Here we attempt to check the consistency of OCO-2 v10 MIP flux estimates and CO2 concentrations simulated using a common and independent atmospheric chemistry transport model (ACTM). NC22 performed sixteen inversions to investigate the dependence of inversion fluxes on the land and ocean prior fluxes as well as prior flux data uncertainty using in situ data only under a single transport model framework namely, the Model for Interdisciplinary Research on Climate (MIROC, version 4.034) based ACTM (MIROC4-ACTM henceforth) developed at the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) in collaboration with the University of Tokyo and the National Institute of Environmental Studies (NIES). All the OCO-2 v10 MIP inversion posterior fluxes in the present study are run forward using MIROC4-ACTM to derive flux evaluation metrics.
In this setting, the forward simulations of concentrations and optimised fluxes are consistent in a single ACTM simulation. In the case of evaluating NC22 fluxes, MIROC-ACTM is a circular model because the same transport model is used to estimate fluxes and to simulate concentrations. Thus, the MIROC-ACTM NC22 CO2 simulations are expected to be more consistent with the measurements compared to the simulation cases using MIROC4-ACTM driven by OCO-2 MIP fluxes, which were estimated using different transport. In a circular model setting, the modelled concentrations are generally close to the observed concentrations (seen in BB23; Friedlingstein et al.22), but estimated fluxes may vary from one model to another depending on the assumptions of the flux inversion system, and more importantly the model transport property, e.g., inter-hemispheric or meridional transport14,15,28,35.
A detailed discussion on the governing transport processes (diffusion, advection and convection) on the forward model simulation is out of scope of this article. We focus on deriving an emergent constraint for estimation of total (ocean + land) CO2 fluxes in broad latitude bands using the model–observation differences as simulated by the MIROC4-ACTM.
Forward transport model description
In this study, forward transport simulations of CO2 fluxes are conducted using MIROC4-ACTM. MIROC4-ACTM uses a dynamical core with triangular truncation at a total of 42 horizontal wave numbers34 (T42; latitude and longitude ~2.8 × 2.8°). MIROC4-ACTM uses a hybrid vertical coordinate system with 67 layers, which allows it to resolve the atmosphere up to 0.0128 hPa (~ 80 km from earth’s surface). For better representation of atmospheric transport, the model simulated horizontal wind (U, V) and atmospheric temperature (T) are nudged with Japanese 55-year Reanalysis36 (JRA-55) data using Newtonian relaxation times of 1 and 5 days, respectively. MIROC4-ACTM has been described and evaluated for chemical tracer transport extensively, for the interhemispheric exchange rates in the troposphere, and age of air in the upper troposphere and stratosphere34,35,37,38.
OCO-2 v10 MIP and MIROC4-ACTM inversion fluxes
Detailed information about the models from various groups that participated in the OCO-2 v10 MIP project are given in Table S1 along with their code name, corresponding meteorological forcing, horizontal and vertical resolutions and prior flux combinations. In a total of 14 groups, GEOS-Chem and TM5 are commonly used, but with different resolutions, nudging data and a variety of prior fluxes which enables every setup to be different and to result different inversion fluxes. All the groups followed a common protocol to generate the inversion fluxes. MIROC4-ACTM simulations during 2015-2020 are conducted using all the 13 flux products (Ames, Baker, CAMS, CMS-Flux, COLA, CSU, CT, JHU, NIES, OU, TM5-4DVAR, UT, WOMBAT) from two different experiments, IS and LNLG. Following BB23, results of the LoFI model (not a traditional inversion) are excluded from this analysis. In addition, we also included two sets of fluxes from MIROC4-ACTM using in situ data only, viz., NC22-gc3t, NC22-gvjf in the analysis, which are not a part of the OCO-2 v10 MIP. Details of these individual flux estimates and their corresponding prior fluxes, model setup etc. are given in NC22. NC22 uses a time-dependent Bayesian synthesis inversion, where fluxes for 84 (54 land + 30 ocean) regions are calculated at monthly time intervals using flask and in-situ air sampling measurements at 50 sites covering a period of 2000-2021 (updated annually). Therefore, a total of 14 models are analysed in this study. An overview of the MIROC4-ACTM MIP experimental setup is schematically presented in Fig. M1.
Each group performed different global flux inversion experiments separately with different combinations of CO2 data, such as:
- In situ CO2 measurements (“in situ” or “IS”) only.
- OCO-2 retrievals over land (“land nadir” + “land glint”, or “LNLG”) only.
- OCO-2 retrievals over land and In situ CO2 (LNLGIS)
The other inversions involving OCO-2 retrievals over water surfaces have biases9 and therefore are not considered in this study. Moreover, our analysis of these inversion fluxes at global and regional scale reveals that the IS and LNLG experiments are the two extreme cases and LNLGIS remains in between them (Fig. S1, S2 and S3). Therefore, IS and LNLG inversion are scrutinised primarily in this study.
Observational datasets
MIROC4-ACTM simulations of CO2 are evaluated mainly using in-situ data at 50 sites, which are located away from the strong emissions/sinks of CO2 (Table S2). CO2 measurements are taken from observation values from the OCO-2 v10 MIP datasets which are primarily based on obspack_co2_1_GLOBALVIEWplus_v6.139. List of sites is given in Table S2. The OCO-2 v10 MIP data are reported in X2007 scale. The simulated growth rates are evaluated using in-situ as well as other data sources such as the total column dry-air mole fraction (XCO2) from the Total Carbon Column Observing Network40 (TCCON), Greenhouse gases Observing Satellite41 (GOSAT) and Orbiting Carbon Observatory-242 (OCO2). Details of the extra datasets and their analyses are given in the supplementary document. The in-situ measurements from remote locations are chosen for the main analysis to avoid local influences (for better representativeness) on the measurement as the MIROC4-ACTM horizontal resolution is relatively coarse (~2.8º × 2.8º). The in-situ measurements also have high accuracy, at about ±0.2 ppm between institutions and consist of no known biases due to environmental conditions19,43.
Forward simulations of OCO-2 v10 MIP fluxes and post-processing
In the MIROC4-ACTM forward transport simulations, the 2015 fluxes at monthly interval from the OCO-2 v10 MIP are run for the period 01 January 2011 to 31 December 2014, as spin up for the tropospheric CO2 concentration fields. The 4-year spin up is also expected to set up the CO2 concentration gradients realistically in most parts of the lower stratosphere. We used the following CO2 flux components from the OCO-2 v10 MIP, a) net land biospheric fluxes (sum of photosynthesis, respiration, fires, biofuels) and b) net air-sea fluxes. The diurnal cycle and daily/synoptic variability in all the fluxes are not considered. The fossil fuel CO2 emissions are taken from GridFED (commonly used in GCP-CO2 annual budget) at monthly intervals44 as used in the MIROC4-ACTM inversion, although the ODIAC FFCO2 emissions with hourly resolution were used in the OCO-2 v10 MIP inversions45. The absolute differences between annual total GridFED and ODIAC emissions are within 0.14 PgC and are unlikely to influence the conclusions of this analysis, because all the OCO-2 v10 MIP models are treated equally in MIROC4-ACTM MIP, and the MIROC4-ACTM estimated fluxes are not used in the EC calculations.
Model simulated hourly CO2 fields are sampled first to the exact location and time of the respective validation datasets, and then averaged temporally before comparison. In case of TCCON, GOSAT and OCO-2 data, columnar concentration (XCO2) is also prepared using the following formula:
XCO2_model = XCO2_prior + aT(CO2_model - CO2_prior)
where
CO2_model: vector representing the vertical profile of CO2 mixing ratios simulated by the model.
XCO2_prior: prior XCO2 value.
a: represents the averaging kernel.
CO2_prior: prior CO2 profile.
In addition, modelled and observed XCO2 data is further sampled to 2.5º × 2.5º horizontal grids for GOSAT and OCO-2 validation. The detailed growth rate comparisons are presented in Fig. S6 and Fig. S7.
Emergent constraint formulation
Reducing uncertainty in climate-carbon cycle projections to enhance their reliability and feasibility is a fundamental challenge and emergent constraints are used here to address it. In this study, weighted ODR46 is used as the linear regression method to find the EC relationship. The major drawback of ordinary least squares is that it considers the errors in the dependent/response variable (total CO2 flux here) only and may therefore provide a biased slope while the independent/explanatory variable (CO2 bias in this study) is also associated with errors. ODR can deal with both the errors. We used standard deviation (SD) of the flux and model–observed CO2 as the scaling weight for the response/predictand and explanatory/predictor variable respectively. Further details are provided in Gaubert et al.25
Flux estimated using ODR fit and with the projection of zero bias line to the flux axis is considered as our BE flux. The calculation involves fifty background sites only (described earlier), and is conducted using 2015-2020 mean values exclusively. To determine the bias uncertainty (BUNC) for EC framing, we conducted calculations based on multi-model mean and 1-s spread of the bias corresponding to each of the fifty sites, as illustrated in Fig. S8. The spread observed in Fig. S8a is identified as site representation error, persisting even after assimilating in-situ CO2 data (IS case). However, in Fig. S8c, where LNLG data is assimilated, this spread does not necessarily represent site representation error. Figures S8b and S8d, on the other hand, illustrate bias error. Consequently, in the computation of BUNC for each subpanel (a, b, c, d) of Fig. S8, we replicated the site representation error (i.e., the spread in Fig. S8a) both for Fig. S8a and S8c. For Fig. S8b and S8d, we combined both site representation error and the corresponding bias error using the standard quadrature formula (combined STDEV of multiple ![](https://myfiles.space/user_files/122228_c8a1650c59388082/122228_custom_files/img1709898124.png)
an independent and non-identical random variable; each site represent one random variable here). BUNC then further subdivided into three latitude bands. Finally, BUNC for each latitude band was calculated by amalgamating the BUNC of the corresponding sites within the respective latitude band and utilized as input for the EC computation.
EC is calculated over each latitude band separately and used further to find the best estimate flux and uncertainty in the corresponding band. Flux is calculated from the Monte-Carlo (MC) simulation on ODR slope and intercepts for 5000 random samples from a bivariate Gaussian distribution with mean zero and respective BUNC spread. Finally, ensemble mean and standard deviation of these fluxes are considered as BE flux and uncertainty of that respective latitude band. In addition, we also calculated 1-s prediction interval corresponding to the ODR fit based on the MC simulated slope and intercepts and ODR residual standard deviation. EC analyses are depicted in Fig. 4 in the main text (prepared combining IS and LNLG data). While plotting, we followed the model–observation CO2 (independent/predictor) in the x-axis and flux (predictand) as y-axis to follow the EC convention as mentioned in Gaubert et al.25
Best estimate Land carbon stockchange and its uncertainty calculation
EC estimated mean CO2 flux (ensemble mean of 5000 MC samples) are considered as BE flux. We considered EC results from MIROC4-ACTM MIP only due to weaker/insignificant correlations in the OCO-2 v10 MIP case (over Tropics in particular). BB23 land/ocean flux (uncertainty) is calculated from muti-model mean (spread) from BB23 fluxes (i.e. OCO-2 v10 MIP flux). Subsequently, mean BB23 ocean fluxes (IS and LNLG) are subtracted from BE fluxes and then corrected with river C export fluxes (at unknown uncertainty) which is considered as our BE land carbon stockchange. EC estimated spread is finally considered as the uncertainty associated to the BE land carbon stockchange. In the same way, BB23 carbon stockchange is also calculated for comparison purpose. The uncertainty of BB23 stockchange is computed combining BB23 IS and LNLG land uncertainty (basically multi-model flux spread from table S3 and S4) [using the quadrature formula described earlier].
Estimated carbon loss/gain from land use change data products
We have compared to three independent estimations of land-atmosphere CO2 fluxes based on land use, land use change and forestry (LULUCF) data products, i.e., (1) the United Nations Framework Convention on Climate Change GHG Data Interface (UNFCCC GHGI), (2) National GHG Inventories (NGHGI) from Grassi et al.31, and (3) forest carbon net flux estimations from Harris et al.5. UNFCCC provides a detailed, categorised and extensive collection of LULUCF CO2 fluxes based on the national inventory data submitted by the individual countries. UNFCCC GHGI contains emission data for 180 countries (43 Annex I countries, https://di.unfccc.int/flex_annex1, and 137 Non Annex I countries, https://di.unfccc.int/flex_non_annex1; Last accessed February 16, 2023). We have taken the net emission/removals product of “Category 4. Land Use, Land-Use Change and Forestry” for the Annex I countries and “Category 5. Land-Use Change and Forestry” for the Non Annex I countries. In the NGHGI database (Grassi et al., 2022, https://doi.org/10.5281/zenodo.7190601; Last accessed February 16, 2023), data are available for a total of 195 countries (15 additional Non Annex I countries). Differences in the country list between the two databases (UNFCCC and NGHGI) are given in Table S3. NGHGI has improved consistency between the UNFCCC country reporting and other data sources such as the Biennial Update Reports (BURs), Reducing Emissions from Deforestation and forest Degradation (REDD+) inventories, Nationally Determined Contributions (NDC).
To process the UNFCCC GHGI data (180 countries) for our analysis period 2015-2020, the UNFCCC data is linearly interpolated during 1990 - 2020 to gap-fill the whole time series. While grouping into various latitudinal belts, data inconsistency (between UNFCCC and NGHGI) is noticed for a few tropical NAI countries. Elimination of these inconsistencies at the individual country level data is beyond the scope of this study and hence we replaced UNFCCC GHGI fluxes for Central African Republic, Guinea and United Republic of Tanzania by the NGHGI values. These 3 countries collectively result in large flux differences of -0.35 and -0.03 PgC yr-1 in UNFCCC GHGI and NGHGI, respectively, for the tropical latitude band. Considering the size of the ecosystem consisting of these three countries, we judge the country emissions were reported mistakenly and those are corrected by the efforts by Grassi et al.31 in preparing NGHGI. Thus, our results of UNFCCC GHGI and those reported in NGHGI may not be considered as completely independent estimations.
Harris et al.5 provides forest carbon net flux (forest, deforestation and others) from a geospatial monitoring framework. This data is available at https://data.globalforestwatch.org (Last accessed February 16, 2023). Their calculation method is based on 30 m global maps of forest-related GHG fluxes by combining IPCC methodologies with spatial data on forests, which includes consideration of global soil carbon and biomass, remotely sensed burned areas, mangroves (extent, soil carbon, biomass), peatlands, plantations, intact forests, tree cover (loss and gain), drivers of forest loss and forest regrowth C rates. Note that they calculated the total GHG fluxes inclusive of CH4, N2O and others, but the values are closely representative of the net land C flux (David Gibbs, WRI; personal comm., February 2023). The global total net forest sink estimations (CO2 equivalent) are in good agreement with that estimated by the Global Carbon Project assessment5.