Main

The terrestrial carbon–climate feedback, resulting from the sensitivity of the terrestrial carbon sink to the physical climate1, dominates the uncertainty in climate projections2,3,4. This feedback depends on the difference between the responses of photosynthesis and respiration to a changing climate5. Estimates of photosynthesis6,7 and respiration8,9,10 vary substantially across terrestrial biosphere models (TBMs)11, however. Furthermore, whereas there has recently been a proliferation of novel measurement techniques to better constrain photosynthesis from regional to global scales, such as solar-induced chlorophyll fluorescence12, near-infrared reflectance of vegetation13 and carbonyl sulfide14,15, respiration remains difficult to constrain at large scales due to the absence of a unique spectral signature or atmospheric tracer.

Accurate climate projections thus hinge on improving our understanding of the magnitude, space–time distribution and climatic sensitivity of respiration. More specifically, constraining the temperature sensitivity of respiration is key to estimating total ecosystem respiration, to assessing the extent to which ecosystem respiration will be amplified by a warming climate and to assessing climate-related risks for regions that can trigger a substantial positive carbon–climate feedback16,17,18,19.

At regional to global scales, ecosystem respiration (RE)—the sum of autotrophic and heterotrophic respiratory fluxes—can be estimated from prognostic TBMs that parameterize respiration based on responses to environmental and biotic drivers20,21, from data-driven models that rely on site-level measurements22, from remotely sensed covariates of respiration23 or from a combination thereof24,25,26. TBMs represent respiratory processes in diverse ways27 but ultimately rely on generalizing locally derived relationships based on sparsely distributed observations to continental and global scales28. This has led to a large spread in estimates of respiration. In addition, estimates of global ecosystem respiration based on TBMs (76–180 Pg C yr−1) vary more widely than those based on data-driven models (94–109 Pg C yr−1; Extended Data Fig. 1).

Within naturally occurring temperature ranges, ecosystem respiration typically shows an exponential response to temperature29,30 as described by the Arrhenius equation31 (Methods). While components of ecosystem respiration are also influenced by moisture32, phenology33, photosynthate input34,35, biomass35, nutrients36, litter quality37 and soil microbial responses38,39, and especially so at the plot scale and for diurnal to monthly timescales, temperature remains the first-order control of ecosystem respiration (and its primary components) at aggregated spatial (biome to continental) and temporal (monthly to decadal) scales17,40,41,42,43. This aggregate temperature sensitivity of ecosystem respiration, which incorporates both the direct response of ecosystem respiration to temperature and indirect influences from other climatic and physiological variables, thereby represents the overall response of biome-scale ecosystem respiration to temperature.

Currently, the only available estimates of the biome-scale temperature sensitivity of respiration are from upscaling of plot-scale estimates, which are largely based on observations from eddy covariance towers (for example, Mahecha et al.44). Such observations are unevenly distributed across ecosystems45 and regions46,47 and represent fluxes for areas only up to several km2 (refs. 48,49,50). Therefore, even a network of hundreds of sites may not adequately represent fluxes at biome or continental scales51. This sampling limitation has led to a large discrepancy between carbon fluxes upscaled from plot-scale observations and those derived from regional-scale observational constraints26, which casts doubt on the robustness of using plot-scale estimates to inform certain biome-scale responses. Moreover, cross-site analyses show that temperature sensitivity is similar across ecosystem types30,44,52, which contradicts anticipated responses from thermal acclimation of autotrophic and heterotrophic respiration; that is, the warmer the climate, the lower the temperature sensitivity53,54,55. Independent empirical estimates of biome-scale temperature sensitivity of ecosystem respiration, such as those based on regional-scale observational constraints, are thus critically needed.

Here we leverage 39,000 atmospheric CO2 concentration measurements from a network of monitoring stations across North America56 during the period 2007–2010 to infer temperature sensitivities of ecosystem respiration for North America and major biomes therein (Extended Data Fig. 2a). To do so, we first use model estimates of ecosystem respiration at monthly temporal and 1° × 1° spatial resolution, obtained from the sum of gross primary productivity (GPP) and net ecosystem exchange (NEE, negative for uptake), to evaluate the biome-scale temperature sensitivity of ecosystem respiration as represented by TBM simulations from the Multi-scale Synthesis and Terrestrial Model Intercomparison Project version 2 (MsTMIP v2) (ref. 57) and Trends in Net Land–Atmosphere Exchange version 6 (TRENDY v6) (ref. 58) ensembles and FLUXCOM machine-learning models26. We then assess the degree to which space–time variability in observed atmospheric CO2 concentrations is captured by carbon flux estimates from this same ensemble of models. Finally, we use the constraint provided by the atmospheric observations to optimize continental- and biome-scale temperature sensitivities of respiration both for individual models and across the model ensemble.

Results

Uncertainty in the temperature sensitivity of respiration

We find that the temperature sensitivity of ecosystem respiration, as represented by the Arrhenius activation energy (Ea, in eV; Methods), ranges widely for the 29 model simulations examined here both for North America (Fig. 1a) and for individual biomes (Extended Data Fig. 3). For North America, for example, Ea ranges from 0.33 to 1.19 eV (Fig. 1a, Extended Data Fig. 4 and Supplementary Table 1), equivalent to Q10 values (that is, the factor by which respiration increases for a 10 °C increase in temperature) of 1.5 to 4.9 at 10 °C (Methods and Extended Data Fig. 5). Inferred temperature sensitivities are highly correlated across biomes within the model ensemble; models with a high temperature sensitivity in one biome also tend to have high sensitivities in other biomes (Supplementary Table 2).

Fig. 1: Using atmospheric observations to constrain the temperature sensitivity of respiration for North America reduces the spread in estimates across models and suggests that the large-scale sensitivity is lower than that implied by the metabolic theory of ecology and by plot-scale studies.
figure 1

a,b, Histograms of the original (a) and optimized (b) aggregate temperature sensitivity of ecosystem respiration for North America, as represented by N = 32 independent estimates of Ea, for TBMs in the MsTMIP v2 (pink) and TRENDY v6 (brown) ensembles and data-driven models in the FLUXCOM ensemble (orange). Grey boxplots summarize the estimates across models, with the centre line, bounds of box, whiskers and dots representing the median, first and third quartiles, smallest and largest estimates falling within 1.5× of the interquartile range from the nearest quartiles and outliers beyond that range, respectively. Green diamonds and vertical dashed lines indicate the reference value of 0.65 eV based on the metabolic theory of ecology29,59,114 and plot-scale estimates52. A two-tailed, paired two-sample t test confirms a statistically significant difference between model-represented temperature sensitivities before (a) and after (b) optimization against atmospheric CO2 observations, as indicated by the t statistic and p value shown in b.

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Approximately two-thirds of the examined TBM simulations (19 of 29) show an Ea estimate for North America that is lower than site-level Ea values derived from flux tower observations30,52, which converge around a universal empirical value of Ea = 0.65 eV for organism- and community-level respiration, according to the metabolic theory of ecology29,59 (Fig. 1a). Note that the model-represented, regional-scale estimates derived here are methodologically comparable with previously reported plot-scale temperature sensitivity (0.65 eV) because both are bottom-up estimates and are derived using temperature as the driver, implicitly accounting for the influence of other covariates30,52. This discrepancy in temperature sensitivity between regional and plot scales is also present for individual biomes (Extended Data Fig. 3). Interestingly, all three FLUXCOM models, which are trained on site-level flux observations, also exhibit Ea estimates for North America (0.48 to 0.61 eV; Fig. 1a and Supplementary Table 1) that are lower than those derived directly from half hourly eddy covariance flux tower observations (approximately 0.65 eV (ref. 52)), indicating that the upscaling of site-level flux observations in space and time impacts the observed aggregate temperature sensitivity of ecosystem respiration.

These biome-scale aggregate temperature sensitivity estimates may differ from those prescribed in models for individual respiratory components because the former characterize large-scale phenomenological properties resulting from a wide array of underlying microscopic respiratory reactions and encompass mediating effects from GPP and other covariates. For example, the Community Land Model version 4.5 (CLM4.5) prescribes a Q10 value of 1.5 for autotrophic and heterotrophic respiration60, but the activation energy estimated from its model output is 0.62 eV for North America (Supplementary Table 1), equivalent to an apparent Q10 value of 2.4 at 10°C. On the other hand, it is precisely the fact that these temperature sensitivity estimates reported here characterize the aggregate properties of biomes, which cannot be readily deduced from model parameterizations, that makes them useful for informing the climatic responses of ecosystem respiration and diagnosing implications of model parameterizations.

Empirical constraint on temperature sensitivities

Next we adjust each model’s activation energy and baseline respiration to maximize consistency with observations of atmospheric CO2 concentrations (Methods) and find that the temperature sensitivity of ecosystem respiration is reduced for most (19 of 29) TBMs and all three FLUXCOM models (Fig. 1a,b and Supplementary Table 1). This indicates that the temperature sensitivity across existing prognostic TBMs and data-driven models is higher than what atmospheric observations suggest. The decrease in the optimized temperature sensitivity of ecosystem respiration is especially large for TBMs with high original sensitivity estimates. As a result of the optimization, model spread of the temperature sensitivity of ecosystem respiration also decreases (Fig. 1b), leading to an ensemble mean (± 1 standard error) of 0.54 (± 0.03) eV (and an ensemble median of 0.51 eV). This ensemble mean temperature sensitivity is statistically significantly lower than the previously reported plot-scale temperature sensitivity of 0.65 eV (p = 0.00019, one-tailed Z test).

Furthermore, we find that the adjustments to Ea needed to maximize the consistency with observed atmospheric CO2 variability, ΔEa, are linearly and negatively correlated with the original Ea estimates of the models (Fig. 2; dashed lines), both for the North American domain (Fig. 2a) and for individual biomes (Fig. 2b–d). This means that atmospheric observations can not only be used to adjust model-specific temperature sensitivities but also to infer an optimal sensitivity (\({\hat{E}}_{{{{\rm{a,opt}}}}}\)) across models. This ensemble optimal sensitivity is represented by the activation energy corresponding to zero adjustment (that is, ΔEa = 0) on the linear relationship between Ea and ΔEa.

Fig. 2: Optimal North American and biome-specific estimates of the temperature sensitivity of ecosystem respiration for individual models and the model ensemble.
figure 2

Adjustments to model-specific estimates of the activation energy are determined by maximizing consistency with observed atmospheric CO2 variability (Methods). a–d, Relationships between adjustments to model-specific estimates of the activation energy needed to maximize consistency with observed atmospheric CO2 variability (ΔEa; vertical axis) and the original estimates of activation energy (Ea; horizontal axis) for models in the MsTMIP v2 (pink), TRENDY v6 (brown) and FLUXCOM (orange) model ensembles in the North American domain (a), croplands (b), evergreen needleleaf forests (c) and deciduous broadleaf and mixed forests (d). Note that only models for which the explanatory power of simulated GPP (\({R}^{2}_{{{{\rm{GPP}}}}}\)) exceeds that of shortwave radiation (\({R}^{2}_{{{{\rm{SW}}}}}\)) are included (Extended Data Fig. 6), leaving two models in the MsTMIP ensemble and one model in the TRENDY ensemble excluded (Methods). The grey dashed lines represent the best orthogonal distance regression (ODR) fit between ΔEa and Ea estimates across the three ensembles of models (N = 29), with light grey shading indicating the 95% prediction interval. The optimal Ea (\({\hat{E}}_{{{{\rm{a,opt}}}}}\)) corresponds to the point where the ODR fit line crosses ΔEa = 0 eV (that is, no adjustment to Ea is needed) and is indicated using a green dashed line and listed for each biome in the corresponding panel.

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We find that the best estimate of the temperature sensitivity of ecosystem respiration (\({\hat{E}}_{{{{\rm{a,opt}}}}}\)) across models is 0.43 ± 0.06 eV (1σ uncertainty; equivalent to Q10 = 1.9 ± 0.2 at 10 °C) for North America. This sensitivity is substantially and significantly lower than the previous global Ea estimate of 0.65 eV (ref. 52) (p = 0.00022, one-tailed Z test) derived from half hourly, site-level flux observations but is remarkably similar to the Ea estimate that represents the temperature sensitivity on an annual timescale (0.42 eV (ref. 52)). Moreover, the optimal sensitivity (0.43 ± 0.06 eV; Fig. 2a) is also lower than the corrected ensemble mean (0.54 ± 0.03 eV, mean ± 1 s.e.) (p = 0.060, one-tailed Z test) or median sensitivity (0.51 eV; Fig. 1b) across the models examined here. This difference also shows that absent an observational constraint, the mean or median responses across a model ensemble may not be a good estimate of actual sensitivity.

We also find substantial variability in temperature sensitivity across biomes, namely, 0.38 ± 0.03 eV (Q10 = 1.7 ± 0.1 at 10 °C) for croplands, 0.50 ± 0.03 eV (Q10 = 2.1 ± 0.1 at 10 °C) for evergreen needleleaf forests and 0.53 ± 0.05 eV (Q10 = 2.2 ± 0.1 at 10 °C) for deciduous broadleaf and mixed forests, which contrasts with earlier site-level studies that had suggested that Ea is uniform across a range of ecosystem types30,52. Tropical and Arctic biomes are not considered individually here due to the low sensitivities of available atmospheric CO2 observations to surface fluxes in these regions (Extended Data Fig. 2b).

Additional analyses confirm that the temperature sensitivities inferred here are not substantially impacted by potential confounding effects of soil moisture or radiation, by co-variability with GPP, by thermal acclimation or by lateral fluxes (Supplementary Notes 1–5 and Supplementary Figs. 1–7). These inferred temperature sensitivities therefore do represent the overall biome-scale response of ecosystem respiration to climatic temperature gradients.

Correcting temperature sensitivity improves model NEE skill

Having obtained observationally constrained estimates of temperature sensitivities of ecosystem respiration (Fig. 2), we then examine how these estimates impact the ability of NEE estimates from TBMs and data-driven models to explain observed atmospheric CO2 variability.

Surprisingly, although space–time variability in atmospheric CO2 concentrations results from space–time patterns in NEE, we find that GPP estimates explain the variability in observed atmospheric CO2 concentrations better than corresponding NEE estimates for 12 of the 29 original TBM simulations in the MsTMIP and TRENDY ensembles (Fig. 3; circles, squares or diamonds; Extended Data Fig. 6). The difference between the explanatory power of monthly averaged NEE estimates and that of GPP estimates (\({{\Delta }}{R}^{2}={R}^{2}_{{{{\rm{NEE}}}}}-{R}^{2}_{{{{\rm{GPP}}}}}\)) ranges from ΔR2 = 0.10 for the simulation for which the improvement from GPP to NEE is greatest to ΔR2 = −0.26 for the simulation where the deterioration relative to the explanatory power of GPP is greatest, highlighting the misrepresentation of ecosystem respiration in the latter set of models. For the FLUXCOM models (not considered TBMs because of their data-driven nature; Methods), NEE estimates neither markedly improve nor degrade the degree to which flux estimates reproduce observed atmospheric CO2 variability relative to GPP estimates (ΔR2 ≤ 0.02; Fig. 3). Note that three of the 29 TBM simulations have GPP estimates that explain an even smaller portion of the observed atmospheric CO2 variability than does shortwave radiation (\({R}^{2}_{{{{\rm{SW}}}}}=0.23\); symbols with empty left portion in Fig. 3; Extended Data Fig. 6), a first-order climatic driver of GPP, and these simulations are therefore excluded from further analysis (consistent with Fig. 2; Methods).

Fig. 3: Rescaling ecosystem respiration by adjusting Ea to optimized values leads to substantial improvement in NEE explanatory power for models for which the explanatory power of NEE originally trailed that of GPP.
figure 3

a, The difference between the explanatory power of NEE (\({R}^{2}_{{{{\rm{NEE}}}}}\)) and GPP (\({R}^{2}_{{{{\rm{GPP}}}}}\)) before and after rescaling based on model-specific optimal adjustments to the temperature sensitivity (ΔEa in Fig. 2a) and the baseline respiration rate at 10∘C for North America (Extended Data Fig. 7a). b, The same information from a after rescaling based on an overall optimal temperature sensitivity derived for North America (\({\hat{E}}_{{{{\rm{a,opt}}}}}=0.43\) eV; Fig. 2a). The R2 differences (\({R}^{2}_{{{{\rm{NEE}}}}}-{R}^{2}_{{{{\rm{GPP}}}}}\)) of the original MsTMIP, TRENDY and FLUXCOM models are represented by squares, circles and diamonds, respectively. A symbol that is filled in the left (right) half indicates that the corresponding model’s GPP (NEE) estimates explain a higher fraction of CO2 variability than does incoming shortwave radiation (\({R}^{2}_{{{{\rm{SW}}}}}=0.23\)). Solid symbols indicate models for which both GPP and NEE estimates outperform shortwave radiation in explaining atmospheric CO2 variability, whereas empty symbols indicate models for which neither GPP nor NEE estimates outperform shortwave radiation. Models for which the explanatory power of GPP lags behind that of shortwave radiation (CLASS-CTEM, VISIT and JPL-HYLAND) are excluded from the rescaling. The blue shaded area highlights models for which the original estimates of NEE outperform GPP in terms of explanatory power, while the red shaded area includes models for which GPP outperforms NEE. The R2 differences after rescaling respiration are indicated by triangles, with upward orientation indicating an improvement in the explanatory power and downward orientation indicating the opposite. Most models for which the explanatory of NEE originally lagged that of GPP (red shaded regions of both panels) show a marked improvement in explanatory power once the temperature sensitivity of ecosystem respiration is adjusted to optimized values. Conversely, adjusting the temperature sensitivity of respiration does not have a large or consistent impact for those models where the explanatory power of NEE was already superior to that of GPP (blue shaded regions). See Supplementary Table 3 for a list of all model names, abbreviations and references.

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Correcting ecosystem respiration by adjusting temperature sensitivity and baseline respiration (Extended Data Fig. 7 and Methods) substantially improves the degree to which NEE estimates reproduce observed atmospheric CO2 variability for those models for which the performance of NEE trailed that of GPP (Fig. 3a, red shaded area). For four of the ten models in this group (SDGVM, CLASS-CTEM-N, CABLE and TRIPLEX-GHG; Supplementary Table 3), NEE estimates in fact outperform GPP estimates once ecosystem respiration is corrected. Only one model, BIOME-BGC (Supplementary Table 3), which has the lowest temperature sensitivity among all investigated models (Ea = 0.33 eV; Supplementary Table 1), shows a minor degradation after respiration is corrected.

By contrast, correcting ecosystem respiration does not consistently improve the performance of NEE estimates for models for which the explanatory power of NEE already exceeded that of GPP (Fig. 3a, blue shaded area). For these models, bias in ecosystem respiration may have been offset by corresponding bias in GPP.

Interestingly, correcting ecosystem respiration using a single value of the ensemble optimal temperature sensitivity (0.43 eV for North America) across all models and biomes yields an improvement in the performance of models’ estimates of NEE that is almost as large (mean increase in \({R}^{2}_{{{{\rm{NEE}}}}}\) of 0.10 for models for which \({R}^{2}_{{{{\rm{NEE}}}}} < {R}^{2}_{{{{\rm{GPP}}}}}\); Fig. 3b) as adjusting both the respiration sensitivity and baseline respiration to model-specific optimized values (mean increase in \({R}^{2}_{{{{\rm{NEE}}}}}\) of 0.12 for the same set of models; Fig. 3a), further supporting the robustness of the overall estimate of temperature sensitivity for North America.

The improvement in model explanatory power of NEE after correcting ecosystem respiration indicates a dominant role of the temperature sensitivity bias in causing the underperformance in carbon flux estimates, although other sources of bias also exist. Attribution of model NEE bias to respiration parameters has been difficult up to now because of equifinality—that is, in the presence of respiration bias, the bias in NEE estimates may still be alleviated by compensation from bias in GPP estimates. Here because rescaling ecosystem respiration based on an overall optimal temperature sensitivity for North America alone (Fig. 3b; Methods) leads to substantial improvement in NEE explanatory power for models for which the performance of NEE trails that of GPP (ΔR2 < 0; Fig. 3b, red shaded area), respiration bias is probably a more important contributor to the NEE bias than is GPP bias for these models. This notion is also corroborated by changes in the seasonal cycles of NEE after imposing the optimal temperature sensitivity on the model ensemble (Supplementary Figs. 8 and 9) and by additional tests on the influences of GPP uncertainty on the inferred temperature sensitivity (Supplementary Figs. 1 and 2).

Discussion

Our findings highlight the spatial-scale dependence of the temperature sensitivity of respiration. Several factors probably contribute to the temperature sensitivity at the biome scale and seasonal to interannual timescales being lower than that reported from plot-scale studies. Temporal aggregation may smooth out short-term (for example, half hourly, typical for plot-scale observations) responses, leading to markedly reduced temperature sensitivity on annual timescales30,52. For soil heterotrophic respiration—a major component of ecosystem respiration—climatological temperature sensitivity has also been shown to differ from instantaneous temperature sensitivity17. Indeed, we find that the relationship between biome-scale temperature sensitivity estimates and mean air temperatures of the studied biomes (Supplementary Fig. 10) is broadly consistent with the previously observed response of climatological Q10 for soil carbon decomposition to the mean air temperature in the temperate domain17. Despite the difference in respiratory components, such qualitative consistency lends support to the robustness of the inferred climatologically relevant temperature sensitivity for temperate North American biomes.

Moreover, biome-scale temperature sensitivities may further differ from plot-scale temperature sensitivities because the responses observed here incorporate indirect sensitivities to temperature via drivers such as soil moisture32, nutrients36 and phenology33. Indeed, some plot-scale studies show a lower temperature sensitivity than the biome-scale temperature sensitivity inferred here after removing influences from low-frequency variability (Q10 = 1.4 ± 0.1 (ref. 44)) or hydrometeorological drivers (Q10 = 1.6 ± 0.1 (ref. 61)). In addition, as ecosystems in cooler (warmer) climates tend to have higher (lower) baseline respiration rates29, accounting for this spatial gradient in baseline respiration potentially dampens the inferred biome-scale temperature sensitivity. Ecosystem state variables such as GPP and phenology may also regulate the baseline respiration62. The relative contribution of these factors at the biome scale merits further research. Given that the sensitivities inferred here encompass these various additional factors, they are likely to more aptly reflect the bulk response of respiration to future warming on aggregate space–time scales and therefore inform climatic responses.

In addition to differences in sensitivity across scales, several known challenges with flux measurements and partitioning may have also led to an overestimate of the temperature sensitivity of ecosystem respiration in earlier studies even at the plot scale. These known challenges can cause ecosystem respiration to be undercounted when temperatures are low (at night or in the dormant season) and overestimated when temperatures are high (during the day or in the growing season). Nighttime respiration can be underestimated in conditions of weak turbulence and canopy CO2 storage build-up63. Moreover, for sites in uneven terrain, there is no accepted way to reliably account for advective CO2 fluxes64, which may lead to a further underestimation of respiratory carbon loss at night. Partitioning daytime respiration from NEE measurements also remains challenging because the relationship between nighttime respiration and temperature often does not hold during the daytime due to light inhibition of leaf respiration65,66,67 and non-temperature controls of nighttime autotrophic respiration68. As a result, using the relationship between nighttime respiration and temperature to partition daytime fluxes often leads to overestimation of daytime respiration69. Furthermore, this overestimation of daytime respiration is particularly strong in the growing season (up to 23%) (ref. 69), further enhancing the bias of inferred temperature sensitivity on an annual timescale. These problems all contribute to a potential positive bias in the plot-scale temperature sensitivity and, in turn, the size of the difference in temperature sensitivity across scales reported here.

The difference in the temperature sensitivity of ecosystem respiration between croplands and forests observed here (Fig. 2b-d) and the absence of such biome specificity in plot-scale studies may arise from several factors. Croplands typically show a higher carbon use efficiency (ratio between net primary productivity and GPP) than unmanaged forests70, that is, a lower autotrophic fraction in ecosystem respiration. This, in turn, means that the fraction of soil heterotrophic respiration, which is less sensitive to air temperature than is aboveground respiration, is higher in croplands than forests, thereby leading to the overall lower temperature sensitivity of ecosystem respiration in croplands. Management practices such as harvest, irrigation and tillage can cause dramatic changes in ecosystem respiration at weekly to monthly timescales71, though their impact on the temperature sensitivity at longer timescales remains poorly understood. The dearth of cropland sites in FLUXNET observations45 may explain the lack of biome specificity in the temperature sensitivity inferred in plot-scale studies and the fact that the FLUXCOM models26, trained on FLUXNET observations, capture the temperature sensitivity best in deciduous broadleaf and mixed forests (Fig. 2d) but least well in croplands (Fig. 2b). To reach a robust understanding of cropland carbon cycling, future investigations may need to examine the partitioning among different respiratory components, quantify the impact of management practices on the temperature sensitivity of ecosystem respiration and expand the eddy covariance network in cropland areas.

Given that the temperature sensitivity of ecosystem respiration constitutes a leading-order positive climate feedback, the findings presented here also open several avenues for advancing the understanding of terrestrial carbon–climate feedbacks.

First, although observed atmospheric CO2 variability incorporates influences of both photosynthesis and ecosystem respiration, the inference of an ensemble optimal temperature sensitivity for respiration for North America (Fig. 2a) and major biomes (Fig. 2b–d) indicates that the current level of uncertainty in GPP7,72,73 does not obscure information about ecosystem respiration (Supplementary Fig. 1). Given this finding, partitioning of net carbon fluxes into photosynthesis and respiration at regional scales is, in principle, achievable in a manner akin to the respiration-based partitioning widely used at eddy covariance sites63,74; such partitioning would overcome a key observational challenge in constraining regional-scale responses of carbon fluxes to climate. Pursuing this goal may require expanding and optimizing atmospheric observational networks to better resolve space–time variability in photosynthesis and respiration75, especially in sparsely sampled tropical and Arctic biomes.

Second, our findings establish a link between the explanatory power of modelled NEE and bias in the temperature sensitivity of ecosystem respiration, which is useful for refining TBMs. Although the temperature sensitivity of either GPP or ecosystem respiration may be adjusted to improve the consistency between NEE and observed atmospheric CO2 concentrations, in reality, GPP and ecosystem respiration are intricately tied by carbon allocation and decomposition processes. Such coupling does not always allow errors in ecosystem respiration to be cancelled by corresponding errors in GPP. Here the substantial improvements in model explanatory power resulting from correcting the temperature sensitivity of ecosystem respiration (Fig. 3) provide robust evidence that current model representation of respiratory processes contribute substantially to uncertainty in NEE estimates, and in turn, uncertainty in the response of the terrestrial carbon sink to future warming. We suggest that calibration of the biome-scale temperature sensitivity of ecosystem respiration against multi-scale constraints be prioritized in model development to reduce compensating errors in ecosystem respiration and GPP, which could otherwise meet model benchmarks but for incorrect reasons.

Finally, if bias in the temperature sensitivity of ecosystem respiration represented by standalone TBM simulations is indicative of that in coupled Earth system model simulations, we may expect the response of ecosystem respiration to warming to be stronger in those models than what current atmospheric CO2 observations suggest as well. This difference also highlights a gap in the predictive understanding of how large-scale carbon sinks respond to future warming, because much of current understanding derives from Earth system model simulations. Meanwhile, in the long run, the response of ecosystem respiration to climatic warming may be additionally influenced by acclimation to a warmer climate53,54,55,76,77, changes in soil microbial community composition78, limitation of labile carbon pools79 and soil warming80, among other factors. As early warning signs of potential saturation and destabilization of regional carbon sinks appear81, there is an urgent need to assess the resilience of large-scale carbon sinks to climatic warming by synthesizing multi-scale observational constraints with Earth system models that embed state-of-the-art mechanistic understanding of respiration. Looking forward, we anticipate that the expanding network of ground-based, airborne and satellite remote-sensing observations of atmospheric CO2 concentrations will further elucidate the climatic sensitivities of ecosystem respiration across regions and spatiotemporal scales and thereby inform respiration-driven terrestrial carbon–climate feedbacks.

Methods

Model estimates of terrestrial carbon fluxes

Monthly model estimates of GPP and NEE were obtained from the MsTMIP (version 2, spanning 1901–2010)57,82,83,84,85,86 and the TRENDY (version 6, spanning 1960–2016)58,87,88 ensembles for the period 2007–2010. We chose this study period because of the overlapping temporal coverage of carbon flux estimates (MsTMIP ends in 2010) and high-resolution atmospheric transport (starting in 2007). Each model ensemble used a set of standardized climate drivers to drive individual model runs, thereby minimizing model divergence contributed from climate drivers. There were 29 simulations from 24 independent TBMs. In addition, we used three machine-learning models from the FLUXCOM ensemble for comparison26. This yielded N = 32 pairs of simulated GPP and NEE estimates for the analysis of ecosystem respiration. The model output was regridded to 1° × 1° resolution. A list of all models is provided in Supplementary Table 3.

Estimating the temperature sensitivity of respiration

Air temperature data were obtained from the North American Regional Reanalysis data89, regridded to the same monthly, 1° × 1° resolution as the carbon flux estimates.

Ecosystem respiration (RE) was calculated from the sum of model estimates of GPP and NEE per definition (note that NEE is negative when there is net ecosystem uptake).

We used the Arrhenius equation to describe the relationship between ecosystem respiration (RE, μmol m−2 s−1) and air temperature (T, K):

$${R}_{{{{\rm{E}}}}}(T)={R}_{{{{\rm{E,ref}}}}} \exp \left[-\frac{{E}_{{{{\rm{a}}}}}}{{k}_{{{{\rm{B}}}}}}\left(\frac{1}{T}-\frac{1}{{T}_{{{{\rm{ref}}}}}}\right)\right],$$
(1)

where Ea (eV) is the activation energy of ecosystem respiration, kB = 8.617333262 × 10−5 eV K−1 is the Boltzmann constant, Tref = 10 °C or 283.15 K is the reference temperature and RE,ref (μmol m−2 s−1) is the baseline ecosystem respiration rate at Tref.

We estimated Ea and RE,ref for each model for North America (Fig. 1a) and then also separately for several major biomes (croplands, evergreen needleleaf forests and deciduous broadleaf and mixed forests; Extended Data Fig. 2a) through a linear regression:

$$\ln {R}_{{{{\rm{E}}}}}(T)=\ln {R}_{{{{\rm{E,ref}}}}}-\frac{{E}_{{{{\rm{a}}}}}}{{k}_{{{{\rm{B}}}}}}\left(\frac{1}{T}-\frac{1}{{T}_{{{{\rm{ref}}}}}}\right).$$
(2)

RE values that were negative or close to zero were filtered out. We used all valid monthly, grid-cell-level RE and corresponding temperature values during the period 2007–2010 to estimate Ea and RE,ref for each study domain (North America or individual biomes), accounting for both spatial and temporal variabilities in temperature and RE. This treatment took the assumption of ‘trading space for time’54,90, given the short span of the study period. Note that we did not consider temperature thresholds in the response of ecosystem respiration52 because monthly mean temperature rarely dips below the previously identified low temperature threshold (−24.8 °C) and most models do not show a discontinuity above the high temperature threshold (15.1 °C) in the study domain.

The Q10 formulation expresses respiration as an exponential function of temperature, that is, a linear relationship between \(\ln {R}_{{{{\rm{E}}}}}\) and T. Hence we linearized \(\ln {R}_{{{{\rm{E}}}}}\) against T to obtain the apparent Q10 as a function of Ea and T to aid interpretation of estimated Ea values in the context of reported Q10 values in the literature:

$${Q}_{10}\left({E}_{{{{\rm{a}}}}},T\right)=\exp \left(\frac{\partial \ln {R}_{{{{\rm{E}}}}}}{\partial T} {\Delta T}_{10}\right)=\exp \left(\frac{{E}_{{{{\rm{a}}}}}}{{k}_{{{{\rm{B}}}}}{T}^{2}}{\Delta T}_{10}\right),$$
(3)

where ΔT10 = 10 K. For example, at T = 283.15 K (10 °C), Ea = 0.65 eV is equivalent to an apparent Q10 of 2.6 (Extended Data Fig. 5).

Optimizing the temperature sensitivity of respiration

Observations of atmospheric CO2 concentrations are sensitive to net CO2 fluxes from large regions (106 km2) (ref. 91) and thus provide top-down constraints on carbon flux estimates for large biomes and continental regions73,92,93,94,95,96, provided that atmospheric transport is adequately resolved to link fluxes to observed concentrations. While atmospheric CO2 observations can inform the mass balance and space–time variability of net carbon fluxes, they lack direct component-level constraints on photosynthesis and respiration. Consequently, TBM-based estimates97 or photosynthetic proxies9,98 have been needed to separately inform estimates of photosynthesis and respiration from atmospheric CO2 observations.

Here we optimized the continental- and biome-scale temperature sensitivity of ecosystem respiration for individual models by maximizing the consistency between transported signals of ecosystem respiration from bottom-up models and the components of space–time variability in CO2 concentrations caused by ecosystem respiration (Extended Data Fig. 2).

To do so, atmospheric measurements of CO2 mixing ratio during 2007–2010 were obtained from 44 tall towers across North America, sourced from the ObsPack CO2 GlobalViewPlus v3.2 data product56,99. We used three hourly averaged CO2 measurements centred in the afternoon (15:00 local time for most sites and 16:00 or 17:00 for a few remaining sites). From these measurements, we subtracted background CO2 values and fossil fuel influences (FFDAS v2 (Fossil Fuel Data Assimilation System version 2)) (ref. 100) to derive the net influence of terrestrial biospheric carbon fluxes on atmospheric CO2 mixing ratio. The resulting observations of CO2 depletion or enhancement were then filtered to remove influences from non-terrestrial fluxes or data points that showed a large model–data mismatch. In sensitivity analyses, we also subtracted the influence of lateral fluxes obtained from the Global Stocktake data product101,102,103,104 (Supplementary Notes 2). We then removed the influence of GPP on atmospheric CO2 observations in the same way. This yielded the respiratory component of the space–time variability in atmospheric CO2 observations. Because biomass-burning emissions (~0.06 Pg C yr−1) (ref. 105) were minor compared with NEE over North America (−0.7 Pg C yr−1) (ref. 95) during the study period (2007–2010)—and certainly dwarfed by model spread in ecosystem respiration—influences from biomass-burning emissions on the temperature sensitivity of ecosystem respiration were not considered.

Sensitivities of CO2 mixing ratio measurements to surface fluxes, also known as transport footprints, were produced from high-resolution (10 km for temperate North America and 40 km for tropical and high-latitude North America) WRF–STILT (Weather Research and Forecasting – Stochastic Time Inverted Lagrangian Transport) model runs106 and post aggregated to a 1° × 1° resolution as part of the CarbonTracker–Lagrange project (https://gml.noaa.gov/ccgg/carbontracker-lagrange/). The potential transport error is demonstrably minor relative to the spread in TBM flux estimates107,108.

We then calculated the adjustments to the temperature sensitivity (Ea) and the baseline respiration rate (RE,ref) by minimizing the mismatch between the transported signal of model estimates of ecosystem respiration and the respiratory component of atmospheric CO2 variability. The original estimates of ecosystem respiration (RE, equation (1)) were adjusted as follows:

$${R}_{{{{\rm{E}}}}}\!^{* }={R}_{{{{\rm{E}}}}} \alpha \exp \left[-\frac{{{\Delta }}{E}_{{{{\rm{a}}}}}}{{k}_{{{{\rm{B}}}}}}\left(\frac{1}{T}-\frac{1}{{T}_{{{{\rm{ref}}}}}}\right)\right],$$
(4)

where \({R}_{{{{\rm{E}}}}}\!^{* }\) (μmol m−2 s−1) is the adjusted estimate of ecosystem respiration, ΔEa (eV) is the adjustment to Ea needed to minimize the mismatch and α > 0 is a dimensionless scaling factor for the baseline respiration rate.

Like the original estimates of Ea, the adjustments ΔEa were estimated over the North American domain and for major biomes. The parameter α accounted for the adjustment to the magnitude of ecosystem respiration (Extended Data Fig. 7), thereby allowing the bias from temperature sensitivity and that from the seasonal cycle amplitude to be separately constrained.

To obtain an estimate of the overall optimal Ea for North America (and for individual biomes) across models, we fitted linear relationships between ΔEa adjustments and the original Ea estimates for individual models using the orthogonal distance regression. Orthogonal distance regression was used because it accounts for errors in both the regressor and the response109. The fitting was performed using the SciPy ODR function110,111. An optimal value of Ea, that is, \({\hat{E}}_{{{{\rm{a,opt}}}}}\) was derived at the intersection of ΔEa = 0 and the best fit line for each domain (North America or individual biomes; Fig. 2).

Evaluating carbon flux estimates using observations

We used in situ measurements of atmospheric CO2 mixing ratio and the transport footprints to determine the extent to which regional-scale estimates of GPP and NEE are consistent with observations. As in Sun et al.73, we calculated the transported signal of GPP or NEE estimates for each individual model and assessed how well the transported signal explains the biospheric component of the observed CO2 space–time variability using the coefficient of determination (R2).

We used the explanatory power of shortwave radiation, \({R}^{2}_{{{{\rm{SW}}}}}=0.23\), as a minimum benchmark to exclude a small subset of models with very low explanatory power (N = 3) from the subsequent analysis on ecosystem respiration. Shortwave radiation data were obtained from the North American Regional Reanalysis data89. Because shortwave radiation is a first-order climatic driver of GPP112 and influential in determining NEE space–time variability113, we would expect carbon flux estimates to explain at least as much portion of observed atmospheric CO2 variability as the shortwave radiation.

Evaluating temperature sensitivity-corrected NEE estimates

We assessed how updating the temperature sensitivity of respiration (‘Optimizing the temperature sensitivity of respiration’) impacted the explanatory power of NEE estimates.

To do so, we adjusted ecosystem respiration estimates for each model according to the optimal ΔEa and α derived for that model in the optimization procedure (equation (4)). Note that correction to the baseline respiration rate through α changes the mean ecosystem respiration magnitude (equation (4)), which avoids erroneously adjusting the temperature sensitivity in response to a bias in overall magnitude.

In a second analysis, we instead adjusted Ea of all models to the optimal value over North America (\({\hat{E}}_{{{{\rm{a,opt}}}}}=0.43\) eV) estimated from the model ensemble. The adjustment of RE was conducted by multiplying RE by the temperature sensitivity adjustment, \(\exp (-\frac{{{\Delta }}{E}_{{{{\rm{a}}}}}}{{k}_{{{{\rm{B}}}}}T})\), followed by rescaling the magnitude to conserve the mean RE. We also capped the adjusted RE at its original maximum value \(\max ({R}_{{{{\rm{E}}}}})\) within a relative tolerance level (≤1%) to prevent unrealistically high values being produced by the exponential function.

The performance of the two sets of adjusted NEE estimates in explaining the space–time variability in atmospheric CO2 measurements was evaluated using the same approach as described in the previous section.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.