We used monthly fluxes of NEE, GPP, and ER produced by the OzFlux regional network of eddy covariance flux towers (https://ozflux.org.au/, last access: 1 April 2023). These data are processed at Level 6 and are freely accessible through the Terrestrial Ecosystem Research Network THREDDS portal (https://dap.tern.org.au/thredds/catalog/ecosystem_process/ozflux/catalog.html; TERN, 2023). All site data used in this study are version “2022_v2”, and in instances where both “site-pi” and “default” versions of the datasets were available, we utilised the “default” datasets. A total of 29 of the 33 freely available sites were selected. The four sites that were excluded showed strong landscape heterogeneity within the flux tower footprint, insufficient temporal duration, or non-representative land cover (e.g. almond farms). A summary of the selected sites and their locations is shown in Fig. A1. The Level 6 OzFlux data used in this study provide two separate estimates of constituent carbon fluxes derived from two methods for partitioning NEE into its component fluxes of GPP and ER. This study uses the “SOLO” data version, which is calculated using a data-driven nocturnal-respiration approach for partitioning, where respiration is modelled using an artificial neural network driven by air temperature, soil temperature, and soil water content (a full description of the SOLO partitioning method is provided within Isaac et al., 2017). We trained ML models with the flux data at a monthly temporal resolution using 2825 monthly observations, equating to 235 site years.

The variables in Table 1 were selected for inclusion in the modelling framework as they were considered to cover most of the expected climate and landscape controls on the terrestrial carbon cycle in Australia. MODIS-derived datasets were temporally resampled to monthly resolution using the mean of all clear observations within a given month and reprojected onto a 1 km × 1 km geographic grid for prediction using averaging resampling techniques. The static variables of land cover fractions and vegetation height were also resampled to 1 km resolution using the average of all pixels within a 1 km grid. The 1 km grid was selected to match the coarsest-native-resolution explanatory variables, namely the climate datasets. The training procedure uses data extracted from the same 1 km gridded data (using the pixel located over the EC tower).

Datasets included for comparative purposes cover the three current categories of methods for estimating the exchange of terrestrial carbon with the atmosphere: process-based models, empirical upscaling of eddy covariance data, and atmospheric inversions. Observation-based GPP products derived from light-use-efficiency methods and solar-induced fluorescence are also included for completeness. Where possible, datasets are processed and plotted in their native resolutions to avoid introducing errors from spatially resampling finer-resolution datasets to very coarse resolutions (or vice versa). The exceptions to this are the higher-resolution MODIS-GPP and DIFFUSE-GPP products (described below), which were resampled to 1 km resolutions to match the resolutions of our ML upscaling product. A summary table of all the comparison datasets is available in the Appendix (Table A1).

We compared our results with two runs of the CABLE model. The first was a regional, fine-resolution (0.25∘) offline run forced by Australian regional climate drivers that follows the protocol from Haverd et al. (2018), but with land use remaining static in the year 2000 (hereafter referred to as CABLE-BIOS3). CABLE-BIOS3 net biosphere production (NBP) includes GPP and autotrophic and heterotrophic respiration but does not include fire disturbances, harvest, erosion, or export of carbon through rivers (a fuller description of the set-up is outlined in Villalobos et al., 2022). A second CABLE run was extracted from the TRENDY v10 ensemble (Friedlingstein et al., 2022), hereafter referred to as CABLE-POP. This dataset has a spatial resolution of 1∘, it is forced by global climate data, and NBP includes additional fluxes from fire emissions and land use change.

Our regional ML upscaling product is compared with the well-known global ML upscaling product, FLUXCOM (Jung et al., 2020; Tramontana et al., 2016). FLUXCOM is built using similar machine learning methods to those used in this study, though trained on the global FLUXNET2015 dataset. Two products are available: FLUXCOM-RS was trained exclusively on MODIS remote sensing data, and FLUXCOM-RS+METEO (FLUXCOM-Met hereafter) was trained on climate reanalysis data and climatological remote sensing data (Jung et al., 2020). For FLUXCOM-Met, we use the multi-model mean of the ERA5-based product. Both RS-METEO and RS products are assessed here and were downloaded at monthly temporal resolution from the Max Planck Institute for Biogeochemistry (https://www.bgc-jena.mpg.de/geodb/projects/Home.php, last access: 13 January 2023).

A regional inverse modelling product, produced by Villalobos et al. (2022), was included for comparison as it provides a wholly independent measure of NEE. This regional inversion estimates carbon fluxes over the Australian continent from 2015–2019 by assimilation of carbon dioxide measurements from the Orbiting Carbon Observatory-2 (OCO-2) satellite. The product is provided at ∼ 81 km spatial resolution and monthly temporal resolution (available for download from 10.5281/zenodo.6649768). NEE in this dataset includes fire emissions and fossil fuel emissions, so to facilitate better comparisons fossil fuel emissions were subtracted from the NEE time series. A second regional satellite-assimilated atmospheric inversion from Metz et al. (2023) is also included. This time series represents the spatially averaged net flux of CO2 over the Australian TRANSCOM region (which includes New Zealand). Therefore, the time series is only shown where Australia-wide, spatially averaged time series are plotted, and some differences between time series may be attributable to the inclusion of the New Zealand land mass in the estimate.

We compare our GPP estimates with a suite of observation-based GPP products: the MODIS Terra GPP product (MOD17A2H), based on a per-biome light-use-efficiency approach (Running et al., 2015); the GOSIF GPP product, generated through a data-driven approach based on OCO-2 solar-induced fluorescence (SIF) soundings, MODIS remote sensing data, and meteorological reanalysis data (Li and Xiao, 2019); and DIFFUSE GPP, which is based on total and diffuse irradiance and the fraction of shortwave irradiance absorbed by foliage (Donohue et al., 2014). All datasets are averaged to monthly temporal resolution, and MODIS-GPP and DIFFUSE-GPP are spatially resampled to 1 km grid cells by averaging the pixels within each 1 km pixel grid.

Fire emissions were added to our estimates of NEE from the Global Fire Assimilation System version 12 (GFASv12) (Kaiser et al., 2012). Daily fire emissions are temporally resampled to monthly totals by summing daily values.

Bioclimatic regions used for separating fluxes into specific ecosystems were identical to those defined in Haverd et al. (2013) and include six bioclimatic classes: tropics, savanna, warm–temperate, cool–temperate, Mediterranean, and desert (Fig. 10a).

The most common ML models implemented in the literature on empirical upscaling of EC data are random forest regression, support vector regression, model tree ensembles, piecewise regression models, and artificial neural networks (Verrelst et al., 2015). Random forest (RF) regression has proven itself to be the go-to model for many remote-sensing-based studies owing to its high accuracy, robustness to overfitting, scalability, and easy-to-configure hyperparameters (Belgiu and Drăguţ, 2016). In recent years, gradient-boosting decision tree (GBDT) learning algorithms have also proven to be highly accurate and robust to overfitting (Chen and Guestrin, 2016; Wei et al., 2019). Here, rather than rely on any one ML method, we rely on both RF and GBDT methods to develop an ensemble of predictions.

Beyond the ML algorithm used, there are numerous other sources of uncertainty associated with the empirical upscaling of EC flux tower data. Epistemic uncertainties arise from the limitations of the training data (e.g. biases in the locations sampled) and uncertainties in the features used for training as well as the hyperparameters used during model optimisation. In addition to these reducible (or at least quantifiable) epistemic uncertainties, aleatoric uncertainties arise from the uncertainties in the eddy covariance measurements themselves (Isaac et al., 2017), along with the non-deterministic dependencies between variables (Hüllermeier and Waegeman, 2021). Here we attempt to account for a portion of the empirical uncertainty by iterating the training data and the models used for fitting. During model fitting, two randomly selected EC sites are removed from the training data, and both a GBDT model (from the Python package LightGBM; Ke et al., 2017) and a RF model are fit on the remaining data (hyperparameter optimisation is conducted on every fit using a random grid search technique with 250 iterations; Table A2). We selected two sites to remove per iteration as we felt it balanced the need to significantly alter the training dataset per iteration while not overly degrading the quality of the model by removing too much data. This procedure is repeated 15 times to increase the likelihood of every site being removed from the training dataset, resulting in 30 unique models. These 30 models are used to generate 30 gridded estimates for each of the variables modelled (GPP, ER, and NEE). In the results that follow, we report the interquartile range of these 30 predictions as our envelope of uncertainty and the “best estimate” as the median of the ensemble predictions.

The overall modelling framework is summarised in Fig. 1. Each flux is independently modelled, and therefore there is no inherent exact mass balance between GPP-ER and NEE. The same predictor variables were used for modelling each flux, so the resulting products originate from a consistent set of drivers. All processing and modelling steps described in the Methods section have been thoroughly documented within a series of Jupyter notebooks, available with the assets of this paper.

The accuracy of each ML model in the ensemble was assessed using a nested, time-series-split cross-validation approach (Fig. 2). This approach ensured minimal data leakage between training and testing sets while still allowing the algorithm to “see” all the sites during training, a desirable feature in the cross-validation technique due to the relatively limited number of sites (n=29), with some ecosystems sampled by only one or two flux towers (e.g. alpine regions, cereal cropping). Five outer cross-validation splits are performed, with each split containing 20 % of test data from every site (as a discrete length of time equal to 20 % of the total length of the dataset; i.e., if a site contained 10 years of data, then testing was conducted on five iterations of 2-year continuous periods), while the remaining 80 % of the data are used for training. Five “inner” cross-validation splits were conducted to optimise the hyperparameter selection for the outer loop. Using a nested approach to cross-validation prevents use of the same data to tune model parameters to those the model is tested on, and thus prevents creation of overly optimistic cross-validation scores (Cawley and Talbot, 2010). Across the five outer cross-validation splits, all samples in the dataset were tested. Mean absolute error (MAE) and the coefficient of determination (R2) are reported to assess the accuracy of the fit for each of the variables modelled. The cross-validation scores reported in the results section summarise the train–test splits of all 30 model fits. Throughout the remainder we use the terms “observed” and “predicted” to refer to in situ measurements from EC towers and the predictions, respectively. We also use the convention of negative NEE values referring to net carbon uptake by the land surface.

In addition to evaluating the overall predictive capacity using temporal cross-validation, we also perform an intercomparison between the results of this study and similar products covering Australia. This is performed through scatterplots of modelled vs. observed fluxes for several products (statistics for comparison are MAE and r2, the square of Pearson's correlation), through comparison of the mean seasonal cycles disaggregated by bioclimatic region, and through the assessment of annual anomalies. It is important to note that NEE calculated through empirical upscaling of EC flux tower data is conceptually distinct from inversion-based NEE and process-model NBP. The addition of fire emissions to our estimates of NEE narrows the conceptual distance between the estimates, and where a conceptual difference still applies, we contend that fluxes from other sources are unlikely to be large enough to warrant the additional complexity of their inclusion.

We adopted the model ensemble median as our best estimate and the interquartile range (IQR) of estimates as a measure of uncertainty. During 2003 to 2022, Australia's terrestrial ecosystems were a strong net carbon sink on an annual mean basis of -0.44 PgC yr-1 (IQR = 0.42 PgC yr-1) (Fig. 7c) (including fire emissions). IAV defined as 1 standard deviation of the annual mean time series is 0.18 PgC yr-1, and the average seasonal range of NEE is 0.85 PgC yr-1. The annual mean estimates of NEE from this study show a greater terrestrial carbon uptake than any of the LSMs or FLUXCOM products, while the regional atmospheric inversion (which also includes fire emissions) predicts a very similar annual mean carbon uptake of -0.47 PgC yr-1 (Fig. 9c; though this is assessed over a much shorter period than the other products). IAV of NEE for the other products ranges from 0.06 PgC yr-1 for FLUXCOM-Met to 0.26 PgC yr-1 for the OCO-2 inversion (Fig. 9f). The GOSAT inversion conducted by Metz et al. (2023) estimated an IAV of 0.207 PgC yr-1 across the Australia TRANSCOM region. CABLE-BIOS3 also shows a comparatively high IAV of 0.23 PgC yr-1 (Fig. 9f). The per-pixel plots of Fig. 8g–i show how annual NEE fluxes are spatially allocated. The strongest carbon sinks are seen along the forested coastal regions of the eastern seaboard from western Tasmania to northern New South Wales; the south-western corner of Western Australia, including the southern part of the Great Western Woodlands; and the tropical part of the Northern Territory. The regions of strongest IAV in NEE are in the savanna regions of northern Australia; the intensive agricultural regions of the MDB; and the Channel Country of south-west Queensland and into South Australia where episodic river basins such as Cooper Creek periodically fill during anomalously large rainfall events (Fig. 8h). The climatological month-of-maximum-NEE plot in Fig. 8i shows the month during which NEE typically achieves its most negative value (greatest carbon uptake), and the plot shows clear delineations along bioclimatic regions.

Annual mean GPP across Australia averaged 4.25 (0.91) PgC yr-1, with an IAV of 0.50 PgC yr-1 and an average seasonal range of 1.47 PgC yr-1 (Fig. 7a). Averaged over Australia, our estimate of GPP closely approximates that of GOSIF and MODIS, with the uncertainty envelope encompassing these two products. In contrast, DIFFUSE, FLUXCOM, and CABLE-POP report lower estimates (Fig. 9a). The IAV between products varies substantially, with both FLUXCOM products showing the lowest IAV in GPP (FLUXCOM-Met: 0.13 PgC yr-1; FLUXCOM-RS: 0.23 PgC yr-1), while this study and CABLE-BIOS3 (0.78 PgC yr-1) display the strongest IAV.

ER averaged 3.64 (1.01) PgC yr-1 (Fig. 7b), with an IAV of 0.34 PgC yr-1 and an average seasonal range of 1.56 PgC yr-1, notably higher than GPP. Agreement between products is generally poor, though the long-term mean of FLUXCOM-Met and this study agree (Fig. 9b). CABLE-BIOS3 shows the most IAV in ER (0.56 PgC yr-1), while the two FLUXCOM products record very low IAV, with FLUXCOM-RS equal to 0.07 PgC yr-1 and FLUXCOM-Met equal to 0.09 PgC yr-1.

Figure 10e–g show the climatological seasonal cycles of the component terrestrial fluxes summed across Australia (climatologies were calculated starting in 2003 and extending over the full remaining length of the time series for each product). The seasonal cycle of this study's NEE differs substantially from those of the LSMs and FLUXCOM-Met (Fig. 10g). According to our results, a climatological peak in terrestrial carbon uptake occurs for Australia during the cooler, drier months of March–September. Examination of the equivalent plots for GPP (Fig. 10e) and ER (Fig. 10f) shows that concomitant increases in ER during periods of peak GPP mean that the time of greatest primary production across Australia (December–March) is not coincident with peak carbon uptake. This result contrasts with the findings of the LSMs and FLUXCOM-Met, which show peak carbon coinciding with peak GPP in austral summer (Fig. 10g). Despite displaying a greater amplitude of seasonal variability, the NEE seasonal cycle of the regional OCO-2 inversion largely matches our estimate. The GOSAT inversion also displays similarities with this study and the OCO-2 inversion. However, the GOSAT inversion shows a second peak in July; it is unclear from the dataset provided if this might be due to the inclusion of New Zealand in the analysis area.

Breaking the fluxes down into bioclimatic zones (Fig. 10a–d), we can observe two processes that predominately dictate the typical seasonal pattern of NEE in Australia. Firstly, seasonal variations in ER in the desert region (peak-to-peak amplitude = 0.66 PgC yr-1) exceed GPP variations (amplitude = 0.46 PgC yr-1). Beginning in March and extending through the autumn and winter period, ER declines more rapidly than GPP, resulting in enhanced carbon uptake during this period. Secondly, in the savanna region we observe a sharp response in ER following the end-of-dry-season rainfall events that exceed the response from GPP, resulting in a net carbon pulse to the atmosphere in the October–December period (fluxes from these regions are re-plotted in Fig. A5a to enhance interpretability). The interaction between these two processes likely explains most of the seasonal variation in Australia's terrestrial carbon cycle and is responsible for peak carbon uptake in Australia occurring in the autumn–winter months, while the carbon sink tends to be weakest during the October–December period.

We found that the largest discrepancies between products also occurs in the desert region (Fig. 10a). The LSMs, FLUXCOM-Met, GOSIF, and this study all report GPP peaking in February–March, with the nadir of GPP occurring during the May–September period (Fig. 9b). On the other hand, MODIS-GPP and FLUXCOM-RS show an inverted climatology with respect to the other products, which are unlikely to be accurate given the monsoonal climate drivers in the region, with >70 % of the typical annual median rainfall falling between November and April (Bowman et al., 2010). The CABLE-POP model appeared to significantly underestimate both GPP and ER in desert regions (Fig. 10b–c). This may explain why the Australia-wide seasonal NEE curve from CABLE-POP (Fig. 10g) does not align with the results of this study despite a similar spatial pattern in the month-of-maximum-NEE flux plot (Fig. A4). The desert and savanna regions typically contribute the most to annual fluxes in other products, but CABLE-POP's NEE fluxes are comparatively more influenced by the savanna and tropical regions. This is most likely due to CABLE-POP's representation of vegetation cover fractions over inland Australia, which shows the desert region as entirely bare (Teckentrup et al., 2021). FLUXCOM-RS follows a similar trajectory in the Australia-wide NEE to that of our estimate, though with considerably lower seasonal amplitude (Fig. 10g). Examining the bioclimatic zones, we see that this is mainly due to an incorrect GPP seasonal cycle in the desert region, combined with a very low amplitude in the seasonal cycle of ER in the desert (Fig. 10c). The seasonal cycle of FLUXCOM-Met is markedly different from FLUXCOM-RS. The per-biome fluxes from FLUXCOM-Met appear more realistic than those of FLUXCOM-RS but produce an inverted Australia-wide NEE seasonal cycle with respect to our estimate (Fig. 10g). This is due to greater amplitude declines in seasonal GPP compared with ER, especially in the warm–temperate and cool–temperate regions.