ORCHIDEE-v3 (ORganizing Carbon and Hydrology in Dynamic EcosystEms) is a state-of-the art process-based land surface model that calculates energy, water, carbon and nitrogen exchanges between the surface and the atmosphere, as well as terrestrial physical and biogeochemical processes. It is composed of two main sub-models : SECHIBA that describes exchanges of energy and water between the atmosphere, the biosphere and the soil, and STOMATE that simulates the phenology and carbon and nitrogen dynamics of the terrestrial biosphere . Fast processes (e.g. latent and sensible heat fluxes, photosynthesis, ecosystem respiration) are computed every 15 min while slow processes (e.g. carbon and nitrogen allocation) are computed daily.

Vegetation is represented by plant functional types (PFTs), i.e. groups of species sharing similar characteristics . These PFTs share the same equations for most processes, but with different parameters. ORCHIDEE-v3 represents 15 PFTs, classified into forests, grasses, crops and bare soil, describing a variety of ecosystems (Table ). PFTs can coexist in every grid box and the fraction occupied by each PFT is read from a prescribed map (which can change on a yearly basis) . For each PFT, carbon and nitrogen are contained in seven plant pools (leaves, below- and above-ground sapwood and heartwood, fruits and fine roots), five litter pools (above- and below-ground metabolic and structural, and woody litter) and three soil pools (active, slow, and passive).

ORCHIDEE-v3 represents energy exchanges between the surface and the atmosphere and takes into account shortwave and longwave radiative fluxes, turbulent latent and sensible heat fluxes, and a ground flux . The turbulent fluxes are calculated separately for each PFT and then summed for each grid box. This coupling with the atmosphere is regulated by vegetation properties such as its albedo and its height (which impacts on surface roughness). Within the ground, heat transfers are represented by a heat diffusion equation and depend on the mineral and organic soil properties (thermal capacity, thermal conductivity, porosity) and soil hydrology. Mineral soil properties are extrapolated from the soil texture map of . Soil thermal dynamics is based on an 18-layer vertical scheme, extending down to 90 m (Table ). The thickness of each layer increases with depth, with thinner layers near the surface. A zero flux condition is imposed at the bottom boundary.

The model also represents exchanges of water between the surface and the atmosphere. Water reaches the land through rain or snowfall, and can be lost through evaporation of water stored in the soil but also intercepted by the canopy, transpiration by vegetation, snow sublimation, surface runoff and percolation and transfer to groundwater (i.e. drainage). Internal water exchanges between land components can also occur through various mechanisms, such as snow melt, or plant root uptake. Soil moisture is resolved on a 11-layer scheme (the same as for soil thermics) down to 2 m, where a free drainage bottom boundary condition is imposed . Therefore, the bedrock differs between soil thermics (90 m) and hydrology (2 m), and a deeper hydraulic scheme is under development. Water is transferred from one layer to another according to a one-dimensional Fokker-Planck equation . Below 2 m, the calculation of soil thermal properties uses the water content of the deepest hydrological layer. Vegetation has a major influence on water exchanges by regulating evapotranspiration through stomatal closure and soil water uptake.

The representation of the carbon and nitrogen cycles have already been described in detail in , and . The following sections are limited to the description of relevant processes for high latitudes and new developments. A more detailed description of ORCHIDEE-v3 can be found in Appendix .

The improvements to permafrost physics (Sect. , and ) have been described in and are summarised here for the sake of completeness. The ground temperature in ORCHIDEE-v3 is calculated using a one-dimensional Fourier equation with a boundary condition at the surface allowing heat exchanges with the atmosphere (Eq. 5 in ): 1capp∂T∂t=∂∂zKth∂T∂z where T is the soil temperature (K) and Kth the soil thermal conductivity (W m⁻¹ K⁻¹). capp is apparent volumetric soil thermal capacity (J K⁻¹ m⁻³). It incorporates volumetric soil thermal capacity and a term representing the latent heat of soil water phase changes during melting and freezing: 2capp=cp-ρiceLΔΘiceΔT where cp is the volumetric soil thermal capacity (J K⁻¹ m⁻³), ρice the ice density (kg m⁻³), L the latent heat of fusion (J kg⁻¹) and Θice the volumetric ice content (m³ m⁻³).

Taking into account the latent heat of water phase change is essential to correctly simulate the soil thermal dynamics in the permafrost region. It acts as a buffer – also called zero-curtain effect – absorbing energy from thawing ice in spring and summer and releasing energy when the water refreezes in autumn and winter, thus reducing the amplitude of the seasonal cycle of ground temperature.

Soil organic carbon (SOC) has been shown to be an important driver of surface-atmosphere energy exchanges at high latitudes and of permafrost thermal dynamics . Its effect is taken into account in our model by weighting the soil thermal properties by the SOC volume fraction (fSOC). fSOC is calculated as: 3fSOC=CSOCCSOCmax where CSOC is the SOC density (kgC m⁻³) and CSOCmax= 500 kgC m⁻³ is a reference value. CSOCmax has been tuned to simulate a realistic high latitude climate , ensuring that its value remains in the range of soil carbon densities from the SoilGrids database . The heat diffusion equation (Eq. ) then uses the total soil thermal conductivity and capacity (mixing mineral and organic soil properties).

Solid and dry soil thermal conductivities and the dry thermal capacity are computed as weighted averages of those of mineral and organic soils : 4λsolid=(1-fSOC)λsolidmineral+fSOCλsolidSOC5λdry=(1-fSOC)λdrymineral+fSOCλdrySOC6cdry=(1-fSOC)cmineral+fSOCcSOC where cmineral (J K⁻¹ m⁻³) and λmineral (W m⁻¹ K⁻¹) are the thermal capacities and conductivities of solid/dry mineral soils, which depend on the dominant soil texture of the grid box. Solid refers to the solid fraction of the soil (excluding pores) while the dry fraction also includes the pores filled with air (not those filled with water). The total thermal capacity is then calculated for each soil layer as: 7c=cdry+Θliqcliq+Θicecice where Θliq (unitless) and Θice (unitless) are the volumetric liquid water and ice contents computed by the model and cliq and cice are the thermal capacities (J K⁻¹ m⁻³) of liquid water and ice, respectively equal to 4.18 × 10⁶ and 2.11 × 10⁶ J K⁻¹ m⁻³. The thermal conductivity of dry organic carbon (cdry) is fixed at 2.5 × 10⁶ J K⁻¹ m⁻³. For each soil layer, the thermal conductivity is computed as: 8λ=Keλsat+(1-Ke)λdry where: 9λsat=λsolid(1-Θsat)λliqΘsatΘliqΘliq+ΘiceλiceΘsatΘiceΘliq+Θice with λliq and λice the thermal conductivities of liquid water and ice, respectively equal to 0.57 and 2.2 W m⁻¹ K⁻¹, and Θsat (unitless) the volumetric moisture content at saturation, which depends on the dominant mineral soil texture. The thermal conductivity of dry organic carbon (λdry) is fixed at 0.25 W m⁻¹ K⁻¹.

Ke is the Kersten number defined for unfrozen soil as: 10Ke=log10(Sr)+1ifSr>0.10.7log10(Sr)+1if0.05<Sr≤0.10ifSr≤0.05 where Sr is the saturation ratio and is calculated as Sr=ΘliqΘsat. For (fully or partially) frozen soils, Ke =Sr.

The modification of soil thermal parameters by soil organic carbon creates a coupling between the carbon cycle and soil thermodynamics, eventually impacting surface-atmosphere energy transfers. Importantly, the porosity calculated by the thermal module of ORCHIDEE-v3 differs from that used in the hydrological scheme (which is equal to that of a mineral soil), which prevents a direct feedback between soil moisture and soil temperature through soil porosity.

In the Arctic, the surface organic layer (SOL) formed by litter and groundcover vegetation (moss, lichens) may significantly reduce surface-atmosphere energy exchanges through their insulative properties and therefore thermally protect permafrost soils from warmer summer air temperatures . In IPSL-Perm-LandN, we decided to modify the thermal capacity and conductivity of the upper soil layers to mimic the effect of such a surface organic layer on soil thermal dynamics. This assumption is made in some land surface models , whereas some other models explicitly represent an organic layer on top of the soil column . We further assumed that the surface organic layer covers a fraction fSOL of each grid box containing boreal PFTs, as bryophytes are widespread in these ecosystems .

The calculation of the effect of the surface organic layer on soil thermal transfers is carried out in two steps. First, a virtual column (not explicitly represented in the model) is defined over a fraction fSOL of the grid box, representing moss, lichen and/or decomposing litter (dashed red in Fig. ). The thermal capacity of the virtual column is calculated as a weighted average of the surface organic layer and soil thermal capacities: 11cvirtualcolumnSID=cSOLSOLT+csoilSID⇔cvirtualcolumn=cSOLSOLTSID+csoil where cSOL is the volumetric thermal capacity of the surface organic layer (J K⁻¹ m⁻³), csoil is the volumetric soil thermal capacity (as calculated in Sect. , J K⁻¹ m⁻³), fSOL is the fraction of the grid box that contains the surface organic layer, SOLT is the surface organic layer thickness and SID is the soil integration depth, i.e. the depth down to which the properties of the soil organic layer are mixed with those of the soil.

Then, the total thermal capacity of the grid box (ctot), which takes into account the fraction not covered by the surface organic layer, is calculated as the weighted average of cvirtual column and csoil: 12ctot=fSOLcvirtualcolumn+(1-fSOL)csoil=fSOLcSOLSOLTSID+csoil

The approach for thermal conductivity is similar but takes into account that it is an intensive property (i.e. its value is independent of the size of the system). The thermal conductivity virtual column (λvirtualcolumn) is the equivalent thermal conductivity of the surface organic layer and soil layers in series: 13λvirtualcolumn=λSOLλsoilSIDSOLTλsoil+SIDλSOL where λSOL is the thermal conductivity of the soil organic layer and λsoil is the thermal conductivity of the soil.

The total thermal conductivity of the grid box is the equivalent thermal conductivity of the surface organic layer column and the soil column in parallel: 14λtot=fSOLλvirtualcolumn+(1-fSOL)λsoil=fSOLλSOLλsoilSIDSOLTλsoil+SIDλSOL+(1-fSOL)λsoil Finally, the mineral soil capacity and conductivity are replaced by ctot and λtot in all the soil layers between the surface and SID.

In this study, we chose fSOL=1, SOLT =0.03 m and SID =0.03 m for evaluating the model. This value of SOLT is consistent with the moss thickness measured in . SID was chosen small enough to allow the soil organic layer to influence surface-atmosphere energy exchanges, but to limit the modification of soil thermal properties to the very top layers.

In addition, the thermal properties of the surface organic layer depend on its water content . They are parameterized using observations made on mosses, using the upper soil water content of each soil layer down to SID as a proxy for the water content of the surface organic layer. The thermal capacity of the soil organic layer is calculated as: 15cSOL=cSOLdry+θ(cSOLwet-cSOLdry)ifT<2°CcSOLdry+θ[(T2+1)cSOLwet-T2cSOLfrozen-cSOLdry]if-2°C≤T≤0°CcSOLdry+θ(cSOLfrozen-cSOLdry)ifT>0°C where cSOLdry, cSOLwet and cSOLfrozen (J m⁻³ K⁻¹) are the thermal capacities of dry, wet and frozen surface organic layers, respectively, and θ is the volumetric moisture content (unitless).

The thermal conductivity of the soil organic layer is calculated as: 16λSOL=λSOLdry+θ(λSOLsat-λSOLdry) where λSOLdry is the thermal conductivity of a dry surface organic layer and λSOLsat is the thermal conductivity of a saturated surface organic layer, calculated as: 17λSOLsat=λSOLliqθsatθliqθliq+θiceλSOLfrozenθsatθiceθliq+θice

The values of surface organic layer thermal properties are taken from in situ measurements and laboratory experiments . Thermal capacities are set to cSOLdry=0.29×106, cSOLwet=4.29×106 and cSOLfrozen=3.26×106 J m⁻³ K⁻¹ . Thermal conductivities are equal to λSOLdry= 0.05, λSOLwet= 0.56 and λSOLfrozen= 1.40 W m⁻¹ K⁻¹ .

ORCHIDEE-v3 uses a 3-layer snow scheme of intermediate complexity with dynamic layer thickness, which was already used in IPSL-CM6A-LR. Snow strongly influences the surface-atmosphere energy transfer at high latitudes due to its insulating properties. Heat diffusion within the snowpack is accounted for by a heat-transfer equation: 18cp∂Tj∂t=∂∂zκj∂Tj∂z+∂R∂z where Tj is the snow temperature of the layer j, cp is the snow heat capacity (J K⁻¹ m⁻³), κj is the thermal conductivity of the snow (W m⁻¹ K⁻¹) and takes into account vapour transfer in the snow, z is the vertical coordinate and t is time. ∂R∂t is the solar-radiative energy source and depends on the incoming solar radiative energy and the snow depth.

Water phase change can occur within the snowpack as snow melts or refreezes, further affecting soil hydrology and surface-atmosphere water exchange. In particular, snow can melt in the upper layer of the snowpack due to solar radiation, infiltrate down to the next layer and may refreeze, releasing latent heat and heating lower layers. Snow compaction is also represented and depends on the weight of the overlying snow. It modifies the density and thickness of snow layers over time. Finally, the snow albedo is included and depends on the snowfall rate and the liquid water content of the snowpack.

Further details on these processes and their implementation can be found in .

Soil organic carbon and nitrogen dynamics in ORCHIDEE follow a CENTURY-based scheme which is schematised in Figs.  and . Plant residues are divided into structural and metabolic litter pools according to their lignin content. Litter decomposition follows a first-order kinetics with pool-dependent decomposition factors, and depends on temperature, moisture and lignin content. Part of the decomposed carbon is respired as CO₂ and the remaining flux is transferred to soil organic carbon (SOC) pools. Importantly, the model only represents CO₂ emissions and does not include CH₄ dynamics. Active, slow and passive SOC pools have different turnover times and can exchange carbon with each other, each time with an associated loss of CO₂ through microbial respiration. SOC decomposition also follows a first-order kinetics with a dependence on soil temperature, moisture and texture (i.e. soil sand, silt and clay content): 19∂Ci∂t|decomposition=ki⋅f(T)⋅f(moisture)⋅f(texture)⋅Ci where Ci is the carbon content of the pool i (kgC m⁻², where i corresponds to active, slow or passive) and ki is the decomposition factor (s⁻¹).

Nitrogen is decomposed at the same rate as carbon. Nitrogen fluxes are driven by carbon fluxes and the C:N ratios of the pools (Fig. ). The nitrogen flux between a pool A and a pool B (kgN m⁻² s⁻¹) is expressed as the product of the corresponding carbon flux and of the N:C ratio of the receiving pool: 20fnitrogen,A→B=fcarbon,A→B⋅N:CB The nitrogen associated with the carbon lost by respiration is assumed to be mineralised. If the decomposed organic nitrogen cannot meet the demand of the receiving pools, mineral nitrogen is immobilised to complete the nitrogen flux. If the amount of nitrogen in the mineral pool is not sufficient, nitrogen is taken from the atmosphere to complete the required immobilisation flux. Conversely, if there is an excess of decomposed nitrogen, it is mineralised and transferred to the mineral nitrogen pool. Furthermore, decomposition rates are independent of C:N ratios. These ratios are dynamic and depend on the concentration of soil mineral nitrogen (NH4+ and NO3-), with a lower nitrogen demand (higher C:N ratios) when mineral nitrogen is scarce, and a higher demand (lower C:N ratios) when mineral nitrogen stocks are high.

Soil mineral nitrogen follows the DNDC model which accounts for ammonium (NH4+), nitrates (NO3-), nitrogen oxides (NO_x) and nitrous oxide (N₂O) . It represents nitrification, denitrification, mineralisation and immobilisation, ammonium adsorption and desorption, plant uptake (NH4+ and NO3- only), gaseous emissions and leaching (Fig. ). Plant uptake is expressed as: 21Nup=vmax×Nmin×kNmin+1KNmin+Nmin×f(NCplant)×Croot where Nup is the plant nitrogen uptake (gN m⁻² d⁻¹), Nmin is the amount of mineral nitrogen available (NH4++ NO3-, gN m⁻²), vmax is the maximum rate of nitrogen uptake (gN gC⁻¹ d⁻¹), kNmin (m² gN⁻¹) and KNmin (gN m⁻²) are Michaelis–Mentens coefficients, Croot the root carbon mass per unit area (gC m⁻²) and f(NCplant) the dependency of plant nitrogen uptake to NC_plant, expressed as: 22f(NCplant)=maxNCplant-ncleaf,maxncleaf,min-ncleaf,max,0 where nc_leaf,min and nc_leaf,max are the minimum and maximum leaf N:C ratios, respectively (PFT-dependent), and NC_plant is defined as the mean N:C ratio of leaves, roots and labile nitrogen pools: 23NCplant=Nleaf+Nroot+NlabileCleaf+Croot+Clabile

Further details can be found in and .

A major improvement from IPSL-CM6A-LR to IPSL-Perm-LandN is the vertical discretisation of soil organic carbon and nitrogen on an 18-layer scheme (the same as for soil thermal dynamics), with depth-dependent decomposition rates depending on environmental conditions. This is particularly important in permafrost regions where the upper soil layers can thaw while deeper layers remain frozen, keeping organic matter thermally protected. Soil mineral nitrogen, however, is not vertically resolved and remains represented on a single soil layer in each grid box. It can exchange nitrogen with all the organic nitrogen layers through mineralisation or immobilisation.

Organic carbon and nitrogen can be exchanged between soil layers through bio- or cryoturbation. This process is described by a diffusion equation: 24∂Ci∂t|cryoturbation=D∂Ci2∂z2 where Ci is the carbon or nitrogen content of the pool i at a given depth and time, and D is the diffusive mixing rate. In the permafrost region (defined as ALT ≤ 3 m), D is set to 10⁻³ m² yr⁻¹ in the active layer and decreases linearly to zero between ALT and 3 × ALT. Thus, the permafrost region where cryoturbation occurs is dynamic. Elsewhere, D is set to 10⁻⁴ mm² yr⁻¹ in the top 2 m of soil to represent bioturbation.

The depth-dependent decomposition of soil organic matter depends on environmental conditions. In particular, it is modulated as a function of temperature (f(T) in Eq. ): 25f(T)=explog(Q10)T-Tref10ifT>0°C(T+1)⋅exp-log(Q10)Tref10if-1°C<T≤0°C0ifT≤-1°C where Q10=2 and Tref= 30 °C. Above 0 °C, decomposition follows a Q10 function (Q10= 2), then decreases linearly to zero between 0 and -1 °C. Below -1 °C no decomposition can take place.

Decomposition also increases monotonically with soil moisture (f(moisture) in Eq. ): 26f(moisture)=max(0.25;-1.1⋅moisture2+2.4⋅moisture-0.29) where moisture represents the humidity profile (unitless) and is between 0 and 1. Below 2 m (the depth to which hydrology is resolved), a constant soil moisture profile is used, taken from the lowest layer.

Overall, for each soil layer, the organic matter dynamics follows the equation below: 27∂Ci(z,t)∂t=Ii(z,t)-ki⋅f(T)(z,t)⋅f(moisture)(z,t)⋅f(texture)⋅Ci(z,t)+D(z,t)∂Ci2(z,t)∂z2 where Ii are the carbon or nitrogen inputs to the pool i, the second term corresponds to decomposition and the third term to vertical mixing.

IPSL-Perm-LandN is unable to build up the observed large permafrost carbon stocks from scratch during spinup (even covering several thousands of years) due to the constant pre-industrial climate forcing of the spinup (i.e. no glacial/interglacial cycles), the long timescales required for carbon burial, missing processes (dust deposition, peat development) and the lack of deep permafrost deposits. Consistent representation of permafrost soil carbon is critical to avoid biases in its insulating effect or underestimation of future permafrost CO₂ emissions. Therefore, soil organic carbon and nitrogen pools are initialised with the contemporary observation-based product SoilGrids, which provides a global map of soil organic carbon and nitrogen with a detailed depth resolution version 2.0,. This allows the unfrozen soil layers to reach an equilibrium state driven by the carbon cycle and climate dynamics, while the organic matter in the frozen layers cannot be decomposed throughout the spinup. SoilGrids gathers observations from about 240 000 locations and uses more than 400 covariates. The original product has a horizontal resolution of 250 m and 6 vertical layers down to 2 m (0–5, 5–15, 15–30, 30–60, 60–100 and 100–200 cm). It has been conservatively regridded to the ORCHIDEE horizontal grid (2.5° × 1.25°) using the CDO “remapcon” command, and vertically interpolated to the 18-layer scheme. Below 2 m, initial organic carbon and nitrogen have been set to zero. Organic carbon and nitrogen stocks were divided into active, slow and passive fractions following the fractions given in (2 % in active, 29 % in slow and 69 % in passive pools). As there is no global gridded map of soil mineral nitrogen, the mineral nitrogen pool is initialised to zero prior to the spinup.

Before running IPSL-Perm-LandN under varying forcings, it is necessary to bring the carbon and nitrogen pools into equilibrium, although such a target is questionable given that parts of the carbon cycle were not at equilibrium in 1850 e.g. permafrost soils and peatlands were accumulating carbon,. This is done by performing a spinup in pre-industrial configuration. The spinup protocol starts with a spinup using ORCHIDEE offline (i.e. not coupled to the atmosphere and the ocean) under pre-industrial conditions for 2600 years. The model is forced by a 50-year cyclic climate from the spinup of IPSL-CM6A-LR (piControl simulation of CMIP6), which has identical atmosphere and ocean physics to that of IPSL-Perm-LandN. The PFT map and nitrogen deposition (National Center for Atmospheric Research-Chemistry-Climate Model Initiative) and fertilisation remain at their 1850 values. Biological nitrogen fixation follows the approach of and is fixed in time . ORCHIDEE is then coupled to LMDZ (atmosphere) and NEMO (ocean) to form IPSL-Perm-LandN. The model is restarted from the offline ORCHIDEE spinup for land variables and from a spinup of IPSL-CM6A-LR for atmosphere and ocean variables. Importantly, the restart state of the ocean is from a 4000-year simulation, providing initial already equilibrated ocean physics and carbon pools. The spinup is run in concentration-driven configuration for 670 years. The land forcings remain the same and the atmospheric and oceanic forcings are fixed at their pre-industrial values. In particular, the atmospheric CO₂ concentration is set to 284 ppm. After the spinup, the coupled model is considered to be sufficiently close to equilibrium to avoid significant drifts in global climate variables and in the land and ocean net carbon fluxes in historical simulations (see Table ).

Three historical simulations (1850–2014) were performed with IPSL-Perm-LandN following the CMIP6 protocol in order to quantify the uncertainty in the simulated processes due to internal model variability. They differed only in their restart state, as the model was restarted from three distinct pre-industrial climate states (years 420, 450, and 480). These restart points were verified to be significantly different in terms of global temperature, thus providing three distinct restart states within the internal variability of IPSL-Perm-LandN. The forcings are provided by the CMIP6 input4MIP project (https://aims2.llnl.gov/search/input4MIPs/, last access: 15 May 2025), including greenhouse gas concentrations, which were taken as global averages from . Tropospheric and stratospheric ozone radiative forcings came from and . Tropospheric aerosols were not simulated interactively by IPSL-Perm-LandN and were prescribed from a historical LMDZOR-INCA simulation (i.e. a coupled surface-atmosphere simulation with tropospheric chemistry). In addition, stratospheric (volcanic) aerosols were prescribed from the version 3 of the dataset from as a latitude-height time-varying climatology. Finally, the solar forcing is provided by .

Atmospheric nutrient deposition to the ocean (iron, phosphorus, and silicate) was provided by LMDZOR-INCA simulations. Wet and dry oceanic deposition of nitrogen (inorganic nitrate and ammonium) came from the National Center for Atmospheric Research-Chemistry-Climate Model Initiative nitrogen deposition rates. The river supply of biogeochemical elements to the ocean was sourced from for dissolved inorganic and organic nitrogen, dissolved inorganic and inorganic phosphorus, and silicate. Dissolved inorganic carbon and alkalinity were provided by the simulations using the Global Erosion Model of . The river supply of iron was calculated from the river supply of inorganic carbon, assuming a constant Fe/dissolved inorganic carbon ratio.

Land cover (i.e. the PFT map), wood harvest and nitrogen fertilisation are provided by the land use harmonisation database LUH2,. Nitrogen deposition is provided by th National Center for Atmospheric Research-Chemistry-Climate Model Initiative and BNF follows the approach of .

A complete description of the implementation of the forcings can be found in .

A necessary but tricky step in the study of permafrost modeling is to clearly define permafrost in the model. A first clarification is needed to avoid the common confusion between the permafrost region and the permafrost area . The permafrost region is defined as the total area covered by permafrost zones (continuous, discontinuous, sporadic and isolated patches). However, each permafrost zone is not completely underlain by permafrost and the actual area underlain by permafrost is smaller than the permafrost region. This area actually underlain by permafrost is called the permafrost area, and takes into account, for example, that there is more permafrost in the continuous than in the sporadic zone. Many observation products provide both the permafrost region and the permafrost area . In Earth System Models, however, each pixel of the grid either contains permafrost or does not. A finer description of permafrost would require the representation of sub-grid land surface heterogeneity and the estimation of a permafrost fraction for each pixel, which is not the case in current ESMs despite promising developments . Thus ESMs can only represent the permafrost region as the total area where grid boxes contain permafrost. However this modeled permafrost region is slightly different from the one estimated from observations. As the ESMs represent the dominant environmental conditions over each grid box, areas with small amounts of permafrost are likely to be missing permafrost. On the contrary, in areas with observed permafrost fractions greater than 50 %, the majority of the area is underlain by permafrost and the models should consider them as pixels containing permafrost. Thus, continuous and discontinuous permafrost zones (>50 % of permafrost) should be similar between models and observations while disagreement is expected for sporadic permafrost and isolated patches (<50 % of permafrost).

Apart from this, a second source of uncertainty comes from the way in which is decided whether a model grid box contains permafrost or not. Comparing 10 different definitions of permafrost in ESMs, found large differences within each model of the CMIP6 ensemble and showed that the spread due to permafrost definition could even be larger than the inter-model spread. Among the classical permafrost definitions, those based on ground-air temperature coupling show a better agreement between models but miss the complexity introduced by ground thermodynamics by implicitly assuming the same ground thermodynamics for all models. More relevant definitions are based on ground thermal properties and are closer to the original definition of permafrost. A direct application of this definition in models would be to define the zero annual amplitude depth (Dzaa) as the minimum soil depth at which the temperature variation within a year is less than 0.1 °C. If the temperature at Dzaa is less than or equal to 0 °C for at least two consecutive years, there is assumed to be permafrost in the grid box . However the Dzaa can be deep, especially in models with a deep soil column such as IPSL-Perm-LandN. With this definition, if deep permafrost is modeled, the grid box is marked as containing permafrost. This can be problematic if the lower soil layers are poorly represented. For instance, the lower ground boundary condition in IPSL-Perm-LandN does not represent the heat coming from the Earth's mantle, resulting in an incorrect geothermal gradient. This can cause deep ground to remain unrealistically frozen and to overestimate the area of permafrost using this definition. This is why in this study, we chose another commonly used permafrost definition, based on the active layer thickness (ALT) . If the ALT is less than 3 m, i.e. if the annual maximum thaw depth is less than 3 m, the grid box is said to contain permafrost. This definition includes surface permafrost but excludes deep permafrost (i.e. below 3 m), which is fine for two reasons:

IPSL-Perm-LandN poorly represents deep soil temperature profile and focusing on surface permafrost avoids overestimating the permafrost region.

Thus we chose to define the permafrost region (Rpermafrost) as the total area where ALT <3 m, i.e.: Rpermafrost=∑ilon=1144∑ilat=1143δ(ilon,ilat)⋅A(ilon,ilat)⋅fland(ilon,ilat) with fland(ilon,ilat) the fraction of land in the grid box, A(ilon,ilat) the grid box area and δ(ilon,ilat)=1ifALT<3m0otherwise.

The permafrost region is calculated for IPSL-Perm-LandN, IPSL-CM6A-LR, C4MIP models and the ESA-CCI observation product . As some C4MIP models have a poorly resolved soil thermal profile, an exponential vertical interpolation at 3 m depth is performed instead of taking the temperature of the nearest soil layer. If the interpolated 3 m-temperature is less than or equal to 0 °C, the ALT is less than 3 m and the grid box contains permafrost. For IPSL-Perm-LandN, the yearly maximum ALT is directly available and is used to calculate the size of the permafrost region (altmax <3 m). The ESA-CCI observation product provides the permafrost fraction (fperm) for each pixel, which allows the calculation of the permafrost region (area where fperm>0), the permafrost area (area weighted by fperm) and the region of continuous and discontinuous permafrost (area where fperm>0.5).

The spatially-averaged time evolution of the active layer thickness is computed using a mask of the permafrost region. This mask is defined as the simulated 2005–2014 permafrost region, using the definition ALT < 3 m.

Instead of prescribing anthropogenic CO₂ emissions to IPSL-Perm-LandN, the historical simulations are run with an imposed atmospheric CO₂ concentration. This prevents the simulated land and ocean carbon fluxes from feeding back onto climate, removing a source of uncertainty for the study of atmospheric processes, despite the use of a spatially homogeneous CO₂ concentration with no vertical gradient. However, these fluxes can be used in addition to atmospheric CO₂ changes to calculate the fossil fuel emissions that are compatible with the prescribed CO₂ concentration scenarios. The rate of compatible fossil fuel emissions is equal to the sum of the rate of atmospheric CO₂ change, the net atmosphere-land and atmosphere-ocean fluxes, i.e. : 28EFF=GATM+FA–O+FA–L with EFF the rate of anthropogenic fossil fuel emissions (PgC yr⁻¹), GATM the rate of change of atmospheric CO₂ concentration (PgC yr⁻¹), FA–O the net atmosphere-ocean flux (PgC yr⁻¹, positive for ocean uptake) and FA–L the net atmosphere-land flux (PgC yr⁻¹, positive for land uptake). Land-use change emissions are included in the NBP, and therefore in FA–L.

On a global scale, gross primary production (GPP) increases slowly until the 1960's and much faster thereafter for both IPSL-Perm-LandN and IPSL-CM6A-LR (Fig. a). As in other ESMs, this bent curve is mainly driven by the fertilisation effect caused by an increase in anthropogenic CO₂ emissions as well as increased nitrogen atmospheric deposition and fertilisation . The change in the slope around the 1960s is more pronounced for IPSL-Perm-LandN than for IPSL-CM6A-LR, primarily driven by the explicit representation of the nitrogen cycle in IPSL-Perm-LandN and its effect in the tropics and mid-latitudes. In IPSL-Perm-LandN, the global GPP reaches 132 PgC yr⁻¹ in the last decade of the simulation, higher than estimates from but within the range of C4MIP ESMs, although there is a large variability across models. GPP is overestimated in the Arctic and mid-latitudes compared to data-driven products, and within the observational range in the tropics (Figs. b and a). This is likely due to IPSL-Perm-LandN simulating larger organic nitrogen stocks in the mid-latitudes and the Arctic than in the tropics, leading to higher mineralisation under warming, and therefore to greater sensitivity of nitrogen limitation to warming (Fig. ). Compared to IPSL-CM6A-LR, GPP has largely increased in the Arctic (+3.3 PgC yr⁻¹) and mid-latitudes (+15.4 PgC yr⁻¹), and decreased in the tropics (-10.1 PgC yr⁻¹), resulting in an overall global increase of 8.6 PgC yr⁻¹. These differences are explained by the introduction of an explicit nitrogen cycle, which replaces an empirical GPP downregulation in IPSL-CM6A-LR (limitation of Vcmax under increasing atmospheric CO₂ to mimic nutrient limitation without explicitly representing it), and to vertically-resolved soil biogeochemistry in IPSL-Perm-LandN. In addition, IPSL-CM6A-LR has been largely tuned using different data sources FLUXNET, atmospheric CO₂, NDVI,, while the new model including the nitrogen cycle has not been extensively calibrated (see Appendix ). The seasonal cycle was improved in the tropics compared to IPSL-CM6A-LR, with a seasonality closer to data-driven estimates (Fig. a). In the northern mid-latitudes, the shape of the seasonal cycle is consistent with the observations but its amplitude is too large. IPSL-Perm-LandN captures the onset of vegetation growth well, but overestimates GPP during the summer peak and vegetation senescence in autumn. In contrast, IPSL-CM6A-LR was very close to data-driven products throughout the year. In the Arctic, IPSL-Perm-LandN overestimates the amplitude of the seasonal cycle, but also shows a delayed decrease in GPP in late summer and autumn. This was already the case for IPSL-CM6A-LR and is partly due to a warm autumn bias in the Arctic which allows vegetation to survive later in the season (Figs.  and ).

For IPSL-Perm-LandN, the soil heterotrophic respiration (RH) follows the same bent shape as GPP over the historical period (Fig. ). This was expected as enhanced GPP leads to increased litter and soil carbon, resulting in higher RH. In the last decade of the simulation, RH reaches 47.4 PgC yr⁻¹ for IPSL-Perm-LandN, close to IPSL-CM6A-LR (45.5 PgC yr⁻¹) and data-driven products (43.4 PgC yr⁻¹ for , 48.8 PgC yr⁻¹ for and 51.9 PgC yr⁻¹ for ). Similar to IPSL-CM6A-LR, IPSL-Perm-LandN is one of the ESMs with the globally simulated RH value that is closest to these data-driven products over the recent period . However, even if the global RH is close to IPSL-CM6A-LR, the use of a discretised soil carbon profile, the inclusion of permafrost and of an explicit nitrogen cycle in IPSL-Perm-LandN leads to very different regional RH patterns. As with GPP, RH has increased in the Arctic and mid-latitudes, and decreased in the tropics compared to IPSL-CM6A-LR. The modeled RH for IPSL-Perm-LandN is in good agreement with the and products globally, but is slightly overestimated over forests (Fig. ). In tropical and mid-latitude grassland ecosystems, RH tends to be underestimated. As expected, given their correlation, GPP and RH show the same regional biases when confronted with independent observational products.

For both models, the net land-atmosphere carbon flux (NBP, positive for land uptake), including land-use change emissions (ELUC), is negative until the 1970's, mainly because of the negative contribution of land-use change . Thereafter, NBP increases, driven by CO₂ fertilisation and nitrogen fertilisation to reach 1.83 ± 0.34 PgC yr⁻¹ for IPSL-Perm-LandN in the last decade (2005–2014), making the land a net carbon sink over the last 50 years (Fig. a). This value is very close to estimates from the 2023 Global Carbon Budget (1.86 ± 1.13 PgC yr⁻¹), which uses offline Dynamic Global Vegetation Models (DGVMs) for the land carbon sink and bookkeeping models for land-use change emissions. The NBP is slightly larger for IPSL-Perm-LandN than IPSL-CM6A-LR (1.52 ± 0.78 PgC yr⁻¹) due to increased net carbon uptake in the Arctic and mid-latitudes, while the tropical NBP remains similar (Fig. b). The inverse modeling approach used by the Copernicus Atmosphere Monitoring Service (CAMS) shows a higher global NBP (2.89 PgC yr⁻¹) and a different latitudinal distribution. This is due to the fact that atmospheric inversions account for lateral carbon fluxes (between the land and the ocean), whereas land surface models (and hence ESMs) typically do not model this flux and have a near-zero land-atmosphere carbon flux in the pre-industrial period. In contrast, the global pre-industrial river flux is estimated to be around 0.65 PgC yr⁻¹ . Subtracting the contribution of lateral fluxes from the inversions generally helps to reconcile both approaches, leading to more comparable NBP values . However, there is still significant uncertainty in these estimates and the 2023 CAMS estimate has a relatively large land sink . In the tropics, the CAMS product diagnoses a net carbon source while all C4MIP ESMs rather show a positive to near-neutral NBP. At mid- and high-latitudes, the NBP is positive and much larger in the inversion than in C4MIP models, indicating a large net carbon sink that more than compensates for the tropical net carbon source. Such discrepancies between models and inversions are a known knowledge gap and an area of active research . Recently, the work of has shown the key role of forest disturbances at mid-to-high latitude to reconcile the estimates of the northern carbon sink between atmospheric inversions and DGVMs. The seasonal cycle of NBP for IPSL-Perm-LandN is consistent with that of CAMS despite differences in amplitude (Fig. a). In general, IPSL-Perm-LandN has a smaller amplitude than CAMS in the tropics and a larger amplitude in the extra-tropics. This difference is greater during periods of negative NBP, especially during autumn and winter of the northern hemisphere. Over the last decade, the mean NBP is positive over most of the globe, with the notable exception of regions of high deforestation (eastern and southern Brazil, equatorial African forest, Indonesia) (Fig. b). Large sinks are simulated over Europe, Amazonian forest, western African forest, eastern China and the boreal forests of Canada, Alaska and Siberia. By removing the contribution of land-use change emissions in the NBP, we can estimate the land carbon sink (SLAND in GCB2023), which is positive almost everywhere with deforested areas close to neutrality (Fig. c). However, we can only approximate SLAND as it is calculated using fixed pre-industrial vegetation in GCB2023, whereas the vegetation evolves over time in our simulations. Therefore, the large spread in ELUC hinders a more precise assessment of the land carbon sink in our simulations .

The global vegetation biomass (above- and below-ground, averaged over 2005–2014) amounts to 479 PgC for IPSL-Perm-LandN, which is lower than the ESA-CCI observation-based product (607 PgC, estimated in 2010), mainly due to the lower tropical biomass, and close to the mean of C4MIP models (Fig. ). Compared to IPSL-CM6A-LR, the tropical biomass remained almost unchanged while it doubled at mid- and high-latitudes. Vegetation in the permafrost region remains limited (23 PgC) and smaller than the ESA-CCI estimate (37 PgC). Comparison with other models is provided for information, but it should be noted that the permafrost mask used here is that of IPSL-Perm-LandN while the permafrost region may differ between models. The total amount of litter carbon has remained similar since CMIP6 (108 PgC for IPSL-Perm-LandN and 107 PgC for IPSL-CM6A-LR) but its distribution has changed, with less carbon in the tropics and more in mid- and high-latitudes. However, there are no global scale observations and the spread across models is large, making it difficult to assess the performance of IPSL-Perm-LandN. Finally, IPSL-Perm-LandN simulates a total amount of SOC of 1985 PgC in 0–1 m (3001 PgC in 0–3 m), distributed between the tropics (521 PgC for 0–1 m, 639 PgC for 0–3 m), mid-latitudes (934 PgC for 0–1 m, 1376 PgC for 0–3 m) and the Arctic (530 PgC for 0–1 m, 985 PgC for 0–3 m). Compared to IPSL-CM6A-LR (total SOC of 550 PgC), it has largely increased in all latitudes, with the highest increases in the mid-latitudes and the Arctic. These changes are due to the discretisation of SOC along a vertical profile, the initialisation of the soil organic carbon and nitrogen pools by observation-based products and the representation of an explicit nitrogen cycle. Observed total SOC is 1204 PgC for HWSD and 2498 PgC for SoilGrids in 0–1 m (3384 PgC in 0–3 m). The large spread across these products and the resulting uncertainty in soil organic carbon content hampers a constrained assessment of ESMs on a global scale. IPSL-Perm-LandN is naturally closer to SoilGrids, which was chosen to initialise the SOC and SON pools due to the large number of observations, the robustness of the machine learning algorithm and the availability of gridded SOC and SON on 6 soil layers. Furthermore, the choice of a product with a high amount of SOC seems justified as global SOC gridded datasets tend to underestimate SOC content when compared to field data e.g.. Compared to CMIP6 models contributing to C4MIP , IPSL-Perm-LandN is the model with the highest amount of SOC, mainly due to large pools in the mid-latitudes and the Arctic. Permafrost SOC amounts to 511 PgC in the first meter of soil (1006 PgC in 0–3 m) and has largely increased compared to IPSL-CM6A-LR (46 PgC), which is a significant improvement of IPSL-Perm-LandN. It is again similar to the SoilGrids product (760 PgC in 0–1 m, 1028 PgC in 0–3 m) and larger than both NCSCD (282 PgC in 0–1 m, 668 PgC in 0–3 m) and HWSD (186 PgC). It is also very close to specific estimates of permafrost SOC stocks from (1014-170+186 PgC) and (1035 ± 150 PgC), both assessing the amount of SOC in the first 0–3 m, which is also what IPSL-Perm-LandN aims to represent. However, IPSL-Perm-LandN does not represent the carbon stored in Yedoma and Arctic river deltas, missing an additional 327–466 and 96 ± 55 PgC, respectively . Deep deposits outside Yedoma or the carbon stored in subsea permafrost are also not represented by the model, but remain challenging to estimate .