Energy balance

The energy balance is the process of computing the balance between influx and outflux of energy in all its form: latent and sensible heat, thermal radiation...

Models overview

Only one model is available to-date:

• Monteith: an implementation of the Monteith et al. (2013) model

You can choose which model to use by passing a model list with an energy balance model set to one of the structs above:

using PlantBiophysics, PlantSimEngine

meteo = Atmosphere(T = 20.0, Wind = 1.0, P = 101.3, Rh = 0.65)

leaf = ModelList(
    Monteith(),
    Fvcb(),
    Medlyn(0.03, 12.0),
    status = (Ra_SW_f = 13.747, sky_fraction = 1.0, aPPFD = 1500.0, d = 0.03)
)

run!(leaf,meteo)
leaf[:Rn]

1-element Vector{Float64}:
 21.40940340906749

Monteith

Leaf energy balance according to Monteith and Unsworth (2013), and corrigendum from Schymanski et al. (2017). The computation is close to the one from the MAESPA model (Duursma et al., 2012, Vezy et al., 2018) here. The leaf temperature is computed iteratively to close the energy balance using the mass flux (~ Rn - λE).

Parameters

The Monteith model has the following set of parameters:

• aₛₕ = 2: number of faces of the object that exchange sensible heat fluxes
• aₛᵥ = 1: number of faces of the object that exchange latent heat fluxes (hypostomatous => 1)
• ε = 0.955: emissivity of the object
• maxiter = 10: maximal number of iterations allowed to close the energy balance
• ΔT = 0.01 (°C): maximum difference in object temperature between two iterations to consider convergence

Input variables

The Monteith model needs three input variables:

inputs(Monteith())

(:Ra_SW_f, :sky_fraction, :d)

Ra_SW_f (W m-2) is the net shortwave radiation (PAR + NIR), most often computed from a light interception model. sky_fraction (0-2) is the fraction of sky the object is viewing compared to everything else. It is given for the 360° viewing angle, i.e. for both faces. d (m) is the characteristic dimension, e.g. the leaf width (see eq. 10.9 from Monteith and Unsworth, 2013).

Output variables

The Monteith model computes a lot of variables, mainly because it is also coupled to a photosynthesis model, itself potentially coupled to a stomatal conductance model:

outputs(Monteith())

(:Tₗ, :Rn, :Ra_LW_f, :H, :λE, :Cₛ, :Cᵢ, :A, :Gₛ, :Gbₕ, :Dₗ, :Gbc, :iter)

Tₗ (°C) is the component temperature, Rn ($W \cdot m^{-2}$) is the net radiation (PAR + NIR + TIR), Ra_LW_f ($W \cdot m^{-2}$) is the longwave radiation (TIR), H ($W \cdot m^{-2}$) is the sensible heat flux, λE ($W \cdot m^{-2}$) is the latent heat flux, Cₛ (ppm) is the air CO₂ concentration at the leaf surface, Cᵢ (ppm) is the intercellular CO₂ concentration, A ($μmol \cdot m^{-2} \cdot s^{-1}$) is the CO₂ assimilation rate, Gₛ ($mol_{CO_2} \cdot m^{-2} \cdot s^{-1}$) the stomatal conductance, Gbₕ ($m \cdot s^{-1}$) the boundary layer conductance to heat, Dₗ (kPa) the difference between the vapour pressure at the leaf surface and the saturated air vapour pressure, Gbc ($mol_{CO_2} \cdot m^{-2} \cdot s^{-1}$) the boundary layer conductance to CO₂, and iter the number of iterations to reach convergence.

Example

Here is an example usage:

meteo = Atmosphere(T = 22.0, Wind = 0.8333, P = 101.325, Rh = 0.4490995)

leaf = ModelList(
    Monteith(),
    Fvcb(),
    Medlyn(0.03, 12.0),
    status = (Ra_SW_f = 13.747, sky_fraction = 1.0, aPPFD = 1500.0, d = 0.03)
)

leaf

PlantSimEngine.DependencyGraph{Dict{Symbol, PlantSimEngine.SoftDependencyNode}}(Dict{Symbol, PlantSimEngine.SoftDependencyNode}(:energy_balance => Monteith{Float64, Int64}
), Dict{Symbol, DataType}())TimeStepTable{Status{(:Ra_SW_f, :sky_fracti...}(1 x 17):
╭─────┬─────────┬──────────────┬─────────┬─────────┬─────────┬─────────┬────────
│ Row │ Ra_SW_f │ sky_fraction │       d │      Tₗ │      Rn │ Ra_LW_f │       ⋯
│     │ Float64 │      Float64 │ Float64 │ Float64 │ Float64 │ Float64 │ Float ⋯
├─────┼─────────┼──────────────┼─────────┼─────────┼─────────┼─────────┼────────
│   1 │  13.747 │          1.0 │    0.03 │    -Inf │    -Inf │    -Inf │    -I ⋯
╰─────┴─────────┴──────────────┴─────────┴─────────┴─────────┴─────────┴────────
                                                              11 columns omitted

The Monteith model implementation can be tested on the data provided by Schymanski et al. (2017). Here is a figure comparing our implementation and the data:

Figure 1. Energy flux measured on an artificial leaf (points) or simulated from its digital twin (lines). Data from Schymanski et al. (2017) figure 6a. The code to reproduce this figure is available in this file.

References

Duursma, R. A., et B. E. Medlyn. 2012. « MAESPA: a model to study interactions between water limitation, environmental drivers and vegetation function at tree and stand levels, with an example application to [CO2] × drought interactions ». Geoscientific Model Development 5 (4): 919‑40. https://doi.org/10.5194/gmd-5-919-2012.

Monteith, John L., et Mike H. Unsworth. 2013. « Chapter 13 - Steady-State Heat Balance: (i) Water Surfaces, Soil, and Vegetation ». In Principles of Environmental Physics (Fourth Edition), edited by John L. Monteith et Mike H. Unsworth, 217‑47. Boston: Academic Press.

Schymanski, Stanislaus J., et Dani Or. 2017. « Leaf-Scale Experiments Reveal an Important Omission in the Penman–Monteith Equation ». Hydrology and Earth System Sciences 21 (2): 685‑706. https://doi.org/10.5194/hess-21-685-2017.

Vezy, Rémi, Mathias Christina, Olivier Roupsard, Yann Nouvellon, Remko Duursma, Belinda Medlyn, Maxime Soma, et al. 2018. « Measuring and modelling energy partitioning in canopies of varying complexity using MAESPA model ». Agricultural and Forest Meteorology 253‑254 (printemps): 203‑17. https://doi.org/10.1016/j.agrformet.2018.02.005.