1. Introduction
Natural terrestrial ecosystems, excluding those subject to land use change, have sequestered about 30% of cumulative anthropogenic carbon emissions since 2005 (Le Quéré et al. 2015). The global terrestrial carbon sink is sensitive to climate variability and climate trends (Forkel et al. 2016; Peylin et al. 2005; Piao et al. 2013; Xuhui Wang et al. 2014). A positive feedback between the terrestrial carbon reservoir and climate change is projected by Earth system models (ESMs), but the magnitude of this feedback differs among models (Friedlingstein et al. 2014, 2006). How to reduce this uncertainty has received increasing attention recently (Cox et al. 2013).
The carbon turnover time, defined as the ratio of mass and outgoing flux from a carbon pool, is one of the key parameters determining terrestrial carbon balance (He et al. 2016; Koven et al. 2015; Todd-Brown et al. 2013). The structure of land carbon cycle models can be summarized by a cascade of pools, each with a different turnover, for different grid points. For example, for live biomass, carbon turnover time in forest is longer than in grasslands; and for dead organic carbon, turnover time in Arctic tundra is much longer than in tropical forests (Bloom et al. 2016). It has been suggested that uncertain carbon turnover time as an emerging property of models dominates the uncertainty in terrestrial vegetation responses to future climate change and rising atmospheric CO2 concentration (Friend et al. 2014). Furthermore, the soil carbon turnover times in ESMs were shown to be significantly underestimated compared to radiocarbon measurements, leading to overestimation of soil carbon sequestration by a factor of nearly 2 (40% ± 27%) (He et al. 2016).
Terrestrial carbon turnover time is closely linked with climate factors such as temperature and precipitation (Carvalhais et al. 2014; Chen et al. 2013; Knorr et al. 2005). For example, Carvalhais et al. (2014) found a negative correlation between temperature and ecosystem carbon turnover time τeco across most of the regions in the world, with the exception of tropical forests and warm arid regions. In the warm arid regions, precipitation showed stronger correlations with τeco than with temperature. In tropical regions, both temperature and precipitation showed a weak spatial correlation with τeco (Carvalhais et al. 2014). It should be noted that since vegetation and soil carbon turnover have different physiological processes and climate responses (Bradford et al. 2016; De Kauwe et al. 2014), vegetation and soil carbon turnover time may have different spatial patterns of correlation with climate, which was not fully investigated by Carvalhais et al. (2014). Furthermore, it is difficult to draw a clear picture of the terrestrial carbon cycle model performance on the magnitude of the sensitivity of carbon turnover time to climate variation from the current literature.
In addition to the uncertainties in the climate sensitivity of carbon turnover time, the bias of ESM climate fields also influences the modeled carbon turnover times. The simulations from phase 5 of the Coupled Model Intercomparison Project (CMIP5) showed large differences between climate models (Flato et al. 2013). For example, the CMIP5 global land annual temperature T during the period of 1986–2005 differed by approximately 3°C among models, and global land annual precipitation P by approximately 250 mm (Anav et al. 2013). This invites the question whether large differences of turnover times between CMIP5 ESMs mainly result from differences between climate models or from structural differences between carbon cycle models.
In this study, we evaluated the spatial patterns of carbon turnover time and its response to climate variation derived from 14 CMIP5 ESMs against observation-based results. Unlike previous studies such as Carvalhais et al. (2014), here we evaluate biomass and soil carbon turnover time separately. Annual net primary production instead of gross primary production was used to calculate carbon turnover time.
2. Dataset and methods
a. Vegetation carbon storage
The spatial distribution of total biomass carbon was derived from recently published global maps of aboveground biomass carbon (ABC) over the period of 1993–2010 (Liu et al. 2015) and biome-specific conversion factors between total biomass carbon (TBC) and ABC (Flato et al. 2013; Liu et al. 2015; Robinson 2007). The global ABC product of Liu et al. (2015) was derived based on global vegetation optical depth (VOD) retrievals from harmonized series of passive microwave satellite sensors (Liu et al. 2011). Similar to Liu et al. (2015), in order to retrieve the TBC we simply multiplied ABC values by vegetation-specific ratios of TBC/ABC, provided by Table 1 in Liu et al. (2015). The information on the spatial distribution of vegetation type was determined using the Moderate Resolution Imaging Spectroradiometer (MODIS) International Geosphere–Biosphere Program (IGBP) land-cover map (Friedl et al. 2010). Our estimation of the global TBC stock was 570 PgC, comparable to the 560 PgC from Gibbs et al. (2006).
b. Soil organic carbon storage
Previous studies usually used the best traditional soil carbon map provided by the Harmonized World Soil Database (HWSD) (FAO/IIASA/ISRIC/ISSCAS/JRC 2012) and the Northern Circumpolar Soil Carbon Database (NCSCD) (Hugelius et al. 2013; Tarnocai et al. 2009) for estimating soil carbon turnover time (Todd-Brown et al. 2013). In this study, we chose the latest global soil carbon dataset provided by the World Inventory of Soil Emission Potentials (WISE) project (Batjes 2016) based on approximately 21 000 available profiles and soil geographical data. The WISE soil carbon dataset has more accurate spatial patterns of soil organic carbon (SOC) especially for the northern circumpolar regions, and reported SOC density for seven depth intervals (0–0.2, 0.2–0.4, 0.4–0.6, 0.6–0.8, 0.8–1.0, 1.0–1.5, and 1.5–2.0 m). Because the CMIP5 models did not include vertically resolved soil profiles, and did not consider carbon cycle processes for burying carbon below the active layer, we used the top 1 m of soil carbon storage to compute soil carbon turnover time as in Todd-Brown et al. (2013). To compare with modeled results, we also used the global litter carbon stock from Bloom et al. (2016) output by a diagnostic ecosystem carbon balance model, Data Assimilation Linked Ecosystem Carbon Model version 2 (DALEC2) (Bloom and Williams 2015). In this study, soil organic carbon storage was calculated from the sum of soil carbon from Batjes (2016) and litter carbon from Bloom et al. (2016).
c. NPP and climate data
The global distribution of net primary production (NPP) with 1-km spatial resolution from 2000 to 2010 was provided by the Numerical Terradynamic Simulation Group (NTSG) at the University of Montana (https://www.ntsg.umt.edu/; Zhao and Running 2010). This NPP product was not an observation but a model with a light-use efficiency formulation driven by satellite-based estimates of the fraction of photosynthetically active radiation, shortwave downward solar radiation, vapor pressure deficit (VPD), and low daily minimum temperature for gross primary production (GPP), and a model for maintenance and growth components respirations to derive NPP from GPP. Detailed information on the techniques used for modeling NPP can be found in related publications (Zhao and Running 2010; Zhao et al. 2005).
The temperature and precipitation data were from the Climatic Research Unit (CRU) time series version 3.24 datasets (Harris et al. 2014) with a spatial resolution of 0.5°. These gridded datasets were obtained from more than 4000 meteorological stations and interpolated based on spatial autocorrelation functions (Mitchell and Jones 2005; New et al. 2000).
d. CMIP5 ESM simulations
We used historical simulations (“historical” experiment, 1850–2005) from the CMIP5 ESMs forced by observed atmospheric composition changes and time-variable land cover (Taylor et al. 2012). Output of biomass carbon, soil organic carbon, litter carbon, NPP, air temperature, and precipitation (cVeg, cSoil, cLitter, npp, tas, and pr in the CMIP5 variable list) from 14 ESMs (see Table S1 in the supplemental information) were used. These monthly output variables were downloaded from the PCMDI server (Cinquini et al. 2014; http://cmip-pcmdi.llnl.gov/cmip5). For models with multiple simulations, all members of the ensemble were averaged following Todd-Brown et al. (2013, 2014). All ESM data were regridded to 1° × 1° spatial resolution using a first-order conservative remapping scheme (Jones 1999) in Climate Data Operators (https://code.zmaw.de/projects/cdo).
e. Analyses
3. Results
a. Carbon turnover time at the global and biome scale
Compared to observation-based τveg (~11 yr), 8 of the 14 CMIP5 ESMs [BCC_CSM1.1(m), CanESM2, IPSL-CM5A-LR, IPSL-CM5B-LR, MIROC-ESM-CHEM, MPI-ESM-LR, MPI-ESM-MR, and MRI-ESM1] underestimate τveg, and 5 ESMs [CCSM4, CESM1(BGC), CESM1(CAM5), CESM1(WACCM), and NorESM1-ME] have a value comparable to observed (Figs. 1a,c). Among the 14 models, the shortest global τveg is simulated by MPI-ESM-MR (4 yr), and BNU-ESM predicted the longest τveg (19 yr), with a factor of 4.8 across the models. As shown in Figs. 1a and 1c, the large differences of τveg across ESMs are correlated with precipitation (r = 0.6, p = 0.0) but not with temperature differences (r = 0.1, p = 0.8), implying that the bias of modeled precipitation rather than temperature may explain some of the differences in τveg at the global scale.
The magnitude of global MAT and MAP with τveg and τsoil estimated by 14 CMIP5 ESMs and observational data, (a) MAT and τveg; (b) MAT and τsoil; (c) MAP and τveg; and (d) MAP and τsoil. Note that r is the Pearson correlation coefficient between MAT or MAP and τveg or τsoil for all models; p is the corresponding significance.
Citation: Journal of Climate 31, 15; 10.1175/JCLI-D-17-0380.1
Global τsoil based on the WISE soil dataset is 26 yr (Fig. 1). The 14 CMIP5 ESMs estimated τsoil ranging from 11 yr [CESM1(WACCM)] to 40 yr (MIROC-ESM-CHEM), with a median value of 16 yr, thus grossly underestimating τsoil (even though 3 models—MIROC-ESM-CHEM, MPI-ESM-LR, and MPI-ESM-MR—overestimate τsoil). The model-estimated global τsoil is weakly positively correlated with temperature (r = 0.0, p = 0.9) and negatively correlated with precipitation (r = −0.1, p = 0.7) across the models (Figs. 1b,d), indicating that the differences of τsoil between models primarily originate from structural differences in terrestrial carbon cycle models rather than from errors in climate models.
For different biomes (see Fig. S1 in the supplemental material), we observed that most models largely underestimated τveg and τsoil in tundra (modeled median of 7 yr vs observed 12 yr for τveg and 40 vs 118 yr for τsoil; Fig. 2a) and in desert and shrubland (modeled median of 4 yr vs observed 14 yr for τveg and 18 vs 54 yr for τsoil; Fig. 2e). In other biomes, model-based carbon turnover times showed large variation, but the median of the models provides similar values to observations for tropical forest (12 vs 14 yr for τveg and 9 vs 11 yr for τsoil; Fig. 2c) and temperate forest (10 vs 9 yr for τveg and 17 vs 18 yr for τsoil; Fig. 2d).
The magnitude of τveg vs τsoil of six biomes estimated by 14 CMIP5 ESMs and observational data, for (a) tundra, (b) boreal forest, (c) tropical rain forest, (d) temperate forest, (e) desert and shrubland, and (f) grassland and savanna.
Citation: Journal of Climate 31, 15; 10.1175/JCLI-D-17-0380.1
b. Spatial distribution of τveg and τsoil
The carbon turnover times derived from observational data show spatial gradients (Figs. 3a and 4a). Longer τveg (>20 yr) prevail in boreal forests and arid and semiarid regions (western United States, western China, the sub-Saharan region, and central Australia), while temperate cropland-dominated regions (e.g., central North America, eastern Europe, and eastern China) have short τveg (<4 yr). The τveg of tropical forests is longer than 12 yr. Similar spatial patterns of τveg are reproduced by most ESMs (except BNU-ESM and MRI-ESM1; Fig. S2 in the supplemental material), although there are large differences in the spatial gradients of τveg (Fig. 3). In fact, τveg is underestimated over more than half the land area (Δτveg < −3 yr, where Δτveg is the difference between observation-based and model-based τveg) for 13 out of 14 models (excluding BNU-ESM). The two models with the largest areas of underestimated τveg are MPI-ESM-LR and MPI-ESM-MR. BNU-ESM has the largest area of mismatch with the observations. It is noticeable that most models underestimate biomass turnover times in arid and semiarid regions as well as in northeastern Siberia, but overestimate τveg in eastern North America, southern Europe, and eastern China (Fig. 3). Across tropical forested regions, 5 of 14 models [CCSM4, CESM1(BGC), CESM1(CAM5), CESM1(WACCM), and NorESM1-ME] largely overestimate τveg (Δτveg > 5 yr). Model-based τveg is weakly correlated with temperature (5.3% land area, p < 0.05; Fig. S4) and with precipitation (4.3% land area, p < 0.05; Fig. S4) across local climate gradients, confirming that differences of τveg mainly generate from the coupled land models rather than climate models.
(a) Global spatial patterns of τveg derived from observation data (obs) and (b)–(o) observation differences with model-based τveg. Areas with no biomass (mean annual NDVI below 0.1) are masked with gray shading.
Citation: Journal of Climate 31, 15; 10.1175/JCLI-D-17-0380.1
In contrast with τveg (Fig. 3a), tropical forested area show lowest τsoil (<20 yr). As shown in Fig. 4a, the largest τsoil are mainly in the temperate arid and semiarid regions as well as high-latitude tundra regions, where τsoil > 80 yr. Note that τsoil in most ESMs generally show similar spatial patterns, with the shortest τsoil in tropical forest regions and longest τsoil in the Arctic tundra region (Fig. S3 in the supplemental material). Compared with τsoil derived from observation, 9 out of 14 models [BCC_CSM1.1(m), BNU-ESM, CCSM4, CESM1(BGC), CESM1(CAM5), CESM1(WACCM), IPSL-CM5A-LR, IPSL-CM5B-LR, and NorESM1-ME] systematically underestimate τsoil (Δτsoil < −5 yr, where Δτsoil is the difference between observation-based and model-based τsoil), with CCSM4 showing the largest underestimated area. On the contrary, MIROC-ESM-CHEM (Fig. 4k), MPI-ESM-LR (Fig. 4l), and MPI-ESM-MR (Fig. 4m) overestimate τsoil (Δτsoil > 5 yr) in about half of the land area. All models largely underestimate τsoil (Δτsoil < −50 yr) in arid and semiarid regions across southwestern North America, western China, the sub-Saharan region, and Australia (Figs. 4b–o). In northern high-latitude regions with permafrost, shorter τsoil than observed (Δτsoil < −10 yr) is predicted by most models except MIROC-ESM-CHEM, which significantly overestimates τsoil (Δτsoil > 50 yr) (Fig. 4k). For spatial correlations between model-based τsoil and climate, there is only a small area showing significant values at the p < 0.05 level for τsoil and temperature (6.2% land area; Fig. S4) and for τsoil and precipitation (5.3% land area; Fig. S4).
As shown in Fig. 5a, model-based τsoil show higher spatial correlation with observation than τveg (correlation coefficients with τsoil generally larger than 0.4 except for BNU-ESM, and correlation coefficients smaller than 0.3 for all models for τveg), implying that ESMs have better performance in the simulation of spatial patterns of τsoil than τveg. Overall, among the 14 models, MIROC-ESM-CHEM shows the highest spatial correlation of τsoil with the observation (r = 0.7), while NorESM1-ME has the highest spatial correlation of τveg with the observation (r = 0.3). In terms of root-mean-square error (RMSE) between the observation and simulations across the globe (Fig. 5b), we found that NorESM1-ME and MPI-ESM-LR show the lowest RMSE for τveg (8 yr) and τsoil (38 yr), respectively. The highest RMSE appears in BNU-ESM for both τveg (36 yr) and τsoil (77 yr).
Matrices of (a) r and (b) RMSE for carbon turnover times between each CMIP5 ESM and observation and between CMIP5 ESMs at the grid cells. Lower-triangular matrix represents r or RMSE for τveg, and upper-triangular matrix represents r or RMSE for τsoil.
Citation: Journal of Climate 31, 15; 10.1175/JCLI-D-17-0380.1
c. Spatial sensitivities of carbon turnover times to climate
To further study the spatial sensitivities of τveg and τsoil to climate (temperature and precipitation), we performed multiple linear regression analysis as explained in the method section. As shown in Fig. 6a, the observation-based sensitivities of τveg to temperature (denoted as 
Spatial sensitivity of 
Citation: Journal of Climate 31, 15; 10.1175/JCLI-D-17-0380.1
Observation-based precipitation sensitivities of τveg (denoted as 
Figure 7 shows the spatial sensitivities of observation-based τsoil to temperature (denoted as 
Spatial sensitivity of 
Citation: Journal of Climate 31, 15; 10.1175/JCLI-D-17-0380.1
In terms of 
Furthermore, we have conducted spatial sensitivity of carbon turnover time to climate in a 7° × 7° moving window (Figs. S9 and S10 in the supplemental material) and in a 9° × 9° moving window (Figs. S11 and S12). In results, most of the spatial patterns are similar based on the three moving window methods, which emphasizes the robustness of the spatial sensitivities of carbon turnover time to climate. Here, we chose the results based on the 5° × 5° moving window, similar to Carvalhais et al. (2014), because larger moving windows, containing more nonuniform biome types and environmental factors, would induce greater uncertainties, especially for the transitional zones of different vegetation types.
4. Discussion
a. Observed global carbon turnover time
Compared to the previous study (τveg = 4 yr based on GPP) of Carvalhais et al. (2014), a much longer global τveg (11 yr) is obtained in this study. This difference is mainly due to the different definition of τveg as we used NPP instead of GPP. NPP is arguably more relevant for the fate of carbon being removed from the atmosphere on time scales longer than a year and stored into terrestrial pools. In contrast to τveg, our estimation of the global value of τsoil (26 yr) is much smaller than derived by Carvalhais et al. (2014) (46 yr). This is because Carvalhais et al. (2014) estimated τsoil using total soil stocks for full depth, while we used soil stocks for 1-m depth. As mentioned in section 2, the main purpose of this study is to evaluate ESMs estimated carbon turnover time, and the CMIP5 ESMs did not consider processes to burying carbon below the active layer (Tian et al. 2015; Todd-Brown et al. 2013). Our estimates are in consistent with the global τveg of 10 yr in Jiang et al. (2015) and with the global τsoil of 24 yr in Todd-Brown et al. (2013).
b. Comparison of observed and ESMs estimated carbon turnover time
Compared with observations, ESMs generally underestimate τveg, particularly in the high northern latitudes and arid and semiarid regions (Fig. 3), where models also do not capture the observation-based spatial climate sensitivity of τveg (Fig. 6). The spatial 
Similar to τveg, ESMs generally underestimate the τsoil. As shown in Fig. 4, 13 out of 14 models predicted shorter τsoil in the northern high latitudes with permafrost, compared with observation. This may be related to the fact that permafrost processes were not taken into account in the CMIP5 ESMs (Burke et al. 2013; Schuur et al. 2015). Permafrost soil contains large amounts of organic carbon, which would be vulnerable with higher decomposition rates under rapid global warming (Koven et al. 2011). Combined reductions in the thawed season length and thawed soil depth during the warm season in these cold regions compared to warm climates could results in higher 
In Carvalhais et al. (2014), negative correlations were found between forest cover and τeco, suggesting that τeco does not increase with in higher forest density. Here, we performed a similar analysis for τveg and τsoil in boreal forest, temperate forest, and tropical rain forest. Five CMIP5 models were used because they output a forest cover variable. In the results (Fig. S13 in the supplemental material), we found that τveg increased with higher forest cover in the three biomes across all the five models; however, there were no consistent relationships between forest cover and τsoil for most models. For observation-based results, τveg showed an increasing trend along with increased forest cover in temperate forest; τveg in boreal forest suggested an increasing trend at a threshold of 35% forest cover and then became flat beyond the threshold; and τveg did not show obvious changes with increasing forest cover in tropical rain forest. Observation-based τsoil decreases with increasing forest cover in boreal forests, while there were no significant relationships between forest cover and τsoil in temperate and tropical rain forest. The differences between the patterns based on observation and model mainly emerged for the relationships between forest cover and τveg. This may be because current land surface models largely simplified the real terrestrial ecosystems, while the observation-based apparent τveg reflects processes including resource competition (Stephenson et al. 2011), fire (Stephenson et al. 2011; Thonicke et al. 2001), insects (Anderegg et al. 2015), and other natural and anthropogenic disturbances (Erb et al. 2016; Fahey et al. 2005) in response to forest density. These underlying mechanisms are difficult to quantify in the present day, and require future research.
c. Uncertainties
It should be noted that there still exist large uncertainties in the estimation of global biomass and soil carbon turnover time. First, biomass carbon stock used in this study from Liu et al. (2015) was indirectly based on aboveground biomass (AGB) and a biome specific conversion factor from AGB to total biomass. It has been suggested that the ratios of above to belowground biomass varied with environmental conditions (Mokany et al. 2006). In addition, AGB derived with satellite-based passive microwave data in Liu et al. (2015) may saturate at a high biomass density (e.g., tropical rain forests) although it remains sensitive to biomass variations in these regions. These may contribute potential uncertainties of τveg. Here, we compared the τveg using TBC from Liu et al. (2015) and the τveg derived from the benchmark map of forest carbon stocks in tropical regions from Saatchi et al. (2011). The results suggested similar histogram patterns between the two (Fig. S14 in the supplemental material), implying that our estimates of τveg in the tropical rain forest are reliable.
Second, although efforts have been made to make global inventories of soil carbon, bias due to the interpolation of point-scale observations remains in the WISE dataset. Most current soil carbon storage data are mainly from temperate and tropical ecosystems, and more inventory data in regions such as Arctic regions are needed. We compared our global estimate of τsoil with that based on soil carbon (using HWSD) and NPP from Bloom et al. (2016). The distribution of τsoil (Fig. S15 in the supplemental material) was found to be similar between the two estimates.
Third, satellite-based NPP data were estimated with a radiation-based approach, through deducting the autotrophic respiration from the GPP (Zhao and Running 2010). Although this NPP observation-based product has been extensively used, including for investigating carbon turnover times (Koven et al. 2017; Thurner et al. 2016) and for benchmarking ecosystem models (Kolby Smith et al. 2016; Todd-Brown et al. 2013), it is subject to uncertainties. For example, satellite-based NPP datasets have large uncertainties in tropical regions (Cleveland et al. 2015), such as from saturation of the fraction of photosynthetically active radiation (FPAR) in high vegetation density areas, cloud and aerosol contamination, scarce meteorological data in tropical regions, and improper parameterization of the maximum light-use efficiency (LUEmax).
Fourth, in this study, we calculated τveg and τsoil based on the steady-state assumption (input equals output), as in previous studies. This seems as an imperative choice because there is no direct measurement on the global distribution of litter fall and heterotrophic respiration. Uncertainties from the steady-state assumption are difficult to quantify from the observations in the present day, such an analysis can be conducted based on modeling output by estimating carbon turnover times from the outflux τout (Carvalhais et al. 2014). Here, outflux from biomass was calculated as in Friend et al. (2014), and outflux from soil is heterotrophic respiration. In the results, the comparisons between NPP and outflux (Figs. S16 and S17 in the supplemental material) and between carbon turnover time and τout (Figs. S18 and S19) show a strong similarity, which emphasizes the robustness of turnover time being defined from input or output under the steady-state assumption.
Fifth, when we evaluate the model-based τveg and τsoil at grid scale, potential discrepancies of vegetation type and forest cover between ESMs and observation increase uncertainties. These differences limit the accuracy of the evaluation of current models for representing the spatial carbon turnover times. Because most of the CMIP5 ESMs did not report the simulated vegetation type and forest cover maps, we are still unable to evaluate the discrepancies in current time. Future model intercomparison projects are recommended to provide these variables. Reducing these apparent influences will help us better understand and improve the internal parameterization and structure related to carbon turnover processes in current ESMs.
d. Conclusions
In summary, our results show that current ESMs underestimate biomass and soil carbon turnover times. This result implies that current ESMs may overestimate the carbon sequestration potential of biomass and soil in response to elevated atmospheric CO2 concentration (He et al. 2016), which has been generally predicted to be the main driver of the enhancement of vegetation productivity (Zhu et al. 2016) and the terrestrial ecosystem carbon sink by ESMs (Cramer et al. 2001; Sitch et al. 2008). To reduce the large bias in the relationships between climate factors and biomass or soil carbon turnover times compared to observation, ESM developers need to calibrate the key processes affecting carbon turnover, especially in the high northern latitudes and arid and semiarid regions, so that ESMs are more closely comparable to the real world. Current limitations include the lack of representation of biotic disturbances, carbon–nutrient interactions, and permafrost–carbon climate responses. In addition, more accurate descriptions of hydrological processes and water–carbon interactions remain as a high priority for the carbon cycle modeling community.
Acknowledgments
This study was supported by the National Key R&D Program of China (2017YFA0604702), the National Natural Science Foundation of China (41530528 and 31621091), and the 111 Project (B14001).
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