JSM is a soil biogeochemical model built on the backbone of the vertically explicit C-only SOC model COMISSION . The COMISSION model was further developed from the conventional one by introducing a scalable maximum sorption capacity based on soil texture for dissolved organic C and microbial residues (Sect. S1.4 in the Supplement) as well as temperature and moisture rate modifiers for microbe-mediated processes and sorption (Sect. S1). We will investigate in a separate study how the maximum sorption capacity for mineral-associated organic C contributes to the observed patterns of SOC content and radiocarbon age. A schematic overview of JSM is presented in Fig. 1, and the mathematical description of the processes is provided in the Supplement. The model is integrated into the QUINCY TBM modelling framework and can either be applied as a stand-alone soil model or coupled to the representation of the vegetation and surface processes. In this study, we applied JSM as a stand-alone model. JSM neither describes the energy and water processes at the atmosphere–soil interface or in the soil profile nor simulates the production of litter. Model inputs (soil temperature, moisture and water fluxes as well as plant litter data) were derived from the QUINCY model.

JSM describes the formation and turnover of SOM along a vertical soil profile, which is explicitly represented as exponentially increasing layer thickness with increasing soil depth (Fig. ). The biogeochemical processes and pools of C, N and P are represented in each layer. Vertical transport of biogeochemical pools between the adjacent layers due to percolation and bioturbation is also modelled. To reflect the development of an organic layer, the model also includes an extra advective transport term which accounts for the upwards/downwards shift of the soil surface when the surface SOM accumulates/diminishes.

SOM is represented as pools of soluble, polymeric or woody litter as well as of dissolved organic matter (DOM), mineral-associated DOM, living microbial biomass, microbial residue (necromass) and mineral-associated microbial residue, each of which contains organic forms of C, N and P. The flows of organic N and P follow the pathways of C, with additional nutrient-specific processes, such as mineralisation and plant uptake, to link organic matter turnover with inorganic nutrient cycles. Microbial biomass is assumed to maintain a fixed stoichiometry in the model. It assimilates organic forms of C, N and P from DOM with fixed element use efficiencies and inorganic forms of N and P from soluble mineral pools. Microbes are assumed to aim to maximise their growth by maintaining high C use efficiency; however, when growth is limited by nutrients, microbes reduce their C use efficiency and increase nutrient mineralisation accordingly (See Sect. S1.5). The stoichiometry of all other SOM pools depends on the C:N:P ratios of influx and efflux, and these fluxes retain the stoichiometry of their source pools unless the formation processes involve respiration. In addition, when microbes decay, nutrients are preferentially recycled to the DOM pool due to the low C-to-nutrient ratio in the cyctoplasma, as proposed by . The inorganic pools of N and P include soluble inorganic ammonium (referred to as NH4), nitrate (referred to as NO3), soluble inorganic phosphate (referred to as PO4), as well as adsorbed PO4, absorbed PO4, occluded PO4 and primary PO4. The inorganic P cycle follows the QUINCY model and accounts for microbial interactions. JSM explicitly traces 13C, 14C and 15N following and .

Enzymes are not explicitly modelled in JSM, although these are described implicitly to regulate processes such as depolymerisation and nutrient acquisition. For enzyme allocation within depolymerisation processes, we extended the microbial adaptation approach of the SEAM model by including P dependence of enzyme allocation and the assumption of a steady state of enzyme production, leading to the prediction that the total enzyme level is always proportional to the microbial biomass. The fractions of enzymes allocated to different depolymerisation sources (litter and microbial residue) are dynamically modelled to maximise the release of the most limiting microbial elements. JSM tracks three potential fractions of enzyme allocation, which represent cases in which microbes only maximise the depolymerisation release of C, N or P, respectively, and then updates the microbial enzyme allocation fraction by acclimating gradually to the potential fraction of the most limiting element (See Sect. S1.5.2). For nutrient competition between plant, microbes and soil adsorption sites (only for phosphate), the potential rates are calculated on the basis of the respective richness and half-saturation level of enzymes and the impacts of other competitors, following the ECA approach (See Sect. S2.2).

The impacts of soil conditions on biogeochemical processes are also represented in JSM. The temperature response of different processes (e.g. microbial growth, decay, and nutrient uptake in Sect. S1.4) are represented by the Arrhenius equation with different activation energies. Moisture responses are described by two rate modifiers – one representing the effects of oxygen limitation (e.g. litter turnover in Sect. S1.2) and the other representing the effects of diffusion limitation (e.g. depolymerisation in Sect. S1.3). JSM also considers the effects of SOM content to correct bulk density (Sect. S3), which in turn affects other processes such as organic matter (Eq. S7) and phosphate (Eq. S25) sorption.

The Vessertal (VES) site is a mature beech (Fagus sylvatica) forest stand with an average tree age of >120 years, located in the central uplands of Germany (Thuringian Forest mountain range). The intermediate elevation is 810 m a.s.l., with a high annual precipitation of 1200 mm and a mean annual temperature of 5.5 ∘C . It is one of the Level II intensive monitoring plots in the Pan-European International Co-operative Program for the assessment and monitoring of air pollution effects on forests (ICP Forests). Since 2013, the VES site has also been one of the main study sites in the German Research Foundation (DFG) priority programme 1685 “Ecosystem Nutrition: Forest Strategies for Limited Phosphorus Resources”.

Soil at the VES site is classified as Hyperdystric Skeletic Chromic Cambisol , with loamy topsoil and sandy loamy subsoil, overlain by a moder organic layer. The current soil developed on trachyandesite, and the development started at the end of the last ice age, 10–12 000 years ago . The soil was sampled up to 1 m, with layer depths of 5–10 cm, for the measurements of total C, N, and organic and inorganic P and basic physical properties such as bulk density and soil texture. Soil from the A horizon alone was extracted for the estimation of microbial C, N and P pools. Detailed sampling and measurement approaches are described in .

The soil contains 19 kgm-2 C, 1.1 kgm-2 N and 464 gm-2 P up to 1 m soil depth, including the forest floor . The soil C content decreases from 510 gCkg-1soil in the forest floor to 126 gCkg-1soil in the A horizon to 5.9 gCkg-1soil at 1 m depth. The C:N ratio of SOM slightly decreases from 19.5 in the forest floor to 14.75 at 1 m depth, whereas the C:P ratio decreases more steeply from 348.7 in the forest floor to 46.6 at 1 m depth. The organic P fraction of total P also decreases from 67 % in the organic layer to 13 % at 1 m depth. The microbial C content decreases from >2000 µgCg-1soil C in the forest floor to 764 µgCg-1soil C in the top mineral soil . The microbial biomass shows a C:N ratio of 13 and a very low C:P ratio of 10.3 .

We tested JSM with different initial SOM contents and different microbial stoichiometry. The simulated SOM profiles, including SOC; C:N and C:P ratios of SOM; microbial C, N and P contents, and bulk density, did not respond strongly to changes in initial SOM contents (Fig. S2) but were notably affected by the assumed microbial stoichiometry (Fig. S1). We further examined the effects of simulation time on soil profile development (Figs.  and S1). SOC in the topsoil (30 cm) reached a stable state (ca. 70 kgCm-3) after approximately 150 years and the subsoil (30–100 cm) reached a stable state (ca. 30 kgCm-3) after approximately 1000 years. The accumulation rate of SOM decreased with time, but the complete soil profile had not yet reached a steady state (Table ) because C continues to accumulate slowly, particularly in deeper soil layers (>1 m). Although the organic P dynamics follow the soil C dynamics, the inorganic P pools inevitably deplete in the long-term simulation (Fig. ) due to high uncertainties in initialisation and P cycling processes. Therefore in this study, we focussed on the stable state of the topsoil (30 cm) at the end of the 200-year simulations and referred to it as a “quasi-equilibrium state” since slow changes are still occurring, particularly in soil inorganic P pools and SOM in deeper soil layers (Figs. S3, S4 and S5).

We first compared the simulated profiles with the in situ observed ones (Fig. ). The modelled results agreed well with observed stock sizes and vertical patterns, indicating that the stocks (here we define the term “stock” as the total amount of all (model) pools within a larger set) of C, N and P pools in SOM show smaller temporal variations than the microbial pools at the quasi-equilibrium state (Fig. a to c) due to strong seasonal variations in microbial biomass. We also found a greater variation in the simulated organic-P-to-inorganic-P (Po-to-Pi) ratio (Fig. d) than for the individual organic and inorganic P stocks (data not shown), inferring that the seasonal dynamics of microbes also impose a seasonal pattern of P immobilisation (from Pi to Po) and mineralisation (from Po to Pi).

The distribution and radiocarbon profile of total organic matter in the simulations varied across soil depths (Fig. ). The first layer (0 cm, O–A horizon) is dominated by the plant litter and microbial component (living or dead microbes), and while the microbial component decreases strongly from ca. 40 % at 0 cm to almost zero at 50 cm soil depth, the litter component still constitutes ca. 10 % of the total SOC at 1 m soil depth. The mineral-associated C (MOC) component switches from a minor component in the O–A horizon (ca. 20 %) to the dominant component (ca. 90 % at 1 m) in deeper soil layers.

The simulated radiocarbon (Δ14C) profile qualitatively agreed with the observed one (Fig. S1e); the Δ14C content increased within the O horizon and started decreasing with increasing soil depth from mineral soil, i.e. the A horizon. This pattern indicates that the “bomb pulse” Δ14C signal significantly affects the apparent 14C age in the organic layer and its impact decreases with soil depth due to the slow turnover in deeper soil. Our simulations further indicated that such a vertical pattern is caused by MOC and microbial components, while the litter component stays modern throughout the profile (Fig. ). Increases in litter 14C with depth suggest that more bomb-derived SOC is still found in subsoils due to slower litter turnover, while it is already replaced by more recent, 14C-poorer SOC in the topsoil. Although the Base Scenario did not reproduce the measured radiocarbon profile, despite producing its vertical pattern, a much better fit with the measured radiocarbon profile and an increase in soil 14C age, driven by MOC, were indeed observed as simulation time increased (Figs. S1e and S4).

The simulated biogeochemical fluxes show strong seasonal and vertical patterns (Figs.  and ), in which the flux rates in summer and in the topsoil are generally higher than those in winter and in the subsoil, respectively. Meanwhile, microbial inorganic N uptake shows a different seasonal pattern, with the lowest rates observed in August and September (Fig. c). In fact, this pattern is supported by the seasonal pattern of net N mineralisation flux, in which the peak is observed in August and September (Fig. b). This result indicates that organic N in DOM is the most abundant for microbial growth during August and September, leading to a large reduction in the microbial inorganic N uptake and an increase in net N mineralisation. In contrast, organic P content in DOM is the lowest during August and September, leading to net P immobilisation and microbial inorganic P uptake elevation (Figs. d and a). While the vertical pattern of plant N uptake parallels root distribution , plant P uptake is lower in the organic layer than in the topsoil due to strong competition from microbes in the organic layer (Figs.  and ).

The sources and sinks of soluble inorganic N and P also show very different patterns (Fig. ). The main source and sink for inorganic N in solution are gross mineralisation and plant uptake of NH4, respectively, whereas for P, microbial uptake is the main sink and biomineralisation is a larger source than gross mineralisation in each scenario.

In general, the SEAM-off scenario did not differ much from the Base Scenario in terms of the main soil stocks and biogeochemical fluxes (Figs.  and ); however, the ECA-off scenario produced a lower microbial biomass and Po-to-Pi ratio in the organic layer and topsoil. Total SOC may not be influenced in either scenario, although its composition and radiocarbon profile were both altered (Fig. ).

We presented the uptake of inorganic PO4 and competition between phosphate adsorption, uptake of inorganic P at three different depths (Fig. ), and seasonal and vertical uptakes of inorganic N and P for both microbes and plants (Fig. ). The simulations showed that microbes outcompeted roots for inorganic P uptake in JSM at all depths. However, the relative competitiveness of roots for phosphate uptake increased with increasing soil depth because the plant P uptake rate decreases less strongly than the microbial P uptake with increasing soil depth. In contrast, the phosphate adsorption rate increased strongly with increasing soil depth and outcompeted biological processes (plant and microbial uptake) in deeper soil layers. The relative competitiveness of phosphate adsorption against microbial and plant uptake also strongly decreased in summer in the topsoil due to high biological activity in warm months (Fig. b). With respect to competition for inorganic N, plants outcompeted microbes along the entire soil profile and throughout the year, particularly in summer when microbes assimilate N mainly from DOM (Fig. c and d).

Turning off the model's feature for nutrient acquisition competition, i.e. ECA-off scenario, led to a notably lower microbial biomass and Po-to-Pi ratio in the topsoil (Fig. ). This is caused by concurrent changes in microbes and plant inorganic P uptake, particularly in the topsoil layer where plants take up more inorganic P than in the Base Scenario (Fig. ) due to reduced competition with microbes. Moreover, there were differences in spatial and temporal variations in uptake and mineralisation fluxes between the ECA-off scenario and the other two scenarios. For instance, the seasonal variation in fluxes was notably lower in the ECA-off scenario. Decrease in P flux rate with soil depth may be weaker in the ECA-off scenario, but the decrease in net N mineralisation with soil depth is marginally stronger (Fig. ). This difference is because geophysical processes, such as adsorption and absorption, play more crucial roles in the soil P cycle than in the N cycle and because these show rather different seasonal and vertical patterns from the biochemical processes, such as mineralisation.

The modelled enzyme allocation for depolymerisation is presented in Fig. . We compared the enzyme allocation curve of polymeric litter (Enzfracpoly in Eq. S17) with three potential allocation curves (αpolyX where X stands for C, N and P in Eq. S15), which represent cases in which microbes only maximise C, N or P release from depolymerisation. All modelled fractions of enzyme allocation to polymeric litter were well below 50 % for the whole soil profile, indicating that polymeric litter is less preferred than microbial residues for depolymerisation in the soil, particularly in very deep soil layers where no roots are present and microbes would thus only produce enzyme to depolymerise microbial residues because the content of residue is much higher than that of polymeric litter. The simulated curve of allocation overlaps with the curve of potential allocation to maximise P release, indicating that depolymerisation is solely driven by P demand. This explains why microbial residues are preferred over polymeric litter since the C:P ratio of microbial residues is much lower than that of polymeric litter (data not shown). Despite rather different enzyme allocation fractions shown in Fig. , the majority of the modelled stocks and fluxes were not significantly influenced when enzyme allocation was turned off (Figs.  and ). More profound differences were observed in the composition and radiocarbon profile of SOC; there was less litter and more SOC in the SEAM-off scenario than in the Base Scenario, resulting a systematic difference in the radiocarbon profiles between the two scenarios (Fig. ).

The interquartile range of outputs (Fig. ) from model sensitivity analysis revealed that all outputs were well centred around the results of the parameterisation of the Base Scenario (Table S2), except microbial inorganic N uptake and N losses. In general, the soil stocks were more stable than the microbial pools and biogeochemical fluxes. N mineralisation was surprisingly insensitive while microbial inorganic N uptake was very sensitive to parameterisation. N mineralisation in JSM was mainly driven by the C:N ratio of DOM, which remains rather stable due to the similar C:N ratios of plant litter, microbes and microbial residues. The very sensitive response of microbial inorganic N uptake was attributed to the high-affinity (low Km,mic value) N uptake transporters of microbes and their sensitivity to changes in NH4 concentration. The RPCC of parameters with outputs (Table ) also demonstrated that the C and N contents of SOM as well as the C and N fluxes were more sensitive to changes in C processes, such as depolymerisation, organic matter sorption and litter partitioning, while the microbial dynamics and the P fluxes were more sensitive to changes in microbial and nutrient processes, such as maximum biomineralisation rate (vmax,biomin) and P recycling during microbial decay (ηres→domP). Overall, most of the selected outputs were strongly influenced by microbial stoichiometry. The five most influencing parameters in JSM were microbial C:N ratio (χmicC:N), microbial N:P ratio (χmicN:P), microbial mortality rate (τmic), soluble litter C fraction transformed into DOM (ηC,sol→dom), and P fraction recycled from res to dom during microbial decay (ηres→domP).

We applied the ECA approach described by to simulate inorganic nutrient competition. In general, our model simulations indicated that microbes take up more inorganic P than plants, which supports the findings of 33P tracer experiments at two other beech forests in Germany . However, our study showed that plants take up more inorganic N than microbes (Figs. a and S1). This pattern seems to disagree with the findings of field studies of 15N addition e.g. and a modelling study using the same approach to simulate competition . The reason for this disagreement is that in JSM, we assumed high microbial N use efficiency from DOM, and the majority of microbial N assimilation was actually fulfilled by DOM uptake. Therefore, plants take up more inorganic N than microbes. However, in 15N tracer experiments and a model study by , there was no distinction between assimilation from organic and inorganic sources; thus, microbes outcompete plants in the sense that the total N assimilated by microbes exceeds the total N taken up by plant roots, which was also true in our study. Another uncertainty related to the plant–microbe competition for inorganic N is the microbial stoichiometry we used in parameterisation. As discussed in the previous section, a change in microbial stoichiometry from the observed field value to the global average value resulted in a switch from microbes outcompeting plants for inorganic N to the opposite trend. Additionally, the choice of microbial nutrient use efficiencies not only affected the microbial demand for inorganic nutrients and the concentrations of inorganic N and P, thereby influencing the potential uptake rates of microbes and roots.

We extended the enzyme allocation approach of the SEAM model by including P dependence and vertical explicitness and by assuming a steady state of enzyme production. Due to the very small microbial C:P ratio used in model parameterisation, our results indicated that depolymerisation is solely driven by P demand; thus, microbial residues are the preferred substrate because they have a much lower C:P ratio than polymeric litter. This is also supported by the massive P biomineralisation flux (Fig. ) independent of depolymerisation and gross mineralisation, indicating that microbial growth is strongly P limited. Even in the scenario using the global microbial stoichiometry, depolymerisation was still solely P driven, and P biomineralisation fulfilled over half of the microbial P demand (Fig. S5). This result is partly supported by the global enzymatic activity data, in which global ratios of specific C, N and P acquisition activities converged on 1:1:1 , while the global microbial stoichiometry was much higher, indicating that relatively more resources are allocated to acquire P than to acquire N and C. This result actually reveals a caveat in the current implementation of enzyme allocation in JSM: the main process via which organic P is hydrolysed, biomineralisation and the mobilisation of sorbed inorganic P due to root exudation are not included in the enzyme allocation calculation. It also explains the very small difference between the Base Scenario and the SEAM-off scenario.

JSM demonstrated a capacity to reproduce the vertical patterns of soil stocks (Fig. ) and to satisfactorily produce both vertical and seasonal patterns of biogeochemical fluxes (Figs.  and ). While the seasonal patterns are primarily driven by the temperature response of the represented processes, the vertical patterns are shaped by the combined effects of biochemical and geophysical factors represented in the model. As seen in Figs.  and , although total SOC decreased with soil depth, the microbial, litter and MOC components showed very different patterns. Following the COMISSION model , we constrained the capacity of organo-mineral association with silt and clay contents and soil bulk density in JSM. In the organic layer and topsoil, the continuous litter input sustains a large microbial biomass and microbial residue pool; however, due to the very low bulk density and relatively low silt and clay contents, sorption is weak and MOC content is very low. As soil depth increases, bulk density and silt and clay contents increase such that microbial residues and DOM stabilise to a greater extent. This hinders microbial DOM assimilation and nutrient immobilisation, leading to a strong decline in microbial biomass and an increase in MOC. As a consequence of the decreasing microbial biomass and litter inputs, much less microbial residue and DOM are available for sorption to the mineral soil, which explains the observed decrease in total SOC in deep soil layers.

Nonetheless, certain caveats of this study and JSM should be discussed. A main challenge is the different simulation times for different purposes. Our results indicated that in the upmost 30 cm of soil, SOM content stabilises after 150 years, while in the upmost 1 m SOM stabilises after 1000 years of simulation (Fig. ), regardless of the initial SOM content (Fig. S2). However, with respect to the radiocarbon profile, as indicated by , a very long simulation time (13 500 years) was required to match both the measured Δ14C and SOC profiles at a nearby Norway spruce forest site. In our study, a 10 000-year simulation time was still not sufficient to match the measured Δ14C profile, indicating that an even longer simulation time is required. Although JSM is very stable in the long term in terms of SOM development and storage, long-term simulation of soil P balance as a result of continuous weathering and occlusion remains a significant challenge (Fig. , Table ). Such a long simulation time is unrealistic for the P cycle due to the unknown conditions of the initial soil P pools and the un-equilibrated soil inorganic P cycling processes . Although we used a much shorter simulation length in this study, noticeable uncertainties remain due to inorganic P cycling parameters (Table ). Additionally, the long simulation time required to match the radiocarbon profiles is also problematic for future coupling to TBMs because these models typically examine centennial timescales. A possible solution is to spin up radiocarbon (>10 000 years) independent of the plant–soil spin-up (1000 years), although this approach needs to be properly tested in the future.

Another caveat involves the model's representation of microbial adaptation schemes. In JSM, we describe enzyme allocation, which is one of the schemes of microbial adaptation proposed by ; however, as discussed above, enzyme allocation to phosphatases might be essential and might thus need to be included. Additionally, we found out that another adaptation scheme, the microbial community shift between fungi and bacteria, is crucial for reproducing the vertical pattern of soil stoichiometry. Although we mimicked such a shift in this study by calibration and parameterisation, a more mechanistic representation is necessary in the future for representing the acclimation of microbial functional properties to climate and environmental changes.

Concerning the model's description of N dynamics, in the current version, N processes such as nitrification–denitrification and abiotic ammonium adsorption are not yet implemented. Although the simplified N dynamics will probably not alter the main findings of this study, it is important to investigate these in the future since plants often have a preference for ammonium uptake . Finally, given the good quality of the input data, JSM could adequately reproduce the soil stocks and flux rates at the selected study site; however, its capacity to extrapolate to other climate and soil conditions needs to be further investigated in the future.

JSM is highly non-linear and sensitive to the parameters controlling microbial growth and decay (Table ). The C and N stocks in SOM as well as respiration and net N mineralisation are highly sensitive to the parameter changes of depolymerisation and organo-mineral association, whereas the organic or inorganic P stocks and P mineralisation are highly sensitive to the microbial processes. These trends support, and also explain, the finding of and that the P cycle is decoupled from the C and N cycles in the soil. A more in-depth explanation of this difference, based on our results, is that the gross mineralisation associated with microbial DOM uptake can supply microbes and plants with sufficient N but not P; thus, a large amount of P needs to be mobilised, particularly from SOM as well as from mineral pools, to sustain microbial growth. Therefore, the microbial pools and soil P stocks or fluxes are highly sensitive to microbial processes.