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Stomatal conductance

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Overview

Stomata regulate gas exchange between the leaf and atmosphere, directly controlling the trade-off between carbon uptake during photosynthesis and water loss through transpiration. Similar to photosynthesis, stomatal conductance, $g_w$, depends on multiple environmental factors, including light availability, CO₂ concentration, and temperature. 

subtypes(Terrarium.AbstractStomatalConductance)
1-element Vector{Any}:
 MedlynStomatalConductance

The Medlyn stomatal conductance model

Terrarium.MedlynStomatalConductance — Type
struct MedlynStomatalConductance{NF} <: Terrarium.AbstractStomatalConductance{NF}

Stomatal conductance following the optimal stomatal conductance model of [24], in the corrected form of [25], which supplies the water/CO₂ diffusivity ratio. The canopy scaling of the minimum conductance and the PFT-specific parameter values follow [21], whose g₁ are in turn those of [26]. Note that PALADYN keeps the diffusivity ratio in λc (its Eq. 71) rather than in the conductance (Eq. 68); this implementation uses the Medlyn convention for both.

Authors: Maha Badri and Matteo Willeit

Properties:

  • g₁::Any: Parameter in optimal stomatal conductance formulation representing the quasi-linear relationship between conductance and net assimilation, [26]. PFT specific.

  • g_min::Any: Minimum stomatal conductance parameter

  • diffusivity_ratio_water_co2::Any = 1.6: Diffusivity ratio of water to CO₂

References

  • [26] Lin et al., Nature Climate Change (2015)
  • [24] Medlyn et al., Global Change Biology (2011)
  • [25] Medlyn et al., Global Change Biology (2012)
  • [21] Willeit & Ganopolski, Geoscientific Model Development (2016)
source
variables(MedlynStomatalConductance(Float32))
Variables
├─ Prognostic: 
├─ Auxiliary: 
├── canopy_water_conductance [m s^-1] on XY{Center, Center, Nothing} of the canopy domain
├─ Inputs: 
├── leaf_area_index [-] on XY{Center, Center, Nothing} of the canopy domain
├── net_assimilation [kg m^-2 s^-1] on XY{Center, Center, Nothing} of the canopy domain
├── soil_moisture_limiting_factor [-] on XY{Center, Center, Nothing} of the ground domain
├─ Namespaces:

This implementation uses the optimal stomatal conductance model of Medlyn (2011) [24], in the corrected form of the 2012 corrigendum [25] which supplies the factor 1.6, with the canopy scaling of $g_0$ and the PFT-specific parameter values taken from PALADYN [21]. It derives stomatal conductance from water-use efficiency optimization as follows

\[\begin{equation} g_w = g_0 + 1.6 \frac{A_n}{c_a} \left(1 + \frac{g_1}{\sqrt{\text{VPD}}}\right) \end{equation}\]

where $g_0$ is the minimum stomatal conductance, $g_1$ is a PFT-specific slope parameter, $\text{VPD}$ is the vapor pressure deficit, $A_n$ is the net photosynthesis and $c_a$ is the atmospheric CO₂ concentration. The factor 1.6 is the ratio of the diffusivities of water vapor and CO₂ in air.

Following PALADYN, $\text{VPD}$ is expressed in kPa, so $g_1$ carries units of $\sqrt{\text{kPa}}$ and the tabulated values of [26] apply directly. Terrarium computes the vapor pressure deficit in Pa and converts before evaluating $g_1/\sqrt{\text{VPD}}$.

The variables $g_w$ and $A_n$ are also related by the diffusion equation

\[\begin{equation} g_w = g_0 + 1.6 \frac{A_n}{c_a - c_i} \end{equation}\]

where $c_i$ is the intercellular CO2 concentration.

Eliminating $A_n$ between the two gives the ratio of intercellular to atmospheric CO₂ concentration $\lambda_c$, in which the factor 1.6 cancels:

\[\begin{equation} \lambda_c = 1 - \frac{1}{1 + \frac{g_1}{\sqrt{\text{VPD}}}} \end{equation}\]

Process interface

Terrarium.compute_auxiliary! — Method
compute_auxiliary!(
    state,
    grid,
    stomcond::MedlynStomatalConductance,
    traits::PlantTraits,
    constants::PhysicalConstants,
    atmos::Terrarium.AbstractAtmosphere,
    args...
)
source

Methods

Terrarium.compute_stomatal_conductance — Function
compute_stomatal_conductance(
    i, j, grid, fields,
    stomcond::AbstractStomatalConductance,
    photo::AbstractPhotosynthesis,
    atmos::AbstractAtmosphere,
    constants::PhysicalConstants,
    args...
)

Cell-level stomatal conductance computation. Returns stomatal/canopy conductance and internal CO₂ ratio for the specified cell.

source
Terrarium.compute_λc — Function
compute_λc(stomcond, vpd)

Computes the ratio of leaf-internal and air CO2 concentration λc = cᵢ/cₐ, derived from the optimal stomatal conductance model ([24]) in the corrected form of [25].

References

  • [24] Medlyn et al., Global Change Biology (2011)
  • [25] Medlyn et al., Global Change Biology (2012)
source

Kernel functions

Terrarium.compute_stomatal_conductance — Function
compute_stomatal_conductance(
    i, j, grid, fields,
    stomcond::AbstractStomatalConductance,
    photo::AbstractPhotosynthesis,
    atmos::AbstractAtmosphere,
    constants::PhysicalConstants,
    args...
)

Cell-level stomatal conductance computation. Returns stomatal/canopy conductance and internal CO₂ ratio for the specified cell.

source

References

[21]
M. Willeit and A. Ganopolski. PALADYN v1.0, a Comprehensive Land Surface–Vegetation–Carbon Cycle Model of Intermediate Complexity. Geoscientific Model Development 9, 3817–3857 (2016).
[24]
B. E. Medlyn, R. A. Duursma, D. Eamus, D. S. Ellsworth, I. C. Prentice, C. V. Barton, K. Y. Crous, P. De Angelis, M. Freeman and L. Wingate. Reconciling the Optimal and Empirical Approaches to Modelling Stomatal Conductance. Global Change Biology 17, 2134–2144 (2011).
[25]
B. E. Medlyn, R. A. Duursma, D. Eamus, D. S. Ellsworth, I. C. Prentice, C. V. Barton, K. Y. Crous, P. De Angelis, M. Freeman and L. Wingate. Corrigendum: Reconciling the Optimal and Empirical Approaches to Modelling Stomatal Conductance. Global Change Biology 18, 3476 (2012).
[26]
Y.-S. Lin, B. E. Medlyn, R. A. Duursma, I. C. Prentice, H. Wang, S. Baig and others. Optimal stomatal behaviour around the world. Nature Climate Change 5, 459–464 (2015).