Global soil profiles indicate depth-dependent soil carbon losses under a warmer climate
WoSIS and permafrost-affected soil profilesThe World Soil Information Service (WoSIS) collates and manages the largest database of explicit soil profile observations across the globe29. In this study, we used the quality-assessed and standardised snapshot of 2019 (ISRIC Data Hub). We further screened the snapshot, and excluded soil profiles with obvious errors (e.g., negative depth values of mineral soil, the value of the depth for the deeper layer is smaller than that of the upper layer). Finally, there is a total of 110,695 profiles with records of SOC content (SOCc, g C kg–1 soil) in the fine earth fraction < 2 mm. The soil layer depths are inconsistent between soil profiles. We harmonised SOCc to three standard depths (i.e., 0–0.3, 0.3–1 and 1–2 m) using mass-preserving splines61,62, which makes it possible to directly compare among soil profiles. We also calculated SOC stock (SOCs, kg C m–2) in each standard depth as:$${{{{{{rm{SOC}}}}}}}_{{{{{{rm{s}}}}}}}=frac{{{{{{{rm{SOC}}}}}}}_{{{{{{rm{c}}}}}}}}{100}cdot Dcdot {{{{{rm{BD}}}}}}cdot left(1-frac{G}{100}right),$$ (1) where D is the soil depth (i.e., 0.3, 0.7, or 1 m in this study), BD is the bulk density of the fine earth fraction 2 mm) of soil. Amongst the 110,695 soil profiles, unfortunately, only 18,590 profiles have measurements of both BD and G. To utilise and take advantage of all SOCc measurements, we used generalised boosted regression modelling (GBM) to perform imputation (i.e., filling 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 110,695 profiles with other 32 soil properties recorded in the WoSIS database. The detailed approach for missing data imputation has been described in ref. 41.Together with the WoSIS soil profiles, a total of 2,703 soil profiles with data of SOCs from permafrost-affected regions were obtained from ref. 30. The original data used in ref. 30 have been obtained, and we used the data of SOCs in the 0–0.3, 0.3–1, and 1–2 m soil layers in this study. These permafrost-affected profiles compensate for the scarce soil profiles in high latitudinal regions in the WoSIS database. Overall, the soil profiles cover 13 major biome groups although the profile numbers vary among biome types (Supplementary Fig. 1). The profiles also cover various climate conditions across the globe with mean annual temperature (MAT) ranging from –20.0 to 30.7 °C and mean annual precipitation (MAP) ranging from 0 to 6,674 mm.Environmental covariatesMAT and MAP for each soil profile were obtained from the WorldClim version 2 (ref. 63). The WorldClim version 2 calculates biologically meaningful variables using monthly temperature and precipitation during the period 1970–2000. We obtained global spatial layers of MAT and MAP at the resolution of 30 arcsecond (i.e., 0.0083° which is equivalent to ~1 km at the equator). Soil profiles in the same 0.0083° grid (i.e., ~1 km2) share the same MAT and MAP. Besides MAT and MAP, other climatic variables for each soil profile were also obtained from the WorldClim version 2. The WWF (World Wildlife Fund) map of terrestrial ecoregions of the world (https://www.worldwildlife.org/publications/terrestrial-ecoregions-of-the-world) was used to extract the biome type at each soil profile. The MODIS land cover map64 at the same resolution of NPP databases was used to identify that if the land is cultivated (i.e., land cover type of croplands and cropland/natural vegetation mosaic) at the location of each soil profile.Space-for-time substitution: grouping soil profilesWe used a hybrid approach of space-for-time substitution and meta-analysis to estimate the response of SOC to warming. Traditionally, space-for-time substitution involves determining regression relationships across gradients at one time31. The regression was then used to predict future status under conditions when one or more of the covariates has changed31. However, the approach was compromised when the effects of other driving variables such as soil type and landform were not minimised. Regarding SOC dynamics, they would show non-linear relationships19 with temperature modulated by a series of other environmental covariates (e.g., precipitation, vegetation type).Based on the idea of space-for-time approach31, first, we sorted all soil profiles by MAT at the soil-profile locations and designated them into MAT classes with an increment of 1 °C (Fig. 1). Then, we derived pairs of soil profiles, with each pair including a “ambient” and “warm” class (i.e., control vs treatment in meta-analysis language) distinguished by MAT (Fig. 1). The ambient class includes soil profiles with MAT ranging from i to i + 1 degree Celsius, where i is the lowest temperature in the class. If 1 °C warming is of interest, for example, the warm class will be identified as the class with MAT ranging from i + 1 to i + 2 degree Celsius (i.e., one degree higher than that of the ambient class; Fig. 1). To control the effects of precipitation, soil type and topography, soil profiles in both ambient and warm classes were further grouped; and each group must have the same following characteristics: (1) Landform. A global landform spatial layer was obtained from Global Landform classification - ESDAC - European Commission (europa.eu), and global terrestrial lands were divided into three general landform types: plains including lowlands, plateaus, and mountains including hills. (2) Soil type. The 12 USDA soil orders were used to distinguish soil types. A global spatial layer of soil orders was obtained from The Twelve Orders of Soil Taxonomy | NRCS Soils (usda.gov). We also independently tested the sensitivity of the results to different soil classification systems by including FAO and WRB soil groups (Soil classification | FAO SOILS PORTAL|Food and Agriculture Organization of the United Nations). (3) Mean annual precipitation (MAP). MAP cannot be exactly the same between the ambient and warm groups. In practice, we considered that soils meet this criterion if the absolute difference of MAP between ambient and warm soils is less than 50 mm. We also tested the sensitivity of the results to this absolute MAP difference using another value of 25 mm, and found that this difference has negligible effect (Supplementary Fig. 11). (4) Precipitation seasonality. Precipitation seasonality indicates the temporal distribution of precipitation. In this study, we focused on warming alone, and global warming would also have less effect on this seasonal distribution of precipitation. The seasonal distribution pattern of precipitation was classified into three categories: summer-dominated precipitation, winter-dominated precipitation and uniform precipitation. Precipitation concentration index (PCI) was calculated in R precintcon package to distinguish the three patterns65: $${{{{{rm{PCI}}}}}}=frac{mathop{sum }nolimits_{{{{{{rm{i}}}}}}=1}^{12}{p}_{{{{{{rm{i}}}}}}}^{2}}{{left(mathop{sum }nolimits_{{{{{{rm{i}}}}}}=1}^{12}{p}_{{{{{{rm{i}}}}}}}right)}^{2}}cdot 100,$$ (2) where pi is the precipitation in month i in a particular year. In this study, we used the monthly precipitation from 1970 to 2000 obtained from WorldClim version 2 (ref. 63) to calculate the average (overline{{{{{{rm{PCI}}}}}}}) at the location of each profile. If (overline{{{{{{rm{PCI}}}}}}}) 8.3 and total precipitation from April to September (from October to March in the Southern Hemisphere) is larger than that from October to March (from April to September in the Southern Hemisphere), precipitation mainly occurs in summer (i.e., summer precipitation); otherwise, it is winter precipitation.By applying these selection criteria to all soil profiles, we obtained pairs (i.e., an “ambient” group vs a “warm” group) of soil profiles mainly distinguished by MAT (i.e., warming). Amongst pairs, they would be different in landform, soil type, MAP and precipitation seasonality, which enables us to address their effects on the response of SOC to warming. We are interested in five warming levels including 1, 2, 3, 4, and 5 °C.Meta-analysis: estimation of the response of SOC to warmingMeta-analysis techniques were used to estimate the percentage response of SOC to warming by comparing SOC content and stock in groups in the warm group to that in the ambient group. The log response ratio of soil C (lnRR) to warming for each pair (i.e., an ambient group vs a warm group) of soil profiles was calculated as:$${{{{{rm{ln}}}}}}{{{{{rm{RR}}}}}}={{{{{rm{ln}}}}}}left(frac{bar{{{{{{{rm{SOC}}}}}}}^{*}}}{overline{{{{{{rm{SOC}}}}}}}}right),$$ (3) where (overline{{{{{{rm{SOC}}}}}}}) and (bar{{{{{{{rm{SOC}}}}}}}^{*}}) are the mean SOC (either content or stock) in groups from ambient and warm class, respectively. In order to provide a robust estimate of global mean response ratio, the individual lnRR values were weighted by the inverse of the sum of within- (v) and between-group (τ2) variances. As such, the global mean response ratio ((overline{{{{{{rm{ln}}}}}}{{{{{rm{RR}}}}}}})) could be estimated as:$$overline{{{{{{rm{ln}}}}}}{{{{{rm{RR}}}}}}}=frac{{sum }_{{{{{{rm{i}}}}}}}left({{{{{{rm{ln}}}}}}{{{{{rm{RR}}}}}}}_{{{{{{rm{i}}}}}}}times {w}_{{{{{{rm{i}}}}}}}right)}{{sum }_{{{{{{rm{i}}}}}}}{w}_{{{{{{rm{i}}}}}}}},$$ (4) where ({w}_{{{{{{rm{i}}}}}}}=frac{1}{{v}_{{{{{{rm{i}}}}}}}+{tau }^{2}}) is the weight for the ith lnRR. In addition, we estimated and compared the mean response ratios under different soil orders, landforms, and precipitation concentration patterns. These mean response rates were calculated in weighted, mixed-effects models using the rma.mv function in R package metafor. To assist interpretation, the results of (overline{{{{{{rm{ln}}}}}}{{{{{rm{RR}}}}}}}) were back-transformed and reported as percentage change under warming, i.e., (({{{{{{rm{e}}}}}}}^{{{{{{rm{RR}}}}}}}-1)times)100. These back-transformed values were also used for subsequent data analyses.An implicit assumption underlying the space-for-time substitution approach is that important events or processes which substantially change the succession direction of studied system (e.g., volcano disruption in one class but not in another class, cultivation in one class but not in another class) are independent of space and time (which includes the past and future)66. We conducted two sensitivity assessment to test this assumption. First, we repeated all above assessment by excluding soil profiles from croplands since preferential choice of land clearing for cultivation should be common. Second, we repeated all assessment by including only groups having at least 20 soil profiles. This allows the assessed pairs to cover a higher diversity of land history and future land cover/use, diluting the effect of a typical event at a specific soil profile on the estimates.Comparison with SOC turnover modelsWe compared our estimation with predictions by SOC models. A simple one-pool SOC model can be written as:$$frac{{{{{{rm{d}}}}}}C}{{{{{{rm{d}}}}}}t}=I-kcdot C,$$ (5) where I is the amount of carbon input, k is the decay rate of SOC, and C is the stock of SOC. At steady state, (C=I/k). A Q10 function can be applied to estimate k under warming (kw):$${k}_{{{{{{rm{w}}}}}}}=kcdot {{exp }}left(0.1cdot triangle Tcdot {{log }}left({Q}_{10}right)right),$$ (6) where (triangle T) is the warming level. Thus, when soil reaches a new steady state under warming, SOC stock (Cw) can be estimated as:$${C}_{{{{{{rm{w}}}}}}}=frac{{I}_{{{{{{rm{w}}}}}}}}{kcdot {{exp }}left(0.1cdot triangle Tcdot {{log }}left({Q}_{10}right)right)},$$ (7) where Iw is the carbon input amount under warming condition. Finally, the response of SOC to warming (R) can be calculated as:$$R=frac{{C}_{{{{{{rm{w}}}}}}}-C}{C}=frac{{I}_{{{{{{rm{w}}}}}}}}{I}cdot {{exp }}left(-0.1cdot triangle Tcdot {{log }}left({Q}_{10}right)right)-1.$$ (8) Using Eq. (8), we calculated R under a series of ensembles of (frac{{I}_{{{{{{rm{w}}}}}}}}{I}), (triangle T), and ({Q}_{10}), and compared R with that estimated using our space-for-time substitution approach.Comparison with field warming experimentsA number of meta-analyses based on data from field warming experiments had been performed to assess the response of SOC to warming7,26,46,47,48,49,50, which enable us to conduct comparisons with the estimates using our hybrid approach combining space-for-time substitution and meta-analysis techniques. A total of five meta-analysis papers have been found by searching the Web of Science. We retrieved the response ratios from the identified papers, and compared them to our estimations. Here, it should be noted that most field warming experiments focused on SOC changes (stock or content) in the top 0.2 m soil layer. We compared them with our estimation of the response of SOC stock in the top 0.3 m soil.Besides the published results of meta-analysis, we also conducted an independent meta-analysis using data from field warming experiments. The meta-analysis dataset was mainly from published papers on meta-analysis from 2013 to 2020 (see Supplementary Data 1). It should be noted that the field warming experiments manipulate temperature using different approaches such as open/closed-top chamber, infrared radiators and heating cables. For the comparison, we did not explicitly distinguish these approaches. The experimental duration ranged from 0.42 to 25 years with a mean of 4.7 years, and the warming magnitude ranged from 0.1 to 7°C with a mean of 1.92 °C. To ease comparison, field warming levels were classified into 0–1, 1–2, 2–3, 3–4, 4–5, and >5 °C. The same meta-analysis to that assessing soil profile data was used to predict the response ratio of SOC to the above six warming levels. In addition, we divided the data into four ecosystems (i.e., tundra, forest, shrublands and grasslands) and estimated the response ratio in each ecosystem. These estimates based on field warming experiments were compared with those estimated using our space-for-time approach.Variable importance and global mappingWe included 15 environmental predictors to derive a meta-forest model, a machine learning-based random forest model adapted for meta-analysis, to map the response of SOC stock/content to warming across the globe at the resolution of 0.0083°. The 15 environmental predictors reflect generally four broad groups of environmental conditions: baseline SOC conditions represented by current standing SOC stock or content, soil order and soil depth; current baseline climatic conditions represented by MAT, MAP, aridity index, precipitation seasonality represented by PCI, the fraction of precipitation in summer, the difference of temperature between ambient and warm groups, the difference of precipitation between ambient and warm groups; topography represented by elevation and landform; and vegetation represented by NPP and biome type.The metaforest function in the metafor package was used to derive the model. To fit the model, a fivefold cross-validation was conducted. That is, 80% of the derived response ratios was used to train the model, and the remaining 20% to validate the model. The best model hypeparameters were targeted by running the model under a series of parameter combinations, and the model performance was assessed by the rooted mean squared error (RMSE) and determination coefficient (R2). The meta-forest model allows the estimation of the relative influence of each individual variable in predicting the response, i.e. the relative 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 are determined by the algorithm when adding more trees cannot reduce prediction residuals. As such, the larger the relative influence of a variable, the stronger the effect of the variable on the response variable.Combining with spatial layers of predictors, the meta-forest model for SOC stock was used to predict the response of SOC to warming across the globe at the resolution of 1 km (most data layers are already at the 1 km resolution as abovementioned, for those layers that are not at the target resolution, they were resampled to the 1 km resolution). In the meta-forest model, current standing SOC stock is the most important predictor (Fig. 4). We use three global maps of SOC stocks including WISE51 (WISE Soil Property Databases | ISRIC), HWSD52 (Harmonized World Soil Database (HWSD v 1.21) – HWSD – IIASA) and SoilGrids53 (SoilGrids250m 2.0) to obtain current standing SOC stocks. These three global maps represent the major mapping products of SOC stock at the global level, and had been widely used for large scale modelling. The derived meta-forest model was applied across the globe to estimate the response ratio of SOC stock in each 1 km pixel. To do so, the same procedure to group the observed soil profiles (Fig. 1) was applied to group global land pixels (section Space-for-time substitution: grouping soil profiles). The only difference is that global mapping uses all pixels instead of the 113,013 soil profiles. In each 1 km pixel, prediction uncertainty was also quantified using estimates of randomly drawn 500 trees of the fitted meta-forest model to calcuate standard deviation of the predictions. More
