ORCHIDEE is a process-based ecosystem model developed for simulating carbon fluxes, and water and energy fluxes in ecosystems, from site level to global scale (Krinner et al., 2005; Ciais et al., 2005; Piao et al., 2007). ORCHIDEE-GM (Chang et al., 2013) is a version of ORCHIDEE that includes the grassland management module from PaSim (Riedo et al., 1998; Vuichard et al., 2007a, b; Graux et al., 2011), a grassland model for field-level to continental-scale applications. Accounting for the management practices such as mowing, livestock grazing and organic fertilizer application on a daily basis, ORCHIDEE-GM proved capable of simulating the dynamics of leaf area index, biomass, and C fluxes of managed grasslands. ORCHIDEE-GM version 1 was evaluated and some of its parameters calibrated, at 11 European grassland sites representative of a range of management practices, with eddy-covariance net ecosystem exchange and biomass measurements. The model successfully simulated the NBP of these managed grasslands (Chang et al., 2013). Chang et al. (2015b) then added a parameterization of adaptive management through which farmers react to a climate-driven change of previous-year productivity. Though a full N cycle is not included in ORCHIDEE-GM, the positive effect of nitrogen fertilizers on grass photosynthesis rates, and thus on subsequent ecosystem productivity and carbon storage, is parameterized with an empirical function calibrated from literature estimates (version 2.1; Chang et al., 2015b). ORCHIDEE-GM v2.1 was applied over Europe to calculate the spatial pattern, interannual variability (IAV), and the trends of potential productivity, i.e. the productivity that maximizes simulated livestock densities assuming an optimal management system in each grid cell (Chang et al., 2015b). This version was further used to simulate NBP and NBP trends over European grasslands during the last 5 decades at a spatial resolution of 25 km and a 30 min time step (Chang et al., 2015a).

ORCHIDEE-GM v1 and v2.1 were developed based on ORCHIDEE v1.9.6. To benefit from recent developments and bug corrections in the ORCHIDEE model, ORCHIDEE-GM is updated in this study with ORCHIDEE Trunk.rev2425 (available at https://forge.ipsl.jussieu.fr/orchidee/browser/trunk#ORCHIDEE). We further made the adjustment of its parameters for the C4 grassland biome (Sect. 2.2) and implemented a specific strategy for wild herbivores grazing (Sect. 2.3; also see Supplement Sect. S1). The updated model is referred to hereafter as ORCHIDEE-GM v3.1.

ORCHIDEE-GM was applied to simulate GHG budgets and ecosystem carbon stocks under climate, CO2, and management changes for Europe. However, an extension of model application to regions outside Europe requires first a calibration of key productivity-related parameters. Two sensitive parameters representing photosynthetic capacity (the maximum rate of Rubisco carboxylase activity at a reference temperature of 25 ∘C; Vcmax25) and the morphological plant traits (the maximum specific leaf area; SLAmax) were reported by Chang et al. (2015a) for simulating grassland NPP. The Vcmax25=55 µmol m-2 s-1 and SLAmax=0.048 m2 per g C in ORCHIDEE-GM were previously defined from observations and indirectly evaluated against eddy-flux tower measurements of GPP for temperate C3 grasslands in Europe (Chang et al., 2013, 2015b). The global TRY database gives SLA values for C4 grasses, of 0.0192 m2 g-1 dry matter (DM) (0.0403 m2 per g C with a mean leaf carbon content per DM of 47.61 %; Kattge et al., 2011). Thus, we have set the value of SLAmax=0.044 m2 per g C for C4 grasses in ORCHIDEE-GM to fit the mean value from the TRY estimate, as we did previously for C3 grasses (Chang et al., 2013). The parameter Vcmax25 cannot be directly measured, but it is usually derived from A/Ci curves in C3 or C4 photosynthesis models (C3: Farquhar et al., 1980; C4: Collatz et al., 1992), where A is the leaf-scale net CO2 assimilation rate and Ci the partial pressure of CO2 in leaf intercellular spaces. Several researches provide observation-based estimates of Vcmax25 (Feng and Dietze, 2013; Verheijen et al., 2013; range of 24–131 µmol m-2 s-1 for C3 grasses and of 15–46 µmol m-2 s-1 for C4 grasses). Based on these estimates, we keep the value of Vcmax25=55 µmol m-2 s-1 previously calibrated in Europe for all C3 grasses and set Vcmax25=25 µmol m-2 s-1 for C4 grasses. These values may reflect neither differences in nitrogen and phosphorus availability between locations nor adaptation or species changes within a C3 or C4 grassland, but they are within the range of observations made under different conditions and consistent with values used by other terrestrial ecosystem models (Table S1 in the Supplement). All other parameters of ORCHIDEE model are kept the same as in Trunk.rev2425. The parameter settings for grassland management module are in consistent with that in ORCHIDEE-GM v1 (Chang et al., 2013) and v2.1 (Chang et al., 2015a, b).

ORCHIDEE-GM v3.1 was run on a global grid over the globe using the 6-hourly CRU+NCEP reconstructed climate data at 0.5∘ × 0.5∘ spatial resolution for the period 1901–2012 (Viovy, 2013). The fields used as input of the model are temperature, precipitation, specific humidity, solar radiation, wind speed, pressure, and long-wave radiation. Other input data are (1) yearly domestic grazing-ruminant stocking density maps, (2) wild-herbivores population density maps, (3) N fertilizer application maps including manure-N and mineral-N fertilizers, and (4) atmospheric-N deposition maps. These input maps all cover the period from 1901 to 2012 and are briefly described below (also see Supplement Sects. S2–S5). Table 1 lists all variables shown in this section, including their abbreviations, units, related equations, and data sources.

Grazing-ruminant stocking density maps: spatial statistical information on grazing-ruminant stocking density is not available at global scale. In this study, we combined the domestic ruminant stocking density maps (Supplement Sect. S2) and historic land-cover change maps (Supplement Sect. S3) to construct gridded grazing-ruminant stocking density.

Assuming that all the ruminants in each grid cell were grazing on the grassland within the same grid, we defined the grazing-ruminant stocking density in grid cell k in year m (Dgrazing,m,k, livestock unit (LU) per ha of grassland area) as Dgrazing,m,k=Dm,kfgrass,m,k, where Dm,k is the total domestic ruminant stocking density (unit: LU per ha of land area; Supplement Sect. S2) and fgrass,m,k is the grassland fraction in grid cell k in year m from a set of historic land-cover-change maps (Supplement Sect. S3). To avoid unrealistic densities of ruminant grazing over grassland (which might cause grasses to die during the growing season), a maximum value of 5 LU ha-1 was set for the density map. In addition, a minimum grazing-ruminant density of 0.2 LU ha-1 was set to avoid economically implausible stocking rates. Figure S1 in the Supplement shows the example maps of domestic ruminant stocking density (D) and the corresponding grazing-ruminant stocking density (Dgrazing) for reference year 2006.

Wild herbivore density maps: gridded maps of wild herbivore density are not available; therefore the gridded population density of wild herbivores (Dwild; unit: LU per ha of grassland area) is derived from the literature data and from Bouwman et al. (1997) (see Table S2 for detail). The population of these herbivores from literature was first converted to LU according to the ME requirement calculated from their mean weight (Table S2) and then distributed to suitable grasslands based on grassland aboveground (consumable) NPP simulated from ORCHIDEE-GM v3.1 (Supplement Sect. S4; Fig. S2). The wild herbivores density was assumed to remain constant during the period of 1901–2012, because no worldwide historical wild-animal population information was available. A specific grazing strategy for wild herbivores is incorporated in the model (Supplement Sect. S1). We assumed wild herbivores eat fresh grass biomass during the growing season and eat dead grass during the non-growing season.

Nitrogen application rates from mineral fertilizers and manure: grassland is fertilized with organic N fertilizer (e.g. manure, slurry) and/or even mineral-N fertilizer, though this is not as common as for cropland. Gridded fertilizer application rates on grassland are not available worldwide. The only exception that we are aware of is for European grasslands (Leip et al., 2008, 2011, 2014; data available for EU-27 as used in Chang et al., 2015a). For countries/regions other than EU-27, the following data were used. The amount of manure-N fertilizer for 17 world regions at 1995 was derived from various sources (e.g. IFA, 1999; FAO/IFA/IFDC, 1999; FAO/IFA, 2001) and synthesized by Bouwman et al. (2002a, b; Table S3). For mineral-N fertilizers on grassland, country-scale data of fertilized area and mean fertilization rate for 1999/2000 are available in FAO/IFA/IFDC/IPI/PPI (2002) with grassland/pasture been fertilized in 13 non-EU countries. The regional/country-scale data were downscaled to a 0.5∘ × 0.5∘ grid and extended to cover the period 1901–2012 (see Supplement Sect. S5 for detail).

Atmospheric-nitrogen deposition maps: the historical atmospheric-N deposition maps were simulated by the LMDz-INCA-ORCHIDEE global chemistry–aerosol–climate model (Hauglustaine et al., 2014). Hindcast simulations for the years 1850, 1960, 1970, 1980, 1990, and 2000 have been performed using anthropogenic emissions from Lamarque et al. (2010). The total nitrogen deposition fields (wet and dry; NHx and NOy) of all nitrogen-containing gas-phase and aerosol species have been simulated at a spatial resolution of 1.9∘ in latitude and 3.75∘ in longitude. Linear interpolation was performed between the hindcast snapshot years to produce temporally variable atmospheric-N deposition maps (Ndeposition, unit: kg N per ha of grassland area per year).

Considering different photosynthetic pathways and management types, six grassland plant functional types (PFTs) are defined: C3 natural (unmanaged) grassland, C3 mown grassland, C3 grazed grassland, C4 natural (unmanaged) grassland, C4 mown grassland, and C4 grazed grassland. In the simulation, we ideally consider that grassland PFTs are distributed all over the world. Post-processing will incorporate the information of grassland distribution in the real world (Supplement Sect. S3). ORCHIDEE-GM v3.1 is run over the globe during the period 1901–2012, forced by increasing CO2, variable climate, and variable nitrogen deposition (Ndeposition). For each grassland PFT, specific forcing and management strategies are used (summarized in Fig. 1). Unmanaged grasslands are forced by wild herbivore density maps (Dwild). Both mown and grazed grasslands are forced by the historical N fertilizer maps described above, which include manure (Nmanure) and mineral fertilizers (Nmineral). Grazed grassland is additionally forced by the historical gridded grazing-ruminant stocking density (Dgrazing).

Figure 1 briefly illustrates the procedures of combining model output, grass-biomass-use data, and grassland area data to reconstruct grassland management intensity maps. This section presents the procedures of the reconstruction in detail. Table 1 lists all variables shown in this section, including their abbreviations, units, related equations, and data sources.

Herrero et al. (2013) established a global livestock production dataset containing a high-resolution (8 km × 8 km) gridded map of grass-biomass use for the year 2000. In this study, this dataset is extrapolated annually over 1901–2012 to constrain the grass-biomass consumption in ORCHIDEE-GM v3.1. Assuming that grass-biomass use for grid cell k in country j and year m (GBUm,j,k, unit: kg DM per year) varies proportionally with the total ME requirement of domestic ruminants in each country, GBUm,j,k can be calculated from its value of the year 2000 given by Herrero et al. (2013), according to GBUm,k=GBU2000,k×Dm,kD2000,k, where Dm.k and D2000,k are the total ruminant stocking density for grid cell k in year m and in year 2000 calculated by Eqs. (S4) and (S5) in Supplement Sect. S2, which take into account the changes in category-specific ME requirement at country scale (1961–2012) or regional scale (1901–1960).

ORCHIDEE-GM v3.1 simulates the annual potential (maximal) harvested biomass from mown grasslands (Ymown, unit: kg DM m-2 yr-1 from mown grassland) and the annual potential biomass consumption per unit area of grazed grassland (Ygrazed, unit: kg DM m-2yr-1 from grazed grassland) in each grid cell. Under mowing, the frequency and magnitude of forage harvests in each grid cell is a function of grown biomass (Vuichard et al., 2007a). The effective yield on grazed grassland (i.e. Ygrazed) depends on the grazing stocking rate (here, Dgrazing) and on the environmental conditions of the grid cell (Chang et al., 2015a); it is calculated as Ygrazed,m,k=IC×Tgrazing,m,k×Dgrazing,m,k, where IC is the daily intake capacity for 1 LU (∼ 18 kg DM per day calculated in Supplement Sect. S1 of Chang et al., 2015b), and Tgrazing,m,k is the number of grazing days in grid cell k at year m. Due to the impact of livestock on grass growth through trampling, defoliation (i.e. biomass intake), etc., and because grassland cannot be continuously grazed during the vegetation period, thresholds of shoot biomass are set for starting, stopping, and resuming grazing (Vuichard et al., 2007a). The “recovery” time required under grazing is obtained in the model using threshold (Vuichard et al., 2007a; Chang et al., 2015a), which determines when grazing stops (dry biomass remaining lower than 300 kg DM ha-1) or when grazing can start again (dry biomass recovered to a value above 300 kg DM ha-1 for at least 15 days). Ygrazed is usually lower than Ymown in temperate grasslands due to the lower herbage-use efficiency of grazing simulated by ORCHIDEE-GM (Chang et al., 2015b). However, in some arid regions the grass biomass does not grow enough during the season to trigger harvest; i.e. it does not reach the threshold in the model at which farmers are assumed to decide to cut grass for feeding forage to animals (see Chang et al., 2015b), so that Ygrazed can become larger than Ymown (Fig. S3). The following set of rules was used to reconstruct historical changes in grassland management intensity, based on NPP simulated by ORCHIDEE-GM v3.1.

Rule 1: for each grid cell and year, the total biomass removed by either grazing and cutting must be equal to the grass-biomass use, GBUm,k.

Thus, for grid cell k in year m, the minimum fraction of grazed (fgrazed,m,k), the minimum fraction of mown (fmown,m,k), and the maximum fraction of unmanaged grassland (funmanaged,m,k) are calculated with the following equations (definitions of minimum and maximum in this context are given below).

If Agrass,m,k×Ygrazed,m,k>GBUm,k, then fgrazed,m,k=GBUm,kAgrass,m,k×Ygrazed,m,kfmown,m,k=0funmanaged,m,k=1-fgrazed,m,k, where Agrass,m,k (unit: m2) is the grassland area for grid cell k in year m of the series of historic land-cover change maps (Supplement Sect. S3).

If Agrass,m,k×Ygrazed,m,k<GBUm,kandAgrass,m,k×Ymown,m,k>GBUm,k then fgrazed,m,k×Agrass,m,k×Ygrazed,m,k+fmown,m,k×Agrass,m,k×Ymown,m,k=GBUm,kfgrazed,m,k+fmown,m,k=1funmanaged,m,k=0. If GBUm,k cannot be fulfilled by any combination of modelled Ygrazed and Ymown, we diagnose a modelled grass-biomass production deficit and apply the following equations: ifYgrazed>Ymown,thenfgrazed,m,k=1,fmown,m,k=0,andfunmanaged,m,k=0,ifYgrazed<Ymown,thenfmown,m,k=1,fgrazed,m,k=0,andfunmanaged,m,k=0. This set of equations is valid for a mosaic of different types of grasslands in each grid cell, some managed (grazed and/or mown) and some remaining unmanaged. In reality, (1) farm owners could increase the mown fraction to produce more forage, which corresponds approximately to the mixed and landless systems of Bouwman et al. (2005); and (2) animals could migrate a long way across grazed and unmanaged fractions (as they do in real rangelands) and only select the most digestible grass in pastoral systems, which corresponds to extensively grazed grasslands. Yet, given the approximations made in this study, fgrazed,m,k and fmown,m,k represent the minimum fractions of grazed/mown grasslands rather than the actual fractions, and funmanaged,m,k corresponds to a maximum fraction of unmanaged grasslands since both mixed and landless and extensive grazing are not modelled.

Herbage-use efficiency (Hodgson, 1979) is defined as the forage removed expressed as a proportion of herbage growth. It can be an indicator of management intensity over managed grassland, in addition to the fraction of managed area obtained above. In this study, the forage removed is modelled annual grass-biomass use including Ygrazed and Ymown, and herbage growth is modelled annual grass GPP.

The gridded grassland management intensity maps are model dependent because they depend on modelled productivity. Thus the evaluation of modelled productivity becomes necessary. In this study, modelled productivity (NPP and GPP) is compared to a new set of site-level NPP measurements (Sect. 2.7.1) and two satellite-based models of GPP (MODIS-GPP, from the Moderate Resolution Imaging Spectroradiometer, Sect. 2.7.2; sun-induced chlorophyll fluorescence (SIF) data, Sect. 2.7.3). Modelled NPP (or GPP) combines grassland productivity of all PFTs (Sect. 2.4), accounting for the variable fractions of grazed, mown, and unmanaged grassland in each grid cell calculated by Eqs. (4–11), and hereafter is referred to as NPPmodel (or GPPmodel). Model–data agreement of NPP and GPP was assessed using Pearson's product-moment correlation coefficients (r) and root mean squared errors (RMSEs).

Figure 2 shows the minimum fractions of mown and grazed grasslands and the maximum fraction of unmanaged out of total grassland (fmown, fgrazed, and funmanaged respectively; Sect. 2.4) in the year 2000. Grazed grasslands comprise most of the managed grasslands in the maps (Fig. 2b). Significant fractions of mown grasslands are only found in regions with high ruminant stocking density such as eastern China, India, eastern and northern Europe, and eastern United States, where Ygrazed cannot fulfil the grass-biomass demand (Fig. 2a). Using the FAO-defined regions (see caption to Table 2), the largest fractions of managed grasslands are modelled in regions of high ruminant stocking density (Fig. S1) such as in eastern Europe with a mean fraction of 90±17 % (the mean is the average fraction of mown and grazed grasslands over all the grid cells in this region, and the standard deviation is taken from differences between grid cells), South Asia (59±46 %), and western Europe (55±36 %). The lowest managed grasslands fractions are modelled in the Russian Federation (17±34 %).

In some grid cells, the simulated grassland productivity is not sufficient to fulfil the grass-biomass use given by Herrero et al. (2013; Fig. 2d). Of the 2.4 billion tonnes of grass-biomass use (in dry matter for the reference year 2000) given by Herrero et al., 16 % cannot be fulfilled by the productivity simulated by ORCHIDEE-GM v3.1. This translates into a modelled grass-biomass production deficit of 0.38 billion tonnes (Table 2). Out of all regions, the largest modelled production deficit (fglobal  in Table 2) is found in South Asia (49 %). This South Asian deficit is predominantly in India (35 % of the modelled global total deficit) and Pakistan (10 % of the modelled global total deficit). Other regions with a biomass production deficit are the Near East and North Africa (18 %) and sub-Saharan Africa (13 %). Overall, 32 % of the global production deficit comes from regions with dry climate and low NPP (less than 50 g C m-2yr-1), and 34 % of it comes from regions with low grassland cover (less than 10 % of total land cover). The causes of this grass-biomass production deficit diagnosed by ORCHIDEE-GM are discussed in Sect. 4.2.

Modelled herbage-use efficiency over managed grassland during the 2000s (grazed plus mown; Fig. 3) ranges between 2 and 20 % in most regions and generally follows the spatial pattern of grazing-ruminant density (Fig. S1). High herbage-use efficiency (over 20 %) is found in regions with significant mown grassland (fmown) simulated due to the larger fraction of biomass removed over mown grassland than that over grazed grassland in the same grid cell (Fig. S3).

Figure 4 displays the NPP per unit area and the production (Prod = NPP × grassland area) of each type of grassland for 10 FAO-defined regions and the globe. Even when grassland management is included, the production of unmanaged grassland (Produnmanaged) still comprises 63 % of the total production (Prodtotal) in the 1990s. The production of grazed grasslands (Prodgrazed) accounts for 34 % of Prodtotal, while the production of mown grasslands (Prodmown) is only 3 %, given the small area under this management practice (Fig. 4). Mown grasslands only contribute to production in the regions where climate conditions and fertilizers maintain a high NPP, and Ygrazedis not enough to fulfil the animal requirement, which triggers the harvest practice in Eqs. (7–11).

Over unmanaged grassland (Fig. S2), ORCHIDEE-GM v3.1 simulated a total annual consumption by wild herbivores of 147–654 million tonnes DM of the 5778 million tonnes DM in aboveground NPP (consumable NPP) over suitable grassland (Table S5), which comprises 3–11 % of the consumable NPP, similar to the range given by Warneck (1988). The fraction of consumption in consumable NPP varied from 1 % in the former USSR to 9 % in Scandinavia, indicating the different significance of wild herbivores on grassland.

The global minimum area of managed grassland (Amanaged-gm) is of 6.1×106 km2 in 1901 and increased to 12.3 × 106 km2 in 2000 (Table 3; Fig. 5) – an increase of 102 % during the 20th century. This expansion of managed grasslands is mainly explained by the increase in the area of grazed lands (+5.7 × 106 km2), while mown grassland increased only marginally (+0.5×106 km2). The largest extension of Amanaged-gm is found in sub-Saharan Africa (+1.8 × 106 km2) and Latin America and the Caribbean (+1.7 × 106 km2; Fig. 5). The regions with the largest relative expansion of managed grasslands (as a percentage of 1901 areas) are sub-Saharan Africa (+219 %), East and Southeast Asia (+204 %), nd Latin America and the Caribbean (+175 %), and the regions where the number of domestic ruminants (Nruminant) increased by nearly or over a factor of 3. Only small increases of Amanaged-gm were modelled in western Europe (+41 × 103 km2; i.e. 8 %) and eastern Europe (+27 × 103 km2; i.e. 8 %), despite an increase of Nruminant by a factor of 1.5 in western Europe (+27×106 LU) and of 1.4 in eastern Europe (+5 × 106 LU). This means that livestock production intensified in those two regions, first by giving crop feedstock given to animals (Bouwman et al., 2005) and second through the optimization of forage harvesting and grazing to feed higher animal-stocking densities. Note that the animal density in eastern and western Europe peaked at 123 × 106 LU near 1990 and has declined by 29 % since then.

Besides the extension of managed grassland area, modelled herbage-use efficiency over managed grassland increased from 6.2 to 6.6 % during the 20th century, indicating the intensification of grassland management. Large increase in herbage-use efficiency is modelled in South Asia (+3.6 %) and eastern Europe (+2.7 %), while marginal decrease of herbage-use efficiency is found in the Near East and North Africa (-0.1 %) and Oceania (-0.2 %; Table 3).

The global mean potential productivity of mown grassland (Ymown) increased by 62 % from 0.29 kg DM m-2 yr-1 for 1900s to 0.48 kg DM m-2 yr-1 for the 1990s, while that of grazed grassland Ygrazed increased by 40 %, from 0.10 kg DM m-2 yr-1 for the 1900s to 0.14 kg DM m-2 yr-1 for the 1990s (Table 3). During the last century, Ymown increased by more than 40 % in most regions except in Latin America and the Caribbean (14 %), while the increase of Ygrazed ranged from 25 % in sub-Saharan Africa and 80 % in eastern Europe (Table 3).

Figure 6 shows the grassland productivity (NPPmodel; Fig. 6a) and the NPP differences between NPPmodel and NPP from unmanaged grassland (Fig. 6b). The effect of including management does not produce a big difference in simulated NPP, which has similar patterns in most regions (Fig. 6b). Nevertheless, there are significant differences of NPP due to management in the central United States, Europe, northeastern India, southern China, South Korea, Japan, and southern Brazil where N fertilizer additions (Tables S3 and S4) cause a higher productivity (Fig. 6b).

The area of managed grasslands obtained in this study is lower than the pasture area of HYDE 3.1 (Apasture-hyde, Klein Goldewijk et al., 2011; Table 3), except in eastern Europe for the year 2000. Apasture-hyde is 3.2 times larger than the minimum area of managed grasslands (mown plus grazed grasslands; hereafter referred to as Amanaged-gm) in the year 1901 and 2.7 times larger in the year 2000. The difference comes from the method used for estimating managed areas between Klein Goldewijk et al. (2011) and this study. Apasture-hyde in Klein Goldewijk et al. (2011) was estimated simply from population density and the country-level-per-capita use of pasture derived from the FAO statistics (FAOSTAT, 2008). In this study, Amanaged-gm is constrained by grass-biomass-use data (i.e. requirement of biomass for animals) and the simulated grassland productivity (i.e. supply of biomass to animals). In fact, the actual (real-world) managed grassland area could be larger than Amanaged-gm in regions where grasslands are not strictly unmanaged, i.e. not fully occupied by Amanaged-gm in the management intensity maps (i.e. funmanaged>0; Fig. 2c). In pastoral systems such as open rangeland and mountain areas, animals keep moving to search for the most digestible grass. Tracts of grasslands can be grazed for a short period, with only a small part of the annual grass productivity being digested (i.e. very low herbage-use efficiency). This type of grassland could be recognized as extensively grazed grassland, whereas it is considered as unmanaged in this study. For example, lower herbage-use efficiency than that simulated in this study (Fig. 3) could be expected in open rangeland of central Asia, the Russia federation, sub-Saharan Africa, Brazil, and Australia and in the mountains of southwestern China and the European Alps. Reclassifying these areas would result in a larger area of extensively managed grassland. Few studies reported the herbage-use efficiency of managed grassland. One exception is the network of European eddy-covariance flux sites. For these sites the average herbage-use efficiency (expressed as forage defoliated as a proportion of GPP) is 7.1%±6.1% for grazed sites, and 13.3%±6.4 % for mown sites (J.-F. Soussana, personal communication, 2015); a similar range, between 2 and 20 %, is simulated in this study (Fig. 3).

The time evolution of Amanaged-gm since 1901 in this study is arguably more realistic than HYDE because it considers changes in animal stocking density from statistics and the evolution in per-head use of pasture. Amanaged-gm takes into account (1) changes in grass-biomass requirement, considering both ruminant numbers and meat/milk productivity (Supplement Sect. S2; Nruminant in Table 3); (2) changes in grassland productivity driven by climate change, rising CO2 concentration, and changes in N fertilization (Ymown and Ygrazed in Table 3); and (3) changes in management types (mown and grazed grassland areas in Table 3 and Fig. 5). For example in intensively managed grasslands, an increase in ruminant stocking density causes a shift from grazed to mown grassland (globally and regionally, except in western Europe; Table 3 and Fig. 5), because mown grassland provides more grass biomass than grazed grassland per unit of area (Fig. S3).

Apasture-hyde is consistent with country-specific pasture area censuses and thus may be suitable for reconstructing land cover, but it does not provide information about management intensity. Amanaged-gm and its split between mown, grazed, and unmanaged fractions provide specific global distributions of pasture management intensity and its historical changes. However, there are several limitations, which may cause uncertainties in our maps of management intensity: (1) the grass fraction in ruminant diet has likely been changing during the last century while, due to a lack of information, we assumed that it was static in each region up to the year 2000; (2) technical developments (such as ruminant breeding) are not considered but may affect the feeding efficiency (meat/milk production per amount of feed) and thus feedback on the grass-biomass requirement; (3) the spatial distribution of ruminants was kept constant in our estimate, whereas it could have changed, depending on geographic changes in human population distribution; and (4) the results depend on the accuracy of NPP modelling in ORCHIDEE-GM. Despite these limitations, the maps of grassland management intensity provide new information for drawing up global estimates of management impact on biomass production and yields (Campioli et al., 2015) and for global vegetation models like ORCHIDEE-GM to enable simulations of carbon stocks and GHG budgets beyond simple tuning of grassland productivities (e.g. like in LPJmL; Bondeau et al., 2007) to account for management. These maps can also be tested in other vegetation models, or the same algorithm can be implemented in other models to give the management intensity consistent with simulated NPP.

Grass-biomass production is constrained by the gridded biomass consumption for the year 2000 (Herrero et al., 2013). In some grid cells, the gridded biomass consumption by year 2000 cannot be fulfilled by the potential grass production simulated by ORCHIDEE-GM v3.1 (Fig. 2d). These modelled grass-biomass production deficits could be due to several reasons.

Land-cover maps used as input to ORCHIDEE-GM v3.1 do not represent grasslands well in the mixed and landless systems and grasslands providing occasional feed to ruminant (e.g. roadside, forest understory grazing land, and small patches). This failing could cause the model to miss a significant part of grass productivity in this study. For example, the largest modelled grass-biomass production deficit is found in India because the simulated grassland productivity is far from agreeing with the grass-biomass-use data. In this country, occasional feed may constitute an important fraction of ruminant diet (30 or 50 % in mixed and landless or pastoral systems of South Asia from Bouwman et al., 2005), which is not represented by the land-cover maps used as input to ORCHIDEE-GM v3.1 and thus is not modelled.

In Sect. 3.3, the spatial patterns of NPPmodel or GPPmodel were compared with observations (NPPobs or MODIS-GPP). ORCHIDEE-GM v3.1 captured well the spatial pattern of grassland productivity, with (i) high rspatial between GPPmodel and MODIS-GPP (Sect. 3.3.2) and (ii) NPPmodel extracted from global simulation showing significant correlation with site-level NPP observation from 129 sites all over the world (Sect. 3.3.1). However, GPPmodel is higher than MODIS-GPP in all latitude bands (Fig. 8). It should be kept in mind that MODIS-GPP had a calculated 18 % uncertainty due to climate forcing (Zhao et al., 2006). Besides, a low bias of MODIS-GPP for grasslands has been reported in a tallgrass prairie in the United States (Turner et al., 2006) and in an alpine meadow on the Tibetan Plateau (Zhang et al., 2008) when compared to the GPP from flux-tower measurements. The underestimate of MODIS-GPP is mostly related to the low value of the maximum light-use efficiency parameters used in the MODIS-GPP algorithm (Turner et al., 2006; Zhang et al., 2008).

The relatively low r value between NPPmodel and site-level NPPobs (r=0.35, p<0.01; Sect. 3.3.1) could be related to the fact that local climate, soil properties, and topographic features are not considered in the model. For example, the r between the site-level climate and that from the CRU+NCEP climate forcing data (0.5∘ × 0.5∘ resolution) is 0.96 for annual mean temperature but only 0.86 for annual total precipitation and 0.86 for solar radiation. The relatively low correlation for annual total precipitation may cause inaccuracy in the model simulations of productivity, because water availability could be a major factor limiting grass growth (e.g. in temperate regions; Le Houerou et al., 1988; Silvertown et al., 1994; Briggs and Knapp 1995; Knapp et al., 2001; Nippert et al., 2006; Harpole et al., 2007). Further, a similar mean belowground NPP and an overestimation of mean aboveground NPP by ORCHIDEE-GM v3.1 is found in Sect. 3.3.1, which suggests that (1) the model tends to overestimate aboveground NPP possibly due to overestimation of GPP (compared to MODIS-GPP) and (2) the model tends to overestimate the ratio of aboveground and belowground biomass allocation (Rabove/below) compared to observation. This overestimation could be the result of nitrogen limitation on the carbon allocation scheme for grassland. For example, a large nitrogen supply has been observed to increase Rabove/below (Aerts et al., 1991; Cotrufo and Gorissen, 1997), while nitrogen limitation might cause it to decrease. However, nitrogen limitation in grassland is not accounted for in ORCHIDEE-GM v3.1, which possibly leads to the model's overestimation of Rabove/below. The model could be improved by incorporating the full nitrogen cycle.

For the seasonal cycle, we compared modelled GPP seasonality to both MODIS-GPP and GOME-2 SIF data. ORCHIDEE-GM v3.1 captures the seasonal variation of productivity in most regions where grassland is the dominant ecosystem (coverage > 50 %), as shown by the high rseasonal between GPPmodel and MODIS-GPP (Fig. S6a) or SIF data (Fig. S6b). However, the model does not capture the seasonal amplitude of grassland productivity in some arid/semi-arid regions (e.g. southwestern United States and central Australia; Fig. S6a and b). In arid/semi-arid regions, grass productivity is triggered by discrete precipitation events and depends on the timing and magnitude of these pulses (Sala et al., 1982; Schwinning and Sala, 2004; Huxman et al., 2004). These precipitation pulses are infrequent, discrete, and not represented in a global climate re-analysis dataset such as CRU+NCEP used in our simulation. In particular, NCEP, like all climate models tends to produce “general circulation model drizzle” (Berg et al., 2010), i.e. too many frequent small rainfall events. This forcing uncertainty could be a major obstacle for our model to capture the seasonality of productivity in these regions. In dry grasslands, the dominant species could change during the season, but the resultant changes in SLA and Vcmax25 by different dominant species cannot be reflected in ORCHIDEE-GM v3.1. This within-season variability could be another reason for the model–data discrepancy in arid/semi-arid grassland seasonality. For the savanna of sub-Saharan Africa, eastern Africa, and South America (Fig. S6), the relatively low rseasonal could be a result of the fact that the frequent fires are not simulated in the current version of the model used here.

ORCHIDEE-GM v3.1 captures the IAV of grassland GPP at global scale and in many regions of the world (40 % of global grassland area) compared to the MODIS-GPP. One exception where IAV is not in phase with MODIS-GPP is sub-Saharan Africa (Fig. 9). Possible causes of this discrepancy are (1) the frequent fires which affect the IAV of GPP, which are not simulated in this study; (2) model biases in the IAV of soil moisture, which could affect the model performances for the productivity of semi-arid Africa, given its two-layer bucket hydrology; (3) the problems with MODIS-GPP dry areas, which may degrade the model–data agreement. The cold Qinghai–Tibet plateau and boreal tundra are the other regions where the model does not capture the GPP IAV (Fig. 9). The low model–data agreement in IAV could be due to shortcomings in (1) the specific characteristics, functioning traits, and nutrient availability of the tundra/alpine-grassland ecosystem that are not well parameterized or accounted for in our model (e.g. Tan et al., 2010, for Qinghai–Tibet plateau) and (2) the snow scheme. The timing of snowmelt will impact the grass phenology, while early spring soil moisture impacted by snow water storage may affect the grassland productivity. The single-bucket snowpack scheme (Chalita and Le Treut, 1994) in the current version of ORCHIDEE-GM may not represent the snow processes sufficiently accurately. The mechanistic intermediate-complexity snow scheme (ISBA-ES; Boone and Etchevers, 2001) implemented into ORCHIDEE-ES (Wang et al., 2013) may improve the model performance in simulating grassland productivity.