The water table depth (WTD) in natural peatlands fluctuates seasonally from above the soil surface to the top of the permanently saturated soil layer, which is often referred to as the boundary between acrotelm and catotelm. The boundary is usually estimated to be 30 cm below the soil surface in wetlands (Canada Committee on Ecological (Biophysical) Land Classification: National Wetland Working Group, 1997), and has been widely used as the bottom of the first soil layer in two-layer soil decomposition models (e.g. Granberg et al., 1999; Yurova et al., 2007; Spahni et al., 2013). To capture the effect of the fluctuating water table on the transfer of water and energy within the soil, we used a multi-layer configuration rather than the standard three-layer configuration of the soil layers in CLASS. We assigned nine organic soil layers, each 10 cm thick, at the top of the soil profile and a 10th soil layer from 90 cm down to the bottom of the organic soil (Fig. 1). Moss was treated as the top first soil layer and the substrate below the 10th soil layer was considered as bedrock. Mineral soil was not included.

The standard configuration of soil layers in CLASS consists of three layers with thickness of 0.10, 0.25, and 3.75 m. Organic soil in CLASS was parameterized by Letts et al. (2000) as fibric, hemic and sapric peat in the three soil layers respectively, representing fresh, moderately decomposed and highly decomposed organic matter. Tests of CLASS on peatlands revealed improved performance in the energy simulations for fens and bogs with this organic soil parameterization. However, the model overestimated energy and water fluxes at bog surfaces during dry periods due to the neglect of the moss cover (Comer et al., 2000).

To take into account the interaction amongst the moss and the soil layers and the overlying atmosphere for energy and water transfer, we added a new soil layer 0.10 m thick above the fibric organic soil to represent living and dead peatland bryophytes, such as Sphagnum mosses and true mosses (Bryopsida). The physical characteristics of mosses differ from those of either the shoots or the roots of vascular plants (Rice et al., 2008). In particular, mosses can hold more than 30 g of water per gram of biomass (Robroek et al., 2009). More than 90 % of the moss leaf volume is occupied by the water-holding hyaline cells (Rice et al., 2008), which retain water even when the water table depth declines to 1–10 m below the surface (Hayward and Clymo, 1982).

The parameter values of the moss layer for water and energy properties were derived from a number of recent experiments measuring the hydraulic properties of mosses (Price et al., 2008; Price and Whittington, 2010; McCarter and Price, 2012) (Table 1). Living mosses range from 2–3 to over 5 cm in height (Rice et al., 2008) and have lower values of dry bulk density and field capacity than fibric peat (Price et al., 2008). Compared to fibric peat, the saturated hydraulic conductivity of living moss is higher by orders of magnitude (Price et al., 2008) and the thermal conductivity is more affected by the water content (O'Donnell et al., 2009). To fully account for the effect of mosses, we set the depth of the living moss (zm) within the top soil (i.e. moss) layer to 3 cm for fens and 4 cm for bogs, and interpolated its water content wm (kg water (kg dry mass)-1) from the water content of the overall layer θl,1 (m3 water (m soil)-3) and the depth of the living moss: wm=zmθl,1ρwBm, where the dry moss biomass (Bm) is converted from moss C (Cm) using the standard conversion factor of 0.46 kg C per kg dry biomass, θl,1 (m3 m-3) is the liquid water content of the top soil layer, and ρw is the density of water (1000 kg m-3). The maximum and minimum moss water contents were estimated from a number of observed moss water contents (e.g. Williams and Flanagan, 1998; Robroek et al., 2009). In CLASS, evaporation at the soil surface is controlled by a soil evaporation efficiency coefficient β (Verseghy, 2012). This parameter is calculated from the liquid water content and the field capacity of the first soil layer following Lee and Pielke (1992). For peatlands, β was assumed to be regulated by the relative moisture of the living moss rather than the ratio of relative liquid water content of the first soil layer: β=0.25[1-cos⁡wm-wm,minwm-wm,max]2, where wm, wm,max, and wm,min are the water content and the maximum and minimum water contents of the living moss in kg water (kg dry mass)-1.

Mosses are an important contributor to the primary production and the C sequestration in peatlands, owing to the low decomposability of the moss tissue. Sphagnum in peatlands grows at 20–1600 g biomass m-2 yr-1 and accounts for about 50 % of the total peat volume (Turetsky, 2003). We have modified CTEM to include a moss C pool and moss litter pool along with the related C fluxes, i.e. photosynthesis, autotrophic respiration, heterotrophic respiration, and humification. The net photosynthesis of moss (Gm) is calculated from the gross photosynthesis (G0,m) and dark respiration (Rd,m): Gm=G0,m-Rd,m. The moss photosynthesis and dark respiration are calculated using the Farquhar (1989) biochemical approach following the MWM (St-Hilaire et al., 2010) and CTEM (Melton and Arora, 2016), with modifications for integration with CLASS–CTEM and moss phenology. The leaf-level gross photosynthesis rate G0,m (µmol CO2 m-2 s-1) is obtained as the minimum of the transportation limited photosynthesis rates (Js) and the first root of the quadratic solution of the light-limited rate (Je) and the Rubisco limited rate (Jc). A logistic factor (ς) is added with values 0 or 1 to introduce a seasonal control of moss photosynthesis. In the MWM, spring photosynthesis starts when the snow depth is below 0.05 m and the soil temperature at 5 cm depth goes above 0.5 ∘C (Moore et al., 2006). Since in our case CLASS sets the minimum depth for melting, discontinuous snow to 0.10 m, this limits the spring photosynthesis to starting only once the snow is completely melted. G0,m=ςmin⁡Js,(Jc+Je)±(Jc+Je)2-4(Jc+Je)2 The dark respiration in mosses (Rd,m) is calculated as a function of the base dark respiration rate (Rd,m,0), which has a value of 1.1 µmol m-2 s-1 (Adkinson and Humphreys, 2011) scaled by the moss moisture (fm,rd) and soil temperature functions (fT,rd). The moss moisture function is based on the volumetric water content of the moss, θm (kg water (kg dry mass)-1). The MWM models the relation between water content in mosses and dark respiration with optimal water content at 5.8 g water per g dry weight, following the approach in Frolking et al. (1996). We modified the relation for water content above the optimal water content, based on a recent discovery of a weak linear positive relation between the dark respiration rate and the water content above the optimal water content during the late summer and fall (Adkinson and Humphreys, 2011): Rd,m=Rd,m,0fm,rdfT,rd,fT,rd=(3.22-(0.046⋅Tmoss)(Tmoss-25/10),fm,rd=0,θm<0.40.35θm2/3-0.14,0.4≤θm<5.80.01θm+0.942,5.8<θm. Photosynthetic photon flux density (PPFD) is measured by the photosynthetically active radiation (PAR), which is defined as the solar radiation between 0.4 to 0.7 µmol that can be used by plants via photosynthesis. In the coupled CLASS–CTEM system, the PAR received by the moss (PARm, unit µmol protons m-2 s-1) is converted from the visible short-wave radiation reaching the ground (K∗g, unit W m-2) in CLASS by a factor of 4.6 µmol m-2 s-1 per W m-2 (McCree, 1972). K∗g is a function of the incoming short-wave radiation (K↓, unit: W m-2), the surface albedo (αg), and the canopy transmissivity (τc): K∗g=K↓τc1-αg. The energy uptake by the moss layer is thus a function of the total incoming short-wave radiation, the aggregated LAI of the PFTs present, the snow depth, the fractional vegetation cover, and the soil water content (Verseghy, 2012). In peatland C models that do not consider vegetation dynamics, the transmissivity of the vegetation canopy is usually assumed to be constant (e.g. St-Hilaire et al., 2010). Compared with such models, CLASS enables a more detailed representation of light incident on the moss surface since it includes partitioning of direct/diffuse and visible/near-IR radiation, PFT-specific transmissivities, and time-varying LAI and fractional PFT coverages (Verseghy, 2012).

CLASS normally categorizes the global vegetation into four broad PFTs that differ in their structure and intra-annual development cycles: needleleaf trees (NDL), broadleaf trees (BDL), crops, and grasses. CTEM further subdivides each PFT in CLASS into PFTs that vary in their phenology, physiology, and their C assimilation rates: evergreen NDL, deciduous NDL, evergreen BDL, deciduous cold BDL, deciduous dry BDL, C3 crops, C4 crops, C3 grasses, and C4 grasses. The evergreen broadleaf PFTs and C3 grasses have been parameterized primarily for tropical and temperate vegetation types that are not representative of peatland plants. Therefore, we introduced three new PFTs for peatlands: evergreen shrubs, deciduous shrubs, and sedges. Evergreen shrubs, for example the ericaceous shrubs, are the common dominant vascular plants in bogs and poor fens while deciduous shrubs, such as the betulaceous shrubs, often dominate rich fens. Both shrubs are categorized as broadleaf trees in CLASS morphologically, but their phenological and physiological characteristics are more similar to those of needleleaf trees. The shrub tundra ecosystem is situated adjacent to needleleaf forest in the Northern Hemisphere (Kaplan et al., 2003) and they share similar responses to climate in ESMs (e.g. Bonan et al., 2002). Table 2 lists the key parameters for the peatland PFTs used in this model. (The photosynthesis and autotrophic respiration of vascular PFTs are modelled the same as in the original CTEM.)

Over the non-peatland fraction, HR is calculated as the sum of the respiration from litter and soil carbon pools as in the original version of CTEM (Arora, 2003). The soil C pool over the non-peatland areas is assumed to be exponentially distributed with depth (Arora, 2003). In peatlands a large amount of humic soil is generally located in the permanently saturated zone and the bulk density increases with soil depth (Loisel and Garneau, 2010). Thus, the assumption of exponentially decreasing distribution of C content with increasing soil depth is not valid in peatlands. We used a quadratic equation to calculate the distribution of soil C content over depth based on an empirically determined bulk density profile (Frolking et al., 2001).

HR over the peatland fraction of a grid cell is modelled using a two-pool approach with a flexible boundary between the pools that depends on the depth of the water table: Ro=CSOM,okofT,oRa=CSOM,akafT,afanoxic, where o and a denote the oxic and anoxic portions of the soil C pool respectively. The respiration rate R (unit: µmol C m-2 s-1) is obtained from the respiration rate coefficient k (µmol C kg C-1 s-1), the temperature functions fT, the soil C mass CSOM (kg), and a scaling factor fanoxic after Frolking et al. (2010, 2001), which represents the inhibition of microbial respiration under anoxic conditions. The value of this parameter is uncertain, varying in those two papers between 0.001, 0.025 and 0.1. Based on calibration runs using two of the data sets described below (MB-Bog and AB-Fen), we adopted a value of 0.025. Q10 is calculated using a hyperbolic tan function of the soil temperatures (Ts) of the oxic and anoxic zones (Melton and Arora, 2016), which are in turn functions of water table depth (Eq. 10). The Q10 values of the anoxic and the oxic zones of the soil are indicated as Q10,a and Q10,o. The values of k, fT, and CSOM are updated along with the water table depth (zwt, unit: m, positive downward) and the peat depth (zp, unit: m) at each CTEM time step. The equations for k and CSOM are derived from Fig. 2 in Frolking et al. (2001), and parameterized differently for fens and bogs (Table 3):

fT,o=Q10,o∫0zwtTj-15/10fT,a=Q10,a∫zwtzpTj-15/10,Q10=1.44+0.56tanh[0.07546.0-Ts],Ts,o=∫0zwtTj/(zwt)Ts,a=∫zwtzpTj/(zp-zwt),ko=0,zwt<0k11-ek2zwt+k3zwt,0.3>zt≥0k4ek5zwt+k6zwt+k7,zwt≥0.3,ka=k4ek5zp+10k6zp+k7,zwt<0k1ek2zwt-k4ek5zp-k3zwt+k8,0.3>zwt≥0k4(ek5zP-ek5zwt)+k6zp-zwt,zwt≥0.3,CSOM,o=0.487∗(k9zwt2+k10zwt),CSOM,a=CSOM-CSOM,o, where 0.487 is a parameter that converts from soil mass to soil C content. The variation of ko and ka with water table depth for bogs and fens is shown in Fig. 2. It will be noted that there is a sharp transition in decomposition rate at a depth of 0.3 m, reflecting the work of Frolking et al. (2001). As noted in Sect. 2.1 above, this value is widely accepted as a representative estimate of the depth dividing the acrotelm and catotelm. In reality, of course, this depth will vary among peatlands. When our peatland model is implemented in climate mode, it is planned that spin-up tests will be run to assess the spatial variability of this depth, and adjustments will be made to Eqs. (13) and (14) if necessary.

As only organic soil is considered in peatlands, the peat soil C is updated from the humification (Chum, kg C m-2 day-1) and soil respiration from the oxic (Ro in kg C m-2 day-1) and anoxic (Ra in kg C m-2 day-1) components during the time step: dCSOMdt=Chum-Ro-Ra Chum is calculated as a PFT-dependent fraction of the decomposition rate. Values of this coefficient are shown in Table 2 (variable “humicfac”). At the end of each time step, the peat depth (i.e. the depth of the organic soil) zp is updated from the updated peat C mass (CSOM in kg) by solving the quadratic equation zp=-k10+k10+4k9CSOM0.487.2k9 The water table depth zwt is deduced by searching for a soil layer below, which the soil is saturated and above which the soil moisture is at or below the retention capacity with respect to gravitational drainage. Within this soil layer j, zwt is calculated as zwt=zb,j-Δzθl,j+θi,j-θret,jθp,j-θret,j, where Δz is the thickness of soil layer (unit: m), θl and θi are the liquid and frozen water contents (unit, m3 m-3), θret and θp are the water retention capacity and the porosity, and zb (unit: m) is the bottom depth of the soil layer.

The model was applied at eight peatland sites to assess its performance in simulating the water, energy, and C fluxes. The peatlands selected consist of four bogs and four fens (Fig. 3). The bogs are the Auchecorth Moss (UK-Amo), 18 km south of Edinburgh, Scotland; the Fajemry bog (SE-Faj), in the south of Sweden; the Fyodorovskoye bog (RU-Fyo), about 340 km north-west of Moscow, Russia; and the Mer Bleue bog (MB-Bog), about 20 km away from Ottawa, Canada. The fens are the Kaamanen Wetland (FI-Kaa), close to Inari in Finland; the Lompolojänkkä northern boreal fen (FI-Lom), in northern Finland; the Degerö Stormyr (SE-Deg) near Uppsala, Sweden; and the Alberta western peatland treed fen (AB-Fen), north of Edmonton, Canada. The characteristics of the eight peatlands represented nutrient gradients from ombrotrophic to minerotrophic, elevations between 65 and 581 m above sea level, mean annual precipitation (MAP) ranging from 473 to 1155 mm per year, mean annual temperature (MAT) between -1.4 and 10.0 ∘C and maximum LAI ranging from 0.7 to 3.5 (Table 4).

Data were obtained from the FLUXNET database (http://fluxnet.ornl.gov/). For each site and for each downloaded variable, the highest available data level was used. The meteorological drivers for the model were obtained from level 4 (gap-filled and quality-controlled) data, except for the wind speed which was obtained from level 3 and surface pressure from level 2 data. Carbon fluxes were obtained from level 4 daily average data when available. The observed GPP and NEP in the FLUXNET database were derived from the observed NEP and the relations between NEP, temperature and photosynthetically active radiation (PAR). The remaining fluxes were averaged from half-hourly level 2 and level 3 data.

In the model evaluation, it must be borne in mind that eddy covariance measurements of turbulent fluxes of energy, water and carbon are subject to inherent uncertainties and errors related to atmospheric conditions such a low turbulence and wind direction, or to equipment malfunction. For this reason we selected a relatively large number of test sites with multi-year data sets, and focused on long-term averages for the validation. We also included in the evaluation variables such as water table depth, soil temperature and snow depth, which are not dependent on turbulent flux measurements.

For each site, the FLUXNET database was used to assign values to background variables such as latitude, longitude, peat depth, areal coverage of the three peatland PFTs, and their roughness lengths, visible and near-infrared albedos, and canopy mass. Other CLASS- and CTEM-related vegetation parameters were assigned their standard values, as listed in Table 2. The parameter values for evergreen shrubs, deciduous shrubs and sedge mostly reflected those used for evergreen needleleaf trees, deciduous needleleaf trees and C3 grasses in CTEM respectively. Exceptions were made for some parameters that determine the length or shape and turnover of the stem and root of the PFT and its tolerance to coldness and dryness (Table 2).

Model C pools in vegetation were spun-up from initial conditions by repeatedly cycling through the inputs for approximately 100 years until the annual mean C pools in consecutive years differed by less than 5 %. The initial soil C mass was calculated from the observation-based estimations of peat depth based on an empirically obtained relation between the soil depth and soil mass (Eq. 15).

The model was forced with half-hourly measured meteorological data: downwelling short-wave radiation, downwelling long-wave radiation, precipitation, atmospheric pressure, air temperature (Ta), specific humidity, and wind speed. The measurement heights for the latter three were obtained from the FLUXNET metadata. Data sets ranged in length from 2 to 9 years. The parameters used for model evaluation include water table depth (zWT), snow depth, soil temperature (Ts), latent heat flux (QE), sensible heat flux (QH), GPP, ER and NEP. Energy and C fluxes were measured every 30 min using the eddy-covariance (EC) technique. The required downwelling long-wave radiation (LW) was available only at MB-Bog, AB-Fen, SE-Deg, and FI-Lom. For the remaining four sites, LW was estimated following the methods of Crawford and Duchon (1999): LW↓=[cf+1-cfεc]σTa4, where σ is the Stefan–Boltzmann constant and cf is the cloud fraction term ranging between 0 and 1. cf is estimated as the ratio between the incoming short-wave radiation and the clear-sky solar radiation, which in turn is a function of the locational character of the site, i.e. latitude, longitude, altitude and time zone. εc is the clear-sky emissivity and is estimated from the vapour pressure (e0) following Ångström (1918): εc=0.83-0.18×10-0.067e0. Water table depths were available for three bogs (RU-Fyo, SE-Faj and MB-Bog) and three fens (AB-Fen, FI-Lom, SE-Deg) sites and snow depths were available for MB-Bog and AB-Fen only. Soil temperatures were available at 1, 5, 10, 20, 40, 80, 150, and 250 cm below the soil surface at the MB-Bog and at 2, 5, 10, 20, 50, and 100 cm below the soil surface at AB-Fen. For the other six sites, the soil temperature was only measured at 5 cm below the surface.

The model was evaluated against observation-based daily sensible and latent heat fluxes at the soil surface, soil water content, water table and snow depth, soil temperature at various depths, and the daily, monthly, and annual C fluxes (GPP, ER, NEP). The root mean square error (RMSE) and linear regression coefficient (r2) were primarily used for evaluation. Statistical analyses were conducted using the free software package R version 3.1.1 (R Core Team, 2014).

Since the ultimate goal is to apply the model globally in an ESM, further experiments were done to investigate the importance of modelling fens and bogs separately. In the version of the model described above, bogs and fens are distinguished primarily through the parameterization of the control of water table depth on soil decomposition (Table 3). Also, the depth of the living moss (dm) is set to 4.0 cm for bogs and 3.0 cm for fens. In a first test, the parameters for soil decomposition (Table 3) for bogs were used for the fen sites and those for the fens were used for the bog sites. In a second test, the living moss layer was set to a single fixed value of 3.5 cm for both bogs and fens. The resulting differences in the surface fluxes and the soil temperatures were then evaluated.

Figure 4 illustrates the simulated daily WTD compared with observations at the six sites where WTD was observed. The model successfully simulated the seasonal dynamics and the zone of fluctuation of the water table in the first two bogs, except for the extremely deep water table observed in RU-Fyo in 2010. Although ponded water is simulated in the model, the simulated WTD did not include the depth of pond above the soil surface, which appears in the observations as a negative value, for example up to -0.14 m in the SE-Faj bog during the winter. The simulated WTD of the FI-Lom fen agreed well with the observations after the spring of the second simulated year (2008). The modelled WTD was calculated as the uppermost surface of the liquid water present in the soil, and thus did not account for the potential occurrence of liquid water below the surface frozen soil layer. As a result, the simulated WTD stayed close to the soil surface over the winter when the soil was frozen. The errors in MB-Bog were consistent over time, which was likely a result of the difference between the observed and modelled peat surfaces. The difference in height between hummocks and hollows at the MB-Bog is about 0.25 m (Lafleur et al., 2005) and the bottom of the fibric peat lies at 0.35 and 0.10 m below the peat surface for hummock and hollow respectively (Dimitrov et al., 2010). The parameterized MB-Bog, with 0.10 m of fibric peat, is therefore closer to a hollow (Table 1). Correcting the modelled WTD by 0.25 m led to a high agreement with the observed WTD in MB-Bog (Fig. 4). For AB-Fen, the model overestimated the inter-annual fluctuation and did not reproduce the trend of increasing WTD seen in the observations, which was likely associated with the change in vegetation cover. It has been observed that the AB-Fen site is currently changing from a rich fen to a poor fen and is now in a phase of rapid tree establishment and increase in LAI and NEP (Flanagan and Syed, 2011).

The model reproduced the annual variation of snow depth quite well for the bog and fen sites where observations were available (Fig. 5). The errors for the MB bog may be associated with uncertainties in the observed data stemming from the combination of a continuous record from one spot with sporadic snow depth data from other locations on the bog surface (Moore et al., 2006).

The model performed similarly well on the daily average QE and QH fluxes for multi-year simulations (Table 5, Fig. 6). The RMSEs ranged from 23.0 to 37.7 W m-2 (QH) and 27.3 to 79.7 W m-2 (QE) for bogs and from 19.6 to 41.5 W m-2 (QH) and 15.8 to 31.5 W m-2 (QE) for fens. When organic soils were first introduced into CLASS by Comer et al. (2000), RMSEs ranged from 16.9 to 47.7 W m-2 (QH) and 23.1 to 65.6 W m-2 (QE) for fens and 67.4 to 182.5 W m-2 (QH) and 78.1 to 153.8 W m-2 (QE) for bogs. Our new model shows a consistent improvement in the energy flux simulations, especially for bogs, where the surface moss cover plays an essential role in regulating the thermal and hydraulic conductivities (Turetsky et al., 2012).

The mean r2 coefficient between the simulated and observed daily average QH was 0.47 and the highest r2 was 0.89 for the AB-Fen site. The poorest agreement in QH occurred in the FI-Kaa fen and the UK-Amo bog. The error in FI-Kaa peaked in the winters of 2002 and 2007 when the snow depth exceeded 0.8 m (not shown). Turbulent fluxes over deep, cold snow packs are notoriously difficult to model accurately (Bazile et al., 2013). In the case of QE, the mean r2 for the eight sites is 0.52, and rises to 0.60 if the outlier UK-Amo is disregarded. The large bias of QH and QE at UK-Amo is thought to be partially attributable to instrumental errors, given the scattered data cloud of the observed QE in 2006 (not shown).

The simulated daily average soil temperature at 5 cm depth across the eight sites agreed well with the observations, with r2 values between 0.77 and 0.98. The comparatively low value found for UK-Amo is perhaps linked to the errors in QE noted above. The RMSE ranged from 1.7 to 4.7 ∘C with a mean of 3.1 ∘C. This is larger than the RMSE range of 0.7 to 2.3 ∘C found for LPJ-WHy v1.2 by Wania et al. (2009a), yet is encouraging considering that the simulation periods for our sites ranged from 2 to 9 years compared to the 1 year simulation with LPJ-WHy, and that we included eight sites in our evaluation compared with two peatland sites for LPJ-WHy. Our model was able to capture the seasonal variation in soil temperature at different depths down to the bedrock. Figure 7 compares the modelled soil temperatures against the observations at 5, 40, 80 cm, and 250 cm depths for the Mer Bleue bog, where good-quality data are available for soil T at various depths.

In eddy-covariance measurements, as noted in Sect. 3.1 above, GPP and ER are obtained by partitioning the observed NEP on the basis of empirically derived relationships. In the case of modelled carbon fluxes, on the other hand, NEP is calculated by subtracting ER from GPP, therefore the error in the NEP simulations accumulates the errors in GPP and ER. Bearing in mind these caveats, examination of the modelled daily GPP, ER, and NEP suggests that the model is capable of capturing seasonal dynamics and climate-driven events consistently in various types of peatlands. Figures 8–10 show the daily average fluxes in time series form. The RMSE (Table 6) is between 0.43 and 0.67 g C m-2 day-1 for GPP and ER for the three sites in Scandinavia and Canada (FI-Kaa, MB-Bog, and SE-Faj, two bogs and a fen) that have high-quality observed data and are not undergoing vegetation shifts. Larger biases of GPP and ER occurred in the blanket bog (UK-Amo) and the Russian ombrotrophic bog (RU-Fyo), the peat depths of which were very deep and relatively shallow respectively – up to 10 m in UK-Amo and 1 m in RU-Fyo (Table 4). Variations in the historical climate have led to variations in the peat accumulation rates over the Holocene and the vertical stratification of the peat and hence the decomposition rates and decomposability of the peat, which become important for deeper, older peat deposits. The Russian bog may be an outlier because warm climate conditions persisted until about 5000 BP in northern Siberia and about 1000 years later in most other areas (Yu et al., 2010). The RU-Fyo bog experienced a period of low GPP due to an abrupt decrease of air temperature in the early fall of 2010, which was well reproduced by the model. The starting and ending periods of photosynthesis in the spring and fall were accurately simulated except for the coldest peatland, FI-Lom, where the length of the growing season was slightly overestimated. Short periods of overestimation of soil temperature at 5 cm existed during that period, by up to 5 ∘C, which may have caused the errors in GPP; Moore et al. (2006) noted a high correlation between soil temperature and the initiation of photosynthesis in the spring.

The RMSE of the daily NEP simulations (Table 6) ranges from 0.486 to 1.65 g C m-2 day-1. The lowest biases were for the SE-Faj bog and the two poor fens (SE-Deg and FI-Kaa) that had little vegetation cover, with the maximum LAI below 1.0 m2 m-2. Values of r2 greater than about 0.3 were observed at six sites. At the other two, SE-Faj and UK-Amo, the observed NEP varied widely, ranging from -1.8 to 2.2 g C m-2 day -1 and from -3.9 to 4.8 g C m-2 day-1 respectively. The discrepancy with the modelled values, contributing to the low r2 values for these two sites, might be due either to weaknesses in the model or to inadequate screening of the eddy covariance measurements. NEP was overestimated at the beginning and the end of the growing season for FI-Lom due to the overestimation of GPP for that period as discussed above. These results may be compared to an evaluation of the MWM using the SE-Deg data set that was conducted by Wu et al. (2013). For daily NEP they obtained an RMSE of 0.49, similar to ours, but a higher r2 of 0.52. It should be noted that the MWM was driven by observed WTD and soil temperature, while in our simulations these were allowed to evolve freely, so our comparable result is gratifying.

Figures 11–13 show the daily modelled vs. observed GPP, ER and NEP in scatter plot form. Although the model performs reasonably well, with r2 values averaging over 0.7 for both GPP and ER, a general tendency can be seen for the modelled GPP to be biased low at high and low values, and high at medium values. The bias in the very low values may be spurious, given the relatively large errors associated with eddy covariance measurements of small fluxes; also, the occasional negative observed values of GPP may be indicative of erroneous partitioning of the measured NEP between GPP and ER. At FI-Lom, FI-Kaa, and UK-Amo, the high model bias at low observed values may be related to early leaf-out and/or delayed leaf drop. The biases at medium values are possibly related to the use of the “big-leaf” assumption in CLASS–CTEM, which neglects sunlit and shaded canopy fractional areas, and may have a dampening effect on photosynthesis. Low biases at high values may be related to water stress caused by a low water table, as seen in Fig. 4 for RU-Fyo and FI-Lom. In the case of ER, the modelled values do not show systematic biases except for RU-Fyo and UK-Amo, which were difficult to model as noted above. Given the fact that a major focus of this study was the incorporation of respiration for organic soils and mosses into CLASS–CTEM, this is encouraging.

Since NEP is the residual of two large terms, GPP and ER, in Fig. 14 we investigate the relationship between the modelled GPP, autotrophic respiration (AR) and HR. Across most sites, simulated AR is approximately 40–50 % of GPP with a relatively consistent relationship between the two. In CLASS–CTEM, autotrophic respiration is sensitive to temperature, the maximum catalytic capacity of Rubsico, and the vertical profile of radiation along the depth of the canopy (Melton and Arora, 2016). GPP is also sensitive to these same factors and thus tends to respond similarly. HR is much more variable than AR and GPP and also shows greater variability between sites. FI-Kaa is relatively consistent in simulated HR, whereas sites such as SE-Faj and FI-Lom have markedly variable HR fluxes. HR in CLASS–CTEM is sensitive to soil matric potential, soil temperature and detrital carbon stocks (Melton and Arora, 2016). The strongest control on the HR variability at these sites appears to be the soil matric potential. The CLASS–CTEM HR parameterization has a maximal rate at a soil matric potential intermediate between wet and dry soils (absolute soil matric potential between 0.04 and 0.06 MPa; see Fig. 1 in Melton et al., 2015). The primary assumption of the HR parameterization is that soil moisture constrains HR when soils are very dry due to limited microbial respiration. As soil become very wet, HR also drops to reflect diminished oxygen supply to microbes. The sites with the high variability of HR tend to reflect soil moisture conditions during the growing season with soil matric potentials fluctuating between the zone of optimal HR production and shutdown due to overly moist soils. For example, in 2007, SE-Faj had high variability of HR with the water table rising from 12 cm to only a few centimetres below the soil surface (indicating saturated soil conditions) resulting in a large shutdown of the HR flux, while 2008 was a drier year with a water table more consistently about 20 cm below the surface and much less variable HR fluxes simulated.

The simulated accumulated monthly NEP from March to November agreed well with the observations in the four bogs and four fens. The outliers for bogs were the overestimations in MB-Bog in October and November due to the underestimation of GPP (Fig. 8). The NEP in RU-Fyo in one August was underestimated owing to the underestimated GPP, which in turn was a result of the underestimated LAI and rooting depth temperature in the summer. Figure 15, showing plots of NEP averaged for each month of the year at each site, demonstrates on the whole larger scatter for the bogs than the fens, with the scatter increasing through the summer and fall. The overall value of r2 was 0.59 for bogs and 0.58 for fens; both values are higher than or similar to those obtained in evaluations of other peatland C models. For example, the r2 value of the monthly NEP for LPJ-WHy was reported to be 0.35 for four peatlands, with three of the sites overlapping those used in this study: SE-Deg, FI-Kaa, and MB-Bog (Wania et al., 2009b). The Finland peatland model simulated the NEP in FI-Kaa with r2 of 0.80 for the same time period tested for our model (Gong et al., 2013), but only the one site was used in the evaluation.

The simulated mean annual NEP values with their standard deviations generally fall within the range of the standard deviations of the observations (Fig. 16), between 9 g C m-2 yr-1 in the rich fen (FI-Lom) and 73 g C m-2 yr-1 in the productive bog (RU-Fyo) (Table 7). The only site with a large bias in annual NEP was AB-Fen. Observation-based estimations of NEP in this fen were extremely high, totalling 176 g C from May to October, in comparison with other sites (Syed et al., 2006). This treed fen had a high peat density and LAI and large variation in the WTD, which, accompanied by high spring temperatures, resulted in high ecosystem photosynthesis capacity and production (Adkinson et al., 2011). Considering nutrient factors and the site-specific peat density could potentially capture the large NEP at this site. The observed annual NEP for the eight sites varied greatly overall, between -17 and 187 gC m-2 yr-1, while the simulated NEP showed slightly less variation, ranging from 13 to 157 g C m-2 yr-1. The simulated mean annual NEP across the sites was 87 g C m-2 yr-1 and was 22 g C m-2 yr-1 higher than the mean observed NEP. In contrast the LPJ-WHy model simulated most of the annual NEP between -5 to 0 g C m-2 yr-1, lower than their observed median of 40 g C m-2 yr-1 (Wania et al., 2009b). As noted above, variations in the depth and age of the peat at the eight sites reflected fluctuations in past climate, leading to site-specific soil properties that were not always captured by the standardized values used in the model. Peatlands in different geographical locations also reflected the effects of local conditions: for example, the blanket bog UK-Amo in a maritime climate accumulated 101 g C m-2 yr-1 in 2007 (Dinsmore et al., 2010) while the dry MB-Bog was estimated to be a source of 13.8 g C m-2 yr-1 (Roulet et al., 2007). The modelled NEP bias tended towards underestimation for the treed fen (AB-fen) and the productive ombrotrophic bog (MB-Bog), and towards overestimation for the remaining sites.

The model errors in GPP were smaller than the standard deviation of the observations, except for the atypical sites (AB-Fen, RU-Fyo) and the sites that had only a few years of data (FI-Lom, SE-Faj) (Table 7). The bias of the simulated ER did not exceed the error bars except for in the RU-Fyo bog, for which a thin peat depth of 1 m was used to initialize the simulation (Table 4). The simulated WTD was consistently shallower in the summer than the observations (Fig. 4), which slowed down the soil respiration in the model and contributed to the discrepancies in ER. The observed WTD showed an abrupt decrease in the summer of 2010 without pulses of large ER being observed during that period (Fig. 9), indicating uncertainties in the WTD observations. Another reason for the errors in ER was the underestimation in soil T. For example, the simulated soil T at 5 cm depth was higher in the summers with RMSE of 4.6 ∘C in RU-Fyo (Table 5). The site is particularly shallow and homogeneous; thus, the standardized living moss layer of 4 cm for bogs was probably too large, leading to an overestimation of the thermal insulation effect from the moss layers and hence less seasonal variation in soil temperature and ER.

An overview of the model's performance is illustrated via a series of Taylor diagrams (Fig. 17). Taylor diagrams provide a graphical summary of how closely modelled data match observed data (Taylor, 2001). The radial spokes represent the level of correlation and the x and y axes show the standard deviation. The standard deviation of the observations is plotted on the x axis, and the RMSE of the modelled values is indicated by the concentric contours around this point. Since we have eight pairs of modelled and observed points for each diagram, we normalized the data by dividing each of the standard deviations and the RMSEs by the standard deviation of the observations associated with each point, so that all the observation points fall at 1 on the x axis. The outliers are the vegetated treed fen (AB-Fen), the maritime blanket bog UK-Amo and the extremely shallow peatland RU-Fyo. The model simulations consistently agreed quite well with the observations except at these sites for some evaluated parameters. The Pearson r was above 0.90 for the soil temperature at 5 cm and above 0.50 and 0.60 for the sensible and latent heat fluxes, except for those at UK-Amo. The modelled daily GPP and ER were highly correlated with the observations, with Pearson r values between 0.80 and 0.95 for GPP, and between 0.70 and 0.96 for ER. The simulated daily NEP accumulated the errors in GPP and ER and was somewhat less well correlated with the observations, with Pearson r values between 0.4 and 0.72.

The original version of our peatland model (referred to as “CONTROL” hereafter) as described above distinguishes bogs and fens through the controls of water table depth on soil decomposition and the depth of the living moss. The parameters for the water table depth regulation of soil decomposition were derived from the empirical relations in the MWM (Eqs. 13, 14). Our first test, “K-SWAP”, involved swapping the values of the decomposition parameters (Table 3) between the bog and fen sites. As shown in Fig. 18, the differences between the test and control runs are generally very small. The relative differences in the simulated values of the fluxes and temperatures between K-SWAP and CONTROL ranged from -1.6 to +5.1 % for RMSE and from -23 to +6 % for r2. The relative differences in RMSE and r2 for GPP, QH, QE, and Ts5 were smaller than ±1 %. The largest differences in r2 between K-SWAP and CONTROL were for NEP at SE-Faj and UK-Amo, which had significantly lower r2 values than the other sites. The long-term effect on the overall carbon balance, as reflected in the cumulative NEP, is shown for six of the sites in Fig. 19. (AB-Fen and RU-Fyo are omitted, since the differences in those two cases were imperceptible for both sensitivity tests.) The cumulative differences were everywhere less than 15 %. The results of K-SWAP indicate that parameterizing fens and bogs differently for the regulation of water table depth on soil decomposition does not make a large difference in the simulation.

The second test, “D-MOSS”, retained the settings in K-SWAP and changed additionally the depth of the living moss in both bogs and fens to 3.5 cm. The RMSE and r2 of D-MOSS show site-specific differences compared to CONTROL (Fig. 18). The relative differences between D-MOSS and CONTROL in RMSE and r2 were in the range of -5 to +7 and -15 to +13 % respectively. The mean differences for all sites and all evaluated variables were less than 5 % for both RMSE and r2. For GPP, ER and the soil temperature at 5 cm depth, the r2 in D-MOSS was similar to that of CONTROL. For QE, the r2 in D-MOSS was higher than the control for all the fens and one unusual bog (UK-Amo), but not for the other three bogs. Compared to CONTROL, the r2 of NEP was higher in D-MOSS for five sites by up to 7 % and less than 2 % lower in the other sites, except for UK-Amo where r2 was also low in CONTROL. Turning to the long-term carbon balance as shown by the cumulative NEP in Fig. 19, it is evident that the depth of the living moss has more of an effect on the simulation than the decomposition parameters. The difference is largest for FI-Kaa at 29 %, and then SE-Faj and SE-Deg at 23 %. However, the effect of the moss depth seems to be more site specific than related to the differences between bogs and fens.

Since as noted in Sect. 2.5 above, there was some uncertainty about what value to assign to the anoxic respiration scaling factor fanoxic, a third test was performed to assess the sensitivity of the simulation to this parameter. Frolking et al. (2010) assigned it a value of 0.001, and Frolking et al. (2001) set it to 0.025 for bogs and 0.1 for fens. For our simulations, based on the results of calibration runs we chose a constant value of 0.025 for all of the sites. Since according to Frolking et al. (2001) this value is more representative of bogs, we ran tests for the four fen sites with fanoxic set first to 0.1 and then to 0.001. The effect of the changes on the cumulative ER is shown in Fig. 20. It can be seen that the maximum cumulative difference is only about 9 % (for fanoxic = 0.1 at SE-Deg), and in the other cases the differences are much smaller. This suggests that we are not incurring any serious errors by using a single value for fanoxic.

Based on the results of the three tests described above, we conclude that when our model is applied at climate time and space scales, as a first-order approximation it will not be necessary to distinguish between fens and bogs through the use of different model parameterizations and coefficients. It will only be necessary to map the locations of peatlands, and whether a given peatland behaves like a bog or a fen will evolve out of the climate forcings, which will determine the vegetation cover and the hydrological characteristics of the peatland in question. This will considerably simplify the global implementation of the model, since global data sets mapping the locations of fens vs. bogs are not available.