Applications
Fitting Model parameters
Fitting functional parameters Procedure
Functional parameter fitting workflow
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Reminder
- hopefully the number of organs (distribution of) per cohort
- organ default properties (for instance their volume set as a constant value in the structural simulation
- The appearance date. For instance, flowering may appear at a given growth stage only)
- The expansion duration: the number of cycles the organ takes to reach its mature stage and end of development
- The functioning duration (specifically for leaves). This duration is greater than the expansion time.
- Allometry parameters are deduced from the collected organ dimensions. (This means collecting organic series, as defined earlier).
- The first level estimated is usually the Sp and r values, with the Beer Law extinction factor k set to 1.
- Organ sinks are then estimated as a single ratio
- Beta laws are then defined for biomass partitioning (the a parameter first, then the b parameter)
- Lastly, the secondary growth is estimated (if required)
As shown earlier, the parameter identification process requires several steps, starting with the structural parameters.
Functional parameter fitting is performed with measured data corresponding to precise development observation stages.
The collected data are usually classic agronomic traits as defined previously. They are usually collected on a plant population, at the various observation stages. Follow-up is often impossible since some traits are often easier to collect by destructive collection (such as organ weights and dimensions).
The hidden functional parameter procedure classically follows this workflow:
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1. The plant structure is simulated at the various observation stages.
This simulation (stochastic in general) helps to define a target file showing,
for each observation date (i.e. for each observation growth cycle):
2. Functional parameters related to organ phenology and allometry are analysed and modelled.
These parameters are mainly related to the definition of the functioning durations of the growth cycle.
3. Building the target file.
This file retrieves output from simulations at different growth cycles, corresponding to different observation stages.
The default agronomic traits generated by the simulation are corrected, and replaced by the data measured at the various observation stages.
4. Fitting the functional hidden parameters.
The parameters to be identified are then fitted, usually in several steps, starting from the production equation.
The fitting iterates on the target file, updating the hidden parameter values until the distance between the simulated traits and the measured ones stays constant (and significantly weak).
The underlying fitting process is, in our implementations, the generalized least square method or renewal annealing.
Once a parameter is fitted, the others are added, according to the sequence given thereby