Summary We estimated carbon and water flows, canopy conductance and the assimilation/transpiration ratio of fruiting and non-fruiting apple trees grown in the field, from daily gas exchange measurements taken during the summer with a whole-canopy enclosure device. The relationships between photosynthetic and transpirational responses and environ-mental conditions were also investigated, as well as the role of canopy conductance in controlling carbon dioxide and water vapor exchange.
Light-saturated net photosynthetic rates, which were higher for the fruiting canopy than for the non-fruiting canopy, showed a general decrease in the afternoon, particularly for the non-fruiting canopy, compared with rates in the morning. When light was not limiting, the afternoon decrease in net photosynthesis appeared to be regulated more by non-stomatal factors than by changes in canopy conductance. Canopy con-ductance, which was higher for the fruiting canopy than for the non-fruiting canopy, may actively regulate photosynthetic ac-tivity and may also be modulated by feedback control in response to assimilation capacity. We conclude that adjust-ments in canopy conductance, which were partially dependent on the vegetative--reproductive status of the tree, control the equilibrium between photosynthesis and transpiration. We also demonstrated that whole-canopy chambers can be used to estimate photosynthetic and transpirational responses thereby overcoming the difficulty of scaling these physiological re-sponses from the leaf to the whole-canopy level.
Keywords: assimilation/transpiration ratio, canopy conduc-tance, whole-canopy enclosure system.
Introduction
Photosynthesis is primarily driven by solar radiation, whereas transpiration also depends on the temperature and humidity of air. Transpiration is induced by evaporative demand resulting from net radiation absorbed by leaves and the drying power of the atmosphere, which in turn is related to wind speed and relative humidity (Monteith and Unsworth 1990).
Stomata, through which CO2 and water vapor diffuse into and out of the leaf, are involved in the regulation of both photosynthesis and transpiration (Jarvis and Morison 1981).
The control of stomatal aperture involves state variables (e.g., leaf water potential and intercellular carbon dioxide concentra-tion), interactions between processes (transpiration and photo-synthetic rates), and is related to environmental conditions, in particular to the water vapor concentration difference between the leaf surface and the bulk air (Jones 1992).
Although the processes of photosynthesis and transpiration have been thoroughly investigated in individual leaves, the contributions of the environmental and physiological factors driving and controlling gas exchange at the whole-canopy level are not well defined. It is difficult to extrapolate the physiological behavior of the whole canopy from single-leaf responses, because a collection of leaves may not accurately represent the complexity of the canopy. Moreover, the control of single-leaf and whole-canopy responses involves several variables and it is reasonable to assume that the same variable has somewhat different effects at the canopy scale than at the leaf level. Also, experimental data for whole-tree performance are required to validate the results obtained by mechanistic approaches (Thornley and Johnson 1990).
For woody perennials, and in particular fruit trees, enclosure systems able to estimate gas exchange between the whole-can-opy, considered as a ‘‘big leaf,’’ and the atmosphere have recently been developed (Palmer and Rom 1986, Snelgar et al. 1988, Adaros et al. 1989, Wibbe and Lenz 1989, Garcia et al. 1990, Buwalda et al. 1992a). The simultaneous monitoring of environmental parameters (incoming photosynthetically ac-tive radiation, CO2 concentration, air temperature and humid-ity) allows estimation of physiological responses (net photosynthesis, dark respiration and transpiration) and calcu-lation of whole-canopy conductance (Lhomme 1991, Avissar 1993, McNaughton 1994) directly from measurements per-formed on the entire canopy.
The present work was undertaken to investigate canopy-level relationships between diurnal trends of environmental variables and photosynthetic and transpirational activities, and the control exerted by plant factors on these responses. Specifi-cally, daily observations were collected with whole-canopy chambers on one heavily cropping and one non-fruiting tree grown in the field. The crop load treatments were chosen to test how source--sink relationships affect the regulation of whole-canopy gas exchange. Canopy conductance for both trees was
Influence of environmental and plant factors on canopy photosynthesis
and transpiration of apple trees
RITA GIULIANI,
1F. NEROZZI,
2E. MAGNANINI
1and L. CORELLI-GRAPPADELLI
11
Dipartimento di Colture Arboree, University of Bologna, via Filippo Re 6, 40126 Bologna, Italy 2 Istituto di Ecofisiologia delle Piante Arboree da Frutto, National Research Council, Bologna, Italy
Received July 5, 1996
calculated, and its role in controlling gas exchange between the whole-canopy, considered as a ‘‘big leaf,’’ and the atmosphere was evaluated.
Materials and methods Plant material
Measurements were carried out on two five-year-old apple trees, in an orchard located in the Po Valley (Northern Italy) near Bologna (44°30′ N; 10°36′ E). The trees, cv. Smoothee grafted on Pajam 2 rootstock, were trained as slender spindles and spaced 2.5 m in rows 4 m apart. At bloom, two trees were chosen of similar trunk diameter, branch development and number of flower clusters. In one tree, all flower clusters were removed by hand. Both trees received the same standard cul-tural (irrigation, fertilization, pest control, etc.) management program throughout the season.
Tree leaf areas were determined after full canopy develop-ment, immediately before the gas exchange measurements. The leaves on each tree were counted and one in 50 leaves was collected and assigned to a spur or extension shoot leaf sample, as reported by Palmer (1987). The area of each sampled leaf was measured with an LI-3000 (Li-Cor, Inc., Lincoln, NE) leaf area meter. The average spur and extension shoot leaf area thus obtained was then multiplied by the corresponding total leaf number. Canopy leaf areas of about 10 and 20 m2 were esti-mated, for the crop load tree (about 20 fruits m−2 final leaf area) and the non-fruiting tree, respectively. Canopy volumes were about 4.2 and 6.2 m3 for the fruiting and the non-fruiting canopy, respectively.
Leaf dry weight per unit area was determined from a sample of 30 bourse shoot leaves per tree, which were collected, at full canopy development, at the end of August. Leaf area was estimated with the Li-Cor LI-3000 leaf area meter and leaves were then dried at 70 °C to constant weight.
Field whole-canopy system and measurements
An open system, similar to that described by Corelli-Grap-padelli and Magnanini (1993), was used to measure canopy gas exchange in the field. The system consisted of a polyeth-ylene chamber enclosing the entire canopy, a centrifugal air-fan, and a butterfly valve to control flow. Because of the rapid and large fluctuations in ambient CO2 concentration occurring in the orchard, a second chamber, acting as a buffer for air mixing, was placed before the assimilation chamber to even out the fluctuations. The various components were connected by lengths of 100-mm diameter plastic pipe.
Air flow rate through each chamber was adjusted, based on canopy leaf area, to obtain CO2 differentials within the linear-ity range of the infrared gas analyzer (IRGA) and, at the same time, to minimize air temperature increases inside the cham-ber. A small thermal differential (chamber air temperatures were 5 and 10% higher than ambient air on fruiting and non-fruiting trees, respectively) between outlet and inlet dry bulb temperatures was recorded. Flow rates were estimated by measuring the time required to fill, through the outlet air stream, a cylindrical polyethylene bag having a volume of
0.767 m3. The average flow rate for the fruiting canopy was 20 dm3 s−1, whereas that for the non-fruiting canopy was 33 dm3 s−1. The time constant of the enclosure system was calculated as the ratio between chamber volume and air flow rate. Because the volume was about 13.5 m3 in both cases, the time constants were about 12 and 7 min for the fruiting and the non-fruiting canopy, respectively.
Canopy gas exchange measurements, which were per-formed on one tree at a time, started in mid-August and continued until mid-September in 1--3 day cycles of uninter-rupted measurements. Incoming photosynthetically active ra-diation (Q) was monitored with a calibrated quantum sensor Li-Cor LI-190SB, placed horizontally above the canopies, outside the chamber. The Q values were corrected for light attenuation caused by the polyethylene canopy enclosure. Al-though the polyethylene film (0.1 mm thick) was spectrally neutral, it caused a 20% reduction in light intensity over the 300--900 nm range.
At the chamber’s inlet and outlet, dry and wet bulb tempera-tures were measured by calibrated solid state detectors, and CO2 concentrations of the inlet and outlet air streams were continuously monitored by a portable IRGA (ADC-LCA2, Analytical Development Co., Hoddesdon, U.K.). All measure-ments were recorded and stored every 3 min by a CR10 data logger (Campbell Scientific Ltd., Loughborough, U.K.).
Leaf gas exchange was also measured, after removal of the enclosure chamber. Over 100 mid-bourse shoot leaves were chosen on external spurs, and light-saturated net photosyn-thetic activity was determined. Data were collected in the morning and afternoon of sunny days with the portable IRGA equipped with a Parkinson broadleaf chamber.
Data analysis (g m−3), and subscripts ‘‘in’’ and ‘‘out’’ refer to inlet and outlet chamber values, respectively. The units of A and E were con-verted and expressed as µmol m−2 s−1 and mmol m−2 s−1, respectively.
Canopy conductance (gc, mm s−1) was calculated as (see Appendix B):
gc=0.462 ET
D,
where T is dry bulb temperature (K) and D is canopy air vapor pressure (Pa).
On the assumption that differences in stomatal conductance entail an energetic trade-off between the potential increments in photosynthesis and the increased costs associated with the corresponding increments in transpiration (Cowan 1990), an assimilation/transpiration ratio (ATR, µg CO2/mg H2O) was calculated for each canopy.
For each canopy, data used for the present analysis were obtained for 3 days between day-of-the-year (DOY) 245 and DOY 255.
Results
Daily trends for environmental parameters (Q, T, D), taken on a day representative of the measurement period, and the con-current physiological responses (A, E, gc) of the fruiting tree are reported in Figure 1. Maximum Q measured outside the canopy enclosure (about 1750 µmol m−2 s−1) was reached
around noon, whereas maximum T (nearly 35 °C) was ob-served in the afternoon (Figure 1a). There was a diurnal trend of decreasing ambient CO2 concentration (Ca) from 350 ppm in the morning to 325 ppm in the afternoon (data not shown). Canopy air vapor pressure deficit and E, which were closely correlated, exhibited maxima of about 1.25 kPa and 2.25 mmol H2O m−2 s−1, respectively, in the afternoon (Figure 1b). Net photosynthetic rate increased until midday and reached a maximum value of about 9.5 µmol CO2 m−2 s−1 coincident with the highest value of gc (nearly 5.5 mm s−1). Both A and gc showed a decreasing trend in the afternoon which was more marked for A (Figure 1c).
There was a nonlinear relationship between E and D for both trees. The fruiting tree values showed a higher slope, and the maximum E was about twice (about 2.5 mmol H2O m−2 s−1) that of the non-fruiting tree (Figure 2).
The relationship between gc and D differed between the fruiting and non-fruiting trees at different temperatures. For the fruiting tree, the relationship between gc and D was nega-tive and exponential at temperatures of 20, 25, 30 and 35 °C (Figure 3a), whereas for the non-fruiting tree the relationship was negative and exponential only at 35 °C, with no relation-ship at the lower temperatures (Figure 3b). There was a posi-tive, linear relationship between gc and T in both canopies (Figure 4), at vapor pressure deficits of 0.5 and 1.0 kPa.
In both canopies, there was a hyperbolic relationship be-tween gc and Q. Stomata responded rapidly to Q values lower than 100 µmol m−2 s−1, whereas at greater Q values, gc in-creased slightly. Moreover, gc of the fruiting tree was about twice that of the non-fruiting tree (Figure 5).
Boundary line relationships (Webb 1972) between A and Q are shown for both canopies in Figure 6. Because the source--sink relationship within the tree may affect A, morning and afternoon data have been treated separately. Under similar light conditions, the boundary line for the fruiting tree showed
Figure 1. Diurnal courses of the environmental parameters and corre-sponding physiological responses for the fruiting canopy during DOY 247: (a) T (dashed line) and Q (continuous line); (b) D (dashed line) and E (continuous line); (c) gc (dashed line) and A (continuous line).
a steeper initial slope and higher light-saturation values than for the non-fruiting tree. Both canopies showed higher A in the morning than in the afternoon. In the fruiting tree, A at saturat-ing Q decreased slightly from about 9.5 µmol CO2 m−2 s−1 in the morning to 9.0 µmol CO2 m−2 s−1 in the afternoon (Fig-ure 6a), whereas this difference, which may reflect a real decrease in potential A, was more pronounced in the non-fruit-ing tree where A was about 25% lower in the afternoon than in the morning (8 versus 6 µmol CO2 m−2 s−1 under saturating light conditions) (Figure 6b).
The relationship between gc and canopy A at irradiances above 500 µmol m−2 s−1 is shown in Figure 7, and data for the general leaf-level relationship between gs and A at irradiances above 500 µmol m−2 s−1 are shown in Figure 8. A Q threshold of 500 µmol m−2 s−1 was chosen on the basis of the weak dependence of A on gc at higher light intensities (cf. Figures 5 and 6). This threshold irradiance was also supported by the finding that, at values lower than 500 µmol m−2 s−1, there was no correlation between A and gc (data not shown). In the fruiting canopy, both morning and afternoon values of A
Figure 3. (a) Effect of D on gc of the fruiting canopy at different temperatures: T = 20 °C (r), T = 25 °C (e), T = 30 °C (d) and T = 35 °C (s) (SEmax = 0.64). (b) Effect of D on gc of the non-fruiting
canopy at different temperatures: T = 25 °C (e), T = 30 °C (d) and
T = 35 °C (s) (SEmax = 0.50). All data points are means of 10 values.
Figure 4. (a) Effect of T on gc of the fruiting canopy at D = 0.5 kPa (s) and D = 1.0 kPa (d) (SEmax = 0.52). (b) Effect of T on gc of the
non-fruiting canopy at D = 0.5 kPa (s) and D = 1.0 kPa (d) (SEmax =
0.49). All data points are means of 10 values.
showed an asymptotic trend with increasing gc (Figure 7a). In contrast, in the non-fruiting canopy, only the morning values of A showed an asymptotic pattern with increasing gc, whereas the afternoon A values were relatively low and nearly constant (Figure 7b). Moreover, for the non-fruiting tree, gc ranged from 2 to 4 mm s−1 in the afternoon, whereas the morning range and the range observed for the fruiting tree during daytime was from 2 to 6 mm s−1.
At the leaf scale, no differences between morning and after-noon values of A with respect to leaf stomatal conductance (gs) were observed (data not shown). Pooled morning and after-noon values of A with respect to gs showed an increasing trend and gs and A values were greater than the corresponding data for both canopies (Figure 8).
For both canopies, ATR plotted against A differed between the morning and afternoon (Figure 9). In the morning, a bell-shaped trend was found, with higher values for the fruiting tree than for the non-fruiting tree. Maximum ATR for both trees occurred at A values of around 150 µg CO2 m−2 s−1 (i.e., 3.4 µmol CO2 m−2 s−1) (Figure 9a). In the afternoon, an
asymp-Figure 6. (a) Effect of Q on A of the fruiting canopy in the morning (d) and afternoon (s). (b) Effect of Q on A of the non-fruiting canopy
in the morning (d) and afternoon (s). The continuous line is the boundary line for morning values and the dashed line is the boundary line for afternoon values.
Figure 7. (a) Effect of canopy conductance on A of the fruiting canopy in the morning (d) and in the afternoon (s). The SEmax was 1.38 and
0.65 in the morning and afternoon, respectively. (b) Effect of canopy conductance on A of the non-fruiting canopy in the morning (d) and
in the afternoon (s). The SEmax was 0.91 and 0.60 in the morning and
afternoon, respectively. Data points are means of 10 values.
totic relationship was shown at lower ATR values, but it was similar for both trees. Moreover, over a range of A values from 100 to 400 µg CO2 m−2 s−1 (i.e., 2.3 to 9.0 µmol CO2 m−2 s−1), ATR remained constant, indicating a nearly linear relationship between A and E (Figure 9b).
Discussion
The functional approach, usually applied to photosynthesis and transpiration data estimated by leaf gas exchange measure-ments, was scaled to the whole canopy, considered as a ‘‘big leaf,’’ and applied to data obtained from a whole-canopy enclo-sure system. We restricted our study to two trees, one fruiting and one non-fruiting, based on the assumption that their widely different vegetative--reproductive conditions would affect the interaction between canopy and environment and induce dif-ferent physiological equilibria.
The diurnal trends in Q, T, D, A, E and gc reported in Figure 1 are similar to those reported by Eckstein and Robin-son (1995) for banana leaves. In accordance with their analy-sis, increasing E in the morning was attributed to increasing D. As stomata began to close around noon, A decreased slightly,
whereas E, driven by D, continued to increase although less than in the morning. The decrease in E that occurred later in the afternoon was induced by decreasing D and partial sto-matal closure. Thus, stosto-matal feedback may be responsible for the nonlinear trend between E and D in Figure 2. This non-linear trend is also in agreement with the leaf data reported by Jones (1992) who showed, over a wide range of D values, a decrease in E beyond a D of 1 kPa. Generally, trees control transpiration by adjustment of stomatal conductance, as shown by the negative relationship between gc and D observed at various air temperatures in the fruiting canopy (Figure 3a). However, in the non-fruiting canopy, a similar negative expo-nential relationship was found only at 35 °C, but not at lower temperatures (Figure 3b). A possible explanation for this lack of correlation between gc and D at low temperatures is that stomatal control of canopy transpiration is strong only when the total boundary layer conductance/stomatal conductance ratio is high (Meinzer and Grantz 1991, Monteith 1995). De-spite the air flow passing through the assimilation chamber, the denser canopy of the non-fruiting tree may have caused condi-tions of low boundary layer conductance and thus a greater degree of decoupling from the environment (Jarvis and McNaughton 1986). The different behaviors of the fruiting and non-fruiting canopies indicate that geometric and structural plant characteristics and source--sink relationships might be involved in a feedback control of canopy conductance. That is, canopy conductance was negatively related to canopy leaf area and positively affected by the presence of crop load. The negative relationship between canopy conductance and leaf area supports observations by Meinzer and Grantz (1991) that, during plant development, increasing stomatal closure with increasing leaf area limits the increase in transpiration per plant, and represents a homeostatic mechanism for maintain-ing nearly constant leaf water status over a wide range of plant sizes and environmental conditions.
Studies of fruiting and non-fruiting peach (DeJong 1986), plum (Gucci et al. 1991) and apple (Jones and Cumming 1984, Lenz 1986) trees all indicate that the presence of fruits tends to have a positive influence on stomatal conductance. Because photosynthesis leads to removal of intercellular carbon diox-ide, it has been postulated that assimilation partially controls stomatal conductance by affecting changes in carbon dioxide concentration, to maintain a constant value (Morison 1987). However, the role of CO2 in stomatal movements is controver-sial. Consequently, it is not clear if stomatal conductance is affected by fruiting as a result of the depletion of CO2 in the substomatal cavity, or as a result of the generally enhanced photosynthetic activity induced by the presence of fruits (Mon-selise and Lenz 1980, Fujii and Kennedy 1985), or if a hormo-nal mechanism is involved (Lenz 1986).
The weak dependence of gc on Q observed above 10% of full sunlight (Figure 5), and which closely resembles the typical single-leaf response reported in the literature (Lakso 1994), confirms the conclusion of Knapp and Smith (1990) that sto-mata of apple trees do not exhibit sun-tracking behavior. Our data support Turner’s suggestion (Turner 1991) that light func-Figure 9. (a) Assimilation/transpiration ratio (ATR) plotted against A
tions as an ‘‘activating factor’’ for stomatal opening; however, light alone is not able to modulate canopy conductance.
The asymptotic relationships between gc and A (Figure 7) and, at the leaf scale, between gs and A (Figure 8) suggest a threshold, when light is not a limiting factor, above which A is controlled by non-stomatal factors. Farquhar and Sharkey (1982) concluded that carbon assimilation rate could increase only marginally with conductance above the values at which regeneration of ribulose bisphosphate carboxylase-oxygenase (RuBP) enzyme becomes limiting.
Our results indicate that non-stomatal factors account for the afternoon decrease in A observed in the non-fruiting canopy. The effects of T and D on canopy conductance and respiratory activity (dark respiration and photorespiration) are of less importance. Mesophyll limitations on carbon fixation, which are related to nonstructural carbohydrates accumulating in leaves (Gucci et al. 1991), limiting phloem loading (Körner et al. 1995) and assimilate distribution (Flore and Lakso 1989), as a result of the low vegetative-sink demand at this time of the growing season, are considered to be responsible for the after-noon decline in A in the non-fruiting canopy. The higher leaf mass per unit leaf area observed in the non-fruiting tree than in the fruiting tree (13.4 versus 11.8 mg cm−2) also supports this explanation (cf. Palmer et al. 1997). In contrast, the strong fruit demand for assimilates in the cropping tree minimized leaf saturating conditions, thereby preventing the afternoon depres-sion of A in the fruiting canopy. Moreover, the lower foliage area density, the consequent lower self-shading and the large carbon allocation to fruits, all contributed to the higher morn-ing A observed in the fruiting canopy than in the non-fruiting canopy.
Because stomata track the adaptative changes in the photo-synthetic apparatus, as a result of their coupling with meso-phyll activity (Wong et al. 1979, Schulze and Hall 1982, Morison 1987), the lower afternoon gc values in the non-fruit-ing canopy were partially a consequence of the decrease in A. Thus, canopy conductance can also be modulated by feedback control in response to assimilation capacity.
For both canopies, the low light compensation point ob-served in the afternoon could be related to the positive effect of T on A (data not shown). Because of the thermal inertia of air, similar Q values tended to occur at higher temperatures in the afternoon than in the morning. Despite their differing photosynthetic and transpiration responses, the fruiting and non-fruiting canopies showed similar diurnal ATR patterns, confirming the assumption that, under well-watered condi-tions, the vegetative--reproductive status of the tree controls the equilibrium between the processes of photosynthesis and tran-spiration by adjusting canopy conductance.
Conclusions
A primary role is ascribed to canopy conductance in control-ling whole-tree gas exchange. However, plant factors such as canopy structure, canopy leaf area and foliage area density also affect conductance, and consequently all contribute to modu-lating gas exchange of the whole canopy. Moreover,
non-sto-matal factors, which were closely related to source--sink rela-tionships and were affected by the presence of fruits, are also able to regulate CO2 exchange and induce adjustments in canopy conductance.
Analysis of the data collected by the whole canopy enclo-sure system indicates that this method offers an opportunity to overcome the complexity of scaling single-leaf data to the whole-canopy level. The technique also yields measured val-ues that can be compared with the results of theoretical scaling from leaf to canopy.
Acknowledgments
Research supported by the National Research Council of Italy, Special Project RAISA, Sub-project No. 2, Paper No. 2855. We thank Prof. E. Baldini and Drs. F. Rossi and S. Poni for critical reading of the manuscript and advice.
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Appendix A
Under the experimental conditions of the study, air mixing inside the chamber allows the assumption that the CO2 concen-tration ([CO2]) and absolute humidity (χ) inside and coming out of the chamber are equal. Hence, the temporal variability of [CO2] and χ inside the chamber can be described by the differential equations:
Because measurements are taken every three minutes and this is a shorter period than the time constant of the system, A, E, [CO2] and χ coming into the chamber are considered to remain stationary in the lagtime between two measurements. Thus, the solutions of the previous equations are:
A=φ
E=φ
S(χout(t+δt)−χin)+ V
Sδt(χout(t+ δt)− χout(t)).
Carbon dioxide concentration is expressed in g per cubic meter and is obtained by converting the direct measurements, ex-pressed in parts per million (ppm):
[CO2]= 103MCO2PT0
V0P0T xppm,
where MCO2 is the molar mass of CO2, V0 is the molar volume
at T0 and P0. The value of T0 is equal to 273 °K and P0 is equal to 1.013×105 Pa. T is the measured dry bulb temperature and P is the atmospheric pressure set equal to P0.
Absolute air humidity (χ) is related to partial water vapor pressure e:
χ =Mwe RT,
where Mw is the molar mass of water, R the gas constant and T the dry bulb temperature. Following a thermodynamic ap-proach, e is calculated from dry (T) and wet bulb temperatures (Tw) (Monteith and Unsworth 1990, Jones 1992):
e=es(Tw)−γ(T−Tw),
where es is the saturation vapor partial pressure, calculated as:
es(T)= 6.13753exp
T(18.564 −T/254.4)
(T+ 255.57)
,
Tw is the wet bulb temperature and γ is the psychrometric constant:
γ= cpP λMw
Mair ,
where λ is the latent heat for water evaporation, cp is the specific heat of air and Mair is the molar mass of air.
Appendix B
From the energy balance equation:
λE=ρcp γ Dgc,
where ρ is dry air density, D is the canopy air vapor pressure deficit, calculated as:
D=es(T)−e,
it is possible to compute the canopy conductance, gc. It is important to observe that the gc is the conductance to the diffusion of water vapor inside the chamber, that is the inverse of the sum of stomatal, boundary layer and aerodynamic resis-tances of the canopy enclosed in the chamber. Hence:
gc=
λγ ρcp
E D .
From the perfect gas law and relations previously reported:
gc= R Mw
ET
D =0.4619 ET
D,
