Reconciling carbon quality with availability predicts temperature sensitivity of global soil carbon mineralization

Significance

Understanding how soil carbon mineralization responds to warming is pivotal for accurate predictions of carbon cycle-climate change feedbacks and effective climate mitigation. By analyzing a comprehensive global dataset encompassing incubations of soils across the globe, we demonstrate that the temperature sensitivity of soil carbon hinges on the interplay between carbon quality and availability. In the absence of carbon limitations, carbon quality dictates sensitivity, with more recalcitrant carbon exhibiting higher temperature sensitivity. In situations of limited carbon availability, substrate availability becomes the decisive factor. Furthermore, we ascertain that temperature sensitivity of global soil carbon is primarily governed by the mineralization of labile carbon. Consequently, potential decline of labile carbon due to global warming may amplify positive carbon cycle-climate change feedbacks.

Abstract

Soil organic carbon (SOC) mineralization is a key component of the global carbon cycle. Its temperature sensitivity Q₁₀ (which is defined as the factor of change in mineralization with a 10 °C temperature increase) is crucial for understanding the carbon cycle-climate change feedback but remains uncertain. Here, we demonstrate the universal control of carbon quality-availability tradeoffs on Q₁₀. When carbon availability is not limited, Q₁₀ is controlled by carbon quality; otherwise, substrate availability controls Q₁₀. A model driven by such quality-availability tradeoffs explains 97% of the spatiotemporal variability of Q₁₀ in incubations of soils across the globe and predicts a global Q₁₀ of 2.1 ± 0.4 (mean ± one SD) with higher Q₁₀ in northern high-latitude regions. We further reveal that global Q₁₀ is predominantly governed by the mineralization of high-quality carbon. The work provides a foundation for predicting SOC dynamics under climate and land use changes which may alter soil carbon quality and availability.

The mineralization of global soil organic carbon (SOC) results in the release of approximately 57 to 80 Pg C to the atmosphere as carbon dioxide (CO₂) each year (1, 2), equal to almost 9% of the atmospheric carbon pool. Climate warming may accelerate SOC mineralization (3), leading to positive soil carbon cycle-climate change feedbacks. However, the rate of this acceleration remains uncertain, particularly across large spatial extents (4, 5), and the underlying controls and mechanisms are also controversial (6, 7). According to the “carbon-quality temperature” hypothesis, recalcitrant SOC is more sensitive to temperature than labile SOC as it requires higher activation energy (8, 9), as depicted by the Arrhenius equation (10, 11). Nevertheless, comparable or even lower sensitivity of recalcitrant SOC has also been widely observed (12–14). This inconsistency could be explained by the low availability of SOC substrates to decomposers, mainly microbes. Indeed, the Michaelis–Menten theory predicts that if microbes cannot access substrates or are limited by metabolically preferred substrates (e.g., labile carbon with high energy density in order to utilize substrates with low energy density), SOC mineralization will be insensitive to temperature (15, 16). Physiochemical isolation of SOC from decomposition and other environmental constraints or unbalanced composition in terms of energy density and activation energy demand for overall SOC mineralization may result in general substrate limitation (17). Due to the high spatial heterogeneity of edaphic properties and high diversity of SOC composition, it is not surprising to observe highly variable apparent temperature sensitivity under different environmental conditions. Simultaneous consideration of carbon quality and availability is vital for reliable prediction of SOC mineralization in response to temperature changes (18).

We propose that combining the effects of carbon quality and availability can provide a universal explanation for the variability in the temperature sensitivity of SOC mineralization in global soils. Both factors affect the temperature sensitivity of SOC mineralization, but their relative importance depends on whether microbial mineralization is more limited by SOC quality or availability. This can be mathematically represented as (18): Q₁₀ = Q_{10_max}•f(A)•f(Q), where Q₁₀ is the observed temperature sensitivity, defined as the change in SOC mineralization with a 10 °C temperature rise. Q_{10_max} represents the maximum potential Q₁₀, while f(A) and f(Q) (both range from 0 to 1) are the availability- and quality-limitation-induced reduction of Q_{10_max}, respectively (Materials and Methods). Specifically, if SOC availability is not or less limited [i.e., f(A) is close to 1], Q₁₀ is primarily limited by carbon quality [i.e., f(Q) < f(A)] with higher values under lower carbon quality, as predicted by the Arrhenius equation (Fig. 1). Conversely, if SOC availability is limited [i.e., f(Q) is close to 1], carbon availability takes precedence [i.e., f(Q) > f(A)], resulting in lower Q₁₀ under conditions of lower carbon availability, as predicted by the Michaelis–Menten equation (Fig. 1).

Fig. 1.

Conceptual diagram of temperature sensitivity of soil carbon mineralization (Q₁₀) as impacted by substrate quality and availability. The effects of substrate availability [f(A)] and quality [f(Q)] are depicted by the Michaelis–Menten and Arrhenius equations, respectively. Parameters in the equations are elucidated in SI Appendix, Table S2.

To test our proposition, we conducted a comprehensive literature review and obtained a global dataset of SOC mineralization from 721 soils collected worldwide (SI Appendix, Fig. S1) under laboratory incubation conditions. We used a continuous interval of 0.2% to calculate the mineralized fraction, which indicates a decreasing gradient of SOC quality and availability over the course of incubation. Then, we estimated changes in the Q₁₀ of SOC mineralization over time by calculating the “equal-carbon” Q₁₀ (19, 20) based on the time required to respire a defined fraction of SOC (0 to 0.2%, 0.2 to 0.4%, 0.4 to 0.6%, etc.). As incubation experiments typically do not involve continuous carbon inputs, the respired fraction provided an opportunity to distinguish between quality- and availability-limited Q₁₀ by evaluating the temporal dynamics of Q₁₀ with the progression of incubation (e.g., depletion of labile SOC and decrease of SOC availability). Using the calculated temporal Q₁₀ values and their corresponding respired fractions, we fitted a model based on the proposed interactions between carbon quality and availability to assess whether the model can accurately capture the temporal dynamics of observed Q₁₀, and the model was applied to infer Q₁₀ at the start of incubation (Q_{10_initial}) and the relative importance of carbon quality and quantity.

Results and Discussion

Two Theoretical Types of Temporal Q₁₀ Dynamics.

If our proposition regarding the interactions between carbon quality and availability is correct, and the incubation period is long enough, we would only observe two types of temporal Q₁₀ dynamics characterized by decreased carbon quality and availability as incubation progresses. Type I involves an initial increase in Q₁₀ to a maximum, followed by a decrease (i.e., an increase phase followed by a decrease phase). For this type, the initial substrate is sufficient, and mineralization is not limited. The initial Q₁₀ and the rate of change toward the turning point would vary depending on the initial substrate quality. However, depending on the initial substrate availability and the length of the incubation, we may only observe the first increase phase (SI Appendix, Fig. S2A). Type II involves a persistent decrease in Q₁₀, regardless of incubation duration, due to persistent availability limitations (SI Appendix, Fig. S2B). The initial Q₁₀ and the rate of decrease depend on the initial intensity of the limitation. These expectations have been confirmed. Specifically, 77% of the trials can be clearly classified into these two types (SI Appendix, Supplementary Data). Among them, 65% are type I, which on average have a higher initial SOC content (i.e., lower probability of substrate limitation) than type II trails (6.5 % vs. 3.3 %, SI Appendix, Fig. S3) which accounts for 12% of the trials (SI Appendix, Supplementary Data). We compared the maximum Q₁₀ values among the two types (SI Appendix, Fig. S4). The maximum Q₁₀ values were expected to be in an order of type I > type II, which was confirmed in our analysis. On average, the maximum Q₁₀ value in Type I trials was 3.9, which was almost as twice as the maximum Q₁₀ value in Type II trials (SI Appendix, Fig. S4).

There are 23% of the trials that do not fall into either type I or type II categories and are referred to as type III dynamics. In these trials, Q₁₀ either remains stable or fluctuates greatly over time (SI Appendix, Fig. S2C). The reason for such dynamics may be due to several factors such as the presence of abundant substrates with similar quality and/or activation energy, very low carbon availability, and unstable incubation environment, among others. Upon examining these trials, we found that they tended to have short pre-incubation periods (which may not allow for microbial stabilization), or larger temperature differences for estimating Q₁₀ (which may result in complex consequences on microbial metabolisms and carbon use strategies).

Spatiotemporal Variability of Q₁₀ and Its Drivers.

Individual Q₁₀ values estimated from the global dataset vary substantially among soils and over time, ranging from 0.1 to 15 with a median of 1.8 (Q₁₀ values exceeding 15, which accounts for 1% of the total data and may be caused by confounding factors such as microbial community shifts, enzyme responses, and desorption of carbon substrates from mineral surfaces (21, 22), have been excluded in this study, Fig. 2A). This spatiotemporal variability of Q₁₀ is well explained (R² = 0.94) by a machine learning–based model—random forest—driven by climatic, vegetation and edaphic properties at the soil location, incubation manipulation, and respired fraction of SOC (Fig. 2A). Respired fraction alone explains 33% of the variance of Q₁₀ (Fig. 2B). As the calculated time-course values of respired fraction are proxies of carbon quality and availability, this result demonstrates the critical role of carbon quality and availability in controlling Q₁₀. Mean annual temperature at soil location and two incubation manipulation-related variables including incubation temperature range and the lower temperature to estimate Q₁₀ are the following three most important variables, explaining 5%, 6%, and 5% of the Q₁₀ variance, respectively. All other variables assessed have less than 5% interpretability (SI Appendix, Fig. S5). Together, incubation manipulation explains 24% of the variance of Q₁₀, while climatic and edaphic properties explain 15% and 22% of the variance of Q₁₀, respectively. Vegetation variables together only explain 6% (SI Appendix, Fig. S5). These findings demonstrate the integrated effects of environmental conditions and experimental manipulation on Q₁₀ estimation and explain why Q₁₀ varies greatly in the literature.

Fig. 2.

Spatiotemporal changes in the temperature sensitivity of soil carbon mineralization (Q₁₀) and their main drivers. Q₁₀ values were calculated for cumulative respired fractions at an interval of 0.2% (0 to 0.2%, 0.2 to 0.4%, 0.4 to 0.6%, etc.). (A) Variation of Q₁₀ values with respired fraction. Inset shows the performance of a random forest model to explain the variance of Q₁₀ values, gray dashed line shows the 1:1 line, and red line shows the regression line. RMSE, root mean squared error; R², determination coefficient. (B) Partial dependence of Q₁₀ values on the four most important controlling factors which explain 5% variance of Q₁₀ at least. Shading area shows the 95% CI. Temperature range is the difference of two temperatures used to calculate Q₁₀, and lower temperature is the low temperature of the range.

Averaging across the globe dataset, Q₁₀ initially increases and then decreases as incubation progresses, in conjunction with the increase of the respired fraction of SOC (SI Appendix, Fig. S6). The average Q₁₀ at the turning point, where it transitions from increase to decrease, is 3.1 (which represents an average maximum Q₁₀). At this point, the corresponding respired fraction of SOC ranges between 4.2 and 4.4%. When we divide the data into two groups with and without carbon inputs, the group with carbon inputs shows a smaller Q₁₀ of 2.6 at the turning point, with the corresponding respired fraction of SOC increasing to 4.8 to 5.0% (SI Appendix, Fig. S6), suggesting that the addition of new carbon delays Q₁₀ from reaching its maximum. The global average temporal pattern of Q₁₀ suggests interactive effects of carbon quality and availability on the temperature sensitivity of SOC. In the first phase, Q₁₀ increases with incubation due to the depletion of labile SOC until reaching the turning point, while in the second phase, Q₁₀ shows a decreasing trend (SI Appendix, Fig. S6). Notably, many laboratory incubation experiments observed only the increase phase of Q₁₀ (19, 23, 24), likely due to abundant substrates or the relatively short duration of the incubation as discussed above.

Interactions between Carbon Quality and Availability.

The global average temporal dynamics of Q₁₀ can be well captured (R² = 0.89) by modeling the interactions between carbon quality and availability (Fig. 3A). Examining the two reduction factors, f(Q) and f(A), which represent the effects of carbon quality and availability, respectively, it is evident that the initial increase phase is primarily controlled by f(Q) while f(A) is larger and closer to 1 than f(Q), and the subsequent decrease phase is primarily controlled by f(A) while f(Q) remains relatively stable and close to 1 (Fig. 3B). The model explains 97% of the spatiotemporal variance of Q₁₀ across the trials (Fig. 3C). For individual trials, the model explains >50% of the Q₁₀ variance in 88% trials (SI Appendix, Fig. S7). Trials with relatively poor model performance mainly belong to type III trials with large fluctuations in Q₁₀ over time (SI Appendix, Figs. S7 and S8). For type III trials, the model explains 94% of the Q₁₀ variance, but the RMSE (root mean squared error) is larger than that of type I and type II trials (Fig. 3C). However, it is interesting to note that the average Q₁₀ of type III trials also presents clear type I dynamics (Fig. 3A), supporting the general global pattern of the two phases albeit potential confounding factors in individual trials.

Fig. 3.

Observed and modeled temperature sensitivity of soil carbon mineralization (Q₁₀). (A) Model performance for predicting the temporal variability of global mean Q₁₀. Shading area represents the 95% CI of the simulation, solid line shows the median of the 200 simulations. Bars represent one SE of observations. Type I shows that Q₁₀ first increases and then decreases with time. Type II represents a persistent decrease in Q₁₀. Type III shows that the temporal dynamic of Q₁₀ do not fall into either type I or type II categories. (B) The temporal dynamics of fitted f(A) and f(Q) values corresponding to the Q₁₀ in (A). Thin lines show 200 estimates considering uncertainties in the data, and bold lines show the median of the 200 estimates. (C) Model performance by pooling individual results together. Vertical and horizontal bars represent one SDs of observed and modeled values, respectively. Gray dashed line shows the 1:1 line, and solid line shows the regression line. (D) the temporal dynamics of f(A) and f(Q) values for the three types. RMSE, root mean squared error; R², determination coefficient. Thin lines show the median of 200 estimates for each individual trial, and bold lines show the mean value of the medians for each type of trials.

The modeling results provide critical insights into the interactions between substrate availability (S) and quality indicated by activation energy (E_a) in regulating Q₁₀ (Materials and Methods). Theoretically, if microbial mineralization is not limited by S, Q₁₀ should be equal to the maximum potential Q₁₀ (i.e., Q_{10_max} in the model) which is inherently determined by substrate chemistry (22). In this case, the Michaelis–Menten equation models a constant Q₁₀ and is incapable of simulating the determinant process underpinning Q_{10_max} and therefore Q₁₀. Simulation of carbon quality represented by the Arrhenius equation compensates such incapability and simulates Q₁₀ as a function of E_a of substrates under sufficient S. At the beginning of the trials, specifically, E_a (i.e., E₀ in the model) was estimated to have a mean value of ${51.1}_{2.4}^{209.8}$ kJ mol⁻¹ (mean with 5% and 95% quantiles) (SI Appendix, Fig. S9). This range of values encompasses a number of empirical observations and theoretical estimates of E_a obtained under various soil environmental conditions (9, 25, 26). When mineralization is limited by S, Q₁₀ is jointly regulated by S and E_a. Although low-quality substrates have a higher E_a and thus a higher Q₁₀, decomposers will be eventually limited by energy availability for activating the mineralization of recalcitrant SOC (27). These evaluations have been verified by comparing the distributions of optimized model parameters among the three types of trials (SI Appendix, Fig. S9). First, Q_{10_max} is on average comparable among the three types (SI Appendix, Fig. S9A). Second, except E₀, all parameters are significantly different between type I and type II trials, while these parameters for type II trials either significantly differ from type I trials or from type II trials (SI Appendix, Fig. S9 B and C). For example, it is expected that the magnitude of initial substrate availability (S₀) at the beginning of Type I trials is greater than that of type II trials. These results align with our proposition that the three types of trails may present distinct status in terms of carbon quality or carbon availability.

Initial Q₁₀ and Its Global Pattern.

In the Q₁₀ model, the effects of both carbon quality f(Q) and availability f(A) are modeled as functions of respired fraction (Materials and Methods), allowing us to estimate initial f(Q), f(A), and thus Q₁₀ at the start of incubation by setting the respired fraction to zero which are, respectively, referred as f(Q)_initial, f(A)_initial, and Q_{10_initial} hereafter. These initial values can help diagnose f(Q), f(A), and Q₁₀ under field conditions, assuming that soil carbon quality and availability at the start of incubation can approximate that in the field.

The optimized Q₁₀ model estimates a Q_{10_initial} of 1.9 ± 1.1 (mean ± one SD), with the highest Q_{10_initial} in tundra (3.3 ± 1.8), followed by cropland (2.2 ± 1.3), forest (1.9 ± 1.1), and wetland (1.8 ± 0.5). Grassland exhibits the lowest Q_{10_initial} of 1.5 ± 0.5 (Fig. 4A). We compare our estimates of Q_{10_initial} for soil incubation with that based on field observations of total soil (Q_{10_Rs}) and heterotrophic respiration (Q_{10_Rh}) (28). The results show that the average Q_{10_initial} for soil incubation across the globe is generally smaller than Q_{10_Rh} (2.2 ± 0.6) which is significantly smaller than Q_{10_Rs} (2.5 ± 0.8, Fig. 4A). While Q_{10_initial} and Q_{10_Rh} are comparable in grasslands, Q_{10_initial} is consistently smaller than Q_{10_Rs} irrespective of ecosystems. These discrepancies would be attributed to factors such as 1) different approaches used to estimate Q₁₀ (i.e., no model can 100% explain the data), 2) model-fitting uncertainties due to data quantity and quality limitations, and 3) inconsistent representativeness of the datasets for estimating the three Q₁₀ metrics. Despite the discrepancies, it is important to note that all three Q₁₀ metrics (especially Q_{10_initial}) show large variability (Fig. 4A), and Q_{10_initial} values less than 1 are not rare. These results highlight the importance of assessing context-dependent Q₁₀ and suggest that warming does not necessarily accelerate SOC mineralization (29). The consistently higher Q_{10_Rs} compared to Q_{10_Rh} and Q_{10_initial} may be due to temperature-dependent root growth and biomass which directly influence the total amount of root respiration and thus the estimation of Q_{10_Rs} (30).

Fig. 4.

Inferred temperature sensitivity of soil carbon mineralization at the start of incubation (Q_{10_initial}) and the impacts of carbon availability [f(A)_initial] and quality [f(Q)_initial]. Q_{10_Rh} Q_{10_Rs} are the Q₁₀ of soil heterotrophic and total respiration (heterotrophic plus autotrophic respiration), respectively, and are derived from ref. 28. Values of <1 and >4.5 are excluded in ref. 28. Red dots show the mean value. Different letters in (A) represent a significant difference among the estimates at the level of P < 0.05. Different letters in (B) represent a significant difference among ecosystems at the level of P < 0.05. The left y-axis in (B) represents the value of reduction factor [i.e., f(A)_initial and f(Q)_initial] and the right y-axis represents the value of log_e [f(Q)_initial:f(A)_initial].

The variability of Q_{10_initial} can be reasonably predicted (cross-validation R² = 0.76) by a random forest model driven by climatic, edaphic, and vegetation properties (SI Appendix, Fig. S10). We apply the random forest model to predict Q_{10_initial} for each 1-km grid across the globe (Fig. 5). The global average Q_{10_initial} is 2.1 (Fig. 5 A and B), which is consistent with another study (28). Digital global mapping shows higher temperature sensitivity of SOC mineralization in northern high-latitude regions (Fig. 5B). The most sensitive areas are located in northern Alaska, northern Canada, and central and eastern Siberia which also have high soil carbon content. Some arid/semi-arid tropical regions, such as northern sub-Saharan Africa and northern regions of the Namib Desert, also have high Q_{10_initial}. However, the data in these regions are very limited (SI Appendix, Fig. S1), which would be also the reason of larger uncertainty compared to other regions (Fig. 5 C and D).

Fig. 5.

Global spatial pattern of Q₁₀ at the start of incubation (Q_{10_initial}) and its uncertainty. (A) and (B) Q_{10_initial} and its latitudinal pattern, respectively. (C) and (D) Uncertainty of Q_{10_initial} and its latitudinal pattern, respectively. Gray area in (B) and (D) shows one SD of the mean. Gray dashed lines show the global mean Q_{10_initial} and its uncertainty. Uncertainty is estimated as the coefficient of variance of 500 estimates in the random forest model for predicting Q_{10_initial}.

The Relative Importance of Carbon Quality and Availability.

The estimated f(Q)_initial and f(A)_initial values provide crucial insights into the relative significance of carbon quality and availability in governing Q_{10_initial}. Across the incubated soils, on average f(Q)_initial is smaller than f(A)_initial, with an average log ratio of f(Q)_initial to f(A)_initial of –1.3 (Fig. 4B). This suggests that substrate quality exerts a stronger influence than availability in limiting Q_{10_initial}. That is, SOC mineralization is dominant by relatively labile SOC components with lower activation energy, and quality limitation of Q₁₀ would be more common than availability limitation in global soils.

However, tundra soils are different from soils in other ecosystems, as they are much less limited by quality, and the importance of quality and availability is comparable with an average log ratio of f(Q)_initial to f(A)_initial of –0.1 (Fig. 4B). Although Arrhenius kinetics predict higher f(Q) for a given carbon quality at lower temperatures, this can be explained by two other factors. On the one hand, carbon availability in tundra for microbial decomposition is often limited by low temperature as most SOC is frozen in peat for most of the year (e.g., permafrost). On the other hand, high-quality carbon substrates with high nutrient content (e.g., nitrogen) are usually scarce in tundra soils (31–33). It has been suggested that tundra soils are often dominated by complex carbon compounds, such as lignin, cellulose, and hemicellulose, which are difficult for microbes to decompose due to nutrient limitation (33). As a result, the Q₁₀ of SOC mineralization in tundra may be vulnerable to shifts in both quality and availability, while Q₁₀ of other ecosystems would be more sensitive to quality changes. Wetland soils show the smallest log ratios of f(Q)_initial to f(A)_initial (Fig. 4B). For wetland soils, they are usually carbon-rich due to inhibited SOC decomposition under anaerobic conditions and therefore have a low probability of availability limitation. Additionally, waterlogging promotes the formation of dissolved SOC, which can be more bioavailable to decomposers and typically has a high quality (34).

It is worth noting that most soil incubations are conducted under optimal soil moisture conditions. Since soil moisture is a critical factor influencing the accessibility of carbon to microbes, incubation data may underestimate the impact of carbon availability on Q₁₀ if optimal soil moisture conditions alleviate the constraints on carbon availability (35). In real field conditions, both drought and waterlogging (as observed in wetland soils) can limit microbial access to or utilization of carbon substrates, subsequently affecting the apparent Q₁₀. Additionally, other aspects of incubation procedures, such as the duration of pre-incubation and soil sieving, can influence the stabilization and destabilization processes of soil carbon, as well as microbial activities. These factors may impact the temporal dynamics of Q₁₀.

Conclusions and Implications

Our results demonstrate that carbon quality–availability interactions universally control the temperature sensitivity of SOC mineralization across the globe and over time. This interaction can be effectively modeled by integrating Arrhenius and Michaelis–Menten kinetics. When mineralization is not limited by substrates, carbon quality explains the increasing Q₁₀ values as SOC quality declines. Conversely, when substrates are limited, Q₁₀ decreases with decreasing availability. The estimated Q₁₀ across the globe is 2.1 with much higher values in colder regions. Furthermore, we found that carbon quality plays a predominant role in controlling Q₁₀ globally. High-quality SOC may contribute to the majority of global SOC mineralization (36), and the sensitivity of SOC to warming may significantly rise if warming results in depletion of high-quality SOC, i.e., positive soil carbon cycle-climate change feedbacks. However, on a global scale, 4% SOC loss would result in availability limitation-induced decrease of Q₁₀.

The carbon quality–availability interactions can serve as a foundation for explaining or inferring whole-profile SOC dynamics in response to changes in carbon quality and availability. Climate and land management changes may alter carbon inputs to soils in terms of both quality and quantity (37), thereby changing SOC quality and availability. The consequences of such changes will depend on the temporal dynamics of carbon quality and availability and their interactions. A long-term field warming experiment has observed multi-phase decay of SOC (13), which can be explained by the shifts in carbon substrate quality and availability during the experiment. Based on the general vertical distribution of carbon quality and availability (38), it is reasonable to infer that topsoil SOC dynamics would be more sensitive to quality changes as topsoil is generally substrate-abundant and has high-quality substrates, while subsoil SOC is more sensitive to availability changes as it is substrate-limited and has low-quality substrates. If high-quality SOC declines due to global change such as warming (39), topsoil SOC may show higher sensitivity to warming than subsoil SOC, which has been confirmed by estimates based on synthesizing SOC measurements in global soil profiles (4) as well as by incubation experiments (24). However, if substrate availability limitation is relieved in subsoil, subsoil SOC would show higher temperature sensitivity than topsoil SOC. Increasing carbon inputs to deep soil layers (e.g., by growing deep-rooting plants), for example, has been suggested as an effective way to promote carbon sequestration (40). Under climate warming, however, increased carbon input would also relax availability limitations, particularly in subsoil layers, thereby enhancing decomposition and offsetting the benefit for carbon sequestration. The global mapping of Q₁₀ can help diagnose hotspots of sensitive areas of SOC mineralization under global warming, promoting soil carbon sequestration and climate change mitigation by managing carbon quality and availability.

Materials and Methods

Data Sources.

A global dataset of SOC mineralization (g CO₂-C kg⁻¹ SOC d⁻¹) measured under laboratory incubation conditions was compiled by searching the Web of Science and the Chinese National Knowledge Infrastructure (CNKI). Topic keywords “soil AND (respir* OR ((carbon OR C OR CO2 OR carbon dioxide OR organic matter OR OM) AND (flux OR efflux OR emission OR release OR loss OR mineralize* OR decompos*))) AND (temperature OR warm* OR cool*) AND (incubat* OR culture)” are used for the search. As a complementary, we also screened five published papers synthesizing SOC mineralization data (41–45) to target publications which may be missed from our search. All publications must meet the following criteria: 1) the soil used for incubation is sampled from the mineral layer; 2) the same soil must be incubated under at least two temperatures under otherwise same incubation conditions, enabling the estimation of Q₁₀; and 3) time-course SOC mineralization rates are reported or can be directly calculated from the reported data. All relevant numerical data were directly extracted from the publication, and data presented in figures were extracted using WebPlotDigitizer (46). Finally, we obtained 21,979 data points observed by incubating 721 soils across the globe (SI Appendix, Fig. S1) from 191 publications (SI Appendix, Table S3).

In the dataset, incubation temperature ranges from –10 °C to 60 °C, and incubation duration ranges from 1 to 924 d. We also extracted, if available, SOC content, soil pH, total nitrogen content, soil C:N ratio, soil bulk density, and texture of the incubated soils before incubation. If these variables are not reported (SI Appendix, Table S1), we extracted them from the Harmonized World Soil Database (47). Ecosystem type (i.e., cropland, desert, forest, grassland, tundra, and wetland), site location (longitude and latitude), and variables relating to incubation manipulation (e.g., incubation temperature and soil moisture) were also recorded. At each soil location, climate attributes were extracted from WorldClim (48).

Temporal Dynamics of Q₁₀.

We calculated the “equal-carbon” Q₁₀ proposed by Rey and Jarvis (20) which can reflect the changes of temperature sensitivity of SOC with time (43). Specifically, Q₁₀ was calculated based on the time required to mineralize a defined fraction of SOC under two temperatures (19):

$$Q_{10}={\left(\frac{t_{T_l}}{t_{T_h}}\right)}^{\frac{10}{T_h-T_l}},$$ [1]

where $t_{T_l}$ and $t_{T_h}$ are the time required to mineralize the defined fraction of SOC under incubation temperature of T_l and T_h, respectively. Considering SOC as a continuum, the fraction of mineralized (or respired) SOC was determined at continuous gradients with an interval of percentage respired SOC of 0.2% (i.e., 0 to 0.2%, 0.2 to 0.4%, 0.4 to 0.6%, …, which represent a gradient of decreasing lability of SOC with the proceeding of incubation). Here, we note that mineralized fraction at the end of incubation in some experiments does not reach to 0.2% (due to very short incubation duration and low incubation temperature), and these experiments are excluded for the assessment (SI Appendix, Table S3). This approach assumes that a certain amount of mineralized SOC comes from a similar fraction of SOC when the soils are at different temperatures, and labile pools will decompose faster/earlier than passive pools (19).

A machine learning–based statistic model—random forest—was used to explore the drivers over the variability of Q₁₀ across the trials. Partial dependence analysis was used to test the relationship between the predicted Q₁₀ and explanatory variables across the entire range of possible values included in the random forest modeling. The considered drivers are shown in SI Appendix, Table S1. Before fitting the model, the variance inflation factor (VIF) method was used to minimize the multicollinearity of explanatory variables. The explanatory variables with a VIF value greater than 10 were excluded. We classified the explanation factors into four main groups: 1) climate conditions, 2) soil properties, 3) vegetation, 4) experimental manipulation (e.g., temperature range used to calculate Q₁₀: T_h–T_l, ΔT—the difference between T_l and mean annual temperature at soil sampling location). The specific explanatory variables in each group after minimizing the multicollinearity are shown in SI Appendix, Table S1. In addition, we included the respired fraction of SOC (i.e., RF) as a proxy to represent the availability and quality of SOC. Nonparametric Kruskal–Wallis test was used to determine the significant difference. The VIF analysis was conducted using the check_collinearity function in R package performance, the random forest analysis was performed using randomForest function in R package randomForest, the partial dependence analysis was conducted using partial function in R package pdp, and the Kruskal–Wallis test was conducted using kruskalmc function in R package pgirmess. All data analyses were performed in R version 4.0.3 (https://cran.r-project.org/).

Data-Model Integration.

Recalling our hypotheses (Fig. 1), we assume that the temporal dynamics of Q₁₀ in each trial are controlled by carbon quality when the substrate availability is not limited, while Q₁₀ is mainly controlled by carbon availability when the substrate availability is limited. A general model aligning with such assumptions can be written as (18):

$$Q_{10}=Q_{10\_\text{max}}·f\left(A\right)·f\left(Q\right),$$ [2]

where $Q_{10\_max}$ is the maximum potential Q₁₀ without limitations of carbon quality and availability, f(A) and f(Q) are the reduction factor due to carbon availability and quality limitations, respectively.

The Michaelis–Menten and Arrhenius kinetics represent mainstream modeling of SOC mineralization as impacted by carbon availability and quality, respectively. Under a typical temperature, the Michaelis–Menten and Arrhenius kinetics can be respectively written as:

$$k_{MM}=V_{\text{max}}·\frac{S}{K_m+S},$$ [3]

$$k_{Arr}={A·e}^{\frac{-E_a}{R·T}},$$ [4]

where $V_{\text{max}}$ is the maximum rate of enzymatic reaction at a given temperature, $K_m$ is the Michaelis–Menten (half-saturation) constant, S is the substrate content, A is the pre-exponential factor, $E_a$ is the activation energy, R is the gas constant (8.314 J K⁻¹ mol⁻¹), and T is the temperature in Kelvin. As Q₁₀ can be generally estimated as the ratio of mineralization rate under a higher temperature (T_h) to that under a lower temperature (T_l), the temperature sensitivity of k_MM ($Q_{k_{\mathit{MM}}}$) and k_Arr ($Q_{k_{\mathit{Arr}}}$) can be, respectively, calculated as:

$$Q_{k_{\mathit{MM}}}=\frac{V_{\mathrm{m}\mathrm{a}\mathrm{x}\_T_h}}{V_{\mathrm{m}\mathrm{a}\mathrm{x}\_T_l}}·\frac{K_{m_{T_l}}+S}{K_{m_{T_h}}+S},$$ [5]

$$Q_{k_{\mathit{Arr}}}=e^{\frac{E_a}{R}·\frac{T_h-T_l}{T_l·T_h}},$$ [6]

where $V_{\mathrm{m}\mathrm{a}\mathrm{x}\_T_h}$ and $V_{\mathrm{m}\mathrm{a}\mathrm{x}\_T_l}$ are the V_max under temperature T_h and T_l, respectively, $K_{m\_T_h}$ and $K_{m\_T_l}$ are the K_m under T_h and T_l, respectively. Both S and E_a keep constant under different temperatures (10, 16). $Q_{k_{\mathit{MM}}}$ and $Q_{k_{\mathit{Arr}}}$ can be normalized to their potential maximum value to represent f(A) and f(Q), respectively:

$$f\left(A\right)=\frac{K_{m\_T_l}+S}{K_{m\_T_h}+S},$$ [7]

$$f\left(Q\right)=e^{\frac{E_a-E_{\mathit{cri}}}{R}·\frac{T_h-T_l}{T_l·T_h}},$$ [8]

where $E_{\mathit{cri}}$ is the critical activation energy (kJ mol^-1) under which k_Arr reaches the maximum. With the proceeding of incubation, S is expressed as an exponential function of the respired fraction of SOC (RF) (SI Appendix, Fig. S11):

$$S=S_0·e^{-\alpha \bullet RF},$$ [9]

where $S_0$ is the initial substrate availability (mg C kg^–1 soil) at the start of the incubation, α is the decreasing rate of substrate availability with RF. This function models that substrate availability decreases with the proceeding of incubation. $E_a$ is expressed as a logistic function of RF (SI Appendix, Fig. S11):

$$E_a=\frac{E_{a\_0}·E_{\mathit{cri}}}{E_{a\_0}+\left(E_{\mathit{cri}}-E_{a\_0}\right)·e^{-\beta ·RF}},$$ [10]

where $E_{a\_0}$ is the initial activation energy (kJ mol^–1) at the start of the incubation, β is the increasing rate of activation energy with RF.

We optimized the model to capture the temporal changes in Q₁₀ calculated under the RF gradients for each trial as well as for their average using a differential evolution algorithm (49). Prior ranges of the eight parameters in the model are shown in SI Appendix, Table S2. The root mean squared error (RMSE) between modeled and observed Q₁₀ was minimized to target the optimal parameters. Considering potential parameter equifinality and observation uncertainty (50), we repeated the optimization for 200 times independently to obtain 200 ensembles of model parameters. For each optimization, specifically, observations were sampled from the probability distribution function of observed Q₁₀ assuming a normal distribution defined by their SD (σ) and mean (μ) at each measurement time point. For each trial and each parameter, the median of the 200 estimates was calculated for comparison purpose. The optimization was performed using the function DEoptim in the package DEoptim in R 4.0.3.

Inferring Initial Q₁₀ and Global Digital Mapping.

At the beginning of incubation, the Q₁₀ (Q_{10_initial}) can be estimated by setting RF = 0 in Eqs. 9 and 10:

$$Q_{10\_\text{initial}}=Q_{10\_\text{max}}·\frac{K_{m\_T_l}+S_0}{K_{m\_T_h}+S_0}·e^{\frac{E_{a\_0}-E_{\mathit{cri}}}{R}·\frac{T_h-T_l}{T_l·T_h}}.$$ [11]

Correspondingly, f(Q) and f(A) can be, respectively, estimated as:

$${f\left(A\right)}_{\text{initial}}=\frac{K_{m\_T_l}+S_0}{K_{m\_T_h}+S_0},$$ [12]

$${f\left(Q\right)}_{\text{initial}}=e^{\frac{E_{a\_0}-E_{\mathit{cri}}}{R}·\frac{T_h-T_l}{T_l·T_h}}.$$ [13]

We estimated Q_{10_initial}, f(A)_initial, and f(Q)_initial for each of the 721 soils. The estimates of Q_{10_initial} were compared with the Q₁₀ values of soil respiration (including heterotrophic—Q_{10_Rh}, and total respiration—Q_{10_Rs}) observed in the field reported in ref. 28 at both global and ecosystem levels.

A random forest model was trained and validated (10-fold cross-validation) to predict Q_{10_initial}. The similar techniques for controlling predictor collinearity as the model for interpreting Q₁₀ in the section Temporal Dynamics of Q₁₀ were used. To facilitate global scale application, the model only includes environmental predictor variables that are meaningful at field conditions (SI Appendix, Table S1). This may damage model performance but can provide more realistic estimates aligning with the purpose of inferring Q₁₀ in situ. Especially, the temperature predictor in the model used mean annual temperature at the site location, soil depth was set to 0 (the depth of layer top) and 30 cm (the depth of layer bottom). The validated model was applied in each 1-km grid across the globe using relevant global mapping products of the predictor variables in the model (SI Appendix, Table S1). Prediction uncertainty was quantified by estimating the SD of predictions from 500 randomly drawn trees in the fitted random forest model. The model training and global mapping were performed in R 4.0.3. The relevant data and code have been provided (see Data, Materials, and Software Availability statements).

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

Data used to generate the results are deposited to figshare through: (51). The field Q₁₀ data were obtained from (28). Code (R scripts) used to assess the data and generate the results are deposited to figshare through: (52).