C3(Sco25 = 2800.0, E_Sco = -24.46e3, Kmc25 = 270.0, E_Kmc = 80.99e3, 
    Kmo25 = 165.0e3, E_Kmo = 23.72e3, Vcmax25 = 120.0, E_Vcmax = 65.33e3, 
    simpleJ = false, k2ll = 0.35, theta = 0.7, Phi2 = 0.82, sigma2 = 0.5, 
    beta = 0.85, fcyc = 0.1, 
    fpseudo = 0.05, Jmax25 = 230.0, E_Jmax = 30.0e3, D_Jmax = 200.0e3, 
    S_Jmax = 650.0, TPU25 = 12.0, E_TPU = 53.1e3, D_TPU = 20.18e3,
    S_TPU = 650.0, Rd25 = 1.2, E_Rd = 46.39e3, gm25 = 0.4, E_gm = 49.6e3, 
    D_gm = 437.4e3, S_gm = 1400.0, gso = 0.01, a1 = 0.85, b1 = 0.14e-3)

Data structure to store all the parameters for the C3 photosynthesis model.

Arguments

• Sco25: Sc/o parameter at 25 C
• E_Sco: Apparent activation energy of Sc/o (J/mol)
• Kmc25: Km for CO2 at 25 C (μmol/mol)
• E_Kmc: Activation energy of Kmc (J/mol)
• Kmo25: Km for O2 at 25 C (umol/mol)
• E_Kmo: Activation energy of Kmo (J/mol)
• Vcmax25: Maximum rate of carboxylation at 25 C (μmol/m2/s)
• E_Vcmax: Activation energy of Vcmax (J/mol)
• theta: Curvature parameter
• simpleJ: Use k2ll rather than calculating from other parameters
• k2ll: Low-light use efficiency for electron transport
• Phi2: Low-light PSII quantum yield
• sigma2: Partitioning of excitation between PSII and PSI
• beta: Leaf absorptance of PAR
• fcyc: Fraction of electrons at PSI that follow cyclic transport around PSI
• fpseudo: Fraction of electrons at PSI that are used by alternative electron sinks
• Jmax25: Maximum rate of electron transport (μmol/m2/s)
• E_Jmax: Activation energy Jmax (J/mol)
• D_Jmax: Deactivation energy of Jmax (J/mol)
• S_Jmax: Entropy term for Jmax (K)
• TPU25: Maximum rate of triose phosphate utilisation (μmol/m2/s)
• E_TPU: Activation energy TPU (J/mol)
• D_TPU: Deactivation energy of TPU (J/mol)
• S_TPU: Entropy term for TPU (K)
• Rd25: Respiration rate at 25 C (μmol/m2/s)
• E_Rd: Activation energy of Rd (J/mol)
• gm25: Maximum rate of CO2 assimilation at 25 C (μmol/m2/s)
• E_gm: Activation energy of gm (J/mol)
• D_gm: Deactivation energy of gm (J/mol)
• S_gm: Entropy term for gm (K)
• gso: Minimum stomatal conductance to fluxes of CO2 in darkness (mol/m2/s/Pa)
• a1: Empirical parameter in gs formula
• b1: Empirical parameter in gs formula

C3Q(Sco25 = 2800.0, E_Sco = -24.46e3J/mol, Kmc25 = 270.0μmol/mol, E_Kmc = 80.99e3J/mol,
     Kmo25 = 165.0e3μmol/mol, E_Kmo = 23.72e3J/mol, Vcmax25 = 120.0μmol/m^2/s, E_Vcmax = 65.33e3J/mol,
     simpleJ = false, k2ll = 0.35, theta = 0.7, Phi2 = 0.82, sigma2 = 0.5, beta = 0.85, fcyc = 0.1, fpseudo = 0.05, 
     Jmax25 = 230.0μmol/m^2/s, E_Jmax = 30.0e3J/mol, D_Jmax = 200.0e3J/mol, S_Jmax = 650.0J/mol/K, 
     TPU25 = 12.0μmol/m^2/s, E_TPU = 53.1e3J/mol, D_TPU = 201.8e3J/mol, S_TPU = 650.0K, 
     Rd25 = 1.2μmol/m^2/s, E_Rd = 46.39e3J/mol, gm25 = 0.4mol/m^2/s, E_gm = 49.6e3J/mol, 
     D_gm = 437.4e3J/mol, S_gm = 1400.0K, gso = 0.01mol/m^2/s, a1 = 0.85, b1 = 0.14e-3/Pa)

Data structure to store all the parameters for the C3 photosynthesis model using Quantity objects from Unitful.jl.

Arguments

• Sco25: Sc/o parameter at 25 C
• E_Sco: Apparent activation energy of Sc/o (J/mol)
• Kmc25: Km for CO2 at 25 C (μmol/mol)
• E_Kmc: Activation energy of Kmc (J/mol)
• Kmo25: Km for O2 at 25 C (umol/mol)
• E_Kmo: Activation energy of Kmo (J/mol)
• Vcmax25: Maximum rate of carboxylation at 25 C (μmol/m2/s)
• E_Vcmax: Activation energy of Vcmax (J/mol)
• theta: Curvature parameter
• simpleJ: Use k2ll rather than calculating from other parameters
• k2ll: Low-light use efficiency for electron transport
• Phi2: Low-light PSII quantum yield
• sigma2: Partitioning of excitation between PSII and PSI
• beta: Leaf absorptance of PAR
• fcyc: Fraction of electrons at PSI that follow cyclic transport around PSI
• fpseudo: Fraction of electrons at PSI that are used by alternative electron sinks
• Jmax25: Maximum rate of electron transport (μmol/m2/s)
• E_Jmax: Activation energy Jmax (J/mol)
• D_Jmax: Deactivation energy of Jmax (J/mol)
• S_Jmax: Entropy term for Jmax (J/K/mol)
• TPU25: Maximum rate of triose phosphate utilisation (μmol/m2/s)
• E_TPU: Activation energy TPU (J/mol)
• D_TPU: Deactivation energy of TPU (J/mol)
• S_TPU: Entropy term for TPU (J/K/mol)
• Rd25: Respiration rate at 25 C (μmol/m2/s)
• E_Rd: Activation energy of Rd (J/mol)
• gm25: Mesophyll conductance at 25 C (mol/m2/s)
• E_gm: Activation energy of gm (J/mol)
• D_gm: Deactivation energy of gm (J/mol)
• S_gm: Entropy term for gm (J/K/mol)
• gso: Minimum stomatal conductance to fluxes of CO2 in darkness (mol/m2/s)
• a1: Empirical parameter in gs formula
• b1: Empirical parameter in gs formula (1/kPa)

C4(Sco25 = 2590.0, E_Sco = -24.46e3, Kmc25 = 650.0, E_Kmc = 79.43e3, Kmo25 = 450e3, 
   E_Kmo = 36380.0, Vcmax25 = 120.0, E_Vcmax = 65.33, theta = 0.7, Phi2 = 0.83, sigma2 = 0.5, 
   beta = 0.85, fQ = 1.0, fpseudo = 0.1, h = 4.0, Jmax25 = 230.0, E_Jmax = 48e3, D_Jmax = 200e3, 
   S_Jmax = 630.0, x = 0.4, alpha = 0.1, kp25 = 0.7, E_kp = 46.39e3, gbs = 0.003, Rd25 = 1.2, 
   E_Rd = 46.39e3, gso = 0.01, a1 = 0.9, b1 = 0.15e-3)

Data structure to store all the parameters for the C3 photosynthesis model.

Arguments

• Sco25: Sc/o parameter at 25 C
• E_Sco: Apparent activation energy of Sc/o (J/mol)
• Kmc25: Km for CO2 at 25 C (μmol/mol)
• E_Kmc3: Activation energy of Kmc (J/mol)
• Kmo25: Km for O2 at 25 C (umol/mol)
• E_Kmo: Activation energy of Kmo (J/mol)
• Vcmax25: Maximum rate of carboxylation at 25 C (μmol/m2/s)
• E_Vcmax: Activation energy of Vcmax (J/mol)
• theta: Curvature parameter
• Phi2: Low-light PSII quantum yield
• sigma2: Partitioning of excitation between PSII and PSI
• beta: Leaf absorptance of PAR
• fQ: Fraction of electrons at reduced plastoquinone that follow the Q-cycle
• fpseudo: Fraction of electrons at PSI that follow cyclic transport around PSI
• h: Number of protons required to produce one ATP
• Jmax25: Maximum rate of electron transport (μmol/m2/s)
• E_Jmax: Activation energy Jmax (J/mol)
• D_Jmax: Deactivation energy of Jmax (J/mol)
• S_Jmax: Entropy coefficient of Jmax (J/mol/K)
• x: Fraction of electron transport partitioned to mesophyll cells
• alpha: Fraction of O2 evolution occuring in the bundle sheath
• kp25: Initial carboxylation efficiency of the PEP carboxylase (mol/m2/s)
• E_kp: Activation energy of kp (J/mol)
• gbs: Bundle sheath conductance (mol/m^2/s)
• Rd25:: Respiration rate at 25 C (μmol/m2/s)
• E_Rd: Activation energy of Rd (J/mol)
• gso: Minimum stomatal conductance to fluxes of CO2 in darkness (mol/m2/s)
• a1: Empirical parameter in gs formula
• b1: Empirical parameter in gs formula (1/kPa)

C4(Sco25 = 2590.0, E_Sco = -24.46e3J/mol, Kmc25 = 650.0μmol/mol, E_Kmc = 79.43e3J/mol,
   Kmo25 = 450e3μmol/mol, E_Kmo = 36380.0J/mol, Vcmax25 = 120.0μmol/m^2/s, E_Vcmax = 65.33J/mol,
   theta = 0.7, Phi2 = 0.83, sigma2 = 0.5, beta = 0.85, fQ = 1.0, fpseudo = 0.1, h = 4.0, 
   Jmax25 = 230.0μmol/m^2/s, E_Jmax = 48e3J/mol, D_Jmax = 200e3J/mol, S_Jmax = 630.0J/mol/K, 
   x = 0.4, alpha = 0.1, kp25 = 0.7mol/m^2/s, E_kp = 46.39e3J/mol, gbs = 0.003mol/m^2/s, 
   Rd25 = 1.2μmol/m^2/s, E_Rd = 46.39e3J/mol, gso = 0.01mol/m^2/s, a1 = 0.9, b1 = 0.15e-3/Pa)

Data structure to store all the parameters for the C4 photosynthesis model using Quantity objects from Unitful.jl.

Arguments

• Sco25: Sc/o parameter at 25 C
• E_Sco: Apparent activation energy of Sc/o (J/mol)
• Kmc25: Km for CO2 at 25 C (μmol/mol)
• E_Kmc3: Activation energy of Kmc (J/mol)
• Kmo25: Km for O2 at 25 C (umol/mol)
• E_Kmo: Activation energy of Kmo (J/mol)
• Vcmax25: Maximum rate of carboxylation at 25 C (μmol/m2/s)
• E_Vcmax: Activation energy of Vcmax (J/mol)
• theta: Curvature parameter
• Phi2: Low-light PSII quantum yield
• sigma2: Partitioning of excitation between PSII and PSI
• beta: Leaf absorptance of PAR
• fQ: Fraction of electrons at reduced plastoquinone that follow the Q-cycle
• fpseudo: Fraction of electrons at PSI that follow cyclic transport around PSI
• h: Number of protons required to produce one ATP
• Jmax25: Maximum rate of electron transport (μmol/m2/s)
• E_Jmax: Activation energy Jmax (J/mol)
• D_Jmax: Deactivation energy of Jmax (J/mol)
• S_Jmax: Entropy coefficient of Jmax (J/mol/K)
• x: Fraction of electron transport partitioned to mesophyll cells
• alpha: Fraction of O2 evolution occuring in the bundle sheath
• kp25: Initial carboxylation efficiency of the PEP carboxylase (mol/m2/s)
• E_kp: Activation energy of kp (J/mol)
• gbs: Bundle sheath conductance (mol/m^2/s)
• Rd25:: Respiration rate at 25 C (μmol/m2/s)
• E_Rd: Activation energy of Rd (J/mol)
• gso: Minimum stomatal conductance to fluxes of CO2 in darkness (mol/m2/s)
• a1: Empirical parameter in gs formula
• b1: Empirical parameter in gs formula (1/kPa)

SimpleOptical(; αPAR = 0.85, αNIR = 0.20, ϵ = 0.95)

Simple optical properties of a leaf.

Arguments

• αPAR: Absorption coefficient of PAR
• αNIR: Absorption coefficient of NIR
• ϵ: Emissivity for thermal radiation

gbAngle(; d = 0.01, ang = 0.0, ar = 1.0, fangm = 1.381, fangk = 0.034,
α = 2.738, b0_0 = 0.455, d_b0 = 2.625, b0_n = 0.373, b0_KAR = 28.125,  db_0 = 0.085,
d_db = 0.437, db_n = 5.175, db_KAR = 0.884,  β_0 = 3.362, d_β = 17.664, β_n = 4.727,
β_KAR = 0.677)

Model of boundary layer conductance that accounts for inclination angle and leaf aspect ratio (see documentation for details).

Arguments

• d: Characteristic leaf length (m)
• ang: Leaf inclination angle (°)
• ar: Leaf aspect ratio (length/width)
• fangm: Maximum enhancement factor due to inclination angle
• fangk: Exponent in response to inclination angle
• α: Effect on back boundary layer conductance due to leaf inclination angle and aspect ratio
• b0_0: Parameter in the effect of aspect ratio (see documentation)
• d_b0: Parameter in the effect of aspect ratio (see documentation)
• b0_n: Parameter in the effect of aspect ratio (see documentation)
• b0_KAR: Parameter in the effect of aspect ratio (see documentation)
• db_0: Parameter in the effect of aspect ratio (see documentation)
• d_db: Parameter in the effect of aspect ratio (see documentation)
• db_n: Parameter in the effect of aspect ratio (see documentation)
• db_KAR: Parameter in the effect of aspect ratio (see documentation)
• β_0: Parameter in the effect of aspect ratio (see documentation)
• d_β: Parameter in the effect of aspect ratio (see documentation)
• β_n: Parameter in the effect of aspect ratio (see documentation)
• β_KAR: Parameter in the effect of aspect ratio (see documentation)

gbAngleQ(; d = 0.01m, ang = 0.0, ar = 1.0, fangm = 1.381, fangk = 0.034,
α = 2.738, b0_0 = 0.455, d_b0 = 2.625, b0_n = 0.373, b0_KAR = 28.125,  db_0 = 0.085,
d_db = 0.437, db_n = 5.175, db_KAR = 0.884,  β_0 = 3.362, d_β = 17.664, β_n = 4.727,
β_KAR = 0.677)

Model of boundary layer conductance that accounts for inclination angle and leaf aspect ratio (see documentation for details) using Quantity for Unitful.jl.

Arguments

• d: Characteristic leaf length (m)
• ang: Leaf inclination angle (°)
• ar: Leaf aspect ratio (length/width)
• fangm: Maximum enhancement factor due to inclination angle
• fangk: Exponent in response to inclination angle
• α: Effect on back boundary layer conductance due to leaf inclination angle and aspect ratio
• b0_0: Parameter in the effect of aspect ratio (see documentation)
• d_b0: Parameter in the effect of aspect ratio (see documentation)
• b0_n: Parameter in the effect of aspect ratio (see documentation)
• b0_KAR: Parameter in the effect of aspect ratio (see documentation)
• db_0: Parameter in the effect of aspect ratio (see documentation)
• d_db: Parameter in the effect of aspect ratio (see documentation)
• db_n: Parameter in the effect of aspect ratio (see documentation)
• db_KAR: Parameter in the effect of aspect ratio (see documentation)
• β_0: Parameter in the effect of aspect ratio (see documentation)
• d_β: Parameter in the effect of aspect ratio (see documentation)
• β_n: Parameter in the effect of aspect ratio (see documentation)
• β_KAR: Parameter in the effect of aspect ratio (see documentation)

simplegb(; d = 0.01)

Simple model of boundary layer conductance.

Arguments

• d: Characteristic leaf length (m)

simplegbQ(; d = 0.01m)

Simple model of boundary layer conductance using Quantity from Unitful.jl.

Arguments

• d: Characteristic leaf length (m)

energybalance(pgb, pAgs, pEb, PAR, NIR, ws, RH, Tair, Ca, P, O2)

Calculate the energy balance of a leaf.

Arguments

• pgb: Boundary layer conductance model
• pAgs: Photosynthesis and stomatal conductance model
• pEb: Optical properties of the leaf
• PAR: Photosynthetically active radiation (umol/m2/s)
• NIR: Near-infrared radiation (W/m2)
• ws: Wind speed (m/s)
• RH: Relative humidity
• Tair: Air temperature (K)
• Ca: Atmospheric CO2 concentration (μmol/mol)
• P: Air pressure (kPa)
• O2: Atmospheric O2 concentration (μmol/mol)

Details

Inputs maybe be either Real or Quantity types (i.e., with physical units). If Quantity types are used, the output will be a Quantity type.

gb(p::gbType, ws, Tleaf, Tair, P)

Compute boundary layer conductance for heat, water vapor and CO2.

Arguments

• p: Model of boundary layer conductance
• ws: Wind speed (m/s)
• Tleaf: Leaf temperature (K)
• Tair: Air temperature (K)
• P: Air pressure (Pa)

Returns

• gbh: Boundary layer conductance for heat (mol/m2/s)
• gbw: Boundary layer conductance for water vapor (mol/m²/s)
• gbc: Boundary layer conductance for CO2 (mol/m²/s)

photosynthesis(par::C3, PAR = 1000.0, RH = 0.75, Tleaf = 298.0, Ca = 400.0, O2 = 210e3, gb = 0.5, net = true)
photosynthesis(par::C4, PAR = 1000.0, RH = 0.75, Tleaf = 298.0, Ca = 400.0, O2 = 210e3, gb = 0.5, net = true)
photosynthesis(par::C3Q, PAR = 1000.0μmol/m^2/s, RH = 0.75, Tleaf = 298.0K, Ca = 400.0μmol/mol, O2 = 210e3μmol/mol, gb = 0.5mol/m^2/s, net = true)
photosynthesis(par::C4Q, PAR = 1000.0μmol/m^2/s, RH = 0.75, Tleaf = 298.0K, Ca = 400.0μmol/mol, O2 = 210e3μmol/mol, gb = 0.5mol/m^2/s, net = true)

Calculate net or gross CO2 assimilation (umol/m2/s) and stomatal condutance to fluxes of CO2 (mol/m2/s) as a function of photosynthetically active radiation (PAR, umol/m2/s), relative humidity (RH), leaf temperature (Tleaf, K), air CO2 partial pressure (Ca, μmol/mol), oxygen (O2, μmol/mol) and boundary layer conductance to CO2 (gb, mol/m2/s). Environmental inputs must be scalar. The argument net indicates whether the net or gross CO2 assimilation should be returned.

solve_energy_balance(Ags::Union{C3Q, C4Q}; gb = simplegbQ(),
                     opt = SimpleOptical(), PAR = 1000.0μmol/m^2/s,
                     NIR = 250.0W/m^2, ws = 1.0m/s, RH = 0.75,
                     Tair = 298.0K, Ca = 400.0μmol/mol, P = 101.0kPa,
                     O2 = 210.0mmol/mol, order = Order2(), xatol = 0.01,
                     maxfnevals = 100, net = true)
solve_energy_balance(Ags::Union{C3, C4}; gb = simplegb(),
                     opt = SimpleOptical(), PAR = 1000.0, NIR = 250.0,
                     ws = 1.0, RH = 0.75, Tair = 298.0, Ca = 400.0,
                     P = 101.0e3, O2 = 210.0e3, order = Order2(), xatol = 0.01,
                     maxfnevals = 100, net = true)

Solve the leaf energy balance coupled to photosynthesis and transpiration.

Arguments

• Ags: Photosynthesis and stomatal conductance model
• gb: Boundary layer conductance model
• opt: Optical properties of the leaf
• PAR: Photosynthetically active radiation (umol/m2/s)
• NIR: Near-infrared radiation (W/m2)
• ws: Wind speed (m/s)
• RH: Relative humidity
• Tair: Air temperature (K)
• Ca: Atmospheric CO2 concentration (μmol/mol)
• P: Air pressure (Pa)
• O2: Atmospheric O2 concentration (μmol/mol)
• order: Order of the root solving algorithm that finds leaf temperature (see Roots.jl package for more information).
• xatol: Absolute tolerance of the root solving algorithm (see Roots.jl package for more information),
• maxfnevals: Maximum number of function evaluations of the root solving algorithm (see Roots.jl package for more information).
• net: Whether to return net or gross CO2 assimilation.

Details

Inputs maybe be either Real or Quantity types from Unitful.jl (i.e., with physical units). If Quantity types are used, the output will be a Quantity type.

Returns

A named tuple with net CO2 assimilation (An, μmol/m^2/s), gross CO2 assimilation (Ag, μmol/m^2/s), transpiration (Tr, mol/m^2/s) and leaf temperature (Tleaf, K).

transpiration(;gsw = 0.1, gbw = 1.0, Tleaf = 300.0, Tair = 298.0, P = 101e3,
               RH = 0.75)

Compute transpiration rate (mol/m^2/s) from conductance to water vapor and environmental variables.

Arguments

• gsw: Stomatal conductance to water vapor (mol/m^2/s)
• gbw: Boundary layer conductance to water vapor (mol/m^2/s)
• Tleaf: Leaf temperature (K)
• Tair: Air temperature (K)
• P: Air pressure (Pa)
• RH: Relative humidity

Organ(f = [0.53, 0.25, 0.05, 0.05, 0.06, 0.06],
      te = 100.0, tm = 50.0, tb = 10.0, wmax = 0.1)

Data structure to store all parameters for the growth model of a plant organ.

Arguments

• f: fraction of dry matter allocated to different carbon pools of newly formed material, [carbohydrates, proteins, lipids, lignin, organic acids, minerals]
• te: time at which growth rate extinguishes, [DD]
• tm: time at which growth rate is maximum, [DD]
• tb: base temperature, [°C]
• wmax: maximum weight, [g]

compute_ASRQ(f::Vector{Float64})

Compute assimilate requirement, CO2 production factor and carbon content according to Penning de Vries et al. 1982. These values can be used to compute growth respiration. Different tissues (species/organ) have different composition. Growth costs are computed given the fraction of dry matter allocated to different carbon pools according to specific composition of the tissue: f = [carbohydrates, proteins, lipids, lignin, organic acids, minerals]

The assimilate requirement (ASRQ, g) is the amount of assimilates required to produce 1 g of dry matter.
The CO2 production factor (CO2PFF, g) is the amount of CO2 produced per g of dry matter.
The carbon fraction (CF, %) is the fraction of dry matter that is carbon.

Citations: Penning de Vries, F. W. T., & van Laar, H. H. (1982). Simulation of growth processes and the model BACROS. In F. W. T. Penning de Vries, & H. H. van Laar (Eds.), Simulation of plant growth and crop production (pp. 114-135). (Simulation monographs). Pudoc. https://edepot.wur.nl/172216

compute_potential_GR(par::OrganType)

Compute potential growth rate of the leaf according to thermal time (Yin et al 2003) The potential growth rate is computed as a function of thermal time (tt, DD), and the parameters of the growth model: - time at which growth rate extinguishes (te, DD), - time at which growth rate is maximum (tm, DD) - base thermal time at which growth starts (tb, DD) - maximum weight (wmax, g)

Citations: Yin, Xinyou & Goudriaan, Jan & Lantinga, Egbert & Vos, Jan & Spiertz, Huub. (2003). A Flexible Sigmoid Function of Determinate Growth. Annals of botany. 91. 361-71. 10.1093/aob/mcg029.