The LoFI flux collection consists of the following six components. Net ecosystem exchange (NEE).

The Carnegie-Ames-Stanford Approach (Randerson et al., 1996) – Global Fire Emissions Dataset version 3 (CASA-GFED 3; van der Werf et al., 2003, 2010) uses satellite-based observations of vegetation and land-cover along with meteorology from MERRA-2 to constrain carbon stocks and fluxes. Notably, net primary productivity (NPP) is determined from Advanced Very-High-Resolution Radiometer (AVHRR) observations of normalized difference vegetation index (NDVI; Pinzon and Tucker, 2014), and biomass burning is determined from observations from Moderate Resolution Imaging Spectrometer (MODIS) burned area estimates (Giglio et al., 2010). This version is available on a 0.5∘ grid with a monthly time step. More details about our implementation and its use in GEOS are available in Ott et al. (2015).

The above separation into component fluxes assumes that, added together, biomass burning and biofuel emissions account for emissions from both naturally occurring wildfires and anthropogenic burning due to gross land-use/land-cover change. Furthermore, emissions from ethanol, biodiesel, and other short-cycle fuels used for transportation are potentially underestimated since they are not included in the ODIAC fossil fuel and CASA-GFED 3 biofuel emissions, yet the removal of carbon due to the corn and soybean harvest in the Midwestern United States is included in CASA-GFED 3 (derived from USDA National Agricultural Statistics Service data for 2005). Excluding the lateral transport of significant amounts of carbon over continental scales, we do not expect these assumptions to have a noticeable effect on the comparisons to follow since they consider only NBE, the sum of all land fluxes except fossil fuel emissions, and not the individual components.

Many of the products used in the above fluxes are unavailable until a few months to years following the end of a given year. In particular, fossil fuel inventories and the NOAA MBL growth rate require data collection and analysis that must necessarily trail real time. Simulations during the current and future years are thus only possible with some type of extrapolation and/or statistical model applied to past values. For all flux components except biomass burning and the empirical sink, we produce estimates during NRT years by first extrapolating a linear fit through the retrospective values for each point and each month. This choice allows different regions and different seasons to have different trend lines. While more complex choices are possible, this is meant as a simple first step as we work to reduce the latency of our baseline satellite-derived flux products.

The primary motivation for using QFED biomass burning instead of GFED was QFED's ability to produce NRT estimates. This ability is particularly important for biomass burning emissions whose interannual variability is comparable in magnitude to its annual mean and seasonal cycle amplitude and is much greater than its long-term trend. While the removal of terrestrial carbon by QFED fires does not match the corresponding fire loss in CASA carbon stocks, QFED emissions are calibrated to GFED (Darmenov and da Silva, 2015), resulting in a difference that is minor compared to that of the empirical sink (see Sect. ).

For the empirical sink, we switch from using an atmospheric growth rate derived from in situ data in retrospective years to a linear functional fit to seasonal SST anomalies and anthropogenic emissions (Jones and Cox, 2005; Betts et al., 2016). This approach estimates the growth rate of CO2 in ppm, ΔCO2, as 2ΔCO2=0.069+0.442N+0.205E, where N is the average of SST anomalies in the Niño 3.4 region (5∘ N to 5∘ S, 170 to 120∘ W) from October of the previous year to September of the current year in units of degrees Kelvin, and E is the global total anthropogenic emissions from fossil fuels and net land-use/land-cover change in units of Pg C. For the SST anomalies, we use the Reynolds analysis (Reynolds et al., 2007) until the last month it is available and fill in the remaining months with SST forecasts from the GEOS Subseasonal to Seasonal (S2S) forecast system (Molod et al., 2020), and for the anthropogenic emissions we use extrapolated totals from the Global Carbon Project (GCP) 2018 budget.

The coefficient 0.205 multiplying the anthropogenic term in the growth rate forecast (Eq. ) represents a constant airborne fraction of 0.44 when converted using a factor of 2.124 Pg ppm-1, roughly in line with the findings of Raupach et al. (2014). Historical data records tend to show that the long-term trend in the airborne fraction is insignificant compared to its interannual variability (Knorr, 2009; Ballantyne et al., 2012), but there is some indication of significant multi-decadal trends, including the possibility of a recent decrease (Keenan et al., 2016).

Over the past few decades, global pCO2sw has increased by roughly 1.5 µatm yr-1, yet with considerable regional differences (Takahashi et al., 2009). At the same time, pCO2atm has increased at an even greater pace, driving an increasing ocean sink. Deviations from these trends are predominantly limited to the tropical Pacific, where the El Niño–Southern Oscillation (ENSO) is the dominant driver of interannual variability (Rödenbeck et al., 2015), and the Southern Ocean, where the net ocean sink switched from increasing to decreasing in the early 1990s and switched back in the early 2000s (Landschützer et al., 2015).

By imposing observed trends in pCO2sw and pCO2atm, our ocean exchange fluxes produce a sink that is generally consistent with the inversion ensemble and GCP 2018 ocean biogeochemical model ensemble (Figs.  and ), again with the provision that the biogeochemical model ensemble does not include outgassing due to riverine input. Averaged over 2000–2010, our mean ocean sink is 1.55 Pg C. This is consistent with annual budgets based on atmospheric measurements of a combination of O2 and CO2 called atmospheric potential oxygen (APO; Stephens et al., 1998): Keeling and Manning (2014) estimate an ocean sink of 2.50±0.60 Pg C for 2000–2010, which reduces to 1.72±0.60 Pg C after removing 0.78 Pg C to account for riverine input (see discussion above). The pCO2sw-based products of Landschützer et al. (2014) and Rödenbeck et al. (2014), which do not require a riverine adjustment, produce sinks of 1.37 and 1.74 Pg C (averages from GCP 2018; Le Quéré et al., 2018), also in line with our budgets (several more comparable estimates are available in Jacobson et al., 2007). Even during the strong ENSO of 2015–2016, the constant growth in pCO2sw that we impose produces a global sink within the ranges of the top-down and bottom-up ensembles (Fig. ). While linear growth is not appropriate for simulations of several decades, over which pCO2sw increases exponentially (Raupach et al., 2014), it is sufficient for our 15-year study period and something we hope to address in future developments.

In comparison to the flux inversion ensemble and the TRENDY version 7, simulation 3 (Sitch et al., 2015) ensemble of dynamical global vegetation models (DGVMs), the baseline fluxes consistently underestimate NBE – the sum of NEE, biofuels, and biomass burning – by over 3 Pg C (see Fig. a and Table ). This is due to the assumption of a neutral biosphere in CASA-GFED, which thus has no long-term net sink, and is the primary motivation for the derivation of the empirical land sink. In the Northern Hemisphere, the neutral biosphere assumption causes CASA to systematically underpredict seasonal cycle amplitudes in comparison to measurements from flux towers (Carvalhais et al., 2008) and a combination of aircraft- and ground-based remote-sensing retrievals (Yang et al., 2007). This effect is seen in the diagnostic fluxes as an underprediction of the global sink strength in March through July (Fig. ) limited primarily to the northern extratropics (Fig. , first column). In contrast, including the empirical sink in the LoFI fluxes moves its annual totals and seasonal cycle significantly closer to the ranges of the comparison ensembles. Since the empirical sink increases the seasonal cycle and its magnitude increases as net terrestrial uptake grows, it produces a seasonal cycle amplitude that increases in time, consistent with observations in high northern latitudes (Graven et al., 2013) and their attribution to increased extratropical terrestrial uptake (Barnes et al., 2016).

Increasingly, modern flux inversions tend to predict a persistent, net sink in the northern extratropics (NE), with the tropics and southern extratropics (T+SE) in near balance with considerably more interannual variability than the NE (Ciais et al., 2019; Gaubert et al., 2019). Stephens et al. (2007) first showed that inversions with neutral T+SE fluxes compared better to profiles of in situ aircraft data than inversions with a significant T+SE source. Inversions from the Regional Carbon Cycle Assessment and Processes (RECCAP; Canadell et al., 2011) intercomparison also showed a clear separation between neutral and source T+SE budgets, with the difference being due to the decision to average observational data over month-long intervals (Peylin et al., 2013). For the RECCAP inversions that used data varying within the month, Peylin et al. (2013) found a sink over 2001–2004 of 1.85±0.25 Pg C in the NE and -0.34±0.27 Pg C in the T+SE. The agreement has become even stronger across more modern inversion systems, with those covering 2004–2014 finding a NE sink of 2.17±0.36 and 0.06±0.11 Pg C in the T+SE (Gaubert et al., 2019). Over this same time period, the LoFI fluxes have a NE sink of 2.50 Pg C and a T+SE sink of -0.41 Pg C, suggesting possibly a slight overestimation of the T+SE source, yet still within a reasonable range of uncertainty (see Table  for comparable ranges from the TRENDY and inversion ensembles).

The net terrestrial sink found by inversions has been shown to be consistent with growth in temperate and boreal terrestrial ecosystems driven primarily by carbon fertilization and forest regrowth (Schimel et al., 2015; Fernández-Martinez et al., 2019) with the possibility of an additional contribution from agriculture (Zeng et al., 2014). Notably, the forest inventory analysis of Pan et al. (2011) estimated a 2000–2007 sink of 1.28±0.17 Pg C in boreal and temperate forests (mostly in the NE) and -0.08±1.17 Pg C in tropical forests. Further evidence for a persistent NE sink and a weak sink or source in the T+SE can be found in estimates of aboveground biomass change derived from vegetation optical depth (VOD; Liu et al., 2015), a product of remotely sensed microwave radiation, and DGVM simulations constrained with forest demography data (Pugh et al., 2019), the global forest age dataset (GFAD; Poulter et al., 2018). Pugh et al. (2019) find a significant sink in the Eastern United States, which is produced by our empirical sink as well (Fig. , third row, third column). These studies do differ with Pan et al. (2011) in important ways, including the attribution of a greater percentage of the net tropical sink to gains in shrublands and savannas than to forest regrowth (Liu et al., 2015) and estimating a significantly smaller tropical regrowth sink (Pugh et al., 2019).

Taken together, the findings described above suggest an empirical sink proportional to the CO2 growth rate (e.g., driven by carbon fertilization) and monthly temperature increase (e.g., focused to the extratropical growing season). The choice of the last remaining factor in Eq. (), heterotrophic respiration (HR) over, for example, net primary production (NPP), requires further investigation. We chose HR rather than NPP for several reasons: (1) boreal forests allocate a much greater percentage of biomass below ground than tropical forests do (Pan et al., 2011); (2) the NDVI driver data of CASA tend to put a strong, observationally driven constraint on NPP; and (3) the uncertainty in the HR response to temperature changes through its so-called Q10 function (Lloyd and Taylor, 1994; Tjoelker et al., 2001; Huntzinger et al., 2020). In any case, the temperature increase factor of the empirical sink makes it relatively insensitive to the choice of the flux factor (e.g., HR, NPP, or ecosystem respiration).

Even after adding the empirical sink, the LoFI fluxes have some discrepancies with the comparison ensembles worth noting. In particular, the LoFI fluxes predict a sink from 0 to 15∘ S during JJA, while the comparison ensembles predict neutral fluxes (Fig. , first column, fourth row, difference between blue line and grey shading). The opposite difference, although less noticeable, is present during DJF (Fig. , first column, second row). It is unclear, however, how accurate either ensemble is in this case: the inversions are hindered by the limitation of in situ data and uncertainties in transport over this latitude band, while the biospheric models are potentially hindered by inaccuracies in meteorological driver data and deficiencies in the representation of disturbance (Molina et al., 2015; van der Laan-Luijkx et al., 2015). This approach may overestimate the net sink over the Midwestern United States, where our version of CASA-GFED 3 already includes a corn and soybean harvest (other harvests are not currently represented). Understanding the interaction of these two adjustments is the subject of ongoing work.

Ultimately, a major goal of this effort is to develop a realistic collection of fluxes that improves the ability of transport simulations to reproduce measurements and support retrospective and NRT studies. As a test of this skill, we transport the LoFI fluxes through the atmosphere with the GEOS GCM and compare the results to in situ measurements from NOAA MBL sites available in NOAA ObsPack GlobalView+ v4.2.2 (Masarie et al., 2014; Cooperative Global Atmospheric Data Integration Project, 2019). We do the same with NOAA's CarbonTracker 2016 (CT2016; Peters et al., 2007, with updates documented at http://carbontracker.noaa.gov, last access: 10 November 2016) fluxes for all components, which functions as a benchmark of the ability of the GEOS GCM to reproduce NOAA MBL measurements when using fluxes from a modern inversion system.

All transport simulations are run using the Heracles 4.0 GEOS GCM version on a 0.5∘×0.625∘ regular latitude–longitude grid with 72 vertical levels, a time step of 15 min, and output instantaneous fields every 3 h. The run uses the GEOS replay approach to reproduce the effect of the meteorological data assimilation system without having to rerun it (see Orbe et al., 2017, for the most up to date description). In this configuration, the large-scale circulation, temperature, and moisture are constrained by analysis fields every 6 h, while physical processes such as convection, turbulence, and radiative transfer are recalculated at a high temporal resolution. This computationally efficient framework provides the ability to simulate realistic meteorology with a tight coupling between fine-scale atmospheric transport processes and trace gas emissions. For the analyzed meteorology, we use MERRA-2, resulting in a transport simulation sharing many of the properties of that used by Ott et al. (2015).

The evaluation of the two model runs (one with LoFI fluxes, the other with CT2016 fluxes) against the NOAA MBL surface sites is shown in Fig. . Neither of the runs is clearly superior. This suggests that, at least in terms of aggregate statistics over multiple years, the empirical sink produces a correction to the baseline, diagnostic fluxes with a similar skill as running a formal inversion system based on MBL data. While our approach may degrade the skill of CT2016 by using a different transport model, it may also improve it by running at a higher resolution, and our calculated differences are consistent with those in the evaluation in the CT2016 documentation. At this level of agreement with the surface sites, it is difficult to say if errors from atmospheric transport or any single component of the LoFI fluxes dominate all other sources of error. Further refinement of any single component then runs the risk of confusing errors in one component with those from another.

At the start of 2016, the LoFI fluxes switch from retrospective mode to NRT. While it would be possible to extend retrospective mode to 2018 at the time of writing, we pick 2016 as an interesting test case where we must forecast a growth rate during a strong El Niño. In practice, NRT runs are limited to 2 years since the flux products in the LoFI collection have at most a 2-year latency. For 2016 and 2017, Eq. () predicts growth rates of 2.93 and 2.63 ppm, while the current NOAA MBL reference values are 2.85±0.09 and 2.15±0.09 ppm. These small differences do not appear to significantly impact the ability of NRT LoFI model runs to reproduce in situ measurements at Mauna Loa (Fig. ) – while there is a notable error near the start of 2016, it is comparable in size to errors during the 2010–2011 El Niño, and all errors after 2016 stay below 1 ppm in magnitude. This suggests that misrepresentations of the spatial and temporal variability of El Niño may have a greater impact on our ability to represent the Mauna Loa data record than errors in the growth rate forecast.

A major factor in the ability of NRT LoFI to reproduce atmospheric CO2 observations is that, even in forecasting mode, it continues to use the retrospective meteorological analysis from MERRA-2. If we were to use meteorological forecasts instead, we would expect the skill to degrade within a few months and last about 2 years or less (Ilyina et al., 2020).