JULES is the land surface model used in the UK Earth System Model (UKESM) . It is a community model that represents the surface energy balance, heat and water fluxes, snowpack dynamics, vegetation dynamics, soil biogeochemistry, and carbon and nitrogen fluxes . As well as being used in UKESM, JULES takes part in multimodel analyses such as the Inter‐Sectoral Model Intercomparison Project and the Global Carbon Project and has been used to make global projections, for example, of future hydrology, permafrost thaw, and carbon and methane emissions and their climate feedbacks

JULES includes a vertically resolved soil carbon scheme , although this has not yet been used in the Earth system model configuration. The scheme is based on Roth-C , with the carbon pools of the Roth-C model simulated separately for each soil layer. Some vertical processes have been added, such as a diffusive mixing, which represents bioturbation and/or cryoturbation (see , for details). This soil carbon scheme has more recently been coupled to a vertically resolved nitrogen model described in . In this paper we build on this vertically resolved soil carbon–nitrogen scheme in JULES. Note that all the simulations in this paper use the same branch of JULES. We generically refer to any configuration with the new peat functionality enabled as “JULES-Peat”, which is further sub-divided into different simulations.

As part of the development of the new, peat-enabled version of JULES we improved the response of soil carbon decomposition both to soil moisture and nitrogen availability. These changes were made based on well-known principles. Firstly, microbial activity drops to zero in completely dry conditions . Secondly, respiration in anaerobic conditions is known to be no higher than 20 % of the maximum rate in aerobic conditions . Finally, when microbes lack nitrogen, they tend to decompose plant litter faster in order to “mine” for nitrogen ; this is in contrast to the original scheme introduced by in which the decomposition of litter is inhibited when nitrogen is in short supply.

The decomposition of soil carbon in JULES is calculated as follows: for each soil carbon pool (Cp kg m-2, where p denotes the pool number), the turnover rate when the nitrogen in the system is not limiting (Rp,pot) is given by 1Rp,pot=kpCpFT(Tsoil)Fθ(θ)Fv(v), where kp is a fixed constant for each pool in s-1 . The functions of temperature (FT(Tsoil)) and moisture (Fθ(θ)) depend on the temperature (Tsoil, K) and moisture content (θ, fraction of saturation) of the soil. The function Fv(v) depends on the vegetation cover fraction (v) . When the vertically resolved soil carbon scheme is used, there is an additional multiplier, exp⁡(-zτresp), where z is depth in the soil and τresp represents an additional decay of carbon decomposition rate with depth.

Fθ is a function of the soil moisture. The standard version of JULES uses the following function, which is also shown in green in Fig. : 2Fθ(θ)=1-0.8(θ-θo)for θ>θo0.2+0.8θ-θmin⁡θo-θmin⁡for θmin⁡<θ≤θo0.2for θ≤θmin⁡, where θo=0.5(1+θw), θw is the wilting point water content as a fraction of saturation and θmin⁡=1.7θw. Fθ takes a value between ∼ 0.6–0.85 in saturated conditions; i.e. the decomposition rate in saturated conditions is between 60 %–85 % of its maximum rate. However, in reality, aerobic respiration essentially stops in saturated conditions, and anaerobic respiration takes place instead, with a rate less than 20 % of the maximum aerobic respiration rate . The fact that decomposition is suppressed under saturated conditions is key to the formation of peat. Therefore, we modified the decomposition function so that it takes a value of 0.2 when the soil moisture is saturated. We also changed the behaviour of this function under dry conditions, since there are a number of studies available that indicate the shape of this function , which should increase in a close-to-linear manner from zero decomposition rate at zero soil moisture content.

In addition, for undecomposed organic soils specifically, critical and wilting point soil moisture can be very small due to the large pore spaces and thus low capillary suction (the critical point can be as low as 10 % saturation). The formulation of θo, on the other hand, limits the optimum soil moisture content for respiration to a minimum of 50 % saturation, which can be up 5 × higher than the critical point. The critical point is defined by a capillary suction of 3.36 m. show in their Fig. 3b that the respiration response to soil moisture reaches a maximum at around this value. They show a moisture response curve for a high carbon soil in their Fig. 3a. The curve reaches a maximum at around 30 %–40 % saturation and stays at a high value until ∼ 75 % saturation, in contrast to the original formulation in JULES, which reaches its maximum only at the point θo. Therefore, for soil layers in which the critical soil moisture is lower than θo, we set the soil respiration to reach its maximum at the critical soil moisture content and remain at its maximum value until the original maximum θo, resembling the “high C content” curve in Fig. 3a. We therefore define a “lower” θo, θo,l=min(θcrit,θo). The old and new functions are shown in Fig. .

The new function used in JULES-Peat is therefore 3Fθ(θ)=1-0.8θ-θo1-θofor θ>θo1for θo,l<θ≤θoθθo,lfor 0≤θ≤θo,l.

In the standard version of JULES, in situations where nitrogen is limiting, the decomposition of the litter carbon pools (decomposable plant material, DPM; and resistant plant material, RPM) is reduced. This is because the more decomposed pools have a higher nitrogen content – or lower C : N ratio – and therefore to decompose the litter carbon into the BIO (biomass) and HUM (hummus) pools requires a source of nitrogen – and nitrogen is thus “immobilised”. Thus, the decomposition terms Rpot for DPM and RPM pools are multiplied by a factor FN, which is given by 4FN=MBIO+MHUM-IBIO-IHUMΔt+NinDDPM+DRPMΔt, where Nin is the total soil inorganic N pool in kg [N] m-2, Mp and Ip are mineralisation and immobilisation of nitrogen, respectively, from pool p in kg [N] m-2 s-1, and Δt is the time step. DDPM and DRPM are the net demand associated with decomposition of each of the litter pools: 5Dp=Ip,pot-Mp,pot, where p is either RPM or DPM; see for details.

However, in reality the microbes would continue decomposing the litter pools in order to access the nitrogen for their own survival. They would not be able to transform all of the decomposed carbon into biomass due to lack of nitrogen, but the carbon would decompose and would simply be released to the atmosphere as carbon dioxide, i.e. their carbon use efficiency reduces . Therefore, instead of modifying the litter decomposition rate with the factor FN, we modify the fraction of decomposed carbon that is released to the atmosphere vs. stored in the soil. This means that the limitation term has to take a slightly different form. The new function is as follows: 6FN=MBIO+MHUM-IBIO-IHUM+MDPM+MRPMΔt+NinIDPM+IRPMΔt, The fraction of decomposed carbon that stays in the soil (rather than being released to the atmosphere), in other words the carbon use efficiency, is then multiplied by FN for the DPM and RPM pools. While nitrogen was not a focus of this study, the need for this modification became apparent once the soil column was allowed to expand with addition of plant litter. This led to an unrealistic positive feedback in which litter carbon was not decomposed due to lack of nitrogen availability, meaning that as litter was added to the layer it took up an ever larger volume, eventually pushing the more nitrogen-rich pools out of the layer completely (further down the column), resulting in zero nitrogen availability and forming unrealistically thick litter layers with no turnover.

showed that the typical soil profile simulated by ESM land surface schemes with vertically resolved soil carbon (JULES and ORCHIDEE) displays a smooth decline with depth that resembles a mineral soil profile. However, in highly organic soils the soil carbon concentration typically increases with depth to a certain point before beginning to decline . This is because the density of the organic material in the surface is usually lower than in the deeper soil, so there is simply less material altogether in the surface layers, and therefore less carbon. The organic material in deeper layers has a higher density: in part because it becomes compressed by soil/water above it, and in a large part because it is generally more decomposed.

The crucial missing factor in global models (e.g. JULES, ORCHIDEE, CLM) is that the models do not account for the volume that is added to the soil when organic material is added via plant litter, or (conversely) the reduction in volume when organic material decomposes. This means that as well as being unable to simulate the typical profile of a peatland (soil carbon increasing with depth near the surface), unrealistically high carbon contents in surface layers are often simulated; see the original JULES version, shown as red lines in Fig. .

In JULES-Peat, the profile of litter inputs into each soil layer and decomposition of soil carbon in the layer is calculated as in , except that the modified decomposition function is used (Sect. ). When these increments come to be applied to the soil carbon profile, however, the thickness of the soil layers is now recalculated based on the volume of organic matter added or removed. We calculate the change in layer thickness by prescribing a density to each carbon pool, using a higher density for the decomposed carbon pools than the litter carbon pools. After addition or removal of carbon in a given time step, the new effective thickness dzeff,n of soil layer n relative to the initial layer thickness dzn is given by 7dzeff,n=dzn+dCdpm,n+dCrpm,n/fcρdpmrpm+dCbio,n+dChum,n/fcρbiohum, where ρdpmrpm and ρbiohum are the bulk densities associated with the carbon pools (in kg m-3), fc is the fraction of organic material that is carbon and dCi,n is the increment in carbon pool i in soil layer n. We picked the density of the litter pools, ρdpmrpm, to be the lowest density that is typically measured for peat (where DPM and RPM are the two litter carbon pools in JULES), and the density of the more decomposed carbon pools (ρbiohum) to be the highest density that is typically observed for peat (where BIO and HUM are the more decomposed carbon pools in JULES). Thus, the bulk density of organic material in any given soil layer will fall somewhere between these two extreme values given that each layer typically contains all four carbon pools (albeit in different ratios). The values we chose were 35 kg m-3 as the minimum, ρdpmrpm, and 210 kg m-3 as the maximum, ρbiohum. These match well with commonly quoted literature values (e.g. ) and were derived from the 5th and 95th percentiles of the bulk densities in the global peat core dataset described in Sect. . These limits are shown by vertical dashed lines in Fig. . The maximum bulk density of 210 kg m-3 corresponds well to the threshold bulk density for peat functioning in, e.g. . We relate the bulk density of the organic material to the carbon content by assuming that fc=0.56 or, in other words, that 56 % of the organic matter is carbon, which was also based on the 95th percentile of the percentage of carbon in the peat core dataset from (see Sect. ) and is consistent with the range of observations, e.g. in .

The new layer thicknesses are labelled as “effective” layer thicknesses (dzeff). In order to avoid technical difficulties and potential numerical problems with variable soil layer thickness (e.g. if surface layers become very thick), the soil carbon profile is then interpolated back onto the original soil layers.

In order to interpolate the carbon profile, the carbon quantities (C+dC; kg m-2) are first transformed to carbon densities (Cden, in kg m-3) by dividing them by the layer thicknesses, dz.

Following this, the interpolation of the effective carbon density on the effective layers back into the original layers depends on whether the centre of the original layer is above or below the centre of the effective layer and is calculated as follows: 8Cdenn,i=Cdeneff,n,i+34Cdeneff,n+1,i-Cdeneff,n,i×zeff,n-znzeff,n-zeff,n+1+14Cdeneff,n-1,i-Cdeneff,n,i×zeff,n-znzeff,n-zeff,n-1, when the original soil layer depth zn is deeper than the effective soil layer depth zeff,n, and 9Cdenn,i=Cdeneff,n,i+34Cdeneff,n-1,i-Cdeneff,n,i×zeff,n-znzeff,n-zeff,n-1+14Cdeneff,n+1,i-Cdeneff,n,i×zeff,n-znzeff,n-zeff,n+1, when the original soil layer depth zn is shallower than the effective soil layer depth zeff,n, where z is the centre of each soil layer and i indicates the carbon pool (DPM, RPM, BIO or HUM).

Mathematically, this represents an approximated second-order Taylor expansion of the function Cdens(z) around the point zeff but with a particular choice regarding the second-order derivative. In order to preserve the vertical structure of the soil, the second-order derivative is assumed to be around z+δz and z-δz, and thus if the gradient of the function changes sharply it will not be smoothed out. This means that a peat layer will not end up being numerically smeared into the rest of the profile. This is explained in detail with equations in the Supplement. Briefly, we used a simple test model where soil carbon inputs and outputs are given prescribed input and turnover rates, we account for the expansion and contraction of the soil column when carbon is added or removed and tested the method of interpolating back onto the original soil layers (i.e. as used in JULES). We ran this simple (and thus much quicker to run) script with very high resolution soil layers to see what the “true” solution for the soil carbon profile would be. We therefore confirmed that our choice of second-order derivative gave the best approximation of the true solution when a lower-resolution soil was used. For details, see the Supplement. Figure S2 in the Supplement shows that in the chosen scheme there does still appear to be some “smearing” in the deeper layers, which are thicker, but using a smaller interval δz′ leads to numerical instability in the thinner surface layers. Thus, for future development a scheme where δz′ depends on the soil layer thickness could be considered.

While the carbon profile is interpolated onto the original soil layers in order to keep the layer thicknesses constant, the thickness of the deepest soil layer is updated in order to track the overall change of soil column height. The minimum thickness for that layer is taken from the soil layer thicknesses specified at runtime, and this corresponds to the layer thickness when there is no carbon in the soil. This base layer is extended based on the total volume of the carbon pools in the soil column, and this extension is considered to be the surface elevation. However, the extra thickness of the bottom layer is neglected when calculating fluxes of heat and water and only applies when calculating carbon and nitrogen stocks and fluxes (which are conserved during layer adjustments). We decided that the complexity of modifying the heat and water calculations to account for the variable-thickness base layer was not worth the added complexity, given that the fluxes at the base of the soil column (8 m depth in this study) are generally very small.

Peat age was simulated following a similar method to , where the fraction of old carbon is traced throughout the simulation. During each update of the soil carbon pools, the age of each carbon pool is tracked and the weighted average of the soil age is taken for each carbon pool in each soil layer.

Each soil carbon pool in each soil layer is assigned an age, A, at the start of the simulation, which currently is either zero on initialising the spin-up or can be initialised from an existing simulation. Each time the carbon pools are updated, the age of each soil carbon pool in each layer is increased by the time step length. These values are then modified as the soil carbon pools are updated, either due to input of fresh carbon from litter (which has an age of zero and therefore reduces the age of the soil pool), due to mixing of carbon between two layers in which the ages are different, or due to input of carbon into BIO and HUM pools from other pools via decomposition. The general formula to update the age (A) for carbon pool Ci (kg m-2), with an increment of carbon Ci→Ci+ΔCi, is as follows: 10ACi→ACiCi+AΔCiΔCiCi+ΔCi.

ΔCi includes both incoming and outgoing fluxes from the pool. For the outgoing fluxes in ΔCi, we assume that A is the same as for the Ci pool. For an incoming litter flux we assume that A is zero, and incoming fluxes from other pools naturally take the age value from the corresponding pool.

If the soil height accumulation is switched on, the age then must be interpolated back onto the original soil layers as described in Sect. . We use the same interpolation method as for the soil carbon, which is given in Eqs. () and ().

In order to dynamically update the soil physical characteristics, we assume that the physical properties of the organic material in the soil are a function of its bulk density. The bulk density that we simulate in JULES-Peat depends on how decomposed the soil carbon is. More highly decomposed organic matter has a higher bulk density, and its properties change as it decomposes. Notably, the hydraulic conductivity becomes much lower as bulk density (or decomposition) increases, which is included in other peat models , but we also fitted relationships between the bulk density and other key physical characteristics, namely porosity, saturated hydraulic suction, the Clapp–Hornberger exponent and thermal conductivity. For the heat capacity we assumed that the heat capacity of the organic material does not significantly change with decomposition status, and therefore we used (1 - porosity, i.e. what fraction of the organic material is solids) multiplied by the heat capacity value of solids of 2.5×106 J K-1 m-3, which we took from .

Since different carbon pools have different bulk densities (see Sect. ), we first calculate the bulk density of the combined organic material in each soil layer, i.e. 11ρorg,n=1fc∑iCn,i/(forg,ndzn), where forg,n is the volumetric fraction of organic matter in the soil layer given by 12forg,n=1fc(Cn,1+Cn,2)/ρdpmrpm+(Cn,3+Cn,4)/ρbiohum/dzn.

Recent studies have shown that bulk density of peat shows strong relationships with its thermal and hydraulic properties . We combined data from these recent syntheses with additional values from the literature in order to get the best estimate of the relationships, which we show in Fig. . We fitted the relationships between bulk density and the other physical characteristics of peat using this combined dataset. Fitting was done using orthogonal least squares after normalising the data so that both variables being fitted had the same range of values. For the saturated hydraulic conductivity, the two available datasets showed markedly different relationships (see Fig. b), and thus we did not combine these but instead used only the data from since this was a global synthesis as opposed to the data which were from a single region. The data in also agreed better with other data, such as , and the original values used for organic soils in JULES, originally given in (also shown in Fig. ). In addition, the fit for porosity was forced to pass through 1 at a bulk density of zero as a physical constraint (this was achieved by modifying the normalisation factor until the intercept of the fit was exactly 1). The additional literature data for saturated hydraulic suction and the Clapp–Hornberger exponent shown in purple in Fig.  were derived from the following papers: , , , , , , and .

Specifically, we relate the following soil properties to bulk density: 13Ψsat,org=exp⁡0.023ρorg-5.08,14borg=0.0304ρorg+1.53,15Ksat,org=exp⁡-0.0532ρorg-6.63,16θsat,org=1-ρorg/1260,17λorg=0.06,18hcaporg=2.5×106ρorg/1260, where Ψsat,org is soil matric suction at saturation (m), borg is the Clapp–Hornberger exponent (unitless), Ksat,org is hydraulic conductivity (in units of m s-1; note that JULES uses kg m-2 s-1 so this is multiplied by 1000 for use in JULES), θsat,org is the volumetric soil moisture at saturation (m3 m-3), λorg is the dry thermal conductivity (W m-1 K-1) and hcaporg is the dry heat capacity (J m-3 K-1). If a soil layer is not 100 % organic then we combine these calculated organic parameters with the properties of the underlying mineral soil, following . The remaining hydraulic parameters θwilt and θcrit, which are the volumetric soil moisture at the wilting point and critical point, respectively (defined in terms of hydraulic suction), are functions of the other parameters and are recalculated when the other parameters are updated (see, e.g. ).

Since JULES is a global model, it is important that adding the functionality to represent peat does not degrade model performance for mineral soils. Therefore, we first evaluate the model at mineral soil sites.

In soils where the organic material is a relatively small fraction of the total soil, the original soil carbon scheme is able to perform well, since the expansion of the soil column due to the addition of organic material will be relatively small. Figure  shows the model performance at mineral soil sites where measured soil carbon profiles were available. While the individual sites are not well simulated, the general form of the profiles – resembling an exponential decline with depth – are recreated reasonably well in the standard JULES configuration.

Figure  also shows two JULES-Peat simulations in light green and dark green (JULES-Peat-B and JULES-Peat-B10, respectively, Table ). As discussed in Sect. , these have different values of τlit and are both plausible. In general, the new model version is also able to simulate a profile that resembles a mineral soil despite forming peaty profiles at a few of the sites, especially Hainich and Carlow (where the carbon is overestimated by all configurations of JULES, Fig. e–f). Aggregated across all sites, the updated model versions produce a profile with somewhat lower carbon density at the surface compared to standard JULES and less of a decline in carbon with depth (Fig. h). The lower carbon density at the surface matches better with observations than the original JULES simulation, but the carbon at depth tends to be overestimated. In terms of root-mean-squared error (RMSE), the aggregated profile is improved in JULES-Peat-B and JULES-Peat-B10 (RMSE 6.2 and 8.1 kg m-3) compared to JULES (RMSE 12.1 kg m-3); Table . Overall we conclude that despite poor model performance at individual sites, the aggregated soil carbon profiles in both JULES and JULES-Peat adequately resemble observed mineral soil profiles (Fig. h).

We assess the performance of the full JULES-Peat model configuration at the selection of simulated sites for which observed soil carbon profiles are available and organic soils are present (Fig. ). A few of the individual sites are well simulated, and almost all sites are simulated significantly better in all of the JULES-Peat configurations than they are in JULES (RMSE of median profile 12.9–13.5 kg m-3 for JULES-Peat configurations shown and 25.5 kg m-3 for JULES; Table ). Note that two additional JULES-Peat simulations are shown in Fig. , JULES-Peat-W and JULES-Peat-W10 (dark blue and light blue lines, respectively), where the lateral water flow is set to zero since we expect that this would lead to a wetter soil and a more realistic simulation of a topographically controlled peatland.

We then evaluate the soil carbon and age–depth profiles in JULES and JULES-Peat against the global dataset of peat cores (described in Sect. ) in Figs.  and . These figures show simulated soil carbon profiles at sites where the model simulates a carbon percentage by mass of more than 15 % for at least 39 cm (see Sect. ) and compares these against the median of the equivalent data (percent carbon > 15 %) from the global dataset of peat cores . It is clear that at these peaty sites, the original JULES configuration simulates a carbon density that is too high in the surface layers and too low in the deeper soil (red lines in Fig. ).

In order to quantify the total improvement in the various JULES-Peat simulations compared with the original JULES configuration we take the RMSE between the median soil carbon profiles for each climate zone, shown in Table . The best-performing version (shown in bold) has a RMSE that is reduced by 35 % for temperate peatland sites (from 23.0 to 14.9 kg m-3, Table ) and by almost 80 % for boreal peatland sites (RMSE reducing from 37.3 to 7.7 kg m-3, Table ). We see that the age at the soil surface was typically too high in the original configuration of JULES (Fig. , red lines). In JULES-Peat, the age at the soil surface is better simulated, age throughout the profile is generally realistic (solid blue and green lines in Fig. , mostly falling within the interquartile range of the observations), and RMSE in age is reduced by 32 % (temperate sites) and 56 % (boreal sites) for the configurations that perform best in terms of carbon profile (JULES-Peat-W and JULES-Peat-B10 respectively, Table ).

We also evaluated the bulk density profiles against the same peat core dataset, and the results are shown in Fig. . The bulk density in JULES-Peat tends to start at realistic values at the surface but increases too quickly with depth. It is remarkable how little the observed bulk density at boreal and temperate peatland sites varies with depth compared with the tundra sites (Fig. ), although this may be related to the larger sample size of boreal and temperate sites (127 and 77 vs. 12 for tundra) leading to a more “smoothed” profile.

The best simulations in JULES-Peat are generally those where drainage is impeded to make the soil wetter (JULES-Peat-W; see the bold numbers in Table ). In particular, JULES-Peat-W simulates a more realistic carbon density profile than the other model configurations for the temperate peatland sites (see the dark blue lines in Fig. ). For the boreal sites, JULES-Peat-W10 accurately captures the gradient of the soil carbon profile in the top 50 cm of soil (light blue lines in Fig. ). The age–depth profiles in JULES-Peat-W and JULES-Peat-W10 also correspond most closely to the median measured age–depth profiles. Since peat generally forms in wetter places, the fact that the simulations without lateral water flow out of the soil (JULES-Peat-W and JULES-Peat-W10) compare best against observations from peat soils is expected if the model realistically forms more peat in wetter soils.

In simulations whose name ends with “10” (e.g. JULES-Peat-W10, shown in light blue) the distribution of litter inputs into the soil is more weighted towards the surface (τlit=10 as opposed to 5, Table ). We generally find that using the lower value of τlit matches better with the data for the temperate peatlands and that the higher value is better for boreal peatlands (see the RMSE values for carbon profile in Table ). This suggests that τlit should depend on plant functional type, which it would in reality (shallower-rooting plants would deposit more of their litter nearer the surface) and implies that smaller or shallower-rooting PFTs should grow in colder regions, as is indeed the case .

JULES-Peat was sometimes able to accumulate peat starting with no carbon in the soil at time = 0 at one of the tundra sites (Iskoras) in selected configurations (JULES-Peat-B and JULES-Peat-W, see Fig. S12). These simulations form a relatively thin organic layer at this site. However, when the simulations were initiated with an existing peat profile instead of zero soil carbon in JULES-Peat-i (see Table ), the peat profile was maintained at Iskoras and continued to accumulate (Fig. S12 and Table S4). This then forms a realistic carbon density profile and a reasonably realistic age–depth profile, shown by dashed cyan lines in Figs. a and a. There are multiple reasons why the model may not accumulate much peat at tundra sites, including a lack of representation of more favourable paleoclimate conditions during spin-up and the simulation of soils that are too dry . Nonetheless, the Iskoras simulation by JULES-Peat-i indicates that when the model does simulate peat at a tundra site it can form a realistic profile (Fig. a, dashed cyan line). Similarly, the bulk density profile simulated for the tundra sites is realistic for the JULES-Peat-i simulation (dashed cyan line in Fig. ).

We initially introduced the additional processes and parameter changes that were incorporated in JULES-Peat into simulations one by one to test each process before running the full model. These simulations are shown in the Supplement (Sect. S2). The key development that allows the shape of the carbon profiles to be more realistic is accounting for the volume of organic material added and removed from the soil column (Eq. ) as described in Sect. . In particular, this process enables more carbon to reach the deeper soil and makes the carbon density in the surface lower since it expands when plant litter (which has low density; ρdpmrpm=35 kg m-3) is added. These differences are clear in all of the JULES-acc and JULES-Peat simulations in comparison to the original JULES (Figs. S3 and ). The majority of the reduction in RMSE is already achieved by adding in this process alone (reduced from 23.0 to 10.4 kg m-3 at temperate sites and 37.3 to 17.3 kg m-3 for boreal sites; Table S2).

While it does not significantly reduce the RMSE by itself, modifying the moisture function to suppress decomposition when saturated (Sect. , Eq. ) allows more peat to form in wetter areas, which is a crucial factor in simulating realistic peatland distribution and future dynamics. Reducing drainage makes the simulation worse for mineral soil sites, which is exactly what would be expected (wetter soil ⇒ more peat forms), and it almost universally improves carbon profiles for organic sites (compare JULES-Peat-B and JULES-Peat-B10 against JULES-Peat-W and JULES-Peat-W10 in Table ).

The other major new process introduced is that JULES-Peat simulates its own soil characteristics (Eqs. –, Sect. ). While we do not have measured profiles of soil characteristics to compare against, we can compare the soil thermal and hydraulic parameters simulated by JULES-Peat against those prescribed in JULES. Comparisons are shown in the Supplement for key parameters: Ksat, Ψsat, θsat and b for the simulations JULES-Peat-B, JULES-Peat-B10 and JULES-Peat-i10 (Figs. S7–S10). For some sites there is a good correspondence between the simulated and prescribed parameters, while for others there are significant differences, but all simulated profiles behave sensibly.

Simulating these soil properties dynamically leads, in many cases, to a thicker organic layer (compare JULES-accC and JULES-accC10 with JULES-Peat-B and JULES-Peat-B10 in Table S4) and more soil organic carbon (Figs. S5 and S6). This increase in carbon results in profiles that are significantly more realistic for organic sites (Fig. S6; RMSE reduced from ∼ 18–20 to 13–14 kg m-3) and marginally less realistic for mineral soil sites (Fig. S5; RMSE increased from ∼ 6–7 to 6–8 kg m-3). This suggests a self-reinforcing feedback of peat accumulation with soil characteristics, e.g. if peat accumulation has started, it is more likely to continue, and can lead to various important dynamics, which are discussed in the following sections.

For the simulations where the lateral flow of water was switched off during spin-up in order to simulate a wetter and more “peaty” soil (JULES-Peat-W and JULES-Peat-W10), we ran an alternative realisation of the 20th century where the lateral flow was switched back on (JULES-Peat-W-drain and JULES-Peat-W10-drain). At many sites the lateral flow is negligible in any case and this does not significantly affect the results. However, at some sites the “wet” (-W) simulation maintains a water table near the surface, whereas the baseline simulation (JULES-Peat-B/JULES-Peat-B10) does not, and the drained simulations therefore experience a major drop in water table and a subsequent degradation of the peat and a drop in the surface elevation (subsidence). Figure  shows the four sites for which the change in water table is most pronounced in JULES-Peat-W-drain (water table change given in Table ).

tracked the surface subsidence rate over time following drainage of peatlands for two different land use practices – forestry and agriculture. They typically see a very high subsidence rate of around 3–10 cm yr-1 in the first few years after drainage. Following this, a more steady subsidence rate of 0.5–2 cm yr-1 can be observed for the next few decades. In the sites in Fig. , we see a surface subsidence rate more in line with the longer-term subsidence rate of 0.5–2 cm yr-1 (e.g. Auchencorth loses > 40 cm in the first 40 years and 60 cm in around 80 years; see Fig. ). The lack of the initial very rapid subsidence suggests that there may be some processes missing in JULES, for example the mechanical raising and lowering of the peat surface by as much as tens of centimetres as the water table fluctuates, known as bog breathing . However, the long-term subsidence rate is at least of the right order of magnitude. After an initial period of subsidence lasting around 50 years, the drop in surface height stabilises or slows. The carbon loss behaves in a similar way, although the slowing of carbon loss is not as pronounced. In these test simulations (noting that the method of “draining” the sites is a proof of concept and is not based on reality), up to 17 kg C m-2 is lost from these sites, which would represent a highly significant addition of carbon to the atmosphere (on the order of tens of gigatons of carbon globally) if it took place across a significant fraction of the world's peatlands.

Both positive and negative feedbacks exist within peatland ecosystems . JULES-Peat is able to capture some of the key feedbacks by simulating dynamic soil properties. Firstly, a negative (damping) feedback takes place following drainage in which the peat compacts and becomes more resistant to water flow, thus re-wetting the soil to some extent; see Fig. . There is a strong correlation between decreased hydraulic conductivity and increased soil moisture: Pearson correlation between soil moisture and log⁡(Ksat) of -0.94 for Auchencorth and -0.87 for Carlow (in the top 3 m) using monthly data points for individual layers for the whole simulation. In these particular simulations, this effect was not strong enough to bring the water table back to the surface by the end of the simulation, but in some test simulations this effect was observed. In reality, it is rare for drained peatlands to self-restore, but it does occasionally happen (Alice Milner, personal communication, 2021​​​​​​​; Morag Angus, personal communication, 2021). On the other hand, a similar mechanism can lead to a positive (amplifying) feedback during spin-up, where the accumulation of peat leads to a lower drainage rate and thus further accumulation of peat. This is seen most strongly at Auchencorth and Carlow, which are the only sites from the UK and Ireland that were simulated (Fig. ). After sufficient peat formation (in particular after being initialised with peat in JULES-Peat-i and JULES-Peat-i10; see Table ), these sites are able to gradually raise their water tables over the course of the spin-up, while accumulating more and more carbon; see Fig. . It is significant that the UK and Ireland sites are the only ones where this mechanism takes place, since this is where the majority of the world's blanket bogs are found – peatlands that are able to maintain themselves autogenically without topographic controls. This indicates that JULES-Peat should be capable of simulating blanket bogs, which are currently missing in global peatland models due to their reliance on TOPMODEL-based wetland fraction to determine peatland area .

Since there are feedbacks in JULES-Peat between soil physics and soil carbon that can be self-reinforcing, the “end state” of the model spin-up now depends on the initial conditions. In mathematical terms there can be more than one equilibrium state. This also implies the existence of tipping points where the system can “tip” from one state to another under sufficient forcing . Essentially, there may be some sites at which initialising the model with peat allows it to further accumulate peat, but initialising the model with mineral soil maintains a stable mineral soil profile. Practically, this means that peat can exist outside of climatic conditions where it would form from scratch, and thus this is very important when we consider the disturbance of existing peatlands for which the original state could be impossible to recover under current climates.

In order to test this we compare the simulations where peat is initialised vs. not initialised in Fig. . We show two sites where peat only accumulates when it is initialised (Abiskomire_noSnowCor and Iskoras), a site where peat always accumulates (CA_WP1), and a site where peat never accumulates and a mineral soil always forms (Twitchell). This behaviour is apparent in the age–depth profiles (bottom row of Fig. ). The age is initialised with the existing age–depth profile of the peat for the runs that are initialised with peat (JULES-Peat-i and JULES-Peat-i10), hence the ages overall can be higher, since the standard runs start from age zero with no carbon. However, when the model converges to a single steady state, the age profile also starts to converge, at least at the surface (Twitchell and CA_WP1 in Fig. ). In contrast, at sites where peat only accumulates when the model is initialised with peat, the age at the surface actually becomes lower in the simulations where it was initialised with an existing age–depth profile than in the simulations where it was initialised at zero. This indicates that carbon is accumulating more quickly when the model is initialised with peat (-i and -i10) (Abiskomire_noSnowCor and Iskoras in Fig. ).

It is interesting to note that the sites where highly distinct steady states are simulated are palsa mires in the sporadic permafrost zone. These sites are on the cusp of the permafrost–non-permafrost transition. Thawing of permafrost peatlands has been shown to increase the carbon accumulation rate in some cases , and, interestingly, the simulations with high peat accumulation rate at Abiskomire_noSnowCor and Iskoras (JULES-Peat-i and JULES-Peat-i10) simulate a thawed soil, whereas the simulations with little peat accumulation (JULES-Peat-B and JULES-Peat-B10) simulate permafrost (Fig. S11).

The different steady states also appear to be associated with the presence of different vegetation types; see Table . The sites that develop very different carbon profiles when initialised with peat (Abiskomire_noSnowCor and Iskoras, JULES-Peat-i and JULES-Peat-i10) also develop a different dominant vegetation type, for example needle-leaf evergreen trees instead of Arctic grass in Abiskomire_noSnowCor (Table ). This interaction between vegetation and soil carbon highlights the importance of further developing the vegetation model to represent peatland vegetation (see Sect.  for further discussion). It is worth noting that for a site that simulates peat accumulation, the “steady-state” condition can be a constant rate of carbon accumulation rather than a constant quantity of carbon, i.e. peatlands are never in equilibrium, which differs from the standard definition of steady state that is currently used when spinning up land surface models.

Simulating landscape-level peatland hydrology is a major challenge. This work has taken a step forward by enabling peat soils to react appropriately to long-term changes in hydrology and to include some of the key feedbacks that the soils then have on the water flows. We have also recently developed an improved methane emissions scheme . However, to model peatlands within the landscape globally, including any methane emissions, the distribution of water around the landscape must be taken into account.

For instance, the majority of peatlands globally are topographically controlled. This means they are found in flat, lowland areas . The standard way of modelling groundwater in ESMs does not explicitly model these areas but simulates a “grid cell average” soil moisture. This means that at typical resolutions, the saturated lowland areas where peat forms would be less than the size of a grid cell, and thus saturated conditions would never be explicitly simulated, and secondly, even with a high enough resolution to resolve peatlands, there is no mechanism for lowland grid cell soils to receive water from the surrounding uplands. Therefore, a key step is to explicitly model different hydrological regimes and features within the landscape. The simplest way to do this is via a tiling approach. found that they were able to recreate the hydrological dynamics in the majority of the world's peatlands by using a tile that was entirely hydrologically disconnected from the rest of the grid cell. A further step would be to simulate the hydrological connection between the tiles in the grid cell, as this is necessary to simulate not only some existing peatlands but also peatland initiation .

Furthermore, the within-soil-column hydrology is not well modelled for organic soils in JULES. While peatlands in JULES-Peat are able to maintain a water table through the hydraulic characteristics of the peat itself, the water table generally does not sit as close to the surface as the observed water table in intact peatlands, which is around 10 cm (see, e.g. Carlow in Fig. ), although it can occasionally reach 10 cm when lateral flow is set to zero (Table ). In cold regions, a representation of ponding can be necessary to prevent too much snowmelt from running off and leaving the soil too dry . On top of this, the hydraulic behaviour of mosses, which form a primary component of high-latitude and temperate peatlands, is very different from that of vascular plants. Mosses do not extract water from the soil and it essentially only evaporates from the surface, which could very well lead to a raised water table . Thus the inclusion of a moss PFT and its unique functions in land surface models like JULES should be a priority, and several models have indeed done this (e.g. ).

It is clearly important to adequately represent the features of peatland vegetation. As well as the hydrological behaviour of mosses, it will be crucial to include an appropriate distribution of plant litter inputs to the soil (see the difference between the simulations with different values of τlit, e.g. in Fig. ), an appropriate recalcitrant litter fraction (for example, mosses are more recalcitrant than grass and therefore more likely to lead to peat accumulation), and suppression of the growth of non-wetland vegetation such as trees under saturated conditions (this is not included in JULES and is necessary to simulate the mossy peat that is found in northern latitudes, since larger vegetation would otherwise outcompete the mosses). In addition, the input of carbon to the peat is determined by the net primary productivity of the ecosystem, and thus this is a key quantity to evaluate when developing peatland-appropriate PFTs.

Finally, the JULES-Peat model configuration has not yet been tested in tropical peatlands, which differ from northern peatlands in terms of hydrology and vegetation and have only recently gained attention in the modelling community . There is a clear need for more focused study of tropical peatlands, given their large spatial extent and carbon stock and the potential impacts of their ongoing drainage . Some of the key principles behind peat dynamics are universal (for example, suppression of decomposition in wet soils, dynamic growth of the soil surface), but model parameters such as those in the relationships used to determine soil characteristics may need to be updated for tropical peat (e.g. Eqs. –).