Changes in global carbon use efficiency in the 21st century and the potential controlling factors

Extensive studies have demonstrated the spatiotemporal changes in carbon use efficiency (CUE) and its driving factors over the past three decades. However, how the global CUE will change and to what extent the CUE is affected by the dominant factor in this century is still unclear. Herein, based on CMIP6 model outputs, we estimated the situation and change trends of CUE in baseline (1982–2014) and future (2015–2100), and identified the controlling factor of CUE variation by boosted regression tree. Further, we predicted the CUE-controlling factor sensitivity (S value, referring to higher/lower controlling factor producing more/less CUE) and its variation under four representative pathways, and revealed the relationship between S value and social economy. Results showed decreased CUE at the end of the 21st century, especially in the SSP5-8.5, its decline rate of CUE is 1.2 × 10−2 ± 5.2 × 10−4/decade, which is 10 times higher than that in the SSP1-2.6. Spatially, 56.9%, 74.5%, 83.1%, and 88.6% of the global land will exhibit a decreased CUE under the SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5 scenarios, and primarily concentrates at the middle-high latitudes of the Northern Hemisphere (30°–60° N). Except in Africa, temperature is the controlling factor for CUE variation, and the S value decreases over time, indicating an enhanced inhibitory effect of temperature on CUE. The turning time of S value change will advance with increases in CO2 emission, presenting prolonged high-temperature stress of vegetation ecosystem under high-emission scenarios. A threshold effect can be found between S value change and precipitation, and the precipitation threshold is higher under the SSP5-8.5 scenario. The negative effect of temperature on CUE is attenuated by economic development and population control but this effect diminishes with rising CO2 concentrations; in the future, developing clean energy and formulating population management policies can be used to enhance the carbon sink ability of the global ecosystem.


Introduction
Globally, much attention has been paid to terrestrial ecosystem carbon cycling, which is driven by carbon uptake through plant photosynthesis and carbon emission by autotrophic (Ra) and heterotrophic (Rh) respiration.Carbon use efficiency (CUE), defined as the ratio of net primary productivity (NPP) to gross primary productivity (GPP) (Liu et al 2024), is crucial for assessing terrestrial carbon cycling and allocation (Wang et al 2023), reflecting the amount of atmospheric carbon captured by an ecosystem (Tucker et al 2013).Higher CUE values mean more growth per unit of carbon, allowing for increased carbon supply to higher trophic levels, detrital pathways, and ecosystem carbon storage (Bradford and Crowther 2013); conversely, lower CUE values may imply carbon loss (Curtis et al 2005).Initially, studies considered CUE to be a constant around 0.47-0.52(Zhang et al 2009), which has been widely used in carbon cycling models to predict fluxes between the atmosphere and terrestrial ecosystems (Chen et al 2015).However, extensive research has indicated that the assumption of constant CUE is difficult to maintain in the real world because CUE is always affected by environmental factors, stand development, management, and ecosystem types (Ogawa 2011).Until now, CUE has been hypothesized to widely exist in various biological communities, tree species, and forest ages (Waring et al 1998), and has become an effective indicator for developing vegetation growth management strategies to address climate change (Piao et al 2010).
Research on the spatiotemporal change of CUE has aroused heated discussion and satellite remote sensing plays an essential role in the CUE studying at large scales and long-term variation.For instance, Liu et al (2019) revealed a slightly decreased CUE in arid regions, and the CUE varied greatly along the arid gradient; while Xiao et al (2023) found that CUE exhibited an increasing trend from 2000 to 2018 in southwest China karst.Dong et al (2020) mapped the spatial gradients of CUE and delineated the hotspots of non-climatic component-driven CUE.Overall, there are certain differences in the spatiotemporal change of CUE due to the variations in data sources, research periods, and scope.At the end of the 21st century, the change trend of global CUE remains unclear, while addressing global climate change and preserving the stability of vegetative ecosystems depends on this.
After understanding the spatiotemporal change of CUE, the climate has imposed a significant impact on the CUE variation, such as temperature, precipitation, and CO 2 concentration (Dewar et al 1998, He et al 2018).Among them, temperature illustrated a negative effect on CUE in most cases, mainly because the activity of respiratory enzymes increases with rising temperature, so the respiratory function may be enhanced with temperature (Li et al 2019); however, some studies have shown that the correlation may vary across different temperature (Zhang et al 2009).CUE was positively correlated with precipitation, primarily attributed to increased precipitation can enhance photosynthesis by amplifying stomatal conductance and intercellular CO 2 concentration in leaves (Kim et al 2018).CO 2 concentration could affect both photosynthesis and respiration, making its impact on CUE more complex (Drake et al 2019).Later, some studies have shown that CUE variation was closely related to vegetation type, forest age, and soil nutrition (Yao et al 2018, Zhang et al 2019).Now, extensive studies have also emphasized the impact of drought on CUE variation (Gang et al 2019).According to statistics, the frequency of drought events will be 1-3 times higher than before with a global temperature rise of 1.5 • C in the future (Price et al 2022); if global temperatures rise by 3 • C, most of the global vegetation cover land will experience extreme droughts lasting at least one year, which will cause the Amazonian tropical forest at risk of becoming a 'carbon source' (Gatti et al 2021), resulting in biodiversity loss, increased tree mortality, wildfire outbreaks, and ecological disruptions (Huang et al 2017), and aggravating food security and poverty challenges (He et al 2022).These studies have greatly enhanced our understanding of how CUE is affected by climatic forcing or non-climatic components individually, while their comprehensive and interactive effects of these factors on future CUE have been generally less discussed.
Here, we selected eight predicted models from CMIP6 to obtain the mean value of GPP and NPP to calculate CUE and examine the spatiotemporal change trend and heterogeneity characteristics of CUE under historical (1982CUE under historical ( -2014) ) and different future scenarios .Subsequently, we selected eight indexes related to climate and background conditions to identify the controlling factor of CUE variation through the boosted regression tree (BRT).Based on this, we used sequential linear regression slope (SeRGS) to assess the sensitivity of CUE to controlling factor under different future scenarios and related the observed changes of sensitivity to both social and economic stressors, to provide a basis for developing transnational environmental protection and management strategies (figure 1).

Data acquisition and pre-processing
In this study, the data output from four SSP-RCPs scenarios in CMIP6 was used to analyze CUE features during historical and future periods.For this work, 8 models were selected, and their specific information is shown in table 1, elements of the model output include precipitation (kg m −2 s −1 ), temperature (K), 2 m dewpoint temperature (K), total soil moisture content (SM) (kg m −2 ), GPP (kg m −2 s −1 ), and NPP (kg m −2 s −1 ).Meantime, SSP-RCPs is a combined matrix of shared socio-economic pathways (SSPs) and representative concentration pathways (RCPs) containing several scenarios, and this study selected four scenarios from SSP-RCPs, namely SSP1-2.6,SSP2-4.5, SSP3-7.0, and SSP5-8.5.Based on the accessibility of the specified variables and scenarios mentioned above and considering reducing variation in simulated data across different models, the first variant level (r1i1p1f1) was selected.An arithmetic mean of selected model simulation values was calculated based on the Traditional Multi-Model Ensemble Mean (MME) method to reduce the uncertainty of multiple simulations and all data was resampled to 0.5 • × 0.5 • resolution.Meanwhile, non-parametric kernel density was employed to characterize the concurrent behavior of observed data and simulated data to evaluate the precision of CMIP6 data (Bellucci et al 2015).
The GPP dataset was collected from https://data.nal.usda.gov.The NPP from the MODIS product (https://lpdaac.usgs.gov)was employed in this study.The land surface temperature and precipitation dataset were downloaded from https://psl.noaa.gov.The SM dataset was obtained from www.GLEAM.eu.The modeled atmospheric CO 2 concentrations (ppm) dataset spanning 1982-2014 was from www.nesdc.org.cn/ (Cheng et al 2022).All of these gridded datasets covered the period from 2000 to 2014 and they were interpolated to a resolution of 0.5 • × 0.5 • .
The vegetation type dataset was obtained from the MODIS land cover type product (https://lpdaac.usgs.gov).The elevation and slope data were collected from the EarthEnv project (www.earthenv.org/topography).Population density data were from the fourth version of the Gridded World Population (https://sedac.ciesin.columbia.edu/data),and we classified the global land into four types of population density regions (figure S7).The data on gross national income was from the World Bank (https:// blogs.worldbank.org/opendata),which was assigned to four income groups (figure S8).

CUE calculation
In this study, CUE is quantified as the ratio of NPP to GPP (Ferna ´ndez-Martınez et al 2014), and its formula is as follows: (1)

Estimation of drought index
In this study, VPD and SM were selected to identify the impact of drought on CUE.Among them, VPD is determined by subtracting the actual water pressure Extensive studies have suggested a robust coupling between high VPD and low SM, which exerts a more pronounced impact on CUE than individual effect (Liu et al 2020).To quantify the coupled effect on CUE variation, we formulated a Compound Drought Index (CDI) according to the related studies (Anderegg et al 2018).Its equation is as follows: (7)

Determination of the terrain niche index (TNI)
A TNI is constructed to characterize the impact of topographic variation on global CUE variation, as outlined by Tong et al (2016).It is calculated as below: where e refers to the elevation and E is the average elevation; whereas s represents the slope and S represents the average slope.

Construction of BRT model
In this study, BRT was proposed to clarify the dominant factor of CUE variation and their interrelationships.Firstly, tree complexity and bagging fraction were set to 0.5 and 5 according to related works (Ceccarelli et al 2023); then, optimal BRT fitting parameters were determined through systematic variations in the learning rate (0.1, 0.05, 0.01, 0.005, 0.001) (Green et al 2022).Subsequently, we used 10fold cross-validation to test the accuracy of the results of the parameter combination with different learning rates (De'Ath et al 2007), from which we selected the parameter combination with the smallest deviation.All BRT operations were executed in 'R' using the 'gem.step'function from the 'dismo' package.

SeRGS model structure
SeRGS proposed by Abel et al (2021) was implemented to assess the sensitivity between CUE and the dominant factor.The method constructed a spatiotemporal moving window of 7 × 7 pixels wide and 4 years long based on continuous series raster data.
Then, the least square regression was employed to establish the relationship between CUE and the dominant factor in the given pixel window, and the regression slope was assigned to the central pixel of the spatial window and the central year of the temporal window, respectively.Finally, the temporal window was moved along the time axis in a 1 year step to capture the temporal variation of the regression slope, and the final value, which was the sensitivity of CUE and dominant factor, known as S value .To exclude outliers, regression fitting was not conducted, and data was not assigned to the central pixel when more than two-thirds of the pixels were of poor quality (figure 2).
To further clarify the nonlinear characteristics of S value change, We calculated mean S value of four future scenarios and compared it with the S value in different scenarios; the last intersection point before the S value in an individual scenario, consistently greater/less than the mean S value , was defined as the turning point of the S value change.

Mann-Kendall (MK) test and Theil-Sen median trend
In this study, the Theil-Sen median trend and the MK test were combined to examine long-term series trends in CUE and S value .The Theil-Sen median trend is a nonparametric statistical method for calculating trends and known for its remarkable computational efficiency and stability (Sen 1968).The MK-test is a rank-based nonparametric method that assumes that no significant monotonic trend is observed in the

CUE under historical and future scenarios
The average global CUE is 0.5 ± 0.11, 0.49 ± 0.1, 0.47 ± 0.11, 0.46 ± 0.1 and 0.45 ± 0.1 under the historical and four future scenarios, respectively, indicating the greatest CUE in the historical period.In the future (2015-2100), the interannual CUE will decrease at 1.1 and1.2 × 10 −2 ± 5.2 × 10 −4 per decade under four future scenarios, respectively (figure 3), the decreasing rate under the SSP5-8.5 scenario is about 10 times higher than that under the SSP1-2.6 scenario, indicating that the capacity of vegetation carbon cycle will be more threatened under the high CO 2 emissions scenario, and it is imperative to control CO 2 emission under this scenario.Spatially, CUE exhibits an obvious latitudinal zonality, the region with high CUE is mostly located in the middle-high latitudes of the Northern Hemisphere (50 • -60 • N), the region with low CUE is primarily concentrated in the lowlatitudes of the Northern Hemisphere (0 • -30 • N) and middle-latitudes regions of the Southern Hemisphere (around 30 • S) (figure 4).
In different continents, the CUE in North America is the highest, while Australia and Africa have a relatively low CUE (figure S10).For different vegetation types, those with higher canopy density, such as the needleleaf forest and broadleaf forest, have a lower CUE than those with lower canopy density such as shrublands and cropland (figure S11).
In terms of the spatial change of CUE, 56.9%, 74.5%, 83.1%, and 88.6% of the terrestrial ecosystem shows a significant decreasing trend under four future scenarios, respectively, mainly in the middlelatitudes of the Northern Hemisphere (30 • -60 • N). 13.1%, 8.1%, 5.3%, and 3.2% of the vegetation cover land indicates a significant increased CUE under different CO 2 emission intensities, respectively, primarily located in the northern Africa, northern South America, and eastern Asia (figure 5).Compared to the low-emissions scenario, regions with a remarkably decreased CUE under the high-emission scenario will increase by 31.7%, demonstrating that over one-third of the region will face a serious carbon loss in the future.Meantime, the region with high CUE is spatially overlapped with the regions of declined CUE.

Controlling factor of CUE variation
For most of the global land, temperature is the controlling factor for the CUE variation in the historical, with a contribution rate among 43.3%-81.1%;while in Africa, precipitation plays a limiting role in its CUE variation (figures 6(a) and (b)).Except for temperature and precipitation, VPD is also a relatively vital factor impacting global change of CUE, particularly in Asia, and North America (figures 6(c) and (f)).The impact of soil nutrition on global CUE variation is not significant and even can be ignored.
In North America, an inverted U-shaped relationship is observed between CUE and temperature, indicating a threshold effect.A U-shaped relationship between CUE and temperature is found in Global land, Australia, and South America, while in Asia and Europe, there is a significant negative relationship between them.For Africa, the CUE first increases and then stabilizes at a high level    with enhanced precipitation.In general, heterogeneity and non-linearity characteristics of the relationship between CUE and its controlling factor in different continents can be found (figure 7).

Differences in the S value trend for future scenarios
The mean S value in four future scenarios is −0.005 ± 0.001, −0.006 ± 0.002, −0.003 ± 0.001, and −0.006 ± 0.001, respectively, indicating that higher temperature will produce less CUE.However, in the SSP1-2.6 and SSP2-4.5, positive S value is found in the 2026 and 2027, implying larger CUE in the high-temperature regions.The S value will significantly decline by the end of the 21st century, and the attenuation degrees of the S value are 1.5 × 10 −4 ± 1.4 × 10 −4 , 3.5 × 10 −4 ± 5.4 × 10 −5 , 3.2 × 10 −4 ± 8.9 × 10 −5 , and 3.2 × 10 −4 ± 5.4 × 10 −5 per decade under four future scenarios, respectively, indicating an enhanced constraint effect of temperature on CUE (figure 8).Comparing the S value in one scenario to the mean S value under four scenarios, a turning time of S value change is found.Under the SSP1-2.6 and SSP3-7.0scenarios, the tuning times of S value occur in 2088 and 2086, respectively, and exceeding the turning time, S value in these two scenarios will be higher than the mean S value , suggesting a diminished constraint effect of warming on CUE (figures 8(a) and (c)); while  under the SSP2-4.5 and SSP5-8.5 scenarios, the turning times will occur in 2084 and 2080, respectively, and after the turning time, S value in these two scenarios will significantly lower than the mean value, which means that the negative influence of temperature on CUE will strengthen (figures 8(b) and (d)).It is worth noting that the turning time of S value change will advance with increased CO 2 emission, presenting a prolonged heat stress of vegetation ecosystem under high CO 2 emission scenarios.
In the historical, the S value change in 19% of the area land was significantly increased, which was located in the middle-high latitudes of the Northern Hemisphere (50 • -70 • N) and western Australia; 17.1% of vegetated land had a decreased S value , which was distributed in the Southern Hemisphere and eastern Australia (figure 9(a)).The spatial distribution of S value change under the SSP1-2.6 scenario is different from the other three scenarios.Under the SSP1-2.6 scenario, 30.4% of the global land shows decreased S value , and is located in the middle-high latitudes of the Southern Hemisphere (10 • -60 • S); while the areas with increased S value account for 28.5% and are primarily distributed in the middlehigh latitudes of Northern Hemisphere (50 • -70 • N) (figure 9(b)).In the other three scenarios, 39.6%, 34.4%, and 40.4% of the global ecosystem exhibit notably decreased S value , respectively, and are mainly distributed in the middle-high latitudes of the Northern Hemisphere (30 • -70 • N); the regions with increased S value account for 24.5%, 29.9%, and 26% of the total area, respectively, and are primarily concentrated in the northern South America, Africa, India and Australia (figures 9(c)-(e)).For different vegetation types, the order of constraint effect of warming on their carbon cycle is shrub > grassland > forest (figure S11).

Future variations in S value change owing to other forces
We analyze the interaction between S value change and another dominant driver (precipitation) and it shows an inverted U-shaped relationship, that is, there is a certain threshold (figure 10).Before reaching the threshold, the downward trend in S value is gradually weakening with increasing precipitation, indicating a strong resilience of the vegetation ecosystem; exceeding the threshold, too much precipitation can influent vegetation growth leading to a reduced CUE.The threshold of precipitation is around 2100 mm under the SSP1-2.6 scenario, and it rises to around 2300 mm, 2500 mm, and 2700 mm under other three future scenarios, respectively, suggesting that vegetation requires more water to maintain the ecosystem carbon storage as CO 2 emission intensity increased.
Clustering characteristic is found in the S value variation response of various vegetation types to precipitation.S value change of vegetation types such as DNF, GL, OSB with low water demand (400-800 mm), and EBF with high water demand (1600-2000 mm) is more sensitive to precipitation.Conversely, precipitation has a minor impact on the change of S value in the vegetation types with moderate water requirements (800-1100 mm), such as MF, WSV, and ENF.In summary, vegetation in drier or wetter environments displays greater sensitivity to changes in precipitation (figure 11).
In terms of income level, the positive trend in S value turns to a negative trend with increased CO 2 emission intensity in high-income countries, indicating the unsustainable advantages of vegetation in high-income countries (figure 12(a)).In uppermiddle-income and middle-income countries, S value changes from an upward to a downward trend; and S value trend is negative, but gradually improves in lowincome countries (figure 12(b)).
From low-emission scenarios to high-emission scenarios, an upward trend in S value gradually changes to a downward trend in high population density areas, mainly located in India, east Asia, and central Africa, meaning a greater pressure of population on the vegetation carbon cycle in these regions (figure 12(b)).However, in low and middle population density areas, the negative trend in S value transfers into a positive trend, demonstrating that applicable population management can lighten the negative effects of climate warming on vegetation CUE to some certain extent (figure 12(b)).
The income level and population density exhibit overlapped effects on the S value change.Under different future scenarios, S value consistently demonstrates a negative trend in low-income countries (figure 13).In high-income countries with high population density, S value shows a transition from an upward to a downward trend, while S value variation is always optimistic in the regions with middle population density.In upper-middle-income countries with high population density, a steadily negative trend of S value is found.That is, when socioeconomic growth lags, lower population density can counterbalance its negative influence on CUE; conversely, when population density is high, a higher socioeconomic level can mitigate population pressure on CUE.

Spatiotemporal changes of global CUE
In this study, the mean value of global CUE is 0.5 ± 0.11 during the historical period , which is close to the result of Gang et al (2022), but lower than the observed CUE of 0.55 derived in this study.This discrepancy can be attributed to the difference in the study scales and data sources.Further, a decreased CUE is found in four future scenarios, especially under the SSP5-8.5 scenario, because under high-emission scenarios, global vegetation ecosystems will be in hotter and drier environments, although GPP will experience a pronounced enhancement, it will be significantly lower than the increased respiration and transpiration rate (Ryan et al 1995).To further validate the accuracy of the modeled CUE, this study calculates CUE using observed GPP and NPP, and then compares the modeled and observed CUE.The result showed that the root mean squared error (RMSE) is 0.15, indicating a high aggregation between these two data, affirming the quality of the modeled CUE (figure S1(c)).Spatially, the distribution of low CUE among these two data is same, located in the African sub-Sahel, northern India, and Australia (figure S2).However, the distribution of high CUE in these two data is different, spatially in the temperate zone of the two hemispheres, which can be attributed to the differences in the parameterization of the two processes of vegetation photosynthesis and autotrophic respiration, which have been reported in related studies (He et al 2018).

Response of CUE to controlling factor
This study selected various driving factors, encompassing climatic parameters, background conditions, etc., and constructed a BRT to clarify the dominant factor for global change of CUE and their interrelationships.The findings reveal that temperature is considered to be the controlling factor for global CUE variation.Temperature, as    an essential element of plant growth, can promote vegetation photosynthetic rate (Dusenge et al 2019), and accelerate the carbon cycle within the optimal temperature; however, exceeding this temperature, it will trigger substantial alterations to metabolic activity and cellular disorganization, Further, to clarify the impact of controlling factor (temperature) on CUE in the future, we analyzed the sensitivity between CUE and temperature under historical and different CO 2 emission scenarios.Results show a declined S value , indicating that the negative influence of temperature on CUE will enhance and the risk of ecosystem carbon loss will persist (Zhang et al 2022).Meanwhile, S value change has an obvious turning time.Among them, the turning time occurs in 2088 and 2086 under the SSP1-2.6 and SSP3-7.0scenarios, respectively, exceeding the turning time, the S value in these two scenarios is continuously greater than the average S value , meaning the negative impact of warming on CUE is weakening.The change of S value under the SSP1-2.6 scenario can primarily ascribed to the validity of the excepted climate mitigation and adaptation policies (Gidden et al 2019).For a heavily transient climate, the oceans are temporarily protected by suppressing warming.What this implies is that CO 2 can be ahead of any detrimental warming (Tian et al 2021), thereby reinforcing the reliability of the conclusion that CUE shows a relatively positive response to warming under the SSP3-7.0scenario.For the SSP2-4.5 and SSP5-8.5 scenarios, the S value remains consistently lower than the mean value of four scenarios after the turning time, and the turning time advances to 2080 under the SSP5-8.5 scenario, presenting a prolonged heat stress for the vegetation under the higher emission scenarios.Some studies have shown that there is a lagged effect in the response of the vegetation's physiological activities to temperature (Desai 2014), this effect can last for 1-2 years in shrubs and grasslands (Wu et al 2018), and for 4 years or longer in forests (Wu et al 2016), and these results reinforce the reliability of our conclusion.
We analyzed the relationship between S value change and another important factor (precipitation), and it was found that there is an inverted U-shaped relationship between them, indicating a certain threshold.Moreover, the precipitation threshold is enhanced with the CO 2 emissions intensity rises, which is because vegetation ecosystems with high temperatures require more water to sustain necessary physiological activities (Luo et al 2008).Meantime, vegetation with water demands between 800-1100 mm is relatively less affected by precipitation change.Studies have pointed out that the critical threshold for precipitation in different vegetation ecosystems is approximately 800-1000 mm yr −1 (Chuai et al 2020), which is consistent with our study.

Potential relationship between socio-economy and S value
Besides climate, the socioeconomic development characterized by the GDP increase and population aggregation is also a critical driver for CUEtemperature sensitivity.The positive trend of S value is weakened with increased CO 2 emission intensity in high-income countries.That is, enhanced economic circumstances confer greater resilience to the warming phenomenon within the region.CUE exhibits greater sensitivity to climate warming in the regions with higher population density, which can be attributed to the deforestation and overgrazing caused by population pressure (Toth and Szigeti 2016).By overlaying economic conditions with population density, we identify that vegetation ecosystems in low-income regions with high population density face the greatest risk of 'carbon sink' turning to 'carbon source' .These phenomena demonstrate that moderate population control can partially offset the negative impact of economic disadvantage on the vegetation carbon cycle (Maja and Ayano 2021).Therefore, suitable population control and economic development measures should be proposed to enhance the resilience of vegetation ecosystems.Specifically, in lowincome countries, sustainable economics should be developed by enhancing agricultural modernization, and population growth should be controlled by improving education and establishing a social security system; in high-income countries, urban planning should be optimized to ease city center overcrowding, and regionally coordinated development should be fostered to redirect population influx.

Limitation and prospect
In this study, the bilinear interpolation is employed to unify the data to 0.5 • × 0.5 • resolution, it performs well in continuous data interpolation, and the reliable results in this study have verified it.However, potential challenges stemming from inadequate precision in the outcomes may manifest due to deficiencies in the design of the interpolation function or other pertinent factors.The incorporation of dynamical downscaling methods, statistical downscaling methods, and synergistic hybrid should be considered in prospective data processing.Meanwhile, this study has revealed the potential relationship between S value variation and precipitation, as well as socioeconomics by statistical analyses.It exhibit complex non-linear features and spatial dependencies, which may be challenging to reveal through statistical analysis (Tao et al 2020).In the future structural equation modeling and spatially weighted regression can be employed to further analyze the influence paths and strengths among them.

Conclusion
Our results show that CUE is expected to experience a decreasing trend, particularly in the middle-latitudes of the Northern Hemisphere (30 • -60 • N) at the end of the 21st century.Temperature is the controlling factor for CUE variation in most global regions.The CUE-temperature sensitivity (S value ) shows consistently downward trend, indicating an intensified negative impact of temperature on CUE.Moreover, this decline trend fluctuates and exhibits a turning time, especially in the SSP 5-8.5 scenario, the turning time occurs earlier, implying a prolonged heat stress on CUE.There is a threshold effect of precipitation on the change of S value and the threshold rises with increasing CO 2 emission intensity.High population density strengthens the inhibitory effect of temperature on CUE but can be improved by increasing economic levels, therefore, sustainable economic development and population control should be considered in improving vegetation carbon absorption capacity.

Figure 1 .
Figure 1.The framework of this study.

Figure 2 .
Figure 2. Conceptual illustration of the SeRGS.(a) serves as long-time series raster input data for the combined spatial window (7 × 7 pixels) and temporal (4 years), (b) represents a linear relationship between independent and dependent, (c) is an assignment of regression slope to the center year.

Figure 5 .
Figure 5. Spatial distribution of changes in the mean annual CUE between 1982-2100 in the four scenarios.The line chart shows the changes in the mean annual CUE variation along the latitudinal gradient, including (a) SSP1-2.6,(b) SSP2-4.5, (c) SSP3-7.0,(d) SSP5-8.5.

Figure 7 .
Figure 7. Relationship between CUE in different continents and their dominant factors between 1982 and 2015, the orange line is fitted function, including (a) Global, (b) Africa, (c) Asia, (d) Australia, (e) Europe, (f) North America, (g) South America.

Figure 9 .
Figure 9. Spatial distribution of changes in the mean annual S value in historical and four scenarios.The left penal shows the changes in the S value change along the latitudinal gradient, the histogram represents the area proportion of different change trends, including (a) Historical, (b) SSP1-2.6,(c) SSP2-4.5,(d) SSP3-7.0,(e) SSP5-8.5.

Figure 12 .
Figure 12.Mean S value trends of the (a) per income group and (b) population density region under the four scenarios.
Funct.28 597-611 Gang C C, Wang Z N, You Y F, Liu Y, Xu R T, Bian Z H, Pan N Q, Gao X R, Chen M X and Zhang M 2022 Divergent responses of terrestrial carbon use efficiency to climate variation from 2000 to 2018 Glob.Planet.Change 208 10 Gang C C, Zhang Y, Guo L, Gao X R, Peng S Z, Chen M X and Wen Z M 2019 Drought-induced carbon and water use efficiency responses in dryland vegetation of Northern China Front.Plant Sci. 10 15 Gatti L V et al 2021 Amazonia as a carbon source linked to deforestation and climate change Nature 595 388 Gidden M J et al 2019 Global emissions pathways under different socioeconomic scenarios for use in CMIP6: a dataset of harmonized emissions trajectories through the end of the century Geosci.Model Dev. 12 1443-75 Green N S, Li S B, Maul J D and Overmyer J P 2022 Natural and anthropogenic factors and their interactions drive stream community integrity in a North American river basin at a large spatial scale Sci.Total Environ.835 12 He Y, Manful D, Warren R, Forstenhäusler N, Osborn T J, Price J, Jenkins R, Wallace C and Yamazaki D 2022 Quantification of impacts between 1.5 and 4 • C of global warming on flooding risks in six countries Clim.Change 170 21 He Y, Piao S L, Li X Y, Chen A P and Qin D H 2018 Global patterns of vegetation carbon use efficiency and their climate drivers deduced from MODIS satellite data and process-based models Agric.For.Meteorol.256 150-8 Huang L, He B, Han L, Liu J J, Wang H Y and Chen Z Y 2017 A global examination of the response of ecosystem water-use efficiency to drought based on MODIS data Sci.Total Environ.601 1097-107 Kim D, Lee M I, Jeong S J, Im J, Cha D H and Lee S 2018 Intercomparison of terrestrial carbon fluxes and carbon use efficiency simulated by CMIP5 earth system models Asia-Pac.J. Atmos.Sci.54 145-63 Li J W, Wang G S, Mayes M A, Allison S D, Frey S D, Shi Z, Hu X M, Luo Y Q and Melillo J M 2019 Reduced carbon use efficiency and increased microbial turnover with soil warming Glob.Change Biol. 25 900-10 Liu L B, Gudmundsson L, Hauser M, Qin D H, Li S C and Seneviratne S I 2020a Soil moisture dominates dryness stress on ecosystem production globally Nat.Commun.11 9 Liu X, Lai Q, Yin S, Bao Y, Tong S, Adiya Z, Sanjjav A and Gao R 2024 Spatio-temporal patterns and control mechanism of the ecosystem carbon use efficiency across the Mongolian Plateau Sci.Total Environ.907 167883 Liu Y Y, Yang Y, Wang Q, Du X L, Li J L, Gang C C, Zhou W and Wang Z Q 2019 Evaluating the responses of net primary productivity and carbon use efficiency of global grassland to climate variability along an aridity gradient Sci.Total Environ.652 671-82 Luo Y, Gerten D, Le Maire G, Parton W J, Weng E, Zhou X, Keough C, Beier C, Ciais P and Cramer W 2008 Modeled interactive effects of precipitation, temperature, and [CO2] on ecosystem carbon and water dynamics in different climatic zones Glob.Change Biol.14 1986-99 Maja M M and Ayano S F 2021 The impact of population growth on natural resources and farmers' capacity to adapt to climate change in low-income countries Earth Syst.Environ. 5 271-83 Mauritsen T, Bader J, Becker T, Behrens J, Bittner M, Brokopf R, Brovkin V, Claussen M, Crueger T and Esch M 2019 Developments in the MPI-M Earth System Model version 1.2 (MPI-ESM1.2) and its response to increasing CO2 J. Adv.Model.Earth Syst.11 998-1038 Müller W A et al 2018 A higher-resolution version of the max planck institute earth system model (MPI-ESM1.2-HR) J. Adv.Model.Earth Syst. 10 1383-413 Ogawa K 2011 Theoretical analysis of change in forest carbon use efficiency with stand development: a case study on Hinoki Cypress (Chamaecyparis obtusa (Sieb.et Zucc.)Endl.) plantation from the seedling stage Ecol.Model.222 437-41 Piao S, Luyssaert S, Ciais P, Janssens I A, Chen A, Cao C, Fang J, Friedlingstein P, Luo Y and Wang S 2010 Forest annual carbon cost: a global-scale analysis of autotrophic respiration Ecology 91 652-61 Price J, Warren R, Forstenhäusler N, Wallace C, Jenkins R, Osborn T J and Van Vuuren D J 2022 Quantification of meteorological drought risks between 1.5 • C and 4 • C of global warming in six countries Clim.Change 174 12 Ryan M G, Gower S T, Hubbard R M, Waring R H, Gholz H L, Cropper W P and Running S W 1995 Woody tissue maintenance respiration of four conifers in contrasting climates Oecologia 101 133-40 Sen P K 1968 Estimates of the regression coefficient based on Kendall's tau J. Am.Stat.Assoc.63 1379-89 Tao T, Wang J Y and Cao X Y 2020 Exploring the non-linear associations between spatial attributes and walking distance to transit J. Transp.Geogr.82 11 Tian C G, Yue X, Zhou H, Lei Y D, Ma Y M and Cao Y 2021 Projections of changes in ecosystem productivity under 1.5 • C and 2 • C global warming Glob.Planet.Change 205 11 Tong X W, Wang K L, Brandt M, Yue Y M, Liao C J and Fensholt R 2016 Assessing future vegetation trends and restoration prospects in the Karst regions of Southwest China Remote Sens. 8 17 Totaro V, Gioia A and Iacobellis V 2020 Numerical investigation on the power of parametric and nonparametric tests for trend detection in annual maximum series Hydrol.Earth Syst.Sci.24 473-88 Toth G and Szigeti C 2016 The historical ecological footprint: from over-population to over-consumption Ecol.Indic.60 283-91 Tucker C L, Bell J, Pendall E and Ogle K 2013 Does declining carbon-use efficiency explain thermal acclimation of soil respiration with warming?Glob.Change Biol.19 252-63

Table 1 .
Basic information of 8 CMIP6 models used.