Carbon Monitoring System Flux Net Biosphere Exchange 2020 (CMS-Flux NBE 2020)

. Here we present a global and regionally-resolved terrestrial net biosphere exchange 28 (NBE) dataset with corresponding uncertainties between 2010–2018: CMS-Flux NBE 2020. It is 29 estimated using the NASA Carbon Monitoring System Flux (CMS-Flux) top-down flux 30 inversion system that assimilates column CO 2 observations from the Greenhouse gases 31 Observing SATellite (GOSAT) and NASA’s Observing Carbon Observatory -2 (OCO-2). The 32 regional monthly fluxes are readily accessible as tabular files, and the gridded fluxes are 33 available in NetCDF format. The fluxes


Introduction
fluxes and uncertainties by comparing the posterior CO2 mole fractions against aircraft 116 observations and the NOAA MBL reference CO2, and a gross primary production (GPP) product 117 (section 5). In Section 6, we discuss the strength and weakness, and potential usage of the data. A 118 summary is provided in Section 7, and Section 8 describes the dataset availability and future plan. 119 120 2 Methods 121

CMS-Flux inversion system 122
The CMS-Flux framework is summarized in Figure 1. The center of the system is the CMS-Flux 123 inversion system, which optimizes NBE and air-sea net carbon exchanges with a 4D-Var inversion 124 system (Liu et al., 2014). In the current system, we assume no uncertainty in fossil fuel emissions, 125 which is a widely adopted assumption in global flux inversion systems (e.g., Crowell et al., 2019), 126 since the uncertainty in fossil fuel emissions at regional scales is substantially less than the NBE 127 uncertainties. The 4D-Var minimizes a cost function that includes two terms: 128 (1) 129 The first term measures the differences between the optimized fluxes and the prior fluxes  Table 1. We run both the forward and adjoint at 4° x 5° spatial resolution, and 137 optimize monthly NBE and air-sea carbon fluxes at each grid point from January 2010 to 138 December 2018. Inputs for the system include prior carbon fluxes, meteorological drivers, and the 139 satellite XCO2 (Figure 1). Section 2.2 (Table 2) describes the prior flux and its uncertainties, and 140 section 2.3 (Table 3)  The prior CO2 fluxes include NBE, air-sea carbon exchange, and fossil fuel emissions (see Table  144 2). The data sources for the prior fluxes are listed in Table 7  We construct the NBE prior using the CARDAMOM framework (Bloom et al., 2016). The 151 CARDAMOM data assimilation system explicitly represents the time-resolved uncertainties in the 152 NBE. The prior estimates are already constrained with multiple data streams accounting for 153 measurement uncertainties following a Bayesian approach similar to that used in the 4D-154 variational approach. We use the CARDAMOM setup as described by Bloom et al. (2016Bloom et al. ( , 2020  The observational coverage of ACOS-GOSAT and OCO-2 is spatiotemporally dependent, with 226 more coverage during summer than winter over the NH, and more observations over mid-latitudes 227 than over the tropics ( Figure S3 Direct NBE estimates from flux towers only provide a spatial representation of roughly 1 -3 252 kilometers (Running et al., 1999), not appropriate to evaluate regional NBE from top-down flux 253 inversions. Thus, we use two methods to indirectly evaluate the posterior NBE and its uncertainties. 254 One is to compare annual NBE anomalies and seasonal cycle to a gross primary production (GPP) 255 product. The other is to compare posterior CO2 mole fractions to independent (i.e., not assimilated 256 in the inversion) aircraft and the NOAA MBL reference observations. The second method has been 257 broadly used to indirectly evaluate posterior fluxes from top-down flux inversions (e.g., Stephens 258 et al., 2007;Liu and Bowman, 2016;Chevallier et al., 2019;Crowell et al., 2019). In addition to 259 these two methods, we also compare the NBE seasonal cycles to three publicly available top-down 260 NBE estimates that are constrained by surface CO2 observations (Tables 3 and 7). 261

Evaluation against independent gross primary production (GPP) product 262
NBE is a small residual difference between two large terms: total ecosystem respiration (TER) 263 and GPP, plus fire. A positive NBE anomaly (i.e., less uptake from the atmosphere) has been 264 shown to correspond to reduced GPP caused by climate anomalies (e.g., Bastos et al., 2018), and 265 the magnitude of net uptake is proportional to GPP in most biomes observed by flux tower 266 observations (e.g., Falk et al., 2008). Since NBE is related not only to GPP, the comparison to GPP 267 only serves as a qualitative measure of the NBE quality. For example, we would expect that the 268 posterior NBE seasonality to be anti-correlated with GPP in the temperate and high latitudes.  (Table  284 3). Figure where P is the total number of grid points and M is the total number of months from the time of 344 the aircraft data to the beginning of the inversion. The numerator of equation (8) quantifies the 345 absolute total sensitivity of the RMSE 2 to the fluxes at the i th grid. Normalized by the total absolute 346 sensitivity across the globe, the quantity " indicates the relative sensitivity of RMSE 2 to fluxes at 347 the i th grid point. Note that " is unitless, and it only quantifies sensitivity, not the contribution of 348 fluxes at each grid to RMSE 2 . 349

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We use the NOAA MBL reference dataset ( We provide posterior NBE from 2010 -2018 using three sets of regional masks (Figure 3), in 360 addition to the gridded product. The regional mask in Figure  in Australia, and seven in Africa. The regional mask in Figure 3B is based on latitude and 365 continents with 13 regions in total, which is referred as Region Mask 2 (RM2) in later description. 366 Figure 3C is the TransCom regional mask with 11 regions on land. can also aggregate the gridded fluxes and uncertainties based on their own defined regional masks. 378 Table 5 provides a complete list of all data products available in the dataset. In section 4, we 379 describe the major characteristics of the dataset. 380 4 Characteristics of the dataset 381

Global fluxes 382
The annual atmospheric CO2 growth rate, which is the sum of fossil fuel emissions and total annual 383 sink over land and ocean, is well-observed by the NOAA surface CO2 observing network 384 (https://www.esrl.noaa.gov/gmd/ccgg/ggrn.php). We compare the global total flux estimates constrained 385 by GOSAT and OCO-2 with the NOAA CO2 growth rate from 2010-2018, and discuss the mean 386 carbon sink over land and ocean. Over these nine years, the satellite-constrained atmospheric CO2 387 growth rate agrees with the NOAA observed CO2 growth rate within the uncertainty of the  4.2 Mean regional fluxes and uncertainties 408 Figure 5 shows the nine-year mean regional annual fluxes, uncertainty, and its variability between 409 2010-2018. Table 6 shows an example of the dataset corresponding to Figure

Interannual variabilities and uncertainties 427
Here we present hemispheric and regional NBE interannual variabilities and corresponding 428 uncertainties (Figures 6 and 7, and corresponding tabular data files). In Figure 6 is small, the R 2 between GPP and NBE is also small (0.0-0.5) as expected. But the increased net 453 uptake generally corresponds to increased productivity. We also do not expect perfect negative 454 correlation between NBE anomalies and GPP anomalies, as discussed in section 2.5. The 455 comparison between NBE and GPP provides insight into when and where net fluxes are likely 456 dominated by productivity. 457

Seasonal cycle 459
We provide the regional mean NBE seasonal cycle, its variability, and uncertainty based on the 460 three regional masks (Table 5) to NBE over a broad region as shown in Figure S5. Note, Figure S5 and Figures  Increasing the resolution of the transport model may reduce transport errors over high latitudes. 550

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We run adjoint sensitivity analysis over the high-latitude regions where the differences between 552 posterior CO2 and aircraft observations are large (Figure 11). The adjoint sensitivity analysis 553 ( Figure S10) shows that the large errors over these regions could be driven by errors in fluxes over 554 Alaska as well as broad NH mid-latitude regions. 555 556

Comparison to MBL reference sites 557
Since MBL reference sites sample air over broad regions, the comparison to detrended MBL 558 observations indirectly evaluates the NBE over large regions. Figure 12  can potentially resolve fluxes at spatial scales smaller than the traditional TransCom regions. Here, 607 we provide regional fluxes at two predefined regions in addition to TransCom. We encourage data 608 users to use the data at propriate regional scales. to the changes of atmospheric CO2 (Liu et al., 2018). Since NBE has high variability and its 627 predicted changes in the future are likely to have large uncertainties, quantifying regional NBE is 628 critical to monitoring regional contributions to atmospheric CO2 growth rate, and ultimately to 629 guide mitigation to limit warming to 1.5°C above pre-industrial levels (IPCC, AR6). 630 631 7 Summary 632 Terrestrial biosphere carbon fluxes are the largest contributor to the interannual variability of the 633 atmospheric CO2 growth rate. Therefore, monitoring its change at regional scales is essential for 634 understanding how it responds to CO2, climate and land use. Here, we present the longest terrestrial 635 flux estimates and their uncertainties constrained by XCO2 from 2010-2018 on self-consistent 636 global and regional scales (CMS-Flux NBE 2020). We qualitatively evaluate the NBE estimates 637 by comparing its variability with GPP variability, and provide comprehensive evaluation of 638 posterior fluxes and the uncertainties by comparing posterior CO2 with independent CO2 639 observations from aircraft and the NOAA MBL reference sites. This dataset can be used in 640 understanding controls on regional NBE interannual variability, evaluating biogeochemical 641 models, and supporting the monitoring of regional contributions to changes in atmospheric CO2.   Figure: 1 Data flow diagram with the main processing steps to generate regional net 1097 biosphere change (NBE). TER: total ecosystem respiration; GPP: gross primary production.

1098
The green box is the inversion system. The blue boxes are the inputs for the inversion system. 1099 The red boxes are the data outputs from the system. The black box is the evaluation step, 1100 and the grey boxes are the future additions to the product.  Table: 6 The nine-year mean regional annual fluxes, uncertainties, and variability. Regions 1225 are based on the mask shown in Figure 5A (Figure 5.