PE EIE[R-Rg RESEARCH ON - HJ Andrews Experimental Forest

where
giving
P = C a Cc
Er
(14 )
Ca = concentration of atmospheri c
CO 2 g cm- 3
Cc = concentration of CO 2 at the
chloroplast g cm 3
Er = resistance to gas diffusion
sec cm- 1
D[CO 2] a
P= 1 + D/KI
where D is the integral exchange coefficien t
D= 1 = 1
ra +rs +rm E r
where ra is boundary layer resistance, rs is
stomatal resistance, and rm is mesophyll
resistance to CO 2 diffusion in sec cm-2 .
Equation 15 is gross photosynthesis, not Pn ,
and thus equation 15 should be corrected for
respiration :
Pn = K[CO 2 /al - R
(16)
I + K1/D
where R is respiration .
These models assume that resistance t o
transfer of CO 2 from respiration site to the
photosynthesis site is negligible . The variable
nature of rs must also be considered, requirin g
an additional model of stomatal behavior .
Brown (1969) notes that the complexity of
equation 16 becomes great when other components
are added, and states that it is
necessary to solve equation 16 by arriving at
the functional relationships of the components
by independent means and substituting
them into the general model .
If the components are truly independent ,
such a tactic is valid . If not, error is introduced
by failing to consider changes in th e
values of the parameters due to interaction, a
violation of our systems criterion .
Lommen and coworkers (1971) took an
approach similar to that of Brown (1969) .
They began with Gaastra 's (1959) derivatio n
from Fick's law of diffusion now familiar to
us. The biochemical relations are described b y
a Michaelis-Menton type equation that de -
scribes the rate of a single enzymatic reaction .
Their model for photosynthesis as a function
(15)
of chloroplast concentration of CO 2 is :
Pm
P 1 + K/Cc
where P = photosynthesis g cm-2 sec- 1
Pm = photosynthesis at saturating CO 2
g cm-2 sec- s
K = concentration of CO 2 at the
chloroplast when P = 1/*Pm
Cc = concentration of CO 2 at the
chloroplast g cm- 3
Equation 14 is solved for Cc and substitute d
into equation 17 giving photosynthesis as a
function of atmospheric CO 2 concentratio n
and stomatal resistance :
(Ca + K + E rPm)
P=
2Er
(18)
- [(Ca + K + ErPm)2 - 4CaErPm] lie
21 r
They also derived a similar though mor e
complex model giving photosynthesis as a
function of Ca, K, Pm, W, and two series of
resistances, S 1 , S 2 ; W is respiration .
They also derived submodels of photosynthesis
as a function of light and temperature ,
Pm(L,T) =
PmLT G(T)
1 + KL/L
(17 )
(19 )
similar to equation 4 but incorporating a term
G(T) representing the temperature dependence
of photosynthesis . The authors implie d
that equation 19 could be incorporated int o
equation 18 and their other model, but the y
did not do so, and dimensional analysis o f
equation 18 with PmLT and KL substituted
for Pm and K, shows that such a substitutio n
is physically unrealistic. Hence the model o f
Lomrnen et al . (1971) is inadequate for
predicting photosynthesis as a function o f
light and temperature as well as CO 2 concentration
and stomatal resistance .
Chartier (1966, 1969, 1970) also developed
a complex model of net assimilation derive d
along the lines of that by Lommen et al .
(1971) . Beginning with the fundamental for m
(Chartier 1970) :
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