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Soil heterotrophic respiration (HR) is an important source of soil-to-atmosphere CO2 flux, but its response to changes in soil water content (θ) is poorly understood. Earth system models commonly use empirical moisture functions to describe the HR–θ relationship, introducing significant uncertainty in predicting CO2 flux from soils. Generalized, mechanistic models that address this uncertainty are thus urgently needed. Here we derive, test, and calibrate a novel moisture function, fm, that encapsulates primary physicochemical and biological processes controlling soil HR. We validated fm using simulation results and published experimental data, and established the quantitative relationships between parameters of fm and measurable soil properties, which enables fm to predict the HR–θ relationships for different soils across spatial scales. The fm function predicted comparable HR–θ relationships with laboratory and field measurements, and may reduce the uncertainty in predicting the response of soil organic carbon stocks to climate change compared with the empirical moisture functions currently used in Earth system models., Empirical moisture functions that describe the relationship between soil heterotrophic respiration and moisture introduce considerable uncertainty in soil CO2 flux predictions. Here, the authors derive a process-based moisture function by incorporating mechanisms that control soil heterotrophic respiration.

Terrestrial ecosystems have absorbed roughly 30 % of anthropogenic CO2 emissions over the past decades, but it is unclear whether this carbon (C) sink will endure into the future. Despite extensive modeling and experimental and observational studies, what fundamentally determines transient dynamics of terrestrial C storage under global change is still not very clear. Here we develop a new framework for understanding transient dynamics of terrestrial C storage through mathematical analysis and numerical experiments. Our analysis indicates that the ultimate force driving ecosystem C storage change is the C storage capacity, which is jointly determined by ecosystem C input (e.g., net primary production, NPP) and residence time. Since both C input and residence time vary with time, the C storage capacity is time-dependent and acts as a moving attractor that actual C storage chases. The rate of change in C storage is proportional to the C storage potential, which is the difference between the current storage and the storage capacity. The C storage capacity represents instantaneous responses of the land C cycle to external forcing, whereas the C storage potential represents the internal capability of the land C cycle to influence the C change trajectory in the next time step. The influence happens through redistribution of net C pool changes in a network of pools with different residence times. Moreover, this and our other studies have demonstrated that one matrix equation can replicate simulations of most land C cycle models (i.e., physical emulators). As a result, simulation outputs of those models can be placed into a three-dimensional (3-D) parameter space to measure their differences. The latter can be decomposed into traceable components to track the origins of model uncertainty. In addition, the physical emulators make data assimilation computationally feasible so that both C flux- and pool-related datasets can be used to better constrain model predictions of land C sequestration. Overall, this new mathematical framework offers new approaches to understanding, evaluating, diagnosing, and improving land C cycle models.

An acceleration of model-data synthesis activities has leveraged many terrestrial carbon datasets, but utilization of soil respiration (RS) data has not kept pace. We identify three major challenges in interpreting RS data, and opportunities to utilize it more extensively and creatively: (1) When RS is compared to ecosystem respiration (RECO) measured from EC towers, it is not uncommon to find RS > RECO. We argue this is most likely due to difficulties in calculating RECO, which provides an opportunity to utilize RS for EC quality control. (2) RS integrates belowground heterotrophic and autotrophic activity, but many models include only an explicit heterotrophic output. Opportunities exist to use the total RS flux for data assimilation and model benchmarking methods rather than less-certain partitioned fluxes. (3) RS is generally measured at a very different resolution than that needed for comparison to EC or ecosystem- to global-scale models. Downscaling EC fluxes to match the scale of RS, and improvement of RS upscaling techniques will improve resolution challenges. RS data can bring a range of benefits to model development, particularly with larger databases and improved data sharing protocols to make RS data more robust and broadly available to the research community.

The feedback between planetary warming and soil carbon loss has been the focus of considerable scientific attention in recent decades, due to its potential to accelerate anthropogenic climate change. The soil carbon temperature sensitivity is traditionally estimated from short-term respiration measurements – either from laboratory incubations that are artificially manipulated or from field measurements that cannot distinguish between plant and microbial respiration. To address these limitations of previous approaches, we developed a new method to estimate soil temperature sensitivity (Q10) of soil carbon directly from warming-induced changes in soil carbon stocks measured in 36 field experiments across the world. Variations in warming magnitude and control organic carbon percentage explained much of field-warmed organic carbon percentage (R2 = 0.96), revealing Q10 across sites of 2.2 [1.6, 2.7] 95 % confidence interval (CI). When these field-derived Q10 values were extrapolated over the 21st century using a post hoc correction of 20 Coupled Model Intercomparison Project Phase 5 (CMIP5) Earth system model outputs, the multi-model mean soil carbon stock changes shifted from the previous value of 88 ± 153 Pg carbon (weighted mean ± 1 SD) to 19 ± 155 Pg carbon with a Q10-driven 95 % CI of 248 ± 191 to −95 ± 209 Pg carbon. On average, incorporating the field-derived Q10 values into Earth system model simulations led to reductions in the projected amount of carbon sequestered in the soil over the 21st century. However, the considerable parameter uncertainty led to extremely high variability in soil carbon stock projections within each model; intra-model uncertainty driven by the field-derived Q10 was as great as that between model variation. This study demonstrates that data integration should capture the variation of the system, as well as mean trends., Biogeosciences, 15 (12), ISSN:1726-4170

Soil carbon has been measured for over a century in applications ranging from understanding biogeochemical processes in natural ecosystems to quantifying the productivity and health of managed systems. Consolidating diverse soil carbon datasets is increasingly important to maximize their value, particularly with growing anthropogenic and climate change pressures. In this progress report, we describe recent advances in soil carbon data led by the International Soil Carbon Network and other networks. We highlight priority areas of research requiring soil carbon data, including (a) quantifying boreal, arctic and wetland carbon stocks, (b) understanding the timescales of soil carbon persistence using radiocarbon and chronosequence studies, (c) synthesizing long-term and experimental data to inform carbon stock vulnerability to global change, (d) quantifying root influences on soil carbon and (e) identifying gaps in model–data integration. We also describe the landscape of soil datasets currently available, highlighting their strengths, weaknesses and synergies. Now more than ever, integrated soil data are needed to inform climate mitigation, land management and agricultural practices. This report will aid new data users in navigating various soil databases and encourage scientists to make their measurements publicly available and to join forces to find soil-related solutions.

Microbes influence soil organic matter decomposition and the long-term stabilization of carbon (C) in soils. We contend that by revising the representation of microbial processes and their interactions with the physicochemical soil environment, Earth system models (ESMs) will make more realistic global C cycle projections. Explicit representation of microbial processes presents considerable challenges due to the scale at which these processes occur. Thus, applying microbial theory in ESMs requires a framework to link micro-scale process-level understanding and measurements to macro-scale models used to make decadal- to century-long projections. Here we review the diversity, advantages, and pitfalls of simulating soil biogeochemical cycles using microbial-explicit modeling approaches. We present a roadmap for how to begin building, applying, and evaluating reliable microbial-explicit model formulations that can be applied in ESMs. Drawing from experience with traditional decomposition models, we suggest the following: (1) guidelines for common model parameters and output that can facilitate future model intercomparisons; (2) development of benchmarking and model-data integration frameworks that can be used to effectively guide, inform, and evaluate model parameterizations with data from well-curated repositories; and (3) the application of scaling methods to integrate microbial-explicit soil biogeochemistry modules within ESMs. With contributions across scientific disciplines, we feel this roadmap can advance our fundamental understanding of soil biogeochemical dynamics and more realistically project likely soil C response to environmental change at global scales.

The feedback between planetary warming and soil carbon loss has been the focus of considerable scientific attention in recent decades, due to its potential to accelerate anthropogenic climate change. The soil carbon temperature sensitivity is traditionally estimated from short-term respiration measurements – either from laboratory incubations that are artificially manipulated, or field measurements that cannot distinguish between plant and microbial respiration. To address these limitations of previous approaches, we developed a new method to estimate temperature sensitivity (Q10) of soil carbon directly from warming-induced changes in soil carbon stocks measured in 36 field experiments across the world. Variations in warming magnitude and control organic carbon percentage explained much of field-warmed organic carbon percentage (R2 = 0.96), revealing Q10 across sites of 2.2, [1.6, 2.7] 95 % Confidence Interval (CI). When these field-derived Q10 values were extrapolated over the 21st century using a post-hoc correction of 20 CMIP5 Earth system model outputs, the multi-model mean soil carbon stock changes shifted from the previous value of 83 ± 156 Pg-carbon (weighted mean ± 1 SD), to 16 ± 156 Pg-carbon with a Q10 driven 95 % CI of 245 ± 194 to −99 ± 208 Pg-carbon. On average, incorporating the field-derived Q10 values into Earth system model simulations led to reductions in the projected amount of carbon sequestered in the soil over the 21st century. However, the considerable parameter uncertainty led to extremely high variability in soil carbon stock projections within each model; intra-model uncertainty driven by the measured Q10 was as great as that between model variation. This study demonstrates that data integration may not improve model certainty, but instead should strive to capture the variation of the system as well as mean trends.

The complexity of processes and interactions that drive soil C dynamics necessitate the use of proxy variables to represent soil characteristics that cannot be directly measured (correlative proxies), or that aggregate information about multiple soil characteristics into one variable (integrative proxies). These proxies have proven useful for understanding the soil C cycle, which is highly variable in both space and time, and are now being used to make predictions of the fate and persistence of C under future climate scenarios. However, the C pools and processes that proxies represent must be thoughtfully considered in order to minimize uncertainties in empirical understanding. This is necessary to capture the full value of a proxy in model parameters and in model outcomes. Here, we provide specific examples of proxy variables that could improve decision-making, and modeling skill, while also encouraging continued work on their mechanistic underpinnings. We explore the use of three common soil proxies used to study soil C cycling: metabolic quotient, clay content, and physical fractionation. We also consider how emerging data types, such as genome-sequence data, can serve as proxies for microbial community activities. By examining some broad assumptions in soil C cycling with the proxies already in use, we can develop new hypotheses and specify criteria for new and needed proxies.

Soil is currently thought to be a sink for carbon; however, the response of this sink to increasing levels of atmospheric carbon dioxide and climate change is uncertain. In this study, we analyzed soil organic carbon (SOC) changes from 11 Earth system models (ESMs) contributing simulations to the Coupled Model Intercomparison Project Phase 5 (CMIP5). We used a reduced complexity model based on temperature and moisture sensitivities to analyze the drivers of SOC change for the historical and high radiative forcing (RCP 8.5) scenarios between 1850 and 2100. ESM estimates of SOC changed over the 21st century (2090–2099 minus 1997–2006) ranging from a loss of 72 Pg C to a gain of 253 Pg C with a multi-model mean gain of 65 Pg C. Many ESMs simulated large changes in high-latitude SOC that ranged from losses of 37 Pg C to gains of 146 Pg C with a multi-model mean gain of 39 Pg C across tundra and boreal biomes. All ESMs showed cumulative increases in global NPP (11 to 59%) and decreases in SOC turnover times (15 to 28%) over the 21st century. Most of the model-to-model variation in SOC change was explained by initial SOC stocks combined with the relative changes in soil inputs and decomposition rates (R2 = 0.89, p < 0.01). Between models, increases in decomposition rate were well explained by a combination of initial decomposition rate, ESM-specific Q10-factors, and changes in soil temperature (R2 = 0.80, p < 0.01). All SOC changes depended on sustained increases in NPP with global change (primarily driven by increasing CO2). Many ESMs simulated large accumulations of SOC in high-latitude biomes that are not consistent with empirical studies. Most ESMs poorly represented permafrost dynamics and omitted potential constraints on SOC storage, such as priming effects, nutrient availability, mineral surface stabilization, and aggregate formation. Future models that represent these constraints are likely to estimate smaller increases in SOC storage over the 21st century.

Stocks of soil organic carbon represent a large component of the carbon cycle that may participate in climate change feedbacks, particularly on decadal and centennial timescales. For Earth system models (ESMs), the ability to accurately represent the global distribution of existing soil carbon stocks is a prerequisite for accurately predicting future carbon–climate feedbacks. We compared soil carbon simulations from 11 model centers to empirical data from the Harmonized World Soil Database (HWSD) and the Northern Circumpolar Soil Carbon Database (NCSCD). Model estimates of global soil carbon stocks ranged from 510 to 3040 Pg C, compared to an estimate of 1260 Pg C (with a 95% confidence interval of 890–1660 Pg C) from the HWSD. Model simulations for the high northern latitudes fell between 60 and 820 Pg C, compared to 500 Pg C (with a 95% confidence interval of 380–620 Pg C) for the NCSCD and 290 Pg C for the HWSD. Global soil carbon varied 5.9 fold across models in response to a 2.6-fold variation in global net primary productivity (NPP) and a 3.6-fold variation in global soil carbon turnover times. Model–data agreement was moderate at the biome level (R2 values ranged from 0.38 to 0.97 with a mean of 0.75); however, the spatial distribution of soil carbon simulated by the ESMs at the 1° scale was not well correlated with the HWSD (Pearson correlation coefficients less than 0.4 and root mean square errors from 9.4 to 20.8 kg C m−2). In northern latitudes where the two data sets overlapped, agreement between the HWSD and the NCSCD was poor (Pearson correlation coefficient 0.33), indicating uncertainty in empirical estimates of soil carbon. We found that a reduced complexity model dependent on NPP and soil temperature explained much of the 1° spatial variation in soil carbon within most ESMs (R2 values between 0.62 and 0.93 for 9 of 11 model centers). However, the same reduced complexity model only explained 10% of the spatial variation in HWSD soil carbon when driven by observations of NPP and temperature, implying that other drivers or processes may be more important in explaining observed soil carbon distributions. The reduced complexity model also showed that differences in simulated soil carbon across ESMs were driven by differences in simulated NPP and the parameterization of soil heterotrophic respiration (inter-model R2 = 0.93), not by structural differences between the models. Overall, our results suggest that despite fair global-scale agreement with observational data and moderate agreement at the biome scale, most ESMs cannot reproduce grid-scale variation in soil carbon and may be missing key processes. Future work should focus on improving the simulation of driving variables for soil carbon stocks and modifying model structures to include additional processes.

Terrestrial ecosystems absorb roughly 30 % of anthropogenic CO2 emissions since preindustrial era, but it is unclear whether this carbon (C) sink will endure into the future. Despite extensive modeling, experimental, and observational studies, what fundamentally determines transient dynamics of terrestrial C storage under climate change is still not very clear. Here we develop a new framework for understanding transient dynamics of terrestrial C storage through mathematical analysis and numerical experiments. Our analysis indicates that the ultimate force driving ecosystem C storage change is the C storage capacity, which is jointly determined by ecosystem C input (e.g., net primary production, NPP) and residence time. Since both C input and residence time vary with time, the C storage capacity is time-dependent and acts as a moving attractor that actual C storage chases. The rate of change in C storage is proportional to the C storage potential, the difference between the current storage and the storage capacity. The C storage capacity represents instantaneous responses of the land C cycle to external forcing, whereas the C storage potential represents the internal capability of the land C cycle to influence the C change trajectory in the next time step. The influence happens through redistribution of net C pool changes in a network of pools with different residence times. Moreover, this and our other studies have demonstrated that one matrix equation can exactly replicate simulations of most land C cycle models (i.e., physical emulators). As a result, simulation outputs of those models can be placed into a three-dimensional (3D) parameter space to measure their differences. The latter can be decomposed into traceable components to track the origins of model uncertainty. Moreover, the emulators make data assimilation computationally feasible so that both C flux- and pool-related datasets can be used to better constrain model predictions of land C sequestration. We also propose that the C storage potential be the targeted variable for research, market trading, and government negotiation for C credits.

We develop a theory for transit times and mean ages for nonautonomous compartmental systems. Using the McKendrick-von F\"orster equation, we show that the mean ages of mass in a compartmental system satisfy a linear nonautonomous ordinary differential equation that is exponentially stable. We then define a nonautonomous version of transit time as the mean age of mass leaving the compartmental system at a particular time and show that our nonautonomous theory generalises the autonomous case. We apply these results to study a nine-dimensional nonautonomous compartmental system modeling the terrestrial carbon cycle, which is a modification of the Carnegie-Ames-Stanford approach (CASA) model, and we demonstrate that the nonautonomous versions of transit time and mean age differ significantly from the autonomous quantities when calculated for that model.

Accurate prediction of future atmospheric CO2 concentrations is essential for evaluating climate change impacts on ecosystems and human societies. One major source of uncertainty in model predictions is the extent to which global warming will increase atmospheric CO2 concentrations through enhanced microbial decomposition of soil organic carbon. Recent advances in microbial ecology could help reduce this uncertainty, but current global models do not represent direct microbial control over decomposition. Instead, all of the coupled climate models reviewed in the most recent Intergovernmental Panel on Climate Change (IPCC) report assume that decomposition is a first-order decay process, proportional to the size of the soil carbon pool. Here we argue for the development of a new generation of models that link decomposition directly to the size and activity of microbial communities in coupled global models. This process begins with the formulation and validation of fine-scale models that capture fundamental microbial mechanisms without excessive mathematical complexity. These mechanistic models must then be scaled up through an aggregation process and validated at ecosystem to global scales prior to incorporation into global climate models (GCMs). Parameterizing microbial models at the global scale is challenging because some microbial properties such as in situ extracellular enzyme activities are very difficult to measure directly. New parameter fitting procedures may therefore be needed to infer the values of important microbial variables. Validating decomposition models at the global scale is also a challenge, and has not yet been accomplished with the land carbon models embedded in current GCMs. Fortunately new global datasets on soil carbon stocks and fluxes offer promising opportunities to validate both existing land carbon models and new microbial models. If challenges in scaling, parameterization, and validation can be overcome, a new generation of microbially-based decomposition models could substantially improve predictions of carbon–climate feedbacks in the Earth system. Development of new models structures would also reduce any bias due to the assumption of first-order decomposition across all of the models currently referenced in reports of the IPCC.

We performed a genome wide association scan in 1,461 patients with bipolar 1 disorder and 2,008 controls drawn from the Systematic Treatment Enhancement Program for Bipolar Disorder (STEP-BD) and University College London sample collections with successful genotyping for 372,193 SNPs. Our strongest single SNP results are found in myosin5B (MYO5B; p=1.66 × 10−7) and tetraspanin-8 (TSPAN8; p=6.11 × 10−7). Haplotype analysis further supported single SNP results highlighting MYO5B, TSPAN8 and the epidermal growth factor receptor (MYO5B; p=2.04 × 10−8, TSPAN8; p=7.57 × 10−7 and EGFR; p=8.36 × 10−8). For replication, we genotyped 304 SNPs in a family-based NIMH sample (n=409 trios) and a University of Edinburgh case-control sample (n=365 cases, 351 controls) which do not provide independent replication after correction for multiple testing. A comparison of our strongest associations with the genome-wide scan of 1,868 patients with bipolar disorder and 2,938 controls completed as part of the Wellcome Trust Case-Control Consortium (1) indicates concordant signals for SNPs within the voltage-dependent calcium channel, L-type, alpha 1C subunit (CACNA1C) gene, but no other single SNP associations are highly significant in both studies. Given the heritability of bipolar disorder, the lack of agreement between studies emphasizes that susceptibility alleles are likely to be modest in effect size and require even larger samples for detection.

A number of nonlinear microbial models of soil carbon decomposition have been developed. Some of them have been applied globally but have yet to be shown to realistically represent soil carbon dynamics in the field. A thorough analysis of their key differences is needed to inform future model developments. Here we compare two nonlinear microbial models of soil carbon decomposition: one based on reverse Michaelis–Menten kinetics (model A) and the other on regular Michaelis–Menten kinetics (model B). Using analytic approximations and numerical solutions, we find that the oscillatory responses of carbon pools to a small perturbation in their initial pool sizes dampen faster in model A than in model B. Soil warming always decreases carbon storage in model A, but in model B it predominantly decreases carbon storage in cool regions and increases carbon storage in warm regions. For both models, the CO2 efflux from soil carbon decomposition reaches a maximum value some time after increased carbon input (as in priming experiments). This maximum CO2 efflux (Fmax) decreases with an increase in soil temperature in both models. However, the sensitivity of Fmax to the increased amount of carbon input increases with soil temperature in model A but decreases monotonically with an increase in soil temperature in model B. These differences in the responses to soil warming and carbon input between the two nonlinear models can be used to discern which model is more realistic when compared to results from field or laboratory experiments. These insights will contribute to an improved understanding of the significance of soil microbial processes in soil carbon responses to future climate change.

©2015. American Geophysical Union. All Rights Reserved. Soil carbon (C) is a critical component of Earth system models (ESMs), and its diverse representations are a major source of the large spread across models in the terrestrial C sink from the third to fifth assessment reports of the Intergovernmental Panel on Climate Change (IPCC). Improving soil C projections is of a high priority for Earth system modeling in the future IPCC and other assessments. To achieve this goal, we suggest that (1) model structures should reflect real-world processes, (2) parameters should be calibrated to match model outputs with observations, and (3) external forcing variables should accurately prescribe the environmental conditions that soils experience. First, most soil C cycle models simulate C input from litter production and C release through decomposition. The latter process has traditionally been represented by first-order decay functions, regulated primarily by temperature, moisture, litter quality, and soil texture. While this formulation well captures macroscopic soil organic C (SOC) dynamics, better understanding is needed of their underlying mechanisms as related to microbial processes, depth-dependent environmental controls, and other processes that strongly affect soil C dynamics. Second, incomplete use of observations in model parameterization is a major cause of bias in soil C projections from ESMs. Optimal parameter calibration with both pool- and flux-based data sets through data assimilation is among the highest priorities for near-term research to reduce biases among ESMs. Third, external variables are represented inconsistently among ESMs, leading to differences in modeled soil C dynamics. We recommend the implementation of traceability analyses to identify how external variables and model parameterizations influence SOC dynamics in different ESMs. Overall, projections of the terrestrial C sink can be substantially improved when reliable data sets are available to select the most representative model structure, constrain parameters, and prescribe forcing fields.

© 2016 Macmillan Publishers Limited. All rights reserved. The majority of the Earth's terrestrial carbon is stored in the soil. If anthropogenic warming stimulates the loss of this carbon to the atmosphere, it could drive further planetary warming. Despite evidence that warming enhances carbon fluxes to and from the soil, the net global balance between these responses remains uncertain. Here we present a comprehensive analysis of warming-induced changes in soil carbon stocks by assembling data from 49 field experiments located across North America, Europe and Asia. We find that the effects of warming are contingent on the size of the initial soil carbon stock, with considerable losses occurring in high-latitude areas. By extrapolating this empirical relationship to the global scale, we provide estimates of soil carbon sensitivity to warming that may help to constrain Earth system model projections. Our empirical relationship suggests that global soil carbon stocks in the upper soil horizons will fall by 30 ± 30 petagrams of carbon to 203 ± 161 petagrams of carbon under one degree of warming, depending on the rate at which the effects of warming are realized. Under the conservative assumption that the response of soil carbon to warming occurs within a year, a business-as-usual climate scenario would drive the loss of 55 ± 50 petagrams of carbon from the upper soil horizons by 2050. This value is around 12-17 per cent of the expected anthropogenic emissions over this period. Despite the considerable uncertainty in our estimates, the direction of the global soil carbon response is consistent across all scenarios. This provides strong empirical support for the idea that rising temperatures will stimulate the net loss of soil carbon to the atmosphere, driving a positive land carbon-climate feedback that could accelerate climate change.

Soil carbon is a recent but critical sub-component of Earth system models that contributes significant uncertainty to carbon cycle simulations in the current Intergovernmental Panel on Climate Change (IPCC) assessment. Understanding and reducing this uncertainty is a high priority for the next round of IPCC assessments. To this end, experts in soil carbon dynamics gathered in Breckenridge, Colo., for 3 days to discuss next steps for global soil carbon modeling.

The relationship between microbial respiration rate and soil moisture content is an important property for understanding and predicting soil organic carbon degradation, CO2 production and emission, and their subsequent effects on climate change. This paper reports a pore-scale modeling study to investigate the response of heterotrophic respiration to moisture conditions in soils and to evaluate various factors that affect this response. X-ray computed tomography was used to derive soil pore structures, which were then used for pore-scale model investigation. The pore-scale results were then averaged to calculate the effective respiration rates as a function of water content in soils. The calculated effective respiration rate first increases and then decreases with increasing soil water content, showing a maximum respiration rate at water saturation degree of 0.75, which is consistent with field and laboratory observations. The relationship between the respiration rate and moisture content is affected by various factors, including pore-scale organic carbon bioavailability, the rate of oxygen delivery, soil pore structure and physical heterogeneity, soil clay content, and microbial drought resistivity. Overall, this study provides mechanistic insights into the soil respiration response to the change in moisture conditions, and reveals a complex relationship between heterotrophic microbial respiration rate and moisture content in soils that is affected by various hydrological, geophysical, and biochemical factors.