The productivity of the vegetation is a function of C, N, and T alone.
As in [9] we assume that the productivity function P(C,N,T) can be presented in
the multiplicative form (accordingly with Liebig's principle):
where is the maximum productivity of the vegetation and
,
are functions:
.
Here
is a unimodular function:
(see Fig. 2),
Figure 2: Function describing the dependence of productivity on temperature T.
according to [10], the function is a monotonous increasing function with
saturation (see Fig. 3).
Figure 3: Function describing the dependence of productivity on carbon content C in the atmosphere.
The function is a monotonous increasing function, tending to one when
(as in Fig. 3). Since C=A-N then the product
can be presented in the form
for fixed A(t) (see Fig. 4).
Figure 4: The function as a function of N.
The function is a unimodular function where
. It is defined
in the interval
.