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Measurements of atmospheric CO2 concentration provide a tight constraint on the sum of the land and ocean sinks. This constraint has been combined with estimates of ocean carbon flux and riverine transport of carbon from land to oceans to isolate the land sink. Uncertainties in the ocean and river fluxes therefore translate into uncertainties in the land sink. Here, we introduce a heat-based constraint on the latitudinal distribution of ocean and river carbon fluxes, and reassess the partition between ocean, river and land in the tropics, and in the southern and northern extra-tropics. We show that the ocean overturning circulation and biological pump tightly link the ocean transports of heat and carbon between hemispheres. Using this coupling between heat and carbon, we derive ocean and river carbon fluxes compatible with observational constraints on heat transport. This heat-based constraint requires a 20–100% stronger ocean and river carbon transport from the Northern Hemisphere to the Southern Hemisphere than existing estimates, and supports an upward revision of the global riverine carbon flux from 0.45 to 0.78 PgC yr−1. These systematic biases in existing ocean/river carbon fluxes redistribute up to 40% of the carbon sink between northern, tropical and southern land ecosystems. As a consequence, the magnitude of both the southern land source and the northern land sink may have to be substantially reduced.

Interannual anomalies in the sea-air carbon dioxide (CO2 ) exchange have been estimated from surface-ocean CO2 partial pressure measurements. Available data are sufficient to constrain these anomalies in large parts of the tropical and North Pacific and in the North Atlantic, in some areas covering the period from the mid 1980s to 2011. Global interannual variability is estimated as about 0.31 Pg C yr-1 (temporal standard deviation 1993-2008). The tropical Pacific accounts for a large fraction of this global variability, closely tied to El Niño-Southern Oscillation (ENSO). Anomalies occur more than 6 months later in the east than in the west. The estimated amplitude and ENSO response are roughly consistent with independent information from atmospheric oxygen data. This both supports the variability estimated from surface-ocean carbon data and demonstrates the potential of the atmospheric oxygen signal to constrain ocean biogeochemical processes. The ocean variability estimated from surface-ocean carbon data can be used to improve land CO2 flux estimates from atmospheric inversions.

Interannual variations in the large-scale net ecosystem exchange (NEE) of CO₂ between the terrestrial biosphere and the atmosphere were estimated for 1957–2017 from sustained measurements of atmospheric CO₂ mixing ratios. As the observations are sparse in the early decades, available records were combined into a 'quasi-homogeneous' dataset based on similarity in their signals, to minimize spurious variations from beginning or ending data records. During El Niño events, CO₂ is anomalously released from the tropical band, and a few months later also in the northern extratropical band. This behaviour can approximately be represented by a linear relationship of the NEE anomalies and local air temperature anomalies, with sensitivity coefficients depending on geographical location and season. The apparent climate sensitivity of global total NEE against variations in pan-tropically averaged annual air temperature slowly changed over time during the 1957–2017 period, first increasing (though less strongly than in previous studies) but then decreasing again. However, only part of this change can be attributed to actual changes in local physiological or ecosystem processes, the rest probably arising from shifts in the geographical area of dominating temperature variations. This article is part of a discussion meeting issue 'The impact of the 2015/2016 El Niño on the terrestrial tropical carbon cycle: patterns, mechanisms and implications'.

Using measurements of the surface-ocean CO2 partial pressure (pCO2) and 14 different pCO2 mapping methods recently collated by the Surface Ocean pCO2 Mapping intercomparison (SOCOM) initiative, variations in regional and global sea–air CO2 fluxes are investigated. Though the available mapping methods use widely different approaches, we find relatively consistent estimates of regional pCO2 seasonality, in line with previous estimates. In terms of interannual variability (IAV), all mapping methods estimate the largest variations to occur in the eastern equatorial Pacific. Despite considerable spread in the detailed variations, mapping methods that fit the data more closely also tend to agree more closely with each other in regional averages. Encouragingly, this includes mapping methods belonging to complementary types – taking variability either directly from the pCO2 data or indirectly from driver data via regression. From a weighted ensemble average, we find an IAV amplitude of the global sea–air CO2 flux of 0.31 PgC yr-1 (standard deviation over 1992–2009), which is larger than simulated by biogeochemical process models. From a decadal perspective, the global ocean CO2 uptake is estimated to have gradually increased since about 2000, with little decadal change prior to that. The weighted mean net global ocean CO2 sink estimated by the SOCOM ensemble is -1.75 PgC yr-1 (1992–2009), consistent within uncertainties with estimates from ocean-interior carbon data or atmospheric oxygen trends.

In 2018, central and northern parts of Europe experienced heat and drought conditions over many months from spring to autumn, strongly affecting both natural ecosystems and crops. Besides their impact on nature and society, events like this can be used to study the impact of climate variations on the terrestrial carbon cycle, which is an important determinant of the future climate trajectory. Here, variations in the regional net ecosystem exchange (NEE) of CO2 between terrestrial ecosystems and the atmosphere were quantified from measurements of atmospheric CO2 mole fractions. Over Europe, several observational records have been maintained since at least 1999, giving us the opportunity to assess the 2018 anomaly in the context of at least two decades of variations, including the strong climate anomaly in 2003. In addition to an atmospheric inversion with temporally explicitly estimated anomalies, we use an inversion based on empirical statistical relations between anomalies in the local NEE and anomalies in local climate conditions. For our analysis period 1999-2018, we find that higher-than-usual NEE in hot and dry summers may tend to arise in Central Europe from enhanced ecosystem respiration due to the elevated temperatures, and in Southern Europe from reduced photosynthesis due to the reduced water availability. Despite concerns in the literature, the level of agreement between regression-based NEE anomalies and temporally explicitly estimated anomalies indicates that the atmospheric CO2 measurements from the relatively dense European station network do provide information about the year-to-year variations of Europe's carbon sources and sinks, at least in summer. This article is part of the theme issue 'Impacts of the 2018 severe drought and heatwave in Europe: from site to continental scale'.In 2018, central and northern parts of Europe experienced heat and drought conditions over many months from spring to autumn, strongly affecting both natural ecosystems and crops. Besides their impact on nature and society, events like this can be used to study the impact of climate variations on the terrestrial carbon cycle, which is an important determinant of the future climate trajectory. Here, variations in the regional net ecosystem exchange (NEE) of CO2 between terrestrial ecosystems and the atmosphere were quantified from measurements of atmospheric CO2 mole fractions. Over Europe, several observational records have been maintained since at least 1999, giving us the opportunity to assess the 2018 anomaly in the context of at least two decades of variations, including the strong climate anomaly in 2003. In addition to an atmospheric inversion with temporally explicitly estimated anomalies, we use an inversion based on empirical statistical relations between anomalies in the local NEE and anomalies in local climate conditions. For our analysis period 1999-2018, we find that higher-than-usual NEE in hot and dry summers may tend to arise in Central Europe from enhanced ecosystem respiration due to the elevated temperatures, and in Southern Europe from reduced photosynthesis due to the reduced water availability. Despite concerns in the literature, the level of agreement between regression-based NEE anomalies and temporally explicitly estimated anomalies indicates that the atmospheric CO2 measurements from the relatively dense European station network do provide information about the year-to-year variations of Europe's carbon sources and sinks, at least in summer. This article is part of the theme issue 'Impacts of the 2018 severe drought and heatwave in Europe: from site to continental scale'.

Atmospheric CO2 inversions estimate surface carbon fluxes from an optimal fit to atmospheric CO2 measurements, usually including prior constraints on the flux estimates. Eleven sets of carbon flux estimates are compared, generated by different inversions systems that vary in their inversions methods, choice of atmospheric data, transport model and prior information. The inversions were run for at least 5 yr in the period between 1990 and 2010. Mean fluxes for 2001-2004, seasonal cycles, interannual variability and trends are compared for the tropics and northern and southern extra-tropics, and separately for land and ocean. Some continental/basin-scale subdivisions are also considered where the atmospheric network is denser. Four-year mean fluxes are reasonably consistent across inversions at global/latitudinal scale, with a large total (land plus ocean) carbon uptake in the north (-3.4 Pg C yr-1 (±0.5 Pg C yr-1 standard deviation), with slightly more uptake over land than over ocean), a significant although more variable source over the tropics (1.6 ± 0.9 Pg C yr-1 ) and a compensatory sink of similar magnitude in the south (-1.4 ± 0.5 Pg C yr-1 ) corresponding mainly to an ocean sink. Largest differences across inversions occur in the balance between tropical land sources and southern land sinks. Interannual variability (IAV) in carbon fluxes is larger for land than ocean regions (standard deviation around 1.06 versus 0.33 Pg C yr-1 for the 1996-2007 period), with much higher consistency among the inversions for the land. While the tropical land explains most of the IAV (standard deviation ~ 0.65 Pg C yr-1 ), the northern and southern land also contribute (standard deviation ~ 0.39 Pg C yr-1 ). Most inversions tend to indicate an increase of the northern land carbon uptake from late 1990s to 2008 (around 0.1 Pg C yr-1 , predominantly in North Asia. The mean seasonal cycle appears to be well constrained by the atmospheric data over the northern land (at the continental scale), but still highly dependent on the prior flux seasonality over the ocean. Finally we provide recommendations to interpret the regional fluxes, along with the uncertainty estimates.

The Southern Ocean (44-75° S) plays a critical role in the global carbon cycle, yet remains one of the most poorly sampled ocean regions. Different approaches have been used to estimate sea-air CO2 fluxes in this region: synthesis of surface ocean observations, ocean biogeochemical models, and atmospheric and ocean inversions. As part of the RECCAP (REgional Carbon Cycle Assessment and Processes) project, we combine these different approaches to quantify and assess the magnitude and variability in Southern Ocean sea-air CO2 fluxes between 1990-2009. Using all models and inversions (26), the integrated median annual sea-air CO2 flux of -0.42 ± 0.07 Pg C yr-1 for the 44-75° S region, is consistent with the -0.27 ± 0.13 Pg C yr-1 calculated using surface observations. The circumpolar region south of 58° S has a small net annual flux (model and inversion median: -0.04 ± 0.07 Pg C yr-1 and observations: +0.04 ± 0.02 Pg C yr-1 ), with most of the net annual flux located in the 44 to 58° S circumpolar band (model and inversion median: -0.36 ± 0.09 Pg C yr-1 and observations: -0.35 ± 0.09 Pg C yr-1 ). Seasonally, in the 44-58° S region, the median of 5 ocean biogeochemical models captures the observed sea-air CO2 flux seasonal cycle, while the median of 11 atmospheric inversions shows little seasonal change in the net flux. South of 58° S, neither atmospheric inversions nor ocean biogeochemical models reproduce the phase and amplitude of the observed seasonal sea-air CO2 flux, particularly in the Austral Winter. Importantly, no individual atmospheric inversion or ocean biogeochemical model is capable of reproducing both the observed annual mean uptake and the observed seasonal cycle. This raises concerns about projecting future changes in Southern Ocean CO2 fluxes. The median interannual variability from atmospheric inversions and ocean biogeochemical models is substantial in the Southern Ocean; up to 25% of the annual mean flux, with 25% of this interannual variability attributed to the region south of 58° S. Resolving long-term trends is difficult due to the large interannual variability and short time frame (1990-2009) of this study; this is particularly evident from the large spread in trends from inversions and ocean biogeochemical models. Nevertheless, in the period 1990-2009 ocean biogeochemical models do show increasing oceanic uptake consistent with the expected increase of -0.05 Pg C yr-1 decade-1 . In contrast, atmospheric inversions suggest little change in the strength of the CO2 sink broadly consistent with the results of Le Quéré et al. (2007).

Quantifying variability in the ocean carbon sink remains problematic due to sparse observations and spatiotemporal variability in surface ocean pCO2. To address this challenge, we have updated and improved ECCO‐Darwin, a global ocean biogeochemistry model that assimilates both physical and biogeochemical observations. The model consists of an adjoint‐based ocean circulation estimate from the Estimating the Circulation and Climate of the Ocean (ECCO) consortium and an ecosystem model developed by the Massachusetts Institute of Technology Darwin Project. In addition to the data‐constrained ECCO physics, a Green's function approach is used to optimize the biogeochemistry by adjusting initial conditions and six biogeochemical parameters. Over seasonal to multidecadal timescales (1995–2017), ECCO‐Darwin exhibits broad‐scale consistency with observed surface ocean pCO2 and air‐sea CO2 flux reconstructions in most biomes, particularly in the subtropical and equatorial regions. The largest differences between CO2 uptake occur in subpolar seasonally stratified biomes, where ECCO‐Darwin results in stronger winter uptake. Compared to the Global Carbon Project OBMs, ECCO‐Darwin has a time‐mean global ocean CO2 sink (2.47 ± 0.50 Pg C year−1) and interannual variability that are more consistent with interpolation‐based products. Compared to interpolation‐based methods, ECCO‐Darwin is less sensitive to sparse and irregularly sampled observations. Thus, ECCO‐Darwin provides a basis for identifying and predicting the consequences of natural and anthropogenic perturbations to the ocean carbon cycle, as well as the climate‐related sensitivity of marine ecosystems. Our study further highlights the importance of physically consistent, property‐conserving reconstructions, as are provided by ECCO, for ocean biogeochemistry studies. Plain Language Summary Data‐driven estimates of how much carbon dioxide the ocean is absorbing (the so‐called “ocean carbon sink”) have improved substantially in recent years. However, computational ocean models that include biogeochemistry continue to play a critical role as they allow us to isolate and understand the individual processes that control ocean carbon sequestration. The ideal scenario is a combination of the above two methods, where data are ingested and then used to improve a model's fit to the observed ocean, also known as, data assimilation. While the physical oceanographic community has made great progress in developing data assimilation systems, for example, the Estimating the Circulation and Climate of the Ocean (ECCO) consortium, the biogeochemical community has generally lagged behind. The ECCO‐Darwin model presented in this paper represents an important technological step forward as it is the first global ocean biogeochemistry model that (1) ingests both physical and biogeochemical observations into the model in a realistic manner and (2) considers how the nature of the ocean carbon sink has changed over multiple decades. As the ECCO ocean circulation estimates become more accurate and lengthen in time, ECCO‐Darwin will become an ever more accurate and useful tool for climate‐related ocean carbon cycle and mitigation studies. Key Points ECCO‐Darwin is a global ocean biogeochemistry model that assimilates physical and biogeochemical observations in a conserving manner Air‐sea CO2 fluxes over seasonal to multidecadal timescales (1995–2017) are largely consistent with interpolation‐based products Contrary to interpolation‐based products, ECCO‐Darwin is impervious to sparse and irregularly sampled observations

A temporally and spatially resolved estimate of the global surface-ocean CO2 partial pressure field and the sea-air CO2 flux is presented, obtained by fitting a simple data-driven diagnostic model of ocean mixed-layer biogeochemistry to surface-ocean CO2 partial pressure data from the SOCAT v1.5 database. Results include seasonal, interannual, and short-term (daily) variations. In most regions, estimated seasonality is well constrained from the data, and compares well to the widely used monthly climatology by Takahashi et al. (2009). Comparison to independent data tentatively supports the slightly higher seasonal variations in our estimates in some areas. We also fitted the diagnostic model to atmospheric CO2 data. The results of this are less robust, but in those areas where atmospheric signals are not strongly influenced by land flux variability, their seasonality is nevertheless consistent with the results based on surface-ocean data. From a comparison with an independent seasonal climatology of surface-ocean nutrient concentration, the diagnostic model is shown to capture relevant surface-ocean biogeochemical processes reasonably well. Estimated interannual variations will be presented and discussed in a companion paper.

In 2018, central and northern parts of Europe experienced heat and drought conditions over many months from spring to autumn, strongly affecting both natural ecosystems and crops. Besides their impact on nature and society, events like this can be used to study the impact of climate variations on the terrestrial carbon cycle, which is an important determinant of the future climate trajectory. Here, variations in the regional net ecosystem exchange (NEE) of CO 2 between terrestrial ecosystems and the atmosphere were quantified from measurements of atmospheric CO 2 mole fractions. Over Europe, several observational records have been maintained since at least 1999, giving us the opportunity to assess the 2018 anomaly in the context of at least two decades of variations, including the strong climate anomaly in 2003. In addition to an atmospheric inversion with temporally explicitly estimated anomalies, we use an inversion based on empirical statistical relations between anomalies in the local NEE and anomalies in local climate conditions. For our analysis period 1999–2018, we find that higher-than-usual NEE in hot and dry summers may tend to arise in Central Europe from enhanced ecosystem respiration due to the elevated temperatures, and in Southern Europe from reduced photosynthesis due to the reduced water availability. Despite concerns in the literature, the level of agreement between regression-based NEE anomalies and temporally explicitly estimated anomalies indicates that the atmospheric CO 2 measurements from the relatively dense European station network do provide information about the year-to-year variations of Europe’s carbon sources and sinks, at least in summer. This article is part of the theme issue ‘Impacts of the 2018 severe drought and heatwave in Europe: from site to continental scale’.