A comparison of two photosynthesis parameterization schemes for an alpine meadow site on the Qinghai-Tibetan Plateau

Abstract

Photosynthesis is a very important sub-process in the carbon cycle and is a crucial sub-modular function in carbon cycle models. In this study, two typical photosynthesis parameterization schemes were compared based on meteorological and eddy covariance (EC) observations at an alpine meadow site. The photosynthesis model parameters were estimated using the Markov Chain Monte Carlo (MCMC) method. The results indicated that the Farquhar-conductance coupled model better predicted the gross primary production (GPP) for the alpine meadow ecosystem at an hourly time scale than the light use efficiency (LUE) model even though the Farquhar-conductance coupled model has a lower computational efficiency than the LUE model. Compared to the Ball–Woodrow–Berry (BWB) stomatal conductance model, coupling the Farquhar model with the Leuning stomatal conductance model more accurately simulated GPP.

Appendix A: photosynthesis model

1.1 Appendix A.1: Scalars in LUE model

f(T) is calculated using the following equation (Xiao et al. 2004b):

$$ f(T)=\frac{\left(T-{T}_{\mathit{\min}}\right)\left(T-{T}_{\max}\right)}{\left(T-{T}_{\min}\right)\left(T-{T}_{\max}\right)-{\left(T-{T}_{\mathrm{opt}}\right)}^2} $$

(A1)

where T _max [°C], T _min [°C], and T _opt [°C] are the maximum, minimum, and optimal photosynthetic temperatures, respectively. Moreover, T [°C] is the air temperature; f(T) [dimensionless] was set to 0 when T was less than T _min or T was greater than T_max. Furthermore, f(VPD) is calculated using the following equation (Running et al. 1999):

$$ f(VPD)=\left({VPD}_{\max}\hbox{-} VV\right)/\left({VPD}_{\max }-{VPD}_{\min}\right) $$

(A2)

VPD_max [Pa] and VPD_min [Pa] are empirical parameters, and VPD [Pa] is the vapor pressure deficit, which is calculated using the air temperature T [°C] and RH [%] (Wu et al. 2009):

$$ \ln {e}_s=21.382-5347.5/\left(T+273.15\right) $$

(A3)

$$ VPD=0.1\cdot {e}_s\cdot \left(1-RH/100\right) $$

(A4)

Furthermore, fAPAR is calculated with an exponential model using the LAI as input (Ruimy et al. 1999):

$$ fAPAR=1-{e}^{-kn*LAI} $$

(A5)

where kn is the light extinction coefficient and LAI is leaf area index.

1.2 Appendix A.2: Ac and Ae in Farquhar model

A_c [μmol CO₂/m²/s] is calculated according to the following equation:

$$ {A}_c={V}_m\frac{C_i-{\varGamma}_{*}}{C_i+{K}_c\left(1+\left({O}_x/{k}_o\right)\right)} $$

(A6)

$$ {C}_i=f{c}_i*{C}_a $$

(A7)

where C _i is the intercellular CO₂ concentration [μmol CO₂/mol], C _a is the ambient CO₂ concentration [365 μmol CO₂/mol], and fc _i is the ratio of the intercellular CO₂ concentration to the ambient air CO₂ concentration. Moreover, O _x is the oxygen concentration in the air [0.21 mol O₂/mol], and V _m is the maximum carboxylation rate [μmol CO₂/m²/s], which is calculated using the canopy temperature T [°C] and activation energy E _vm according to the Arrhenius equation:

$$ {V}_m={V}_m^{25}\cdot \exp \left(\frac{E_{Vm}\cdot \left(\left(T+273.15\right)-298\right)}{R\cdot \left(T+273.15\right)\cdot 298}\right) $$

(A8)

where ${V}_m^{25}$ is the maximum carboxylation rate at 25 °C and R is the universal gas constant [8.314 J/K/mol]. The CO₂ compensation point without dark respiration is represented by Γ _* [μmol CO₂/mol] and is also calculated using the Arrhenius equation:

$$ {\varGamma}_{*}={\varGamma}_{*}^{25}\cdot \exp \left(\frac{E_{\varGamma_{*}^{25}}\cdot \left(\left(T+273.15\right)-298\right)}{R\cdot \left(T+273.15\right)\cdot 298}\right) $$

(A9)

where ${\varGamma}_{*}^{25}$ is the CO₂ compensation point without dark respiration at 25 °C; ${E}_{\varGamma_{*}^{25}}$ describes the temperature dependence ofΓ _*. Two Michaelis–Menten constants are temperature dependent based on the Arrhenius equation, similarly to V _m .K _c is the Michaelis–Menten constant for carboxylation [μmol/mol] and is calculated using the following equation:

$$ {K}_c={K}_c^{25}\cdot \exp \left(\frac{E_{K_c}\cdot \left(\left(T+273.15\right)-298\right)}{R\cdot \left(T+273.15\right)\cdot 298}\right) $$

(A10)

where ${E}_{K_c}$ is the activation energy and ${K}_c^{25}$ is the Michaelis–Menten constant for carboxylation at 25 °C. Moreover, K _o is the Michaelis–Menten constant for oxygenation (mol/mol) and is calculated according to the following relationship:

$$ {K}_o={K}_o^{25}\cdot \exp \left(\frac{E_{K_o}\cdot \left(\left(T+273.15\right)-298\right)}{R\cdot \left(T+273.15\right)\cdot 298}\right) $$

(A11)

where ${E}_{K_o}$ is the activation energy and ${K}_o^{25}$ is the Michaelis–Menten constant for oxygenation at 25 °C. The light electron transport-limited CO₂ assimilation rate, Ae [μmol CO₂/m²/s], is calculated as follows:

$$ {A}_e=\frac{\alpha_q\cdot I\cdot {J}_m}{\sqrt{J_m^2+{\alpha}_q^2\cdot {I}^2}}\cdot \frac{Ci-{\varGamma}_{*}}{4\cdot \left( Ci+2{\varGamma}_{*}\right)} $$

(A12)

where I is the absorbed PAR [μmol photons/m²/s], α _q is the quantum efficiency of photon capture [mol/mol photons], and J _m is the maximum electron transport rate [μmol CO₂/m²/s]. Furthermore, Jm depends on temperature and is calculated by

$$ {J}_m={r}_{JmVm}\cdot {V}_m^{25}\cdot \exp \left(\frac{E_{Jm}\cdot \left(\left(T+273.15\right)-298\right)}{R\cdot \left(T+273.15\right)\cdot 298}\right) $$

(A13)

where r _JmVm is the ratio of Jm to ${V}_m^{25}$ at 25 °C; E _Jm is the activation energy.