dataesr/scientific-paragraphs-categorization huggingface dataset:
For the monthly-based bias correction, we applied CDF-t, on a monthly basis, to the daily data ensemble of each grid cell, given that the days belong to the same month. During the yearly-corrected bias correction, we applied CDF-t to the full data ensemble of each grid cell, regardless of the month. Within the two options for bias correction with CDF-t (on a monthly or yearly basis) there is potential to test if one or the other methodology has a significant impact on the result. It must be recognized that bias correcting on a per month basis does not guarantee to maintain the seasonality changes at a period where the orbital configuration is significantly different. The performance of the bias correction was analysed by calculating the root-mean-square error (RMSE), Pearson's correlation coefficient (R), and standard deviation (SD) between the values of the bias-corrected iLOVECLIM simulations and the EWEMBI values.
Their findings indicated that dynamically downscaled iLOVECLIM simulations result in a better agreement with proxy-based reconstructions and other climate model studies, compared to the coarse resolution grid, particularly in the Mediterranean and complex mountainous terrain. In the current study, the dataset used for the data-model comparison was extracted from the global database of Holocene paleotemperature records Temperature 12k at version 1. 0. 0  (Kaufman et al 2020) , where data is represented as absolute temperature values, rather than anomalies. It consists of reconstructed through the inverse modelling absolute near-surface air temperature data points derived from lake sediment, marine sediment, peat, glacier ice, and other natural archives. Temperature reconstructions were done by numerous independent studies using a wide variety of proxy data (i.
e. alkenones, d18O), associated with several uncertainties (see section 4. 1). The design of the Temperature 12k database is further described by  Kaufman et al (2020) , while the sources of each data point are included in the metadata of the database. For the purpose of this study, we extracted the Temperature 12k terrestrial mean annual values dated between 5. 5-6. 5 ka (MH), and 20. 5-21. 5 ka (LGM). For the sake of comparing with the iLOVECLIM model outputs, we resampled the Temperature 12k data points to T21 and hi-res grid, using the aggregated average resampling method. This method assigns to the new output cell the most common values of the cells in the input map within the limits of the output cell (Díaz-Pacheco et al 2018). We then analysed the differences between the modelled and reconstructed near-surface air temperatures before and after the CDF-t application at corresponding grid cells.
The CARAIB model is made of five modules: hydrological, canopy photosynthesis and stomatal regulation, carbon allocation-growth-respiration, heterotrophic respiration, and plant competition and biogeography. Vegetation is distributed in 26 PFTs, which, with respect to climatic parameters, are classified into 20 biomes. As an input, CARAIB requires six variables with a daily frequency: near-surface air temperature, precipitation, relative humidity, wind speed, sunshine hours and daily temperature amplitude. In all simulations of this study, wind speed was taken from the EWEMBI dataset, and sunshine hours were used directly from iLOVECLIM. The iLOVECLIM model does not have a daily cycle, thus daily temperature amplitudes were taken from observations (Climatic Research Unit (CRU) data, mean over 1901-2015) and kept constant for all time periods.
To assess the effect of the CDF-t application on the accuracy of simulated biome distribution, we used different sets of surface temperature, precipitations, and relative humidity taken (a) from the EWEMBI observation dataset (b) from the iLOVECLIM model, and (c) from the iLOVECLIM model after the CDF-t application to the outputs. The observation-enforced simulation was used as a control for the PI simulations. The resulting computed biome distribution was compared to the BIOME6000 reconstruction  (Harrison 2017). This reconstruction is based on the Paleovegetation Mapping Project  (Prentice et al 1998 (Prentice et al , 2000)). In BIOME6000, biomes are represented based on degrees of affinity of PFTs with each biome  (Prentice et al 1996). In this work, we used megabiomes from BIOME6000, described by  Harrison and Bartlein (2012).
The 20 biomes in CARAIB were then reclassified into the nine megabiomes used in the BIOME6000 pollen database using the methodology of Extier (2019) (supplementary table  1 ). Similarly to the inverse approach, we resampled BIOME6000 data points to the T21 and hi-res grids, using the majority resampling method (figure  6 ). The agreement was tested by calculating matching ratios between the resampled BIOME6000 and CARAIB-derived biomes before and after the CDF-t application. To account for the discrepancies in biome classification and spatial incoherency we also present the biome distribution in data and model in a form of contingency tables (supplementary tables 2-11), that outline frequency for particular combinations of biomes. We found that the spatial irregularity of the data distribution of BIOME6000 and its absence in certain bioclimatic zones led to major regional inconsistencies.
To overcome this data scarcity and irregularity across different regions and biomes (see section 4. 1), we thus further compared our results with the statistically modelled gridded potential natural vegetation (PNV) distribution of  Levavasseur et al (2012). The PNV is relying on BIOME6000 at the PI period as a predictand for a multinomial logistic regression on a high-resolution grid worldwide. Besides its regular grid spacing without missing data, it also has the advantage of including a prediction of climatic zones where biomes remain are scarce or non-existent such as desertic areas (see section 4. 1). To test differences between the matching ratios before and after correction, we used the generalized Pearson chi-squared test of independence.
Inverse mode. Comparison with paleotemperature record The results of the comparison between the modelled climate parameters and proxy-reconstructed values from the Temperature 12k dataset are represented as scatterplots (figure  2 ). We observe significant improvement after the CDF-t application for the MH on the hi-res grid over Europe and on a T21 grid globally. No statistical difference was detected for the LGM. In supplementary figures 2-7 we can observe a reduction in known large-scale iLOVECLIM biases, outlined in the literature  (Goosse et al 2010). After the CDF-t application, North America is getting colder (supplementary figure  2 ) and, in parts, dryer (supplementary figures 3 and 4), which corrects the overestimation of temperatures in low latitudes in iLOVECLIM. Similarly, we observed a decrease in precipitations in subtropics, in particular in Asia and Australia (supplementary figure  3 ).
Forward mode. Comparison with pollen-based vegetation reconstructions To quantify the performance of the CDF-t bias correction method to simulate the global biome distribution, we compare the resulting biome maps with biome reconstructions provided by the BIOME6000 project  (Harrison 2017). Since there is an inherent bias related to the use of the CARAIB model as well as the reconstruction dataset, we first compute biomes from CARAIB vegetation output using the EWEMBI observations (control) as an input. This biome output represents the best attainable fields using the bias correction. The difference between that reference field and the other biome fields is indicative of the remaining error in the climatic field. Table  2  shows that after the CDF-t correction, the modelled biomes better match the BIOME6000 pollen data in all experiments except for the T21 PI, as opposed to non-corrected values.
The improvement is    1 ). The figure with reference data before resampling can be found in supplementary materials (supplementary figure  9 ). Table  2. Matching ratios between megabiomes in pollen reconstructions (BIOME6000) and biomes predicted by the CARAIB model using: unaltered iLOVECLIM climatic variables (before correction); bias-corrected iLOVECLIM climatic variables using the CDF-t method on a monthly basis (after correction); and EWEMBI climatic variables (control). Hi-res: downscaled simulation over Europe; T21: standard global simulation. The megabiome classification consists of 9 biomes. A ' * ' marks when differences between the data before and after the CDF-t bias correction is statistically significant at the 0. 05 level with a chi-squared test. biome reconstructions for each continent separately (figures 6-8).
Europe The area is also well-represented in the BIOME6000 database. However, the number of records for LGM is quite low, and mostly represented by the grassland and dry shrubland data points near PD coastal areas, generally clustered around the Mediterranean. This lack of diversity in the reconstructions hampers obtaining a full picture for other biomes. At PI, in the Mediterranean region CARAIB simulates temperate (before CDF-t) and boreal forest (after CDF-t), thus no significant improvement in matching ratios is observed. However, the results indicate a significant improvement in biome representation for PI (57 versus 65%) and MH (50 versus 85%) after the CDF-t application. The lack of improvement in comparison with  Levavasseur et al (2012)  on a T21 grid (matching ratio 51% before and 39% after CDF-t) could be attributed to the coarse resolution of the model, since the downscaled simulation results in a significant increase in the matching ratios between the models after the CDF-t application (39 and 49% correspondingly) (table  3 ).
Asia Asia appears to have lower matching ratios after the bias correction for each studied period, compared to non-bias corrected results, but these differences are not statistically significant (PI: 37 versus 36%, MH: 38 versus 35%, LGM: 33 versus 29%). Comparison with the PNV of  Levavasseur et al (2012) , however, indicates significant improvement in matching ratios after correction (35 versus 44%). This suggests that the results of comparison with reconstructions are negatively influenced by poor BIOME6000 data spatial coverage in Siberia, and highlights the role of spatial distribution and continuity of the reconstructions. CARAIB classifies cold desert as 'desert' , and therefore, large areas of Siberia are assigned to this distribution. This negatively reflects on matching ratios for the region of Asia.
Another aspect that contributes to the decrease in matching ratios over the entire continent, is the fact that the conditions of warm temperate forest are The superimposed circles are the data from the BIOME6000 Version 4. 2 reconstruction resampled to the T21 grid using the majority resampling method. The biome classification of CARAIB has been adapted to match the megabiomes of BIOME6000. Matching ratios are presented in % per continent between megabiomes in pollen reconstructions (BIOME6000) and biomes predicted by the CARAIB model. NA-North America; SA-South America; EU-Europe; AF-Africa; AU-Australia; AS-Asia; Obs-CARAIB results with the use of the EWEMBI climatic variables (observations) as an input (control). A ' * ' marks when differences between the data before and after the CDF-t bias correction is statistically significant at the 0.
05 level with a chi-squared test. The figure with reference data before resampling can be found in supplementary materials (supplementary figure  10 ). attributed to temperate forest in CARAIB. After CDF-t correction, the model overestimates the extent of tundra compared to reconstructions for all the studied time periods. However, the southern extent of the boreal forest after the CDF-t application is in better agreement with the BIOME6000 records and PNV of  Levavasseur et al (2012).
South America The extent and location of the Amazon rainforest after correction seem visually better represented (supplementary tables 3-7). However, this is not supported by the matching ratios. We observe a significant decrease in accuracy after bias correction for the MH (52 versus 26%). This is probably a consequence of the low number of pollen samples in the rainforest. The vast majority of data points from the region are found on the borders of the rainforest with other biomes and are, due to the coarse spatial resolution of our The superimposed circles are the data from the BIOME6000 Version 4. 2 reconstruction resampled to the T21 grid using the majority resampling method. The biome classification of CARAIB has been adapted to match the megabiomes of BIOME6000. Matching ratios are presented in % per continent between megabiomes in pollen reconstructions (BIOME6000) and biomes predicted by the CARAIB model.
NA-North America; SA-South America; EU-Europe; AF-Africa; AU-Australia; AS-Asia; Obs-CARAIB results with the use of the EWEMBI climatic variables (observations) as an input (control). A ' * ' marks when differences between the data before and after the CDF-t bias correction is statistically significant at the 0. 05 level with a chi-squared test. The figure with reference data before resampling can be found in supplementary materials (supplementary figure  11 ). simulations, attributed to temperate, warm temperate forest, savannah, and dry woodland. Comparison with  Levavasseur et al (2012)  indicated no significant improvement (table  3 ), since the PNV of  Levavasseur et al (2012)  is based on BIOME6000 data, and thus tropical forest is largely replaced by warm-temperate forests in both datasets.
Australia Due to the low number of BIOME6000 data points and model resolution, CDF-t has no significant impact on the matching ratios on the continent compared both to reconstructions and to PNV of  Levavasseur et al (2012). Due to the lack of representation of biomes, not specific to pollen-based climate reconstructions, the desert is not reflected in the BIOME6000 dataset. Thus, here, as well as in North Africa and the Himalayas, the matching ratios are negatively biased by the absence of an important biome class in one of the compared LGM on T21 grid before and (b) after the CDF-t correction. The superimposed circles are the data from the BIOME6000 Version 4. 2 reconstruction resampled to the T21 grid using the majority resampling method. The biome classification of CARAIB has been adapted to match the megabiomes of BIOME6000.
Matching ratios are presented in % per continent between megabiomes in pollen reconstructions (BIOME6000) and biomes predicted by the CARAIB model. NA-North America; SA-South America; EU-Europe; AF-Africa; AU-Australia; AS-Asia; Obs-CARAIB results with the use of the EWEMBI climatic variables (observations) as an input (control). A ' * ' marks when differences between the data before and after the CDF-t bias correction is statistically significant at the 0. 05 level with a chi-squared test. The figure with reference data before resampling can be found in supplementary materials (supplementary figure  12 ). datasets. Taking this aspect into account, it is evident from figure  6  and supplementary figure 10 that the expansion of the Australian desert resulting from the bias correction in the model leads to a spatial distribution in better agreement with its PD size and location, and the biome distribution modelled by  Levavasseur et al (2012)  (supplementary figure  8 ).
Limitations related to multivariate correlations in vegetation modelling As an input, CARAIB model requires six variables: near-surface air temperature, precipitation, relative humidity, wind speed, sunshine hours, and daily temperature amplitude. However, due to data availability of the observational dataset, we were only able to apply the CDF-t method to three of them (surface temperature, precipitation, relative humidity). CFD-t bias correction has been applied independently for each of the three variables. However, the application of univariate calibrations by CDF-t should not disrupt existing spatial coherency and dependence among variables. Indeed, as it is a QQ-based technique, CDF-t respects the dependence (i. e. coherency) between the variables of the simulations to be corrected. This means that a high (or low) simulated value is transformed to a high (respectively, low) corrected value and, more generally, that a simulation value corresponding to the p% percentile is transformed to the p% percentile of the correction values.
Limitations related to paleovegetation reconstructions While being a quantitative approach to denote a similarity between datasets, there are several limitations to consider while interpreting paleovegetation reconstructions. Firstly, the BIOME6000 is an amalgamation of multiple data sets, each containing significant reconstruction uncertainties  (Hengl et al 2018)  related to pollen sampling and analysis methods  (Prentice and Webb 1998, Harrison 2017). There are relatively little data for tropical South America, Africa, and Asia  (Hengl et al 2018) , where lower confidence in the results is expected. This is also true for other regions for the LGM because of the very few data points. BIOME6000 is a point-based dataset, which represents biomes of specific locations, often influenced by the local micro-climate and geo-environmental parameters.
In this study, we resampled the BIOME6000 dataset to match the native grid of iLOVECLIM, which led to the loss of spatial detail in the reconstructions. Additionally, it created a bias in the regions, poorly represented in the BIOME6000 database, since scarcely located data points were considered representative of entire grid cells. This bias is particularly strong on a coarser resolution T21 grid, at bordering regions between the biomes, and in cases where the BIOME6000 data points were located near an edge of a grid cell. An example of such bias can be seen on the Western border of the Sahara desert at PI (figure  6 , supplementary figure  10 ), where several reconstruction data points associate the region with grassland and dry woodland. While being in close vicinity with the corresponding biome class in CARAIB, a few of them fall at the edge of a desert grid cell, and therefore, do not contribute to the increase in matching ratios.
The biomization technique has been applied for the LGM but the conversion from PFT to biomes based on bioclimatic limits for the PI is considered constant over time which may not be the case. This may contribute to lower matching ratios at LGM compared to PI and MH (tables 2 and 3). The abovementioned patterns persist after the CDF-t application, as well as for the control simulation, which indicates that differences in biomization methods of BIOME6000 compared to CARAIB significantly influenced the inter-comparison of the two datasets.
Limitations related to paleotemperature reconstructions Most published studies present the reconstructed, as well as modelled climate data in a form of anomalies (differences) to modern values  (Mauri et al 2015 , Cleator et al 2020). The CDF-t approach, however, preserves the evolutions of the input climate values by design, since the CDF-t corrects stationary biases under different mean states and preserves simulated by climate models anomalies. Therefore, useful data for the evaluation of the CDF-t methodology are scarce. Among the few available options, we selected the Temperature 12k dataset (Kaufman et al 2020) as a reference dataset for paleotemperature reconstructions. While being a compilation of non-continuous point data and featuring exclusively temperatures, it presents the data in a form of absolute values, which allows direct comparison with the modelled values prior to and following the CDF-t correction.
In addition, the Temperature 12k is composed of consistent, quality-controlled paleotemperature records derived from the lake and marine sediments, peat, glacier ice, and other natural archives  (Kaufman et al 2020). High standards of quality control of the featured data and consistency throughout a large number of records allow the use of the dataset as a reference in the context of the current study. Being largely based on pollen samples, the Temperature 12k dataset shares a similar spatial bias as the BIOME6000 dataset regarding quantification of deserts and other not specific to pollen-based reconstructions biomes  (Chevalier et al 2020). Other uncertainties of the dataset are related to calibration and proxy biases, chronology, and spatiotemporal coverage  (Kaufman et al 2020). In addition, a vast majority of the Temperature 12k data points were derived from marine proxies and thus were not used in this study, which is focused on the land surface.
The effect of the limitations of the reconstruction datasets is more likely to be significant when the number of data points is low. This can be seen in the example of the downscaled MH. In figure  3 , we compare the results of our simulations to the observation-based simulation. Temperature 12k indicates higher temperatures in Scandinavia than iLOVECLIM. This was also noted in comparison between the temperature reconstructions and PMIP4-CMIP6 simulations, where annual mean temperatures of the reconstructions for the MH were warmer at most latitudes, with maximum warming in the Arctic  (Brierley et al 2020). However, the EWEMBI data show that this region is colder than in iLOVECLIM at the PD, thus it further lowers the temperatures over the region when applying the CDF-t. A similar phenomenon is observed in the Northern Hemisphere for the LGM.
Better representation of these regions in pollen databases, compared to rather poorly-covered South America, Africa, and Asia  (Hengl et al 2018) , attributes to higher confidence in the results of the comparison for the aforementioned regions. The T21 coarse grid is rather disadvantageous for capturing regionally confined biomes (i. e. savannah and dry woodland), which are better represented at finer downscaled resolution. However, large biome belts (such as tropical forest) are well captured following the bias correction procedure on both studied resolution grids (figures 6-9). The use of the CDF-t bias correction improves the agreement for the PI with predicted PNV distribution based on multinomial logistic models  (Levavasseur et al 2012)  and the BIOME1 model results  (Dallmeyer et al 2019).
We have demonstrated that placing the CDF-t technique as an additional post-processing step of modelled data is a clear advantage to correct palaeoclimate model data for systematic biases. Our conclusion is supported by a set of statistical parameters (matching ratios, R, RMSE) showing better agreement between the models and the reconstruction datasets for the PI and MH. We found higher correlation between the reconstructed  (Kaufman et al 2020)  and the modelled temperatures after bias correction on both 5. 625 • (R = 0. 88, RMSE = 6. 32, SD = 9. 37 before correction; R = 0. 91, RMSE = 4. 71, SD = 10. 05 after correction) and 0. 25 • grid (R = 0. 15, RMSE = 4. 13, SD = 3. 46 before correction; R = 0. 46, RMSE = 2. 79, SD = 1. 97 after correction). Comparison with BIOME6000 reconstructions resulted in significant increase in matching ratios after bias correction for the MH at T21 grid at the 0.
Figure6. Model-data comparison of the biome distribution simulated from offline CARAIB run forced with iLOVECLIM climatic results for (a) pre-industrial on T21 grid before and (b) after the CDF-t correction. The superimposed circles are the data from the BIOME6000 Version 4. 2 reconstruction resampled to the T21 grid using the majority resampling method. The biome classification of CARAIB has been adapted to match the megabiomes of BIOME6000. Matching ratios are presented in % per continent between megabiomes in pollen reconstructions (BIOME6000) and biomes predicted by the CARAIB model. NA-North America; SA-South America; EU-Europe; AF-Africa; AU-Australia; AS-Asia; Obs-CARAIB results with the use of the EWEMBI climatic variables (observations) as an input (control). A ' * ' marks when differences between the data before and after the CDF-t bias correction is statistically significant at the 0.