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.

Abstract. Terrestrial ecosystems have absorbed roughly 30 % of anthropogenic CO 2 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 timedependent 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 threedimensional (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 computationPublished by Copernicus Publications on behalf of the European Geosciences Union. 146Y. Luo et al.: Land carbon storage dynamics ally 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.

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.

Soil organic matter (SOM) supports the Earth's ability to sustain terrestrial ecosystems, provide food and fiber, and retains the largest pool of actively cycling carbon.Over 75% of the soil organic carbon (SOC) in the top meter of soil is directly --

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