## Summary

Almost all terrestrial biosphere models (TBMs) still assume infinite mesophyll conductance (

*g*_{m}) to estimate photosynthesis and transpiration. This assumption has caused low accuracy of TBMs to predict leaf gas exchange under certain conditions.In this study, we developed a photosynthesis-transpiration coupled model that explicitly considers

*g*_{m}and designed an optimized parameterization solution through evaluating four different*g*_{m}estimation methods in 19 C_{3}species at 31 experimental treatments.Results indicated that temperature responses of the maximum carboxylation rate (

*F*_{cmax}) and the electron transport rate (*J*_{max}) estimated by fusing the Bayesian retrieval algorithm and the Sharkey online calculator together with*g*_{m}temperature response estimated by fusing the chlorophyll fluorescence-gas exchange method and anatomy method predicted leaf gas exchange more accurately. The*g*_{m}temperature response exhibited activation energy (Δ*H*_{a}) of 63.13 ± 36.89 kJ mol^{-1}and entropy (Δ*S*) of 654.49 ± 11.36 J K^{-1}mol^{-1}. The*g*_{m}optimal temperature (*T*_{opt}_g_{m}) explained 58% of variations in photosynthesis optimal temperature (*T*_{optA}). The*g*_{m}explicit expression has equally important effects on photosynthesis and transpiration estimations.Results advanced understandings of better representation of plant photosynthesis and transpiration in TBMs.

## Introduction

The leaf photosynthesis-transpiration coupled model is the basis of vegetation photosynthesis and transpiration estimations performed using terrestrial biosphere models (TBMs) (Dai *et al*., 2003; Rogers *et al*., 2017). The model is based on the biochemical-based photosynthesis theory developed by Farquhar *et al.* (1980), which considers the leaf stomatal aperture as the primary gauge of CO_{2} influx and water vapor efflux and assumes an infinite conductance of CO_{2} diffusion from sub-stomatal cavities to the chloroplast stroma (i.e. mesophyll conductance, *g*_{m}). In such cases, there is no CO_{2} concentration drawdown between the intercellular airspace and the chloroplast stroma. However, now it is widely accepted not only that there is a significant CO_{2} diffusion drawdown from the intercellular airspace to the chloroplast stroma, but that the resistance that causes this drawdown can be similar or greater than stomatal resistance in land plants (Flexas *et al*., 2012; Evans and von Caemmerer, 2013; von Caemmerer and Evans, 2015; Gago *et al*., 2019). Currently, almost all TBMs do not explicitly consider *g*_{m} (Rogers *et al*., 2017; Knauer *et al*., 2019; 2020; Iqbal *et al*., 2021), primarily because of (1) huge disputes in response characteristics of *g*_{m} to ambient environment, particularly the temperature response (von Caemmerer and Evans, 2015; Bahar *et al*., 2018; Shrestha *et al*., 2019; Li *et al*., 2020; Evans, 2021), and (2) lack of a *g*_{m} finite photosynthesis-transpiration coupled model that can be applied to as many C_{3} species as possible (Niinemets *et al*., 2009; Xue *et al*., 2017; Knauer *et al*., 2020).

Mesophyll conductance cannot be directly measured mainly because it is not possible to determine the CO_{2} concentration within the chloroplast stroma. Thus, modeling methods are required to estimate *g*_{m}, which could be grouped into four classes according to the algorithm principle and field measurement tools: the chlorophyll fluorescence-gas exchange method (i.e. *g*_{m_F}) (Harley *et al*., 1992); the anatomy method (i.e. *g*_{m_A}) (Tosens *et al*., 2012; Tomas *et al*., 2013); the ^{13}C isotope discrimination method (Evans *et al*., 1986; Barbour *et al*., 2007; Pons *et al*., 2009; Evans and von Caemmerer, 2013; Flexas *et al*., 2013); and the curve-fitting parameter retrieval methods (Sharkey *et al*., 2007; von Caemmerer *et al*., 2009; Yin and Struik, 2009; Gu *et al*., 2010; Zhu *et al*., 2011; von Caemmerer, 2013, Han *et al*., 2020; Xiao *et al*., 2021). These methods have their own advantages and weakness in terms of model parameter assumptions made during estimation, resulting in large discrepancies in the estimated temperature response of *g*_{m} (Pons *et al*., 2009; Evans, 2021). Therefore, we decided to select the best *g*_{m} estimation method in terms of accuracy in predicting leaf gas exchange at any temperature, namely a good criterion to select at each temperature which *g*_{m} estimation method works best is the one that could predict leaf gas exchange more accurately.

Effects of the *g*_{m} finite expression on photosynthesis have been widely demonstrated, whereas few attentions are paid on transpiration. Considering the indirect effects of *g*_{m} on transpiration and the direct effect on photosynthesis through its control on chloroplast CO_{2} concentration, Knauer *et al*. (2020) determined that *g*_{m} has a greater effect on photosynthesis but no significant effects on transpiration in most species and hence proposed the ‘the asymmetric effects on photosynthesis and transpiration estimations’ hypothesis. Kumarathunge *et al.* (2019) found that variations in photosynthesis optimal temperature (*T*_{optA}) can be primarily explained by changes in the ratio of the apparent maximum electron transport rate and the apparent maximum carboxylation rate at 25°C (*J*_{a,25}/*V*_{a,25}, *JV*r), thus proposing ‘the *JV*r biochemical limitations’ hypothesis. *J*_{a,25} and *V*_{a,25} estimations in their study were derived from the *A*_{n}/C_{i} curve without explicitly considering *g*_{m}. Previous results indicated significant changes in *T*_{optA} under different intercellular CO_{2} concentrations (*C*_{i}) in C_{3} species (Farquhar *et al*., 1980; Rogers *et al*., 2017), suggesting that the CO_{2} substrate levels significantly affect *T*_{optA}. The CO_{2} substrate levels inside the chloroplasts in turn are strongly controlled by *g*_{m}. We speculated that the plausibility of the *T*_{optA}-*JV*r relationship reported by Kumarathunge *et al.* (2019) is questionable in reality. The observed variations in *T*_{optA} among plant species may not be solely explained by biochemical limitations.

As a first step towards the better representation of plant photosynthesis and transpiration in most TBMs, we attempted to develop a *g*_{m} finite model that could be directly implemented in most TBMs, in addition to design an optimized parameter configuration solution that is physiologically meaningful for as many C_{3} species as possible. The optimized parameterization solution was designed by comparing multiple different parameter estimation methods used for *g*_{m}, *V*_{cmax}, and *J*_{max} estimations. The response features of *g*_{m}, *V*_{cmax}, and *J*_{max} to temperature were therefore determined. Dynamic changes in apparent *g*_{m} in response to irradiance were not of main consideration in the current study, since the underlying conductance at the cellular level may remain unchanged with varying light environments (Evans, 2021). Validation of the predictability of the *g*_{m} finite model compared to a traditional photosynthesis model assuming infinite *g*_{m} (abbreviated as the *g*_{m} infinite model) was performed in 19 C_{3} species under 31 experimental conditions. The effects of the *g*_{m} finite expression on leaf photosynthesis and transpiration estimations were quantified to evaluate the ‘the *JV*r biochemical limitations’ hypothesis proposed by Kumarathunge *et al.* (2019) and ‘the asymmetric effects on photosynthesis and transpiration estimations’ hypothesis proposed by Knauer *et al*. (2020).

## Materials and methods

### Model description

In line with the photosynthesis-transpiration coupled model adopted by most TBMs, the Farquhar, von Caemmerer & Berry (1980) (FvCB) photosynthesis model and a stomatal conductance sub-model (Ball *et al*., 1987; Leuning, 1995) were coupled to quantify leaf carbon uptake and water loss through transpiration. *A*_{n} is limited either by the Rubisco carboxylation rate at a low CO_{2} concentration (*W*_{c}) or the RuBP regeneration rate at a relatively high CO_{2} concentration because of low electron transport rates (*W*_{j}) or deficit inorganic phosphate for photophosphorylation (*W*_{p}). *A*_{n} can be expressed as follows:
where *V*_{cmax} is the maximum carboxylation rate; *Γ** is the CO_{2} compensation point without mitochondrial respiration; *K*_{c} and *K*_{o} are the Michaelis-Menten constants for CO_{2} and O_{2}, respectively; *R*_{d} and *J* are dark respiration in the light and the electron transport rate, respectively; *TPU* is the rate of triose phosphate export from the chloroplasts. *C* is *C*_{i} for the *g*_{m} infinite model or CO_{2} concentration inside the chloroplasts (*C*_{c}) for the *g*_{m} finite models, which can be determined using Eqns. 9 and 10. *J* is modeled as a function of incident photosynthetically active radiation (*PAR*), which is calculated using the non-rectangle hyperbola equation (Eqn. 5) (Farquhar *et al*., 1980; Medlyn *et al*., 2002; Sharkey *et al*., 2007; Rogers *et al*., 2017; Kumarathunge *et al*., 2019) as follows:
where *ρ* is the quantum yield of electron transport; *Θ* is the curvature of the non-rectangle hyperbola equation (Table 1).

Under well-watered conditions, the correlation between photosynthetic parameters and temperature can be expressed by the peak Arrhenius function (Dreyer, 2001; Medlyn *et al*., 2002; Xue *et al*., 2017; Kumarathunge *et al*., 2019; Knauer *et al*., 2019) as follows:
where *k*_{25} is the photosynthetic parameter value at 25C (*V*_{cmax},25, *J*_{max,25}, or *g*_{m,25}); Δ*H*_{a} is the activation energy; Δ*H*_{d} is the deactivation energy; Δ*S* is the entropy term which characterizes the changes in reaction rate caused by substrate concentration (Table 1); *T*_{k} is leaf temperature in Kelvin unit; and *R* is the gas constant (8.314 Pa m^{3} K^{-1} mol^{-1}).

*V*_{cmax}, *J*_{max}, and *g*_{m} can be estimated from field measurements, whereas *C* remains unknown in the leaf photosynthesis model. The leaf photosynthesis model is therefore required to be coupled with the stomatal conductance sub-model for predicting the behavior of stomatal conductance by depending on environmental drivers and *A*n. The stomatal conductance sub-model can be expressed as follows:
where *C*_{s} is leaf surface CO_{2} concentration; *a* is a constant (default as 35kPa); *g*_{min} is the value of *g*_{sw} when *A*_{n} is zero; *g*_{fac} is the stomatal sensitivity to the assimilation rate; and *VPD* is the vapor pressure deficit between the leaf surface and atmosphere; *g*_{sw} is the stomatal conductance to water vapor; and *g*_{fac} and *g*_{min} are the slope and intercept of the linear relationship between *g*_{sw} and *A*_{n}, respectively, which were extracted from the diurnal gas exchange data.

To predict the response of *A*_{n} to leaf temperature at ambient and relatively high CO_{2} concentrations and light saturation levels (i.e. *A*_{max}-*T*_{leaf} curve) for the species derived from literature, we needed to determine the *g*_{fac} and *g*_{min} values, without the diurnal gas exchange information. According to our field measurements, *g*_{fac} was set to 3.0 for the woody species and 4.0 for the herbaceous species. The *g*_{min} was set to 10.0 mmol m^{-2} s^{-1} for both C_{3} woody and herbaceous species, as commonly adopted by most TBMs (Sellers *et al*., 1996). An initial value was set for *C*, and then, *A*_{n} was determined using Eqn. 1. The known *A*_{n} was substituted into Eqn. 7 for *g*_{sw} estimation, which in turn was substituted into Eqn. 8 or 9 to generate a new *C* value. The new *C* value was then compared with the previous value. This new *C* value was adjusted and then considered as the second initial value for Eqn. 1 until the difference between the generated *C* and the previous one became less than 0.05 ppm. The iteration procedure used here (i.e. the Newton-Raphson iteration method) was consistent with that used by most TBMs (Dai *et al*., 2003; Sellers *et al*., 1996).

#### (1) The *g*_{m} infinite model and parameterization

In the *g*_{m} infinite model, the CO_{2} diffusion conductance from intercellular airspace to the chloroplast stroma was assumed to be infinitely large, a common practice in line with almost all TBMs. Photosynthesis is considered to be limited either by stomatal aperture/closure or by CO_{2} fixation, which depends on the functioning of leaf photochemistry and/or photosynthetic enzymes. *C* is the intercellular CO_{2} concentration. According to the Fick’s first law, *C* can be expressed as:

*V*_{a} was estimated using the linear phase of the *A*_{n}/*C*_{i} curve (*C*_{i} from 50 to 200 ppm) and *J*_{a} was estimated using the saturated phase (*C*_{i} > 400 ppm) by referring to the studies by Xu and Badocchi (2003) and Kumarathunge *et al.* (2019). Other input parameters for the *g*_{m} infinite model were clarified in Methods S1.

#### (2) The *g*_{m} finite model and parameterization

In the *g*_{m} finite model, the total conductance of CO_{2} diffusion from the leaf surface to the chloroplast stroma consists of *g*_{sw} and *g*_{m}. Photosynthesis is limited by three major factors: stomatal conductance, mesophyll conductance, and biochemical/photochemical limitations. *C* is the CO_{2} concentration inside the chloroplasts that depends on *A*_{n}, *g*_{sw}, *g*_{m}, and *C*_{s}. It can be expressed according to the Fick’s first law as follows:

*V*_{cmax} and *J*_{max} are the maximum carboxylation rate and the maximum electron transport rate based on the CO_{2} concentration in the chloroplasts, respectively. In this study, *V*_{cmax}, *J*_{max}, and *g*_{m} values were estimated using four different parameter estimation methods. The Bayesian retrieval algorithm (Zhu *et al*., 2011; Han *et al*., 2020) and the Sharkey online calculator (Sharkey *et al*., 2007) were used to estimate *V*_{cmax}, *J*_{max}, and *g*_{m} values by using the *A*_{n}/*C*_{i} curve only (abbreviated as *V*_{cmax_B}, *J*_{max_B}, *g*_{m_B} and *V*_{cmax_S}, *J*_{max_S}, and *g*_{m_S}, respectively). The chlorophyll fluorescence-gas exchange method was used to estimates *g*_{m} by using the variable *J* method (abbreviated as *g*_{m_F}), according to methods used by previous studies (Harley *et al*., 1992; Niinemets *et al*., 2009; Xue *et al*., 2016; 2017; Carriquí *et al*., 2020; 2021). The anatomy method for *g*_{m} estimation is constrained to a narrow range of leaf temperature around 25°C (*g*_{m_A,25}) (Tosens *et al*., 2012; Tomas *et al*., 2013). In this study, the prior range of parameters for the Bayesian retrieval algorithm adopted the range recommended by Zhu *et al*. (2011) and Han *et al*. (2020). The prior ranges of *R*_{d} for woody plants and herb plants were 0.01-2.0 μmol m^{-2} s^{-1} and 0.01-5.0 μmol m^{-2} s^{-1}, respectively. Notably, the unit of *g*_{m} estimated using the Sharkey online calculator and the Bayesian retrieval algorithm was μmol m^{-2} s^{-1} Pa^{-1}; therefore, it was required to be converted into mol m^{-2} s^{-1} by using the formula: [(g_{m}(mol m^{-2} s^{-1}) = *g*_{m}(μmol m^{-2} s^{-1} Pa^{-1}) × P/10], where *P* is the actual atmospheric pressure (Pa). The explicit clarity on the parameter values assumed for each parameter estimation method was referred to the Methods S1.

*V*_{cmax}, *J*_{max}, and *g*_{m} estimated using the Sharkey online calculator, Bayesian retrieval algorithm, chlorophyll fluorescence-gas exchange method, and anatomy method were grouped to develop eight parameterization solutions to drive the *g*_{m} finite and infinite models (Table 2). For the plant species without *g*_{m_A,25} data, model parameterization solutions adopted *g*_{m_B}, *g*_{m_S}, and *g*_{m_F}. *g*_{m_FA} at a leaf temperature of 25°C was the mean of *g*_{m_F,25} and *g*_{m_A,25}. *g*_{m_FA} values at other temperatures were approximated by *g*_{m_F} only.

Variation in the Rubisco kinetic parameters measured *in vitro* was less than 10% amongst C_{3} plant species (von Caemmerer, 2020); thus these parameters may be assumed to be identical for all vegetation types. In this study, the use of the Rubisco kinetic parameters (*K*_{c}, *K*_{o}, and *Γ**) for the *g*_{m} finite model was consistent with Bernacchi *et al*. (2002) (Table 1). However, Knauer *et al*. (2019; 2020) used two types of Rubisco kinetic parameters for model comparisons, of which one type was adopted from the study by Bernacchi *et al*. (2002) for the *g*_{m} finite model and the other type was adopted from a study by Bernacchi *et al*. (2001) for the *g*_{m} infinite model. Similarly, the Rubisco kinetic parameters in study of Bernacchi *et al*. (2001) were used for parameterization of the *g*_{m} infinite model in 141 C_{3} species by Kumarathunge *et al*. (2019). The hypotheses proposed by Knauer *et al*. (2019; 2020) and Kumarathunge *et al*. (2019) were evaluated in this study. Hence, it is necessary here to parameterize the *g*_{m} infinite model by using the 2001 version in association with the Rubisco kinetic parameters.

### Data collection for model validation

*V*_{cmax}, *J*_{max}, and *g*_{m} estimations by the four parameter estimation methods were performed using field measurements of the *A*_{n}/*C*_{i} curve plus chlorophyll fluorescence at leaf temperatures ranging from 10-15°C to 40°C in 19 species under 31 experimental treatments (four tropical deciduous tree species, four deciduous broadleaf tree species, seven evergreen broadleaf tree species, three C_{3} crops species, and one C_{3} herb and grass species) (Methods S2 and S3). Diurnal gas exchange rates were measured in 15 species under 25 treatments (Methods S2 and S3). Leaves were sampled *in-situ* immediately after the gas exchange measurement to determine the leaf anatomical structure (Methods S4). For parameter correlation analysis, the *A*_{n}/*C*_{i} curve and chlorophyll fluorescence data at 25°C in seven gymnosperms specie, five ferns species and four herbs species were collected from literature (Carriquí *et al*., 2020; Nadal *et al*., 2018) (Methods S5). For the *T*_{optA}-*T*_{opt_gm} correlation analysis, data on *T*_{optA} and optimum temperature of *g*_{m} (*T*_{opt_gm}) estimated using the carbon isotope discrimination method (*g*_{m}_^{13}c) and the chlorophyll fluorescence-gas exchange method in five C_{3} crops species, two C_{3} herbs and grasses species, and one deciduous broadleaf tree species were collected from literature (Evans and von Caemmerer, 2013; Li *et al*., 2020; Scafaro *et al*., 2011; von Caemmerer and Evans, 2015; Warren and Dreyer, 2006; Xue *et al*., 2016) (Methods S6). Abbreviations of sampled species under different experimental treatments were referred to Methods S2-S6.

### Evaluations of the *g*_{m} infinite and finite models

Independent field data, including the *A*_{max}-*T*_{leaf} curve, *T*_{optA}, and diurnal gas exchange, were used to validate the *g*_{m} infinite and finite models. We fitted the *A*_{max}-*T*_{leaf} curve in Eqn. 10 to obtain *T*_{optA} (Sall and Pettersson, 1994; Battaglia *et al*., 1996; Gunderson *et al*., 2009; Kumarathunge *et al*., 2019),
where *A*_{opt} is the *A*_{n} at *T*_{optA}, and parameter *b* (unitless) describes the curvature of *A*_{max} and *T*_{leaf}.

Root mean square error (RMSE) and Nash-Sutcliffe efficiency (NSE) coefficients were used to quantify the performance of the model (Methods S7).

## Results

### Temperature responses of *V*_{cmax}, *J*_{max}, and *g*_{m}

The temperature curve-fitting lines for *V*_{cmax_B}, *V*_{cmax_S}, *V*_{cmax_SB}, and *V*_{a} increased rapidly with increase in *T*_{leaf} from 10C to 35C, and began to decrease after reaching a peak (about 300 μmol m^{-2} s^{-1} for *V*_{cmax_B}, *V*_{cmax_S}, and *V*_{cmax_SB}; 180 μmol m^{-2} s^{-1} for *V*_{a}) at a leaf temperature around 35C. *V*_{cmax_B}, *V*_{cmax_S}, and *V*_{cmax_SB} presented a similar behavior *(p* > 0.1, Fig. 1a and Figs. S1a-ae), except at high leaf temperatures ≥ 35°C. Despite *V*_{cmax_SB} was significantly higher by 43.9% in average than *V*_{a} at 25°C, considerable scatter in the difference for the two variables was observed (Table S1). There were similar values at each leaf temperature among temperature response curves of *J*_{max_B}, *J*_{max_S}, *J*_{max_SB}, and *J*_{a} (Fig. 1b), with the difference among them being less than 6% at 25C and the optimal temperatures changing around 32-34C (Figs. S2a-ae and Table S2). The *g*_{m_B} temperature curve-fitting line was overlapped with that of *g*_{m_S} (Fig. 1c), whereas both had significantly higher values by 69% and 58% than that of *g*_{m_FA} at 25°C, respectively (Table S3). However, the *g*_{m_S} temperature curve-fitting line did not well overlap with the 95% confidence interval because of irregular observations in *g*_{m_S} temperature response among sampled species/treatments (Figs. S3a-ae). The temperature curve-fitting lines for *g*_{m_B}, *g*_{m_S}, and *g*_{m_FA} exhibited larger variations in *T*_{opt_gm}, ranging from 27 to 32°C, which were lower by 15.7% and 10.6% in average as compared to optimal temperatures for *V*_{cmax} (i.e. *V*_{cmax_B}, *V*_{cmax_S}, and *V*_{cmax_SB}) and *J*_{max} (i.e. *J*_{max_B}, *J*_{max_S}, *J*_{max_SB}), respectively.

The boxplot minimum value of Δ*H*_{a} was 49.2 KJ mol^{-1} for *V*_{cmax_B}, 52.3 KJ mol^{-1} for *V*_{cmax_S}, 37.6 KJ mol^{-1} for *V*_{cmax_SB}, and 65.6 KJ mol^{-1} for *V*_{a} (Fig. 1d). For *J*_{max_B}, *J*_{max_S}, *J*_{max_SB}, and *J*_{a}, their minimum values were 22.2, 20.8, 22.6, and 23.6 KJ mol^{1}, respectively (Fig. 1e). Similarities in the minimum value that was close to zero were observed for *g*_{m_B}, *g*_{m_s}, and *g*_{m_FA} (Fig. 1f). Zero value in Δ*H*_{a} was found in Pop_WC for *g*_{m_B}, in Pop_CW for *g*_{m_s}, and in E_sal and E_mdel for *g*_{m_FA} (Table S3 and Figs. S3u, t, q, and r). There were similarities in the interquartile range (IQR) of Δ*H*a among *V*_{cmax_B}, *V*_{cmax_S}, *V*_{cmax_SB}, and *V*_{a}, so did the Δ*H*_{a} of the four *J*_{max} types and the Δ*H*a of the three *g*_{m} types. However, larger ranges in the IQR of Δ*H*_{a} for *g*_{m} (i.e. *g*_{m_B}, *g*_{m_S}, and *g*_{m_FA}) than those of *J*_{max} and *V*_{cmax} were clearly observed and coefficient of variation *(CV)* in Δ*H*a of *g*_{m} (i.e. *g*_{m_B}, *g*_{m_S}, and *g*_{m_FA}) was amplified in average by 135.2% (Table S3). The IQR of Δ*S* for *V*_{cmax_B}, *V*_{cmax_S}, *V*_{cmax_SB}, and *V*_{a} was 5.1, 20.2, 8.3, and 15.6 J K^{-1} mol^{-1}, respectively (Fig. 1g). Similarities in the IQR of *ΔS* among *J*_{max_B}, *J*_{max_S}, *J*_{max_SB}, and *J*_{a} temperature responses were evident (Fig. 1h and Table S2). Whereas, the first quartile (Q1) values of Δ*S* for *g*_{m} (i.e. *g*_{m_B}, *g*_{m_s}, and *g*_{m_FA}) were similar or slightly higher than the third quartile (Q3) values of *V*_{cmax} (i.e. *V*_{cmax_B}, *V*_{cmax_S}, and *V*_{cmax_SB}) and *J*_{max} (i.e. *J*_{max_B}, *J*_{max_S}, and *J*_{max_SB}) (i.e. mean of the Q1 value for *g*_{m} was 644.5 J K^{-1} mol^{-1}; mean of the Q3 value for *V*_{cmax} was 644.1 J K^{-1} mol^{-1}, and mean of the Q3 value for *J*_{max} was 647.5 J K^{-1} mol^{-1}). The mean value of Δ*S* across *g*_{m_B}, *g*_{m_S}, and *g*_{m_FA} temperature curves was 654 J K^{-1} mol^{-1}, whereas it was 639 J K^{-1} mol^{-1} for *J*_{max} (i.e. *J*_{max_B}, *J*_{max_S}, and *J*_{max_SB}) and 637 J K^{-1} mol^{-1} for *V*_{cmax} (i.e. *V*_{cmax_B}, *V*_{cmax_S}, and *V*_{cmax_SB}) (Table S1-S3). The *CV*s of Δ*S* for *g*_{m_B}, *g*_{m_S}, and *g*_{m_FA} temperature curves were 1.74%, 2.88%, and 2.2%, respectively, while the corresponding *CV*s of Δ*H*_{a} were 58.45%, 78.98%, and 53.26%, respectively (Table S3). These results suggested: greater variations in Δ*H*_{a} and Δ*S* of *g*_{m} than those of *V*_{cmax} and *J*_{max}; large variations in Δ*H*_{a} and relatively small variations in Δ*S* for *g*_{m}; and greater values in Δ*S* for *g*_{m} than those for *V*_{cmax} and *J*_{max}.

### Comparisons between gas exchange observations and simulations by the *g*_{m} finite and infinite models

For the *A*_{max}-*T*_{leaf} curves measured at ambient *C*_{a} = 400-450 ppm, the slopes of the linear regression between observations and simulations by the S_S, S_SBFA, and S_FA parameterization schemes were 0.87, 0.91, and 1.00, respectively (Figs. 2a-c). The adjusted R^{2} (adj.R^{2}) values for the three schemes were 0.81, 0.86, and 0.90, respectively, and the corresponding NSE values were 0.79, 0.84, and 0.88. The RMSE values of the three parameterization schemes accounted for 24%, 22%, and 19% of the mean *A*_{max} (*A*_{max,mean} = 12.47 μmol m^{-2} s^{-1}). The predicted *A*max values from the S_S and S_SBFA schemes were 11% and 7% higher than the *A*_{max,mean}, respectively (Figs. S4a-ae). These results suggested that *g*_{m} estimation using the chlorophyll fluorescence-gas exchange method and anatomy method was more reasonable. In line with the results obtained from S_S, S_SBFA, and S_FA schemes, the B_FA scheme fitted *A*_{max} at each temperature better than the B_B and B_SBFA schemes (Figs. 2d-f and Figs. S4a-ae), which further suggested that the configuration of *g*_{m_FA} for *g*_{m} estimation was more reasonable. As shown in Figs. 1a and b, the values of *V*_{cmax_B} and *V*_{cmax_S} and those of *J*_{max_B} and *J*_{max_S} at each temperature were similar to each other. Therefore, we considered the possible effects of the combination of *V*_{cmax} or *J*_{max} estimations using the Bayesian retrieval algorithm and Sharkey online calculator on *A*_{max} simulations (the SB_FA scheme in Figs. S4a-ae). The NSE value for the SB_FA scheme (0.92) was 5% and 1% higher, whereas the ratio of RMSE to *A*_{max,mean} was 21% and 12% lower than those for the S_FA and B_FA schemes suggesting better *A*_{max} predictions using the parameter configuration scheme by considering *V*_{cmax_SB}, *J*_{max_SB}, and *g*_{m_FA}. The adj.R^{2}, NSE, and the ratio of RMSE to *A*_{max,mean} were 0.85, 0.73, and 28%, respectively (Fig. 2h), indicating that although the *g*_{m} infinite model is generally credible in estimating the *A*_{max}-*T*_{leaf} curve, the prediction errors in this model are relatively larger. We found that *A*_{max} predictions using the *g*_{m} infinite model were significantly higher (16%) than the observations (partially for 30-40°C, Figs. S4a-ae). Additionally, numerical simulation indicated that the *g*_{m} finite model driven by the *g*_{m} temperature function without considering the deactivation stage significantly overestimated *A*_{max} at higher temperatures 30-35-40°C by 10.99%, 32.51%, 64.06%, respectively. The results obtained from the eight parameterization schemes at *C*_{a} = 600-630 ppm were similar to those at *C*_{a} = 400-450 ppm (Figs. 2a-h and Figs. S5a-ae). These results indicated that the *g*_{m} finite model driven by the SB_FA scheme could predict *A*max more accurately than the *g*_{m} infinite model.

Figs. 2i-l shows the comparisons in diurnal *A*_{n}, *E,* and *g*_{sw} between observations and predictions using the *g*_{m} infinite model and the *g*_{m} finite model that is forced by the parameterization scheme SB_FA (detailed comparisons in each species/treatment shown in Figs. S6-S8). The adj.R^{2} values for *A*_{n}, *E*, and *g*_{sw} predicted using the *g*_{m} finite model were 0.88, 0.85, and 0.78, respectively, whereas those predicted using the *g*_{m} infinite model were 0.87, 0.83, and 0.76, respectively. The NSE values for the three variables for the *g*_{m} finite model were 0.88, 0.85, and 0.76, respectively, and those for the *g*_{m} infinite model were 0.76, 0.75, and 0.74, respectively. The ratio of RMSE to the mean of *A*_{n}, *E*, and *g*_{sw} for the *g*_{m} finite model was 27%, 34%, and 40%, respectively, whereas that for the *g*_{m} infinite model was 38%, 45%, and 42%, respectively. Meanwhile, significant overestimations in simulated *A*_{n} under heat shocking conditions (i.e. *T*_{leaf} from > 30°C) by 25%-40% by using the *g*_{m} infinite model were observed (Fig. 2l and Fig. S9). These results suggested that the *g*_{m} finite model is superior to the *g*_{m} infinite model in predicting diurnal gas exchange under a wide range of growth conditions.

For the diurnal changes in *A*_{n}, the adj.R^{2} and NSE for the *g*_{m} finite model were improved by 1% and 12% compared with those for the *g*_{m} infinite model. For the diurnal changes in *E*, the adj.R^{2} and NSE for the *g*_{m} finite model improved by 2% and 10% compared with those for the *g*_{m} infinite model. These results suggested that the effects of *g*_{m} finite expression on photosynthesis and transpiration estimations were almost equally stronger.

### Statistical correlations between *T*_{optA} and photosynthetic parameters

The linear regression slope and adj.R^{2} values between *T*_{optA} predictions using the *g*_{m} finite model and observations were 0.67 and 0.85, respectively, whereas those obtained using the *g*_{m} infinite model were 0.88 and 0.18, respectively (Fig. 3a). *T*_{optA} predicted using the *g*_{m} finite model displayed a better correlation with the observations. We observed that *T*_{optA} observations had a significant positive correlation with the *T*_{opt_gm} derived from *g*_{m_FA} and *g*_{m}_^{13}C temperature responses, and the adj.R^{2} value reached 0.58 (Fig. 3b). No significant correlations were found among *T*_{optA}-Δ*H*_{a} of *g*_{m_FA}, *T*_{optA}-*g*_{m_FA,25}, and *T*_{optA}-*J*_{max_SB,25}/*V*_{cmax_SB,25} (Fig. S10).

### Statistical correlations among photosynthetic parameters estimated by four parameter estimation methods

*g*_{m_F,25} was positively correlated with *g*_{m_A,25}, whereas the adj.R^{2} was 0.22, and the linear regression slope was 0.57, which is much lower than 1.0 (Fig. 4a), primarily because of large discrepancies between the two variables in rice plants. The two variables strongly correlated in other sampled species/treatments with the adj.R^{2} of 0.76 and the slope of 0.80. A significant exponential correlation was found between *g*_{m_FA,25} and *g*_{m_SB,25} (adj.R^{2} = 0.67, *p* < 0.01, Fig. 4b), so did the correlation between *g*_{m_F,40} and *g*_{m_SB,40} (gray circles in Fig. 4b), with a close agreement found at low *g*_{m} < 0.15 mol m^{-2} s^{-1}. A negative correlation for *g*_{m_FA,25} and the difference between *V*_{cmax_SB,25} and *V*_{a,25} was found (adj.R^{2} = 0.47,*p* < 0.05, Fig. 4c). *J*_{max_SB,25} was closely related to *V*_{cmax_SB,25} (adj.R^{2} = 0.83,*p* < 0.01, Fig. 4d).

## Discussion

### Superiority of the *g*_{m} finite model and an optimized parameterization solution that excludes the equifinality phenomenon

The *A*_{max}-*T*_{leaf} curves were accurately predicted using the *g*_{m} infinite model only in 15 species/treatments (Figs. S4d, j-s, y, aa, ad, and ae), whereas *A*_{max} values at higher temperatures (30-40°C) were largely overestimated in other sampled species/treatments. Poor modeling accuracies were also evident in the simulation of diurnal gas exchange rates (Fig. 2l and Figs. S6c, e, h, k, l, n, p, and q). It aligned with the previous reports in rice and winter wheat by Xue *et al*. (2016) and in *Quercus ilex* by Niinemets *et al*. (2009) who found that the photosynthesis model that does not explicitly consider *g*_{m} cannot always predict leaf gas exchange accurately. The *g*_{m} finite model considers the dependent effects of chloroplast CO_{2} concentration on the assimilation rate, stomatal and mesophyll resistance, and leaf surface CO_{2} concentration (von Caemmerer, 2013; 2020). The relationships among CO_{2} diffusion flux, CO_{2} concentration gradient between the leaf surface and chloroplasts, and gas diffusion resistance may be approximated using the Fick’s first law (Harley *et al*., 1992; Xue *et al*., 2017), as shown in Eqn. 9. Simulation results in gas exchange in 19 species under a wide range of growth conditions proved that the *g*_{m} finite model has good transferability and high prediction capacity, due to which the model can be applied to as many C_{3} species as possible. The *g*_{m} finite model developed in this study can be conveniently substituted into most TBMs by simply replacing (*C*_{i} = *C*_{s} – 1.56*A*_{n}/*g*_{sw}) as given in Eqn. 9.

*V*_{cmax}, *J*_{max}, and *g*_{m} temperature responses are key photosynthetic parameters of the *g*_{m} finite model. Despite a “one-point” method has been proposed to quantify *V*_{cmax}, there is no consensus that this method can be widely used (Burnett *et al*. 2019). One way to determine *V*_{cmax} is from the *A*_{n}/*C*_{c} curve that is converted from the *A*_{n}/*C*_{i} curve using a value for *g*_{m} determined at ambient CO_{2} and assuming a constant *g*_{m} for the entire range of *C*_{i} (Manter and Kerrigan, 2004; Bahar *et al*., 2018). Whereas, the conversion of *A*_{n}/*C*_{i} to *A*_{n}/*C*_{c} may not be true at low *g*_{m} values under certain conditions (Flexas *et al*., 2007). The key photosynthetic parameters can also be quantified using the curve-fitting methods applied to the *A*_{n}/*C*_{i} curve; for example, the Bayesian retrieval algorithm and the Sharkey online calculator (Sharkey *et al*., 2007; von Caemmerer*et al*., 2009; Gu *et al*., 2010; Zhu *et al*., 2011; von Caemmerer, 2013). The curve-fitting methods that simultaneously quantify the three key photosynthetic parameters may have the equifinality phenomenon (i.e., similar simulation results can be achieved with different initial conditions), because of a curvilinear negative correlation between *V*_{cmax} estimation and *g*_{m} (von Caemmerer, 2013) that changes steeply at the lower range of *g*_{m} (generally < 0.1 mol m^{-2} s^{-1}) (Bahar *et al*., 2018). For the parameterization of the *g*_{m} finite model, *V*_{cmax}, *J*_{max}, and *g*_{m} values were simultaneously estimated by the Bayesian retrieval algorithm, so did the Sharkey online calculator. Importantly, *g*_{m} was also determined using the chlorophyll fluorescence-gas exchange method and the anatomy method. Our results indicated that the *g*_{m_B} temperature responses were significantly different from the *g*_{m_S} temperature responses in terms of absolute values at 25°C and Δ*H*_{a} in most sampled species/treatments (Figs. S3a-b, d, f-i, l, o-t, y, aa-ac), whereas similarities in the temperature response for either *V*_{cmax} or *J*_{max} were found between the two curve-fitting methods. It implied that the differences in *V*_{cmax} observed at high temperatures between the two methods (Fig. 1a) were likely not related to *g*_{m} estimation. A close agreement between the *g*_{m_F,25} and *g*_{m_A,25} (Fig. 4a) and between *g*_{m_FA,25}/40 and *g*_{m_SB,25}/40, especially at the lower range < 0.15 mol m^{-2} s^{-1} (Fig. 4b), was evident, respectively. Furthermore, there is a close agreement in *T*_{opt_gm} between the chlorophyll fluorescence-gas exchange method and the Bayesian retrieval method (adj.R^{2} = 0.58 and the regression slope = 0.81, Fig. S3a-ae). Results suggested that the four parameter estimation methods give similar *g*_{m} estimations, especially at the lower range. The consequence of variations in *g*_{m} on estimation of *V*_{cmax} on *C*c and *C*_{i} bases in this study was consistent with the reports by Bahar *et al.* (2018) (Fig. 4c). Hence, the estimations in *V*_{cmax} by fusing the Bayesian retrieval algorithm and the Sharkey online calculator are reasonable. Furthermore, we found a significantly linear correlation between *V*_{cmax_SB,25} and *J*_{max_SB,25} (Fig. 4d), which falls between the reports by Bahar *et al.* (2018) and Sun *et al.* (2014) and overlaps with the reports by Gago *et al*. (2019). These results suggested that the four parameter estimation methods are independent in the measurements taken for parameter estimation and optimization algorithms, namely the optimized parameterization scheme (i.e. the SB_FA scheme, discussed below) is physiologically meaningful, which excludes the equifinality phenomenon.

In the present study, a close relationship between *g*_{m_F,25} and *g*_{m_A,25} was observed in most sampled species/treatments (Fig. 4a). The close correspondence between the two variables has been also reported in many other C_{3} species (Tosens and Laanisto, 2018; Carriquí *et al*., 2019; 2020; 2021) (grey symbols shown in Fig. 4a). Mesophyll conductance is a complex three-dimensional trait that is probably determined by both biochemical and anatomical features. The chlorophyll fluorescence method compares gas exchange signal with the optical signal which may vary with the depth through the mesophyll tissue (Evans, 2021). These variations may explain minor discrepancies between *g*_{m_A,25} and *g*_{m_F,25} in most sampled species/treatments (Fig. 4a). Carriquí *et al*. (2020) reported that the cell wall composition is a key factor in the *g*_{m} setting in sclerophyll species. The constant values in model parameters of the anatomy *g*_{m} estimation method for vascular plants such as the ratio of cell wall porosity to tortuosity (*P*_{cw}) may also contribute to the discrepancies. In this study, *g*_{m_F,25} was found to be significantly higher than *g*_{m_A,25} in rice. An extremely dense distribution of mesophyll cells in rice was observed (ultrastructure images not shown). The total length of the chloroplast facing the intercellular space (*l*_{c}) in association with *g*_{m_A,25} by using the ultrathin sections was probably underestimated in rice because of the exclusion of tightly adjacent parts of two mesophyll cells in the sampling fields of view.

As shown in Figs. 2a and d, *g*_{m} estimation using the *A*_{n}/*C*_{i} curve only through the Bayesian retrieval algorithm or the Sharkey online calculator can accurately predict leaf gas exchange rates in some species/treatments, whereas cannot in others. A better modeling performance was obtained by the S_FA scheme (i.e. *V*_{cmax_S}+*J*_{max_S}+*g*_{m_FA}) than the S_S scheme (i.e. *V*_{cmax_S}+*J*_{max_S}+*g*_{m_s}). Our results are similar to reports by Sharkey *et al*. (2007): if chlorophyll fluorescence data are available, it could be possible to estimate *g*_{m} from those data to ameliorate reliability of modeling performance. Results suggested the SB_FA solution (i.e. *V*_{cmax_SB}+*J*_{max_SB}+*g*_{m_FA}) that can predict the photosynthesis and transpiration better than other parameterization solutions as the optimized parameterization solution for the *g*_{m} finite model.

### Temperature responses characteristics of *g*_{m}

A *g*_{m} response to temperature has been reported in some species, but not in others (Scafaro *et al*., 2011; von Caemmerer and Evans, 2015; Shrestha *et al*., 2019; Evans, 2021; Li *et al*., 2020), partially due to differences in *g*_{m} estimation methods used by them, as seen in great variations in *g*_{m} temperature response obtained by different estimation methods (Fig. 1c and Figs. S3a-ae). We argued that the *g*_{m} estimated using the parameter estimation method that can accurately fit the *A*_{max}-*T*_{leaf} curve and diurnal gas exchange rates has higher credibility than those that cannot predict accurately. Results of our study suggested that 90% of the sampled species under well-watered conditions exhibit a significant response of *g*_{m} to temperature. Inter-species variations in both Δ*H*a and Δ*S* for *g*_{m} were significantly greater than those of *V*_{cmax} and *J*_{max}. Large variations in Δ*H*a signify significant changes in *g*_{m} temperature response across species, which is in agreement with the results of the studies by Shrestha *et al.* (2019), von Caemmerer and Evans (2015), and Evans (2021). The two-components modeling method developed by von Caemmerer and Evans (2015) produced Δ*H*_{a} for CO_{2} permeability through the membranes, ranging between 36 and 76 kJ mol^{-1}. Using the isolated pea leaf plasma membranes, Zhao *et al.* (2017) reported Δ*H*_{a} for CO_{2} permeability of 30.2 and 52.4 kJ mol^{-1} at high and low internal carbonic anhydrase (CA) concentrations. Results of our study reported the lower and upper limits of the 95% confidence interval of Δ*H*_{a} for *g*_{m_FA} were 50.14 and 76.12 kJ mol^{-1}, respectively. The determined Δ*H*_{a} values of our study are similar to the ranges reported by von Caemmerer and Evans (2015) and Zhao *et al.* (2017). The rates of CO_{2} diffusion in the membranes and during the liquid phase reflect the amount of CO_{2}-permeable and transport enzyme proteins, their thermal stabilities, and the structural components of cell wall. A common or distinct set of aquaporins in the membranes and the associating proteins such as CA inside the vesicles that affect Δ*H*_{a} for CO_{2} permeability/diffusion (Zhao *et al*., 2017) likely vary greatly in expression levels and the associating heterotetramers among C_{3} species (Otto *et al*., 2010; Momayyezi *et al*., 2020). Hence, the determined large variations in temperature response attributes of *g*_{m} are reasonable.

The temperatures at which *V*_{cmax} and *J*_{max} deactivate were usually higher than 35°C and even 40°C in most sampled species. They are similar to the findings in tobacco (Bernacchi*et al*., 2001), rice (Xue *et al*., 2016), and poplar (Silim *et al*., 2010; Xu *et al*., 2020). We found that *g*_{m} deactivation temperatures were lower than those for *V*_{cmax} and *J*_{max} (Figs. 1a-c), which are similar to reports by Xu *et al*. (2020) and Warren and Dreyer (2006). Meanwhile, better accuracy in leaf gas exchange predictions was obtained using the temperature peak function for *g*_{m} than the monotone increasing function. Results highlighted importance of incorporating the deactivation stage of *g*_{m} into leaf photosynthesis model for better modeling accuracy. A rapid change in fluidity of plasma membrane was observed within 1-3 min after heat shock of 37°C in *A. thaliana* and wheat (Zheng *et al*., 2012; Abdelrahman *et al*., 2020). Elevated temperature increases membrane permeability. During a 40°C, 5-15 min heat stress Triandafillou *et al.* (2020) found that *Saccharomyces cerevisiae* cells rapidly acidify from a pH of 7.5 to a range of slightly acidic pH values around 6.8 due to proton influx, which could constrain the CA stability by 20-30% (Wang *et al*., 2016). The transient intracellular acidification induced by heat stress is broadly conserved in eukaryotes. Changes in fluidity and permeability of plasma membrane at elevated temperatures (Niu and Xiang, 2018) that cause proton influx and impact the CA stability may cause the decline of *g*_{m} by 10-20% at elevated temperature from 30°C to 40°C (Fig. 1c).

### Effects of the *g*_{m} finite expression on photosynthesis and transpiration

Kumarathunge *et al*. (2019) proposed that the variation in *T*_{optA} among species can be explained by biochemical restrictions (*J*_{a,25}/*V*_{a,25}). *V*_{a} and *J*_{a} are referred to as the apparent maximum carboxylation rate and electron transport rate, respectively, and both these parameters, particularly *V*_{a}, are numerically and physiologically different from *V*_{cmax} and *J*_{max}. A similar result of an asymmetric effect of *g*_{m} estimation on *V*_{cmax} and *J*_{max} estimations was reported by Manter and Kerrigan (2004) and Sun *et al*. (2014). Hence, we may argue that *V*_{a} not only represents the Rubisco carboxylation rate but also embeds the *g*_{m} effects. Stripping off the *g*_{m} effects from *V*_{a,25} would cause changes in *J*_{a,25}/*V*_{a,25} and then cause significant changes in the *T*_{optA}-*J*_{a,25}/*V*_{a,25} correlation. Our results suggested that *T*_{optA} has a significant linear correlation with *T*_{opt_gm} but not *JV*r, Δ*H*_{a} of *g*_{m_FA}, and *g*_{m_FA,25}, implying that *T*_{optA} is probably related to *g*_{m} temperature response characteristics. Whereas, the plasticity in *T*_{optA} was not fully related to *g*_{m} because only 58% of the variations in *T*_{optA} were explained by *g*_{m}. Changes in the Rubisco kinetic properties, such as thermal stability of Rubisco activase (Salvucci and Crafts-Brandner, 2004), could be an important mechanism.

Knauer *et al.* (2020) argued that the *g*_{m} finite expression has significant effects on photosynthesis estimation and that the effects of *g*_{m} on transpiration are marginal. Conversely, we found that the effects of the *g*_{m} finite expression on photosynthesis and transpiration simulations are equally stronger. Significant effects on transpiration estimation were probably achieved through better predictions of *g*_{sw} because transpiration is a product of *VPD* and *g*_{sw}. Across diverse species, *g*_{m} is strongly linked with *g*_{sw} and leaf hydraulic conductance through the *g*_{m} linkage to extra-xylem components (Flexas *et al*., 2013) such as the plasma membrane intrinsic proteins (PIPs) subfamily of aquaporins (Groszmann *et al*., 2017). Physiological mechanisms underlying the integrated hydraulic-photosynthetic system explained the observed effects of the *g*_{m} finite expression on photosynthesis and transpiration.

## Conclusions

In this study, we developed a *g*_{m} finite photosynthesis-transpiration coupled model that can be directly applicable for most TBMs and also proposed an optimized parameterization solution. The *g*_{m} finite model driven by the parameterization theme of *V*_{cmax_SB}, *J*_{max_SB} and *g*_{m_FA} could well predict *A*_{max}-*T*_{leaf} curves and diurnal gas exchange rates in all sampled species under various experimental treatments. However, the *g*_{m} infinite model cannot always accurately track variations in photosynthesis and transpiration. Results suggested large variations in Δ*H*_{a} and Δ*S* for *g*_{m}. *T*_{optA} was related to thermal attributes of *g*_{m} not *JV*r. Meanwhile, the explicit *g*_{m} expression had equally important effects on photosynthesis and transpiration estimations at plant species level. Results of our study proved that the *g*_{m} finite expression in most TBMs is important for better understanding effects of *g*_{m} on photosynthesis and transpiration under climate change.

## Author contributions

WX: design of the research and funding, data analysis, collection and interpretation, and manuscript writing and revision. HL: data analysis, collection and interpretation, and manuscript writing. JE, MC, MN, TH, and CW: data collection and analysis, manuscript revision. J-F H, J-L Z, Z-G Y and X-W F: data collection and part work of data analysis.

## Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request. MATLAB script for Bayesian retrieval algorithm and the *g*_{m} finite photosynthesis-transpiration coupled model compiled by FORTRAN can be obtained through directly contacting the correspondence author.

## Supporting Information

Additional supporting information may be found in the online version of this article: **Fig. S1** The temperature response curves of *V*_{cmax}.

**Fig. S2** The temperature response curves of *J*_{max}.

**Fig. S3** The temperature response curves of *g*_{m}.

**Fig. S4** Temperature response curves of the net assimilation rate under ambient CO_{2} concentration (400-450 ppm) and high radiation derived from field measurements and predictions.

**Fig. S5** Temperature response curves of the net assimilation rate under ambient CO_{2} concentration (600-630 ppm) and high radiation derived from field measurements and predictions.

**Fig. S6** Comparisons in diurnal photosynthesis rate between field observations and predictions.

**Fig. S7** Comparisons in diurnal transpiration rate between field observations and predictions.

**Fig. S8** Comparisons in diurnal stomatal conductance between field observations and predictions.

**Fig. S9** Comparisons in diurnal *An* at PAR greater than 1500 μmol m^{-2} s^{-1} and across a wide range of leaf temperatures between observations and predictions using the *gm* infinite model and the *g*_{m} finite model that is forced by the parameterization scheme SB_FA.

**Fig. S10** Statistical relationships for photosynthesis optimal temperature and the ratio of the maximum carboxylation rate to the maximum electron transport rate (*JV*r) (a), *T*_{optA}-*g*_{m_F,25} (b), and *T*_{optA}--activation term of *g*_{m_F} (Δ*H*_{a}) (c).

**Table S1** Temperature response characteristic parameters of *V*_{cmax}.

**Table S2** Temperature response characteristic parameters of *J*_{max}.

**Table S3** Temperature response characteristic parameters of *g*_{m}.

**Methods S1** The explicit clarity on the parameter values assumed for each parameter estimation method

**Methods S2**

**Methods S3**

**Methods S4**

**Methods S5**

**Methods S6**

**Methods S7**

## Acknowledgements

This research was supported by the Fundamental Research Funds for the Central Universities (lzujbky-2020-28) and the National Natural Science Foundation of China (32001129). Sincere thanks are dedicated to Dr. John R. Evans for his comments on the manuscript. We are also grateful to Dandan Liu and Xiao Song for their helps on field data collection. The authors declare that they have no conflicts of interest.