GreenLab Course
Production-Expansion
Organ dimensions
Organ geometry
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Organ weight
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We have seen that the weight is the total biomass allocated to a given organ o:
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Qo,p(n) = Σj=n-l;n qo,p(j)
where
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n-l stands for the first appearance cycle of the current organ.
l stands for the expansion duration (in number of cycles) of the current organ.
Using (equation 2) describing organ biomass allocation we can then write:
Qo,p(n) = Σj=n-l;n qo,p(j) = Σj=n-l;n Q(j-1) . φo,p(j-n+l) / D(j)
where
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n is the current growing cycle
o stands for the organ type
p stands for the physiological age
n-l stands for the first appearance cycle of the current organ.
j-n+l (= j-(n-l)) stands for the organ age (expressed in cycles since the beginning of its expansion)
D(j) is the total plant demand at cycle j (the sum of all sinks of organs in expansion)
Q(n-1) is the available biomass in the common pool. By definition Q(0) defines the seed biomass.
In this expression, production is expressed according to the cycle number, as well as the sink function.
An alternate writing is to express these quantities relatively to organ age:
Qo,p(n) = Σj = 1 ; l φo,p(j) . Q(j + n - l - 1) / D(j + n - l) (equation 4)
Organ sizes
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In the GreenLab model, the relation relating sizes to fresh biomass is defined from allometries
(see here).
A remider of the allometry rules defining organ dimensions from their volume (i.e. from their biomass) is given here:
Organ allometry relations in the GreenLab model
Blade Area
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With a constant leaf thickness e, the total functioning blade area S(n) at cycle n
can then be expressed as follows:
| S(n) = | 1 | ( | Σi = 1 ; Tb ( Σj = 1 ; i φb(j) | Q ( n - i + j - 1) | ) | ) | (equation 5) |
| e | D ( n - i + j ) |
where:
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φb(j) stands for the leaf blade sink function at age j
i,j stand for the blade age with Tb >= i >= j
Tb is the number of cycles before the leaf becomes senescent (i.e. the number of functional cycles)
e is the blade thickness (the SLW)