dataesr/scientific-paragraphs-categorization huggingface dataset:
S2 and S3 in the Supplement). When N observations of the radar backscatter are available, a final estimate of GSV, with higher accuracy compared to the individual estimates, is obtained by means of a weighted linear combination of the individual estimates of GSV obtained by inverting Eq. (  1 ) for each backscatter observation  (Santoro et al. , 2011; Kurvonen et al. , 1999). V mt = N i=1 w i Vi N i=1 w i (2) In Eq. (2), the weights w i are defined as the difference (σ 0 veg,i -σ 0 gr,i ) so that GSV estimates obtained from images with the strongest sensitivity to GSV are preferred to those obtained from images with no sensitivity to GSV  (Santoro et al. , 2011). In this study, the BIOMASAR-C implementation was tailored to ingest ASAR data (Sect. S2 in the Supplement) and generated a GSV map at 1000 m spatial resolution by combining individual estimates from the ASAR dataset.
AGB = GSV × WD × BEF (5) The spatial variations in WD and BEF result from biological processes that respond to local conditions, as has been demonstrated in regional studies showing environmental controls on the patterns of WD and BEF  (Chave et al. , 2009; Thurner et al. , 2014). Towards a global assessment of WD patterns, we collected published databases based on inventory data where wood density (WD) is reported and explored machine learning methods to maximize the information content in relevant environmental variables (Sect. S5 in the Supplement). The final dataset of WD was obtained by integrating several individual predictions (Sect. S5 in the Supplement). To estimate the BEF, we used the generalized power-law function relating branch and leaf biomass to stem biomass (SB)  (Thurner et al.
, 2014). BEF = p 1 SB p 2 + SB SB (6) Because of the uneven distribution of samples for which biomass component measurements were available (Sect. S5 in the Supplement), the model in Eq. (  6 ) was fitted to measurements of BEF and stem biomass for tropical and extratropical forests only, each stratified by leaf type (broadleaves, evergreen conifers, and deciduous conifers). All BEF models decreased rapidly for increasing stem biomass reaching an asymptote for low-to medium-stem biomass depending on ecoregion and leaf type. The asymptotic BEF for tropical broadleaf species was modelled with a value of 1. 36, higher than other forest types, which were characterized by values of 1. 15-1. 20. Spatially explicit estimates of WD and BEF were obtained at 0. 01 • spatial resolution and resampled to the pixel size of the GSV dataset using bi-cubic interpolation.
In Eq. (  11 ), the scaling factor between standard deviations was represented by the ratio between the pixel areas of the rescaled product (A c+ ) and the BIOMASAR-C data product (A c ): δV C+ = δV C A C+ A c. (11) The standard deviation of the GSV estimates was obtained with the same weighted linear combination of the standard deviations of the BIOMASAR-L and the BIOMASAR-C+ datasets: δGSV = δV C+ × w C + δV L × w L. ( 12 ) The standard deviation of AGB was expressed in terms of partial derivatives of its components: δAGB = ∂AGB ∂WD 2 × δWD 2 + ∂AGB ∂BEF 2 × δBEF 2 + ∂AGB ∂GSV 2 × δGSV 2. ( 13 ) The standard deviation of the wood density estimates, δWD, was obtained by computing the variance of the predictions for each measurement of wood density and fitting a linear model (Fig. S4  in the Supplement).
Validation To assess the accuracy of the AGB estimates, we used a reference dataset of AGB observations from 110 897 forest field inventory plots. The data were gathered from a variety of surveys undertaken by national forest inventories and research networks (Sect. S6 in the Supplement). The opportunistic nature of our validation database led to an uneven spatial distribution of the reference samples (Fig. S5  in the Supplement) as well as a variety of plot sizes, survey methods, and allometric equations used (Tables  S3  and S4  in the Supplement). The plots were mostly smaller than 1 ha (Table  S3  in the Supplement), implying that they often represented a small fraction of the area covered by a 1 ha map pixel. To reduce the effect of random errors caused by the mismatch in resolution between the reference dataset and our map model, we aggregated our map and the plot data to 0.
1 • grid cells. This represented a trade-off between capturing the local-scale variability in AGB whilst allowing a number of plot measurements deemed sufficient to compute an average AGB representative of the area within the grid cell. In the end, our assessment cannot provide an indication of the validity of pixel-based AGB estimates. Instead, it provides a measure of the accuracy of generalized spatial AGB patterns. This is, however, a pragmatic approach when using measurements not designed for validation of estimates from remote sensing imagery but which often provide the only source of information on AGB in poorly inventoried regions or regions where national inventory data are not publicly available. To provide a more comprehensive overview of the reliability of the spatial patterns in areas not covered by the database of plot inventory measurements, the analysis was supplemented by a comparison of average GSV or AGB at the level of inventory reference units (polygons, counties, provinces, and ecoregions).
Inter-comparison of AGB maps The spatial distribution of AGB map estimates from our dataset was compared with biome and global forest AGB maps based on satellite remote sensing observations  (Saatchi et al. , 2011b; Baccini et al. , 2012; Thurner et al. , 2014; Liu et al. , 2015; Avitabile et al. , 2016; Santoro et al. , 2015a)  or ancillary datasets  (Kindermann et al. , 2008). While an additional assessment of our dataset against regional maps of AGB would further contribute to building confidence in the data product, it is felt that such investigations require their own framework also making use of local reference data and expert knowledge, as for example undertaken for Europe  (Avitabile and Camia, 2018) , the US  (Spawn et al. , 2020) , and Tanzania  (Naesset et al. , 2020). To do this, the datasets were first harmonized to a common geographic map projection and resampled to a pixel size of 0.
01 •. Datasets expressing AGB in carbon units (Mg C ha -1 ) were converted to AGB using a carbon fraction default value of 0. 47  (IPCC, 2006)  (Table  S5  in the Supplement). All datasets span a decade of input observations from 2000 to 2010 but could not be harmonized to reflect the conditions of a single epoch due to the lack of information on growth rates. This, however, is not expected to have significant effects on the interpretation of the latitudinal profiles. As a way of assessing the AGB patterns of each map, we compared latitudinal averages based on values from the 0. 1 • validation grid cells with corresponding values from the database of forest inventory plots. To obtain a homogeneous representation of all latitudes, we grouped grid cells in 10 • wide intervals.
Global AGB dataset The global AGB dataset (Fig. 2 ) was obtained by scaling global estimates of GSV (Fig. S6  in the Supplement) using model-based estimates of wood density (Fig. S7  in the Supplement) and stem-to-total biomass expansion factors (Fig. S8  in the Supplement). The uncertainty in the AGB estimates is reported as standard deviation (Fig. 2 ). The models for retrieving GSV and converting it to AGB were developed for woody vegetation, so we evaluated the estimates corresponding just to forest cover by regrouping the classes from the Climate Change Initiative Land Cover (CCI-LC) dataset of 2010 into forest and non-forest land (Sect. S1, Table  S7  in the Supplement). At the 1 ha scale, the largest predicted value was 757 Mg ha -1 , corresponding to a GSV of 1087 m 3 ha -1 , in forests of the US Pacific Northwest.
2 , which scale with the AGB level. The relative standard deviation was smaller than 100 % for approximately 95 % of the mapped pixels, which explains truncating the colour bar of the AGB standard deviation map in Fig. 2  at 100 %. The large majority of the AGB estimates for which the standard deviation exceeded the 100 % level were below 20 Mg ha -1 , such as in sparsely vegetated regions corresponding to the transition to tundra in Canada and Alaska, the Siberian Lowlands and Far East Russia, or in poorly stocked forests such as in northern China and western Madagascar. The small-scale variability in AGB in forest landscapes is captured by the 1 ha pixel spacing of the dataset (Figs. 3  and 4 ). The example in Fig. 3  shows the region of the Bratsk Reservoir formed by the Angara River in central Siberia, where forests are heavily managed for timber production.
4 , top left panel), and some isolated, smallscale patches of deforestation are also visible. For comparison, Fig. 4  shows AGB estimates by three pan-tropical maps based on remote sensing observations  (Saatchi et al. , 2011b; Baccini et al. , 2012; Avitabile et al. , 2016). Because it was based on satellite data acquired around the year 2000, the deforestation patterns are less extended in the map by  Saatchi et al. (2011b)  compared to the maps by  Baccini et al. (2012) , based on observations taken in 2007, and  Avitabile et al. (2016) , which merged the other two pan-tropical datasets. The level of detail in our map is much greater because of the 1 ha spatial resolution compared to 25 ha in  Baccini et al. (2012)  and nearly 100 ha in  Avitabile et al. (2016)  and  Saatchi et al. (2011a)  3.
2 Validity of AGB estimates AGB averages were obtained for 6456 0. 1 • grid cells including at least five inventory plots (Sect. S6 in the Sup-plement). These grid cells represented approximately 1 % of the Earth's forest cover. The grid cell average AGB from the field inventory database ranged from 0 to 1670 Mg ha -1 (median: 43 Mg ha -1 ; mean: 60 Mg ha -1 ; 99th percentile: 351 Mg ha -1 ). The AGB histogram was skewed towards low values (Fig. 5a ) because of the large proportion of measurements from the National Forest Inventories of Spain and Sweden (Table  S4  in the Supplement). The grid cell average AGB from the map ranged from 0 to 358 Mg ha -1 (median: 57 Mg ha -1 ; mean: 67 Mg ha -1 ; 99th percentile: 278 Mg ha -1 ). The AGB histograms from the map (Fig. 5b ) and the field inventory (Fig.
Spatial distribution of AGB Combining our AGB dataset with the CCI Land Cover dataset and the FAO ecological zones, we estimated a total AGB of 521 Pg for a forest area of 4825 million ha, corresponding to a global average forest AGB of 108 Mg ha -1 (Table  1 ). Using the carbon fraction default value of 0. 47  (IPCC, 2006) , we estimated a total above-ground carbon stock of 246 Pg C. Tropical forests had the highest average AGB (147 Mg ha -1 ), representing 64 % of the total forest AGB and 47 % of the total forest area. The second-largest average AGB was found in temperate forests (102 Mg ha -1 ), which accounted for 14 % of the total AGB and 15 % of the total forest area. Subtropical and boreal forests had similar average AGB (75 and 60 Mg ha -1 , respectively), but the area covered by the latter was almost 3 times larger.
Global and continental statistics The statistics on forest area, average AGB, and total AGB from the FRA 2010 and from the combination of our AGB dataset with the CCI Land Cover dataset are reported by continent (Table  2 ). Our total AGB estimate of 522 Pg was 11 % higher than the value of 468 Pg reported by the FRA. This difference is a consequence of the 23 % larger forest area estimated from the CCI Land Cover dataset (Table  2 ) despite the FRA reporting 9 % higher global average AGB than our estimate (119 vs. 108 Mg ha -1 ; Table  2 ). Compared to Table  1 , based on the FAO global ecological zones dataset to delineate land surfaces, we estimate an additional 8 × 10 6 ha of forest area and an additional 1. 5 Pg of total AGB as a consequence of the more precise delineation of the land surface by the Database of Global Administrative Areas used as reference Table  3.
Source Latitude range 60-30 • S 30-10 • S 10 • S-10 • N 10-30 for the countries' boundaries (GADM, http://www. gadm. org, last access: 9 August 2021). For the three continents spanning the tropics, we found the highest average AGB in South America, although our estimate (183 Mg ha -1 ) was 11 % lower than the corresponding value from the FRA (206 Mg ha -1 ) (Table  2 ). South America also contained the largest total AGB pool. Although our estimate (155. 9 Pg) was only 4 % smaller than the FRA (162. 3 Pg), the FRA did not provide AGB for approximately 10 % of the forest area of South America (Table  2 ). We found a larger difference between our results and those of FAO for Africa. The average AGB from our dataset was 24 % lower than the FRA (108 Mg ha -1 vs. 142 Mg ha -1 ; Table  2 ), whilst the total AGB was only 11 % smaller than in the FRA (84.
8 vs. 95. 3 Pg) due to the larger forest area we used from the CCI Land Cover dataset. In contrast, for Asia the average AGB from our dataset (115 Mg ha -1 ) was 17 % higher than in the FRA (98 Mg ha -1 ) (Table  2 ), while our estimate of total AGB exceeded that from the FRA by 64 % (89. 4 vs. 54. 3 Pg) mainly because of the 40 % larger forest area estimated from the CCI Land Cover dataset. For the two continents spanning the northern boreal and temperate zones, the average AGB values from our estimates were well below 100 Mg ha -1 (Table  2 ). The average AGB estimate for Europe differed by less than 1 % (Table  2 ) compared to the FRA, whereas for North and Central America the difference was 15 %. Because the forest area estimated from the CCI Land Cover dataset was larger than the FRA values, the total AGB estimated from our dataset was larger than the values reported in the FRA by 20 % for Europe and 14 % for North and Central America.
National statistics At the level of individual countries, the agreement between the total and average AGB values from out dataset and from the FRA differed depending on the continent (Figs. 7  and 8 , Table  S7  in the Supplement). The largest difference between our average AGB and FRA AGB was in Africa (median difference: -60 %; 51 countries), where for most countries the average AGB reported in the FRA exceeded the value from our dataset (Fig. 7 ). This is probably due to ei-   S7  in the Supplement for details). ther AGB underestimation in countries dominated by highdensity forests or to high biomass conversion and expansion factors (BCEFs) used by countries with low-density forest when estimating values of AGB from their original measurements of GSV (Table  S7  in the Supplement). In addition, several countries used a small sample of plots for the calculations as well as small-sized plots for heterogeneous forest areas, leading to large uncertainties in the values reported to the FRA.
In Europe and South America, where the span of the average AGB was similar to Africa, we also saw underestimation patterns above 200 Mg ha -1 (Fig. 7 ). Nonetheless, we did not identify the trend in the range 0-200 Mg ha -1 seen in Africa. For European and South American countries, the assessment of the reliability of our AGB averages at the country level was more meaningful because of the better developed national inventories (Fig. 8b ) and the direct estimation of AGB from the inventory measurements, thus bypassing the use of a standard BCEF like in African countries (Table  S7  in the Supplement). Indeed, the smallest differences between the average AGB from the FRA and from our dataset were obtained in Europe (median difference: -8 %; 42 countries) and South America (median difference: 2 %; 9 countries) (Fig.
8a ). For North and Central America (19 countries), Asia (35 countries), and Oceania (9 countries), the median difference between our average AGB estimates and the FRA numbers was between -23 % and -27 % (Fig. 7 , Table  S7  in the Supplement). The disagreement for North and Central America was largest for the Caribbean countries (Fig. 8a ), for most of which the reference data used in the FRA had low to moderate quality, and the NFI capacity was mostly low or limited. The scatterplot for Asian countries shows data points of average AGB clustered along the identity line (Fig. 7 ) but with two distinct regions. For the Asian Middle East, stretching as far as Pakistan and the former Soviet countries of the Asian continent, the average AGB from our dataset was on average 70 % smaller than the values reported in the FRA (Fig.
8a ). The FRA country reports were based on highly stocked forest, which may not be representative of the true average AGB. In contrast, the average AGB estimated from our dataset was approximately 27 % larger than the values reported in the FRA for the southern and eastern regions of the Asian continent (Fig. 8a ). Several countries of Southeast Asia assumed their forests to be strongly degraded, which justified the use of low reference values for the average GSV, and hence AGB, when reporting to the FRA. Our estimates of average AGB for Australia (brown marker, Fig. 7 , Oceania panel) and Papua New Guinea (green marker, Fig. 7 , Oceania panel) exceed the values in the FRA while being smaller for New Zealand (cyan marker, Fig. 7 , Oceania panel). Australia reported their biomass stock based on models calibrated with a small number of inventory measurements.
5 ) were associated with an intermediate NFI capacity level (Fig. 8b ), which partly explains the somewhat poor agreement between our average AGB and the average AGB reported in the FRA (Fig. 8c-e ). In terms of forest area, the orders of magnitude in the map and the FRA agreed, but in most cases the area obtained from the CCI Land Cover dataset was larger than the country values reported to the FRA. The CCI value was on average 24 % greater than in the FRA except for the countries of North and Central America, where the average difference was 81 %. The discrepancy can be explained in terms of the different definitions of forest used in CCI when generating land cover maps and in the FRA when using national data of different quality to generate the country estimates. However, the estimate of forest area obtained in this study is likely to be an underestimate since it excluded land cover classes with a sparse tree and vegetation component that could be attributed to forest under less restrictive definitions of percentage tree cover  (Mermoz et al.
, 2018). As a result, our country estimates of total AGB were only slightly different from the FRA estimates (Fig. 9 ) because the lower AGB densities from our dataset were compensated by the larger forest area values in the CCI Land Cover dataset (Table  S7  in the Supplement). For Asian and European countries, the difference was 7 % and 5 % on average, respectively. The difference was larger throughout the American continent, where total AGB estimated in this study exceeded that in the FRA on average by 33 % (North and Central America) and 23 % (South America). Only for Africa and Oceania did we obtain a total AGB smaller than the FRA, on average -37 % for Africa and -29 % for Oceania, because of the large difference between average AGB values obtained in this study and those reported by the FAO.
Comparison of map estimates of AGB All map datasets analysed in this study including ours (Table 3) showed similar latitudinal trends (Fig. 10a ), with the highest AGB in the Southern Hemisphere at 40 • S and across the Equator and low AGB in the dry tropics at around 20 S and north of 10 • N. However, there were some large differences between the maps (Fig. 10a ), illustrating the current uncertainty about the global forest carbon pools. For the wet tropics between 15 • S and 10 • N, the AGB from our dataset was close to that from the pan-tropical dataset by  Saatchi et al. (2011a)  (Fig. 10b ) but is between 10 % and 50 % lower than the values by  Baccini et al. (2012) , and the GEOCARBON dataset. The analysis of the latitudinal averages based on the 0. 1 • grid cell AGB values show an overestimate of AGB in these two datasets by about 10 % to 60 %.
In contrast, the average AGB values from our dataset were only higher than the corresponding values from the plot inventory database by a few per cent (Fig. 11a  and b ). The differences between our dataset and each of the pantropical AGB datasets were much larger in tropical and subtropical regions north and south of the wet tropics. In the Northern Hemisphere, between 10 and 30 • N,  Saatchi et al. and Baccini et al. (2011a, 2012)  exceeded our estimates by between 40 % and 110 % (Fig. 9b ). For the same latitude range, the GEOCARBON dataset differed from our values by 110 % to -47 % with increasing latitude (Fig. 10b ). The latitudinal averages at the 0. 1 • grid cells confirmed that all three maps were strongly biased, while our dataset was closer to the values obtained from the plot inventory dataset (Fig.
11 ). The GEOCARBON dataset presented both positive and negative biases, being about 50 % of the average AGB from the plot inventory dataset (Fig. 11a ). The overestimate exceeded 100 % of the average AGB from the plot inventory dataset in the case of  Saatchi et al. and Baccini et al. (2011a, 2012)  (Fig. 11b ). In the Southern Hemisphere, between 35 and 15 • S, the GEOCARBON dataset and  Baccini et al. (2012)  exceeded our AGB by 20 % to 160 %, whereas  Saatchi et al. (2011a)  differed from our values by between +20 % and -60 % (Fig. 10b ). The comparison at the level of the 0. 1 • grid cells indicates an overestimate by  GEOCARBON and Baccini et al. (2012)  between 20 % and 60 % of the average AGB from the plot inventory data (Fig. 11a  and b , respectively). The difference between the average AGB from our dataset and from  Saatchi et al.
(2011a)  with respect to values from the plot inventory dataset were instead mostly below 20 %. For the Southern Hemisphere temperate forests south of 35 • S, our AGB exceeded the values from  Saatchi et al. (2011a)  and the GEOCARBON dataset. The comparison was, however, of limited value because of the incomplete coverage by the former and the coarse-resolution estimates used to fill gaps in the latter. North of 30 • N, we did not observe differences between our dataset,  Thurner et al. (2014)  and the GEOCARBON dataset. This was expected since all studies were based on the same Envisat ASAR dataset and the BIOMASAR algorithm. The only difference was visible at about 70 • N (Fig. 9b  and 6c ) because of the tendency of ASAR to overestimate biomass in sparse tree vegetation. This difference is, however, of minor importance in the context of global estimation of AGB stocks because the AGB hardly ever exceeded 30 Mg ha -1 at these latitudes in any of the datasets (Fig.
10a ), this being consistent with values based on forest inventory measurements  (Stolbovoi and McCallum, 2002; Gillis et al. , 2005). Figure  11a  and c confirm that the three maps present similar spatial patterns of AGB; the difference with respect to the plot inventory dataset was about 20 %-30 % for all datasets except for GEOCARBON at 60 • N, where the difference was 60 % of the plot inventory value. These results were attributed to the higher spatial resolution of our map. The coarse-resolution AGB datasets by  Liu et al. and Kindermann et al. (2015, 2008)  agreed with our estimates in the large unbroken tracts of forest in the wet tropics between 10 • S and 10 • N and in the boreal zone around 60 • N (Fig. 10d ). However, the estimates of AGB by  Liu et al. (2015)  were up to 70 % lower than our estimates in fragmented forest landscapes, e.