The Joint UK Land Environment Simulator (JULES; Best et al., 2011; Clark et al., 2011) is the land surface component of the UK Earth System Model (UKESM; Jones and Sellar, 2016). This paper uses a permafrost-adapted version of JULES (version 4.3; Chadburn et al., 2015a). JULES describes the physical, biophysical and biochemical processes that control the exchange of radiation, momentum, heat, water and carbon between the land surface and the atmosphere. It can be applied at a point or over a grid and requires temporally continuous meteorological forcing data along with atmospheric CO2 concentration. Each point or grid box can contain several different land-cover types or “tiles”, including five plant functional types (broadleaf trees, evergreen trees, C3 and C4 grasses, and shrubs) as well as non-vegetated tiles (urban, water, ice and bare soil). Each tile has its own surface energy balance, but the soil underneath is treated as a single column and receives aggregated mean fluxes from the surface tiles. TRIFFID, the dynamic vegetation model (Clark et al., 2011), was used to simulate the vegetation distribution and its response in a changing climate.

Several new modifications have been added into JULES to improve the representation of physical and biogeochemical processes in the cold regions. These include the additional impact of the insulation effects of a fractional moss layer at the soil surface; updated soil thermal and hydraulic properties to take account of the presence of organic matter; and a deeper and better-resolved soil column (total depth 18.3 m), with an additional thermal column at the base of the soil to represent bedrock (Chadburn et al., 2015a, b). These changes lead to a significant reduction of the error in the annual cycle of soil temperature along with a reduction in the active layer bias, from over 1.0 m too deep to only about 0.4 m too deep. All these developments are included here in an improved JULES version better suited for the permafrost simulations discussed here.

The standard soil carbon model in JULES is a four-pool model (decomposable plant material, resistant plant material, biomass and humus). When added together, these pools represent the total soil carbon storage. The model is based on the RothC soil carbon model and described in detail in Clark et al. (2011). Burke et al. (2017) adapted the soil carbon model in JULES to include a soil vertical dimension within each of the carbon pools. This results in a set of pools in every layer of the soil column. The respiration rate is determined at each depth (z) for each soil carbon pool (i) and is given by Ri=kiCi(z)FTTsoil(z)Fs(s(z))Fv(v)exp⁡-z/ζresp. Here ki is a pool-specific decay constant (s-1); Ci is the amount of soil carbon in pool i (kg m-2); and FT, Fs and Fv parameterize the response of the respiration rate to temperature (Tsoil(z) in K), soil moisture (s(z) as a fraction of saturation) and vegetation fraction (v) respectively. The soil respiration is additionally modified by including an extra exponential decay of respiration with depth. This accounts for factors that are currently missing in the model such as priming effects and microscale anoxia (Koven et al., 2013). The e-folding depth (ζresp in m) of this function is very uncertain, and the soil carbon vertical distribution depends significantly on its value (Burke et al., 2017). A smaller ζresp means the respiration is more suppressed with depth and results in more soil carbon particularly in the deeper soils.

Two different parameterizations (JULES-suppressResp and JULES-deepResp) of the response of respiration to temperature (FT) are available within JULES (Clark et al., 2011), and we test both. JULES-suppressResp uses an Arrhenius function (FT,Q10 from Eq. 2) with Q10 = 2.0 and ζresp = 0.56 m, whereas JULES-deepResp uses FT,Roth in Eq. (3) and ζresp = 2.5 m. These are shown in Fig. 1 in Burke et al. (2017). Both functions have some decomposition at temperatures below freezing. FT,Q10Tsoil=Q10Tsoil-298.1510FT,RothTsoil=47.91+exp⁡106.0Tsoil-254.85 Burke et al. (2017) showed there was very little difference in the timing of the peak soil respiration in summer between these two temperature response functions when combined with appropriate e-folding depths (ζresp).

There is a vertical mixing term representing either bioturbation (i.e. the soil mixing by, for example, animals and plant roots) or, in permafrost regions, cryoturbation (soil mixing is from frost heave and freeze–thaw processes). The mixing rate changes depending on whether permafrost is present or not (Burke et al., 2017; Koven et al., 2013). In the absence of permafrost, the bioturbation mixing rate is constant at 1 cm2 yr-1. The cryoturbation mixing rate is set at 5 cm2 yr-1. This drops off linearly below 1 m, reaching zero at 3 m depth. Permafrost is diagnosed at any location where the deepest soil layer is below 0 ∘C, assuming that there is only a very minor seasonal cycle in temperature at this depth.

Soil carbon increases, though vegetation litter falls. Although the majority of the litter enters at the soil surface, a small amount enters the deeper soil layers, for example, from roots. In JULES the litter distribution drops off exponentially with depth with an e-folding parameter of 5 m-1. The litter is mixed through the soil profile by either bioturbation or cryoturbation. The amount and quality of litter directly impact the soil carbon stocks; therefore it is important for the simulated vegetation distribution to be as accurate as possible.

Using pan-Arctic JULES simulations with this vertically resolved soil carbon model, Burke et al. (2017) showed that, at the large scale, the depth distribution of soil organic carbon approximately follows that of the observations. Chadburn et al. (2017) suggests that, given the correct input (litter), the depth distribution of soil organic carbon is well simulated for mineral soils but that the model is currently unable to reproduce the peat layers of organic soils.

Unique to the analysis is that in JULES a tracer was added to enable the “old carbon” initially within the permanently frozen soils to be easily distinguished from the rest of the soil carbon (Burke et al., 2017). This enables the old permafrost carbon, defined as carbon within the permanently frozen soil at the start of the simulation, to be traced throughout the simulation.

Our second land surface model is the Organizing Carbon and Hydrology in Dynamic Ecosystems (ORCHIDEE-MICT) model, again enhanced with several new processes related to cold-region soils. The new soil processes include the implementation of the thermal and hydrological effects of soil freezing in a multi-layered soil hydrology scheme (Gouttevin et al., 2012). Gouttevin et al. (2012) state that the modelling of the soil thermal regime is generally improved by the representation of soil freezing processes. This enables the dynamics of the active layer to be more accurately captured. This process is important when simulating the response of frozen carbon stocks to future warming (Koven et al., 2009, 2011). Also added is a more advanced multi-layer snow scheme, which improves the estimation of permafrost physics (Wang et al., 2013). This three-layered snow module includes a varying snow density and a varying snow thermal conductivity along with the thawing and refreezing of water within the snowpack. More specifically, the snow module has been introduced to account for the water freezing–thawing processes within snow capturing more accurately the impact of the overlying snow cover on soil temperature (Wang et al., 2013). An evaluation of snow depth, snow water equivalent, surface temperature, snow albedo and snowmelt runoff demonstrate the improvement in the simulation of snow processes by this version of ORCHIDEE-MICT over previous versions. To account for the effects of cryoturbation on redistribution of soil organic carbon (SOC), a vertical mixing scheme based on a diffusion equation was introduced into ORCHIDEE-MICT (Koven et al., 2009), with the diffusion length being set to 3 times the local active layer thickness. In the model version used here, carbon and temperature are discretized down to the depth of the bottom layer (47.6 m), whereas the soil depth for hydrology is 2 m. Soil water content in each layer below 2 m is assumed to be equal to the monthly average soil moisture at the bottom layer of the top 2 m, and its frozen fraction depends on soil temperature of the layer below 2 m.

The soil carbon model of ORCHIDEE-MICT is based on the equations in the CENTURY model (Parton et al., 1992). It contains seven pools, namely, above- and below-ground metabolic and structural litter, along with active, slow and passive soil organic carbon pools. Decomposition of carbon is modulated by soil temperature and moisture functions along with a clay function. Transfer functions between pools are described using the CENTURY equations (Parton et al., 1992). The temperature function FT follows Eq. (2) for temperatures above 0 ∘C. At colder soil temperatures below 0 ∘C, FT is reduced linearly to reach zero at -1 ∘C (Koven et al., 2011). In this paper, heat production by decomposing soil carbon (the “heating” experiment in Koven et al., 2011) is turned off. Unlike JULES the old carbon cannot be traced throughout the simulation, which means the old carbon below the active layer and within the permafrost is only identified at the start of the simulation. As with JULES, the dynamic vegetation model was used to simulate the vegetation distribution and litterfall. Both of these have a significant impact on the soil carbon stocks.

The Integrated Model Of Global Effects of climatic aNomalies is an intermediate-complexity climate model developed specifically to quantify geographical and seasonal variation in meteorological conditions over land in response to changing atmospheric gas composition. It can be operated for different anthropogenic-emission scenarios and can capture global land–atmosphere carbon feedbacks. IMOGEN is calibrated to emulate different GCMs and, for example, has recently been used to investigate the risk of Amazon dieback under a large range of climate projections (Huntingford et al., 2013). Here it provides a test bed for evaluating the impact of the permafrost feedback on the global carbon cycle for a variety of emission scenarios, driving GCMs and alternative land surface parameterizations describing the northern latitude terrestrial cryosphere response.

IMOGEN contains a simple energy balance model to relate changes in atmospheric greenhouse gas concentrations to the global mean land temperature via changes in a radiative forcing. The radiative forcing itself depends on any pathway in altered atmospheric gas concentrations since the pre-industrial period. The EBM requires four parameters which are readily calibrated against a given climate model (Huntingford et al., 2010). The four parameters are climate feedback parameters over land and over sea, the oceanic effective thermal diffusivity representing the ocean thermal inertia and a land–sea temperature contrast parameter which linearly relates warming over the land to warming over the ocean (Huntingford and Cox, 2000).

IMOGEN forces its coupled land surface model with local meteorological data temporally downscaled from calculated mean monthly values to 30 min timescales using a weather generator. These driving data, required by both JULES and ORCHIDEE-MICT, are 1.5 m temperature, relative humidity, wind speed, precipitation, downward shortwave and longwave radiation, and pressure. The mean monthly data (that are downscaled) are derived for each GCM, assuming simple linear regressions between the local and monthly variations in meteorology and the amount of annual global mean warming over land. This “pattern-scaling” concept (Huntingford and Cox, 2000) takes these regression values and multiplies them by the mean warming over land calculated from the EBM in IMOGEN. The patterns of changing meteorological conditions plus the four energy balance model parameters to give mean land warming were calibrated for the 22 CMIP3 climate models (Huntingford et al., 2013). These 22 patterns represent the uncertainty in the driving climate models. The monthly anomalies of climate change (from EBM and patterns combined) are added to the 1961–1990 Water and Global Change forcing data (WFD) climatology (Weedon et al., 2011), which is assumed here to be also representative of pre-industrial conditions. Any biases introduced by neglecting anthropogenically induced climate change up to that date are assumed to be small compared with the errors from using earlier years in the WFD climatology with poorer observational coverage (Huntingford et al., 2013). This also removes individual GCM biases in the estimation of the pre-industrial state.

IMOGEN has a closed global carbon cycle when its operation includes a land surface model (Huntingford et al., 2013). At the end of each modelled year, atmospheric CO2 concentration is modified using the difference between prescribed emissions and the global mean ocean–atmosphere and land–atmosphere fluxes of CO2 for that year. The values of net ecosystem productivity (NEP) are integrated over all land points for that year and used to derive the land–atmosphere flux. The NEP is output from either JULES or ORCHIDEE-MICT. A single “box” model is used to calculate the ocean sink. It is a function of both global temperature increase and atmospheric CO2 level (Huntingford et al., 2004). Any changes in atmospheric CO2 concentration then feed back via the energy balance model on modelled surface climate changes, which drives the scaled patterns of local and monthly climatology.

The pre-industrial spin-up state for each of the different land surface models was estimated using the 1961–1990 WFD climatology and pre-industrial atmospheric CO2 concentration at the IMOGEN resolution of 2.5∘ latitude and 3.75∘ longitude. This was done independently for each of the three different global land surface model configurations, but in each case it was sufficient to give stable soil carbon and vegetation carbon distributions for 1860. In both JULES and ORCHIDEE-MICT competition of vegetation was enabled, allowing the models to determine both their initial vegetation distributions and litterfall and the response of the vegetation distribution and litterfall to climate change. Anthropogenic land use change was ignored in these simulations, as it is relatively small at northern high latitudes (Klein Goldewijk, 2001).

In JULES a “modified accelerated decomposition” numerical technique (modified-AD; Koven et al., 2013;) was adopted to more quickly spin the JULES soil carbon to an initial equilibrium distribution. The decay rates of the four soil carbon pools were set to the rate of the fastest pool. In order to appropriately adopt the modified-AD method, the diffusion coefficients for the four pools were multiplied by the same factors. The model was then initially spun up for 500 model years using this modified-AD technique and the fixed WFD climatology representative of pre-industrial times. The decay rates for the four pools were then reset, and the model was spun up for another 2000 years again using the WFD climatology. This needed to be done independently for both JULES-suppressResp and JULES-deepResp – although these two model versions have the same physics and vegetation carbon, they have different soil carbon distributions. ORCHIDEE-MICT was initially spun up by running the full version of the land surface model (30 min time step) for 150 years first, again with the WFD climatology. Following this, the soil carbon sub-model forced by above- and below-ground litter input (FORCESOIL) was run 10 times for 10 000 model years, with each time followed by a 2-year run of the full ORCHIDEE-MICT. This was followed by another 200 years of ORCHIDEE-MICT to complete the numerical spin-up. Note that, due to its permanent burial of carbon below the active layer even after 100 000 years of spin-up, ORCHIDEE-MICT's soil carbon pools continue to gain carbon, albeit at a very small rate (mean net ecosystem productivity over the last 50 years of spin-up is 0.16 Gt C yr-1). The permafrost area, soil and vegetation carbon distributions for these pre-industrial states are described here and used to initialize the transient simulations.

To quantify the permafrost carbon feedback separately, paired simulations were carried out for each of the JULES and the ORCHIDEE simulations: one which includes the response of the climate to the CO2 emissions from the perturbed (thawing) permafrost carbon (indexed “PF”) and one which excludes it (indexed “non-PF”). In JULES the permafrost carbon and non-permafrost carbon are diagnosed separately at each time step. For the non-PF case, only the non-permafrost carbon is visible to IMOGEN, whereas for the PF simulation all the soil carbon is visible to IMOGEN. In ORCHIDEE-MICT, for the case of the non-PF simulations, the pre-industrial permafrost carbon is subtracted from the total soil carbon at each time step.

The spun-up coupled system is forced with historical fossil fuel and cement production CO2 emissions followed by the emissions representing three of the RCPs used in the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR5; IPCC, 2013) – RCP2.6, RCP4.5 and RCP8.5 (Moss et al., 2010; Meinshausen et al., 2011). Simulations were carried out until the year 2300 using the RCP extensions (Meinshausen et al., 2011) to examine the long-term relationship between permafrost and climate. Non-CO2 greenhouse gases and aerosols were not included in this set of simulations, nor were land use change emissions. The impact of these extra emissions will be minor for the purpose of our study focusing on the differences between PF and non-PF simulations.

The models were assessed to ensure that the permafrost physics and the soil and vegetation carbon are not inconsistent with the observations. Permafrost is assumed to exist in grid cells where the soil is frozen at 3 m depth for a period of 2 years or more. Figure 1 (left panels) shows the simulated permafrost extent for JULES (JULES-suppressResp and JULES-deepResp have the same physics and hence the same permafrost) and ORCHIDEE-MICT. Superimposed on the simulated permafrost extent are the observations from Brown et al. (1998). Both JULES and ORCHIDEE-MICT capture all of the observed continuous permafrost (more than 90 % of a grid cell underlain by permafrost). They might be expected to also capture the regions of discontinuous permafrost (more than 50 % but less than 90 % of a grid cell underlain by permafrost) and simulate a permafrost area similar to the observed area of continuous and discontinuous permafrost (15 million km2). JULES has slightly too much permafrost overall with extra permafrost in Eurasia and not enough in North America – this is possibly caused by biases in the winter snow depth. ORCHIDEE-MICT systematically simulates more permafrost than either the observations or JULES. Compared with the 0 ∘C isotherm for the 2 m air temperature (Fig. 1, right panels), ORCHIDEE-MICT has some permafrost where the annual mean temperature is greater than 0 ∘C, suggesting it might be missing a process which increases the thermal insulation in winter between the air and the deeper soil.

The simulated vegetation carbon distribution is shown in Fig. 2. There are no feedbacks from the soil carbon onto the vegetation – via, for example, changing soil hydraulic properties or nitrogen limitation; therefore both versions of JULES also have the same vegetation distribution. In general both of the models simulate more vegetation carbon than observed, which will lead to more litter carbon input. Some model overestimation might be expected because there is no land use change included in the models. There are also some differences in spatial patterns; for example, in JULES the simulated boreal forest does not extend far enough east in Siberia. This will reduce the litter inputs in eastern Siberia and potentially result in relatively smaller simulated soil carbon stocks in these regions. ORCHIDEE-MICT has slightly more vegetation carbon than JULES, but its spatial distribution is more comparable to the observations.

Figure 3 shows the soil carbon distribution simulated by the three different model versions (top three row panels), with the left-hand panels being the total soil carbon in the top 2 m and the right-hand panels being the soil carbon in the permafrost in the top 3 m. Also shown, bottom row, are two different observational data sets. The first is the ISRIC-WISE-derived soil property estimates on a 30-by-30 arcsec global grid (WISE30sec; Batjes, 2016). The second is the Northern Circumpolar Soil Carbon Database version 2 (NCSCDv2; Hugelius et al., 2014). The WISE30sec soil carbon distribution for the top 2 m of soil is shown at the bottom left, and the NCSCDv2 for the top 3 m of the soil is shown at the bottom right. These observed distributions are interpolated from a number of discrete soil pedons and therefore have a large associated uncertainty not reflected in these figures. The two different observational data sets have different amounts of soil carbon in the polar region. In the top 2 m of the region mapped by the NCSCDv2 there is 873 Gt C in NCSCDv2 but only 622 Gt C in the WISE30sec data set. The NCSCDv2 was specifically created for the northern high latitudes, so it is likely to be more suitable for any assessment of the northern high-latitude soil carbon, but it only covers a limited region of the northern latitudes.

On inspection of Fig. 3 the models have more soil carbon in the top 2 m than the WISE30sec observations, but this might be expected if the WISE30sec underestimates the northern high-latitude soil carbon. All three models have large amounts of soil carbon in the permafrost regions of Siberia and northern Canada. The right-hand column shows the simulated soil carbon in the top 3 m of the simulated permanently frozen soil volume. These are not directly comparable with the NCSCDv2 observations, which show the total soil carbon in the top 3 m; the NCSCDv2 observations provide an upper limit on the permafrost carbon (586 Gt C for regions > 60 ∘ N). The permafrost carbon in both JULES simulations falls below this threshold (314 and 488 Gt C for regions > 60 ∘N), but ORCHIDEE-MICT (959 Gt C for regions > 60 ∘N) has more than the total soil carbon in NCSCDv2.

The simulated distribution of permafrost carbon is strongly controlled by the simulated permafrost extent: ORCHIDEE-MICT has too much permafrost and hence too much permafrost carbon; JULES has too little permafrost in North America and western Russia and consequently low permafrost carbon in that region. Although JULES-suppressResp has suppressed respiration with depth and relatively more soil carbon deeper in the profile, it has a smaller proportion of its total global soil carbon at northern high latitudes than JULES-deepResp because of the dependence of FT on temperature (Eqs. 2 and 3). Despite obvious model biases, these three different models provide reasonable approximations of the land surface state, and we consider them to zero order as suitable for estimating the permafrost carbon feedback.

The simulated areal loss of the top 3 m or permafrost, or near-surface permafrost, under the different RCP scenarios considered is shown in Fig. 4. For a grid cell to lose permafrost, it must have a temperature greater than 0 ∘C at a depth of 3 m for at least 1 month of the year. ORCHIDEE-MICT has a much larger initial permafrost extent but loses a smaller fraction of its permafrost than JULES under the RCP scenarios. The models simulate an increasing rate of permafrost loss with time over the next ∼ 100 years and then tend towards stabilization after 2200 in the RCP scenarios that stabilized forcing around 2100. By 2100 between 5 and 63 % of the permafrost is lost, depending on model configuration and emissions scenario (comparing Fig. 4 changes with annotations in Fig. 1). This potentially very big change in permafrost extent falls within the spread given by Koven et al. (2013) for the CMIP5 models. This might be expected because Koven et al. (2013) found that structural differences in snow physics and soil hydrology had a significant impact on uncertainties – our set of model simulations has a smaller range of these structural uncertainties. Across all scenarios, the near-term sensitivity of future permafrost area to global mean temperature change is 1.95 to 2.10 million km2 ∘C-1 for JULES and 2.30 to 2.55 million km2 ∘C-1 for ORCHIDEE-MICT. This is less than the 4.0 ± 0.9 million km2 ∘C-1 found after stabilization of permafrost by Chadburn et al. (2017) but falls within the 1.8–2.6 million km2 ∘C-1 (Chadburn et al., 2015b) found using transient model simulations. By 2300 between 6 and 90 % of the near-surface permafrost is lost, a range more consistent with the stabilized estimate of Chadburn et al. (2017). In JULES the permafrost area has stabilized by 2300, but ORCHIDEE-MICT is still losing near-surface permafrost, in particular for the RCP8.5 scenario, suggesting that ORCHIDEE-MICT has greater thermal inertia than JULES.

Figure 5 shows the change in northern high-latitude vegetation (top row panels) and soil carbon (middle and bottom) over the region polewards of 60∘ N. In the case of soil carbon two different quantities are shown – the non-PF soil carbon in the middle row and the total soil carbon in the bottom row. At the start of the simulation the non-permafrost soil carbon is defined as the soil carbon within the active layer; i.e. any old carbon below the active layer in the permanently frozen soil is excluded. In any given subsequent year, this non-permafrost soil carbon is defined for the same soil volume, i.e. within the active layer defined for 1860. This non-permafrost soil carbon is taken to be equivalent to the soil carbon assessed by Ito et al. (2016) and Qian et al. (2010), who present results from simulations of the northern high-latitude carbon balance without any specific permafrost carbon included. The bottom row in Fig. 5 shows the total northern high-latitude soil carbon including both the old carbon below the active layer and the non-permafrost soil carbon. The tables in the Supplement summarize these changes for four different regions (polewards of 60∘ N, polewards of 55∘ N, the land surface where permafrost is observed and the land surface where permafrost is simulated by each model version in 1860).

Warming and CO2 fertilization effects stimulate vegetation growth and increase land carbon storage in all three land surface model configurations (Fig. 5, top row panels). This results in an increase of vegetation carbon of between 10 and 60 Gt C by 2100 with a greater increase in ORCHIDEE-MICT than JULES and a greater increase for the higher-emissions scenarios, due to higher atmospheric CO2. Ito et al. (2016) used offline land surface models driven by weather data from global climate models under a high-emissions scenario and showed the vegetation carbon change was between -5 and 80 Gt C: a much larger spread than found here. Qian et al. (2010) assessed the C4MIP (Coupled Climate Carbon Cycle Model Intercomparison Project) models under a high-emissions scenario and found an increasing vegetation carbon of 17 ± 8 Gt C by 2100 – this range falls within the spread shown here. The vegetation carbon increase is slower in JULES than ORCHIDEE-MICT and continues to increase after 2300, whereas in ORCHIDEE-MICT the vegetation is stabilizing by 2300. This is probably linked to the different rates of establishment and growth of the boreal forest as it expands polewards in the two models.

This enhanced vegetation productivity leads to increased soil carbon storage in biomass litter and input to soil organic matter pools. In a warming climate, the soil organic matter decomposition also accelerates, decreasing the soil carbon. The balance between increased soil carbon input and increased decomposition (or reduced turnover time of soil carbon) is relatively uncertain (Jones et al., 2005), leading to simulations of either an increase or decrease in non-permafrost soil carbon at northern high latitudes under future climate change. All three models show an increase in non-permafrost soil carbon before 2100. Across all the different climate responses and emission scenarios examined these increases range from 10 to 100 Gt C and suggest that the increase of litterfall dominates over increased respiration. By 2100, Qian et al. (2010) found that the soil carbon in the C4MIP models increases by 21 ± 16 Gt C. Ito et al. (2016) showed that, although the majority of their model ensemble members have an increase in soil carbon before 2100, there are a few with a decrease. This decrease is not reflected in this ensemble of model simulations and is probably caused by a combination of unsampled structural uncertainty in the current ensemble and unrealistic soil organic carbon distributions in some of the models in the Ito et al. (2016) ensemble. The spread of the future response of the non-permafrost soil carbon in RCP8.5 (caused by differences in the driving GCMs) is larger than the differences between the different RCP scenarios. JULES-suppressResp and ORCHIDEE-MICT have an increase in non-permafrost soil carbon of similar magnitudes; these increases are slightly larger than in JULES-deepResp. After 2100, in the majority of simulations, the non-permafrost soil carbon is relatively stable. The exception to this is RCP8.5 for JULES-deepResp, where there is a significant loss of non-permafrost soil carbon for a few of the simulations.

Qian et al. (2010) and Ito et al. (2016) did not include any specific permafrost carbon. However when permafrost carbon is included in the simulations (Fig. 5, bottom row panels), the increase in the total soil carbon before 2100 is reduced, and in some cases there is a slight decrease. The impact of including permafrost soil carbon in northern high-latitude soils is highly model-dependent. In JULES-suppressResp, although the total soil carbon increases more than the non-permafrost soil carbon, there is little noticeable difference in Fig. 5. However in ORCHIDEE-MICT and JULES-deepResp there is a significant decrease in total soil carbon compared with non-permafrost soil carbon, which continues past 2300, especially for RCP8.5. In JULES, uncertainties in the total northern high-latitude soil carbon (given by the spread in the bottom row of Fig. 5) caused by uncertainties in the climate response are larger than the differences between scenarios. However, the differences between the different model versions dominate any differences in scenario or driving climate.

For the ensemble mean of the RCP8.5 scenario, including permafrost carbon in JULES-deepResp and ORCHIDEE-MICT results in a reduction in the total carbon in the northern permafrost region by 2150 (when compared with 1860). The majority of the RCP2.6 and RCP4.5 scenarios and JULES-suppressResp still have more total carbon in the northern permafrost region in 2300 than in 1860, even when permafrost carbon is included.

Changes in biomass and in global soil carbon drive the land–atmosphere flux of CO2, which then feed backs, influencing the global climate change. IMOGEN can capture this effect. Globally, there is an initial uptake of carbon by the land, which reduces over time as the vegetation and soil begin to uptake less, and in some cases the soil becomes a source of carbon as respiration carbon loss overtakes litterfall carbon input (Fig. 6, top row panels). By 2300 the global land surface has a net carbon balance very close to zero for many of the RCP2.6 and RCP4.5 simulations. The RCP8.5 simulations are very uncertain, with some climate patterns driving a source of global land carbon and some patterns a sink of global land carbon.

The contribution of permafrost carbon to the global land flux is also shown in Fig. 6 (bottom row panels). Including the permafrost carbon increases the global land CO2 flux to the atmosphere, only slightly for JULES-suppressResp but more notably for the other two model versions. This brings the time of peak annual uptake earlier in the permafrost enabled simulations – it is 10 years earlier for JULES-deepResp and ORCHIDEE-MICT and 4 years earlier for JULES-suppressResp and suggests that permafrost thaw could cause a significant positive feedback on the climate system.

The impact of including these additional permafrost-related carbon fluxes on the global mean temperature is less than ∼ 0.46 ∘C (Fig. 7: PF – non-PF simulations). However, the impact is very different between the three different model configurations, for example, JULES-deepResp, giving an additional increase of 0.02–0.28 ∘C (5th–95th percentile), and JULES-suppressResp, giving an additional increase of 0.01–0.05 ∘C (5th–95th percentile). These results appear relatively independent of scenario, but there are some notable differences between the different model configurations.

Figure 8 shows the temperature change caused by permafrost carbon loss as a percentage of the global mean temperature change. RCP2.6 has a much lower overall temperature increase (∼ 2 ∘C) than RCP8.5 with a ensemble mean temperature increase of ∼ 7 ∘C. This is reflected by the larger relative impact of the permafrost carbon for the RCP2.6 scenario than for the RCP8.5 scenario. For the RCP2.6 scenario the permafrost carbon loss increases the global mean temperature by between 4 and 18 %, however. Even for JULES-suppressResp, where the loss of permafrost carbon is relatively low, the temperature change caused by permafrost carbon is still a relatively large fraction (5–8 %) of the global mean temperature change. The percentage impact of permafrost carbon is lower (less than 4 % of the global mean temperature change) for the high-emissions scenario. This is because the radiative forcing from CO2 is a logarithmic function of CO2 concentration – at higher CO2 concentrations, 1 kg of CO2 increases the radiative forcing less than at lower concentrations. These results, in line with MacDougall et al. (2012) and Crichton et al. (2016), suggest that permafrost carbon should be taken into account particularly when evaluating scenarios of strong mitigation and stabilization.

The carbon cycle response in a changing world can be described via two components, firstly the climate–carbon response (γ), which determines the change in carbon storage caused by changes in climate. The climate–carbon response, γ, is formally defined as the change in land carbon per degree of global mean temperature change (Friedlingstein et al., 2006). The second component is the concentration–carbon response (β), which determines the change in carbon storage caused by changes in CO2 concentration – sometimes referred to as the “fertilization” effect. Chapter 6 of the most recent IPCC report (Ciais et al., 2013) assessed results from models without permafrost carbon and stated that there is high confidence that increasing the atmospheric CO2 will increase land uptake and medium confidence that climate change will reduce the land uptake. The latter can exhibit regional variation, potentially with different signs, and is predominantly due to the direct effects of higher temperatures. The inclusion of permafrost carbon will have a minor impact on the concentration–carbon response (β) but will reduce the land carbon uptake and hence increase the climate–carbon response (γ).

At the start of the simulation the carbon that is below the active layer is defined as permafrost carbon. In JULES this carbon is numerically labelled, and its (depth) location can be traced throughout the simulation. It is denoted “old permafrost carbon” and is assumed to be the cryogenically stabilized carbon pool within the permafrost under pre-industrial conditions. This can only remain the same or decrease during the simulation period. It cannot be added to. In ORCHIDEE, although the old permafrost carbon can be identified under pre-industrial conditions, it cannot be traced throughout the simulations.

Figure 9 shows the time series of the old permafrost carbon – by 2100 JULES-deepResp loses between 20 and 50 Gt of old permafrost carbon, and JULES-suppressResp loses about 20 Gt of old permafrost carbon. There are relatively small differences between emissions scenarios compared with the large differences between JULES-deepResp and JULES-suppressResp. Koven et al. (2015b) found a similar result for RCP4.5 with permafrost soil carbon losses of 12.2–33.4 Gt C, but they found a much larger loss of permafrost carbon for RCP8.5, the high-warming scenario. Loss of old permafrost carbon in JULES continues out to 2300, with no sign of stabilization.

Figure 10 shows the change in permafrost carbon as a function of global temperature change for three time slices: 2100, 2200 and 2300. For each time slice and each model version there is a well-defined relationship which is relatively independent of the driving climate model and the emissions scenario. The permafrost carbon–climate feedback parameter, or γPF, is defined as the slope of the relationship between the loss of old permafrost carbon and global mean temperature change, i.e. the slope of the relationship in Fig. 10. γPF increases with the time over which the warming has been applied; for example, for JULES-deepResp, γPF is ∼ 10 Gt C K-1 at 2100, ∼ 20 Gt C K-1 at 2200 and ∼ 30 Gt C K-1 by 2300. These differences are caused by inertia in the permafrost system related to the ongoing low temperatures which slow the decomposition rate of the thawed old permafrost carbon. This significant time dependence of the permafrost climate feedback (expressed in Gt C K-1) means that an alternative method of quantifying the permafrost carbon–climate response is required.

Here we quantify the FCRt, defined for any time over the simulations as the ratio of remaining permafrost carbon to the permafrost carbon loss rate at that time. FCRt can be used to estimate permafrost carbon loss given any pathway of global mean temperature and an assessment of the initial permafrost carbon. It is derived independently for the two different versions of JULES using the old permafrost carbon traced throughout the simulations and the simulated global temperature change. FCRt is defined for any given year as the old permafrost carbon still in the permafrost divided by the loss of permafrost carbon in that year. Figure 11 shows the FCRt as a function of global mean temperature change (GMT) for the two available versions of JULES. There is a clear relationship between the FCRt and the global mean temperature change. This is relatively independent of scenario but remains highly model-dependent.

The results of an exponential fit between the FCRt and the global temperature change (Eq. 4) are shown in Fig. 11 and Table 1. The data for the fit were restricted so that the global temperature change was between 0.2 and 5 ∘C, and this relationship should only be applied within that range. FCRt=FCRt0exp⁡-ΔTΓwhereΔT>0.2∘C FCRt0 is a reference timescale representing the permafrost carbon turnover time at the transition point from accumulation of soil carbon to loss of soil carbon. ΔT is the temperature above which this transition occurs. If permafrost carbon were totally inert, FCRt0 would be infinite at ΔT = 0 ∘C. However in JULES this is a large but finite number of years, and the old permafrost carbon simulated within JULES can be considered stable over centennial timescales. There are a couple of process within JULES which cause this. Firstly, there is mixing of soil carbon throughout the profile. This mixing reduces exponentially with increasing depth but still occurs within the permafrost. In addition, the soil carbon is still decomposing, albeit at a very slow rate, at temperatures below 0 ∘C. FCRt0 is slightly larger for JULES-suppressResp because the respiration is much slower at depth than in JULES-deepResp. The decay term, Γ, represents the temperature change at which the number of years taken for all of the old permafrost carbon to be emitted reduces by 1/e of its initial value. As expected this is much larger for JULES-suppressResp than JULES-deepResp.

The relationship found in Eq. (4) can be used to reconstruct a simple estimate to quantify the loss of old permafrost carbon given an annual time series of global mean temperature change and the initial permafrost carbon. An example of a reconstructed time series of permafrost carbon is shown in Fig. 12. The JULES simulations of old permafrost are the individual curves from Fig. 11 for RCP4.5. The reconstructed curves fall within the spread of the original results.