On the potential of ICOS atmospheric CO 2 measurement network for the estimation of the 1 biogenic CO 2 budget of Europe 2

Introduction Conclusions References

synthetic "true" data used for the OSSE, any simulation can be used to build this truth, while, 149 when using fraternal twin experiments with nonlinear models in other application fields of data 150 assimilation, it is critical to ensure that the truth is realistic enough (Halliwell et al., 2014). Still, 151 the reliability of the OSSEs in CO 2 atmospheric inversion critically depends on the realism of 152 their input error statistics since their configuration in the inversion system is perfectly consistent 153 with the sampling of synthetic errors that are used in these experiments. In this study, our 154 confidence in the realism of the statistical modeling approach and of the input error statistics, 155 and thus in the inversion set-up, is based on the statistical modeling studies of Chevallier et al. 156 (2012) and Broquet et al. (2013) that were themselves based on real data. 157 The manuscript first documents the potential for constraining NEE, through the use of a state-of-158 the-art (i.e. which solves the NEE at high spatial and temporal resolution, and which has been 159 submitted to a high level of evaluation) variational atmospheric inversion system, and of the 160 ICOS23 network containing existing sites and other stations that could be installed on tall towers 161 over Europe in the coming years. We also consider two longer-term ICOS configurations with 50 162 (hereafter ICOS50) and 66 stations (hereafter ICOS66), respectively. For the time domain, we 163 consider results for NEE aggregated at the two-week scale, for two different periods of the year 164 (in July and in December). Shorter aggregation scales, like the day, result in a significant 165 dependency of NEE to specific synoptic events. Longer scales imply computing resources that 166 are beyond the scope of this study with this high-resolution inversion system. We pay special 167 attention to the analysis of the results at different spatial scales, from the native transport model 168 grid scale of about 50x50 km 2 up to the national scale that is the most relevant for supporting 169 environmental policy, and the full European domain considered in this study (which extends to 170 western Russia and Turkey). We also present the sensitivity of our results to parameters in comparison to the other type of errors that have to be accounted for in the inversion hourly averages of the atmospheric CO 2 data from these networks (over restricted time windows 206 everyday depending on the type of sites that are considered, see Sect. 2.2.2.). A regional 207 atmospheric transport model (see its description below) is used to estimate the relationship 208 between the CO 2 fluxes and the CO 2 mixing ratios. The inversion system solves for 6-hour mean 209 NEE on each grid point of the 0.5º by 0.5º resolution grid used for the transport modeling. It also 210 solves for 6-hour mean ocean fluxes at 0.5° spatial resolution in order to account for errors from 211 air-sea fluxes when mapping fluxes into hourly mean mixing ratios. However, analyzing the 212 uncertainty reduction for ocean fluxes is out of the scope of this paper. Peylin et al. (2011) 213 indicate that uncertainties in anthropogenic fluxes yield errors when simulating CO 2 mixing 214 ratios at ICOS stations that are smaller than atmospheric model errors. Furthermore, the relative 215 uncertainty in anthropogenic emissions is smaller than that in NEE, while on short timescales, 216 the anthropogenic signal is generally smaller than the signature of the NEE at sites that are not 217 very close (typically at less than 40km) to strong anthropogenic sources such as cities (see the 218 analysis for the Trainou ICOS station near Orléans, in France by Bréon et al. 2015). Relying on 219 such indications, we assume that the errors due to uncertainties in anthropogenic emissions are 220 negligible compared to errors from NEE and atmospheric model errors. This is a fair assumption 221 as long as most ICOS stations are relatively far from large urban areas, which should be the case 222 since the ICOS atmospheric station specification document (https://icos-223 atc.lsce.ipsl.fr/?q=doc_public) recommends that the measurements sites are located at more than 224 40km from the strong anthropogenic sources (such as the cities). Zhang et al. (2015) yield 225 conclusions from their transport experiments at 1° resolution which contradict this assumption 226 and this clearly raises an open debate. However, the evaluation of the inversion configuration 227 from Broquet et al. (2013) supports our use of this assumption for our study. Therefore, in order 228 to simulate the full amount of CO 2 in the atmosphere, the inversion uses a fixed estimate of the 229 fossil fuel emissions (see below) without attempting at correcting it nor at accounting for 230 uncertainties in these fluxes. The inversion also uses a fixed estimate of the CO 2 boundary 231 conditions at the lateral and top boundaries of the regional modeling domain without attempting 232 at correcting it or at accounting for uncertainties in these conditions. This follows the protocol 233 from Broquet et al. (2011) which assumed that the error from the boundary conditions for the 234 European domain is mainly a bias and which corrects for such a bias in a preliminary step that is 235 independent to the subsequent application of the inversion. Again such an assumption is  In principle, the inversion mainly exploits the smaller scale signal of the gradients between the 244 sites to constrain the NEE, and it is thus weakly influenced by the large scale signature of the 245 uncertainty in the boundary conditions. In this section we only summarize the main elements of 246 the inversion system, starting with the theoretical framework, while the detailed description can 247 be found in Broquet et al. (2011).
We define the control vector x of the atmospheric inversion as the 6-hour and 0.5°x0.5° mean 249 NEE and ocean fluxes. The atmospheric inversion seeks the mean x a and covariance matrix A of 250 the normal distribution N(x a , A) of the knowledge on x based on (i) the atmospheric transport 251 model, (ii) the prior knowledge x b of x , (iii) the hourly mean atmospheric measurements y, (iv 252 and v) the covariances B and R of the distributions of the prior uncertainty and of the 253 observation error assuming that these uncertainties are normal and unbiased (i.e., equal to N(0, 254 B) and N(0, R) respectively), and (vi) a Bayesian relationship between these distributions. The 255 observation error is the combination of all sources of misfit between the atmospheric transport 256 model and the concentration measurements other than the prior uncertainty, in particular the 257 measurement errors, the model transport, aggregation and representation errors, and the errors 258 from the model inputs that are not controlled by the inversion.

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With this theoretical framework, x a is the minimum of the quadratic cost function (Rodgers, simulating the atmospheric transport from the 1-hour resolution fluxes at 0.5° resolution. The inversion system derives an estimate of x a by performing an iterative minimization of 273 with the M1QN3 algorithm of Gilbert and Lemaréchal (1989). The gradient of J is derived using 274 the adjoint operator of H thanks to the availability of the adjoint version of the CHIMERE code.

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The covariance of the posterior uncertainty in inverted NEE A, of main interest for this study, is 276 given by the formula: posterior fluxes x ai is derived from an ensemble of inversions using synthetic prior flux x bi and 304 data y i whose random errors (x bi -x true and y i -Hx true respectively) to a known truth (x true , whose 305 value does not influence the results analyzed here, and which is thus ignored hereafter) sample

Practical set-up
In this study, the operator H is based on the CHIMERE mesoscale atmospheric transport model 322 (Schmidt et al., 2001) forced with ECMWF winds. We use a configuration with a 0.5ºx0.5º 323 horizontal grid and with 25 σ-coordinate vertical levels starting from the surface and with a 324 ceiling at ~500 hPa (such a ceiling being usual for regional transport modeling when focusing on 325 mole fractions close to the ground, e.g. Marécal et al. 2015). The spatial extent of the 326 corresponding domain is described below. CHIMERE is an off-line transport model. Hourly In this study, we use the European domain shown in Fig. 1a  Three week experiments allow retrieving information about uncertainties at the two-week scale 344 without being biased by edge effects, i.e., they allow accounting for the impact of uncertainties 345 from the days before the 14 targeted days and for the impact of the assimilation of measurements during the days after these 14 targeted days. Indeed, the advection of CO 2 throughout Europe can 347 last more than three days, but the atmospheric diffusion ensures that the signature at ICOS sites 348 of the NEE during a 6-hour window is generally negligible after three days of transport (not 349 shown). Thus, the windows 3-17 July and 5-19 December were chosen for analysis respectively. 350 We consider the results for July and December to be representative for the summer and winter

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It is chosen to represent the typical uncertainty in estimates from the biosphere models (for NEE) winter than that during the summer. It is given for each site in Table A1 for the two months 418 (July, December) considered in this study. We assume that the errors for two different sites are 419 independent and that they do not bear temporal autocorrelations. Thus, the observation error  less than 10% relative difference to this theoretical minimum except for few cases (for these 437 cases, 18 iterations were used to reach a relative difference to the theoretical minimum that is 438 smaller than 10%).    The spatial structure of the uncertainty reduction and the underlying spatial extrapolation from a 505 site is a complex combination of transport influence and of the structure of the prior uncertainty.  Regions lacking stations in ICOS23 have an uncertainty reduction which is more sensitive to the 521 atmospheric transport than regions with a dense network. The uncertainty reduction in December 522 is significantly larger in the east and in the southeast part of domain compared to July, due to 523 more occurrences of winds from the east during December than during July.

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Complementing the uncertainty reduction, Fig. 3 shows prior and posterior uncertainty standard  Table A2. The results suggest the ability of the mesoscale inversion 537 framework to derive estimates of the NEE at the national scales with relatively low uncertainties.

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The uncertainty reduction is particularly large for countries such as Germany, France and the UK 539 e.g., more than 80% for France during July. It is larger than 50% for a large majority of the 540 countries in Western Europe and Scandinavia both in July and December.
The smallest uncertainty reduction applies to southeastern European countries where it can be 542 smaller than 10 % (e.g., for Greece in July) indicating that the presence of stations very close to 543 or within a given country is a requisite for bringing significant improvement to the estimates of 544 NEE in this country. In general, the differences of the inversion skill between July and December 545 look consistent with what has been analyzed at the pixel scale. In particular the uncertainty 546 reduction is higher in July for western countries but higher in December for eastern countries for 547 the same reasons as that given when analyzing the same behavior at the pixel scale.  Table 1 shows that the uncertainty in two-week-mean NEE in July averaged over the full 551 European domain (6.8 ×10 6 km 2 of land surface) is reduced by the inversion by 50% down to a 552 value of ~ 43 TgCmonth -1 (see Table 1 for details) using the default configuration. The  The five locations used for this analysis are representative of the diversity of the situation 583 regarding the differences between grid scale uncertainty reduction in July and in December.

584
While the uncertainty reduction is slightly larger in July than in December for TRN, much larger 585 in July for PRS and HYY, it is slightly larger in December at OXK and much larger in December 586 at SW1. Furthermore, the values for these grid scale uncertainty reductions range from 15% to 587 50% in July and from 7% to 47% in December at these locations (Fig. 5).

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The maximum scores of uncertainty reduction occur for spatial scales of aggregation ranging 589 from 10 5 km 2 to 10 6 km 2 when considering the sites located in Western Europe. These scales approximately correspond to the range of the sizes of the European countries and it is larger than 591 the typical area of correlation of the prior uncertainty (as defined by prior correlation lengths of 592 250 km). Increasing the spatial resolution generally increases the uncertainty reduction since 593 posterior uncertainties have generally smaller correlation lengths than prior uncertainties, due to 594 the spatial attribution error when trying to link the measurement information to local fluxes 595 despite the atmospheric mixing. This explains the increase of uncertainty reduction from the grid 596 scale to the "national scales". This also explains why, for a given regional density of the 597 measurement network, larger countries bear larger uncertainty reductions (Fig. 4). However, 598 above such national scales, the corresponding domains include parts of Eastern Europe being 599 poorly sampled by the ICOS23 network which explains the decrease in uncertainty reduction.

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The convergence of the results around TRN, PRS and OXK to nearly 65% uncertainty reduction 601 in both December and July for the western European domain, and of the results at all sites to 602 53% in July and 66% in December for the whole Europe, when increasing the spatial averaging 603 area, starts between the same 10 5 km 2 and 10 6 km 2 (national scale) averaging areas. For smaller 604 areas, the differences between July and December or between different spatial locations stay configuration of the inversion (see Fig. 2  the uncertainty reduction at 0.5° resolution even in Western Europe in July, e.g., with uncertainty 631 reduction increased from ~40% using ICOS23 to ~60% using ICOS66 in Switzerland. The 632 impact of adding new sites is larger in December than in July, and, consequently, results for 633 western Germany and Benelux quite converge between July and December when increasing the 634 network to ICOS66.

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The impact on the scores of uncertainty reduction of the increase of the ICOS network is also 636 significant at the national (compare Fig. 4 and Fig. 8) and European scales (see Table 1 and Fig.   637 9) when comparing results with ICOS50 or ICOS66 to those obtained with ICOS23. The

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ICOS66 network delivers uncertainty reductions as high as 80% for countries like France and to ~15 TgCmonth -1 posterior uncertainty in December, and 64% down to ~33 TgCmonth -1 641 posterior uncertainty in July. However, the increase from ICOS50 to ICOS66 does not seem to 642 impact much the uncertainty reduction at these scales, especially in July. The impact of reducing the correlation e-folding length (from 250 km to 150 km) of the prior 656 uncertainty in the inversion configuration is tested using ICOS66 in July (compare Fig. 7b and   657 10a, Fig. 8b and 11a, and the corresponding curves in Fig. 9). Such a change of correlation  Even though these decreases can be very large, it is critical to keep in mind that they refer to 670 uncertainty reductions compared to a prior uncertainty which is decreased by the new 671 configuration of B (as illustrated at the country scale in Fig. A1). The posterior uncertainty in the 672 European and two-week mean NEE in July using ICOS66 is decreased from ~33 TgC month -1 to 673 29 TgCmonth -1 when changing the configuration of B from B 250 to B 150 (Table 1) The impact of dividing the standard deviation of the observation error by two in the inversion 687 configuration is tested using ICOS50 in July (compare Fig. 7a and 10b, Fig. 8a and 11b and the 688 corresponding curves in Fig. 9). The decrease of observation error increases the weight of the 689 measurements in the inversion and the resulting uncertainty reduction. This increase is visible at all spatial scales for the aggregation of the NEE, and relatively constant as a function of these 691 spatial scales except at the European scale for which it is quite smaller, from 64% to 67%. This 692 provides the highest scores of uncertainty reduction of this study at any spatial scales, the impact 693 of division of the observation error by two being larger than that of increasing the ICOS network 694 configuration from ICOS50 to ICOS66. 695 696 4 Synthesis and conclusions 697 We assessed the potential of CO 2 mole fraction measurements from three configurations of the 698 ICOS atmospheric network to reduce uncertainties in two-week mean European NEE at various 699 spatial scales in summer and in winter. This assessment is based on a regional variational inverse  Table A2. The relative posterior 729 uncertainty could be less than 20% for the countries gathering the largest NEE such as France,

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Germany, Poland or UK (if using ICOS66 in the three last cases, otherwise it should be less than 731 30% if using ICOS23), even though it would not be the case for Scandinavian countries with a 732 high NEE too. For some Eastern European countries, the posterior uncertainty could be very 733 close to the estimate of NEE from ORCHIDEE but the general tendency is to obtain posterior 734 uncertainties much lower than the estimate of the NEE from ORCHIDEE even when using 735 ICOS23. This tendency is reflected at the European scale (Table 1)  indicates that the inversion is required to reach the target from the CarbonSat report for mission 747 selection. It also indicates that this target is likely not reached in a large part of South Eastern 748 Europe even when using ICOS66 but that for countries like the Czech Republic and Poland, 749 extending the network from ICOS23 to ICOS66 allows reaching it. Finally, it indicated that the 750 ICOS23 network is sufficient to reach this target in Western Europe.

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The comparison of the sensitivity of the results in July to changes in the observation network,         high/low uncertainties (with min = 0 gCm -2 day -1 , max = 3 gCm -2 day -1 in the color scale).