The model and simulation is explained in detail in Kleinen et al. (2023a) and Dallmeyer et al. (2022). The transient experiment was performed using the Max-Planck-Institute Earth System Model MPI-ESM, version 1.2 (Mauritsen et al., 2019) at T31GR30 spatial resolution, including the JSBACH land surface model and its dynamic vegetation module (Reick et al., 2013, 2021). Vegetation is represented as natural plant functional type (PFT) cover fraction per grid cell. JSBACH distinguishes several tree, shrub, and grass PFTs whose distributions are limited by bioclimatic temperature thresholds that reflect the physiological constraints and bioclimatic tolerance (e.g. chilling or heat requirements and cold resistance) of the plants. Changes in PFT cover are regulated by NPP-based competition, reflecting differences in e.g. moisture availability and physiological requirements. JSBACH also determines the fraction of bare ground, in contrast to the reconstructions in which the vegetation always sums up to 100 %.

The JSBACH version used lacks permafrost, dynamic soil development, and seed-dispersal modules (Dallmeyer et al., 2022). Soils therefore remain fixed, and all PFTs are assumed to have unlimited seed availability. Consequently, JSBACH, like most vegetation modules in Earth System Models, represent potential vegetation in quasi-equilibrium with the climate.

In this model, a transient simulation from 22 to 0 ka has been conducted (Kleinen et al., 2023a), prescribing orbital forcing from Berger (1978), greenhouse gas forcings from Köhler et al. (2017), and ice sheet extent from GLAC-1D (Tarasov et al., 2012). To better match climate reconstructions, meltwater from the Laurentide ice sheet was stored between 15.2 and 12.8 ka to mimic proglacial lakes (e.g., Lake Agassiz). A subsequent 1200-year release into the Mackenzie basin triggered an AMOC collapse and North Atlantic cooling consistent with the occurrence of the Younger Dryas, followed by rapid recovery after 11.8 ka. The simulated temperature trend from the Bølling-Allerød to the Early Holocene aligns well with reconstructions (Dallmeyer et al., 2022).

In line with the reconstructions, we bin the simulation output in 500-year intervals. This means, the time step 19 500 BP contains the simulated vegetation for the years 20 000 to 19 500 BP. For comparing MPI-ESM with reconstructions, we only use grid cells and time periods for which reconstructions are available.

Such temporal aggregation inevitably smooths out short-term variability and may dampen rapid vegetation changes, particularly during periods of abrupt postglacial transitions. As a consequence, the magnitude of submillennial variability, correlations during abrupt centennial-scale climate changes, and the detectability of sub-millennial non-linear responses may be somewhat reduced. Therefore, the comparison focusses on differences in multi-millennial trends and sensitivities, instead of submillennial vegetation changes.

We use the REVEALS-based quantitative tree cover reconstruction by Schild et al. (2025) that contains 2752 records, distributed over the Northern Hemisphere. This dataset is based on the LegacyPollen 2.0 synthesis (Li et al., 2025b), that was compiled from individual publications and the Neotoma Paleoecology Database, which includes data from the European Pollen Database and the North American Pollen Database (Fyfe et al., 2009; Giesecke et al., 2014; Williams et al., 2018) and underwent standardized age modelling and taxonomic harmonization. Vegetation cover was reconstructed using the REVEALS model (Sugita, 2007), which corrects pollen counts for taxon-specific productivity and dispersal characteristics. The implementation followed the REVEALSinR routine (Theuerkauf et al., 2016), which incorporates repeated simulations with randomized input parameters to estimate uncertainty. The resulting dataset provides time-series of vegetation cover per taxon, including associated standard deviations and percentile-based confidence intervals. In general, REVEALS-based forest cover is characterized by a slight overestimation. This arises partly from persistent taxon-specific biases and partly from the presence of unvegetated areas. REVEALS-based vegetation cover reflects the composition of vegetated areas but does not capture the overall extent of vegetation. As a result, forest cover can be overestimated when large unvegetated areas occur within the pollen source area. Further details are described in Schild et al. (2025).

In this study, we extend the dataset by Schild et al. (2025) to the last 19 500 years and map them to the T31 grid used in the MPI-ESM simulation. Our analysis is based on all available reconstructions (see Appendix A). The distribution of the reconstructions in space and time is seen in Fig. 1.

The present-day pattern of simulated and reconstructed tree cover fractions is compared to remote sensing data (MODIS, year 2000–2019; DiMiceli et al., 2022) (Fig. 2). Tree cover in Europe and China is relatively well-represented by REVEALS, whereas REVEALS strongly overestimates tree cover in Alaska, Northeastern North America, and Eastern Siberia, often exceeding 20 %. These discrepancies between MODIS and REVEALS tree cover may provide a first-order indication of the magnitude by which REVEALS could overestimate tree cover due to the reconstruction of vegetation composition only. However, this potential bias is unlikely to be temporally constant, as it depends on changing environmental conditions, vegetation dynamics, and the extent of non-vegetated surfaces.

The MPI-ESM model shows too little tree cover in Alaska and Western North America. However, it significantly overestimates tree cover along the East Asian Summer Monsoon (EASM) margin and in Central and Eastern North America, as well as in Europe. It is important to note that land-use is not included in this version of MPI-ESM, and many of these regions are heavily influenced by historical and contemporary land-use practices, which contributes to overestimated tree cover. Furthermore, validation studies indicate that the MODIS tree cover exhibits substantial uncertainties in boreal and transition regions, particularly at low tree cover fractions (< 20 %) (Montesano et al., 2009), further challenging the comparison with the simulation and reconstructions.

We use three statistical measures for evaluating the similarity of the REVEALS data and the MPI-ESM simulation, the Pearson correlation coefficient, the mean absolute error and the variance difference. The Pearson correlation coefficient (r) is used to assess the similarity in the temporal evolution of the tree cover in each grid cell. It is invariant to differences in the mean and variance. As such, it is well-suited for assessing if the REVEALS data and the MPI-ESM tree cover simulation follow a similar trajectory over time. We consider all grid-cells where the correlation between reconstructions and model data was significant at p < 0.1 in order to maintain spatial representativeness, particularly in regions with sparse data availability and low tree cover where correlations tend to be less statistically significant due to lower signal-to-noise ratios.

In contrast, the mean absolute error (MAE) quantifies the average absolute deviation between the two datasets. As a scale-dependent metric, it is highly sensitive to differences in the temporal mean and amplitude of changes. Consequently, MAE provides a direct measure of absolute agreement and reflects how closely the tree cover values simulated by MPI-ESM aligns in magnitude with the REVEALS-based estimates.

Third, the temporal variance captures the degree of fluctuation or variability within a signal. It complements the other measures by highlighting whether MPI-ESM captures not only the correct magnitude and trend but also the extent of variability inherent in the REVEALS data. We here consider the difference between the variance in the simulated and reconstructed tree cover.

For clarity of presentation, we assign the grid cells for each metric into different groups. For MAE and the correlation coefficient, we categorize the group by thresholds that are multiplier of the median (x) of all values. The variance difference values are categorized into three groups based on a threshold (y) defined as 10 % of the overall range (maximum minus minimum) of the variable. Grid cells with variance difference below this threshold indicate an underestimation of the variance in MPI-ESM compared to REVEALS, those exceeding the positive threshold are indicating an overestimation of the variance compared to REVEALS, and values within the interval ± threshold are defined to be of similar variance. The group definitions are provided in Table 1. Please note that grid cells with non-significant r-values are assigned to the group “no-correlation”.

To disentangle the effects of precipitation, soil moisture, temperature, and CO₂ on the simulated tree cover, we additionally train a statistical emulator to the simulation output of MPI-ESM, following the procedure of Adam et al. (2021). The emulator is based on generalized additive models (GAMs; Wood, 2017), which are non-parametric, non-linear statistical models, in which tree cover is the response variable and mean temperature of the coldest month (Tc), mean temperature of the warmest month (Tw), annual mean precipitation (P), annual soil moisture (Sw), and atmospheric CO₂-concentration are used as predictors.

The selection of these variables is motivated by their known importance for vegetation productivity and the implementation of bioclimatic thresholds for Tw and Tc in JSBACH. We train one GAM, which we call emulator in the following, using the data from all grid points, time steps, and climate predictors. Thereby, we estimate the modeled climate-CO₂-vegetation relationship across the full climate, CO₂, and vegetation gradients, independent of any specific location. This approach is justified by JSBACH modeling the vegetation independently for each grid box, without considering horizontal vegetation interactions such as seed dispersal. We use the function gam in the R package mgcv to fit the emulator (Wood, 2017). Following (Adam et al., 2021), we use a binomial response function due to tree cover being restricted to the interval 0 % to 100 %, and a full tensor product smooth with a cubic regression spline basis for modeling the vegetation-CO₂-climate relationship (Wood, 2006). Thereby, we estimate not just the non-linear effects of the individual predictors but also interactions between them. The number of smooth terms was determined with the default optimization routine in mgcv (Wood, 2017). To keep the fitting procedure computationally feasible, we use only every second time step for training.

We simulate sets of surrogate tree cover time series using transient climate forcing by all five variables, and by each individual variable alone, to disentangle the main climatic driver. For the latter, we employ the full emulator but set all predictors to time mean value in the respective grid box. The emulator explain the major vegetation changes over the deglaciation as indicated by predominantly high grid box correlations between the simulated and emulated tree cover (Fig. 3). Lower correlations are mainly concentrated in subtropical South America, the Sahara, arid regions in Asia and the Mediterranean region, and thus include mostly regions with marginal (Sahara) or low changes in tree cover. Marginal tree cover change may lead to spurious correlations, while low correlations in regions with low tree cover changes points to unresolved climate-vegetation dynamics in these regions.

In a second set of emulations, we employ the emulator trained on the MPI-ESM climate and force it with a bias-corrected climate, assuming that grid cell-specific model biases (e.g., related to orography) remain constant over time (Maraun and Widmann, 2018). To construct the bias-corrected climate forcing, we apply the delta method following Beyer et al. (2020), using additive corrections for temperature and multiplicative corrections for precipitation, both downscaled to a 0.5°-grid to align with the CRU-TS 4.08 baseline (University of East Anglia Climatic Research Unit et al., 2024; Harris et al., 2020). Soil moisture was only interpolated to the 0.5°-grid due to the lack of an equivalent observational dataset in CRU-TS 4.08. More details on the preparation of the climate forcing data, time-series and maps for some time-slices are given in the Appendix B.

Complementing the emulation approach, which mimic the response of trees in the MPI-ESM model to climate changes, we assess the non-linearity of climate–vegetation relationships by distinguishing linear from non-linear behaviour. Linear relationships are quantified using Pearson correlation coefficients between simulated or reconstructed vegetation and the individual climate variables. Non-linear relationships are explored using generalized additive models (GAMs; Wood, 2017), with simulated tree cover as the response and the full set of climate variables as predictors. In contrast to the emulations, GAMs are fitted separately for each grid cell here, using 500-year binned datasets smoothed with a Loess filter. Each predictor is represented by a smooth, flexible function capable of capturing curves and other complex patterns. The effective degrees of freedom (edf) associated with each smooth term indicate the degree of non-linearity, with edf ≈ 1 reflecting near-linear relationships and higher values indicating stronger non-linear effects. F-values quantify the importance of each term in explaining variation in the response. For our analysis, we consider only grid cells with edf > 1.2 and p < 0.05, so that we can use the corresponding F-values as indicators of the non-linear climate–vegetation relationships. The most influential variable is identified as the predictor with the highest F-value.

For the Last Glacial Maximum (LGM), only ∼ 50 vegetation records are available (Fig. 4). REVEALS indicates a predominantly open landscape, consistent with previous reconstructions (Cao et al., 2019a; Davis et al., 2024; Kern et al., 2025; Li et al., 2025a; Prentice et al., 2000). Dense forests occurred mainly in eastern North America (up to 75 % tree cover) and eastern Asia (up to 100 % in Japan), with moderate cover in western North America (up to 60 %). Isolated cells with moderate or high tree cover appear in western central Europe (up to 35 %), the Mediterranean (up to 20 %), Alaska (up to 50 %), and eastern Siberia (up to 20 %). MPI-ESM broadly agrees but shows higher tree cover in Europe and temperate North America, and lower cover in most other regions, including Siberia and the rim of the Tibetan Plateau. The isolated high-cover cells in REVEALS are not reproduced by MPI-ESM, likely reflecting glacial refugia not captured at the model's spatial scale (Leroy et al., 2020).

By 10.5 ka, regions of reconstructed high tree cover expanded markedly. Dense forests developed across eastern North America (70 %–80 %) and western Canada (Pacific coast), and most Siberian records show 60 %–80 % tree cover. Southern China changed little from the LGM, while the northern part of China has experienced a moderate increase in tree cover (30 %–50 %) and up to 70 % in the north eastern part along the Pacific coast. In Europe, REVEALS indicates only modest increases to 30 %–60 %. MPI-ESM captures the general trends but deviates regionally, underestimating forest cover along the North American Pacific coast, in eastern North America's temperate zone, the Mediterranean, and parts of Siberia, while overestimating it in central North America, western and central Europe, northern Siberia, and the East Asian monsoon region.

Towards 7 ka, reconstructions indicate a further increase in tree cover fractions in the Northern Hemisphere north of approximately 50° N, particularly across boreal latitudes and Europe, similar to previous studies (Sweeney et al., 2025). In contrast, MPI-ESM simulates a small but widespread decline, since the maximum Northern Hemispheric tree cover is already reached during early Holocene (Dallmeyer et al., 2022). Exceptions to this trend include periglacial areas in North America and Scandinavia, where tree coverage remains relatively stable or increases slightly. In boreal regions of North America and parts of Siberia, MPI-ESM simulates much less tree cover (∼ 30 % to 80 %) than suggested by the reconstructions. The pattern of disagreement is similar as in 10.5 ka, but much more pronounced in 7 ka. Only in some parts of Europe and eastern North America, tree cover is consistent with the reconstructions, showing dense forests.

At 0 ka, the absence of land-use effects in MPI-ESM likely leads to overestimated tree cover, especially in Europe. Overall, the spatial mismatch between REVEALS and MPI-ESM remains similar to 7 ka: the model simulates too little forest in boreal Asia and North America, but too much in East Asia and central North America.

Overall, MPI-ESM captures the continental-scale patterns and temporal evolution of tree cover reasonably well, but its performance decreases substantially at regional scales.

To identify regional differences between the REVEALS-based reconstructions and the MPI-ESM simulation, we calculate three different metrics (Fig. 5): (a) the Pearson correlation coefficient measuring the synchronicity of the time-series, (b) the MAE measuring the absolute difference in the tree cover estimates and (c) the tree cover variance difference as estimate of differences in the amplitude of tree cover changes. For easier accessibility, we group these measures into statistical categories, aligned on the median value over all grid cells (MAE and r) or the range of the variance difference values (see methods, Table 1).

Overall, most of Europe demonstrates a highly positive correlation between REVEALS and MPI-ESM, indicating that the model generally captures the European climate and vegetation dynamics. The Mediterranean region stands out as an exception, experiencing a low or even highly negative correlation. The MAE is moderate for most of Europe, but the model has a higher variance than the reconstructions. These differences could be enhanced by the ignorance of land-use change in Europe which leads to systematic differences in the late Holocene tree cover. However, previous studies report no substantial large-scale human impact on vegetation composition before 2 ka (Roberts et al., 2018; Trondman et al., 2015), thus land use cannot be the only driver of model-data differences. Estimates of potential tree cover for the present time slice indicate more than 80 % tree cover in most parts of Europe except for Spain (Roebroek et al., 2025). This is in line with MPI-ESM.

In North America, mid-latitude regions (40–60°) display a strongly positive correlation, particularly in the eastern part, where also the MAE is low despite a mostly lower variance in the model. However, Central North America exhibits notable weak or even negative correlations and exceptionally high MAE. As the variance difference is low in most grid cells, the high MAE points to a systematic bias and/or diverging trends of the tree coverage in this region. Most grid cells in Western Canada show high MAEs with differing correlations. Coastal regions, also in Alaska, experience negative or weak correlations, while in inland Western Canada correlations are positive in some grid cells only.

In Asia, the correlation indicates no clear pattern, reflecting no robust alignment between REVEALS and MPI-ESM. Siberia displays rather weak or negative correlations, while positive correlations can be observed in non-forested regions, in Western China and along the Pacific coast. Positive correlations are also observed in certain grid cells in Western Siberia. The MAE is high in most grid cells in East Asia, particularly in Central and Eastern Siberia and along the northern rim of the East Asian monsoon region. The variance difference is low in most grid cells, which eliminates amplitude differences as reasons for high MAEs.

These regional discrepancies between the model and the reconstructions point to several key challenges in comparing the REVEALS-based reconstructions with vegetation models. Possible reasons include methodological caveats such as shortcomings in the process of reconstructions, including the REVEALS model (Githumbi et al., 2022; Kaplan et al., 2017; Li et al., 2023b; Schild et al., 2025), biases in the simulated climate, missing or idealized model components (Dallmeyer et al., 2022, 2023; Li et al., 2025a; Zhang et al., 2025) and differences in the vegetation-climate relationship. These factors may lead to local ecological processes, migration lags, and disturbance regimes affecting the reconstructions, while being inadequately represented in the model. This may be particularly problematic in ecotones, where small climatic changes or disturbances can cause large shifts in vegetation composition because multiple vegetation types coexist near their ecological limits.

One important source of divergence lies in the fundamental assumptions underlying each approach: REVEALS estimates plant cover fractions that always sum to 100 % vegetation cover, as it is based on pollen assemblages that represent only vegetated areas without accounting for the proportion of bare ground. Consequently, REVEALS reflects the relative composition of vegetation types within the vegetated area, rather than the absolute area (fi) covered by each vegetation type (i). In contrast, MPI-ESM explicitly calculates both, a bare soil fraction and the composition of plant functional types (ci) on the vegetated area (V), with ci=fi/V. While in principle this allows a comparison to REVEALS cover fractions, we have not applied it in this study, because this approach is only valid for regions and time periods where overall tree and vegetation cover is high, such as during the Holocene in Europe (Dallmeyer et al., 2023). In rather open landscapes, this comparison suffers from the artefact of high relative PFT fractions (ci), because for numerical reasons, PFT cover fractions always have to be non-zero in the model. We therefore use the absolute area covered by the PFTs (fi). This fundamental difference (vegetated area vs. vegetation ratios) influences the MAE.

We therefore analyse the differences in tree cover estimates (MPI - REVEALS) grouped by REVEALS tree cover fraction classes. The results demonstrate a clear, non-linear trend across the vegetation gradient (Fig. 6): In areas/time-slices for which REVEALS indicates low tree cover (0 %–20 %), MPI tends to overestimate vegetation cover, with a mean positive bias of approximately 14 %, turning into a negative bias for high REVEALS tree cover classes (-32 % for the 80 %–100 % class). Part of this pattern, however, is methodological, because the difference metric (MPI - REVEALS) is analysed as a function of REVEALS tree cover. This mathematical dependence tends to produce increasingly negative values at high REVEALS fractions even in the absence of ecological effects. The figure should therefore primarily be interpreted as illustrating the magnitude of model–data deviations along the vegetation gradient rather than a purely ecological non-linear response.

This pattern is nevertheless consistent with the increase in MAE from the LGM (open landscapes) to the Holocene (forested period) (Fig. A3 in the Appendix A) and underlines that the comparison of tree cover fraction of grid cells in the model against tree cover fractions of total vegetation in the reconstructions increase the MAE, particularly in highly forested landscapes.

The positive bias in sparsely wooded regions may result from the model's omission of environmental constraints such as wetlands, permafrost, or water-logged soils, while the negative bias in regions of dense forest may arise from limited number of PFTs, the global, relatively simple definitions of PFTs and their interaction, as well as tuning parameters calibrated for modern rather than past conditions (Dallmeyer et al., 2023; Horvath et al., 2021; Zhao et al., 2025). In addition, the coarse grid resolution of the MPI-ESM leads to a smoothing of regional vegetation patterns. Local maxima, such as tree refugia or areas of particularly dense forest due to local climate conditions, are not adequately captured, resulting in a more homogenized vegetation distribution that overlooks the fine-scale structural heterogeneity evident in the reconstructions.

The differences in absolute tree cover levels expressed by the MAE show a pattern that shares features with the modern deviations to the MODIS observations (Fig. 2, method part). This could point to systematic errors in the REVEALS data and simulation results. REVEALS rather seems to overestimate tree cover in boreal latitudes (Schild et al., 2025) and thus may be too sensitive in cold climates such as glacial periods with open landscapes. Some taxa can occur as trees or shrubs, and their differentiation is not possible based on pollen, especially as the pollen taxonomy was harmonized at the genus level (Herzschuh et al., 2022). More generally, each taxon is assigned to a single plant functional type (PFT), which inherently departs from ecological reality, as many taxa comprise species belonging to different PFTs. Although the reconstruction method by Schild et al. (2025) applies a static threshold that assigns shrub status to common tree taxa (e.g. Betula, Alnus, Corylus) north of 60° N, this adjustment is unlikely to eliminate all biases in tree and shrub PFT representation at northern latitudes. Consequently, the distinction between shrubs and trees in REVEALS may remain imprecise, potentially leading to overestimated tree cover in boreal regions.

On the other hand, the MPI-ESM simulation might suffer from the fixed bioclimatic limits and a tendency towards too cold conditions in the boreal latitudes. For Central North America and the East Asian monsoon margin, the spatial pattern of the MAE diverges from the pattern of disagreement with the MODIS data. In terms of MAE, these regions, which are both forest–steppe transition zones, thus represent the most challenging areas in the comparison.

Many methodological limitations in both the model and the REVEALS reconstructions cannot be quantified directly, and their individual contributions to the model–data tree cover discrepancies therefore remain unresolved. However, we can assess the extent to which systematic climatic biases or differences in the climate–vegetation relationships contribute to the observed mismatches in tree cover patterns. To this end, we analyze the regional climatic drivers of the simulated vegetation dynamics and evaluate which factors distinguish grid cells with close model–data agreement from those exhibiting substantial deviations. Additionally, we employ the trained emulator with bias-corrected climate inputs to further isolate the influence of climatic biases.

To evaluate the climate–vegetation relationships, we apply a statistical emulator (see Methods) that captures both linear and non-linear responses of vegetation to climatic forcing. To maximize the training data we use the complete global model domain, although reconstructions are limited to the Northern Hemisphere. Pearson correlation coefficients and generalized additive models (GAMs) are additionally used to disentangle the linearity and non-linearity of the climate–vegetation relationship (see Methods). The tested predictors include temperature of the warmest and coldest month (Tw, Tc), annual precipitation (P), annual mean soil moisture (Sw), and atmospheric CO₂ (Fig. B1) and we determine the locally most influential predictor as the emulated tree cover curve with the highest correlation to the simulated/reconstructed tree cover. We emphasize that the emulator diagnoses sensitivities intrinsic to the model itself, and thus characterizes model behavior rather than real-world sensitivities.

The emulator results show coherent regional patterns. In high-latitude and high elevation regions (Siberia, Alaska, northern Canada, Tibetan Plateau), the emulation forced with Tw (orange) shows the strongest correlation with simulated tree cover (Fig. 7), consistent with the well-established control of growing-season warmth on vegetation in cold environments (Adam et al., 2021; Dallmeyer et al., 2021; Li et al., 2022a; Seddon et al., 2016; Tucker et al., 2001). In the tropics and subtropics (Africa, South America, Southeast Asia), tree cover is predominantly governed by precipitation (P, light blue), reflecting the central role of water availability (Adam et al., 2021; Gosling et al., 2022; Zhao et al., 2018).

Temperate regions display mixed controls. In Central North America, Tw dominates, whereas in Europe both P and Tc are influential. In large parts of northwestern Asia, precipitation emerges as the primary driver. CO₂ (yellow) dominance is spatially scattered, with occurrences in South America, East Africa, Australia, and southern Asia, particularly in the East Asian monsoon region. This strong impact of CO₂ has also been found in time-slice-based biome change analysis for the deglaciation period (Tian et al., 2018). However, this relationship should be interpreted as a model-derived sensitivity rather than direct evidence of physiological CO₂ fertilisation. The apparent CO₂ control may partly reflect a proxy for hemispheric deglacial trends that are not fully captured by the other climate predictors. Soil moisture shows weak influence overall, except in arid regions (e.g. North East Africa) and in tropical monsoon margins.

The spatial patterns inferred from the emulations, correlations, and GAMs are largely consistent and remain robust when the analysis is repeated with a data subset matched to the spatial and temporal structure of the reconstructions. In addition to the dependency of tree cover on Tw in the boreal latitudes, GAMs indicate a non-linear influence of Tc in temperate regions (Central North America and Europe) and around the Tibetan Plateau (Fig. 8c), consistent with physiological evidence that winter cold constitutes a major limitation for tree survival and recruitment. Extremely low temperatures can cause cellular freezing, xylem embolism, and bud mortality, while repeated freeze–thaw cycles and deep soil frost disproportionately damage roots and seedlings (Charrier et al., 2017; Sakai and Larcher, 1987). Juvenile trees, with shallow roots and limited carbohydrate reserves, are more vulnerable than grasses or shrubs, favoring cold-tolerant vegetation. Many temperate species require a chilling period to break dormancy, but excessively low temperatures can exceed frost tolerance and prevent establishment, creating a narrow climatic window for regeneration. In JSBACH, these constraints are represented by PFT-specific minimum-temperature thresholds for the coldest month, below which tree establishment is suppressed, contributing to the non-linear response of trees to Tc.

In contrast to the spatially coherent patterns in MPI-ESM, the relationships between reconstructed REVEALS tree cover and emulated tree cover show a much more fragmented structure of climate drivers (Fig. 8d). Moreover, the dominant climatic drivers inferred from REVEALS and the simulated climate differ markedly from those in the model. Most notably, the strong influence of Tw in boreal regions is absent in the reconstructions. Instead, REVEALS tree cover correlates more strongly with P and Tc, even at high latitudes. This finding contradicts the commonly assumed dominance of growing-season temperature in controlling boreal vegetation dynamics and indicate that MPI-ESM does not sufficiently capture the past real-world climate change or that the strong restriction of the extratropical trees by warm season temperature limitations are oversimplified and regionally inappropriate.

A substantial number of grid cells shows the highest correlation of REVEALS tree cover with CO₂. Although time-slice experiments have demonstrated a strong impact of the ecophysiological CO₂ effect on vegetation differences between the LGM and the present (Claussen et al., 2013; Woillez et al., 2011), the strong correlation between REVEALS-derived tree cover and the CO₂ signal in this study rather suggests that the local REVEALS reconstructions follow the overall deglacial warming trend – reflected in the CO₂ record – more closely than they follow the simulated local climate or climate-vegetation relationship. This statistical agreement may therefore primarily reflect the shared large-scale deglacial trend in both variables, rather than a direct plant-physiological CO₂ response in the real-world.

Because the emulator diagnoses model-internal sensitivities within the MPI-ESM framework, discrepancies between simulated and reconstructed patterns do not necessarily indicate model failure; they may also arise from characteristics of the reconstructions, including their temporal resolution, chronological uncertainties, and spatial aggregation, which can enhance alignment with long-term trends while smoothing local variability.

The dominant climatic drivers in MPI-ESM according to the emulation vary through time. While energy limitations (i.e. Tw or CO₂ as most influential variables) are a key driver during the deglaciation, moisture availability (i.e. precipitation and soil moisture dominant driver) becomes increasingly important toward the Holocene (Fig. 9). The moisture availability influence peaks at 7.5 ka, indicating a widespread shift from energy- to water-limited environments in the early Holocene before shifting back to higher energy-limited influences in the late Holocene. The reconstructions reflect the transitions between energy- and water-limited regimes (in terms of their correlation with the emulations), with a maximum area of water-limited regimes reached at 8.5 ka. The influence of Tc stays relatively constant through time in the simulations, whereas it increases by ∼ 10 % in the Holocene in the reconstructions.

Based on the correlation, mean absolute error (MAE), and variance differences between simulated and reconstructed tree cover, we classify all grid cells into statistical categories (cf. Fig. 5 and Table 1) and analyse differences in tree cover responses to climate change among these groups. Additionally, we assess whether the observed group differences arise from insufficient data (e.g., incomplete or short time series) or are related to geographic position (latitude or longitude), and whether they affect the representability of the tree cover dynamic by the emulation. To this end, we pre-select variables that show significant differences between the groups based on pairwise comparisons using the Wilcoxon rank-sum test (Appendix C, Table C1 in the Appendix C). Then, we use this preselection of predictors for running a PCA-analysis to determine the most influential variables for group-separation.

It should be noted that high MAE values and low correlations do not necessarily indicate deficiencies in the climate-vegetation relationship in the model. They may also reflect the fact that the reconstructions capture local ecological processes, migration lags, or microclimatic conditions that are not represented in the coarse-resolution simulation. Since these factors cannot be filtered out, all grid cells are included in the analysis to examine the dependence on climatic conditions.

Grid cells exhibiting a synchronous dynamic in simulated and reconstructed tree cover (positive correlation-group) differ markedly in their tree cover response to climate change from those with negative correlations (Fig. C1 in the Appendix C). High agreement occurs where both simulated and reconstructed tree cover follow the simulated climate linearly as indicated by strong Pearson correlations with CO₂, precipitation (P), soil moisture (Sw), and temperature of the coldest month (Tc). In these cells, Tc shows high correlations with precipitation (r ≈ 0.85), which itself closely follows CO₂ changes (r ≈ 0.7). The temperature of the warmest month, in contrast, is only moderately correlated with CO₂ and precipitation (r ≈ 0.45 and r ≈ 0.3). Good agreement can also arise in cells with more non-linear responses to precipitation, which the GAM analysis identifies as the main driver in significantly more cells of the positive-correlation-group than in the negative-corelation-group. In contrast, disagreement (negative correlation) is linked stronger to non-linear responses to Tw, which emerges significantly more often as the main driver in grid cells of the negative-correlation–group according to the GAM analysis. In grid cells of the negative-correlation-group, Tw is furthermore rather negatively correlated with CO₂. Neither the variance difference nor the MAE are deviating significantly between grid cells in the negative- and the positive-correlation-group. The agreement is furthermore independent of the time-series length, including the timing of the first data point and the number of missing values.

The PCA on the preselected key variables (F-statistics and Pearson correlations) confirms the significant (Wilcoxon test, p = 6.75 × 10⁻¹¹) separation between the correlation-groups, with PC1 and PC2 jointly explaining 49.5 % of the variance (Fig. 10a). High agreement aligns with strong positive loadings of the Pearson correlation coefficients between tree cover and CO₂ and Tc, as well as the strong positive precipitation-CO₂- and precipitation-Tc-correlations, which most strongly differentiate the positive-correlation-group. In contrast, the non-linear response to Tw is clearly oriented towards the centroid of the negative-correlation-group (negative loadings on PC1), substantially contributing to its separation from the positive-correlation-group. Other variables (including the linear and non-linear relationship to precipitation (R_P, F_P), and correlation to soil moisture (R_Sw) load mainly on PC2 and play only a minor role in distinguishing the groups.

MAE groups do not match with any correlation-group classification. However, grid cells with low MAE differ in climate response from high-MAE cells typically located at mid-latitudes (∼ 50° N) (Fig. C2 in the Appendix C). In the mean, grid cells with early starting reconstructions have a significantly lower MAE than grid cells with later starting reconstructions. High-MAE cells exhibit significantly higher linear correlations of the simulated tree cover with Tc and CO₂. No significant differences in dominant climate drivers are found between the MAE groups, indicating that the prevalence of a particular variable as the main driver does not systematically vary with model error. The PCA of MAE groups (PC1 66.8 %, PC2 26.4 %) confirms the statistically significant (Wilcoxon test, p = 2.04 × 10⁻³) separation, mainly by the linear correlation to Tc, and CO₂.

For the tree cover variance difference, we compare all three groups. Grid cells with overestimated variance in the model are characterized by earlier, more complete time series, stronger linear correlation with CO₂, and Tc, and also higher correlations between precipitation and CO₂ and Tc compared to grid cells with similar variance (Fig. C3 in the Appendix C). Moreover, overestimated variance co-occurs with much higher linear correlation between Tw and CO₂ (r ≈ 0.6), but can be less well represented by the full-forcing-emulator.

Grid cells with underestimated variance in the model mainly cluster in Eastern North America and show higher linear correlations with Tw, Tc, P, and CO₂ and lower non-linear relationship to Sw, Tw and CO₂ compared to grid cells with similar variance. Consistently, correlation between P and CO₂, Tw and Tc are significantly higher compared to grid cells with similar variance. Interestingly, grid cells within both groups (overestimated and underestimated variance) exhibit higher correlations between simulated and reconstructed tree cover than grid cells with similar variance, despite larger MAEs. This indicates that the temporal structure can be preserved even when variability and amplitude is misrepresented. The lower correlations and low MAE in the group with similar variance points to poor temporal coherence despite a reasonable magnitude fit.

The PCA of the preselected variables confirms the significant separation between the variance groups (Kruskal-Wallis, p = 1.66 × 10⁻⁵) in their multivariate environmental characteristics, with PC1 and PC2 explaining 43.6 % of the variance. Along PC1, the most influential contributors to group separation are the contrasting non-linear vs. linear responses of the tree cover to CO₂. The non-linear relationship to CO₂ (F_CO2) loads positively and aligns with the overestimated-variance–group, while the linear correlation to CO₂ exhibits negative loadings associated with the underestimated-variance–group. Additional separation along the horizontal axis arises from variation in linear correlations with Tc, Tw, and P, which load negatively towards the underestimated-variance-group. Separation along PC2 is driven primarily by differences in the Tw–CO₂ relationship and by the length of the time-series.

Overall, these analyses show that the agreement between simulated and reconstructed tree cover is strongly influenced by the choice of evaluation metric and the specific ways in which vegetation responds to climate drivers. The temporal evolution is best captured when tree cover responds linearly to the hemispheric warming and moistening trends, reflecting the coherent signal shared by precipitation, cold-season temperature, and the global CO₂ trajectory. In these grid cells, reconstructed tree cover appears to follow the large-scale trend closely, probably indicating regions where vegetation dynamics are primarily controlled by broad-scale climatic forcing and are therefore well captured by the model.

In contrast, grid cells in which a non-linear response to summer temperature fosters poor temporal correlations could coincide with regions in which the reconstructions indicate strong regional or local vegetation trajectories that are not governed primarily by hemispheric climate forcing. This pattern suggests that the mismatches to REVEALS do not necessarily arise from shortcomings in the model's representation of large-scale vegetation–climate interaction, but rather highlights areas where regional ecological or climatic processes play a comparatively larger role, influencing the reconstructions.

MAE reflects differences in simulated tree cover sensitivity to cold-season temperature and CO₂, with greater disagreement when tree cover is more linearly aligned with Tc and CO₂. Deviations in variance do not increase model–data asynchronicity but tend to coincide with higher MAE, indicating that the timing of changes can be accurately reproduced even when amplitude is misrepresented. Strong linear correlations with CO₂ lead to overestimated variance, whereas non-linear relationships tend to produce underestimated variance. Overall, the response of the climate–vegetation system to CO₂ forcing emerges as one key controlling factor. Linear alignment of climate with the CO₂ signal co-occurs with synchronous tree-cover changes in reconstructions and MPI-ESM, but simultaneously increases MAE and exaggerates amplitudes in the model, pointing to a too strong sensitivity of forests to CO₂ variations in MPI-ESM. This high sensitivity to CO₂ in MPI-ESM has also been observed in other studies (Arora et al., 2020; Kleinen et al., 2023a; Rogers et al., 2017).

The trained emulator is forced with a bias-corrected climate to test the impact of potential, systematic climate offsets on the tree cover change. The bias-corrected climate and examples of the resulting tree cover emulation in comparison with the original simulation is provided in Figs. B1–B3 in the Appendix B. To evaluate where the bias-corrected emulation enhances model-data agreement (i.e. it shows higher r or lower MAE values or variance differences), we statistically compare the distribution of grid cells with relative improvement (> 25 % percentile) or worsenings (< -25 % percentile) for the correlation-, MAE-, and variance-groups, using the same classification as in Fig. 5 and Table 1. Note that a relative improvement in model-data agreement does not necessarily imply a good absolute agreement, as r or MAE values may still indicate substantial discrepancies.

The bias correction enhances the model–data agreement at the regional scale, but not in the mean across all grid cells. Correlation coefficients and variance differences improve in only about one third of the grid cells, and the MAE improves in roughly 40 %, while around 25 % of the grid cells in all groups remain unaffected, respectively. The remaining cells show deteriorated performance. MAE improvements (blue areas, Fig. 11) concentrate in Western/Central North America Scandinavia, Southern Europe and Eastern Asia and mostly coincide with an increase in the tree cover correlation, except for Asia. Variance differences increase across much of North America, Europe, and China, but decrease north of 40° N in Asia and south of 40° N in North America, pointing to a high degree of regional sensitivity in the model's ability to reproduce reconstructed variability patterns. The bias correction is most effective in grid cells with initially poor performance, such as those exhibiting negative correlations, high MAE, or large variance mismatches. For correlation and variance, the improvements show no systematic association with the dominant climate driver, suggesting that errors in these metrics are broadly distributed and more difficult to correct with this kind of bias correction. In contrast, MAE improvements occur disproportionately more in grid cells where temperature (Tw) is the primary driver, while deteriorations are more frequent in precipitation-dominated (P) cells.

The results indicate that MPI-ESM performs reasonably well at the hemispheric scale, so that regional bias corrections often come at the expense of other areas, producing localized improvements but limited overall gain. The corrections primarily reduce large systematic errors, leading to improvements in MAE and correlation, but they do not consistently preserve the amplitude of variability, and variance is degraded across large areas. Consequently, the bias-correction methods tend to redistribute errors rather than uniformly improving the model performance across the domain. Furthermore, tree-cover dynamics driven by temperature are more amenable to correction, whereas precipitation-driven dynamics remain more sensitive and are more likely to deteriorate under bias correction, reflecting the differing spatial and temporal characteristics of these climate drivers.

To better understand the regional behaviour, we compare the time series of tree cover fractions (Fig. 12) from reconstructions (red), the MPI-ESM simulation (black), and statistical emulations (blue) with bias correction for the six regions with the largest MAE. Overall, the (bias-corrected) emulated tree cover aligns better with the reconstructions than the simulation in most high-MAE regions. Particularly, in the temperate forest–steppe transition zones in Central North America and Northern China (EASM margin), the emulation produces substantially lower tree cover and aligns more with the reconstructions than the simulation, indicating that the large simulation–reconstruction discrepancies in these regions mainly stem from systematic climate biases.

In Western Canada, bias-corrected warmer summers advance postglacial tree-cover growth and reduce offsets with reconstructions by 30 %, but neither simulation nor emulation capture the mid-Holocene maximum. The model appears to miss the prolonged early- to mid-Holocene warming, pointing to deficiencies in the simulated climate trajectory

In Central Siberia, the bias correction increases emulated tree cover too strongly during deglaciation and leads to a too early peak, indicating an overestimated sensitivity to warm-month temperature and explaining the worsening of the correlation despite an improved MAE in this region. The simulation with much lower temperatures agrees with reconstructions until 9.5 ka, after which their trends diverge, while the emulation and reconstructions only converge in the late Holocene. Neither simulation nor emulation reproduce the reconstructed Holocene increase, pointing to a wrong driver or structural vegetation deficiencies in the model. This mismatch may partly be caused by the missing permafrost processes in this version of MPI-ESM. Permafrost is a major regulator of tree cover across northern high-latitude regions, including Siberia, western Canada, and Alaska. It controls soil thermal and hydrological conditions that limit tree establishment and growth (Cao et al., 2019b; Helbig et al., 2016; Jin et al., 2022, 2021; Kruse et al., 2022; Stuenzi et al., 2021), influences fire regimes (Kim et al., 2024) and shapes forest–tundra mosaics (Viereck, 1973) that may decrease the absolute forest cover in the REVEALS reconstructions. Thus, permafrost can maintain unsuitable ground conditions and can cause significant temporal lags in postglacial forest expansion (Herzschuh et al., 2016; Li et al., 2022b; Tian et al., 2018).

In Eastern Europe, bias correction slightly improves pre-Holocene agreement, but the emulation substantially underestimates Holocene tree cover and fails to capture the reconstructed mid-Holocene rise and 4 ka maximum. This indicates that the model-data mismatch in this region is not related to systematic climate biases. Tree cover in the emulation closely follows the precipitation that is much lower in the bias-correction than in the simulation. This strong relationship may be incorrect, but also none of the other considered climate variables indicate a mid- to late-Holocene peak that could explain the reconstructed late tree cover maximum.

On the Tibetan Plateau, warmer conditions in the emulation would raise tree cover, but reduced precipitation limits its growth. Nonetheless, emulated trends better match reconstructions, highlighting the combined influence of multiple climate variables on tree-cover dynamics and that JSBACH in principle captures the vegetation-climate relationships in this region well.

Overall, bias correction is most effective in regions with strong model–data mismatches, where systematic climate biases are the main cause of discrepancies, such as in Western Canada, Central North America or Northern China. In these regions, the MAE can be substantially reduced, but whether the correlation to the reconstructed tree cover is improved, depends on the relationship between the climate variables and there joint effect on the tree cover. The interactions among climate variables (or with CO₂) are often non-linear, so that changes in one variable can alter the importance or sensitivity of the tree cover response to another. Significant mismatches persist in regions where non-climatic factors, such as missing processes in the model, cause the mismatch (Eastern Europe, Central Siberia). The effectiveness of bias correction is further limited in regions with inappropriate climate-temperature relationships, either due to incorrect dependencies or an overestimated tree-cover sensitivity to temperature changes. In addition, the applied bias correction can not reduce errors in the temporal temperature evolution. Therefore, the mismatch in the timing of the Holocene tree cover maximum persists across large parts of the Northern Hemisphere in the emulation with bias-corrected climate, particularly in boreal latitudes. This can partly be expected because the applied bias correction removes only stationary offsets.

At the same time, the results indicate that the absence of a mid-Holocene vegetation maximum is unlikely to be explained solely by biases in the simulated climate. Instead, they point toward structural limitations in the representation of boreal vegetation dynamics and associated land–surface feedbacks in the model, which the emulator does not correct for.

This interpretation is consistent with findings from transient Holocene simulations. Several studies highlight the importance of vegetation feedbacks for Holocene climate evolution, in particular mid-Holocene warmth in the Northern Hemisphere (Thompson et al., 2022). However, models with dynamic vegetation frequently underestimate the magnitude and spatial extent of vegetation changes inferred from proxy records (Dallmeyer et al., 2019; Harrison et al., 2015; Tian and Jiang, 2013), potentially limiting the strength of these feedbacks.

Transient Holocene simulations also show strong regional differences in the timing and magnitude of the Holocene Thermal Maximum, particularly in boreal regions. While models agree reasonably well in regions strongly influenced by residual ice sheets, substantial model–proxy discrepancies persist in areas such as Alaska and Siberia (Zhang et al., 2017, 2018). In these regions, simulated temperature trends during the Early Holocene often differ from pollen-based reconstructions (i.e. warming in reconstructions, cooling in models), highlighting persistent uncertainties in both climatic forcing of vegetation and regional feedbacks (Hao et al., 2025).

In addition, the varying impact of bias correction across regions and time periods may at least partly result from the fact that different climatic factors constrain vegetation at different times. While temperature corrections may improve model–data agreement particularly during the deglaciation, Holocene mismatches may relate to insufficient representation of precipitation dynamics.