Estimation of Area! Evapotranspiration(?vocte,dmgs of a workshop held at
Vancouver,B.C., Canada, August 1987). IAHSPubl. no. 177,1989.
213
Estimation of forest transpiration and C0 2 uptake using
the Penman-Monteith equation and a physiological
photosynthesis model
1
D.T. Pricei and T.A. Black2
Department of Forest Sciences
University of British Columbia
Vancouver, B.C. V6T1W5
Canada
2Department of Soil Science
University of British Columbia
Vancouver, B.C. V6T 2A2
Canada
Abstract A physiologically-based canopy photosynthesis model of a
young Douglas-fir stand was developed using equations from the recent
literature of Farquhar and coworkers, and canopy conductance
characteristics determined at a site on eastern Vancouver Island, using a
modified Bowen Ratio/energy balance measurement technique. Canopy
transpiration was then estimated using the Penman-Monteith equation.
In this paper, the model's output was compared with measured data for a
single day, remarkable for a dramatic decrease in solar irradiance around
noon, and therefore considered a good test of the model's response to
changing conditions. Changes in canopy transpiration were predicted by
the model fairly well, but canopy photosynthesis was modelled less
satisfactorily. Possible reasons for the latter and required improvements
are discussed.
Evaluation de la transpiration forestière et de l'ascendance du COz à
partir de l'équation de Penman-Monteith et d'un modèle de
photosynthèse physiologique
Résumé C'est sur des principes physiologiques que l'on a fondé le
développement d'un modèle de photosynthèse du couvert forestier d'un
peuplement de jeunes pins Douglas. On s'est servi des équations tirées
des récentes publications de Farquhar et de ses collègues et on a
déterminé les caractéristiques de la conductance du couvert forestier
dans un site de l'est de l'île de Vancouver à l'aide de la méthode de
mesure du rapport de Bowen/bilan énergétique modifié pour la
circonstance. On a ensuite évalué la transpiration du couvert par
l'équation de Penman-Monteith. Dans notre étude, on a comparé les
résultats du modèle aux relevés effectués pendant une seule journée qui
se distingua par un ralentissement remarquable du rayonnement solaire
vers midi, ce qui en fait un excellent test de la réponse du modèle à des
changements de conditions. Le modèle a assez bien prédit les variations
de la transpiration du couvert forestier mais la photosynthèse du couvert,
D.J. Price and T.A Black
214
elle, n'a pas été reproduite de façon aussi satisfaisante. On en a étudié
les causes possibles et proposé les améliorations qui s'avèrent
nécessaires.
INTRODUCTION
Understanding the relationship between canopy (surface) conductance, transpiration (E)
and net photosynthesis (Fc) is of importance because: (i) it may allow simple estimates of
crop productivity from seasonal transpiration estimates (e.g. Tanner, 1981; Tanner &
Sinclair, 1983); and (ii) recent work by plant physiologists (Farquhar & Wong, 1984;
Wong et al., 1979, 1985) suggests that crop water use may be governed by the
photosynthesis rate (Monteith, 1986), instead of being largely a passive response to
environmental conditions. The latter builds on the hypothesis (Cowan, 1982; Farquhar &
Sharkey, 1982) that as a result of selective adaptation, many plants optimise water use
by maintaining 3E/8FC more or less constant, through stomatal control.
Recently conceived models of coniferous canopy E and Fc, (e.g. Jarvis et al.
1985) may help decide whether conifers also adopt water use optimization strategies,
and hence whether seasonal transpiration estimates can be used to assess forest
productivity. This paper reports recent progress in the development and testing of a
physiologically-based model of canopy photosynthesis and transpiration. Test data were
obtained from energy balance measurements made during the growing seasons of 1983
and 1984, over a coniferous canopy on eastern Vancouver Island, near Nanaimo, B.C.
METHODS
Measurements
The site is described in detail elsewhere (Price & Black, 1988; Price, 1987; Osberg,
1986). It is located at 49°02'N, 124°12'W at an elevation of about 450 m. The overstory
consists predominantly of 22 year old Douglas-fir {Pseudotsuga menziesii (Mirb.)
Franco), with a leaf area index (LA) of about 3, while the understory consists mainly of
salal (Gaultheria shallon Pursh.), with LA of about 2. Tree height is generally in the range
7-8 m, and the stocking density is generally greater than 2000 stems ha-i.
Measurements of water vapour and CO2 flux densities above the canopy were made
using a modified Bowen Ratio/energy balance method (Price, 1987; Price & Black, 1988).
A reversing psychrometric apparatus (McNaughton & Black, 1973; Spittlehouse & Black,
1980) with 3 m vertical sensor separation, was mounted on an 8 m meteorological tower
with approximately 300 m fetch in the prevailing wind direction. The lower sensors were
approximately 0.5 m above the tops of the nearest trees. Air intakes were attached to the
sensors and sample air drawn via 8.5 mm ID Dekabon tubes and 4 L glass mixing
vessels to an infra-red gas analyser (IRGA) modified for field use and operating in
differential mode. Air samples were dried so that the vertical CO2 concentration
difference (Ac) was measured assuming dry air at constant temperature inside the IRGA
measurement cells (Webb et al., 1980, Leuning et al., 1982). The remaining variables
measured were dry and wet bulb temperatures (T, Tw) vertical differences AT, ATW, solar
and net irradiances (S, Rn) and soil heat flux density (Go) (using two heat flux plates at
Estimation of forest transpiration and C02 uptake
215
50 mm depth with soil heat storage above 50 mm determined from vertically integrating
thermometers and periodic determinations of surface soil volumetric water content). A
low power field microcomputer was constructed which controlled the measurement
system, monitored sensor outputs and calculated and recorded values every half-hour.
The measurement system determined each of the terms in the stand energy
balance (Price & Black, 1988; Price, 1987) so that energy flux densities of water vapour
and CO2 (LE and XFC respectively) could be calculated from:
LE = (Rn - Go - M)/(1 + p + A)
(1)
XFc = A(R n -Go-M)/(1+p + A)
(2)
and
where p is the Bowen Ratio and A is the canopy water use efficiency, (= XF,JLE), both
corrected for the effects of small vertical wind velocities associated with the sensible and
latent heat flux densities, as discussed by Webb et al. (1980). The rate of canopy
transpiration (mg[H20] m-2 s-1) was calculated from E = LE/L where L, the latent heat of
vaporization of water, was corrected for temperature. Similarly, the net canopy mass flux
density of CO2 (u.g[C02] m-2 s-1) was calculated from Fc = XfJX where X is the energy
associated with photosynthetic fixation.
Subsequent analysis corrected these
calculations for the rates of change in canopy heat storage (M) (following Stewart &
Thorn, 1973, Jarvis era/., 1976; McCaughey, 1985), and in surface soil heat storage.
Bulk canopy resistance to water vapour diffusion (rc) was determined from the
Penman-Monteith equation (Monteith, 1965):
r
c=ff +r AKP S/ ^~ 1 l
(3)
where D is the atmospheric vapour pressure deficit recorded at the measurement height,
s is the slope of the saturation vapour pressure curve at T, and TA is the canopy
aerodynamic resistance to heat and mass diffusion. The latter was estimated from the
hourly mean wind velocity approximately corrected for the Monin-Obukhov stability
function (Dyer & Hicks, 1970; Webb, 1970; Thorn et al., 1975) using an iterative
procedure (Price, 1987). Canopy conductance for water vapour (gc) was then calculated
as the reciprocal of rc.
Other weather data, recorded hourly at an automated station nearby, included
wind direction, wind velocity and rainfall (P). Barometric pressure was also measured
daily. Measurements of root-zone soil water storage (W) and profile average soil water
potential (*PS) using a neutron hydroprobe and soil thermocouple psychrometers respectively, were made routinely throughout the two growing seasons. ¥s was also estimated
using laboratory-determined soil water retention curves and the measurements of W. A
simple water balance procedure was used to estimate daily values of W and *PS from the
measured W and weather station records of S and P. Soil respiration (Rs) was estimated
using a soda-lime technique following that of Monteith et al. (1964).
The Model
The model, described in Price (1987), consists of four distinct submodels. Of these, the
solar radiation submodel partitions measured S into diffuse and direct components, and
the canopy light penetration submodel estimates average quantum flux density (Q) for
each 1 m2 increment in LA from the top of the canopy following Jones (1983). For
simplicity, the overstory and understory were treated as one canopy, with LA « 5.
D.J. Price and T. A Black
216
Canopy Conductance and Transpiration Submodel
The canopy conductance submodel estimates average stomatal conductance (gs) for
each 1 m2 canopy layer, using an empirical approach based on boundary line functions
(Jarvis, 1976; Jones, 1983) which describe the observed dependence of all measured
values of g c on daily W, and half-hourly D, S and time since dawn (t). This approach was
necessary because, to date, no practical mechanistic model of stomatal behaviour exists
(Farquhar & Wong, 1984). The equations finally selected were:
9l(W) - gmax 0.3344 W0.23
(4a)
g2(D) = gmax 2.2434 exp[-1.6D0.45]
(4b)
g3(S) = gmax (1 - exp[-0.003S])
(4c)
04(t)« 9max (1-0.0661)
(4d)
where maximum conductance (gmax) was 22 mm s-1 for the canopy or 4.4 mm s-1 for
each 1 m-2 layer (Fig. 1). The forms of the functions used in (4) were selected following
consideration of the empirical relationships determined from porometer studies of
Douglas-fir and salal stomatal characteristics (e.g. Tan et al., 1977; Livingston & Black,
1987). The values of the coefficients were determined initially on a trial-and-error basis,
assuming the four functions should be multiplied together, following Jarvis (1976).
However, poor correlation between measured and predicted data led to an alternative
approach being investigated. Using "limiting factor analysis" (gs = minimum (gi(W),
92(D), g3(S), g4(t)}), significantly higher correlations between measured and predicted
data were achieved.
Canopy Photosynthesis Submodel
The canopy photosynthesis submodel was based on work of Farquhar and coworkers
(Caemmerer & Farquhar, 1981; Kirschbaum & Farquhar, 1984; Brooks & Farquhar,
1985). First, suitable values for the maximum rates of carboxylation, as limited by foliar
carboxylase activity (Vcmax) and electron transport rate (Jmax) were selected. From
consideration of the canopy measurements, these were estimated to be 33 and 66 u,mol
m-2 s-1 respectively (about one third of those reported in the literature). These values
were then modified to take account of the effects of W and (together with the value of the
CO2 photocompensation point, r*) of T, using empirical relationships.
For each half-hour and each canopy layer, the CO2 "demand function" was
determined as the minimum of the two rates of carboxylation (limited by foliar carboxylase
activity (Wc) and by the rate ofribulosediphosphate regeneration (Wj) respectively), while
the stomatal limitation to CO2 flux density, (the CO2 "supply function"), was determined
using the modelled value of g s obtained above (Fig. 2 and appendix). The model then
found an iterative solution for the rate of foliar photosynthesis (F|) (photorespiration
included) satisfying both demand and supply functions, by varying the value of the
canopy layer intercellular CO2 concentration (d).
For each half hour, gA, gs and the solution value of F| were estimated for each 1
m2 of canopy leaf area. Canopy conductance (gc) and canopy net CO2 flux density at the
top of the canopy (Fc) were calculated as
n
oc = Z g si
i=1
<5a>
Estimation of forest transpiration and CO- uptake
Fc= SFii-Rn
FL
217
(5b)
i=i
where n is the number of 1 m2 layer increments (i) in the canopy, Rms is an estimate of
nonfoliar maintenance respiration and Rs is the measured soil respiratory efflux
(appendix). Canopy transpiration was estimated from the modelled g c (5a) using the
Penman-Monteith equation:
s ( R n - G 0 - M ) + gADpcD
(6)
L(s + Y(1 + g A /g c ))
Finally, water use efficiency (WUE) was calculated from Fc/E and expressed as a mass
percentage.
S(Wm
FIG. 1. Relationships between measured canopy conductance (gc) and functions used in
the canopy conductance submodel for the four environmental variables found to
be important (eqs. 4a-4d). The data are half-hourly values estimated from daytime energy balance measurements of canopy évapotranspiration using (3),
taken on seven days with varying conditions. The variables are (a) soil water
storage, (b) atmospheric vapour pressure deficit, (c) solar irradiance and (d) time
since dawn.
RESULTS AND DISCUSSION
The measurement system was found to work well, with daytime resolution of canopy net
CO2 flux densities of about ±20ugrcr2s-i. Night-time measurements were less
satisfactory because of low available energy and low atmospheric diffusivity which often
caused overranging of the IRGA. Measurements were made successfully for 16 days
during August 1983 and 59 days in July and August 1984, of which 32 days were
D.T. Price and 7. A Black
218
selected for detailed analysis and determining boundary line relationships between
measured physical variables and go.
Measured and modelled data are presented and compared for one day, 4 August
1984, noteworthy for a dramatic decline in irradiance occurring around noon, when
extensive cloud moved in (Fig. 3). This day was considered arigoroustest of the model's
prediction of canopy responses to changing conditions.
300
' ^r^
Z^—-—^"
~
150 •
/
^
^
^
3.
•
C
/
^
:
^
.y
co
-150
6 August 1984
!
.„.,!
200
1
1,.
1
400
1
600
1
800
Foliar c, (mg m" )
FIG. 2. Diagram showing the functioning of the canopy photosynthesis model for a single
half-hour (12:15 PST on 6 August 1984, a predominantly cool and cloudy day),
following Farquhar and Sharkey (1982). The family of curves are the CO2
demand functions (Pn) for 1 m2 canopy leaf area increments (top line is for the
top layer of the canopy where light is least attenuated, and hence has least effect
on the foliar electron transport rate). The left hand curve represents the canopy
layer photosynthesis rates as limited by foliar carboxylase activity, here assumed
constant for all layers, which intersects the abscissa at the CO2 compensation
point (T). The straight dashed lines are C02 supply functions (Fi) derived from
the measured (right) and modelled (left) values of canopy conductance, which
intersect the abscissa at the ambient CO2 concentration (c^. Conditions were
as follows: S: 709 Wm-2, T: 17.3 °C, measuredgc: 13.6 mm s-i, modelledgc:
9.8 mm s-U Modelled non-foliar maintenance respiration rate, Rms, was
285 g m-2 s-1 while the estimated soil respiratory CO2 efflux, Rs was
100 \ig rrr2 s-1. To calculate the net CO2 flux density at the top of the canopy
(Fc), one would sum the five solution values of F/ and subtract Rms and Rs.
Canopy Energy Balance
Fig. 3 shows the diurnal energy balance. After a perfectly clear morning, heavy cloud
developed rapidly soon after midday and within an hour both S and Rn declined to about
one third of their noon values, while p declined from about 2.3 to 0.4. It is evident that the
Estimation of forest transpiration and C02 uptake
-200 H
0
'
1
4
'
1
8
'
1
'
12
1
16
'
1
20
219
'
24
HOURS (PST)
FIG. 3. Canopy energy balance for the stand on 4 August 1984. Plotted variables are
the solar irradiance (S), net irradiance (Rn), the sum of canopy heat storage and
soil surface heat flux densities (G0 + M) and the flux densities of sensible heat
(H), latent heat (LE) and photosynthetic fixation energy (kFJ. Soil water content
(W) was about 71 mm, profile average soil water potential (*¥s) was about -0.35
MPa and maximum S was 840 Wm-2 at 12:15.
rapid decrease in available energy was accompanied by a similar decline in H, while LE
was relatively unaffected. This demonstrates a strong "coupling" of forest canopy
transpiration to the imposed vapour pressure deficit, in accordance with the work of
McNaughton & Jarvis (1983).
Canopy Conductance
Fig. 4 compares diurnal variation in "measured" canopy conductance with that predicted
by the empirical canopy conductance submodel using the minimum function approach
described above ("model A"), and an alternative estimate of conductance obtained by
calculating the product of the boundary line functions (as originally proposed by Jarvis
(1976), and referred to as "model B"). The significant underestimation by model B is
attributed to two variables, D and W, both imposing a significant limitation to g c for much
of the day, which may well demonstrate a significant weakness in the multiplicative
approach. By comparison, model A shows generally very good agreement on this day,
marred slightly by a tendency to underestimate the measured values in the later
afternoon. The minimum factor analysis approach therefore seems better suited for
modelling g c when more than one environmental factor is likely to affect it simultaneously.
All the days studied in detail showed better agreement with the measured data
when using model A, although it should be emphasised that the agreement was not
always as good as seen in Fig. 4. For seven such days, covering a range of conditions of
solar irradiance, temperature and root-zone water storage, the overall regression
equation was
220
D.T. Price and T. A Black
= 0.755gcmod + 1.181 (mm s-1)
(7)
9cn
with an r2 of 0.755 determined from 316 half-hourly data pairs. Nevertheless, it is thought
the success of the model on this day, when S and D both changed so dramatically,
demonstrates its realistic response to the dominant variables affecting Douglas-fir
stomatal conductance in the forest.
ZD-
• Measured
— Model A
2 0 - . - -Model B
4 August 1984
15- •
to
b
10-
go
• ^ - N :
6-
v
0-
-B-
J
••
^ ^ - ' ^ X
•
*""
—:_,—.—|—,—|—,—|—,—,—,—
4
8
12
16
20
24
HOURS (PST)
FIG. 4. Comparison of measured and modelled canopy conductance when soil water
storage (W) was about 128 mm. The solid line given by Model A is derived as
the minimum of four conductance functions, whereas the dashed line given by
Model B, estimates gc as the product of these same four functions.
Canopy Transpiration
Fig. 5 shows the diurnal variation in canopy transpiration (E) measured by the Bowen
Ratio/energy balance system and estimated from the canopy conductance predicted by
model A using the Penman-Monteith equation (6). While the overall agreement is very
satisfactory, it should be noted that E was not predicted as successfully for all days
studied. However, in general the agreement between measured and modelled data was
slightly better than for g^. This was due to non-linearity in the dependence of E on g c
when using (6). (When D is small, and g 0 characteristically high, large errors in g c result
in relatively small errors in E.)
Canopy Net Photosynthesis
Fig. 6 shows the measured and modelled diurnal variation in canopy net photosynthesis.
Model A data were calculated using values of J m a x and Vcmax approximately one third of
those reported in the literature, compared to one fifth for model B. It can be seen that the
overall agreement is poor, although the general diurnal trend is apparent in both models.
Model A appears to overestimate in the morning and underestimate in afternoon, while
model B is closer in the morning and converges with model A in late afternoon (when the
Estimation of forest transpiration and C02 uptake
221
200
Measured
175 - . - Modelled
4 August 1984
150
125
100
75
OJ
50
25
0
-25
8
12
16
20
24
HOURS (PST)
FIG. 5. Comparison of measured canopy evaporation (from energy balance
measurements shown in Fig. 3) with that estimated using the Penman-Monteith
equation (6), and the values of modelled canopy conductance shown in Fig. 4.
Aerodynamic resistance was estimated from the wind velocity, corrected for the
Monin-Obukhov stability function, while available energy and vapour pressure
deficit were obtained from the original energy balance measurements.
1000
4 August 1984
-500 - •
-750
8
12
16
20
24
HOURS (PST)
FIG. 6. Comparison of measured canopy net photosynthesis (from energy balance
measurements shown in Fig. 3) with values predicted by the physiologically
based model. Model A used values of
Vcmax snd Jmax approximately one third of
those reported in the literature by Farquhar and coworkers, whereas Model B
used values of approximately one fifth.
D.T. Price and T.A. Black
222
respiratory functions dominate Fc). This diurnal trace was typical of many days studied,
perhaps indicating that the respiration functions were overly responsive at higher
temperatures, or that the decrease in Jmax with time since dawn was too severe.
It was found that modelled F0 was much more sensitive to changes in Jmax than
in Vcmax. which is consistent with the observation that the major diurnal limitation to
photosynthesis is in irradiance. On hot days, Fc will tend to be limited by high rates of
maintenance respiration, and, on the basis of this study, low stomatal conductance will
rarely become significant in restricting CO2 uptake. These observations are consistent
with others reported in the literature for coniferous species (Beadle & Jarvis, 1977;
Beadle et al., 1985; Leverenz, 1981).
The overall agreement between measured Fc and model A had the following
regression equation:
Fcmeas = 0.98F c m od + 48.2 (ug t r r 2 s-1)
(8)
with an r2 of 0.515 calculated from 262 half-hourly data pairs. Model B produced slightly
lower correlation even though the absolute values often appeared more comparable to
the measured data.
Part of the explanation for the poor agreement may lie in the measurements
rather than in deficiencies of the model. Considering the consistency in LE for this day
(Figs. 3 and 5) it is unlikely that there were serious problems with the CO2 measurement
system or the upwind fetch (the IRGA was checked and calibrated routinely and found to
perform well throughout both field seasons). However it is postulated that fluctuating
wind direction caused the air arriving at the tower to pass over trees of varying sizes and
productivity (due perhaps to varying soil nutritional status), which resulted in much
greater variation in Fc than in LE.
Canopy Water Use Efficiency
Fig. 7 shows measured and modelled WUE for the daytime hours. The agreement is poor
for both model A and model B (where these correspond to the A and B canopy
photosynthesis models). Since canopy transpiration was modelled very successfully, it is
evident that the poor agreement is attributable mainly to the limited success of the
canopy net photosynthesis model. Because Fc was overestimated (at least by model A)
in the morning and underestimated in the cloudy cool conditions of the afternoon, WUE
behaved similarly.
CONCLUSIONS
For a young Douglas-fir stand, measurements of canopy transpiration (E) and CO2 flux
density at the top of the canopy (Fc) were successfully accomplished using a modified
Bowen Ratio/energy balance technique. The model of canopy processes predicted
canopy conductance (gc) almost as well as it could be calculated from measurements of
E. For the particular day reported here, a dramatic change in solar irradiance was
accompanied by only a slight change in E as expected from consideration of McNaughton
& Jarvis (1983). The simple empirical model of gc was responsive enough to enable
diurnal E to be estimated from climatic variables using the Penman-Monteith equation.
However, the more complex physiologically-based canopy photosynthesis model was
only moderately successful in estimating Fc and canopy water use efficiency, mainly
Estimation of forest transpiration and CO- uptake
223
because of deficiencies in the information required to characterize diurnal responses in
Fc. The improvements required are:
(i) a more detailed simulation of the canopy light regime,
(ii) correct values for foliar carboxylase activity and electron transport rate,
(iii) better analysis of the factors influencing canopy respiration
1.0
4 August 1984
0.5
0.0
UJ
-0.5
-1.0
0
4
8
12
16
20
24
HOURS (PST)
FIG. 7. Comparison of measured and modelled canopy daytime water use efficiency ratio
(WUE) (from the half-hourly values of E and Fc shown in Figs. 5 and 6). Nighttime values were omitted because low evaporation rates combined with large
respiratory fluxes resulted in very large and erratic ratios. As in Fig. 6, Model A
used values of Vcmax and Jmax approximately one third of those reported in the
literature by Farquhar and coworkers, whereas Model B used values of
approximately one fifth.
ACKNOWLEDGEMENTS
This research was funded partly by grants from the Canadian Natural Sciences and
Engineering Research Council, and partly through Section 88 funding from the British
Columbia Ministry of Forests to MacMillan Bloedel Ltd. The assistance and logistical
support arranged by MrD.G. Dunsworth of MacMillan Bloedel Woodlands Services
Division is gratefully appreciated. D.T.P. acknowledges the award of University of British
Columbia Graduate and Donald S. McPhee Fellowships.
APPENDIX
The maximum potential rate of carboxylation limited by the rate of ribulose diphosphate
(RUP2) regeneration, in the absence of photorespiration (V\max) was determined from
(Caemmerer & Farquhar, 1981; Farquhar & Caemmerer, 1982; Kirschbaum & Farquhar,
1984):
0.7". Price and 7". A Black
224
Vjmax = JmaxQ/[(Q + 2.1 Jmax)4.5]
(A1 )
where Q is the absorbed (assumed equal to incident) quantum flux density, Jmax is the
maximum potential (light saturated) rate of whole chain electron transport expressed in
u,Eq rrr-2s-i, and the factor 4.5 converts it to the equivalent net mole rate of carboxylation
(in u.mol rrr 2 s-1).
Seasonal decreases in soil water storage (W) were found to reduce canopy
photosynthesis for days that were otherwise comparable, so W was considered to affect
the RuP2 regeneration-limited carboxylation rate (Vj) and the apparent maximum rate of
carboxylation (Vc) (in the presence of saturating RuP2 and CO2). Measured afternoon
photosynthesis rates were lower than morning rates, for conditions that were otherwise
similar, which indicated that time since dawn should also be considered a factor
influencing photosynthesis, so simple empirical corrections (similar to the ones used for
stomatal conductance) were introduced:
Vj = Vjmax(1 - 0.045t)(0.45W0.17)
(A2)
V c = (1 - 0.045t)(0.45W0.17)VCmax/(1 + Ka/Doi)
(A3)
where Vcmax is the maximum (RuP2~saturating) rate of carboxylation for full activation of
RuP2-carboxylase-oxygenase (Rubisco), pCi is the intercellular CO2 partial pressure, and
Ka is the Michaelis-Menten constant for activation of Rubisco, assumed constant
following Kirschbaum & Farquhar (1984).
Temperature dependence of photosynthesis was represented by empirical
adjustments to Vj and Vc of the form suggested by Jones (1983), i.e.
v
x =
2b 1 (T
+
b 2 ) 2 (Tmax + b 2 ) - ( T + b 2 ) 4
( Tmax + b 2 )"
(A4)
where bi and bz are constants, T*max is the temperature at which the maximum reaction
rate occurs, and x is the multiplicative factor applied to Vj or Vc. Tmax was taken to be
22.7 °C for Vj and 21.3 °C for Vc. The values used for bi and b2 respectively were 1.31
and 4.0 for VJ and 1.0 and 5.5 for Vc. Temperature sensitivity of r*, was estimated using
the equation provided by Brooks & Farquhar (1985):
r, = 4.27 + 0.168(T - Tref) + 0.0012(T - Tref)2
(A5)
where r* is expressed in Pa and Tref is 25 °C (although slightly better results were
obtained in this study using 28 °C). Following Kirschbaum & Farquhar (1984), the lightlimited rate of carboxylation (Wj) was then calculated from
Wj = Vj/(1 + (7/3)r*/Pcj)
(A6)
where pd is initially assumed equal to the ambient partial pressure (pea) (see below),
while the RuP2 saturating rate of carboxylation (Wc) was given by
Wc = V ^ l + Kc/poi)
(A7)
where Kc is the effective Michaelis-Menten constant for carboxylation at ambient oxygen
partial pressure. The gross photosynthesis rate (Pg) was then determined as
Pg = minimum{Wc,Wj} (1 - rVpa)
(A8)
where Pg allows for photorespiration. Growth respiration of the foliage (Rg) was
estimated as one tenth of foliar net photosynthesis (Pn) although it is recognised that this
is only a rough approximation. Foliar maintenance respiration for each canopy layer
(Rmf) was computed from
Rmf = Rmax(Rf/LA){1 - exp[Rk(T-TR0)]}
(A9)
Estimation of forest transpiration and C02 uptake
225
where LA is the canopy leaf area index, T is the ambient temperature and TRO is the
temperature at which canopy respiration appears to become zero, found by inspection of
the data to be about 10.0 °C. The constants Rf, Rmax and Rk represent: the proportion of
canopy respiration contributed by the foliage (taken to be 50%); the assumed maximum
possible canopy respiration rate; and an empirical coefficient set to -0.047, respectively.
Equation (A9) was derived empirically to resolve the difference between measured and
modelled photosynthesis rates. The negative exponential implies a Qio that decreases
with increasing temperature, which suggests that all the components of canopy
respiration could not be modelled realistically with a simple maintenance respiration
function. Hence Pn (the CO2 "demand function") and Rd (the "daytime" respiration) could
be calculated using
P„-(P„-Rmf)/1.1
Rd = Rmf + 0.1Pn
(A10)
(A11)
while non-foliar maintenance respiration (Rms) (i.e. where respired CO2 does not exit
through foliage), was determined from
Rms = (1-Rf)Rmf/R{
(A12)
The CO2 "supply function" is the net flux density of CO2 from the atmosphere to the
inside of the leaves (F|) calculated from
F| = gt(Pca-Pci)/PA
(A13)
where PA is barometric pressure, and total conductance of the canopy layer to CO2
diffusion (gt) is given by
g t = gAigsPADc/[Dv(gAi + gs)RT«]
(A14)
where Dc and Dv are the binary diffusion coefficients in air for CO2 and water vapour
respectively, R is the universal gas constant and gs is the mean layer stomatal
conductance with units of u.mol rrr 2 s-1 (Jones 1983). Following Wesely et al. (1978) and
Kelliher et al. (1986), the corresponding canopy layer mean aerodynamic conductance,
gAi, was assumed to originate mainly from within the canopy (i.e. as leaf and branch
boundary layer terms), so that gAi *= (LArAH-
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