A global scale mechanistic model of the photosynthetic capacity

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Introduction
Photosynthesis is one of the major components of the ecosystem carbon cycle (Canadell et al., 2007;Sellers et al., 1997) and is thus central to Earth system models (ESMs) (Block and Mauritsen, 2013;Hurrell et al., 2013).Most of the ESMs are based on photosynthesis models developed by Farquhar et al. (1980), which are particularly sensitive to photosynthetic capacity.The maximum carboxylation rate scaled to 25 • C (i.e., V c,max25 (µmol CO 2 m −2 s −1 )) and the maximum electron transport rate scaled to 25 • C (i.e., J max25 (µmol electron m −2 s −1 )) have been generally accepted as the measure of photosynthetic capacity.V c,max25 and J max25 are the key biochemical parameters in the photosynthesis models as they control the carbon fixation process (Farquhar Figures Back Close Full  , 1980).There exist large variations in estimates of gross primary productivity in space and time across ESMs (Schaefer et al., 2012), which have been partly attributed to uncertainties in V c,max25 (Bonan et al., 2011).Accurate estimations of V c,max25 and J max25 are needed to simulate gross primary productivity because errors of V c,max25 and J max25 may be exacerbated when upscaling from leaf to ecosystem level (Hanson et al., 2004).
Our ability to make reliable predictions of V c,max25 and J max25 at a global scale is limited.One of the reasons is that we do not have a complete understanding of the processes influencing V c,max25 and J max25 (Maire et al., 2012;Xu et al., 2012) despite the fact that V c,max25 has been measured and studied more extensively than many other photosynthetic parameters (Kattge and Knorr, 2007;Leuning, 1997;Wullschleger, 1993).Many empirical studies have shown that V c,max25 and J max25 (or field-based surrogates) correlate with leaf nitrogen content (Medlyn et al., 1999;Prentice et al., 2014;Reich et al., 1998;Ryan, 1995;Walker et al., 2014).Therefore, a constant relationship between the leaf nitrogen content and V c,max25 or J max25 is commonly utilized by many ecosystem models (Bonan et al., 2003;Haxeltine and Prentice, 1996;Kattge et al., 2009).The relationship between leaf nitrogen content, V c,max25 and J max25 varies with different light, temperature, nitrogen availability and CO 2 conditions (Friend, 1991;Reich et al., 1995;Ripullone et al., 2003), and therefore, the prescribed relationship of V c,max25 , J max25 and leaf nitrogen content might introduce significant biases into predictions of future photosynthetic rates, and also the downstream carbon cycle and climate processes that are dependent on these predictions (Bonan et al., 2011;Knorr and Kattge, 2005;Rogers, 2014).
To better account for the relationships between photosynthetic capacities and their environmental determinants, we developed a mechanistic model of leaf utilization of nitrogen for assimilation (LUNA V1.0) at the global scale that accounts for the key drivers (temperature, radiation, humidity, CO 2 and day length) contributing to the variability in the relationship between leaf nitrogen, V c,max25 and J max25 .Based on the theoretically optimal amount of leaf nitrogen allocated to different processes, the LUNA model Introduction

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Full predicts V c,max25 and J max25 under different environmental conditions.We estimate the LUNA model parameters by fitting the model predictions to observations of V c,max25 and J max25 .In order to assess the impacts of future climate change on photosynthesis, we used the calibrated LUNA model to estimate the summer season net photosynthetic rate using predicted V c,max25 and J max25 under historical and future climate conditions.

Overview
Our LUNA model (version 1.0) is based on the nitrogen allocation model developed by Xu et al. (2012), which optimizes nitrogen allocated to light capture, electron transport, carboxylation, and respiration.Xu et al. (2012) considered a series of assumptions on the model to generate optimized nitrogen distributions, these were (i) that storage nitrogen is allocated to meet requirements to support new tissue production; (ii) respiratory nitrogen is equal to the demand implied by the sum of maintenance respiration and growth respiration; We used an efficient Markov Chain Monte Carlo simulation approach, the Differential Evolution Adaptive Metropolis Snooker Updater (DREAM-ZS) algorithm (Laloy and Vrugt, 2012), to fit the nitrogen allocation model to a large dataset of observed V c, max and J max collected across a wide range of environmental gradients (Ali et al., 2015).After model fitting, a sensitivity analysis was Introduction

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Full performed to gauge the response of the model to parametric variation and to environmental drivers (temperature, photosynthetic active radiation, day length, relative humidity and atmospheric CO 2 concentration).Finally, using climate projections from the Community Climate System Model (CCSM), mean summer-season V c,max25 and J max25 and their impacts on net photosynthesis were estimated for the globe.

Model description
The structure of LUNA model is based on Xu et al. (2012), where plant leaf nitrogen is divided into four pools: structural nitrogen, photosynthetic nitrogen, storage nitrogen and respiratory nitrogen.We assume that plants optimize their nitrogen allocation to maximize the photosynthetic carbon gain, defined as the gross photosynthesis (A) minus the maintenance respiration for photosynthetic enzymes (R psn ), under specific environmental conditions and given the leaf nitrogen use strategy determined by four parameters in the LUNA model.These four parameters include (1) J maxb0 (unitless) specifies baseline proportion of nitrogen allocated for electron transport rate; (2) J maxb1 (unitless) determines electron transport rate response to light; (3) t c,j 0 (unitless) specifies the baseline ratio of Rubisco-limited rate to light-limited rate; and (4) H (unitless) determines electron transport rate response to relative humidity.A complete description of the LUNA model and the detailed associated optimization algorithms are provided in Appendix A. This optimality approach was introduced and tested by Xu et al. (2012) for only three test cases, and here we assess its fidelity at large spatial scale with improvement to account for large scale variability.Optimal approaches are an important tool of land surface models, in that they provide a specific testable hypothesis for plant function (Dewar, 2010;Franklin et al., 2012;Schymanski et al., 2009;Thomas and Williams, 2014).Introduction

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Data and temperature response functions
Details of data collection are stated in Ali et al. (2015).We used all of the data from Ali et al. (2015) with the exception of one study that collected seasonal data on V c,max and J max during prolonged drought (Xu and Baldocchi, 2003), in view that our model only consider the optimal nitrogen allocation based on the monthly climate conditions but did not consider the potential enzyme deterioration due to long-term droughts.In summary, we used 766 data points for V c,max and 643 data points for J max ranging from tropics to the arctic with a total of 125 species.
To allow comparisons of V c,max and J max data collected at different temperatures, we first standardized data to a common reference temperature ( 25• C).To do this, we employed temperature response functions (TRFs).Because of issues related to the possibility of acclimation to temperature, the appropriate TRF to use is not yet a matter of scientific agreement (Yamori et al., 2006).To test the potential impact of our decision on the outcome of the study, we used two alternative temperature response functions in this study.The first temperature response function (TRF1) used Kattge & Knorr's (2007)'s algorithm, which empirically accounts for the potential for acclimation to growth temperature.Following the Community Land Model version 4.5, the growth temperature is constrained between 11 and 35 • C (Oleson et al., 2013) to limit the extent of acclimation to growth temperatures found in the calibration data set.The second temperature response function (TRF2) did not consider change in temperature response coefficients to growth temperature (Kattge and Knorr, 2007).See Appendix B for details of TRF1 and TRF2.
Because LUNA model is based on the C 3 photosynthetic pathway, in this study, we only consider C 3 species.Typically, plant species are grouped into several simple plant functional types (PFTs) in ESMs because of computational limitations and gaps in the ecological knowledge.In view that the processes considered in LUNA model are universal across all C 3 species and limited coverage of environmental conditions for Introduction

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Full individual plant functional types, our LUNA model does not differentiate among PFTs for C 3 species.Namely, we have a single model for all C 3 PFTs.

Parameter estimation
The four parameters in the LUNA model are difficult to measure in the field.In this study, we estimate these parameters by fitting out model against observations of V c,max25 and J max25 data using the Differential Evolution Adaptive Metropolis (DREAM (ZS) ) method (Vrugt et al., 2008(Vrugt et al., , 2009;;Laloy and Vrugt, 2012).We used the DREAM (ZS) algorithm (Vrugt et al., 2008(Vrugt et al., , 2009;;Laloy and Vrugt, 2012) to calibrate our model because this method uses differential evolution (Storn and Price, 1997) as genetic algorithm for population evolution with a Metropolis selection rule to decide whether candidate points should replace their parents or not.This simple MCMC method exhibits excellent sampling efficiencies on a wide range of model calibration problems, including multimodal and high-dimensional search problems.A detailed description of DREAM (ZS) appears in Vrugt et al. (2008Vrugt et al. ( , 2009) ) and Laloy and Vrugt (2012) and interested readers are referred to these publications.A simple Gaussian likelihood function (No.4 in DREAM (ZS) ) was used to compare our model simulations of V c,max25 and J max25 with their observed counterparts.Examples of convergence of the parameters are presented in Figs.S1 and S2 in the Supplement.

Model evaluations
In this study, we considered two statistical metrics to analyze the performance of the LUNA model against the V c,max and J max data.They are the coefficient of determination efficiency is given as where y i are observations, ŷi are model estimates and y is the mean of observations.It estimates the proportion of variance in the V c, max or J max data explained by the 1 : 1 line between model predictions and observations (Mayer and Butler, 1993;Medlyn et al., 2005).The ME can range between 0 and 1, where a ME = 1 corresponds to a "perfect" match between modelled and measured data and a ME = 0 indicates that the model predictions are only as accurate as the mean of the measured data.

Model sensitivity analysis
We conducted two sensitivity analyses of our model to identify the importance of the model parameters and the environmental variables.In the first sensitivity analysis, each value of the model parameter (J maxb0 , J maxb1 , t c,j 0 , and H) was perturbed, one at a time, by ±15 % of their fitted values, to measure the importance of model parameters to modeled V c,max25 and J max25 .In the second sensitivity analysis, the environmental variables (day length (hours), daytime radiation (W m −2 ), temperature ( • C), relative humidity (unitless), and carbon dioxide (ppm)) were perturbed, one at a time, by ±15 % of their mean values to identify which environmental variable was most likely to drive modeled V c,max25 and J max25 . in different regions.In this study, we aim to investigate the importance of changes in V c,max25 and J max25 as predicted by the LUNA model to the net photosynthesis rate (A net ) estimation in future.The importance is measured by the percentage difference in the estimation of future mean A net for the top canopy leaf layer during the summer season by using V c,max25 and J max25 estimated for historical climate conditions or the V c,max25 and J max25 estimated for future climate conditions (See Appendix C for details of A net calculation).
We used Coupled Climate Carbon Cycle Model Intercomparison Project Phase 5 (CMIP5) (Meehl et al., 2000) model outputs to obtain projections of the future climate.Climate modelers have developed four representative concentration pathways (RCPs) for the 21st century that correspond to different amounts of greenhouse gas emissions (Taylor et al., 2013).In this study, we used the historical and future climate conditions simulated by the CCSM 4.0 model under the emission scenario of RCP8.5, which considers the largest greenhouse gas emissions.We did not consider other models and emission scenarios because our main purpose is to estimate the potential impact of our nitrogen allocation model on photosynthesis estimation but not to do a complete analysis under all CMIP5 output.Specifically, we used ten-year climate conditions between 1995 and 2004 for historical and the ten-year climate conditions between 2090 and 2099 for future.We present optimal V c,max25 and J max25 predictions for the peak growing season months.Data from the NOAA Earth System Research Laboratory over the years 1950 to 2010 (Riebeek, 2011) showed that the maximum amount of carbon dioxide drawn out of the atmosphere occurs in August and February by the large land masses of Northern and Southern Hemisphere, respectively.As a result, June, July and August months were used in this study as the summer season for Northern Hemisphere and December, January and February months were considered as the summer season for the Southern Hemisphere.V c,max25 and J max25 were predicted using the average values of the climate variables for June, July, August and December, January and February for Northern, Southern Hemispheres, respectively.Introduction

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Full In order to identify the importance of changes in different climate variables (temperature, CO 2 , radiation and relative humidity) to modeled changes in V c,max25 and J max25 in the future, we conducted a sensitivity analysis of the impact of changes in climate variables on model results.Specifically, we measured the importance of changes in a specific climate variable by the difference in V c,max25 and J max25 predicted by the LUNA model driven by historical values or future values of the specific climate variable of interest with all other climate variables set as their historical values.

Model-data comparison of V c,max25 and J max25
The DREAM inversion approach allowed us to estimate the four parameters in our LNUE model (Table 1).Using the fitted model parameters, the LUNA model explained 54 % of the variance of observed V c,max25 across all of the species (Fig. 1a) and 65 % of the variance in observed J max25 (Fig. 1b) using temperature response function TRF1 (a temperature response function that considered the potential of acclimation to growth temperature).When temperature response function TRF2 (a temperature response function that did not consider change in temperature response coefficients to growth temperature) was used, the LUNA model explained 57 % of variance in observed V c,max25 (Fig. 1c) and 66 % of the variance in observed J max25 (Fig. 1d) across all of the species.By comparing the model predictions with only the studies that reported seasonal cycles of V c,max25 and J max25 , we found the model explained 67 and 53 % of the variance in observed V c,max25 and J max25 , respectively, when TRF1 was used (Fig. S3a and b in the Supplement).The model explained 67 and 54 % of the variance in observed V c,max25 and J max25 , respectively, when TRF2 was used (Fig. S3c and d).
Our model also performed well for different PFTs.When using TRF1, for herbaceous plants, the LUNA model explained about 57 % of the variance in observed V c,max25 (Fig. S4a).The model explained about 58 and 47 % of the variance in observed V c,max25 Introduction

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Full for shrubs (Fig. S4b) and for trees (Fig. S4c), respectively.For the electron transport, the LUNA model explained about 49, 85 and 46 % of the variances in observed J max25 for herbaceous plants (Fig. S4d), shrubs (Fig. S4e) and trees (Fig. S4f), respectively.When we used a fixed temperature response curve under different growth temperatures (TRF2), for shrubs, the LUNA model has a higher predictive power (about 63 % of the variances in observed V c,max25 (Fig. S5b)).Across TRF1 and TRF2, the LUNA model explained similar amount of variance in observed V c,max25 for herbaceous and trees (Fig. S5a and c).For J max25 , the LUNA model explained a similar amount of variability for herbaceous, shrubs and trees for TRF1 (Fig. S4d-f) and TRF2 (Fig. S5d-f).

Model sensitivity analysis
Sensitivity analysis of the four model parameters (Table 1) showed that all the four parameters had positive effects on V c,max25 (Fig. 2a and c) and J max25 (Fig. 2b and d) regardless of the temperature response function used.t c,j 0 had the strongest effect on V c,max25 (Fig. 2a and c) while J maxb0 had the strongest effect on J max25 (Fig. 2b and d).H had little impact on either V c,max25 and J max25 (Fig. 2a-d).
Sensitivity analysis of the climate variables showed that, under both temperature response functions (TRF1 and TRF2), the key drivers of change in V c,max25 were radiation, day length, temperature, CO 2 and relative humidity in order of decreasing importance (Fig. 3a and c).For J max25 , the main drivers of change in J max25 were day length, temperature, radiation, relative humidity and CO 2 in order of decreasing importance (Fig. 3b and d), irrespective of which temperature response functions were used.

Impacts of climate change on V c,max25 and J max25
Across the globe, the gradient of V c,max25 and J max25 is similar irrespective of whether TRF1 or TRF2 was used (Figs. 4 and S6).Under historical conditions, regions from higher latitudes are predicted to have relatively high V c,max25 and J max25 while lower latitudes are predicted to have relatively low V c,max25 and J max25 (Fig. 4a and c  Fig. S6a and c for TRF2).Future climatic conditions are likely to decrease V c,max25 in many continents mainly due to the predicted increase in temperature and CO 2 concentration (Fig. 4b for TRF1; Fig. S6b for TRF2).J max25 is predicted to decrease at higher latitudes but slightly increasing at lower latitudes (Fig. 4d for TRF1and Fig. S6b for TRF2).
Our results showed that V c,max25 was most sensitive to CO 2 , temperature, radiation and relative humidity in order of decreasing importance (Fig. 5a-d for TRF1 and Fig. S7a-d for TRF2).J max25 was most sensitive to temperature, radiation, relative humidity and CO 2 in order of decreasing importance (Fig. 6a-d for TRF1 and Fig. S8a-d for TRF2).Across the globe, temperature had negative impacts on V c,max25 when using TRF1 (Fig. 5a); however, V c,max25 was found to be increasing at the lower latitudes when using TFR2 (Fig. S7a).
Our model showed that the future summer-season mean photosynthetic rate at the top leaf layer could be substantially overestimated if we does not consider the acclimation of V c,max25 and J max25 for the future (i.e., using the V c,max25 and J max25 estimated for historical climate conditions) (Fig. 7a and b), especially for regions with high temperatures (Fig. S9).Compared to the model using TRF1, the overestimation of future summer-season mean photosynthesis rates is much higher than the model using TRF2 (Fig. 7b).The overestimation of total global net photosynthetic rate is 10.1 and 16.3 % for TRF1 and TRF2, respectively.

Model limitations
The assumption that nitrogen is allocated according to optimality principles explained a large part of variability in V c,max25 (approximately 55 %) and in J max25 (approximately 65 %) at the global scale, regardless of the temperature response functions used.It also well captured the seasonal cycles and the PFT-specific values of V c,max25 and

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Full  -5).These results suggest our model is able to capture many of the key components of the drivers of V c,max25 and J max25 across the globe both in space as well as in time.The remaining portion of uncertainty that cannot be explained by our LUNA model could be related to variability within the 125 species considered in this study.Data availability limited the number of species considered and favored the universal LUNA that we used as separate species normally did not cover a large range of environmental conditions; however, we should be able to fit our model to specific PFTs when additional data become available that provides more complete coverage of environmental conditions and PFTs.We expect that such a model would be able to capture more of the variability observed in V c,max25 and J max25 .
Unexplored nutrient limitations and other plant physiological properties could also play a factor in the limitation of our model.For example, the nitrogen use efficiency of tropical plants (typically modest to low nitrogen) can be diminished by low phosphorus (Cernusak et al., 2010;Reich and Oleksyn, 2004;Walker et al., 2014), suggesting that our model could be improved by considering multiple nutrient limitations (Goll et al., 2012;Wang et al., 2010).Our treatment of photosynthetic capacity could also be improved by incorporating species-specific mesophyll and stomatal conductance (Medlyn et al., 2011), by analyzing leaf properties such as leaf life span (Wright et al., 2004), or by considering soil nutrient and soil water availability.
Another potential reason why the model is unable to explain a significant part of uncertainty in the observation is due to that fact that the measurement error on V c,max25 and J max25 is rarely reported in the literature.Measurement errors on V c,max25 and J max25 could result from many sources.Firstly, through different statistical fitting approaches used to fit the Farquhar et al. model (Dubois et al., 2007;Manter and Kerrigan, 2004) to determine the transition C i value (the value of C i used to differentiate between Rubisco and RUBP limitations), which are not yet consistent in the literature (Miao et al., 2009).Secondly, obtaining accurate or biologically realistic estimates of dark respiration is often challenging (but see Dubois et al., 2007), and as such, dark respiration is sometimes not reported (Medlyn et al., 2002b).Introduction

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Full Our model predicts that higher temperatures generally lead to lower values of V c,max25 and J max25 (Fig. 3a and c ).As temperature increases, the nitrogen use efficiencies of V c,max and J max also increase and thus plants need a lower amount of nitrogen allocated for carboxylation and electron transport.This is true for all the sites except for V c,max25 in the hotter regions when TRF2 was used (Fig. S7a).The reason is because LUNA model will use a higher increase in night-time temperature (e.g., 22 to 30 • C) than daytime temperature (e.g., from 31 to 33 • C) as constrained by the maximum temperature for optimization in TRF2 (i.e., 33 • C).Thus, the nitrogen use efficiency of daily respiration increases much strongly than the nitrogen use efficiency of V c,max .Photosynthesis and respiration is balanced within the model, so plants do not need to invest a lot of nitrogen in respiratory enzymes under hot regions.Therefore, more nitrogen is available for other processes, and the proportion of nitrogen allocated to carboxylation and thus V c,max25 increased accordingly.
Our model predicts that CO 2 has negligible effects on J max25 , which is supported by reports from other studies (e.g.Maroco et al., 2002).A meta-analysis of 12 FACE experiments indicated reductions of J max of approximately 5 % but a 10 % reduction in V c,max25 under elevated CO 2 (Long et al., 2004).Our model also predicts that relative humidity has little effect on V c,max25 .This may be due to the fact that most of the values of V c,max25 and J max25 used in our dataset were reported with relatively high humidity values.But, our model, may have underestimated the effects of prolonged drought on V c,max25 under low humidity conditions (Xu and Baldocchi, 2003), which we did not consider.Under prolonged drought, plants close their stomata and photosynthesis is greatly reduced (Breshears et al., 2008;McDowell, 2011).Without carbon input and high temperatures during drought, photosynthetic enzymes may degenerate, which could decrease V c,max25 substantially (Limousin et al., 2010;Xu and Baldocchi, 2003).

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Full Our model suggests that most regions of the world will likely have reductions in V c,max25 (Figs.4b and S6b), because higher temperature (Fig. S10) coupled with elevated CO 2 will increase nitrogen use efficiency of Rubisco and thus plants are able to reduce the amount of nitrogen allocated for Rubisco to reduce the carbon cost required for enzyme maintenance.Similarly, J max25 will also decrease globally, except in regions where the present growing temperatures are high (Fig. S9b).The increase of J max25 can be attributed to leaf temperature limitation and increased shortwave radiation.Temperature will have little impact on nitrogen allocation in regions with historically high growing temperatures because leaf temperature in already close to or high than the upper limit of optimal nitrogen allocation (42 • C for TRF1 and 33 • C for TRF2).Based on Eq. (A11), higher levels of shortwave solar radiation will increase nitrogen allocation to electron transport (Evans and Poorter, 2001).If we do not account for the potential acclimation of V c,max25 and V c,max25 under future climate conditions as predicted by the LUNA model, our analysis indicates that ESM predictions of future global photosynthesis at the uppermost leaf layer will likely be overestimated by as much as 10-14 % if V c,max25 and J max25 are held fixed (Fig. 7).Therefore, to reliably predict global plant responses to future climate change, ESMs should incorporate models that use environmental control on V c,max25 and J max25 .It has been recently suggested that nitrogen-related factors are not well represented in ESMs (Houlton et al., 2015;Wieder et al., 2015).Our nitrogen partitioning scheme would help alleviate biases into the predictions of future photosynthetic rates, and also climate processes that are dependent on these predictions (Bonan et al., 2011;Knorr and Kattge, 2005;Rogers, 2014).Introduction

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Full The photosynthetic nitrogen, N psn , is further divided into nitrogen for light capture (N lc ; gN m −2 leaf), nitrogen for electron transport (N et ; gN m −2 leaf), and nitrogen for carboxylation (N cb ; gN m −2 leaf).Namely, The structural nitrogen, N str , is calculated as the multiplication of leaf mass per unit area (LMA: g biomass/m 2 leaf), and the structural nitrogen content (SNC: gN g −1 biomass). Namely, where SNC is set to be fixed at 0.002 (gN g We assume that plants optimize their nitrogen allocations (i.e., N store , N resp , N lc , N et , N cb ) to maximize the photosynthetic carbon gain, defined as the gross photosynthesis (A) minus the maintenance respiration for photosynthetic enzymes (R psn ), under specific environmental conditions and given plant's strategy of leaf nitrogen use.Namely, the solutions of nitrogen allocations {N store , N resp , N lc , N et , N cb } can be estimated as follows, Nstore , Nresp , Nlc , Net , Ncb = argmax The gross photosynthesis, A, was calculated with a coupled leaf gas exchange model based on the Farquhar et al. (1980)  In the LUNA model, the maximum electron transport rate (J max ; µmol electron m −2 s −1 ) is simulated to have a baseline allocation of nitrogen and additional nitrogen allocation to change depending on the average daytime photosynthetic active radiation (PAR; µmol electron m −2 s −1 ), day length (hours) and air humidity.Specifically, we have The baseline electron transport rate, J max0 , is calculated as follows, where J maxb0 (unitless) is the baseline proportion of nitrogen allocated for electron transport rate.NUE J max (µmol electron s −1 g −1 N) is the nitrogen use efficiency of J max Introduction

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Full (see Eq. D2 for details).J maxb1 (unitless) is a coefficient determining the response of the electron transport rate to amount of absorbed light (i.e., αPAR).f (day length) is a function specifies the impact of day length (hours) on J max in view that longer day length has been demonstrated by previous studies to alter V c,max25 and J max25 (Bauerle et al., 2012;Comstock and Ehleringer, 1986) through photoperiod sensing and regulation (e.g.Song et al., 2013).Following Bauerle et al. (2012), f (day length) is simulated as follows, f (humidity) represents the impact of air humitidy on J max .We assume that higher humidity leads to higher J max with less water limiation on stomta opening and that low relative humidity has a stronger impact on nitrogen allocation due to greater water limitation.When relative humidity (RH; unitless) is too low, we assume that plants are physiologically unable to reallocate nitrogen.We therefore assume that there exists a critical value of relative humidity (RH 0 = 0.25; unitless), below which there is no optimal nitrogen allocation.Based on the above assumptions, we have where H (unitless) specifies the impact of relative humidity on electron transport rate.Replacing Eq. (A7) with Eqs.(A8), ( A9) and (A10), we have The efficiency of light energy absorption (unitless), α, is calculated depending on the amount of nitrogen allocated for light capture, N lc .Following Niinemets and Tenhunen (1997), we have, where 0.292 is the conversion factor from photon to electron.C b is the conversion factor (1.78) from nitrogen to chlorophyll.After we estimate J max , the actual electron transport rate with the daily maximum radiation (J x ) can be calculated using the empirical expression of Smith (1937), where PAR max (µmol m −2 s −1 ) is the maximum photosynthetically active radiation during the day.
Based on Farquhar et al. (1980) and Wullschleger (1993), we can calculate the electron-limited photosynthetic rate under daily maximum radiation (W j x ) and the Rubisco-limited photosynthetic rate (W c ) as follows, where K j and K c as the conversion factors for J x , V c,max (V c,max to W c and J x to W J x ), respectively (see Eqs. where t c,j is the ratio of W c to W J x .We recognize that this ratio may change depending on the nitrogen use efficiency of carboxylation and electron transport (Ainsworth and Rogers, 2007) and therefore introduce the modification as follows, where t c,j 0 (unitless) is the ratio of Rubisco-limited rate to light limited rate, NUE c0 (µmol CO 2 s −1 g −1 N), NUE j 0 (µmol CO 2 s −1 g −1 N) are the daily nitrogen use efficiency of W c and W j under reference climate conditions defined as the 25 determines that the higher nitrogen use efficiency of W c compared to that of W j will lead to a higher value of t c, j (or a higher value of W c given the same value of W j ).The exponent 0.5 was used to ensure that the response of V c,max to elevated CO 2 is down-regulated by approximately 10 % when CO 2 increased from 365 to 567 ppm as reported by Ainsworth and Rogers (2007).Replacing Eq. (A16) with Eqs.(A14), (A15) and (A17), we are able to estimate the maximum carboxylation rate (V c,max ; µmol CO 2 m −2 s −1 ) as follows, Following Collatz et al. (1991a), the total respiration (R t ) is calculated in proportion to

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Full Accounting for the daytime and nighttime temperature, we are able to estimate the daily respirations as follows, where D day and D night are daytime and nighttime durations in seconds.f r (T night ) and f r (T day ) are the temperature response functions for respiration (see Eq. B1 for details).
In summary, given an initial estimation of N lc , we are able to first estimate the efficiency of light energy absorption α using Eq.(A12).With that, we are able to estimate the maximum electron transport rate, J max , using Eq.(A11).The nitrogen allocated for electron transport can thus be calculated as follows, Then, based on Eq. (A18), we are able to estimate the corresponding the maximum carboxylation rate V c,max and the nitrogen allocated for carboxylation as follows, where NUE V c ,max is the nitrogen use efficiency for V c,max .See Eq. (D1) for details of calculation.Using Eq. (A 20), we are able to estimate R td and thus the nitrogen allocated for respiration as follows, where NUE r is nitrogen use efficiency of enzymes for respiration.See Eq. (D3) for details of calculation.Finally, the "storage" nitrogen is calculated as follows,

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Full Note that this "storage" nitrogen is mainly a remaining component of FNC a .Its formulation is different from the formulation of Xu et al. (2012) where N store is set as a linear function of net photosynthetic rate.This modification is based on the observations that the preliminary fitting to data using the linear function shows no dependence of N store on net photosynthetic rate.To make the solutions realistic, we set minimum of N store as 5 % of NC a in view of potential nitrogen for plant functionality that is not accounted for by photosynthesis and respiration.By exploring different values of nitrogen allocated for light capture N lc and using the Eqs.(A21-23), we will find the "optimal" nitrogen allocations ( Nstore , Nresp , Nlc , Net , Ncb ) until the net photosynthetic rate is maximized (see Eq. A5) given a specific set of nitrogen allocation coefficients (i.e., J maxb0 J maxb1 , H, and t c,j 0 ).The detailed optimization algorithms are implemented as follows: 1. Increase the nitrogen allocated (N lc ) for light capture (from a small initial value of 0.05) and calculate the corresponding light absorption rate α with Eq. (A12); 2. Calculate J max from Eq. (A11) and derive the nitrogen allocated to electron transport, N et , using Eq.(A21); 3. Calculate V c,max from Eq. (A18) and derive the nitrogen allocated to Rubisco, N cb , using Eq.(A22); 4. Calculate the total respiration R td from Eq. (A20) and derive the nitrogen allocated to respiration, N resp , using Eq.(A23); 5. Calculate the total nitrogen invest in photosynthetic enzymes including nitrogen for electron transport, carboxylation and light capture using Eq.(A2); 6. Calculate the gross photosynthetic rate, A, and the maintenance respiration for photosynthetic enzymes, R psn , by Eq. (A6); 7. Repeat steps (1) to ( 6) until the increase from previous time step in A is smaller or equal to the increase in R psn .Introduction

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Full Community land model version 4.5 (CLM4.5)(Oleson et al., 2013) uses the partial pressures of oxygen, O as 20 900 Pa.The kinetic properties of Rubisco which depend on temperature are Rubisco specific factor, τ (Jordan and Ogren, 1984), K cc and K o , which are the Michaelis-Menten constants for CO 2 and O 2 , respectively.The temperature response function of R d and kinetic properties of Rubisco (K cc , K o , τ) are described below, where the fixed coefficients of the equations are values at 25 • C.

Temperature dependence of V c,max and J max
Temperature sensitivities of V c,max and J max were simulated using a modified Arrhenius function (e.g.Kattge and Knorr, 2007;Medlyn et al., 2002a;Walker et al., 2014).Because the temperature relationship could acclimate, we examined Kattge and Knorr (2007)'s formulation of with and without temperature acclimation to plant growth temperature.We used two temperature dependence functions of V c,max and J max , which are described below.

Temperature response function one (TRF1)
Fundamentally, TRF1 is a temperature dependence of V c, max and J max , which is based on the formulation and parameterization as in Medlyn et al. (2002a) but further modi-

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Full fied by Kattge and Knorr (2007) to make the temperature optima a function of growth temperature (T g ; • C).
where V c,max25 is the value of V c,max at the reference temperature (T 0 = 298.15K).H a (J mol −1 ) is energy of activation and H d (J mol −1 ) is the energy of deactivation.The entropy term, S v (J mol −1 K −1 ), is now a function of temperature (Kattge and Knorr, 2007): S v = a+bT g , where a and b are acclimation parameters for S v , R is the universal gas constant (8.314J mol −1 K −1 ) and the leaf temperature is T 1 (K ).
TRF1 is implemented in CLM4.5 by Oleson et al. (2013), who uses the form of temperature dependence of V c,max and J max as shown in Eq. (B5), but with limited temperature acclimation, where S v = 668.39− 1. 07 • min (max (tgrowth, 11) , 35).Other parameters that are present in CLM4.5 model include, H a = 72 000 J mol −1 and H d = 200 000 J mol −1 .The values of the acclimation parameters (a = 668.39 and b = −1.07) were taken from Table 3 of Kattge and Knorr (2007), which were fixed across our data set.The same values of a and b are used by CLM4.5.A equation similar to Eq. (B6), f J max T 1 , T g , is used to describe the temperature dependence of J max with the corresponding S v equation (that considers limited temperature acclimation).The corresponding values of the acclimation parameters (a and b), were again taken from Table 3 of Kattge and Knorr (2007) and were fixed across our data set.The same values of a and b are used by CLM4.5.We used the remaining parameter values as in CLM4.5 that included, H a = 50 000 J mol where W c is the Rubisco limited rate and W j is the electron transport limited rate.The Rubisco-limited carboxylation can be described by, with where V c,max is the maximum rate of carboxylation, competitive with respect to both CO 2 and oxygen, and K cc and K O are Michaelis constants for carboxylation and oxygenation, respectively.τ is the specificity factor for Rubisco (Jordan and Ogren, 1984), while C i , and O are the partial pressures of CO 2 and O 2 in the intercellular air space, respectively.Likewise, the electron-limited rate of carboxylation can be expressed by, with where J is the potential rate of electron transport, and the factor 4 indicates that the transport of four electrons will generate sufficient ATP and NADPH for the regeneration of RuBP in the Calvin cycle (Farquhar and von Caemmerer, 1982).The potential rate of electron transport is dependent upon irradiance, I, according to the empirical expression of Smith (1937), Full where α, the efficiency of light energy conversion is considered as 0.292 (unitless) (Niinemets and Tenhunen, 1997) and J max is the maximum rate of electron transport.

Ball-Berry model
The stomatal conductance (g, m s −1 ) was evaluated by the Ball-Berry empirical stomatal conductance model (Ball et al., 1987): where RH is the relative humidity (unitless) at the leaf surface, C a is the CO 2 concentration at the leaf surface, and g 0 (0.0005 s m −1 ) and m are the maximum stomatal conductance and slope (9, constant across all C 3 species), respectively.The estimation of A could be sensitive to the choice of maximum stomatal conductance slope, which we set the same for all species, despite the evidence that this parameter varies both within and across species (Harley and Baldocchi, 1995;Wilson et al., 2001).A recent synthesis provides the first analysis of the global variation in stomatal slope based on an alternative algorithm that considers representation of optimal stomatal behavior (Lin et al., 2015).However, following CLM4.5, which uses the Ball-Berry empirical stomatal conductance model (Ball et al., 1987), we fixed the value of stomatal slope (m) as 9 for all PFTs in our study.

Calculation of photosynthesis and stomata conductance
We solved Farquhar's non-linear equation (A vs. C i ), the Ball-Berry equation (g s vs. A) and the diffusion equation (A = g s (C a -C i ) simultaneously by taking an iterative approach (Collatz et al., 1991a;Harley et al., 1992;Leuning, 1990) until values of A, g s , and C i were obtained.The three equations were solved in two phases; the first phase included solving the equations for which Rubisco was limiting while the second phase considered light limitation.The following steps were followed:

GMDD Introduction
Full 1.Given the initial values of C i (where initial value of C i was assumed 0.7 × ambient CO 2 concentration), the temperature dependence functions of V c, max and J max (see Appendix B), and the temperature dependence of Rubisco kinetics (O, τ, K c and K O , Appendix B), A was calculated from Eq. (C1).
2. CO 2 concentration at the leaf surface (C a ) was determined by calculating the difference between C i and the partial pressure due to A, wind speed and the dimension of the leaf.
3. Given A and C a , and using Eq.(C7), stomatal conductance (g) was determined.
4. C i was determined by calculating the difference between C a and partial pressure due to A and boundary conditions of the stomata.
5. Using the leaf energy balance based on absorbed short-wave radiation, molar latent heat content of water vapor, air temperature, and a parameter that governs the rate of convective cooling (38.4 J m −2 s −1 K −1 ) (Jarvis, 1986;Moorcroft et al., 2001), leaf temperature was calculated.
The above five steps were repeated in a systematic way until g was equilibrated.The final value of A was then recorded.

Appendix D: Nitrogen use efficiencies
The nitrogen use efficiency for V c,max (NUE V c,max , µmol CO 2 g −1 N s −1 ) is estimated from a baseline nitrogen use efficiency 25 • C (NUE V c,max25 ) and a corresponding temperature response function at as follows, where the constant 47.3 is the specific Rubisco activity (µmol CO 2 g −1 Rubisco s −1 ) measured at 25 • C and the constant 6.25 is the nitrogen binding factor for Rubisco (g Rubisco g −1 N) (Rogers, 2014).f V c,max (T , T g ) is the function specifying the temperature dependence of V c,max with T as the leaf temperature and T g as the growth air temperature (See Appendix B for details of the temperature dependence of V c, max ).
The nitrogen use efficiency for J max (NUE J max , µmol electron g −1 N s −1 ) is estimated based on a characteristic protein cytochrome f (Niinemets and Tenhunen, 1997), where the coefficient 156 is the maximum electron transport rate for cytochrome f at 25 • C (µmol electron µmol cytochrome f ); 8.06 is the nitrogen binding coefficient for cytochrome f (µmol cytochrome f g −1 N in bioenergetics).f Jmax (T , T g ) is a function specifies the dependence of J max on temperature (See Appendix B for details of the temperature dependence of J max ).
The nitrogen use efficiency of enzymes for respiration (µmol CO 2 g −1 N day −1 ), NUE r , is assumed to be temperature-dependent.Specifically, it is calculated as follows, where NUE rp25 is the nitrogen use efficiency at 25 • C. NUE rp25 is estimated from the observation of J max25 and V c,max25 as follows, NUE rp25 = 0.8 × 0.5 × 0.015 × V c,max25 where the total respiration is set as 1.5 % of V c,max (Collatz et al., 1991b).We assume that 50 % of the total respiration is used for maintenance respiration (Van Oijen et al., 2010) and 80 % of the maintenance respiration is used for photosynthetic enzyme.In view that the light absorption rate is generally around 80 % (Niinemets and Tenhunen, 1997), we set the nitrogen for light capture as 0.2 based on Eq. (A12) in Appendix A. NUE J max25 and NUE V c,max25 are the nitrogen use efficiency for J max25 and V c,max25 estimated from Eqs. (D1) and (D2).In this study, we used the estimated mean value of 0.715 for NUE rp25 based on the data of Ali et al. (2015).The nitrogen use efficiency for carboxylation (NUE c ) is calculated as the multiplication of conversion factor K c and the nitrogen use efficiency for V c,max follows: where K j is calculated based on the actual internal CO 2 concentrations and leaf temperature (see Eq. C5 in Appendix C for details).Correspondingly, the reference nitrogen use efficiency for electron transport (NUE j 0 ) is calculated using the Eq.(D6) except that Discussion Paper | Discussion Paper | Discussion Paper | et al.
Discussion Paper | Discussion Paper | Discussion Paper | (iii) light capture, electron transport and carboxylation are colimiting to maximize photosynthesis.Xu et al. (2012)'s model need to be calibrated, and has thus far been tested for three test sites.Here, we expand on the work of Xu et al. (2012) to allow global predictions of nitrogen allocation, by fitting the model parameters to an expanded photosynthetic capacity data set.To make global predictions feasible, we also made important refinements to Xu et al. (2012)'s model by considering the impacts of both day length and humidity, and the variations in the balance between light-limited electron transport rate and the Rubisco-limited carboxylation rate in accordance with recent theory.
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | the model efficiency (ME) (Whitley et al., 2011).The r 2 is estimated using the linear regression model for observed values vs. the predicted values.It measures the proportion of variance in V c,max or J max data explained by the model.The model Discussion Paper | Discussion Paper | Discussion Paper |

2. 7
Changes in V c,max25 and J max25 under future climate projections Global surface temperature by year 2100 (relative to present day) could increase by 3.9 • C (Friedlingstein et al., 2014), with large spatial variations across different regions of the globe (Raddatz et al., 2007).Given the dependence of photosynthesis on temperature, it is critical to examine how much future photosynthesis is likely to change Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | J max25 (Figs.S3 Discussion Paper | Discussion Paper | Discussion Paper | 4.2 Importance of environmental control on V c,max25 and J max25 Discussion Paper | Discussion Paper | Discussion Paper | 4.3 Importance of changes in V c,max25 and J max25 to future photosynthesis estimation Discussion Paper | Discussion Paper | Discussion Paper | Appendix A: Leaf Utilization of Nitrogen for Assimilation (LUNA) Model The LUNA model considers nitrogen allocation within a given leaf layer in the canopy that has a predefined leaf-area-based plant leaf nitrogen availability (LNC a ; gN m −2 leaf) to support its growth and maintenance.The structure of the LUNA model is adapted from Xu et al. (2012), where the plant nitrogen at the leaf level is divided into four pools: structural nitrogen (N str ; gN m −2 leaf), photosynthetic nitrogen (N psn ; gN m −2 leaf), storage nitrogen (N store ; gN m −2 leaf), and respiratory nitrogen (N resp ; gN m −2 leaf).Namely, LNC a = N psn + N str + N store + N resp .(A1) −1 biomass), based on data on C : N ratio from dead wood (White et al., 2000).The functional leaf nitrogen content (FNC a ; gN m −2 leaf) is defined by subtracting structural nitrogen content, N str , from the total leaf nitrogen content (LNC a ; gN m −2 leaf), FNC a = LNC a − N str (Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | C3 and C5 in Appendix C for details of calculation).Based on Xu et al. (2012), Maire et al. (2012) and Walker et al. (2014), we assume that W c is proportional to W J x .Specifically, we have W c = t c,j W J x Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | plants were assumed to acclimate to growth temperatures (Temperature response function one; TRF1) or not (Temperature response function two; TRF2).
Discussion Paper | Discussion Paper | Discussion Paper | −1 and H d = 200 000 J mol −1 .Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | D1) with NUE V c,max25 = 47.3 × 6.25, Discussion Paper | Discussion Paper | Discussion Paper | NUE r = 33.69[Dday f r (T day ) + D night f r (T night )] (D3) where 33.69 is the specific nitrogen use efficiency for respiration at 25 • C (µmol CO 2 g −1 N s −1 ) (Makino and Osmond, 1991) and f r (T ) specifies the dependence of respiration on temperature.D day and D night is the daytime and nighttime length in seconds.The maintenance respiration cost for all photosynthetic enzymes (NUE rp , µmol CO 2 g −1 N s −1 ) is calculated as follows: NUE rp = NUE rp25 f r (T , T g ), (Discussion Paper | Discussion Paper | Discussion Paper | D6)where K c is calculated based on the actual internal CO 2 concentrations and leaf temperature (see Eq. C3 for details).Correspondingly, the reference nitrogen use efficiency for carboxylation (NUE c0 ) is calculated using the Eq.(D5) except that K c is calculated based on the reference internal CO 2 concentration of 26.95 Pa and the reference leaf temperature of 25 • C. The reference internal CO 2 concentration is estimated by assuming 70 % of the atmospheric CO 2 concentration of 380 ppm and an air pressure of 101 325 Pa.The nitrogen use efficiency for electron transport (NUE j ) is calculated as the multiplication of conversion factor K j and the nitrogen use efficiency for J max follows: NUE j = K j NUE J max , (Discussion Paper | Discussion Paper | Discussion Paper |

Figure 1 .
Figure 1.Percentage of variations (r 2 , ME; model efficiency) in observed V c,max25 (µmol CO 2 m −2 s −1 ) explained by modeled V c,max25 (a, c) and in observed J max25 (µmol electron m −2 s −1 ) explained by modeled J max25 (b, d) across all of the species, using TRF1 (a, b) andTRF2 (c, d), where the nitrogen allocation model, the environmental variables, leaf mass per leaf area, and the leaf nitrogen contents were used.TRF1 was a temperature response function that considered the potential for acclimation to growth temperature while TRF2 was a temperature response function that did not consider change in temperature response coefficients to growth temperature.The r 2 is derived by a linear regression between observed and modeled values.The dashed line is the 1 : 1 line.
• C leaf temperature and atmospheric CO 2 concentration of 380 ppm, with leaf internal CO 2 concentration set as 70 % of the atmospheric CO 2 concentration.NUE c (µmol CO 2 s j (µmol CO 2 s −1 g −1 N) are the nitrogen use efficiency of W c and W j at the current climate conditions.See Eqs.(D6) and (D7) for details of calculation.The term NUE c /NUE j NUE c0 /NUE j 0