Depth distribution of belowground net primary production across global biomes

The depth distribution of belowground net primary production (BNPP) has been unquantied globally, hindering our understanding of belowground carbon dynamics. We synthesize global observational data sets to infer the depth allocation of BNPP down to 2 m, and map depth-specic BNPP globally at 1 km resolution. We estimate that global average BNPP in the 0–20 soil layer is 1.1 Mg C ha –1 yr –1 , accounting for >50% of total BNPP. Across the globe, the depth distribution of BNPP shows large variability, and more BNPP is allocated to deeper layers in hotter and drier regions. Edaphic, climatic and topographic properties (in the order of importance) can explain >80% of such variability in different soil depths; and the direction and magnitude of the inuence of individual properties (e.g., precipitation and soil nutrient) are soil depth- and biome-dependent. Our results provide global benchmarks for predictions of whole-soil carbon proles across global biomes.


Introduction
Plant net primary production (NPP) is a fundamental ecosystem property, providing food, energy and ber for higher trophic organisms, and mediating the global carbon cycle by linking atmospheric and soil carbon reservoirs (1)(2)(3).In mineral soils -the largest terrestrial carbon reservoir (4), belowground NPP (BNPP) is the predominant source of soil carbon and its depth distribution is critical for understanding whole-soil pro le carbon dynamics.On the one hand, the vertical distribution of BNPP couples with a series of belowground processes such as plant water uptake and nutrient acquisition, microbial and soil fauna activities which are important processes modulating soil carbon turnover behaviors in different soil layer depths (5).On the other hand, BNPP represents the major new carbon inputs to different soil depths, together with carbon outputs mainly through the respiration of soil microorganisms, determining soil carbon balance in soil depths (6).The new carbon may actively interact with bulk soil old carbon via the priming effect (i.e., new carbon promotes or retards native carbon decomposition in the bulk soil) (7,8), regulating soil carbon stability (9).Overall, it is vital to quantify the depth distribution of BNPP to elucidate belowground processes and making reliable depth-speci c predictions of soil carbon and relevant biogeochemical cycles (e.g., nutrients) in the soil pro le.
The BNPP can be reasonably estimated by root growth measurements (10)(11)(12) or using state-of-the-art tracer (e.g., carbon isotopes) techniques (13).Data synthesis based on BNPP measurements enables us to rigorously address questions relating to soil carbon dynamics at large spatial scales such as carbon turnover times based on the ratio of soil carbon stocks to BNPP (6,14).Indeed, by synthesizing eld measurements of aboveground NPP (ANPP), combining with satellite-derived NPP, total BNPP (i.e., satellite-derived NPP -ANPP) has been quanti ed at a global scale (15).Nevertheless, the vertical distribution of BNPP in the soil pro le remains unexplored, especially across large extents, due to technical challenges in un-destructively measuring belowground carbon budgets depth by depth in situ (16).Moreover, factors controlling BNPP and particularly its depth distribution may be diverse and vary across space (17,18), resulting in the di culty to construct uni ed models to accurately estimate the depth distribution of BNPP.In Earth system models, for example, BNPP and its depth distribution are usually assumed to be a constant fraction of total NPP.The fraction only varies with plant functional types; and climate is generally considered to be the dominant determinant (19,20).This simpli cation of controls over BNPP would be the major source of the uncertainty in predictions of climate-carbon cycle feedbacks as well as belowground processes such as soil carbon sequestration potential over space and time (21).We need an advanced understanding of whether and how soil depth-speci c BNPP (i.e., the vertical distribution of BNPP) is modulated by environmental factors such as edaphic and topographic attributes.
This study builds upon the ORNL DAAC legacy global data set of eld NPP measurements with the partitioning of aboveground and belowground fractions ( i.e., ORNL DAAC data set, https://daac.ornl.gov/cgi-bin/dataset_lister.pl?p=13).We further update this data set by searching data from peer-reviewed literature (i.e., literature-derived data set).At last, we have obtained 725 soil pro les (NPP obs hereafter which includes 367 and 358 pro les in the ORNL DAAC and literature-derived data sets, respectively) across the globe which enable us to estimate above-and below-ground NPP (Figs. 1a and  S1a).It should be noted that the ORNL DAAC data set is quality-contronlled in order to minimize the potential effects of different measurement techniques on the estimation of NPP and its allocation.
Although the potential discrepancies in measurement techniques, we nd that overall the ORNL DAAC and literature-derived data sets do not show signi cant differences in terms of belowground NPP (BNPP) estimates except in several speci c biomes (Fig. S1b).In addition, the two data sets present a very similar latitudinal pattern of BNPP and are complementary in terms of both spatial (Fig. S1a) and latitudinal coverage (Fig. S1c).In this study, we pool all data together to amplify the usage of the two valuable data sets and the underlying consequences are quanti ed by uncertainty assessment.
Combining the NPP obs data set with another data set of the vertical distribution of root biomass in 559 soil pro les (Root obs hereafter; Fig. 1a and Table S1), we estimate the allocation of BNPP to seven sequential soil layers (i.e., 0-20, 20-40, 40-60, 60-80, 80-100, 100-150, and 150-200 cm) by assuming that BNPP depth allocation is proportional to root biomass distribution in soil pro le.Using a suite of environmental covariates including climatic, edaphic and topographic properties (Table S2), we assess the underlying drivers regulating the depth distribution of BNPP across the globe as well as in different biome types.Machine learning-based models are developed to map the depth distribution of BNPP and its uncertainty across the globe at the resolution of 0.0083° (which is equivalent to approximately 1 km at the equator).
The depth distribution of BNPP Using root pro les (i.e., the Root obs data set) to infer the proportional depth distribution (PDD, unit in %) of BNPP in the seven soil layers, the results indicate that on average roughly 60% of BNPP is allocated to the 0-20 cm soil layer (Fig. 2a); and the top 40 cm soil layer holds around 80% of BNPP (Fig. 2a).In other deeper soil layers, BNPP allocation is relatively small and shows much less variance than in upper layers (Fig. 2a).In the top 20 cm soil layer, for example, the proportional allocation of BNPP ranges from 37% (2.5% quantile) to 78% (97.5% quantile).For proportional BNPP allocation to a typical soil layer, it is signi cantly (P < 0.05) different among biomes (Fig. 2c).Boreal forests and tundra relatively allocate more (~70% of BNPP) to upper layers (e.g., 0-20 cm) than other biome types (e.g., <50% in tropical/subtropical grasslands/savannas and deserts which allocate more BNPP to deeper layer depths, Fig. 2c).
Because the locations of NPP obs soil pro les do not match with that of Root obs (Fig. 1a), we develop machine learning models trained by Root obs data set to predict PDD in NPP obs locations (Fig. S2).
Multiplying the observed BNPP at NPP obs locations by PDD predictions, the absolute amount of BNPP in the seven soil layers is estimated with the consideration of prediction uncertainties by the model.As the PDD (Fig. 2a), the absolute amount of BNPP also decreases exponentially with soil depths, with greater variances in upper soil layers than in deeper layers.Across the globe, an average BNPP of 1.60 Mg ha -1 yr -1 is estimated in the top 20 cm soil (Fig. 2b).In the 20-40 cm soil layer, the average BNPP is reduced to 0.69 Mg ha -1 yr -1 .In deeper layers, BNPP is relatively small and comparable (< 0.30 Mg ha -1 yr -1 ) with smaller variances (Fig. 2b).Among biomes, the absolute BNPP shows signi cant disparities (Fig. 2d).In the top layers (e.g., 0-20 cm), higher BNPP is observed in Mediterranean/Montane shrublands (2.37 Mg ha -1 yr -1 ) and temperate forests (2.11 Mg ha -1 yr -1 ) than in boreal forests (0.94 Mg ha -1 yr -1 ) and tundra (0.52 Mg ha -1 yr -1 ).In deeper soil layers, the variations in absolute BNPP among biomes are in general consistent with those in the top 0-20 cm soil (Fig. 2d).

Drivers of BNPP allocation
As might be expected, soil depth is the most important predictor for the depth distribution of BNPP (Fig. 3a and b).An exponential model using depth as the only predictor can explain 23-56% of the variance in the depth distribution of BNPP across the globe (R 2 = 0.34) and in different biome types (R 2 ranges from 0.23 to 0.56; Fig. 3a, Table S3).The coe cients of the exponential model indicating BNPP allocated to the top layer and decreasing rate of BNPP with soil depth are signi cantly different among biomes (Table S3), further demonstrating that the depth distribution of BNPP is signi cantly different among biomes (Fig. 2).
A random forest model taking into account soil depth, biome type and additional 55 environmental covariates (Table S2), after controlling multicollinearity among the covariates (Figs.S3, S4), can explain 92% (R 2 = 0.92) of the variance in the depth distribution of BNPP in the whole 0-200 cm soil pro le across the globe (Fig. 3b).Following soil depth, MAT (mean annual temperature, which is shown as BIO1 in the gure), AE (mean actual daily soil evaporation), biome type, BD (soil bulk density) and MAP (mean annual precipitation, BIO12) are the most important ve predictors (Fig. 3b).Grouping the environmental predictors into climatic (temperature-and precipitation-related, a total of 7 variables in the model), edaphic (12 variables) and topographic (7 variables) ones, the result indicates that the contributions of climate, soil and topography are 26%, 28%, 13% (Table S4).Focusing on BNPP in speci c soil layer depths, the tted random forest models can explain over 80% of BNPP variances in each of the seven soil layers (Fig. S5).MAT is consistently the most important factor, followed by AE, MAP, soil carbon:nitrogen ratio (i.e., SCN) in deeper layers (Fig. 3b; Fig. S5).In terms of the overall in uence of climatic, edaphic and topographic variables, climatic variables together contribute 33-40% depending on soil layer depths; and edaphic and topographic properties contribute 33-40% and 18-28%, respectively (Figs. 3b, S5; Table S4).
Besides the relative importance of various environmental variables identi ed by the random forest models, linear mixed-effects modelling is further conducted to identify the direction and magnitude of their rst-order relationship with BNPP depth allocation (Fig. 3c).As expected, BNPP depth allocation is negatively correlated to soil depth (Fig. 3c).In general, the effects of all climate-related variables are positive; while the effects of soil-related variables are negative except the positive effects of AE and soil carbon to nitrogen ratio.In different biomes, however, the magnitude and, in some cases, the direction of the regression coe cient are substantially different (Fig. 3c).For example, MAT (i.e., BIO1) has a positive effect in most biomes, but its effect is negative in tropical/subtropical grasslands/savannas.Overall, the varying regression coe cients of the predictor variables in terms of both magnitude and direction among biome types (Fig. 3c) indicate that the effects of environmental controls are biome-dependent.However, it should be noted that the rst-order effects of all variables on BNPP are relatively weak at the global scale albeit signi cant (Figs.3c and S6).A partial correlation analysis controlling the effect of soil depth is also conducted to assess whether the effects of soil-, climate-and topography-related variables are modulated by soil depth.The results of the zero-order correlations between BNPP and the assessed predictors are generally consistent with the results of the mixed-effects regression (Fig. 3c vs Fig. S6a).After controlling the effect of soil depth by conducting a partial correlation analysis, however, most correlation coe cients have been changed, particularly the correlations with soil properties (Fig. S6b,c) which suggest that the effects of soil properties are depth-dependent.

Global pattern of the depth distribution of BNPP
The depth distribution of BNPP is mapped across the globe at the 0.0083° resolution (which is equal to ~1 km at the equator; Fig. 4).Using the NPP obs data set, machine learning-based models are rst developed to predict BNPP (Fig. S7).Combining with models for estimating the proportional depth distribution of BNPP (PDD, Fig. S2), then BNPP in each 1 km grid and each of the seven depths is estimated (i.e., BNPP ×PDD) taking into account uncertainties in the estimation of both BNPP and PDD (Fig. 4).Across the globe, BNPP in the 0-200 cm soil pro le is Mg ha -1 yr -1 (Figs. 4, 5a).The largest BNPP on average occurs in ~20° N (Fig. 5a).In all soil layers, it is general that BNPP is relatively low in desert and northern Hemisphere high latitudinal regions (Fig. 4) with an apparent decreasing trend from 40° N to 80° N (Fig. 5a).The highest BNPP is in tropical/subtropical forests, temperate forests and croplands; and the lowest in tundra, boreal forests and deserts (Fig. 4).For the proportional depth distribution, averaging across the globe, it is 57% and 77% in the top 20 and 40 cm soil layers, respectively (Fig. 5b).With increasing latitudes from 40° N to 80° N, more BNPP is allocated to upper soil layers (Fig. 5b).Fig. 6 shows the uncertainty (i.e., coe cient of variance in each 1 km grid) in predicted depth-speci c BNPP.The uncertainty is greater in deeper soil layers, particularly in the northern Hemisphere high latitudinal regions such as tundra and boreal forests.Indeed, the uncertainty is markedly higher in tundra and boreal forests than in other biomes in deeper soil layers.Across the globe, the average uncertainty in the top 20 cm layer is , and increased to in the 150-200 cm layer, respectively (Fig. 6).

Discussion
Using root biomass distribution to infer depth distribution of BNPP, we generated eld observational dataderived global maps of BNPP down to 200 cm at a resolution of ~1 km.In the 0-200 cm soil pro le, the global average BNPP is estimated to be ~2 Mg ha -1 yr -1 with a global total BNPP of ~21 Pg yr -1 .This estimate is close to the value of 2.2 Mg ha -1 yr -1 (with a global total BNPP of 24.7 Pg yr -1 ) by Gherardi and Sala (15) who estimated total BNPP as the difference between satellite-derived NPP and eld measurements of aboveground NPP.According to our data of f BNPP , f BNPP is estimated to be 39% which is slightly lower than the estimation of 46% by Gherardi and Sala (15).
Our results further suggest that the majority of total BNPP (>50%) is allocated to the top 20 cm soil layer, and additional ~20% to the 20-40 cm soil layer.This is consistent with a series of studies with eld observations of BNPP depth distribution at individual sites across the globe (22)(23)(24).Among biomes, however, the depth distribution of BNPP is signi cantly different.Generally, more BNPP is allocated to deeper layers in drier biomes (e.g., deserts and grasslands).This may due to the close coupling of plant root growth with soil moisture pro le (25,26).More assimilated carbon would be allocated to deeper soil layers in drier environments to acquire water (27,28).A synthesis of literature data has found that tropical grasslands/ savannas and deserts have the deepest rooting depth compared with other biomes (29).There is also a clear pattern of higher allocation of BNPP to upper layers in higher latitudes.Due to low temperature in high latitudinal regions, deep soil permafrost (e.g., in tundra) exists even in growing season, which inhibits root growth into the subsoil (29)(30)(31), resulting in a large fraction of BNPP allocated to surface layers.As biome type is inherently determined by climate conditions, it is reasonable to expect that climatic factors would play a key role in regulating BNPP depth distribution.Indeed, climatic variables have signi cant effects on BNPP and its depth distribution.Mean annual temperature (MAT) and mean annual precipitation (MAP) are identi ed amongst the most important.MAP is the predominant, if not the only for most soils, source of soil moisture; while MAT determines the loss rate of soil moisture via evaporation and plant transpiration and the depth of active layer above the permafrost.Previous assessments at broad scales mainly focused on MAT and MAP, and have demonstrated the importance of these two climatic variables (15,(32)(33)(34).Our result further con rms that the climatic control is general on BNPP allocation in different soil layer depths.However, the linear mixedeffects regression indicates that the degree and even the direction of the correlation of BNPP with MAT and MAP are biome-dependent (Figs.3c and S6).This may attribute to the differential responses of biomes to temperature and precipitation shifts depending on plant functional types and carbon allocation strategies (35,36).For example, the growth of tropical species is more vulnerable to high temperature or drought than temperate or boreal trees.High temperature in humid ecosystems may induce more frequent drought or wild re which deplete soil moisture in the top soil layer (37)(38)(39), resulting in stimulated root growth and/or deeper rooting to obtaining moisture.For MAT, its effect is positive in most biomes but negative in tropical/subtropical grasslands/savannas, which may relate to the shift from tree-(which has deep rooting depth) to grass-dominant vegetation (which has relatively shallow rooting depth) with increasing MAT.Intriguingly, the general positive effect of both MAP and MAT is strongest in tundra.Warming experiments across the tundra biome have found that warming stimulates the growth of deciduous shrubs and graminoids and retards the growth of mosses and lichens (40), while former species have much deeper rooting depth and thus higher BNPP.A simulation study using the dynamic tundra vegetation model has reported that increasing precipitation under climate change bene ts graminoids outcompeting shrubs, resulting in more root biomass in deeper soils as graminoids have higher rooting depth than shrubs (41).The tundra biome may be particularly sensitive to climate change in terms of BNPP allocation and the relevant soil processes.
Except for MAT and MAP, other climatic variables indicating climate seasonality and inter-annual variability also play a role in regulating BNPP allocation.Mean temperature diurnal range (i.e., BIO2) and mean temperature of the wettest quarter (i.e., BIO8) are the most important climatic variables after MAT and MAP (Figs. 3b and S5).Overall, these results suggest that both the mean and variability of climatic conditions are important determinants of BNPP and its depth distribution; and, more importantly, the direction and magnitude of their effects are biome-speci c probably depending on local plant functional types and their response to soil water dynamic regimes.Future climate (e.g., warming and precipitation change) and land cover changes (e.g., vegetation shift) may signi cantly alter the amount of carbon allocated to different soil layer depths thereby potentially modifying soil pro le biogeochemical processes regulated by fresh carbon inputs.
Despite the leading role of climate, soil properties also play a vital role in cotrolling BNPP depth distribution.Indeed, mean actual daily soil evaporation (which is affected by both soil properties and climate conditions) is as important as MAT and MAP positively associating with BNPP, in line with the ndings in global grasslands (34).A major reason would be that high soil evaporation means a higher probability of water stress, given otherwise similar to other environmental conditions.Soil carbon to nitrogen ratio also exerts signi cant positive effect, particularly in deeper layers (Fig. 3b, c).High soil carbon to nitrogen ratio may indicate poor nutrient availability in the soil.In nutrient-pool soils, the plant would have to invest more assimilated carbon to root growth for nutrient acquisition in deeper layers (10).
Together with the general positive relationship between BNPP and climatic variables, these results re ect the key role of energy (e.g., temperature) and soil resource pro les (e.g., water and nitrogen) in regulating BNPP depth allocation.Other soil properties also cannot be ignored.For example, both soil bulk density and sand show negative effects on BNPP.They are key soil physical parameters determining the suitability of the soil environment for root growth (42).Another noteworthy phenomenon is that the effect of a typical soil property is soil layer-dependent, while the dependence of the effects of climatic and topographic variables is much weaker (Fig. S6c).These results demonstrate that depth distribution of BNPP is driven by complex interplay among edaphic, climatic and topographic variables, which is further modulated by biome type as different biomes may adopt distinct BNPP allocation strategies (16,43,44).
The data used in this study builds upon quality-checked legacy data sets, and we further update the data via literature synthesis to generate a more comprehensive one that improves spatial coverage and bene ts robust assessment at the global scale.Although we show evidence that the two data sets are not statistically different in terms of BNPP estimates (derived from peer-reviewed publications vs the ORNL DAAC legacy data; Fig. S1), we note several limitations in the estimation of BNPP depth allocation due to the di culty in eld measurements and adopted assumptions (45,46).First, not all data include all BNPP components such as root exudates.BNPP allocated to root exudates and mycorrhizae may account for a signi cant fraction of BNPP (particularly in forest systems), but is challenging to measure in the eld (45,47).As such, BNPP in the data would be an underestimation of real BNPP and depend on the approach used to measure BNPP in speci c studies.We do not explicitly distinguish measurement techniques and the underlying consequences on the estimation of BNPP.Second, most data only include BNPP in a single year, but BNPP would present inter-annual variability.Given that we focus on the spatial variability of BNPP across the globe, however, the consequences of temporal variability on our estimates would be small if we accept that inter-annual variability is smaller than spatial variability.This also can be evidenced by the comparable estimates of global BNPP in this study to that by Gherardi and Sala (15) in which the temporal variability of BNPP is considered.Third, our approach implicitly assumes that roots in different soil depths have the same turnover times.For some plants, roots in different soil layers (e.g., coarse vs ne roots) may have different functions, and roots with different functions may distribute unequally in soil layer depths (31,48).Thus, turnover times of different root functional types may be different, resulting in biases in the estimation of the proportional depth distribution of BNPP acrodding to root biomass alone.BNPP and its depth distribution are the least constrained component of the global carbon budget (49).To our knowledge, we are the rst to spatially, explicitly predict depth-speci c BNPP allocation across the globe with the quanti cation of prediction uncertainties.The quantitative information is critical for explicit representation of soil layer-speci c carbon inputs.By quantifying the spatial pattern of BNPP depth distribution, our maps provide the information on plant carbon allocation that can be potentially used to promote their application across large extents at resolutions meaningful for land management.
The maps also can be used to parameterize, scale or benchmark spatially explicit model predictions of carbon allocation and thus facilitate simulation of soil carbon turnover and dynamics.

Materials And Methods
To quantify the depth distribution of BNPP across the globe, we integrated observational global datasets, including NPP datasets of eld observations of aboveground and belowground fractions (NPP obs ) and root biomass (Root obs ) in the soil pro le.In general, the data sets span across the globe (Fig. 1a) covering various climatic, edaphic and topographic conditions.We also used soil, climate, and topography databases along with biome types and soil order to obtain environmental covariates (edaphic, climatic, topographical variables; Table.S1).Combing these environmental covariates with NPP obs and Root obs , we developed models to predict the depth distribution of BNPP, identify its drivers, and map it across the globe.
Data acquisition.We collected eld net primary production (NPP) data from 725 soil pro les (Fig. 1a; NPP obs hereafter).NPP obs contain NPP, belowground NPP (BNPP) and aboveground NPP (ANPP).The dataset was compiled by a thorough literature search and data synthesis from 54 published peerreviewed papers (Supplementary references) and the ORNL DAAC NPP data collection (https://daac.ornl.gov/cgi-bin/dataset_lister.pl?p=13).We obtained root biomass and its depth distribution from 559 soil pro les to infer the depth distribution of BNPP (see the section Estimation of the depth distribution of BNPP).The root biomass data set (Root obs ) was originally compiled by Schenk and Jackson (50).
We obtained a set of global layers of environmental covariates including soil properties, climate, topography and biome type (Table S1) as potential predictor variables of BNPP and its depth distribution.A total of 20 soil physical and chemical properties (Table S2) were obtained from ISRIC-WISE soil pro le database (4) with a spatial resolution of 1 km.We obtained 19 climatic attributes with the same resolution as the WISE database from WorldClim (51), which quanti es biologically meaningful variables using monthly temperature and precipitation.Actual soil evaporation (AE) counted as the liquid water supply plus the soil water utilized was obtained from TerraClimate (52).In addition, we derived spatial layers of biome type by aggregating two land cover maps (i.e., the MODIS land cover map (53) and the Terrestrial Ecoregions of the World ( 54)) to generate a map consisting of nine biome types.Finally, we calculated 13 topographic attributes from SRTM-DEM at 90 m resolution (http://srtm.csi.cgiar.org)using 'elevatr', 'spatialEco' and 'dynatopmodel' packages in R 3.6.1 (55) and SAGA (56).More details of these global spatial covariate layers are given in Table S1.
Estimation of the depth distribution of BNPP.Total BNPP has been recorded in the NPP obs data set.To quantify BNPP allocated to different soil layer depths, the most straightforward way is to directly measure BNPP in different soil layers.However, no sites have such measurement with BNPP in the NPP obs data set.In this study, we assume that BNPP allocated to a speci c layer is proportional to root biomass in that layer.Using the Root obs data set, we calculated the depth distribution of root biomass in seven sequential layers in the 0-200 cm soil pro le (i.e., 0-20, 20-40, 40-60, 60-80, 80-100, 100-150 and 150-200 cm), using the following equations(6, 50): Linear mixed-effects models (using the 'lmer' function of the 'lmerTest' package in R) were performed to further identify the correlations between BNPP depth allocation and the individually selected environmental covariates, and investigate whether and how biome type regulates those correlations by treating biome type as the random effect factor.In addition, we conducted correlation analysis to evaluate the general relationship between selected controlling factors (i.e., the most important ones) and depth distribution of BNPP.Partial correlation was also conducted to assess that whether the correlations between BNPP and environmental predictors are soil depth-dependent by controlling the effect of soil depth.
Global and prediction uncertainty.We explored machine-learning-based models, including random forest (RF), extreme gradient boosting (XGBoost), Cubist, support vector machines (SVM), bayesian regularized arti cial neural networks (BRANNs) and lasso regression (LASSO), and selected the best models for predicting BNPP (using NPP obs ), the proportional depth distribution of BNPP (using Root obs ) across the globe.For each model, the selected environmental covariates after minimizing multicollinearity via VIF selection and MFA dimensionality reduction were used; 80% soil pro les were randomly selected for training and the remaining 20% for validation.A 'tuneGrid' method (R package 'caret') was used to compute model performance metric (i.e., rooted mean squared error-RMSE) for a set of tuning hyperparameters required by each model, and the best model with its tuning hyperparameters was targeted with the smallest RMSE.
Using the best models (random forest is consistently the best model; Fig. S2 and Fig. S7), we predicted BNPP, the proportional depth distribution (PDD) of BNPP inferred from roots across the globe with gridded driver variables at the resolution of 0.0083 o (~1 km at the equator).The BNPP in each soil depth can be nally calculated in BNPP PDD.Prediction uncertainty in each 1 km pixel was quanti ed using a Monte Carlo approach by randomly drawing 500 individual trees with replacement from the random forest model to predict BNPP, PDD.These 500 estimates were used to calculate the mean (m) and standard deviation (sd) of BNPP and PDD at each of the seven-layer depths.The prediction uncertainty (U) was expressed as the coe cient of variation (CV), i.e., sd/m.The total uncertainty of BNPP depth allocation (BNPP PDD) was estimated as .Boxplots show the median and interquartile range, with whiskers extending to the most extreme data indicate that the coe cients are signi cant at P < 0.05, and R2 is the determinant coe cient for the corresponding predictor.See Table S1 for the details of the environmental predictors.

Figures Figure 1
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Figure 2 Depth
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Figure 4 Global
Figure 4