-> About this Resource
Scope *______
Map *____

-> Preliminary Courses
Contents & Objectives *__________________
Map *____
-> Botany
Contents & Objectives *__________________
Map *____
-> Axis Typology Patterns
Typology basis *___________
Pictograms *_________
Sexuality & development *___________________
Growth *______
Branching rhythms *______________
Branching delays *_____________
Branching positional *________________
Branching arrangement *__________________
Axis orientation *_____________
Architectural models *________________
-> Architectural Unit
About Arc. Models *______________
Models limitations *______________
Architectural Units *______________
Reiteration *_________
Sequence of development *___________________
Morphogenetic gradients *___________________
Physiological age *_____________
-> An Example
Wild Cherry (young) *_______________
Wild Cherry (adult) *______________
Wild Cherry (mature) *________________
Quiz *____
Case study Quiz *_____________
Supplementary resources *____________________

-> Eco-Physiology
Contents & Objectives *__________________
Map *____
-> Growth Factors
Factors affecting Growth *___________________
Endogenous Processes *_________________
Environmental Factors *_________________
Thermal Time *___________
-> Light interaction
P.A.R. *_____
Light absorption *_____________
Photosynthesis *___________
Respiration *_________
Maintenance respiration *__________________
L.U.E. Model *__________
Density effect *___________
Density effect on crop *__________________
-> Biomass
Biomass Pool *__________
Biomass Partitioning *_______________
Crop models *__________
A Crop model example *__________________
Quiz *____
Supplementary resources *___________________

-> Applied Mathematics
Contents & Objectives *__________________
Map *____
-> Probabilities
Section contents *____________
Discrete Random Variable *___________________
Expected value, Variance *___________________
Properties *________
-> Useful Laws
Bernoulli Trials *___________
Binomial Law *__________
Geometric Law *____________
Negative Binomial Law *_________________
-> Dynamic systems
Section contents *_____________
Useful functions *____________
Beta density *__________
Exercises *________
Negative Exponential *________________
Systems functions *______________
Discrete dynamic systems *___________________
Parameter Identification *__________________
Parameter estimation *________________
Supplementary Resources *____________________

-> GreenLab courses
GreenLab presentation *__________________
-> Overview
Presentation & Objectives *____________________
Map *____
Growth and components *___________________
Plant architecture *_______________
Biomass production *________________
Modelling - FSPM *______________
GreenLab principles *________________
Applications *__________
Supplementary resources *_____________________
-> Principles
Presentation & Objectives *____________________
Map *____
-> About modelling
Scientific disciplines *________________
Organs: tree components *___________________
Factors affecting growth *___________________
Model-simulation workflow *____________________
GreenLab inherits from *__________________
GreenLab positioning *_________________
The growth cycle *______________
Inside the growth cycle *___________________
Implementations *______________
Supplementary resources *____________________
-> Development
Presentation & Objectives *____________________
Map *____
Modelling Scheme *______________
Tree traversal modes *________________
-> Stochastic modelling
Principles *_______
-> Development
Growth Rhythm *____________
Damped growth *____________
Viability *______
Rhythmic axis *___________
Branching *________
Stochastic automaton *_________________
-> Organogenesis equations
Principles *_______
Organ cohorts *___________
Organ numbering *_____________
Substructure factorization *____________________
Stochastic case *____________
-> Structure construction
Construction modes *_______________
Construction basis *______________
Axis of development *________________
Stochastic reconstruction *___________________
Implicit construction *________________
Explicit construction *________________
3D construction *____________
Supplementary resources *____________________
-> Production-Expansion
Presentation & Objectives *____________________
Map *____
-> EcoPhysiology reminders
Relevant concepts *______________
Temperature *__________
Light interception *______________
Photosynthesis *___________
Biomass common pool *_________________
Density *______
-> Principals
Growth cycle *__________
Refining PbMs *___________
Organ cohorts *___________
GreenLab vs PbM & FSPM *___________________
-> GreenLab's equations
Summary *_______
Production equation *_______________
Plant demand *__________
Organ dimensions *______________
A dynamic system view *__________________
Equation terms *____________
Full Model *________
Model behaviour *______________
Supplementary resources *____________________
-> Applications
Presentation & Objectives *____________________
Map *____
-> Measurements
Agronomic traits *_____________
Mesurable/hidden param. *___________________
Fitting procedure *______________
-> Fitting structure
Principles *_______
-> Development
Simple development *_______________
Damped growth *____________
Rhythmic growth *_____________
Rhythmic growth samples *___________________
Mortality *_______
Branching *________
-> Crown analysis
Analysis principles *______________
Equations *________
Example / Exercise *_______________
-> Case study
Plant Architecture *______________
Development simulation *__________________
Introducing Biomass *_______________
Biomass partitioning *_______________
Equilibrium state *_____________
Supplementary resources *____________________

-> Tools (software)
Presentation & Objectives *_____________________
Map *____
Fitting, Stats *___________
Simulation *_________
Online tools *__________

GreenLab Course


Modelling principles.

GreenLab specificity

From individual plant to crop level

FSPM approaches show heavy reliance production computation, since they use the plant structure as a biomass storing and transportation pathway.
The main specificity of the GreenLab models lies in the fact that structure is only used as an organ compartment classifier, and not as a transportation network.
    Indeed, an interesting way of overcoming this difficulty is to use the crop production model approach, defined at m2 level to estimate the photosynthesis.
    The structural approach precisely defines organ compartments sharing the same fate, making biomass allocation easier, but does not require exhaustive definition, be it topological (graph), or geometrical.

    This positioning, between individual plant and crop models is specific to the GreenLab model.
    Taking into account the simplifications established by agronomists from experimental studies, i.e. the common biomass pool, the use of net photosynthesis and, biomass computation from Beer's Law, this approach does away with use of the topological structure in production computation.
    The classic crop model equation (Eq. 1) is adapted to the plant scale as follows:

    Q = LUE . PAR . Sp . (1 - e - k Sf/Sp) (Eq. 2)

      Q is the increase in biomass of the plant cycle
      Sf is the leaf area of the plant
      Sp is a parameter which has the dimension of a surface
      Sp allows equation (2) to operate even when the canopy is not very dens.
      In an high density d stand, the canopy is uniform and Sp verifies:

          Sp = 1 / d (Eq. 3)

      This relation has been verified experimentally on crops (see below).
    Equations (Eq. 1) and (Eq. 2) are thus equivalent, but the formula (Eq. 2) allows a switch from the individual plant to the plant stand.


In the GreenLab model, organogenesis is modelled by meristem production equations, according to their physiological age, and deduced from observations.
Growth, mortality and, branching are described by probability laws.

For each cycle of growth, new organ population (cohors) occurrences are simulated.

Each organ takes up biomass from the common biomass pool according to the srentgh of its sink function; (this function varies during organ maturation).
Since all organs of the same cohort and of the same type are in the same state, efficient factorization can be applied. For instance, plant demand D is simply the sum of the demand of all the cohorts.

The biomass increment Δ q of a given organ depends on its sink φ, the available biomass in the common pool Q calculated by equation (Eq. 2) and plant demand D according to the formula:

    Δ q = φ . Q / D     (Eq. 4)

Organ weight is then simply defined by summing up the biomass increments (Eq. 4).
Its dimensions (length, diameter, area) are assessed by applying geometric (allometric) rules.
The weight of the organ compartments is obtained by summing up all cohorts of the same organ.
In particular, the total functioning leaf area of the plant Sf is deduced, using the equation (Eq. 2).

Plant Growth Modelling, Simulation with GreenLab model
Simulation of plant growth and plasticity with the GreenLab model (© Digiplante and LIAMA).
    These virtual plants are obtained from field data thanks to the software that takes particular account of how organs (leaves, roots, fruits, etc.) change, which can be very different depending on environmental conditions.
    (a) simulating morphological gradients.
    The base effect due to low biomass availability at early stages is shown on the right. The left-hand tree is only a structural simulation
    (b) structural plasticity simulation on the beech tree.
    Left and Right are respectively simulated with the same parameter, except for the Sp (Eq. 2) area value (shown as a grey disk) standing for reversed density.
    Other calibrated simulations are for: (c) arabsisdosis, (d) beetroot, (e) sunflower,
    (f) maize, (g) cotton, (h) rice, (i) tomato,
    (j) chrysanthenum, (k) sweet pepper, (l) Mongolian pine

The GreenLab model is therefore a dynamic model of plant growth which operates by feedback between growth and development.
The calculation of plant production does not need to rely on the details of the architecture, but only on the equations of production and source-sink relations.
Such a model offers efficient computing costs and enables model calibration, optimisation and control methods to be implemented.