List of the models :: ARCHIMED user documentation

List of the models

Here is a list of all models available for each process.

Interception

There are three different models available in ARCHIMED-φ to compute their light interception and scattering: Translucent, ignore and VirtualSensor.

Translucent

This model has two set of parameters :

transparency: between 0 and 1. 0 is not transparent (opaque), and 1 fully transparent. If it is set to e.g. 0.3, 70% of the incoming light is intercepted by the component (interception = radiation * (1-transparency)), and 30% is directly transmitted (not being part of the interception). Not to be confused with the scattering of the light (transmitted + scattered light) after the first order interception,
optical_properties. Used to parametrize the scattering factors for each waveband to compute how much light is absorbed, reflected and transmitted by the component (i.e. a range of wavelength).

Decomposition of light paths after a hit.

Usually the radiation remaining for each component is computed using coefficients, such as the sum of all coefficients is equal to 1:

\(\alpha + \rho + \tau = 1\)

with \(\alpha\) the coefficient of absorptance, \(\rho\) the reflectance and \(\tau\) the transmittance.

Then, the absorbed (\(R_a\)), reflected (\(R_r\)) and transmitted (\(R_t\)) light are computed using the the intercepted radiation (\(R_i\)) as follows:

\(R_a = \alpha \cdot R_i\)
\(R_r = \rho \cdot R_i\)
\(R_t = \tau \cdot R_i\)

But in ARCHIMED-φ we consider the reflectance coefficient equal to the transmittance coefficient (\(\rho = \tau\)), so we use only one value to parameterize the model: the scattering factor (\(\sigma\)). It is the sum of \(\rho\) and \(\tau\), such as \(\sigma = \rho + \tau\). Then we can compute \(R_a\), \(R_r\) and \(R_t\) as:

\(R_a = R_i \cdot (1 - \rho - \tau)\)

\(R_r = R_i \cdot \frac{(1-\sigma)}{2}\)

\(R_t = R_i \cdot \frac{(1-\sigma)}{2}\)

In ARCHIMED-φ, the components are considered lambertian surfaces, i.e. they scatter the light uniformly in all directions.

The scattering factors are given for each waveband to be simulated by the model. This is typically for the photosynthetically active radiation (PAR, typically 400 to 700 nm) and the near-infrared (NIR, typically 700 nm to 3000 nm) but the user can also define custom wavebands, e.g. for the red band: red: 0.20.

The user must provide the radiation incoming from the atmosphere for the custom band in the meteorology file (e.g. Ri_red_f) if the computation for its interception and scattering is required. See this section for more information.

Here is an example parameterization using this model:

Interception:
    use: Translucent_1
    Translucent_1:
      model: Translucent
      transparency: 0
      optical_properties:
          PAR: 0.15
          NIR: 0.9

The PAR and NIR bands are mandatory for the computation of the energy balance and the photosynthesis using the Farquhar model (see this section for more details).

ignore

This model totally ignore the object, so it is not used during the computation of light interception, as if it never existed. No parameter.

Here is an example parameterization using this model:

Interception:
    model: ignore

VirtualSensor

This model is used for special components called virtual sensors. They are used to know the incoming radiation for a given point in space. See this chapter for more details. No parameter.

Here is an example parameterization using this model:

Interception:
    model: VirtualSensor

Example parameterization

Here is an example parameterization of a component with all three models, and using the first one:

Group: test
Type:
  example_component:
      Interception:
          use: Translucent_model
          Translucent_model:
            model: Translucent
            transparency: 0
            optical_properties:
                PAR: 0.15
                NIR: 0.9
          ignore_model:
            model: ignore
          sensor:
            model: VirtualSensor

The name of a parameterization group is free. For example we can replace Translucent_model by anything, such as foo.

Interception:
    use: foo
    foo:
      model: Translucent
      transparency: 0
      optical_properties:
          PAR: 0.15
          NIR: 0.9

Photosynthesis

There are two models to compute the photosynthesis in ARCHIMED-φ: FarquharEnBalance and NRH. Here is an example parameterization using those models:

Photosynthesis:
    use: Farquharcoffee_1
    Farquharcoffee_1:
        model: FarquharEnBalance
        tempCRef: 25
        jMaxRef: 250
        vcMaxRef: 200
        rdRef: 0.6
        theta: 0.853
        LWratio: 1.5
        nFaceStomata: 1
        leafEmissivity : 0.98
        delta_T_init: -2
        epsilon: 0.1 
        iter_T_max: 10
        iter_A_max: 50
    NRH_coffee:
        model: NRH
        theta: 0.6711
        pmax: 32.91
        alpha: 0.06906
        rd: 1.612

FarquharEnBalance

This model is the most complete. It couples the photosynthesis model of Farquhar, von Caemmerer, and Berry (1980), a model for stomatal conductance (see next paragraph), and a detailed energy balance model to iteratively solve the stomatal conductance and the leaf temperature.

This model has 12 parameters:

tempCRef (°C): reference temperature of measurements
jMaxRef (\(\mu mol_{CO_2} \cdot m^{-2} \cdot s^{-1}\)): value of maximum rate of electron transport (Jmax) at the reference temperature
vcMaxRef (\(\mu mol_{electron} \cdot m^{-2} \cdot s^{-1}\)): Maximum carboxylation rate at the reference temperature
rdRef (\(\mu mol_{CO_2} \cdot m^{-2} \cdot s^{-1}\)): mitochondrial respiration in the light at reference temperature (other than that associated with the PCO cycle).
theta: the curvature of the light-response curve of electron transport.
LWratio: average length / width ratio for the component. Used to compute the boundary layer conductance.
nFaceStomata: number of faces of the component with stomata (1: hypostomatal, 2: amphistomatal leaf).
leafEmissivity (0-1): Ratio between the leaf radiant emittance (also called radiant exitance) compared to the one of a black body.
delta_T_init (°C): initialization of the leaf temperature in relation to Tair (Tleaf = Tair - delta_T_init). This initialization is done every time the function is called (at every iteration of the assimilation computation), then the leaf temperature is computed by iteration, and its last value is used on the computation of the assimilation, but is reset to delta_T_init before re-doing the calculation of Tleaf. This is done to avoid heavy divergence of both optimization algorithms.
epsilon (°C): criteria for convergence of the leaf temperature computation (difference between previous Tleaf and current Tleaf)
iter_T_max (-): maximum number of iterations allowed for leaf temperature computation
iter_A_max (-): maximum number of iterations allowed for assimilation and conductance computation

NRH

The NRH (Non-Rectangular Hyperbola) model is used to compute the photosynthesis much more simply (but less reliably). It has four parameters:

pmax (\(\mu mol_{CO_2} \cdot m^{-2} \cdot s^{-1}\)): maximum (i.e light-saturated) net photosynthetic rate
theta (-): convexity of the PLR (photosynthetic Light Response) curve
alpha (\(\mu mol_{CO_2} \cdot \mu mol_{photon}^{-1}\)): quantum yield of assimilation (initial slope of the PLR)
rd (\(\mu mol_{CO_2} \cdot m^{-2} \cdot s^{-1}\)): dark respiration rate.

Stomatal Conductance

The stomatal conductance is crucial to estimate the water and carbon fluxes from the leaves to the environment. There are two models of stomatal conductance yet: Medlyn and 'Yin-Struik'. Here is an example parameterization of the models:

StomatalConductance:
  use: Medlyn_generic
  Medlyn_generic:
      model: Medlyn
      g0: -0.03
      g1: 12
  Medlyn_caturra:
      model: Medlyn
      g0: -0.03
      g1: 12.5
  'Yin-Struik_caturra':
      model: 'Yin-Struik'
      g0: 0.02089956
      a1: 0.9
      b1: 0.15

Please note the “’” around the name of the Yin-Struik model. It is used to escape the “-” character inside the name, and is mandatory.

Medlyn

The model of Medlyn et al. (2011) computes the leaf stomatal conductance using the vapor pressure deficit (VPD) such as:

\(G_s=G_0+\left(1+\frac{G_1}{\sqrt{VPD}}\right)\cdot\frac{A}{C_a-\Gamma}\)

where \(G_s\) is the stomatal conductance in \(mol_{CO_2} \cdot m^{-2} \cdot s^{-1}\), VPD is the vapor pressure deficit in kPa, A is the net assimilation rate in \(\mu mol_{CO_2} \cdot m^{-2} \cdot s^{-1}\), \(C_a\) the atmospheric \(CO_2\) concentration in ppm, and \(\Gamma\) the \(CO_2\) compensation point of assimilation in the presence of dark respiration (so in the absence of day respiration (Rd)). The model has two parameters:

g0 (\(mol_{CO_2} \cdot m^{-2} \cdot s^{-1}\)): residual conductance
g1 (-): slope of the conductance

‘Yin-Struik’

The model from Yin and Struik (2017) (equ. 11) also relates the stomatal conductance to the VPD using the following equation:

\(G_s=G_0+\frac{A+R_d}{C_s-C_s^\ast}f\left(VPD\right)\)

with \(C_s\) the \(CO_2\) concentration at the leaf surface, and \(C^{\star}_s\) is the equivalent of \(\Gamma\) based on \(C_s\) (see full article, eq. 11).

In ARCHIMED-φ, \(C^{\star}_s\) is given by \(\Gamma^\star_{ref}\) corrected by the temperature, and \(C_i\) is used instead of \(C_s\).

The \(f\left(VPD\right)\) function is computed as:

\(f_{VPD}=\frac{1}{\frac{1}{\max\left(a_1-b_1\cdot VPD,\ 0.01\right)-1}}\)

The model has three parameters:

g0 (\(mol_{CO_2} \cdot m^{-2} \cdot s^{-1}\)): the residual conductance
a1 (-): Ci:Ca ratio in water vapour-saturated air
b1 (-): slope of the decrease of this ratio with increasing VPD.

References

Farquhar, G. D., S. von Caemmerer, and J. A. Berry. 1980. “A Biochemical Model of Photosynthetic Co2 Assimilation in Leaves of C3 Species.” Planta 149 (1): 78–90.

Medlyn, Belinda E., Remko A. Duursma, Derek Eamus, David S. Ellsworth, I. Colin Prentice, Craig V. M. Barton, Kristine Y. Crous, Paolo De Angelis, Michael Freeman, and Lisa Wingate. 2011. “Reconciling the Optimal and Empirical Approaches to Modelling Stomatal Conductance.” Global Change Biology 17 (6): 2134–44. https://doi.org/10.1111/j.1365-2486.2010.02375.x.

Yin, X., and P. C. Struik. 2017. “Can Increased Leaf Photosynthesis Be Converted into Higher Crop Mass Production? A Simulation Study for Rice Using the Crop Model GECROS.” J Exp Bot 68 (9): 2345–60. https://doi.org/10.1093/jxb/erx085.