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Modeling gas exchange in a closed plant growth chamber
Adv. Space Res. Vol. 14, No. 11, pp. (11)337-(11)341, 1994 1994 COSPAR Printed in Great Britain. 0273-1177/94 $7.00 + 0.00
Pergamon
MODELING GAS EXCHANGE IN A CLOSED PLANT GROWTH CHAMBER J. D. Cornett,* J. E. Hendrix,* R. M. Wheeler,** C. W. Ross* and W. Z. Sadeh*** * Department of Plant Pathology and Weed Science, Center for Engineering Infrastructure and Sciences in Space, Colorado State University, Fort Collins, CO 80523, U.S.A. ** NASA Biological Research and Life Support Office, Kennedy Space Center, FL 32899, U.S.A. *** Department of Civil Engineering, Center for Engineering Infrastructure and Sciences in Space, Colorado State University, Fort Collins, CO 80523, U.S.A.
ABSTRACT Fluid transport models for fluxes of water vapor and CO2 have been developed for one crop of wheat and three crops of soybean grown in a dosed plant growth chamber. Correspondence among these fluxes is discussed. Maximum fluxes of gases are provided for engineering design requirements of fluid recycling equipment in growth chambers. Furthermore, to investigate the feasibility of generalized crop models, dimensionless representations of water vapor fluxes are presented. The feasibility of such generalized models and the need for additional data are discussed. INTRODUCTION To design fluid management hardware for Controlled Ecological Life Support Systems (CELSS), quantitative gas exchange data are required for complete crop growth periods. Such data are rare; however, Corey and Wheeler/1/have generated useable data. The goal of this study was to generate models in the form of selected empirical equations describing fluid transport in a closed plant growth chamber. Such models, or equations, are necessary to establish fluid recycling apparatus requirements. This is a preliminary evaluation of initial efforts to 1) use this method to model whole season gas exchange by plants and 2) develop more generalized models that could be utilized without regard to plant species or environmental parameters. METHODOLOGY Plants were grown by Corey and Wheeler/1/at the Breadboard Project, NASA Kennedy Space Center (KSC). Specific environmental parameters for each crop are provided in figure legends. Data include fluxes of water vapor produced by evapotranspiration (ET), CO2 used by net photosynthesis (PS,) and CO2 produced by dark respiration (Ra). Molar ratios of OJC02 for PS. and Rd are assumed to be 1.0. Lamps utilized were high pressure sodium (lIPS), metal halide (MH) and a mixture of the two (HPS/MH). Models of gas fluxes were produced using TableCurve software (Jandel Scientific). Carbon dioxide exchange was not detectable early in crop development and ET data for the first few days of crop development were not used because water vapor was added to facilitate seedling establishment. As a result of these limitations, an artificial zero-zero was added to each data set to limit candidate equations to those that have increasing slopes between zero and the first data point. Extrapolations beyond data points should be considered artifacts of the equations. This adjustment of the data sets is defensible from a physiological standpoint since gas exchange in small seedlings is minimal. Polynomials of 5 ~ to 8~ order were selected as compromises between best fit on the basis of degrees of freedom adjusted R 2 and physiologically acceptable models. These high order polynomials accommodate data fluctuations and determine flux maxima for design criteria. To (11)337
(11)338
J.D. Corner et al.
evaluate the feasibility of generalized modeling, the flux equations were made dimensionless by using respective function maxima and harvest date (DAP) as unity. RESULTS AND DISCUSSION Croo ET. PS.. R, Models Models of ET, PS, and 1~ for wheat (Triticum aestivum, L. cv. Yecora rojo) are plotted in Figure 1. Coefficients for these ~and for soybean models are in Table 1. Rates of the three processes increased almost linearly before rounding to their maxima. Maximum PS, occurred 23 days after planting (DAP) then fell sharply, leveling to a shoulder about 60 DAP before falling to about 25% of Figure 1
Figure 2
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Figs. 1-4. Models for ET, PSo and Ra for crop growth period. CO2 concentration, 1000 #tool/tool. 1. Wheat: light source, HPS; photon flux (PPF), 650 #mol/m2s or 130 W/m2; light/dark, 20/4 h; temperature, 20116*(]. 2. Soybean: light source, HPS; PPF, 815 #mol/m2s or 163 W/mS; light/dark, 12112 h; temperature, 26/20°C. 3. Soybean: light source, MH; PPF, 477/~mol/m2s or 104 W/m2; otherwise as Figure 2. 4. Soybean: light source, mixture of HPS and MH; PPF, 645 #mol/m2s or 134 W/m2; light/dark, 10/14 h; temperature, 26/20°C.
:2: _J
Modeling Gas Exchange in a Closed Plant Growth Chamber
(11)339
TABLE 1 Equation Parameters. Selected equations for wheat 0V) and soybean (SB) conform to the following general forms: y=a+bx+cx2+dx3+ex4+fx 5, y=a+bx+cx2+dx3+ex%fxS+gx%hx 7 and y f a + b x + c x 2 + d x 3 + ex4+ fxS+gx6+hxT+ixS. a
b
W-HPS ET PS. Rd
-8.8e-03 -1.4 -3.2e-01
3.1e-01 4.4e-01 -5.8e-02
3.2e-03 2.8e-01 1.5e-01
-4.3e-04 -2.1e-02 -1 .le-02
7.8e-06 6.3e-04 3. le-04
-4.3e-08 -9.7e-06 -4.6e-06
7.4e-08 3.3e-08
-2.2e-10 -9.7e-ll
SB- HPS ET PS. Rd
8.1e-02 5.7e-01 7.3e-02
-4.3e-01 -6.7 -8.8e-01
5.6e-02 9.5e-01 1.2e-01
-I .7e-03 -4.4e-02 -4.4e-03
2.0e-05 9.8e- 04 7.3e-05
-8. Ie-08 -I .2e-05 -5.0e-07
7.2e-08 4.5e-10
-I .Te- I0 6.3e- 12
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-3.7e-02 1.6e-01 - I . 5e-01
-3.7e-01 1.4 - 2.5e-01
4.6e-02 -3.5e-01 3.4e-02
-1.3e-03 3.5e-02 -9.9e-04
1.4e-05 - I . 5e-03 I . 2e-05
-5.1e-08 3.3e- 05 -4.8e- 08
-4. Ie-07
2.6e-09
5.5e-02 1.4e-01 9.1e-03
-4.9e-01 -4.2 -5.4e-01
5.2e-02 5.3e-01 6.0e-02
-I .4e-03 -2.1e-02 -2.0e-03
1.5e-05 4.3e-04 3.2e-05
-5.7e-08 -4.7e-06 -2.3e-07
2.7e-08 5.3e-I0
-6.0e-11 7.6e-13
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maximum at harvest. The pattern for P~ was similar. Fluxes of CO2 for PS, exceeded those for Rd at all times except at the end of the growth period. These patterns are expected, because maximum PS, usually occurs in newly expanded leaves, and maximum P~ generally occurs following high carbohydrate production/2,3,4/. The shoulder of PS. occurred during grain filling, a time of high carbohydrate demand. The ET maximum lagged the other two maxima by about 8 d and the second ET peak lagged the PS, shoulder even more. Figures 2, 3 and 4 represent models for three crops of soybean (Glycine max, [L.] Merr. cv. McCall) grown under three different light regimes. Curves exhibited distinct maxima for PS. that varied between 35 and 48 DAP. Furthermore, each PS, curve describes a shoulder late in the growth period, as was observed for wheat. Timing of computed P~ maxima were similar to those of PS,. Early in development, ET curves tracked PS. curves well. ET maxima lagged those of PS, for HPS and MH crops, but the ET maximum of the HPS/MH crop preceded the PS, maximum. For soybean, a shoulder on ET curves appeared late in development. Only under MH did that shoulder correspond to the PS. shoulder. Failure of correspondence of PS, and ET maxima for both wheat and soybean indicates that PS. was influenced by factors other than stomatal aperture, e.g. variable sink demand. Maximum Fluxe~ ~ d Rates Maximum fluxes and total daily rates (TDR) of H20 and CO: are in Table 2. These maxima are needed to determine design capacity of a growth chamber. Fluxes and TDR of ET were higher for all crops of soybean than for wheat. This was unexpected, because the light period that drives most of the ET was longer for wheat; however, the higher temperature of the soybean crops resulted in a greater vapor pressure deficit and may explain these differences in fiuxes and TDR. CO2 fluxes driven by PS, for two of the soybean crops were higher than for wheat, whereas the flux of the other crop was marginally lower. This was a result of taller soybean canopies receiving highest light intensity. However, the TDR of PS. were lower for soybeans than for wheat because soybeans were exposed to a shorter photoperiod. On a mass basis, the maximum flux of water vapor was 47 to 66 times that of CO2. Therefore, water is the major component to be cycled in the plant growth chamber. The Rcdriven CO2 flux for wheat was higher than those for soybean crops even though soybeans attained a greater biomass. This greater Rd flUX for wheat likely occurred because the
(11)340
J.D. Corner etal.
TABLE 2 Gas Exchange. Maximum fluxes and total daily rates CrDR) for wheat (W) and soybean (SB). Environmental parameters in legend for Figures 1-4. MAXII4UM FLUX ET W-HPS SB" HPS SB'NH SB" HPS/NH
L/m2 d** 5.8 6.7 6.9 6.6
PS. W'HPS SB" HPS SB-NH SB'HPS/MH
g/~h*** 232 268 276 264
4.2 5.6 4.2 5.1
X
kg/d
La. n~ 0.6 0 (1. <( > 0.4
116 134 138 132
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#mot/m2s * * 26.6 35.4 26.2 31.9
DIMENSIONLESS ET
11.6 6.6 4.8 4.8
1.8 1.0 0.76 O. 76
* Based on 24 h r a t e s in 20 m2 KSC chamber. * * Nax|mum model values. * * * Assuming 80~ o f ET during photoperfod. COz f o r PS. baaed on p h o t o p e r i o d s ; f o r R,, based on dark period.
0.15 0.25 0.18 0.21
Fig. 5. Dimensionless evapotranspiration for the four crops represented in Figures 1-4 such that flux and growth cycle are varied from zero to one for each crop separately.
longer photoperiod supplied more carbohydrate substrate used in Rd. The TDR of P,~-derived CO2 production for soybean were higher because of longer dark periods. Dimensionless Renresentations Dimensionless representations were developed for PS,, P~ and ET to study the possibility of developing generalized models. As an example, dimensionless plots for ET are presented in Figure 5. For soybeans, fluxes of water vapor increased almost linearly to their maxima at about 0.44 of the growth cycle and all had a shoulder between 0.85 and 0.90. The similarity of these curves indicates that a generalized model for a single cultivar under different environments may be feasible. For wheat, the curve profile was similar to those for soybean up to maximum flux except for a shift to an earlier portion of the growth cycle. These similarities indicate that a generalized model may be feasible across species for this early, most critical part of development, if a time shift is introduced. The second peak in ET for wheat at 0.85 was near the shoulders of soybean ET. The difference in relative magnitude between the shoulders for soybean and the second peak for wheat would argue against a generalized model across species; however, the correspondence in timing of shoulders for soybeans and the second peak for wheat supports the possibility of a generalized model. CONCLUDING REMARKS Some interesting preliminary generalizations regarding the interaction between environment and species have been discussed. These generalizations include correspondence and magnitude of flux maxima, comparison of relative fluxes throughout crop development, and interaction of processes. These results have borne out, in general terms, traditional physiological findings that there exists a relationship between the occurrence of maximal PS, and ET; and that maximum 1~ follows periods of high substrate production (PS.). This suggests that modeling whole season gas fluxes of crop stands has a sound physiological basis. Likewise, differences in calculated TDR for all three processes can be explained by widely accepted physiological principles. It is especially important to note that
Modeling Gas Exchange in a Closed Phmt Growth Chamber
(11)341
calculations of TDR for ET demonstrate that liquid water and water vapor will be the major fluids to be considered in designing a closed plant growth chamber. The possibility of developing generalized models of gas flux by plants using dimensionless plots shows promise. Preliminary results suggest that such modeling may be possible for single cultivars without regard to environmental conditions; however, this type of modeling across species lines may be possible only during early growth stages. Experiments should be conducted to specifically test the validity of these generalizations and conclusions. As noted above, existing data appropriate for this type of modeling are rare. Most modeling efforts are concerned with early growth and thus whole season measurements are ignored. This study suggests that important information can be gained by extending gas exchange measurements throughout the growing season. If gas exchange fluxes in plants can be simplified to fit widely applicable, generalized models, these models must be based on data collected from experiments designed to accommodate the various interactive processes that control these fluxes. Moreover, such models will provide a new perspective on physiological processes of whole plants. Acknowled2en~e~ts: The support of the Advanced Life Support Division, NASA Ames Research Center and the Controlled Ecological Life Support Systems Program, Life Sciences Division, Office of Space Science and Applications, NASA Headquarters is gratefully acknowledged. Partial support from NASA Space Grant College and Fellowship Program is also acknowledged. Suggestionsby Dr. Frank D. Moore, Professor of Horticulture, are appreciated. REFERENCES 1. K. A. Corey and R. M. Wheeler. Gas exchange in NASA's bi.omass production chamber. A preprototype human life support system. BioScience 42:503 (1992). 2. J. T. Baker, F. Laugel, K. J. Boote, and L. H. Allen, Jr. Effects of daytime carbon dioxide concentration on dark respiration in rice. Plant, Cell and Environ. 15:231 (1992). 3. K.J. McCree. Equations for the rate of dark respiration of white clover and grain sorghum, as functions of dry weight, photosynthetic rate, and temperature. Crop Sci. 14:509 (1974). 4. F. B. Salisbury, and C. W. Ross. Chapter 13. Plant Physiology, 4th ed., Wadsworth Publ. Co., Belmont, CA (1991).
JASR 14:11-W
Pergamon
MODELING GAS EXCHANGE IN A CLOSED PLANT GROWTH CHAMBER J. D. Cornett,* J. E. Hendrix,* R. M. Wheeler,** C. W. Ross* and W. Z. Sadeh*** * Department of Plant Pathology and Weed Science, Center for Engineering Infrastructure and Sciences in Space, Colorado State University, Fort Collins, CO 80523, U.S.A. ** NASA Biological Research and Life Support Office, Kennedy Space Center, FL 32899, U.S.A. *** Department of Civil Engineering, Center for Engineering Infrastructure and Sciences in Space, Colorado State University, Fort Collins, CO 80523, U.S.A.
ABSTRACT Fluid transport models for fluxes of water vapor and CO2 have been developed for one crop of wheat and three crops of soybean grown in a dosed plant growth chamber. Correspondence among these fluxes is discussed. Maximum fluxes of gases are provided for engineering design requirements of fluid recycling equipment in growth chambers. Furthermore, to investigate the feasibility of generalized crop models, dimensionless representations of water vapor fluxes are presented. The feasibility of such generalized models and the need for additional data are discussed. INTRODUCTION To design fluid management hardware for Controlled Ecological Life Support Systems (CELSS), quantitative gas exchange data are required for complete crop growth periods. Such data are rare; however, Corey and Wheeler/1/have generated useable data. The goal of this study was to generate models in the form of selected empirical equations describing fluid transport in a closed plant growth chamber. Such models, or equations, are necessary to establish fluid recycling apparatus requirements. This is a preliminary evaluation of initial efforts to 1) use this method to model whole season gas exchange by plants and 2) develop more generalized models that could be utilized without regard to plant species or environmental parameters. METHODOLOGY Plants were grown by Corey and Wheeler/1/at the Breadboard Project, NASA Kennedy Space Center (KSC). Specific environmental parameters for each crop are provided in figure legends. Data include fluxes of water vapor produced by evapotranspiration (ET), CO2 used by net photosynthesis (PS,) and CO2 produced by dark respiration (Ra). Molar ratios of OJC02 for PS. and Rd are assumed to be 1.0. Lamps utilized were high pressure sodium (lIPS), metal halide (MH) and a mixture of the two (HPS/MH). Models of gas fluxes were produced using TableCurve software (Jandel Scientific). Carbon dioxide exchange was not detectable early in crop development and ET data for the first few days of crop development were not used because water vapor was added to facilitate seedling establishment. As a result of these limitations, an artificial zero-zero was added to each data set to limit candidate equations to those that have increasing slopes between zero and the first data point. Extrapolations beyond data points should be considered artifacts of the equations. This adjustment of the data sets is defensible from a physiological standpoint since gas exchange in small seedlings is minimal. Polynomials of 5 ~ to 8~ order were selected as compromises between best fit on the basis of degrees of freedom adjusted R 2 and physiologically acceptable models. These high order polynomials accommodate data fluctuations and determine flux maxima for design criteria. To (11)337
(11)338
J.D. Corner et al.
evaluate the feasibility of generalized modeling, the flux equations were made dimensionless by using respective function maxima and harvest date (DAP) as unity. RESULTS AND DISCUSSION Croo ET. PS.. R, Models Models of ET, PS, and 1~ for wheat (Triticum aestivum, L. cv. Yecora rojo) are plotted in Figure 1. Coefficients for these ~and for soybean models are in Table 1. Rates of the three processes increased almost linearly before rounding to their maxima. Maximum PS, occurred 23 days after planting (DAP) then fell sharply, leveling to a shoulder about 60 DAP before falling to about 25% of Figure 1
Figure 2
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Figs. 1-4. Models for ET, PSo and Ra for crop growth period. CO2 concentration, 1000 #tool/tool. 1. Wheat: light source, HPS; photon flux (PPF), 650 #mol/m2s or 130 W/m2; light/dark, 20/4 h; temperature, 20116*(]. 2. Soybean: light source, HPS; PPF, 815 #mol/m2s or 163 W/mS; light/dark, 12112 h; temperature, 26/20°C. 3. Soybean: light source, MH; PPF, 477/~mol/m2s or 104 W/m2; otherwise as Figure 2. 4. Soybean: light source, mixture of HPS and MH; PPF, 645 #mol/m2s or 134 W/m2; light/dark, 10/14 h; temperature, 26/20°C.
:2: _J
Modeling Gas Exchange in a Closed Plant Growth Chamber
(11)339
TABLE 1 Equation Parameters. Selected equations for wheat 0V) and soybean (SB) conform to the following general forms: y=a+bx+cx2+dx3+ex4+fx 5, y=a+bx+cx2+dx3+ex%fxS+gx%hx 7 and y f a + b x + c x 2 + d x 3 + ex4+ fxS+gx6+hxT+ixS. a
b
W-HPS ET PS. Rd
-8.8e-03 -1.4 -3.2e-01
3.1e-01 4.4e-01 -5.8e-02
3.2e-03 2.8e-01 1.5e-01
-4.3e-04 -2.1e-02 -1 .le-02
7.8e-06 6.3e-04 3. le-04
-4.3e-08 -9.7e-06 -4.6e-06
7.4e-08 3.3e-08
-2.2e-10 -9.7e-ll
SB- HPS ET PS. Rd
8.1e-02 5.7e-01 7.3e-02
-4.3e-01 -6.7 -8.8e-01
5.6e-02 9.5e-01 1.2e-01
-I .7e-03 -4.4e-02 -4.4e-03
2.0e-05 9.8e- 04 7.3e-05
-8. Ie-08 -I .2e-05 -5.0e-07
7.2e-08 4.5e-10
-I .Te- I0 6.3e- 12
SB-NH ET PS. Rd
-3.7e-02 1.6e-01 - I . 5e-01
-3.7e-01 1.4 - 2.5e-01
4.6e-02 -3.5e-01 3.4e-02
-1.3e-03 3.5e-02 -9.9e-04
1.4e-05 - I . 5e-03 I . 2e-05
-5.1e-08 3.3e- 05 -4.8e- 08
-4. Ie-07
2.6e-09
5.5e-02 1.4e-01 9.1e-03
-4.9e-01 -4.2 -5.4e-01
5.2e-02 5.3e-01 6.0e-02
-I .4e-03 -2.1e-02 -2.0e-03
1.5e-05 4.3e-04 3.2e-05
-5.7e-08 -4.7e-06 -2.3e-07
2.7e-08 5.3e-I0
-6.0e-11 7.6e-13
SB-HPS/NH ET PS. Rd
c
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-6.8e- 12
Degrees of freedom adjusted R= for each equation as fottows: tJ-HPS: ET, 0.824; PS,, 0.903; R=, 0.87'6; SB-HPS: ET, 0.644; PS,, 0.936; Rd, 0.851; SE-NH: ET, 0.820; PSn, 0.964; Rd, 0.871; SB-HPS/NH: ET, 0.891; PS., 0.962; R~, 0.%3.
maximum at harvest. The pattern for P~ was similar. Fluxes of CO2 for PS, exceeded those for Rd at all times except at the end of the growth period. These patterns are expected, because maximum PS, usually occurs in newly expanded leaves, and maximum P~ generally occurs following high carbohydrate production/2,3,4/. The shoulder of PS. occurred during grain filling, a time of high carbohydrate demand. The ET maximum lagged the other two maxima by about 8 d and the second ET peak lagged the PS, shoulder even more. Figures 2, 3 and 4 represent models for three crops of soybean (Glycine max, [L.] Merr. cv. McCall) grown under three different light regimes. Curves exhibited distinct maxima for PS. that varied between 35 and 48 DAP. Furthermore, each PS, curve describes a shoulder late in the growth period, as was observed for wheat. Timing of computed P~ maxima were similar to those of PS,. Early in development, ET curves tracked PS. curves well. ET maxima lagged those of PS, for HPS and MH crops, but the ET maximum of the HPS/MH crop preceded the PS, maximum. For soybean, a shoulder on ET curves appeared late in development. Only under MH did that shoulder correspond to the PS. shoulder. Failure of correspondence of PS, and ET maxima for both wheat and soybean indicates that PS. was influenced by factors other than stomatal aperture, e.g. variable sink demand. Maximum Fluxe~ ~ d Rates Maximum fluxes and total daily rates (TDR) of H20 and CO: are in Table 2. These maxima are needed to determine design capacity of a growth chamber. Fluxes and TDR of ET were higher for all crops of soybean than for wheat. This was unexpected, because the light period that drives most of the ET was longer for wheat; however, the higher temperature of the soybean crops resulted in a greater vapor pressure deficit and may explain these differences in fiuxes and TDR. CO2 fluxes driven by PS, for two of the soybean crops were higher than for wheat, whereas the flux of the other crop was marginally lower. This was a result of taller soybean canopies receiving highest light intensity. However, the TDR of PS. were lower for soybeans than for wheat because soybeans were exposed to a shorter photoperiod. On a mass basis, the maximum flux of water vapor was 47 to 66 times that of CO2. Therefore, water is the major component to be cycled in the plant growth chamber. The Rcdriven CO2 flux for wheat was higher than those for soybean crops even though soybeans attained a greater biomass. This greater Rd flUX for wheat likely occurred because the
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J.D. Corner etal.
TABLE 2 Gas Exchange. Maximum fluxes and total daily rates CrDR) for wheat (W) and soybean (SB). Environmental parameters in legend for Figures 1-4. MAXII4UM FLUX ET W-HPS SB" HPS SB'NH SB" HPS/NH
L/m2 d** 5.8 6.7 6.9 6.6
PS. W'HPS SB" HPS SB-NH SB'HPS/MH
g/~h*** 232 268 276 264
4.2 5.6 4.2 5.1
X
kg/d
La. n~ 0.6 0 (1. <( > 0.4
116 134 138 132
0
0.8
r4
,,'II;IMH
/
........
"i- 0.2
1.69 1.35 1.00 1.01
°°
0.0
0.2 '
0i 4
0i 8
0.8 '
1.0
GROWTH CYCLE
R,, W-HPS SB-HPS SB-MH SB-HPS/NH
1.0
TDR*
#mot/m2s * * 26.6 35.4 26.2 31.9
DIMENSIONLESS ET
11.6 6.6 4.8 4.8
1.8 1.0 0.76 O. 76
* Based on 24 h r a t e s in 20 m2 KSC chamber. * * Nax|mum model values. * * * Assuming 80~ o f ET during photoperfod. COz f o r PS. baaed on p h o t o p e r i o d s ; f o r R,, based on dark period.
0.15 0.25 0.18 0.21
Fig. 5. Dimensionless evapotranspiration for the four crops represented in Figures 1-4 such that flux and growth cycle are varied from zero to one for each crop separately.
longer photoperiod supplied more carbohydrate substrate used in Rd. The TDR of P,~-derived CO2 production for soybean were higher because of longer dark periods. Dimensionless Renresentations Dimensionless representations were developed for PS,, P~ and ET to study the possibility of developing generalized models. As an example, dimensionless plots for ET are presented in Figure 5. For soybeans, fluxes of water vapor increased almost linearly to their maxima at about 0.44 of the growth cycle and all had a shoulder between 0.85 and 0.90. The similarity of these curves indicates that a generalized model for a single cultivar under different environments may be feasible. For wheat, the curve profile was similar to those for soybean up to maximum flux except for a shift to an earlier portion of the growth cycle. These similarities indicate that a generalized model may be feasible across species for this early, most critical part of development, if a time shift is introduced. The second peak in ET for wheat at 0.85 was near the shoulders of soybean ET. The difference in relative magnitude between the shoulders for soybean and the second peak for wheat would argue against a generalized model across species; however, the correspondence in timing of shoulders for soybeans and the second peak for wheat supports the possibility of a generalized model. CONCLUDING REMARKS Some interesting preliminary generalizations regarding the interaction between environment and species have been discussed. These generalizations include correspondence and magnitude of flux maxima, comparison of relative fluxes throughout crop development, and interaction of processes. These results have borne out, in general terms, traditional physiological findings that there exists a relationship between the occurrence of maximal PS, and ET; and that maximum 1~ follows periods of high substrate production (PS.). This suggests that modeling whole season gas fluxes of crop stands has a sound physiological basis. Likewise, differences in calculated TDR for all three processes can be explained by widely accepted physiological principles. It is especially important to note that
Modeling Gas Exchange in a Closed Phmt Growth Chamber
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calculations of TDR for ET demonstrate that liquid water and water vapor will be the major fluids to be considered in designing a closed plant growth chamber. The possibility of developing generalized models of gas flux by plants using dimensionless plots shows promise. Preliminary results suggest that such modeling may be possible for single cultivars without regard to environmental conditions; however, this type of modeling across species lines may be possible only during early growth stages. Experiments should be conducted to specifically test the validity of these generalizations and conclusions. As noted above, existing data appropriate for this type of modeling are rare. Most modeling efforts are concerned with early growth and thus whole season measurements are ignored. This study suggests that important information can be gained by extending gas exchange measurements throughout the growing season. If gas exchange fluxes in plants can be simplified to fit widely applicable, generalized models, these models must be based on data collected from experiments designed to accommodate the various interactive processes that control these fluxes. Moreover, such models will provide a new perspective on physiological processes of whole plants. Acknowled2en~e~ts: The support of the Advanced Life Support Division, NASA Ames Research Center and the Controlled Ecological Life Support Systems Program, Life Sciences Division, Office of Space Science and Applications, NASA Headquarters is gratefully acknowledged. Partial support from NASA Space Grant College and Fellowship Program is also acknowledged. Suggestionsby Dr. Frank D. Moore, Professor of Horticulture, are appreciated. REFERENCES 1. K. A. Corey and R. M. Wheeler. Gas exchange in NASA's bi.omass production chamber. A preprototype human life support system. BioScience 42:503 (1992). 2. J. T. Baker, F. Laugel, K. J. Boote, and L. H. Allen, Jr. Effects of daytime carbon dioxide concentration on dark respiration in rice. Plant, Cell and Environ. 15:231 (1992). 3. K.J. McCree. Equations for the rate of dark respiration of white clover and grain sorghum, as functions of dry weight, photosynthetic rate, and temperature. Crop Sci. 14:509 (1974). 4. F. B. Salisbury, and C. W. Ross. Chapter 13. Plant Physiology, 4th ed., Wadsworth Publ. Co., Belmont, CA (1991).
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