The model has two litter C pools (metabolic and structural) and three soil C pools (active, slow, and passive); all pools are vertically discretized into 32 layers, with exponentially coarser vertical resolution as depth increases and a total depth of 38 m. Decomposition of the C in each pool and the C fluxes between the pools are calculated at each layer, with each pool having a distinct residence time. A detailed description of the litter and soil C pools and carbon flows between them can be found in the Supplement Text S2.

In grid-based simulations, each grid cell is characterized by fractional coverages of PFTs. The dynamic coverage of each non-peatland PFT is determined by the dynamic global vegetation model (DGVM) equations as functions of bioclimatic limitations, sapling establishment, light competition, and natural plant mortality (Krinner et al., 2005; Zhu et al., 2015). Here, a cost-efficient TOPMODEL from the DYPTOP model (Stocker et al., 2014) is incorporated and calibrated for each grid cell by present-day wetland areas that are regularly inundated or subject to shallow water tables to simulate wetland extent (Sect. 2.2.1). Then, the criteria for peatland expansion are adapted from DYPTOP to distinguish peatland from wetland (Sect. 2.2.2).

The base decomposition rates of active, slow, and passive peat soil carbon pools in the model are 1.0, 0.027, and 0.0006 a-1 at a reference temperature of 30 ∘C, respectively (Table 1, Sect. 5: Choice of model parameters). The e-folding depth of the depth modifier (z0, Eq. 2) determines the general shape of increases in soil C turnover time with depth; the prescribed threshold to allow downward C transfer between soil layers (fth, Eq. 5) and the prescribed fraction of C to be transferred (f, Eq. 4) determine movement and subsequent distribution of soil C along the soil profile. We compare simulated C vertical profiles with observed C profiles at 15 northern peatland sites (Table S1) (Loisel et al., 2014) using different combinations of parameters (z0=(0.5,1.0,1.5,2.0), fth=(0.5,0.7,0.9), and f=(0.1,0.2,0.3)) and eventually selected z0=1.5 m, fth=0.7, and f=0.1 based on visual examinations to match the observed C content. Model sensitivity to the selection will be discussed in Sect. 5.

We conduct both site-level and regional simulations with ORCHIDEE-PEAT v2.0 at 1∘×1∘ spatial resolution. Regional simulations are performed for the Northern Hemisphere (>30∘ N), while site-level simulations are performed for 60 grid cells containing at least one peat core (Table S1, Fig. S2). Peat cores used in site-level simulations are from the Holocene Perspective on Peatland Biogeochemistry (HPPB) database (Loisel et al., 2014). Both site-level and regional simulations are forced by the 6-hourly meteorological forcing from the CRUNCEP v8 dataset, which is a combination of the CRU TS monthly climate dataset and NCEP reanalysis (ftp://nacp.ornl.gov/synthesis/2009/frescati/temp/land_use_change/original/readme.htm, last access: 10 July 2019).

All simulations start with a two-step spin-up followed by a transient simulation after the pre-industrial period (Fig. S3). The first spin-up (Spin-up1) includes N cycles of a peat carbon accumulation acceleration procedure consisting of (1) 30 years with the full ORCHIDEE-PEAT (FullO) run on a 30 min time step followed by (2) a stand-alone soil carbon sub-model (SubC) run to simulate the soil carbon dynamics in a cost-effective way on monthly steps (fixed monthly litter input, soil water, and soil thermal conditions from the preceding FullO simulation). Repeated 1961–1990 climate forcing is used in Spin-up1 to approximate the higher Holocene temperatures relative to the pre-industrial period (Marcott et al., 2013). The atmospheric CO2 concentration is fixed at the pre-industrial level (286 ppm). Each time we run the SubC for 2000 years in the first N-1 sets of acceleration procedures, and the value of N and the time length of the last set of acceleration procedures (X) are defined according to the age of the peat core in site-level simulations, and are defined according to the reconstructed glacial retreat in regional simulations (Figs. S4, S5). The reconstructed glacial retreat used in this study is from Dyke (2004) for North America and from Hughes et al. (2016) for Eurasia (Text S6).

In the second spin-up step (Spin-up2), the full ORCHIDEE-PEAT model was run for 100 years, forced by looped 1901–1920 climate forcing and pre-industrial atmospheric CO2 concentration so that physical and carbon fluxes can approach the pre-industrial equilibrium. After the two spin-ups, a transient simulation is run, forced by historical climate forcing from CRUNCEP and rising atmospheric CO2 concentration. For site-level simulations, the transient period starts from 1860 and ends at the year of coring (Table S1). For regional simulations, the transient period starts from 1860 and ends at 2009.

We first evaluate the performance of ORCHIDEE-PEAT v2.0 in reproducing peat depths and vertical C profiles at the 60 sites from HPPB (Table S1). Out of the 60 grid cells (each grid cell corresponding to one peat core), ORCHIDEE-PEAT v2.0 produces peatlands in 57 of them. The establishment of peatlands at Zoige, Altay, and IN-BG-1 (Table S1) is prevented in the model by the summer water balance criterion of these grid cells. Peat depths are underestimated for most sites (Fig. 2). Simulated depth of these 57 sites ranges from 0.37 to 6.64 m and shows a median depth of 2.18 m, while measured peat depth ranges from 0.96 to 10.95 m, with the measured median depth being 3.10 m (Table 2). The root-mean-square error (RMSE) between observations and simulations is 2.45 m.

The measured and simulated median peat depths for the 14 fen sites are 3.78 and 2.16 m, compared to 3.30 and 2.18 m, respectively, for the 33 bog sites (Table 2). The model shows slightly higher accuracy for fens than for bogs, with the RMSE for fens being 2.08 and 2.59 m for bogs. RMSEs for peat depths of sites that are older than 8 ka are greater than those of younger sites, but are smaller than the measured mean depth (3.5 m) of all peat cores. Simulated median depth of the six arctic sites is larger than observations, but that of the 47 boreal sites and the four temperate sites is smaller than observations (Table 2). The RMSE for temperate sites is larger than that for arctic or boreal sites.

The simulated and observed vertical profiles of soil C for the 15 sites are shown in Fig. 3, simulated C concentrations are generally within the range of measurements at most of the sites, but are underestimated at Sidney bog, Usnsk Mire 1, Lake 785, and Lake 396. In the model, the buildup of peat is parameterized by downward movement of C between soil layers, with the empirical amount of C that each layer can hold being calculated from median observed bulk density and C fraction of peat core samples (Sect. 2.1.2). High C concentration of cores that have significantly larger bulk density and/or C fraction than the median of the measurements thus cannot be reproduced. This is the case of Lake 785 and Lake 396 (Table S1), where C concentrations are underestimated and depths are overestimated (Fig. 2), while simulated total C content is close to observations (for Lake 785, measured and simulated C content is 86.14 and 96.13 kg C m-2, respectively, while values for Lake 396 are 57.2 and 70.2 kg C m-2).

As shown in Fig. 4, there is considerable variability in depth and C concentration profiles among peat cores within a grid cell, even though these cores have a similar age. We rerun the model at the five grid cells where more than one peat core has been sampled, with time length of the simulation being defined as the mean age of cores in the same one grid cell. The simulated peat depth and C concentration profiles at G2, G4, and G5 are generally within the range of peat core measurements (Fig. 4). Observed C fraction at grid cell G1 and G3 is much greater than the median value of all peat core samples (Sect. 2.1.2); thus simulated C concentration along the peat profile is smaller than observations, but peat depth is still overestimated by the model. This is also the case with Lake 785 and Lake 396.

We found a general underestimation of peat depth (Figs. 2, 10), possibly due to the following reasons. Firstly, there is a lack of specific local climatic and topographic conditions. The surfaces of peatlands are mosaics of microforms, with accumulation of peat occurring at each individual microsite of hummocks, lawns, and hollows. Differences in vegetation communities, thickness of the unsaturated zone, local peat hydraulic conductivity, and transmissivity between microforms result in considerable variation in peat formation rate and total C mass (Belyea and Clymo, 2001; Belyea and Malmer, 2004; Borren et al., 2004; Packalen et al., 2016). Cresto Aleina et al. (2015) found that the inclusion of microtopography in the hummock–hollow model delayed the simulated runoff and maintained wetter peat soil for a longer time at a peatland of northwest Russia, thus contributing to enhanced anoxic conditions. Secondly, site-specific parameters are not included in gridded simulations. Parameters describing peat soil properties, i.e. soil bulk density and soil carbon fraction, determine the amount of C that can be stored across the vertical soil profile. Hydrological parameters, i.e. the hydraulic conductivity and diffusivity, and the saturated and residual water content regulate vertical fluxes of water in the peatland soil and expansion–contraction of the peatland area, and hence influence the decomposition and accumulation of C at the sites considered. Plant trait parameters, i.e. the maximal rate of carboxylation (Vcmax), and the light saturation rate of electron transport (Jmax⁡) determine the carbon budgets of the sites (Qiu et al., 2018). The depth modifier, which parameterizes depth dependence of decomposition, controls C decomposition at depth and is an important control on simulated total C and the vertical C profile. A third reason is sample selection bias. Ecologists and geochemists tend to take samples from the deepest part of a peatland complex to obtain the longest possible records (Gorham, 1991; Kuhry and Turunen, 2006). In contrast, the model is designed to model an average age and C stock of peatlands in a grid location, and thus preferably the simulated C concentrations of a grid cell should only be validated against grids represented by a number of observed cores. We do try to compare the model output with multiple peat cores (Figs. 4, 10), but we need to note that shallow peat is not sufficiently represented in field measurements. A fourth source of error is that simulated initiation time of peat development at some sites is too late compared to ages of measured cores. The model multiple-spin-up strategy accounts for coarse-scale ice sheet distribution at discrete Holocene intervals (Sect. 3.2, Fig. S3), and if the modelled occurrence of peatland is too late, the accumulated soil C may be underestimated. For example, at the Patuanak site, where the core age is 9017 years, the model was run with 4 times' SubC (Table S1). However, there was no peatland before the first SubC, meaning that simulated peatland at this grid cell was 2000 years younger than the observation and that our simulation missed C accumulation during the first 2000 years at this site. This may be another source of bias associated with the model resolution, namely that local site conditions fulfilled the initiation of peatland at specific locations, but the average topographic and climatic conditions of the coarse model grid cell were not suitable for peatland initiation. Also, one has to keep in mind that a single (a few) sample(s) from a large peat complex may not be enough to capture the lateral spread of peat area, which may be an important control on accumulation of C (Charmen, 1992; Gallego-Sala et al., 2016; Parish et al., 2008). The underestimation of peat depth can also come from biased climate input data: spin-ups of the model are forced with repeated 1961–1990 climate, assuming that Holocene climate is equal to recent climate. While peatland carbon sequestration rates are sensitive to climatic fluctuations, centennial- to millennial-scale climate variability, i.e. cooling during the Younger Dryas period and the Little Ice Age period and warming during the Bølling-Allerød period, is not included in the climate forcing data (Yu et al., 2003a, b). An early Holocene carbon accumulation peak was found during the Holocene Thermal Maximum when the climate was warmer than present (Loisel et al., 2014; Yu et al., 2009). Finally, effects of landscape morphology on drainage as well as drainage of glacial lakes are not incorporated and can represent a source of uncertainty.

We note that caution is needed in interpreting the comparison between simulated peat C profile and measured C profile from peat cores (Figs. 3, 4). In reality, peat grows both vertically and laterally since inception, with peat deposits tending to be deeper and basal age tending to be older at the original nucleation sites/center of the peatland complex (Bauer et al., 2003; Mathijssen et al., 2017). As mentioned earlier, field measurements tend to take samples from the deeper part of a peatland complex and shallow peat is underrepresented. The model, however, only simulates peat growth in the vertical dimension and lacks an explicit representation of the lateral development of a peatland in grid-based simulations; thus simulated peat C (per unit peatland area) is diluted when the simulated peatland area fraction in the grid cell increases. In addition, we cannot compare the simulated peat C profile against the observed profile from dated peat cores because the model does not track age bins explicitly.

The above-noted discrepancies between the simulation and the observation highlight both the need for more peat core data collected with more rigorous sampling methodologies and the need to improve the model. In parallel with this study, 14C dynamics in the soil have been incorporated into the ORCHIDEE-SOM model (Tifafi et al., 2018), which may give us an opportunity to compare simulated 14C age–depth profiles with dated peat C profiles in the future after being merged with our model.

The initiation and development of peatlands in NA followed the retreat of the ice sheets, as a result of the continuing emergence of new land with the potential to become suitable for peatland formation (Gorham et al., 2007; Halsey et al., 2000). To take glacial extent into account for simulating the Holocene development of peatlands, we use ice sheet reconstructions in NA and Eurasia (Figs. S4, S5). Not surprisingly, when ice cover is considered, the area of peatlands that developed before 8 ka is significantly decreased, while the area that developed after 6 ka is increased (Fig. 13). We use observed frequency distribution of peat basal age from MacDonald et al. (2006) as a proxy of peatland area change over time, following the assumption proposed by Yu (2011) that peatland area increases linearly with the rate of peat initiation. We grouped the data of MacDonald et al. (2006) into 2000-year bins to compare with simulated peatland area dynamics (Fig. 13). The inclusion of dynamic ice sheet coverage triggering peat inception clearly improved the model performance in replicating peatland area development during the Holocene, though the peatland area before 8 ka is still overestimated by the model in comparison with the observed frequency distribution of basal ages (Fig. 13). In spite of the difference in peatland area expansion dynamics between the simulation that considered dynamic ice sheets and the one that did not, the model estimates of present-day total peatland area and carbon stock are generally similar (Fig. S10). Without dynamic ice sheets, the model would predict only 0.1 million km2 more peatland area and 24 Pg more peat C over the Northern Hemisphere (>30∘ N). We are aware of two studies that attempted to account for the presence of ice sheets during the Holocene (Kleinen et al., 2012) and the Last Glacial Maximum (Spahni et al., 2013) while simulating peatland C dynamics. Kleinen et al. (2012) modelled C accumulation over the past 8000 years in the peatland areas north of 40∘ N using the coupled climate–carbon cycle model CLIMBER2-LPJ. A decrease of 10 Pg C was found when ice sheet extent at 8 ka BP (from the ICE-5G model) was accounted for. Another peatland modelling study conducted by Spahni et al. (2013) with the Land surface Processes and eXchanges (LPX) model also prescribed ice sheets and land area from the ICE-5G ice sheet reconstruction (Peltier, 2004), but influences of ice sheet margin fluctuations on simulated peatland area and C accumulation were not explicitly assessed in their study.

The peatland carbon density criterion for peatland expansion (Clim) is an important factor impacting the simulated Holocene trajectory of peatland development. Without the limitation of Clim, a larger expansion of northern peatlands would occur before 10 ka (Fig. S11). Such a premature, “explosive” increase in peatland area would result in the overestimation of C accumulated in the early Holocene in the model. In the meantime, peatland area in regions that only have small C input, i.e. Baffin Island and northeast Russia, would be overestimated (Fig. S12).

For the active, slow, and passive peat soil carbon pool, the base decomposition rates are 1.0, 0.027, and 0.0006 a-1 at a reference temperature of 30 ∘C, respectively, meaning that the residence times at 10 ∘C (no moisture and depth limitation) of these three pools are 4, 148, and 6470 years. In equilibrium/near-equilibrium state, simulated C in the active pool takes up only a small fraction of the total peat C, while generally 40 %–80 % of simulated peat C is in the slow C pool and about 20 %–60 % is in the passive C pool. Assuming that in a peatland, the active, slow, and passive pools account for 3 %, 60 %, and 37 % (median values from the model output of the year 2009) of the total peat C, we can get a mean peat C residence time of 2500 years. If depth modifier is considered, the C residence time will vary from 2500 years at the soil surface to 13 200 years at the 2.5 m depth. For the record, in previous published large-scale diplotelmic peatland models, at 10 ∘C, C residence time for the acrotelm (depth = 0.3 m) ranged from 10 to 33 years and ranged from 1000 to 30 000 years for the catotelm (Kleinen et al., 2012; Spahni et al., 2013; Wania et al., 2009b). We performed sensitivity tests to show the sensitivity of the modelled peat C to model parameters at the 15 northern peatland sites where observed vertical C profiles can be constructed (Table S1). Tested parameters are the e-folding decreasing depth of the depth modifier (z0, Eq. 2), the prescribed thresholds to start C transfer between soil layers (fth, Eq. 5), and the prescribed fraction of C transferred vertically (f, Eq. 4). We found that changing fth or f leads to only small effects on the vertical soil C profile (see, e.g. Burnt Village peat site in Fig. S13). The parameter z0, by contrast, exerts a relatively strong control over C profiles. It is noteworthy that while our model resolves water diffusion between soil layers according to the Fokker–Planck equation (Qiu et al., 2018), simulated soil moisture does not necessarily increase with depth (Fig. S14). z0 is therefore an important parameter to constrain peat decomposition rates at depth. With smaller z0, decomposition of C decreases rapidly with depth, resulting in a deeper C profile (Fig. S14). Regional-scale tests verified these behaviours of the model: when fth=0.9 is used (instead of fth=0.7), changes in peatland area and peat C stock are negligible (Fig. S15). Without z0, simulated northern peatland area will not change (3.9 million km2), but northern peatland C stock will be underestimated (only 300 Pg C). If z0=0.5 m is applied (instead of z0=1.5 m), the simulated total peat C would triple while the total peatland area would only increase by 0.2 million km2 (Fig. S16).

There are large uncertainties in estimates of peatland distribution and C storage. Some studies prescribe peatlands from wetlands. However, in spite of the fact that there are extensive disagreements between wetland maps, it is a challenge to distinguish peatlands from non-peat-forming wetlands (Gumbricht et al., 2017; Kleinen et al., 2012; Melton et al., 2013; Xu et al., 2018). Estimates based on peatland inventories are impeded by poor availability of data, non-uniform definitions of peatlands among regions, and coarse resolution (Joosten, 2010; Yu et al., 2010). In addition, as peatlands are normally defined as waterlogged ecosystems with a minimum peat depth of 30 or 40 cm, shallow peat is underrepresented. Another approach to estimate peatland area and peat C is to use a soil organic matter map to outline organic-rich areas, such as Histosols and Histels (Köchy et al., 2015; Spahni et al., 2013). This approach overlooks local hydrological conditions and vegetation composition (Wu et al., 2017). Our model estimates of peatland area and C stock generally fall well within the range of published estimates, except in the southeastern US, where there is only 0.05–0.10 million km2 of peatland in observations but 0.37 million km2 in the model prediction (Fig. 7d, Table 3). From the early 1600s to 2009, ∼50 % of the original wetlands in the lower 48 states of the US have been lost to agricultural, urban development, and other development (Dahl, 2011; Tiner, 1984). Although wetlands are not necessarily peatlands, the reported losses of wetlands in the US indicate that a potentially large area of peatlands in the US may have been lost to land use change. However, historical losses of peatlands due to land use change and the impact of agricultural drainage of peatlands have not been taken into account by our model. Another factor that might have contributed to the overestimation is a limitation of TOPMODEL, namely that the “floodability” of a pixel in the model is determined by its compound topographic index (CTI) value regardless of the pixel's location along the stream, and thus the floodability of an upstream pixel with a large CTI might be affected by downstream pixels that have a small CTI. The model's inability to resolve small-scale streamflows might be another cause of the overestimation.

The simulated mean annual NPP, HR, and NEP of northern peatlands increase from about 1950 onwards. We find positive relationships between NPP and temperature, NPP and atmospheric CO2 concentration, and HR and temperature over the past century (Fig. S9). From a future perspective, it is unclear whether the increasing trend of NEP can be maintained. While photosynthetic sensitivity to CO2 decreases with increasing atmospheric CO2 concentration and photosynthesis may finally reach a saturation point in the future, decomposition is not limited by CO2 concentration and may continue to increase with increasing temperature (Kirschbaum, 1994; Wania et al., 2009b).

Our model applies a multilayer approach to simulate process-based vertical water fluxes and dynamic C profiles of northern peatlands and highlights the vertical heterogeneities in the peat profile in comparison to previous diplotelmic models (Kleinen et al., 2012; Spahni et al., 2013; Stocker et al., 2014; Wania et al., 2009b). While simulating peatland dynamics, large-scale models used a static peatland distribution map obtained from peat inventories and soil classification maps (Largeron et al., 2018; Wania et al., 2009b, a), prescribed the trajectory of peatland area development over time (Spahni et al., 2013), or used wetland area dynamics as a proxy (Kleinen et al., 2012). We adapt the scheme of DYPTOP to simulate spatial and temporal dynamics of northern peatland area by combing simulated inundation and a set of peatland expansion criteria (Stocker et al., 2014).

As a large-scale LSM which is designed for large-scale gridded applications, ORCHIDEE-PEAT v2.0 cannot explicitly model the lateral development of a peatland. The model therefore aims to simulate large-scale average peat depth and C profile rather than capturing local peat inception time and age–depth profiles at the location of specific peat cores. Tracers like 14C are not included in the model, making some site-to-site evaluation in particular regarding peat inception time and age–depth profiles of peat cores difficult. For tropical peatlands, the model needs to be improved to represent its tree dominance, oxidation of deeper peat due to pneumatophore (breather roots) of tropical trees, and the greater water table fluctuations as a result of the higher hydraulic conductivity of wood peats and tropical climates (Lawson et al., 2014). In addition, tropical peat is formed in riparian seasonally flooded wetlands with water coming from upstream river networks, whereas the TOPMODEL equations used here implicitly assume a peatland is formed in a grid cell only from rainfall water falling into that grid cell. Further work to improve this simulation framework is needed in areas such as an accurate representation of the Holocene climate, higher spatial resolution, and distinguishing bogs from fens to better parameterize water inflows into peatland. Including CH4 emissions and leaching of DOC will be helpful to get a more complete picture of peatland C budget.