Photosynthesis of C3 plants in ORCHIDEE is based on Farquhar and Sharkey (1982), with the stomatal conductance (gs) implemented according to Yin and Struik (2009): gs=g0+A+RdCi+Ci∗×fVPD, with g0 the stomatal conductance when irradiance is null, A the rate of CO2 assimilation, Rd the dark respiration rate, Ci the intercellular CO2 partial pressure and Ci∗ the Ci-based CO2 compensation point in the absence of dark respiration. fVPD is a function describing the effect of leaf-to-air vapour pressure difference (VPD), described empirically following Yin and Struik (2009): fVPD=1[1/a1-b1×VPD-1], with a1 and b1 empirical constants. This function limits the stomatal conductance under dry air conditions.

Vascular plants have stomata (Kirkham, 2005; Ruszala et al., 2011) to regulate gas fluxes (i.e. CO2, transpiration). For NVPs, the situation is more complex and diverse (Williams and Flanagan, 1996; Chater et al., 2013): some species have “non active” stomata (Ruszala et al., 2011) like Oedipodium, others have only “pseudo-stomata” like Sphagnum, and some have no stomata like Andreaeobryum (Haig, 2013). For the sake of simplicity and given the lack of a well-established photosynthesis model for each NVP type, we considered all NVPs to have “pseudo-stomata”. Thus we kept Eq. (1) for gs (Yin and Struik, 2009) but with a conductance that only weakly depends on the VPD. Observation of NVP transpiration suggests that their conductance has a small dependence on humidity and atmospheric CO2 concentration, but a large mean value. We thus defined the coefficients a1 and b1 (see Table 2) so that the VPD dependence of leaf stomatal conductance fvpd in Eq. (2) is almost independent of VPD and chose a large value for g0 to simulate a high stomatal conductance. This solution is close to that used by Dimitrov et al. (2011), i.e. a constant conductance.

ORCHIDEE has five biomass carbon reservoirs for C3 grasses: leaves, root, reserve, reproductive organs (fruits), and sapwood below and above ground. We chose to keep only the leaf reservoir to represent the NVP biomass and the fruits pool for reproduction (see Table 2). Furthermore, C3 grasses are deciduous vegetation with only reserve pools during wintertime. Using the leaf pool to represent NVP biomass means considering NVPs as an evergreen PFT (see Table 2) with leaves present all year long. The main challenge is then to adapt the leaf biomass turnover rate in order to represent the observed temporal dynamic of lichens and bryophytes biomass.

We first modified the original leaf senescence parameter from 120 days (for grasslands) to 470 days for NVPs (Table 2). We then defined an energy cost (i.e. an extra turnover of biomass) for NVP survival in cold winter conditions and limited photosynthesis due to the thickness of the NVPs reducing light penetration.

Bryophytes and lichens have a very good resistance to extreme conditions introduced by lower leaf senescence and no leaf fall. However, this adaptation has an energy and thus a biomass cost, modelled through an additional carbon loss (tnpp0 in  gC m-2 d-1) based on the cumulative number of day (dcum) when the NPP is negative or null: tnpp0=b×klkl=0,dcum<d0klmax×dcum-d0dm-d0,d0<dcum<dmklmax×dcum-dfdm-df,dm<dcum<df, where b is the (leaf) biomass of NVPs (gC m-2) and kl the additional fraction of biomass lost during extreme conditions (or turnover rate in d-1) with a maximum value of klmax (in d-1), d0 is the threshold delay time (in days) before increasing the turnover, df (days) the maximum number of days for applying the extra turnover, and dm (days) the day number when kl reaches its maximum value after d0. The values of all parameters are summarised in Table 2. Figure 1 illustrates the increasing biomass turnover linked to extreme conditions with kl as a function of time in the season with negative or zero NPP. After a maximum, the turnover decreases in order to represent the induced resistance and thus survival to extreme conditions, i.e. under snow cover in winter or under dryness.

Using NPP to determine the period of the year with extreme conditions allows us to combine different stress factors such as cold temperature and very low moisture. Hence, the combination of short-term stress episodes (periods when d0 >  0) such as a short drought followed by a snowfall (blocking of light and cold temperature stress) on the NVPs could result in a long-term impact (increase in turnover) on vegetation.

The second turnover rate is related to favourable conditions with a large growth of biomass during the growing season (such as in peatlands). Given their large NPP under favourable conditions, NVPs can accumulate biomass over several tens of centimetres. In this case, sunlight cannot reach the lower portion of the canopy due to light penetration decreasing, although this biomass is still considered as leaf material (see Sect. 2.2.1). The underneath biomass usually dies from a lack of light and possibly a lack of oxygen in wet conditions. Given that oxygen concentration is not simulated in this model, the effect of anoxic conditions and severe light limitation are simply parameterised by increasing the overall leaf biomass turnover rate during the growing season. We chose the leaf area index (LAI) to define this additional turnover: when the maximum LAI (LAIlim) is reached, the underlying layers will not receive any sunlight, resulting in an increase of their turnover rate (tmissL) represented by tmissL=b×elcoef×(LAI-LAIlim)-1if LAI>LAIlim, where b is the leaf biomass of NVPs (gC m-2), lcoef a coefficient (d-1) and LAIlim a threshold leaf area index. These two parameters are optimised in Sect. 2.6.1 and their values reported in Table 2.

In ORCHIDEE, all vegetation types have access to soil water through a root system. The ability of roots to extract water depends on soil moisture in the different soil layers (11 currently, see Sect. 2.1) and the root density profile (R; de Rosnay, 1999): Rz=e-rp×z, with z the soil depth (in metres) and rp a PFT-dependent parameter to control the shape of the root profile.

NVPs do not have roots to absorb water (or nutrients from the underlying substrate). Some of them, such as Sphagnum, can have threadlike rhizoids, but only to anchor to the soil. So they can only access the surrounding surface water. However, ORCHIDEE does not include a surface liquid water reservoir; thus for simplicity we have assumed that NVPs have access to water stored in the first top-soil layers. This assumption allows us to keep an internal coherence between PFTs and facilitates the treatment of competition for water between PFTs. The value of the rp parameter (Table 2) for NVPs was defined through the optimisation (see Sect. 2.6.1). With 50 % water uptake (without roots) at 2.5 cm and 95 % at 11 cm, we obtained water access values close to those proposed by Dimitrov et al. (2011) and Chadburn et al. (2015). Figure 2 illustrates the soil water uptake profile for NVPs, and the root profiles for C3 grasses and boreal trees (used in ORCHIDEE).

During and after a water stress period, the water content of NVPs decreases significantly (desiccation), which reduces the plant photosynthetic capacity (Williams and Flanagan, 1996; Wania et al., 2009; Dimitrov et al., 2011). As for the other PFTs in ORCHIDEE, the instantaneous effect of soil water limitation will reduce photosynthesis through a soil water stress function imposed on the maximum photosynthetic capacity (Farquhar et al., 1980 photosynthesis model). Additionally, for NVPs, plant desiccation occurs and the time needed before recovery to optimum photosynthetic capacity must be taken into account.

To account for this effect, Wania et al. (2009) reduced gross primary production as a function of the annual mean water table position. In ORC-HL-VEGv1.0 we chose to use a monthly running mean hydric stress factor (ws) computed from the relative water content in each soil layer weighted by the specific water uptake profile of NVPs defined in Fig. 2. We defined a desiccation function, dess, as a linear function of ws (Eq. 6 and Fig. 3) varying between 1 (no impact) and a minimum value doff, when ws decreases to zero under maximum water stress. The function dess (ws) illustrated in Fig. 3 scales the maximum rate of carboxylation (Vcmax) as well as the maintenance respiration. The maximum rate of electron transport (Vjmax) is scaled through Vcmax. Indeed, leaf maintenance respiration defined in ORCHIDEE being a function of the leaf carbon content (biomass) and LAI, should then be reduced when NVPs get desiccated. With this formulation, we can take into account the impact of a drought on a monthly timescale: dess=doff+1-doffwsmin×ws,ifws<wsmin1,ifws≥wsmin, with wsmin being the minimum threshold hydric stress for desiccation (a constant defined in Table 2).

Non-vascular plants, and more precisely bryophytes, form an insulating layer above the soil with thus a strong control on the heat exchange between the atmosphere and the soil (Dyrness, 1982; Beringer et al., 2001; Blok et al., 2011a). In its standard version, ORCHIDEE does not account for the thermal insulation properties of vegetation in the calculation of the surface energy budget. For the sake of simplicity and following the same approach as in Chadburn et al. (2015), we modified in ORC-HL-VEG the upper soil layer characteristics to describe the effects of NVPs on the heat transfers to the soil over a depth that is equivalent to the NVP thickness and for the fraction of each grid cell covered by NVPs.

First we estimate the thickness of NVPs (h) assuming a fixed biomass density: h=bρ, with b the total NVP biomass (g m-2) and ρ its density (gC m-3; see Table 2).

The thermal capacity/conductivity (Eqs. 8 and 9) of the upper soil layers (equivalent to the depth of the NVP layer) are modified based on the soil volumetric moisture content (as in the standard ORCHIDEE version) and the heat conductivity and capacity of NVPs, following Soudzilovskaia et al. (2013). The heat thermal capacity of the top-soil thickness h occupied by NVPs, C, follows from C=Cdry+mvol×(Cwet-Cdry), where mvol is the volumetric relative moisture content over a thickness h, Cdry the dry thermal capacity of dry NVPs and Cwet the wet heat capacity of wet NVPs (from Soudzilovskaia et al., 2013; see Table 2). Note that in the standard case without NVPs, Cwet and Cdry are defined from the soil texture (see Wang et al., 2016). In the case of frozen soil we use an ice capacity (Cice) for NVPs, deduced relative to the Cice of soil. When the soil is partly frozen a weighting average between the two thermal capacities is calculated (using x, the unfrozen soil fraction). The overall thermal conductivity, λ, follows from λ=λdry+mvol×λsat-λdryλsat=λsat_wetx×λsat_ice1-x, with λdry being the dry soil thermal conductivity, λsat_wet the unfrozen wet thermal conductivity (from Soudzilovskaia et al., 2013) and λsat_ice the frozen thermal conductivity of NVPs (derived relative to the λsat_ice of soil). See Table 2 for values and units. Note that the current version of ORCHIDEE only calculates one energy budget (being the average of all vegetation types present in a grid cell); the overall thermal soil characteristics thus correspond to a weighted average of the soil characteristics according to the fraction of NVPs covering a grid cell.

In the standard version of ORCHIDEE, two important factors, temperature and moisture, exert control over litter and soil organic matter decomposition (following the CENTURY model; Parton et al., 1988). These factors are computed from weighted mean soil temperature and soil moisture profiles, assuming an exponential profile of soil organic matter content and associated decomposition processes between 0 and 2 m depth. For the moisture control of decomposition, the original function (Parton et al., 1988; Krinner et al., 2005) is increasing with soil moisture content (maximum at saturation), which is not adapted for water-saturated soils, where anoxic conditions reduce soil microorganism activity (such as in peatlands). As these conditions may prevail for NVP covers, we modified the original scheme.

First, we introduced a vertical discretisation of below-ground litter carbon pools, assuming it follows the same distribution as the root profile for vascular plants or soil water uptake profile for NVPs (exponential decay as Eq. (5), in de Rosnay, 1999), as in Frolking et al. (2001). Moreover, we consider that there is no above-ground litter for NVPs, so that leaf litter is treated like below-ground litter, as in Frolking et al. (2001) and Chadburn et al. (2015). With this new vertical discretisation, we chose to use the temperature and soil moisture of each layer to control litter decomposition.

To account for anoxic conditions often prevailing in water-saturated NVP ecosystems causing slow decomposition rates (Frolking et al., 2001), we changed the moisture decomposition function (RSR) applied for each layer as in Moyano et al. (2012), using a look-up table approach. Equation (10) and Fig. 4 describe the new function and the reduced decomposition with soil moisture content (applied for the litter from all PFTs): PRSL(mvol)=mc(3)×mvol3+mc(2)×mvol2+mc(1)×mvol+mc(0)SRmvol=∏k=0mvolPRSL(k)RSR(mvol)=SR(mvol)max0<k<1(SR(k)), with SR being the soil respiration (coefficient), PRSR the proportional response of SR to soil moisture, RSR the relative respiration, mvol the soil volumetric moisture content (unitless), and mc(1-3) three parameters taken from Moyano et al. (2012). SR is equal to the product of all PRSL values (denoted by Π symbol) at each 0.01 moisture interval (k), from zero to the computed SR moisture. To obtain RSR, SR is divided by the maximum of SR for all k intervals (0 to 1). See Table 2 for constant values. Note that the temperature function decomposition is not modified.

Other parameters and processes used for NVPs are set equal to those of C3 grasses, such as albedo and roughness as described by Krinner et al. (2005). We have optimised specific parameters of NVPs (marked with an “a” in Table 2) against observation (see Sect. 2.5.1), following a Bayesian optimisation framework (see Sect. 2.6.1). The values of the main parameters for the NVPs including the optimised ones are reported in Table 2.

Tree allometry in ORCHIDEE is based on a pipe tune model (Smith et al., 2001). It represents the relation between height and diameter as a power (or log-linear) function, with no height limit. Shrub development is more horizontal than vertical (Bentley et al., 1970; Sitch et al., 2003; Lufafa et al., 2009), which requires modification of the tree allometry. We implemented the allometry rules described by Aiba and Kohyama (1996) with specific values for shrubs from Martínez and López-Portillo (2003). Equation (11) gives the allometry relation between individual height (H, in metres), diameter (D, in metres), volume (V, m3), the number of individuals (ni), the total crown area (Ca, m2), the total stem basal areal (T, m2), the total woody biomass (mw, gC m-2) and wood density (ρw, between 0 and 1). The height of a shrub is related to a logarithmic function of its diameter (Eq. 11a) and its volume is represented by a cylinder (Eq. 11b). The shrub vegetation cover is defined as a function of the total stem basal area (Eq. 11c). With simple geometric relations (Eq. 11d) and assuming a fixed crown area (Ca becomes a constant) the system can be solved and all key variables expressed as a function of shrub woody biomass (mw). The height is given by Eq. (11e) and the number of individuals is adapted in order to keep the crown area fixed (Eq. 11c and d). If the crown area is not fixed (e.g. with dynamic vegetation), there is no analytical solution to obtain the height: 1/H=1/A×Dγ+1/HmaxV=π/4×Hmax×A×D2+γHmax+A×DγCa=β×Tα=β×ni×π/4×D2αmw=ni×V×ρwandH=ni×VTH=mwρw×Ca/β1/α, where A, β, γ, α and Hmax are parameters adapted from Martínez and López-Portillo (2003) (see Table 4). Here, the parameter Hmax defining the maximal height (in metres) was optimised (see Sect. 2.6.1). In accordance with imposed vegetation coverage, a minimum woody vegetation height (Hmin, in metres) was prescribed based on the maximum height, according to Hmin=Hmax/hc, where hc is a factor defined in Table 4. Based on the new shrub allometry equations (Eq. 11), new parameters can be derived for shrubs with the pipe tune model (Table 4).

Shrub vegetation affects snow cover through snow compaction and spatial heterogeneity of snow deposition (due to lateral wind transport). Shrub (and tree) branches support part of the snow cover. As a result, the snow weight on lower snow layers is smaller and the compaction of snow crystals is reduced. Moreover, wind is reduced by the presence of a shrub (and tree) canopy, which further reduces snow compaction compared to short vegetation cover. We kept the original snow compaction equation in ORCHIDEE (Wang et al., 2013, their Eqs. 11, 12 and Table A1) but chose new values for the parameters controlling compaction depending upon low or high vegetation (Table 3) in order to model a different depth and density over the fraction of a grid cell covered with shrubs (and tree).

Currently there is no sub-grid simulation of snow cover and energy balance in ORCHIDEE, so there is no distinction according to the fraction of different PFTs present in a grid cell. To account for differences between PFTs we computed snow compaction separately for short vegetation (bare soil, grasses and NVPs), shrubs and trees. The resulting average snow depth and density over a grid cell is obtained by weighting each vegetation-dependent compaction by its fraction. The deposition of snow is assumed to be identical among the different PFTs. A PFT-dependent snow depth is needed to compute the protection of vegetation by snow (Sect. 2.3.3). To compensate for the lack of an explicit PFT-dependent snow depth, an empirical correction is applied to account for the effect of vegetation type on snow compaction and deposition on shrubs: ds_v=ds_f×dsds_f=1+fv,fv≤0.52-fv,fv>0.5, with ds_v being the snow depth of high vegetation (shrubs and trees, in metres), ds the average snow depth (in metres) over the grid-cell, and ds_f a function of fv, the fraction of high vegetation. Note that this equation is a heuristic formulation discussed in Sect. 4.

ORCHIDEE includes a tree mortality during extremely cold days, calculated as the percentage of biomass lost at the end of each day, when used to compute the vegetation distribution dynamically (see Zhu et al., 2015). This mortality depends on a minimum temperature, as defined in Eq. (14). We used the same equation but assigned a critical minimum survival temperature to all boreal (including needleleaf) trees: IfTmin<Tmin,crit,Mce=kce×Tmin,crit-Tmin, with Mce being the mortality rate due to cold extremes, Tmin,crit the minimum critical survival temperature (defined for each PFT), Tmin the daily minimum air temperature and kce a mortality coefficient. The values of these parameters are given in Table 4.

For shrubs we used a similar approach to control for loss of biomass due to extreme cold temperatures. A mortality rate similar to Eq. (14) is applied to the highest parts of shrubs that are not covered by snow. For the part of shrubs situated inside snow layers (see Sect. 2.3.2 and Eq. 13 for the shrub snow depth calculation), snowpack temperature is used in Eq. (15). We defined a daily vertical profile of the minimum temperature Tmin(z) function of shrub height above ground (z), by linear interpolation between soil, snow layers and air temperatures above the shrub height emerging from the snow pack. To simulate the mortality of shrub parts being exposed to extreme cold, the following mortality equation is applied for the top part of shrubs: Mce=∫HminHkce×fnTHdzfnz=0,Tmin≥TmincritTmincrit-TminzTmin<Tmincrit, with Mce being the extreme cold mortality, Tmincrit a minimum critical temperature (defined by PFT), kce a coefficient, H the shrub height and Hmin its minimum height (Eq. 12). The values of the parameters of Eq. (14) for shrubs are given in Table 4. This equation is the integral of Eq. (14) applied to the height of shrubs.

In ORCHIDEE, the surface roughness length is directly computed from the height of the vegetation. Similarly, surface albedo depends on the vegetation type. Because shrubs can be partially or entirely covered by snow, the computation of surface roughness and albedo in the presence of shrubs needs to take into account snow height. The calculation of surface roughness length has thus been modified. First vegetation height is computed separately for shrubs (using Eq. 11) and for trees (using the original pipe tune model equation of Smith et al., 2001). The height of the snow cover over shrubs is then subtracted from the vegetation height in order to estimate the height of the vegetation above the snow surface (i.e. the relative height), which determines the surface roughness. The relative difference between the relative height and the total height is not substantial for trees (height > 5 m), but it can be important for shrubs (> 30 cm), which can be totally covered by snow. To represent the spatial heterogeneity of snow cover, when the snow thickness is close to the height of vegetation, a linear function is applied to estimate the height above snow: HPFTas=HPFT-ds,ifHPFT>ds×1+Δz00,ifHPFT<ds×1-Δz0(HPFT-ds(1-Δz0))/2,otherwise, where HPFT is the height of the PFT, HPFT_as is the height of the PFT above the snow, ds is depth of snow, and Δz0 the width of the transition zone due to spatial heterogeneity of snow cover (see Table 4).

The fraction of vegetation (fv) is used to compute the roughness length z0. For trees and shrubs the maximum fraction of vegetation fv=fv_max (prescribed if the vegetation cover is static, or calculated when the vegetation cover is dynamic, and independent of LAI) is used to take into account the influence of trunks and branches even if there are no leaves. For grasses and NVPs, to take into account the variation of leaf cover (for example absent for grasses in winter) only the projected surface of the foliage in the canopy fv=fv_max(1-e-LAI/2) is used because there are no woody elements. The rest of the surface is treated as bare soil with a constant roughness length value.

Finally the roughness length of a given PFT is calculated as its height above snow multiplied by a roughness parameter z0_c, as initially in ORCHIDEE. If this value is lower than the bare soil roughness (z0_bs fixed), then the latter value is used. The grid cell mean roughness length is computed (from Vihma and Savijärvi, 1991) as a function of each PFT roughness weighted by the vegetation cover, fv: log⁡z0=∑PFTfv×log⁡maxHPFT_asz0_c,z0_bs, where z0 is the grid-cell averaged roughness (m), z0_bs the roughness of the bare soil (m), fv the fraction of each PFT and z0_c a constant roughness parameter. The values of the parameters of Eq. (17) are given in Table 4.

The mean albedo of a grid cell depends on the vegetation, bare soil and snow albedo and their fractional coverage. While snow albedo is a function of snow age (computed for each vegetation type), bare soil and vegetation albedo are constant in time. A critical parameter to weigh the different terms is the fraction of the grid cell covered by snow, snowfrac, on bare soil and vegetation. In ORCHIDEE this fraction only depends on the snow mass, as defined in Chalita and Le Treut (1994). We chose to modify this approach in order to account for the effect of the vegetation structure as in Douville et al. (1995) and Boone (2002), using the roughness length calculated from Eq. (17), which is given by snowfrac=snowdzsnowdz+ξ×z0, with snowfrac being the fraction of the grid covered by snow, snowdz the snow thickness, z0 the roughness length and ξ a parameter (defined in Table 4).

Table 4 summarises the main parameter values used in the equations described previously as well as a few other parameters modified for the shrub PFT (compared to the initial tree PFT).

The calibration of the parameters entered in the equations of NVPs, shrubs and cold climate grasses is based on observations for the period 1993–2001 gathered in Peregon et al. (2008) and extended up to 2013 for this study. The data set contains georeferenced point-scale observations of the total summertime living biomass (g m-2) and annual net primary productivity NPP (g m-2 yr-1) for non-vascular plants (mosses and lichens) and vascular plants (grasses and shrubs) in boreal wetlands. Test sites for field observations are located in western Siberia (lat 55 to 71∘ N, long 63 to 91∘ E), which is suited for spatial analysis of NPP and biomass due to its flat topography along a wide latitudinal gradient and large variety of natural ecosystems, with minor anthropogenic influence.

At each test site, detailed geobotanical descriptions were recorded and biomass sampling was conducted. Sampling was repeated two or three times during the growing season at the same test sites for several consecutive years to obtain information on interannual variability. Field studies were conducted between June and October at more than 99 % of the test sites, and between July and September for 90 % of them. General descriptions of in-field and laboratory methods used to estimate NPP and biomass are described in Peregon et al. (2008, 2016).

The data set takes into account all components of NPP and living biomass: above-, land-surface and below-ground fractions measured in situ at different topographical features (such as hummocks, hollows, ridges). In order to avoid the “bound” effect and use of values at the border between two vegetation classes, we chose to exclusively take into account observations where the studied vegetation represented at least 10 % of the surface. Spatial differences in these microsite characteristics (i.e. hydrologic and thermal regimes, nutrient availability) strongly determine vegetation characteristics, as well as NPP and biomass, and small-scale heterogeneity induced by these microsite characteristics can be as large as the large-scale variability due to climatic gradients across the area covered by the data set. Because the small-scale variability cannot be represented in a large-scale model like ORCHIDEE, and small-scale information on microsite hydrological and topographical characteristics were not available, no perfect model–data fit can be expected, and we should rather seek for a broad model–data agreement.

The data have therefore been grouped into supersites at 0.5∘ spatial resolution, giving 36 supersites. The 36 sites have data on mosses (comprising in total 1209 individual observations), but only 16 supersites presenting non-vascular plants, shrubs and grasses (comprising in total 660 individual observations; Fig. 5). Note, finally, that using a single data set in western Siberia (mainly lowlands) for the model calibration may introduce some biases, which will have to be evaluated.

For this study we prescribe the spatial distribution of the vegetation, while a follow-up study will focus on the dynamics of the vegetation. We thus had to update the vegetation map used by the standard version of ORCHIDEE in order to include the spatial distribution of the new PFTs. The land cover product used to define PFT distribution in ORCHIDEE is derived from the land cover product of the European Space Agency (ESA) Climate Change Initiative (CCI; available at http://www.esa-landcover-cci.org/). The product is based on medium-resolution satellite observation and provides information on the vegetation distribution using land cover classes (LCC) defined by the United Nations Land Cover Classification System (UNLCCS). In order to match the satellite land cover classes with the PFTs coverage in ORCHIDEE, we use a conversion table established by Poulter et al. (2015). Note that the climate classification system of Köppen (Peel et al., 2007) is also used to further partition some vegetation types into tropical, temperate and boreal zones (see also Poulter et al., 2015). The new vegetation map is thus obtained from this Land Cover data set (version 1.6.1) transformed with a conversion table (tool available from http://maps.elie.ucl.ac.be/CCI/viewer/), from 300 m LCC data. From the standard conversion table used in ORCHIDEE, the three new PFTs were included using the following modifications (Table S1 in the Supplement): i.

The C3 grasses (initially defined globally) that were located in class 5 of Köppen classification (polar and alpine climates) were assigned to the new cold climate C3 grasses PFT.

The resulting spatial distribution north of 60∘ N is consistent with CAVM and Loveland et al. (2000), with 2.9, 2.2 and 2.8 million km2 NVPs, shrubs and cold climate grasses, respectively.

The distribution of the different circumboreal PFTs is presented in Fig. 6. NVPs are mainly present in northern latitudes, where climate conditions for the other PFTs are too extreme. Shrubs are present everywhere in northern latitudes but sparsely, with the tree PFTs always dominating. This is due to the approach we chose, because shrubs are diagnosed from the same LCCs as trees, with a smaller fractional coverage (Table S1). The cold climate C3 grasses come mainly from boreal forest LCCs in northern latitudes and from meadows further south (Table S1). They are dominant only in the latter.

We used a Bayesian optimisation procedure to improve the value of selected parameters of the new NVPs, shrubs and boreal C3 grass PFTs. Prior information on the parameter is combined with the information that can be extracted from an ensemble of observations (see Sect. 2.5.1). Assuming that the errors associated with the parameters, the observations and the model follow Gaussian distributions, the optimal parameter set corresponds to the minimum of a cost function J(x), that measures the mismatch between (i) the observations (y) and the corresponding model outputs H(x) (where H is the model operator), and (ii) the a priori (xb) and optimised parameters (x), weighted by their error covariance matrices (Tarantola, 1987; Eq. 21): Jx=12Hx-yTR-1Hx-y+x-xbTB-1x-xb, where R represents the error variance/covariance matrix associated with the observations and B the parameter prior error variance/covariance matrix. Note that R includes the errors on the measurements, model structure and the meteorological forcing. Model errors are rather difficult to assess and may be much larger than the measurement error itself. Therefore, we chose to focus on the structural error and defined the variances in R as the mean squared difference between the prior model and the observations (as in Kuppel et al., 2013). For simplicity we assumed that the observation error covariances were independent between the different observations and therefore we kept R diagonal (off-diagonal terms set to zero).

The determination of the optimal parameter vector that minimises J(x) is performed using a Monte Carlo approach based on a genetic algorithm following the implementation of Santaren et al. (2014). The algorithm works iteratively, starting with a pool of vectors of parameters (i.e. the chromosomes) defined from randomly perturbed parameters. At each iteration, it randomly perturbs or exchanges parameters of the chromosomes and ranks them based on the cost function values, so that the best chromosomes (parameter combinations corresponding to the lower cost function values) produce more descendants (following the principle of natural selection). For details of the implementation see Santaren et al. (2014). Note that this algorithm is more efficient to find the minimum of J than a gradient-based method as discussed in Bastrikov et al. (2018).

For each optimised parameter (Table S2), the initial values were taken from the literature or from the values used for the ORCHIDEE boreal deciduous tree PFT for shrubs and from the C3 grasses PFT for NVPs and cold climate C3 grasses. We defined the observation errors (R diagonal) as 50 gC m-2 (1σ standard deviation) for the biomass and for NPP, based on field measurement errors (Peregon et al., 2008) and a priori model data mismatch. The number of iterations was set to 25 and the number of chromosomes to 15 for NVPs and 10 for C3 grasses and shrubs, after some initial check of the convergence of the algorithm. The simulation for the optimisation was done with CRU-NCEP meteorological forcing (Wei et al., 2014; Viovy, 2015), at 0.5∘ resolution. In order to spin up the model with respect to the living biomass, each simulation starts 10 years before the observation period for NVPs and grasses, and 19 years for shrubs.

To illustrate the impact of new boreal vegetation compared to standard PFTs we show the results of two different simulations: one with the standard 13 PFTs of ORCHIDEE (ORC13) and the second with the new circumboreal PFTs (13 standard + 3 new PFTs: ORC16). Both simulations use the CRU-NCEP meteorological forcing (Wei et al., 2014; Viovy, 2015) based on gridded monthly observations from the Climatic Research Unit (CRU) at 0.5∘ and the climate re-analysis from the National Center for Environmental Prediction (NCEP) model (reduced to 2∘ resolution), available from 1901 to 2013. We first spun up the model carbon pools (above and below ground) with a 5000-year simulation (recycling the forcing files from 1901 to 1950 randomly). We then used a transient simulation from 1901 to 2004 with linked CO2 concentration. The spatial domain is also limited to the latitudes above 40∘ N.

First, the total biomass and NPP are evaluated against observations using extended data from Peregon et al. (2008). We further compare the simulated biomasses with two other Arctic transects. The first one is the North America Arctic Transect (NAAT). It is situated in a continental area, and includes eight field locations (70∘ N 149∘ W to 79∘ N 100∘ W) sampled from 2002 to 2006 (Walker et al., 2011b) chosen as representative of zonal conditions. The second, located in a marine-influenced area, is the Eurasian Arctic Transect (EAT). It includes six field locations (58 to 73∘ N, between 67 and 81∘ E) sampled from 2007 to 2010 (Walker et al., 2008, 2009a, b, 2011a). In order to evaluate the simulated LAI, we use the GLASS (Global Land Surface Satellite) LAI product (Liang et al., 2013; Xiao et al., 2014). This product has a temporal resolution of 8 days and is available from 1982 to 2012. Data used in this study cover the period from 2004 to 2013 and were derived from MODIS (moderate resolution imaging spectroradiometer) land surface reflectance (MOD09A1), at a resolution of 1 km. In order to compare this GLASS product with our 2∘ resolution simulations, an extrapolated map of the 1 km resolution to the 2∘ resolution was built and a mask was applied to remove 2∘ resolution grid cells with a land fraction below 0.7. Finally we analyse key variables (such as NPP, albedo, soil temperature, total evaporation) to provide further insight on the impacts on carbon, energy and water fluxes. The analysis is carried out on multiple spatial and temporal scales.

Following the optimisation protocol described in Sect. 2.6.1, we calibrated 12, 6 and 7 parameters for the NVPs, shrubs and cold climate grasses respectively (see list in Tables 2, 4, 5 and S2). The optimisation relied on observations of living biomass and NPP observations presented in Sect. 2.5.1.

To evaluate the modelled biomass in other Arctic sites (not used in the calibration step), including uplands and lowlands, Fig. 9 shows scatter plots of observed and simulated biomass along two transects: the NAAT (North America) and the EAT (Eurasia) Arctic Transect. The NVPs and shrub biomasses are relatively well reproduced by the model (i.e. within the error bars). For both PFTs, the standard deviation of the observations includes the 1:1 line, but the observed biomasses are on average higher than the simulated biomasses. Simulated shrub biomasses are biased low for the NAAT transect but not for the EAT transect.

In contrast, the mean value of observed biomass for boreal C3 grasses (Fig. 9c) is low compared to the simulated biomasses for both cases. For half of the sites the simulated low biomass is in accordance with the observations, but for the other half the values are much larger (> 300 gC m2 whereas the observation do not exceed 54 gC m2). Despite the optimisation with observations from western Siberia (Fig. 7; leading to a decrease of biomass compared to temperate C3 grasses) there is likely an overestimation of the biomass for boreal C3 grasses, probably associated with an overestimated productivity.

Overall, the main spatial patterns of LAI simulated with ORC16 match the patterns of the GLASS product well (Fig. 10) with (i) a latitudinal band with higher LAI around 60∘ N in Eurasia and below 60∘ N in northern America and (ii) lower LAI at low latitudes in central Siberia and in above 65∘ N in Siberia and North America. However, the model underestimates LAI in the central-west of Siberia. Comparison between GLASS product and the two model simulations (ORC16 and ORC13) indicates an overall improvement of the simulated LAI with the inclusion of the new boreal PFTs. A substantial decrease of LAI in northern Europe (from 55∘ N), northern-western Siberia (from 55∘ N and until 135∘ E) and northern America (from 50∘ N) is simulated in ORC16 compared to ORC13, which is in better accordance with GLASS product. This improvement with ORC16 is directly due to significantly lower LAI values in these regions (north of 55∘ N) compared to ORC13. North of 65∘ N in Asia and America, these lower values in ORC16 are attributed to the introduction of NVPs in replacement of C3 grasses (Sect. 2.5.2) with lower LAI (see Sect. 3.3). In addition, the introduction of cold climate C3 grasses and shrubs with lower maximum LAI (e.g. 2.5 for shrubs against around 4 for tree PFTs) also contributes. Elsewhere, ORC16 and ORC13 simulations present on average similar LAI anomalies compare to GLASS (mainly located in the south), except for Alaska and eastern Siberia where ORC16–GLASS anomalies are slightly more negative than with ORC13.

On average, a similar latitudinal gradient in terms of biomass (Fig. 11a) and productivity (Fig. 11b) for all PFTs is obtained with a maximum of biomass and productivity around 60∘ N. Further north and until 80∘ N, an important decrease of NPP and biomass can be observed, with an even steeper slope for shrubs. The shape of these latitudinal gradients is primarily controlled by the climate (Fig. S1 in the Supplement), in particular for precipitation and temperature gradients and with a strong influence of the topography.

On average, boreal C3 grasses have comparable living biomass but lower NPP than temperate C3 grasses in the southern latitudes where both PFTs are present. NVPs on the other hand always have a much lower productivity and living biomass than grasses (more than 50 % lower). Despite the NVP implementation being based on C3 grasses, we notice that the latitudinal gradients of both productivity and living biomass differ between these two PFTs, with smoother latitudinal variations for the NVPs than the ones for boreal C3 grasses, illustrating the importance of the added processes for the NVPs (resistance to extreme conditions, see Sects. 2.2.3 and 2.2.4). Similarly, shrubs systematically display a lower NPP (by a factor of 2) and much lower biomass (factor 20, see Fig. S3) than the corresponding boreal deciduous trees, although with similar latitudinal patterns. The reduced biomass accumulation for shrubs is controlled by the new allometry relations described in Sect. 2.3.1, a lower residence time (i.e. higher mortality) and a higher fraction of GPP lost as growth respiration (Sect. 2.3.5).

These lower biomass and NPP of the new boreal PFTs compared to the PFT from which they are derived reflect a globally lower value in simulation ORC16 than in ORC13 (without the new PFT). For example, the NPP is lower by 31 % north of 55∘ N.

On average, the simulated productivity increases for the three regions (Figs. 11d and S2) by around 27 % for boreal C3 20 grasses, 210 % for NVPs and 80 % for boreal shrubs (versus 35 % for trees, Fig S3) from 1950 to 2013. The simulated biomass increases (Figs. 11c, S2) by the same proportion as the NPP for cold climate grasses and NVPs (+23 and +200 %, respectively), while for shrubs the increase is stronger (+85 %). It is also of interest that the biomass increase for shrubs is much larger than for boreal broadleaf trees (+20 %, S3).

Globally, the increase of both NPP and biomass over the last 60 years is substantial for all PFTs, but largest for non-vascular plants and shrubs (see above), which are more sensitive to climate change and CO2 increase in the model. For shrubs, climate change at high northern latitudes has a direct impact on mortality in winter (Sect. 2.3.3); an increase of the minimum temperature implies a lower mortality. Importantly, we expect that the impact of climate change in the transient simulation would be small before 1950, because the model spin-up was done with climate forcing randomly taken from the period 1901–1950 (Sect. 2.6.2).

The mean seasonal cycle of NPP is slightly different for NVPs (Fig. S4), for which the NPP starts earlier in spring, followed by maximum reach earlier (in June). Considering that the impact of the global increase in temperature is large in spring and autumn, the NVPs can take better advantage of it. During these two periods, more than 20 % of the annual increase in NPP for NVPs occurs (Fig. 11), while there is almost no increase for other PFTs. The small NPP decrease over the summer (Fig. S4) is due to the impact of desiccation during summertime (due to an increase of the water stress, see Sect. 2.2.4) that decreases the maximum potential photosynthesis rate.