We evaluated carbon fluxes from ESMs and SCMs in historical and future periods. In the historical period, the differences between estimates by simple and complex models could be attributed to the procedure of observational constraining that is present in the majority of SCMs but not applied in ESMs. In the future period, the differences could be partly explained by a few model outliers (both ESMs and SCMs). Besides, the differences in future scenarios arose from the differences in the way how LUC emissions were calculated and the assumptions on carbon-concentration and carbon-climate feedbacks. In this section, we discuss these sources of the differences in projections between simple and complex model.
3.1 Performance of models in the historical period
The larger warming estimated by CMIP6 ESMs than by SCMs over the historical period was discussed in the existing studies and can be attributed to (i) a higher climate sensitivity of CMIP6 ESMs (on average) and (ii) the fact that SCMs are constrained to historical observations (Liddicoat et al. 2021; Nicholls et al. 2021) (Figure 2a). The estimates of total (FF and LUC) compatible CO2 emissions by CMIP6 ESMs are in their majority within the uncertainty range. The corresponding estimates by SCMs are lower than the GCB2021 historical CO2 emissions (Figure 2c). CMIP6 ESMs tend to estimate higher compatible FF emissions than SCMs and higher cumulative compatible FF emissions than observation-based FF emissions over the last three decades (Figure 2f, h–m). Consistent with GCB2021 estimates of total compatible emissions and higher than GCB2021 estimates of compatible FF emissions by ESMs imply their underestimation of LUC emissions, discussed before (Melnikova et al. 2022) (Figure 2g).
In the concentration-driven model simulations, the estimates of compatible FF emissions are directly linked to the land and ocean carbon uptakes. Both ESMs and SCMs underestimate decadal ocean carbon uptake relative to estimates by Li et al. (2016), who reduced the carbon flux uncertainty using a Bayesian fusion approach. But the cumulative ocean carbon uptake estimates by the models are within the uncertainty range of historical estimates by Gruber et al. (2019) and GCB2021. ESMs, with a few exceptions, estimate slightly higher land carbon sink than historical observation-based estimates and SCMs over the historical period (Figure 2b, h–m). The higher estimates of cumulative land carbon uptake by ESMs are not fully compensated by the lower estimates of cumulative ocean carbon uptake (relative to historical observation-based datsets), which leads to higher compatible FF emissions. Most SCMs estimate decadal and cumulative land carbon uptake consistently with historical observation-based estimates. Still, the lower estimates of cumulative ocean carbon uptake by SCMs lead to lower compatible FF emissions estimates.
3.2 Emergent constraints
We evaluated the model response to the future forcing using emergent constraints (EC). EC approaches were broadly used in CMIP5 and CMIP6 communities on future warming (Tokarska et al. 2020; Schlund et al. 2020) and carbon cycle (Cox et al. 2013; Varney et al. 2020; Wenzel et al. 2014). While existing studies offer ECs on specific aspects of the carbon cycle, such as tropical carbon sensitivity to warming (Cox et al. 2013; Wenzel et al. 2014) or soil carbon turnover (Varney et al. 2020), we attempted to develop a statistical relationship between global carbon fluxes. To this end, we plotted the estimates of 2015–2049 and 2065–2099 cumulative carbon fluxes against the estimates of 1980–2014 cumulative fluxes over the historical period (Figures S9 and S10). We showed that the ESMs that estimate higher land and ocean uptakes during the historical period give higher future carbon uptake in high CO2 concentration scenarios. The ECs developed for ESMs weaken (in terms of statistical significance) with time so that they are more reliable in the earlier future period and are not sustained in the low CO2 concentration and overshoot pathways. This may be related to the more complex nature of mitigation scenarios that include ramp-up and ramp-down phases of CO2 concentration and GSAT, as well as assumptions on implementing the land-based CO2 removal technologies in the climate mitigation scenarios that influence the land carbon sink. A few model outliers also weaken the ECs. For example, compared to other models, WASP2 and CanESM5 simulate much larger increases in ocean and land carbon uptake under high-concentration scenarios. The time series of the future carbon fluxes for each model confirmed these deviations (Figures S13–S18). There is a weaker (less reliable) EC for SCMs due to the larger range of carbon cycle feedbacks to the changes in CO2 and GSAT under SSPs, as well as the historical constraining of SCMs’ carbon cycle feedbacks (see section 3.4.3).
3.3 Performance of models in the future scenarios
The discrepancies in the estimates of GSAT increase between CMIP6 ESMs and SCMs in future scenarios are consistent with those in the historical period (Figure 3a). While the temperature response is always higher in ESMs than in SCMs, the compatible CO2 emissions are nearly consistent between ESMs and SCMs (Figures 3, S11–18). ESMs estimate slightly lower (although within ensemble spread) cumulative emissions in high-concentration and slightly higher emissions in low-concentration SSPs compared to SCMs. The larger GSAT increase estimated by ESMs, and consistent cumulative compatible emissions between ESMs and SCMs indicate that ESMs have higher TCRE than SCMs in the historical period and future SSP scenarios if we do not consider the contributions from non-CO2 forcing (Figure S19).
LUC emission data are largely inconsistent between ESMs and IAMs partly because of the discrepancies that emerge during the translation of the data from IAMs to ESMs (Melnikova et al. 2022) (Figure 3a). ESMs estimate lower positive LUC emissions, possibly because they do not include forestry and managed land practice. Still, they also estimate smaller negative LUC emissions relative to emissions created by IAMs, possibly because LUC emissions reported by ESMs do not account for future forest regrowth.
Both ESMs and SCMs estimate higher future compatible FF emissions than those simulated by IAMs (Figure 3c). This issue has been previously discussed by Liddicoat et al. (2021) and may be related to lower estimates of land and ocean carbon uptakes by MAGICC7.0, which was used with IAMs to generate the CMIP6 ScenarioMIP input CO2 concentrations. MAGICC7.0 was calibrated to CMIP5 ESM carbon cycle to include permafrost CO2 and methane feedbacks (slightly different version from MAGICCv7.5.1 of RCMIP phase 2) (Meinshausen et al. 2020; Nicholls et al. 2021). MAGICCv7.5.1 estimates a lower land carbon uptake than observation-based datasets during the historical period and than the model ensemble means in future scenarios (Figures 1, S15–16). However, the lower land carbon uptake estimates by MAGICCv7.5.1 are partly compensated by higher ocean carbon uptake estimates, especially in future scenarios. Thus, the total future carbon uptake simulated by MAGICCv7.5.1 is lower than those by other models. Such deviation of the carbon cycle behaviour of MAGICC from other models has broader implications because MAGICC is widely used for future projections informing policies and for translating the IAM emissions to concentrations used by ESMs.
Despite the general agreement of the estimates of cumulative compatible FF emissions between ESMs and SCMs, the estimates of land and ocean carbon uptakes deviate. SCMs estimate higher ocean carbon uptake than ESMs in the historical period and future SSPs. The inter-model spread of cumulative ocean carbon flux in future scenarios is also larger in SCMs (Figure S9). The estimates of cumulative NBP are larger in ESMs than SCMs over the historical period and all future scenarios, except for SSP4-3.4, which assumes low FF but high LUC emissions relative to other SSPs (Figure 1, Table 3).
3.4 The sources of discrepancies in the carbon cycle between ESMs and SCMs
The discrepancies between ESM- and SCM-ensemble mean may originate from differences in the representation of some specific climate or carbon cycle processes and due to single or few model outliers that impact ensemble means. Here we discuss how both could lead to the discrepancies in the carbon cycle between ESMs and SCMs.
3.4.1 Model outliers
We defined outlier models simply as the ESMs/SCMs that estimate maximum/minimum global land and ocean carbon uptake (maximum/minimum, or upper/lower ends) over 1850–2014 historical and 2015–2100 future SSP scenarios (Tables S1 and S2). The model outliers vary depending on the target carbon flux and SSP scenario, e.g., low- vs. high- FF or LUC emission pathways, increasing CO2 concentration, and temperature vs. mitigation pathways. Besides, the models that provide data vary with the target scenario.
In the case of land carbon flux, CanESM5 and CNRM-ESM2-1 estimate the highest NBP during historical and future periods among ESMs; OSCARv3.1 and ACC2 estimate the highest NBP among SCMs. The two ESMs, CanESM5 and CNRM-ESM2-1, do not include an nitrogen cycle explicitly, a process that is shown to limit the land carbon uptake through nitrogen limitations of plant growth (Arora et al. 2020). As for SCM outliers, the land carbon cycle of the version of ACC2 adopted in this study has limited sensitivity to GSAT increase. The land carbon uptake by OSCARv3.1 was not historically constrained (Quilcaille et al. 2022).
In the case of ocean carbon flux, ESMs are fairly consistent with each other (Figures S5 and S17). However, CanESM5 estimates slightly lower ocean carbon uptake than other ESMs in all future SSPs. This has been shown in an existing study (Arora et al. 2020), but the reasons remain unclear. On the contrary, SCMs show a large inter-model spread. WASP-v2 (followed by MAGICCv7.5.1) and MCE-v1-1 give maximum and minimum ocean carbon fluxes, respectively, in the majority of future scenarios. MCE-v1-1, which shows the lowest future ocean uptake among SCMs, provides an estimate of ocean carbon uptake closest to ESMs. Furthermore, the response of ocean carbon fluxes to declining CO2 and temperature is somewhat delayed in some SCMs, particularly SCM4OPTv2.1 (Figure S17). Removing the ESMs and SCMs that produce the maximum/minimum cumulative fluxes over a target scenario improves the agreement of the carbon flux estimates between concentration-driven ESMs and SCMs and reduces their ensemble spreads but not for all the scenarios (Figure S20). Removing model outliers is less effective on improving the agreement between models in the scenarios that were run by few (<5) models.
3.4.2 LUC emissions
The presence of outliers cannot fully explain the discrepancy in the carbon cycle between ESMs and SCMs. After removing outliers, although, of a smaller magnitude, the discrepancy in the future ocean carbon uptake between ESMs and SCMs persists in all SSPs (Figure S9). The differences in the land carbon fluxes by ESMs and SCMs arise from several sources. They are partly explained by the LUC emissions that are highly uncertain already over the historical period (van Marle et al. 2022).
On the one hand, CMIP6 ESMs provide the simulation outputs of NBP, i.e., land carbon uptake accounting for incompletely quantified LUC emissions via the “fLuc” ESM variable, thus, underestimating LUC emissions (Melnikova et al. 2022) (Figures 3 and S14). Additional simulations for each SSP scenario with a fixed land cover (similar to the “hist-noLu” simulation of Land-Use MIP (LUMIP)) are required to separate the “natural” land sink from the gross LUC emissions, including the foregone sink of land exposed to LUC. On the other hand, most SCMs do not estimate LUC emissions but directly use the prescribed values that come from several methods and models (Le Quéré et al. 2016; Gütschow et al. 2016) in the historical period and from IAMs in future scenarios. This may lead to underestimating the impact of LUC on the land carbon uptake, e.g., the reduced carbon turnover time in LUC-impacted ecosystems (Erb et al. 2016; Melnikova et al. 2022). Furthermore, during the historical period, the global net LUC emissions are positive (i.e., directed to the atmosphere), but they may be either negative or positive in future scenarios. Thus, the deviations in LUC emission estimates between ESMs and SCMs (via IAMs) may go in either direction.
3.4.3 Carbon-concentration and carbon-climate feedbacks
Besides the discrepancy in the LUC component, ESMs and SCMs differ in the response of future cumulative land and ocean carbon fluxes to the CO2 and GSAT changes (Figure 4). ESMs estimate higher land carbon uptake per CO2 and temperature increases. During the ramp-down phases of peak and decline scenarios, ESMs show larger inertia of the land carbon uptake (e.g., SSP1-1.9, SSP1-2.6, and SSP5-3.4-OS). In addition, unlike SCMs, ESMs show a saturation of NBP with increasing GSAT. Here we put forward two possible explanations for the discrepancy in the land carbon cycle feedbacks.
First, a large spread of NBP estimates by ESMs reaches ca. 20 GtC year-1 in 2100 under the high-concentration SSP5-8.5 scenario (Figure S14). It is primarily driven by the differences in the carbon-concentration (ꞵ) feedback, i.e., the impact of CO2 concentration changes on carbon uptake (Figures 4 and S20). The differences in the ꞵ feedback may root in the inclusion of the nitrogen cycle by the models and in carbon turnover differences(Friend et al. 2014). Most ESMs analyzed in this study include the nitrogen cycle (Table 2). Introducing the nitrogen cycle to an ESM generally weakens the ꞵ feedback at high CO2 concentrations because ecosystem nitrogen contents cannot keep up with the increased photosynthetic production, thus limiting carbon assimilation (Arora et al. 2020).
Second, some SCMs may estimate higher uptake due to their lack of carbon-climate (γ) feedback on the carbon cycle. The carbon cycle of most SCMs is historically constrained. While ꞵ feedback dominates the historical land carbon uptake (Tharammal et al. 2019), its impact is projected to decrease with future warmer temperatures (Figures 4 and S20). The γ feedback is characterized by a complex spatial variation. It is mostly positive to land in the high northern latitudes and negative in the tropics (Melnikova et al. 2021), so simulating the γ feedback requires a regional division of the models’ outputs, which is usually not available or limited to macro-regions in SCMs outputs. Besides, γ feedback to date has relatively little observational evidence on a global scale, so it is more challenging to tune in models. This adds to uncertainty in the estimates of future land carbon fluxes by ESMs.
We have used outputs of ESMs that, in addition to fully-coupled (COU) simulations, provided biogeochemically-coupled (BGC) simulations, where only the biogeochemical impact of atmospheric CO2 concentration, and not the radiative impact, is accounted for. A suite of BGC and COU simulations enables analyzing the ꞵ-driven and γ-driven changes in the carbon uptake (Figure 5). In both SSP-3.4-OS overshoot and high-CO2-concentration SSP5-8.5 scenarios, the ESM inter-model spread is dominated by the ꞵ feedback, especially over high northern latitudes. The inter-model spread for γ-driven changes in the land carbon uptake is also large, varying from globally positive to negative values (carbon source or sink) over high northern latitudes. Under an overshoot pathway, feedback amplification (Melnikova et al. 2021) may lead to either an increase γ-driven sink or source over high latitudes, depending on the utilized ESM. The SCMs that lack spatial disaggregation (with the exception of OSCAR) cannot account for the spatial heterogeneity of the γ feedback.
3.4.4 Mixing of carbon in the ocean
The differences between ESMs and SCMs also emerge in the response of ocean carbon flux to the CO2 growth rate, CO2 concentration, and GSAT (Figure 4). The increase in cumulative ocean carbon uptake with increasing CO2 growth rate, CO2 concentration, and GSAT slows down in the ESMs but not SCMs. The discrepancies in the ocean carbon flux may be attributed to the nonlinearities of the carbon-concentration and carbon-climate feedbacks that are the changes in the carbon storage in response to the changes in CO2 concentration and GSAT, respectively (Gregory et al. 2009; Schwinger and Tjiputra 2018; Melnikova et al. 2021). The behavior of carbon-concentration feedback in the ocean is complex, with change in CO2 growth rate dominating the flux variability on year-to-year timescales (i.e., system response to the forcing rate of change) and change in CO2 concentration dominating the variability on decadal timescales (i.e., system response to the forcing magnitude) (Schwinger and Tjiputra 2018; Melnikova et al. 2021). Thus, while the ocean carbon storage response to the forcing rate of change is nearly equal among the two types of models, the storage response to the forcing magnitude is slower in SCMs. We speculate that the discrepancy may be rooted in a faster mixing of carbon from the surface to the deep ocean in SCMs. Schwinger and Tjiputra (2018) showed that the cumulative uptake of the water masses of different ages varies in the magnitude of hysteresis, with water masses at short renewal timescales having smaller carbon uptake response hysteresis to the changes in CO2 concentrations. Similarly, the ocean carbon uptake increases less with increasing GSAT and starts to decrease sooner with decreasing GSAT under climate change mitigation overshoot-like scenarios when estimated by ESMs compared to SCMs. This may indicate the weaker ocean carbon-climate feedback of SCMs. We recommend that the discrepancies in the response of ocean carbon uptake by ESMs and SCMs are further investigated using the set of idealized experiments, including those that have abrupt CO2 increases.