Five different estimates of global soil carbon stock (Csoil) were obtained from independent datasets. The main features of the datasets and the approaches used are briefly described below: a.

SoilGrids is an automated soil mapping system that provides consistent spatial predictions of soil properties and types at the spatial resolution of 250 m (Hengl et al., 2017). A global compilation of in situ soil profile measurements is used to produce an automated soil mapping based on machine learning algorithms. The dataset contains global soil organic carbon content at soil depths of 0, 5, 15, 30, 60, 100 and 200 cm. In addition, physical and chemical soil properties such as bulk density and carbon concentration are provided. A total of 158 remote-sensing-based covariates including land cover classes and long-term averaged surface temperature were used to train the machine learning model at the site level. According to Hengl et al. (2017), the current version of the dataset explains 68.8 % of the variance in soil carbon stock compared to a mere 22.9 % in the previous version (Hengl et al., 2014). However, it has also been recognized that SoilGrids may overestimate carbon stocks due to high values of bulk soil density (Tifafi et al., 2018). In general, the estimation of Csoil is mainly caused by the geographically biased availability of measured data especially in the circumpolar regions. Even though in situ measurements had a large spatial extent and cover most of the continents, the remote regions that are characterized by severe climate were sampled much less.

Four different datasets of biomass were used to produce the total vegetation biomass (Cveg) data on the global scale. a.

Thurner et al. (2014) estimated the aboveground biomass (AGB) and belowground biomass (BGB) for Northern Hemisphere boreal and temperate forests based on satellite radar remote sensing retrievals of growing stock volume (GSV) and field measurements of wood density and biomass allometry. The carbon stocks of tree stems were estimated from GSV retrieval of the BIOMASAR algorithm. The BIOMASAR algorithm uses remote sensing observations from the Advanced Synthetic Aperture Radar (ASAR) instrument on the Envisat satellite (Santoro et al., 2015). The remote sensing retrievals are then converted to biomass using information on wood density and allometry. The other tree biomass compartments (BCs) including roots, foliage and branches were estimated from stem biomass using field measurements of biomass allometry. The total carbon content of the vegetation was then derived as the sum of the biomass in different compartments and converted to carbon mass units using carbon fraction parameters. A comparison between the data and inventory-based estimates shows good agreement on regional scales in Russia, the United States and Europe (Thurner et al., 2014). The data from Thurner et al. (2014), at 0.01∘ spatial resolution and representative for the year 2010, only cover the northern boreal and temperate forests between 30∘ and 80∘ N latitudes.

The data for global distribution of soil depth were obtained from the Global Soil Texture and Derived Water-Holding Capacities database (Webb et al., 2000). The data contain standardized values of soil depth and texture selected from the values from the same soil type within each continent. The total soil depth depends on soil texture and water availability, and it is usually deeper than 100 cm. In regions with permafrost, total soil depth can extend beyond 400 cm (Fig. S1 in the Supplement).

The GPP datasets used to calculate ecosystem carbon turnover times were obtained from the FLUXCOM initiative (http://fluxcom.org/, last access: 28 February 2018). In FLUXCOM, the global energy and carbon fluxes are upscaled from eddy covariance flux measurements using different machine learning approaches with meteorological and Earth observation data (Jung et al., 2017). In this study, we used GPP derived from the two different FLUXCOM setups based on (1) only remote sensing covariates and (2) both remote sensing and meteorology forcing (Tramontana et al., 2016; Jung et al., 2020). In this study, we derived the long-term mean annual GPP across different machine learning methods over the time period from 2001 to 2015.

The high spatial resolution (∼1 km) climate dataset WorldClim (Fick and Hijmans, 2017) was used to investigate the relationship between τ and climate. The data included monthly maximum, minimum, and average temperature, precipitation, solar radiation, vapor pressure, and wind speed. The WorldClim data were produced by assimilating 9000–60 000 ground-station measurements and covariates such as topography, distance to the coast and remote sensing satellite products including maximum and minimum land surface temperature, as well as cloud cover in model fitting. For different regions and climate variables, different combinations of covariates were used. The 2-fold cross-validation statistics showed a very high model accuracy for temperature-related variables (r>0.99) and a moderately high accuracy for precipitation (r=0.86).

As a result of the balance between influx and outflux of carbon, the terrestrial carbon pool can be approximated to reach the steady-state condition (influx equals outflux) when long timescales are considered. This simplifies the calculation of τ to the ratio between the total terrestrial carbon storage and the influx or the outflux of carbon. The approach is advantageous in representing the highly heterogeneous intrinsic properties of the terrestrial carbon cycle as an averaged apparent ecosystem property which is more intuitive to infer large-scale sensitivity of τ to climate change. Instead of focusing on the heterogeneity of individual compartment turnover times, we show the change in the carbon cycle on the ecosystem level using τ as an emergent diagnostic property. The total land carbon storage can be estimated by summing soil carbon stocks derived from extrapolation and vegetation biomass. Assuming a steady state in which the total efflux (autotrophic and heterotrophic respiration, fire, etc.) equals the influx (GPP), then τ can be calculated as the ratio between carbon stock and influx: 1τ=Csoil+CvegGPP, where Csoil and Cveg are the total soil and vegetation carbon stocks, respectively, and GPP is the total influx to the ecosystem. An ensemble of τ estimates is generated by combining three soil carbon stocks at three different soil depths (1 m, 2 m, full soil depth), four vegetation biomass products, and 24 GPP values resulting in an ensemble with 864 members.

Two different corrections had to be addressed in order to assess the whole vegetation carbon stock from current observation-based products. First, the aboveground biomass datasets only consider the biomass within woody vegetation (mostly trees), while the biomass of herbaceous vegetation is missing. To account for herbaceous biomass, we used a previously developed method in which the live vegetation fraction is assumed to have a mean turnover time of 1 yr and a uniform distribution of respiratory costs of carbon (Carvalhais et al., 2014). The carbon in herbaceous vegetation can then be expressed as a function of GPP: 2CH=GPP×1-α⋅fH, where CH is the carbon stock of the herbaceous vegetation, GPP is the gross primary productivity from FLUXCOM, α is respiration cost of carbon (0.25–0.75), and fH is the fraction of a grid cell covered by herbaceous vegetation, which was obtained from the SYNMAP database (Jung et al., 2006).

Second, two of the vegetation biomass datasets (GlobBiomass and Avitabile; see Table 1) do not include BGB. For consistency across all Cveg datasets, we estimated the BGB using a previously developed empirical relationship (Saatchi et al., 2011) between AGB and BGB: 3BGB=0.489×AGB0.89.

We used observed soil profiles and multiple empirical models to extrapolate soil carbon stock to full soil depth (Fig. S1 and Table S1 in the Supplement). This approach is necessary to obtain the accumulated carbon stock from the surface to full soil depth because the soil datasets only extend up to 2 m below the surface. However, a large amount of Csoil is stored below this depth, especially in peatland regions where soil carbon content can be substantially higher in deeper soil layers (Hugelius et al., 2013). To estimate the total carbon storage in the land ecosystem, different empirical mathematical models were used (Table S1 in the Supplement). The covariance matrix adaptation evolution strategy (CMA-ES) method, which is based on an evolutionary algorithm that uses the pool of stochastically generated parameters of a model as the parents for the next generation (Hansen et al., 2001), was used to optimize parameters of the models.

Extrapolation using empirical numerical models may cause arbitrary bias and higher uncertainty if the models are not appropriately chosen. Here we used the in situ observational data from the World Soil Information Service (WOSIS) (Batjes et al., 2020) and the International Soil Carbon Network (ISCN) (Nave et al., 2017) to select the ensemble of the models that could best simulate soil carbon stocks at full depth. We used a global dataset of soil depth (Webb, 2000) as the maximum soil depth to which we extrapolated. The approach fit each empirical model against cumulative Csoil with all data points and then predicted the cumulative Csoil at full soil depth for each soil profile independently. The ability of a particular empirical model or combination of models was then evaluated by comparing the predictions of Csoil at full depth against the observations (see Sect. S3.2 in the Supplement). This procedure was applied to the two different in situ datasets: WOSIS, which covers most of the biomes, and ISCN, which has more coverage in circumpolar regions. Finally, after comparing different model averaging methods (see Table S2 in the Supplement), we chose two model ensembles that could best represent circumpolar and non-circumpolar regions based on observational datasets. The performance of the chosen ensembles is synthesized in Figs. S3 and S4 in the Supplement. Finally, each model ensemble is applied to extrapolate Csoil to full depth in corresponding regions (see Sect. S3 in the Supplement).

To estimate the sources of uncertainty in τ, we performed an n-way analysis of variance (ANOVA) on the different variables (Csoil, Cveg and GPP). The ANOVA provides the sum of squares of each variable and the total sum of squares of all variables. The contribution of each variable (data from different sources) to the total uncertainty can then be calculated as follows: 4Cn=SSnSStotal, where Cn is the relative contribution of uncertainty from the nth variable, SSn is the sum of the square of the nth variable, and SStotal is the total sum of the square of all variables. Note that the uncertainty was quantified in two domains:

grid cell – the relative contributions of different variables to uncertainty in τ were calculated independently for each grid cell;

The local correlation between τ and climate across latitudes was obtained by using a zonal moving window approach in which the Pearson partial correlations between τ and T and P were calculated using a 360∘ (longitudinal span) × 2.5∘ (latitudinal span) moving window. This approach allowed for the assessment of the correlation strength between τ and each climate parameter. The τ values below the local 1st percentile and above the 99th percentile were removed in each moving window to avoid the effect of potential outliers in the correlations with climate. In order to investigate the effect of latitudinal span, we chose different band sizes of 0.5∘, 2.5∘ and 5∘ and performed the correlation analysis in the same manner for each selection.

Table 2 summarizes the estimates of Csoil, Cveg and GPP. Globally, estimates of soil carbon stocks within the top 2 m of soil are 2863, 3969 and 3710 PgC for the datasets of Sanderman, SoilGrids and LandGIS, respectively (bulk density corrected; see Sect. S2 in the Supplement). The significant differences among different datasets indicate a high uncertainty in the current estimation of global soil carbon storage. The extrapolation of Csoil to the full soil depth (FD) shows that approximately 18 % of soil carbon is stored below the depth of 2 m. Compared to the previous generation of HWSD Csoil data (available only for top 1 m), the current state-of-the-art datasets show significantly higher Csoil within the top 1 m (Table 2). On the other hand, the current datasets of vegetation biomass show global Cveg ranges from 392 to 437 PgC and substantially lower relative uncertainty than Csoil. The estimation of the uncertainty that is derived from different GPP members shows a range of 100 to 123 PgC (10th percentile to 90th percentile) from different products. Note that the GPP members are different realizations from FLUXCOM and encompass a wide range of sources of uncertainty such as different climate forcing, use of remotely sensed data and machine learning methods (see Sect. 2.4). Overall, the results show that the differences in Csoil estimates are substantially larger than the differences in Cveg and GPP datasets.

A significant amount of soil organic carbon is stored in high-latitude terrestrial ecosystems, especially in the permafrost regions (Hugelius et al., 2013). However, in comparison with low latitudes, the uncertainties of Csoil distribution and storage in high latitudes are potentially higher due to fewer available observations of soil profiles. We therefore divided the global soil carbon into the non-circumpolar (Fig. 1) and the circumpolar (Fig. 2) regions based on the northern permafrost region map of the NCSCD. The results show that the mean value and range (maximum–minimum) of Csoil in non-circumpolar regions (Table 2) in the top 2 m are 2136 and 537 PgC and in the circumpolar regions within the top 2 m are 1278 and 574 PgC.

We used in situ observed soil profiles (Fig. S1 in the Supplement) and multiple empirical models to select an ensemble of models to extrapolate soil carbon stock to full soil depth (Fig. S2 and Table S1 in the Supplement). It was apparent that a unique ensemble would be limited to represent Csoil profiles globally, resulting in two different model ensembles being selected to represent the soil vertical distribution: one for the circumpolar regions, and another for non-circumpolar regions. In general, the results show good model performances for predicting in situ soil carbon stocks up to full soil depth, although non-circumpolar regions (Fig. S3 in the Supplement) show a higher model performance than that in circumpolar regions (Fig. S4 in the Supplement). The global estimation of Csoil to full soil depth results in a higher mean value of 2678 PgC in non-circumpolar regions and 1637 PgC in circumpolar regions. Our results show that there are approximately 500 and 400 PgC of carbon stock stored in the deep soil layer below 2 m in non-circumpolar and circumpolar regions, respectively.

The spatial distribution of Csoil is more consistent across datasets in the non-circumpolar regions than in the circumpolar regions (Fig. 1). The Pearson correlation coefficients (r) between each pair of datasets in the non-circumpolar regions are generally higher than in the circumpolar regions. Our results show a moderate agreement among the datasets in the spatial distribution of Csoil globally (r>0.65). However, there are significant differences in the spatial patterns between the HWSD and each dataset (Fig. 1) as the correlation coefficients are all below 0.3. In addition, there is a 2-fold lower carbon storage in the HWSD than the other datasets. Ratios between the total Csoil in the top 100 cm (Fig. 1, upper off diagonal plots) show that LandGIS, SoilGrids and Sanderman are consistent in temperate regions but show poor agreement in the tropical and the boreal regions. The comparison also shows that the gradient in carbon stocks between Europe and the lower latitudes diminished in the HWSD soil map. In addition, the spatial distribution and the amount of carbon stocks in insular Southeast Asia are significantly different in the HWSD.

Greater dissimilarities of spatial patterns across the datasets in the circumpolar regions are shown in Fig. 2. We included the NCSCD dataset which specifically focuses on the circumpolar regions. The spatial correlations between each pair of the four datasets show low correlation values (r) which range from 0.2 to 0.5. In contrast to the non-circumpolar regions, the high spatial dissimilarity in circumpolar regions indicates higher uncertainty regarding the estimation of total carbon storage. However, there is no evidence on which dataset is more credible in terms of total carbon storage and spatial pattern. The large differences are possibly due to fewer observational soil profiles in the northern high-latitude regions, which are crucial in the model training process (Hugelius et al., 2013; Hengl et al., 2017).

The comparison between all datasets shows good agreement in the vertical structure of terrestrial carbon stocks. The Csoil in the top 1 m is about half of the total terrestrial carbon and 80 % of the top 2 m of Csoil regardless of region or data source. For the non-circumpolar regions, all the datasets show significantly higher carbon storage in the top 1 m than that in the HWSD while showing less divergence of carbon storage among these three datasets (Table 2). In general, the current datasets show a similar vertical distribution of Csoil with consistent values and ratios between 1 and 2 m soil. The extrapolation results indicate that about 20 % of carbon is stored below 2 m in the non-circumpolar regions. For the circumpolar regions, the four datasets show a clear trend that the difference of Csoil increases with soil depth, as shown in Table 2. The difference between the top 1 m of Csoil among datasets has a higher difference than that of 2 m. However, the ratio between storage in 1 and 2 m is similar across all datasets.

Different from the spatial distribution of soil carbon, most vegetation carbon is stored in the tropics, whereas much less carbon resides in the higher latitudes. In fact, the Cveg in the circumpolar regions is only 10 % of that in the non-circumpolar regions (Table 2). In comparison with soil carbon, the results show higher consistency and convergence in global estimates of carbon stock among the four global vegetation datasets (Fig. 3). Our results show that the global vegetation carbon stock is 10 % to 25 % of the global soil carbon stock depending on the soil depth considered. The significant spatial correlations (r>0.75, α<0.01) between each of the estimates indicate a consistent global spatial distribution of vegetation across the different data sources. However, the results show more heterogeneity in the regional distribution of vegetation biomass and uncertainty of Cveg. Specifically, Cveg in arid and cold regions has higher relative uncertainty than that in the moist and hot regions.

The Cveg consists of three components including AGB, BGB and herbaceous biomass. The herbaceous biomass is estimated from mean annual GPP (see Sect. 3.2; Carvalhais et al., 2014) and globally represents 5 % of the total Cveg and less than 1 % of the total Csoil, indicating the minor role of herbaceous biomass in affecting the global estimates and the spatial distribution of τ. The comparison among the four vegetation datasets shows a mean of 410 PgC in Cveg with a spread of 11 % across the different datasets and a consistent spatial distribution across the different sources. Locally these differences can be higher, as observed in the relatively higher level of disagreement in sparsely vegetated arid regions and some cold regions (Fig. 3, upper off-diagonal panels).

The global spatial distribution of GPP is similar to that of Cveg, i.e., high in the tropical regions and low in the higher latitudes (Fig. 4). The GPP datasets show high consistency in both the spatial patterns and global values. The spread in GPP estimates is higher (>50%) in arid and polar regions than the other regions (Fig. 4, upper off-diagonal plots). Although the differences among different vegetation and GPP estimations, in general, are not as high as in soil carbon, the regionally high uncertainties can be significant.

The ecosystem turnover time and its uncertainty were estimated using different combinations of Csoil, Cveg and GPP data. We calculated τ using full soil depth, which results in a global estimate of 43 yr and ranges from 36 yr (25th percentiles) to 50 yr (75th percentiles). The uncertainty in the global estimate of τ is mainly contributed by soil (84 %) and GPP (15 %), whereas vegetation contributes only marginally (less than 1 %). In addition, we derived a global τ of 37 yr and ranges from 31 to 40 yr by assuming the maximum active layer thickness to be the full soil depth in the circumpolar regions instead of using only 1 m Csoil as was done in the previous study (Carvalhais et al., 2014). The incorporation of deep soil in the circumpolar regions increased the global mean value of τ by 6 yr and uncertainties in the estimations of τ as well. The global spatial distribution of τ (Fig. 5) shows a large heterogeneity which ranges from 7 yr (1st percentile) in the tropics to over 1452 yr (99th percentile) in northern high latitudes. The results show a U-shaped distribution of τ along latitudes in which τ increases by nearly 3 orders of magnitude from low to high latitudes (Fig. 7a). Fig. 5b shows the map of relative uncertainty that is derived from different datasets. The higher relative uncertainty indicates more spread among the datasets used to estimate τ. Our result shows that τ estimates at higher latitudes, especially in circumpolar regions, have higher uncertainties than those at lower latitudes. We found several regions with large spreads in τ among the datasets including northeast Canada, central Russia and central Australia where the relative uncertainties can span beyond 100 %.

The latitudinal distributions of τ can be best represented by a second-degree polynomial function (Fig. 7b). After fitting the data of all ensemble members, the rate of τ change with latitude can be obtained by taking the first derivative of the fitted polynomial function. We found that the rate of τ change with latitude has very consistent zonal patterns for different τ ensemble members from different data sources (Fig. 7c). The result shows a consensus in the change in τ with latitude of different datasets. We also found that the zonal τ gradients were not significantly (p>0.05) different from each other for different selections of soil depth, indicating that soil depth has no significant effect on the τ gradient along latitude. It is worth noting that there is a significant difference in the zonal τ gradient between the Northern Hemisphere and Southern Hemisphere (p<0.0001) and that τ increases faster from low to high latitudes in northern latitudes than in the southern latitudes. The results show a high confidence in the zonal distribution of τ and that the difference across datasets does not affect the robustness of the pattern.

The correlations between τ and temperature and precipitation are analyzed for all the ensemble members on the global scale (see Sect. 3.5). The τ–T correlation (Fig. 8a) is the strongest in northern middle to high latitudes between 25 and 60∘ N, and it decreases rapidly from 20∘ N to the Equator. In the Southern Hemisphere, it increases until 40∘ S, albeit with a weaker gradient than in the Northern Hemisphere. The uncertainties due to differences in the ensemble members (shown by the shaded area) are higher in the transition between the temperate and Arctic regions (50 to 70∘ N), as well as between tropical humid and semiarid regions (20∘ N to 20∘ S). Similar to the contribution of different sources to global uncertainty, the spread in the τ–T correlation is mostly due to Csoil, whereas GPP only affects the zonal correlation to a limited extent (Fig. 8c). However, we find that the τ–T zonal correlation varies negligibly due to data source and soil depth. All ensemble members agree that the τ–T correlation is negative with stronger associations in cold regions than in warm regions.

The τ–P correlation, in general, has larger variability across latitude and a higher uncertainty related to differences in Csoil (Fig. 8e). Contrary to the τ–T relationship, the uncertainty of the τ–P correlations from both different data sources and soil depths is smaller in the tropics than at high latitudes. Negative correlations dominate the high latitudes between 20 and 50∘ N and between 20 and 40∘ S. On the other hand, stronger positive correlations prevail in the tropics. The τ–P correlation changes the direction from negative in the temperate zone to positive in the tropics, indicating the role of moisture availability in transitions from arid to humid regions. We also find that the τ–P relationship does not change with different soil depths (Fig. S11 in the Supplement).

We found that there is a significant difference across the current soil carbon datasets in both circumpolar and non-circumpolar regions (Figs. 1 and 2). The results show that the uncertainty of Csoil estimations in the circumpolar regions (52 %) is much larger than that in the non-circumpolar regions (37 %). The spatial patterns of total ecosystem Csoil among the soil datasets are more consistent in the non-circumpolar regions, indicating a higher confidence in the current estimation of soil carbon stock in these regions. In contrast to the non-circumpolar regions, there is lower confidence in the circumpolar regions in estimating Csoil due to the fact that there is a low spatial correlation across datasets (Fig. 1). The difference can be caused by a variety of reasons: for example, (i) as an important input to the machine learning methods, in situ soil profiles are very important factors that influence the final results of the upscaling and, using different training datasets, can lead to relevant differences in outputs, and (ii) the sparse coverage of soil profiles in the circumpolar regions may cause the large divergence in the northern circumpolar region. A major difference in the Sanderman soil dataset compared to the other two soil datasets (SoilGrids and LandGIS) is that here the direct target of upscaling was the soil carbon stock, while in the other two datasets, the targets were each individual component used to calculate Csoil (carbon density, bulk density and percentage of coarse fragments) which were predicted individually. Additional discrepancies may also be associated with the differences in climatic and other input covariates used in the upscaling which may yield a different estimation of Csoil (see Sect. 2.1).

The estimation of a whole ecosystem turnover time is dependent on an estimate of soil carbon stock up to full soil depth. Here, we rely on the available global datasets to follow an ensemble approach for predicting Csoil at full depth that selects models with a minimum distance between prediction and observations by using in situ soil profiles (see Sect. S3 in the Supplement). The final results depend on the information from the global soil datasets and also on the characteristics of the empirical models. Recent studies have shown the advantage of convolutional neural networks, in comparison to random forest approaches (Hengl et al., 2017; Wheeler et al., 2018), for more robust predictions of soil organic carbon (SOC) with depth (Wadoux et al., 2019; Padarian et al., 2019), which could improve the geographical representation of SOC with depth, although random forest approaches already tend to provide unbiased estimates. Overall, the extrapolation provides insights into the carbon storage vertical distribution in deeper soil layers globally, showing that there is approximately 18 % of carbon stored below 2 m globally and over 20 % of carbon stored below 2 m in the circumpolar regions. This results from the fact that, in contrast to the non-circumpolar regions, the circumpolar Csoil does not have a decreasing trend up to 4 m of soil depth (Fig. S1 in the Supplement), which indicates that there is a significant amount of carbon stored in deep soil and emphasizes the perspective that deep soil turnover is a key aspect of the global carbon cycle still poorly understood (Todd-Brown et al., 2013).

Compared to soil carbon, the higher level of consistency in the Cveg estimates indicates the stronger agreement on the current estimations in the aboveground carbon components. We show that due to much lower uncertainties in the Cveg estimates, the effect of vegetation on the global τ estimates is minor regardless of which soil depth is used (Table S3). Although the contribution of vegetation to the uncertainties in global τ estimates is less than 2 %, our results show that, locally, vegetation can be the major factor that causes the difference in τ estimates. As shown in Fig. S10 in the Supplement, vegetation dominates the uncertainties of τ in part of the tropics and part of the temperate region in Southeast Asia which in total account for 7 % of the global land area if only 1 m of Csoil is used to estimate τ. The land area where τ uncertainties are dominated by vegetation carbon stocks decreases to 3 % and 1 %, respectively, when Csoil of 2 m and full soil depths is considered. Although our results indicate that vegetation plays a minor role in the global estimates of τ, it is an important factor that can largely affect local patterns of the distribution of τ.

The contribution of vegetation and GPP to the uncertainties in global τ is modest compared to the contributions from soil carbon stocks. However, we note that the regional differences in the products can significantly affect the spatial distribution and uncertainty of τ (Figs. 3 and 4). Alternate GPP estimates are likely to impact τ estimates, although marginally. For example, on global scales, the estimate of a GPP of 123 PgCyr-1 by Zhang et al. (2017) would lead to a reduction in τ of ∼10% compared to our current estimates (43 yr). However, the difference is well within the range of our estimated uncertainty in τ (∼20%) using all the ensemble members. Given the robustness in spatial patterns in GPP estimate from Zhang et al. (2017) compared to the FLUXCOM estimates (r≥0.9, p<0.01; Fig. S8 in the Supplement), the spatial variability in τ shows a high correlation (r≥0.92, p<0.01) (See Fig. S9 in the Supplement).

The current global estimates of τ are substantially larger than previously (60 %), although the global patterns are comparable to previous estimates. Our results show an overall agreement of r=0.95 between the current estimation and the previous estimation of the latitudinal gradient of τ (Carvalhais et al., 2014). The patterns in the latitudinal correlations between climate and τ are also qualitatively similar to the previous patterns found with some particular exceptions in the strength of correlations between τ and temperature in northern temperate systems and changes in τ–precipitation correlations, especially in the tropics. A further investigation on the causes behind these differences between the previous and current studies reflects that Csoil has a substantial contribution to these changes in the correlation between τ and climate, while GPP has only a modest role in altering the τ–temperature correlation changes in northern temperate regions (see Fig. S6 in the Supplement). This is consistent with the assessment of the largest differences in the spatial distribution of Csoil between the three soil datasets used in this study and the HWSD soil dataset used before (Fig. 1).

The uncertainty analysis showed that our current estimation of τ has a considerable spread which is derived from state-of-the-art observations of carbon stocks in soils and vegetation and of carbon fluxes. The uncertainty mainly stems from the soil carbon stocks (84 %) and GPP fluxes (15 %), in which the former dominates the vast areas in the circumpolar regions and the tropical peatland, while the latter dominates the semiarid and arid regions (Fig. 6). Although GPP shows a strong agreement in global spatial patterns, local differences between estimates can lead to significant differences in the estimation of τ. This result is consistent with previous observations and model-based studies that also refer to the biases in estimated primary productivity in affecting the carbon turnover estimations to a large extent (Todd-Brown et al., 2013).

In contrast to global modeling approaches, previous studies have shown that the global soil carbon stocks across observation-based datasets are much less divergent than the ESM simulations included in CMIP5 (Carvalhais et al., 2014). The CMIP5 results show that the simulated carbon storage ranges from 500 to 3000 PgC, implying a 3-fold variation in τ across models (Todd-Brown et al. 2013; Carvalhais et al., 2014). Our current results show that the total amount of carbon in terrestrial ecosystems is substantially higher than the estimation by ESMs, in which even the lowest estimation of total carbon storage (in the Sanderman dataset) is about 300 PgC higher than the highest ESM estimation (MPI-ESM-LR; Todd-Brown et al., 2013). The spatial distribution of carbon stocks among ESMs shows a large variation across models (Carvalhais et al., 2014), while the observation-based datasets are more consistent in the non-circumpolar regions. However, the uncertainty analysis shows that our current estimation of τ has a considerable spread resulting mainly from the spread in state-of-the-art estimates of soil carbon stocks, followed by the spread in estimates of GPP. The estimation of τ is dependent on the assumption of a maximum soil depth used to estimate soil C stocks that particularly in the circumpolar regions contribute 54 % to the overall uncertainty, while the data source contributes 25 %. Soil depth itself is characterized by a large uncertainty given the difficulty in assessing in situ measurement uncertainties in defining a depth at which the soil becomes metabolically inactive and in determining the role of vertical transport to a depth-dependent concentration. The challenge in circumpolar regions relates additionally to the influence of active layer dynamics on the spatial and temporal variability in metabolic activity. From an ESM perspective, it is difficult to avoid relying on a whole soil, or ecosystem, estimate to compare it with observation-based estimates given that these models abstract from depth-dependent soil carbon decomposition dynamics or have not reported the depth of the soil carbon stocks (Carvalhais et al., 2014). In this aspect, an explicit consideration of soil C stocks at depth in ESMs would be instrumental in understanding and evaluating the distribution of ecosystem carbon stocks and turnover times against observations.

It is worth noting that here the estimation of τ is based on the steady-state assumption, which is the assumption of a balanced net exchange of carbon between terrestrial ecosystems and the atmosphere. Here, the assumption is that integrating at larger spatial scales, by averaging the local variations in sink and source conditions, reduces the differences between assimilation and outflux relative to the gross influx and that the integration of stocks and fluxes for long-term spans reduces the effects of transient changes in climate and of interannual variability in τ estimates. However, this assumption is valid to a significantly lesser extent at smaller spatial scales (site-level) and shorter time intervals since the ecosystem–atmosphere exchange of carbon is most of the time not in balance, and forced steady-state assumptions can lead to biases in estimates of turnover times and other ecosystem parameters (Ge et al., 2018; Carvalhais et al., 2008).

Despite the large uncertainty in the τ estimations, we identified robust patterns in the τ–climate relationship that can be instrumental in addressing the large uncertainties in modeling the sensitivity of terrestrial carbon to climate, which are reflected in the spread of τ estimates by the different ESMs (Tod-Brown et al., 2013). The zonal distribution of τ is a robust feature that changes little across different datasets, which indicates that the current state-of-the-art datasets all agree on the latitudinal gradient of the carbon turnover time (Fig. 7). In addition, the latitudinal change rate of τ is robust against any considered soil depth (Fig. 7), which reflects pattern comparability between assumptions of τ gradients up to 1 m (Koven et al. 2017; Wang et al., 2018) or to full soil depth (Carvalhais et al., 2014). The robustness of the latitudinal patterns in the ensemble is likely to emerge from the latitudinal gradient in temperature, shaping the zonal distribution of τ that increases towards the poles as mean annual temperatures substantially decrease.

This study addresses the robustness of the τ–climate association by investigating the zonal correlations between τ and temperature and between τ and precipitation. The τ–temperature correlation varies with latitude in which high correlations are found at higher latitudes and low to moderate correlations are found closer to the tropics (Fig. 8). The latitudinal gradient in the τ–T relationship is similar when compared with previous results (Carvalhais et al., 2014), although the strength of the correlations can vary marginally by changing GPP products but more substantially when exchanging the Csoil datasets (Fig. S6 in the Supplement). However, these relationships show strong robustness across state-of-the-art datasets (Fig. 8). On the other hand, the zonal patterns of τ–precipitation are more challenging to converge across different Csoil sources (Fig. 8e) when compared with uncertainties stemming from GPP (Fig. 8f) regardless of the depth considered (Fig. S11 in the Supplement). Overall, the correlation between turnover times and precipitation in the tropics is higher than that with temperature, as shown in Fig. 8d, indicating a potentially more dominant role of precipitation in the tropics (Wang et al., 2018).

Overall, the τ–P correlations, although varying in strength, are robust across the data ensemble except when controlling for Csoil source (Fig. 8e). The role of Csoil in the τ–P relationships is independent of depth (Fig. S11 in the Supplement) and explains most of the differences found in the patterns of previous results (Carvalhais et al., 2014), which are mainly caused by the differences in the soil carbon stock (Fig. S6 in the Supplement). Given that the data and methodological support are substantially shared across the different approaches (see Sect. 2.1) and given the potential limitations in representing contributions of soil moisture to τ at deeper layers, even shallower than 2 m, these results highlight the relevance of better understanding and diagnosing the effects of the hydrological cycle on τ. The limitation may be linked to the realization that methods based on random forests tend to show high correlations between predicted top soil and deeper soil estimates of Csoil, as well as lower correlations to deeper Csoil geographic variability (Wadoux et al., 2019; Padarian et al., 2019).

Ultimately, given the recognition that the sensitivity of the terrestrial carbon to climate is a major uncertainty reflected in the spread of τ across different ESMs, the reliable estimation of τ and identification of robust patterns in τ–climate associations is key to provide robust constraints to improve the performance of the current ESMs. Notwithstanding, the intimate interaction of energy and water along with other factors such as land use change all affect τ but on different spatial and temporal scales. Further research directions would gain by exploring the contribution of addition potential factors that may influence the spatial distribution of τ, such as mortality and disturbance regimes, human impact via management regimes or land cover change dynamics, and the vertical distribution of the hydrological cycles.