GreenLab Course
Production-Expansion
Full model equations
GreenLab Equations
-
In the following equations
-
n is the current cycle
o is the organ type (internode, leaf, fruit, ring, root, etc.)
p is the physiological age
φo,p defines the sink function of organ o at physiological age p
Q(n-1) is the biomass available in the common pool. By definition Q(0) defines the seed biomass.
Structure: The Number of organs at cycle n, appeared at cycle t
-
Ntp(n) = [ ∏p≤q≤P up,q(t+1-n)
( Ntq(n-1) )bp,q(t+1-n) ]
Ntp(n-1)
where:
-
up,q corresponds to the number of phytomers mp,q(t) in growth units of
physiological age p appearing at growth cycle t
bp,q corresponds to the number of axillary sub-structures of physiological age q in growth units of physiological age p that appeared at growth cycle t
These sequences can be deterministic or stochastic.
Plant demand at cycle n
-
D(n) = Σo,p Σt1=n-l;n No,p(t1) . φo,p(t1-n+l)
where:
-
t1 stands for the different appearance cycles of cohort Co,p
t1 stands for the different appearance cycles of cohort Co,p
t1-n+l if therefore the age of the organ (belonging to [0..l])
The biomass allocated to organs
-
qo,p(n) = Q(n-1) . φo,p(i) / D(n)
where i stands for the organ age (expressed in cycles since the beginning of expansion)
The total functioning Leaf area S(n) at cycle n
| S(n) = | 1 | ( | Σi = 1 ; Tb ( Σj = 1 ; i φb(j) | Q ( n - i + j - 1) | ) | ) | |
| e | D ( n - i + j ) |
where:
-
φb(j) stands for the leaf blade sink function at age j
i,j stands for the blade age with Tb >= i >= j
Tb is the number of cycles before the leaf becomes senescent (the number of functional cycles)
e is blade thickness (the SLW)
The Production equation
| Q(n) = | E(n) . Sp | ( | 1 - exp ( -k | Sl(n) | ) | ) | |
| r | Sp |
where:
-
Q(n) is the fresh biomass produced at cycle n
E(n) is an aggregate variable standing for the environmental resource conditions, typically LUE and PAR
r represents the water resource, proportional to the Water Use Efficiency inverse (WUE-1)
k stands for the Beer law extinction coefficient
Sp stands for the projection area, as defined above
Sl(n) stands for the total functional leaf area