We reserved the following annual C fluxes for post-calibration model evaluation: AGNPP_spruce and AGNPP_tamarack, available for year 2022 in the ten treatment enclosures; AGNPP_shrub, available for year 2023 in all eleven plots; the growing season average NEE of the shrub-moss community (NEE_shrubmoss, gC m⁻² gs⁻¹, “gs”), available for year 2023 in the ten treatment enclosures. The data sources of AGNPP_spruce, AGNPP_tamarack, and AGNPP_shrub are the same as in Sect. 2.5. The growing season mean NEE_shrubmoss was calculated from the average of gapfilled 15 min automated chamber measurements made on the shrub-moss community (Stelling et al., 2024). Growing season is defined as 1 May to 31 October, to match the observational period (27 April to 27 October 2023). The gapfilling method is adapted from previous work at the SPRUCE site (Walker et al., 2017) and is described in detail in Sect. S1.3. Note the automated chamber measurements and the gap-filling method used here are preliminary and were applied solely for the purposes of this study, pending availability of the full analysis of the automated chamber data (J. Stelling, personal communication, 2006). To obtain the modelled equivalence of NEE_shrubmoss, we considered what component fluxes were included in the observed NEE_shrubmoss. The chambers only enclosed shrubs and moss aboveground. Therefore, the chamber fluxes included aboveground shrub and moss GPP and respiration. The belowground collars of the chambers did not exclude tree roots. Therefore, the chamber fluxes included belowground soil HR, tree root respiration, shrub root respiration, and belowground moss respiration. Furthermore, because the chambers have small footprints, the sampled shrub and moss growths were often not representative of the average plot conditions. Therefore, we down-scaled the modelled plot-level shrub and moss GPP and respiration to the chamber-level using each PFT's ratio of measured aboveground biomass in the chamber (gC m⁻²) to the measured aboveground biomass in the corresponding plot (gC m⁻², Table S8). We assumed the soil HR and tree root respiration components of the chamber fluxes correspond to plot-level averages due to lack of prior information. In summary, the modelled equivalence of NEE_shrubmoss is calculated as (Plot-average HR + Plot-average tree root respiration + Scaled shrub autotrophic respiration + Scaled moss autotrophic respiration – Scaled shrub GPP – Scaled moss GPP).

To evaluate the simulated C biomass, we compared the models against the annual maximum leaf area index (LAI) of the two trees and shrub, measured using LICOR LAI 2200 device during 2015–2020 (McPartland et al., 2019). The annual C fluxes and LAI observations all have direct correspondence with modeled variables. AGNPP_spruce and AGNPP_tamarack have strong pre-treatment variation that impacts the interpretation of results (Hanson et al., 2025). Therefore, we fitted ordinary least squares linear regression models to remove the pre-treatment effect; because LAI is closely related to aboveground NPP, we used the same method to remove the pre-treatment variation in the LAI of the two tree species (Sect. S1.2). We did not compare the models against observed net C exchange or methane flux data because the net C exchange has small components of lateral outflow of organic C and dissolved inorganic C (Hanson et al., 2020a), which are not yet considered in ELMv2-SPRUCE, and the model cannot yet fully capture methane dynamics.

For nutrient cycling, we evaluated the models against several forms of observations. The first of those was porewater ammonia (NH4+), nitrate (NO3-), and inorganic P (PO43-) concentrations, which characterize the pool of dissolved nutrients in soil. The porewater concentrations were measured roughly twice per month during the non-frozen months of 2015–2020 near the bottom of the rooting profile (30 cm) in the hollow (Griffiths et al., 2016). The pore water nutrient concentrations were measured on a per water volume basis (mg N L⁻¹, mg P L⁻¹), but ELM can only simulate nutrient concentrations on a per soil volume basis (gN m⁻³ soil, gP m⁻³ soil). Therefore, we divided the simulated NH4+, NO3-, and soluble P (as defined in Yang et al., 2019) concentrations by the simulated volumetric soil water content to bring them to the same unit as the observations. Because the sampling interval was irregular and relatively infrequent, and nutrient concentrations in water can exhibit sharp, episodic fluctuations (Basu et al., 2010), we chose not to interpolate the observations to annual level like the annual C fluxes (Hanson et al., 2018a, b, 2020a; Norby et al., 2019). Instead, we down sampled the model outputs to only include the dates on which pore water concentrations were measured, ensuring that both observed and modeled data reflect the same seasonality. For each enclosure, we then summarized the observed and down-sampled modeled porewater nutrient concentrations into two statistics: the mean value and the temporal linear trend, to facilitate concise comparison. Here, the temporal linear trend is defined as the slope of a least-squares regression between the modeled/observed values and the elapsed days since 1 January 2015. We chose enclosure-specific temporal trends, instead of cross-enclosure temperature sensitivity (as done in Sect. 2.5), because the former metric captures well the behavior of the data when plotted as a time series, whereas scatterplots between the observed porewater nutrient concentrations and the air temperature on the corresponding dates do not show clear correlation.

The second form of nutrient cycling observations we used is resin-exchange NH4+ and PO43- (Iversen et al., 2017a). Those values approximately represent plant-available nutrients but previous study suggests that in shallow soil layers (10 cm), competition with roots invalidates this interpretation (Iversen et al., 2017a, 2022). Therefore, we focus on the resin-exchange nutrients measured at 30 cm in both the hummock and hollow, and at 60 cm in the hollow during 2015–2018, at which depths few roots exist in the anaerobic peatland environment (Iversen et al., 2017a). The raw measurements were cumulative absorbed weights of NH4+ or PO43- per resin capsule surface area during roughly monthly intervals; the values used in this study are the aggregated annual averages by the data collector (Iversen et al., 2017a). Following previous study, we compared the temperature sensitivities of the observed resin-exchange nutrients to the temperature sensitivities of the most comparable modeled variable, annual average net nutrient mineralization rates (NET_NMIN [gN m⁻³ s⁻¹], NET_PMIN [gP m⁻³ s⁻¹]) for a qualitative comparison (Iversen et al., 2022). To remove unit difference between the observed and modeled quantities, we divided the observed values and the modeled values, respectively, by the mean value of each during the observational period, separately for each nutrient species and soil depth. The resulting regression slopes against temperature represent relative (mean-scaled) changes per unit change in soil temperature. This normalization approach is commonly used in elasticity analysis for comparing effects across variables with different units (Sydsaeter and Hammond, 1995).

The final observation of nutrient cycling we used for evaluation are pre-treatment vertical profiles of C, N, and P stocks in the peat (Griffiths et al., 2017; Salmon et al., 2021). The compared model variables are the summed C, N, and P contents of all four SOM pools (1, 2, 3, 4) in all the soil layers in the decomposition processes (Sect. S1.1.3; Oleson et al., 2013) in the control plot.

In both ELM-OLD and ELM-MYCI, the soil decomposition process uses column-level parameters that are shared between hummock and hollow. Vegetation processes like photosynthesis, respiration, and nutrients uptake/acquisition use PFT-specific parameters that are also shared between hummock and hollow. We used observed parameter values as much as possible in ELM-OLD (Table S2) and ELM-MYCI (Table S4). For those unobserved, we used either optimized values obtained from 4000-member ensemble simulations that are described below (Tables S3 and 1) or manually set default values (Tables S2 and S4) if a parameter has relatively minor influence on the quantities of interest in this study. All the parameter optimization simulations excluded moss parameters for the purpose of consistency – because moss is not modified in this study, the newly added parameters do not cover moss.

We selected eleven preexisting parameters in ELM-OLD to optimize based on previous sensitivity findings (Meng et al., 2021; Ricciuto et al., 2018). Those parameters affect photosynthesis, plant respiration, plant allocation, and soil decomposition processes (Table S3). For each parameter, we generated an equal number of uniform random samples between predetermined upper and lower bounds from previous studies (Griffiths et al., 2017; Meng et al., 2021; Ricciuto et al., 2018; Table S3). We then formed all possible combinations of these samples across the parameters to create a total of 4000 samples. We then ran the model with these 4000 parameter sets. Finally, we ranked these parameter sets by relative absolute error (RAE) and selected the sample with the lowest RAE as the optimized parameter values. The RAE formula is shown in Eq. (5) and considers the relative errors in mean and in temperature sensitivity of annual C fluxes: 5RAE=1V∑v∈Vc∈ambient,elevated⋅Asim,v,c-Aobs,v,cUobs,v,c+Ssim,v,c-Sobs,v,cQobs,v,c where the subscripts sim means simulated, obs means observed, v is variable, c is the CO₂ treatment (ambient or elevated), V is the set of variables compared, |V| is the number of variables, A is the mean magnitude of the variable across all the treatments and years, S is the linear regression slope of the variable against annual mean air temperature across all the treatments and years, U is the observational uncertainty in mean, Q is the observational uncertainty in slope. During calibration, the performance metric calculated on the annual C fluxes that are items 1–6 in Sect. 2.5, because those are directly comparable to model outputs. Other observations are either reserved for validation (Sect. 2.6.1–2.6.2), not directly comparable to model outputs (Sect. 2.6.3–2.6.4), or pretreatment (Sect. 2.6.5). We did not include the aggregate NPP (item 7) or annual maximum LAI because of strong overlap with items 1–6. The Uobs,v,c values were estimated from pre-treatment standard deviation across the enclosure locations (Hanson et al., 2020a, 2025) by assuming that the relative uncertainty stays the same, i.e. the ratio of pre-treatment standard deviation to pre-treatment mean is the same as the ratio of Uobs,v,c to Aobs,v,c. The Qobs,v,c values are the 1σ uncertainty in the linear regression slopes (DeGroot and Schervish, 2018). We chose normalization by uncertainty to ensure the BGNPP_treeshrub variable, which are based on ingrowth core samples that had limited spatial representativeness and only span two years, was not overemphasized compared to the other C fluxes, which have five-year estimates (Hanson et al., 2020a; Iversen et al., 2021b). The normalization additionally ensured that all the variables are unitless, making them intercomparable.

For ELM-MYCI, the total number of preexisting and newly added parameters resulted in an extremely large search space that cannot be covered by 4000 samples. Therefore, we focus on perturbing the most sensitive half (18) of the 37 newly added parameters (Table 1). The most sensitive half was predetermined using one-at-a-time (OAT) perturbation – for each parameter, we generated 50 uniform random samples per parameter between pre-defined upper and lower bounds (Tables S4, 1). The perturbation ranges were based on observations or previous studies when possible (Table S4). The range for q10 of mycorrhizal acquisitions was set wider than the range of q10_hr for HR (Table S3) to explore more values (Table 1). The ranges for the rate constants (vN/P,froot,j, vN/P,fungi,j, uN/P,fungi,j) always span exactly two orders of magnitudes, and were selected based on experimental measurements (Table S5) and similar rate constants in past modelling studies (He et al., 2021; Shao et al., 2023b; Wu and Blodau, 2013). The geometric centre of each range was a manually tuned value that produced acceptable performance at the site during preliminary simulations. The ranges for the half-saturation points (kN/P,j) were set at approximately the modelled annual average soil inorganic NP levels at the SPRUCE site, because experimentally measured values (Table S6) were found to cause PFTs to die in test simulations. The ranges for the C-cost factor of mycorrhizal N acquisition (cN) were selected based on past observed exchange ratios for EcM (Bogar et al., 2022), assuming ErM has similar behaviour. We did not include the high-end of the observed exchange ratios (>100; Bogar et al., 2022) because those severely restricted mycorrhizal nutrient uptake in the modelling context, possibly due to the 50 % net photosynthesis cap.

We then calculated the standard deviations of Asim,v,c and Ssim,v,c over all the random samples for each variable and CO₂ treatment. This approach resulted in a 4th order tensor of 37 parameters × 6 variables × 2 CO₂ treatments × 2 coefficients [mean or temperature response slope]. We converted the standard deviation tensor to a same-dimensioned rank tensor by ranking the standard deviations high-to-low across the parameters separately for each variable, CO₂ treatment, and mean or slope. We show the ranks in Fig. S4, with the last three dimensions of the rank tensor compressed into the form of boxplots. The selected most sensitive parameters are those with lowest median ranks in Fig. S4 and are listed in Table S5. We then perturbed those most sensitive 18 parameters in a 4000-member ensemble simulation, calculated the RAE in the same way as done for ELM-OLD, and selected the sample with lowest RAE as the optimized set of parameters.

It is desirable to understand whether our structural change can improve ELM-OLD beyond the capability of parameter optimization. Therefore, we conducted two sets of 4000-member ensemble simulations for ELM-MYCI: one with the preexisting parameters fixed at default levels, and one with the preexisting parameters fixed at optimized levels. Table 2 lists the final four simulations compared in this study. Comparing ELM-OLD_optim to ELM-OLD gives the effect of parameter optimization. Comparing either ELM-MYCI to ELM-OLD, or ELM-MYCI_optim to ELM-OLD_optim, gives the effect of structural modification. Comparing ELM-MYCI_optim to ELM-OLD gives the combined effects of parameter optimization and structural modification.

Equation (5) only uses C fluxes but the optimized new parameters are mainly relevant to NP. To examine whether the selected optimal parameter values are indeed from a constrained subregion of the search space by Eq. (5), or simply perform best by chance, we used a clustering metric. This metric, though not using a formal likelihood framework, is consistent with the equifinality concept, where parameters are considered identifiable if the high-likelihood parameter values are concentrated in a small region, and non-identifiable if broadly distributed across the parameter space (Raue et al., 2009). We first normalized all the sampled parameter values to between 0 and 1 using the predefined ranges (Tables S3 and S5). Then, we calculated the Euclidean distances between the normalized parameter values of two types of ensemble member pairs. The first type was all the pairs that can be formed between the best performing 1 % (i.e. 40) members. The second type was all the pairs formed between one value from the best performing 1 % members, and one value from the bottom 99 % (4000 - 40 = 3960) members. If the pairwise distances in the first group are systematically lower than the pairwise distances in the second group, it means the better-performing parameter sets are clustered, which we interpret as being constrained by Eq. (5).

While the OAT perturbation helps us to downsize the number of parameters to perturb, it offers limited insight into the full sensitivity of model outputs, because it omits potential interactions among parameters. Using the 4000-member ensembles, we therefore applied a previously established procedure on ELM to calculate Sobol's main-effect and total-effect indices between selected model outputs and all the perturbed parameters (Ricciuto et al., 2018). Sobol's sensitivity indices are based on variance decomposition, where the total variance in a model output is decomposed into fractions attributed to individual parameters and interactions among parameters (Saltelli et al., 2004). The main effect measures the relative fraction attributed to a parameter excluding all interactions. Due to the omission of interactions, the sum of main effects across all the parameters is less than 1. The total effect measures the relative fraction attributed to a parameter including itself and all higher-order interactions involving the parameter. Due to duplicated counting of interactions, the sum of total effects across all the parameters is greater than 1.

On the calibration set of C fluxes, ELM-MYCI_optim best captures the mean and temperature sensitivity of the C fluxes (RAE = 1.54), followed by ELM-OLD_optim (RAE = 1.61), ELM-OLD (RAE = 1.80), and lastly ELM-MYCI (RAE = 1.82; Fig. 2). Also, ELM-MYCI_optim and ELM-OLD_optim have the fewest number of variables falling outside the ± one standard deviation observational uncertainty window (6 out of 28), followed by ELM-MYCI (8 out of 28), and lastly ELM-OLD (9 out of 28; the number of “×'s” of Fig. 2). Among the individual variables, the mean NPP_moss under elevated CO₂, the temperature sensitivity of BGNPP_TreeShrub under ambient and elevated CO₂, and the temperature sensitivity of aggregate NPP under elevated CO₂ are least well-captured, with all four model setups simulating outside the observational uncertainty (Fig. 2a, c, d). ELM-MYCI captures mean HR better than the other three model setups but performs worse on several other variables (mean AGNPP_shrub, temperature sensitivity of AGNPP_spruce under ambient CO₂, mean NPP_moss under ambient CO₂, and temperature sensitivity of NPP_moss under elevated CO₂; Fig. 2). Consistent with our hypothesis (see end of Sect. 1), structural modification improves model performance in capturing the observed large positive response of shrub growth to warming. The temperature sensitivity of AGNPP_shrub under ambient and elevated CO₂ are outside the observational uncertainty in ELM-OLD (Fig. 2c). Using optimized preexisting parameters, ELM-OLD_optim simulates the temperature sensitivity of AGNPP_shrub within the observational uncertainty range, but still underestimates it by ∼ 50 % under elevated CO₂ (Fig. 2c). With structural modification on top of optimized preexisting parameters, ELM-MYCI_optim best captures the temperature sensitivity of AGNPP_shrub, with only 17 %–35 % underestimation (Fig. 2c). Structural modifcation appears to negtatively influence the simulated mean AGNPP_spruce, which is more severely underestimated in ELM-MYCI and ELM-MYCI_optim than in the other two model setups.

The results of Fig. 2 show aggregated statistics for all the plots. To reveal more detailed causes of model biases, Fig. S7 shows the plot-wise observed and modelled annual time series of the calibration C fluxes. The interannual and inter-plot variabilities are much larger in the observations than all four model setups, especially in 2015, suggesting spatial variability in the real world remains a source of uncertainty in the model-observation comparison (Sect. S1.2). Increase in AGNPP_shrub, decrease in NPP_moss, and increase in HR from the coldest to the warmest treatments are visually discernible in both the observations (Fig. S7c1, d1) and the simulations (Fig. S7c2–c5, d2–d5). Using root mean squared error (RMSE) as a metric on each individual C flux, one can see that ELM-MYCI_optim best captures AGNPP_shrub (Fig. S7c2–c5) as well as the aggregate NPP (Fig. S7f2–f5), ELM-MYCI best captures HR (Fig. S7g2–g5), but the structural modifications did not result in clear improvements on AGNPP_spruce or AGNPP_tamarack (Fig. S7a1–b5). These are consistent with calibration-period performance evaluated on mean and temperature sensitivity (Fig. 2).

On the evaluation set of C fluxes, ELM-MYCI_optim has the best RAE (4.65), followed by ELM-OLD_optim (RAE = 5.03), ELM-MYCI (RAE = 7.22), and ELM-OLD (RAE = 7.31; Fig. 3). RMSE and RAE values calculated on the individual C fluxes show that ELM-MYCI_optim outperforms the other three model setups on AGNPP_spruce, AGNPP_shrub, and NEE_shrubmoss, but not on AGNPP_tamarack. This is consistent with the better performance of ELM-MYCI_optim on shrub than trees during the calibration period (Figs. 2, S7). None of the model setups correctly captures the positive temperature sensitivities of AGNPP_spruce under both CO₂ treatments and of AGNPP_tamarack under the ambient CO₂ treatment in 2022 (Fig. 3a, b). The high RAE on NEE_shrubmoss likely arises from an underestimation of observational uncertainty for this variable, since it was estimated from the RMSE of the gapfilling algorithm (Figs. S4–S5), not considering pre-treatment spatial variability or uncertainty in the chamber- and plot-level biomass measurements used to harmonize model and observations (Sect. 2.6.1). Nonetheless, such bias does not affect the within-variable ranking across the model setups based on RAE or RMSE.

In addition to C fluxes, we used annual maximum LAI, which is not a calibration variable, as a proxy to compare modelled C biomass to observed. Based on RMSE, ELM-MYCI_optim has lower overestimation in spruce LAI and lower underestimation in shrub LAI compared to the other three model setups, although higher overestimation in tamarack LAI (Fig. S8).

The observed resin-exchangeable nutrients increase by about two orders of magnitude with warming in all observed combinations of depth, nutrient, and hummock-hollow (Fig. 4). The net mineralization rates increase only by about one order of magnitude in ELM-OLD and ELM-OLD_optim. ELM-MYCI and ELM-MYCI_optim better capture the observed increases (yellow line in Fig. 4a, yellow and red lines in Fig. 4b, e, f, red line in Fig. 4c).

The modelled soil NH4+ and soluble P concentrations, converted to per volume soil water basis to compare with observed porewater values, show mean levels that are ELM-MYCI > ELM-OLD > ELM-MYCI_optim > ELM-OLD_optim (Fig. S9a, c). The ELM-OLD_optim values are closest to observed NH4+ values but still about one order of magnitude higher. The ELM-MYCI values are closest to observed soluble P values but more than one order of magnitude smaller. The observed NO3- mean concentrations are captured more accurately than NH4+ or soluble P, with ELM-OLD_optim being closest to observations, followed by ELM-MYCI_optim, while ELM-OLD and ELM-MYCI remain within one order of magnitude of the observations (Fig. S9b). These large discrepancies call into question if these observed and simulated quantities are comparable, even after the units are nominally aligned. Like the mean concentrations, the observed and simulated trends differ substantially in magnitudes. ELM-OLD and ELM-MYCI better capture the observed qualitative transition from negative to positive trends NH4+ towards the warmer enclosures than ELM-MYCI_optim; ELM-OLD_optim did not capture this transition for the ambient CO₂ enclosures (Fig. S9d).

All the model setups overestimate the peat C and N stock in the shallow soil layers (0–30 cm; Fig. 5a, b). In the deeper layers (30–200 cm), ELM-OLD exhibits underestimation that is exacerbated in ELM-MYCI and remedied in ELM-OLD_optim and ELM-MYCI_optim (Fig. 5a, b). All model setups severely underestimate P stock below 30 cm (Fig. 5c). The total simulated soil organic C stock of all the soil layers is about 190 kg C m⁻² by ELM-OLD, 240 kg C m⁻² by ELM-OLD_optim, 140 kg C m⁻² by ELM-MYCI, and 210 kg C m⁻² by ELM-MYCI_optim. This places ELM-OLD_optim outside the observational uncertainty of the estimated 176 ± 40 kg C m⁻² of the S1 bog (McFarlane et al., 2018), probably due to the overestimation in the shallow layers (Fig. 5a).

Simulation results from ELM-MYCI and ELM-MYCI_optim show that the total N acquisition from organic sources by PATH^myc,org across the three vascular PFTs are about 2.5 gN m⁻² yr⁻¹, and the total P acquisition by PATH^myc,org about 0.07 gP m⁻² yr⁻¹, in the unenclosed ambient plot (TAMB; Fig. 6). The PFT-total N acquisition by PATH^myc,org is mainly accounted by spruce (about 50 % of the total spruce N uptake, Fig. 6a) and shrub (30 %–50 % of the total shrub N uptake in TAMB, lower in the warmed enclosures, Fig. 6c). The total organic P acquisition mainly comes from tamarack (>50 % of the total tamarack P uptake; Fig. 6e). Those numbers and percentages are comparable to the coarse pretreatment estimates for the SPRUCE site, which suggests organic N sources account for about 30 % of total plants N acquisition (2.4 gN m⁻² yr⁻¹ out of 7.6 gN m⁻² yr⁻¹), and organic P sources account for a negligible fraction of total plants P acquisition (0.7 gP m⁻² yr⁻¹; Salmon et al., 2021).

ELM-MYCI and ELM-MYCI_optim simulates higher total spruce N acquisition through all three pathways, and greater warming-induced increases in total tamarack and shrub NP acquisitions across all three pathways, than ELM-OLD and ELM-OLD_optim (Fig. 6). The low spruce P acquisition simulated by ELM-MYCI_optim, especially under elevated CO₂, can explain the underestimation of AGNPP_spruce by this model setup (Fig. 2a). The large increases in shrub NP acquisition are driven by PATH^root (Fig. 6c, f), consistent with declining fungal colonization rates and rising soil inorganic nutrients under warming (Figs. S9a–c, S10c).

In addition to changing the responses of plants nutrient acquisition to warming (Fig. 6), ELM-MYCI and ELM-MYCI_optim simulate more flexible responses of plants nutrient acquisition to soil inorganic nutrient contents (Fig. S11). In ELM-OLD and ELM-OLD_optim, the uptake always displays a logistic shape where they first increase with soil inorganic N or P and then plateaus. In ELM-MYCI and ELM-MYCI_optim, the total acquisition across all three pathways can show linear relationships (e.g. Fig. S11b, e, f, ELM-MYCI_optim) or logistic shapes that saturate at higher or lower levels (e.g. Fig. S11a, b, ELM-MYCI).

All model setups simulate a transition from C sink to C source, that is, negative to positive net ecosystem exchange (NEE), with warming (Fig. 7a). Except for the +0.00 °C elevated CO₂ treatment, the C source strength is ELM-OLD > ELM-OLD_optim > ELM-MYCI > ELM-MYCI_optim. NEE is mainly driven by the balance between gross primary productivity (GPP), heterotrophic respiration (HR), and autotrophic respiration (AR), i.e. NEE ≈ - (GPP - AR - HR). All model setups simulate decreasing GPP with warming, especially in the ambient CO₂ plots, while the sum of AR and HR remains relatively stable. The latter's apparent stability is due to cancellation between decreasing AR, consistent with the GPP change, and increasing HR under warming.

The low NEE of ELM-MYCI_optim is because it has the lowest fraction of GPP lost to AR, especially in the warmest enclosures, among all the model setups (Fig. 7c). Like ELM-MYCI_optim, ELM-MYCI has a low AR-to-GPP ratio, but its low NEE is likely driven by the low GPP per se (Fig. 7b, c). In contrast, ELM-OLD_optim has lower NEE than ELM-OLD is because of a high GPP (Fig. 7b) and a smaller fraction of GPP lost as HR (Fig. 7d). Structural modification has little effect on HR to GPP ratios (ELM-OLD vs. ELM-MYCI, ELM-OLD_optim vs. ELM-MYCI_optim; Fig. 7d). The temperature sensitivities of NEE, GPP, AR and HR are generally insignificant within individual enclosures, but exhibit consistent increasing, decreasing, or bell-shaped patterns across the enclosure warming levels in all the model setups (Fig. 7e–l).

The difference between structural modification and parameter optimization on AR-to-GPP ratios can be better understood by examining the individual components of AR (Fig. 7). In ELM, AR is the sum of excess, maintenance, and growth respiration (AR = XR + MR + GR). XR represents respiration loss due to nutrient limitation, and is calculated as an nonlinearly increasing function of the percentage of plant biomass existing as NSC (Sect. S1.1.2); MR represents respiration for maintaining regular plant metabolism and is approximately proportional to total living biomass; GR is a small and constant fraction of structural growth and therefore of low interest here (Oleson et al., 2013).

At grid level, the lower fraction of GPP lost as AR in the structurally modified model setups than their unmodified counterparts (Fig. 7c) is mainly driven by lower XR-to-GPP ratios, especially under warming (ELM-MYCI_optim vs. ELM-OLD_optim, ELM-MYCI vs. ELM-OLD; Fig. 8a). Interestingly, parameter optimization induces large decreases in the MR-to-GPP ratio that are offset by large increases in the XR-to-GPP ratio (ELM-OLD and ELM-MYCI vs. ELM-OLD_optim and ELM-MYCI_optim), resulting in small net changes (Fig. 8a). This “trade-off” between XR and MR can be explained by their implicit relationship. At a higher XR-to-GPP ratio, the higher nutrient limitation prevents GPP from being assimilated into structural growth, leading to lower biomass-to-GPP ratio and therefore lower MR-to-GPP ratio. By the same logic, lower XR-to-GPP ratio implies a higher biomass-to-GPP ratio, and therefore higher MR-to-GPP ratio.

Compared to the grid-level ratios, structural modification has strong effects on the ratios calculated between PFT-specific XR, MR, and GPP. For spruce, ELM-MYCI and ELM-MYCI_optim have much higher XR-to-GPP ratio and lower MR-to-GPP ratio than ELM-OLD and ELM-OLD_optim, especially in the colder enclosures (Fig. 8b), which indicates a XR-MR trade-off similar to observed at grid level. For tamarack, ELM-MYCI_optim has much lower XR-to-GPP ratio than ELM-OLD_optim in all the enclosures (Fig. 8c). For shrub, ELM-MYCI and ELM-MYCI_optim have much lower XR-to-GPP ratio than ELM-OLD and ELM-OLD_optim in the warmest enclosures (Fig. 8d). As such, spruce and shrub are likely the main drivers behind the more rapid decline of the grid-level XR-to-GPP ratio in the structurally modified models than ELM-OLD or ELM-OLD_optim (Fig. 8a). The weaker XR-MR trade-off in tamarack and shrub likely reflects the lower importance of MR in the two PFTs compared to spruce.

Nutrient limitation of HR occurs in the default and modified models when the available soil inorganic N or P cannot satisfy the total demand of the plants and immobilization demand from soil litter and organic matter decomposition (Eq. S4, Sect. S1.1.3). The immobilization demand arises mainly in the decomposition step from plant litter to SOM (Oleson et al., 2013; Schimel and Bennett, 2004). The C : N and C : P in the plant litter pool depend on litter inputs and are usually higher than the C : N and C : P of the downstream SOM pools, which are fixed parameters (Oleson et al., 2013). As a result, the process immobilizes additional soil inorganic NP to meet the C : N and C : P of the SOM pools. Because ELM-MYCI and ELM-MYCI_optim allow plants to access the NP in plant litter pools via mycorrhizal roots (Sect. 2.2), the C : N and C : P the litter pools increase, resulting in greater immobilization demand per unit decomposition, which is proportional to HR. Consistent with this expectation, for each unit of HR, the corresponding actual immobilized inorganic N in ELM-MYCI and ELM-MYCI_optim are higher than in ELM-OLD_optim and ELM-OLD at the same level of HR (Fig. S12a). The same effect is not seen in P (Fig. S12b). Instead, ELM-OLD_optim exhibits considerably higher P-immobilization per unit HR than the other three model setups. All the model setups exhibit sensitivity to warming, which suggests P-limitation on HR is more affected by litter quality changes created by relative changes in primary productivity among the PFTs than N-limitation on HR (Fig. 2).

The distance metric (Sect. 2.7.2) shows the top-performing 1 % parameter values are statistically significantly closer to each other (smaller distances) than to the remaining 99 % parameter values (larger distances) in all three ensemble simulations (Table 2, Fig. 9). The significant separation means the C fluxes can constrain the preexisting and newly added parameters. The distances are least well-separated for ELM-MYCI_ENS (Fig. 9b), which uses the same un-optimized parameters as ELM-OLD for the unchanged model processes. Those suboptimal parameter values may have caused biases that the new model processes cannot compensate for, leading to unstable optimized values in the new parameters in the ELM-MYCI_ENS simulations.

We show the parameter sensitivities of ELM-MYCI_optim_ENS in the main text (Fig. 10), since the finding of Sect. 3.3.1 suggests this may be a more reliable perturbed parameter ensemble than ELM-MYCI_ENS (Fig. S11), and the sensitivities of preexisting parameters (Fig. S12) are similar to the well-reported findings of past studies (Meng et al., 2021; Ricciuto et al., 2018).

The relative sensitivity of model outputs to each parameter is approximately the same whether assessed using total effects or main effects (compare the rows in Fig. 10). The grid total GPP is sensitive to the parameters of all three vascular plants and grid-level parameters (topmost bar in each panel of Fig. 10). The grid total NEE and vegetation C (TOTVEGC) are most sensitive to spruce parameters, especially the sensitivity of fungal colonization rate to soil inorganic N (bj, Eq. S12) and maximum rate of inorganic N acquisition via mycorrhizal association (vN,myc,j, Eq. S23). The grid total HR and total soil organic C (TOTSOMC) are most sensitive to shrub parameters, especially the maximum rate of N uptake via fine root (vN,froot,j, Eq. S33). The C variables in any vascular PFT are mainly determined by the parameters specific to that PFT, especially the maximum uptake/acquisition rates of NP (uN,myc,j and uP,myc,j for spruce (Eq. S17), vP,froot,j for tamarack (Eq. S33), and vN,froot,j for shrub (Eq. S33)). Moss C variables are sensitive to the parameters of all three vascular plants and grid-level parameters.

Compared to ELM-MYCI_optim_ENS, the sensitivities derived from ELM-MYCI_ENS are similar for tamarack and shrub parameters (Figs. 10b, c, f, g, S11b, c, f, g). For spruce parameters, the model outputs of ELM-MYCI_ENS are more sensitive to the fungal colonization rate to soil inorganic N (bj, Eq. S12 and Fig. S11a, e), whereas ELM-MYCI_optim_ENS are more sensitive to the maximum organic NP acquisition rates via mycorrhizal association (uN,myc,j and uP,myc,j for spruce, (Eq. S17; Fig. 10a, e). Still, the two sets of parameters fulfil similar functions, with the former controlling all the nutrient uptake/acquisition pathways (see Mmyc,j in Eqs. S17, S23, and S33) and the latter only controlling the organic pathway (Eq. S17). For column level parameters, ELM-MYCI_ENS is mainly sensitive to the Q10 of NP acquisition rates (q10, Eq. S13) and has little sensitivity to the C cost of mycorrhizal nutrients acquisition to the plant (cN, Eqs. S25, S30) (Fig. S11d, h). ELM-MYCI_optim_ENS exhibits the same contrast, albeit less strongly (Fig. 10d, h).

Comparing between the newly added (Figs. 10, S11) and preexisting parameters (Fig. S12), one can see the newly added parameters exhibit more inter-PFT interactions. That is, the C variables of each PFT are even more strongly determined by the parameters specific to that PFT in ELM-OLD_optim_ENS (Fig. S12a, b, c, e, f, g) than in ELM-MYCI_optim_ENS (Fig. 10a, b, c, e, f, g) or ELM-MYCI_ENS (Fig. S11a, b, c, e, f, g). Additionally, the grid-level C variables are mainly responsive to spruce parameters in ELM-OLD_optim_ENS (Fig. S12a, e), compared to both spruce and shrub parameters in ELM-MYCI_optim_ENS (Fig. 10a, c, e, g) and ELM-MYCI_ENS (Fig. S11a, c, e, g). Moss C variables are more responsive to spruce parameters in ELM-OLD_optim_ENS (Fig. S12a, e), compared to shrub parameters in ELM-MYCI_optim_ENS (Fig. 10c, g) and ELM-MYCI_ENS (Fig. S11c, g). The main and total effects of ELM-OLD_optim_ENS are close to 1 when summed over all the parameters (Fig. S12 grey lines), while the main effects of ELM-MYCI_ENS and ELM-MYCI_optim-ENS are much smaller than 1 and the total effect much greater than 1 (Figs. 10, S11, grey lines). The larger difference between total and main effects in the modified models means the newly added parameters have stronger statistical interactions than the preexisting parameters in the default model.

In ELM-MYCI, the partitioning of plant nutrient demand between non-mycorrhizal and mycorrhizal pathways is a linear function of soil inorganic N concentration (Eq. 1). The focus on N is likely acceptable for northern boreal regions, where plant growth is N limited or co-limited by N and P, but extending the model into temperate or tropical regions will require considering P limitation (Du et al., 2020). A second question is whether the covariate, soil inorganic nutrient concentration (Eq. 1), is simplistic and should be replaced with plant nutrient status. Plant exudates and phytohormones play a large role in the early establishment of EcM and AM, making plant nutrient status a mechanistically defensible choice (Garcia et al., 2015), but this mechanism is much less established in ErM (Genre et al., 2020). EcM colonization may also respond to soil inorganic N directly, because assimilating inorganic N is more C-expensive than assimilating organic N (Garcia et al., 2015). Therefore, the relative appropriateness of the two covariates will be best determined via multi-site, multi-PFT simulations across N and P gradients. The current ELM-MYCI equations already have two terms related to plant nutrient status: the N-limitation and NSC availability multipliers (Eqs. 3–4). Therefore, to implicitly encode an effect on colonization rate, one can simply let the parameter value in the N-limitation multiplier (Eq. S15) differ between PATH^root and the two mycorrhizal pathways.

The current formulation for PATH^myc,org makes a few significant simplifications that do not conform to real world processes (Sect. 2.3). The restriction of mycorrhizal organic NP acquisition to plant litter pools may underestimate total mycorrhizal organic NP acquisition. This, in turn, could lead to underestimation of mineral NP limitation on HR and overestimation of the NP limitation on plant growth, contributing to the biases shown in Fig. 2. The acquisition rate does not vary with soil organic NP content or the recalcitrance of the accessed plant litter pools (Eq. 4), and the upper bound (0.0001 ⋅ total plant litter pool size per hourly time step) is more a sanity constraint rather than a realistic upper bound on fungi-accessible organic matter. This may result in underestimation of the changes in acquisition rates across environmental gradients. In reality, mycorrhizal nutrient acquisition involves two sequential steps: depolymerization followed by uptake of small organic molecules for N (Talbot and Treseder, 2010), and enzymatic hydrolysis and uptake of released phosphate for P (Plassard et al., 2011). Each step is describable by Michaelis-Menten kinetics (Näsholm et al., 2009; Plassard et al., 2011). In the organic matter-rich peatland environment, the first step would be much more limited by fungal enzyme availability than substrate availability, making a colonization-proportional formulation (Eq. 4) acceptable. Extending the model to mineral soil environments will require revisiting the formulation. Although the rate of the first step may be higher for labile than recalcitrant organic matter (Talbot and Treseder, 2010), current understanding of mycorrhizal enzyme activity is largely from a biochemical perspective, i.e. characterizing individual compounds, rather than from an ecological perspective, i.e. classifying numerous compounds into measurable fractions that significantly differ in rates (Lavallee et al., 2020; Oleson et al., 2013). Therefore, the current even distribution of organic NP acquisition across the plant litter pools, proportional only to pool sizes, serves as a starting point that can be refined as ecological-scale data become available. Modelling the second step in Michaelis-Menten form would require explicit representation of the turnover of mono- and oligomeric fractions of organic N pools, or of soluble P pools in microsites, which are beyond the scope of this study.

The total mycorrhizal acquisition of inorganic and organic NP is capped by 50 % of net photosynthesis per time step (Sect. 2.3). In the real world, belowground C allocation to mycorrhizal fungi peaks later in the growing season than aboveground photosynthesis (Högberg et al., 2010). Therefore, the current model formulation may underestimate mycorrhizal NP acquisition later in the growing season. In principle, this could lead to underestimated NP limitation on the heterotrophic microbes later in the growing season and overestimated NP limitation during leaf expansion in the following spring. The practical effect in the current ELMv2-SPRUCE, however, may be minor. The model also does not yet separate heterotrophic microbes and mycorrhizal fungi in soil decomposition. The model also uses fixed C : N : P ratios for plant structural tissues, and always evaluates nutrient limitation based on concurrent soil nutrient availability rather than nonstructural nutrient storage pool sizes.

The new equations in ELM-MYCI introduces a fairly large number of new parameters (in total 37 in Tables S4 and 1) compared to ELM-OLD. Although the annual C fluxes demonstrated ability to constrain these parameters (Fig. 9), the ability may have benefited from the temperature gradient, with implied inorganic nutrient gradient, across the SPRUCE treatments. Extending ELM-MYCI to other sites will therefore require more direct constraints.

The highest priority should be given to uptake rate constants (vN/P,froot,j, vN/P,fungi,j, uN/P,fungi,j) and half-saturation points (kN/P,j) because of the high sensitivity of model outputs to these parameters (Sect. 3.3.2). Many experimental measurements of these parameter exist, but the data points are concentrated in temperate regions and crop species, and exhibit high cross-species uncertainty (Craig et al., 2025; Griffiths and York, 2020; Tables S5–S6). Therefore, these data points are likely useful for large-scale simulations, but less so for site-scale simulations involving only a few species or simulations targeting underrepresented ecosystems like peatlands. In those cases, total plant NP uptakes, estimated from paired NPP and whole-plant C : N and C : P measurements, provide a reasonable nutrient-centred constraint. The efficiency of the parameter search can be increased in future studies by constraining the search space with well-validated qualitative findings in experimental data – for example, mycorrhizal roots generally have higher rate constants for inorganic NP on a per unit fine root biomass basis than uncolonized roots (Craig et al., 2025; Plassard and Dell, 2010).

Other large sources of uncertainty in the modified model include the fungal colonization fractions (Fig. S10), relative contributions of different pathways to total plant NP acquisition (Fig. 8), and the transfer of plant C to mycorrhizal fungi (Sect. S1.1.8). EcM colonization is known to respond to large temperature, water, and nutrient gradients and covary with fine root traits (Ostonen et al., 2011, 2017; Xie et al., 2021). Stable isotope fractionation studies (δ15N, δ13C) provide the most direct constraint on mycorrhizal contribution to plant demand and plant C allocation to mycorrhizal fungi (Hawkins et al., 2023; Hilman et al., 2024; Hobbie and Hobbie, 2006; Yin et al., 2022). Observations of all these quantities vary between 0 %–100 % (Hawkins et al., 2023; Hilman et al., 2024; Hobbie and Hobbie, 2006; Ostonen et al., 2011, 2017; Xie et al., 2021; Yin et al., 2022) and root tip counts at SPRUCE corroborate the high uncertainty (Fig. S10). Therefore, multi-site model-data integration will be needed to capture the broad pattern and prevent overfitting.

Root morphology parameters come from measurements in this study (root diameter – rj and root tissue density – ρj in Table S5). These two traits belong to, respectively, the collaboration and conservation gradients in the root economics space, and both are correlated with other traits (Bergmann et al., 2020; Craig et al., 2025). Thinner roots tend to depend less on fungal partners and have higher uptake rate constants. Lower root density tends to be associated with higher root N content, turnover rates, uptake rate constants, yet higher half-saturation points. These qualitative understandings, along with global root trait observations from, e.g. the Fine-Root Ecology Databases (Iversen et al., 2021a), provide good constraints for ELM-MYCI in future multi-site or regional extensions.

Several process developments in ELM are being carried out during the same time as this work, including division of fine root biomass into transport, absorption, and mycorrhizal pools (Wang et al., 2023), nutrient-responsive dynamic above-belowground allocation (Knox et al., 2024), and explicit microbial biomass pools and dissolved organic matter dynamics (Ricciuto et al., 2021). These developments can be merged with this work to relax many of the assumptions listed in Sect. 4.3.1 and improve the model results. Explicit simulation of fungal and heterotrophic microbial biomass will enable separating mycorrhizal fungal from non-mycorrhizal respiration and the modelling of fungal necromass, which has different decomposability from saprotrophic residues due to higher melanin content, particularly in ErM fungi (Fernandez et al., 2019). Other efforts of interest may include separating the behaviours of EcM and ErM, spruce photosynthesis and MR, Sphagnum growth, and considering direct plant uptake of small organic N molecules (Näsholm et al., 2009). Nonetheless, process-development should consider the limited constraint available from empirical observations (Fig. 9) and ensure the complexity is commensurate with our ability to check model accuracy and interpret cause and effect in model responses.

The modified ELMv2-SPRUCE has extended capabilities compared to the default model, e.g. fine tune nutrients competition relationships between PFTs using the maximum uptake/acquisition rates and half-saturation parameters (Tables S4–S5), assimilating nutrient uptake kinetics data, and testing the ecosystem impacts of changing fine root traits. Those improvements will enable new hypothesis testing and more accurate modelling of peatland C, N, and P cycling. It will also be interesting to compare the modified ELMv2-SPRUCE with other models that use similar fine root-based uptake rules (Knox et al., 2024; Zhu et al., 2019) and/or have mycorrhizal representations (He et al., 2018; Shao et al., 2023b; Sulman et al., 2019), and to test the performance of the model at multi-site to regional scale and its implications for carbon cycle feedbacks to the climate system.