Our regional inversion system optimizes monthly mean grid-based surface carbon emissions x using a four-dimensional variational data assimilation method that was configured to utilize the Community Multiscale Air Quality (CMAQ, version 5.3) model and its adjoint version 4.5.1;. Each year of the 5-year period was run independently, with a spin-up of 1 month for each year. Our system optimizes CO2 surface fluxes by finding the minimum of the cost function J(x) shown in Eq. (). Notation in this study follows . 1J(x)=12x-xbTB-1x-xb+12H(x)-yTR-1H(x)-y

This cost function measures the mismatch between the CMAQ forward model simulation H and OCO-2 satellite observations y as well as the deviation of the control vector x from its background (also termed prior) estimate xb. In our case, the control vector x (the vector of unknowns) consists not only of the gridded CO2 surface fluxes but also incorporates initial and boundary conditions (BCs). These two latter variables were incorporated into the control vector to reduce any potential biases related to the boundary inflow that could affect our system details of how we treat the boundary and initial conditions in our system can be found in Sect. 2.2 in, and a brief description of this treatment is found in Sect. . R represents the observational error covariance matrix, which was defined as a diagonal matrix a full description of this covariance matrix is found in Sect. 2.3 in, and a brief explanation of how it was constructed is found in Sect. . B is the associated error covariance matrix of xb, boundary and initial concentrations, and includes off-diagonal terms. In these off-diagonal values, we only include spatial and non-temporal correlations of the prior fluxes details of the structure of the prior error covariance matrix are found in Sect. 2.4 in, and a summary of its description is found in Sect. .

The minimization procedure involves iterative calculations of J(x) and its gradient ∇xJ(x), using the CMAQ forward model H and its adjoint HT, as shown in Eq. (): 2∇xJ=B-1x-xb+HTR-1H(x)-y.

The method that our inversion system uses to minimize the J(x) is the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS-B) algorithm , implemented in the “SciPy” Python module. The L-BFGS-B algorithm iteratively adjusts x until J(x) reaches a minimum. We reached a reasonable convergence for each year run after iteration 25. The ratio between the cost function and the number of observations was close to the theoretical expected value (see details in Sect. ). Posterior uncertainties in this study were assumed to be the same as Sect. 2.4; however, we increase their value by a factor of 1.2 to satisfy the theoretical assumption in the variational optimization p.211,.

To avoid the effect of initial conditions (ICs) and boundary conditions (BCs) on our OCO-2 assimilated carbon fluxes, we optimized them within the control vector x. Each lateral boundary (south, east, north, and west) of our regional WRF-CMAQ (Weather Research and Forecasting – Community Multiscale Air Quality) model domain was split into two regions. Lateral BCs in the lower layer of the atmosphere were taken from σ=1 to σ=0.96, corresponding (on average) to a pressure of 972.5 hPa, whereas the upper boundary layer was solved from 972.5 up to 50 hPa. Each lateral BC was solved at a monthly scale. Boundary and initial concentrations were taken from CAMS (Copernicus Atmosphere Monitoring Service) global CO2 atmospheric inversion product data (v19r1) (Frédéric Chevallier, personal communication, 2019). BC uncertainties were assumed to be the standard deviation (1σ uncertainty) in the perimeter of each region of the boundaries, and IC uncertainties were set at 1 % (approximately 4 ppm). A diagram of the WRF-CMAQ domain is illustrated in Fig. .

The CMAQ model was used to simulate atmospheric transport and dispersion. These simulations, which were run offline from the meteorological model, were conducted without atmospheric chemistry. The meteorological data used as input for the CMAQ model were taken from the WRF model, version 4.1.1 . We run the CMAQ model at an hourly resolution at a grid cell scale of 81 km. The model has 32 vertical levels using the terrain-following σ vertical coordinate system. Details of the parameterizations are listed in Sect. 2.4, Table 1. We run WRF at a spatial resolution of 81 km on a single domain (i.e. non-nested). WRF initial conditions were taken from the ERA-Interim global atmospheric reanalysis , which has a resolution of approximately 80 km on 60 vertical levels from the surface up to 0.1 hPa. Sea surface temperatures were obtained from the National Centers for Environmental Prediction/Marine Modeling and Analysis Branch (NCEP/MMAB). The WRF model was run with a spin-up period of 12 h.

The prior flux estimates used in our inversion consisted of four datasets: land–biosphere fluxes, fossil fuel, fires, and ocean fluxes. Biosphere carbon fluxes were simulated by the Community Atmosphere Biosphere Land Exchange (CABLE) model set up in the BIOS3 modelling environment, a fine resolution offline environment built on capability developed for the Australian Water Availability Project (AWAP) (King et al., 2009), hereafter referred to as CABLE BIOS3 . The CABLE land surface model consists of a biophysical core: a biogeochemical module including a nitrogen and phosphorous cycle , the “Populations-Order-Physiology” (POP) module for woody demography and disturbance-mediated landscape heterogeneity , and a module for land use and land management POPLUC;. However, the functionality of POPLUC was not considered in BIOS runs, and the land use change remained static at the year 2000. CABLE can be run at global or regional scales. For our regional study case, CABLE was run at a regional scale (resolution 0.25∘), and it was forced with Australian regional drivers and observations (BIOS3 set-up). Biosphere fluxes from CABLE (roughly net biome productivity – NBP) include gross primary productivity (GPP) and net ecosystem respiration (autotrophic and heterotrophic respiration); however, they do not include carbon losses from fire disturbances, harvest, erosion, and export of carbon in river flow. We used the averages of 3-hourly NBP estimates as input for CMAQ further details of how we constructed NBP can be found in Sect. 2.3 in. The prior error covariance matrix of the terrestrial biosphere flux from CABLE was assumed to be an approximation of the net primary productivity (NPP), following the approach of , with a ceiling of 3 gC m-2 d-1. We assumed that these uncertainties were spatially correlated with length scale of 500 km over land, following . Within our inversion system, no temporal correlations were considered.

Fossil fuel emissions used here were based on two different inventory datasets: the Open-source Data Inventory for Anthropogenic CO2 (ODIAC, version 2019; ) and the Emissions Database for Global Atmospheric Research (EDGAR; ). We added some missing sectors from the EDGAR inventory to ODIAC (such as aviation climbing and descent, aviation cruise, and aviation landing and take-off datasets). ODIAC is a global gridded product distributed at a 0.1∘ × 0.1∘ spatial resolution over land that uses power plant profiles (emission intensity and geographical location) and satellite-observed night-time lights. We used ODIAC monthly fluxes and incorporated a diurnal scale factor to estimate diurnal CO2 emission variability . Given that the ODIAC product only covers the period from 2015 to 2018, we repeated the data from 2018 in 2019 but increased the value in each grid cell by 1.7 %, which represents the mean annual growth rate of these emissions from 1970 to 2018. EDGAR is also gridded at 0.1∘ × 0.1∘ with a monthly temporal resolution. There is no EDGAR gridded product for 2016–2019, so we repeated the 2015 product to cover the other years. We increased EDGAR aviation emissions by 2.5 %, which represents the mean growth rate in this emissions sector from 2016 to 2019. Fossil fuel prior uncertainties were assigned to be 0.44 times the value of the monthly fossil fuel estimates described above see details in Sect. 2.3 in. Errors in fossil fuel emissions were assumed to be uncorrelated.

Ocean flux estimates were selected from CAMS global data (v19r1) (Frédéric Chevallier, personal communication, 2019). Ocean prior uncertainties were assumed to be 0.2 gC m-2 d-1 and uniform across the ocean, as in . Similar to correlations for biosphere prior uncertainties, uncertainties in ocean fluxes were assumed to be correlated in space with a length scale of 1000 km. Fire prior emissions were selected from the Global Fire Emissions Database (GFED, version 4.1s), which includes emissions from small fires. Fire emission uncertainties were assumed to be 20 % of the GFED emissions and correlated in space with a length scale of 500 km, but they were not assumed to be correlated in time. The combination of all prior fluxes was regridded to the spatial resolution of the CMAQ model.

Our regional inversion assimilates satellite observations derived from NASA's Orbiting Carbon Observatory-2 OCO-2;. The OCO-2 satellite instrument carries a single instrument that incorporates three-channel imaging grating spectrometers developed to measure sunlight reflected by the Earth's surface in three spectral bands: two CO2 spectral bands in the short-wave infrared (SWIR) at 1.6 and 2.1 µm respectively and one in the near-infrared (NIR) at 0.76 µm (O2 A-band). From these radiance spectra, it is possible to calculate the column-averaged dry-air mixing ratio of carbon dioxide. The OCO-2 employs three different sampling strategies to collect data: nadir mode, glint mode, and target mode. Nadir observations provide useful information over land because the satellite points straight down at the surface of the Earth (surface solar zenith angle is less than 85∘). In glint mode, the instrument points to the bright glint spot on Earth where solar radiation is directly reflected off the Earth's surface (local solar zenith angle is less than 75∘). In target mode, the instrument points towards a specific location on the ground. Target mode is use for validation, where the performance of the instrument is validated against ground-based observations from the Total Carbon Column Observation Network (TCCON) .

In this study, the regional inversion was performed using a combination of both land (nadir and glint – LNLG) OCO-2 observations (version 9). We used the combination of both datasets, as demonstrated that combining both modes provides a stronger and better constraint on CO2 fluxes at regional scales. Moreover, both datasets present negligible bias . We did not incorporate ocean glint measurements in our inversion, as ocean observations still have undetermined biases that might impact the Australian carbon flux estimates.

OCO-2 LNLG data from December 2014 to December 2019 were selected. We considered OCO-2 data from December 2014, as we ran CMAQ with a spin-up of 1 extra month. As an example, Fig.  in the Appendix shows the spatial pattern of OCO-2 soundings (LNLG) that fall in our CMAQ domain for 2015. In this figure, we can see that OCO-2 data provide a very good coverage of the Australian region. Such spatial coverage offers good potential to help constrain regional biosphere CO2 fluxes.

Given that the OCO-2 spatial resolution (1.29 km × 2.25 km) is higher than the CMAQ model grid cell resolution (81 km × 81 km), the OCO-2 data were averaged to the CMAQ model grid level following the two-step process described in Sect 2.3,: the first step involves averaging all OCO-2 soundings across 1 s intervals, while the second step involves averaging these 1 s averages into the CMAQ vertical column (approximately 11 s averages). The algorithm to estimate the uncertainties across 1 s averages follows . Here, we considered three different forms of uncertainty calculation. First, we assumed that uncertainties that fall within a 1 s span were perfectly correlated in time and space (uncertainties defined as σs). Second, given that the average of OCO-2 uncertainties (σs) is relatively low compared with the real OCO-2 uncertainties (mainly because they only consider the errors from measurement noise and are not systematic errors), we also used the spread (standard deviation) of the OCO-2 retrievals in the 1 s average (uncertainties defined as σr). Third, we also considered a baseline uncertainty (defined as σb) for cases where the number of OCO-2 soundings was not high enough to compute a realistic spread. Our baseline uncertainties were assumed to be 0.8 ppm over land and 0.5 ppm over ocean. Finally, we selected the maximum value between these three uncertainties (σs, σr, and σb). For each grid cell, we also added (in quadrature) 0.5 ppm to this term as the contribution of the CMAQ model uncertainty (defined as σm). We also increased the final observation uncertainty by a factor of 1.2 to satisfy the theoretical assumptions of the inversion . We interpolated the retrieval OCO-2 profile to the CMAQ model vertical profile as described in Sect. 2.6. Note that we only selected bias-corrected data and OCO-2 retrievals with a quality flag of “0”, as described by .

To understand which ecosystems contributed the most to the Australian interannual carbon flux variability between 2015 and 2019, we divided the continent into six bioclimatic classes: tropics, savanna, warm temperate, cool temperate, Mediterranean, and sparsely vegetated (Fig. ). We used the same six bioclimatic regions at a 0.05∘ spatial resolution as in . The classes were regridded over our CMAQ grid (81 km × 81 km) resolution.

In order to analyse the impact of climatic drivers on Australian terrestrial carbon cycle variability, we investigated the anomalies of rainfall and temperature across Australia for the 2015–2019 period. Rainfall data were selected from the Australian Water Availability Project (AWAP), Bureau of Meteorology (BOM) , for the 2015–2019 period. AWAP is a gridded product at a 0.05∘ resolution. It is generated by spline interpolation of in situ rainfall observations. We also used air temperature data at 2 m above the land surface from ERA5, the fifth generation of European Centre for Medium-Range Weather Forecasts (ECMWF) atmospheric reanalyses. The dataset selected from ERA5 was monthly and was gridded at a 0.25∘ spatial resolution. We constructed 3-month running means of rainfall anomalies and air temperature anomalies relative to a mean across 2015–2019. These anomalies were calculated by subtracting their long-term mean (2015–2019) for each month from the raw time series and constructing the 3-month running mean on the resultant time series. We regridded the rainfall anomalies onto the grid of the CMAQ model in order to simplify the comparison with the estimated terrestrial carbon uptake from the flux inversions.

Plant photosynthesis and respiration are two fundamental physiological processes in the carbon cycle. Physiological and structural changes in vegetation modulate the exchange of CO2 between the land and atmosphere. In order to understand what physiological factors drive the interannual variability in our posterior fluxes, we studied the anomalies of the enhanced vegetation index (EVI). The EVI provides information on vegetation state, and we used it to characterize changes in Australian vegetation greenness and activity (e.g photosynthesis) from 2015 to 2019. The EVI product was derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) – which flies on board Terra, a NASA Earth-observing satellite – MOD13C1 Version 6 data product. The MODIS EVI is a gridded product that has a 16 d composite temporal resolution and a 0.05∘ spatial resolution. The EVI ranges from -0.2 to +1, where values less than 0 indicate a lack of green vegetation or arid areas. We calculate the 3-month running mean of EVI anomalies in Australia relative to the long-term mean from 2015 to 2019 and subtract the mean seasonal cycle. These monthly EVI MODIS products were also regridded into the CMAQ domain to calculate the temporal correlation between prior and posterior flux anomalies.

To understand the difference between posterior and prior fluxes, we compared the climatological seasonal cycle of the gross primary productivity (GPP) from the CABLE BIOS3 model against the remote-sensing-based DIFFUSE model and against the latest MODIS Terra GPP product (MOD17A2H Version 6) for the 2015–2019 period. We also calculated the 3-month running mean GPP anomalies for these three datasets.

The DIFFUSE GPP estimates are taken to be the product of the fraction of photosynthetically active radiation (PAR) absorbed by vegetation and the light use efficiency. These datasets have a temporal resolution of 16 d at a 250 m spatial resolution. Similar to the DIFFUSE estimates, the MODIS GPP product is based on a light use efficiency approach and provides a cumulative 8 d composite product gridded at 500 m. For comparison, the CABLE BIOS3, DIFFUSE, and MODIS GPP products were averaged to a monthly resolution and regridded over the CMAQ domain.

We compared our Australian assimilated fluxes against nine independent global atmospheric inversions: AMES, PCTM, CAMS, CMS-Flux, CSU, CT, OU, TM5-4DVAR, and UT (Sect. ). These global inversions are part of the OCO-2 Model Intercomparison Project (OCO-2 MIP) . In this study, we used the OCO-2 MIP flux version found in . In , the global inversions were performed using the assimilation of OCO-2 data (version 9, bias corrected) from 2015 to 2018. A summary of these nine global inversions is given in Table , and a complete description of them and their input fields can be found in Appendix A: model information. We can see from Table  that all global inversions were run using different inverse systems and were configured at different spatial resolutions with different atmospheric transport models and prior fluxes. Some global inversion methods use a four-dimensional variational (4D-Var) approach, whereas others utilize a technique known as ensemble Kalman filter (EnKF) or Bayesian synthesis.

We also compared our assimilated fluxes against the FLUXCOM net ecosystem exchange (NEE) ensemble mean product. The FLUXCOM dataset is created using machine learning approaches, which combine data from FLUXNET eddy covariance towers (site-level observations) with satellite remote sensing, and meteorological data to estimate carbon fluxes, such as NEE, along with their uncertainties . For this study, we downloaded the products at a monthly temporal resolution from the data portal of the Max Planck Institute for Biogeochemistry (https://www.bgc-jena.mpg.de, last access: 6 April 2022).

In our inversion system, the L-BFGS-B algorithm iteratively adjusts the control vector until the cost function reaches an optimal solution. In Bayesian inverse problems, we require that the observational residuals (simulated – observed) and increments (posterior – background) are consistent with the assumed probability density functions (PDFs). This implies that the cost function should be approximately half the number of observations p. 211. Table  shows the analysis of convergence for our 5-year inversion. In this table, we can see that, for each year, the ratio between final cost function J(x) and observation was about 0.5, indicating that our system is self-consistent.

Figure  shows the monthly bias and the root-mean-square error (RMSE) between the prior and posterior column-integrated concentrations simulated by CMAQ against the OCO-2 observations. In this figure, we can see that the inversion generally reduces prior biases significantly to values close to zero. As an indication of the overall inversion performance, the Australian mean prior bias for 2015–2019 was reduced from 0.23 to 0.06 ppm and the RMSE was reduced from 0.90 to 0.76 ppm (Fig. ).

While we see that inversion reduces the prior biases significantly, relatively small positive systematical posterior biases remain (0.05 ppm). These systematic positive posterior biases across Australia are likely driven by sampling and residual retrieval biases in the OCO-2 data. Some studies suggest that the existing OCO-2 cloud-screening algorithm has difficulty identifying clouds near the surface (shallow-layer clouds). Unresolved low-level clouds introduce significant biases in the retrieved column of CO2 concentration.

We note that the data gap in August and September was caused by a satellite outage. In November 2017, we observed that the prior concentration underestimated the observations significantly, with biases of about -0.56 ppm and an RMSE of 1.29 ppm. High prior biases in this month were found along the east coast of Australia, suggesting that the CABLE model might likely be underestimating the carbon outgassing in this area and, therefore, the prior retrieval column CO2 concentration. The reduction of the prior biases in this month was about 90 % (-0.06 ppm with an RMSE of 0.94).

Before assessing the interannual variability in the fluxes derived by the assimilation of OCO-2 observations, we first examine the monthly, seasonal, and annual means between the prior and posterior fluxes. This step is relevant for the subsequent evaluation of how well the posterior column-averaged concentrations simulated by the CMAQ model fit with independent data. Assessing the robustness of our inversion with independent data will allow us to better explain the posterior flux anomalies derived by our inversion.

Figure a shows the long-term mean of the prior and posterior carbon fluxes aggregated across Australia for the 2015–2019 period, and Figs. b and c show the annual and seasonal cycle of these estimates. Posterior flux uncertainties from 2016 to 2019 were assumed to be the same as those calculated for 2015, which were estimated by five different observing system simulation experiments OSSEs; see more details in.

Our 5-year inversion suggests that Australia was a carbon sink of -0.46 ± 0.09 PgC yr-1, compared with the prior flux estimate of 0.11 ± 0.17 PgC yr-1 (Fig. a). Here, the prior flux estimate (fluxes derived by the CABLE model) represents the current knowledge of the Australian carbon budget. Due to the size of the uncertainties in the prior estimate, it cannot be concluded with high confidence whether Australia was a sink or source of CO2 for the 2015–2019 period. The annual posterior fluxes also suggest that Australia's terrestrial biosphere is able to absorb more carbon from the atmosphere than the CABLE model estimate (Fig. b). Moreover, we see that 2016 was the year that contributed most to the long-term mean sink estimated by the OCO-2 inversion.

In terms of a seasonal cycle, we can see that the posterior flux estimates show a stronger seasonality compared with the prior flux estimate (Fig. c). Over the 5 years from 2015 to 2019, we observe that OCO-2 sees a strong seasonal biospheric carbon uptake each year between June and September (winter and early spring in Australia) as well as a stronger carbon source from November to December (late spring and early summer in Australia). As we showed in Fig. , the stronger carbon uptake seen in winter and early spring occurs because the prior column-averaged concentration simulated by CMAQ model overestimates OCO-2 observations during this period.

To identify the Australian regions in which the OCO-2 satellite sees a stronger carbon uptake, we plotted the annual difference between the posterior and the prior fluxes (Fig. ). In Fig. a, we see that the majority of the posterior long-term mean flux for the 2015–2019 period is distributed in one half of the continent (in the north-east, central, and southern regions of the continent). However, we note that this was not the case for the coastal region in these areas, where we observe that OCO-2 recorded a stronger carbon release compared with the prior estimate.

The substantial difference between the prior and posterior flux in 2015 and 2016 comes from the northern and south-eastern regions of Australia (excluding coastal areas in the south-east of the continent). In Sect. , we show that the stronger carbon uptake recorded by the inversion (relative to the prior) in these 2 years was driven by an increase in vegetation productivity due to a rise in rainfall and lower temperatures across these regions. Despite the fact that 2016 was one of the strongest El Niño events on record in the Pacific Ocean, the rain over Australia was above average for most of the continent. The annual climate report from the Bureau of Meteorology for 2016 indicates that the annual rainfall over Australia was 17 % above the 1961–1990 average. In 2017, prior and posterior differences were seen in the northern, central, and eastern coastal areas of Australia. Rainfall in 2017 was below average for much of eastern Australia and along the west coast of Australia. For 2019, OCO-2 recorded a stronger carbon release in western and central Australia. These results are not unexpected, as 2019 was an exceptional year (the hottest and driest year on record in Australia) with a mean temperature that was 1.52 ∘C above the 1961–1990 average . We also noticed a large carbon uptake (relative to prior) in the south-eastern corner of Australia in 2019 (Fig. f).

To further examine what might potentially be the cause of the difference between the posterior and prior fluxes described above, we compared the climatological seasonal cycle (Fig. ) against the climatological seasonal cycle of the gross primary productivity (GPP) fluxes derived from CABLE BIOS3, MODIS, and the DIFFUSE model (Fig. ). We made this comparison by aggregating the fluxes over six bioclimatic regions.

It is evident that the largest difference between prior and posterior flux estimates is over savanna (Fig. b) and sparsely vegetated (Fig. d) ecosystems. Over the savanna region, the most notable difference is seen from June to September. The absolute difference in this period is about 0.4 to 0.5 PgC yr−1. According to MODIS and DIFFUSE GPP estimates, the stronger posterior sink observed in this period may be due to an underestimation of GPP simulated by the CABLE BIOS3 model (Fig. b). The GPP estimated by MODIS from June to September was about 0.90 PgC yr−1 compared with the CABLE BIOS3 estimate of 0.59 PgC yr−1. DIFFUSE GPP estimates were around 0.68 PgC yr−1.

Over the sparsely vegetated region, the seasonal discrepancy between the prior and posterior flux is more evident than for savanna. The seasonality of the posterior flux is stronger (relative to the prior estimate) from April to September. In this ecosystem, the largest absolute difference between the prior and posterior fluxes is seen from June to August (0.5 PgC yr−1). In July, for example, the inversion shifts the prior flux from -0.05 ± 0.09 to -0.56 ± 0.06 PgC yr−1. Again, in Fig. d, we can see that a possible reason of this shift may be associated with an underestimation of the GPP by CABLE BIOS3. It is evident that MODIS and DIFFUSE GPP have a stronger seasonality than CABLE BIOS3 GPP. For example, from June to August, the CABLE BIOS-3 GPP was about 0.4 PgC yr−1 compared with DIFFUSE and MODIS, which were 0.9 and 1.3 PgC yr−1 respectively. We did not find a seasonal correlation between the prior fluxes and MODIS and DIFFUSE GPP fluxes (Table ), but we did find a positive correlation between the posterior fluxes and the GPP estimated by MODIS and DIFFUSE (R=0.44 and R=0.45 respectively).

Regarding the tropical, warm temperate, cool temperate, and Mediterranean ecosystems, the seasonal correlations with the MODIS or DIFFUSE GPP estimates were stronger for the prior than for the posterior fluxes (Table ). A stronger correlation between the prior flux and MODIS and DIFFUSE might be attributable to the fact that the assimilated coastal fluxes might somehow be less constrained by the inversion in these ecosystems, mainly because they are mostly influenced by ocean fluxes where the uncertainties have less freedom to be modified by the inversion.

To evaluate the accuracy of the posterior fluxes discussed in the previous section, we assess the fit between the posterior concentration CO2 field (derived by running the CMAQ model with the fluxes assimilated by OCO-2) and independent CO2 measurements: TCCON (Darwin, Wollongong, and Lauder) and in situ measurements (Gunn Point, Ironbark, Burncluith, and Cape Grim).

Figure a and b illustrate the 3-month running mean of the prior and posterior flux anomalies and the 3-month running means of EVI, rainfall, and air temperature anomalies for the 2015–2019 period aggregated over sparsely vegetated and savanna ecosystems. Figure  shows the spatial distribution pattern of the annual anomalies of the posterior flux estimate for the 2015–2019 period.

It is clear that the anomalous prior and posterior carbon land sink recorded over the sparsely vegetated ecosystem from August 2016 to April 2017 is likely due to the combination of a higher-than-average increase in land productivity (positive EVI anomalies) and rainfall (positive rainfall anomalies) as well as a lower-than-average decrease in air temperature (negative temperature anomalies). It is also evident that the strong carbon release (positive carbon flux anomalies) recorded after April 2017 is due to a lower-than-average greenness of the vegetation (negative EVI anomalies) and rainfall (negative rainfall anomalies) as well as an increase in the air temperature (positive temperature anomalies). In this ecoregion, we found that the temporal correlation between EVI anomalies and carbon flux anomalies is in better agreement with the posterior (R=-0.5) than the prior (R=-0.32) anomalies. The posterior and EVI correlations become even stronger when we see them at each grid point Fig. b (R=0.5–0.9). Spatial averaging smooths grid point anomalies and, thus, dilutes signals. The spatial distribution of correlations between rainfall anomalies (Fig. d), temperature anomalies (Fig. f), and posterior carbon anomalies also improved in some areas in this large ecosystem.

Similar to the findings for sparsely vegetated regions, we also see a higher-than-average increase in land productivity (positive EVI anomalies) and rainfall as well as a decrease in air temperature recorded from August 2016 to April 2017 over the savanna ecosystem. However, unlike the results for sparsely vegetated regions, the carbon sink anomaly only coincides with the negative posterior carbon anomaly in 2016. In 2017, we see that the positive EVI and rainfall as well as the negative anomalies recorded from January to April do not align with the larger-than-average posterior carbon release in this period. We believe that the few OCO-2 soundings found in this period limit the potential of our inversion to constrain the surface fluxes in the savanna ecosystem (see Fig. S2a, b, and c in the Supplement). We found similar results in September and November 2017. As mentioned in Sect. , there was a long data outage of 51 d from August to September 2017. In September, the number of OCO-2 observations in Australia was only 221, and most of the soundings were seen over sparsely vegetated regions (in central Australia) compared with the savanna ecosystem (see Fig. S2h and i in the Supplement). In 2019, we also see that a lower-than-average land productivity, in combination with a rainfall deficit and an increase in temperature, led to a stronger carbon release into the atmosphere. In this category, the temporal correlation between the posterior anomalies and EVI anomalies was moderate (R=-0.38) compared with the prior flux anomalies and EVI anomalies (R=-0.52). We note that the time series temporal correlation between EVI anomalies and posterior anomalies at the grid-cell-scale resolution (Fig. a) is slightly stronger for the prior than the posterior correlations (Fig. b). Similar results were found between the link of the rainfall and posterior flux anomalies, where the correlation tends to degrade compared with the prior. The spatial correlation between temperature anomalies and posterior correlation is more variable, and we see that correlations for the posterior flux anomalies are stronger in the north-west area of the continent.

In general, the better agreement between posterior, climate, and vegetation parameters over regions with sparse vegetation is because the CABLE model likely underestimates GPP anomalies. We found that the correlation between the posterior anomalies and CABLE BIOS3, DIFFUSE, and MODIS GPP anomalies was stronger than that for the prior anomalies. For example, the correlation between the prior and CABLE BIOS3 GPP anomalies was -0.46 compared with the posterior (R=-0.61). Correlations between the posterior anomalies and DIFFUSE and MODIS GPP (-0.5) were also stronger than the prior (R=-0.3) (more details in Table D2). These findings are significant for Australia because they suggest that our OCO-2 inversion might likely be better at capturing the anomalies of this ecosystem (the largest ecosystem in Australia) compared with the biosphere–land model.