -"...the inversion system may have applied corrections in response to events registered by only a single station at a time". I am not sure what the authors mean here. Do the authors imply that even though observations from a particular site were available for a few years, it negatively impacted the analyses over other time periods? Based on my understanding, in the variational system the analysis window spanned the full period from 2002-2010. If so, did the authors consider breaking up the analysis window into smaller time-chunks, for example, 2 or 3 year periods with overlapping 2-3 months in between?

A) Our statement was a bit confusing and has been reformulated. Corrections applied in response to a specific event at a given site should not spread in time to such an extent that it would impact the results during years when there is no data available at this site, and we do not think that we should verify it by conducting inversions on 2-3 year periods (however, see the analysis of the results for 4-5
year periods in answer to the Referee #1, in figure S1, which helps isolate the impact of the different sites; see also the results for the year 2003 when SAN data only were available in answer to the General Comment Q.5 of Referee #2). Still, these specific corrections would have less weight in the average increments in the area if the data availability was higher. We confusingly made a shortcut between giving more weight to a short term event in the mean corrections and applying mean corrections in answer to such short term events.
In the revised manuscript we discuss this topic based on the answers to the Referee #1 and to the General Comment Q.5.