Pervasive decreases in living vegetation carbon turnover time across forest climate zones Kailiang Yua,1, William K. Smithb, Anna T. Trugmana,c, Richard Conditd, Stephen P. Hubbelld,e, Jordi Sardansf,g, Changhui Pengh,i, Kai Zhuj, Josep Peñuelasf,g, Maxime Cailleretk,l, Tom Levanicm, Arthur Gesslerk,n, Marcus Schaubk, Marco Ferrettik, and William R. L. Anderegga a School of Biological Sciences, University of Utah, Salt Lake City, UT 84112; bSchool of Natural Resources and the Environment, University of Arizona, Tucson, AZ 85721; cDepartment of Geography, University of California, Santa Barbara, CA 93106; dThe Morton Arboretum, Lisle, IL 60532; eDepartment of Ecology and Evolutionary Biology, University of California, Los Angeles, CA 90095; fConsejo Superior de Investigaciones Científicas, Global Ecology Unit (Center for Ecological Research and Forestry Applications–Consejo Superior de Investigaciones Científicas–Universitat Autònoma de Barcelona), 08193 Bellaterra (Catalonia), Spain; gCenter for Ecological Research and Forestry Applications, 08193 Cerdanyola del Vallès (Catalonia), Spain; hDepartment of Biological Sciences, University of Quebec at Montreal, Montréal, QC H3C 3J7, Canada; iState Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Northwest Agriculture and Forestry University, Yangling, 712100 Shaanxi, China; jDepartment of Environmental Studies, University of California, Santa Cruz, CA 95064; kThe Swiss Federal Institute for Forest Snow and Landscape Research (WSL) 8903 Birmensdorf, Switzerland; lUMR RECOVER, University of Aix-Marseille, Institut National de Recherche en Sciences et Technologies pour l’Environnement et l’Agriculture, 13182 Aix-en-Provence, France; mSlovenian Forestry Institute, 1000 Ljubljana, Slovenia; and nInstitute of Terrestrial Ecosystems, Eidgenössische Technische Hochschule Zürich, 8092 Zürich, Switzerland Edited by Christopher B. Field, Stanford University, Stanford, CA, and approved October 15, 2019 (received for review December 15, 2018) Forests play a major role in the global carbon cycle. Previous studies been approximated as the ratio of the averaged carbon stock to on the capacity of forests to sequester atmospheric CO2 have mostly the averaged carbon flux such as net primary productivity (NPP) focused on carbon uptake, but the roles of carbon turnover time and (7, 9, 10). This steady-state approach has been applied to eco- its spatiotemporal changes remain poorly understood. Here, we used systems across large spatial and temporal scales and allows for an long-term inventory data (1955 to 2018) from 695 mature forest plots understanding of the spatial variation of average carbon turnover to quantify temporal trends in living vegetation carbon turnover time in different vegetation types/biomes and its spatial corre- time across tropical, temperate, and cold climate zones, and com- lations with climate (7, 9, 10). However, a steady-state approach pared plot data to 8 Earth system models (ESMs). Long-term plots fails to capture any temporal variations in carbon turnover time consistently showed decreases in living vegetation carbon turn- that underlie forest–climate feedbacks. over time, likely driven by increased tree mortality across all major Predicting future changes in the forest carbon sink requires a climate zones. Changes in living vegetation carbon turnover time fundamental understanding of the drivers and mechanisms gov- were negatively correlated with CO2 enrichment in both forest erning the changes in carbon turnover time across time and plot data and ESM simulations. However, plot-based correlations space. Ongoing environmental changes are expected to alter plant between living vegetation carbon turnover time and climate drivers growth and mortality, carbon allocation, and species composition, such as precipitation and temperature diverged from those of ESM all of which will affect plant carbon pools and carbon loss from simulations. Our analyses suggest that forest carbon sinks are likely to be constrained by a decrease in living vegetation carbon turn- Significance over time, and accurate projections of forest carbon sink dynamics will require an improved representation of tree mortality processes With a limited understanding of spatiotemporal trends of car- and their sensitivity to climate in ESMs. bon turnover time and its drivers, we are unable to quantify future changes in the forest carbon sink strength. By compar- | | carbon cycle carbon turnover forest carbon stocks | ing long-term forest plot data and Earth system model (ESM) | forest productivity tree mortality projections, we found a pervasive increase in carbon loss from tree mortality, likely driving declines in living aboveground orests cover ∼33% of the terrestrial surface area and play a F prominent role in the global carbon cycle, sequestering roughly 25% of anthropogenic carbon emissions each year. Forests thus vegetation carbon turnover time across forest climate zones. The climate correlations between temperature or precipitation and temporal trends of living vegetation carbon turnover time have the potential—via carbon–climate feedbacks—to either differed between forest plots and ESMs. Our results indicate amplify or dampen the increasing trend in atmospheric CO2 that a mechanistic representation of tree mortality in ESMs and concentrations, and affect future climates (1, 2). The capacity of its sensitivity to climate is a crucial uncertainty in predicting the forests to sequester atmospheric CO2 in a changing climate depends future forest carbon sink. not only on the response of carbon uptake (plant productivity) but also on the timescale over which the accumulated carbon stock Author contributions: K.Y. and W.R.L.A. designed research; K.Y. performed research; K.Y., would theoretically be depleted by outflux (hereafter, carbon turn- W.K.S., A.T.T., R.C., S.P.H, J.S, C.P, K.Z., J.P., M.C., T.L., A.G., M.S., M.F., and W.R.L.A. contributed new data and analytic tools; K.L.Y. analyzed data with input from W.K.S.; over time) (3–6). When considering aboveground living vegetation and K.Y., W.K.S., A.T.T., and W.R.L.A. wrote the paper. carbon in forests, outflux is largely dominated by tree mortality (7, The authors declare no competing interest. 8). While decomposition dynamics influence the rate at which dead This article is a PNAS Direct Submission. vegetation carbon enters the atmosphere, tree mortality directly This open access article is distributed under Creative Commons Attribution-NonCommercial- affects the living vegetation carbon turnover time and thus mediates NoDerivatives License 4.0 (CC BY-NC-ND). the net exchange of CO2 between land and the atmosphere over the Data deposition: The forest plot dataset containing time series of growth, carbon stock, long term. Spatiotemporal trends of living vegetation carbon carbon loss from mortality, and living vegetation carbon turnover time at each plot have turnover time and the underlying drivers remain poorly under- been archived on the Hive, the University of Utah’s Open Access Institutional Data stood (7–10), thus limiting our ability to predict forest carbon Repository (https://doi.org/10.7278/S50D-D656-FSP2). sinks and their feedbacks to climate. 1 To whom correspondence may be addressed. Email: ky9hc@virginia.edu. Previous studies of carbon turnover time have primarily relied This article contains supporting information online at https://www.pnas.org/lookup/suppl/ on the steady-state assumption that carbon stock on the land doi:10.1073/pnas.1821387116/-/DCSupplemental. surface is not changing with time. Thus, carbon turnover time has First published November 18, 2019. 24662–24667 | PNAS | December 3, 2019 | vol. 116 | no. 49 www.pnas.org/cgi/doi/10.1073/pnas.1821387116 mortality and thus influence aboveground living vegetation carbon turnover time (see Eq. 3 in Materials and Methods) (8, 11). However, the large-scale effects of these environmental drivers on living vegetation carbon turnover time are poorly quantified. Studies in tropical forests suggest that CO2 fertilization not only favors tree growth and productivity but also might accelerate rates of tree mortality, which may thus lead to shorter turnover time of vegetation carbon (12). Earth system models (ESMs) were found to consistently underestimate the spatial correlations of the hy- drological cycle (i.e., precipitation) with carbon turnover time (7). Critically, however, climatic correlations in space do not necessarily indicate climate change-induced temporal changes in carbon turnover (9, 13). We applied a dynamic approach to calculate instantaneous living vegetation carbon turnover time (Materials and Methods) and used linear mixed-effects models to quantify temporal trends and correlations with atmospheric CO2, precipitation, and tem- perature across forest climate zones. Using this dynamic approach Fig. 1. Long-term forest plot data ranging from 1955 to 2018 over at least 3 (8), a previous study reported divergent predictions of temporal censuses across tropical (n = 128), temperate (n = 87), and cold climate zones trends of vegetation carbon turnover time across global vegetation (n = 480) in South and North America and Europe. The forest climate zones models, and indicated that vegetation carbon turnover time is a are defined based on Köppen–Geiger climate classification. major uncertainty for carbon sinks in terrestrial ecosystems with climate change. However, because long-term data for vegetation Comparing temporal trends in plot data to ESMs, ESMs dis- carbon stocks and NPP are scarce in continental-scale forest in- played generally consistent trends with forest plot data, with both ventories (10), studies of temporal changes in the turnover time of vegetation carbon using a dynamic approach have not been esti- datasets showing positive trends in carbon loss from mortality, and negative trends in living vegetation carbon turnover time ECOLOGY mated using observational data. To this end, we compiled a long- term dataset of mature, largely unmanaged (SI Appendix) forest across climate zones (Figs. 2 and 3A and SI Appendix, Figs. S6 plots spanning from 1955 to 2018 that contained at least 3 cen- and S7). The estimated temporal trends (mean ± 1 SE after a suses across tropical (n = 128), temperate (n = 87), and cold natural log transformation: −2.2 ± 0.4% per year) in living climate zones (n = 480) in South and North America and Europe vegetation carbon turnover time at pan biome scale, however, that have been minimally disturbed by humans (Fig. 1 and SI Appendix, were greater in forest plot data, compared to ESMs with mean Table S1, and Dataset S1). We further compared the emergent values of negative trends ranging across the 8 models from −0.5 patterns of aboveground living vegetation carbon turnover time to 0% per year after the same natural log transformation (Figs. 2 from the forest plots to estimates of living vegetation carbon and 3A and SI Appendix, Figs. S1 and S7). This suggests that turnover time from long-term remote sensing data of NPP and ESMs likely underestimate the negative trends of living vegeta- aboveground vegetation carbon stock from 1993 to 2011 (14, 15), as tion carbon turnover time, although we note that our forest plots well as from 8 ESMs from phase 5 of the Coupled Model In- are not spatially comprehensive across the globe. Furthermore, it tercomparison Project (CMIP5). is important to note that forest plot data and ESM-estimated growth are not completely analogous. Growth was quantified Results and Discussion as increment of mainly aboveground wood vegetation carbon The forest plot data provide cross-climate zone estimates of the including components of recruitment of new trees and growth of temporal trends in growth (mainly aboveground wood pro- surviving trees in forest plot data; in the ESMs, growth (NPP) duction), carbon loss from mortality, and carbon turnover time was calculated for total vegetation carbon (all plant tissues and of aboveground living vegetation of undisturbed forests. We aboveground plus belowground components), and thus living found an increase in both carbon losses (1.9%, 2%, 0.9% per vegetation carbon turnover refers to all vegetation carbon. year) and a decrease of aboveground living vegetation carbon However, a sensitivity test using ESM estimates of aboveground turnover time (−2.3%, −2.7%, −2% per year) across tropical, NPP and vegetation carbon stocks (available in IPSL-CM5A- temperate, and cold climate zones, respectively (Fig. 2 and SI MR) showed no meaningful difference with estimates of total Appendix, Fig. S1). Decreases in aboveground living vegetation NPP and vegetation carbon stocks (SI Appendix, Fig. S8). carbon turnover time were significant even when accounting for While ESM trends were generally consistent with those of differences in stand density (forest basal area) and forest suc- forest plot data, we further sought to quantify the variation among cessional status or age (16) (SI Appendix, Figs. S2 and S3). As an ESMs. To this end, range (Fig. 3A) and coefficient of variation exploratory analysis, we calculated living vegetation carbon (CV) (Fig. 3B) were used to quantify the variations among ESMs turnover time using satellite remote sensing estimates of growth in predictions of temporal changes in NPP, carbon loss, and (NPP) and carbon stocks (Materials and Methods) (14, 15) and living vegetation carbon turnover time. ESMs generally indicated found the decreasing trends in living vegetation carbon turnover a negative trend and a relatively low value (<1) of CV in living time that were generally consistent with forest plot data in most vegetation carbon turnover time across all forest climate zones but not all analyses (SI Appendix, Figs. S4 and S5). However, except cold forests (Fig. 3 A and B and SI Appendix, Fig. S7). given the limitations in current estimates of living vegetation ESM-simulated NPP exhibited an increasing trend and a relatively carbon turnover time from satellite remote-sensing data, in- low CV (<0.6) across all forest climate zones except tropical forests cluding a relatively short time range, uncertainty in productivity (Fig. 3B and SI Appendix, Figs. S6 and S7). Collectively, these re- and carbon stocks trends, and challenges in accounting for the sults suggest that ESM simulations differ in projections of temporal potential effects of CO2 fertilization on productivity (see Materials changes in living vegetation carbon turnover in cold forests and and Methods and SI Appendix for details), we primarily focus on NPP in tropical forests. Temporal trends in living vegetation carbon estimating the emergent patterns from forest plot data and com- turnover time for future climatic scenarios (2006 to 2100) showed paring these observational estimates to simulations in 8 ESMs similar signs as historical simulations (1971 to 2005) but were from CMIP5. more uncertain, particularly for temperate and cold climate zones Yu et al. PNAS | December 3, 2019 | vol. 116 | no. 49 | 24663 likely drove the decreased living vegetation carbon turnover time across forests biomes, although changes in carbon allocation and/ or species composition may play a role as well. The regrowth of human-disturbed forests could be another factor in affecting living vegetation carbon turnover time (21), but the forest plots used in this study were largely mature and unmanaged and we found no significant role of successional stages or forest age in living vegetation carbon turnover trends. Declines in living vege- tation carbon turnover time associated with increased tree mor- tality have previously been suggested in Amazon rainforest (12). Our study compiles a dataset that spans a larger area of tropical forests but does not include tropical forests in Africa or Asia due to data limitations. With projected increases in tree mortality in a changing climate (i.e., drought and warming) (20, 22, 23), living vegetation carbon turnover time may decline further, potentially constraining forest carbon sinks under future climate scenarios. We further investigated the degree to which atmospheric CO2 concentrations and variations in precipitation and temperature were correlated with the temporal trends in carbon turnover time. Increased resource availability (e.g., resulting from increased CO2) associated with global change can favor forest growth and Fig. 2. Living vegetation carbon turnover time decreases across forest climate productivity (3, 24, 25), but it may also accelerate the rate of tree zones as observed by forest plot data. Temporal trend of growth (in kilograms mortality, reducing vegetation carbon turnover time (26, 27). This per square meter per year), carbon stock (in kilograms per square meter), pattern of “faster growth–higher mortality–shorter carbon turn- carbon loss (in kilograms per square meter per year), and aboveground living over time” has been suggested at local scales, particularly in vegetation carbon turnover time (in years) quantified by forest plot data tropical forests (12, 26, 27) and was recently demonstrated in boreal ranging from 1955 to 2018 over at least 3 censuses across tropical (n = 128), forests (28). We observed in the forest plot data that increasing temperate (n = 87), and cold (n = 480) climate zones. Data were natural log- transformed before analysis. Temporal trends were quantified by linear mixed-effect models accounting for each plot in each forest climate zone as a random effect. The y axes are coefficients of the independent variable (time) ± 95% CIs. Coefficient estimate of each variable refers to proportional change per year when data are log-transferred. Percent change per year in each variable was quantified as follows: (exp (β) – 1) * 100, where β is the coefficient estimate. (Fig. 3A and SI Appendix, Fig. S7). A sensitivity test that consid- ered a historical period between 1971 and 2018 in ESMs, corre- sponding to the census period of the majority of forest plots (>95%) (SI Appendix, Fig. S9), showed very similar historical trends in simulated NPP, carbon loss, and living vegetation carbon turnover time across climate zones (SI Appendix, Fig. S10). While there is generally consistency of the temporal trends in living vegetation carbon turnover time at scales of forest climate zones across forest plot data and models, we note that estimates of NPP and particularly carbon stocks used to calculate living vegetation carbon turnover time in ESMs have substantial un- certainty (13), which is reflected in our study by the large vari- ation in temporal trends of carbon stocks across ESMs (SI Appendix, Fig. S6D), a result that is consistent with previous Fig. 3. ESMs show a pervasive decrease of historical living vegetation car- studies (4, 17). Forests in Africa generally showed decreasing bon turnover time across forest climate zones but with large cross-model (−2 to 0% per year) trends of living vegetation carbon turnover differences. (A) Historical (1971 to 2005) and future (2006 to 2100) temporal time, in contrast to Australian forests. Some locations showed trends in living vegetation carbon turnover time across forest climate zones increasing (even >2% per year) trends of living vegetation car- quantified by the 8 ESMs (CanESM2, CCSM4, GFDL-ESM2G, HadGEM2-ES, bon turnover time, particularly in the Amazon, despite the IPSL-CM5A-MR, MIROC-ESM, MPI-ESM-LR, NorESM1-M) from phase 5 of the Coupled Model Intercomparison Project (CMIP5). Temporal trends were general decreasing trends at pan biome scale. Moreover, the quantified by linear mixed-effect models accounting for pixel in each forest large spatial variations of trends in NPP, carbon stocks, carbon climate zone as a random effect. Data were natural log-transformed before losses, and carbon turnover time from the remotely sensed data analysis. The y axes are the minimum, mean, and maximum of the temporal (SI Appendix, Fig. S11) were not identified by ESMs (Fig. 3C and trends in the 8 ESMs. (B) Coefficient of variance quantified as the ratio of the SI Appendix, Figs. S6 and S12) and highlight key knowledge gaps SD to the absolute value of mean across the 8 ESMs in CMIP5 while pre- in understanding the spatial patterns of changes in vegetation dicting historical and future temporal trends in loge-transformed values of carbon turnover time that are essential to quantify the changes in NPP and living vegetation carbon turnover time across forest climate zones. (C) Global patterns of historical (1971 to 2005) percent change of living the global forest carbon sink. vegetation carbon turnover time quantified by the ensemble mean of the Carbon loss associated with widespread tree mortality has 8 ESMs in CMIP5. Percent change is quantified as an increase or reduction attracted much attention and has been documented in multiple (percentage) per year relative to initial value at year 1971. The temporal regions in the last decade (18–20). As the dominant outflux of trend was quantified by a linear regression model and expressed as co- aboveground vegetation carbon (7, 8), increased tree mortality efficient of the independent variable (time). 24664 | www.pnas.org/cgi/doi/10.1073/pnas.1821387116 Yu et al. atmospheric CO2 concentrations were strongly and negatively cor- related with living vegetation carbon turnover time across multiple climate zones (Fig. 4E) and positively correlated with growth and carbon loss associated with plant mortality (Fig. 4 A and C) (26, 27, 29). We emphasize, however, that this correlation of living vege- tation carbon turnover time and CO2 does not necessarily imply causation, as it could arise from 2 concurrent trends. Thus, further research is needed to examine potential mechanistic links between faster growth and decreased living vegetation carbon turnover time. Decreased precipitation was correlated with increased carbon loss (tree mortality), and thus decreased carbon turnover time is significant in cold forests in forest plot data (Fig. 4 C and E) when accounting for other potential drivers, consistent with pre- vious studies (30, 31). At the plant community scale, increased growth under resource (CO2, precipitation, or temperature) en- richment could potentially lead to biomass accumulation and higher water usage, thereby increasing drought stress and plant mortality associated with competition for limited soil water re- sources in drought years (32). Similarly, we observed the positive influences of rainfall variability on carbon loss, thereby decreasing living vegetation carbon turnover time in cold forests (SI Appen- dix, Fig. S13). These patterns related to precipitation are robust to considering an estimate of plant competition (i.e., basal area) (SI Appendix, Fig. S14) (33). At climate zone scale, the impacts of rising temperature on damping forest growth, increasing mortality, and thus decreasing carbon turnover are evident in temperate Fig. 4. The decrease in living vegetation carbon turnover time across forest ECOLOGY forests but not in cold forests (Fig. 4 A, C, and E), even when climate zones is primarily associated with CO2 fertilization. (A, C, and E) accounting for an estimate of competition (SI Appendix, Fig. S14). Standardized response coefficients between CO2, precipitation (Prn), tem- Evaluating ESM climate correlations compared to those of perature (TAS), and growth (A), carbon loss (C), and aboveground living forest plots, ESMs exhibited similar temporal trends in their vegetation carbon turnover time (E) quantified for forest plot data using simulated responses of living vegetation carbon turnover time to linear mixed models. The y axes are coefficients of each independent rising CO2 concentrations (Fig. 4F and SI Appendix, Fig. S15). variable ± 95% CIs. (B, D, and F) Standardized response coefficients between CO2, Prn, and TAS and NPP (B), carbon loss (D), and living vegetation carbon The order of magnitude in the standardized coefficients between turnover time (F) for 8 ESMs using linear mixed models. The y axes are min- climate variables (precipitation and temperature) and temporal imum, mean, and maximum coefficients of each independent variable in 8 trends of NPP, carbon loss from mortality, and living vegetation ESMs. The data for NPP, carbon stock, carbon loss, and living vegetation carbon turnover was comparable between forest plot data and carbon turnover time were natural log-transformed before analysis in both ESMs (Fig. 4 and SI Appendix, Fig. S15). In contrast to the forest plot data and ESMs. forest plot data, however, ESMs predicted much lower corre- lations in temporal trends of NPP, carbon loss from mortality, and living vegetation carbon turnover with CO2 (Fig. 4 and SI impacts of the hydrological cycle (precipitation) (7). Our forest plot Appendix, Fig. S15). data suggest that living vegetation carbon turnover strongly in- Positive relationships between precipitation and NPP and creases with precipitation in cold forests, potentially because of precipitation and carbon loss, leading to a negative relationship lower rates of tree mortality in wetter regions (30, 31). ESMs, between living vegetation carbon turnover time and precipita- however, predict an opposite pattern, likely because of the tion, were observed across tropical and temperate climate zones simplified processes of carbon loss (tree mortality and other in ESMs, which was in contrast to the forest plot data (Fig. 4). In disturbances) (13, 24). Our forest plot data, however, show the cold forests, the impacts of precipitation on NPP, carbon loss, weak dependence of temporal trends in living vegetation carbon and living vegetation carbon turnover time from forest plot data turnover time on temperature in cold forests or show a negative also largely diverged from those in ESMs (Fig. 4 B, D, and F). correlation between these 2 in temperate forests, which is gener- Temperature damped growth (Fig. 4B) and thus increased living ally not observed in ESMs. vegetation carbon turnover time (Fig. 4F), except in cold forests By analyzing long-term forest plot data and ESMs, we docu- with higher growth in a warmer climate (34). Collectively, these mented pervasive declines in living vegetation carbon turnover results appear to suggest that, in ESMs, the factors that favor time across multiple climate zones. Given that we consider only growth also accelerate carbon loss, thus leading to the decrease in living vegetation carbon here, we note that disturbance and de- living vegetation carbon turnover time, whereas the climate in- composition dynamics will be critical in quantifying the net ex- fluences on mortality are more complex and multifaceted in forest change of carbon between the biosphere and atmosphere on the plot data. Indeed, our analysis shows strong and positive corre- lations between growth and mortality and carbon stock across scale of years to decades. Our study also found little spatial co- climate zones in ESMs (SI Appendix, Fig. S16), which are not herence among models and observations, highlighting a key observed in forest plot data (SI Appendix, Fig. S17). This strong knowledge gap in understanding the spatial patterns of changes association is likely because ESMs poorly represent carbon loss in living vegetation carbon turnover time. Our results further (tree mortality), frequently as a static process via a background highlight that the beneficial effects of CO2 fertilization on the rate (10, 13) or function of forest growth or carbon stock. terrestrial carbon sink may be transitory due to the accelerating Our study quantifies the temporal changes in living vegetation mortality, particularly in a changing climate with increased risks carbon turnover time, which are highly relevant to evaluate the of drought. Collectively, our findings suggest that a better un- impacts of climate change. Previous studies using a steady-state derstanding and representation of tree mortality processes in approach that examined the spatial relationships of carbon turnover ESMs is central to constrain future forest carbon sinks and their time with climate found that ESMs consistently underestimated the feedbacks to climate in the 21st century. Yu et al. PNAS | December 3, 2019 | vol. 116 | no. 49 | 24665 Materials and Methods on datasets of forest plot, remote sensing, and ESMs, CO2, and climate data Quantification of Living Vegetation Carbon Turnover Time. We quantified are provided in SI Appendix. living vegetation carbon turnover time (τ) across forest climate zones based on a previously established approach (8, 11), where changing vegetation Statistical Analysis. We evaluated trends over time in growth, carbon stock, carbon stock (dCS) over time (dt) is determined by changes in growth and carbon loss, and living vegetation carbon turnover time in each forest climate the turnover time of carbon in living vegetation: zone (tropical, temperate, and cold) using linear mixed-effects models in which each plot or pixel in each forest climate zone was treated as a random effect: dCS CS  = Growth − . [1] Log Variable i,j = β t ij + bi + «ij , [4] dt τ Changes in vegetation carbon stock ðCSÞ can equivalently be modeled as where i refers to plot or pixel; j is census interval; the dependent “Variable” follows: refers to either growth, carbon stock, carbon loss, or carbon turnover time; tij is the time of the ith plot and the jth census interval and quantified as dCS mean value of time between consecutive time steps j and j + 1; β is the = Growth − carbon loss , [2] standardized fixed effect associated with an individual model parameter; bi dt represent the random effect of the ith plot; and «ij is random error, which is where carbon loss is flux of vegetation carbon out of living vegetation pools. assumed to follow a normal distribution with mean zero and SD σ. For forest plot Assuming no human disturbance, aboveground living vegetation carbon loss data, data of growth (mainly aboveground wood production), carbon stock, is primarily associated with tree mortality. carbon loss, and aboveground living vegetation carbon turnover time were nat- By rearranging Eqs. 1 and 2, we have the following: ural log-transformed to meet the requirement of normal distribution of residual in linear mixed models. For remote sensing and ESMs that had long-term and CS τ= . [3] annual time series of data, we used 2 approaches (see SI Appendix for details). carbon loss We evaluated the association between growth, carbon stock, carbon loss, Thus, Eq. 3 divides a time-varying stock over a time-varying outflux (woody or carbon turnover time on CO2 concentration (CO2), total annual pre- mortality flux) to quantify the instantaneous living vegetation carbon cipitation (Prn), and mean annual temperature (TAS) in forest plot data and turnover time (35). We note that growth refers to mainly aboveground ESMs. We have the following: wood production in forest plots and thus τ represents the aboveground living vegetation carbon turnover time, while in ESMs growth is NPP in-  Log Variablei,j = β1 CO2i,j + β2 Prni,j + β3 TASi,j + bi + «ij , [5] cluding belowground components and τ refers to carbon turnover time by total living vegetation. We also caution that one should not interpret τ quantified in this study as the amount of time carbon resides in terrestrial where parameters were identical to Eq. 4 and the dependent variables living vegetation at equilibrium state because the ecosystem is not indeed in were natural log-transformed before analysis. Nitrogen deposition, which a steady state (35). Rather, τ is an instantaneous rate of carbon loss nor- could influence forest growth at local and regional scales, is not expected malized by the carbon stock (technically the inverse of the rate). It quantifies to change the observed relationships between vegetation carbon turnover the timescale for the aboveground vegetation carbon stock to be depleted and climate over our entire plot sample because many of our forest plots (i.e., at the rate of woody mortality flux. This approach of using woody mor- most all plots in tropical regions and much of the North American cold forest tality flux does not include short-term phenological turnover (i.e., leaf and plots) are generally located in low nitrogen deposition zones (38). root turnover), since this study focuses on multiannual changes in above- In all of the analysis on temporal trends and their associations with climate ground vegetation. This dynamic approach considering carbon losses has variables, when investigating the patterns in global forests, the ratio of total advantages over using the input as the flux to calculate τ (13) because aboveground vegetation carbon stock in each forest climate zone (0.55, 0.32, the growth-based vegetation carbon turnover time generated (i.e., τ = and 0.14 in tropical, temperate, and cold climate zone, respectively) to global CS/growth) quantifies the timescale for replenishment of the current car- scale was used as weighting coefficients (39). The temporal trends of growth, bon pool, which includes leaves and roots, and because tree mortality rate carbon loss, and vegetation carbon turnover time and its association with and longevity are increasingly realized as critical controls of vegetation climate were not affected by other factors such as competition and forest carbon stocks and turnover (12, 27, 28). The approach of using outflux is succession and spatial autocorrelations. More information about testing the also a reasonable way to compare with forest plot observations, where influences of these factors are provided in SI Appendix. woody mortality flux is directly measured. We note, however, that our study only quantified one of the key carbon turnover times, which is pri- ACKNOWLEDGMENTS. We thank the editor and 2 anonymous reviewers for marily affected by woody mortality flux. Indeed, turnover rate of leaves insightful comments that improved the manuscript. We thank Thomas A. M. and roots, carbon allocation to leaves and roots, and decomposition of Pugh and Thomas Ward Crowther for discussion of this paper during the litterfall also influence the overall vegetation carbon turnover time when revisions. W.R.L.A. acknowledges funding from the David and Lucille Packard we consider the total vegetation pool including litterfall and belowground Foundation, National Science Foundation Grants 1714972 and 1802880, the components. US Department of Agriculture (USDA) National Institute of Food and Agricul- Eqs. 1–3 can be solved at different spatial scales. Previous studies have ture, the Agricultural and Food Research Initiative Competitive Programme, aggregated vegetation carbon stock and NPP on global scale to quantify and Ecosystem Services and Agro-ecosystem Management Grant 2018-67019- 27850. J.S. and J.P. acknowledge funding from European Research Council vegetation carbon turnover time (8) (see SI Appendix for details). However, Synergy Grant ERC-SyG-2013-610028 IMBALANCE-P. W.K.S. acknowledges this method may misrepresent critical local scale processes that have been funding from NASA Terrestrial Ecosystems Grant 80NSSC19M0103. A.T.T. found to compensate locally and thus damp the patterns of carbon cycle acknowledges support from USDA National Institute of Food and Agricul- observed on large (global) scale (36). Thus, we quantified carbon turnover ture Postdoctoral Research Fellowship Grant 2018-67012-28020. K.Z. ac- time on local scale (in each forest plot or grid cell) and then used a linear knowledges funding from the Faculty Research Grant awarded by the mixed model to quantify the temporal trend of carbon turnover time in each Committee on Research from the University of California, Santa Cruz. All CMIP5 forest climate zone by accounting for the random effect in each forest plot data are available at https://pcmdi.llnl.gov/mips/cmip5/data-portal.html. We ac- or grid cell. The Köppen–Geiger climate classification was used to determine knowledge the World Climate Research Programme’s Working Group on Cou- pled Modelling, which is responsible for CMIP, and we thank the climate the climate zones (i.e., tropical, temperate, and cold) of these forest plots or modeling groups (listed in SI Appendix) for producing and sharing their model grid cells (37). More information on quantification of living vegetation output. For CMIP, the US Department of Energy’s Program for Climate Model carbon turnover time are provided in SI Appendix. Diagnosis and Intercomparison provided coordinating support and led the de- velopment of software infrastructure in partnership with the Global Organiza- Data Availability. Three long-term datasets—forest plot, remote sensing, and tion for Earth System Science Portals. The evaluation was partly based on data ESMs—were used. The forest plot dataset, containing time series of growth, that was collected by partners of the official United Nations Economic Commis- carbon stock, carbon loss from mortality, and aboveground living vegetation sion for Europe International Cooperative Programme Forests Network (http:// icp-forests.net/contributors). 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