Here, the dependence of photosynthesis intensity on solar radiation is described
by the Michaelis – Menten type function [25, 26] and presented as:
,
max
max
P
aI
aIP
E
+
=
(13)
where I is radiation intensity, a is initial slope of the productivity curve,
max
P
is
the maximum rate of photosynthesis per unit leaf surface.
As shown in the monographs [27, 28], the intensity of solar radiation inside the
vegetation cover is determined by external and internal factors; the latter is the amount
and distribution of the leaf surface. The dependence of the radiation attenuation by
vegetation cover can be expressed by Monsie and Sayek’s model [29], according to
which the light transmission factor depends on the density and thickness of the plant
layer.
Thus, following the course of the studies, which are presented in [30], we will
consider a model in which it is believed that the tree receives energy only by
photosynthesis, free energy is spent on the needs of photosynthesis, on constructing
living tissue and on uptaking the solution from the soil. The growth equation is written
in the form of the law of conservation of energy. The growth of an individual tree is
described by a system of equations, which allows calculating the volume, height and
diameter of the trunk at each step of the simulation, taking into account the effect of
competition from trees that grow nearby:
,
cVH
Pb
dt
dV
−
=
(14)
,
)
exp(
ln
max
3
2
max
−
+
+
=
d
pV
aQ
Pm
aQ
P
p
V
P
P
(15)
,
)))
(
(
exp
1
(
)
(
3
0
2
c
t
t
c
c
t
H
−
−
−
=
(16)
,
)))
(
(
exp)
1
(
)
(
3
0
2
1
d
t
t
d
d
t
D
−
−
−
=
(17)
,
4
−
=
HaV
V
D
(18)
where V, H, D are the volume, height and diameter of a tree stem; a is initial slope
of the productivity curve; P is the photosynthesis intensity of a tree; P
m
is the maximum
photosynthesis rate per unit leaf surface; p is light absorptance; d is crown fractal
dimension; b is the coefficient of energy conversion into the stem volume increment;
c is the coefficient of proportionality of energy consumption for transport of
assimilates; Q is the proportion of solar radiation incidence on the outer surface of the
crown; c
1
, c
2
, c
3
are species-specific parameters of tree height increment; d
1
, d
2
, d
3
are
species-specific parameters of diameter increment at a height of 1.3 m; α, γ is the form-
factor stem-volume dependence ratio.
- 1772 -