Deciduous forests use carbon more efficiently than evergreen forests

doi:10.21203/rs.3.rs-3989566/v1

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Deciduous forests use carbon more efficiently than evergreen forests

https://doi.org/10.21203/rs.3.rs-3989566/v1

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Terrestrial ecosystems have been serving as a strong carbon sink that offsets one quarter of anthropogenic CO₂ emissions. Carbon use efficiency (CUE), the percentage of photosynthesized carbon that is available for biomass production and other secondary carbon products, is one factor determining the carbon sink size. The global variation in CUE remains unclear, however, as recent reports disagree over the responses of CUE to temperature, dryness, forest types and stand age, and there are limited direct observations to constrain the related uncertainty. Here, we propose to infer CUE from spatially distributed observations of land-atmosphere CO₂ exchange from global eddy covariance sites based on first principles of ecosystem respiration - photosynthesis coupling. Across 2737 site-years, CUE derived from eddy covariance observations is 0.43 ± 0.11, consistent with previous inventory-based estimates (0.46 ± 0.12, n = 244) but with a better representation of spatial-temporal variation in CUE. We find that CUE consistently decreases with temperature, precipitation, light availability and stand age, with a significant difference in the baseline CUE among biomes. Importantly, CUE of deciduous forests is typically 15% higher than that of evergreen forests, suggesting that over long-term deciduous forests are more efficient in using photosynthate. Our study advances the understanding of the global variation in CUE and provides new insights to guide best practices of forest conservation, management, and restoration for carbon sequestration.

Earth and environmental sciences/Ecology/Climate-change ecology

Earth and environmental sciences/Biogeochemistry/Carbon cycle

Forest conservation and restoration are the most cost-effective nature-based solutions for climate change mitigation ^1–3, as protected old-growth trees and newly planted trees can remove CO₂ from the air and fix it into biomass in their lifetime. Many global and regional initiatives, such as Reducing Emissions from Deforestation and Degradation (REDD+) ⁴ and the Trillion Tree Campaign ⁵, are leveraging the carbon fixation ability of trees to offset part of the anthropogenic CO₂ emissions. Successful implementations of forest conservation and restoration initiatives require knowledge on how efficient different forests fix carbon. Greater efficiency of forests to fix carbon means a greater likelihood of achieving carbon neutrality goals in a pledged time frame (e.g., mid-21^st century ⁶), and fewer conflicts with land use needed for food production ^2,7 and urbanization ⁸.

Ecological studies have historically used the concept of carbon use efficiency (CUE) – which is more recently updated to biomass production efficiency (BPE) ^9–11 -- to describe the efficiency of forests to fix and store carbon. Trees take up carbon through leaf photosynthesis (denoted as gross primary productivity; GPP) and lose a portion of the fixed carbon due to autotrophic respiration (Ra). The net amount of carbon available for biomass production and other secondary products (i.e., soluble organic compounds and biogenic volatile organic compounds) comes from net primary productivity (NPP = GPP-Ra), and its ratio to GPP is defined as CUE. At the same rate of photosynthetic assimilation, a higher CUE often indicates faster accumulation of biomass and production of other secondary products. Previous studies have suggested that global CUE converges to a constant around 0.47 with little variation (± 0.04; mean ± standard deviation, n = 12) ¹², though this notion has been challenged recently ¹³, as regional and global syntheses have reported that CUE varies considerably due to physical (i.e., climate, soil fertility) ^9,10, biological (i.e., biome type, stand age) ^14–17 and management ^11,18 factors. While these studies reveal substantial variation in CUE, they differ in the inferred responses of CUE to temperature ^10,19–21, dryness ^10,22,23 and biome types ^9,11,14,15, leading to conflicting interpretations of the global variation in CUE.

This lack of understanding of CUE variation hinders our ability to predict the land carbon sink ^22–25 and calls into question whether current conservation and reforestation practices are optimal for mitigating climate change. Part of the difficulty stems from the scarcity of direct CUE observations, as globally we only have ~250 CUE records to represent its variation so far ¹⁰, mostly because of the difficulties related to continuous measurements of NPP or Ra. In this study, we propose to fill the knowledge gap by leveraging distributed and high-frequency carbon flux observations of the land surface from a global network of eddy covariance towers. Using first principles of the coupling between plant photosynthesis and respiration and recent theoretical advances in estimating Ra ¹⁷, we develop a novel method to estimate CUE for more than 2700 site-years of observations across diverse biomes and climates worldwide (see Methods). The newly derived CUE dataset enables us to examine the spatiotemporal variation in CUE and its dependence on biotic and abiotic factors. Furthermore, we use the international tree ring data bank (ITRDB) to investigate changes in basal area increment (BAI) across various tree species ²⁶ and infer the relative magnitude of CUE among biomes. Using these new data sources and methods, we map the spatial variability of global CUE, which is a critical element in guiding best practices of forest conservation and restoration for effective and efficient offset of CO₂ emissions.

Across biomes and years, the CUE derived from eddy covariance observations (CUE_EC) was 0.43 ± 0.11 (mean ± one standard deviation), comparable to the CUE estimated based on inventory data (CUE_IN), which was 0.46 ± 0.12 (Fig. 1a). When comparing CUE_EC and CUE_IN across nine sites that have both records, we found that the two metrics were similar at seven sites, aligning closely along the 1:1 line (Fig. 1b). While CUE_IN is only available for forest types (n = 244), CUE_ECis available for both forest biomes (n = 1365) and non-forest biomes (n = 1372). The CUE_EC of forest biomes was 0.41 ± 0.11, significantly lower (p < 0.01; one-way ANOVA) than the CUE_EC of 0.45 ± 0.12 for non-forest biomes (Fig. 1a). Among the non-forest biomes, which include grasslands (GRA), wetlands (WET), shrublands (SH), savannas (SAV) and croplands (CRO), SAV had significantly lower (p < 0.01) CUE_EC(CUE_EC = 0.32 ± 0.12) than other non-forest biomes (CUE_EC = 0.46 ± 0.11).

Among forest biomes, we noticed that the CUE_ECof deciduous broadleaf forests (DBF) was 0.46 ± 0.10, significantly higher (p < 0.01) than other forest types, such as evergreen needleleaf forests (ENF; CUE_EC= 0.39 ± 0.10) and evergreen broadleaf forests (EBF; CUE_EC = 0.32 ± 0.12). In total, CUE_EC of DBF was 15% greater than that of evergreen forests. Across all biomes, CUE_EC of DBF was among the largest, trailing slightly behind those of CRO (CUE_EC = 0.50 ± 0.09). Inventory data also showed a relatively higher CUE_IN of DBF (CUE_IN = 0.49 ± 0.13) than other forest types (CUE_IN = 0.45 ± 0.11), though the difference was not statistically significant, unlike the difference in CUE_EC.

We further used an independent metric - paired basal area increment (pBAI) of deciduous trees and evergreen trees at the same site - as a proxy for the relative difference in CUE between DBF and ENF (see Methods). pBAI greater than 1 indicates that the CUE of DBF is greater than that of ENF. Despite the wide range of pBAI estimates, especially for young stands, the average of pBAI was consistently greater than 1 across all stand ages, further confirming the CUE of DBF is greater than that of ENF. Across all stand ages, pBAI averaged to 1.09, suggesting that the CUE of DBF was 9% greater than ENF, which was consistent with the relative difference in CUE_ECbetween DBF and ENF.

Using the newly derived CUE_EC estimates, we applied a linear mixed effect model to quantify the impacts of various biotic and abiotic factors on CUE (see Methods). We found that CUE decreased significantly (p < 0.01) with mean annual air temperature (MAT) and mean annual precipitation (MAP), and insignificantly (p = 0.48) with mean annual photosynthetically active radiation (PAR). CUE also decreased with stand age (p = 0.50), though its impact was not significant (Fig. 2a-e). One significant contributor to CUE variability is the inherent difference in baseline CUE associated with each biome, revealing that CRO, DBF, and GRA exhibit greater CUE compared to other plant functional types (PFTs) (Fig. 2e). In particular, the baseline CUE of DBF was 0.10 and 0.08 higher than that of EBF and ENF, respectively, accounting for almost all the observed differences in CUE between DBF and other forest types (Fig. 2e).

The newly derived CUE_EC allows the calculation of NPP from GPP, and further enables us to partition the ecosystem respiration (Reco) into Ra and heterotrophic respiration (Rh) at eddy covariance sites. We found that for all PFTs, areas sampled by eddy covariance sites act as carbon sinks, with GPP exceeding Reco by 10-50% on average (Fig. 3a). Upon partitioning Reco into Ra and Rh components, our analysis revealed that Rh was typically smaller than Ra at eddy covariance sites. On site-year average, Rh was about 39 ± 10% (mean ± one standard deviation), 31 ± 11%, 45 ± 10%, 41 ± 10%, 45 ± 11%, 32 ± 12%, 44 ± 10%, 45 ± 11% and 50 ± 9% of Reco for ENF, EBF, DBF, MF, SH, SAV, GRA, WET and CRO, respectively.

We also examined the relationship between CUE and the key parameters determining Ra ¹⁷(see Methods), including the coefficient of growth respiration (g_R; unitless), the fraction of live biomass turned into non-respiratory biomass per unit time (𝜏; unitless) and the temperature sensitivity of maintenance respiration (E_a; eV). These parameters were concurrently derived alongside CUE using our method (see Methods). We found that CUE was negatively related to g_R, while g_R was constrained in a narrow range from 0.2 to 0.22. With a 0.01 increase in g_R, CUE decreased by 0.13. Meanwhile, 𝜏, a factor determining how fast live biomass turns into non-respiratory materials (e.g., sapwood to hardwood), was positively related to CUE. 𝜏 predominantly falls within the range of 0.7 to 0.9 across various PFTs. Swift turnover, indicated by a higher 𝜏, suggests a reduced respiratory cost to maintain live biomass, leading to a corresponding increase in CUE. Finally, we observed a positive association between E_a and CUE, with the average site-year E_a = 0.35 ± 0.15 eV. This implies that for the site-years where maintenance respiration is less responsive to temperature (i.e., lower E_a values), more carbon is likely lost through maintenance respiration, thereby reducing CUE

We generated a global map of CUE by utilizing a random forest model trained by CUE_EC (see Methods). Our estimates of CUE ranged from 0.3 to 0.6, with a clear latitudinal gradient - increasing from the tropics to high latitudes (Fig. 4a). For more than 50% of the global vegetated land surface, CUE converged in a relatively small range between 0.4 and 0.5. Meanwhile, the CUE derived from an ensemble of dynamic global vegetation models (DGVMs) exhibited a similar latitudinal gradient, though with a broader distribution, ranging from 0.3 to 0.7 (Fig. 4c). Notably, the CUE estimated from DGVMs showed substantial spread across models (Fig. 4d and S5), with an average uncertainty of 0.15 (i.e., one standard deviation of DGVMs CUE) and the largest uncertainty of 0.21 in the high latitudes. Meanwhile, the uncertainty from CUE estimated from the random forest was spatially homogeneous and generally less than 0.05 (Fig. 4d).

In this study, we leveraged a global network of eddy covariance sites to estimate CUE and revealed that CUE averaged 0.43 ± 0.11 across 2737 site-years. We then analyzed the biotic and abiotic factors responsible for the global variation in CUE. Among these factors, plant functional types (PFTs) emerged as the pivotal contributor to CUE variability, with deciduous broadleaf forests exhibiting notably higher CUE compared to other forest ecosystems. Meanwhile, non-forest biomes have greater CUE than forest biomes. We found consistently negative impacts of temperature, radiation, rainfall and stand age on CUE. Based on the CUE we obtained from eddy covariance data, we further partitioned ecosystem respiration into heterotrophic and autotrophic components, and estimated the global pattern of CUE.

1. Reasons for differences in CUE between PFTs

Previous studies have examined whether and how CUE varies by PFT. While some found no discernible distinction in CUE among PFTs ¹¹, others identified substantial differences ¹³. However, these studies have not reached a consensus regarding the specific impact of PFTs on CUE. For instance, temperate deciduous forests have been reported to have either greater CUE ^13,14 or lower CUE ¹⁵ than boreal forests. Importantly, our findings indicate that DBF exhibits a significantly (p < 0.01) higher CUE than other forest ecosystem types. This finding aligns with previous research demonstrating that deciduous trees tend to grow at a faster rate than evergreen trees in similar climatic conditions ²⁷ - with similar input of photosynthesis, the faster biomass growth implied a higher CUE of deciduous trees.

From a physiological perspective, the higher CUE was jointly determined by lower g_R and higher 𝜏 (Fig. S4). The lower g_R means the carbon cost of DBF building new tissues and components is less than other forests. This difference may manifest in the form of a lower leaf mass per area in DBF compared to other forest ecosystems ^28,29. Meanwhile, higher 𝜏 indicates that there is less live biomass to incur maintenance respiration for DBF than for other biomes.

Our study also examined the CUE of non-forest types, which lacks observations previously as inventory-based CUE studies were biased towards forests. We reported significantly (p < 0.01) higher CUE for non-forests than for forests, except the low CUE of the savanna ecosystems. The generally higher CUE of non-forests is likely caused by the low carbon stocks and fast turnover rate of their live biomass (Fig. S4), and thus less maintenance respiration. CRO has the highest CUE, reflecting the selection of productive varieties for efficient biomass accumulation (a.k.a., crop yield) and better management ^11,30. Consistent with our results, a study using an emergent constraint approach to estimate CUE also reported greater CRO CUE (i.e., CUE = 0.55) than forests ¹⁵. Interestingly, we found that SAV demonstrates significantly (p < 0.01) lower CUE than other herbaceous species (Fig. 1a), potentially reflecting the high energy and carbon costs of C₄ photosynthesis pathway compared to the more prevalent C₃ pathway in temperate grasslands. Some leaf-level studies indicated that C₄ plants show higher dark respiration rates than C₃ plants ³¹, implying a higher respiratory need for C₄ and therefore a lower CUE. This high demand of respiration of C₄vegetation is also indicated by the great g_Rvalues of savanna ecosystems (Fig. S4). Meanwhile, we also hypothesize that the warm and dry conditions associated with the growth of C₄ grasses ^32,33 may suppress photosynthesis and enhance respiration, potentially resulting in a lower CUE for savanna ecosystems compared to other ecosystems.

2. Climate, soil, and stand age impacts on CUE

Other than PFTs, we found CUE is also impacted by climate (i.e., temperature, precipitation, and light) and stand age. CUE derived from eddy covariance exhibited a linear decline with stand age, although this trend was not statistically significant (p = 0.50). This finding aligns with outcomes reported in earlier research studies ^10,14. However, we noted that a linear model might not be the most suitable way to describe the CUE - stand age relationship, since our estimated CUE generally increased with stand age up to ~30-50 years, and then gradually decreased after the peak (Fig. 2a). A few studies have noted this non-linearity in the CUE - stand age relationship ^10,16,34. Considering that GPP is not as sensitive to stand age as NPP ³⁵, we hypothesize that the non-linear association between CUE and stand age suggests an initial rise in NPP with increasing stand age followed by a subsequent decline as in Odum’s ecological theory. In fact, this pattern has previously been documented for the primary tree species in the continental United States ³⁶.

Prior studies utilizing survey data have reported a positive impact of soil N content on CUE ^9,21, as nutrient limitation may hinder photosynthesis and biomass production or demand stronger metabolic activities (i.e., respiration) for nutrient acquisition. In our attribution analysis (Fig. 2), we did not include soil N as an explanatory factor, as the soil N extracted from Soilgrids for eddy covariance sites demonstrated large biases when validated against the observed soil N (Fig. S8), and the statistical performance of our attribution model declined after including soil N (Table S1). If we indeed include soil N in our attribution analysis (Fig. S7), a positive impact of soil N on CUE_ECwas detected, consistent with the previous understanding. The increase of CUE with soil N also seems nonlinear, with CUE steeply increasing with soil N under low nitrogen conditions, and plateauing when soil N is greater than 0.02 g N/kg (Fig. S7f).

The negative impacts of climate variables on CUE collectively signify that under warmer, wetter, and brighter conditions, a greater portion of photosynthate is lost through Ra (Fig. 2). Increasing temperatures are expected to enhance Ra, while their effect on GPP can be either positive or negative. If there is a decline in GPP or if the rise in Ra outpaces that of GPP, it is plausible that rising temperatures could result in a decrease in CUE ¹⁹. It is worth noting that the response of CUE to temperature we observed differs from those reported in a recent synthesis ¹⁰. We speculate that this difference may arise from three potential factors:

1) the previous synthesis omitted PFTs as an explanatory variable. Given that PFTs are influenced by climate variations and play a significant role in CUE dynamics, the absence of PFTs could potentially alter the CUE-MAT relationship. For example, we attributed the low CUE in the boreal zone to the presence of ENF, which has a lower CUE baseline than temperate DBF (Fig. 2f). However, if ENF is not accounted for in our attribution analysis, the low CUE in the boreal zone may be attributed to low temperature, thus resulting in a positive CUE-MAT relationship.

2) the shift of CUE-MAT relationship with MAT. We analyzed the univariate regressions of CUE_IN and CUE_EC against MAT, and found both CUE_IN and CUE_EC exhibit a change in their relationship with MAT around 10°C (Fig. S6). Specifically, when MAT is less than 10°C, CUE_IN increases with MAT, and CUE_EC only slightly decreases with MAT. However, when MAT exceeds 10°C, both CUE_IN and CUE_EC decrease rapidly with MAT. The shift indicates that the positive impact of MAT on CUE_IN reported in the previous synthesis may primarily arise from the CUE records obtained under low temperatures. The shift in CUE-MAT relationship around 10°C, identified by both CUE_IN and CUE_EC, merits further examination (Fig. S6).

3) Thermal acclimation of respiration. Experiment evidence has suggested that thermal acclimation - the declines of base respiration rate or the temperature sensitivity of respiration with the increase of growth temperature - could impact CUE ^37,38. While the exact impact of growth temperature on CUE is still subject to debate, it is conceivable that CUE may increase with MAT if GPP increases with growth temperature while the increase of Ra is mitigated by thermal acclimation³⁹. This seems to be consistent with our point 2) above where the increase of CUE with temperature is noted predominantly within the low temperature range. Additionally, we found that E_a (i.e., the temperature sensitivity of maintenance respiration) decreases with MAT (Fig. S6c), providing further evidence for the existence of temperature acclimation of respiration across global eddy covariance sites.

Water availability directly impacts GPP, as water deficits lead to the downregulation of stomatal openness ⁴⁰ and light use efficiency ⁴¹. However, the decrease in GPP may not translate into a decrease in NPP or CUE during droughts ²². In fact, forests are likely to experience a decrease in biomass residency time (i.e., high tree mortality rate) and then a decrease in Ra, ultimately leading to a CUE increase during droughts ²². This mechanism offers a plausible explanation for the negative relationship observed between CUE and precipitation (Fig. 2) and is in line with the notably lower 𝜏 values found in the case of wet EBF compared to other forest types (Fig. S4).

The influence of light on CUE has received less attention. Nonetheless, the synthesis study we mentioned ¹⁰ did find a positive correlation between latitude (i.e., equivalent to a negative impact of light availability) and CUE. One plausible mechanism is that leaves tend to incur higher construction costs in regions with greater light intensity ⁴², which can result in higher g_R and consequently lower CUE. In alignment with this mechanism, our investigation revealed that EBF and SAV in low-latitude regions exhibit significantly higher g_R values (p < 0.01) compared to the global average (Fig. S4).

3. The interpretation of CUE derived from eddy covariance observations

Our method of deriving CUE assumes that there is a strong coupling between Reco and GPP (Fig. S1), and within a short period of similar temperature in the growing season, variations in Reco are predominantly influenced by changes in Ra. Given that we initially determined Ra and then subtracted it from GPP to represent NPP, our NPP estimates encompass not only the carbon available for building biomass but also the carbon utilized in nonstructural and secondary carbon compounds (i.e., reserves, root exudates, biogenic volatile organic compound). Those secondary carbon products might use a considerable part of photosynthate ^43,44. Therefore, our estimate of CUE (i.e., NPP/GPP) would be greater than the narrowly defined biomass production efficiency (BPE) ¹³. With the strong dependence of maintenance respiration on temperature ¹⁹, it is also anticipated that CUE will exhibit seasonal fluctuation. While our method allows the derivation of seasonal CUE (Fig. S3), we did not explore its variation as we lack independent observations to validate seasonal CUE, and the environmental dependences of CUE at the seasonal scale might be different to those at the interannual scale.

During our validation of CUE_EC against CUE_IN, we observed good agreement between the two metrics at seven out of the nine sites (Fig. 1b). Nevertheless, at one site (i.e., CA-TP2), we observed that CUE_EC was considerably greater than CUE_IN, and at another site (i.e., US-MMS), CUE_EC was lower than CUE_IN. CA-TP2 is one of the pine plantation sites (i.e., CA-TP1, CA-TP2, CA-TP3, CA-TP4) distributed along a stand age gradient in Southern Ontario, Canada. The stand ages for the four sites were 5, 18, 33, and 68 in 2007 ⁴⁵. Our derived CUE_EC for the four sites were 0.62, 0.58, 0.54, and 0.35, respectively, demonstrating a clear negative CUE-stand age relationship. Meanwhile, CUE_IN for the four sites were 0.57, 0.31, 0.51, 0.44, with CA-TP2 deviating from the negative CUE-stand age relationship. Given the similar species, climate, topography, and soil conditions across the four sites, with stand age being the primary differing factor, we posit that our estimate of CUE_EC at CA-TP2 might provide a more accurate reflection of CUE than CUE_IN. US-MMS is a diverse deciduous forest (i.e., including 29 tree species) in southcentral Indiana, USA ⁴⁶. The CUE_IN reported there was 0.70 and the CUE_EC was 0.48. We noted that the biometric measurements for CUE_IN derivation were mostly conducted in plots within 200m of the tower ⁴⁷, while the footprint climatology of the US-MMS tower extending to 500m in daytime, especially the southwest fetch was underrepresented by the plots ⁴⁸. Considering the diverse species composition and variable topography of this site, the discrepancy in spatial representativeness between the plots and flux footprint could potentially account for the disparity between CUE_IN and CUE_EC.

4. Implications for land carbon sink

Land carbon sink has been increasing proportionally to human emissions of CO₂ and playing a critical role in climate change mitigation. The increase in land carbon sink has been largely attributed to elevated CO₂ ^49,50, changes in other environmental variables ⁵¹ and natural regrowth after disturbance ^52,53, meanwhile, the impact of shift in vegetation biomes on carbon uptake has been rarely studied though large-scale biome shifts have been reported as the expansion of deciduous trees in boreal zones ⁵⁴ and savannas ⁵⁵. Our study indicates that the shift in biome types would potentially impact land carbon sink by changing CUE. Moreover, the disparities in CUE among biomes carry significant implications for large-scale tree-planting initiatives and forest management strategies. While the restoration of native trees and natural forest regrowth is advocated as the optimal approach for forest restoration ^56,57, our findings suggest that we could enhance the carbon use and the land carbon sink more effectively by prioritizing native DBF species given a fixed amount of GPP, particularly in regions where deciduous and evergreen trees coexist.

In summary, our study offers a timely and critical insight into the variability of global CUE. It advances our understanding of the terrestrial carbon cycle by employing a new method to derive advanced ecological metrics (e.g., CUE) from eddy covariance data. It offers valuable guidance for the implementation of reforestation, afforestation, and conservation plans aimed at optimizing the land carbon sink's potential.

1. Theoretical basis to estimate CUE from eddy covariance observations

We used eddy covariance observations of CO₂ flux between ecosystems and the atmosphere provided in the standard FLUXNET2015 dataset ⁵⁸, as well as the flux data acquired from Ameriflux and ICOS, processed by the FLUXNET2015 pipeline. The pipeline to produce the data includes the quality control of raw flux data and the partitioning of the net CO₂ exchange into GPP and Reco. Our main analysis used the GPP and Reco values based on the daytime partitioning method (GPP_DT_REF and Reco_DT_REF), though we have also tested GPP and Reco from the nighttime partitioning method and got similar results (Fig. S2).

According to the definition of CUE, CUE = (GPP-Ra)/GPP = 1 – Ra/GPP. Between any two timestamps, we can obtain:

ΔRa = (1-CUE) × ΔGPP (Equation 1)

in which we assume CUE to be constant between the two timestamps. Meanwhile, we further expanded autotrophic respiration (Ra) to growth respiration (R_G) and maintenance respiration (R_M). R_G is the cost of producing new biomass (G) and R_M is the cost of maintaining the existing biomass (W_live). Therefore, R_G and R_M can be further expanded to the product of their respective respiration coefficients (g_R and m_R) and biomass amounts (G and W_live)¹⁷, leading to Equation 2 below:

Ra = R_G+R_M = g_RG+m_RW_live(Equation 2)

Substituting Equation 2 into Equation 1, the change in Ra between two timestamps can be described as ΔRa = g_RΔG+m_RΔW_live. The change in new biomass growth (ΔG) is proportional to the change in NPP between two timestamps (ΔNPP = ΔGPP × CUE). The changes in live biomass (ΔW_live) that needs maintenance are proportional to the accumulated NPP between the two timestamps ΔcNPP = ΔcGPP×CUE×(1-𝜏), where cNPP and cGPP are the cumulative NPP and GPP from day one of the year, respectively. 𝜏 represents the fraction of live biomass turned to non-respiratory biomass per unit time. Therefore, we can adjust the Equation 2 to:

ΔRa = g_R×CUE×ΔGPP + m_R×CUE×ΔcGPP×(1-𝜏) (Equation 3)

Note that in equation 3, we assume all ΔGPP × CUE between the two timestamps is used for growth, neglecting the carbon allocated for root exudation or symbiosis of mycorrhizal. This assumption would not affect the estimation of CUE, but may lead to an overestimation of g_Rif carbonallocated for non-growth purposes is significant between the two timestamps.

Since m_R has a strong temperature dependence¹⁹ and changes substantially within a year, to facilitate the comparison between site-years we further include the temperature sensitivity of maintenance respiration (i.e., E_ain eV, the Arrhenius activation energy for respiration) into equation 3:

ΔRa = g_R×CUE×ΔGPP + e^(-E^a^/K^B^)(1/T-1/T⁰⁾ ×m_R0×CUE×ΔcGPP× (1-𝜏) (Equation 4)

where m_R0refers to the baseline m_R of the site-year and T₀(in K) is the temperature corresponding to m_R0. T is the mean temperature of the temperature bin. K_B = 8.617333262 × 10⁻⁵ eV K⁻¹ is the Boltzmann constant.

We further used two criteria to organize daily flux data for the derivation of CUE - 1) we grouped flux observations using windows of 5 consecutive days in the growing season, and 2) we grouped flux observations by daily mean temperature (i.e., the difference in temperature) should be less than 1 °C and remove the days with rainfall greater than 2 mm/day to avoid sudden pulses of respiration after rewetting the soil (e.g. Birch effect) ^59,60. The criteria are to ensure there are limited changes in soil organic matter (i.e., majority of the soil organic matter have turnover time longer than a week) and no changes in Rh under similar temperatures. Therefore, we can regard ΔRa = ΔReco in these data groups. A side effect of these criteria is relevant to the interpretation of the results. The criterion 1) assumes there are limited changes in the biomass of leaf and fine roots within the short time window (i.e., 5-day), therefore the estimated m_R and 𝜏 mostly reflect the characteristics of live biomass in stems, branches and coarse roots where most biomass is stored ⁶¹.

2. The workflow to estimate CUE from eddy covariance observations

Following the theoretical basis above, we designed the following workflow to estimate CUE, g_R, 𝜏 and E_a for each site-year (Fig. S3):

Step 1. Organize daily flux data in the growing season into groups of 5 consecutive days. Within each 5-day window, we obtained ΔGPP, ΔRa and ΔcGPP between every two days. For example, if in a 5-day window the daily GPP are 1.1, 1.2, 1.3, 1.4, 1.5 g/m²/day, then the ΔGPP between day 5 and day 1 would be 1.5 – 1.1 = 0.4, and the ΔcGPP between day 5 and day 1 would be (1.1+1.2+1.3+1.4+1.5) – 1.1 = 5.4.

For each time window, we got approximately 20 samples of ΔGPP, ΔRa and ΔcGPP. The growing season was defined as when daily GPP was above 20% of the maximum daily GPP of the site-year.

Step 2. Apply the data obtained in step 1 to equations 1 and 3, and estimateCUE, g_R, 𝜏 and m_Rfor each 5-day time window. In this step, since we have 20 samples and 4 unknown parameters, we used the Markov Chain Monte Carlo (MCMC) method ⁶² to estimate the optimal values of CUE, g_R, 𝜏 and m_Rfor each 5-day time window. When running MCMC, the prior of variables for CUE, g_R, m_R and 𝜏 were set within the ranges of (0, 1), (0.15, 0.3), (0.0, 0.5) and (0 1), respectively.

Step 3. Obtain m_R0 and T₀ for the site-year, where m_R0is the bottom ten percentile of the m_Rvalues of all 5-day windows in the site-year (from step 2). T₀is the mean temperature corresponding to m_R0. We used the bottom ten percentile to avoid obtaining an extreme m_R0value which is not representative of the ecosystem.

Step 4. Obtain g_R and 𝜏 for the site-year, where g_R and 𝜏 are the average g_R and 𝜏 of all 5-day windows (from step 2). The step aligns with the observations that g_Rhas a small range based on the construction cost of key chemicals in plants and should have limited seasonality ^42,63. There were no previous reports on the seasonality of 𝜏, therefore we assume that it is also a constant for each site-year.

Step 5. Organize daily flux data by temperature and remove the days with precipitation greater than 2 mm. Within each temperature bin (the range of temperature is less than 1K), we obtained ΔGPP, ΔRa and ΔcGPP between every two days. For each temperature bin, we got approximately 20-200 samples of ΔGPP, ΔRa and ΔcGPP.

Step 6. Apply the data obtained in step 5, the m_R0 and T₀obtained in step 3, and the g_R and 𝜏 obtained in step 4, to equations 1 and 4, and estimateCUE and E_afor each temperature bin. In this step, since we have 20-200 samples and 2 unknown parameters, we used MCMC again to estimate the optimal values of CUE and E_afor each bin. When running MCMC, the prior values for CUE and E_a were set within the ranges of (0, 1) and (0.2 1.5), respectively.

Step 7. Obtain CUE and E_afor the site-year, where CUE and E_a are the average CUE and E_a of all bins from step 6. We acknowledge that while our method provides seasonality of CUE and E_a, we only examined CUE and other parameters at the annual time scale in this study.In total, we obtained 2737 site-years of CUE record for our analysis. We also got the average CUE for each site for validation (Fig. 1b; Table S2).

3. Quantify relative CUE from paired basal area increment (pBAI)

In parallel to CUE, the carbon accumulation rate of individual trees is assessed by another metric - basal area increment (BAI). BAI is indicative of NPP, as NPP allocated to stem, NPP_stem, can be estimated by scaling BAI with stem density (i.e., number of trees per unit area), wood density and tree height. Similar to CUE, many studies have examined BAI and its associated changes in biomass production with abiotic (i.e., temperature ⁶⁴ and droughts ⁶⁵) and biotic factors (i.e., stand age ⁶⁶, tree size ⁶⁷, mortality ⁶⁸, forest types ⁶⁹), however, they often had a regional focus and thus lack global implications. Following these studies, we have:

NPP_stem = BAI × tree height × wood density × stem density (Equation 5)

Meanwhile, we estimated that the CUE for stem is CUE_stem = NPP_stem/GPP, and assume that the difference in CUE_stemis indicativeof the difference in total CUE. To compare the relative difference between the CUE of deciduous trees (DB) and evergreen trees (EV) at the same locations (i.e., similar climate and thus GPP), we have:

CUE_stem__DB/CUE_stem__{EV ~}= BAI_DB/BAI_EV = pBAI (Equation 6)

where pBAI means the paired BAI of DB and EN trees at the same locations. In this study, to obtain pBAI, we used a clean and high-quality version of tree-ring width data from international tree-ring data bank (ITRDB) ²⁶ and estimated BAI from tree-ring width using the functions in an open R package “dlpR”. We classified the trees into DB and EV, based on the species information compiled at https://www1.ncdc.noaa.gov/pub/data/paleo/templates/tree-species-code.txt (accessed in 2021, now archived at https://github.com/lxzswr/CUE_fluxnet/blob/main/tree-species-code.txt). Note the EV trees are mostly evergreen needleleaf trees in ITRDB while evergreen broadleaf trees in the tropics are underrepresented.

4. Ancillary climate, soil and model datasets

For site-level analysis, we used the daily meteorological observations from the eddy covariance datasets. The climate variables we used include air temperature, precipitation and photosynthetic active radiation. The stand age of flux sites is acquired from a previous study⁷⁰ wherever there is a record. For sites lacking stand age data, we sourced the required information from the Global Forest Age Dataset (GFAD v1.1) ⁷¹. The stand age of non-forest biomes is assumed to be 1 in all attribution analyses. We extract the soil total nitrogen content (soil N content) for each flux site from Soilgrids at 250 m resolution ⁷².

We further used the TS4.04 version of monthly gridded air temperature, precipitation, and solar radiation data at 0.5° provided by the Climate Research Unit (CRU) ⁷³, along with the aforementioned GFAD v1.1 stand age dataset and the soil N content from soilgrids, to estimate global CUE using a random forest model (see Section 5 of Methods). All gridded datasets were resampled to 0.5 degree. The gridded climate data were averaged to annual values, including mean annual temperature (MAT), mean annual precipitation (MAP) and mean annual photosynthetic active radiation (PAR).

Meanwhile, we studied the CUE estimated by 15 Dynamic Global Vegetation Models (DGVMs) participating in the TRENDY v9 project in our study ^74,75. For each DGVM, we estimated their CUE as the ratio of mean annual NPP to mean annual GPP from 1980 to 2019 (Fig. S5). The simulations of NPP and GPP were conducted under the S3 scenario (i.e., considering elevated CO₂, climate change, and land use and land cover changes).

5. Linear mixed effect model and random forest model

We used the linear mixed effect (LME) model ⁷⁶ to quantify the sensitivities of CUE to abiotic and biotic factors. LME model suffers less from correlations of samples from similar groups and can quantify the impacts of grouping as the random effect term. This is especially useful in our study to understand the impact of PFTs on CUE, while obtaining the sensitivity of CUE to continuous variables such as climate and soil properties. We tested multiple LME models and selected the one that has the lowest Akaike information criterion (AIC) and Bayesian information criterion (BIC), and considers the major factors found in previous studies (Table S1). The final LME model to estimate CUE was based on MAT, MAP, PAR, stand age, and PFTs, where PFTs were set as a random effect, and the others were fixed effect. The analysis was conducted using the function ‘fitlme’ in MATLAB.

We then trained a random forest model using the 2737 records of CUE_EC and the in-situ variables identified by the LME model as inputs. Subsequently, the random forest model was employed to estimate global CUE using gridded MAT, MAP, PAR, stand age, soil N and PFTs. External validation of the random forest model shows good performance in extrapolating CUE (R = 0.72, RMSE = 0.08). We chose the random forest model as it can utilize both continuous variables (i.e., climate) and categorical variables (i.e., PFT) as inputs, capture the nonlinear dependence of CUE on some variables, and demonstrate stronger statistical performance in predicting CUE compared to LME. The random forest model has been widely used for upscaling in ecology and is often regarded as one of the better performing models ^77–79.

Data availability

This study used openly available eddy covariance measurements provided by FLUXNET2015 dataset (https://fluxnet.fluxdata.org/data/fluxnet2015-dataset/), Ameriflux (https://ameriflux.lbl.gov/introducing-the-ameriflux-fluxnet-data-product/) and ICOS (https://www.icos-cp.eu/data-products). We acquired the global tree ring dataset from the international tree-ring database bank (ITRDB;https://www.ncei.noaa.gov/products/paleoclimatology/tree-ring). The TRENDY v9 DGVM simulations can be requested on the website https://blogs.exeter.ac.uk/trendy/. We will reposit the carbon use efficiency of eddy covariance sites and global carbon use efficiency map at https://zenodo.org/record/XXXX.

Code availability

The code used to support the findings of this study will be publicly available upon publication atwww.github.com/lxzswr/CUE_fluxnet.

Acknowledgement

XL, RZ and LY are supported by the NUS Presidential Young Professorship awarded to XL (A-0003625-03-00) and a Tier 2 Academic Research Fund from Singapore Ministry of Education (MOE-T2EP50222-0006). AC thanks the support from National Recovery and Resilience Plan (NRRP), Mission 4 Component 2 Investment 1.4 - Call for tender No. 3138 of 16 December 2021, rectified by Decree n.3175 of 18 December 2021 of Italian Ministry of University and Research funded by the European Union – Next Generation EU under award Number: Project code CN_00000033, Concession Decree No. 1034 of 17 June 2022 adopted by the Italian Ministry of University and Research, CUP B83C22002930006, Project title “National Biodiversity Future Centre - NBFC”. SF acknowledges the support of Singapore's Ministry of Education (MoE) under its Academic Research Fund Tier 2, Project ID: MOE-000379-00/MOE-000379-01.

Authors contribution

XL designed the study and carried out the analysis. RY aided in producing figures. XL, HC, AC, SF, TFK, NN and ICP participated in discussions at various stages. RY, HC, XLu and LY aided in data collection. All authors contributed to the interpretation of the results and writing.

Competing Interests Statement

The authors declare no competing interests.

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Deciduous forests use carbon more efficiently than evergreen forests

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