The Variability of Air-sea O₂ Flux in CMIP6: Implications for Estimating Terrestrial and Oceanic Carbon Sinks

Human beings are now faced with continuous growth of the climate risk in the warming world. The climate change, occurring mainly as a consequence of anthropogenic CO₂ emissions, is already wielding its influences on ecosystems, economic sectors and people's health (Bopp et al., 2013; Huang et al., 2016; Frölicher et al., 2018; Wei et al., 2021). An increasing number of evidence warns us that actions should be taken urgently to minimize dangerous anthropogenic interference with the climate system, limiting global warming to 2 degrees – a threshold laid down by the Paris Agreement (Seneviratne et al., 2016; Huang et al., 2017b). Under this circumstance, the carbon neutrality, which refers to the balance of emissions of carbon dioxide with its removal, has become one of the most essential things human society needs to achieve in the mid-late 21st century (Dhanda and Hartman, 2011; Niu et al., 2021).

The land and ocean play an important role in the storage of atmospheric CO₂ (Dai et al., 2013; DeVries et al., 2019). It has been reported that the land and ocean have sequestered approximately half of the anthropogenic CO₂ emitted to the atmosphere in the past decades, which helps greatly buffer climate change (Friedlingstein et al., 2019; Gao et al., 2019, 2020). Thus, for a reasonable design of global warming mitigation and carbon neutrality strategies, there is a pressing need to address the effectiveness of terrestrial and oceanic carbon uptake and their susceptibility to climate change. According to this view, the measurement of atmospheric O₂ concentrations and related oxygen budget could provide us a concise and effective method to estimate carbon-uptake capacity of land and ocean on the basis of the close relationship between oxygen and carbon (Huang et al., 2018, 2021; Han et al., 2021; Li et al., 2021).

The accuracy of this O₂-based carbon uptake estimation largely depends on how the oxygen data, especially the air-sea O₂ exchange, is processed in the calculation. Early studies used to assume that there was no long-term oceanic effect of O₂ on the atmosphere (Keeling and Shertz, 1992; Battle et al., 2000). However, a number of indications have revealed the huge oceanic heat uptake under climate change (Willis et al., 2004; Cheng et al., 2018; Cheng and Zhu, 2018; Li et al., 2019), which implies the air-sea O₂ exchange could vary as a consequence of warming-induced solubility and circulation changes (Bopp et al., 2002; Li et al., 2020). Later studies have thus taken air-sea O₂ flux into consideration (Manning and Keeling, 2006; Tohjima et al., 2019), where the oceanic O₂ outgassing to the atmosphere is approximately estimated by a linear regression with ocean heat content, assuming the relationship between gas flux and heat flux bears a proportional relationship at the air–sea interface. In fact, mechanisms that control the variability of air-sea O₂ flux are rather complicated. Its temporal and spatial variations could be affected by changes in ocean primary production, ventilation and stratification, as well as oceanic internal modes such as El Niño-Southern Oscillation(ENSO) (Resplandy et al., 2015; Yang et al., 2017). The intensified ocean heat uptake in the past few decades (Trenberth et al., 2014; Cheng et al., 2017) also wields its influences in the long-term period. How to accurately quantify the air-sea O₂ flux has therefore been one of the most important questions in the field of O₂-based carbon uptake estimations.

Here, based on recent CMIP6 model simulations, we systematically investigate the characteristics of air-sea O₂ flux and from it, we subsequently calculate the terrestrial and oceanic carbon sinks. We hope to provide a better understanding of air-sea O₂ flux under ongoing climate change. We also hope the applications of process-based air-sea O₂ flux from CMIP6 model simulations can provide a more comprehensive and reliable carbon sink estimation, compared with results from previous studies where the air-sea O₂ flux is not considered or simply approximated by a linear relationship between O₂ outgassing and heat content.

The paper is arranged as follows. Section 2 describes the detailed method of O₂-based carbon sink estimations and the datasets, especially air-sea O₂ flux, used in this study. The climatology characteristics of air-sea O₂ flux and its variability under climate change in CMIP6 are shown in section 3.1. Section 3.2 provides our estimations of terrestrial and oceanic carbon sinks with the use of this air-sea O₂ flux. Discussion and conclusion are presented in section 4.

The assessments of land and ocean carbon sinks in this study are based on the strong relationship between oxygen and carbon, which can be written as follows (Keeling and Manning, 2014; Li et al., 2021):

where ∆CO₂ and ∆O₂ represent changes in atmospheric CO₂ and O₂; F_fossil is the industrial CO₂ emissions, which mainly comes from fossil fuel combustion; F_air-sea represents the air-sea O₂ flux; α_F and α_B are dimensionless parameters which represent the globally averaged O₂: CO₂ mole exchange ratios for fossil fuel burning and biological process; S_land and S_ocean represent the net land carbon sink and ocean carbon sink, respectively. These two equations briefly describe the human impacts on the oxygen and carbon cycles. All variables in the equations mentioned above use the units of mole.

The concentrations of CO₂ in the atmosphere ($X_{{\rm{CO}}_2} $) are measured using the unit of “ppm” (parts per million). Its change can be expressed as

where M_air represents the global total number of moles of dry air (M_air=1.769×10²⁰). The change of atmospheric O₂ concentrations, however, is typically measured as the mole ratio changes of O₂/N₂ rather than the mole fraction such as ppm, due to its high abundance in the atmosphere. Following Keeling and Shertz (1992), the O₂ content of an air sample can be defined as

where (O₂/N₂)_sample is the mole ratio of O₂ to N₂ in the sample air and (O₂/N₂)_ref is the ratio in an arbitrary reference gas. Note that δ(O₂/N₂) is typically multiplied by 10⁶ and expressed as “per meg” unit. The observed changes of δ(O₂/N₂) in the atmosphere could thus be written as

where ∆O₂ and ∆N₂ are changes in moles of atmospheric O₂ and N₂; $X_{{\rm{O}}_2} $ and $X_{{\rm{N}}_2} $ are the standard mole fraction of O₂ and N₂ in the atmosphere ($X_{{\rm{O}}_2} $ = 0.2094 and $X_{{\rm{N}}_2} $ = 0.7808).

According to Eqs. (1)−(5), the land and ocean carbon sink can be written as

The observed timeseries of atmospheric CO₂ and O₂ concentrations [i.e. $X_{{\rm{CO}}_2} $ and δ(O₂/N₂)] can be downloaded from Scripps O₂ Program (https://scrippso2.ucsd.edu/), which provides records of both CO₂ and O₂ concentrations at 12 stations. In this study, we choose the longest three timeseries, at Alert (82.5°N, 62.3°W), La Jolla (32.9°N, 277.3°W), and Cape Grim (40.7°S, 144.7°E), respectively, and calculate the average with weights of 0.25, 0.25, 0.5 (given the equal weight in both hemispheres).

The global CO₂ emissions (F_fossil) are derived from Carbon Dioxide Information Analysis Center (CDIAC, Andres et al., 2016), which counts the consumptions of each type of fossil fuel. It should be noted that each fuel type has its own combustion ratio (α_F), as shown in Table 1 (Liu et al., 2020). The global averaged α_F therefore slightly varies with time due to changes of global energy sources [Fig. S1 in the Electronic Supplementary Material, (ESM)]. The oxidative ratio α_B also exhibits temporal variations due to modifications to global vegetation cover by human activities, however, it is generally believed the decrease of α_B is less than 0.01 over 100 years (Randerson et al., 2006). We thus set the typical value of α_B as 1.10 according to previous studies (Keeling and Manning, 2014; Battle et al., 2019).

Due to the importance of O₂ flux (F_air-sea) in estimating the carbon uptake, here we discuss it in greater detail. The air-sea O₂ flux evaluated in this study builds on the process-based ocean physical and biochemical models developed as part of Coupled Model Intercomparison Project phase 6 (CMIP6), which can be downloaded from https://esgf-node.llnl.gov/search/cmip6/. The detailed descriptions of these models are presented in Table 2. Here we choose the historical experiments of these models to match the timeseries of O₂ observations. Note that the air-sea O₂ flux is calculated by the model in mol m⁻² s⁻¹, so we convert to mol of oxygen per year (mol m⁻² yr⁻¹). For sake of comparisons and analysis, all the model results are gridded to 1°×1° resolution.

Furthermore, it should be noted that, due to import of N₂ in the atmospheric O₂ observations, oceanic N₂ outgassing must be considered in the calculations. The total effect of the ocean on carbon sinks could thus be expressed as Eq. (8). Here we apply the tuning parameter β=0.88 to represent the negative effect of N₂ outgassing (Keeling and Manning, 2014); it can be shown that the equation can be written as

The related ocean physics variables such as sea temperature, salinity, and mixed layer depth in CMIP6 are also used in this study to analyze mechanisms of O₂ flux change.

We use the ensemble empirical mode decomposition (EEMD) method to separate the human-induced long-term signals from natural decadal variability in the time series of air-sea O₂ flux. This noise-assisted method can separates scales naturally without any prior subjective criterion (Ji et al., 2014; Huang et al., 2017a). EEMD performs operations that partition a series into different “modes” (Intrinsic Mode Functions, IMFs), which are expressed by the following equation:

where IMF_i(t) is the ith IMF, and r_n(t) is the residual of data X(t). The detailed descriptions of the steps on how to execute EEMD method can be found in Text S1 in the ESM. In this study, the noise added to the data has an amplitude that is 0.2 times the standard deviation of the raw data, and the ensemble number is 400. The number of IMFs is 6. A python version of EEMD is available at https://www.github.com/laszukdawid/PyEMD (Laszuk, 2017).

The transfer of gases across the air-sea interface is controlled by several physical, biological and chemical processes in the atmosphere and ocean, which could influence not only the partial pressure differences but also the efficiency of transfer processes (Wanninkhof, 1992; Liang et al., 2013). The air-sea O₂ flux thus varies considerably among the ocean regions. Figure 1a presents the model-ensemble-mean of annual air-sea O₂ flux averaged from 1985 to 2014 in CMIP6 historical experiments (positive means a flux to the atmosphere). Spatial distributions of O₂ flux in each individual model can be found in Fig. S2 in the ESM. The results show an overall net O₂ outgassing from ocean to the atmosphere at low latitudes, while a significant influx of O₂ occurs at high latitudes. The tropical and subtropical ocean (30°S−30°N) emits approximately 250.8±38.4 Tmol O₂ per year (1 Tmol = 10¹² mol), which is partly compensated by O₂ absorption in the high-latitude ocean, about −105.2±24.8 and −87.2±41.4 Tmol yr⁻¹ in the Northern (>30°N) and Southern Hemisphere (>30°S), respectively, eventually leading to a net O₂ outgassing of ~58.5±9.6 Tmol yr⁻¹ over the global ocean. This pattern highlights the solubility effect driven by meridional temperature gradients, as well as combinations of the dynamical and biological effects, which lead to a surplus of oceanic O₂ production in low latitudes (Bopp et al., 2002).

Figure 1.  The spatial distributions of annual mean air-sea O₂ flux (a) averaged from 1985 to 2014 in CMIP6 historical simulations, and (b) compared with two other studies. Positive flux in Fig. 1a means O₂ outgassing from ocean to the atmosphere. For sake of comparisons, the ocean is partitioned into 13 regions as shown in Fig. S3 in the ESM. The results from Li et al (2020) are similar with Resplandy et al 2015, which are not shown here.

Furthermore, the simulated O₂ flux is evaluated against results derived from previous studies (Gruber et al., 2001; Resplandy et al., 2015), which are found in Fig. 1b . The ocean is divided into 13 regions for sake of comparison (Fig. S3 in the ESM). The patterns presented by the ensemble-mean of the suite of models in CMIP6 correspond well with estimations based on ocean inversions (Gruber et al., 2001), except for the Sothern Ocean. The results derived from Gruber et al. (2001) exhibit a much stronger O₂ outgassing in the subpolar South Atlantic [95.0 Tmol yr⁻¹ differences between this study and Gruber et al. (2001)]. However, this difference could roughly cancel out when we integrate the whole Southern Ocean regions, as it also exists a larger O₂ influx in subpolar Indian-Pacific Ocean and Oceans >58°S (differences of −58.1 and −26.2 Tmol yr⁻¹, respectively). Besides, the spatial distribution shows a remarkable consistency with preindustrial experiments presented by Resplandy et al. (2015), indicating the robust of models in simulating O₂ flux.

Temporal evolution of the air-sea O₂ flux reveals that significant modifications have been occurring in response to ongoing climate change (Fig. 2). In Fig. 2a, we can see sizable oscillations of air-sea O₂ flux during the period 1950−85. Also obvious is the increase of oceanic O₂ outgassing found since the mid-1980s, with an upward trend of ~1.49 Tmol yr⁻² (significant at 0.01 level). Based on EEMD method, here we split the evolution of air-sea O₂ flux into decadal variability (i.e. sum of IMFs 2−5 from EEMD) and the long-term trend (i.e. IMF 6). As shown in Fig. 2b, the time series of air-sea O₂ flux from 1950 to 1985 is primarily dominated by natural decadal variability, while the human-induced long-term changes gradually wields its influence after 1985. The combination of the two terms eventually lead to an overall upward trend since the 1980s, with natural variability modulating the long-term trend.

Figure 2.  Time series in the historical period (1950−2014) of (a) air-sea O₂ flux and (b) its EEMD decomposition. The red dashed line in (a) represents linear regression from 1980 to 2014, significant at the 0.01 level. Shaded area is the uncertainty of the flux represented by the standard deviation of these models. The decadal variability in (b) (the blue solid line) is the sum of IMF2-5 from the EEMD and the long-term trend (the red solid line) is the IMF6. Positive values in both panels indicate oceanic O₂ outgassing to the atmosphere.

The EOF analysis was applied to the de-trended global air-sea O₂ flux over the 1985−2014 period to explore the spatio-temporal distributions of decadal variability (Fig. 3). The first two modes explain approximately 58% of the total variance. The highest decadal variability of O₂ flux is found in the North Pacific, the North Atlantic and the Southern Ocean (Figs. 3a, 3b). The most significant changes in the Atlantic are mainly in the high-latitude areas where the sinking branch of the Atlantic Meridional Overturning Circulation (AMOC) is located, the changes of which could significantly influence climate (Yang et al., 2016; Wen et al., 2018; Yang and Wen, 2020). In the Southern Ocean, the spatial pattern exhibits opposite phase between 40°S and 65°S, suggesting the potential relationship with the Southern Annular Mode (SAM). Time series associated with EOF modes reveal a cycle of ~15 years with different phases in PC1 and PC2 (Fig. 3c). The standard deviation of the decadal variability derived from EEMD also shows a similar spatial distribution compared with the EOF analysis (Fig. S4 in the ESM).

Figure 3.  EOF analysis of de-trended global air-sea O₂ flux over the 1985−2014 period. The spatial patterns of the first and second EOF mode are presented in panel (a) and (b), respectively. The black and blue lines in (a) represent the temporal coefficient of the two modes. Note that the original timeseries is pre-processed with a pentad running average to remove the influence of the high-frequency oscillations.

The long-term changes of air-sea O₂ flux, which are generally considered as modifications to anthropogenic forcing, is presented in Fig. 4. Positive values are mainly found in the high latitude areas (Fig. 4a), where strong O₂ uptake in the climatological state is seen (Fig. 1a), revealing the weakening of the oceanic O₂ absorption capacity from the atmosphere. The maximum increase of the flux occurs in the Southern Ocean (SO>58°S), where it reaches 5.39±0.34 Tmol yr⁻¹. The next two highest increases occur in the North Pacific (Temp NPac) and North Atlantic (N NAtl), with an increase about 4.39±0.17 and 3.25±0.11 Tmol yr⁻¹, respectively (Fig. 4b). This long-term change could be attributed to human-induced solubility and circulation changes. The solubility of dissolved O₂ has been decreasing in the warming ocean. This effect could be written as:

Figure 4.  15-year changes in the long-term trend of air-sea O₂ flux since 1985. The error bars in panel (b) represent the uncertainty of flux change.

where Q is the total sea-surface downward heat flux; C_p represents the heat capacity of sea water; ∂O₂/∂T is the temperature dependence of O₂ solubility which could be derived from Garcia and Gordon (1992). Our calculations reveal that roughly one quarter of the increase is directly associated with reduced solubility in the warming ocean, which is consistent with results found by Li et al. (2020) and Plattner et al. (2002). Warming-induced ocean stratification also plays an important role in the modifications of air-sea O₂ flux. Strong shoaling of the mixed layer is found in the North Atlantic and widespread areas in the Southern Ocean (Fig. S5 in the ESM), which prevents oxygen supplies from reaching the deeper layers and eventually result in a positive contribution to the air-sea O₂ flux.

In Li et al. (2020), the air-sea O₂ flux derived from CMIP5 is applied to investigate the terrestrial and oceanic carbon sinks. It is therefore necessary to clarify the difference of the flux between the CMIP5 and CMIP6 as well as its influences on carbon sink estimations.

For a simulated historical period from 1975 to 2005, the comparisons between CMIP6 (this study) and CMIP5 [derived from Li et al. (2021)] reveal pronounced temporally varying differences of air-sea O₂ flux (Fig. 5). Except for a short period of time around year 1990, the ocean in CMIP6 exhibits an overall smaller oceanic O₂ outgassing, up to −22 Tmol yr⁻¹, than in CMIP5. Spatial patterns shown in Fig. 5b reveal that this difference is mainly caused by the intensified high-latitude oceanic O₂ uptake in CMIP6, especially in the North Atlantic and Southern Ocean. Although there still exists relatively large uncertainties, this intensified uptake in CMIP6 is more consistent with the regional observations in the Southern Ocean (Bushinsky et al., 2017), reflecting the improvement of simulations in CMIP6. Furthermore, slight difference also exists in the long-term trend of air-sea O₂ flux. An upward linear trend of ~1.52 Tmol yr⁻² has been found in CMIP6 during the period 1985 to 2005, while the trend is approximately 1.12 Tmol yr⁻² in CMIP5. This indicates an accelerated oceanic O₂ outgassing in CMIP6, which is tightly associated with ocean deoxygenation (Bopp et al., 2013; Palter and Trossman, 2018; Li et al., 2020).

Figure 5.  Differences of air-sea O₂ flux between CMIP6 and CMIP5 during period 1975−2005 (i.e. FLUX_CMIP6 minus FLUX_CMIP5). The black line in (a) is the time series of the difference and (b) shows the spatial distribution of the difference averaged from 1975−2005.

According to Eqs. (6)−(8), this difference in O₂ flux could lead to a total fluctuation as large as 0.4 GtC yr⁻¹ in the estimated carbon sink. It should be noted that, besides the air-sea O₂ flux, the estimated carbon sink could also be influenced by the choice of other oxygen datasets in the study, which is therefore rather complicated. Comparisons of O₂-based carbon sinks between this study and Li et al. (2021), as well as other previous studies, will be discussed in detail in the following section.

Simulations of the air-sea O₂ flux in CMIP6 provide a valuable complement for the O₂-based carbon uptake estimations. With the use of air-sea O₂ flux as well as other O₂-related variables, the global terrestrial and oceanic carbon sinks could be calculated based on Eqs. (1)−(9). The processes are briefly diagrammed in Fig. 6.

Figure 6.  Changes in observed atmospheric concentrations of O₂/N₂ and CO₂ from 1990 to 2014. The blue dots represent the annual averaged O₂ and CO₂ anomaly (here we choose the concentrations in 1990 as the reference value). The vectors in the diagram schematically illustrate the contribution of each process related to the changes in O₂ (vertical axis) and CO₂ (horizontal axis) during this period. The effect of air-sea O₂ flux is highlighted in red.

The dots in Fig. 6 are the observed anomalies of global atmospheric CO₂ (horizontal axis) and O₂/N₂ concentrations (vertical axis) from 1990 to 2014. Here we set the concentrations in year 1990 as the base point (0 ppm, 0 per meg). These dots show an increase of CO₂ concentration and a simultaneous decline in O₂/N₂ concentration with time. For example, the concentrations in 2014 could be written as (44 ppm, −465 per meg) in this coordinate system, which means a 44 ppm increase of CO₂ concentration and a 465 per meg decrease of O₂/N₂ concentration in the atmosphere since year 1990. The arrows in Fig. 6 reveal the effect of related processes on atmospheric CO₂ and O₂/N₂ concentration changes. For example, the fossil fuel combustion is marked by the black arrow in Fig. 6, starting at (0, 0) and ending at (89.0, −584.7), meaning that the fossil fuel burning would have contributed to a total 89.0 ppm increase of CO₂ (that is, a release of 189.0 GtC CO₂, 1 Gt = 10¹⁵ g, 1 ppm = 2.12 GtC) and 584.7 per meg decrease of O₂/N₂ concentration during 1990−2014, if no other processes were involved. This is to say, the observed decline of O₂/N₂ (~465.1 per meg) is a bit smaller compared with the decline directly derived from fossil fuel combustion (584.7 per meg) during 1990−2014. More importantly, the observed atmospheric CO₂ concentration only increases by about half of the value derived from fossil fuel combustion (that is, ~44 ppm, as shown in Fig. 6 and Fig. 7), from which we can thus infer huge land and ocean carbon sinks, absorbing a total of 96.6 GtC carbon. The projections of these arrows on the x- axis are also drawn in Fig. 6, which reflect how the atmospheric CO₂ concentrations are influenced by the related processes. The land and ocean carbon sinks can be separated from the total carbon uptake according to Eq. (6) and Eq. (7), as 33.5 GtC and 63.2 GtC, respectively, during this period.

Figure 7.  The observed time series of atmospheric O₂/N₂ and CO₂ concentrations. The blue, green and red lines represents observations in La Jolla (32.9°N, 277.3°W), Alert (82.5°N, 62.3°W), and Cape Grim (40.7°S, 144.7°E), respectively. The black line is the annual mean concentrations averaged among the three stations with a weight of 0.25, 0.25 and 0.5.

It should be especially noted that the air-sea O₂ flux plays an important role in the carbon uptake estimations. The ocean emits ~1.54 Pmol O₂ (1 Pmol = 10¹⁵ mol) to the atmosphere (sum of the air-sea O₂ flux from 1990 to 2014 in Fig. 2a), making a positive contribution of about 36.7 per meg to the atmospheric O₂/N₂ concentration (red vector in Fig. 6). Despite this air-sea O₂ flux being relatively small, it plays an important role in the estimation of land and ocean carbon sinks. Figure 8 describes the situation assuming that the air-sea O₂ flux is negligible on a multiannual-to-decadal timescale, as proposed in the early studies (Bender and Battle, 1999; Battle et al., 2000). If the air-sea O₂ flux is not considered in the O₂ budget, the ocean carbon sink would be apparently underestimated by approximately 14.8 GtC during 1990−2014, while the land carbon uptake would be largely overestimated (bar charts in the top right of Fig. 8).

Figure 8.  Role of air-sea O₂ flux in O₂-based carbon sinks estimations. The diagram is same as Fig. 6, except for no air-sea O₂ flux considered in the calculation. The bar charts in the top right show the comparisons between estimated ocean/land carbon sink with and without O₂ flux correction.

We subsequently calculated the averaged terrestrial and oceanic carbon uptake over several different periods and compared them with previous O₂-based carbon uptake estimations (Table 3). Here, we use the linear trend of atmospheric O₂/N₂ and CO₂ concentrations in the period to represent the O₂/N₂ and CO₂ changes in Eqs. (6)−(7) (∆δ(O₂/N₂) and ∆CO₂). For observed atmospheric concentration changes and fossil fuel consumption (F_fossil), our results are relatively consistent with Keeling et al. (2014) (differences less than 0.06 ppm yr⁻¹ in ∆CO₂ and 0.12 GtC yr⁻¹ in F_fossil). The effect of air-sea flux in our study (which are derived from process-based CMIP6 model simulations, as described above) shows a relatively large discrepancy with that in Keeling et al. (2014) (which is calculated based on the linear regression between O₂ flux and net changes of ocean heat content). Our results show an averaged ocean and land carbon sink of 2.10±0.43 and 1.14±0.52 GtC yr⁻¹, respectively, during 1990−2000. An increase is found in both ocean and land carbon sinks during 2000−10, while results from Keeling et al. (2014) show an increase in ocean sink but a decline in land sink. Furthermore, the averaged carbon sinks from 2004 to 2008 in our study (2.64±0.66 GtC yr⁻¹ for ocean and 1.84±0.79 GtC yr⁻¹ for land) are generally larger than that in Tohjima et al. (2019) (1.97±0.62 GtC yr⁻¹ for ocean and 2.17±0.82 GtC yr⁻¹ for land), which could also be partly attributed to the discrepancy in the air-sea flux (Table 3).

To further explore the temporal changes of ocean and land carbon sinks over the past two decades, the averaged ocean and land carbon sinks were calculated for several representative periods: 1991−97, 1994−2000 and 2004−10 were selected for the estimates of averaged ocean sinks; meanwhile, 1994−2000, 2002−08 and 2008−14 were selected for the estimates of averaged land sinks. These results are shown as the asterisks in Fig. 9, accompanied by time-continuous estimations from the Global Carbon Project (GCP, Friedlingstein et al., 2019), Landschützer et al 2016 and Carbon Tracker (CT, Jacobson et al., 2020). The estimates by GCP clearly show a quasi-monotonous increase of the oceanic carbon sink over the past few decades (Fig. 9a, red line). However, the oceanic uptake in our results show a decline from 2.04±0.47 GtC yr⁻¹ in 1991−97 to 1.85±0.45 GtC yr⁻¹ in 1994−2000. A significant upward trend is subsequently found in the 21st century, with ocean uptake increasing to 2.87±0.47 GtC yr⁻¹ in 2004−10. This temporal pattern is generally consistent with results derived from observed surface partial pressure of CO₂ in Landschützer et al. (2016) (Fig. 9a, green line), which may occur as consequences of the combined influence of anthropogenic forcing and oceanic internal modes. The net terrestrial carbon uptake estimated in this study corresponds well with the results derived from GCP. An increase of land carbon uptake (from 1.23±0.60 GtC yr⁻¹ to 1.91±0.50 GtC yr⁻¹ according to our estimations) could be found in the 2000s (Fig. 9b) which has been reported by several atmospheric inversion and model-based studies (Keenan et al., 2016; Ballantyne et al., 2017; Piao et al., 2018). Despite the fact that the mechanisms behind this increase are still under discussion, it is generally believed that the changes in land use, modifications of terrestrial productivity and respiration, as well as climatic variations of temperature and moisture are responsible for changes in terrestrial carbon uptake (Chen et al., 2020; Piao et al., 2020a, b; Yue et al., 2020).

Figure 9.  Estimated ocean and land carbon sinks in different studies. The asterisks and triangles are seven-year averaged carbon sinks in this study and Li et al 2021, with error bars representing uncertainties of the estimations. The time series of carbon sinks derived from Global Carbon Project 2019, Landschützer et al 2016 and Carbon Tracker 2019 are colored in red, green and blue, respectively. The thin dashed lines and the thick solid lines are annual and seven-year running averaged carbon sinks, respectively.

In this section, we specifically investigate the differences of the carbon sinks from that in Li et al. (2021). As mentioned in section 3.1.3, the air-sea O₂ flux used in Li et al. (2021) is derived from CMIP5, while CMIP6 simulation of the flux is used in this study. Meanwhile, the other O₂-related variables (such as atmospheric O₂ decline) in Li et al. (2021) are derived from the oxygen budget proposed by Huang et al. (2018), which is also different from this study. Terrestrial and oceanic carbon uptakes estimated by Li et al. (2021) are depicted by the triangles in Fig. 9. From the comparisons between this study and Li et al. (2021), we can discern the role of oxygen data in carbon sink estimations.

For the terrestrial carbon sink, both of the two studies corresponds well with GCP in the 21st century, which exhibit an enhanced uptake mentioned in section 3.2.2. However, the result from Li et al. (2021) seems to present an unrealistically high land carbon uptake (1.50 GtC yr⁻¹) in the 1990s, while the current study behaves in good agreement with GCP during this period (1.06 GtC yr⁻¹). The oceanic carbon uptake in both this study and Li et al. (2021) exhibits a similar variability with that in Landschützer et al. (2016) (that is, a downward trend in the 1990s subsequently followed by an upward trend in the 2000s). Despite this, discrepancy occurs around year 2010, as shown in Fig. 9a. The estimated oceanic carbon uptake in this study (2.87 GtC yr⁻¹) is relatively larger than it in Li et al. (2021) (2.45 GtC yr⁻¹) and GCP (2.36 GtC yr⁻¹).

Overall, both of the two studies reveal an enhanced carbon uptake in the 21st century. This study provides a more reliable estimate of the terrestrial carbon uptake in the 1990s, while the oceanic carbon sink in Li et al. (2021) is more consistent with the Global Carbon Project after year 2010. Our calculations show that the differences in air-sea O₂ flux ($ {F}_{\mathrm{a}\mathrm{i}\mathrm{r}-\mathrm{s}\mathrm{e}\mathrm{a}} $) and atmospheric O₂ change ($ \Delta {\mathrm{O}}_{2} $) are the main contributors to the discrepancies. If the difference in O₂ flux is expressed as $\Delta {F}_{{\rm{air-sea}}}$ (the other variables remain unchanged), its influence on the terrestrial and oceanic carbon uptake could then be respectively expressed as $\Delta B=-{\beta }/{{\alpha }_{{\rm B}}}{\Delta F}_{\mathrm{a}\mathrm{i}\mathrm{r}-\mathrm{s}\mathrm{e}\mathrm{a}}$ and $\Delta O={\beta }/{{\alpha }_{{\rm B}}}{\Delta F}_{\mathrm{a}\mathrm{i}\mathrm{r}-\mathrm{s}\mathrm{e}\mathrm{a}}$_, according to Equations 6−8. This implies that a weakened oceanic O₂ outgassing, approximately −22 Tmol O₂ yr⁻¹, would lead to an increase of 0.21 GtC yr⁻¹ land carbon sink and a simultaneous opposite effect on ocean carbon sink. For the period 1990−95, Li et al. (2021) shows a smaller declining trend of atmospheric O₂ and oceanic outgassing in 1990−95, which could eventually lead to a larger land uptake in Li et al. (2021) during this period. These results highlight the vital importance of oxygen datasets on carbon sink estimations.

We use the coupled ocean biogeochemistry models in CMIP6 to investigate the modifications of air-sea O₂ flux under climate change and its influences on the estimations of global terrestrial and ocean carbon uptake. Our results show an enhanced global oceanic O₂ outgassing to the atmosphere since the 1980s, accompanied by a strong decadal variability dominated by oceanic internal modes. Consistent with Li et al. (2020), this study shows maximum changes of flux mainly occurring in the high latitudes, with roughly one quarter of the outgassing directly associated with reduced solubility in the warming ocean, and the rest mainly linked with circulation changes and ocean stratification. This modification of air-sea O₂ flux plays an important role in estimating carbon uptake, as described in section 3.2.

The application of air-sea O₂ flux in CMIP6 provides a valuable complement for studies of O₂-based global carbon sinks estimations under climate change. Our results reveal the significant increases of terrestrial and oceanic carbon sinks in the 21st century, reflecting the human impacts on the carbon cycle and Earth’s environments. The model biases of air-sea O₂ flux between CMIP5 and CMIP6 are also investigated in this study, which could lead to a total discrepancy up to 0.4 GtC yr⁻¹ in the estimations, indicating the importance of improvement of air-sea O₂ flux parameterizations in the model.

Some limitations should also be acknowledged. Our estimation of carbon sinks still suffers from relatively large uncertainties (0.4−0.8 GtC yr⁻¹) due to the accumulations of uncertainty of each term in the calculations. Furthermore, the earliest observations of O₂/N₂ we could obtain are from the late 1980s, which greatly limits the lengths of estimated time series. The comparisons between this study and Li et al. (2021) also reveal the importance of the accuracy of oxygen datasets on the carbon uptake estimations. Presently, we are working on structuring the global oxygen budget (Huang et al., 2018) under the constrain of O₂/N₂ observations, from which we hope to extend the time series of atmospheric O₂ changes back to the 1900s as well as provide a more reliable oxygen dataset. Further explorations and investigations of the O₂-based carbon uptake estimations should be done in the future.

Acknowledgements. The authors acknowledge the Scripps O₂ Program for providing the observations of atmospheric O₂ and CO₂ data. The authors also acknowledge the World Climate Recruitment Programme’s (WCRP) Working Group on Coupled Modelling (WGCM), and the Global Organization for Earth System Science Portals (GO-ESSP) for producing outputs of CMIP6 model simulations. This work was jointly supported by the National Science Foundation of China (Grant Nos. 41991231, 91937302) and the China 111 project (Grant No. B13045). The data processes and analysis are supported by Supercomputing Center of Lanzhou University.

Electronic supplementary material: Supplementary material is available in the online version of this article at https://doi.org/10.1007/s00376-021-1273-x.

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