Forests are one of the largest conduits in the transfer of carbon from Earth's atmosphere to the terrestrial biosphere, providing a sink for ca. 2.4 Pg C annually and accounting for nearly half of terrestrial net primary productivity (NPP) (Field, 1998;Pan et al., 2011). However, NPP represents only a fraction of the total amount of carbon fixed during photosynthesis (GPP), as a substantial amount of CO 2 is released back to the atmosphere through autotrophic respiration (R a ) (Field, 1998). Indeed, observations from trees around the world show between ca. 20 and 80% of GPP may be partitioned to R a (Collalti & Prentice, 2019;DeLucia et al., 2007). This translates to a similarly large range in tree carbon use efficiency (CUE), or the ratio of tree NPP to GPP, which is an integrated index that tracks and allows direct comparison of tree carbon metabolism across a range of productivity (DeLucia et al., 2007). Some of the spatial patterns in tree CUE can be explained by tree age (DeLucia et al., 2007;Mäkelä & Valentine, 2001), disturbance history (Kunert et al., 2019), species richness (Kunert et al., 2019) and tree functional type (Chen & Yu, 2019;Collalti & Prentice, 2019). Tree CUE also varies appreciably across climate-space, tending to decrease with increasing temperature in juvenile (Drake et al., 2019) and mature trees (Chen & Yu, 2019;He et al., 2018). Yet, how tree CUE may change as a result of increasing atmospheric CO 2 (eCO 2 ) has been given less attention. On one hand, eCO 2 stimulates leaflevel photosynthesis (i.e. GPP) (Ainsworth & Rogers, 2007) and has driven increases in tree leaf area (Zhu et al., 2016), which may be reflected in higher NPP (Mathias & Thomas, 2018;Norby et al., 2005;Walker et al., 2019), and result in increasing tree CUE, especially if NPP is stimulated proportionally more than GPP. Alternatively, if eCO 2 -driven increases in leaf area, which requires similar additional investment in roots for water uptake and transport (Litton et al., 2007;Nie et al., 2013), result in proportionately higher costs (R a ) than benefits (NPP or GPP), tree CUE may decline.
The future trajectory of tree CUE may be even more uncertain when considering the combined effects of eCO 2 and climate change on NPP, GPP and R a . While the shortand long-term responses of leaf-level photosynthesis to eCO 2 and environment are relatively well documented (Ainsworth & Rogers, 2007;Bernacchi et al., 2001Bernacchi et al., , 2013;;Farquhar et al., 1980;Farquhar & Sharkey, 1982) and have been incorporated widely into process-based models, future changes in R a may contribute a large source of uncertainty, and therefore a potential source of variability in estimates of future forest CUE and the terrestrial carbon cycle. Some uncertainty is related to the nature and extent of acclimation of R a over longer time periods (Atkin & Tjoelker, 2003;Lombardozzi et al., 2015;Slot et al., 2014;Smith et al., 2016). However, the explicit representation of the temperature-respiration relationship is also critical to consider (Heskel et al., 2016;Reich et al., 2016). A wide range of functions grounded on robust empirical relationships has been developed to represent how R a varies across a range of temperatures (Arrhenius, 1889;Gillooly, 2001;Heskel et al., 2016;Lloyd & Taylor, 1994), with each predicting similar R a at moderate temperatures. However, across the suite of temperaturerespiration functions, predictions of R a diverge at novel high temperatures that are anticipated in some regions of the globe with warming under future climate change, with potential CUE and carbon cycle consequences that are important to understand.
Here, we leverage a physiologically based tree model that couples carbon allocation to local environmental conditions through gas exchange and plant hydraulic transport (Trugman, Detto, et al., 2018) to examine the consequences of eCO 2 and climate change on future tree CUE globally. We first update the model to incorporate the temperature dependency of C 3 photosynthesis and tissue respiration. We then ask 1) how does the modelpredicted CUE across six different respiration functions commonly utilised in Earth system models compare with observations of CUE from trees around the world across a range of climates, 2) what are the consequences of eCO 2 and future projections of climate change on tree CUE globally and 3) what do changes in the distribution of CUE globally tell us about the future of forests in a changing climate?
The physiologically based tree model, adapted from Trugman, Detto, et al. (2018), couples carbon allocation to local environmental conditions through gas exchange and plant hydraulic transport. The original model (see Trugman, Detto, et al., 2018 for full model description) requires inputs of atmospheric CO 2 (C a , ppm), vapour pressure deficit (VPD, Pa) and soil water potential (Ψ soil , MPa). Here, we update the model to include a tree physiological response of photosynthesis and respiration to temperature (T air , °C), such that in the updated model inputs include C a , VPD, Ψ soil and T air , as described below. The rate of carbon fixation during photosynthesis is assumed to be limited by Rubisco (Trugman, Detto, et al., 2018) with a full description in the supporting information.
The temperature dependence of respiration has been documented empirically using a range of functions, all of which result in similar predictions for R a at temperatures below 36.5°C. However, estimates of R a diverge at temperatures above 36.5°C. The divergence of dataconstrained respiration functions at higher temperatures has significant consequences for our understanding of carbon partitioning under novel expected high temperatures and therefore tree CUE under climate change. Thus, we calculated the sensitivity of leaf (light and dark), stem (xylem and phloem) and root respiration using each of six temperature-respiration response functions (Figure S1) which represent a spectrum of decreasing sensitivity to temperature, in turn: 1) Arrhenius, 2) fixed Q 10 , 3) universal temperature dependence, 4) log-polynomial, 5) Lloyd-Taylor or a 6) variable Q 10 function in the absence of short-or long-term thermal acclimation (see Supporting Information Methods for the full equations). When simulating the sensitivity of CUE to respiration functional form, the same respiration function was used across all biomass pools. Across all respiration functions, leaf respiration in light (R leaflight ) was calculated as a temperaturedependent variable fraction (0.66-0.80) of leaf respiration in dark (R leafdark ) following Way et al. (2015) using A tree stem respiration at 25°C of 0.719 µmol CO 2 m -2 s -1 was used (Edwards & Hanson, 1996) and partitioned into the xylem (~21% of total stem respiration) and phloem respiration (~79% of total) following Stockfors and Linder (1998). Whole-tree NPP is calculated as GPP minus R a , and tree CUE as the ratio of NPP to GPP.
We validated model performance in two ways. First, we directly compared model-simulated CUE with a compilation of site-level estimates of forest CUE (N = 228) (Collalti & Prentice, 2019) across a range of mean growing season temperatures (10-28°C). We ran separate model simulations for each of the six respiration functions, in turn. Second, we examined model skill in capturing vegetation transitions at dry range edges by (1) R leaflight = R leafdark × (0.0039 × T + 0.6219) .
performing a series of global simulations and examining spatial patterns of CUE.
For the first model validation (Figure S2, Table S2), we held all model parameters and inputs constant except T air , which we varied from 10 to 45°C. Given that most measurements did not include detailed demographic or climate information, we used CO 2 , DBH, Ψ soil , and VPD values of 415 ppm, 30 cm, -0.3 MPa and 800 Pa, respectively. Tree leaf area (m 2 ) was calculated to maximise whole tree NPP (Trugman et al., 2019) while varying T air across 10-45°C and keeping other climate factors fixed using the optimise() function from the 'stats' package in R (R Core Team, 2018). We limited the maximum leaf area to 1600 m 2 , assuming the relationship between tree DBH and leaf area described in Forrester et al. (2017) for broadleaf and needle leaf trees is widely conserved (Figure S3). We then compared model-predicted CUE with the distribution of published tree CUE observations across temperatures (Collalti & Prentice, 2019). Given that growing season T air was not included with the CUE observations (Collalti & Prentice, 2019), we extracted growing season T air for the time period 1980-2009 for each study location (based on documented site GPS coordinates) with a unique CUE observation using the Climatic Research Unit (CRU TS4.03) globalgridded data product (Harris & Jones, 2019), which we then used to calculate 30-year growing season mean T air , assuming that photosynthesis primarily occurs during June, July and August for the northern hemisphere (≥0° latitude) and December, January and February for the southern hemisphere (≤0° latitude). To determine where model-prognosed CUE significantly diverged among the functions examined, we performed a breakpoint analysis of the range in model-predicted CUE (i.e. CUE max -CUE min ) as a function of temperature across the six respiration functions using the R package 'segmented' (Muggeo, 2008). Linear regression was used to determine the relationship between temperature and modelled tree CUE prior to the estimated breakpoint.
For the second model validation, we ran global simulations with one modelled tree per grid cell and examined the spatial patterns in CUE (Figure S3). We compared spatial patterns in model-predicted CUE to a LIDARbased canopy height data set that documents transitions from forests to shrubland to examine whether the model was a useful tool for predicting where trees could exist at dry range edges. Specifically, for our global model simulations, we initialised each pixel with a tree 14 m in height (though we found CUE to be invariant to tree size, Table S3) and calculated tree DBH (13.5 cm) from height following Farrior et al. (2013). Functional tree xylem crosssectional area (A x , m 2 ) was estimated from DBH as ca. 62% of total xylem cross-sectional area (Trugman, Detto, et al., 2018). Environmental forcings for the model including mean temperature (T air , °C; calculated as the average of T max and T min ) and VPD were extracted from TerraClimate (Abatzoglou et al., 2018). Soil moisture (SM, kg H 2 O m -2 soil) was extracted from the NASA Global Land Data Assimilation System Version 2 (GLDAS-2) (Beaudoing & Rodell, 2020;Rodell et al., 2004) for 2005, the same year during which LIDAR canopy height retrievals were made. We converted SM to soil volumetric water content (θ, m 3 H 2 O m -3 soil), integrating over the soil depth profile for each soil layer down to 2 m, which we weighted by the biome-specific distribution of roots throughout the soil horizon (Schenk & Jackson, 2002) within each respective biome in which trees grow, excluding mangroves (Dinerstein et al., 2017). We then calculated soil water potential (Ψ soil , MPa) from θ using where Ψ sat is the saturated soil water potential (MPa), θ sat is the saturated volumetric water content of the soil (m 3 H 2 O m -3 soil), and b is the Clapp-Hornberger coefficient (unitless) (Clapp & Hornberger, 1978), which are specific to a given soil type and were determined using data products from the Global Soil Wetness Project -Phase 2 (Dirmeyer et al., 2002). In cases, where Ψ soil became highly negative (i.e. <-10 MPa), a value of -10 MPa was assigned. We calculated growing season means for each environmental factor for each respective period as described previously. All global gridded data products were resampled to the same extent (0.1° × 0.1°) using the resample() function in the 'raster' package in R using a bilinear method (Hijmans, 2020) for analyses. We optimised leaf area for each tree within each grid cell, given grid-specific environmental forcings to calculate the tree CUE.
We compared simulated tree CUE against a highresolution (1 × 1 km) LIDAR vegetation canopy height data product from the Geoscience Laser Altimeter System (GLAS) on the Ice, Cloud, and land Elevation Satellite (ICESat) retrieved during 2005 (Simard et al., 2011). Vegetation with canopy height <2 m was excluded from analyses following the International Geosphere-Biosphere Land classification system (Loveland & Belward, 1997). This analysis allowed us to examine the relationship between forest canopy height and model-predicted CUE for each grid cell using a two-dimensional density kernel estimation, breakpoint analysis, and linear regression.
To understand the sensitivity of forest CUE to potential changes in climate associated with anthropogenic climate change, we used globally gridded data products from a representative subset of 7 coupled climate-Earth System Models (ESMs) from the Coupled Model Intercomparison Project-Phase 5 (CMIP5) for the periods 1976-2005 (historical) and 2071-2100 (future Respective Concentration Pathway 8.5, hereafter RCP8.5) for our
(2)
, analyses (see, Figure S5, Table S4) (Taylor et al., 2012). We accessed the Centre for Environmental Data Access data portal (https://www.ceda.ac.uk) to download monthly averages for each climate variable, mean air temperature (T air , °C), surface air pressure (P s , Pa), soil moisture (SM, kg H 2 O m -2 soil), and relative humidity (RH, %) for each respective period of interest. We calculated vapour pressure deficit (VPD, Pa) from RH, T air , and P s using the function RHtoVPD() in the 'plantecophys' R package (Duursma, 2015) and Ψ soil from soil moisture as described previously. Similar to our model validation simulations, we calculated growing season mean climatologies over the 30-year period for all environmental factors. We then computed the multi-model median value for each environmental factor for each grid cell when forcing the physiologically based tree model under historical and future scenarios. All global gridded data products were resampled to the same extent (0.1° × 0.1°) and were masked using the vegetation canopy height LIDAR product. Concentrations of atmospheric CO 2 used in our analysis for the historical and future periods were 354 ppm and 807 ppm (Meinshausen et al., 2011), respectively. We used two-dimensional kernel density estimation using the function kde2d() from the R package 'MASS' (Venables & Ripley, 2002), and linear regression, to quantify the relationship between temperature and tree height with modelled CUE at the global scale.
We examined the sensitivity of model-predicted CUE to two distinct climatological periods of 30 years: historical and end-of-century (2071-2100, RCP8.5). Tree height was assigned according to LIDAR estimates (Simard et al., 2011). Tree leaf area was optimised based on grid cell-specific climate for each respective period (historical and future) using the CMIP5 growing season multi-model median value for each environmental factor (i.e. VPD, Ψ soil , T air ) and the respective mean mid-year atmospheric CO 2 concentration (historical: 354 ppm, future: 807 ppm). We assumed no change in tree characteristics beyond leaf area between the historical and future simulations. We performed a series of model experiments designed to understand the sensitivity of tree CUE and forest extent to eCO 2 and climate change by first simulating historical and then future tree CUE, using leaf area and environmental factors specific to each time period. Finally, we examined the relative contribution of each environmental factor, CO 2 , VPD, Ψ soil and T air , in isolation to the change in CUE between historical and future periods (∆CUE) through factorial model experiments where we varied the environmental factor of interest each in isolation between the historical and future periods. For our global model experiments, we performed a one-way ANOVA to determine the change in global CUE across all respiration functions between historical and future climate scenarios.
Our two-dimensional kernel density estimation indicated that model-predicted decreases in CUE corresponded to decreases in observed vegetation canopy height associated with transitions from taller forests to shorter shrubland at dry edge range limits for forests. Thus, we used model-predicted CUE to diagnose geographic areas where future forest range shifts may occur due to changes in hydroclimate. We consider geographic areas where future environmental conditions are insufficient to support tree growth as diagnosed by model-predicted negative CUE (i.e. R a >GPP), as well as those areas that may experience possible forest expansion where future CUE is positive and historical CUE is negative. For this analysis, we examine three potential cases leveraging results from our historical-future climate simulations: 1) no change in forest range (i.e. no change in sign of CUE), 2) forest range expansion (i.e. negative CUE historical to positive CUE future ) and 3) forest range decline (i.e. positive CUE historical to negative CUE future ). We then examine the nature of the relationship between environmental factors and model CUE-derived range shifts, including non-forested biomes such as grasslands and shrublands, where future forest encroachment could be possible.
In the current model formulation and model predictions, we neglected the effects of spatial variability in plant traits that mediate forest biogeographic patterns. Although we do not account for spatial variability in functional traits, we found that model adjustments in leaf area covary with key traits regulating plant water demand (Table S1), largely compensating for potential spatial variability in traits such as V cmax25 . We also do not explicitly represent tree age in our framework. However, model predictions for forest transitions at dry range limits are consistent with observed spatial patterns in vegetation canopy height. Thus, we contend that our simple model framework will help inform understanding of how climate change and CO 2 fertilisation will impact forest extent and inform the uncertainty in these projections associated with our understanding of R a .
Compared to a meta-analysis of observed CUE across a range of climates globally spanning mean growing season temperatures of 12-28°C, model-predicted CUE intersected median observed CUE for temperatures 15 and 21°C (Figure 1a). As the temperature increased, model-predicted CUE fell well within the interquartile range of observed CUE, however, model predictions were biased low relative to the observed median CUE values at a given temperature by 0.033 ± 0.008 (Table S2). Further, across the observed temperature ranges, model performance did not differ appreciably across the six respiration functions.
Despite the fact that model performance was roughly independent of respiration function choice across the observed range of CUE, the choice of respiration matters for high-temperature conditions expected with anthropogenic climate change. Specifically, across all six respiration functions, model-predicted CUE decreased, on average, by 0.12 for each 10°C increase in temperature (R 2 = 0.97, p < 0.001) up to 36.5 ± 0.45°C (Figure 1a), which is ~4.5°C higher than current average highs (ca. 32°C) observed in the tropics. However, as temperature increased above 36.5°C, CUE significantly diverged across the six respiration functions considered (Figure S5). At high temperature, the choice of respiration function is of critical importance, as CUE is least sensitive to increasing temperature under a variable Q 10 representation of respiration sensitivity to temperature (analogous to some acclimation of respiration to temperature) and is most sensitive under an Arrhenius representation of respiration sensitivity to temperature (Figure 1a). Notably, no current observations of CUE exist at the high-temperature limit (36.5°C), where we find the respiration functions significantly diverge (Figure 1a, Figure S6). Thus, it is not currently possible to evaluate the functional performance of these respiration functions when it matters most. As a result, there is significant uncertainty related to future plant CUE in locations such as central North America, central South America and central Eurasia, where climate change is projected to increase growing season temperature above 36.5°C under some emissions scenarios (Figure S7).
Plant CUE is sensitive not only to temperature, because of the impact of temperature on respiration and GPP, but also plant available water, which influences the balance of plant productivity relative to maintenance respiration. We therefore quantified the sensitivity of plant CUE through our model to changes in environmental factors that influence water use based on global climatologies. Interestingly, we found that model-predicted CUE varies with the environment globally and the spatial variation is driven by two climatic regions with distinct mechanisms at play-cool high latitude forest areas with a relatively high CUE due to low respiration and warm forested areas that transition from wet forests with intermediate CUE values to dry forests with low CUE (Figure 2a; Figure S8), and ultimately shrublands and grasslands (which our model is not designed to represent). The bimodal distribution of modelled CUE values ranged from ca. 0-0.70, with a median value of 0.42 across the six respiration representations (Figure 2), and the highest densities of model-predicted CUE occurred at growing season temperatures ca. 14.7 and ca. 26.5°C, corresponding to tree CUE of 0.48 and 0.35, respectively (Figure 2b, Figures S9, S10a). Compared to observations of canopy height across hydroclimate gradients, we found that transitions from taller forests at 13.4 ± 0.01 m to shorter shrubland corresponded with rapid decreases in model-prognosed CUE from ~0.5 to values that are unsustainable by trees over prolonged periods at a rate of ~0.021 CUE/m decrease in canopy height (p < 0.001) (Figure 2c; Figures S10b, S11), particularly at dry range limits of forests (Figure 2a). Thus, the model was able to reproduce dry range edges based on tree CUE.
At the global scale, model-predicted CUE increased, on average, by 6.2% (ca. 0.024 ± 0.002, mean ± SE) between the historical and the future (2071-2100) time periods (F = 21.7, p < 0.001; Table 1), driven predominantly by large increases in CO 2 which stimulated GPP (Figure 3). Future increases in T air and VPD (Table S4) strongly reduced the realised increases due to CO 2 , while future changes in Ψ soil did not have an appreciable impact on mean global CUE (Figure 3, Table S4). However, the choice of respiration function introduced uncertainty F I G U R E 1 Model-predicted CUE across a range of temperature for six temperature-respiration functions (a) and locations of tree CUE observations (b). Solid colour lines in (a) represent model-predicted CUE using each of six temperature-respiration representations, while the boxplots in (a) correspond to published observations of CUE globally (Collalti & Prentice, 2019). Boxplots highlight the median, interquartile range and 95% CI for CUE observations across a range of temperatures. The colour of location markers in (b) represent the site-level estimate of CUE from Collalti and Prentice (2019) and correspond to the boxplots in panel (a). The horizontal dashed line in (a) is at 0, which represents the point at which model-predicted autotrophic respiration equals gross primary productivity. All respiration functions were solved to 25°C and exhibit larger differences as temperature increases above 36.5 ± 0.45°C, denoted by the vertical dark blue line and grey shading in (a) into our predictions for both historical and future CUE, primarily due to the function-specific response of increasing T air on respiration and therefore CUE (Table 1). Importantly, the variable Q 10 respiration-temperature response function had the highest historical and future mean CUE values across all forested pixels (due to lower respiratory fluxes), while the fixed Q 10 respiration representation showed the lowest global mean CUE within each respective period (Table 1), with a range in CUE across the six respiration functions (including historical and future CUE) of 0.036 or ca. 8.7%.
Given model skill in determining dry range limits in forest extent, we used model-predicted CUE to constrain where forest range shifts may occur under future climate scenarios. We found, on average across all respiration functions, a net reduction in ca. 105,124 km 2 of the forested area by 2100, driven by a decline of forested lands by 0.34% and an increase in forested lands by 0.19% (Table S5). Importantly, the balance between forest decline and increase is variable spatially, such that some biomes only experience forest range expansion or encroachment (i.e. flooded grasslands and tropical dry broadleaf) or no change (i.e. tundra), which is unsurprising because the model does not include mechanisms expected to govern forest cold edge limits, while the majority exhibit a variable range in the balance between forest range decline and increase (Figure 4, Table S6). Model-predicted CUE between historical and future periods shows boreal forests exhibit the largest net decline in forest range (-61,895 ± 528 km 2 ) through the end of the 20th century, while land areas currently designated as flooded grasslands exhibit the largest potential for net forest area increase (+373,939 ± 74,545 km 2 ) (Table S6). Furthermore, the choice of temperature-respiration representation mediated the sensitivity of our estimates of changes in future forested areas, with a variable Q 10 representation resulting in larger increases and smaller declines in the net forested area and an Arrhenius representation resulting in larger declines and smaller increases in the net forested area (Figure 4, Table S6). As such, the differences in the temperature-respiration representation resulted in as little as a ca. 38,097 km 2 decline (variable Q 10 ) or as much as a ca. 150,313 km 2 decline (Arrhenius) in the net forested area globally in this analysis.
In this study, we use a physiologically based tree model to diagnose the underlying mechanisms and future uncertainties for forest resilience with anthropogenicdriven climate change. We capture observed dry range forest edges using a CUE framework where progressively lower model-predicted CUE corresponds with global vegetation height transitions from taller forested areas to shorter shrubland (Figure 2). We find that the future resilience of forests globally is nuanced, such that total Variable Q 10 0.432 0.452 +4.6 Lloyd-Taylor 0.418 0.448 +7.2 Log-Poly 0.425 0.447 +5.2 UTD 0.421 0.446 +5.9 Fixed Q 10 0.416 0.445 +7.0 Arrhenius 0.425 0.447 +5.2
forested area declines at dry range edges, but core forested areas exhibit overall higher mean CUE by the end of the 21st century (Figures 3, 4, Table 1). We show that uncertainty in our understanding of the sensitivity of R a to increasing temperature introduces significant variability into predictions of CUE. Importantly, uncertainty is highest at higher temperatures that are expected with climate change but is currently unconstrained with observational data.
There currently exists no standardised representation of the temperature-R a response in many widely used terrestrial biosphere models, with some adopting a fixed Q 10 temperature-R a function (e.g. Pnet-CN, ED2) (Medvigy et al., 2009;Thorn et al., 2015), others incorporating a variable Q 10 function (e.g. CABLE) (Wang et al., 2007) and some scaling R a with temperature and tissue nitrogen concentration (CLM4, JULES) (Clark et al., 2011;Oleson et al., 2013;Reich et al., 2008). Our results highlight the consequences of the choice of temperature-R a function by illustrating the large range in model-predicted CUE (driven primarily by R a ), which is too large to be ignored at high temperature (Figure S1). As autotrophic carbon fluxes, including R a , increase towards warmer equatorial regions (Banbury Morgan et al., 2021), careful consideration of differences in modelled R a becomes increasingly important for simulating future forest CUE, particularly when the temperature exceeds 36.5°C (Figure S7). Large-scale, data-rich experiments like SPRUCE (Hanson et al., 2017) will be invaluable in helping to constrain estimates of CUE at higher temperatures and CO 2 .
Tree R a is one of the largest, and also most challenging to measure, carbon fluxes globally. Yet, it is critical to accurately represent R a in terrestrial biosphere models to understand climate change impacts on forest resilience and the terrestrial carbon cycle. Multiple independent observations show that tree CUE declines with increasing temperature across the range of temperatures considered in this study (Chen & Yu, 2019;Dillaway & Kruger, 2014;He et al., 2018;Piao et al., 2010;Zhang et al., 2009), a phenomenon our physiologically based tree model reproduces. When considering the combined effects of multiple environmental factors globally, we find model-predicted tree CUE is higher in cool, moist ecosystems and lower in warm, dry ecosystems, trending to zero at forest dry range edges (Figure 2, Figure S8), similar to recent predictions using large-scale Earth-system models (which couple terrestrial biosphere models to the rest of the Earth system) and satellite retrievals (He et al., 2018). However, uncertainty remains. In an analysis by Collalti et al. (2020), the authors find that CUE increased with temperature in an observational range of up to ca. 28°C. Further, though the model and observations are in agreement with absolute CUE values in our analysis (Figure 1), a clear temperature trend is not evident in the observations. There are many reasons why these diverse measurements across space may not exhibit a clear temperature trend including diversity in species, diversity in tree ages, lack of site-specific soil moisture and VPD measurements at the time of observations and measurement uncertainty. Collectively, these results contextualise that our model results are in broad agreement with and additive to the literature but also highlight several future avenues of research (which we detail below).
Globally, variation in model-simulated tree CUE is driven by air temperature, VPD and soil water potential, reflecting our current knowledge of large-scale drivers of forest carbon cycling (Banbury Morgan et al., 2021;Fernández-Martínez et al., 2019;Humphrey et al., 2021). However, when considering end-of-century mean changes in simulated tree CUE, the effect of increasing atmospheric CO 2 stimulating GPP, on average, outweighs those environmental factors that either diminish GPP or stimulate R a (Figure 4). The effects of increasing CO 2 and VPD on forest function have gained notable attention in recent years (Novick et al., 2016;Swann et al., 2016;Yuan et al., 2019), given their simultaneous, but often counteracting influences over tree physiology. In this context, our findings provide a unique framework to diagnose the areas where forests are vulnerable to climate driven die-off based on tree CUE (Figure 4). Indeed, the world's boreal forests, which are currently showing evidence of increasing browning and forest decline (Barber et al., 2000;Trugman, Medvigy, et al., 2018;Walker & Johnstone, 2014;Walker et al., 2015), experience the largest range decline of all biomes examined at dry range edges by the end of the 21st century as inferred through model-simulated CUE (Figure 4), and overwhelmingly contribute to the model-predicted global decline in forest range extent. The model-predicted declines in temperate broadleaf forests are also consistent with reports from the southeastern United States (White et al., 2021). Moreover, these findings also agree with findings from a recent meta-analysis showing observations of widespread drought-induced tree mortality at dry range edges (Anderegg et al., 2019). However, despite modelpredicted declines in the total forested area, projected increases in CO 2 resulted in higher mean CUE in areas that are predicted to maintain a positive CUE (Figure 3, Table 1). Targeted measurements of tree-level photosynthesis and respiration under experimental warming will be invaluable for assessing the extent to which these predictions are realised.
In conclusion, our analysis of tree CUE and forest dry range edges through the lens of a physiologically based tree model highlights the potential consequences and uncertainty of the choice of the temperature-R a representation is widely used process-based models. Particularly, at higher temperatures, we show a variable Q 10 representation, which represents some acclimation of respiration sensitivity to temperature, resulting in much less carbon being lost to R a and consequently higher CUE. In contrast, an Arrhenius type representation yields the lowest tree CUE due to larger predicted R a costs. Importantly, we find that model-predicted decreases in CUE correspond to decreases in observed vegetation canopy height associated with transitions from taller forests to shorter shrubland at dry range edges, indicating that model-predicted CUE is a useful tool for understanding future forest resilience to climate change-induced drought stress. Under future climate conditions, model predictions indicate an expected higher mean CUE in intact forest regions due to CO 2 fertilisation, but the declining geographic extent, highlighting that the resilience of forests under future climate change may be nuanced and controlled by multiple competing mechanisms.
We acknowledge the World Climate Research Programme's Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modelling groups (listed in the supplementary materials) for producing and making available their model output. A.T.T. acknowledges funding from the NSF (Grant 2003205), the USDA National Institute of Food and Agriculture, Agricultural and Food Research Initiative Competitive Programme (Grant No. 2018-67012-31496) and the University of California Laboratory Fees Research Program Award (No. LFR-20-652467).
JMM and ATT designed the study. ATT developed the original model which was updated by JMM in this study. JMM performed analyses and JMM and ATT wrote the final manuscript.