The World Soil Information Service (WoSIS) collates and manages the largest database of explicit soil profile observations across the globe (Batjes et al., 2017) which forms the foundation of a series of digital soil mapping products such as the global SoilGrids (Hengl et al., 2017). The WoSIS dataset is still growing. When we visited the dataset last on 25 March 2019, there were a total of 141 584 profiles which were used in this study. These profile observations were quality-assessed and standardized, using consistent procedures (Batjes et al., 2017). In each soil profile, multiple layers were sampled for determining SOC content and/or other soil properties. A total of 48 soil properties were recorded with multiple variates of the same property (e.g. pH measured in H2O, CaCl2, KCl). In the data assessment, we considered nine principal soil physicochemical properties other than SOC itself in the data analysis (Table 1). Taking the advantage of all measurements, however, other soil properties were used for missing data imputation (see the Sect. 2.2). The layer depths are inconsistent between soil profiles. We harmonized all soil properties including SOC to four standard depths (i.e. 0–20, 20–50, 50–100 and 100–200 cm) using mass-preserving splines (Bishop et al., 1999; Malone et al., 2009). This harmonization enables the calculation of SOC stock in the defined standard layers, making it possible to directly compare among soil profiles.

We calculated SOC stock (SOCs, kg C m-2) in each standard depth as 1SOCs=OC100⋅D⋅BD⋅1-G100, where OC is the weight percentage SOC content in the fine earth fraction <2 mm, D the soil depth (i.e. 0.2, 0.3, 0.5 or 1 m in this study), BD the bulk density of the fine earth fraction <2 mm (kg m-3) and G the volume percentage gravel content (>2 mm) of soil. Amongst the 141 584 soil profiles, unfortunately, only 9672 profiles have all the measurements of OC, D, BD and G to enable direct calculation of SOC stock. We call these profiles “stock profiles”.

Another 82 734 profiles have measured OC (i.e. the weight percentage SOC content), but BD and/or G are missing. We call these profiles “content profiles”. To utilize and take advantage of all OC measurements, we used generalized boosted regression modelling (GBM) to perform imputations (i.e. fill missing data). As such, SOCs can be estimated. To do so, for BD and G in each standard soil depth, GBM was developed based on all measurements of that property (e.g. BD) in the 141 584 profiles with 32 other soil properties. Total carbon which includes organic and inorganic carbon and another nine soil properties (Table 1) which were used as predictors of SOC stocks were excluded as covariates (i.e. predictors). The final GBM model was validated using 10-fold cross validation repeated 10 times and applied to predict missing values of BD and G. A total of 92 406 SOC profiles including stock profiles and content profiles with relevant measurements of nine soil properties (Table 1) was obtained and used to assess the effects of various variables on SOCs (Sect. 2.4). These soil profiles cover 13 major biome groups although the profile numbers vary from 472 in flooded grasslands and savannas to 24 382 in temperate broadleaf and mixed forests (Fig. 1). The profiles also cover various climate conditions across the globe with the mean annual temperature ranging from -19.6 to 30.7 ∘C and mean precipitation ranging from 0 to 667.4 cm yr-1 (Fig. 1). The prediction error of the GBM was propagated into the calculation of SOCs to account for uncertainty resulting from data imputation (see Sect. 2.4).

For each SOC profile, NPP was extracted from the MODIS NPP product (Zhao and Running, 2010). The NPP product includes the annual NPP from 2001 to 2015 at the resolution of 1 km2, which was estimated by analysing satellite data from MODIS using the global MODIS NPP algorithm (Zhao et al., 2005; Zhao and Running, 2010). NPP is the net carbon gained by plants (i.e. the difference between gross primary productivity and autotrophic respiration). If assuming a steady state of the vegetation (i.e. no long-term directional change of carbon biomass in plants), NPP will end up in soil via rhizodeposition and litter fall and will be equal to total carbon input into soil. Here we calculated the average NPP based on the data from 2001 to 2015 and called this average NPP the apparent carbon input to soil, acknowledging that not all ecosystems are at strict steady state, particularly those ecosystems (e.g. croplands) actively interacting with human activities. The WWF (World Wildlife Fund) map of the terrestrial ecoregions of the world (Olson et al., 2001; https://www.worldwildlife.org/publications/terrestrial-ecoregions-of-the-world, last access: 18 March 2021) was used to extract the biome type for each location. The MODIS land cover map (Friedl et al., 2010) at the same resolution of NPP databases was used to identify whether or not the land is cultivated (i.e. land cover type of croplands and cropland/natural vegetation mosaic) at the location of each soil profile.

In addition to NPP, land cover and biome type, 19 climatic variables (Table 1) for each SOC profile were obtained from the WorldClim version 2 (Fick and Hijmans, 2017). The WorldClim version 2 calculates biologically meaningful variables using monthly temperature and precipitation during the period 1970–2000. The data at the same spatial resolution of the NPP data (i.e. ∼1 km2) were used in this study. Eleven of the 19 climatic variables are temperature-related (Table 1), and eight are precipitation-related (Table 1). These variables reflect the seasonality, intra- and inter-annual variability of climate, which would have both a direct (via decomposition thus carbon outputs from soil) and an indirect (via carbon assimilation thus carbon inputs to soil) effect on SOC stock.

A machine learning-based statistical model – boosted regression trees (BRTs) – was performed to explain the variability of SOCs across the globe and identify important controlling factors. A big advantage of the BRT model is its ability to model high-dimensional dataset, taking into account non-linearities and interplay (Elith et al., 2008). Using the BRT model, we modelled SOCs in each standard depth as a function of edaphic variables in that depth, climatic and biotic variables (Table 1): 2SOCs=fedaphic,climatic,biome,NPP,cultivation. We used a 10-fold cross validation to constrain the BRT model in R 3.6.1 (R Core Team, 2019) using algorithms implemented in the R package dismo. The amount of variance in SOCs explained by the model was assessed by the coefficient of determination (R2). To assess the potential uncertainty induced by the uneven distribution of soil profiles across the globe as well as the imputation of missing BD and G for estimating SOCs, we conducted 200 bootstrapping simulations (i.e. resample all soil profiles with replacement). For each bootstrap sample, SOCs, if BD and G are missing, was recalculated using BD and G imputed by GBM plus an error randomly sampled from the distribution of imputation error. Using the new SOCs estimations, then, a new BRT model was fitted.

Considering the potential collinearity in the 19 climatic variables as well as in the nine soil properties, the BRT model was conducted using their principal components. That is, a principal component analysis (PCA) was performed to eliminate potential correlations in the soil and climatic variables, respectively. The important principal components (PCs) with variances of greater than 1 were retained in the BRT model based on Kaiser's criterion (Kaiser, 1960). The PCA was performed using the function prcomp in the package stats in R 3.6.1 (R Core Team, 2019). In addition, in order to demonstrate the importance of soil properties, we fitted another set of BRT models without soil properties. The model performance with and without soil properties were compared in terms of explaining the variance of SOC stocks across the globe.

The BRT model allows the estimation of the relative influence of each individual variable in predicting SOCs, i.e. the percentage contribution of variables in the model. The relative influence is calculated based on the times a variable selected for splitting when growing a tree, weighted by squared model improvement due to that splitting, and then averaged over all fitted trees which were determined by the algorithm when adding more trees cannot reduce prediction residuals (Elith et al., 2008; Friedman and Meulman, 2003). As such, the larger the relative influence of a variable, the stronger the effect on SOCs. In addition, we also calculated the 95 % confidence intervals as the 2.5 % and 97.5 quantiles of the relative influence estimated by 200 bootstrapping simulations, which represent the uncertainty in the importance of variables. To facilitate interpretation, the relative influence of each variable is scaled so that the sum of the influence of all variables is equal to 100. The overall relative influences of edaphic (i.e. the sum relative importance of all soil-related variables) and climatic (i.e. the sum relative importance of all climate-related variables) variables as well as biome type, NPP and cultivation were also calculated and compared. As we have 200 estimations (i.e. 200 bootstraps) of the relative influence, we calculated a weighted average relative influence for each variable with weights based on the R2 of each BRT model.

A series of soil properties may directly or indirectly affect SOC dynamic processes via influencing carbon inputs to soil, microbial activity and accessibility of carbon substrates to microbes and thereby SOC stocks. Sand content (which is the most important contributor to the first PC of soil), for example, has significant effects on the formation and transformation of soil aggregates which regulate the stability of SOC as well as soil porosity and thereby oxygen availability for microbial decomposition of SOC (Dungait et al., 2012; Six et al., 2002). In addition, soil properties such as LL15 and DUL have dominant control over soil water dynamics, which further influence water availability for plant growth. Theoretically, LL15 is close to the permanent plant wilting point; it thus may strongly regulate plant growth therefore carbon inputs into soil and final SOC stocks. Together with DUL (i.e. drained upper limit – soil water content obtained at the matric potential of 33 kPa), LL15 determines the available water capacity of soil (AWC, i.e. the difference between DUL and LL15), and thus LL15 would affect SOC stock via its determination on soil AWC, while AWC couples with a series of soil hydrological processes such as runoff and drainage, which have direct effects on the vertical/horizontal translocation of SOC (Luo et al., 2020; Kaiser and Kalbitz, 2012). Soil properties are more important for controlling SOC stocks in deeper layers than in upper layers. This phenomenon may be due to the fact that soil structure may have substantial effects on water and oxygen diffusion in deeper layers. Potentially more frequent waterlogging and low oxygen in subsoil result in additional environmental constraints inhibiting microbial decomposition of SOC (Huang et al., 2020).

Our results demonstrate the primary control of soil properties on SOC stocks in the whole-soil profile across the globe. Indeed, the results suggested that soil-related principal components were consistently the most important individual influential variables in three deeper soil layers except in the assessed 0–20 cm soil layer. Soil physical and chemical properties directly determine the activity of the decomposer community which mediates the decomposition of soil carbon (Derrien et al., 2014; Foesel et al., 2014; Bernard et al., 2012). More importantly, soil carbon can be physically protected from decomposition via occlusion with soil aggregates and binding with minerals (Lehmann and Kleber, 2015; Dungait et al., 2012; Schmidt et al., 2011), while the protection capacity is largely determined by soil physicochemical properties (Six et al., 2000). These physical protection processes may lead to soil-dependent stabilization/destabilization of different soil carbon substrates (Waldrop and Firestone, 2004; Keiluweit et al., 2015; Six et al., 2002). However, it should be noted that complex interplays of various soil properties are involved in SOC stabilization and destabilization processes. It is also difficult to obtain a cause–effect conclusion on the relationship between a particular soil physicochemical property and SOC stocks.

Few studies have paid particular attention to the dynamics of SOC in subsoils across large scales. One might expect greater importance of climate in surface soils as topsoil is at the frontline of the interaction with the atmosphere. But our results do not show a clearly decreasing importance of climate with soil depth. Rather, the overall influence of climatic variables on SOC stocks is statistically similar in all soil layers. In a forest soil, a recent study found that SOC in the whole-soil profile down to 1 m is sensitive to warming (Pries et al., 2017). This sensitivity may be general across the globe. However, it is noteworthy that neither mean annual temperature nor mean annual precipitation was the most important individual climatic variable. Rather, climatic variables reflecting seasonal variability were more important. This result may suggest that, except for average change trend, it is important to understand the change patterns of temperature and precipitation under climate change. For example, a number of studies have demonstrated that extreme climate events (e.g. drought and heatwaves) have significant effects on the carbon cycle, including soil carbon, due to their dramatic influence on the transport and availability of water and energy as well as ecosystem functional processes (Reichstein et al., 2013). Field observations, particularly via manipulative experiments of whole-soil profile, are certainly needed to detect how deep soil carbon responds to climate change as the result may have significant implications on the fate of deep soil carbon under future climatic conditions.

The effect of apparent carbon input, NPP, on SOC stock is generally small in all assessed soil layers (Fig. 5). This result is in line with findings from a continental-scale study across sub-Saharan Africa where climate and geochemistry are more important predictors of SOC content than aboveground carbon inputs (von Fromm et al., 2020). The importance of NPP may largely depend on how much NPP ends up in the soil and how it is translocated to different depths (Wang et al., 2021). Total NPP may not be a useful indicator of actual carbon inputs into different soil depths, particularly in deeper layers. Cultivation, for example, may substantially change the fate of plant biomass – a large fraction of plant biomass may be harvested as yield or consumed by livestock and thus does not contribute to soil carbon. This could explain the phenomena that cultivation (cultivated vs. non-cultivated in this study) and NPP show the similar importance in general. In addition, the final importance of carbon inputs may also depend on their quality (e.g. carbon-to-nitrogen ratio), while NPP alone does not bring such information. The quality of carbon inputs represented by their nutrient content and chemical structure plays a vital role in SOC formation and transformation (Hessen et al., 2004; Jastrow et al., 2007). In our study, biome type (which shows similar importance to NPP) would partially reflect the importance of carbon input quality as different biome types have distinct carbon biomass quality (e.g. wood vs. leaf litter, which are the main component of NPP). However, here we must to point out that the minor role of carbon inputs in determining the global spatial distribution of SOC stocks does not mean that they are not important for local carbon management. Under the same climatic and edaphic conditions, indeed, carbon inputs should be the predominant factor controlling if the soil is a carbon sink or source (Luo et al., 2017).

Although we have used a diverse and representative dataset across the globe for the analysis, there are still some limitations in the datasets and assessment. First, our study did not bring detailed land use history and intensity (such as the time length of cropping and the intensity of grazing) into the analysis, which may significantly affect SOC stabilization processes and thus SOC stocks in managed landscapes (Sanderman et al., 2017). As anthropogenic land use may change from year to year, it is challenging to accurately explain SOC stock changes in those systems that experience intensive human disturbances across large extents. Second, all soil properties including SOC were treated as constant. In reality, however, some soil properties, particularly chemical variables such as pH, may actively respond to external disturbance including human activities. Treating these variables as constant may result in under- or overestimations of the variable importance if a variable shows marked temporal variability. Third, in managed systems, the apparent carbon input represented by NPP may not accurately reflect the real carbon input into soil (Luo et al., 2018; Pausch and Kuzyakov, 2018) as discussed above, leading to biased estimation of the importance of C inputs. In cropping areas, for example, yield harvesting and crop residue removal certainly reduce the fraction of NPP ending up in the soil. Fourth, we would like to point out that, albeit edaphic factors appear to be the dominant individual controls on SOC stock, climate might have an impact on those edaphic factors and hence SOC stocks in the long term (Jenny, 1941). Indeed, Luo et al. (2017) have provided evidence that climate not only directly but also indirectly (via its effect on edaphic factors) exerts significant effect on SOC dynamics. All these limitations should be overcome to provide more robust predictions on the role of different factors in SOC stabilization and stock, which will be particularly important for understanding long-term SOC dynamics in managed systems. Fourth, we would like to note that this study focused on the controls over the global spatial pattern of SOC stocks and did not explicitly assess the potential variability of controls at small scales. Under different land use types, for example, factors controlling SOC stock would change. A recent study focused on SOC component fractions has found that continental drivers of SOC stocks were modulated by regional environmental factors (Viscarra Rossel et al., 2019). In order to better understand regional-scale factors controlling SOC dynamics, we should further explore the controls over different spatial scales. Considering that we only included limited soil properties in our assessment and different soil properties may play different roles at different scales, scale-dependent understanding of controls over SOC stocks is important to make site-specific management practices for sustainable soil use and carbon management. Finally, soil samples are still limited in some areas (e.g. tundra and flooded grasslands and savannas) (Batjes, 2016). We do not know much about whether some of the relationships we find between SOC stocks and predictor variables are universal or maybe fundamentally different in less studied soils. The uneven distribution of soil samples may also help to explain the model bias in explaining low and high SOC stocks (Fig. 3). Our results indicate that there are large uncertainties in the relative importance of climate and soil depending on the data used to fit the model (Fig. 5).