Leaf Ci optimization
Given: gs (stomatal conductance), gbc (boundary layer conductance for CO₂)
Vcmax, J, Kc, Ko, Γ*, Rd (all temperature-adjusted)
ca (atmospheric CO₂), oi (atmospheric O₂)
│
▼
┌───────────────────────────────────┐
│ Calculate gleaf = total CO₂ │ ← Eq. 11.75
│ conductance (series combination) │
└───────────────────────────────────┘
│
┌─────────┴─────────┐
▼ ▼
Rubisco-limited Light-limited
(solve quadratic (solve quadratic
for Ac) for Aj)
Eq. 11.28 + 11.78 Eq. 11.29 + 11.78
│ │
└─────────┬─────────┘
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┌───────────────────────────────────┐
│ Co-limitation: blend Ac and Aj │ ← Eq. 11.31
│ Θ·A² - (Ac+Aj)·A + Ac·Aj = 0 │
└───────────────────────────────────┘
│
▼
An = Ag - Rd ← Eq. 11.30
cs = ca - An/gbc ← Eq. 11.75
ci = ca - An/gleaf ← Eq. 11.76leaf_ci_optimization
def leaf_ci_optimization(
atmos:Atmos, # Atmospheric forcing variables:
- o2air : float
Atmospheric O2 concentration (mmol/mol).
- co2air : float
Atmospheric CO2 concentration (umol/mol).
leaf:Leaf, # Leaf physiological parameters:
- c3psn : int
Photosynthetic pathway: 1 = C3, 0 = C4 plant.
- colim : int
Photosynthesis co-limitation: 0 = no, 1 = yes.
- colim_c3 : float
Empirical curvature parameter for C3 co-limitation (-).
- colim_c4a : float
Empirical curvature parameter for C4 co-limitation (-).
- colim_c4b : float
Empirical curvature parameter for C4 co-limitation (-).
- qe_c4 : float
C4 quantum yield (mol CO2 / mol photons).
flux:Flux, # Flux variables with the following inputs:
- vcmax : float
Maximum carboxylation rate (umol/m2/s).
- cp : float
CO2 compensation point (umol/mol).
- kc : float
Michaelis-Menten constant for CO2 (umol/mol).
- ko : float
Michaelis-Menten constant for O2 (mmol/mol).
- je : float
Electron transport rate (umol/m2/s).
- kp_c4 : float
C4 initial slope of CO2 response curve (mol/m2/s).
- gs : float
Leaf stomatal conductance (mol H2O/m2 leaf/s).
- gbc : float
Leaf boundary layer conductance for CO2 (mol CO2/m2 leaf/s).
- apar : float
Leaf absorbed PAR (umol photon/m2 leaf/s).
- rd : float
Leaf respiration rate (umol CO2/m2 leaf/s).
)->Flux: # Updated flux object with the following attributes:
- ac : float
Rubisco-limited gross photosynthesis (umol CO2/m2 leaf/s).
- aj : float
RuBP regeneration-limited gross photosynthesis (umol CO2/m2 leaf/s).
- ap : float
Product-limited (C3) or CO2-limited (C4) gross photosynthesis
(umol CO2/m2 leaf/s).
- ag : float
Leaf gross photosynthesis (umol CO2/m2 leaf/s).
- an : float
Leaf net photosynthesis (umol CO2/m2 leaf/s).
- cs : float
Leaf surface CO2 concentration (umol/mol).
- ci : float
Leaf intercellular CO2 concentration (umol/mol).
Calculate leaf photosynthesis for a specified stomatal conductance, then calculate Ci from the diffusion equation.
This routine uses a quadratic equation to solve for net photosynthesis (An). A general equation for C3 photosynthesis is:
a*(Ci - Cp)
An = ----------- - Rd
e*Ci + dwhere:
An = Net leaf photosynthesis (umol CO2/m2/s)
Rd = Leaf respiration (umol CO2/m2/s)
Ci = Intercellular CO2 concentration (umol/mol)
Cp = CO2 compensation point (umol/mol)Rubisco-limited photosynthesis (Ac):
a = Vcmax, e = 1, d = Kc * (1 + Oi / Ko)
RuBP regeneration-limited photosynthesis (Aj):
a = J, e = 4, d = 8 * Cp
where:
Vcmax = Maximum carboxylation rate (umol/m2/s)
Kc = Michaelis-Menten constant for CO2 (umol/mol)
Ko = Michaelis-Menten constant for O2 (mmol/mol)
Oi = Intercellular O2 concentration (mmol/mol)
J = Electron transport rate (umol/m2/s)Ci is calculated from the diffusion equation:
1.4 1.6
An = (Ca - Ci) / (--- + ---)
gb gs
1.4 1.6
Ci = Ca - (--- + ---)*An
gb gswhere:
Ca = Atmospheric CO2 concentration (umol/mol)
gb = Leaf boundary layer conductance (mol H2O/m2/s)
gs = Leaf stomatal conductance (mol H2O/m2/s)
1.4 = Corrects gb for the diffusivity of CO2 compared with H2O
1.6 = Corrects gs for the diffusivity of CO2 compared with H2OThe resulting quadratic equation is: aAn^2 + bAn + c = 0, which is solved for An. Correct solution is the smaller of the two roots.
A similar approach is used for C4 photosynthesis.
The total leaf conductance for CO2 (gleaf, mol CO2/m2/s) is computed from the boundary layer conductance gbc (mol CO2/m2/s) and stomatal conductance gs (mol H2O/m2/s) acting in series:
gleaf = 1 / (1/gbc + 1.6/gs)where the factor 1.6 converts gs from H2O to CO2 basis.
Parameters:
Atmos: Atmospheric forcing variables
- o2air: Atmospheric O2 concentration (mmol/mol).
- co2air: Atmospheric CO2 concentration (umol/mol).
Leaf: Leaf physiological parameters
- c3psn: Photosynthetic pathway: 1 = C3, 0 = C4 plant.
- colim: Photosynthesis co-limitation: 0 = no, 1 = yes.
- colim_c3: Empirical curvature parameter for C3 co-limitation (-).
- colim_c4a: Empirical curvature parameter for C4 co-limitation (-).
- colim_c4b: Empirical curvature parameter for C4 co-limitation (-).
- qe_c4: C4 quantum yield (mol CO2 / mol photons).
Flux: Flux variables with the following inputs
- vcmax: Maximum carboxylation rate (umol/m2/s).
- cp: CO2 compensation point (umol/mol).
- kc: Michaelis-Menten constant for CO2 (umol/mol).
- ko: Michaelis-Menten constant for O2 (mmol/mol).
- je: Electron transport rate (umol/m2/s).
- kp_c4: C4 initial slope of CO2 response curve (mol/m2/s).
- gs: Leaf stomatal conductance (mol H2O/m2 leaf/s).
- gbc: Leaf boundary layer conductance for CO2 (mol CO2/m2 leaf/s).
- apar: Leaf absorbed PAR (umol photon/m2 leaf/s).
- rd: Leaf respiration rate (umol CO2/m2 leaf/s).
Returns:
Flux: Updated flux object with the following attributes
- ac: Rubisco-limited gross photosynthesis (umol CO2/m2 leaf/s).
- aj: RuBP regeneration-limited gross photosynthesis (umol CO2/m2 leaf/s).
- ap: Product-limited (C3) or CO2-limited (C4) gross photosynthesis (umol CO2/m2 leaf/s).
- ag: Leaf gross photosynthesis (umol CO2/m2 leaf/s).
- an: Leaf net photosynthesis (umol CO2/m2 leaf/s).
- cs: Leaf surface CO2 concentration (umol/mol).
- ci: Leaf intercellular CO2 concentration (umol/mol).