The equation for production at crop level.
We have seen that crop-based models may express biomass growth per unit area m², as follows:

dW = LUE . PAR . (1 - exp ( -k LAI ) )
where:

LUE is the Light Use Efficiency,
LAI the Leaf Area Index
PAR the Photosynthetic Active Radiation incident on the crop (per m²)

Expression of the crop model at single plant level.

Let d define plant density.
Then Sd = 1 / d represents the potential available area at single plant level.
Let S_l also define the total area of functional leaves. We can then write:

LAI = S_l / S_d

The production equation can thus be expressed as:

dW = LUE . PAR . S_d(1 - exp ( -k S_l / S_d ) )

Now, at low density, we introduce S_p, a virtual surface area such that

S_p = F(S_d)
with F(S_d) -> S_d when the crop cover closes (at a significant density value).

Moreover, we can integrate these equations over the duration of a growth cycle.
Assuming that the leaf area remains constant during a growth cycle, we obtain the first GreenLab equation, defining fresh biomass production as follows:

Q(n) =	E(n) . Sp	(	1 - exp ( -k	Sl(n)	)	)	(equation 1)
	r			Sp






where:

Q(n) is the fresh biomasss produced at cycle n
E(n) is an aggregate variable standing for 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
S_p stands for the projection area, as defined above
S_l(n) stands for the total functional leaf area