Photosynthesis

To model photosynthesis and hence calculate GPP we apply a vairant of the Farquhar-von Caemmerer-Berry model ([Farquhar:1980]) adapted from [Liu:2021].

  1. The absorbed photosynthetically active radiation (APAR) driving photosynthesis is calculated using the Beer-Lambert law [Campbell:1998] :

\[APAR = PAR \cdot (1 - \rho_\text{leaf}) \cdot (1 - e^{(-K \cdot LAI \cdot \Omega)})\]
  • \(PAR\) is the photosythnetically active radiaion
    \(PAR = \frac{SRAD}{2 \cdot E_{photon} \cdot N_A} \cdot 10^6\)

    • \(PAR\) is the photosynthetically active radiation (μmol photons m⁻² s⁻¹)

    • \(SRAD\) is the incident shortwave radiation (W m⁻²)

    • \(E_{photon} = 2.0 \times 10^{-25} / (500.0 \times 10^{-9})\) J (Planck constant times speed of light divided by light wavelength)

    • \(N_A = 6.02 \times 10^{23}\) mol⁻¹ (Avogadro’s constant)

  • \(K\) is the vegetation extinction coefficient [Campbell:1998]

  • \(LAI\) is the leaf area index

  • \(\Omega\) is the clumping index [Braghiere:2019]

  • \(\rho_\text{leaf}\) parameter describing the reflected portion of photosynthetically active radiation due to canopy reflectance

  1. Net carbon assimilation is calculated based on C3 photosynthesis biochemistry to determine potential leaf-level photosynthesis (unstressed by water availability). This is expressed in terms of two potentially limiting rates:

  1. Rubisco-limited rate (\(a_1\)):

    \[a_1 = V_\text{cmax} \cdot \frac{c_i - c_p}{c_i + K_c \cdot (1 + 209/K_o)}\]
  • \(V_\text{cmax}\) (mol CO2 m-2 s-1) is the maximum rate of carboxylation.
    \(V_{cmax} = \frac{V_{cmax25} \cdot q_{10}^{0.1(T_C - 25)}}{\left(1 + e^{0.3(T_C - (T_{upp} - T_0))}\right) \left(1 + e^{0.3((T_{down} - T_0) - T_C)}\right)}\)

    • \(V_{cmax25}\) is the maximum rate of carboxylation at 25°C

    • \(q_{10}\) parameter describing temperature sensitivity

    • \(T_C\) is the air temperature in °C

    • \(T_{upp}\) parameter describing the upper temperature limit for photosynthesis (in K)

    • \(T_{down}\) parameter describing the lower temperature limit for photosynthesis (in K)

    • \(T_0\) is the freezing point of water in Kelvin (273.15 K)

  • \(c_i\) is the intercellular CO2 concentration
    \(c_i = c_{a} \cdot \left(1 - \frac{1}{1 + \frac{g_1}{\sqrt{VPD}}}\right)\)

    • \(c_{a}\) is the atmospheric CO2 concentration

    • \(g_1\) is the stomatal slope parameter

    • \(VPD\) is the vapor pressure deficit

  • \(c_p\) is the CO2 compensation point (the CO2 concentration at which photosynthesis equals respiration)
    \(c_p = 36.9 + 1.18(T_C - 25) + 0.36(T_C - 25)^2\)

    • \(T_C\) is the air temperature in °C

  • \(K_c\) is the Michaelis-Menten concentration for CO2
    \(K_c = 300 \cdot e^{0.074(T_C - 25)}\)

    • \(T_C\) is the air temperature in °C

  • \(K_o\) is the Michaelis-Menten concentration for O2
    \(K_o = 300 \cdot e^{0.015(T_C - 25)}\)

    • \(T_C\) is the air temperature in °C

  1. Light-limited rate (\(a_2\)):

    \[a_2 = J \cdot \frac{c_i - c_p}{4(c_i + 2c_p)}\]
  • \(J\) is the rate of electron transport.
    \(J = \frac{0.3 \cdot PAR + V_{cmax} \cdot e - \sqrt{(0.3 \cdot PAR + V_{cmax} \cdot e)^2 - 1.08 \cdot PAR \cdot V_{cmax} \cdot e}}{1.8}\)

    • \(PAR\) is the photosynthetically active radiation

    • \(V_{cmax}\) is the maximum rate of carboxylation

    • \(e\) is the mathematical constant (approximately 2.71828)

  1. The total net carbon assimilation (\(A_n\)) is

\[A_n = \min(a_1 \cdot \beta, a_2) - R_d\]

  • \(\beta\) is the minimum of the moisture stress factor related to the mean soil moisture concentration in the root zone, and the temperature stress factor

  • \(R_d\) is the leaf dark respiration.

  1. GPP, representing the total canopy photosynthesis, is calculated by integrating leaf-level photosynthesis over the entire canopy leaf area index:

\[GPP = A_n \cdot \frac{1 - \exp(-K \cdot LAI \cdot \Omega)}{K}\]
[Braghiere:2019]

Braghiere, R.K., Quaife, T., Black, E., He, L. and Chen, J.M., 2019. Underestimation of global photosynthesis in Earth system models due to representation of vegetation structure. Global Biogeochemical Cycles, 33(11), pp.1358-1369. https://doi.org/10.1029/2018GB006135

[Campbell:1998] (1,2)

Campbell, G.S. and Norman, J.M., 2000. An introduction to environmental biophysics. Springer Science & Business Media.

[Farquhar:1980]

Farquhar, G.D., von Caemmerer, S.V. and Berry, J.A., 1980. A biochemical model of photosynthetic CO 2 assimilation in leaves of C 3 species. planta, 149, pp.78-90. https://doi.org/10.1007/BF00386231

[Liu:2021]

Liu, Y., Holtzman, N.M. and Konings, A.G., 2021. Global ecosystem-scale plant hydraulic traits retrieved using model–data fusion. Hydrology and Earth System Sciences, 25(5), pp.2399-2417. https://doi.org/10.5194/hess-25-2399-2021