An overview of model functions is given in the Appendix, Table A1. Plant growth is simulated according to a “radiation use efficiency approach” in which the rate of photosynthesis is assumed to be proportional to the global radiation absorbed by the canopy, but limited by temperature, water conditions, and N availability (Eq. 1, Table A1a). Assimilated C is allocated into five different plant C compartments: Croot, Cleaf, Cstem, Cgrain, and Cmobile. The same compartments also represent the corresponding N amounts. The “mobile” pool (Cmobile, Nmobile) contains embedded reserves that are reallocated during certain time periods of the year, e.g., during leafing. Respiration is distinguished between maintenance and growth respiration, where a Q10 function response is used (Eq. 2.1, 2.2; Table A1a). Plant litter is calculated as fractions of standing biomass (Eq. 3, Table A1a).

The ECM are closely linked to the trees' fine roots and consist of C and N pools. The C pool is distinguished between the mycelia, which are responsible for N uptake, and the fungal mantle, which covers the fine-root tips. The C pool is the difference between C gains from plant supply and C losses due to respiration and litter production (Eq. 8.1, Table A1b). Accordingly, the fungal N pool is the result of the difference between N gains by uptake, N losses by litter production, and N transfer to the plant (Eq. 8.2, Table A1b). ECM fungal C and N pools distinguish between mycelia and mantle, which is of importance when simulating N uptake (only the mycelia are able to take up N), and also when simulating litter production if the more complex approach is chosen (see Sect. 2.1.4). The ratio between mycelia and mantle is determined by the parameter FRACMYC, which defines the fraction of mycelia C in total ECM fungal C. For all other N and C exchange processes (growth, respiration, and N transfer to plant), the separation between mycelia and mantle is disregarded.

ECM growth is limited by a defined maximum, i.e., only a certain amount of tree host assimilates are directed to the ECM. This maximum ECM growth is determined by a potential C supply from the plant and limited by N availability (Eq. 5.1, Table A1b). The C supply is defined by a constant fraction of the root C gain and is leveled off by the function f(cfungiavail) as soon as a defined value of soil-available total N is exceeded, i.e., in the model the potential ECM growth declines with rising soil N. This scaling function is based on observations from field and laboratory experiments, which showed that the ECM biomass of mycelia and mantle can be as much as 30–50 % of fine-root biomass, and the majority of ECM decrease in abundance and functioning when the soil N levels are high (e.g., Wallander, 2005; Wallenda and Kottke, 1989; Högberg et al., 2010). The actual ECM growth is limited by the maximum growth and calculated by a predefined fraction of assimilated root C, assuming that the production of an optimum mycorrhization degree requires a certain amount of ECM biomass (Eq. 5.2, Table A1b: FRACOPT×cfrt). This is further dependent on the N supply from the ECM to the roots, f(nsupply). The model thus follows the assumption that plants feed the ECM with C as long as their investment is outweighed by the benefits obtained (Nehls et al., 2008). A minimum C supply to prevent ECM fungi death during C shortage is guaranteed by the term during time periods when plant photosynthesis is limited and belowground C supply to root and ECM becomes zero (Eq. 5.3, Table A1b).

Respiration is separated into two components (maintenance and growth) for both ECM and root respiration (see Eqs. 2 and 6, Table A1). Two approaches are available to simulate ECM fungal litter production that differ in complexity. The simple approach (Eq. 7.1, 7.2; Table A1) uses one common litter rate L for both the fungal mantle and mycelia. Consequently, possible specific effects of the mantle and mycelia tissue on litter production are neglected. The alternative “detailed” approach (Eq. 7.3, 7.4; Table A1) has specific litter rates for ECM mantle and mycelia (LM,LMYC). This setup is recommended when investigating different biomass ratios between mycelia and mantle and their effects on overall litter production. Irrespective of the approach used for litter production, ECM have the capability to retain a defined amount of N during senescence (Eq. 7.2, 7.5; Table A1b: nretfungi). In this study, the simple approach is applied.

According to field investigations, the mycorrhization degree can vary considerably between species. For spruce (Picea abies), typical mycorrhization degrees of over 90 % have been reported (Fransson et al., 2010; Leuschner, 2004). The impact of the ECM mantle on fine-root nutrient uptake has been controversially discussed, but the majority of studies indicate that the root is isolated from the soil solution, i.e., the nutrient uptake is hampered so that the plant is highly dependent on ECM supplies (Taylor and Alexander, 2005). Therefore, the mycorrhization degree is of major importance when plant–ECM–soil N exchange and plant nutrition are of interest. In the explicit Coup-MYCOFON model, mycorrhization degree is calculated as the ratio between ECM C pool and the defined optimum ECM C pool, divided by the defined optimum mycorrhization degree (Eq. 9, Table A1b). It should be noted that the optimum mycorrhization degree needs to be defined with care as there is often a discrepancy between the applied root diameter in experimental studies and models: in experiments, mycorrhization degrees usually refer to fine roots ≤ 1 mm, whereas models often consider fine roots as roots with a diameter of up to 2 mm.

The mycorrhizal mantle has an impact on the mineral plant N uptake. This is because plant ammonium and nitrate uptake is largely driven by the plant N demand (Eq. 4.1, 4.2; Table A1) but also regulated by the N availability function (Eqs. 15, 16, 17; Table A1: f(navail), f(nmhumavail)) based on the assumption that only a certain fraction of soil ammonium and nitrate is available for plant uptake. The ECM fungal mantle reduces this availability in such a way that reduction is highest at maximum biomass. In a balanced symbiosis, the fungus provides nutrients to the plant in exchange for the plant's C supply. In the Coup-MYCOFON model, the amount of ECM fungal N transferred to the plant is determined by either the plant N demand or, if the plant N demands exceed the ECM fungal capacity, the available fungal N (Eq. 10.1, 10.2; Table A1). This is the amount of “excess” N that is available after the ECM have fulfilled their defined minimum demand as calculated by the fungal C / N ratio (Eq. 10.2, Table A1). This relation is again based on the assumption that the ECM fungi will only supply the plant with N as long as its own demand is fulfilled (Nehls et al., 2008).

In the Coup-MYCOFON model, ECM can take up both mineral and organic N. For both N forms, the potential ECM uptake is first defined. This is determined by the size of ECM C pool, the fraction of ECM C that is capable of N uptake (the mycelia, FRACMYC), and an uptake rate (NO3RATE, NH4RATE, NORGRATE (Eq. 11.1, 11.3, 11.4, 11.6; Table A1b). This function is based on the assumption that only the ECM fungal mycelia can take up N. Values for NO3RATE, NH4RATE, and NORGRATE are derived from published values but with wide ranges (Table 2). The actual N uptake is dependent on the available soil N as well as the ECM N demand (Eq. 11.2, Table A1). The N availability function f(navfungi) determines the fraction of soil N that is available for ECM fungal uptake and is controlled by the parameters NUPTORGFRACMAX (the fraction of organic N available for uptake) and NUPTFRACMAX (the fraction of mineral N available for uptake). N availability for ECM corresponds to the plant-available N (Eq. 16, Table A1), but as ECM are more efficient in the uptake of nutrients, the availability is enhanced for both mineral and organic N (Eq. 17.1, 17.2, 17.3; Table A1). To prevent the ECM N demand being covered by only one N form, the parameters rNO3, rNH4, rLIT, and rHUM are included, corresponding to the ratio of nitrate to ammonium in total available soil N (litter and humus). If the potential N uptake exceeds the available soil N, the actual uptake corresponds to the available N (Eq. 11.2 and 11.5; Table A1b).

Three modeling approaches of different complexity were applied in this study. The basic nonlim approach was conducted to test if plant N uptake can be described as proportional to the C demand of the plants of the respective sites. In this case, the plant N uptake is not regulated by the actual soil N availability, and N is used from a virtual source potentially exceeding the soil N availability, thus as an open N cycle. The ECM implicit approach simulates plant uptake of organic N, which is assumed to be via ECM, i.e., ECM are considered implicitly as being responsible for N uptake but are not physically represented in the model. The rate of the organic N uptake is determined by the plant N demand and restricted by the availability of organic N in the soil humus pools (Eq. 4.4, 4.5; Table A1). Plants can also additionally take up ammonium and nitrate (Eq. 4.1, 4.2; Table A1). In the ECM explicit approach, ECM are fully physically considered as described above. ECM growth interacts dynamically with plant growth and responds to changes in soil N availability and soil temperature. ECM can take up both mineral and organic N forms.

Simulations were performed for four forests sites – Lycksele, Mora, Nässjö, and Ljungbyhed – situated along a climate and N deposition gradient in Sweden (Fig. 2). Climate and site information is given in Table 3 and the climate data were taken from the Swedish Meteorological and Hydrological Institute (SMHI). Data on forest standing stock volumes and forest management were derived from the database and practical guidelines of the Swedish Forest Agency (2005) and applied as previously described by Svensson et al. (2008a). Soil C content as well as soil C / N ratio, previously determined by Berggren Kleja et al. (2008) and Olsson et al. (2007), were used to describe soil properties in the initial model setup. For all simulated sites and modeling approaches, the development of managed Norway spruce forests was simulated in daily steps over a 100-year period from a newly established forest to a closed mature forest. Available daily climate data (1961–1986) were repeated four times in order to cover the entire period, and thus climatic warming effects are not considered here. A minimum of specific regional data including the meteorological data, N deposition, and soil data were used as input values (Table 3). Otherwise, model parameters were kept identical between modeling approaches in order to evaluate the general model applicability. An overview of the parameter values is shown in Table A1d in the Appendix. For a more detailed site description and CoupModel setup, see Svensson et al. (2008a).

We performed a Bayesian calibration for all modeling approaches and sites. In this study, we emphasize the models' predictability in precisely describing the long-term plant and soil developments, also aiming at maximized model flexibility. This allows us to compare the different model approaches in terms of explaining the measured data and also to investigate distributions and uncertainty of key parameters. The previous modeling study by Svensson et al. (2008a) demonstrated that the changes of soil C at these sites were rather small over a 100-year period while the soil C / N ratio showed large variabilities with different N supply assumptions. Therefore, in this study the measured C / N ratio of soil organic matter and standing stock biomass were used as observational constraints. The measured error (also called relative uncertainty in Table 4) for both the soil C / N ratio and the standing stock biomass were difficult to assume due to lack of information. An uncertainty estimate of 30 % was generally recommended under such conditions (van Oijen et al., 2005). In order to reduce the weight of values close to zero on behalf of large peaks, a minimum measured error that is 10 % of the measured value was defined in this study (Klemedtsson et al., 2008). This is also because our intention was to force the model to simulate tree biomass and soil C / N ratio precisely to better constrain posterior parameter distributions for the respective model approach and site. The Bayesian calibration as applied in this study is briefly described below; however, for a detailed description of the general methodology see Klemedtsson et al. (2008) and van Oijen et al. (2005), for example.

The different ECM modeling approaches were calibrated for a comprehensive set of key parameters, which are chosen according to their function as regulating factors of the C and N fluxes in the plant–soil–mycorrhiza continuum (Table 2). In the nonlim approach, the constant N supply parameter ConstantNsupply for the spruce tree was a calibration parameter. In the implicit approach, the fraction of organic N available for plant uptake (NUPTORGFRACMAX) was included in the calibration based on Svensson et al. (2008a). For the ECM explicit approach, all ECM fungal parameters in MYCOFON including ECM growth (C and N assimilation and uptake, C and N losses), overall N uptake and plant N supply, respiration, and littering were calibrated. For all three approaches, the humus decomposition rate (KH), the C / N ratio of microbes (CNmic) regulating soil mineralization and thus soil N availability, and the fraction of plant C assimilates allocated to the rooting zone (FROOT) regulating ECM fungal growth were additionally calibrated.

The prior distributions of the parameters were chosen as uniform and uncorrelated, with wide ranges of possible values (Table 2). Bayesian calibration combines the prior information about the parameters and the observational constraints on model outputs to obtain a revised probability distribution called posterior distribution (Yeluripati et al., 2009). The posterior probability of any parameter vector is proportional to the product of its prior probability and its corresponding likelihood (Eq. 1). The likelihood function that determines acceptance of the parameter sets as the posterior distributions is based on the assumption that the model errors (the differences between simulated and observed values) are normally distributed and uncorrelated (van Oijen et al., 2005). Furthermore, model errors are assumed to be additive so that the log-likelihood function reads log⁡L=∑i=1n-0.5yi-f(ωi⋅θi)σi-0.5⋅log⁡(2π)-log⁡(σi), where yi is observed values, f(ωi⋅θi) is simulated values for a given model input vector ωi and parameter set θi, σi is standard deviation across the measured replicates, and n is number of variables measured.

To construct the posterior parameter distribution, many sets of parameter θ were sampled. In this study, candidate parameter sets were generated using the Metropolis–Hastings random-walk Markov chain Monte Carlo (MCMC) algorithm (van Oijen et al., 2005; Vrugt, 2016). Briefly, a parameter ensemble of “walkers” move around randomly and the integrand value at each step was calculated. A few number of tentative steps may further be made to find a parameter space with high contribution to the integral. MCMC thus increases the sampling efficiency by using information about the shape of the likelihood function to preferentially sample in regions where the posterior probability is high (Rubinstein and Kroese, 2016). For each simulation, the model's likelihood was evaluated for a certain parameter set. After each run, a new parameter set was generated by adding a vector of random numbers ε to the previous parameter vector: θi+1=θi+ε, where θi is the previous parameter vector, θi+1 the new parameter vector, and ε random numbers.

The normally distributed random numbers ε have a mean of zero and a step length of 0.05, i.e., 5 % of the prior parameter range as proposed by van Oijen et al. (2005). After a sufficiently long iteration (referred to as the “burn-in” period), the Markov chain reaches a stationary distribution that converges to the joint parameter posterior (Ricciuto et al., 2008). Van Oijen et al. (2005) recommended chain lengths in the order of 104–105 for modeling forest ecosystems with many observational constraints. In this trial study, we performed 104 runs for each ECM modeling approach and site. This is because a length of 104 model runs with a burn-in length of around 103 runs results in numerically stable results for our current considered problem. The step sizes used in this study result in acceptance rates between 25 and 50 % (Table 4), which is also generally the most efficient range for the MCMC algorithm (Harmon and Challenor, 1997).

The three modeling approaches show different accuracies in reproducing current plant growth and soil C / N ratio after calibration (Table 4b). The posterior model in the implicit and explicit approaches shows better performance of simulating soil C and N, as indicated by the soil C / N ratio, than the nonlim approach. The latter tends to simulate a lower soil C / N ratio, indicated by the negative mean errors (ME, difference between the simulated and measured values) in the posterior model (Table 4b). The ME by the nonlim approach is also 2 to 5 times higher than that when using the implicit or explicit approach (Table 4b). The nonlim approach tends to overestimate plant growth as the posterior mean of ME for plant C is always positive, while the implicit and explicit approaches tend to show an underestimation (Table 4b).

All posterior models underestimate soil C / N for the northern sites, which are generally more N limited, but gradually switch to overestimation at the southern sites. The model with the nonlim approach simulates better plant growth for the southernmost site, Ljungbyhed, than the other sites. Further, modeled plant growth at Ljungbyhed is overestimated by the implicit approach but underestimated when the explicit approach is used (Table 4b). The acceptance of model runs in posterior is higher for the nonlim (25 to 48 %) and implicit approaches (42 to 50 %), followed by the explicit approach (30 to 33 %). No major differences are found for the summed log likelihood for both calibration variables (Table 4b).

Modeled major ecosystem N fluxes in the posterior are shown in Fig. 3. The modeled N litterfall, uptake, and leaching fluxes differ significantly from one modeling approach to another, where the nonlim approach always gives the highest fluxes. The explicit and implicit approaches show similar modeled N fluxes for the northernmost site, Lycksele. However, the differences between these two approaches become larger when moving south where higher fluxes are simulated by the explicit approach (Fig. 3). For instance, modeled N litter production in the explicit approach increases by 1 to 30 % compared to the implicit approach, but N losses due to uptake and leaching also increase by 10 to 50 % for Lycksele and Ljungbyhed, respectively (Fig. 3). The modeled N pool sizes for these two sites also differ, where the explicit approach shows a larger mineral N in the soil and a smaller organic N pool compared to the implicit approach (Fig. 4).

Figure 5 shows the modeled major ecosystem C fluxes and comparison with previous results by Svensson et al. (2008a) and measured data from three other Swedish sites (Flakaliden, Knottåsen, and Åsa ; Fig. 2) at comparable latitudes and on comparable soils by Lindroth et al. (2008). The simulated plant gross primary production (GPP) using three approaches all show an increasing trend from the northern sites to the southern sites due to a more favorable climates and N availability for spruce forest growth. For the studied four sites, the nonlim approach simulates the highest GPP followed by the explicit approach and lastly the implicit approach. The variation in modeled GPP between the explicit and implicit approach ranges from 12 % at northernmost Lycksele site to 7 % at the southernmost Ljungbyhed site (Fig. 5). Simulated GPP in this study is generally higher than that by Svensson et al. (2008a) but comparable with the measured data from Lindroth et al. (2008). It should be noted that the GPP at the southern site, Åsa, was only measured for 1 year and thus can show large uncertainties due to annual variations. Modeled ecosystem respiration generally follows the pattern of GPP. The net ecosystem exchange (NEE) values predicted by the three approaches all show an overall atmospheric C uptake for all the sites where the explicit approach seems to have a higher uptake strength than the others (Fig. 5). Current estimates of NEE are again within the measured range by Lindroth et al. (2008), although a small net release of C was measured at Knottåsen, likely caused by the abnormal high temperature during those measured years. In addition, explicitly including ECM also increases the soil respiration for the four sites except the northernmost Lycksele site. The simulated ranges are however somehow smaller than those by Svensson et al. (2008a).

The nonlim approach generally shows much higher uncertainties in the modeled N fluxes than either the implicit or explicit approaches. The nonlim approach simulated soil N sequestration of up to 2 g N m-2 yr-1 for all the sites, but values much lower or close to zero were found when using the other two modeling approaches (Fig. 5). The simulated soil C balance by the nonlim approach also contrasts with that of soil N, in which the soil sequesters C at the northernmost site, Lycksele, but loses C at a rate of 6 to 17 g C m-2 yr-1 for the other three sites (Fig. 5). Therefore, soil C and N are not in steady state and are decoupled in the nonlim approach over the simulated 100-year period. The implicit and explicit approaches, however, show a strong coupling between soil C and N (Fig. 5). That is, for the implicit approach, Lycksele and Mora soils lose 6 and 5 g C m-2 yr-1, respectively, while Nässjö and Ljungbyhed soils gain 3 and 13 g C m-2 yr-1, respectively. Similarly, Lycksele and Mora lose N by 0.2 and 0.1 g N m-2 yr-1, while Nässjö and Ljungbyhed gain N by 0.3 and 0.6 g N m-2 yr-1. For the explicit approach, soil C and N losses at the two northern sites are slightly higher than those in the implicit approach. The respective net change in the soil C and N pools of the implicit approach corresponds well to the results by Svensson et al. (2008a), who also suggest a small loss of soil C in the north, whereas soils in the south gain C. However, when the explicit approach is used, the soils in the south are also predicted to lose C and N. Lindroth et al. (2008) found a similar trend in the soil net C change as simulated by the explicit approach here, but with a higher loss rate between 24 and 133 g C m-2 yr-1 (Fig. 5). Overall, our results show that accounting for ECM in boreal forest ecosystems can have a considerable impact on the predicted C and N dynamics for both the plants and soil.

The posterior distributions differ from the prior uniform distributions for all modeling approaches and parameters, reflecting the efficiency of Bayesian calibration (Figs. 6 and 7). The posterior constantNsupply parameter in the nonlim approach shows the lowest values at Lycksele and the highest at Ljungbyhed. This means a higher N supply is necessary at the southern sites to explain the observed tree biomass and soil C / N ratio. No significant differences in parameter values – microbial C / N ratio (CNMIC), humus decomposition coefficient (KH), and the fraction of C allocated to roots (FROOT) in the nonlim approach are found for the different sites (data not shown). The organic N uptake parameter in the implicit and explicit approaches (NUPTORGFRACMAX) shows an opposite pattern with the highest values for Lycksele and lowest for Ljungbyhed and larger parameter uncertainties are found for the explicit approach (Fig. 6). Parameter values for the northern sites also have a much wider range compared with the southern sites (Fig. 6), which also explains the larger simulated ME of soil C / N at the northern sites (Table 4). Both approaches demonstrate that the plant and soil conditions at the northern sites could not be simulated without an enhanced uptake of organic N.

When the implicit approach is used, the posterior humus decomposition coefficient KH shows higher values for the northern sites and decreases along the studied transect, demonstrating a modeled enhancement of organic matter decomposition and soil mineralization for northern sites (Fig. 7). A less-clear tendency towards higher values at the southern sites is identified for the fraction of C allocated to roots, the FROOT parameter. The microbial C / N ratio (CNMIC) parameter for both implicit and explicit approaches show similar posterior distributions for the three northern sites. However, much lower values are obtained for the southernmost Ljungbyhed site (Fig. 7), reflecting a more N-rich soil environment. Overall, parameters are less constrained and only minor differences among sites are found when the explicit approach is used (Fig. 7).

The posterior distributions of all ECM fungal-specific parameters are constrained to log-normal or normal distributions (data not shown). The mean values of N uptake parameters (NORGRATE, NH4RATE, NO3RATE) show a decreasing trend from the northern to southern sites (Fig. 8). This again means an enhanced ECM fungal N uptake is necessary to explain the observed soil and plant data at the more N-limited northern sites. Similarly, lower values for the northern regions and higher values for the southern regions are also found for the minimum ECM fungal C / N ratio parameter (CNFMIN). The optimum ratio between ECM and root C content, FRACOPT, tends to be higher at the northern sites and lower at the southern sites, also implying a higher modeled ECM biomass at the northern sites (Fig. 8). MINSUPL, the minimum supply of N from ECM to the host plant parameter, does not show a clear trend. Further, differences in the other ECM parameters for the four sites are minor (Fig. 8).

An overview of correlations for all posterior model parameters can be found in Tables A2, A3, and A4. Key parameter sets showing correlation with each other (defined here as a Pearson correlation coefficient r≥0.3 or ≤-0.3) are shown in Fig. 9. When the implicit approach is used, a significant positive correlation is obtained between the humus decomposition rate, KH, and the fraction of C allocated to the rooting zone, FROOT. The organic N uptake parameter, NUPTORGFRACMAX, and microbial C / N ratio, CNMIC, are significantly negatively correlated, except for a weak correlation for Ljungbyhed (Fig. 9). A weak correlation between NUPTORGFRACMAX and FROOT is also found for the Nässjö site (Table A2). For the explicit approach, the correlation coefficients between KH and FROOT are decreased, and there is also a weaker correlation between NUPTORGFRACMAX and CNMIC for all sites compared to the implicit approach (Fig. 9). No clear correlation between common and ECM fungal parameters is obtained. Further, a negative correlation occurred among microbial C / N ratio, CNMIC, and the fungal N uptake rates (NorgRATE, NH4RATE, NO3RATE), but only for the northern sites Lycksele and Mora (Table A4). A moderate correlation is found for KH and the fungal litter rate, L, for Ljungbyhed. Among fungal parameters, the N uptake rates moderately correlate to the litter production rate, L, at the northern sites, but correlations at Nässjö and Ljungbyhed are either weak or nonexistent (Table A4).