Variability of ecosystem carbon source from microbial respiration is controlled by rainfall dynamics

Significance

The variability of the different ecosystem carbon fluxes directly influences the global carbon budget and future climate trajectory. Heterotrophic respiration is particularly uncertain and the extent to which its dynamics are driven by climate, soil, and vegetation properties remains poorly understood. Here we combine a global carbon flux dataset with a probabilistic model of microbial growth to show that despite its complexity the ecosystem-scale heterotrophic respiration can be described as a function of rainfall characteristics and vegetation primary productivity, regardless of ecosystem type. This emergent simplicity in ecosystem-scale heterotrophic respiration may help close the ecosystem carbon budgets and provide a quantitative framework to forecast the possible impacts of climate change on the soil carbon balance.

Abstract

Soil heterotrophic respiration (R_h) represents an important component of the terrestrial carbon cycle that affects whether ecosystems function as carbon sources or sinks. Due to the complex interactions between biological and physical factors controlling microbial growth, R_h is uncertain and difficult to predict, limiting our ability to anticipate future climate trajectories. Here we analyze the global FLUXNET 2015 database aided by a probabilistic model of microbial growth to examine the ecosystem-scale dynamics of R_h and identify primary predictors of its variability. We find that the temporal variability in R_h is consistently distributed according to a Gamma distribution, with shape and scale parameters controlled only by rainfall characteristics and vegetation productivity. This distribution originates from the propagation of fast hydrologic fluctuations on the slower biological dynamics of microbial growth and is independent of biome, soil type, and microbial physiology. This finding allows us to readily provide accurate estimates of the mean R_h and its variance, as confirmed by a comparison with an independent global dataset. Our results suggest that future changes in rainfall regime and net primary productivity will significantly alter the dynamics of R_h and the global carbon budget. In regions that are becoming wetter, R_h may increase faster than net primary productivity, thereby reducing the carbon storage capacity of terrestrial ecosystems.

Soil respiration (R_s), the sum of autotrophic (i.e., root) respiration (R_a) and heterotrophic (i.e., microbial) respiration (R_h), is the second largest flux in the terrestrial carbon cycle (1). R_s plays a deciding role in the global carbon budget and understanding the dynamics of R_s and its components is of significance to climate modeling and the global carbon cycle. For example, the magnitude of R_h and net primary productivity (NPP) determines the stability of soil carbon pools and whether ecosystems serve as carbon sources or sinks (Fig. 1). Although R_h releases approximately five times more CO₂ than anthropogenic emissions annually (2), it remains one of the least-documented carbon fluxes, probably due to the difficulty in partitioning R_s into R_a and R_h (3) and in disentangling the diverse biotic and abiotic processes influencing R_h (4, 5). Despite some efforts that have been made to explore the dependence of R_h on environmental factors such as soil temperature and moisture (6–8), the integrated effects of climate, soil, and vegetation properties on the dynamics of R_h remain a recalcitrant problem. A better understanding of the dynamics of R_h and to what extent this variability can be attributed to climatic and edaphic factors will not only reduce the current high uncertainty in the global estimates of R_h but also improve the forecasting capability of Earth system models (ESMs), which usually require a separate parameterization of R_h (3, 5).

Fig. 1.

Schematic diagram of carbon and water cycles. Ecosystem gross primary productivity (GPP) is the total amount of carbon fixed through photosynthesis. NPP is the net carbon gain by plants and usually stored as vegetation biomass. Vegetation carbon use efficiency (CUE_p) is the proportion of GPP converted to NPP. A proportion of the fixed carbon is lost by plant respiration (autotrophic respiration, R_a). A proportion of NPP is eventually converted to organic substrates (e.g., litter) that are utilized by soil microbes for both catabolism (energy production) and anabolism (biomass production). Microbial carbon use efficiency (CUE_m) is the ratio of microbial biomass growth to carbon uptake. Some of the substrates are lost through leaching. Heterotrophic respiration (R_h) is the carbon respired by soil organisms, mainly soil microbes. Soil water gained from precipitation (R) is lost through evapotranspiration (ET), runoff (Q), and deep drainage.

The spatial heterogeneity in soil resources (e.g., water, labile carbon, and nutrients) and environmental conditions (e.g., temperature, precipitation, soil structure, and vegetation type) exert important controls on microbial growth and the decomposition of soil organic carbon (9–12). Vegetation carbon uptake (i.e., productivity) and turnover influence the dynamics of R_h by determining the amount of organic substrate (e.g., litter and root exudates) available for microbial activity (13). R_h may also be strongly driven by stochastic rainfall dynamics in addition to temperature (7, 14). Increased soil water availability after rainfall pulses accelerates microbial activity and the decomposition of soil organic carbon by increasing the substrate availability (15, 16) and by directly enhancing microbial metabolism and growth (11, 17, 18). Ultimately, however, the microbial growth rate and R_h are also controlled by the availability of O₂ or other electron acceptors in soil microsites, a fact that is largely controlled by soil structure (19). Although empirical evidence suggests that R_h will increase with increasing precipitation (20), a combination of model and data is needed to interpret mechanistically the variability of R_h across ecosystems, examine whether the variability of R_h can be described by a universal probabilistic distribution, and identify how the main drivers among climate, soil, and vegetation characteristics simultaneously affect R_h in the long term.

Water availability is a limiting factor for most terrestrial ecosystems (17, 21). Both climate models and empirical observations suggest that rainfall regimes will tend to be more extreme in the future, with rainfall events becoming fewer but larger (22, 23). Previous work has shown that changes in rainfall variability (rainfall frequency λ and intensity h) can significantly influence ecosystem fluxes such as NPP (24–26). In fact, ecosystem behaviors such as vegetation growth are strongly driven by soil moisture dynamics and the stochastic nature of rainfall input, R(t), which has often been approximated by a marked Poisson process (27–30). Similarly, the stochastic behavior of rainfall events needs to be accounted for to understand how microbial respiration will respond to climate change. Analyzing R_h data and estimating its variability thus requires a probabilistic approach that can incorporate rainfall stochasticity and propagate it to microbial activity.

We analyze the FLUXNET 2015 database aided by a stochastic microbial model to explore the statistics (i.e., probabilistic density function, pdf) of R_h across different ecosystems. Specifically, we 1) explore the existence of a universal probability law of R_h across different ecosystems and 2) disentangle the role of climate, soil, and vegetation characteristics in determining the mean, variance, and probability distribution of R_h. We then discuss how future global changes may affect R_h dynamics and, in turn, the ecosystem carbon budget.

Empirical Evidence from FLUXNET Data

We consider six ecosystems (shrubland, grassland, savanna, deciduous broadleaf forest, evergreen broadleaf forest, and evergreen needleleaf forest) and select 13 qualified sites across the globe (SI Appendix, Fig. S1) after the necessary filtering procedures (see Materials and Methods). The daily R_h is calculated using a top-down approach, i.e., $R_{\text{h}}=\text{RECO}-\left(1-{\text{CUE}}_{\text{p}}\right)*\text{GPP}$, where RECO and GPP are ecosystem respiration and gross primary productivity, respectively, and CUE_p is the carbon use efficiency of vegetation (31). We also introduce the seasonal dynamics of CUE_p, following Konings et al. (3), to account for the positive correlation between CUE_p and GPP. To eliminate the effects of daily temperature variations on the temporal dynamics of R_h, for each site we adjust all R_h values to a common site-specific mean temperature using the Q₁₀ approach. For sites with a clear bimodal distribution of soil moisture, the whole year is divided into wet and dry seasons. The numeric values of climate, soil, and vegetation parameters except the potential evapotranspiration (PET) for each site are estimated empirically (SI Appendix, Table S1). Detailed descriptions of data processing can be found in Materials and Methods.

After analyzing the variability in R_h across sites, we notice that the empirical pdf of R_h varies consistently along two key dimensions, i.e., wetness and NPP (Fig. 2 and SI Appendix, Figs. S2–S5). These patterns suggest that despite the large variations in environmental conditions among different ecosystems and the complex biogeochemical processes underlying R_h, the probabilistic behavior of ecosystem-scale R_h may be mainly controlled by stochastic rainfall forcing and NPP, which determines the substrate availability. Below, we further explore whether the probabilistic behavior of R_h can be quantitatively interpreted by a probabilistic microbial growth model linked to key environmental drivers.

Fig. 2.

The theoretical and empirical probability distribution of effective relative soil moisture (x) and soil heterotrophic respiration (R_h). One example site was chosen to represent each of the climate (dry and wet) and NPP (high and low) combinations. (A) A savanna site AU-Gin. (B) An evergreen needleleaf forest site NL-Loo. (C) A shrubland site US-Whs. (D) A grassland site US-Wkg. Black lines show the fitted pdfs (SI Appendix, Eqs. S2 and S14) and blue lines show the theoretical pdf of R_h expressed by rainfall characteristics and NPP only (SI Appendix, Eq. S18).

A Stochastic Microbial Model

We develop a stochastic model to describe the observed pdfs of soil moisture and R_h across ecosystems. Here we focus on the dynamics of the soil microbial population and account for the key processes affecting its growth and turnover over time. The goal of our model is to analytically examine the universal probability law of R_h based on first principles of microbial growth, instead of modeling the whole-ecosystem dynamics by incorporating all the biogeochemical processes involved in R_h. In SI Appendix we also present a soil water balance model capturing the stochastic behavior of the soil water content, which as we detail below controls the growth of the microbial population.

We consider a soil microbial community quantified by its total biomass B, whose dynamics is the result of the variety of species populating the soil environment and their different traits (e.g., growth rate, growth yield, etc.). The growth of soil microbes depends on how they partition the organic substrate between catabolism and anabolism (Fig. 1). The growth rate of B is thus equal to the soil microbial carbon use efficiency CUE_m times the carbon uptake rate U. The growth G can also be expressed as a function of B, i.e., $G={\text{CUE}}_{\text{m}}\times U=\mathit{\alpha }\phi \left(x\right)B$, where $\mathit{\alpha }$ is the intrinsic biomass growth rate and $\phi \left(x\right)$ is introduced to make the soil moisture (x) dependence of microbial growth explicit. Here we use “effective” relative soil moisture similar to Porporato et al. (28) which is defined as $x=\left(s-s_w\right)/\left(s_1-s_w\right)$, where s is the relative soil moisture (or degree of saturation), at the wilting point, and s₁ is the relative soil moisture threshold for deep infiltration and runoff. Although soil moisture usually exhibits a vertical gradient in the soil profile, in this study we account for the mean effect of soil moisture on the growth of the whole microbial community because our focus is on ecosystem-scale R_h and this simplification allows analytical tractability. The dynamics of B can thus be expressed as

$$\frac{\text{d}B}{\text{d}t}=\mathit{\alpha }\phi \left(x\right)B-\delta B,$$ [1]

where $\delta$ is the biomass loss rate per unit of microbial biomass.

In this parsimonious representation of microbial dynamics, the substrate not utilized for anabolism is used for catabolism, so that the soil microbial respiration rate R_h can be expressed as $R_{\text{h}}=\left(1-{\text{CUE}}_{\text{m}}\right)\times U={\mathit{\alpha }}_1\phi \left(x\right)B$, where ${\mathit{\alpha }}_1=\left(1/{\text{CUE}}_{\text{m}}-1\right)\mathit{\alpha }$. Considering the dependence of microbial activity on soil moisture and making use of the above equations, the temporal dynamics of R_h can be described by the following differential equation:

$$\frac{\text{d}{R}_{\text{h}}}{\text{d}t}=K_{1}R\left(t\right)-K_2{R}_{\text{h}},$$ [2]

where the only two parameters K₁ and K₂ embed key information on microbial physiology and soil moisture dynamics, respectively, affecting the growth and decay of the microbial population. These parameters are not constant in principle, because B and x can change over time. However, they can be considered constant for each site because the biological processes (microbial growth) occur on a much longer time scale than hydrological processes (rainfall events) and we anticipate that they are strongly correlated with ecosystem productivity and rainfall characteristics, respectively, as supported by the linear regression analyses below (see Results and Discussion). More details on this assumption are provided in SI Appendix. Eq. 2 suggests that the dynamics of R_h is a function of stochastic, intermittent rainfall pulses and a decay term resulting from endogenous (microbial mortality) and exogenous factors (soil water losses). This leads to the important result that for ecosystems that are in a stationary rainfall regime and land cover (or that these vary over much longer time scales than daily/seasonal scales), the pdf of R_h is a Gamma distribution,

$$p\left(R_{\text{h}}\right)=C{e}^{-\frac{R_{\text{h}}}{K_{1}h}}{R}_{\text{h}}{}^{\frac{\lambda }{K_2}-1},$$ [3]

where $C=\frac{{\left(K_{1}h\right)}^{-\frac{\lambda }{K_2}}}{\mathrm{\Gamma }\left(\frac{\lambda }{K_2}\right)}$ and Γ(⋅) is the gamma function. From Eq. 3, all the statistics of R_h, such as mean and variance, can be readily computed if K₁ and K₂ are known. The detailed derivation of the probabilistic model is given in SI Appendix.

Results and Discussion

To analyze the influence of climate, soil, and vegetation on the dynamics of R_h, we fit the theoretical pdfs of x and R_h to empirical data for each site by estimating the values of PET and two model parameters K₁ and K₂. We note that the major focus of this study is on the dynamics of R_h while the soil moisture pdf is used in this study only to confirm that soil moisture in these ecosystems is mainly driven by rainfall and not groundwater, lateral flow, etc. The results show that the fitted analytical pdfs of x and R_h describe well the empirical observations for all study sites (Fig. 2 and SI Appendix, Figs. S2–S5). We then study how they are correlated with climate, soil, and vegetation conditions. We therefore conduct linear regressions to examine the dependence of K₁ and K₂ on climate, soil, and vegetation characteristics. Fig. 3 shows that K₁ is primarily controlled by NPP (log-log slope = 0.43, R² = 0.42, P = 0.01), whereas K₂ is primarily controlled by mean rainfall rate $\langle R\rangle$ (log-log slope = 0.48, R² = 0.47, P < 0.01). These correlations lend strong support to the stochastic model. In fact, the model anticipates the strong dependence of K₁ on NPP because the numerator of K₁, ${\mathit{\alpha }}_1\langle B\rangle$, can be conceived as the mean maximum R_h when there is no soil water stress (i.e., $g\left(x\right)=1$) which should be closely correlated with NPP (since NPP directly determines the substrate availability for microbial activity). The model also suggests that K₂ is related to climatic factors, a fact confirmed by its correlation with rainfall.

Fig. 3.

The dependence of model parameters K₁ (A–D) and K₂ (E–H) on climate, soil, and vegetation conditions. Nonsignificant linear regressions (P > 0.05) are not shown. The shaded areas represent the 95% CI range. NPP: annual NPP (g C⋅m⁻²⋅y⁻¹); $\langle R\rangle$: mean rainfall rate (cm⋅d⁻¹); PET: potential evapotranspiration (cm⋅d⁻¹); $\langle x\rangle$: mean effective relative soil moisture.

Considering these correlations, the theoretical pdf of R_h becomes only dependent on rainfall characteristics and NPP, after substituting $K_2=0.37{\langle R\rangle }^{0.48}$ and $K_1=0{.\text{1NPP}}^{0.43}$ (see SI Appendix, Eq. S18), suggesting that the variation in the pdfs of x and R_h among ecosystems indeed span the two key dimensions of wetness and NPP. As shown in Fig. 2 and SI Appendix, Figs. S2–S5, the theoretical pdf based on SI Appendix, Eq. S18 (blue lines) is very close to both the fitted theoretical pdf (Eq. 3) and the empirical pdf (indicated by histograms). This demonstrates the remarkable power of using only rainfall characteristics and NPP in describing the dynamics of R_h across different ecosystems. We emphasize that although soil properties are not explicit in the pdf of R_h, vegetation characteristics (such as vegetation cover and biomass) are strongly linked to soil structure (e.g., soil porosity and aggregation), which further affects soil hydrological responses (32, 33). Thus, NPP may indirectly account, at least partially, for these soil properties. Interestingly, after a scrutiny of the pdf of R_h, we notice that R_h can be rescaled by NPP, $R_{\text{h}}{}^{\prime }={R_{\text{h}}/\text{NPP}}^{0.43}$ (see SI Appendix, Eq. S24), without affecting the shape of the pdf. The result is a pdf of NPP-corrected R_h, i.e., $R_{\text{h}}{}^{\prime }={R_{\text{h}}/\text{NPP}}^{0.43}$, which no longer depends on NPP. In other words, the dynamics of $R_{\text{h}}{}^{\prime }$ is only controlled by rainfall characteristics and the pdf of $R_{\text{h}}{}^{\prime }$ evolves only along the wetness dimension, irrespective of site-specific NPP (Fig. 4 and SI Appendix, Figs. S2–S5). In summary, while NPP only affects the amplitude of R_h fluctuations, rainfall characteristics alone determine the shape of its pdf.

Fig. 4.

The probability distribution of NPP-corrected heterotrophic respiration ($R_{\text{h}}{}^{\prime }$). (A) A shrubland site US-Whs. (B) A savanna site AU-Gin. (C) An evergreen needleleaf forest site NL-Loo. (D) A grassland site US-Wkg. Black lines show the fitted pdf of $R_{\text{h}}{}^{\prime }$ (SI Appendix, Eq. S22) and blue lines show the theoretical pdf expressed by rainfall characteristics and NPP only (SI Appendix, Eq. S24).

These results hint at a universal stochastic behavior of $R_{\text{h}}{}^{\prime }$ across sites of different vegetation and soil characteristics. The distinct role of hydrological versus biological processes in controlling the R_h dynamics can be also illustrated by recasting Eq. 2 as $\text{d}{R}_{\text{h}}/\text{d}t=R_{\text{h}}\left({\tau }_{\text{hydro}}{}^{-1}+{\tau }_{\text{bio}}{}^{-1}\right)$, where τ_hydro is a hydrological time variable related to rainfall statistics filling the root zone and evapotranspiration and drainage emptying them (i.e., τ_hydro is stochastic) and τ_bio is a biological time variable related to microbial biomass growth. Since the biological time scales are likely to be longer than the hydrological time scales (i.e., we have seen empirically that it is dictated by NPP) (34), the biological time scale (slow component) must integrate all the hydrological fluctuations (fast component) such that the shape of the stationary pdf of R_h is likely to be determined by rainfall statistics. This ubiquitous distinction between hydrological and biological time scales leads to the universal probability law (Gamma distribution) of R_h, demonstrating the fundamental role that rainfall dynamics plays in determining the variability of R_h.

An important implication of the above results is that only rainfall characteristics and NPP quantitatively determine the mean and variance of R_h. After substituting K₁ and K₂ with their corresponding relations to NPP and $\langle R\rangle$, respectively, the theoretical mean and variance of R_h are described as $\langle R_{\text{h}}\rangle =0.27{\langle R\rangle }^{0.52}{\text{NPP}}^{0.43}$ and ${\sigma }_{R_{\text{h}}}^2=0.03h{\langle R\rangle }^{0.52}{\text{NPP}}^{0.86}$. The results show that the theoretical estimates of $\langle R_{\text{h}}\rangle$ and ${\sigma }_{R_{\text{h}}}^2$ are very close to the empirical observations from the FLUXNET data across the study sites (Fig. 5 A and B). In addition, the rainfall- and NPP-corrected $\langle R_{\text{h}}\rangle$ are positively correlated with NPP and rainfall, respectively (Fig. 5 C and D), further supporting the high dependence of R_h dynamics on rainfall characteristics and NPP. The slope of the scaling relationship of rainfall-corrected R_h with NPP is 0.38 (95% CI = 0.19 to 0.57) and the slope of the scaling relationship of NPP-corrected R_h with rainfall is 0.49 (95% CI = 0.27 to 0.70), which are close to the theoretical values 0.43 and 0.52, respectively. Furthermore, it is expected that increases in rainfall and NPP will lead not only to enhanced $\langle R_{\text{h}}\rangle$ but also to a higher degree of variability in R_h. This is particularly important given that both theoretical and empirical evidence suggests a global trend of more extreme rainfall regimes (22, 23), which will significantly alter the R_h dynamics and terrestrial carbon cycling.

Fig. 5.

Comparisons of theoretical mean and variance of R_h with observed data across 13 study sites. The theoretical estimates and empirical data are strongly correlated around the red 1:1 line (A and B). The green solid lines represent the theoretical estimates based on the equations shown in the figure (C and D).

To further test the robustness of our model, we estimate the global 10-y average annual R_h during 2004 to 2013 using the historical rainfall and NPP data from the Coupled Model Intercomparison Project Phase 6 (CMIP6) (35) and compare its performance with a recently published Random Forest (RF) model (36) by testing model estimates with empirical observations from two independent datasets, i.e., the FLUXNET data from 130 sites worldwide and the Global Soil Respiration Database (SRDB) version 5.0 (37) (see SI Appendix). The analysis shows that our model estimates are more consistent with the FLUXNET and SRDB data (slope = 0.98 and 1.11, respectively) than the RF model estimates (slope = 0.59 and 0.49, respectively; SI Appendix, Fig. S6). In addition, our model performs better than the RF model in terms of predicting the high R_h in tropical regions. Intriguingly, our model relies on only two predicting factors, i.e., rainfall characteristics and NPP, while the RF model involves many other explanatory variables such as radiation, soil properties, and land-cover type.

Despite the complexity of biological and physical factors controlling R_h, our model shows that the ecosystem-scale dynamics of R_h can be simply described as a function of rainfall characteristics and vegetation NPP. This is in accord with recent work suggesting that ecosystem productivity and climate are important predictors of the variability of ecosystem functions (38). Clearly, our probabilistic modeling approach requires some simplifications of the underlying processes. We consider the soil microbial community as a whole without accounting for the spatial variations in the proportion of different groups (bacteria, archaea, and fungi). The vertical gradient of soil moisture and substrate availability in the soil profile is also not explicitly accounted for. The well-recognized Birch effect, i.e., the stimulation of soil CO₂ flux due to enhanced carbon and nitrogen mineralization by microbes in response to rewetting after an extended dry period (39–41), is also not considered because it operates at smaller spatial scales and the underlying mechanisms remain debated (42). In addition, the increasingly recognized photodegradation (i.e., the decomposition of plant litter on soil surface through the photodegradative action of ultraviolet solar radiation), which is not considered here, can also contribute to the dynamics of R_h, especially in arid ecosystems (11). These aspects remain poorly understood globally and therefore difficult to quantify at the ecosystem scale (43). In this regard, our approach follows the popular quote “Better be approximately right than precisely wrong.” The parsimonious approach is in line with the available data and the spatiotemporal scale of interest and provides solid empirical and theoretical support for the fundamental effect of key environmental variables (NPP and rainfall) on the dynamics of R_h. Incorporating more complex processes will significantly increase the difficulty of testing the probabilistic model and introduce further uncertainties that hamper the accuracy of model predictions. Yet, the probabilistic model performs remarkably well and its estimates may be used as a reference to calibrate ESMs and improve their forecasting capability.

Finally, our probabilistic model also provides insights into how global change will alter the dynamics of R_h. For example, a 10% increase in λ, h, and NPP in the future will lead to approximately a 15% increase in $\langle R_{\text{h}}\rangle$ and a 32% increase in ${\sigma }_{R_{\text{h}}}^2$. This indicates that in regions where annual rainfall is becoming greater it is possible that increases in $\langle R_{\text{h}}\rangle$ may outpace increases in NPP, thereby reducing the carbon storage capacity of ecosystems, with further impacts on the climate system. This is consistent with previous work suggesting that some ecosystems are on the verge of switching from carbon sinks to carbon sources (44). However, other factors such as land use change may also directly affect ecosystem fluxes (31, 45). Our findings highlight the important role of climate and vegetation in regulating the stochastic behavior of R_h, which may further influence ecosystem carbon balance under ongoing global change. Future investigations will explore the response of the stochastic dynamics of R_h (e.g., mean and variance) to climate change (including temperature, rainfall, and NPP) projected by the CMIP6 under different socioeconomic pathways.

Materials and Methods

FLUXNET 2015 Dataset.

The FLUXNET 2015 Tier 1 dataset contains in situ ecosystem-scale measurements of CO₂, water, and energy fluxes and other meteorological and biological variables from >200 sites across the globe (46). The sites represent nine major vegetation cover types defined by the International Geosphere-Biosphere Program (IGBP) classification. The FLUXNET 2015 dataset for each site provides data products at four different temporal resolutions (half-hourly or hourly, daily, monthly, and yearly). We used the daily-scale dataset, which captures well the variability introduced by rainfall intermittency while excluding hourly and subhourly environmental noise. We applied several criteria to select appropriate sites to test the theoretical prediction of probabilistic distributions of soil moisture and heterotrophic respiration. First, we excluded croplands and wetlands due to their complex soil moisture regimes and consider the following ecosystems: shrubland, grassland, savannas, and three forest types (DBF: deciduous broadleaf forest; EBF: evergreen broadleaf forest; ENF: evergreen needleleaf forest). Second, we excluded sites without records of soil moisture, soil temperature, or net ecosystem exchange (NEE). Third, we excluded sites with soil depth at which soil moisture was measured lower than 5 cm since this shallow soil layer might not fully represent the typical rooting depth. Fourth, we also excluded sites with records of relative soil moisture (soil moisture divided by soil porosity; see below) greater than 1. Fifth, sites that experienced significant disturbances (fire, harvest, etc.) were also excluded to meet the model assumption that ecosystems are at a relatively stationary state. For each site, rainfall characteristics were checked to confirm that rainfall regime was relatively stable across the study years. Data of months with freezing events (temperature ≤0 °C) were removed from further analysis because freezing stress inhibits soil microbial activity and also fails to capture the response of microbial respiration to soil moisture dynamics. Finally, we only selected data with quality control (QC) index of the soil moisture and NEE ≥0.5 to ensure data quality. The QC index of daily-scale data ranged from 0 to 1 and a higher value indicates a higher percentage of good-quality data aggregated from half-hourly or hourly data (46).

Data Processing and Analysis.

We adopted a top-down approach to calculate the heterotrophic (or microbial) respiration (R_h, g C⋅m⁻²⋅d⁻¹), i.e.,

$$R_{\text{h}}=\text{RECO}-R_{\text{a}}=\text{RECO}-\left(1-{\text{CUE}}_{\text{p}}\right)*\text{GPP,}$$ [4]

where RECO is the ecosystem respiration (g C⋅m⁻²⋅d⁻¹), R_a is the autotrophic respiration (g C⋅m⁻²⋅d⁻¹), GPP is the gross primary productivity (g C⋅m⁻²⋅d⁻¹), and CUE_p is the carbon use efficiency of vegetation. The RECO and GPP were obtained through the partitioning of NEE and have been provided in the FLUXNET 2015 dataset. For consistency, we used RECO and GPP derived from the daytime partitioning method (47) for all sites. The annual CUE_p from 2000 to 2015 at each site was calculated as the ratio of NPP to GPP using the MOD17A3 GPP and NPP products at a spatial resolution of 30 arcseconds (∼1 km²) (48). We did not use the C data model framework (CARDAMOM) to calculate CUE_p due to its coarse spatial (1°) and temporal (10-y average) resolutions. Although the seasonal variability in CUE_p remains poorly understood, here we introduced the seasonal dynamics of CUE_p following Konings et al. (3), i.e.,

$${\text{CUE}}_{\text{p}}={\text{CUE}}_{\text{MOD}}+\frac{0.1\times \left(\text{GPP}-\overline{\text{GPP}}\right)}{SD\left(\text{GPP}-\overline{\text{GPP}}\right)},$$ [5]

where CUE_MOD is the raw CUE_p value calculated from MODIS products, SD represents standard deviation, and $\overline{\text{GPP}}$ is the mean GPP over the specific entire year. This approach assumes a proportional relationship between CUE_p and GPP to reflect that vegetation has a higher CUE_p during the growing season. These calculations resulted in a small proportion of negative values of R_h for each site’s data, likely due to the uncertainties in the estimation of CUE_p and the partitioning of NEE into RECO and GPP in the FLUXNET 2015 dataset. These few negative R_h values were removed from further analyses since they should have limited effects on the final results.

To eliminate the effects of temperature variations on R_h, we used a Q₁₀ function (49) to adjust all the original heterotrophic respiration R_ho to a site-specific mean temperature T_mean:

$$R_{\text{h}}=R_{\text{ho}}{Q}_{{}_{10}}^{\frac{T_{\text{mean}}-T_s}{10}},$$ [6]

where T_s is the soil temperature (°C) at which daily R_h was measured and T_mean is the site-specific mean annual soil temperature (°C). Q₁₀ can be estimated from the empirical relationship between log-transformed R_h and T_s. Specifically, Q₁₀ can be calculated using the following equation based on Eq. 6:

$$Q_{10}=e^{\text{β}\times 10},$$ [7]

where β is the slope of the scaling relationship between ln(R_ho) and T_s. The scaling slope was estimated by fitting the empirical data using ordinary least-squares regression analysis.

The values of climate, soil, and vegetation parameters in the model were estimated from available data. For each site, the rainfall frequency (day⁻¹) was calculated as the ratio of number of rainy days to the number of total days. The mean rainfall depth (centimeters) was calculated as the total rainfall amount (centimeters) divided by the number of rainy days. The relative soil moisture s was calculated as the volumetric soil moisture divided by soil porosity. Soil porosity for each site was calculated as soil bulk density divided by a standard particle density 2.65 g/cm³. Site-specific soil bulk density was retrieved from the Regridded Harmonized World Soil Database v1.2. The “effective” relative soil moisture was then defined as $x=\left(s-s_w\right)/\left(s_1-s_w\right)$, where s_w is the relative soil moisture at the wilting point and s₁ is the relative soil moisture threshold for deep infiltration and runoff (28). Here, the values of s_w and s₁ for each site were directly estimated as the minimum and maximum relative soil moisture observed in the FLUXNET 2015 dataset, to avoid introducing further uncertainty from the choice of these parameters. In the model, soil moisture was interpreted as the soil moisture vertically averaged over the rooting zone. However, in the FLUXNET 2015 dataset soil moisture was measured only at a point instead of along a vertical soil profile. Therefore, we assumed that the measured soil moisture at soil depth of D (centimeters) was the average value over the rooting zone with a depth of Z_r = 2D.

We visually examined the pdf of x for each site to test whether the soil moisture dynamics is primarily driven by the rainfall forcing. Sites were excluded from further analyses if the theoretical pdf did not match the empirical pdf. After applying all the above filtering criteria, 13 sites were selected for our analysis (SI Appendix, Fig. S1). For sites with a clear bimodal distribution of x, the whole year was divided into wet and dry seasons and the values of climate, soil, and vegetation parameters were estimated independently for wet and dry seasons. In this study, the theoretical pdf of soil moisture is fitted by estimating the value of PET for each site using the maximum likelihood estimation approach via the fitdist function from the R package fitdistrplus (50). The hydroclimatic regime (dry and wet) of each site was defined based on the mode of soil moisture distribution. For example, sites with a mode ≤0.3 were defined as dry regimes and sites with a mode >0.3 were defined as wet sites.

Data Availability

Previously published data were used for this work. The FLUXNET 2015 dataset is available at https://fluxnet.org/data/fluxnet2015-dataset/. The soil bulk density data can be accessed at https://daac.ornl.gov/SOILS/guides/HWSD.html. The annual MOD17A3 GPP and NPP products can be accessed at http://files.ntsg.umt.edu/data/NTSG_Products/MOD17/.

Change History

January 21, 2022: The byline has been updated.