Spatial Inhomogeneity of Atmospheric CO₂ Concentration and Its Uncertainty in CMIP6 Earth System Models

Since the industrial revolution, the global surface temperature has significantly increased, causing widespread and rapid climate change in the atmosphere, ocean, cryosphere, and biosphere, which has profoundly affected the survival and development of human beings (IPCC, 2021). Global warming is mainly caused by the rapid increase of atmospheric greenhouse gases (mainly carbon dioxide) (IPCC, 2013, 2021). The sixth assessment report (AR6) issued by the Intergovernmental Panel on Climate Change (IPCC) makes it clear that the observed increase in the concentration of atmospheric CO₂, which has risen from about 280 ppm (parts per million) before the industrial revolution to 410 ppm in 2019, is due to human activities (IPCC, 2021). Relevant studies find that more than half of anthropogenic CO₂ is absorbed by land and ocean, and the remainder is retained in the atmosphere (IPCC, 2021; Friedlingstein et al., 2022). Meanwhile, due to the combined effect of complex and interacting factors of the Earth’s multi-sphere, such as anthropogenic CO₂ emission sources, land-atmosphere-ocean CO₂ exchanges, and atmospheric circulation, the atmospheric CO₂ concentration exhibits inhomogeneity in its spatial distribution and variations in time.

Earth System Models (ESMs) are among the most advanced tools available for studying the historical distributions and future changes in atmospheric CO₂ concentration (Flato et al., 2013; Chen et al., 2021). The use of ESMs in research on the impact of anthropogenic CO₂ emissions on climate change and the interaction between the global carbon cycle and the climate system has become a crucial scientific issue attracting the attention of scientists, policymakers, and citizens worldwide. The Coupled Climate–Carbon Cycle Model Intercomparison Project (C4MIP) was included in the Coupled Model Intercomparison Project Phase 5 and 6 (CMIP5 and CMIP6) to understand and quantify the long-term changes in terrestrial and oceanic carbon storage and carbon fluxes as well as their impact on climate projections (Eyring et al., 2016; Jones et al., 2016). Previous assessments have shown that the ESMs that participated in CMIP5 could reasonably reproduce the global distribution and interannual variability of CO₂ flux (Anav et al., 2013; Wu et al., 2013; Dong et al., 2016), and the simulation results have been used to quantify the feedback between the climate and carbon cycle (Arora et al., 2013; Liu et al., 2017).

Over the past two years, progress has been made in the study and simulation of the carbon cycle using the current generation of ESMs that participated in CMIP6, especially the simulation of time and spatial variations in CO₂ fluxes (e.g., Lerner et al., 2021; Peng et al., 2021; Wieder et al., 2021). However, there are few relevant assessments of atmospheric CO₂ concentration in simulations with CMIP6 ESMs, and those assessments that do exist have mainly used either satellite retrievals or a small number of ground-based observations to analyze changes in global average or site-specific CO₂ concentrations (Sellar et al., 2019; Gier et al., 2020; Ito et al., 2020; Patra et al., 2021). Therefore, research on the long-term historical evolution and regional distribution features of CO₂ concentration is still lacking. In this paper, we analyze the spatial distribution and time evolution features of the near-surface atmospheric CO₂ concentration in the historical period, as simulated by ESMs in CMIP6, explore the uncertainties in the simulations, and identify the possible causes of inter-model disagreements.

The remainder of this paper is organized as follows. Section 2 describes the data and methods. Section 3 evaluates the historical evolution, spatial distribution, and seasonal variability of the near-surface atmospheric CO₂ concentrations, as simulated by the ESMs in CMIP6, and explores the causes of differences between the simulation results. Section 4 summarizes our main conclusions and some prospects for future work.

The model data used in this study is the simulation results of historical experiments of 12 ESMs from CMIP6 and 11 ESMs from CMIP5. Table 1 shows model information for those in CMIP6 and Table 2 for those in CMIP5. The analyzed variables include the near-surface CO₂ concentration and anthropogenic and natural CO₂ fluxes. Anthropogenic CO₂ fluxes comprise those due to anthropogenic emissions, including the combustion of fossil fuels, cement production, agricultural practices, and sources associated with anthropogenic land-use changes (excluding forest regrowth). Natural CO₂ fluxes are the sum of land–atmosphere CO₂ exchanges (i.e., net ecosystem productivity) and ocean–atmosphere CO₂ exchanges. The analysis and discussion of anthropogenic and natural CO₂ fluxes are based on output from BCC-CSM2-MR, MRI-ESM2-0, and UKESM1-0-LL since these models provided all the necessary flux variables. Due to the different resolutions used in these ESMs, all model output is interpolated to a global grid of 1.125° × 1.125° with bilinear interpolation to facilitate analysis and comparison. The CMIP6 model data are interpolated from the model grids to each site using the site observations.

The reference data used to evaluate the performance of the models’ historical simulations includes a) the global site observation data of monthly mean atmospheric CO₂ concentration from 1968 to 2021 provided by the World Data Centre for Greenhouse Gases (WDCGG) (WMO, 2021) at the 49 representative sites (shown by the triangles in Fig. 1) which have continuous observations from 1995 to 2014, b) the monthly mean data of zonal mean observed atmospheric CO₂ concentration (Meinshausen et al., 2017) and global anthropogenic CO₂ emissions (Hoesly et al., 2018) from 1850 to 2014, as recommended by CMIP6, c) the annual observed atmospheric CO₂ concentration data from 1850 to 2014 provided by the Scripps CO₂ program, which are obtained by combining ice core data from 1850 to 1958 (MacFarling Meure et al., 2006) and data observed in Mauna Loa and the South Pole from 1959 to 2014 (Keeling et al., 2001), and d) the global carbon budget data from 1850 to 2014 (GCB2021; Friedlingstein et al., 2022).

Figure 1.  Geographical location of 154 WDCGG observation sites (WMO, 2021). The 49 sites marked with red triangles are representative sites selected for this study with continuous monthly CO₂ concentration data for 1995–2014.

Figure 2a shows the time series of the global annual mean surface CO₂ concentration from 1850 to 2014, as simulated by CMIP6 ESMs. The reference data is the time series of the Scripps CO₂ concentration and the CMIP6 recommended CO₂ concentration based on observational and reconstructed data. The two sets of reference data have a high level of agreement on the concentration and evolution of CO₂, as the correlation coefficient exceeds 0.99. The average difference between the multi-model ensemble mean (MME) and the reference data is within 2.5 ppmv, and the MME can reasonably simulate both the slow increases in observed CO₂ concentration before the 1950s and the more rapid growth thereafter. The 12 ESMs can also basically reproduce the trend of CO₂ concentration change, but the differences in CO₂ concentration between the ESMs show an increase with time. The simulated CO₂ concentrations range from 282.2 to 291.4 ppmv (an ensemble spread of 9.2 ppmv), in 1850, to between 368.5 and 432.1 ppmv (a spread of 63.6 ppmv), in 2014. Table 3 shows the changes and trends in CO₂ concentration simulated by each ESM during the period of rapidly increasing CO₂ (1950–2014). Although the MME long-term trend is in good agreement with the observation, the inter-model differences in CO₂ concentrations increase with time from 27.7 ppmv in 1950 to 63.6 ppmv in 2014. This leads to a large range of simulated trends (1.00 to 1.57 ppmv yr^–1). In contrast, the CMIP5 ESMs systematically overestimate the CO₂ concentration after 1950 (Fig. 2b), which is consistent with the results of Hoffman et al. (2014) and Friedlingstein et al. (2014). These biases are much smaller in CMIP6 ESMs, which may be due to the more comprehensive biogeochemical processes included in CMIP6 ESMs, such as nitrogen and nutrient limitations on land plant growth and iron limitations in ocean ecosystems (Canadell et al., 2021).

Figure 2.  Time series of the globally averaged annual mean of CO₂ concentration during 1850–2014 for (a) CMIP6 and 1850–2005 for (b) CMIP5: ESMs (colored thin solid lines), MME (red thick solid line), the observation data provided by Scripps CO₂ program (gold thick solid line) and the CMIP6 recommended observation data (black thick solid line). Units: ppmv.

Figure 3 shows the time evolution of the zonally-averaged annual mean of CO₂ concentration anomalies for the CMIP6 reference data and ESMs simulation from 1850 to 2014. The average CO₂ concentrations along each latitude circle for both CMIP6 reference data and ESMs simulations increase with time, consistent with the global average time series. The growth rate of CO₂ concentration in the northern hemisphere (NH) is slightly higher than that in the southern hemisphere (SH). The change of zonal mean CO₂ concentration simulated by the MME is consistent with observations (Fig. 3b), but the ensemble spread (e.g., twice the standard deviation, 2σ) increases from 3 ppmv in 1850 to over 40 ppmv in 2014 (Fig. 3c). For all latitudes, the zonal mean CO₂ concentration shows remarkable increases from the year 1950. Hence, we estimate the trends of the zonally averaged annual mean of CO₂ concentration from 1950 to 2014 relative to 1850–1879. As shown in Fig. 4, the highest CO₂ concentration growth rate values in the NH are between 30°–50°N. As for the CMIP6 reference data, the average growth rate of CO₂ concentration in the NH from 1950 to 2014 is estimated to be about 1.39 ppmv yr^–1, and its SH counterpart is close to 1.33 ppmv yr^–1. The CO₂ concentration growth rate for the MME is slightly lower than the CMIP6 reference data by 0.03 ppmv yr^–1. The MME can reasonably reproduce the main features of the meridional distribution of CO₂ concentration trends with high (low) rates of increase in the northern (southern) hemisphere, with the largest values located in the mid-latitudes in the NH. The ESMs can also reasonably simulate the meridional distribution of CO₂ concentration trends, indicating that the model biases are mainly due to a systematic deviation in CO₂ concentration trends on the global scale.

Figure 3.  Time evolution of zonally averaged annual mean of CO₂ concentration for 1850–2014 relative to 1850–1879: (a) the CMIP6 recommended observation data, (b) MME, and (d)–(o) ESMs. Panel (c) shows the model spread among the 12 ESMs expressed as twice the standard deviation (2σ). Units: ppmv.

Figure 4.  Trends of the zonally averaged annual mean of CO₂ concentration for 1950–2014 relative to 1850–1879: ESMs (colored thin solid lines), MME (red thick solid line), and the CMIP6 recommended observation data (black thick solid line). Units: ppmv yr^–1.

The inter-model differences in the historical evolution of CO₂ concentration in ESMs (as shown in Figs. 2 and 3) are mainly attributed to their biases in simulated CO₂ fluxes. Variation of the global mean of CO₂ concentration in the atmosphere is generally determined by anthropogenic CO₂ emissions and natural CO₂ exchanges between land and atmosphere and between ocean and atmosphere, which are generally presented in terms of CO₂ flux. Figure 5 shows the yearly global mean CO₂ concentration and CO₂ flux to the atmosphere for BCC-CSM2-MR, MRI-ESM2-0, and UKESM1-0-LL from 1850 to 2014, in which negative values of CO₂ flux denote uptake by terrestrial or marine ecosystems. Only these three models provided CO₂ flux data to download from the CMIP6 website (https://esgf-node.llnl.gov/search/cmip6/). Among the three models, the values of net CO₂ flux (i.e., the sum of anthropogenic CO₂ emissions and natural CO₂ exchange with land or ocean) in BCC-CSM2-MR are relatively low, corresponding to low atmospheric CO₂ concentration; the net CO₂ flux in UKESM1-0-LL is relatively high after the 1930s, corresponding to the higher atmospheric CO₂ concentration in the second half of the 20th century (Figs. 5a, b).

Figure 5.  Time series of the globally averaged annual mean of (a) CO₂ concentration, (b) net CO₂ flux (9-yr running average), (c) net CO₂ flux, (d) anthropogenic CO₂ flux, (e) land-atmosphere CO₂ flux, and (f) ocean-atmosphere CO₂ flux for 1850–2014: BCC-CSM2-MR (deep-pink thin solid lines), MRI-ESM2-0 (cyan thin solid lines), UKESM1-0-LL (purple thin solid lines), the CO₂ observation data provided by Scripps CO₂ program (gold thick solid line), the CMIP6 recommended CO₂ observation data (black thick solid line), the CO₂ flux estimated by GCB2021 (G_ATM is the growth rate of atmospheric CO₂ concentration) (dark blue thick solid lines), and the CMIP6 recommended anthropogenic CO₂ emissions (gray thick solid line). Positive values in panels (b)–(f) represent a flux to the atmosphere. Units: ppmv for CO₂ concentration and GtC yr^–1 for CO₂ flux.

As shown in Fig. 5, both the globally averaged CO₂ concentration and CO₂ flux show rapid increases after 1960. The main source of increased CO₂ in the atmosphere is anthropogenic CO₂ emissions. The anthropogenic emissions of CO₂ into the atmosphere are over 4 GtC yr^–1 (Fig. 5d), although their values vary slightly between the ESMs. These differences likely arise from the pre-processing of CMIP6-prescribed emissions to the resolution of the models. The anthropogenic CO₂ emissions in Fig. 5d exceed the total CO₂ uptake by the land and ocean and cause a net CO₂ flux into the atmosphere almost every year (Fig. 5c). Referring to the calculation method of Friedlingstein et al. (2022), we quantified the 1960–2014 averaged partitioning of anthropogenic CO₂ emissions burden into the atmosphere (AF), the land (LF), and the ocean (OF) from the three ESMs (Table 4). Compared with GCB2021 (Friedlingstein et al., 2022), the AF value simulated by BCC-CSM2-MR and UKESM1-0-LL is about 3% lower, while the LF value is about 5% higher; the LF value simulated by MRI-ESM2-0 is 6% lower, while the OF value is 7% higher. BCC-CSM2-MR and UKESM1-0-LL reproduce a stronger CO₂ uptake by terrestrial ecosystems than by marine ecosystems, as derived by GCB2021.

It is noted that land-atmosphere CO₂ fluxes exhibit much more remarkable year-to-year variations than the ocean–atmosphere CO₂ fluxes. The average amplitude of variations in land–atmosphere CO₂ flux among ESMs is 1.8 GtC yr^–1, which is about three times that in ocean–atmosphere CO₂ flux (Figs. 5e, f). Given the long lifetime of CO₂, the strong interannual variability of land–atmosphere CO₂ flux may lead to a cumulative increase in the inter-model differences of CO₂ concentration. Therefore, the uncertainty of the net CO₂ flux mainly comes from the land–atmosphere CO₂ flux, which is consistent with the conclusions of IPCC AR5 and AR6 (Ciais et al., 2013; Friedlingstein et al., 2014; Canadell et al., 2021).

Exploring the global spatial distribution of CO₂ concentration is helpful for understanding the uncertainties in ESMs. Utilizing the relatively abundant observational data from recent years, we compared the site-based observations and ESM simulations of the annual-mean atmospheric CO₂ concentrations from 1995–2014 (Fig. 6). From the site observations, Europe, East Asia, and the eastern United States can be considered as regions with high CO₂ concentration (e.g., 5–10 ppmv above the global average) (Fig. 6a). The MME reproduces the distribution of high-CO₂ concentration in these regions (Fig. 6b). All ESMs can simulate the meridional and regional features of CO₂ concentration (Figs. 6d–o), but the spatial variations of CO₂ concentration are quite different among the ESMs. The model spread (2σ) of CO₂ concentration differences is higher than 10 ppmv in northern Russia, Eastern China, the eastern United States, northern South America, and southern Africa (Fig. 6c). It seems that these inter-model differences are mainly due to the contributions of two model outliers: MIROC-ES2L and UKESM1-0-LL.

Figure 6.  Global distribution of annual mean CO₂ concentration anomalies relative to the global mean for 1995–2014: (a) site observations, (b) MME, and (d)–(o) ESMs. Panel (c) shows the model spread among the 12 ESMs expressed as twice the standard deviation (2σ). The global mean is marked at the top-right corner of each panel. Units: ppmv.

Figure 7 shows the multi-model ensemble mean simulation and the model spread of the spatial distribution of CO₂ concentration differences for 1995–2005 in CMIP6 and CMIP5 ESMs. BCC-CSM1-1 is not included in the CMIP5 ensemble as it does not consider the spatial distribution of atmospheric CO₂, and only the global mean of the carbon budget is considered (Wu et al., 2013). Both the CMIP6 MME and the CMIP5 MME can simulate the north-south difference of CO₂ concentration and the three high-CO₂ concentration centers over Europe, eastern China, and the eastern United States (Figs. 7a, b). Compared with CMIP6, although the global mean CO₂ concentration is about 8 ppmv larger in the CMIP5 MME, the spatial distribution of CO₂ concentration is relatively smoother with smaller CO₂ concentration over the three high CO₂ concentration centers. The model uncertainties of CO₂ concentration anomalies are large in the three high-CO₂ concentration centers in the NH in CMIP6 and CMIP5 ESMs. In addition, the model uncertainties are also large over the tropical rain forests, such as tropical Africa, Southeast Asia, and South America (Figs. 7c, d).

Figure 7.  Global distribution of annual mean CO₂ concentration anomalies relative to the global mean for 1995–2005: (a) CMIP6 MME, (b) CMIP5 MME (BCC-CSM1-1 is not included). The model spread among (c) the 12 CMIP6 ESMs and (d) the 10 CMIP5 ESMs expressed as twice the standard deviation (2σ). The global mean is marked at the top-right corner of each panel. Units: ppmv.

The model uncertainties of CO₂ concentration over the ocean in ESMs, which may be mainly caused by the difference in ocean–atmosphere CO₂ fluxes among ESMs, are less than those over land. As described in Wu et al. (2013), the air-sea CO₂ flux depends on the difference between the CO₂ concentration of the water vapor-saturated air and the sea-surface aqueous CO₂ concentration, and the magnitude of wind speed near the surface. The simulation deviation of sea surface CO₂ concentration due to the biases of sea surface temperature (SST), dissolved inorganic carbon, and total alkalinity may be the main reason for the difference in the simulations of air-sea CO₂ flux (Jing et al., 2022).

Noticeable simulation uncertainty of CO₂ concentration over land may be mainly related to the large difference in land–atmosphere CO₂ fluxes among ESMs. The land–atmosphere CO₂ flux mainly involves the net change in carbon storage in the ecosystem, commonly called net ecosystem productivity (NEP), including fluxes from vegetation, detritus, and mineral soil. It is just the residual of gross primary productivity (GPP) of terrestrial vegetation by deducting the plant autotrophic respiration (R_veg) and the heterotrophic soil respiration (R_soil). The magnitude of NEP is less than that of all the three terms, GPP, R_veg, and R_soil, and easily introduces a large uncertainty to the land–atmosphere CO₂ flux simulations among ESMs, within which different treatments are used in land CO₂ schemes. As listed in Table 5.4 of IPCC AR6 on the characteristics of land carbon cycle components of most CMIP6 ESMs (Arora et al., 2020; Canadell et al., 2021), the number of carbon pools and the number of plant functional types in the land CO₂ schemes are different among the ESMs. Only a few ESMs represent fire, dynamic vegetation cover, permafrost carbon, and nitrogen cycles in land CO₂ schemes, and most ESMs do not or just partially represent them. The simulated deviation of climate (such as temperature, precipitation, etc.) in ESMs may also cause large uncertainties in the simulation of terrestrial carbon flux by affecting these terrestrial carbon cycle processes (Ahlström et al., 2017; Bonan et al., 2019).

A comparison of the simulated CO₂ concentration with the data at 49 observation sites in the globe (Fig. 8) shows that the mean difference between the MME results and the observations (2 ppmv) is smaller than that between each ESM and the observations (–27.3 to 28.8 ppmv). As shown in Figs. 8b–m, large model biases exist in MIROC-ES2L and UKESM1-0-LL, and their spatial standard deviations reach 6.8 and 7.2 ppmv, respectively, while the other ESMs range around 2–3 ppmv. Meanwhile, the correlation coefficients (0.86–0.88) between these two models and the site observations are also relatively lower than those between other models and site observations (0.98–0.99).

Figure 8.  Comparison of the annual mean CO₂ concentrations from 1995 to 2014 at 49 observation sites with those simulated by (a) MME and (b–m) ESMs at the corresponding sites. Here, the model simulation at each site shows the data interpolated from the model grids to each site. The black dashed line shows a 1:1 straight line for reference. Each panel also shows the mean and uncertainty (±1 standard deviation, ±1σ) of the deviations (DEV) between simulated and observed CO₂ concentrations and the correlation coefficient (r) between simulation and observation. Units: ppmv.

At regional scales, the CO₂ concentration can have strong seasonal cycles; thus, we calculated the seasonal amplitude of atmospheric CO₂ concentration, defined as the difference between the maximum and minimum monthly mean CO₂ concentration during a year. Figure 9 shows the temporal evolution of the seasonal amplitude of zonal mean CO₂ concentration for 1850–2014 from CMIP6 reference data and ESMs simulations. Similar to the zonal distribution of CO₂ concentration, the seasonal amplitude of CO₂ concentration in the NH is generally higher than that in the SH and has an increasing trend after the 1950s, with the largest trends located near 60°N (Fig. 9a). Compared with the CMIP6 reference data, the MME reasonably reproduces the meridional variations of the seasonal amplitude of zonal mean CO₂ concentration and the increasing amplitudes in the later period. The largest seasonal variation of CO₂ occurs near 60°N, with increases of more than 6 ppmv by the 2010s compared with the 19th century (Fig. 9b). Most ESMs can also capture the meridional difference and increasing seasonal amplitudes of zonal mean CO₂ concentration (Figs. 9d–o). However, there is a remarkable spread across the ESMs. As shown in Fig. 9c, the spread (2σ) exceeds 24 ppmv in the vicinity of 40°–70°N, significantly higher than the MME values. This means that the ESMs simulation of the seasonal amplitude of CO₂ concentration is highly uncertain. As the mean of three ESMs (BCC-CSM2-MR, MRI-ESM2-0, and UKESM1-0-LL) in Fig. 10 shows, the seasonal amplitude increase of natural CO₂ fluxes is much larger than that of anthropogenic CO₂ fluxes after 1950, especially around 60°N, so the increase in seasonal amplitude of atmospheric CO₂ concentration is mainly related to seasonal variations of natural CO₂ fluxes. In Fig. 9, the increase in seasonal amplitude of CO₂ concentration with time may be strongly correlated with the amplified vegetation productivity in the NH caused by the interaction of recent climate change and vegetation dynamics that have been suggested by previous studies (Graven et al., 2013; Forkel et al., 2016; Piao et al., 2018; Bastos et al., 2019).

Figure 9.  Time evolution of the seasonal amplitude of zonal mean CO₂ concentrations for 1850–2014: (a) CMIP6 recommended observation data, (b) MME, and (d)–(o) ESMs. Panel (c) shows the model spread among the 12 ESMs expressed as twice the standard deviation (2σ). Units: ppmv.

Figure 10.  The increase in the seasonal amplitude of zonal mean (a) anthropogenic CO₂ flux, (b) natural CO₂ flux, and (c) net CO₂ flux of ensemble mean of BCC-CSM2-MR, MRI-ESM2-0, and UKESM1-0-LL for 1950–2014 relative to 1950. Units: gC m^–2 mon^–1.

We further explored the global distribution of the annual mean of the seasonal amplitude of CO₂ concentrations for 1995–2014 (Fig. 11). Observations and MME results show that the seasonal amplitude of CO₂ concentration over land is higher than that over the ocean and that the mid-high latitudes of the NH, such as Europe, Eastern China, eastern United States, and Alaska, are areas with high seasonal amplitude of CO₂ concentration (Figs. 11a, b). MME results show that the seasonal amplitudes are higher than 22 ppmv in Europe, North Asia, eastern China, and eastern North America and higher than 12 ppmv in northern South America and southern Africa. Most ESMs can simulate the meridional and regional differences in the seasonal amplitude of CO₂ concentrations (Figs. 11d–o). However, there are some notable exceptions: for example, compared with site observations, MIROC-ES2L overestimates the seasonal amplitude of CO₂ concentration by 30 ppmv in the NH, Southern Africa, and South America.

Figure 11.  Global distribution of the annual mean of the seasonal amplitude of CO₂ concentrations for 1995–2014: (a) site observations, (b) MME, and (d)–(o) ESMs. Panel (c) shows the model spread among the 12 ESMs expressed as twice the standard deviation (2σ). The global mean is marked at the top-right corner of each panel. Units: ppmv.

The regions with high seasonal-amplitude values of CO₂ concentration correspond to those areas that show a large model spread (Fig. 11c), further noting that the value of the model spread is even larger than that of the seasonal amplitude of CO₂ concentration in the MME results (Fig. 11b). In general, the seasonal amplitude of CO₂ concentration and its model spread over oceans are smaller than those over land at the same latitude; the seasonal amplitude of CO₂ concentration and its model spread over land in the NH are higher than those in the SH.

We further examine the mean seasonal variation of CO₂ concentration for 1995–2014 (Fig. 12) in the NH, SH, and eight major sub-regions (Fig. 11a). MIROC-ES2L was not included in the analysis because the simulated amplitude is anomalously strong compared with observations. The observed seasonal amplitude of CO₂ concentration in the NH is 11.7 ppmv (Fig. 12a) and about 4.1 ppmv in the SH (Fig. 12b). The relatively large portion of the SH covered by oceans may be one of the important factors for the relatively small seasonal variability of CO₂ concentration there. In the NH, winter and summer are the peak and trough periods of CO₂ concentration, respectively. This seasonal cycle is mainly caused by the release of CO₂ from the decomposition of soil organic matter in winter and the absorption of CO₂ by the photosynthesis of terrestrial ecosystems in summer (Keeling et al., 1996; Wenzel et al., 2016). The seasonal cycles of CO₂ concentration simulated by the MME are generally consistent with the site observations, but the amplitude is slightly smaller, and the period of low values in the year is slightly earlier than the observations. Both observations and the MME show that the seasonal amplitudes of CO₂ concentrations in Europe, North Asia, and northern North America are generally higher than those in East Asia and southern North America (Figs. 12c–g). Notably, the MME results over the SH show that the seasonal amplitudes in South America and southern Africa are about 5 ppmv, and those in Australia are only around 2.5 ppmv (Figs. 12h–j).

Figure 12.  Mean seasonal cycle (expressed as monthly anomalies) of CO₂ concentration for 1995–2014: (a) Northern Hemisphere, (b) Southern Hemisphere, (c) Europe (35°–70°N, 0°–50°E), (d) North Asia (50°–70°N, 60°–150°E), (e) East Asia (25°–50°N, 90°–150°E), (f) Northern North America (50°–72°N, 165°–60°W), (g) Southern North America (25°–50°N, 120°–60°W), (h) South America (55°S–0°, 75°–45°W), (i) Australia (45°–10°S, 115°–155°E), and (j) Southern Africa (40°S–0°, 10°–40°E). Colored thin solid lines, red thick solid lines, and black thick solid lines represent the ESMs, MME, and observations, respectively. The observation values are the average of all sites in the selected area. MIROC-ES2L was excluded due to the large deviation of the simulated seasonal amplitude from the observation. Each panel also shows the mean and uncertainty (±1 standard deviation, ±1σ) of the simulated seasonal amplitude and the observed seasonal amplitude. Units: ppmv.

It is worth noting that the spatial distribution of the simulated seasonal amplitude of CO₂ concentration (Fig. 11b) is not only consistent with that of annual-mean CO₂ concentration (Fig. 6b) but is also correlated with the global distribution of forests (Hansen et al., 2013) and the type of vegetation (Olson et al., 2001). In ESMs, the seasonal amplitudes over the mid- and high-latitude forests in the NH are generally higher than those in the broad-leaved forest belts in East Asia and the eastern United States (Figs. 11d–o; Figs. 12c–g); the desert areas in North Africa, West Asia, and the western United States, and the Qinghai-Tibet Plateau are areas with low seasonal amplitudes (Figs. 11d–o); as the land in the SH is mainly covered by tropical rain forests, tropical grasslands, and deserts, the seasonal amplitudes of CO₂ concentrations in these areas are also smaller (Figs. 11d–o; Figs. 12h–j).

The simulation of atmospheric CO₂ concentration is closely related to the CO₂ fluxes. Figure 13 shows the MME results of the annual mean and seasonal amplitude of anthropogenic CO₂ flux, natural CO₂ flux, and net CO₂ flux for 1995–2014 (colored figure), as well as the zonal mean for three ESMs (BCC-CSM2-MR, MRI-ESM2-0, and UKESM1-0-LL) (colored curves). The high-value areas of anthropogenic CO₂ emissions are located around 45°N, and the highest values are mainly in Europe, eastern China, and the eastern United States (Fig. 13a). The MME results show that land areas, other than deserts (such as the Sahara Desert) and high-altitude areas (such as the Qinghai-Tibet Plateau and the Rocky Mountains), are natural CO₂ sinks, and most ocean areas except for tropical oceans are also CO₂ sinks (Fig. 13b), which is consistent with the results of Takahashi et al. (2009) and Friedlingstein et al. (2022). From the meridional distribution of the zonal mean, the simulated difference of natural CO₂ flux is significantly larger than that of anthropogenic CO₂ flux, which is the main factor causing the inter-model differences in the net CO₂ flux (Figs. 13a–c).

Figure 13.  The global distribution of the annual means of (a) anthropogenic CO₂ flux, (b) natural CO₂ flux, and (c) net CO₂ flux of the ensemble mean of BCC-CSM2-MR, MRI-ESM2-0 and UKESM1-0-LL for 1995–2014 are shown. The global distribution of the annual means of the seasonal amplitude of (d) anthropogenic CO₂ flux, (e) natural CO₂ flux, and (f) net CO₂ flux of the ensemble mean of BCC-CSM2-MR, MRI-ESM2-0 and UKESM1-0-LL for 1995–2014 are shown. The right parts of panels (a)–(c) and panels (d)–(f) represent the meridional distribution of the zonal mean of CO₂ fluxes and their seasonal amplitudes, respectively: BCC-CSM2-MR (deep-pink thin solid lines), MRI-ESM2-0 (cyan thin solid lines), UKESM1-0-LL (purple thin solid lines) and the MME (black thick solid lines). The global mean value is marked at the top-right corner of each panel. Positive values represent a flux to the atmosphere for CO₂ flux. Units: gC m^–2 yr^–1 for CO₂ flux and gC m^–2 month^–1 for the seasonal amplitude of CO₂ flux.

As shown in Fig. 13c, yearly mean net CO₂ fluxes in the NH mid-latitudes over land except for the Tibetan Plateau and the Mongolia Plateau, and in the subtropical regions of Southern Africa and South America, are mainly due to anthropogenic emissions, while in other regions they mainly come from natural contributions. But the seasonal variation of CO₂ concentration is substantially determined by the seasonal cycles of natural CO₂ fluxes (Figs. 13d–f), and the highest values of seasonal amplitude of CO₂ concentration well correspond with those of the seasonal amplitudes of net CO₂ fluxes (Fig. 11, Fig. 13f). There are weak seasonal variations in anthropogenic CO₂ emissions data that are provided for the CMIP6 experiments. Therefore, the simulation difference in the seasonality of natural CO₂ fluxes is the main reason for the simulation uncertainty in the seasonal variation of CO₂ concentration among CMIP6 ESMs.

This paper evaluates the performance of 12 CMIP6 ESMs in their ability to reproduce the spatial inhomogeneity of atmospheric carbon dioxide concentration and discusses the sources of uncertainty in model predictions. The main findings are as follows.

(a) The MME can reasonably simulate the historical evolution and spatial structures of CO₂ concentration, including the slightly faster growth rate of CO₂ concentration in the NH compared with the SH and the CO₂-concentration centers located in Europe, East Asia, and the eastern United States. Compared with CMIP5, the CMIP6 MME reduces the overestimation of CO₂ concentration after 1950 and simulates an average spatial distribution closer to surface site observation. However, the inter-model differences in CO₂ concentration are substantial on regional scales and grow with time. The model spread of interannual variability in CO₂ concentration is related to differences in the net CO₂ flux among ESMs, mainly due to contributions from natural land–atmosphere CO₂ exchanges.

(b) The CO₂ concentration shows strong seasonal variations. Regions with large seasonal variations are generally found where the climatological, annual-mean CO₂ concentrations are also high. The amplitude of the CO₂ seasonal variation is also affected by the types of surface vegetation. The MME can reasonably reproduce the meridional dependencies of the seasonal amplitude of CO₂ concentration, and the trend towards larger seasonal amplitudes after the 1950s are mainly due to increased amplitudes of natural CO₂ fluxes. There are also large uncertainties in the seasonal amplitudes simulated by the ESMs, especially in the regions with high-amplitude seasonal cycles. Analysis of the CO₂ fluxes shows that the seasonal variation of CO₂ concentration is mainly attributed to the seasonal variation of natural CO₂ flux and that the inter-model differences in seasonal variability of natural CO₂ flux are the main source of model uncertainty in seasonal variability of CO₂ concentration.

In general, we find that the inter-model differences in the interannual and seasonal variability of CO₂ concentrations are closely correlated to the simulation of natural CO₂ fluxes. Therefore, improving the ability of models to simulate land–atmosphere and ocean–atmosphere CO₂ exchanges is key to improving their predictions of CO₂ concentration and its variability. To do so, we must investigate inter-model differences in the parameterized processes regarding the land, atmosphere, and ocean components that influence the carbon cycle within the ESMs.

Aside from the horizontal distribution of CO₂ concentration, the vertical distribution of the CO₂ concentration, as simulated by the ESMs, is also of interest and needs to be evaluated. Meanwhile, in addition to CO₂ flux, the spatial inhomogeneity and vertical distribution of atmospheric CO₂ concentration are also affected by atmospheric circulation. The vertical distribution of CO₂ concentration and the effects of atmospheric circulation upon it are to be analyzed and discussed in a forthcoming paper.

Data availability. All the CMIP6 and CMIP5 model data can be freely downloaded from the Earth System Grid Federation (ESGF) nodes (https://esgf-node.llnl.gov/search/cmip6/, https://esgf-node.llnl.gov/search/cmip5/). The WDCGG data is freely available at https://gaw.kishou.go.jp/. Both the CMIP6 recommended CO₂ concentration data and anthropogenic CO₂ emission data are available at https://esgf-node.llnl.gov/search/input4mips/. The CO₂ concentration from the Scripps CO₂ program is available at https://scrippsco2.ucsd.edu/data/atmospheric_co2/icecore_merged_products.html. The GCB2021 data are available at https://doi.org/10.18160/gcp-2021.

Acknowledgements. This work was supported by the National Natural Science Foundation of China (Grant No. 42230608) and the UK-China Research & Innovation Partnership Fund through the Met Office Climate Science for Service Partnership (CSSP) China as part of the Newton Fund.