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is a PAR vector (W/m
2
); n is the normal to the leaf surface;
where F
p
e
3
;
4
is
quantum ef
ciency of CO
2
assimilation (mol);
x
p
is the dispersion coef
cient for
PAR.
The third limitation w
s
is written as:
V
m
=
2 for C
3
;
w
s
¼
V
m
p
=
2 for C
4
where p is atmospheric pressure (Pa).
The photosynthesis intensity A as a minimum of functions w
c
,w
e
, and w
s
is
estimated in a simplest way, but observations show that the transition from one
limitation to another is not that spasmodic. Therefore Collatz et al. (1992) proposed
a method of combining the contributions of all the three limitations in the form of
two equations, which have to be solved with the least values:
b
ce
w
p
w
p
w
c
þ
w
e
ð
Þ þ
w
e
w
c
¼ 0
;
þ
w
p
w
s
¼ 0
b
ps
A
2
Aw
p
þ
w
s
;
where
ʲ
ce
and
ʲ
ps
are coef
cients of correlation; w
p
is a
“
smoothed
”
minimum
between w
c
and w
e
, (mol/m
2
s).
Theoretically
ʲ
ps
can have values from unity (lack of relationships
between limitations) to zero. Real estimates vary from 0.8 to 0.99.
Pure assimilation of CO
2
by a plant A
n
is equal to A
n
=A
ʲ
ce
and
R
d
, where R
d
is CO
2
losses resulting from respiration connected with the content of carboxylase in
cellulose: R
d
=f
d
V
m
where f
d
= 0.015 for C
3
, f
d
= 0.025 for C
4
.
The connection of the Collatz model of photosynthesis with the Ball semi-
empirical model of vegetation bud conductivity is written as
−
g
s
¼ m
A
n
c
s
h
s
p
þ
b
where g
s
is the vegetation bud conductivity (mol/m
2
s); g
s
m/
ðÞ
¼0
p
0
0224
T
f
:
p
;
g
s
mol/m
2
cient (=9 for vegetation of class C
3
, =4 for
C
4
, =6 for coniferous forests); b is an empirical coef
=
s
m is an empirical coef
cient (mol/m
2
/s or m/s, =0.01
for C
3
, =0.04 for C
4
); h
s
is a relative moisture of the leaf surface; c
s
is the CO
2
partial pressure in the stem, (Pa); p is atmospheric pressure (Pa); p
0
is the normal
atmospheric pressure
;
¼
1
:
013
10
5
Pa
T
f
is the absolute zero temperature
(=273.16
°
K).
There is a relationship between partial pressure of CO
2
(c
i
,c
s
) and relative
humidity h
s
. This dependence can be obtained by the analysis of the processes
taking place on the border
“
vegetation bud
atmosphere
”
,
the
respective
-
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