The processes of vertical water movement in the soil column have remained unchanged since their initial description by and . However, infiltration of daily rainfall and applied irrigation amounts (P; in mm) is now influenced by topography and is modified by accounting for a contribution to surface runoff (βHAG), which depends on the mean slope gradient of the stand (β): 5infil=P⋅(1-βHAG+α⋅βHAG), where α is the factor representing the dependence on soil water conditions as described in : 6α=1-Wliq(1)+Wice(1)(θsat(1)-wpwp(1))⋅z(1)1Φinf, based on the first layer's relative volumetric soil water content at saturation (θsat(1)), the relative soil water content at the wilting point (wpwp(1)), and its actual soil water content (Wliq(1) in mm) and the actual ice content (Wice(1) in mm) of the first layer. z(1) is the layer thickness (in mm). The factor α is scaled with Φinf, a dimensionless infiltration parameter that controls the sensitivity of infiltration to the relative soil water content of the upper soil layer and is adjusted according to the actual above-ground litter layer cover fraction as described in . To improve numerical stability during vertical soil-water routing, precipitation was internally partitioned into increments of at most 4 mm, which were sequentially routed through the soil column within the daily time step. The newly added Haggard function relates the slope gradient (β) to the fraction of non-infiltrating water contributing to surface runoff : 7βHAG=0.06⋅ln⁡(β+0.1)+0.220.43.

Infiltrated water is routed through the soil column depending on the hydraulic conductivity of the soil layer and the soil moisture of the layer below down to the layer of the water table. The percolation of the last unsaturated layer recharges the ground water, and thus the model is able to simulate the temporal variation of the water stored in the unconfined aquifer (Wa). Lateral runoff is determined by the groundwater–soil water interactions which is adopted from the CLM4.5 model .

Subsurface drainage (i.e. groundwater discharge) (qdrain) is distinguished between completely and partially frozen and completely unfrozen conditions of the layers below the groundwater table. In the unfrozen state: 8qdrain=qdrain,max⋅exp⁡(-fdrain⋅zΔ), where fdrain=2.0 m⁻¹ is the decay factor controlling the exponential reduction of subsurface drainage with increasing mean water-table depth (z¯Δ), following the default CLM 2.0 parameterization described by . The local maximum subsurface drainage rate (qdrain,max at zΔ=0) depends on the stand-specific topographic slope β: 9qdrain,max=maxdrain⋅tan⁡2(β).

The reference parameter max_drain is set to 50 mm d⁻¹ following . For agricultural land, max_drain is increased to 100 mm d⁻¹ and interpreted as an effective upper limit for managed drainage rather than as a site-specific drainage parameter. This reflects the assumption of enhanced water removal on agricultural land and prevents unrealistically persistent waterlogging under managed conditions. The subsurface drainage rate for the at least partially frozen state is: 10qperched=Θice⋅maxperch⋅ks⋅(zfrost-zΔ).

Lateral drainage above the frozen soil column depends on the saturated hydraulic conductivity (ks), and the maximum rate max_perch, equivalent to max_drain for sub-soil dynamics, is assumed to be 50 mm d⁻¹, but is strongly limited by Θice that gives the ice impedance factor . zfrost is the depth at which the soil is frozen. Drainage only occur when zfrost>zΔ. Θice is calculated from the ice content of the layer that is partly frozen. It describes the increased tortuosity of the water flow when parts of the pore space are filled with ice: 11Θice=10-Ω⋅icefrac and 12icefrac=∫0soildepthFice(z)/soildepthdz, where Fice=θiceθsat is the frozen part of the water filled pore space relating θsat, the relative water content at saturation (m³ water pro m³ soil), to the ice content relative to the soil porosity. If the soil is saturated and all water is frozen Fice is at unity. Ω is a parameter set to 6 following , to meet the impedance of frozen ground.

This section describes how the water table depth (and therefore the groundwater level) changes depending on the exchange of water between the saturated zone (below the water table) and the unsaturated zone (above it). The equilibrium matric potential and corresponding water content follow the hydrostatic formulation of , as implemented in the Community Land Model-CLM4.5 , and used for dynamic groundwater–soil coupling and recharge calculation following . The recharge rate qrecharge of the water table depth can be determined by applying Darcy's law to zΔ: 13qrecharge=-kaq⋅ΨΔ-Ψ(lwt)zΔ-z(lwt), where ΨΔ and Ψ(lwt) are the soil matric potential at zΔ and of the layer above zΔ, where lwt is the index of this layer. kaq is the hydraulic conductivity of the layer which contains the water table and is calculated as follows: 14kaq=Θice,(lwt+1)⋅ks⋅θ(lwt+1)θsat,(lwt+1)2⋅B(lwt+1)+3. Ψ(lwt) is not simply a constant, it depends on how the soil would behave under hydrostatic equilibrium at the current water–table depth (zΔ). Ψ(lwt) represents the equilibrium potential at the interface between saturated and unsaturated zones and is described by the saturated soil matric potential of the different soil types (Ψsat), the relation of the volumetric water content above the water table (θ(lwt) in m³ water pro m³ soil) and θsat: 15Ψ(lwt)=Ψsat,(lwt)⋅θ(lwt)θsat,(lwt)-B(lwt). The Clapp – Hornberger exponent (B(lwt)) is an empirical parameter that controls the steepness of the soil water retention curve , describing how rapidly soil suction increases as the soil dries. When the soil is saturated (θ=θsat), the matric potential is close to zero and the soil water is under little or no tension. As the soil dries, the matric potential becomes increasingly negative, reflecting stronger capillary and adsorptive forces that hold water within smaller pores. Following the approach from , both B(lwt) and Ψsat,(lwt) are adjusted based on the soil's fraction of organic material using a weighted combination approach: 16B(lwt)=(1-fsc,(lwt))⋅Bmin+fsc,(lwt)⋅Bsc and 17Ψsat,(lwt)=(1-fsc,(lwt))⋅Ψmin+fsc,(lwt)⋅Ψsc, where fsc,(lwt) is the fraction of organic material in this layer and Bmin is the Clapp – Hornberger exponent for mineral soils (Table S1) and Bsc=2.7 for organic soils respectively Ψmin the saturated matric potential for mineral soils and Ψsc=10.3 for organic soils (parameters for mineral soils are given in Table S1).

Within the soil bucket, the equilibrium state between the water table and the layers above is reached when the water entering the soil layer equals the water leaving it. The adjustment of the water table reflects the balance of water fluxes between the saturated zone and the unsaturated zone.

qrecharge determines from the hydraulic properties (Eq. ) if the water table rises or falls. zΔ is initially set to the maximum soil depth and gradually reaches equilibrium during the spin-up simulation. This adjustment is based on changes in saturated zone storage. From the balance of the recharge rate (qrecharge) and drainage (qdrain or qperched for partly frozen soils) the water table can be adjusted using the following equation: 18ΔzΔ=qrecharge-qdrainSy, where Sy is the specific yield ranging between 0 an 1. It depends on the water table location and saturated soil properties: 19Sy=θsat,(lwt)1-1+zΔΨsat,(lwt)-1B(lwt). The stand-specific aquifer (Wa in mm) represents a vertically and spatially constrained water pool that is associated with individual stands within a grid cell. Its volume is limited to a maximum of 5000 L and is updated by the balance of qrecharge and qdrain if the water table is below the calculated soil column Wa: 20Wa=qrecharge-qdrain. Wa is stand specific and becomes hydraulically active and declines only when the water table falls below the maximum soil depth or the maximum storage is not reached, allowing the compartment to store additional water or release it through drainage. For the ground water dynamics an additional pool is introduced as described in Sect. .

A spatially explicit groundwater storage compartment was implemented for each grid cell to account for subsurface water dynamics. The groundwater pool is recharged by two components: (i) the percolation flux, defined as the downward drainage from the bottom soil layer, and (ii) the lateral runoff generated in the lowest saturated soil layer, representing subsurface flow contributing to groundwater recharge.

To simulate the temporal evolution of groundwater discharge, we apply a baseflow‐recession approach . The dimensionless baseflow recession coefficient (kbf∈[0,1]) characterises the rate at which baseflow declines (Fig. ). The specific formulation used here was developed in the ERMITAGE project () and is defined separately for each grid cell to account for spatial heterogeneity in hydrogeological properties such as aquifer transmissivity, soil texture and topographic gradient. High values of kbf denote fast‐draining soils or shallow aquifers, leading to rapid groundwater release, whereas low values represent deep or low‐conductivity aquifers with slow recession and more sustained baseflow contributions. The release of groundwater to streamflow (baseflow) is described by a first‐order linear recession function: 21Qbf(t)=kbf⋅GW(t), where Qbf(t) denotes the baseflow at time t, GW(t) is the current groundwater storage.

The residual groundwater storage after baseflow release is retained in the groundwater compartment and contributes to subsequent discharge events, thereby introducing a memory effect in the hydrological system. This parameterization ensures both spatial differentiation and temporal delay in the subsurface runoff component, improving the realism of long-term streamflow simulations.

In cells with irrigated agriculture the groundwater storage pool also serves as an additional source for irrigation that is accessed only when surface water availability is insufficient to meet irrigation demand.

As the slope has an enormous importance for the infiltration and the runoff formation, but there is no information about the exact location of different stands within the grid cell, we distinguish only the mean slope for the wetland (βwet) and for the upland area (βup), respectively. To derive stand-specific slopes for wetlands and uplands, we therefore make a simple statistical assumption about the subgrid distribution of slope. Within each grid cell, the subgrid slope m is treated as a random variable which is assumed to follow a negative exponential probability distribution with cumulative distribution function (CDF) 22F(m)=1-exp⁡(-λm). The rate parameter λ is chosen such that the mean of this distribution equals the DEM-derived grid-cell mean slope (βmean) 23E[m]=1λ=βmean. where E[m] denotes the expectation (statistical mean) of m. After computing the wetland area fraction (Awet) of the grid cell (see Sect. ), we determine a threshold slope mw,max such that F(mw,max)=Awet, assuming that the fraction of the cell with m≤mw,max is equal to the wetland area fraction. Using the inverse CDF of the exponential distribution this yields 24mw,max=-1λln⁡(1-Awet), which is then constrained to the range [mmin,mmax] of the grid cell. Slopes between mmin and mw,max are assigned to the wetland stand, and slopes between mup,min and mmax to the upland (natural or agricultural) stand. The mean slope of the wetland part is obtained from the truncated exponential distribution over [mmin,mw,max] as 25βwet=∫mminmw,maxmλe-λmdm∫mminmw,maxλe-λmdm, and is additionally constrained not to exceed βmean. In the code these integrals are evaluated analytically using the antiderivative -exp⁡(-λm)(m+1/λ). Analogously, the upland mean slope βup is computed as the conditional mean of the same exponential distribution over [mw,max,mmax⁡] (see Fig. ). The DEM-derived minimum and maximum slopes of the cell are denoted mmin and mmax. All non-rice agricultural stands are assigned the upland mean slope, whereas rice paddies are assumed to be levelled fields and therefore receive a slope of exactly zero.

The evolution of the CH₄ concentration in the soil is characterized by the diffusive transport of CH₄ through the soil column (first part of the equation) and the production of CH₄ (methanogenesis (Rprod)) and losses through CH₄ oxidation above the water saturated layer if enough oxygen is available (Roxic), the de-gassing through forming of bubbles in water filled pores (ebullition (Qebull)), and the plant mediated transport (Qplant,CH4) by vascular plants through their aerenchyma: 26ϵCH4∂CCH4(z,t)∂t=∂∂zDCH4(z)∂CCH4(z,t)∂z-Qebullout(z,t)+Qebullin(z,t)-Qplant,CH4(z,t)+Rprod(z,t)-Roxic(z,t). The O₂ concentration is calculated analogously to the CH₄ concentration equation including the O₂ consuming processes of oxic decomposition of soil organic matter (RCO2),the plant mediated transport (Qplant,O2), nitrification of NH4+ to NO3- (RNO3-), and aerobic root respiration (Rroot): 27ϵO2(z)∂CO2(z,t)∂t=∂∂zDO2(z)∂CO2(z,t)∂z-Qplant,O2(z,t)-WO2WCRCO2(z,t)-2WO2WCH4Roxic(z,t)-2WO2WNRNO3-(z,t)-WO2WCRroot(z,t). where ϵO2 resp. ϵCH4 are the O₂ and CH₄ porosities, that convert concentration per soil volume to the gas concentration per air volume and are calculated as 28ϵO2=v+ϕ⋅θsat⋅BO2,ϵCH4=v+ϕ⋅θsat⋅BCH4, where ϕ is the volumetric soil water content expressed per unit pore volume (mm³ of water per mm⁻³ of soil porous volume; here θsat is used as an equivalent measure of the pore‐volume fraction), and v is the soil air content (m³ air per m³ soil). WC, WO2, and WCH4 are the molar masses of Carbon (12 g mol⁻¹), O₂ (32 g mol⁻¹), and CH₄ (16 g mol⁻¹), respectively. The Bunsen coefficients of O₂ (BO2) and CH₄ (BCH4) describe the solubility of these gases in water as a function of temperature. Due to the decreasing capacity of water to dissolve gases with rising temperature, this dependence is commonly expressed using exponential decay functions. Following and , we apply the following empirical relationships: 29BO2=0.0647⋅e-0.0257⋅Tsoil,BCH4=0.0523⋅e-0.0236⋅Tsoil. The net CH₄ flux to the atmosphere, Fatm, represents the total upward CH₄ transfer from the soil to the atmosphere. It is considered positive when the soil acts as a net CH₄ source and negative when it acts as a net sink. This flux is composed of three contributing terms 30Fatm(t)=-DCH4(z)∂CCH4(z,t)∂zz=0+Qebullout(0,t)+Fplant(t), where the diffusive flux at the soil-atmosphere interface, -DCH4(z)∂CCH4(z,t)∂z, and the ebullition flux, Qebullout(z=0,t), escape directly to the atmosphere. Note that ebullition contributes directly to the atmospheric flux only from the surface layer (z=0), as ebullition from deeper layers is transferred to the layer above instead of escaping directly (see Sect. ). The third term, Fplant(t), represents the flux of CH₄ transported through plant tissues (see Sect. ), particularly aerenchyma structures, which provide a low-resistance conduit for CH₄ transfer from anaerobic soil layers directly to the atmosphere, bypassing diffusion and ebullition pathways.

Oxic decomposition of organic carbon follows the principles described by . The anoxic decomposition model is adapted from . Aerobic conditions promote the generation of CO₂ in all soil carbon pools and anaerobic conditions lead to CH₄ production. The soil carbon pools consist of an intermediate and a slow pool with turnover rates for the oxic decomposition of 0.03 and 0.001 respectively at 10 °C and a fast so-called active pool with a turnover rate of 0.3 . For realistic decomposition dynamics, introduced a vertical soil distribution which improved the simulation of the carbon, which can be released by permafrost thawing (see also ). Decomposition follows first order kinetics: 31∂C(z,t)∂t=RCO2(z,t)-Rprod(z,t)⋅WCWCH4, where oxic (RCO2) and anoxic decomposition (Rprod) is reciprocally exclusive.

Oxic decomposition is computed as 32RCO2(z,t)=mink1(z,t)⋅C(z,t),∂Cmax(z,t)∂t where C is the carbon pool size at time t and soil depth z, k1 is the daily oxic decomposition rate, and ∂Cmax is the mass of carbon corresponding to O₂ which is available for oxic decomposition: 33∂Cmax(z,t)∂t=O2(z,t)⋅WCWO2 O2(z) is the mass of molecular soil O₂ at depth z. The oxic decomposition rate is expressed as: 34k1(z,t)=k⋅g(Tsoil(z,t))⋅fϕ(z). k1 incorporates the rate constant (k) that represents the reciprocal of the mean residence time τ for the litter components, as described by for the litter components. Additionally, k1 is influenced by the temperature dependency function gTsoil(z,t), and the soil moisture function f(ϕz) as outlined in related to the non–frozen water. The temperature dependence function is based on an Arrhenius relationship as described in 35gTsoil(z,t)=exp⁡[308.56⋅(156.02-1Tsoil(z,t)+46.02)], where Tsoil is the soil temperature in degree Celsius. The soil moisture function has its maximum around field capacity of the soil and is given by f(ϕ(z))=0.0402-5.005⋅ϕ(z)3+4.269⋅ϕ(z)2+0.719⋅ϕ(z).

The anoxic decomposition (Rprod) is calculated as follows: 36Rprod(z,t)=k2(z,t)⋅C(z,t). The methanogenesis rate (k2) is expressed as 37k2(z,t)=k⋅rk⋅exp⁡-CO2(z,t)O2*⋅g(Tsoil(z,t)). CO2(z,t) is the O₂ concentration at depth z, while O2* represents a threshold O₂ concentration of 10 g m⁻³. As demonstrated by methanogenesis is significantly suppressed by higher O₂ concentrations. rk is an empirical parameter reflecting the reduced methanogenesis rate under anoxic conditions, which is considerably slower than oxic decomposition and is set to 0.1 for the fast soil carbon pool and 0.5 for the fast decomposing litter pool. Components of the carbon pool, such as lignin, degrade much more slowly in anoxic environments due to their recalcitrant structure and resistance to microbial breakdown, further limiting methanogenesis. The decomposition rate under anoxic conditions is 4–10 times lower than under oxic conditions, with reported rates ranging from 0.02 to 1.44 mg CH₄ g⁻¹ over 500 d . This corresponds to a decomposition rate between 1.46×10-5 and 0.00105. Methanogenesis rate k2 has the same temperature dependence gTsoil(z,t) and rate constant (k) as the oxic decomposition.

The representation of the CH₄ oxidation (Roxic) follows the approach by . Roxic occurs above the saturated soil layer, where enough O₂ is available. 38Roxic(z,t)=min⁡[Vmax⁡⋅WCH4⋅CCH4z,tKm⋅WCH4+CCH4z,t⋅gTsoilz,t,CO2z,t⋅WCH42WO2⋅O2,frac], where Km and Vmax⁡ are the Michaelis-Menten coefficients. These are defined in the model for Km=5 µM and Vmax⁡=20 µM h⁻¹ . CCH4 is the CH₄ concentration at time t and depth z in g m⁻³. g(Tsoil) is the temperature response function given in Eq. (). Vmax⁡ and Km need to be multiplied by the molecular mass of CH₄. O₂ consumption is limited by O2,frac=0.95, accounting for O₂ use for oxidation of reduced compounds, where 5 % is assumed . O₂ consumption from aerobic microbial respiration, plant root respiration. nitrification and CH₄ oxidation is taken into account by reducing the O₂ content of the respective layer.

For the temperature dependency of CH₄ oxidation a Q10 relationship is used 39gTsoil(z,t)=Q10Tsoil(z,t)-Tsoil,mean(z)10 where Tsoil,mean is the annual mean soil temperature and the Q10 is set to 1.8.

CH₄ diffusion, which describes the movement of gas from higher to lower concentrations between layers and the air, is governed by Fick’s law: 40Fdiffz,t=DCH4z⋅∂CCH4∂xz,t, where DCH4z is the diffusivity at depth z and CCH4z,t is the CH₄ concentration at time t and depth z. DCH4 is calculated depending on soil water conditions: 41DCH4=(DairCH4⋅v+DwaterCH4⋅w⋅θsat⋅BCH4)⋅η where DairCH4 is the diffusivity of air (1.82×10-5 m² s⁻¹, ) and DwaterCH4 the diffusivity of water (1.6×10-9 m² s⁻¹, ). BCH4 is the Bunsen coefficient for CH₄ (see Eq. ) and η=2/3 denotes the soil tortuosity. O₂ diffusion is calculated analogous to Eqs. () and (). Initial conditions of all soil layers are: CCH4=1.207 g m-3,CO2=266 g m-3 The lower boundary for both CH₄ and O₂ conditions are: 42∂CCH4(z=soildepth)∂z=∂O2(z=soildepth)∂z=0 and the upper boundary conditions are: 43C(z=0)=psR⋅Tair⋅ACgas⋅W, where ps is the atmospheric surface pressure (101 000 Pa), Tair is the air temperature (in K), ACgas is the atmospheric content (0.209 for O₂, transient over time for CH₄), W is the molar mass of O₂ and CH₄, respectively and R is the universal gas constant (8.314 J mol⁻¹ K⁻¹).

CH₄ ebullition is the process by which CH₄ gas produced in anaerobic soil environments escapes into the atmosphere through gas bubbles. This occurs when the concentration of dissolved CH₄ in soil porewater exceeds its solubility threshold, causing bubble nucleation and release. The process is modulated by factors such as CH₄ concentration, soil moisture, and vegetation cover, which influence both the formation and migration of gas bubbles. The change in CH₄ concentration in a soil layer over time due to ebullition is governed by a balance between CH₄ loss via ebullition and CH₄ flux received from the layer below.

Ebullition is active only when the local CH₄ concentration exceeds a critical threshold required for bubble formation , and the outgoing ebullition flux is then calculated as 44Qebullout(z,t)=ke⋅max⁡((CCH4(z,t)-Cthresh),0), where ke is the ebullition efficiency constant controlling the rate of CH₄ release, which typically ranges between 0.1 to 1 d⁻¹, and Cthresh is the threshold CH₄ concentration for bubble formation. In this study we set ke=1. The functional form of the threshold concentration is given by 45Cthresh=Cmin⋅1+1-∑pft=1nPFT(αpfte⋅FPCpft), Experimental studies have shown that the presence of vegetation can substantially suppress CH₄ ebullition due to competition with plant-mediated transport and structural alterations to sediment or soil (Deshmukh et al., 2020). Therefore, to represent the vegetation-dependent reduction in ebullition flux, we introduce plant functional type (PFT)-specific suppression (αe) factors in the model (see Tables S3 and S4 for parameter values). These account for the observed differences in ebullition across vegetated and non-vegetated systems, as supported by field measurements. FPC is the fractional plant cover of the PFT, which influences bubble formation by altering gas exchange dynamics. Cmin is the minimum CH₄ concentration required for bubble formation under standard conditions and has been observed to range between 500 and 1000×10-6 M which corresponds to 0.008 to 0.016 g m⁻³. We use 0.012 g m⁻³ in LPJmL6. Eq. () ensures that ebullition only occurs when the gas pressure exceeds the critical pressure threshold.

The outgoing ebullition flux is transferred upwards and is added to the incoming ebullition flux Qebullin(z,t) in a layer above in case of z<0, or to the atmosphere in case of z=0. At the shallowest soil depth, there is no overlying material to impede the upward migration of gas bubbles. Therefore, the ebullition flux originating from this depth contributes directly to the CH₄ flux emitted to the atmosphere.

At deeper soil depths, the fate of CH₄ released via ebullition depends on the moisture content of the overlying soil column. If the overlying layer is not saturated (θ<0.9), the bubbles are trapped and remain in the overlying layer, preventing direct transfer. However, if the overlying layer is water-saturated (soil moisture >0.9), bubbles migrate further upward and are transferred to the next layer above.

This recursive upward propagation continues through the saturated soil profile until an unsaturated soil layer is found or the surface is reached. This mechanism determines whether CH₄ from deeper soil zones contributes to atmospheric emissions or remains retained within the subsurface environment.

Certain vascular plants possess aerenchyma, a specialized tissue forming interconnected air-filled channels within their stems, leaves, and roots. This tissue facilitates the movement of O₂ and CH₄ between the plant and its environment, playing a crucial role in gas exchange, particularly in waterlogged or anaerobic soils. O₂ is transported from the atmosphere through the stems and leaves into the roots, supporting root respiration. Conversely, CH₄ produced in anaerobic soils can diffuse into the aerenchyma through the roots and be transported upward through the plant, being released into the atmosphere, bypassing the oxidizing zones in the soil. We hypothesize that this gas exchange via aerenchyma is more prominent in grasses compared to trees, as aerenchyma is predominantly observed in herbaceous plants and is largely absent in woody species . To quantify these processes, we adopt the approach outlined by which shows that gas diffusion through aerenchyma (Fplant) depends on both the cross-sectional area of plant tillers available for gas transport (Atiller, in m2) and the volumetric soil liquid water content (θliq, in m³): 46Fplant(t)=∫rootingdepthsoilsurfaceQplantz,t⋅dz, where 47Qplant(z,t)=Cgas(z,t)-Cgasair⋅exp⁡(-kgas⋅Atillerθliq(z,t)).

This equation is applied to both O₂ and CH₄ in the model, reflecting the bidirectional transport of these gases. Atiller is defined as: 48Atiller=max⁡0.001,π⋅rtiller2⋅Ntiller⋅ϕtiller, where rtiller is the radius of an individual plant tiller defined to be rtiller=0.0345 m . The variable ϕtiller is the porosity of the tiller structure, expressed as a dimensionless fraction (ϕtiller=0.7). The use of the max⁡ function ensures that Atiller maintains a minimum value of 0.001 m², preventing numerical instability when the calculated tiller area becomes very small. Ntiller represents the tiller fraction, which depends on plant biomass and root distribution within the soil layer: 49Ntiller=Cleaf⋅(γ/Wtiller)⋅Froot(l), where Cleaf is the leaf carbon per square meter for PFTs that are able to form aerenchyma and γ is the phenology status of the PFT. Wtiller=0.22 g is the weight of the tillers and Froot(l) is the fraction of the root in the respective layer.

The gas exchange coefficient, (kgas in m d⁻¹), represents the piston velocity between the water and the atmosphere. Following , (kgas) is obtained by scaling a reference transfer velocity for a Schmidt number (Sc) of 600, (k600=2.07 m d⁻¹) with the actual Schmidt number of the respective gas: 50kgas=k600⋅Scgas600np, where np is the Schmidt-number exponent, here set to -0.5. Sc can be calculated specifically for O₂ and CH₄: 51ScCH4=1898-110.1⋅Tair+2.834⋅Tair2-0.02791⋅Tair3 and 52ScO2=1800.6-120.1⋅Tair+3.7818⋅Tair2-0.047608⋅Tair3

In summary, CH₄ and O₂ fluxes are based on concentration gradients, gas transfer velocities, and tiller geometry, while accounting for soil moisture, porosity, and air content. These fluxes reflect the dynamic movement of gases between the soil and atmosphere, influenced by soil properties, plant structure, and environmental conditions.

Dissolved oxygen in each soil layer is consumed by nitrification of ammonium and aerobic root respiration. Nitrification is represented by the overall reaction NH4++2O2→NO3-+2H++H2O, i.e. one mole of N nitrified requires two moles of O₂. For the nitrification rate RNO3-(z,t) (g N m⁻³ s⁻¹), the associated O₂ consumption is 53SO2nitr(z,t)=2WO2WNRNO3-(z,t), where WN is the molar mass of N (14 g mol⁻¹). In the numerical implementation RNO3(z,t) corresponds to the depth-dependent analogue of the nitrification flux FNO3- limited by O₂, NH4+ availability, soil moisture, temperature and pH (see ).

Aerobic root respiration represents the metabolic consumption of O₂ by living roots to sustain maintenance and growth. The model provides a depth-dependent root respiration rate Rroot(z,t) (g C m⁻³ s⁻¹), which is distributed over the soil profile according to the vertical root density. Because the O₂ balance is formulated in units of O₂ mass, this carbon–based respiration flux is converted into an equivalent O₂ sink SO2root using a constant mass-conversion factor, yielding 54SO2root(z,t)=WO2WCRroot(z,t).

Numerical solutions to the CH₄ and O₂ diffusion equations are obtained using the finite difference method for the heat diffusion problem described by Sect. 4.1. For time stepping the forward Euler, Crank-Nicolson and backward Euler methods were tested. The backward Euler scheme was the only method that provided sufficient stability and was thus chosen for the solution of the diffusion problems. All other elements of the methane and oxygen balance, including the reaction terms, are solved using the forward Euler method.

Experiments with the time step showed that the default daily time step of LPJmL is not sufficient to obtain accurate and stable numerical solutions for the coupled methane and oxygen balance. A baseline sub-daily time step of 4 h was therefore adopted. Additionally, an adaptive sub-stepping scheme was implemented that rejects this baseline time step and reduces it to six 40 min increments whenever the baseline time step causes a relative change of CH₄ or O₂ concentration larger than 20% in any soil layer.

The numerical errors resulting from the temporal discretization were estimated by performing a global run of LPJmL6 using a smaller baseline time step of 80 min while leaving the adaptive sub-stepping scheme untouched. The global sum and temporal mean of CH₄ and O₂ concentrations in soils changed by less than 1% compared to the default 4 h baseline time step. Global methane emissions decreased by 5.2% when switching to the increased temporal resolution.

The global constraints on CH₄ sources and sinks outlined above allow a more detailed comparison of LPJmL6-simulated emissions with other global estimates. LPJmL6 simulates CH₄ emissions from wetlands, rice fields, and wildfires, and can distinguish between emissions from agricultural land and natural land. Furthermore, LPJmL6 explicitly represents soil CH₄ uptake via diffusion from the atmosphere into the soil. To derive the possible range of CH₄ emissions compatible with observations, source categories that are not explicitly calculated by LPJmL6 have to be added. These include anthropogenic emissions from enteric fermentation and manure management, and from landfills and waste (about 170–205 TgCH₄ a⁻¹), as well as fossil fuel–related emissions (about 145 TgCH₄ a⁻¹) and biomass combustion (about 28 TgCH₄ a⁻¹). Together, these account for 462–481 TgCH₄ a⁻¹ . Additional natural sources not represented in LPJmL6, such as emissions from freshwater systems, geological sources, termites and the ocean, account for a further 64–259 TgCH₄ a⁻¹, with particularly large uncertainty for freshwater emissions. For the illustrative period 2010–2019, the atmospheric CH₄ sink is estimated to be between 523 and 649 TgCH₄ a⁻¹.

Depending on the estimated CH₄ lifetime in the atmosphere given by , between 31 and 242 TgCH₄ a⁻¹ remain attributable to land net sources, for which LPJmL6 simulates about 142.1 TgCH₄ a⁻¹ (wetlands, fire, rice cultivation, and other agricultural soil emissions and the explicitly simulated soil sink; mean over the years 2000 to 2019; see Table ). If, however, we enforce global budget consistency by combining the lower (upper) estimates of the atmospheric sink with the lower (upper) estimates of CH₄ sources not simulated by LPJmL6, the residual range attributable to land net sources narrows to 116–157 TgCH₄ a⁻¹, which still encompasses the LPJmL6 estimate (see Fig. ).

When all emissions simulated by LPJmL6 are combined with estimates for the remaining anthropogenic and natural sources, the resulting overall CH₄ budget matches well with the observationally constrained overall emissions Fig. . We construct two such combined estimates: one using bottom-up (BU) values for the non-LPJmL sources and one using top-down (TD) values. Adding the same LPJmL6 land emissions to these two source data sets shifts both curves upwards by the modelled land flux; in our set-up this makes the BU-based combination systematically higher and the TD-based combination lower. Consequently, the BU+LPJmL6 series forms the upper envelope and the TD+LPJmL6 series the lower envelope of the total-budget range shown by the red and orange lines in Fig. , respectively.

Table  summarizes CH₄ emissions from wetlands as estimated by the Global Methane Budget project . For the period 2000–2009, BU estimates range between 147 and 175 TgCH₄ a⁻¹, whereas TD estimates range from 180 to 217 TgCH₄ a⁻¹. The discrepancy between these methodologies is evident across all decades examined. Notably, the differences are largest in the 1980s and 1990s, exceeding 50 TgCH₄ a⁻¹. MOre recent estimates show reduced discrepancies, with TD estimates decreasing significantly while BU estimates remain relatively stable. LPJmL6 aligns closely with BU estimates, reflecting its process-based methodology and explicit integration of wetland hydrology.

The site-level comparison, shown in the Supplement (Figs. S5–S21), indicates that LPJmL6 reproduces the observed seasonal and cumulative CH₄ emissions at some sites, for example RU–Ch2, US–Tw1, and US–Myb, but performs less well at others. This behaviour is expected because eddy-covariance CH₄ measurements often represent relatively small and heterogeneous source areas, whereas LPJmL6 simulates grid-cell mean fluxes. Individual tower footprints may therefore be dominated by local wetland patches, drainage features, vegetation composition, management, or water-table dynamics that are not representative of the corresponding 0.5° grid cell. Consequently, mismatches at individual sites do not necessarily indicate a failure of the large-scale model process representation, but may reflect a scale mismatch between local observations and grid-cell averages.

The cumulative comparison is often more robust than the month-to-month comparison because it integrates over short-term variability and gaps in the observations. However, the FLUXNET-CH₄ records are frequently incomplete, and missing periods can affect both monthly sums and cumulative totals, especially when data gaps occur during peak emission periods. Therefore, the site-level evaluation should mainly be interpreted as a diagnostic of seasonal timing and order-of-magnitude agreement, rather than as a strict validation of local flux magnitudes at every site.

Figure  compares the spatial and latitudinal distribution of wetland CH₄ emissions simulated by LPJmL6 with the WetCHARTs ensemble . Both data sets show a pronounced tropical maximum in the latitudinal profile, reflecting the dominant contribution of tropical wetlands to the global wetland CH₄ emissions. In terms of zonally summed emissions, LPJmL6 agrees reasonably well with the WetCHARTs ensemble median across broad latitude bands and remains mostly within the WetCHARTs min–max range, particularly outside the tropical peak region.

However, the spatial comparison indicates that similar latitudinal totals can arise from different regional emission patterns. The anomaly map shows regional offsets between LPJmL6 and the WetCHARTs median, including areas where LPJmL6 underestimates or overestimates emissions relative to WetCHARTs despite comparable zonal sums. This suggests that agreement in the latitudinal profile should not be interpreted as full spatial agreement. Part of this mismatch is expected because the comparison is made only against the WetCHARTs ensemble median, while the ensemble spread reflects substantial uncertainty in wetland extent and CH₄ flux estimates. In addition, LPJmL6 is run on a coarse spatial grid and does not explicitly represent bank infiltration or river–floodplain exchange processes, which limits its ability to resolve narrow floodplains, riparian wetlands, and seasonal inundation features that can contribute substantially to local CH₄ emissions.

Quantifying the exact global contribution of each pathway is challenging because of spatial and temporal variability in wetland extent, hydrology and vegetation, as well as differences in wetland types and environmental conditions. Table  therefore summarises the LPJmL6 global methane budget separated into atmospheric flux pathways (diffusion, plant-mediated transport, ebullition and fire emissions) and source categories (natural wetlands, rice fields, grasslands and other cropland), together with soil oxidation and the resulting net methane sink. This pathway- and source-resolved budget provides a process-level decomposition of the simulated CH₄ emissions and complements the spatial evaluation against WetCHARTs. It allows the relative importance of the main atmospheric transport pathways to be assessed separately from the contributions of different land-use and wetland source categories. In this way, the table provides an additional diagnostic for interpreting the model behaviour beyond the total wetland CH₄ flux and the latitudinal emission patterns.

The atmospheric flux partitioning shows that diffusion remains by far the dominant CH₄ emission pathway, with global emissions increasing from 117.6 to 157.5 Tg CH₄ a⁻¹ between the 1980s and 2010–2019. Plant-mediated transport roughly doubles from 19.5 to 40.6 Tg CH₄ a⁻¹ over the same period, whereas ebullition remains comparatively small (about 2 Tg CH₄ a⁻¹) and exhibits no clear trend, in line with the minor contribution of ebullition reported by . Fire emissions are simulated at around 10 Tg CH₄ a⁻¹, consistent with independent estimates of global wildfire CH₄ emissions of approximately 10 Tg CH₄ a⁻¹ and contributing about 5 % of the total natural source .

The soil methane sink in LPJmL6 can be compared with independent constraints. estimated a global soil CH₄ sink of 33.5 Tg CH₄ a⁻¹ for 1990–2009, whereas LPJmL6 simulates a stronger net uptake of about 52 Tg CH₄ a⁻¹ over the same period (Table ). A key difference is that LPJmL6 does not explicitly represent the atmospheric CH₄ sink associated with methanotrophic activity in well-aerated soils; instead, CH₄ oxidation is treated as part of the soil CH₄ balance. The gross soil oxidation flux in LPJmL6 is close to 150 Tg CH₄ a⁻¹, reflecting the substantial fraction of CH₄ that is oxidized while diffusing through the unsaturated zone. Despite these structural differences, the simulated net soil sink lies within, albeit towards the upper end of, the range of 9–51 Tg CH₄ a⁻¹ reported by atmospheric inversions and bottom-up estimates .

Because LPJmL6 explicitly represents both natural and managed ecosystems, including land use and land-use change, it can attribute global CH₄ emissions to distinct source categories. In our simulations, emissions from natural wetlands increase from 117 to 166 Tg CH₄ a⁻¹ between the 1980s and 2010–2019, while emissions from rice fields rise from 13.3 to 20.9 Tg CH₄ a⁻¹. This corresponds to an increase of about 57 % in rice-field emissions compared to only about 13 % growth in harvested rice area. Emissions from other agricultural land (excluding rice and grasslands) grow from 2.0 to 4.5 Tg CH₄ a⁻¹, and grassland emissions from 6.7 to 9.4 Tg CH₄ a⁻¹. For comparison, estimated that other agricultural CH₄ sources contribute roughly 20 Tg CH₄ a⁻¹ for 2005–2020, which is higher than the LPJmL6 estimate but broadly consistent when considering that the EPA category also includes savanna and residue burning. Overall, all simulated source categories exhibit increasing CH₄ emissions over recent decades, likely reflecting the combined effects of climate change and evolving land management; however, the relative contributions of these drivers warrant further investigation.

Another important aspect of LPJmL6 is the explicit representation of both natural and managed ecosystems, including land-use and land-use change dynamics. This structure allows us to attribute simulated changes in global CH₄ emissions to distinct source categories and regions across the terrestrial surface and to link emerging trends to underlying drivers. Such source-resolved information is essential for understanding, and ultimately mitigating, the role of wetlands and agricultural systems in global greenhouse gas budgets. The LPJmL6 model allows us to separately quantify global CH₄ emissions from natural wetlands, rice fields, grasslands and other agricultural land. In the simulations, emissions from natural wetlands increase from 117 Tg CH₄ a⁻¹ in the 1980s to 166 Tg CH₄ a⁻¹ in 2010–2019. Emissions from rice fields rise from 13.3 to 20.9 Tg CH₄ a⁻¹ over the same period, corresponding to an increase of about 57 %, whereas harvested rice area increases by only about 13 %. Emissions from other agricultural land (excluding rice and grasslands) grow from 2.0 to 4.5 Tg CH₄ a⁻¹, and grassland emissions from 6.7 to 9.4 Tg CH₄ a⁻¹. Over the same period, simulated global grassland area increases by only about 5 %, implying that the roughly 40 % rise in grassland CH₄ emissions is driven primarily by changing environmental conditions and management rather than by areal expansion alone. For comparison, estimated that other agricultural CH₄ sources contribute roughly 20 Tg CH₄ a⁻¹ for 2005–2020, which is higher than the LPJmL6 estimate but broadly consistent when considering that the EPA category also includes savanna and residue burning. Overall, all simulated source categories exhibit increasing CH₄ emissions over recent decades, consistent with the combined effects of changing climate conditions and evolving agricultural practices; however, the relative contributions of these drivers require further investigation.

Table  summarizes literature estimates of global CH₄ emissions from rice cultivation, aggregated over the growing seasons, together with the corresponding LPJmL6 simulations. Most literature values are multi-year means for the period indicated in the table (rather than single-year snapshots). They are based on a range of methodological approaches, including emission-factor inventories, statistical upscaling from field measurements, and FAOSTAT-based accounting, and span roughly 18.3 to 38.8 TgCH₄ a⁻¹. LPJmL6 simulates an increase from a global mean of 13.0 TgCH₄ a⁻¹ in the 1980s to 20.4 TgCH₄ a⁻¹ during 2010–2019, which places our results toward the lower end of the published range (Table ). A likely explanation is that the current representation of rice production systems assumes one cropping season per grid cell, whereas multi-cropping (double or even triple rice) is widespread in parts of South and Southeast Asia and eastern China . In such regions, annual emissions exceed the values simulated by LPJmL6 because emissions from multiple growing seasons within a calendar year are not explicitly represented. In annual sums of LPJmL6 simulated emissions, we combine planted rice area with those from wetland-setaside emissions on these fields, which captures major biogeochemical controls but may still under-represent management effects such as straw incorporation, organic amendments, and deliberate drainage. In the LPJmL6 simulations, the unproductive (non-growing) period contributes about 4 TgCH₄ a⁻¹. While the emission estimates obtained with other methodologies are strongly influenced by how the contributing days are defined, the very wide range of 8–78 Tg CH₄ a⁻¹ simulated by by the process-based model CH4MOD is mainly driven by differing assumptions about management.

Across rice-growing regions, methane emissions from rice fields exhibit strong spatial and temporal variability. LPJmL6 simulates country-mean cumulative growing-season emissions that range from a few to more than 100 gCH₄ m⁻² a⁻¹, with local grid-cell values reaching up to 328 gCH₄ m⁻² a⁻¹ in the most strongly emitting areas (Table ). The observed values compiled in Table  span a comparable order of magnitude, with maximum values extending from about 13 up to 347.5 gCH₄ m⁻² a⁻¹, indicating pronounced sub-national heterogeneity within the sampled regions. Independent field studies further highlight the very strong variability of rice CH₄ emissions. report substantial year-to-year differences in growing-season emissions from Chinese rice fields, with high emissions of 36.8 gCH₄ m⁻² a⁻¹ in 2018 and low emissions of 5.3 gCH₄ m⁻² a⁻¹ in 2019, while document even higher plot-scale values approaching 580 gCH₄ m⁻² a⁻¹ under specific conditions, illustrating the potential for extreme fluxes in certain regions or management settings. It is important to note that LPJmL6 always provides spatially complete coverage of each national rice area, whereas most literature values in Table  are derived from individual sites or sub-regions and therefore cannot be interpreted as true national means, even in the comparatively extensive dataset of . This mismatch in spatial representativeness, together with differences in local management practices, environmental conditions and measurement protocols, explains part of the discrepancies between simulated and observed ranges, while the overall overlap in magnitude supports the ability of LPJmL6 to capture first-order patterns of rice CH₄ emissions.

Globally, grasslands exhibit simulated CH₄ emissions that are half those from rice paddies, as indicated in Table . This important source of CH₄ emissions arises from two primary factors. First, the vast spatial extent of grasslands worldwide provides a substantial area for CH₄ production and emission, despite the generally lower CH₄ fluxes per unit area compared to rice paddies. Second, many grassland regions, particularly those converted from historical peatlands, are characterized by drained organic soils. The drainage of these former peatlands for agricultural use not only alters the hydrological regime but also influences the soil carbon dynamics, creating conditions conducive to CH₄ emissions . Residual croplands constitute a small but non-zero CH₄ source that is highly sensitive to field-scale hydrology. Even in nominally aerated systems, shallow or perched water tables, episodic waterlogging after irrigation or storms, and poorly drained depressions can create anoxic microsites where methanogenesis occurs. The resulting emissions are intermittent and heterogeneous, governed primarily by water-table depth and inundation frequency. Although flux magnitudes are typically far lower than those from wetlands, such emissions can be regionally relevant in poorly drained landscapes and in wet seasons, and they carry high spatial and interannual variability.

The release of soil carbon is decelerated due to the representation of wetlands in the LPJmL6 models. The anoxic decomposition is about 10 times slower and thus carbon is sequestered in soils for a much longer time. Thus the model can well reproduce the magnitude of the global carbon sink – including land-use change (LUC) emissions – within the estimate range of the Global Carbon Budget (GCB) 2023 from Dynamic Global Vegetation Models (DGVM) and from the bookkeeping approach (DGVM-LU-BK) (see Table  and Fig. ). Table  shows that LPJmL6 reproduces decadal terrestrial sink magnitudes within the GCB 2023 DGVM and DGVM-LU-BK uncertainty ranges and exhibits the expected strengthening from the 1990s to the 2010s; across the two GCB methods, residual differences can be traced to land-use-change treatment – bookkeeping versus implicit DGVM dynamics – and no systematic decadal bias is evident; this also holds for LPJmL6, indicating robust, method-invariant trends in the net land carbon sink. In Fig. , the simulated terrestrial sink follows the independently constrained apparent sink and the atmospheric CO₂ growth rate with comparable interannual variability, indicating that LPJmL6 captures the major climate-driven fluctuations and the multi-decadal increase in sink strength without long-term divergence from independent estimates.

We used eddy-covariance flux tower data to benchmark simulated NEE (Fig. ; full data description in Sect. ). As noted there, comparisons are constrained by scale mismatches between grid cells and tower footprints, possible vegetation (PFT) mismatches, and the use of large-scale meteorological forcing rather than site-specific observations, which limits the ability to capture site-specific variability in carbon fluxes.

Nevertheless, the comparison demonstrates that correlations between simulated and observed fluxes are generally high across many sites, indicating that the model captures the overall temporal dynamics of NEE reasonably well. However, the centered root mean square difference (CRMSD) and the normalized standard deviation reveal larger discrepancies, suggesting that while the timing of seasonal and interannual variability is reproduced, the magnitude of fluxes is often either over- or underestimated.

The ILAMB comparison demonstrates that the model successfully reproduces gross primary production (GPP) within the same order of magnitude as reported by (global mean 119 ±6 PgC a⁻¹ for 1982–2008 vs. 126 PgC a⁻¹ simulated by LPJmL6). This agreement is also in line with later FLUXCOM syntheses that place global GPP roughly in the 106–130 PgC a⁻¹ range, depending on predictors and machine-learning methods used .

Across the ILAMB benchmark, reference biomass products differ in scope (forest AGB vs. all vegetation; above- vs. below-ground components), spatial/temporal coverage, and retrieval/inversion methodology, yielding a wide spread in implied global stocks. LPJmL6 estimates global woody biomass to be 422 PgC (mean 2000–2019). Among reference datasets, products that resolve high biomass in humid tropical and high-latitude forests report totals comparable to LPJmL6, for example, GEOCARBON 408 PgC ; the Xu–Saatchi synthesis 381 ± 2 PgC for 2000–2019 . By contrast, ESA CCI Biomass provides forest AGB of 300 PgC (above-ground forest only) , and NBCD2000 is regional (conterminous U.S., sim∼2000 baseline), serving primarily for spatial pattern evaluation rather than global sums . These definitional and methodological contrasts account for the spread in ILAMB intercomparisons and explain why LPJmL6 aligns more closely with datasets emphasizing woody stocks across humid tropical and boreal forests, whereas ESA CCI implies lower global totals.

From the reference data sets used in ILAMB, only the Xu–Saatchi product (381 PgC) aligns closely with the LPJmL6 simulation result of 422 PgC, whereas most other datasets imply substantially higher global biomass totals ranging from 300 to 408 PgC.

Table  synthesizes ranges of data-driven and model-based estimates for the principal terrestrial water fluxes – evapotranspiration (ET), transpiration (T), total runoff from land, groundwater recharge, and irrigation withdrawals. ET (62×103 km³ a⁻¹) and T (39×103 km³ a⁻¹) fall within published model ranges and are near the lower bounds of data-driven syntheses, indicating a conservative global partitioning of ET. Total runoff and river discharge (47 and 40×103 km³ a⁻¹) lie near the centers of reported ranges, consistent with independent constraints. Groundwater recharge (31×103 km³ a⁻¹) exceeds data-driven and modeled estimates; this difference reflects varying definitions (diffuse vs. focused recharge and return flows), considered land areas, and averaging periods, also examined spatially in Sect. , with discharge and ET evaluations provided in Sect.  and . Nevertheless, the LPJmL6 estimate is near the upper end of published values and coincides with greater groundwater storage in the simulations than reported (Fig. ).

Figure  compares long-term mean groundwater storage (GWS) and groundwater recharge for 1981–2010 from WaterGAP 2.2 and LPJmL6. Recharge is highest in humid tropics and monsoon regions (Amazon, Congo, SE Asia, eastern India), and is moderate in temperate wet zones, and near zero across arid belts (Sahara, Arabian Peninsula, central Australia); orographic bands (Andes, Himalaya) are evident. Storage broadly tracks persistently wet lowlands and large sedimentary basins, with minima in deserts and high-latitude regions. LPJmL6 tends to display sharper spatial gradients and stronger orographic signals, while WaterGap is smoother and often more conservative in semi-arid interiors.

The comparison of discharge data shows that LPJmL6 is able to reproduce the seasonal hydrographs (see Fig.  and in the Supplement Fig. S28, especially in the southern latitudes. There are small improvements compared to LPJmL5.10. The far northern discharge levels are also reproduced quite well, with the largest discrepancy in the mid-latitudes. In some regions with low R2, errors are dominated by timing mismatch: the model typically leads the observed cycle (peaks occur earlier), while amplitudes are reasonably captured (see the Supplement Fig. S28).

Simulated ET was compared against eddy-covariance flux tower measurements. While towers provide high-frequency and highly localized ET estimates, the coarse spatial resolution of the simulations introduces a scale mismatch similar to that encountered for NEE.

Model-data agreement of ET is even higher than for NEE, in terms of both correlation coefficients (the model reproduces the temporal variability of ET with greater accuracy) and the CRMSD and the normalized standard deviation (the magnitude of ET fluxes is represented more consistently across sites). This likely reflects the fact that ET is primarily controlled by atmospheric demand and canopy conductance, processes that are more directly constrained by meteorological forcing and vegetation structure in the model, whereas NEE additionally depends on complex carbon turnover processes and ecosystem-specific dynamics.