Simulated responses of soil carbon to climate change in CMIP6 Earth System Models: the role of false priming

. Reliable estimates of soil carbon change are required to determine the carbon budgets consistent with the Paris climate targets. This study evaluates projections of soil carbon during the 21 st century in CMIP6 Earth System Models (ESMs) under a range of atmospheric composition scenarios. In general, we find a reduced spread of changes in global soil carbon ( ∆ C s ) in CMIP6 compared to the previous CMIP5 model generation. However, similar reductions were not seen in the derived contributions to ∆ C s due to both increases in plant Net Primary Productivity (NPP, named ∆ C s,NPP ) and reductions in the 5 effective soil carbon turnover time ( τ s , named ∆ C s,τ ). Instead, we find a strong relationship across the CMIP6 models between these NPP and τ s components of ∆ C s , with more positive values of ∆ C s,NPP being correlated with more negative values of ∆ C s,τ . We show that this emergent relationship is the result of ‘false priming’, which leads to a decrease in the effective soil carbon turnover time as a direct result of NPP increase and occurs when the rate of increase of NPP is relatively fast compared to the slower timescales of a multipool soil carbon model. The inclusion of more soil carbon models with multiple pools in 10 CMIP6 compared to CMIP5, therefore seems to have contributed towards the reduction in the overall model spread in future soil carbon projections.


Introduction
The response of soil carbon to human-induced climate change represents one of the greatest uncertainties in determining future atmospheric CO 2 concentrations (Canadell et al., 2021).Global soil carbon stocks contain at least 3 times more carbon than https://doi.org/10.5194/egusphere-2023-383Preprint.Discussion started: 24 March 2023 c Author(s) 2023.CC BY 4.0 License.node.llnl.gov/search/cmip6/,last access: 8 April 2022) and CMIP5: (https://esgf-node.llnl.gov/search/cmip5/,last access: 12 April 2022).Specific soil carbon related updates within ESMs from CMIP5 to CMIP6 are included in Varney et al. (2022) within the 'Earth system models' section of the Methods, and more general model updates are presented within the 'Model descriptions' section of the Arora et al. (2020) Appendix.
The analysis in this study considers 3 future climate scenarios defined by CMIP, which are used to consider different levels of global warming and associated climate policies.The CMIP6 'Shared Socioeconomic Pathways' (SSPs) considered in this study are: SSP126, SSP245, SSP585, which run from 2015 to 2100 (O'Neill et al., 2014;O'Neill et al., 2016).These pathways are chosen to allow for comparison with the CMIP5 'Representative Concentration Pathways' (RCPs): RCP2.6,RCP4.5 and RCP8.5, which run from 2005 to 2100 (Meinshausen et al., 2011).It is noted that the SSP and RCP concentration scenarios are not identical, but they are similar enough to enable helpful comparisons between CMIP5 and CMIP6 projections.For the reference period from which change is calculated, the CMIP Historical simulation was considered, where the simulation runs from 1850 to 2005 in CMIP5 and from 1850 to 2015 in CMIP6.A change (∆) was defined as the difference between the last decade of the 21 st century (time-averaged between 2090 and 2100) and the last decade of the CMIP5 historical simulation (time-averaged between 1995-2005), which allows for consistency between the CMIP generations.If a timeseries is considered, the historical reference period (historical simulation time-averaged between 1995-2005) was taken away from the entire future climate simulation (e.g.SSP126 minus the historical reference period).

C4MIP experiments
This study also uses model experiments set up by the Coupled Climate-Carbon Cycle Model Intercomparison Project (C4MIP), which are idealised experiments designed to separate the effects of CO 2 increases and climate change on land and ocean carbon stores.In these experiments additional effects such as land-use change, aerosols or non-CO 2 greenhouse gases are not included, and nitrogen deposition is fixed at pre-industrial values (Jones et al., 2016).The experiments included are: (1) a 'full 1% CO 2 simulation' (CMIP6 simulation 1pctCO2), which is a simulation that sees a 1% increase in atmospheric CO 2 per year, starting from pre-industrial concentrations (285 ppm) and running for 150 years, (2) a biogeochemically coupled 'BGC simulation' (CMIP6 simulation 1pctCO2-bgc), where the 1% CO 2 increase per year only affects the carbon cycle component of the ESM and the radiative code remains at pre-industrial CO 2 values, and (3) a radiatively coupled 'RAD simulation' (CMIP6 simulation 1pctCO2-rad), where the 1% CO 2 increase per year affects only the radiative code and the carbon cycle component on the ESM remains at pre-industrial CO 2 values.These simulations are used with 10 CMIP6 ESMs for further analysis: 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, and where '2xCO 2 ' and 4xCO 2 are defined as 70 and 140 years into the simulations, respectively.

Climate variables
Using ESM output variables, soil carbon (C s ) is defined as the sum of carbon stored in soils and surface litter (CMIP variable cSoil + CMIP variable cLitter).This allows for a more consistent comparison between the models due to differences in how soil carbon and litter carbon are defined.For models that do not report a separate litter carbon pool (cLitter), soil carbon is https://doi.org/10.5194/egusphere-2023-383Preprint.Discussion started: 24 March 2023 c Author(s) 2023.CC BY 4.0 License.taken to be simply the cSoil variable.Spatial C s is given in units of kg m −2 , and global total C s is given in units of PgC, which are calculated using an area weighted sum (using the model land surface fraction, CMIP variable sftlf ).
Additionally, ESM output variables were used to define the soil carbon driven climate feedbacks.Net Primary Productivity (NPP, CMIP variable npp) is defined as the net carbon assimilated by plants via photosynthesis minus loss due to plant respiration and is used to represent the net carbon input flux to the system.Heterotrophic Respiration (R h , CMIP variable rh) is defined as the microbial respiration within global soils and is used to define an effective global soil carbon turnover time (τ s ), see Equation 1. τ s (years) is defined as the ratio of mean soil carbon to annual mean heterotrophic respiration (where the mean represents an area weighted global average).Carbon fluxes (NPP and R h ) are considered as area weighted global totals in units of PgC yr −1 .

Breaking down the projected changes in soil carbon
From Equation 1, soil carbon (C s ) can be defined as shown by Equation 2. Future soil carbon stocks can be defined as initial soil carbon (C s,0 ) plus a change in soil carbon (∆C s ), as shown by Equation 3, where the subscript 0 denotes the initial state (historical simulation time-averaged between 1995-2005).Equation 3 can be expanded to give Equation 4, which can be simplified to give Equation 5.
To isolate the above and below ground effects on soil carbon, the separate effects due to changes in NPP and changes due to τ s are considered (Todd-Brown et al., 2014).For carbon to be conserved however, the difference between the global fluxes NPP and R h in a transient climate must be taken into account, where the difference is defined as the Net Ecosystem Productivity (NEP), as shown in Equation 6. Equation 6 can be substituted into Equation 5, to obtain an equation for ∆C s in terms of NPP, NEP and τ s (Equation 7).
If the initial state is a steady-state, the initial NEP (NEP 0 ) will be approximately equal to zero.However, as our initial state is defined as the end of the historical simulation, NEP 0 will therefore be non-zero as a result of the contemporary global land carbon sink.ESMs may also include additional carbon fluxes that cause changes to the resultant soil carbon inputs, such as: grazing, harvest, land-use change, and fire (Todd-Brown et al., 2014).The ∆NEP terms in Equation 7 implicitly includes these effects.
Finally, Equation 7 can expanded to give Equation 8, and the individual responses which make up the total change in soil carbon (∆C s ) can be broken-down into 6 components:

Projected changes in soil carbon
A reduced spread in projected end of 21 st century estimates of ∆C s is seen in CMIP6 compared to CMIP5 (Fig. 1).This reduced spread is shown in Fig. 1, where projections of ∆C s by 2100 in CMIP6 are compared with those from CMIP5 across the different future scenarios.The reduced range of projected changes is seen across all future scenarios (SSP126 and RCP2.6,SSP245 and RCP4.5, SSP585 and RCP8.5), with the range in CMIP6 consistently less than 50% of the equivalent range in CMIP5 (Fig. 1).This reduced spread in projections is also suggested by a reduced standard deviation about the ensemble mean ∆C s in CMIP6 compared with CMIP5, which is consistently reduced by 50% across all future climate scenarios (Tables 1 and A1, bottom rows).It is noted that the large range in CMIP5 estimates is mostly a result of large increases in C s in HadGEM2-ES and MPI-ESM-LR, together with the large C s losses in GISS-E2-R (Fig. 1).An updated CMIP6 version of the GISS-E2-R model is not included in this analysis of this study, which could contribute to the reduced uncertainty from CMIP5.However, the updated equivalent CMIP6 models UKESM1-0-LL (from HadGEM2-ES) and MPI-ESM1-2-LR (from MPI-ESM-LR) have projected estimates of ∆C s which are more consistent with the other models in the CMIP6 ensemble.
Nearly all of the ESM projections in CMIP6 suggest an increase in C s by 2100, however CMIP5 models project both increases (positive ∆C s ) and decreases (negative ∆C s ) in soil carbon during the 21 st century (Fig. 1).In CMIP5 projections, the future responses of soil carbon range from an increase of 23.2% (HadGEM2-ES) to a decrease of 6.50% (GISS-E2-R) in RCP8.5, where across all future scenarios approximately half of the models show increases and half show decreases in ∆C s (Table A1).In CMIP6, the future responses of soil carbon range from an increase of 12.5% (MPI-ESM1-2-LR) to a decrease of 2.25% (ACCESS-ESM1.5) in SSP585, however the majority of models predict an increase in ∆C s across all future scenarios (Table 1).
Despite more consistent projections of increased ∆C s in CMIP6 compared with CMIP5, it is apparent that greater CO 2 forcing (i.e.SSP585 compared with SSP126) does not always imply a greater magnitude of increased C s .By contrast to what is seen in CMIP6, the majority of CMIP5 models project an increased magnitude in estimated ∆C s with increased CO 2 forcing (Fig. 1).In CMIP6, half the models (CESM2, CNRM-ESM2-1, IPSL-CM6A-LR, NorESM2-LM, and UKESM1-0-LL) estimate less soil carbon accumulation by 2100 (i.e. a smaller increase or a greater decrease) in SSP585 when compared with SSP126.This effect is most prominent in BCC-CSM2-MR and UKESM1-0-LL, where a turning point from increasing to decreasing soil carbon is seen in the mid-century of the SSP585 projections (Fig. 2).This is opposed to an estimated increase in soil carbon storage with increased forcing, which is generally seen in CMIP5 and the remaining CMIP6 models (CanESM5,

MIROC-ES2L, and MPI-ESM1-2-LR)
. This finding suggests a potential limit to ∆C s increase and a reduced likelihood of a carbon sink under more extreme levels of climate change.
The spatial pattern of estimated ∆C s (Fig. 3) is quite variable between CMIP6 ESMs.For example in the tropical regions, where increases in soil carbon can be seen in 6 of the CMIP6 ESMs (BCC-CSM2-MR, CanESM5, CESM2, MIROC-ES2L, and NorESM2-LM), but decreases are seen in the remaining 4 (ACCESS-ESM1-5, CNRM-ESM2-1, IPSL-CM6A-LR, and UKESM1-0-LL).There is a lack of agreement in the high northern latitudes amongst the CMIP6 ESMs (Fig. 3), where it is known that the uncertainty surrounding the fate of soil carbon stocks in these regions is particularly important due to the large magnitude of carbon stored (Burke et al., 2020;Jackson et al., 2017).It has previously been found that a high accumulation of northern latitude C s is predicted amongst CMIP5 ESMs, however this C s response has not been suggested in empirical studies (Todd-Brown et al., 2014).The results here suggest that this accumulation (increased ∆C s ) remains in the majority of CMIP6 ESMs (Fig. 3), although reductions in northern latitude soil carbon stocks were found in 3 CMIP6 ESMs (BCC-CSM2-MR, CESM2 and NorESM2-LM, with BCC-CSM2-MR seeing reductions in a greater area).These ESMs which predicted northern latitude C s reductions were previously found to simulate historical northern latitude soil carbon stocks which are more consistent with the observational estimates seen in these regions (Varney et al., 2022).

Future changes to land-atmosphere fluxes
The projected ∆C s is a result of the changing input and output land-atmosphere fluxes under climate change.To a first order, the response of soil carbon will be determined by changes to NPP and to τ s (see Equation 7).In this section, future projections of these fluxes are analysed in both CMIP6 and CMIP5 ESMs.

Net Primary Productivity
NPP is projected by CMIP6 ESMs to increase during the 21 st century, with a greater increase with increasing climate forcing (across SSP scenarios).This result is consistent with the projections of ∆NPP amongst the CMIP5 models (Fig. 4; Todd-Brown et al. ( 2014)).Projections amongst ESMs however, show disagreement in the magnitude of ∆NPP by 2100 across all future climate scenarios, where a projected CMIP6 ensemble increase of 24.6 ± 16.9 PgC yr −1 is seen in SSP585.The largest projections of ∆NPP amongst the CMIP6 models are seen in CanESM5 and BCC-CSM2-MR, where increases of 65.8 PgC yr −1 (47% increase) and 39.4 PgC yr −1 (43% increase) are projected by 2100 under SSP585, respectively.This is compared to ACCESS-ESM1-5 which has the lowest projected changes amongst the CMIP6 models with an increase of only 4.07 PgC yr −1 (10% increase) by 2100 under SSP585 (Table 2).
The CMIP6 ensemble sees a slightly increased range in end of century ∆NPP compared with CMIP5, across all future scenarios (Tables 2 and A2).

Soil carbon turnover time
Future τ s is projected by CMIP6 ESMs to decrease by 2100 across all future SSP scenarios (Fig. 5).A greater reduction in τ s is seen with increased climate forcing scenario, where a reduced τ s is a faster soil carbon turnover time, and implies that carbon is cycled back to the atmosphere in less time due to an increased carbon output from the soil (increased R h , see Equation 1).
This result is consistent with the projections of ∆τ s amongst the CMIP5 models (Fig. 5; Todd-Brown et al. ( 2014)).However, it is found that greater variation exists amongst the CMIP6 ESMs end of century estimates, where a projected CMIP6 ensemble ∆τ s value of -7.65 ± 5.65 years is seen in SSP585 compared to -6.13 ± 3.03 years for CMIP5 ESMs in RCP8.5 (Tables 2 and     A2).  2).The increased range in CMIP6 from CMIP5 is primarily due to the large τ s reductions seen in the CMIP6 models NorESM2-LM, CESM2 and BCC-CSM2-MR (Fig. 5).

Breaking down the projected changes in soil carbon
To understand the projected end of century changes in soil carbon storage (∆C s ) in ESMs, the individual responses of soil carbon due to changes in NPP (∆C s,N P P , see Equation 9) and the response due to changes in τ s (∆C s,τ , see Equation 12) were diagnosed for both CMIP5 and CMIP6 as shown in Fig. 6.Future ∆C s (blue bars) is found to mostly a result of the net effect of the linear terms: ∆C s,N P P (dark green bars) and ∆C s,τ (red bars).However, there are also non-negligible contributions from the non-linear term: ∆NPP∆τ s (black bars), and a small addition due to the non-equilibrium terms: ∆C s,N EP (light green bars), ∆C s,τ N EP (pink bars), and ∆NEP∆τ s (grey bars).
The importance of investigating the individual processes which contribute to the net ∆C s in ESMs can be seen (Fig. 6).In relationship between all the contributing terms to the net ∆C s response, as opposed to the absolute size of a given contribution (Fig. 6).
Surprisingly, a very strong correlation is found amongst the ESMs in CMIP6 (r 2 value of 0.97) between the linear terms ∆C s,N P P and ∆C s,τ (Fig. 7(a)).This leads to the partially cancelling of the terms, with a resultant relatively small net ∆C s .
When comparing with the CMIP5 ensemble, a lower correlation between ∆C s,N P P and ∆C s,τ is seen (r 2 value of 0.084, Fig.

7(a)
).This correlation amongst CMIP6 ESMs results in net ∆C s being more clustered in CMIP6 compared to CMIP5 (Fig. 1), despite a similarly large variation in the individual contributions (Fig. 6).The strong CMIP6 correlation (r 2 = 0.97) remains when the fractional changes (∆C s,N P P /C s,0 and ∆C s,τ N P P /C s,0 , where C s,0 is initial soil carbon stocks) are plotted instead (Fig. 7(b)).
Fig. 6 also shows that the differences in ESM projections of ∆C s are partly due to differing magnitudes of the nonlinear term (∆NPP∆τ s ).The non-linear ∆NPP∆τ s term having non-negligible contributions to future ∆C s means the initial ∆NPP/NPP << 1 and ∆τ s /τ s << 1 assumptions were not valid in this case.The ESM projected magnitudes of ∆NPP∆τ s are found to be relatively large, especially in the more extreme climate scenarios (Fig. 6).In SSP585, a range from a decreased C s of 11 PgC (ACCESS-ESM1-5) to a decreased C s of 599 PgC (BCC-CSM2-MR) is found amongst the CMIP6 models due to only the ∆NPP∆τ s term, and in some cases values greater magnitudes are seen than the net ∆C s (BCC-CSM2-MR, CanESM5, CESM2, NorESM2-LM, and UKESM1-0-LL).The term is greater when there are large and counteracting magnitudes of ∆NPP and ∆τ s , which results in a non-negligible product.
Additionally, to obtain the overall change in soil carbon seen in the models, contributions from the non-equilibrium terms (∆C s,N EP , ∆C s,τ N EP , and ∆NEP∆τ s ) must also be included (Fig. 6).The ∆C s,N EP term represents the change in soil carbon due to the net carbon sink during the 21 st century, which exists while the climate is in a transient state due to continuous climate change.By definition, the magnitude of ∆C s,N EP is negative if ∆NEP is positive, which implies a greatest or faster increase in NPP with respect to R h seen in the majority of ESMs.The contribution from these terms is found to be relatively small in most models, but not in all.In SSP585, projections of ∆C s,N EP amongst CMIP6 models range from a reduction of 333 PgC (NorESM2-LM) to a gain of 8.74 PgC (ACCESS-ESM1-5).In CMIP5, exceptions where greater ∆C s,N EP terms are found in the GISS-E2-R and MPI-ESM-LR models, implying the models are far from equilibrium at the end of the century.
The change in soil carbon due to the change in NEP (∆C s,N EP ) is often found to be greater in the models which see greater magnitudes of ∆C s,N P P and ∆C s,τ .
3.4 Investigating the emergent relationship between ∆C s,N P P and ∆C s,τ In this subsection, the emergent relationship between ∆C s,N P P and ∆C s,τ present across the CMIP6 ensemble is further investigated using the idealised C4MIP simulations (see Methods).Fig. 8 presents the relationship between ∆C s,N P P and ∆C s,τ for each CMIP6 ESMs as in Fig. 7, but for the full 1% CO 2 , BGC, and RAD simulations.It is found that ∆C s,N P P and ∆C s,τ are strongly correlated in the full 1% CO 2 simulation, at both 2xCO 2 (r 2 value of 0.925) and 4xCO 2 (r 2 value of 0.839).
The correlation is found to remain in the BGC simulation, where r 2 values are found to be 0.838 and 0.708 for 2xCO 2 and 4xCO 2 , respectively.The slightly reduced correlation in the BGC simulation at 4xCO 2 suggests a potential limit to the effect at high levels of atmospheric CO 2 .A correlation is also seen in the RAD simulation at 2xCO 2 (r 2 value of 0.601), however the correlation in the RAD simulation does not hold at 4xCO 2 , where the r 2 value reduces to 0.265.The reduced correlation in the RAD simulation at 4xCO 2 suggests a reduced relationship between NPP and τ s at the more extreme temperature changes that are projected at high levels of atmospheric CO 2 .
For each CMIP6 ESM, NPP and τ s are found to be strongly inversely correlated in the full 1% CO 2 simulation (Fig. 9).The r 2 values between NPP/NPP 0 and τ s,0 /τ s (where the subscript 0 denotes the historical state) are found to be greater than 0.95 in all models except for ACCESS-ESM1-5 (where an r 2 value of 0.65 is found due to a breakdown at high CO 2 levels).In the BGC simulation, a similar relationship between NPP/NPP 0 and τ s,0 /τ s is seen up until approximately 2xCO 2 in all ESMs (approximately 50% of the simulation).However, how the relationship between NPP/NPP 0 and τ s,0 /τ s changes throughout the BGC simulation (between 2xCO 2 and 4xCO 2 ) varies between models.A greater rate of NPP/NPP 0 increase compared to τ s,0 /τ s is seen at greater levels of climate forcing for the majority of CMIP6 ESMs (BCC-CSM2-MR, CanESM5, GFDL-ESM4, IPSL-CM6A-LR, MIROC-ES2L, MPI-ESM1-2-LR and UKESM1-0-LL), where the τ s changes appear to saturate and a limit to the increase is seen.In these ESMs, the changes seen in the full and BGC simulations differ due to a climate effect (shown by the RAD simulation), which appears to negate the apparent limit or saturation seen in the τ s,0 /τ s increase in the BGC simulation (Fig. 9).In CESM2 and NorESM2-LM (containing the same land surface model component), a consistent relationship is seen in both the full 1% CO 2 and BGC simulations, suggesting the changes in NPP and τ s are primarily due to changes in CO 2 concentrations, or that the climate affects cancel out to a resultant net zero change.In ACCESS-ESM1-5, a consistent relationship is seen in the full 1% CO 2 , BGC and RAD simulations, suggesting a greater sensitivity of NPP to environmental climate changes compared to the other CMIP6 ESMs (Fig. 9).Koven et al. (2015) presents the concept of 'false priming', which describes a reduction in effective carbon turnover (τ s ) due to increases in productivity (NPP).It was defined as false priming due to the impact being similar to the 'true priming' process, but occurs without simulating the priming mechanisms; where priming is defined as the stimulation of decomposition of soil carbon (reducing τ s ) due to input of carbon to the soil (Liu et al., 2020).The false priming reduction in effective τ s is a transient phenomenon that arises in soil models that represent multiple carbon pools with different turnover times.Under continually increasing NPP, proportionally more of the additional input litter carbon is put into the faster soil carbon pools than the slow, which brings down the global average effective τ s value of the soil.
In this subsection, false priming is explored as a possible explanation for the correlations seen between NPP changes and τ s changes, which are seen even in the BGC simulations where the climate does not change significantly (second row of Fig. 8).
where, C s,1 , C s,2 , C s,3 represent the carbon stored in soil carbon pools 1, 2, and 3 and make up the total soil carbon (C s ).Similarly, τ s,i are the respective soil carbon turnover times, which are given defined values of increasing turnover times in years: fast (1 year), medium (10 years) and slow (100 years).NPP represents the carbon input into the system, where carbon is inputted into pool 1 (C s,1 ), then flows to pool 2 (C s,2 ) and then 3 (C s,3 ).The coefficients e i represents the fraction of carbon that is passed to the next pool rather than outputted as heterotrophic respiration (R h ).
At equilibrium, the change in the soil carbon pools will be zero (dC s,i /dt = 0), so the amount of soil carbon present within each pool depends on the input carbon and turnover time of the pool (τ s,i ).Under increasing NPP, the three-box model can be used to investigate the subsequent changes to soil carbon in the 3 carbon pools (C s,1 , C s,2 , C s,3 ) based on changing input alone, due to each pool having a fixed τ s,i value.This removes the ∆τ s from changing environmental and microbial conditions (Koven et al., 2015;Wieder et al., 2015;Exbrayat et al., 2013).Fig. 10(a) produces a simulation of the response of this threebox model to an NPP input flux that increases at 0.3% per year (reproducing Fig. 12 in Koven et al. (2015)).The false priming decline in effective τ s with increasing NPP is clear, and for this set of parameters offsets about 40% of the increase in soil carbon that would arise from the NPP increase alone.Fig. 10(b) demonstrates that false priming is a transient effect associated with a disequilibrium in the distribution of soil carbon between the 3 pools.It shows results from the same model, but for a step increase in global NPP from 50 PgC yr −1 to 70 PgC yr −1 at year 100.The instantaneous decline in τ s of about 10% eventually reduces to return the soil to the original τ s , but this occurs on the timescale of the slowest carbon pool and so may take many centuries.
The same three-box model can also be used to investigate the relationship between the contributions of changes in NPP (∆C s,N P P ) and τ s (∆C s,τ ) to net soil carbon change that was noted in both Fig. 7  suggesting that these correlations in CMIP6 (and to a lesser extent in CMIP5) are predominantly due to false priming.
It is noted that the influence of false priming was stronger in the full 1% CO 2 and BGC (CO 2 only) simulations, compared to the RAD (climate only) simulation.This is likely due to the RAD simulation not seeing sufficient NPP change for the false priming affect to be significant (see Fig. A2), opposed to false priming being a direct result of atmospheric CO 2 change.
Additionally, the direct effect of temperature changes on τ s in the RAD simulation is likely to dampen the correlation to NPP changes, due to both direct and indirect ∆τ s in this case (Varney et al., 2020).

Conclusions
In this study, future projections of soil carbon change (∆C s ) have been analysed using ESM output from the latest CMIP6 ensemble and were investigated under differing levels of climate change (future scenarios SSP126, SSP245 and SSP585).The future projections made by CMIP6 ESMs were also compared against equivalent projections made by the previous generation of ESMs in the CMIP5 ensemble (future scenarios RCP2.6,RCP4.5 and RCP8.5) to investigate whether recent model improvements have reduced the uncertainty surrounding the future soil carbon response.Additionally, ∆C s was broken down into the individual components which contribute to the net change within ESMs, with a specific focus on increases due to increases in NPP (∆C s,N P P ) and decreases due to reductions in turnover (∆C s,τ ).Below the key conclusions from this study are listed: 1.An apparent reduction in uncertainty of end of 21 st century ∆C s projections is suggested in CMIP6 compared to CMIP5.
2. However, the same reduction in projection uncertainty is not suggested surrounding the soil carbon controls: Net Primary Productivity (NPP) and the effective soil carbon turnover time (τ s = C s /R h ), and the subsequent effects on future soil carbon storage (∆C s,N P P and ∆C s,τ , respectively).
3. It is noted that the results in this study suggest the inclusion of a interactive nitrogen cycle within simulations constrains the future responses to NPP and shows progress in CMIP6 models.
4. The derived linear terms which contribute to net soil carbon change, the response of soil carbon due to changes in NPP (∆C s,N P P ) and the response due to changes in τ s (∆C s,τ ), are found to have a strong relationship in CMIP6, with a more significant correlation than what was seen in CMIP5.This correlation is likely to be a cause of the reduction in the ∆C s projection spread across the CMIP6 ensemble.
5. The apparent emergent relationship between ∆C s,N P P and ∆C s,τ in CMIP6 ESMs was found to be a result of false priming, which describes a transient increase in effective turnover time due to increased input of carbon to the soil.The net effect of false priming is a coupling affect between ∆NPP and ∆τ s , and results in a reduced range of future ∆C s predictions in CMIP6.Understanding and quantifying soil carbon feedbacks under anthropogenic emissions of CO 2 is critical for calculating an accurate global carbon budget, which is required if Paris Agreement targets are to be met (Friedlingstein et al., 2022).This study           year run with a different assumed rate of increase of NPP (∼ 0.0% to 0.8% per year in increments of 0.05%).
Fig. 4 suggests that the increased range is mostly due to outlying projections of ∆NPP (CanESM5), where greater increases are seen compared to the majority of models within the ensemble.It is noted that a cluster of ESMs which have similar projections of ∆NPP is seen within CMIP6 (CESM2, MIROC-ES2L, MPI-ESM1-2-LR, NorESM2-LM, and UKESM1-0-LL).The cluster is found to be made up of ESMs which include the simulation of an interactive nitrogen cycle (shown by the dashed lines throughout this study), which is a common addition within CMIP6 ESMs (ACCESS-ESM1.5,CESM2, MIROC-ES2L, MPI-ESM1-2-LR, NorESM2-LM and UKESM1-0-LL; Davies-Barnard et al. (2020)).ACCESS-ESM1-5 is the only model which simulates interactive nitrogen and does not predict consistent ∆NPP with the other nitrogen ESMs in CMIP6, however the projections of ∆NPP in ACCESS-ESM1-5 is consistent with the projections of NorESM1-M in CMIP5, which is the only CMIP5 model considered here to simulate interactive nitrogen (Fig. 4).https://doi.org/10.5194/egusphere-2023-383Preprint.Discussion started: 24 March 2023 c Author(s) 2023.CC BY 4.0 License.
The CMIP6 ESMs with the greatest reductions in effective global τ s by 2100 is seen in BCC-CSM2-MR, CESM2 and NorESM2-LM, where global carbon turnover in the soil is at least 14 years faster at the end of the SSP585 simulation compared to the start of the 21 st century (historical reference).The CMIP6 models with the least change in effective global τ s are ACCESS-ESM1-5, IPSL-CM6A-LR, and MPI-ESM1-2-LR, where global carbon turnover in the soil is only around 2 years faster at the end of the SSP585 simulation (Table

Fig. 6
Fig.6it is seen that the net ∆C s is relatively small compared to the individual changes from the derived components, where especially large magnitudes are seen in the increased C s due to increased ∆NPP (∆C s,N P P ) and the decreased C s due to reduced ∆τ s (∆C s,τ ).For example, in SSP585 there is a range of approximately 170 PgC in net ∆C s , from an increase of 132 PgC (CNRM-ESM2-1) to a reduction of 35 PgC (BCC-CSM2-MR).However, the ∆C s,N P P contribution has a much larger range of 1442 PgC, from an increase of 95 PgC (ACCESS-ESM1-5) to an increase of 1517 PgC (NorESM2-LM).Similarly, ∆C s,τ has a range of 756 PgC, from a decrease of 115 PgC (ACCESS-ESM1-5) to a decrease of 871 PgC (NorESM2-LM).The magnitude of change seen from the individual feedbacks (∆C s,N P P and ∆C s,τ ) is not obviously related to the resultant magnitude of soil carbon change (Fig.A1).For example, NorESM2-LM projects large ∆C s,N P P and ∆C s,τ values (1517 PgC and -871 PgC in SSP585, respectively), however a relatively small net change in soil carbon (49 PgC in SSP585).Conversely, CNRM-ESM2-1 projects smaller ∆C s,N P P and ∆C s,τ values (667 PgC and -413 PgC in SSP585, respectively), but a larger net soil carbon change (132 PgC in SSP585).Within ESMs, it is found that the change in soil carbon is determined by the https://doi.org/10.5194/egusphere-2023-383Preprint.Discussion started: 24 March 2023 c Author(s) 2023.CC BY 4.0 License.
Koven et al. (2015) demonstrates false priming with a simple three-box soil carbon model, which has been adapted here to use notation consistent with the rest of this study: https://doi.org/10.5194/egusphere-2023-383Preprint.Discussion started: 24 March 2023 c Author(s) 2023.CC BY 4.0 License.
and Fig. 8. Fig. 11 plots ∆C s,N P P against ∆C s,τ from the three-box model after 70 years of runs that assume different rates of increase of NPP (0% to 0.8% per year in https://doi.org/10.5194/egusphere-2023-383Preprint.Discussion started: 24 March 2023 c Author(s) 2023.CC BY 4.0 License.increments of 0.05%).A clear relationship between ∆C s,N P P and ∆C s,τ is seen, with greater false priming (more negative ∆C s,τ ) when the NPP increase is larger (more positive ∆C s,N P P ).The similarity of Fig. 11 to both Fig. 7 and Fig. 8 is clear, https://doi.org/10.5194/egusphere-2023-383Preprint.Discussion started: 24 March 2023 c Author(s) 2023.CC BY 4.0 License.6.It is recommended that the full extent of false priming on future soil carbon is understood, where if increased carbon inputs to soil carbon pools preferentially enters fast soil carbon pools, this could limit the maximum increase in soil carbon storage in the future.
the importance of considering the individual soil driven carbon feedbacks under climate change when determining the overall response of global soil carbon storage, and suggests the need for constraints on the magnitudes of these feedbacks in CMIP6 to reduce uncertainty in projections of future land carbon storage.https://doi.org/10.5194/egusphere-2023-383Preprint.Discussion started: 24 March 2023 c Author(s) 2023.CC BY 4.0 License.

Figure 1 .
Figure 1.Projected future change in soil carbon (∆Cs) in CMIP5 (top row) and CMIP6 (bottom row) ESMs, for future climate scenarios RCP2.6 and SSP126, RCP4.5 and SSP245, RCP8.5 and SSP585, respectively.The dashed lines represent ESMs which include the representation of interactive nitrogen in these simulations.

Figure 3 .
Figure 3. Map plots showing the change in soil carbon (∆Cs) in SSP585 for each CMIP6 ESM.

Figure 4 .
Figure 4. Projected future change in Net Primary Production (∆NPP) in CMIP5 (top row) and CMIP6 (bottom row) ESMs, for future climate scenarios RCP2.6 and SSP126, RCP4.5 and SSP245, RCP8.5 and SSP585, respectively.The dashed lines represent ESMs which include the representation of interactive nitrogen in these simulations.

Figure 6 .
Figure 6.A bar chart showing the contributions of NPP and τs to end of 21 st century changes in soil carbon (∆Cs) in CMIP5 (top row) and CMIP6 (bottom row) ESMs, for future scenarios: RCP2.6 and SSP126, RCP4.5 and SSP245, RCP8.5 and SSP585, respectively.The included terms are: the linear term representing changes in soil carbon due to the changes in NPP (∆Cs,NP P ), the linear term representing changes in soil carbon due to the changes in τs (∆Cs,τ ), the non-linear term (∆NPP∆τs), and then additional terms to account for the non-equilibrium climate in 2100 (∆Cs,NEP , ∆Cs,τ N EP , and ∆NEP∆τs).

Figure 10 .
Figure 10.Timeseries plot showing the results from the simple three-box model.(a) For normalised changes in NPP, R h , τs and Cs and fractional change in each of the 3 soil carbon boxes and in the total soil carbon (recreation of Fig. 12 in Koven et al. (2015)).(b) For an abrupt change in global NPP, from 50 PgC yr −1 to 70 PgC yr −1 at year 100.

Figure 11 .
Figure 11.Relationship between ∆Cs,NP P and ∆Cs,τ derived from the three-box model.Each dot represents the results at the end of a 70
∆C s,N P P is the change in soil carbon due to changes in NPP, ∆C s,N EP is the change in soil carbon due to changes in NEP, and ∆C s,τ is the change in soil carbon due to changes in τ s (with ∆C s,τ N EP accounting for non-equilibrium).

Table 2 .
Table presenting the absolute (PgC) and relative (%) change in 21 st century soil carbon (∆Cs) for each CMIP6 model and the ensemble mean ± standard deviation, for each future SSP scenario.Table presenting the change in 21 st century NPP and τs for each CMIP6 model and the ensemble mean ± standard deviation, for each future SSP scenario.

Table A2 .
Table presenting the change in 21 st century NPP and τs for each CMIP5 model and the ensemble mean ± standard deviation, for each future RCP scenario.