The Coupled Climate-Carbon Cycle Model Intercomparison Project (C4MIP) was set up to provide a common framework to allow for comparison and consistent evaluation of carbon cycle feedbacks within ESMs and has been used across CMIP generations . This framework includes a set of idealised experiments to simplify and quantify the impact of increasing atmospheric CO2 on the climate system. In these experiments, additional effects such as land-use change, aerosols and non-CO2 greenhouse gases are not included, and nitrogen deposition is fixed at pre-industrial values .

The control simulation is known as the 1 % CO2 run (CMIP simulation 1pctCO2), where a consistent 1 % increase in atmospheric CO2 per year is prescribed (referred to in this study as the full 1 % CO2 simulation), starting from pre-industrial concentrations and running for 150 years. Additional experiments were designed to enable the CO2 and climate effects to be isolated, and these are known as biogeochemically coupled (referred to here as the “BGC” simulation) and radiatively coupled (referred to here as the “RAD” simulation) runs. In the BGC runs (CMIP6 simulation 1pctCO2-bgc and CMIP5 simulation esmFixClim1), the 1 % CO2 increase per year only affects the carbon cycle component of the ESM, while the radiation code continues to see pre-industrial CO2 values. Conversely, in the RAD runs (CMIP6 simulation 1pctCO2-rad and CMIP5 simulation esmFdbk1), the 1 % CO2 increase per year affects only the radiation code, and the carbon cycle component of the ESM continues to see just the pre-industrial CO2 value (285 ppm).

This study uses the full 1 % CO2, BGC and RAD C4MIP experiments with 10 CMIP6 ESMs : ACCESS-ESM1-5, BCC-CSM2-MR, CanESM5, CESM2, GFDL-ESM4, IPSL-CM6A-LR, MIROC-ES2L, MPI-ESM1-2-LR, NorESM2-LM and UKESM1-0-LL (see Table ). For comparison, the soil carbon feedback parameters were calculated using six CMIP5 ESMs : CanESM2, GFDL-ESM2M, IPSL-CM5A-LR, MPI-ESM-LR, NorESM1-ME and HadGEM2-ES (see Table ). The ESMs included were chosen due to the availability of the data required at the time of analysis (CMIP6: https://esgf-node.llnl.gov/search/cmip6/, last access: 4 February 2024, CMIP5: https://esgf-node.llnl.gov/search/cmip5/, last access: 6 February 2024).

To isolate the processes which make up each soil carbon feedback, we follow the framework presented in . An equation for soil carbon (Eq. ) is derived using the definition of soil carbon turnover time (τs=Cs/Rh), which is defined as the ratio of soil carbon storage (Cs) to the carbon output flux from the soil (heterotrophic respiration, Rh; ). Future soil carbon can then be defined as initial soil carbon (Cs,0) plus a change in soil carbon (ΔCs), as shown by Eq. , where the subscript 0 denotes the initial state (decadal time average at the start of C4MIP simulation). Equation () can be expanded to give Eq. (), which can be simplified to give Eq. (), as shown below. 8Cs=Rhτs9Cs,0+ΔCs=Rh,0+ΔRhτs,0+Δτs10Cs,0+ΔCs=Rh,0τs,0+τs,0ΔRh+Rh,0Δτs+ΔRhΔτs11ΔCs=τs,0ΔRh+Rh,0Δτs+ΔRhΔτs

To consider the above- and below-ground effects on soil carbon separately, the effects due to changes in vegetation productivity, represented by net primary productivity (NPP), and effects due to changes in soil carbon turnover time due to increased heterotrophic respiration (τs) are considered . However, due to the difference between the global fluxes NPP and Rh in a transient climate, an additional term is included which is defined as net ecosystem productivity (NEP=NPP-Rh). Using the definition of NEP, this can be substituted into Eq. () to give Eq. () and expanded to give an equation for ΔCs in terms of NPP, NEP and τs (Eq. , where the subscript 0 denotes the initial state). 12ΔCs=τs,0Δ(NPP-NEP)+NPP0-NEP0Δτs+Δ(NPP-NEP)Δτs13ΔCs=τs,0ΔNPP+NPP0Δτs+ΔNPPΔτs-τs,0ΔNEP-NEP0Δτs-ΔNEPΔτs

The individual terms in Eq. () are the change in soil carbon due to NPP changes (ΔCs,NPP≈τs,0ΔNPP), the change in soil carbon due to the NEP transient term (ΔCs,NEP≈-τs,0ΔNEP), the change in soil carbon due to τs changes (ΔCs,τ≈NPP0Δτs) and the transient effect on τs (ΔCs,τNEP≈-NEP0Δτs). The two additional terms are the non-linear term between NPP and τs (ΔNPPΔτs) and the non-linear term between NEP and τs (ΔNEPΔτs).

The NEP term is used to represent the transient state of the system where NPP ≠ Rh. However, it is noted that, if the initial state is in equilibrium, then the initial NEP (NEP0) will be approximately equal to zero. This would mean the ΔCs,τNEP term (representing the difference in τs from using NPP or Rh in the definition) will be negligible. Despite initialising at the start of the C4MIP simulations (decadal time average at the start of C4MIP simulation), this term is included within the analysis for completeness to ensure exact values of ΔCs.

Following on from this framework, the equation for ΔCs (Eq. ) can also be defined for the change in soil carbon in both the BGC simulations (ΔCsBGC, Eq. ) and RAD simulations (ΔCsRAD, Eq. ), where the superscripts denote the BGC and RAD simulations, respectively. 14ΔCsBGC=τs,0BGCΔNPPBGC+NPP0BGCΔτsBGC+ΔNPPBGCΔτsBGC-τs,0BGCΔNEPBGC-NEP0BGCΔτsBGC-ΔNEPBGCΔτsBGC15ΔCsRAD=τs,0RADΔNPPRAD+NPP0RADΔτsRAD+ΔNPPRADΔτsRAD-τs,0RADΔNEPRAD-NEP0RADΔτsRAD-ΔNEPRADΔτsRAD

These equations can be used to investigate the sensitivity of these isolated processes to changes in atmospheric CO2 and global temperature (T), as shown by Eqs. () and (). This is done by the explicit differentiation of Eqs. () and () with respect to CO2 and T, respectively. 16ΔCsBGC=∂∂CO2ΔCsBGCΔCO217ΔCsRAD=∂∂TΔCsRADΔT

Equations () and () can be used to relate these CO2 and T sensitivities to the βγ formulation, where β is used to represent the sensitivity to CO2 and γ is used to represent the sensitivity to T. Equation (), which defines ΔCs in terms of the soil carbon-concentration (βs) and carbon-climate (γs) feedback parameters, can be rewritten in terms of partial derivatives, as shown by Eq. (). 18ΔCs=∂Cs∂CO2ΔCO2+∂Cs∂TΔTwhere,βs=∂Cs/∂CO2andγs=∂Cs/∂T

Then, Eqs. () and () can be used together with Eq. () to combine the βγ formulation with the framework. In this case, therefore, βs and γs can be defined as the contributions to ΔCs based on the individual sensitivities of the soil carbon controls to CO2 and T (by substituting Eqs. () and () into Eqs. () and (), respectively), as shown by Eqs. () and (). 19ΔCs=∂∂CO2ΔCsBGCΔCO2+∂∂TΔCsRADΔT, where 20βs=τs,0BGC∂NPPBGC∂CO2+NPP0BGC∂τsBGC∂CO2+∂ΔNPPBGCΔτsBGC∂CO2-τs,0BGC∂NEPBGC∂CO2-NEP0BGC∂τsBGC∂CO2-∂ΔNEPBGCΔτsBGC∂CO2,21γs=τs,0RAD∂NPPRAD∂T+NPP0RAD∂τsRAD∂T+∂ΔNPPRADΔτsRAD∂T-τs,0RAD∂NEPRAD∂T-NEP0RAD∂τsRAD∂T-∂ΔNEPRADΔτsRAD∂T.

Equations () and () can be rewritten by defining the βs and γs contribution terms, where each component of the equations makes up the total βs and γs sensitivities, as shown below for βs (Eq. ) and γs (Eq. ): 22βs=βNPP+βτ+βΔNPPΔτ-βNEP-βNEPτ-βΔNEPΔτ,23γs=γNPP+γτ+γΔNPPΔτ-γNEP-γNEPτ-γΔNEPΔτ, where βNPP and γNPP are the βγ contributions due to ΔNPP, βτ and γτ are the βγ contributions due to Δτs, βNEP and γNEP are the βγ contributions due to the transient NEP term, including βNEPτ and γNEPτ representing the βγ contributions due to the transient NEP term on Δτs, and then βΔNPPΔτ, βΔNEPΔτ, γΔNPPΔτ and γΔNEPΔτ are the non-linear effects on βγ.

Projections of soil carbon change in CMIP6 ESMs for the full 1 % CO2 (ΔCs), BGC (ΔCsBGC) and RAD (ΔCsRAD) simulations are presented in Fig. . Soil carbon is projected to increase in the full 1 % CO2 simulation amongst CMIP6 ESMs (ensemble mean 88.2 ± 40.4 PgC at 2 × CO2 and 177 ± 141 PgC at 4 × CO2). However, the magnitude of the increase varies amongst the ESMs, with a range of 38 PgC (NorESM2-LM) to 145 PgC (BCC-CSM2-MR) at 2 × CO2 and a range of 15 PgC (ACCESS-ESM1-5) to 502 PgC (CanESM5) at 4 × CO2. Six of the ESMs (CanESM5, CESM2, GFDL-ESM4, MIROC-ES2L, MPI-ESM1-2-LR, NorESM2-LM) see an increased ΔCs value with increasing climate forcing. However, the remaining four ESMs (ACCESS-ESM1-5, BCC-CSM2-MR, IPSL-CM6A-LR, UKESM1-0-LL) see a saturation in the rate of increase or even a turning point where carbon starts to decrease again, from 70 years (≈ 2 × CO2) in the simulation (Fig. a).

The projected increase in soil carbon can be approximated by the increases projected in the BGC run (ΔCsBGC; ensemble mean 132 ± 66.5 PgC at 2 × CO2 and 348 ± 203 PgC at 4 × CO2, Fig. b) and the decreases projected in the RAD run (ΔCsRAD; ensemble mean -45.5 ± 22.9 PgC at 2 × CO2 and -170 ± 94.7 PgC at 4 × CO2, Fig. c). The responses due to increases in atmospheric CO2 (BGC simulation) are found to dominate the overall response (full 1 % CO2 simulation) in the majority of the models, where greater magnitudes of change are seen compared with the RAD simulation (exception ACCESS-ESM1-5). The BGC simulation also sees a greater spread in projected ΔCs, with ranges of 218 PgC at 2 × CO2 and 603 PgC at 4 × CO2 (ΔCsBGC) compared with ranges of 68 PgC at 2 × CO2 and 312 PgC at 4 × CO2 in the RAD simulation (ΔCsRAD).

Figure  shows patterns of soil carbon changes at 4 × CO2 for the full 1 % CO2 (ΔCs), BGC (ΔCsBGC) and RAD (ΔCsRAD). In the BGC simulation, increases in ΔCsBGC are seen across the majority of regions within CMIP6 ESMs, though exceptions are found at the northern latitudes for two ESMs (CanESM5 and NorESM2-LM). Across the ensemble, the projected increases in ΔCsBGC have spatially varying magnitudes, where generally the greatest increases are seen in the tropical regions. Conversely, the RAD simulation generally sees reductions in ΔCsRAD globally, with the greatest reductions seen in the tropical regions. However, disagreement is seen at the northern latitudes, where four models (ACCESS-ESM1-5, CanESM5, MIROC-ES2L, UKESM1-0-LL) see an increased ΔCsRAD and three models (BCC-CSM2-MR, CESM2, NorESM2-LM) see a decreased ΔCsRAD. The overall ΔCs values seen in the full 1 % CO2 simulation are again found to be mostly dominated by the BGC simulation (Fig. ), though exceptions are seen where the RAD simulation is shown to dominate the response for certain regions. Specifically, the reduced ΔCs within the RAD simulation dominates the net response at the northern latitudes of three ESMs (BCC-CSM2-MR, CESM2 and NorESM2-LM, the only models where decreases were seen) as well as in the tropical regions of three different ESMs (ACCESS-ESM1-5, GFDL-ESM4 and UKESM1-0-LL).

The calculated βs and γs values for CMIP6 ESMs are presented in Table . Values for βs are found to be positive amongst the CMIP6 ESMs, which is consistent with increased Cs with increasing CO2, and values for γs are found to be negative, which is consistent with decreased Cs with increasing temperature (Fig. ). The magnitudes of the feedback parameters (βs and γs) are found to vary amongst the CMIP6 ensemble, suggesting uncertainty in the magnitude of the soil carbon response to climate change. Generally, models with higher sensitivities to CO2 (βs) also have higher sensitivities to temperature (γs), where r2 values of 0.64 (2 × CO2) and 0.60 (4 × CO2) are found between the βs and γs values (Table ). The ranges in projected βs parameters are found to be relatively consistent between 2 × CO2 and 4 × CO2 (where a small decrease is seen), with a range of 0.704 PgC ppm-1 and a range of 0.636 PgC ppm-1, respectively. Conversely, the ranges of calculated γs parameters are found to be less consistent between 2 × CO2 and 4 × CO2 (increasing range with increased global warming), with ranges of 42.7 and 68.0 PgC °C-1, respectively (Table ).

The linearity of future soil carbon changes can be investigated by comparing the 2 × CO2 and 4 × CO2 lines for βs and γs in Fig. . A future linear response is shown to be a good approximation. However, the figure suggests a slight non-linearity in the soil carbon response to both CO2 (ΔCsBGC) and temperature (ΔCsRAD) in the majority of ESMs. The BGC simulation generally sees greater consistency between 2 × CO2 and 4 × CO2 βs values, for example in the CESM2 and NorESM2-LM models. However, the majority of ESMs (ACCESS-ESM1-5, BCC-CSM2-MR, GFDL-ESM4, IPSL-CM6A-LR, MIROC-ES2L, MPI-ESM1-2-LR and UKESM1-0-LL) see a reduction in βs and a saturation in the sensitivity with greater CO2 levels (Fig. a). In the RAD simulation, generally inconsistencies are seen between 2 × CO2 and 4 × CO2 (exception MPI-ESM1-2-LR), and an increased sensitivity of CsRAD to temperature (T) with increased climate forcing is suggested by the majority of CMIP6 ESMs (Fig. b). As an example, in CESM2, where one of the lowest sensitivities to T at 2 × CO2 is seen, the ESM sees an approximate 50 % increase in γs by 4 × CO2 (Table ).

The βs and γs values were also calculated for CMIP5 ESMs (Table ), which can be compared with a subset of generationally related CMIP6 ESMs considered in this study (Fig. ). The CMIP6 ensemble means for both βs and γs parameters are found to be lower compared with the CMIP5 ensemble means (Tables  and ). The relationship of βs and γs values between CMIP5 and CMIP6, however, is not found to be consistent amongst the ensembles. For βs, reductions are seen in four ESMs (GFDL-ESM2M vs. GFDL-ESM4, IPSL-CM5A-LR vs. IPSL-CM6A-LR, MPI-ESM-LR vs. MPI-ESM1-2-LR and HadGEM2-ES vs. UKESM1-0-LL) compared with increases in the remaining two (CanESM2 vs. CanESM5 and NorESM1-ME vs. NorESM2-LM). For γs, a greater value (closer to 0) is seen in four ESMs (CanESM2 vs. CanESM5, GFDL-ESM2M vs. GFDL-ESM4, IPSL-CM5A-LR vs. IPSL-CM6A-LR and MPI-ESM-LR vs. MPI-ESM1-2-LR) compared with a lower value (greater negative) seen in the remaining two ESMs (NorESM1-ME vs. NorESM2-LM and HadGEM2-ES vs. UKESM1-0-LL).

In this section, βs and γs are broken down into the individual sensitivities of drivers of soil carbon change which make up the net response. As shown in Fig. , the total soil carbon sensitivities (βs and γs, blue bars) can be considered as the sum of the sensitivity due to ΔNPP (βNPP and γNPP, green bars), the sensitivity due to Δτs (βτ and γτ, red bars) and additional terms due to the transient land carbon sink, such as NEP (βNEP and γNEP, light green bars) and the NEP effect on τs (βτNEP and γτNEP, pink bars). Additionally, there are non-negligible contributions due to non-linear sensitivities between NPP and τs (βΔNPPΔτ and γΔNPPΔτ, black bars) and a small contribution from non-linear sensitivities between NEP and τs (βΔNEPΔτ and γΔNEPΔτ, grey bars).

Investigating the sensitivity of soil carbon to ΔNPP, βNPP is found to be positive amongst CMIP6 ESMs (Fig. ). At 2 × CO2, βNPP ranges from 0.567 PgC ppm-1 (ACCESS-ESM1-5) to 5.62 PgC ppm-1 (BCC-CSM2-MR), with an ensemble mean of 2.37 ± 1.37 PgC ppm-1. There is some evidence of a saturation of global NPP at higher CO2, with the sensitivity of NPP to CO2 (βNPP) decreasing at 4 × CO2 to an ensemble mean of 1.44 ± 0.933 PgC ppm-1. The sensitivity of NPP to global temperature changes (γNPP) is found to be more variable in the ensemble. The majority of models find γNPP to be negative. However, it is found to be positive in two ESMs (CanESM5 and MPI-ESM1-2-LR). The sensitivity of NPP to temperature (γNPP) is found to be more consistent with climate change than the sensitivity to CO2 (βNPP), where the γNPP ensemble mean changes from -29.4 ± 40.1 PgC °C-1 at 2 × CO2 to -35.3 ± 33.1 PgC °C-1 at 4 × CO2 (Fig. ). At 4 × CO2, the lowest sensitivity of NPP to temperature is seen in CanESM5 (3.95 PgC °C-1) and the highest sensitivity in BCC-CSM2-MR (-90.8 PgC °C-1).

Investigating the sensitivity of soil carbon to Δτs, negative βτ and γτ values are mostly found amongst the CMIP6 models (Fig. ). An anomaly is found where τs is found to increase with temperature in the ACCESS-ESM1-5 model, where the reason for this is unclear (Fig. ). The sensitivity of τs to T (γτ) is also found to be more consistent with increasing climate change than the sensitivity to CO2, where an ensemble mean of -25.2 ± 27.9 PgC °C-1 at 2 × CO2 and -20.5 ± 29.5 PgC °C-1 at 4 × CO2 is seen. At 4 × CO2, the greatest sensitivity of τs to temperature is seen in the MIROC-ES2L model (-54.6 PgC °C-1) and the lowest sensitivity is seen in the NorESM2-LM model (-2.80 PgC °C-1). τs is found to decrease non-linearly with increasing CO2 (βτ). At 2 × CO2, βτ ranges from -0.329 PgC ppm-1 (ACCESS-ESM1-5) to -1.90 PgC ppm-1 (BCC-CSM2-MR), with an ensemble mean of -0.900 ± 0.574 PgC ppm-1. Due to the non-linearity, a reduced ensemble mean of -0.450 ± 0.359 PgC ppm-1 is found at 4 × CO2 compared with 2 × CO2 (Fig. ).

It is apparent from Fig.  that the sensitivities of NPP and τs to both CO2 and T must be accounted for to understand and quantify the sensitivities of soil carbon. The magnitude of βτ is found to be approximately one-third of the magnitude of βNPP at both 2 × CO2 and 4 × CO2 but with counteracting signs of change. Models with the lowest βNPP sensitivities also see the lowest βτ sensitivities (e.g. ACCESS-ESM1-5) and vice versa. The magnitude of γNPP is generally found to be greater across the ensemble compared with γτ, with however a greater range of sensitivities. Additionally, the apparent sensitivity of soil carbon to CO2 is less than the individual sensitivities of NPP and τs, due to a cancellation effect from opposing signs, leading to a lower apparent βs. The magnitudes of βNPP and βτ are lower at 4 × CO2 than 2 × CO2, which means a reduced sensitivity of NPP and τs to CO2 at greater levels of climate change. However, due to this cancellation effect, the same reduced sensitivity is not seen in βs. Conversely, a reduced sensitivity of NPP and τs to temperature is not suggested under increasing climate forcing. No clear relationship between γNPP and γτ is seen amongst the CMIP6 ESMs (Fig. ).

The contribution of the non-linearity between NPP and τs to the net soil carbon sensitivity is also investigated (βΔNPPΔτ and γΔNPPΔτ). Figure  suggests that the non-linearity between NPP and τs is more robustly projected to result from increasing CO2 (βs). However, non-linearities in γs are also seen in the models with the greatest temperature sensitivities. The ensemble mean predicted βΔNPPΔτ is found to be -0.462 ± 0.462 at 2 × CO2 and -0.463 ± 0.468 PgC ppm-1 at 4 × CO2. As expected from Fig. , predicted γΔNPPΔτ is found to have a low sensitivity, where the ensemble means of -0.374 ±  3.12 at 2 × CO2 and -0.0478 ± 7.42 PgC °C-1 at 4 × CO2 are found. Additionally, the NEP terms (βNEP and γNEP) are shown to contribute to both CO2 and T sensitivities (Fig. ), due to the disequilibrium of land carbon changes under 1 % increasing CO2.

Projections of ΔCs in ESMs in the full 1 % CO2 simulation were compared with the estimated ΔCs derived using Eq. (), which uses the derived βs and γs feedback parameters together with model-specific ΔT and estimates for ΔCO2 (Fig. ). This investigates the approximation that changes in the full 1 % CO2 simulation are equal to the sum of changes in the BGC and RAD simulations. At 2 × CO2, the approximation is found to predict ΔCs within 20 % of the actual projected values in the 1 % CO2 simulation for 7 out of the 10 CMIP6 ESMs (BCC-CSM2-MR, CESM2, GFDL-ESM4, IPSL-CM6A-LR, MIROC-ES2L, MPI-ESM1-2-LR and UKESM1-0-LL). At 4 × CO2, the robustness of the assumption between the BGC and RAD simulations decreases for future changes in soil carbon. However, βsΔCO2+γsΔT is within 20 % of the projected ΔCs for 5 out of the 10 ESMs (GFDL-ESM4, IPSL-CM6A-LR, MIROC-ES2L, MPI-ESM1-2-LR and UKESM1-0-LL). The models where the approximation is the least consistent with projected ΔCs are ACCESS-ESM1-5 and BCC-CSM2-MR, where at 4 × CO2 the greatest non-linearities are present between BGC and RAD simulations (Fig. ).

The contribution of the sensitivity of soil carbon stocks (Cs) to the total sensitivity of land carbon stocks (CL) was investigated by comparing the β and γ feedback parameters for land (Table ) and soil (Table ) for both 2 × CO2 and 4 × CO2 in CMIP6 ESMs (Fig. ). Here, the assumption from Eq. () is followed that the land sensitivity is made up of the sum of the soil and vegetation responses. For the carbon-concentration feedback (β), the portion of the land sensitivity to CO2 (βL) that is due to global soils (βs) ranges from 19 % (NorESM2-LM) to 53 % (BCC-CSM2-MR), with a mean of 38 ± 11 % seen across the CMIP6 ESMs at 2 × CO2 (Fig. a). Similar proportions are found at 4 × CO2, ranging from 22 % (NorESM2-LM) to 58 % (MIROC-ES2-L), with a mean of 42 ± 12 % seen across the CMIP6 ESMs (Fig. b). The portion of βL due to βs is estimated to be close to half of the total land response. For the carbon-climate feedback (γ), the portion of the land sensitivity to climate (γL) that is due to global soils (γs) ranges from approximately 42 % (CESM2) to 147 % (MPI-ESM1-2-LM), with a mean of 75 ± 30  % seen across the CMIP6 ESMs at 2 × CO2 (Fig. a), and at 4 × CO2 the range is from 48 % (ACCESS-ESM1-5) to 157 % (MPI-ESM1-2-LM), with a mean of 75 ± 31  % seen across the CMIP6 ESMs (Fig. b). Therefore, the portion of γL due to γs is estimated to be the majority of the sensitivity, suggesting that soil dominates the response of land carbon to climate. Note that the MPI-ESM1-2-LR model sees a greater γs value compared with γL, resulting in the percentage of the land response attributed to soil being greater than 100 %. This suggests a positive γv response in this model, meaning a predicted increased vegetation carbon globally with global warming.