Leaf stomatal Medlyn

source

leaf_stomatal_medlyn


def leaf_stomatal_medlyn(
    physcon:PhysCon, # Physical constants.
    atmos:Atmos, # Atmospheric forcing variables.
    leaf:Leaf, # Leaf parameters including:
- g0 : float
    Minimum stomatal conductance (mol H2O/m2/s).
- g1_medlyn : float
    Medlyn slope parameter (kPa^0.5).
- minl_wp : float
    Minimum leaf water potential (MPa) — the cavitation threshold.
    flux:Flux, # Flux variables. Must have tleaf, qa, psi_leaf, lsc, etc. set.
)->Flux: # Updated flux object with converged gs, An, Tleaf, psi_leaf, etc.

Compute stomatal conductance using the Medlyn et al. (2011) model, coupled with leaf energy balance, photosynthesis, and plant hydraulics.

The Medlyn equation (Medlyn et al. 2011, Eq. 11) is:

gs = g0 + 1.6 * (1 + g1 / sqrt(D)) * An / cs

where:

  • gs = stomatal conductance to water vapor (mol H2O/m2/s)
  • g0 = minimum stomatal conductance (mol H2O/m2/s)
  • g1 = slope parameter (kPa^0.5)
  • D = vapor pressure deficit at the leaf surface (kPa)
  • An = net photosynthesis (umol CO2/m2/s)
  • cs = CO2 concentration at the leaf surface (umol/mol)

The factor 1.6 converts from CO2 conductance to H2O conductance (ratio of molecular diffusivities: D_H2O / D_CO2 = 1.6).

The coupling problem: gs depends on An (more photosynthesis → more stomatal opening) An depends on gs (wider stomata → more CO2 → more photosynthesis) Tleaf depends on gs (wider stomata → more transpiration → cooler leaf) An depends on Tleaf (enzyme kinetics change with temperature)

Solution approach — fixed-point iteration:

1. Start with an initial guess for gs
2. Compute Tleaf from energy balance (leaf_temperature)
3. Compute An, cs, VPD from photosynthesis (leaf_photosynthesis)
4. Update gs from Medlyn equation
5. Repeat until gs converges

After convergence, a hydraulic safety check is applied: If the resulting leaf water potential drops below the minimum safe value (leaf.minl_wp), gs is iteratively reduced until hydraulic safety is restored. This prevents xylem cavitation.

The Medlyn equation (Medlyn et al. 2011, Eq. 11):

gs = g0 + 1.6 * (1 + g1 / sqrt(D)) * An / cs

where:

  • g0 is the baseline conductance (always present)

  • 1.6 represents the H2O/CO2 diffusivity ratio

  • (1 + g1/sqrt(D)) represents the VPD sensitivity factor:

    • i.e. When D is small (humid): g1/sqrt(D) is large → gs is high
    • i.e. When D is large (dry): g1/sqrt(D) is small → gs is low
    • g1 controls the magnitude of this VPD response

  • (An / cs) represents the photosynthetic demand factor: - High An and low cs → stomata open wide for CO2 - Low An (shade) → little need to open stomata

  • Example with g0 = 0.01, g1 = 4.45, D = 1.5 kPa, An = 10, cs = 350:

    gs = 0.01 + 1.6 * (1 + 4.45/sqrt(1.5)) * 10/350 gs = 0.01 + 1.6 * (1 + 3.633) * 0.02857 gs = 0.01 + 1.6 * 4.633 * 0.02857 gs = 0.01 + 0.212 gs = 0.222 mol H2O/m2/s

Example leaf_stomatal_medlyn()