The PFT cover fractions simulated by the individual dynamic vegetation models are converted into nine different mega-biomes (Fig. 1), using few bioclimatic limits and assumptions on the maximum required coverage of certain PFTs. The aggregation into the mega-biomes is in line with the definitions of the BIOME6000 project (cf. Harrison, 2017) that are also commonly used for grouping pollen-based biome reconstructions. Bioclimatic limits and the differentiation rules basically follow the biome assignment of the BIOME4 model (Kaplan et al., 2003). As input data, only climatological mean growing degree days (GDD0 and GDD5), monthly mean 2 m air temperature and multi-year mean PFT cover fractions (e.g. averaged over 100 years) are required. The limitation to few climatic rules and few variables needed enables the application of the method to all state-of-the-art dynamic vegetation models.

In detail, the PFTs calculated by the respective dynamic vegetation models are aggregated into the groups “trees”, “woody PFTs” (i.e. shrubs and all tree PFTs), “grass” and “desert”, which is calculated as 1 minus the total vegetation. If the model includes land-use types, the affected areas are redistributed to the other PFTs by simply scaling up the other PFT fractions proportionally to their ratio of the total natural vegetation. Based on these groups, regions dominated by trees and regions in which the cover fraction of the woody PFTs exceeds 25 % (with the additional constraint of the total vegetation cover exceeding 50 %) are identified, as these are necessary conditions for the assignment of the land cover to forest biomes. Afterwards, the groups “trees” and “woody PFTs” are split into boreal (GDD5 ≤ 900 ∘C), temperate (GDD5 > 900 ∘C) and tropical trees or woody PFTs (Tc > 15.5 ∘C) via temperature limits (cf. Table 2). If any of these tree PFTs are simulated directly in the vegetation model (e.g. in LPJ or ORCHIDEE), the original distributions are taken and the PFT group is assigned to the dominant tree type, i.e. the tree type that covers the largest fraction of the grid cell. These PFT groups (i.e. boreal woody PFTs, temperate trees and woody PFTs, tropical trees, grass and desert) are the first consistent vegetation classification shared by all input simulations, so that model-to-model comparison is also possible on this PFT level.

For the biomisation, the forests are considered first; i.e. regions in which trees or woody PFTs are dominant or cover an area more than 25 % are assigned to tropical, temperate and boreal forests according to the PFT groups. From the temperate forest, warm regions (i.e. GDD5 > 3000 ∘C) revealing a dominant temperate tree fraction are subtracted and assigned to the biome “warm–temperate forest”. The remaining area is then tested for fulfilling the constraints for the non-forest biomes. First, the savanna and dry woodland region is identified by bioclimatic limitations (GDD5 > 1200 and Tc > 10 ∘C) and a woody PFT coverage of at least 25 %. The remaining vegetated area is assigned to the biome “grassland and dry shrublands”, if GDD0 exceeds 800 ∘C, or to the biome “tundra”, if GDD0 is below 800 ∘C (cf. BIOME4; Kaplan et al., 2003). The non-vegetated area, i.e. regions in which the total vegetation cover is less than 20 %, is either assigned to warm or to cold desert, depending on whether the annual mean temperature is above or below 2 ∘C. For the biome “tundra”, only 10 % vegetation cover is needed. A flow chart summarising the details of the PFT-based biomisation is shown for the VECODE model in Appendix A.

We are aware of the simplicity of this approach, calculating the tundra and the grassland and dry shrubland biomes as a residual of the non-forested area, not directly depending on the simulated grass PFT fraction. We decided to attribute the main priority to the forested biomes as this is also the strategy commonly used in DGVMs and biome models.

To assess the performance of the biomisation based on simulated PFTs, we additionally biomise the simulated climate fields corresponding to the PFT distributions in each model. This is the conventionally used procedure to biomise general circulation model (GCM) or ESM output (further referred to as the classical approach or climate-based method). For this purpose, we use the biome model BIOME1 (Prentice et al., 1992) that calculates the biome distribution in equilibrium to the input climate. As forcing, BIOME1 needs the monthly mean climatological precipitation, near-surface temperature and cloudiness, which were taken from each simulation considered in this study, respectively. This classical biomisation approach can only handle climate data as input; the simulated PFT distributions from the ESMs used in the here-introduced PFT-based method are ignored. The original biomes have been grouped into the same mega-biome classification that is used for the PFT-based approach.

Simulations from nearly all state-of-the-art global dynamic vegetation models that are included in Earth system models have been selected for biomisation. Six different models could be considered (i.e. JSBACH, TRIFFID, ORCHIDEE, SEIB, LPJ and VECODE). Overall, eight simulations for the pre-industrial climate (PI) and vegetation, four for mid-Holocene (6 ka) conditions and five for Last Glacial Maximum (LGM) conditions have been used (Table 3). Most of these simulations were performed within CMIP5/PMIP3 under strict simulation and output protocols enabling direct comparison between the models (Braconnot et al., 2011; Taylor et al., 2012). These include the models MPI-ESM-P, IPSL-CM5A-LR, MIROC-ESM and HadGem2-ESM. Further details on the models and simulations are described in Appendix B.

For the pre-industrial time slice, two out of eight simulations (MPI-ESM-T63 and IPSL-ESM-T31) were performed with fixed vegetation distribution, but this has essentially no effect on the biomisation procedure. Therefore, we include these simulations in our analysis. Nevertheless, the PFT-based biome distributions for these simulations are expected to fit better to the references than the other simulations that ran with interactive vegetation.

We emphasise that this study is thought of as an introduction and detailed evaluation of a new biomisation method. It is not seen as evaluation of the different vegetation models with respect to the skill of simulating biome or vegetation distributions. For this purpose, the different vegetation models would have to be forced by the same climate state. Such an ensemble including all DGVMs (used here) does not exist. Therefore, we had to take individual simulations that all deviate with respect to the prescribed or simulated climate in the coupled models. These differences in the climatic field among the models and between the models and observations (general climate biases) lead – per se – to differences in the simulated vegetation distributions and biases to the reference vegetation distribution.

As reference, we use the estimated global potential natural vegetation map by Ramankutty and Foley (1999, referred to as RF99 in the following), which is a combination of modern satellite-based vegetation observations (i.e. the DISCover land cover dataset) and the vegetation compilation prepared by Haxeltine and Prentice (1996) that has been taken for regions dominated by land use at present day. The RF99 dataset is available at 5 min resolution and distinguishes 15 different biome types that are similar to the mega-biome classification used here. Thus, most biomes could directly be assigned to the mega-biome types (Table C1 in Appendix C). The preparation of the RF99 reference dataset is explained in more detail in Appendix C.

As further reference data, we use pollen-based biome reconstructions that are available for the modern, mid-Holocene and Last Glacial Maximum time slices within the Biome6000 database (Harrison, 2017). The biome reconstructions have been grouped into the mega-biomes according to the suggestions made by the Biome6000 project.

Both vegetation datasets are derived for the modern time slice not exactly corresponding to the pre-industrial period (around 1850 AD) simulated in the models. While the ice sheet, the topography and the orbital conditions used for the pre-industrial control simulations are prescribed from modern conditions, greenhouse gases are set to pre-industrial values in the models. These differences in, e.g. atmospheric CO2 concentration between the reference datasets and the simulations may lead to small discrepancies in the model. In addition, the references may be disturbed by anthropogenic influences.

Climatological monthly mean data of the years 1901–1930 from the University of East Anglia Climate Research Unit Time Series 4.00 (CRU TS4, University of East Anglia, 2017) have been taken as the pre-industrial reference climate. This is the earliest period available. The CRU TS4 reference climate has additionally been used as forcing for the BIOME1 model to provide a best guess for the pre-industrial biome map. We assume that neither the biomisation of simulated climate states (i.e. the classical method) nor the biomisation of simulated PFTs can agree better with any reference than this biome distribution, derived with a highly tuned biome model and the best global climate observation available. Therefore, we use the level of agreement between the CRU TS4 biome map and the RF99 or the Biome6000 reconstructions as target value for our new biomisation method. The reference biome distributions and the CRU TS4-based biome map are displayed in Fig. 2.

For the pre-industrial time slice, the PFT coverage of eight different Earth system model simulations has been converted into mega-biome distributions (Fig. 3). Additionally, the underlying pre-industrial climate states are used as forcing for the BIOME1 model (i.e. the classical way of biomisation) to calculate the mega-biome distributions in equilibrium with the simulated climate states (Fig. 4). Overall, the PFT-based biome maps look similar to the climate-based ones. All major biome belts can be reproduced using the new method, independent of the resolution or the complexity of the vegetation models. The biomisation based on the PFT coverage generally assigns more grid cells to forest or woody biomes (e.g. savanna instead of grassland or desert) than the classical method. This is most noticeable in South America, where the area covered by tropical forests is strongly increased in the PFT-based biome distribution (Table D1), being more in line with observations. Likewise, the savanna and/or forest biomes are more spread out on the African continent for nearly all biomisations with the exception of the CLIMate-BiosphERe 2 (CLIMBER-2) model and IPSL-ESM-T63.

The Asian forest regions are slightly larger in most PFT-based biome distributions compared to the climate-based ones. This impression is reinforced by the fact that for CLIM-LPJ and IPSL-ESM-T63 the PFT method suggests a pronounced boreal forest belt in northern Asia, not only reducing the size of the grassland but also that of the temperate forest area.

For North America, the PFT-based approach yields less forest for MPI-ESM-T63 and IPSL-ESM-T31 than shown by the climate-based biomisation. As a consequence, the North American prairie fits better to observations for the PFT-based biome distributions. In Alaska and north-western Canada, parts of the tundra regions suggested by BIOME1 tend to be replaced by boreal forest when using the new approach, which is generally more consistent with the observed vegetation.

The differences between the PFT-based and climate-based biome distributions can be caused by deficiencies in the biomisation methods, biases related to the imperfect vegetation models or biases in the simulated climate. While the effect of shortcomings in the vegetation models cannot be disentangled, the caveats of the PFT-based method and the effect of climate biases on the PFT-to-biome conversion are further discussed in Sect. 4.

To quantify the skill of the new method to represent the global biome distribution, we compare the resulting biome maps with the modern potential natural vegetation cover estimated by Ramankutty and Foley (1999, RF99 in the following) and the pre-industrial biome reconstructions provided by the Biome6000 project (Harrison, 2017). As target for the skill, the level of agreement between the BIOME1 derived biome distribution of the observed climate (CRU TS4, 1901–1930; cf. Fig. 2) and the reference datasets is taken, i.e. κ of 0.68 and FSS of 0.13 (Fig. 5) with respect to RF99 and a κ of 0.46 and BNS of 0.73 with respect to the biome reconstructions.

The PFT-based biome distributions agree well with the references, independent of the model. The kappa statistic shows an overall agreement to RF99 between 0.54 (for MIROC-ESM) and 0.79 (for MPI-ESM-T63) revealing a good to very good agreement (Fig. 5). Likewise, all models reach in total the level of good skill in the FSS metric (0.01–0.27). This agreement is in line with or even better than the match between RF99 and the climate-based biomisation and that between RF99 and the CRU TS4 biomisation that is taken as the target skill (Fig. 5). However, the spread between the individual models is larger for the PFT-based method than for the classical approach.

As expected, the kappa statistic indicates that the PFT-based biome maps compare worse with the reconstructions than with RF99, underestimating the similarity to the point reconstructions. κ ranges from 0.2 (poor) to 0.49 (fair), which is in line with the target skill and the metrics for the climate-based biome maps. The BNS, additionally considering accordance in the neighbouring grid cells of the record sites, reveals a good to very good agreement of the PFT-based biome distributions and the records (between 0.40 and 0.74), not much lower than the target skill and in accordance with the climate-based biomisations. For the MPI-ESM, IPSL-ESM-T31, HadGEM2-ESM and CLIMBER biomisations, the PFT-based method even produces biome distributions that fit better to the biome reconstructions than the climate-based biome maps.

Despite the overall agreement between the PFT-based biome distributions and the references, a closer look at the representation of individual mega-biomes in the converted maps indicates large differences among the models as well as among the individual mega-biomes (Fig. 6). While tropical forests and deserts compare best with RF99, the biome “warm–temperate forest” is not reproduced, independent of the underlying model simulation.

The skill for simulating the other biomes is very different for the diverse models. κ spreads from poor for one model to very good for other models. Correcting the PFT distribution in land-use areas by redistributing the area fraction to the other tiles has no impact on the performance of the method. The biome maps based on simulations applying land use do not compare worse with RF99 than the maps of other simulations. Likewise, the complexity of the vegetation model and the number of distinguished PFTs have no significant effect on the representation of the biome distribution, indicating that the climate limits used in the biomisation procedure are appropriate for the assignment of the PFTs to the distinct PFT groups. The differentiation of the PFT types (e.g. the different forest types) in vegetation models is often based on similar climate limits, regardless of whether the model is a complex dynamic vegetation model or a simple biome model. With the exception of the PFT-based biomisation for CLIMBER, in which the coarse grid is clearly disadvantageous for capturing the reconstructed desert belts and the rather regionally confined biomes (savanna, warm–temperate forest), the spatial resolution of the models is not the primary factor for the spread in the metrics. The PFT-based method performs equally well for simulations using T63 as for simulations using T31 (in total); only the regionally distributed warm–temperate forest is better represented in finer resolutions.

In general, the skill in representing the individual mega-biomes is similar for the PFT- and climate-based methods. Both approaches have the same strengths and weaknesses, but the spread between the models is larger for the PFT-based biomisations. In comparison to the climate-based method, the tropical, the warm–temperate and the boreal forest biomes tend to be slightly better represented by the PFT-based method. In contrast, the temperate forest, savanna and grassland distribution – averaged over all models – fit better to RF99 when using the climate-based approach, although for individual simulations, κ derived for the PFT biomisation exceeds the climate-based one. The savanna and grassland biomes are particularly misrepresented in the biome maps that are based on the PFT distributions simulated by MIROC-ESM, CLIMBER, CLIM-LPJ and HadGEM2-ESM. The temperate forest is poorly reproduced only in the PFT-based biomisation of CLIM-LPJ. Overall, the metrics indicate that the PFT-based method works as well as the classical approach of biomising climate states via the BIOME1 model. Likewise, the method is able to keep up with the method by Prentice et al. (2011), further discussed in Appendix E.

The sensitivity of the PFT-based method to changes in the vegetation cover is assessed by evaluating palaeo-biome distributions. For the mid-Holocene time slice, four different simulations have been analysed. The main vegetation changes described by biome reconstructions are the northern shift of the Northern Hemisphere forest belts, in particular a northward displacement of the taiga–tundra boundary, and the decrease of the desert areas compared to pre-industrial time slice. According to the BIOME6000 records, grassy vegetation reached at least up to 26∘ N at 6 ka, far into the modern central Sahara (Fig. 7). For none of the models is this biome shift reproduced, neither in the PFT-based (Fig. 7) nor in the climate-based biome distributions (not shown). The mean Sahara desert border shifts northward by one to two grid cells in the biomisations (i.e. approximately 1.875 to 3.75∘, Table 4). This shift collocates with substantial reductions in the desert fractions simulated by the individual ESMs (Fig. 8). Only in MPI-ESM-T63 is vegetation increased in the entire western and central Sahara, but this increase is lower than 20 %, not leading to a change in the biome assignment from desert to grassland. As the climate-based biomisations performed with BIOME1 reveal a reduction of the Sahara desert area in the same magnitude as the PFT-based ones, we conclude that the new biomisation method shows a reasonable sensitivity to the simulated changes in the desert fractions.

For all models with the exception of MIROC-ESM, the PFT-based biomisation reproduces an increased forest biome fraction in Eurasia north of 60∘ N during the mid-Holocene compared to pre-industrial time slice, in line with the biome reconstructions (Table 5). However, the magnitude of the change differs between the models, ranging from 0 % within MIROC-ESM to 12 % within CLIM-LPJ. For nearly all models (except for MIROC-ESM), the expansion of the forested area in the high northern latitudes seen in the PFT biomisation is of similar magnitude to that in the climate-based biomisation, confirming that the method covers past vegetation changes with reasonable sensitivity.

Overall, the biome distributions for the mid-Holocene compare equally well to the reconstruction as they do for the pre-industrial time slice (Fig. 9). Although κ is similarly low, ranging from 0.17 for the CLIM-LPJ biomisation to 0.38 for the MPI-ESM-T63 biomisation (poor agreement), the spread in the models and the differences in κ between the PFT-based biomisations and the climate-based biomisations is nearly identical to the results for the pre-industrial biome distributions. In line with the results for PI, the BNS indicates a good to very good agreement to the biome reconstructions (ranging from 0.44 for MIROC-ESM to 0.72 for MPI-ESM-T63). The skill to capture the reconstructed individual mega-biomes strongly depends on the number of available pollen records; thus, temperate and boreal forests are represented best (Fig. 7), while the simulated savanna regions are not supported by the biome reconstructions.

For the Last Glacial Maximum time slice, five different simulations have been analysed. According to BIOME6000, the main reconstructed vegetation differences at LGM compared to PI are a strong equatorward retreat of the forest biomes and an expansion of tundra and steppe regions. The northernmost record indicating boreal forest during LGM is located at approximately 51∘ N in Asia (Fig. 10). The PFT biomisations mostly reproduce this reduction and the shift in Northern Hemisphere forest biomes (Fig. 10), though the extent of the shift is underestimated. Forest reaches up to 50∘ N (for CLIMBER) to 65∘ N (for MPI-ESM-T63). The boreal forest position in the MIROC-ESM biomisation is not much changed compared to PI, but the boreal forest nearly replaces the temperate forest biome.

The overall agreement of the PFT-based biome distributions with the biome reconstructions is rather fair but in line with the results for the climate-based biome distributions. κ ranges from 0.07 for MPI-ESM-T31 to 0.23 for CLIMBER, only indicating a poor similarity of the biome maps and records (Fig. 11). The BNS ranges from 0.24 (for MIROC-ESM) to 0.57 (for MPI-ESM-T63) revealing a fair to good agreement. The values for both metrics are in the same magnitude as for the climate-based biomisations. Similar to the PI time slice, neither the complexity nor the spatial resolution is the main reason for the differences between the PFT biomisations. The spread in the skill of representing the individual biomes is large, and no systematic bias for one model can be found. With the exception of the biomisation for CLIMBER, the savanna biome is misrepresented in all biomisations, independent of whether the PFT-based or the climate-based method was used. Within the model ensemble, tropical and temperate forest can be reproduced best.

Even if the biomisation is restricted to mega-biome level, no clear definitions exist to distinguish biomes in terms of plant functional type compositions. While the bioclimatic limits used in the biome models are based on empirical analysis, no equivalent classification regulates the biomisation of PFTs. We particularly face this problem in finding a meaningful threshold of maximum tree cover needed for defining forests. When is an accumulation of trees identified as forest? As models tend to underestimate the forest coverage and forest extent in the high northern latitudes (cf. Loranty et al., 2013), we choose the assumption of tree cover being just dominant in forested grid cells, although this limit is very low. We test other limits (e.g. absolute dominance, i.e. fractional coverage exceeding 50 %), but these work worse for most simulations used in this study as well as for other simulations.

The mega-biome “warm–temperate forest” (e.g. subtropical forest) includes PFTs that can be assigned to several biomes and is rather defined by a coexistence of certain PFTs. For instance, in the BIOME4 model, it is not only defined by the dominance of temperate evergreen broadleaved trees but can also be defined by a dominance of cool conifers (with a sub-PFT of temperate evergreen broadleaved trees). The cool conifers – in turn – are also part of temperate forest biomes. Given the limited number of PFTs in the DGVMs, the confinement of biomes via PFT mixtures is not possible. As biome models such as BIOME4 generally manage to simulate warm–temperate forests at the correct locations, we adopt the bioclimatic limits from BIOME4 (limit for temperate evergreen broadleaved trees) for defining this mega-biome. Nevertheless, the calculated warm–temperate forest distribution strongly disagrees with the reference datasets. The reconstructed biome “warm–temperate forest” shares some subtropical PFTs with the tropical evergreen forest (Ni et al., 2010). These biomes are quite different in key species, but not on genus or family level, on which the pollen identification in the reconstructions is performed. Thus, these biomes tend to overlap in some regions and are sometimes mixed up in reconstructions (Chen et al., 2010). In addition, this mega-biome includes the warm–temperate rainforest and the wet sclerophyll forest and woodland in the BIOME6000 reconstructions (cf. Harrison, 2017), which may not be able to be identified with our biomisation method. Regarding the modern reference of RF99, we decided to assign the biome “temperate needleleaf evergreen forest and woodland” of the RF99 dataset to the mega-biome “temperate forest”, although this biome is also located, e.g. in the southern US, which should be assigned to the warm–temperate forest. Therefore, the evaluation of this method with respect to warm–temperate forest might be ambiguous. Furthermore, warm–temperate forests are small and rather patchily distributed and are thus rarely dominant in the coarse grid cells to which the RF99 reference had to be interpolated to. The coarser the grid is, the more warm–temperate forest regions get lost during the interpolation. Therefore, the warm–temperate forest biome is generally better represented for models using a higher spatial resolution (i.e. MPI-ESM-T63, CLIM-LPJ and IPSL-ESM-T63).

In addition, not all biomes can be differentiated by the structural composition or climatic tolerance. The biome “savanna” is the second-largest ecosystem in the tropics, covering approximately one-fifth of the global land surface (Scholes and Hall, 1996). It occurs in climatic zones that are also suitable for forest and grasslands (Lehmann et al., 2011) and is thus very variable regarding the plant composition. Tree fraction can vary from very dense (open forest savanna) to nearly zero (Torello-Raventos et al., 2013). While tropical savannas require the coexistence of trees and C4 grass, they can only be distinguished from forests by their unique functional ecology, fire tolerance and shade intolerance (Ratnam et al., 2011). These features make savannas unstable and vulnerable to changes in, e.g. grazing, fire regime and climate, transforming savannas into forest or grasslands (Franco et al., 2014). The functional diversity of savannas is not adequately included in DGVMs nor considered in the biomisation method presented here. As even C4 grass is not simulated in all models, we had to define the savanna biome in a very rudimentary manner by a mixture of woody PFTs and grass and by bioclimatic limits, i.e. a mean temperature of the coldest month exceeding 10∘ which is taken as a limit for C4 grass in dynamic vegetation models (e.g. Jena Scheme for Biosphere Atmosphere Coupling in Hamburg; JSBACH; cf. Reick et al., 2013). The savanna biome might therefore not be represented well. At least in the palaeo-simulations, most biomisations do not capture the reconstructed savanna area, but this may partly also be related to the fact that only few records exist indicating savanna during LGM and 6 ka. Modern pollen rain analysis reveals that woody plant taxa typically characterising savannas are underrepresented or even absent in the pollen/vegetation ratios. Given the lack of savanna indicators, this biome may be overlooked in fossil pollen records (Jones et al., 2011).

Similar to dynamic vegetation models, the priority in the biomisation procedure is given to forest biomes. It is first tested whether forest biomes are suitable for covering the grid cell, before the savanna is distributed. Grasslands and tundra are assigned to the residual grid cells, independent of the real grassy PFT cover fractions. The only restriction is a total vegetation coverage exceeding 10 % for tundra or 20 % for grassland to be distinguishable from deserts. This method has the large disadvantage that biases in the forest distribution propagate throughout the assignment of all biomes with the exception of deserts. The forest biome distribution calculated for the different models is further tested in Sect. 4.3 for the pre-industrial time slice.

Another problem is the inclusion of anthropogenic plant functional types (i.e. land use) in some simulations, making the biome distribution less comparable to the reference data. Although land use is often prescribed in the models, this process cannot be reversed in the final output data. The area chosen for land use is historically determined and is based on human decisions and not primarily on climate conditions. These human pathways cannot be reproduced in simple biomisation methods nor in the current dynamic vegetation models. We artificially rescale the natural vegetation in human-affected regions by redistributing the fraction of anthropogenic PFT coverage proportionally to the natural PFTs. This is a very simple approach and only partly in line with the implementation of land use in the dynamic vegetation models. For instance, within JSBACH, pasture is preferentially assigned to natural grasslands; forests are only affected if prescribed pasture fraction exceeds the natural grassland area (cf. Reick et al., 2013). This rule is plausible but not reversible and therefore not appropriate for the biomisation method presented here. The results show that biome maps based on models including land use do not agree worse with the references than the other simulations, underlining that the redistribution method used here provides a good approximation of the natural vegetation cover.

The method of PFT biomisation basically uses bioclimatic limits that have been inferred for the modern vegetation–climate relationships. These limits may not be valid for all time periods. During LGM, the atmospheric CO2 concentration was substantially lower than today, which may also affect the response of the plants to the background climate. Likewise, the matrices for the assignment of taxa into PFTs and from PFTs into biomes have been constructed on the basis of the recent vegetation. These matrices do not have to be constant in time; i.e. they may not be applicable for glacial vegetation. Furthermore, the classification of the biomes itself corresponds to the modern vegetation and does not necessarily have to reflect the palaeo-vegetation. There might be other biomes in glacial climates that remain unconsidered. This may lead to biases in the modelling results and the biome reconstructions taken as reference. The κ values for the LGM time slice were quite low, indicating disagreement between the simulated and reconstructed biome distributions.

A rather technical problem is the interpolation of the PFT distributions to the T31 or T63 grid that partly leads to a decrease in the global area to be compared with the reference datasets due to a mismatch of the land–sea masks. In regions with a strong change of the PFT fractional composition (e.g. desert border, coastal region), the interpolation may produce blurry transitions in the PFT distributions resulting in an erroneous conversion into the mega-biomes.

The classical method of biomising climate states via biome models (here BIOME1 by Prentice et al., 1992) and the new PFT-based method result in similar biome distributions for most models and all time slices. Generally, the PFT-based method produces more forest in comparison with the classical approach. This is mainly related to the rather low limit of forest fraction needed in the assignment of forest in the PFT-biomisation procedure. In forest regions, where Earth system models tend to produce large biases in the climate state, the PFT-based approach may be more suitable for the biomisation. Therefore, the tropical, warm–temperate and boreal forests are probably better represented by the PFT method. However, the biomisation of the PFT distributions itself strongly depends on the underlying climate, affecting both the differentiation into the biomes as well as the simulation of the PFT coverage in the different dynamic vegetation models. To accurately compare the performance and the skill of the different vegetation models to represent biome distributions, the models should therefore be forced by the same climate state, but only few models can be run offline. This study is thus not thought of as a model evaluation but as an introduction to the biomisation method and as a test of whether the procedure works for models of different complexity and simulations for different time slices.

To assess the contribution of the effect of biases in the underlying climate to the differences in the PFT-based biomisations and the references, we compare the pre-industrial climate-based biomisations with the biomisation of the CRU TS4 dataset. A sensitivity study is performed following Dallmeyer et al. (2017) to relate differences in the biome distributions to precipitation or temperature deviations in the background climate (Fig. 12). For this purpose, we successively replace the temperature or the precipitation in the CRU TS4 forcing file for the BIOME1 model with the respective pre-industrial temperature or precipitation distributions simulated by the models. Afterwards, we compare the differences between the calculated biome distributions.

Generally, disagreement in the high northern latitudes is associated with biases in temperature, while disagreement in low latitudes co-occurs with precipitation biases for the pre-industrial time slice. The similarity of the PFT biomisations and RF99 is lowest for CLIMBER, MIROC-ESM and CLIM-LPJ. While for CLIMBER the coarse resolution (i.e. the very different land–sea masks) may be the main responsible factor for disagreement, total κ is reduced by an underestimation of grasslands and savanna and an overestimation of the forests in the PFT-based biomisation of MIROC-ESM. This is exactly opposite to the biases occurring in the climate-based biomisation, indicating that the climate is not the primary origin of the differences. For this specific model, the PFT-based biomisation strongly differs from the climate-based one. This may at least partly be related to the handling of vegetation in the model. The spatially explicit individual-based (SEIB) vegetation model included in MIROC-ESM is a forest gap model, not using the tiling approach (Sato et al., 2007). PFT fractions have only been estimated during the CMIP5 post-processing, based on the net primary productivity ratios of the different vegetation categories. This approach might lead to an overestimation of forest. On the other hand, according to BIOME1, the underestimation of the tropical forest domain in the climate-based biomisation of MIROC-ESM is caused by the way to dry climate in South America.

In the PFT biomisation of CLIM-LPJ, κ is basically reduced by an overestimation of boreal forest at the expense of temperate forest and an underestimation of the savanna regions. Both errors are mainly not climate driven. Within dynamic vegetation models explicitly calculating boreal and temperate forest, these forest types can coexist. To give a clear assignment, we decided to differentiate both forest types by the dominant tree PFT, i.e. if the boreal tree fraction exceeds temperate tree fraction, forest fraction is assigned to boreal forest, and vice versa. This partly disagrees with the handling in biome models; e.g. in cool mixed forest, boreal trees could be the dominant PFT and temperate trees only the subdominant PFT (cf. Kaplan et al., 2003), but this biome would be assigned to the mega-biome “temperate forest”. We assume that due to a slight overestimation of boreal forest coverage in Europe and at the modern boreal to temperate forest transition zone within CLIM-LPJ, the vegetation in these regions is grouped into the mega-biome “boreal forest”. In South America, tropical forest fraction is overestimated by CLIM-LPJ, with values exceeding 80 % in most regions of Brazil, precluding the savanna biome. Within north Africa, CLIM-LPJ simulates hardly any regions with coexisting substantial forest and grass fractions. Either tropical trees are clearly the dominant PFT (assigned to tropical forest) or forest fraction is too low (below 10 %) to be assigned to savanna. The defined limits for savanna are only fulfilled for very few grid cells.

For MPI-ESM-T31, the boreal forest biome is strongly underestimated in the PFT-based biomisation. The BIOME1 results clearly relate this bias to a too-cold climate (GDD5 limit is not reached in BIOME1), which also affects the simulation of trees in JSBACH sharing the same bioclimate limits. Therefore, forest fraction in MPI-ESM-T31 is underestimated for the northern latitudes.

IPSL-ESM-T31 shows a dry bias in South America resulting in a too-low tropical forest biome cover in both the climate-based and the PFT-based biomisations. BIOME1 reveals another systematic bias for the MIROC-ESM biomisation indicating too much temperate forest in North America at the expense of grassland and partly of boreal forests. This overestimation of temperate forest is induced by a too-wet climate favouring growing of trees and a rather too-warm climate in the high northern latitudes.

Due to the forest priority rule in the biomisation method, the skill of representing the non-forested biomes depends on how well the forest distribution can be reproduced. To further assess the performance of the method with respect to the forest biomisation, we analyse the pre-industrial zonal mean forest fraction in the form of the zonal sum of forested area per latitude to be independent of the different grid sizes used for the individual simulations (Fig. 13). In nearly all PFT biomisations, the zonal forest fraction is underestimated in the high northern latitudes and the zonal maximum is shifted southward, although the defined limit of minimum required tree fraction is already quite low in the PFT method. This bias is most obvious in the biomisation for MPI-ESM-T31 and IPSL-ESM-T63. While for MPI-ESM-T31, the coexistence of the bias in both the climate-based and the PFT-based biomisations underlines the effect of the too-cold climate on the forest distribution, the strongly shifted high-latitude forest maximum in the IPSL-ESM-T63 PFT biomisation is probably not climate driven.

In the tropical regions, the forest fraction tends to be underestimated when using the climate-based method, whereas forest fraction is often too high in the PFT-based biomisations, probably related to the low tree fraction limit needed for forest assignment in the PFT method. The tropical forest fraction based on the simulated climate and PFT distribution by CLIMBER is strongly overestimated. This is at least partly caused by the coarse grid and specific land–sea mask used in the model.

To further quantify the biases in forest fraction, we compare the centred root mean square error (cRMSE), the Pearson correlation coefficient (r) and the zonal variability between the biomisations of the ESM simulations and the RF99 reference, combined in a Taylor diagram (Fig. 14). Overall, the zonal forest fraction in the biomisations agrees well with the reference. All biomisations show a good to nearly perfect pattern correlation with values exceeding 0.77, independent of the chosen method. For most models, the Pearson correlation coefficient even exceeds 0.9. The PFT-based biomisation is worst for CLIMBER and MIROC-ESM, revealing a too-large standard deviation and a cRMSE of 0.83 and 0.73, respectively. For MPI-ESM-T31, spatial variability is slightly too low and the cRMSE is 0.61 using the PFT-based method and 0.63 in the climate-based biomisation, reflecting the common underestimation of the boreal forest. As expected, best performance can be observed for the biomisations based on simulations with prescribed PFT coverage (MPI-ESM-T63 and IPSL-ESM-T31), sharing a similar standard deviation with RF99, a pattern correlation coefficient of 0.98 and a cRMSE of 0.21, which is even better than the biomisation of the CRU TS4 data (cRMSE of 0.28).