The 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 few model assumptions to derive the optimized nitrogen distributions, including (i) 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; and (iii) light capture, electron transport and carboxylation are co-limiting to maximize photosynthesis. The model of Xu et al. (2012) has been tested for three different sites only without global-scale calibration of its parameters. Here, we expand the work of Xu et al. (2012) by using a global data set of observations of photosynthetic capacity to derive accurate values of the model parameters and by incorporation of several refinements to support global-scale prediction of Vc,max25 and Jmax25. Specifically, this revised model considers additional environmental variables such as day length and humidity, and honors variations in the balance between the light-limited electron transport rate and the Rubisco-limited carboxylation rate. We use an efficient Markov chain Monte Carlo simulation approach, the Differential Evolution Adaptive Metropolis algorithm (DREAM(ZS)) (Laloy and Vrugt, 2012; Vrugt et al., 2008, 2009), to fit the nitrogen allocation model to a large data set of observed Vc,max and Jmax values collected across a wide range of environmental gradients (Ali et al., 2015). After model fitting, sensitivity analyses are performed to gauge the response of the model to changes in its parameter values and the key environmental drivers including temperature, photosynthetic active radiation, day length, relative humidity and atmospheric CO2 concentration. Finally, mean summer-season Vc,max25 and Jmax25 values and their impacts on net photosynthesis are estimated for the globe, using climate projections from the Community Climate System Model (CCSM) (Gent et al., 2011).

The structure of the LUNA model is based on Xu et al. (2012), where the leaf nitrogen is divided into four different pools including structural nitrogen, photosynthetic nitrogen, storage nitrogen and respiratory nitrogen. We assume that plants optimize their nitrogen allocation to maximize the net photosynthetic carbon gain, defined as the gross photosynthesis (A) minus the maintenance respiration for photosynthetic enzymes (Rpsn), under given environmental conditions and a leaf nitrogen use strategy as determined by the parameters of the LUNA model. The model includes the following four unitless parameters: (1) Jmaxb0, which specifies the baseline proportion of nitrogen allocated for electron transport rate; (2) Jmaxb1, which determines response of electron transport rate to light; (3) tc,j0, which defines the baseline ratio of Rubisco-limited rate to light-limited rate; and (4) H, which determines the response of electron transport rate to relative humidity. The LUNA model predicts the values of Vc,max25 and Jmax25 based on the optimal amounts of nitrogen allocated for carboxylation and electron transport. The model inputs are area-based leaf nitrogen content, leaf mass per unit leaf area and the driving environmental conditions including temperature, CO2, radiation, relative humidity and day length.

It is important to stress here that the outcome of the optimality concept used in LUNA is conditional on the plant's nitrogen use strategies built into the model. Thus, it is possible that the optimal values of Vc,max25 and Jmax25 predicted by the LUNA model for future climate conditions could produce lower values of the net photosynthetic carbon gain than fixed values of Vc,max25 and Jmax25 without the use of a nitrogen use strategy. An example of this is shown in Fig. S1 in the Supplement, where the net photosynthetic carbon gain pertaining to the optimal nitrogen allocations predicted by the LUNA model for the elevated temperature is lower than its counterpart derived from a fixed nitrogen allocation for the ambient temperature. A complete description of the LUNA model and the associated optimality hypothesis and algorithms appears in Appendix A. This optimality approach is introduced and tested by Xu et al. (2012) for only three different sites, and here we evaluate its usefulness and applicability at the global scale with improvements to account for large-scale variability. Optimality approaches are important tools for land surface models because they provide testable hypotheses for specific plant functions (Dewar, 2010; Franklin et al., 2012; Schymanski et al., 2009; Thomas and Williams, 2014).

Details of data collection are reported in Ali et al. (2015). Specifically, we conducted an exhaustive literature search with Google Scholar to obtain publications that contained the words Vc,max, Jmax, maximum carboxylation rate or maximum electron transport rate. To rapidly subset the most appropriate and relevant publications, we use simultaneously the wording leaf nitrogen content, leaf mass per area or specific leaf area. Individual values of Vc,max, Jmax, area-based leaf nitrogen content (LNCa; g N m-2 leaf) and leaf mass per unit leaf area (LMA; g dry mass m-2 leaf) are then obtained by digitizing the experimental data depicted graphically in the selected papers. We use all of the data from Ali et al. (2015) with the exception of one study that collected seasonal data on Vc,max and Jmax during a prolonged drought (Xu and Baldocchi, 2003), as the LUNA model does not take into consideration the potential enzyme deterioration due to water stress but rather simulates only the optimal nitrogen allocation based on monthly climate conditions. This resulted in a data set of 766 observations of Vc,max and 643 data points of Jmax ranging from the tropics to the arctic with a total of 125 species. The data include evergreen and deciduous species from arctic, boreal, temperate and tropical areas at different times of the year and from various canopy locations (Fig. S2).

To allow comparisons of Vc,max and Jmax data collected at different temperatures, we first standardize our data to a common reference temperature (25 ∘C). To do this, we employ temperature response functions (TRFs) for Vc,max and Jmax. Because of issues related to the possibility of acclimation to temperature, there is not yet scientific consensus on which TRF to use (Yamori et al., 2006). Therefore, we use two alternative temperature response functions to evaluate the potential impact of our selection of the TRFs on the outcome of our analysis. The first temperature response function (TRF1) uses the formula of Kattge and Knorr (2007), which accounts empirically for the potential of thermal 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) does not consider the thermal acclimation by fixing the acclimation coefficients in TRF1 (Kattge and Knorr, 2007). Please refer to Appendix B for details on TRF1 and TRF2 used herein.

Because the LUNA model is based on the C3 photosynthetic pathway, in this study, we only consider C3 species. Typically, plant species are grouped into several simple plant functional types (PFTs) in ESMs because of computational limitations and gaps in ecological knowledge. The LUNA model does not differentiate among the PFTs of C3 species due to a limited coverage of environmental conditions for individual PFTs. Thus, a single set of parameter estimates is used for the PFTs of all C3 species.

The four parameters of LUNA are difficult to measure directly in the field. In this study, we estimate their values by fitting our model against observations of Vc,max25 and Jmax25 using the DREAM(ZS) algorithm (Vrugt et al., 2008, 2009; Laloy and Vrugt, 2012). This method uses differential evolution as a genetic algorithm for population evolution with a Metropolis selection rule to decide whether candidate points should replace their parents or not. This simple Markov chain Monte Carlo (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. (2008, 2009) and Laloy and Vrugt (2012) and interested readers are referred to these publications for further details. Uniform prior parameter distributions are used to constrain the potential parameter values and the Gaussian likelihood function is used to quantify the distance between the modeled Vc,max25 and Jmax25 values and their observed counterparts. Convergence plots of the DREAM(ZS) sampled LUNA parameters to the posterior distribution are presented in Figs. S3 and S4.

In this study, two different goodness-of-fit metrics are used to quantify the performance of the LUNA model against the Vc,max and Jmax data. These are the coefficient of determination (r2) (Whitley et al., 2011) and the model efficiency (ME) (Whitley et al., 2011). The r2 metric ranges between 0 and 1 and measures how much of the observed dispersion of Vc,max or Jmax is explained by the model. A related metric, the model efficiency is calculated using ME=1-∑yi-y^i2∑yi-y¯2, where yi and y^i denote the observed and LUNA-simulated values, respectively, and y¯ signifies the mean of the observations. This metric measures the proportion of the variance in Vc,max or Jmax explained by the 1:1 line between model predictions and observations (Mayer and Butler, 1993; Medlyn et al., 2005). The ME ranges between 0 and 1, where a ME of unity corresponds to a perfect match between the modeled and measured data and a ME of zero indicates that the model predictions are only as accurate as the mean of the measured data.

To better understand how the simulated LUNA output of Vc,max25 and Jmax25 depends on its four parameters and the key model inputs, a one-at-a-time (OAT) sensitivity analysis is performed. In the first analysis, we focus on the model parameters only, and perturb their calibrated values, one at a time, with ±15 %. The second sensitivity analysis considers separately the effect of the key environmental variables on the simulated values of Vc,max25 and Jmax25 and perturbs the mean values of the day length (hours), daytime radiation (W m-2), temperature (∘C), relative humidity (unitless) and carbon dioxide (ppm) with ±15 %.

The global surface temperature could increase as much of 3.9 ∘C by the year 2100 relative to present day (Friedlingstein et al., 2014), with large 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 in different regions. In this study, we investigate how the LUNA predicted values of Vc,max25 and Jmax25 will change under future climate conditions and how they will affect future estimates of Anet, the net photosynthesis rate. The impacts of future climate on Vc,max25,Jmax25 and Anet are quantified by calculating their values for the leaf layer at the top canopy during the summer season under historic and future climate conditions. Appendix C summarizes the calculation of Anet.

We use model outputs from the climate carbon cycle Coupled Model Intercomparison Project Phase 5 (CMIP5) (Meehl et al., 2000) to obtain projections of future climate. Climate modelers have developed four representative concentration pathways (RCPs) for the 21st century (Taylor et al., 2013). Each of them corresponds to a different level of greenhouse gas emission. In this study, we use historic and future climate conditions simulated by the CCSM 4.0 model under scenario RCP8.5, which considers the largest greenhouse gas emissions. We do not consider herein other models and emission scenarios as the main purpose of our study is not to do a complete analysis under all CMIP5 outputs but rather to estimate the potential impact of nitrogen allocation on photosynthesis. Specifically, the 10-year climate record between 1995 and 2004 is used as a benchmark for historic conditions, whereas the climate data between 2090 and 2099 is used for future conditions. We present the LUNA's predicted Vc,max25 and Jmax25 values for the months of the peak growing season. Data from the NOAA Earth System Research Laboratory (Riebeek, 2011) showed that the maximum amount of carbon dioxide drawn from the atmosphere occurs in August and February for the large land masses of the Northern and Southern hemispheres, respectively. As a result, June, July and August are assumed herein to best represent the summer season for the Northern Hemisphere and December, January and February are considered representative for the summer season on the Southern Hemisphere. In this study, Vc,max25 and Jmax25 values are predicted by LUNA using the average values of climate variables for the summer season.

We conduct a third sensitivity analysis to quantify the impacts of future changes in climate variables such as temperature, CO2 concentration, radiation and relative humidity on the simulated values of Vc,max25 and Jmax25. While the first two sensitivity analyses in section 2.6 assume current mean climate conditions, this sensitivity analysis investigates global patterns in sensitivity of Vc,max25 and Jmax25 to future changes in climate variables across different biomes. Specifically, we calculate the percentage difference in the LUNA predicted values of Vc,max25 and Jmax25 using historic and future values of each climate variable. All other climate variables are set at their default (or historic) values.

The DREAM(ZS) algorithm provides us with the posterior means and standard deviations of the four LUNA parameters (Table 1). The calibrated LUNA model explains ∼ 54 % of the variance in the observed values of Vc,max25 across all species (Fig. 1a) and ∼ 65 % of the variance in the observed values of Jmax25 (Fig. 1b) using the temperature response function TRF1. This response function considers explicitly the thermal acclimation. If TRF2 is used in LUNA, the model is able to explain ∼ 57 % of the variance in the observed values of Vc,max25 (Fig. 1c) and ∼ 66 % of the variance in the observed values of Jmax25 (Fig. 1d) across all species. When the LUNA predictions with TRF1 are compared with the observation data with seasonal cycles, the model explains ∼ 67 and ∼ 53 % of the variance in the observed values of Vc,max25 and Jmax25, respectively (see Fig. S5a, b in the Supplement). The model performs similarly when TRF2 is used (Fig. S5c, d).

Our model also performs well for different PFTs. With TRF1, the LUNA model explains about 57, 58 and 47 % of the variance in the observed values of Vc,max25 for herbaceous plants (Fig. S6a), shrubs (Fig. S6b) and trees (Fig. S6c), respectively. For Jmax25, LUNA explains approximately 49, 85 and 46 % of the variances in the observed values of Jmax25 for herbaceous plants (Fig. S6d), shrubs (Fig. S6e) and trees (Fig. S6f), respectively. The predictive power of LUNA increases for shrubs when TRF2 is used. About 63 % of the variance in the observed Vc,max25 values is explained by the model (Fig. S7b), yet a similar performance is observed for herbaceous plants and trees (Fig. S7a, c). The statistics for the predictions of Jmax25 are very similar to those reported previously for TRF1 (Fig. S6d–f).

Sensitivity analysis shows that all four LUNA model parameters (Table 1) have a positive effect on Vc,max25 (Fig. 2a, c) and Jmax25 (Fig. 2b, d) regardless which temperature response function is used. The parameter tc,j0 has the strongest effect on Vc,max25 (Fig. 2a, c) while Jmaxb0 has the strongest impact on Jmax25(Fig. 2b, d). Parameter H has a much lesser control on the simulated values of both Vc,max25 and Jmax25 (Fig. 2a–d).

Sensitivity analysis of the LUNA model output to its main climate variables shows that radiation most strongly affects the simulated Vc,max25 values, whereas an increasingly smaller impact is observed for the day length, temperature, CO2 concentration and relative humidity (Fig. 3a, c). The LUNA predicted values of Jmax25 appear most sensitive to day length, followed by temperature, radiation, relative humidity and CO2 concentration (Fig. 3b, d). These findings are independent of the TRF being used.

Across the globe, a similar pattern is observed for TRF1 and TRF2 in the simulated values of Vc,max25 and Jmax25 (Figs. 4 and S8). Under historical climate conditions, the higher latitudes are predicted to have relatively high values of Vc,max25 and Jmax25 while lower latitudes are predicted to have relatively low values of Vc,max25 and Jmax25 (Fig. 4a, c for TRF1; Fig. S8a, c for TRF2). Future climate conditions are likely to decrease significantly the Vc,max25 values for most vegetated lands in large part due to a predicted rise in the temperature and CO2 concentration (Fig. 4b for TRF1 and Fig. S8b for TRF2). A somewhat opposite trend is observed for Jmax25 with decreasing values at higher latitudes and increasing values at the lower latitudes (Fig. 4d for TRF1 and Fig. S8b for TRF2).

Our results show that the LUNA-simulated Vc,max25 values are most sensitive to the changes in CO2 concentration, followed by temperature, radiation and relative humidity (Fig. 5a–d for TRF1 and Fig. S9a–d for TRF2). The variable Jmax25 appears most sensitive to the changes in temperature, and then radiation, relative humidity and CO2 (Fig. 6a–d for TRF1 and Fig. S10a–d for TRF2). Across the globe, temperature has negative impacts on Vc,max25 when using TRF1 (Fig. 5a); however, when TRF2 is used, Vc,max25 is found to increase at the lower latitudes (Fig. S9a).

The simulations of LUNA demonstrate that the future summer-season mean photosynthetic rate at the top leaf layer might be substantially overestimated if acclimation of Vc,max25 and Jmax25 under future climate conditions (i.e., using historic values of Vc,max25 and Jmax25) is not explicitly considered (Fig. 7a, b). This is especially true for regions with high temperatures (Fig. S11). Future estimates of the summer-season mean photosynthesis rate are much higher under TRF1 than TRF2 (Fig. 7b). The omission of acclimation could lead to a 10.1 and 16.3 % overestimation in the global net photosynthetic rate at the top canopy layer for TRF1 and TRF2, respectively.

The LUNA model built on the assumption that nitrogen is allocated according to optimality principles explains a large part of the global-scale variability observed in Vc,max25 (∼ 55 %) and Jmax25 (∼ 65 %), regardless which TRF is used. This approach used by LUNA also mimics accurately seasonal cycles and PFT-specific values of Vc,max25 and Jmax25 (Figs. S5–S7), and has a much better overall predictive power than a multiple linear regression with LNCa and LMA as main predictors. Such a linear model is able to explain only, for both TRFs, about 22 % of the variance in the observed Vc,max25 values (Fig. S12a, d) and approximately 13 % of the variance in the observed Jmax25 values (Fig. S12b, d). These results suggest that our model includes many of the key variables that determine the spatial and temporal variation of Vc,max25 and Jmax25 across the globe. The remaining portion of the variance that cannot be explained by the LUNA model can be related to variability within the 125 species considered in this study. There are inherent intraspecific variations in leaf traits (Valladares et al., 2000) and in photosynthetic capacity (Moran et al., 2016). Data availability limits the number of species that can be considered in the present analysis and favors a single LUNA calibration for all species. Indeed, the data for individual species normally did not cover a sufficiently large range of environmental conditions. When more data become available for individual species in the future, we can revisit the calibration procedure and fit our model to specific PFTs pending a sufficiently large enough coverage of environmental conditions. We posit that such a model will be able to adequately capture a larger portion of the variability observed in Vc,max25 and Jmax25.

Other deficiencies of LUNA might be related to unexplored nutrient limitations and other plant physiological properties. For example, low phosphorus concentrations can reduce considerably the nitrogen use efficiency of tropical plants with typically modest to low nitrogen (Cernusak et al., 2010; Reich and Oleksyn, 2004), suggesting that our LUNA model can be enhanced by considering multiple different nutrient limitations simultaneously (Goll et al., 2012; Walker et al., 2014; Wang et al., 2010). Our treatment of the photosynthetic capacity can also be improved by incorporating a species-specific mesophyll and stomatal conductance (Medlyn et al., 2011), by analyzing properties such as leaf life span (Wright et al., 2004), and by considering soil pH, nutrient availability and water availability (Maire et al., 2015). 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), suggesting that our model could be improved by considering multiple nutrient limitations (Goll et al., 2012; Walker et al., 2014; 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, soil water availability and soil pH (Maire et al., 2015).

Measurement errors of Vc,max25 and Jmax25 also affect negatively the ability of LUNA to describe perfectly the observational data. These errors can originate from many different sources but are rarely quantified in the literature. They can play a significant role in parameter fitting. Indeed, previous research has shown that the value of Ci in the Farquhar et al. (1980) model used to differentiate between Rubisco and Ribulose-1,5-bisphosphate (RuBP) limitations, could be estimated from different methods in the literature (Miao et al., 2009). Furthermore, it is particularly difficult to obtain accurate and biologically realistic estimates of dark respiration (but see Dubois et al., 2007), and consequently, dark respiration is sometimes not reported (Medlyn et al., 2002b).

Our model predicts that higher temperatures generally lead to lower values of Vc,max25 and Jmax25 (Fig. 3a, c). As temperature increases, the nitrogen use efficiencies of Vc,max and Jmax 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 Vc,max25 in the warmest regions of our planet when TRF2 is used (Fig. S9a). This is explained by a large increase in the nighttime temperature of LUNA (e.g., 22 to 30 ∘C) as the daytime temperature (e.g., from 31 to 33 ∘C) is constrained by the maximum temperature for optimization in TRF2 (i.e., 33 ∘C). To maximize the net photosynthetic carbon gain, the model predicts a higher proportion of nitrogen allocated to carboxylation to compensate for a higher nighttime respiration rate. Therefore, the LUNA model predicts higher values of Vc,max25. Yet, this may result from a deficiency of TRF2 in that this response function does not allow for thermal acclimation under global warming (Lombardozzi et al., 2015).

Our model predicts that the future changes in atmospheric CO2 concentration has a negligible effect on Jmax25, a finding that is in agreement with results from other studies (e.g., Maroco et al., 2002). A meta-analysis of 12 Free-Air Carbon dioxide Enrichment (FACE) experiments demonstrated reductions in Jmax on the order of 5 % but with a 10 % reduction in Vc,max25 under elevated CO2 concentrations (Long et al., 2004). Our model also predicts that the relative humidity has a relatively minor effect on Vc,max25. This may be due to the fact that most of the values of Vc,max25 and Jmax25 in our data set coincide with relatively high values of the humidity. As LUNA does not consider the effects of drought on photosynthesis, it may have underestimated the effects of water scarcity on Vc,max25 under low humidity conditions (Xu and Baldocchi, 2003). Under prolonged drought, plants close their stomata and photosynthesis is greatly reduced (Breshears et al., 2008; McDowell, 2011). Without sufficient carbon input, photosynthetic enzymes may degenerate during the high temperatures of a drought, which could decrease Vc,max25 substantially (Limousin et al., 2010; Xu and Baldocchi, 2003).

There are many different ways to incorporate environmental controls on Vc,max25 and Jmax25. One such approach is to use relatively simple empirical relationships between environmental variables and Vc,max25 and Jmax25 (e.g., Ali et al., 2015; Verheijen et al., 2013). Such functions can improve the model performance (Verheijen et al., 2015), yet may exhibit rather poor extrapolative capabilities under future climate conditions. The optimality hypothesis used by LUNA is arguably better rooted in ecologic theory, and is therefore expected to exhibit a better predictive quality when confronted with novel future climate conditions. Indeed, the concept of optimality has been applied to the prediction of many different plant functions and structures under a wide array of environmental conditions. Examples include carbon allocation (Franklin et al., 2012), leaf C : N (Thomas and Williams, 2014), root distribution (McMurtrie et al., 2012) and stomatal conductance (Cowan and Farquhar, 1977). For photosynthetic capacity optimization, Haxeltine and Prentice (1996) have predicted Vc,max25 based on a trade-off analysis of photosynthesis and respiration. This concept has been incorporated in different land surface models such as LPJ-GUESS (Smith et al., 2001) and LPJmL (Sitch et al., 2003). Both LUNA and the model of Haxeltine and Prentice (1996), hereafter conveniently referred to as HP, consider Vc,max25 and respiration. The LUNA model is currently limited to prediction at the leaf level only while the HP model is applicable for both the leaf and canopy level. Nevertheless, key improvements of LUNA over HP include an explicit consideration of light capture, electron transport and storage. Furthermore, the parameters of LUNA have been derived from a much larger global data set, with many different environmental conditions.

Our model suggests that most regions of the world will likely experience reductions in Vc,max25 (Figs. 4b and S8b) due to global warming. An increase of the temperature (Fig. S13) and atmospheric CO2 concentration is expected to increase the 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, Jmax25 will also decrease globally, except in regions where the present temperatures of the growing season are relatively high (Fig. S12b). The increase of Jmax25 can be attributed to leaf temperature limitations and increased shortwave radiation (Figs. S14 and S15). Temperature will have a relatively small impact on nitrogen allocation in regions with historically high temperatures during the growing season because leaf temperature is already close to or higher 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 Vc,max25 and Jmax25 under future climate conditions, our analysis based on the LUNA model indicates that ESM predictions of future global photosynthesis at the uppermost leaf layer will likely be overestimated by as much as 10–16 % if Vc,max25 and Jmax25 are held fixed (Fig. 7). This overestimation is larger for TRF2 (16.3 %) than TRF1 (10.1 %) and can result from the fact that TFR2 does not account for thermal acclimation under future climate conditions. Consequently, LUNA predicts a large nitrogen allocation acclimation under climate change. In both cases, our results suggest that, to reliably predict global plant responses to future climate change, ESMs should take into explicit consideration environmental controls on Vc,max25 and Jmax25. It has been suggested recently that nitrogen-related factors are not well represented in ESMs (Houlton et al., 2015; Wieder et al., 2015). Our nitrogen partitioning scheme would help remove the prediction bias of future photosynthetic rates, which will also improve considerably related climate processes that are dependent on these predictions (Bonan et al., 2011; Knorr and Kattge, 2005; Rogers, 2014).

The LUNA model has been implemented in CLM5.0 and will be made publicly available with its release in 2016. Stand-alone codes of LUNA are available in MATLAB, FORTRAN and C. These source codes can be obtained from the corresponding author upon request.