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Plant Evapotranspiration in a Greenhouse on Mars

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PAGE 1

PLANT EVAPOTRANSPIRATION IN A GREENHOUSE ON MARS By ERIN GEORGETTE WILKERSON A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2005

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Copyright 2005 by Erin Georgette Wilkerson

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Dedicated to the memory of my grandmothe r, Elsie Bell Wilkerson, whose sweet spirit and strong faith will always challenge and encourage me

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iv ACKNOWLEDGMENTS I thank the engineers and sc ientists who took time from their busy schedules to invest in my professional development and my work. My major professor, Dr. Ray Bucklin, was a patient advisor and source of wisdom. He gave me freedom to explore my research topic, yet was readily available when problems arose. My committee, Dr. Khe Chau, Dr. Dennis McConnell, Dr. Jim Jone s, and Dr. Charles Beatty, very kindly challenged me to be a better engineer and re searcher. Dr. Ray Wheeler, Dr. Phil Fowler, and Dr. John Sager welcomed me to the Space Life Sciences Lab and took me under their wings while I learned the ropes at KSC. Dr. Hyeon-Hye Kim and the folks from Dynamac taught me how to grow radishes and always had answers to my many questions. The KSC Prototype Shop guys built some beautiful bases for me in exchange for a few cookies. I may have learned a lot of math, biology, a nd physics these past three years, but I have learned so much more about myself and the wonderful people in my life. Dr. Stephanie Reeder may have grown up in Florid a, but she was destined to find her way to the mountains and my life. The most beauti ful engineers I know, Dr. Czarena Crofcheck, Dr. Mari Chinn, and Dr. Grace Danao, are the be st colleagues and friends a girl could ask for. Jennifer DeFoe and Angela Archer have supported me for many years. Im so blessed to have two such amazing cheerleader s in my corner! My beautiful, awesome big sis Kathy has enriched my life in so ma ny ways. I always wanted a sister and I sure picked a good one! Newman Webb has very patiently put up with my fussing and

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v complaining the past couple of years, all th e while reminding me what I was here for and all that I have to look forward to. And my wonderful family, Daddy, Momma, and Wesley, have loved and suppor ted me unconditionally. They have taught me how to work hard and how to treat people right.

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vi TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES.............................................................................................................ix LIST OF FIGURES.............................................................................................................x ABSTRACT.....................................................................................................................xiii CHAPTER 1 GENERAL INTRODUCTION....................................................................................1 Low-Pressure, Inflatable Greenhouse...........................................................................2 Growing Plants in Reduced Pressures..........................................................................3 Evapotranspiration Model............................................................................................5 Research Objectives......................................................................................................8 Dissertation Organization.............................................................................................9 2 DEVELOPMENT OF SMALL-SCALE PRESSURE-CONTROLLED PLANT CHAMBERS..............................................................................................................11 Literature Review.......................................................................................................11 Objectives...................................................................................................................13 Bell Jar System...........................................................................................................14 Data Acquisition and Control.....................................................................................20 Instrumentation....................................................................................................20 Temperature and Humidity Control....................................................................22 Pressure and Carbon Dioxide Concentration Control.........................................23 Light Control.......................................................................................................25 Performance Testing...................................................................................................26 Pressure................................................................................................................26 Carbon dioxide....................................................................................................27 Air Temperature and Relative Humidity.............................................................29 Conclusions and Future Development........................................................................31 3 EFFECTS OF PRESSURE ON LEAF CONVECTIVE HEAT TRANSFER...........33

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vii Literature Review.......................................................................................................33 Convection Heat Transfer....................................................................................34 External resistance........................................................................................37 Boundary layer thickness.............................................................................38 Objectives...................................................................................................................39 Materials and Methods...............................................................................................39 Results and Discussion...............................................................................................46 Model Performance.............................................................................................51 Boundary Layer Thickness..................................................................................54 Conclusions.................................................................................................................56 4 SURFACE RESISTANCE TO EVAPOTRANSPIRATION IN REDUCED PRESSURE ENVIRONMENTS................................................................................57 Literature Review.......................................................................................................57 Effects of Environmental Vari ables on Stomatal Control...................................57 Vapor pressure deficit..................................................................................58 Carbon dioxide.............................................................................................59 Photosynthetically active radiation..............................................................60 Mass Diffusivity and St omatal Resistance..........................................................60 Plant Adaptation and Surface Resistance............................................................62 Objectives...................................................................................................................63 Materials and Methods...............................................................................................64 Plant Material......................................................................................................64 Evapotranspiration Measurement........................................................................65 Experimental Design...........................................................................................66 Model Development............................................................................................67 Results and Discussion...............................................................................................70 Conclusions.................................................................................................................77 5 EVAPOTRANSPIRATION MODEL PERFORMANCE IN MARS GREENHOUSE CONDITIONS................................................................................78 Objectives...................................................................................................................79 Materials and Methods...............................................................................................79 Results and Discussion...............................................................................................80 Sensitivity Analysis.............................................................................................81 Error Analysis......................................................................................................82 Conclusions.................................................................................................................85 6 LEAF TEMPERATURE IN A MARS GREENHOUSE...........................................86 Literature Review.......................................................................................................86 Objectives...................................................................................................................87 Materials and Methods...............................................................................................88 Results and Discussion...............................................................................................89 Infrared Thermocouple Performance..................................................................89

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viii Effects of Evapotranspiration at Redu ced Pressures on Leaf Temperature........90 Leaf Temperature in a Mars Greenhouse............................................................92 Conclusions.................................................................................................................95 7 CONCLUSIONS AND FU TURE RESEARCH........................................................96 LIST OF REFERENCES.................................................................................................101 APPENDIX A SENSOR CALIBRATIONS.....................................................................................106 Pressure..............................................................................................................106 Leaf Temperature..............................................................................................106 Air Temperature................................................................................................109 Weight...............................................................................................................109 Carbon Dioxide Concentration..........................................................................110 Oxygen concentration........................................................................................112 B SENSOR ERROR BUDGETS.................................................................................113 Voltage Input Module (SNAP-AIV-4)..............................................................113 Voltage Input Module (SNAP-AITM-2)...........................................................113 Pressure..............................................................................................................114 Relative Humidity.............................................................................................114 Oxygen..............................................................................................................115 Carbon Dioxide.................................................................................................115 Leaf temperature................................................................................................115 Air temperature..................................................................................................116 C BELL JAR BASE DRAWINGS..............................................................................117 D BELL JAR CONTROL ALGORITHM...................................................................122 Data Buffer Routine..........................................................................................122 Variable Update Routine...................................................................................126 Fan Control Routine..........................................................................................128 Carbon Dioxide and Pressure Control...............................................................129 Temperature and Relative Humidity Control....................................................135 E EVAPOTRANSPIRATION MODEL......................................................................140 BIOGRAPHICAL SKETCH...........................................................................................143

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ix LIST OF TABLES Table page 2-1 Descriptions and applications of Opto 22 I/O modules used in this research..........20 2-2 Calibrated sensor accuracies....................................................................................21 2-3 Performance of pressu re control algorithm..............................................................26 2-4 Bell jar leakage rates................................................................................................27 2-5 Performance of CO2 control algorithm at 12 kPa with plants..................................29 2-6 Performance of the air te mperature and relative humid ity control algorithm at 12 kPa with plants.........................................................................................................31 4-1 Controlled environment chamber conditions...........................................................65 4-2 Evapotranspiration treatment structure....................................................................67 4-3 Evapotranspiration and resistance results................................................................73 4-4 Root mean square error of surface resistance model................................................77 5-1 Parameter descriptions and reference values...........................................................79 5-2. Sensitivity analysis of the evap otranspiration model for Mars greenhouse conditions.................................................................................................................82 5-3 Change in evapotranspira tion rate and estimated error of parameters for overall error calculation........................................................................................................83 6-1 Comparison of temperature sensors for leaf temperature measurement..................89 6-2 Effects of pressure on evapotrans piration rate and leaf temperature.......................91 6-3 Leaf temperature model results for 12 and 101 kPa.................................................94 A-1 Slope and intercept equations for carbon dioxide sensors.....................................111 A-2 Slope equations for the oxygen sensors.................................................................112

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x LIST OF FIGURES Figure page 1-1 Artists conception of a future Mars colony...............................................................1 1-2 Leaf to air vapor pres sure deficit approximation.......................................................7 2-1 Schematic of pressure controlled plant chambers....................................................15 2-2 Pressure controlled plant chambers..........................................................................15 2-3 Schematic of one pressure controlled plant chamber...............................................16 2-4 Picture of one of the three pr essure controlled plant chambers...............................17 2-5 Light level control....................................................................................................25 2-6 CO2 control without plants at standard pressure......................................................27 2-7 Effect of vacuum pump on CO2 control at low pressures........................................28 2-8 CO2 control with plants at 12 kPa............................................................................29 2-9 Air temperature and relative humidity control at 12 kPa with plants......................31 3-1 Velocity boundary layer ove r a horizontal flat plate................................................34 3-2 Thermal boundary layer over a horizontal flat plate that is warmer than the surrounding air.........................................................................................................35 3-3 Thermal boundary layer over a horizontal flat plate that is cooler than the surrounding air.........................................................................................................35 3-4 Leaf replica...............................................................................................................40 3-5 Convection heat transf er experimental setup...........................................................41 3-6 Temperature profile for leaf replica du ring heating and subse quent cooling phase at 101 kPa and an air velocity of 5.8 m s-1...............................................................42 3-7 Transformed cooling data for the leaf re plica at 101 kPa and an air velocity of 5.8 m s-1....................................................................................................................45

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xi 3-8 Surface temperature of leaf replica du ring heating and subsequent cooling phase for four air velocity treatments at 12 kPa.................................................................47 3-9 Transformed surface temperature da ta for leaf replica at 12 kPa............................47 3-10 Surface temperature of leaf replica du ring heating and subsequent cooling phase at 33 kPa...................................................................................................................48 3-11 Transformed surface temperature da ta for leaf replica at 33 kPa............................48 3-12 Surface temperature of leaf replica du ring heating and subsequent cooling phase at 66 kPa...................................................................................................................49 3-13 Transformed surface temperature da ta for leaf replica at 66 kPa............................49 3-14 Surface temperature of leaf replica du ring heating and subsequent cooling phase at 101 kPa.................................................................................................................50 3-15 Transformed surface temperature da ta for leaf replica at 101 kPa..........................50 3-16 Measured and predicted values for ex ternal resistance of leaf replica as a function of pressure and four levels of air velocity..................................................52 3-17 Rate of heat transfer from leaf replica as a function of pressure and air velocity....52 3-18 External resistance model performance...................................................................53 3-19 External resistance model error................................................................................54 3-20 Effect of atmospheric pressure on b oundary layer thickness of a horizontal flat plate..........................................................................................................................55 3-21. Effect of air velocity on boundary laye r thickness of a horizontal flat plate............55 4-1 The effect of pressure on ma ss diffusivity of water in air........................................61 4-2 Leaf temperature transient respons e to changes in total pressure............................66 4-3 Visual observations of water status at 101 and 12 kPa............................................74 4-4 Effects of pressure and CO2 on evapotranspiration.................................................75 4-5 Effect of CO2 on surface resistance..........................................................................75 4-6 Effects of pressure and PAR on evapotranspiration.................................................76 4-7 Actual and predicted values of surface resistance at 40 Pa and 341 mol m-2 s-1...76 5-1 Predicted and measured evapotranspira tion rate as a function of pressure..............81

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xii 5-2 Model performance at reference conditions.............................................................83 5-3 Model performance in elevated CO2........................................................................84 5-4 Model performance in low PAR conditions.............................................................84 6-1 Leaf temperature measurement at 25 kPa................................................................90 6-2 Effect of pressure on leaf -to-air temperature difference..........................................91 6-3 Effect of evapotranspiration rate on leaf-to-air temperature difference...................92 6-4 Effects of net radiation on l eaf-to-air temperature difference..................................94 A-1 Pressure sensor calibration.....................................................................................107 A-2 Infrared sensor calibration......................................................................................108 A-3 Thermocouple calibration......................................................................................108 A-4 Load cell calibration...............................................................................................109 A-5 Carbon dioxide sensor calibration..........................................................................111 C-1 Top view of bell jar base........................................................................................118 C-2 Bottom view of bell jar base..................................................................................119 C-3 Bell jar base top plate.............................................................................................120 C-4 Cooling coil............................................................................................................121

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xiii Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy PLANT EVAPOTRANSPIRATION IN A GREENHOUSE ON MARS By Erin Georgette Wilkerson December 2005 Chair: Ray A. Bucklin Major Department: Agricultur al and Biological Engineering Successful crop production is vital to manned missions to Mars. Plants play integral roles in conceptual life-support systems as sources of food, oxygen, and waste treatment. Constraints of building a structure on the Martian surface to withstand Earth-similar interior air pressures make it necessary to develop plant growth systems capable of operating in air pressures as low as 0.1 to 0.3 atm (10 30 kPa). Research has shown that plants are capable of surviving in such environments, but have increased rates of water loss. The enormous costs associated with launching a manned mission to Mars make it crucial that plants be not only capable of survival, but also of producing fruit and seed. Plant growth and development, and t hus, performance of a biological life-support system are highly dependent on plant environmen tal responses. Theref ore, it is important that the interactions between plants and th e environment of a Mars greenhouse are well understood.

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xiv A model was used to predict the rate of evapotranspiration in response to changes in pressure, CO2, and light. The model was compared to empirical data obtained in experiments performed in a system of three small-scale low pressure controlled environment chambers built for this research. The system provided control of pressure, CO2 concentration, air temperatur e, and relative humidity and measured plant weight and leaf temperature. The rate of evapotranspiration changed little when pressure was 33 kPa and greater, but increased significantly at 12 kPa. Plants quickly wilted when pressure was 12 kPa and CO2 was 40 Pa. Reduced pressure increased the rate of evapotranspiration by decreasing resistances to sensible and la tent heat loss as well as reducing the effectiveness of convection. However, when CO2 concentration was increased from 40 to 150 Pa, stomata closed and evapotranspiration decreased even at the lowest pressure. Thus, plants are capable of gr owing at extreme low pressures, but are more sensitive to changes in other environmental parameters. In a low pressure Mars greenhouse, failure of the control system will likely result in crop failure.

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1 CHAPTER 1 GENERAL INTRODUCTION For a long-term manned mission in space (~ 3 years), the costs of transporting and storing consumable resources (e.g. food, oxygen) are not feasible and resources must be produced in situ. Preliminary strategies for a manned mission to Mars include a greenhouse for the production of vascular plants. Growing pl ants provide essential life support functions such as food producti on, oxygen production and waste treatment (Drysdale et al., 1999) and psyc hological benefits associated with the sensory value of fresh food and of nurturing plan ts (Corey et al., 2002). Figure 1-1. Artists conception of a future Mars colony. The settlement includes an inflated greenhouse for food and pr oduction, oxygen production, and waste treatment.

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2 Low-Pressure, Inflatable Greenhouse One possible concept, currently being devel oped by researchers at the University of Florida and the Kennedy Space Center, is an inflatable greenhouse system. Such a system would be autonomous and could be deployed during an unmanned mission 100 to 120 days prior to the crew's arrival (Fowle r et al., 2001). The purpose of a greenhouse on Mars is no different than on Earth to ove rcome "climatic adversity" (Hanan, 1998). However, the Martian climate presents se veral new and interesting challenges. Reductions in gravity, atmospheri c pressure, light levels, and temperature all significantly affect the design and control of a greenhouse (B ucklin et al., 2004). The climatic factor of greatest concern for plant grow th and development is pressure. The atmospheric pressure on Mars varies greatly with location, but is always less than one-hundredth that of Earth sea level (101.3 kPa) and for stru ctural design purposes can be considered equal to zero (Bucklin et al., 2004). It is possible to build a structure capable of withstanding a pressure diffe rential of 100 kPa as would result for a greenhouse maintaining Earth-similar pressures on Mars. However, the costs associated with such a massive structure are prohibitive. Also, it is desirable fo r the structure to be transparent in order to make use of the s un's radiant energy for plant photosynthesis as well as heating (Corey at al., 2002; Ferl et al., 2002). Consequently, it is important to minimize the pressure differential across the structure surface by maintaining a low atmospheric pressure within. No official deci sions have been made regarding the internal pressure of a Mars greenhouse. Present st rategies call for less than one-third the atmospheric pressure of Earth (Bucklin et al. 2004; Fowl er et al., 2001).

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3 Growing Plants in Reduced Pressures Based on the results of previous studies, avoiding excessive water losses and subsequent dehydration is likely to be a challenge in maintain ing productivity of plants in a low atmosphere Mars greenhouse (0.1 0.2 atm). Large reductions in atmospheric pressure have been shown to significantly in crease the rate of evapotranspiration (Andre and Massimino, 1992; Corey at al., 1997; Dauni cht and Brinkjans, 1992; Goto et al., 1995; Goto et al., 1996; Goto et al., 2002; Ma ssimino and Andre, 1999; Rule and Staby, 1981; Rygalov et al., 2002). The most likel y explanation for these increases is the inversely proportional relationship between pr essure and mass diffusivity. As the mass diffusivities of CO2 and water increase, so do the boundary layer and stomatal conductances to CO2 and water exchange (Nobel, 1999; Monteith and Unsworth, 1990). Because evapotranspiration is increased at low pressure, the health and productivity of plants grown at low pressures depends on their ability to mainta in turgidity in an environment with a high transpirational load. In their studies on tomato plants, Daunicht and Brinkjans (1992), showed slight decreas es (<10%) in biomass and leaf area and a slight increase (10%) in th e dry weight of plants grow n at 40 kPa versus 100 kPa ( Earth atmospheric pressure). On the last day of their study, the photosynthesis and transpiration rates were 12 and 39% higher, respectively, for the plants grown at the lower pressure. They concl uded that, in spite of having a higher photosynthesis rate, plants grown at the lower pressure were mo st significantly affected by the increase in transpiration rate, which they considered to be the cause of reduced growth. In experiments by Goto et al. (2002) vegetative rice plants were grown in one of three total pressure environments: 34, 50, and 100 kPa. Growth, as measured by plant height and

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4 dry weight, were statistically similar for 50 and 100 kPa, but significantly reduced at 34 kPa. They also concluded that this grow th inhibition at extreme low pressures was caused by water stress. This is a reasonabl e conclusion based on ear lier studies by the same research group in which rates of transp iration for maize were approximately four times higher at 10 kPa than at 100 kPa (Goto et al, 1996). Experiments to measure the open water surface evaporation by Rygalov et al (2002) showed marked increases at total pressures less than 25 kPa. These low pressures ( 25 kPa) correspond to the design internal pressure range current ly being considered for the Mars greenhouse (Bucklin et al., 2004). Increases in mass diffusivity may not be the only reason for increases in evapotranspiration at low pressu res. Goto et al. (1996) inco rporated a simple model for the changes in stomatal and boundary layer resistances at low pressures to predict transpiration rate as a function of vapor pre ssure deficit (VPD) and resistance to water vapor transfer. In this model, the resistan ces were adjusted proportional to changes in mass diffusivity as pressure decreased. In ot her words, it was assumed that the stomatal opening remained the same at all pressures and changes in stomatal resistance were caused only by an increase in the mass diffusivi ty of water vapor. With their assumptions that stomatal and boundary layer resistances were affected only by pressure and VPD remained constant, the measured transpirati on rates showed smaller incremental increases than simulated rates. Goto et al. (1996) hypot hesized that stomatal control might also be affected by pressure changes. Decreases in stomatal aperture at low pressures, but constant VPD, seem likely considering the increases in evaporation rate and recent research claiming that stomatal control is a f unction of the rate of water loss rather than

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5 humidity (Monteith, 1995). It was also s hown in work by Paul et al. (2004) that Arabidopsis plants subjected to reduced pressures show gene e xpressions as if they are in drought stress despite no visible signs of desiccation. Stomatal controls, and consequently transpiration and photosynt hesis rates, are also affected by CO2 concentration, VPD, and photosynthetically ac tive radiation (PAR) (Jarvis, 1976). The effects of interaction between pr essure and these vari ables have not been explored. Evapotranspiration Model The Penman-Monteith evapotranspiration model (Monteith, 1965) has been used extensively over the past several decades to predict plant water loss rates in field and greenhouse conditions. Based on work by Penman (1948) and later modified by Monteith, the model predicts the evapotranspira tion of plants as driv en by convective and radiative forces and incorporat es the resistances of the cr op canopy to water vapor loss. Derivation of the Penman-Monteith evapotra nspiration model begins with a steadystate energy balance of the plant canopy (equation 1-1). 0 LE H Rn (1-1) where: Rn = net radiation, W m-2 H = sensible heat flux, W m-2 LE = latent heat flux, W m-2 Sensible heat flux, H, is estimated by equation 1-2. h air leaf p ar ) T T ( c H (1-2) where: a = density of air, kg m-3 cp = specific heat of air at constant pressure, J kg-1 oC-1 Tleaf = leaf temperature, oC Tair = air temperature, oC rh = external resistance for sensib le heat transfer by convection, s m-1

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6 Equation 1-3 gives the estimation for the latent heat flux, LE. ) r r ( VPD c LEh s air leaf p a (1-3) where: VPDleaf-air = leaf to air vapor pressure deficit, kPa ) e e ( VPDa sleaf air leaf (1-4) esleaf = saturation vapor pressure at leaf temperature, kPa ea = vapor pressure, kPa = psychrometric constant, Pa oC-1 622 0. Pcp (1-5) = latent heat of vaporization, kJ kg-1 P = pressure, Pa rs = surface resistance of canopy to water vapor transfer, s m-1 Calculation of the sensible and latent h eat fluxes of equations 1-2 and 1-3 requires surface temperature, a variable that is typi cally unknown. Penman (1948) incorporated a simplifying assumption to eliminate leaf te mperature from the model. Equation 1-6 shows an approximation for VPDleaf-air calculated from air vapor pressure deficit (VPDair), the leaf to air temperature difference, and th e slope of the saturation vapor pressure curve (). ) T T ( VPD VPDair leaf air air leaf (1-6) An example is shown in Figure 1-2. Cons ider a leaf whose surface temperature is 20 oC in a 24 oC airstream. Saturation vapor pressu re at a given temperature, T, is calculated by equation 1-7. T T s* ) T ( e3 237 5 710 61078 0 (1-7)

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7 where: es(T) = saturation vapor pressu re at temperature T, kPa T = temperature, C In Figure 1-2 the dashed line is a straight line with slope equal to the saturation vapor pressure curve at the air temperature, 24 oC. The difference between the actual VPDleaf-air and the estimation from equation 1-6 is only 0.08 kPa. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 182022242628303234 Temperature, CSaturation vapor pressure, kPa VPDair = esa ea = 2.98 2.24 = 0.74 kP (Tair Tleaf) = 0.18*(24-20) = 0.72 ea = 1.49 kPa (esleaf ea) = 2.34 2.24 = 0.1 kP slope = =0.18 Figure 1-2. Leaf to air vapor pressure deficit approximation. To eliminate leaf surface temperature from the evapotranspiration model, Penman (1948) introduced an approximation for VPDleaf-air. This approach assumes that the saturation vapor pressure curve can be approximated by a straight line with slope calculated at air temperature for small differences be tween leaf and air temperature (figure adapted from Jones, 1992). Substituting equation 1-6 into 1-3 yields an equation for latent heat flux as a function of leaf to air temper ature difference. The leaf temperature can be eliminated by combining this new equation with 1-3. Subs titution into the heat balance of equation 1-1 and rearranging gives a standa rd from of the Penman-Monteith equation (Monteith, 1965) that does not require knowle dge of leaf temperature.

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8 h s h air pa a nr r r VPD c R LE 1 (1-8) The Penman-Monteith model requires the measurement or estimation of five variables to calculate the rate of evap otranspiration. The net radiation, Rn, and air vapor pressure deficit, VPDair, are environmental parameters. The external and surface resistances to evapotranspiration are estimated via heat transfer and biological models. The external resistance, rh, is the resistance to sensible heat transfer from the leaf and is calculated by convection heat transfer models. The surface resistance, rs, is the resistance of water vapor transfer through the leaf cuticle laye r and the stomata. Models for surface resistance account for the effects of e nvironmental conditions (e.g PAR, VPD, CO2) on stomatal behavior. The remain ing model parameters are physi cal constants for particular environmental conditions. Research Objectives Several researchers have show n that, despite increases in transpiration rate, plants are capable of surviving in low pressures a nd at moderate pressures may even experience enhanced growth due to higher photosynthesis rates. However, it is important that plants be not only capable of surviv al, but also of thriving to produce fruit and seed. To optimize life support functions plant responses must be considered along with physical constraints in the design of a greenhouse system for Mars. There is a significant amount of research modeling the effects of environmental factors on plant growth and development and a pplying these models to control systems in order to optimize the plant environment. Ther e is also an increasi ng amount of research on the effects of reduced atmospheric pressu re on short-term plant growth. This proposed research would extend and complement this previous research in several ways.

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9 Extreme low atmospheric pressure (< 20 kPa) is an environmental factor that has not yet been fully explored with regard to its effect on plant response especi ally with regard to interactions CO2, PAR, and VPD. Furthermore, leaf temperature has not been measured during reduced pressure experi ments and should provide useful information with regard to evapotranspiration rates and pl ant water status. The goal of this research is to improve the current understanding of the effe cts of atmospheric pressure on plant evapotranspiration via the use of short-duration experiments and mathematical modeling. Using a modeling approach makes it possible to test current understa nding of the effects of pressure on plant evapotra nspiration including stomatal conductance, which cannot be measured during low pressure expe riments using current technology. The objectives of this research are to: 1. Quantify the effects of pressure on external and surface resistances to canopy sensible and late nt heat transfer. 2. Investigate the effects of changes in ev apotranspiration rate at low pressures on leaf temperature of mature radish plants. 3. Incorporate the effects of atmospheric pressure into an evapotranspiration model and apply the model to predict wa ter loss rates of pl ants growing in a greenhouse on Mars. Dissertation Organization This dissertation is organized topically with chapters two through six each focusing on a different component of the research obj ectives. The development and performance of a small-scale low pressure sy stem is described in chapter two. This system was used to measure the effects of pressure on su rface resistance (chapter three), external resistance (chapter four), and leaf temperatur e (chapter five). Ch apters three and four

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10 include the development of mathematical m odels for surface and external resistances, respectively. In chapter six, these models are incorporated into a model to simulate evapotranspiration rate of radish plants as a function of pressure. Chapter seven addresses the overall co nclusions and future recommendati ons resulting from this body of work. The references list for the entire di ssertation is included following chapter 7. Appendices include supplementar y information such as sens or calibrations engineering drawings, and the control algorithm.

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11 CHAPTER 2 DEVELOPMENT OF SMALL-SCALE PRESSURE-CONTROLLED PLANT CHAMBERS Simulation of a Mars greenhouse environment is complex. It requires a chamber capable of maintaining low pressures for exte nded periods of time and a control system for many linked environmental parameters. The objective of this chapter is to describe the development of three small-scale pressure -controlled plant chambers used in this research. Literature Review As interest in advanced life support sy stems for Mars exploration missions has increased during the past severa l years, so has research activ ity regarding plant responses to low pressure environments. Researchers at Kennedy Space Center, Texas A&M University, University of Guelph, and Universi ty of Tokyo, as well as the University of Florida have each developed their own unique low pressure growth systems for studying the effects of Mars greenhouse conditions on plants. The Mars Dome, developed by research ers at Kennedy Space Center and the University of Florida, is a polycarbonate dome joined to a stainless steel base (Fowler at al., 2002). It was originally de signed to operate as a pressu rized vessel insi de a larger vacuum chamber, but added reinforcement ma de it possible to grow plants at reduced pressures ( 25 kPa) inside with Earth normal pr essure outside. A microcontroller system monitored and controlled temperature, pressure, humidity and plant irrigation.

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12 The main component of the Mars Dome was a central tower that contained all electronic components and temperature and humidity control devices. Nine scales surrounded the tower. Plants were weighe d throughout an expe riment to quantify evapotranspiration rates and activate irrigation events. A group of engineers and plan t scientists at Texas A&M University designed and built small cylindrical low-pressure plant growth chambers (Brown, 2002; Purswell, 2002). Six clear acrylic cyli nders each measuring 0.31 m in diameter and 0.91 m in height were placed in a larger environment ch amber to control light and temperature. A distributed control system m onitored and controlled pressure and concentrations of oxygen and carbon dioxide. A cooling co il provided a condensing surface for dehumidification. The University of Guelph developed two different types of lo w-pressure growth systems. They developed large vacuum ch ambers with hydroponics systems and some smaller steel cylindrical growth chambers. Both types of growth chambers offered control of critical environmental parameters pressure, light, temperature, relative humidity, and carbon dioxide concentration. Engineers at the University of Florid a designed and built two new low pressure systems. One was a large vacuum chamber placed inside a large freezer. The environment inside the vacuum chamber closel y resembled that of the Martian surface virtually no atmospheric pressure and temp eratures below freezing. A polycarbonate dome with steel base, similar to the Mars Dome described above, was placed inside the vacuum chamber and pressurized to simulate a greenhouse on Mars. Experiments were performed with this system to better understa nd heat transfer in a Martian greenhouse and

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13 develop temperature and humidity control syst ems for reduced pressures. A small-scale system for detailed plant experiments wa s also developed at UF and KSC and is described in the remainder of this chapter. Replication is necessary in plant experime nts to perform statistical analysis, draw sound conclusions, and extrapolat e conclusions to other situ ations. Plant experiments performed in the large low-pressure systems described above such as the Mars Dome and the UF low temperature vacuum chamber must be replicated in time. To save time and ensure identical treatments, it is desirable to perform replications simultaneously. Three bell jars were used in this research for plant experiments (see Figures 1 and 2). An aluminum base was designed and constructe d to house the temperature and humidity controls and wiring. A PC based data acqui sition and control system was developed to monitor and control pr essure, temperature, humidity, and carbon dioxide concentration. Plant weight and leaf temperature were also measured to evaluate evapotranspiration and water stress. Objectives The objective of the work described in th is chapter was to design and construct plant growth chambers to meet the following design criteria: Steadily maintain pressures as low as 10 kPa over long periods of time, Allow exterior lighting to reach plant canopy, Three simultaneous replications, Control pressure, air temperature, humidity, CO2 concentration, and Monitor environmental parameters, le af temperature, and plant weight.

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14 Bell Jar System Bell jars were selected as the primary component of the plant growth chambers because they were readily available and easy to replace. Glass bell ja rs, routinely used in vacuum studies, are strong and relatively easy to seal. The inside a nd outside diameter of each bell jar was 213 and 222 mm, respect ively They were 381 mm tall. New aluminum bases constructed by the Kennedy Space Center Design and Development Integration Branch (prototype s hop) were designed to house a cooling coil, humidifier, two fans, sensors, wiring, and fittings. Preliminary plant experiments performed in bell jars with off-the-shelf plas tic bases emphasized their small volume. It was difficult and awkward to accommodate a ll instrumentation, heating and cooling equipment, scale, and the plant. The new bases were deep enough to house these components below the plant as shown in Figures 3 and 4. Detailed engineering drawings of the base are in appendix 3. Ports for gases, water, and wiring were made in the bottom of the bell jar bases. Fittings for water and gases were fitted with o-rings and installed tightly to minimize leakage. To minimize costs, wire feedthr oughs were constructed in -house. Art clay was packed into the center of 1.905-cm bushings to hold wires in place. The thickness of the clay was 1.25 cm. Solid wires cut to length were inserted through th e clay. To minimize air passing through the wire insulation, about 0.5 cm was stripped away before wires were inserted. Epoxy was poured into both sides of the bushing so that the exposed portion of each wire was completely covered. Three wire feedthroughs containing nine wires and one with two type-T and one type -K thermocouples were made for each bell jar.

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15 Figure 2-1. Schematic of pressure controlled plant chambers. Expe rimental replication was achieved using three independently controlled bell jars. Figure 2-2. Pressure controlled plant chambers The small chambers were placed inside a larger plant growth chamber for high-quality exte rnal lighting.

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16 Figure 2-3. Schematic of one pre ssure controlled plant chamber.

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17 Figure 2-4. Picture of one of the thr ee pressure controlled plant chambers.

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18 The cooling coil was designed for dehu midification. From preliminary experiments (data not shown) the average ev apotranspiration rate for a single mature radish plant at 10 kPa was estima ted to be approximately 0.075 g H2O min-1. Since the lowest pressure treatment applied in this re search was 12 kPa, the evapotranspiration rate for 10 kPa was assumed to be a good approxi mation for the maximum expected in this research. Thus, the coil was designed to conde nse water at a rate equal to the assumed evapotranspiration rate for two mature radish plants at 10 kPa, 0.15 g H2O min-1. The steady-state heat transfer rate re quired to condense water was calculated by equation 1. ) h )( m ( qfg O H2 (2-1) where: q = heat tran sfer by condensation, W m = mass rate of water condensed, kg s-1 hfg = latent heat of vaporization, kJ kg-1 At 10 kPa, the latent heat of vaporization is 2389 kJ kg-1. The rate of heat transfer required to condense water at 0.15 gH2O min-1 was 6 W. The rate of heat transfer by water co ndensing on the coil was calculated by equation 2 with the average conve ctive heat transfer coeffici ent taken from Incropera and DeWitt (1996) for water condensation on a horizontal tube (equation 3). ) T T ( hA qcoil air coil (2-2) where: q = rate of heat transfer, W h = convective heat transfer coefficient, W m-2 K-1 Acoil = coil surface area, m2 Tair = air temperature, K

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19 Tcoil = coil surface temperature, K 4 1 3729 0 D ) T T ( N h k ) ( g hs sat l fg l v l l (2-3) where: h = convective heat transfer coefficient, W m-2 K-1 g = acceleration due to gravity, m s-2 l = density of liquid, kg m-3 v = density of vapor, kg m-3 kl = thermal conductivity of liquid, W m-1 K-1 hfg = latent heat of vaporization, kJ kg-1 N = number of horizontal tubes l = viscosity of liquid, kg s-1 m-1 Tsat = saturation temperature, K Ts = coil surface temperature, K D = tubing diameter, m The following values for properties of wa ter vapor and saturated liquid at 10 kPa were used: v = 0.111 kg m-3; l = 0.997 kg m-3 ; kl = 0.606 W m-1 K-1; and l = 934 x 10-6. The number of horizontal tubes, N, was a ssumed to be two for a coil and the tube diameter, D, was 0.0635 m (0.25 in). The resu lting heat transfer coefficient was 39.8 W m-2 K-1. Equating the two expressions for the rate of heat transfer (equ ations 1 and 2) and rearranging, yields an equation for calc ulating the coil surf ace area needed. ) T T ( h q Acoil air coil (2-4)

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20 Assuming that the coil temperature was 3 oC and air temperature was 24 oC, the coil surface area needed to condense 0.15 g H2O min-1 was calculated to be 0.0075 m2 (11.6 in2). Designed with a factor of safety of 2.5, the coil surface area was approximately 0.0187 m2 (29 in2). Data Acquisition and Control Environmental parameters within the bell jar were monitored and controlled by a PC-based data acquisition a nd control system. Pressure air temperature, and CO2 concentration of each bell jar we re controlled independently. Instrumentation An Opto 22 system was used for data acquisition and control. An I/O and communications processor (SNAP ultimate br ain, Opto22, Temecula, CA) managed 16 digital and analog I/O modules. Table 1 lists the modules used in this research and their application. The control program was written in ioControl 6. 0 (Opto 22, Temecula, CA), a flowchart based software designed for the Op to system. A user interface and display program was written in ioDisplay 6.0 software (Opto 22, Temecula, CA). Table 2-1. Descriptions and applications of Opto 22 I/O mo dules used in this research. Opto 22 module description Quantity Application SNAP-OAC5, 412-250 VAC input 1 Vacuum pump, solenoid valve SNAP-AOV-25, 0 to +10 VDC anal og output 1 Mass flow controller SNAP-ODC5SNK, 5-60 VDC output, sink 4 Solenoid valves, heaters, humidifiers, and fans SNAP-AITM, mV or thermocouple input 2 Infrared thermocouples SNAP-AITM2, mV or thermocouple input 5 Oxygen sensors, type-T thermocouples SNAP-AIV-4, 0 to +10 VDC analog input 3 Pressure, CO2, and relative humidity sensors and load cells

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21 All sensors were calibrated within one year prior to the start of experiments. Table 2 lists the calibrated accuracy of each sensor. Calibration data and error budget calculations for all sensors (e xcluding RH sensors which we re factory calibrated) are included in appendix A. Air temperature was measured by t ype-T thermocouples placed just below the height of th e plant canopy. They were sh ielded to reduce measurement error caused by the high radiation environmen t of the outside growth chamber. The thermocouples were calibrated using a two point calibration (10 oC and 40 oC) in a thermometer calibrator (TCAL, Sun Electronic Systems, Inc., Titusville, FL). Small integrated circuit sensors were used to monitor pressure (MPXH6115A6U, Freescale Semiconductor, Inc., Austin, TX) and rela tive humidity (HIH3610-003, Honeywell, Freeport, IL). The oxygen concentration was me asured using a galvanic cell type oxygen sensor (MAX-250, Maxtec, Salt Lake City, UT ). A low-cost OEM ultrasonic sensor was used to measure ca rbon dioxide (6004 CO2 module, Telaire, Goleta, CA). Leaf temperature was measured with infrared thermocouples (OS36SM-K-140F, Omega, Stamford, CT). Load cells were used fo r measuring plant weight (LPS-2kg, Celtron Technologies, Inc., Colvina, CA). Table 2-2. Calibrated sensor accuracies. All se nsors were calibrated within one year of the start of experiments. Parameter Sensor description Accuracy Air temperature Type-T thermocouples 0.5 oC Pressure Integrated circuit pressure sensor 0.53 kPa Relative humidity Integrated circuit RH sensor 2.1 % Oxygen Galvanic cell sensor 1.0 % Carbon dioxide Ultrasonic sensor 100 ppm (at 2000 ppm) Leaf temperature Mini infrared thermocouples 0.8 oC Plant weight Load cell 0.1 g

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22 Temperature and Humidity Control The air temperature of each bell jar was determined by the outside temperature of the bell jar, the coil temperature, and a heater At the beginning of the control loop, the current air temperature of each jar was compared to the setpoint temperature. The heater or cooling coil was activated as needed. Only one solenoid valve was available for controlling the water flow through the cooling coils. Thus, cooling coil temperature was not controlled independently and was simila r in the three bell jars at all times. Relative humidity was determined by the rate of plant evapotranspiration and the cooling coil temperature. When the relative humidity of any one of the three bell jars was higher than setpoint, the solenoid valve was opened to allow chilled water to flow through the coils. On the other hand, if relative humidity wa s too low in a bell jar, the humidifier for that bell jar was tu rned on until setpoint was achieved. The surface temperature of the copper cooling coils was determined by the temperature and flow rate of water flowing th rough them. Both of these factors were controlled by a chilled water ba th and were the same for a ll three bell jars. A solenoid valve in the chilled water lin e was opened to allow water to pass through the cooling coil if the air temperature or relative humidity of any one of the bell jars was too high. A 50 W, 1 power resistor was used as the he ating source in each bell jar. The power output of the resistor was set by vary ing the voltage across it. The Opto modules used to turn the heaters on/off were rated at 4 A. The resistors were 1 so the theoretical magnitude of the cu rrent draw (A) was equal to the magnitude of the voltage drop (V). However, at 8 A the current draw was only 4 A, within the limit of the Opto module. The power output of the heater was 28 W as calculated by equation 5.

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23 IV P (2-5) where P = power, W I = current, A V = voltage, V Each bell jar had two manually controlled fans (BM5115-04W-B50-L00, NMB Technologies, Chatsworth, CA) to maintain air ci rculation. The specifi ed air flow rate at standard pressure was 1.42 L s-1 (3 cfm) per fan. To reduce disturbance caused by high air velocities within the pl ant canopy, a pulse width modul ation routine was applied to reduce the fan flow rate. Power to the fans (12 V) was cycled on/off every 500 milliseconds. The volumetric flow rate of a gi ven fan is proportional to the fan speed and diameter (Henderson et al., 1997). Therefore, although th e mass flow rate of air decreased at lower pressures due to decreased air density, air velocity was not affected by pressure. Some leaf movement was observed at pressures as low as 12 kPa, leading to the conclusion that the fan output was ade quate for air mixing w ithin the range of pressures used in this research. All fans were turned on at the start and remained on throughout the duration of each experiment. Pressure and Carbon Dioxide Concentration Control Internal pressure and carbon dioxide concen tration control for a ll three bell jars were carried out in the same ioControl chart to avoid timing conf licts. At the beginning of the control loop, the current CO2 concentration (ppm) in each bell jar was compared to the setpoint concentration (ppm) for that bell jar. The measured and setpoint concentrations, given in units of parts per million, were converted to units of mass by equation 6 derived from the ideal gas law.

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24 airK bjT V p CO mass CO 3144 8 10 446 2 2 (2-6) where CO2_mass = mass of carbon dioxide inside, g [CO2] = carbon dioxide c oncentration, ppm p = bell jar pressure, Pa Vbj = bell jar volume, m3 TairK = absolute temperature of air inside bell jar, K The current mass of CO2 in each bell jar was compared to the setpoint mass for that particular jar. If the curr ent level was more than 120 ppm below setpoint, the mass of CO2 required to reach the setp oint was calculated and CO2 was added by the mass flow controller (FMA3202-CO2, Omega, Stamford, CT). To avoid overshoot that sometimes occurs when the mass flow controller (MFC)w as first turned on, the MFC is turned on and vented for 12 seconds before the thre e-way solenoid valve was switched to permit CO2 flow into one of the three bell jars. On e of three solenoids was opened to allow CO2 into the desired bell jar. The MFC flow ra te was always set at 40 ml/min. After time elapsed to add 70% of the calculated mass of CO2 needed to the bell jar the MFC was turned off. The bell jar solenoid valve remained open for 30 seconds to allow CO2 in the tubing to diffuse into the bell jar. With pl ants present, mixing within the bell jar was allowed for 60 seconds before the next CO2 addition. Without plants, mixing was allowed for ten minutes. Pressure control logic occu rred immediately following the carbon dioxide control. As in the CO2 control logic, pressures of the three bell jars were independently controlled one at a time. The pressure of each bell jar was compared to th e setpoint pressure of that

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25 jar. If pressure exceeded the setpoint by 1 kP a, the solenoid valve fo r that bell jar opened and the vacuum pump was turned on. The vacuum pump remained on until the current pressure was equal to the setpoint. After pr essure control of the bell jar, the entire CO2/pressure control loop began again. Light Control The light within the bell jars was controll ed externally to the system. The light level on the bases without the bell jars was 349.9, 372.8, 353.2 mol m-2 s-1 for chambers 1, 2, and 3 respectively. With the bell jars in place the light level were 338.4, 351.4, and 333.3 mol m-2 s-1. Thus, the average transmissivity of the bell jars was 95%. It is believed that the highly reflective surfaces of the external growth chamber contributed to such a large amount of light transmitted through the bell jar. A sock made of a lightweight screening material was configur ed for each bell jar to reduce the internal light level for low light treatments (see Figure 5). With the socks in place, the light levels inside the thre e bell jars were 158.5, 166.5, and 156.5 mol m-2 s-1. Figure 2-5. Light level control. Fine mesh screening material was used to reduce the PAR level inside the bell jars from an average of 341 mol m-2 s-1 to 161 mol m-2 s-1.

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26 Performance Testing Data from several experiments were used to quantify the perfor mance of the smallscale chambers. When applicable, environm ental data are reported as described in ANSI/ASAE Standard EP411.1 Guidelines for Measuring and Reporting Environmental Parameters for Plant Experiments in Growth Chambers. Pressure The system was operated for one hour at a pr essure setpoint of 12 kPa for all three bell jars. Pressure was recorded every minute during this time. The maximum, minimum, average, and standard deviation of the pressure data for each bell jar are given in Table 2-3. Since leakage increases at lo w pressure, data for a setpoint of 12 kPa are given as a worst case situation. Table 2-3. Performance of pr essure control algorithm. Descriptive statistics are given for data recorded at oneminute intervals for a one hour period. All values are in kPa. Bell Jar 1 Bell Jar 2 Bell Jar 3 Average 12.61 12.49 12.55 Maximum 13.05 13.06 13.07 Minimum 12.12 12.04 12.09 Standard deviation 0.26 0.03 0.30 To quantify the leakage rate of each bell jar, the pressure was reduced to 12, 33, or 66 kPa and the pressure contro l algorithm was turned off. Pressure data were again recorded every minute for a one-hour period. The leakage rate was taken as the pressure increase per minute as determined by slope of a linear regression line. Table 4 shows the rate of pressure increase for each bell jar at 12, 33, and 66 kPa.

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27 Table 2-4. Bell jar leakage rates. The rate of pressure increase is given for each bell jar in kPa min-1. Initial pressure, kPa Bell Jar 1 Bell Jar 2 Bell Jar 3 12 0.07 0.15 0.12 33 0.03 0.14 0.08 66 0.02 0.08 0.06 Carbon dioxide The CO2 control algorithm was te sted with and without pl ants. Figure 2-6 shows the CO2 concentration as a function of time withou t plants at standard pressure with the setpoint equal to 1000 ppm. CO2 was added incrementally until the concentration was within 120 ppm of the setpoint. Within 45 minutes, the CO2 concentration was within 60 ppm of the 1000 ppm setpoint. Achieving se tpoint took much longer without plants because ten minutes was allowed for mixing ve rsus the one minute allowed when plants were present. This longer mixing time wa s required to avoid overshoot that often occurred when no plants were in side the bell jar to take up CO2. 400 500 600 700 800 900 1000 1100 020406080100 Time, minCO2 concentration, ppm Bell jar 1 Bell jar 2 Bell jar 3 Figure 2-6. CO2 control without plants at standard pressure. The CO2 concentration within all three bell ja rs was within 60 ppm of the 1000 ppm setpoint approximately 45 minutes from the activation of the CO2 algorithm.

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28 The CO2 control algorithm was also tested at a reduced pressure. Figure 2-7 shows the CO2 concentration and pressure for a one-hou r period. Data were recorded at oneminute intervals. The pressure setpoint wa s 12 kPa with a hysteresis of 1 kPa and the CO2 setpoint was 9000 ppm. The CO2 concentration dropped by approximately 800 ppm each time the pump was activated, a reducti on of only about 8.2%. This corresponded well to a 8.3% decrease in pressure in reduc ing it from 13 to 12 kPa, indicating that the air within the bell jar was well mixed. At higher pressures, the vacuum pump activity had less effect on CO2 concentration. For example, if the total pressu re was 67 kPa and the vacuum pump was turned on to reduce the pressure by 1 kPa, assuming the air inside the bell jar is well mixed, the decrease in CO2 would be only 1.5%. 7000 7500 8000 8500 9000 9500 10000 10500 0102030405060 Time, minCO2, ppm10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15Pressure, kpa Carbon dioxide Pressure Figure 2-7. Effect of vacuum pump on CO2 control at low pressures. At 12 kPa, with no plants, the activity of the vacuum pump to maintain the pressure setpoint had a considerable effect on the CO2 concentration. Another test of the CO2 algorithm was performed with pl ants inside the bell jar. With a total pressure setpoint of 12 kPa, the CO2 setpoint was 3367 ppm (0.04 kPa partial

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29 pressure). Figure 2-8 shows the CO2 concentration over time for each of the three bell jars with two mature radish plants inside. Summary statistics for the same data as in Figure 2-7 are given in Table 2-5. The control system wa s successful in responding to plant CO2 uptake and reductions cau sed by vacuum pump activity and maintained the CO2 setpoint with a maximum sta ndard deviation of 267 ppm. 100 600 1100 1600 2100 2600 3100 3600 4100 4600 020406080100120 Time. minCO2, ppm Bell jar 1 Bell jar 2 Bell jar 3 Figure 2-8. CO2 control with plants at 12 kPa. The CO2 control algorithm reached the 3367 ppm setpoint in less than 40 minutes from the start of the experiment. Table 2-5. Performance of CO2 control algorithm at 12 kPa with plants. Descriptive statistics are given for data recorded at one-minute inte rvals for a one hour period. The CO2 setpoint was 3367 ppm. All values are in ppm. Bell Jar 1 Bell Jar 2 Bell Jar 3 Average 3574 3383 3335 Maximum 3885 3656 3786 Minimum 3204 2935 2738 Standard deviation 181 157 267 Air Temperature and Relative Humidity The air temperature and relative humidity control algorithm was also tested at 12 kPa. The setpoints, 24 oC and 70%, were chosen to achieve a VPDair of 0.9 kPa. Figure

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30 2-9 shows the air temperature and relative humidity for the 50-minute period beginning one hour after the start of the experiment. The air temperature of bell jar 3 was the last to reach its setpoint. As previously mentioned, th e power resistors that se rved as the bell jar heating elements could not be operated si multaneously to avoid exceeding the current rating of the Opto output modules. The contro l algorithm placed prior ity numerically. In other words, power was given to the resistor in bell jar 3 only if the air temperatures in bell jars 1 and 2 were at or a bove setpoint. Furthermore, h eating occurred slowly because current was limited to only 4 A. From equa tion 5, the power output of the resistor was calculated to be 28 W. Although it took some time to achieve the setpoint in bell jar 3, once the air temperature reached 24 oC, the heater was sufficient to maintain temperature as demonstrated by a maximum air temp erature standard deviation of 0.3 oC (see Table 26). Relative humidity was maintained fairly constant throughout the duration of the setpoint. From Table 2-6, which gives de scriptive statistics for air temperature and relative humidity, the maximum standard de viation over the 50-minute period was only 1.1%. The mean values for bell jars 1 and 2 were slightly below the 70% setpoint. This occurred because chilled water flow to the three cooling coils was controlled together. The coil remained on as long as the humidity in any one of the bell jars was above the setpoint. However, it should be pointed out that humidity in a ll three bell jars was within the 5% deviation from setpoint recommende d by ASAE standard ANSI/ASAE Standard EP411.1 during the entire experiment.

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31 20 20.5 21 21.5 22 22.5 23 23.5 24 24.5 25 6065707580859095100105110 Time, minAir temperature, C45 50 55 60 65 70 75 80 85RH, % Tair (1) Tair (2) Tair (3) RH (1) RH (2) RH (3) Figure 2-9. Air temperature a nd relative humidity control at 12 kPa with plants. The control algorithm successfully achieved and maintained the 24 oC and 70% setpoints one hour after the start of the experiment. Table 2-6. Performance of th e air temperature and relative humidity control algorithm at 12 kPa with plants. Descriptive statistics are given for data recorded at oneminute intervals for a 50-minute period. The air temperature and relative humidity setpoints were 24 oC and 70% to achieve a VPDair of 0.9 kPa. Bell Jar 1 Bell Jar 2 Bell Jar 3 Air temperature, oC Average 24.0 24.0 23.8 Maximum 24.2 24.2 24.1 Minimum 23.7 23.8 23.0 Standard deviation 0.1 0.1 0.3 RH, % Average 66.4 68.2 70.6 Maximum 69.7 71.0 72.4 Minimum 65.0 66.0 68.4 Standard deviation 1.1 1.1 0.9 Conclusions and Future Development The bell jar based small-scale controlled environment chambers described in this chapter worked well for the purposes of this research to study short term effects of pressure, CO2, and light on plant evapotranspiration. The control algorithm successfully

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32 maintained pressure, CO2 concentration, air temperatur e, and relative humidity while measuring plant weight and leaf temperature. There were a few limitations of the syst em. Leakage rates were higher than desired. The wire feedthrough and water fit tings built in the lab were adequate, but did not perform as well as commercial vacuum fittings. For this research, maintaining pressure and CO2 setpoints was a primary objectiv e. The vacuum pump and CO2 algorithm were capable of overcoming leakage to sufficiently maintain the pressure and CO2 setpoints. In other applications of this system, such as monitoring CO2 drawdown to measure photosynthesis, hi gh leakage rates may be of more concern. Another limitation of this system was the heating power limitations. The current rating of the output modules limited the power for heating to 28 W for a single bell jar at a time. If more current could be applied to the 50-W resistors for heating, the air temperature setpoints could be achieved more quickly. For th e purposes of this research the ambient environment was buffered by the external growth chamber and the heat output of the power resistor was capable of overcoming the temperature decrease that occurred when the cooling coil was turned on. However, in settings with a higher heating load, more power may be needed to maintain the temperature setpoint.

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33 CHAPTER 3 EFFECTS OF PRESSURE ON LEAF CONVECTIVE HEAT TRANSFER The rate of water loss from leaves is governed by the leaf energy balance that includes the effects of radiation, water evapor ation, and convection. Heat transfer by convection occurs when air passes over the l eaf surface and is significantly affected by the density of air, which is determined by total pressure. This chapter presents convective heat transfer analysis for a leaf represented by a horizontal flat sheet as affected by pressure and air velocity. Literature Review The rate of sensible heat transfer by convection (equation 1-2) has a significant impact on the leaf energy balance. Convecti on determines the degree to which the leaf is affected by the ambient aerial environment. Wh en convective heat transfer is high, as for a plant outdoors in windy c onditions, leaf temperature a pproaches air temperature regardless of the radiative load (Jarvis and McNaughton, 1986; Jones, 1992). On the other hand, if the rate of conv ective heat transfer is low, ra diation heat transfer dominates the leaf energy balance. Convective heat transfer analysis is also significant because it provides a way to estimate the thickness of boundary layers. K nowledge of the thickne ss of the velocity and thermal boundary layers that form over the surface of a leaf are important in order to accurately quantify the ambien t environment. Within the boundary layer there are gradients of air velocity, gas concentration, and temperature. Sensors must be located outside the boundary layer in the free stream to best measure the surrounding

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34 environment. On the other hand, locati ng sensors within the boundary layer provides information about the leaf microclimate. Convection Heat Transfer Resistance to convective heat transfer is caused by the boundary layer that forms above the leaf as air passes over. Figure 31 shows a theoretical di agram of the velocity boundary layer over a horizontal thin plate. The air above the pl ate surface can be thought of as a series of infinitely thin horizon tal layers of particles. The air particles that come in contact with the surface of th e plate have zero velocity and exert a shear stress on the layer just above it, slowing it down. This second layer slows down the third by exerting a shear force and so on until the eff ect is negligible and the local velocity reaches the free stream velocity, u. A horizontal velocity gr adient exists between the plate surface (u = 0) a nd the free stream (u = u). The boundary layer thickness, is defined as the vertical dist ance, y, at which u = 0.99 u (Incropera and DeWitt, 1996). Figure 3-1. Velocity boundary layer over a hor izontal flat plate (adapted from Incropera and DeWitt, 1996). A thermal boundary layer similar to the velocity boundary layer also develops over the surface of a flat plate. Figures 32 and 3-3 show the thermal boundary layer over a horizontal flat plate with a surface temperat ure warmer (Figure 3-2) and cooler (Figure 3-3) than the free stream air temperature. A horizontal temperatur e gradient develops

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35 between the surface temperature, Ts, and the free stream temperature, T. The thickness of the thermal boundary layer, t, is defined as the vertical distance at which the air temperature, T, is equal to 0.99T (Incropera and DeWitt, 1996). Figure 3-2. Thermal boundary layer over a horizont al flat plate that is warmer than the surrounding air (adapted from Incropera and DeWitt, 1996). Figure 3-3. Thermal boundary layer over a horizont al flat plate that is cooler than the surrounding air (adapted from Incropera and DeWitt, 1996). The mathematical derivati ons involved in boundary la yer analysis are beyond the scope of this review and are not includ ed. To simplify analysis, the following nondimensional groups Reynolds, Prandtl, Gr ashof, and Nusselt numbers are employed in the solutions. The Reynolds and Grashof numbers are used to determine if forced, free, or mixed convection is dominant. Then, based on the dominant mode of convection, non-dimensional groups are used to calculate resistances a nd boundary layer thicknesses.

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36 Forced convection occurs when the flui d movement across the surface is driven externally by a pump, fan, or wind. Free convection is driven by buoyancy forces created by temperature gradients in the fluid. Mixed convection occurs when the effects of forced and free convection are similar in ma gnitude and neither can be neglected. The Reynolds number, Re, is the ratio of iner tia to viscous forces and is calculated as: L u Re (3-1) where: u = free stream air velocity, m s-1 L = characteristic length, m = kinematic viscosity, m2 s-1 Kinematic viscosity, a function of fluid dens ity, is highly pressure dependent. As a result, assuming all other parameters are held constant, Reynolds number will decrease as pressure is dropped. Prandtl number, ratio of viscosity to ther mal conductivity, is calculated as follows in equation 3-2. Pr (3-2) where: = thermal diffusivity, m2 s-1 Grashof number, ratio of buoyancy to viscous forces, is calculated by equation 3-3. 2 3 L ) T T ( g Gra s (3-3) where: g = gravitational constant, m s-2 = 1/Ta =coefficient of thermal expansion, K-1

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37 TS = surface temperature, K Ta = air temperature, K External resistance The method of calculatio n of the rate of sensible h eat transfer from the crop canopy is determined by the dominant mode of convectiv e heat transfer forced, free, or mixed. In typical field conditions wind velociti es are in the range of 1 to 5 m s-1 and forced convection is the primary mode of sensible heat transfer (Han an, 1998). In Earth greenhouse applications typical ai r velocities of 0.5 to 0.7 m s-1 are considered acceptable (ASHRAE, 2001). In these lowe r air velocities, free convecti on plays a larger role and a mixed convection model is most accurate (Bai ley and Meneses, 1995; Stanghellini, 1987; Zhang and Lemeur, 1992). The magnitude of the ratio Gr/Re2 determines the principal mode of convection. If Gr/Re2 1, both free and forced convection must be considered (mixed convection). If Gr/Re2 <<1, forced convection dominates and free convection may be neglected. Likewise, if Gr/Re2 >>1, forced convection may be neglected The Nusselt number is a measure of the magnitude of convection heat transfer occurring at a surface. Calculation of the Nusselt number depends on the dominant mode of convection heat transfer. In the case of forced convection, th e Nusselt number for a horizontal thin plate is (Incropera and DeWitt, 1996): 3 1 2 1664 0 Pr Re Nu (3-4) For free convection of the upper surface of a horizontal, heated plate, the Nusselt number is (Incropera and DeWitt, 1996): 4 154 0 Pr) Gr ( Nu (3-5)

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38 Equation 3-5 for a heated upper surface was a pplied in this analysis because it is most appropriate for the convect ion experiments performed in this research. In the case of an actual leaf at reduced pressures equa tion 3-6 for a cooler than air surface may be more appropriate considering evaporative co oling caused by high tran spiration rates. 4 127 0 Pr) Gr ( Nu (3-6) In free convection conditions equation 3-7 fo r characteristic length, L, suggested by Incropera and DeWitt (1996) was applied to improve model accuracy. P A L (3-7) Stanghellini (1987) developed equation 3-8 for the Nusselt number in mixed convection conditions that worked well for horizontal leaves in a greenhouse. 4 1 292 6 37 0) Re Gr ( Nu (3-8) From the Nusselt number, the external resistance to sensible heat transfer for a single leaf can be calculated by equation 3-9. Nu L re (3-9) The external resistance of a crop canopy, rh, was estimated by Zhang and Lemeur (1992) from the re of a horizontal flat plate by equati on 3-10. This equation assumes that all leaves contribute equally to sensible heat transfer. LA I r re h2 (3-10) Boundary layer thickness The average thickness of the velocity boundary layer for forced flow over a horizontal, thin flat plate is given by equation 3-11 (Incropera and DeWitt, 1996).

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39 2 15 R e L (3-11) The Prandtl number, a measure of the ratio of the viscosity forces to diffusion, can be used to estimate the thickness of the thermal boundary layer, t, based on 3 1Prt (3-12) Objectives The objective of this chapter was to use cl assical convection heat transfer analysis to determine the effects of pressure and air velocity on the external resistance and boundary layer thickness of radish plants grow ing at atmospheric pressures as low as 12 kPa. The theoretical heat transfer model de scribed above was compared with data from a series of controlled lab experiments. Materials and Methods The sensible heat transfer from a leaf re plica was measured to evaluate the effects of pressure and air velocity on external resistance. The rectangular-shaped replica (Figure 3-4) was made by wra pping a 12.7 cm x 2.54 cm (5 in x 1 in) flexible 10-W Kapton heater (model BKL3005, Birk Manufacturing, Inc., East Lyme, CT) with standard grade aluminum foil (thickness = 0.16 mm). A small type-T thermocouple was sandwiched between the heater upper surface and the foil. It was assumed that there was no temperature gradient along the thickness of the foil so that the temperature measured by the thermocouple was equal to the upper surf ace temperature of th e leaf replica. Power to the heater was supplied by a DC pow er supply. The voltage input was 13.2 V and the current draw was 0.82 A.

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40 Figure 3-4. Leaf replica. A leaf replica made by wrapping a thin, flexible heater with aluminum foil was used to measure the effects of pressure and air velocity on convective heat transfer. A fan (BM5115-04W-B50-L00, NMB T echnologies, Chatsworth, CA) was positioned about 2.5 cm in front of the leadi ng edge of the heated sheet as shown in Figure 3-5. The fan output was varied by cyc ling power to the fan (1 second delay) and positioning layers of screening material over the fan outlet. The volumetric flow rate of a given fan is proportional to the fan speed and diameter (He nderson et al., 1997). Therefore, although the mass fl ow rate of air decreased at lower pressures due to decreased air density, air velocity was not aff ected by pressure. At standard pressure, air velocity was measured about 5 cm above th e sheet with a hot wire anemometer (model 407123, Extech Instruments, Waltham, MA). On e of the bell jar chambers and the data acquisition system described in chapter 2 was modified for these experiments to control pressure.

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41 Figure 3-5. Convection heat tran sfer experimental setup. A fan was positioned in front of a thin heated sheet inside one of the bell jar chambers. External resistance was determined from cooling curves generated for the heated foil sheet at four levels of pressure (12, 33, 66, and 101 kPa) and air velocity (0, 1.8, 2.9, and 5.8 m s-1). Power was turned on to the heat ing element of the sheet until the surface temperature approached 80 oC. The power supply was then turned off and the sheet was allowed to cool until the surface temperatur e approached the ambient air temperature measured by a type-K thermocouple located abou t 5 cm above the sheet. Figure 3-6 is an example of a cooling curve at 5.8 m s-1 and 101 kPa.

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42 0 10 20 30 40 50 60 020406080100120140 Time, sTs-Ta, C Figure 3-6. Temperature profile for leaf re plica during heating a nd subsequent cooling phase at 101 kPa and an air velocity of 5.8 m s-1. The slope of the cooling curve was related to the rate of sensible heat loss as determined by a mass balance of the foil sheet given by equation 3-13. nR H C (3-13) where: C = rate of change of heat content of foil sheet, W m-2 H = rate of sensible heat transfer, W m-2 R = rate of radiation heat transfer, W m-2 The rate of change in the heat content of the foil sheet is given by equation 3-14. dt ) T T ( d L c dt dT L c Ca s ps s s ps s (3-14) where: s = density of leaf replica sheet, kg m-3 cps = specific heat of leaf replica sheet, kJ kg-1 K-1 L = length of sheet, m Ts = sheet surface temperature, oC

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43 Ta = air temperature, oC The rate of sensible heat transfer, H, is given by equation 1-2. Note that the canopy resistance term, rh, was replaced by the resistance for a single flat plate, re, for this analysis. Net radiation was calculated by the following equation 3-15. Variables in bold denote absolute temperature. ) ( Rsur s n4 4T T (3-15) where: = Stefan-Boltzmann constant = 5.670 x 10-8 W m-2 K-4 = emissivity of sheet surface Tsur = average temperature of surrounding surfaces, K It was assumed that the system was in equilibrium and the temperature of the surroundings could be well approximated by air temperature. An approximation was employed to elimin ate the fourth order terms of the radiation equation 3-14 and simply the solution of the heat balance. A coefficient, hr, was introduced to cast the net radiation equation in a form similar to the convection equation. ) T T ( h ) ( Ra s r a s n 4 4T T (3-16) where: hr = radiation heat transfer coefficient, W m-2 K Rearranging to solve for hr and expanding the fourth order polynomial ) ( ) )( )( ( ) ( ) )( ( ) ( ) ( ha s a s a s a s a s a s a s a s a s rT T T T T T T T T T T T T T T T T T 2 2 2 2 2 2 4 4 (3-17) and simplifying ) )( ( ha s a s r2 2T T T T (3-18)

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44 To further simplify the equa tion two more variables, Tm and e, were introduced. Tm was the mean of the sh eet surface temperature, Ts, and the air temperature, Ta. The difference between Ts and Ta was 2e so that: m aeT T (3-19) and m seT T (3-20) Combining equations 3-18, 3-19, and 3-20 and simplifying, 2 2 22 2) ( ha s m m rT T T T (3-21) Assuming that the difference between the surface and air temperatures, Ts-Ta, was significantly less than the absolute temperature of either the surface or air, the last term could be neglected. Therefore, the radiat ion heat transfer coefficient was given by equation 3-22. 34m rhT (3-22) Substituting equations 1-2, 3-14, 3-16, and 3-22 into the heat balance of equation 313 gave the following differential equation. ) T T ( h r ) T T ( c dt ) T T ( d L ca s r e a s pa a a s ps s (3-23) Dividing both sides by scpsL ) T T ( L c h L c r ) T T ( c dt ) T T ( da s ps s r ps s e a s pa a a s (3-24) and rearranging to simplify yielded equation 3-25. ) T T ( L c h L c r c dt ) T T ( da s ps s r ps s e pa a a s (3-25)

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45 The solution to the differential equation 3-25 was 3-26. ) t t ( L c h L c r c ) T T ln( ) T T ln(ps s r ps s e pa a a s a s 1 2 1 2 (3-26) Equation 3-26 was related to th e cooling curves (as in Figure 3-6) to solve for the external resistance. Figure 3-7 shows a plot of the natural logarithm of Ts-Ta of the same data as Figure 3-6 for time equal 50 to 110 s econds. Equating the sl ope, m, of a linear regression line through this data with equa tion 3-26 and rearranging gave equation 3-27 for external resistance, re. r ps s pa a eh ) L c ( m c r (3-27) y = -0.0617x + 7.1408 R2 = 0.9996 0 1 2 3 4 5 455565758595105115 Time, sln(Ts-Ta) Figure 3-7. Transformed cooling data for the leaf replica at 101 kPa and an air velocity of 5.8 m s-1. The slope of a linear regressi on line was related to Equation 3-26 to determine the external resistance to sensible heat transfer. The slope of the linear regr ession line for the transformed data of Figures 3-6 and 3-7 was -0.0617. This value and the follo wing properties for air and the sheet were

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46 applied to Equation 3-27 to calcu late the external resistance: a=1.16 kJ kg-1 K-1; cpa=1.007 kJ kg-1 K-1; s=1800 kJ kg-1 K-1; cps=0.98 kJ kg-1 K-1; and L=0.22 mm. The average air temperature dur ing all testing was 25 oC. Assuming an emissivity of bright aluminum foil of 0.05 (McQuistan and Pa rker, 1994) and a maximum sheet surface temperature of 80 oC, the radiation heat transfer coe fficient calculated by equation 3-22 was 0.393 W m-2 K. This gave an external resistance of 50.1 m s-1. Results and Discussion The external resistance of a thin, heated sheet was empirically determined at four levels of pressure and air velocity using temperature profiles dur ing a cooling phase. Figures 3-8, 3-10, 3-12, and 3-14 show the difference between surface temperature of the sheet and air temperature duri ng heating and subsequent co oling at 12, 33, 66, and 101 kPa, respectively. Figures 3-9, 3-11, 3-13, and 3-15 show the na tural logarithm of Ts-Ta during cooling. The slopes from linear regression analysis for each curve were used to determine the external resistance, re, in equation 3-27. At each pressure, cooling occurred at a faster rate with increasing air velocity. Decreasing pressure also decreased the rate of cooling. As previously menti oned, volumetric flow rate and, therefore, air velocity was not affected by pressure. Ho wever, air density and mass flow rate decrease with pressure. Decreasing the air density reduced th e cooling capacity of the air passing over the sheet. Note that differences in maximum temperature were due to the time period that the heating element was turned on, which was controlled manually.

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47 0 10 20 30 40 50 60 70 80 020406080100120140 Time, sTs-Ta, C 5.8 m/s 2.9 m/s 1.8 m/s still air Figure 3-8. Surface temperature of leaf repl ica during heating and subsequent cooling phase for four air velocity treatments at 12 kPa. m5.8= -0.0376 m2.9 = -0.0256 mstill = -0.0161 m1.8 = -0.0187 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 455565758595105115 Time, sln(Ts-Ta) 5.8 m/s 2.9 m/s 1.8 m/s still air Figure 3-9. Transformed surface temperatur e data for leaf re plica at 12 kPa.

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48 0 10 20 30 40 50 60 70 020406080100120140 Time, sTs-Ta, C 5.8 m/s 2.9 m/s 1.8 m/s still air Figure 3-10. Surface temperature of leaf repl ica during heating and subsequent cooling phase at 33 kPa. mstill = -0.0198 m1.8 = -0.0249 m2.9 = -0.0364 m5.8 = -0.0495 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 455565758595105115 Time, sln(Ts-Ta) 5.8 m/s 2.9 m/s 1.8 m/s still air Figure 3-11. Transformed surface temperatur e data for leaf re plica at 33 kPa.

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49 0 10 20 30 40 50 60 70 020406080100120140 Time, sTs-Ta, C 5.8 m/s 2.9 m/s 1.8 m/s still air Figure 3-12. Surface temperature of leaf repl ica during heating and subsequent cooling phase at 66 kPa. mstill = -0.0235 m1.8 = -0.0328 m2.9 = -0.0436 m5.8 = -0.0613 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 455565758595105115 Time, sln(Ts-Ta) 5.8 m/s 2.9 m/s 1.8 m/s still air Figure 3-13. Transformed surface temperatur e data for leaf re plica at 66 kPa.

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50 0 10 20 30 40 50 60 70 020406080100120140 Time, sTs-Ta, C 5.8 m/s 2.9 m/s 1.8 m/s still air Figure 3-14. Surface temperature of leaf repl ica during heating and subsequent cooling phase at 101 kPa. mstill = -0.0255 m1.8 = -0.0375 m2.9 = -0.0604 m5.8 = -0.0618 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 455565758595105115 Time, sln(Ts-Ta) 5.8 m/s 2.9 m/s 1.8 m/s still air Figure 3-15. Transformed surface temperatur e data for leaf replica at 101 kPa.

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51 Model Performance The empirically determined values for exte rnal resistance were compared with the classical heat transfer model of equation 3-9. Figure 3-16 shows the empirical values and model predictions at each level of air velo city as a function of pressure. The model accurately predicted the proporti onal effects of both pressure and air velocity on external resistance. Resistance to heat transfer increas ed with increasing pressure and air velocity. Equation 1-2 predicted that the rate of convective heat transf er was inversely proportional to external resistance. That is, if air density, specific heat, and temperature difference remained the same, convective heat transfer should increase as resistance decreases. However, as previously mentioned, the si gnificant decrease in air density at lower pressures reduced the heat transfer capacity of air passing over the surface. This was demonstrated by calculating the rate of sensible heat transfer, H, from the heated sheet for the external resistance values determined e xperimentally. Figure 317 shows the rate of heat transfer for the sheet with a surface area of 0.0032 m2 as a function of pressure and air velocity. The rate of heat transfer was an average of 50% higher at standard pressure than at 12 kPa. This increase was much less than the 88% decrease in air density from 101 to 12 kPa demonstrating the effect of ex ternal resistance. Higher values of re at standard higher pressures reduced the magn itude of the effect on convection.

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52 0 20 40 60 80 100 120 140 102030405060708090100 Pressure, kPaExternal resistance, s m-1 5.8 m/s 2.9 m/s 1.8 m/s still air 5.8 m/s theory 2.9 m/s theory 1.9 m/s theory still air theory Figure 3-16. Measured and pred icted values for external resi stance of leaf replica as a function of pressure and four levels of air velocity. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 020406080100120 Pressure, kPaSensible heat transfer, W 5.8 m/s 2.9 m/s 1.8 m/s still air Figure 3-17. Rate of heat transfer from leaf replica as a function of pressure and air velocity.

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53 The ability of the theoretical model to pr edict external resistance was evaluated by comparison to the experimentally determined values. Figure 3-18 and 3-19 show two tests for model performance. In Figure 318 the predicted values were plotted against empirical values. The 1:1 line represents pe rfect model fit. The points lined up nicely along the 1:1 line which indicated that th e predicted values closely matched the experimental values for both free and forced convection conditions. Forced convection dominated at air velo cities above 1.8 m s-1 and free convection was dominant in still air. None of the combinations of pressure a nd air velocity tested resulted in mixed convection. The actual mode l error as given by the diffe rence between predicted and experimentally determined values was plotted as a function of pressu re in Figure 3-19. The maximum error was 21.1 s m-1 and the average error was only 2.6 s m-1 for all conditions tested. 0 40 80 120 160 200 04080120160200 re (experimental), s m-1re (predicted), s m-1 5.8 m/s 2.9 m/s 1.8 m/s 0 m/s 1:1 Figure 3-18. External resistance model perfor mance. Predicted values of re are shown plotted against empirically determined values.

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54 -25.0 -20.0 -15.0 -10.0 -5.0 0.0 5.0 10.0 15.0 20.0 25.0 020406080100120 Pressure, kPare (predicted) re(experimental), s m-1 5.8 m/s 2.9 m/s 1.8 m/s still air Figure 3-19. External resistance model erro r. The difference between predicted and experimental external resistance is plotted as a function of pressure. Boundary Layer Thickness Pressure and air velocity also play sign ificant roles in the thickness of the boundary layer, that forms over the horizontal surface. Figure 3-20 and 3-21 show the effects of pressure and air velocity, respectively, on boundary layer thickness (equation 3-11). In Figure 3-20 the velocity boundary layer thickness was plotted as a function of pressure for an air velocity of 1.0 m s-1. The thickness of the boundary layer increased exponentially as pressure decreased so that it was greater than 2 cm as pressure approached zero. Boundary layer thickness at standard pressure was plot ted as a function of air velocity in Figure 3-21. At air velocities of 1.0 m s-1 and above, there was little change in However, when the air velocity was lo w the boundary layer in creased significantly.

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55 Note that this predicted trend held true for all pressures. Changes in pressure only shift the magnitude of these curves. 10 20 30 40 50 60 70 80 90 100 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 Pressure (kPa)Boundary Layer Thickness (cm) Figure 3-20. Effect of atmos pheric pressure on boundary la yer thickness of a horizontal flat plate. Air velocity wa s held constant at 1.0 m s-1. 0 1 2 3 4 5 6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Air velocity (m/s)Boundary Layer Thickness (cm) Figure 3-21. Effect of air velo city on boundary layer thickness of a horizontal flat plate. Pressure was held constant at 101 kPa.

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56 Conclusions To predict the external re sistance and boundary layer thic kness for a mature radish leaf, convection heat transfer analysis was performed both theoretically and experimentally for a horizontal flat plate. A classical heat transfer model for both free and forced convection regimes was compared with data from controlled experiments. The model fit well for all levels of pressure (12, 33, 66, and 101 kP a) and air velocities (still air, 1.9, 2.8, and 5.8 m s-1) tested. The average error between the predicted and empirical resistances was 2.6 s m-1. As predicted by the model and observed in experiments, external resist ance was proportional to both pressure and air velocity. Boundary layer thickness, howev er, increased significantly at low pressures and air velocities less than 1 m s-1. The external resistance model developed here was a necessary component of the ev apotranspiration model that was the overall goal of this research. This analysis also served as a mechanism for testing conventional convection heat transfer equation in low pressure conditions. Predictions of boundary layer thickness, although not tested experimenta lly, provided some guidance for choosing appropriate locations to meas ure environmental conditions. Large boundary layers that occurred at low pressures and low air velociti es should be considered in the design of low pressure systems.

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57 CHAPTER 4 SURFACE RESISTANCE TO EVAPOTRAN SPIRATION IN REDUCED PRESSURE ENVIRONMENTS Evapotranspiration, the total water lost by plant transpiration a nd evaporation from the plant and surrounding ground surfaces, can be predicted by the Penman-Monteith model (equation 1-8). Monteith (1965) m odified an evaporati on model developed by Penman (1948) to account for resistances of the crop canopy to water vapor loss. In this research, surface resistance is defined as the resistance to water vapor transfer through the leaf cuticle layer and stomata. Changes in surface resistance are caused by the opening and closing of stomata while the cuticle resistance remains relatively constant. This chapter examines the effect of atmospheric pressure and other environmental variables on the surface resistance to ev apotranspiration. Literature Review The rate of water loss by evapotranspi ration is determined by both physical and biological parameters. Water vapor diffuse s mostly through stomata, and to a lesser extent through the le af cuticle, from saturated air in side the leaf to the surrounding environment. The rate of water diffusion th rough the leaf surface is limited by stomatal aperture allowing the plant some control of transpiration rate. Effects of Environmental Variables on Stomatal Control Stomata reduce plant water loss while allowing CO2 diffusion into the leaf for photosynthesis. Therefore, it is no surprise th at stomatal control is significantly affected

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58 by the ambient environment. Photosynt hetically active radiation (PAR), CO2 concentration, vapor pressure deficit (VPD), and plant water status are all known to have an effect on stomatal action. Vapor pressure deficit During the past two decades a considerable amount of research has been done to investigate stomatal control with regard to ambient humid ity. In question is whether guard cells sense humidity or the rate of evapotranspiration. Most researchers have concluded that plants use a feedback met hod of control in which they detect and respond to changes in the rate of evapotrans piration and/or water status and not humidity (Comstock, 2002; Lhomme, 2001; Monteith 1995; Mott and Parkhurst, 1991; and Outlaw, 2003). If the rate of water loss is great er than the rate of water uptake, the water potential of the tissue surrounding the guard cells decreases. Although the exact mechanism is not known, these desiccating cells are believed to send a signal to nearby guard cells causing them to close and the rate of ev apotranspiration to decrease (Comstock, 2002). High rates of evapotranspi ration may also have a direct affect on guard cell action. Accordi ng to Outlaw (2003), solutes accumulate in the guard cell apoplast (dead tissue includi ng cell walls, intrace llular spaces, and xylem elements through which water flows) as the transpir ation stream evaporates. The solute concentration increases at high rates of tran spiration and, by osmosis, water flows into the apoplast leaving the guard cells less turgid and causing them to close. The relationship between stomatal resist ance, evapotranspiration rate, VPD, and mass diffusivity was cleverly demonstrated in experiments by Mott and Parkhurst (1991). They compared stomatal resistance of seve ral plant species in air and in helox (79% helium and 21% oxygen). Water evaporates 2.33 times faster in helox than in air due to

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59 the higher mass diffusivity of water in helox. Therefore, in cases of equal stomatal aperture and VPD, evapotranspiration occurred fa ster for plants in the helox mixture. Carbon dioxide In normal and slightly above Earth ambient CO2 concentrations in the range of 400 to 1000 ppm (Pco2 = 40.4 to 101 Pa) decreases in con centration cause stomatal opening (Assmann, 1999; Wheeler et al., 1999) and thus an increase in surface resistance. At CO2 concentrations above approximately 1000 ppm there is little to no change in stomatal resistance (Jarvis, 1976; Stanghellini and Bunce, 1993). However, in plants exposed to super-elevated CO2 concentrations greater than 10,000 ppm (PCO2 = 1.01 kPa) stomatal resistance was shown to decrease in potato and wheat plants leading to decreased water use efficiency (Wheeler et al., 1999). Some plants may acclimate to higher CO2 concentrations as shown by Stanghellini and Bunce (1993). Stomatal re sistance increased less as CO2 concentration was increased from 500 to 2000 ppm for tomato plan ts grown at 700 ppm ve rsus plants grown at 350 ppm. The decreased sensitivity to changes in CO2 may mean that plants grown at higher concentrations have increased wate r use. Soybeans grown at 800 ppm of CO2 had similar values of canopy surface resistance during short-term exposure to 330 ppm as plants grown at 330 ppm (Jones et al., 1985). Likewise, the surface resistance of plants grown at 330 ppm was similar during shortterm exposure to 800 ppm as the plants grown at the higher CO2 concentration. A more signifi cant effect of long-term exposure to higher CO2 concentrations was the increase in l eaf area. The leaf area of soybeans grown at 800 ppm was 1.8 times greater than those grown at 330 ppm. Increased leaf area led to higher transpiration rates for plants grown at 800 ppm when the surface resistance decreased during exposure to an ambient CO2 concentration.

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60 Photosynthetically active radiation Stomata respond to light both directly a nd indirectly. As the intracellular CO2 concentration decreases due to photosynthe sis, stomata open to take in more CO2 (Outlaw, 2003). Stomatal resi stance of poinsettia cuttings decreased significantly when incident radiation was in creased from 50 to 300 W m-2 (400-700 nm) in work by Zolnier et al. (2001). There is less of an effect of the magnitude of PAR on stomatal resistance at levels above 500 mol m-2 s-1 (Jarvis, 1976). Mass Diffusivity and Stomatal Resistance Because mass diffusivity is pressure depende nt, growing plants in reduced pressure environments can be expected to yield resu lts similar to those of Mott and Parkhursts (1991) helox experiments. Equation 4-1 give s the relationship derived from the ideal gas law to quantify the effect of pressure on mass diffusivity (Incropera and DeWitt, 1996). It is assumed that the ideal gas law is valid fo r the range of pressures used in this research ( 10 kPa). P P D Dw w 0 0 (4-1) where Dw = mass diffusivity of water at pressure P, m2 s-1 P0 = standard pressure= 101.3 kPa 0 wD= mass diffusivity of water at standard pressure = 2.50 x 10-5 m2 s-1 A plot of mass diffusivity as a function of pressure, calculated by equation 4-1, is shown in Figure 4-1. Note that the rate of water diffusion incr eases significantly at pressures less than 25 kPa. A sharp increas e in mass diffusivity at pressures below 25 kPa was verified in experime nts by Rygalov et al. (2002).

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61 0.0E+00 5.0E-05 1.0E-04 1.5E-04 2.0E-04 2.5E-04 3.0E-04 020406080100Pressure, kPaMass diffusivity of water in air, m2 s-1 Figure 4-1. The effect of pressu re on mass diffusivity of water in air. At pressures lower than 30 kPa, such as those being c onsidered for a greenhouse on Mars, water diffusion occurs much faster than at standard pressure. Nobel (1999) gives equation 4-2 to calculat e stomatal conductance, the inverse of stomatal resistance. s sr D g 1 (4-2) where gs = surface conductance, mm s-1 D = mass diffusivity, mm2 s-1 l = effective path length for diffusion through stomatal pore, mm rs = surface resistance, s mm-1 If stomatal density and pore depth does not change the effect path length, l, is a function of stomatal aperture only (Mott and Parkhurst, 1991). Note from equation 4-2 that surface resi stance is negatively proportional to mass diffusivity. As an example, consider a plant at 10 kPa and one at standard earth pressure

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62 (101.3 kPa). If all other conditions remain the same and stomatal opening does not change, stomatal conductance will increase by th e ratio of the mass diffusivity at 10 kPa to the mass diffusivity at 101.3 kPa. The resu lt is an increase in stomatal conductance by approximately a factor of 10 (see equation 43). The corresponding ch ange in stomatal resistance would be a decrease by a factor of 10. 5 4 3 101 3 101 10 3 101 1010 5 2 10 53 2x x g D D g g. s . s s (4-3) where: gs10 = stomatal conductance at 10 kPa, m s-1 gs101.3 = stomatal conductance at 101 kPa, m s-1 D10 = mass diffusivity of water at 10 kPa, m2 s-1 D101.3 = mass diffusivity of water at 101.3 kPa, m2 s-1 Plant Adaptation and Surface Resistance This research focused on short term response of surface resistance to changing environmental conditions and did not consider effects of adaptations of plants grown at high CO2 concentrations or low pressures. Adaptation of plants to Mars greenhouse conditions may affect surface resistance. Fo r example, stomatal density has been shown to be significantly affected by environm ental conditions during development. In a study by Schoch et al. (1980), a decrease in the stomatal index (ratio of stomatal cells to total number of cells) of new, developing leaves of Vigna sinensis plants growing in high light conditions was observed following exposure to only one day of shade. Gay and Hurd (1975) found that to matoes grown under high light conditions (100 W m-2) had 30 stomata mm-1 on the upper surface of the leaf compared to less than one stomata mm-1 for those grown in low light (20 W m-2).

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63 Humidity and carbon dioxide concentrations have also been shown to impact stomatal frequency. A study by Bakker ( 1991) compared the stomatal density and average size of stomata for cucumber, tomato and sweet pepper grown in a range of air vapor pressure deficit (VPDair) treatments from 0.2-1.6 kPa. Their results showed that both stomatal density and size, and, conseque ntly, total pore area, increased with lower VPDair (high humidity). Woodward (1987) f ound that stomatal frequencies have decreased by about 40% since before the industrial revolution when atmospheric CO2 concentration was about 60 ppm lower than curr ent levels. Similarly, during exposure to the same VPDair and PAR levels tomato plants grown at 700 ppm experienced higher rates of water loss than plants grown at 350 ppm (Stanghellini and Bunce, 1993). It should be noted that there is significant va riation between species with regard to the effect of carbon dioxide concen tration on stomatal density. Environmental conditions may also affect the leaf area and/or size of stomata so that changes in stomatal density do not necessarily denote changes in total pore area. Bakker (1991) showed that statistical change s in stomatal pore area may not necessarily result in significant changes in stomatal c onductance. In a study by Jones et al. (1985) leaf area was a factor of 1.8 greater for soybeans grown at 80 0 ppm than plants grown at 330 ppm. Surface resistance was similar fo r both sets of plants at the same CO2 concentration leading the author s to conclude that increased water loss rates of plants acclimated to higher CO2 conditions was caused by enhan ced leaf area an d not surface resistance adaptations. Objectives The objective of this chapter is to quan tify the effects of atmospheric pressure, CO2, and PAR on evapotranspiration and surface resistance. These effects will be

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64 incorporated into an empirical model of surface resistance for mature radish plants acclimated to standard pressure. Materials and Methods Experiments to collect data for calculat ion of surface resistance were performed in controlled environment conditions as s uggested by Jarvis (1976) Evapotranspiration rates of radish plants were measured during short-term exposure to different levels of pressure, CO2 concentration, and PAR inside the small-scale pressure controlled chambers described in chapter 2. Each of the three bell jar-based chambers was considered a replication as it offere d independent control of pressure, CO2 concentration, air temperature, and relative humidity. Ma ximum PAR was determined by the external growth chamber and screens were a dded to reduce the light level. Plant Material A group of twelve pots each containing two 18-to-24-day-old radish plants (Raphanus sativa L. Cherry Bomb II) were available for each three-hour measurement period. Seeds were pretreated for 15-20 mi nutes in a 10% trisodium phosphate solution prior to planting. Three or f our pretreated seeds were plan ted per pot containing in metro mix media. All plants were grown in the same controlled environment chamber as the small-scale pressure controlled chambers. The chamber environmental conditions are given in Table 4-1. Plants were culled after one week to leave two similar sized seedlings per pot. Plants were watered daily with a 1 X Hoaglands solution. Planting dates were staggered so that 12 pots of 18-to24-day-old radish plants were available for each week of experimentation. One pot per chamber was randomly selected for each measurement period. Each pot was never us ed more than once per day to allow for complete recovery following stress event.

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65 Table 4-1. Controlled environment chamber c onditions. The radish plants used in this research were grown in the following conditions for 24 days. Parameter Setpoint Air temperature 24 oC Relative humidity 70% PAR 360 mol m-2 s-1 Photoperiod 16/8 Evapotranspiration Measurement To measure evapotranspiration, a randomly selected pot of radish plants was centered on the load cell of the bell jar chamber. Before the start of each run, 20 mL of nutrient solution was added to a small tray pl aced underneath the pot of radishes to make certain that plants were we ll-watered throughout the measur ement period. The bell jar was then placed on top of the base and, if necessary, the shading material was slipped over the bell jar to reduce the light level. Environment setpoints were added to the control program and data logging was activat ed. One hour was allowed for the system and plants to stabilize. The rate of evapot ranspiration was taken as the slope of a linear regression line fit to the weight data for the subsequent twohour period. Each run of three replications lasted a total of three hours. A preliminary experiment was performed to determine the amount of time needed for plants to reach steady-state. Leaf te mperature was measured with an infrared thermocouple while plants were subjected to 12 kPa for three hour s (see Figure 4-2). Plants reached steady-state, as indicate d by stabilization of leaf temperature, approximately 45 minutes after the pre ssure was reduced to 12 kPa.

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66 15 17 19 21 23 25 27 00.511.522.53Time from start, hrTemperature, C0 20 40 60 80 100 120Pressure, kPa Leaf temperature Pressure Steady-state Figure 4-2. Leaf temperature transient res ponse to changes in tota l pressure. Radish plants subjected to 12 kPa reached stea dy-state within one hour of initial pressure drop. Experimental Design Experiments were completely rando mized with a 4x2x2 factorial treatment structure. Table 4-2 gives the levels of pressure, CO2, and PAR treatments applied. Data not used in the development of the surface re sistance model were used for validation of the evapotranspiration model (chapter 6). As previously mentioned, a pot containing two radish plants inside each of the bell jars for the three-hour measurement period was considered a replication.

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67 Table 4-2. Evapotranspirati on treatment structure. A 4x2x2 factorial treatment structure was used in this research to determine the effects of pressure, CO2, and PAR on evapotranspiration and surface resistance of radish plants. Treatment Levels Pressure 12, 33, 66, and 101 kPa CO2 40 and 150 Pa PAR 340 and 160 mol m-2 s-1 Model Development Empirical models for surface resistance ba sed on the work of Jarvis (1976) have been widely used in greenhouse applicatio ns (Baille et al., 199 4; Stanghellini, 1987; Zolnier et al., 2001) to pred ict the effects of environmental conditions on surface resistance, rs. These models predict surface resistance as a reference value multiplied by a dimensionless function that accounts for the change in surface resistance caused by changes in environmental conditions. Equation 4-4 gives an example of a Jarvis-type model for surface resistance that accounts for th e effects of solar radiation (PAR), air vapor pressure deficit (VPDair), and carbon dioxide concentration (CO2). Note that the functions for environmental factors are not n ecessarily of the same mathematical form. ) CO ( f ) VPD ( f ) PAR ( f r rref s s 2 3 2 1 (4-4) The reference resistance, rsref, is a physiological value and can be determined from experimentation or from literature (S tanghellini, 1987). This model assumes that there are no interactions among environmental va riables. The nature of the functions for environmental factors is best determined by regression analysis from controlled environment data (Jarvis, 1976). The simple, empirical model of equation 4-4 is often chosen over more complex, mechanistic models for predicting surface resi stance. Stomatal control is complicated and likely involves signals from a number of sources throughout the plant. The level of

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68 detail required for development and applicati on of a mechanistic mode l of stomatal action is often not feasible or necessary. Aubine t et al. (1991) found that when considering a crop grown in protected culture external resistances caused by leaf boundary layers were typically much larger than th e surface resistances. Their data suggest that stomatal opening and closing has little e ffect on evapotranspiration rate compared to the external resistance on a canopy scale. Surface resistance, equations 4-5 and 4-6, was calculated from evapotranspiration rates measured in the previously described ex periments by inversion of a) the latent heat loss equation (1-3) and b) the Penman-Monteith evapotranspiration model (equation 1-8). Values of surface resistance estimated by these two equations were compared to determine the applicability of the Penman-M onteith model for low-pressure conditions. Inversion of equation 1-3 yielded the following equation for surface resistance. h air leaf a air sr LE VPD c r (4-5) where: a = density of air, kg m-3 cp = specific heat of air at constant pressure, J kg-1 oC-1 VPDleaf-air = leaf-to-air vapor pressure deficit, kPa = psychrometric constant, Pa oC-1 LE = latent heat flux, W m-2 rh = canopy external resistance for sensible heat transfer, s m-1 Equation 4-6 was obtained by inversion of the Penman-Monteith model. LE ) R LE ( r LE VPD c rn h air a air s1 (4-6)

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69 where: VPDair = air vapor pressure deficit, kPa = slope of saturation vapor pressure curve, Pa oC-1 Rn = net radiation, W m-2 Equations 4-5and 4-6 required estimation of several heat fluxes and air properties. Latent heat flux, LE, was estimated by equati on 4-7. The latent heat of vaporization, was assumed to be 2442 kJ kg-1 for an air temperature of 24 oC. ET (g m-2 s-1) was the measured evapotranspiration from the experiments described above. ET LE (4-7) The procedure for estimating net radiation, Rn, was the same as used in Zolnier et al. (2004). Net radiation, e quation 4-8, was the sum of th e effects of longand shortwave radiation. Incoming shortwave radiation, Rsw, was measured at canopy height beneath the bell jar with and without shading material by an Eppley pyranometer (Model PSP, The Eppley Laboratory, Inc, Newport, RI). The average incoming short-wave radiation was 95 W m-2 without shading and 48 W m-2 with shading in place. Long wave radiation was calculated by the Stefan-Boltzmann equation. The reflectance and emissivity of the canopy was assumed to be 0.27 and 0.90 respectively (Zolnier et al., 2004). ) ( R ) ( Rs sur sw n 4 41T T (4-8) where: = reflectivity, dimensionless = Stefan-Boltzmann constant, W m-2 K-4 = emissivity, dimensionless Tsur = average absolute temperature of surroundings, K Ts = average absolute temperature of canopy, K

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70 It was assumed that the bell jar was in e quilibrium with the external chamber and that Tsur could be well estimated by the chamber temperature of 24 oC. The canopy external resistance, rh, was calculated by equatio n 3-10 from values of re predicted by the model described in chap ter 3 for air velocity equal to 1.3 m s-1. Leaf area of each plant was measured on day 24 by a leaf area meter (LI-3000A, Licor Biosciences, Lincoln, NE). A preliminary experiment was performed to determine the change in leaf area from day 18 to day 24. There were no statistical differences between total leaf area of radish plants on days 18, 20, 22, and 24 ( = 0.05). From this, it was concluded that measuring leaf area each da y during experimentation was not necessary. Functional relationships for the effects of many environmental factors including PAR, CO2, VPD, and leaf temperature have been de veloped for a variety of crops. In this research, data from short duration controll ed environment experiments with mature radish plants were used to determine the effect of pressure on rs. Effects of CO2 and PAR were incorporated in rsref. Although it is recognized that there may be adaptations, such as changes in stomatal density, that occur during long term exposure to different environmental conditions, only the short term re sponses were considered in the scope of this research. Results and Discussion Mean values of eva potranspiration, canopy external resistance (rh), and surface resistance (rs) calculated by equation 4-5 are shown in Table 4-3. Values of surface resistance estimations made by the Penman-Mon teith model at the lowest pressures were negative. Negative values of surface resistance are not physically possible and this estimation error was attributed to the lower le af temperatures that occurred at 12 kPa (see chapter 6). Thus, the remaining results a nd conclusions are based on surface resistance

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71 calculated by the latent heat equation. Reference condi tions were at 101 kPa. The effects CO2 and PAR on evapotranspiration and surface resistance were evaluated by comparison to these reference conditions. Evapotranspiration (ET) wa s negatively proportional to pressure (Figures 4-3 and 4-3). At reference levels of CO2 and PAR (40 Pa and 341 mol m-2 s-1) average ET increased from 2.3 g m-2 min-1 at 101 kPa to 3.3 g m-2 min-1 at 12 kPa. The same trend in ET as a function of pressure was obs erved in different levels of CO2 and PAR. In elevated CO2 conditions (150 Pa) ET incr eased from 2.0 to 2.7 g m-2 min-1 between 101 and 12 kPa. Likewise, ET increased from 1.4 to 3.1 g m-2 min-1 in a low PAR environment (161 mol m-2 s-1). Because the observed trend in evapotranspiration as a function of pressure was similar to that of mass diffusivity (Figure 4-1), it is hypothesized that increases in ET were dire ct results of increases in st omatal conductance at reduced pressures. This agreed with the relati onship given by Mott and Parkhurst (1991) for stomatal conductance. Surface resistance (Table 4-3), calculated by equation 4-5, decreased with pressure as predicted by e quation 4-4. The lowest resistances were observed at 12 and 33 kPa (Figur e 4-5). ET was also influenced by decreases in external resistance at low pr essures (Chapter 3). Elevated CO2 concentrations decreased ET (data shown in Table 4-3). When the concentration of CO2 was increased from 40 to 150 Pa, ET decreased some, although not significantly, at 33, 66, and 101 kPa (Figure 4-4). At 12 kPa, however, ET decreased from 3.3 to 2.7 g m-2 min-1 which was statistically significant ( =0.05). This decrease in ET at elevated CO2 corresponded to an increase in rs from at 12 kPa from 178.6 s m-1 to 228.3 m-1 (Figure 4-6). The mass diffusivity of water vapor, a functi on of pressure, was

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72 the same for these two treatments. Therefore, the increase in rs in elevated CO2 conditions could only have been a physiologi cal response. As in research by Assmann (1999) and Wheeler et al. ( 1999), stomata closed when CO2 levels rose from 40 to 150 Pa causing an increase in rs. The increase in rs was enough to protect the plants from the severe water stress observed at 12 kPa and 40 Pa of CO2 (see photo in Figure 4-3). In fact, there were no statistical differen ces between ET at 12 kPa and elevated CO2 (ET = 2.7 g m-2 min-1) and 101 kPa and 40 Pa of CO2 (ET = 2.3 g m-2 min-1). There was a slight decrease in ET, although not significant at all pressures, when PAR was reduced from 341 to 161 mol m-2 s-1 (Table 4-3 and Figure 4-6). Th e decrease in incident radiant energy reduced the energy available for water evaporation. An empirical equation for surface resi stance as a function of pressure was determined by linear regression in Figure 4-7. This equation was developed for incorporation in the surface resistance model of equation 4-4. This additional function (equation 4-7) accounted for th e effect of pressure on rs in the multiplicative model. ) P ( r rs s36 0 0066 0101 (4-7) To estimate surface resistance, a refere nce value was multiplied by an empirical linear function as in equation 4-7. The reference value, rs101, was the surface resistance determined at a particular set of environmen tal conditions. In this research, reference values were taken as the average surface resistance at 101 kPa for a particular CO2and PAR setpoint. No functions were de veloped to account for changes in CO2 and PAR. 463.9 (CO2 = 40 Pa; PAR = 341 mol m-2 s-1), 518.7 (CO2 = 150 Pa; PAR = 341 mol m2 s-1), and 446.4 s m-1 (CO2 = 40 Pa; PAR = 161 mol m-2 s-1).

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73 Table 4-3. Evapotranspirati on and resistance results. Shown below are mean values ( standard deviation) of evapotranspi ration, canopy external resistance (rh), and surface resistance (rs) for three replications. Letter superscripts indicate statistical differences among values in a column per pressure treatment and symbolic superscripts indicate diffe rences between pressures for each treatment ( = 0.05). Treatment Evapotranspiration (g m-2 min-1) rh (s m-1) rs (s m-1) 12 kPa CO2 = 40 Pa PAR = 341 mol m-2 s-1 3.3 (.1)A* 15.0 (.68) 178.6 (.9)A* CO2 = 150 Pa PAR = 341 mol m-2 s-1 2.7 (.06)B* 19.5 (.1) 228.3 (.8)B* CO2 = 40 Pa PAR = 161 mol m-2 s-1 3.1 (.1)A* 16.3 (.5) 210.3 (.5)B* 33 kPa CO2 = 40 Pa PAR = 341 mol m-2 s-1 2.9 (.2)A* 23.0 (.6) 293.9 (.5)A** CO2 = 150 Pa PAR = 341 mol m-2 s-1 2.8 (.1)A* 24.7 (.9) 296.2 (.0)A* CO2 = 40 Pa PAR = 161 mol m-2 s-1 2.3 (.2)B** 31.0 (.8) 378.8 (.0)B* 66 kPa CO2 = 40 Pa PAR = 341 mol m-2 s-1 2.4 (.2)** 34.0 (.6) 369.8 (.1)A*** CO2 = 150 Pa PAR = 341 mol m-2 s-1 2.0 (.3)** 35.6 (.9) 477.6 (.3)A** CO2 = 40 Pa PAR = 161 mol m-2 s-1 2.0 (.2)*** 40.6 (.4) 436.8 (.9)B** 101 kPa CO2 = 40 Pa PAR = 341 mol m-2 s-1 2.3 (.3)A** 46.1 (.6)A 463.9 (.2)A**** CO2 = 150 Pa PAR = 341 mol m-2 s-1 2.0 (.2)A** 49.4 (.5)B 518.7 (.3)A** CO2 = 40 Pa PAR = 161 mol m-2 s-1 1.4 (.4)B*** 62.6 (.2)B 664.1 (.0)B***

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74 Figure 4-3. Visual observations of water status at 101 and 12 kPa. Photo A shows a turgid radish plant at 101 kPa inside the bell jar system. Photo B shows a radish plant 45 minutes after pressure was reduced to 12 kPa. The CO2 concentration for the plants in both photos is 40 Pa. A B

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75 1.5 2 2.5 3 3.5 020406080100 Pressure, kPaEvapotranspiration, g s-1 m-2 40 Pa 150 Pa Figure 4-4. Effects of pressure and CO2 on evapotranspiration. Evapotranspiration rates increased with decreasing pressure and CO2 concentration. PAR was 341 mol m-2 s-1. 150 250 350 450 550 020406080100120 Pressure, kPaSurface resistance, s m-1 40 Pa 150 Pa Figure 4-5. Effect of CO2 on surface resistance. At 12 kPa, surface resistance increased somewhat when the CO2 concentration was increased from 40 to 150 Pa. PAR was 341 mol m-2 s-1.

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76 1 1.75 2.5 3.25 4 020406080100 Pressure, kPaEvapotranspiration, g min-1 m-2 341 161 mols m-2 s-1 mols m-2 s-1 Figure 4-6. Effects of pressure and PAR on ev apotranspiration. Ev apotranspiration rates increased with decreasing pressure. There were no statistical differences between light levels at the lowest pressure treatment. CO2 was 40 Pa. rs = rs101(0.0066*P + 0.36) R2 = 0.910 100 200 300 400 500 020406080100 Pressure, kPaSurface resistance, s m-1 Figure 4-7. Actual and predicted values of surface resistance at 40 Pa and 341 mol m-2 s1.

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77 The root mean square error (RMSE) of the model, calculated by equation 4-8, is shown in Table 4-4 for different environmental conditions. N i i i N) y y ( RMSE0 2 1 (4-7) where: N = number of predictions y = ith actual value y = ith predicted value Table 4-4. Root mean square error of surface re sistance model. Environmental conditions RMSE (s m-1) CO2 = 150 Pa PAR = 341 mol m-2 s-1 92.7 CO2 = 40 Pa PAR = 161 mol m-2 s-1 77.3 Conclusions Surface resistance is the resistance of th e leaf surface to water vapor loss. It accounts for the effects of stomata and the le af cuticle. Since cu ticle resistance is constant, changes in surface resistance can be used to understand stomatal control in response to environmental conditions. Surf ace resistance for mature radish plants, calculated from measured values of evapotra nspiration, increased significantly with increasing pressure while evapotranspiration decreased. An empirical model developed to predict rs as a function of pressure and a refe rence value determined at standard pressure performed well. There was also a significant effect of CO2 on stomata. Surface resistance increased and ET decreased when CO2 rose from 40 to 150 Pa for all pressure treatments. Decreasi ng PAR from 340 to 160 mol m-2 s-1 had little effect on rs or ET.

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78 CHAPTER 5 EVAPOTRANSPIRATION MODEL PERFORMANCE IN MARS GREENHOUSE CONDITIONS The evapotranspiration models described in Chapter 1 provides a way to calculate the water loss rate of a crop of plants. It accounts for the physical environment as well as physiological control of plant stomata to li mit water loss. Because water stress is anticipated to be a limiting fact or in growing plants in a low pressure Mars greenhouse, understanding the effects of environmental parameters on evapotranspiration rate is important in designing the struct ure and control system. Thorough analysis of a mathematical model provides a great deal of information. The sensitivity of the prediction to each para meter identifies the parameters with the most influence. To reduce water stress of plants in a Mars greenhouse, more attention should be focused on those parameters that have the strongest affect on the rate of water loss. Design decisions regarding parameters with little influence on ET can be based solely on other factors besides plant water stress. Error analysis quantifies the performance of the model. One method to quality error is to calculate the anticipated error of the prediction resulti ng from error in the estimation or measurement of parameters. A nother method of error analysis is validation of the prediction in comparis on with actual data. Strong co rrelation of the model with actual data establishes confid ence in the model predictions.

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79 Objectives The objective of this chapter is to ev aluate the performance of the PenmanMonteith model including the resistance m odels of Chapters 3 and 4 to predict evapotranspiration rate of radish pl ants in Mars greenhouse conditions. Materials and Methods The sensitivity of evapotra nspiration rate predictions to pressure, air velocity, surface resistance, temperature of surroundings, and incident radiation was determined by varying one parameter at a time with rema ining parameters held constant. The parameters evaluated and their referen ce values are listed in Table 5-1. Evapotranspiration rate was calculated by equation 1-3 for air velocity, surface resistance, and incident radiation varied by -90, -50, +50, and +100% of the reference value. Pressure was varied 90, -25, -50, and -75% and VPDleaf-air -90, -50, +50 % from their reference values. The percent cha nge in evapotranspiration was calculated by equation 5-1 for each parameter perturbation. o oE T ET ET change % (5-1) where ET = evapotranspiration rate with one parameter varied, g m-2 s-1 ETo = evapotranspiration calculated at reference parameters, g m-2 s-1 Table 5-1. Parameter descrip tions and reference values. Parameter Description Reference value P Atmospheric pressure 101 kPa u Air velocity 1.3 m s-1 rs Surface resistance 464 s m-1 VPDleaf-air Leaf-to-air vapor pressure deficit 2.65 kPa The error of the evapotranspiration model was evaluated in two ways. First, the propagation of error from environmental meas urements to predicted evapotranspiration

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80 was calculated by equation 5-2 (Dally et al., 199 3). Errors associated with measurement of pressure, air velocity, inci dent radiation, temperature of surroundings and estimation of surface resistance were included in the cal culation of evapotranspiration error. 2 2 2 2 2 1 1 i idp p ET dp p ET dp p ET dET (5-2) where ip ET =change in ET per unit change in parameter pi dpi = error in estimation of pi The unit change in ET per unit of each parameter was determined by sensitivity analysis. The errors associated with P, u, and VPDleaf-air were estimated as typical errors for that particular type of sensor. Surface resistance error was estimated as the standard error of the regression model in Chapter 4. The second method for evaluating the error of the evapotranspiration model was by validation using independent data. Two se ts of the evapotranspiration experiments described in Chapter 4 were performed with th ree replications each. One set was used to develop the surface resistance model and the other was for validation of the evapotranspiration model. The model was validated by computing the RMSE of the model compared to the actual data for different environmental conditions. Results and Discussion Evapotranspiration rate was predicted as a function of atmospheric pressure above 10 kPa in Figure 5-1 for the reference conditi ons. The model predicted a gradual increase in ET as pressure dropped from 101 to a pproximately 35 kPa and a more significant increase in ET at pressures below 35 kPa. The actual data shown in Figure 5-1 were also used to develop surface resistance model in Chapter 4.

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81 1.5 2.0 2.5 3.0 3.5 4.0 020406080100 Pressure, kPaEvapotranspiration, g m-2 min-1 Model Measured Figure 5-1. Predicted and meas ured evapotranspiration rate as a function of pressure. Sensitivity Analysis The change in evapotranspiration rate for th e parameters in Table 5-1 varied one at a time is given in Table 5-2. Predicted ET and the percent change from the ET at reference conditions calculated by equation 5-1 are shown. Predicted ET when all parameters were at refe rence values was 2.22 g m-2 min-1. Air velocity was negatively pr oportional to the external re sistance to sensible heat transfer. Increasing air veloci ty decreased the resistance to heat transfer. When air velocity was increased by 50%, ET increased to 2.26 g m-2 min-1, 1.8% of the reference ET. Surface resistance was also negatively proportional to ET. With pressure held constant, increasing the surface resistance by 50% from 464 to 696 s m-1 decreased ET by 31%. Conversely, decreasing rs by 90% increased ET four-fold. At constant pressure,

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82 changes in surface resistance were caused by other environmental parameters such as CO2 concentration and PAR availability (see chapter 4). Table 5-2. Sensitivity analysis of the evapotranspiration model for Mars greenhouse conditions. Given are the evapotranspi ration rate and percent change from reference conditions when only one parameter is varied. The evapotranspiration rate at the reference conditions was 2.47 g m-2 min-1. Parameter ET g m-2 min-1 % change Pressure 10.1 kPa 3.02 36 50 kPa 2.60 17 Air velocity 0.13 m s-1 (rh = 146.2 s m-1) 1.87 -16 0.65 m s-1 (rh = 66.8 s m-1) 2.14 -4 1.95 m s-1 (rh = 38.6 s m-1) 2.26 1.8 2.60 m s-1 (rh = 33.4 s m-1) 2.28 2.7 Surface resistance 46.4 s m-1 12.23 451 232 s m-1 4.07 83 696 s m-1 1.53 -31 928 s m-1 1.16 -47.7 VPD leaf-air 0.27 kPa 0.23 -90 1.3 kPa 1.09 -51 4.0 kPa 4.00 81 Error Analysis The expected error in predicted evap otranspiration rate caused by error in parameter estimation was calculated by equation 5-2. Table 5-3 lists the change in ET per unit change in each parameter and error fo r estimation of each parameter. Error in the estimation of pressure, ai r velocity, incident radiati on, and surrounding temperature are typical errors for sensors for that particular parameter. The estimation error for surface resistance is the RMSE error of the m odel in Chapter 4 for reference conditions. The expected error in prediction of evapotranspiration rate was 0.36 g m-2 min-1.

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83 Table 5-3. Change in evapotranspirati on rate and estimated error of parameters for overall error calculation. Parameter ET/pi dpi Pressure, kPa -0.009 0.5 kPa Air velocity, m s-1 0.46 (< 2.5 m s-1) 0.172 ( 2.5 m s-1) 0.1 m s-1 Surface resistance, s m-1 -0.011 35 s m-1 VPDleaf-air 0.84 0.1 kPa Performance of the evapot ranspiration model was validated by comparison to independent data. Equation 4-7 was used to ca lculate the root mean square error of the model at 12, 33, 66, and 101 kPa. The model was validated (Figures 5-2, 5-3, and 5-4) for the reference conditions (CO2 = 40 Pa; PAR = 340 mol m-2 s-1), elevated CO2 (CO2 = 150 Pa; PAR = 340 mol m-2 s-1); and reduced PAR (CO2 = 40 Pa; PAR = 160 mol m2 s-1). The RMSE error was 0.2 g m-2 min-1 in reference conditions, 0.4 g m-2 min-1 in elevated CO2, and 0.3 g m-2 min-1 in reduced PAR. 0 20 40 60 80 100 120 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 Pressure, kPaEvapotranspiration, g m min-2 -1 Figure 5-2. Model performance at referen ce conditions. Carbon dioxide concentration was 40 Pa and PAR was 340 mol m-2 s-1.

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84 0 20 40 60 80 100 120 1 1.5 2 2.5 3 3.5 Pressure, kPaEvapotranspiration, g m min -2 -1 Figure 5-3. Model performance in elevated CO2. Carbon dioxide concentration was 150 Pa and PAR was 340 mol m-2 s-1. 0 20 40 60 80 100 120 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 Pressure (kPa)Evapotranspiration, g m min-2 -1 Figure 5-4. Model performance in low PAR conditions. Carbon dioxide concentration was 40 Pa and PAR was 160 mol m-2 s-1.

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85 Conclusions The evapotranspiration model incorporat ing the external and surface resistance models developed in this research performed well to predict evapotranspiration rate of mature radish plants in Mars greenhous e conditions. The value of the predicted evapotranspiration was close to the independe nt evapotranspiration rate measurements. The root mean square error of the model comp ared to independent data was less than 0.5 g m-2 min-1 for all conditions tested.

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86 CHAPTER 6 LEAF TEMPERATURE IN A MARS GREENHOUSE Leaf temperature is an im portant component of the l eaf energy balance. Leaf temperature influences the rate of the eva potranspiration, convecti on and radiation heat fluxes. High rates of evapotranspiration at low pressures and the extremely cold environment in a Mars greenhouse may cause le af temperatures below typical values on Earth. This chapter examines the impacts of reduced pressures on leaf temperature and how this affects evapotranspiration. Literature Review The temperature of a leaf is determined by the leaf heat balance (equation 1-1). If the rate of heat gain is greater than the ra te of heat loss leaf temperature will rise. Conversely, if the rate of heat loss exceeds heat gains, the leaf temperature will decrease. The primary modes of heat transfer for a cr op canopy are radiation, c onvection, and latent heat loss by evapotranspiration. The vapor pressure deficit between the crop canopy and ambient air (VPDcrop-air) is the driving force for evapotranspiration (Zolnier et al., 2000). Accura te calculation of the VPDcrop-air requires that the temperature of the leaf is known to calculate the vapor pressure of the saturated surface of the leaf. A simplification in the derivation of the Penman-Monteith model described in chapter 1 assumes that the leaf temperature is approximately equal to the air temperatur e. This simplification introduces a new variable, which is the slope of the saturation vapor pressure curve (see Figure 1-2). The slope is evaluated at the air temper ature and is assumed to provide a good

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87 approximation of leaf temperature. This si mplification eliminates the need to measure leaf temperature in order to predict evapotrans piration rates. For many situations in Earth greenhouses the difference between leaf and air temperature is small and this assumption is reasonable (Stanghellini, 1987; Zolnier et al., 2000). The rate of radiation heat transfer to or from a leaf is driven by the difference between the leaf and the temper ature of its surroundings. In a subalpine environment in the mountains of Wyoming, frost was observed on plants even when air temperature was above freezing (Jordan and Smith, 1995). Long wave radiation heat transfer from the leaf to the night sky during clear conditions account ed for 30% of the frost events. Leaf temperature depressions (Tleaf-Tair) of up to -5 oC were observed in response to radiative cooling. Several factors of a Mars greenhouse environment may cause leaf temperatures less than those commonly observed in Earth gree nhouse conditions. It was shown in Chapter 4 that, depending on the CO2 concentration, higher rates of evapotranspiration (ET) can be expected at lower atmospheric pressures. It is hypothesized that these higher rates of ET will cool the leaf causing the temperature to drop. Radiative cooling is also expected between the interior surface of the Mars greenhouse structure and the leaf. The average temperature on the surface of Mars is -63 oC (NASA, 2005). If the greenhouse structure is assumed to be in equilibrium with the out side environment, the direction of radiation heat transfer will be away from the plant canopy. Objectives The objectives of this chap ter were to examine how the components of the leaf energy balance would be affected in a gree nhouse on Mars. Specifically, the effects of high rates of evapotranspiration and radiative cooling on leaf temperature were examined.

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88 Materials and Methods The effects of reduced pressure on leaf temperature were determined via the use of evapotranspiration experiments. Evapotra nspiration rate and leaf temperature were measured during a series of experiments in th e pressure controlled chambers described in chapter 2. Leaf temperature experiments were perf ormed in conjunction with the surface resistance experiments of chapter 4. L eaf temperature was measured by non-contact infrared thermocouples (OS36SM-K-140F, Om ega, Stamford, CT) directed at the underside of a leaf. Each bell jar chamber c ontained one infrared thermocouple (IRt/c). Replacement of the analog input module used to read the IRt/c sensors from bell jars 2 and 3 solved the interference problem, but a new module was not available until the end of the experiments. Performance of the infrared thermocouples was compared with fine gauge type-T thermocouples during a preliminary study. Leaf temperature of a single radish plant was measured by two IRt/c sensors, one above and one below a leaf, and three type-T thermocouples inserted in the midvein of leav es. Three replications were performed at each of three pressure treatments: 10, 25, and 50 kPa. The potential effects of the cold surfaces of a Mars greenhouse on the leaf energy balance were determined by a theoretical model. A model to predict the leaf-to-air temperature difference was derived from the en ergy balance of equation 1-1. Equations 1-1, 1-2, and 1-8 were combined and simplified to give equation 6-1. h s air p a n h s air Leafr r VPD c R ) r r ( T T 1 (6-1)

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89 Results and Discussion Infrared Thermocouple Performance As shown in Table 6-1, the average difference between the mean reading of the infrared thermocouples and the mean of th e type-T thermocouples over a two-hour period (one minute sampling interval) was only 0.4 oC. This is within the error of the IRt/c reading (including analog input module) of 0.8 oC. T-tests performed on the mean data sets confirmed that there was no differen ce between the average of the infrared thermocouples and the average of the type-T thermocouples. Figure 6-1 shows data from a single replication at 25 kPa. The in frared temperature readings matched closely with the type-T thermocouple readings. Al-F araj et al. (1994) recommended the use of infrared thermometry for measuring leaf te mperature. They argued that thermocouple measurements are more affected by local air a nd lead wire temperatures than by the leaf temperature. Table 6-1. Comparison of temp erature sensors for leaf temperature measurement. There was no statistical difference in leaf te mperature data measured by non-contact infrared thermocouples and type-T ther mocouples inserted in a radish leaf. Pressure (kPa) mean IR (oC) mean TC (oC) Difference (oC) 10 17.9 18.5 0.5 10 15.8 16.5 0.6 10 16.7 15.8 0.9 25 16.9 17.0 0.1 25 16.9 17.3 0.5 25 16.7 16.8 0.1 50 18.5 18.7 0.2 50 18.4 18.9 0.4 50 18.8 18.4 0.4

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90 16.0 16.5 17.0 17.5 18.0 18.5 020406080100120Time from start, minTemperature, C IRt/c type-T Figure 6-1. Leaf temperature measurement at 25 kPa. Leaf temperature readings from infrared and type-T thermocouples were similar over the course of a two-hour 25 kPa treatment. Effects of Evapotranspiration at Re duced Pressures on Leaf Temperature The average values of evapotranspirati on, leaf temperatur e, and leaf-to-air temperature difference for each pressure treatm ent in bell jar 1 are given in Table 6-2. The data presented here included both levels of CO2 and PAR treatments. As first shown in chapter 4, there was no change in the rate of evapotranspiration at 33, 66, and 101 kPa. Evapotranspiration at 12 kPa was 3.6 g m-2 min-1, significantly highe r than at higher pressures. Higher rates of evapotranspiration at 12 kP a caused the lowest leaf temperature, 19.3 oC, and the largest leaf-to-air temperature difference, -5.3 oC. Note that negative leaf-to-air temperature differences occurred when leaf temperature was less than air

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91 temperature. Leaves were cooler than air at all pressures except 101 kPa, when leaves were an average of 1.1 oC warmer than air. Figures 6-2 and 6-3 show leaf-to-air temperature di fference as a function of pressure and evapotranspiration rate, respectiv ely. The relationship between pressure and leaf-to-air temperature difference (R2 = 0.57) was a bit stronger than it was for evapotranspiration rate (R2 = 0.30). This suggested that there were other modes of heat flux away from the leaf in addition to evaporative cooling. Table 6-2. Effects of pressure on evapotranspiration rate and leaf temperature. Shown in the table below are the average values ( standard deviation) for all eight measurements made in bell jar 1 at e ach pressure. Different superscripts indicate statistical difference ( =0.05). Pressure (kPa) ET (g m-2 min-1) Tleaf (oC) Tleaf -Tair (oC) 12 3.6 (.0)A 19.3 (.3)A -5.3 (.8)A 33 2.5 (.6)B 22.6 (.0)B -1.9 (.6)B 66 2.1 (.27)B 23.5 (.8)BC -1.1 (.6)BC 101 2.5 (.6)B 25.6 (.7)C 1.1 (.3)C Tleaf -Tair = 2.9692*Ln(P) 12.709 R2 = 0.57-10 -5 0 5 020406080100120 Pressure, kPaTleaf Tair, C Figure 6-2. Effect of pressure on leaf-t o-air temperature difference. The largest differences between leaf and air temper atures occurred at 12 kPa when leaves were always cooler than air.

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92 y = -2.0436x + 3.7336 R2 = 0.31 -10 -5 0 5 0123456Evapotranspiration rate, g m-2 min-1Tleaf Tair, C Figure 6-3. Effect of eva potranspiration rate on leaf-toair temperature difference. Higher rates of evapotrans piration led to leaf temperatures several degrees below the ambient air. Leaf Temperature in a Mars Greenhouse Figure 6-4 shows the leaf-to-air temperatur e difference predicted by equation 6-1 as a function of the temperature of surrounding surfaces for 12, 33, 66, and 101 kPa. Surface resistance was estimated by the model in chapter 4 with a reference value, rsref, of 75 s m-1. Canopy external resistance was estimat ed by the model in chapter 3 for air velocity equal to 1.3 m s-1 and a leaf area index of 1. Ne t radiation was estimated using equation 4-7 with an incoming s hort wave radiation of 150 W m-2, reflectance of 0.27, and emissivity of 0.9. Leaf temperature was held constant and the temperature of the surroundings ranged from -70 oC (Rn = -180 W m-2) to 20 oC (Rn = 110 W m-2). At the lowest values of net radiation, estimates of la tent heat flux, equation 1-8, were negative. Because evapotranspiration can onl y be a heat loss, not a gain, these values were replaced with LE = 0. The heat balance wa s then reduced to equation 6-2.

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93 0 H Rn (6-2) Substitution of equation 1-2 into 6-2 and rea rranging gave equation 6-3 for leaf-to-air temperature difference when evapotranspiration was zero. p a h n air Leafc r R T T (6-3) In Figure 6-4, the sharp decrease in leaf-to-air temperature difference occurred when LE = 0. Table 6-3, gives the predicted latent and sensible heat fluxes and the leafto-air temperature difference for range of Tsur values from -70 to 20 oC. At the colder Tsur, leaves had no latent heat loss and all heat gained by convection from the warmer air surrounding the canopy, was lost by radiation heat transfer to the cold surroundings. The sensible heat loss decreased the temperature of the leaf. When Tsur was warmer, a portion of the heat gain by convection was lost by ev aporative cooling during transpiration. The magnitude of the difference between l eaf and air temperatures increased as pressure decreased. For the conditions applie d in the model for Figure 6-4 and Table 6-3, the only mode of heat gain was convection from the warmer ambient air. At lower pressures the decrease in air density reduces th e effectiveness of convection heat transfer. Evapotranspiration and radiat ion become the dominant heat transfer modes, thereby cooling the leaves. For example, when Tsur was -40 oC net radiation for both 12 and 101 kPa was -117 W m-2 and there was no latent heat loss. The resistance to sensible heat transfer by convection was higher for 101 kPa, 47 versus 16.5 s m-1. Therefore, although the magnitude of sensible heat loss was the same for both pressures, the smaller resistance at 12 kPa resulted in a lower pred icted leaf temperature than at 101 kPa.

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94 -25 -20 -15 -10 -5 0 5 -75-55-35-15525Temperature of surroundings, CTleaf Tair, C 12 kPa 33 kPa 66 kPa 101 kPa Figure 6-4. Effects of net radiation on leaf -to-air temperature difference. Leaf-to-air temperature difference was predicted by equation 6-1 as a function of net radiation for 12, 33, 66, and 101 kPa. Net radiation varied from -180 W m-2 when the temperature of the surroundings was -70 oC, as on Mars, to 110 W m-2 at 20 oC. Table 6-3. Leaf temperature model result s for 12 and 101 kPa. Shown below are the latent and sensible heat fluxes and th e leaf-to-air temperature differences predicted by the Penman-Monteith model for radiation heat exchange between leaves and surroundings as cold as -70 oC. 12 kPa 101 kPa Tsur (oC) Rn (W m-2) LE (W m-2) H (W m-2) TLeaf Tair(oC) LE (W m-2) H (W m-2) TLeaf Tair(oC) 20 110 135 -26 -3.0 109 0.4 0.0 0 17 48 -32 -3.7 61 -44.6 -1.8 -10 -23 11 -34 -4.0 41 -63.7 -2.5 -40 -117 0 -117 -13.7 0 -117 -4.6 -70 -180 0 -180 -21.2 0 -180 -7.2 As previously mentioned, a simplificati on was employed in the derivation of the Penman-Monteith evapotranspiration model to eliminate leaf temperature as an independent variable. This simplification required the assumption that the slope of the saturation vapor pressure curve at the leaf temperature was approximately equal to the slope at air temperature. This assumption wa s valid for cases when the absolute value of

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95 the leaf-to-air temperature difference was less than 10 oC (Jones, 1992). For the conditions applied to the leaf temperature m odel for Figure 6-4, at 12 kPa this assumption was valid for Tsur as low as -30 oC. If the temperature of th e interior surface of a Mars surrounding the plant canopy is much less than freezing, this assumption should be reevaluated. For it is likely that the slope of the vapor pressure curve at the leaf temperature would be signifi cantly different than the slop e at the air temperature. Another consequence of very low leaf temperatures is chilling injury. Sensitive plant species show signs of wilting or i nhibited growth and reproduction when tissue temperature is lowered about 10 oC (Jones, 1992). Long term exposure to conditions causing leaf temperatures lower than plants were adapted for coul d significantly reduce productivity. The effects of environmenta l conditions on leaf temperature should be considered in the design of a greenhous e on Mars. Conclusions The heat balance for a plant in a Mars gr eenhouse will be much different than for a plant on Earth. It is anticipated that the pressure inside a Mars greenhouse will be less than 30 kPa. At these low atmospheric pre ssures, evapotranspiration will occur faster than on Earth causing more latent heat loss a nd cooler leaf temper atures. Leaves will also lose heat by radiation to the cold greenhouse structure. In fact, it is likely that more heat will be lost than gained by radiation. In this case, sensible heat transfer by convection will be the only mode of heat gain. Since, conv ection heat transfer is less effective at reduced pressure s; the leaf temperature in a low pressure Mars greenhouse will be significantly lower than air temperature. This could invalidate some of the assumptions made during the derivation of the Penman-Monteith model. Low leaf temperatures could also cause chilling injury in plants adapted for warmer conditions.

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96 CHAPTER 7 CONCLUSIONS AND FUTURE RESEARCH When astronauts embark on a long-term exploration mission to Mars, they will need reliable, efficient life-support systems. Plants will play important roles in these systems as sources of food and oxygen production and waste treatment. Plant growth and development, and thus, performance of a biological life-support system are highly dependent on plant environmental responses. Ther efore, it is critical that the interaction between plants and the environment of a Mars greenhouse is well understood. The constraints of building a structure on the Martian surface to withstand interior air pressures equal to that of earth make it essential to develop crop production systems capable of operating at pressures as low as 0.1 to 0.3 atm (10 30 kPa). Recent research has shown that plants are capable of surviv ing in such environm ents; however, they experience increased rates of evapotranspirati on. The enormous costs associated with launching a manned mission to Mars make it critical that plants be not only capable of survival, but also of producing fruit a nd seed. Even slight environmental stress throughout the life of a plant can greatly aff ect growth, quality, and reproduction. The effect of the environment on the rate of pl ant water loss should be considered in the design of a Mars greenhouse. In this research, water loss of mature radish plants in response to their environment was evaluated by application of a mathematical model. An evapotranspiration model was used to predict the rate of evapotranspiration of 18-to-24-day-old radish plants in

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97 response to changes in pressure, CO2 concentration, and photosynthetically active radiation (PAR). A system of three low-pr essure bell jar based controlled environment chambers were designed and built for this research. The system provided control of pressure, CO2 concentration, air temperature, and relative humidity and measured plant weight and leaf temperature. The rate of convection heat transfer is an important component of the canopy energy balance and the evapotranspiration model. The effects of reduced pressure and air velocity on convection were determined by comparison of a theoretical model for the external resistance to sensible heat transfer with empirical values cal culated from the rate of cooling for a thin, heated sheet. Theoreti cal versus empirical data were compared for four levels of pressure (12, 33, 66, and 101 kPa) and four air velocities (still air, 1.9, 2.8, and 5.8 m s-1). The theoretical model fit the empiri cal data well with an average error of only 2.6 m s-1. As predicted by the model, external resistance was proportional to both pressure and air velocity. Another important parameter in the evapot ranspiration model was the resistance to water loss by the canopy surface. The rate of water evaporation from the interior of the leaf is inhibited by the cuticle and stomata. The surface resistance acco unts for this effect and is influenced mostly by the opening and closing of stomata. Changes in surface resistance can be interprete d as the stomatal response to environmental conditions. A model was developed to predict surface resistance as a functio n of pressure for elevated CO2 and reduced PAR. The model calculated surface resistance as a reference value (taken at standard pressure) for particular levels of CO2 and PAR multiplied by an empirically determined function. The pr edicted values of surface resistance were

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98 compared with values calculated from measur ed rates of evapotranspiration. At 12 kPa there was a more significant decrease in resistance and corresponding increase in evapotranspiration. There was al so a significant effect of CO2 on stomatal control. When CO2 rose from 40 to 150 Pa surface resist ance increased and evapotranspiration decreased. In fact, the decrease in evapotranspiration rate for elevated CO2 at 12 kPa was significant enough to prevent wilting. Decreasing PAR from 340 to 160 mol m-2 s-1 had little effect on surface resistance or evapotranspiration. The resistance models accounting for th e effects of pressure and other environmental variables on convection heat tran sfer and stomatal cont rol were built into the evapotranspiration model. The overall m odel performed adequately well with a root mean square error compared to inde pendent data of less than 0.5 g m-2 min-1. The heat balance for a plant in a greenhous e on Mars will be much different than for a plant on Earth. Evapotranspiration will occur faster and plants may lose heat rather than gain it by radiation. The result will li kely be leaf temperatures much lower than typically faced by plants on earth. These lower leaf temperatures will invalidate some of the underlying assumptions made in the derivation of the Penman-Monteith model with regard to leaf temperature. Parameters often taken at air temperature should be taken at leaf temperature to improve model accuracy. Chilling injury may also occur in plants adapted for warmer conditions. Application of an evapotranspiration m odel for Mars greenhouse conditions was useful for understanding how plants will respond in those conditions with regard to the rate of water loss by evapotranspiration. Reduced pressure increases the rate of evapotranspiration by decreasing re sistances to sensible and latent heat loss as well as

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99 reducing the effectiveness of convection. Howe ver, selecting appropriate values for other environmental parameters may enable plants to withstand very low pressures. For example, in elevated CO2 concentrations plants close their stomata. This increases surface resistance and, consequently, evapotrans piration decreases. The structure itself may also reduce the rate of water loss. In a Mars greenhouse the co ld interior surface temperature will cool leaves by radiation heat transfer. This cooling will also reduce the rate of evapotranspiration. Properly selecting environmental parameters will make it possible to grow plants at super low pressures; however, they will be much more dependent on the performance of the environm ental control system. If, for example, the CO2 control system fails, plants growing in pre ssures below 25 kPa will wilt within a half hour of a decrease in CO2. In other words, at super low pressures failure of the control system will almost definitely result in failure of the crop. The model applied in this research was useful for better understanding how plants will respond to environmental conditions in a Mars greenhouse. Yet more research is needed to develop a more reliable evapotrans piration model that can be incorporated into the Mars greenhouse control system. In particular, the model for surface resistance should be expanded to include more crops a nd environmental parameters. Only mature radish plants were used in this research. The effect of reduced pressures on development should also be examined. It is hypothesized that stomatal density of plants grown in reduced pressures will be less than plants gr own at standard pressure. Such changes in stomatal density would affect surface resi stance and should be accounted for in the reference surface value. The model should al so be expanded to predict surface resistance as a function of CO2, PAR, and VPD. Such functions have already been developed for

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100 many crops. Genetic modifications are likely for plants selected for the Mars greenhouse to improve their ability to withstand stressfu l conditions such as low temperatures. Any changes in stomatal control as a result of genetic modification shoul d be accounted for in the surface resistance model.

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101 LIST OF REFERENCES Al-Faraj, A., G. E. Meyer, and J. B. F itzgerald. 1994. Simulated Water Use and Canopy Resistnace of New Guinea Impatiens ( Impatiens X hb.) in Single Pots Using Infrared Heating. Transactions of the ASAE 37(6): 1973-1980. Andre, M. and D. Massimino. 1992. Growth of Plant at Reduced Pressures: Experiments in Wheat-Technological Advant ages and Constraints. Advances in Space Research 12(5): 97-106. American Society of Heating, Refrig eration, and Air-Conditioning Engineers (ASHRAE). 2001. ASHRAE Handbook: Fundamentals. Atlanta, GA: ASHRAE. Assmann, S. M. 1999. The Cellular Basi s of Guard Cell Sensing of Rising CO2. Plant, Cell, and Environment 22(6): 629-637. Aubinet. M., J. Deltour, and D. DeHalle ux. 1989. Stomatal Regulation in Greenhouse Crops: Analysis and Simulation. Agricultural and Fo rest Meteorology 48:21-44. Bailey, B. J. and J. F. Meneses. 1995. Modelling Leaf Convective Heat Transfer. Acta Horticulturae 399: 191-198. Baille, M., A. Baille, and J. C. Laury. 1994. Canopy Surface Resistances to Water Vapour Transfer for Nine Greenhouse Pot Plant Crops. Scientia Horticulturae 57: 143-155. Bakker, J. C. 1991. Effects of Humidity on Stomatal Density and its Relation to Leaf Conductance. Scientia Horticulturae 48: 205-212. Brown, D. L. 2002. A Distributed Control System for Low-Pressure Plant Growth Chambers M.S. thesis. College Station, TX: Texas A&M University, Department of Biological and Agricultural Engineering. Bucklin, R. A., P. A. Fowler, V. Y. Rygalov, R. M. Wheeler, Y. Mu. I. Hublitz, and E. G. Wilkerson. 2004. Greenhouse Design for th e Mars Environment: Development of a Prototype, Deployable Dome. Acta Horticulturae 659: 127-134. Comstock, J. P. 2002. Hydraulic and Chemical Signalling in the Control of Stomatal Conductance and Transpiration. Journal of Experimental Botany. 53(367): 195200.

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102 Corey, K. A., D. J. Barta, and D. L. He nninger. 1997. Photosynthesi s and Respiration of Wheat Stand at Reduced Atmospheri c Pressure and Reduced Oxygen. Advances in Space Research 20(10): 1869-1877. Corey, K. A., D. J. Barta, and R. M. Wheeler. 2002. Toward Martial Agriculture: Responses of Plants to Hypobaria. Life Support & Biosphere Science 8: 103-114. Dally, J. W., W. F. Riley, and K. G. McConnell. 1993. Instrumentation for Engineering Measurements, Second Edition New York, NY: John Wiley and Sons, Inc. Daunicht, H. J. and H. J. Brinkjans. 1992. Gas Exchange and Growth of Plants Under Reduced Pressure. Advances in Space Research 12(5): 107-114. Ferl, R. J., A. C. Schuerger, Paul A., W. B. Gurley, K. Corey, and R. A. Bucklin. 2002. Plant Adaptation to Low Atmospheric Pre ssures: Potential Molecular Responses. Life Support & Biosphere Science 8: 93-101. Fowler, P. A., V. Y. Rygalov, R. A. Bu cklin, and R. M. Wheeler. 2001. Design and Control of Interior Climate of Martian Greenhouses. ASAE Paper No FL01104 American Society of Agricultural Engineers, St Joseph, MI. Gay, A. P. and R. G. Hurd. 1975. Influen ce of Light on Stomatal Density in Tomato. New Phytologist 75(1): 37-46. Goto, E., K. Iwabuchi, and T. Takakura. 1995. Effect of Reduced Total Air Pressure on Spinach Growth. Journal of Agricultural Meteorology 51(2): 139-145. Goto, E., H. Ohta, K. Iwabuchi, and T. Takakura. 1996. Measurement of Net Photosynthetic and Transpiration Rates of Spinach and Maize Plants under Hypobaric Condition. Journal of Agricult ural Meteorology 52(2): 117-123. Goto, E., Y. Arai, and K. Omasa. 2002. Grow th and Development of Higher Plants Under Hypobaric Conditions. 2002 International Conference of Environmental Systems Meeting Paper No 2002-01-2439 Society of Automotive Engineers, San Antonio, TX. Hanan, J. J. 1998. Greenhouses: Advanced Technology for Protected Horticulture Boca Raton, FL: CRC Press. Henderson, S. M., R. L. Perry, and J. H. Young. 1997. Principles of Process Engineering, Fourth Edition. St. Joseph, MI: ASAE. Incropera, F. P. and D. P. DeWitt. 1996. Fundamentals of Heat and Mass Transfer, Fourth Edition. New York, NY: John Wiley and Sons, Inc. Jarvis, P. G. 1976. The Interpretation of th e Variations in Leaf Water Potential and Stomatal Conductance Found in Canopies in the Field. Phil Trans R Soc Lond B 273: 593-610.

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103 Jarvis, P. G. and K. G. McNaughton. 1986. St omatal Control of Transpiration: Scaling Up from Leaf to Region. Advances in Ecological Research 15: 1-45. Jones, H. G. 1992. Plants and Microclimate: A Quantita tive Approach to Environmental Plant Physiology, Second Edition. New York, NY: Cambridge University Press. Jones, P., L. H. Allen, J. W. Jones, and R. Valle. 1985. Photosynthesis and Transpiration Responses of Soybean Canopies to Short-Term and Long-Term CO2 Treatments. Agronomy Journal 77(1): 119-126. Jordan, D. N., and W. K. Smith. 1995. Micr oclimate Factors Influencing the Frequency and Duration of Growth Season Frost for Subalpine Plants. Agricultural and Forest Meteorology 77: 17-30. Lhomme. J. P. 2001. Stomatal Control of Tran spiration: Examination of the Jarvis-type Representation of Canopy Resistan ce in Relation to Humidity. Water Resources Research 37(3): 689-699. Massimino, D. and M. Andre. 1999. Grow th of Wheat Under one-Tenth of the Atmospheric Pressure. Advances in Space Research 24(3): 293-296. Monteith, J. L. 1965. Evaporation and Environment. Symp Soc Exp Biol 19: 205-234. Monteith, J. L. 1995. A Reinterpretation of Stomatal Responses to Humidity. Plant, Cell, and Environment 18: 357-364. Monteith, J. L. and M. H. Unsworth. 1990. Principles of Environmental Physics, Second Edition. Boston, MA: Butterworth Heinemann. Mott, K. A. and D. F. Parkhurst. 1991, St omatal Responses to Humidity in Air and Helox. Plant, Cell, and Environment 14: 509-515. Mu, Y. 2005. A Distributed Control System for Lo w Pressure Plant Growth Chambers. Ph.D. dissertation. Gainesville, FL: Un iversity of Florida, Agricultural and Biological Engineering Department. National Aeronautics and Space Administra tion (NASA). 2005. Mars Fact Sheet: NASA. Available at: http://nssdc.gsfc.nasa .gov/planetary/factsheet/marsfact.html. Accessed 15 August 2005. Nobel, P.S. 1999. Physicochemical and Environm ental Plant Physiology, Second Edition. San Diego, CA: Academic Press. Omega Engineering, Inc. 2005. Thermoc ouples An Introduction. Available at: http://www.omega.com/thermocouples.html. Accessed 26 August 2005. Outlaw, W. H. 2003. Integration of Cellular and Physiological Functions of Guard Cells. Critical Reviews in Plant Science 22(6): 503-529.

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104 Paul A., A. C. Schuerger, M. P. Popp, J. T. Richards, M. S. Manak, and R. J. Ferl. 2004. Hypobaric Biology: Arabidopsis Gene Expr ession at Low Atmospheric Pressure. Plant Physiology 134: 215-223. Penman, H. L. 1948. Natural Evaporation Fr om Open Water, Bare Soil and Grass. Proc Roy Soc London (A) 193: 120-145. Purswell, J. L. 2002. Engineering Design of a Hypobaric Plant Growth Chamber M.S. thesis. College Station, TX: Texas A&M Un iversity, Department of Biological and Agricultural Engineering. Rule, D. E. and G. L. Staby. 1981. Growth of Tomato Seedlings at Sub-atmospheric Pressures. HortScience 16(3): 331-332. Rygalov, V. Y., P. A. Fowler, J. M. Me tz, R. M. Wheeler, and R. A. Bucklin. 2002. Water Cycles in Closed Ecological Syst ems: Effects of Atmospheric Pressure. Life Support & Biosphere Science 8: 125-135. Schoch, P. G., C. Zinsou, and M. Sibi. 1980. Dependence of the Stomatal Index on Environmental Factors during Stomatal Differentiation in Leaves of Vigna-Sinensis L. 1. Effect of Light Intensity. Journal of Experimental Botany 31(124): 12111216. Stanghellini, C. 1987. Transpiration of Greenhouse Crops: An Aid to Climate Management Ph.D. dissertation Landbous universiteit, Wageningen. Stanghellini, C. and J. A. Bunce. 1993. Re sponse of Photosynthesis and Conductance to Light, CO2, Temperature, and Humidity in Tomato Plants Acclimated to Ambient and Elevated CO2. Photosynthetica 29(4): 487-497. Wheeler, R. M., C. L. Mackowiak, N. C. Yorio, and J. C. Sager. 1999. Effects of CO2 on Stomatal Conductance: Do Stomata Open at Very High CO2 Concentrations? Annals of Botany 83: 243-251. Woodward, F. I. 1987. Stomatal Number s are Sensitive to Increases in CO2 from Preindustrial Levels. Nature 327(6123):617-618. Zhang, L. and R. Lemeur. 1992. Effect of Aerodynamic Resistance on Energy Balance and Penman-Monteith Estimates of Eva potranspiration in Greenhouse Conditions. Agricultural and Forest Meteorology 58: 209-228. Zolnier, S., R. S. Gates, J. Buxton, and C. Mach. 2000. Psychrometric and Ventilation Constraints for Vapor Pre ssure Deficit Control. Computers and Electronics in Agriculture 26: 343-359. Zolnier, S., R. S. Gates, R. L. Geneve, and J. W. Buxton. 2001. Surface Diffusive Resistances of Rooted Poinsettia Cu ttings Under Controlled-Environment Conditions. Transactions of the ASAE 44(6): 1779-1787.

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105 Zolnier, S., G. B. Lyra, R. S. Gates. 2004. Evapotranspiration Estimates for Greenhouse Lettuce Using an Intermittent Nutrient Film Technique. Transactions of the ASAE 47(1):271-282.

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106 APPENDIX A SENSOR CALIBRATIONS All sensors used in this research to mon itor radish plants and bell jar environment were calibrated within one year of all e xperiments. With the exception of relative humidity sensors, which were factory calib rated, all sensors and thermocouples were calibrated in place. Pressure Pressure sensors (Bell jars 1 a nd 3: MPXH6101A6U and Bell jar 2: MPXH6115A6U, Freescale Semiconductor, Inc., Austin, TX) were calibrated by linear regression analysis in comparis on to a dial pressure gauge (Model CM, Heise, Stratford, CT) in line between the vacuum pump and bell jars over the range of 10 101 kPa. Figure A-1 shows the data, best fit line, regression coefficien t, and standard error for each sensor. The standard error was less than 0.2 kPa for each sensor. Leaf Temperature Leaf temperature was measured using mi niature infrared thermocouples (model OS36SM, Omega, Stamford, CT). These infrared thermocouples had a type-K thermocouple output, but had significantly hi gher internal impedances. A three-point calibration was performed by comparing the thre e infrared thermocouples to a precision infrared sensor (Model 4000.4GL, Everest In terscience, Inc, Tucson, AZ) with NIST traceable calibration. One by one an infrared thermocouple and the precision infrared sensor were directed at an open container of water just above the surface and the readings recorded. Some drift was observed in the offset of the calibration equation. As a result, a

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107 one-point calibration was performed daily as described above to determine the offset. The slope of the calibration curve remained cons tant over the course of all experiments. Figure A-2 shows the calibration da ta and best fit line for infrared sensors in bell jar 1. The infrared thermocouples were read by an Optp22 SNAP-AITM analog input module. According to manufacturers specifications, the calibrate d sensor accuracy was 0.8 oC. P = 18.99* V1 + 9.41 R2 = 1, SE = 0.1 kPa P = 19.06* V2 + 9.30 R2 = 0.9999, SE = 0.2 kPa P = 22.53*V3 + 8.74 R2 = 1, SE = 0.2 kPa0.0 25.0 50.0 75.0 100.0 125.0 0123456 Sensor reading, VPressure, kPa Sensor 1 Sensor 2 Sensor 3 Figure A-1. Pressure sensor cal ibration. The microchip sensors used to monitor pressure inside the bell jars were calibrated in comparison to a vacuum gage. Linear regression analysis was used to determin e the best fit lines and error for each sensor.

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108 T = 1.3466* IR1 45.93 R2 = 0.9997 15 20 25 30 35 40 454749515355575961IR sensor readingTemperature, C Figure A-2. Infrared sensor calibration. Th e data and best-fit line for a three-point calibration is shown for IR1. T = 1.01* TC1 0.53 T = 1.01* TC2 0.83 T = 1.00*TC3 0.2516 21 26 31 36 41 46 16212631364146 Thermocouple reading, CActual temperature, C TC 1 TC 2 TC 3 Figure A-3. Thermocouple calib ration. The type-T thermocouples used to monitor air temperature inside the bell jars were calibrated using a two point temperature calibration.

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109 Air Temperature The temperature inside each bell jar wa s measured by type-T thermocouples. A two point calibration (Figure A-3) was pe rformed using a thermocouple calibrator (TCAL, Sun Electronic Systems, Inc., Titusvi lle, FL). Estimated er ror of the calibrated thermocouples was 1.0 oC (Omega, 2005). Weight The load cells inside each bell jar were calibrated by linear regression analysis using standard weights. Figur e A-4 shows the calibration data best fit lines, regression coefficient, and standard error for each load cell. Standard error was less than 0.2 g for all three load cells. As for the infrared th ermocouples, some drift was observed in the offset of the calibration equation. As a resu lt, a routine was added to the control program to perform a one-point calibration with no weight on the scale to zero it. The slope of the calibration curve remained constant over the course of all experiments. m = 88.334*V1 182.39 R2 = 1, SE = 0.18 g m = 79.928*V3 263.4 R2 = 1, SE = 0.03 g m = 85.351*V2 677.06 R2 = 1, SE = 0.16 g0 50 100 150 200 024681012 Load cell output, mVMass, g load cell 1 load cell 2 load cell 3 Figure A-4. Load cell calibration. The load cells were calibrated us ing standard weights and linear regression analysis.

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110 Carbon Dioxide Concentration The response of the carbon dioxide sensors us ed in this research was sensitive to pressure. The calibration equation developed acc ounted for the effect of pressure using a method similar to Mu (2005). A two point calibration was applied to each carbon dioxide sensor at approximately 10, 30, 50, 70, 90, and 101 kPa. The sensor reading was compared to the CO2 concentration as measured by a gas chromatograph. For each sensor an equation was fit to the slopes and intercepts of the linear regression equations as a function of pressure. The form of final calibration equations is below. ) P ( g V )* P ( f COCO 2 2 (A-1) where [CO2] = CO2 concentration, ppm VCO2 = CO2 sensor output, V f(P) = slope as a function of pressure (from Table A-1) g(P) = intercept as a functi on of pressure (from Table A-1) Figure A-5 shows the functions determin ed by linear regression analysis of CO2 concentration as a function of sensor output for sensor 1 at six pressures. Only the plots for sensor 1 are shown. The slope and intercept equations fo r all three sensors are given in Tables A-1. To obtain the CO2 concentration, these pre ssure dependent slope and intercept equations were plugged into equation A-1.

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111 [CO2] = 519.75*VCO2 131.29 [CO2] = 728.75*VCO2 201.31 [CO2] = 1602.9*VCO2 373.26 [CO2] = 1921.9*VCO2 29.121 [CO2] = 4037*VCO2 + 287.74 [CO2] = 1324.7VCO2 546.92500 600 700 800 900 1000 1100 1200 1300 00.511.522.5Sensor output, VCarbon dioxide concentration, ppm 10.1 29.4 47.5 64.0 83.3 101.6 Figure A-5. Carbon dioxide sens or calibration. Linear f unctions determined by linear regression analysis for sensor 1 at si x pressures ranging from approximately 10 to 101 kPa. Table A-1. Slope and intercept equa tions for carbon dioxide sensors. Sensor Slope Intercept 1 4645e-0.0208*P 0.2486*P2 33.492*P + 656.87 2 2791e-0.0184*P 0.0558*P2 8.264 + 300 3 4547.1e-0.0254*P 0.0857*P2 11.424*P + 418.07 The accuracy of the carbon dioxide sens ors is listed by the manufacturer as 40ppm + 3% of the reading. Since the sens or accuracy is a function of the sensor output, the accuracy of car bon dioxide readings is depe ndent on concentration and pressure. It ranges from 52 ppm for an ambient CO2 concentration of 400 ppm at standard pressure to 490 ppm for a c oncentration of 15000 ppm at 10 kPa.

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112 Oxygen concentration Like the carbon dioxide sens ors, the oxygen sensors used in this research were sensitive to changes in total pressure. Th e calibration procedure for the oxygen sensors was the same as for the CO2 sensors. A two-point calib ration was performed with one point determined by comparing the sensor output to oxygen concentration measured by a gas chromatograph. The second calibrati on point was obtained by assuming that the sensor output was zero volts when the oxygen concentration was zero. Table A-2 gives the slope equation for the thre e oxygen sensors. The assumption of zero voltage when no oxygen was present meant that there was no offs et term in the calibration equation. The resulting oxygen sensor calibrati on equation is given below. 2 2 OV ) P ( f O (A-2) where: [O2] = O2 concentration, % VO2 = O2 sensor output, mV f(P) = slope as a function of pressure (from Table A-2) Table A-2. Slope equations for the oxygen sensors. Sensor Slope 1 158.6*P-0.9783 2 148.7*P-0.9892 3 146.0*P-0.9893

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113 APPENDIX B SENSOR ERROR BUDGETS The error budget for each measured parame ter was the accumulated error of the sensor and measurement system. Total error was estimated as the root sum square error (Root SSE) calculated by the followi ng equation (Dally et al., 1993). 2 2 m se e SSE Root where es = sensor error, em = error of the measurement system The error of each sensor and measurement sy stem accounted for the accuracy and sources of error as appropriate. E rror estimation calculations for the Opto 22 analog input modules used in this research and each environmental parameter are given here. Voltage Input Module (SNAP-AIV-4) accuracy = 2.5 mV at 5 VDC offset temperature coefficient = 15 ppm/oC gain temperature coefficient = 30 ppm/oC Offset drift (25 oC) = (15 x 10-6 ppm/oC)(25 oC)(5 VDC full scale) = 1.875 mV Gain drift (25 oC) = (30 x 10-6 ppm/oC)(25 oC)(5 VDC full scale) = 3.75 mV The overall root sum square error: mV mV mV mV SSE Root 9 4 ) 75 3 ( ) 875 1 ( ) 5 2 (2 2 2 Voltage Input Module (SNAP-AITM-2) accuracy = 0.1% at 50 mV

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114 offset temperature coefficient = 5 V/oC gain temperature coefficient = 2 V/oC Accuracy = (0.001)(50 mV) = 0.05 mV Offset drift (25 oC) = (5 x 10-6 V/oC)(25 oC) = 0.125 mV Gain drift (25 oC) = (2 x 10-6 V oC)(25 oC) = 0.05 mV The overall root sum square error: mV mV mV mV SSE Root 14 0 ) 05 0 ( ) 125 0 ( ) 05 0 (2 2 2 Pressure Accuracy from calibration = 0.52 kPa Voltage-to-pressure relationship (from calibration) = 22.47 kPa/V SNAP-AIV-4 error = 4.9 mV Input module error = (0.0049 V)(22.47 kPa/V) = 0.11 kPa The overall root sum square error: kPa kPa kPa SSE Root 53 0 ) 11 0 ( ) 52 0 (2 2 Relative Humidity Sensor accuracy = 2% RH Linearity = 0.5% RH Full scale = 5 VDC SNAP-AIV-4 error = 4.9 mV The sensor root sum square error: % 1 2 %) 5 0 ( %) 2 ( ) (2 2 sensor SSE Root Input module error = (0.0049 V) (1/5 V) = 0.1 % RH

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115 The overall root sum square error: % 1 2 %) 1 0 ( %) 1 2 (2 2 SSE Root Oxygen Sensor accuracy = 1.0 % full scale at constant temperature and pressure SNAP AITM-2 accuracy = 0.14 mV Voltage-to-oxygen relationship (theoretical) = 1.67 % O2/mV Full scale = 59.9 mV Sensor accuracy = (1.0 %) (59.9 mV) = 0.6 mV The overall root sum square error: 2 2 20 1 62 0 14 0 6 0 O % mV ) mV ( ) mV ( SSE Root Carbon Dioxide Sensor accuracy = 40 ppm + 3% of reading Voltage-to-carbon dioxide respon se (theoretical) = 500 ppm/V SNAP-AIV-4 accuracy = 4.9 mV Sensor accuracy (at 2000 ppm) = 40 ppm + (0.03)(2000 ppm) = 100 ppm = 0.2 V Sensor accuracy (at 1000 ppm) = 40 ppm + (0.03)(1000 ppm) = 70 ppm = 0.14 V The overall root sum squa re error (at 2000 ppm): ppm V V V SSE Root 100 2 0 ) 0047 0 ( ) 2 0 (2 2 The overall root sum squa re error (at 1000 ppm): ppm V V V SSE Root 70 14 0 ) 0047 0 ( ) 14 0 (2 2 Leaf temperature Module and calibrated sensor accuracy (SNAP-AITM module specifications) = 0.8 oC

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116 Air temperature Module and calibrated sensor accuracy (S NAP-AITM2 module specifications) =2.0 oC

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117 APPENDIX C BELL JAR BASE DRAWINGS As part of this research new bell jar bases were designed to house the cooling coil, fans, humidifier, and wiring connections below the bell jar itself to maximize space for the plants. The bases were constructed out of aluminum by machinists at the Kennedy Space Center prototype shop. The following figures show the actual dimensions and details of the bell jar bases.

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118 Fi g ure C-1. To p view of bell j ar base. All dimensions are in inches ( not to scale )

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119 Fi g ure C-2. Bottom view of bell j ar base. All dimens ions are in inches ( not to scale )

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120 Figure C-3. Bell jar base top plate. All dimensions are in inches (not to scale).

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121 Figure C-4. Cooling coil. All dimens ions are in inches (not to scale).

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122 APPENDIX D BELL JAR CONTRO L ALGORITHM An Opto 22 system was used for data acquisition and control for the bell jar chambers. The control program, written in ioControl 6. 0, is shown below. ioControl is a flowchart based software. The flowchart for each routine is shown followed by the instructions and code for each block of th e chart. The user interface, written in ioDisplay 6.0 is also included. Data Buffer Routine Action Block: Delay (sec) (Id: 0) Exit to: Buffer sensor readings (Id: 9) Delay variable buffer Delay (mSec) 500 OptoScript Block: Buffer sensor readings (Id: 9) Exit to: Delay (sec) (Id: 0) // Get sensor readings for k = 1 to 10 step 1 // Bell jar 1 TC1 = TC_0; // thermocouple IR1 = IR_0; // IR thermocouples rh1 = rh_0; //Relative humidity sensor

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123 prsr1= prsr_0; //Pressure sensor co21 = co2_0; //Carbon dioxide sensor o21 = o2_0; //Oxygen sensor lc1 = lc_0; //Load cell // Bell jar 2 TC2 = TC_1; // thermocouple IR2 = IR_1; // IR thermocouples rh2 = rh_1; //Relative humidity sensor prsr2= prsr_1; //Pressure sensor co22 = co2_1; //Carbon dioxide sensor o22 = o2_1; //Oxygen sensor lc2 = lc_1; //Load cell // Bell jar 3 TC3 = TC_2; // thermocouple TC4 = TC_3; IR3 = IR_2; // IR thermocouples rh3 = rh_2; //Relative humidity sensor prsr3= prsr_2; //Pressure sensor co23 = co2_2; //Carbon dioxide sensor o23 = o2_2; //Oxygen sensor lc3 = lc_2; //Load cell // Ignore out of range load cell readings if (lc1>1000) then lc1 = 0; elseif (lc1<0) then lc1 = 0; endif if (lc2>1000) then lc2 = 0; elseif (lc2<0) then lc2 = 0; endif if (lc3>1000) then lc3 = 0; elseif (lc3<0) then lc3 = 0; endif // Buffer sensor readings to eliminate noise // Bell jar 1

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124 TC1_sum = TC1_sum + TC1; // thermocouple IR1_sum = IR1_sum + IR1; // IR thermocouples rh1_sum = rh1_sum + rh1; //Relative humidity sensor prsr1_sum = prsr1_sum + prsr1; //Pressure sensor co21_sum = co21_sum + co21; //Carbon dioxide sensor o21_sum = o21_sum + o21; //Oxygen sensor lc1_sum = lc1_sum + lc1; //Load cell // Bell jar 2 TC2_sum = TC2_sum + TC2; // thermocouple IR2_sum = IR2_sum + IR2; // IR thermocouples rh2_sum = rh2_sum + rh2; //Relative humidity sensor prsr2_sum = prsr2_sum + prsr2; //Pressure sensor co22_sum = co22_sum + co22; //Carbon dioxide sensor o22_sum = o22_sum + o22; //Oxygen sensor lc2_sum = lc2_sum + lc2; //Load cell // Bell jar 3 TC3_sum = TC3_sum + TC3; // thermocouple TC4_sum = TC4_sum + TC4; IR3_sum = IR3_sum + IR3; // IR thermocouples rh3_sum = rh3_sum + rh3; //Relative humidity sensor prsr3_sum = prsr3_sum + prsr3; //Pressure sensor co23_sum = co23_sum + co23; //Carbon dioxide sensor o23_sum = o23_sum + o23;

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125 //Oxygen sensor lc3_sum = lc3_sum + lc3; //Load cell next // Reset intermediate variable sums // Bell jar 1 TC1_avg = TC1_sum/10; // thermocouple IR1_avg = IR1_sum/10; // IR thermocouples rh1_avg = rh1_sum/10; //Relative humidity sensor prsr1_avg = prsr1_sum/10; //Pressure sensor co21_avg = co21_sum/10; //Carbon dioxide sensor o21_avg = o21_sum/10; //Oxygen sensor lc1_avg = lc1_sum/10; //Load cell // Bell jar 2 TC2_avg =TC2_sum/10; // thermocouple IR2_avg = IR2_sum/10; // IR thermocouples rh2_avg = rh2_sum/10; //Relative humidity sensor prsr2_avg = prsr2_sum/10; //Pressure sensor co22_avg = co22_sum/10; //Carbon dioxide sensor o22_avg = o22_sum/10; //Oxygen sensor lc2_avg = lc2_sum/10; //Load cell // Bell jar 3 TC3_avg = TC3_sum/10; // thermocouple TC4_avg = TC4_sum/10; // thermocouple IR3_avg = IR3_sum/10; // IR thermocouples rh3_avg = rh3_sum/10; //Relative humidity sensor prsr3_avg = prsr3_sum/10; //Pressure sensor co23_avg = co23_sum/10; //Carbon dioxide sensor o23_avg = o23_sum/10; //Oxygen sensor lc3_avg = lc3_sum/10; //Load cell // Bell jar 1 TC1_sum = 0; // thermocouple IR1_sum = 0; // IR thermocouples rh1_sum = 0; //Relative humidity sensor prsr1_sum = 0; //Pressure sensor co21_sum = 0; //Carbon dioxide sensor o21_sum = 0; //Oxygen sensor lc1_sum = 0; //Load cell // Bell jar 2 TC2_sum = 0; // thermocouple

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126 IR2_sum = 0; // IR thermocouples rh2_sum = 0; //Relative humidity sensor prsr2_sum = 0; //Pressure sensor co22_sum = 0; //Carbon dioxide sensor o22_sum = 0; //Oxygen sensor lc2_sum = 0; //Load cell // Bell jar 3 TC3_sum = 0; // thermocouple TC4_sum = 0; IR3_sum = 0; // IR thermocouples rh3_sum = 0; //Relative humidity sensor prsr3_sum = 0; //Pressure sensor co23_sum = 0; //Carbon dioxide sensor o23_sum = 0; //Oxygen sensor lc3_sum = 0; //Load cell Variable Update Routine Action Block: Delay 1 sec (Id: 0) Exit to: Update variable values (Id: 1) variable update delay Delay (mSec) 1000 OptoScript Block: Update variable values (Id: 1) Exit to: Delay 1 sec (Id: 0) // This block assigns sensor readings to variables //For bell jar 1, if online if (bJar1 == 1) then

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127 Ta[0] = 1.01* TC1_avg 0.53; Tl[0] = 1.35* IR1_avg-21.96; // Leaf temperature, IR sensors RH[0] = 23.9* rh1_avg-21.96; //Relative humidity Prsr[0] = prsr1_avg 18.99 + 9.41; //Pressure CO2[0] = 4645 RaiseEToPower(-0.0208 Prsr[0]) co21_avg + (0.2486 Prsr[0] Prsr[0] 33.492 Prsr[0] + 656.87); //Carbon dioxide O2[0] = 158.6 power(Prsr[0],-0.9783) o21_avg; //Oxygen weight[0] = 88.334 (1000 lc1_avg) 182.39 + offset[0]; //Plant weight else Ta[0] = 0; // Air temperatures, T thermocouples Tl[0] = 0; // Leaf temperature, IR thermocouples RH[0] = 0; //Relative humidity Prsr[0] = 0; //Pressure CO2[0] = 0; //Carbon dioxide O2[0] = 0; //Oxygen weight[0] = 0; //Plant weight endif //For bell jar 2, if online if (bjar2 == 1) then Ta[1] = 1.01 TC2_avg 0.88; // Air temperatures, T thermocouples Tl[1] = IR2_avg 1.29 + IRoffset_2; // Leaf temperature, IR sensors RH[1] = rh2_avg* 23.7 21.9; //Relative humidity Prsr[1] = prsr2_avg 19.06 + 9.30; //Pressure CO2[1] = 2791 RaiseEToPower(-0.0184 Prsr[1]) co22_avg + (0.05586 Prsr[1] Prsr[1]-8.2642 Prsr[1]+300); //Carbon dioxide O2[1] = 148.7 power(Prsr[1],-0.9872) o22_avg; //Oxygen weight[1] = 85.351 (1000 lc2_avg) 677.06 + offset[1]; //Plant weight else Ta[1] = 0; // Air temperatures, T thermocouples Tl[1] = 0; // Leaf temperature, IR thermocouples RH[1] = 0; //Relative humidity Prsr[1] = 0; //Pressure CO2[1] = 0; //Carbon dioxide O2[1] = 0; //Oxygen weight[1] = 0; //Plant weight endif //For bell jar 3, if online if (bjar2 == 1) then Ta[2] = TC3_avg 0.25; // Air temperatures, T thermocouples Tc[2] = TC4_avg; // Coil temperature, T thermocouples Tl[2] = IR3_avg 1.2696 + IRoffset_3; // Leaf temperature, IR sensors RH[2] = rh3_avg* 23.9 21.4; //Relative humidity Prsr[2] = prsr3_avg 22.53+8.74; //Pressure CO2[2] = 4547 RaiseEToPower(-0.0254 Prsr[2]) co23_avg + (0.0857 Prsr[2]

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128 Prsr[2]11.429 Prsr[2]+418.1); //Carbon dioxide O2[2] = 146.0 power(Prsr[2],-0.9893) o23_avg; //Oxygen weight[2] = 79.928 (1000 lc3_avg) 263.4 + offset[2]; //Plant weight else Ta[2] = 0; // Air temperatures, T thermocouples Tl[2] = 0; // Leaf temperature, IR thermocouples RH[2] = 0; //Relative humidity Prsr[2] = 0; //Pressure CO2[2] = 0; //Carbon dioxide O2[2] = 0; //Oxygen weight[2] = 0; //Plant weight endif Fan Control Routine Action Block: Delay 1 sec (Id: 0) Exit to: Is fan flag high? (Id: 3) Delay (Sec) 1.0 Action Block: Fans OFF (Id: 7) Exit to: Delay 1 sec (Id: 0) turn fans off Turn Off doFans Action Block: Fans ON (Id: 2) Exit to: Delay 1 sec (Id: 0) turn fans on Turn On doFans Condition Block: Is fan flag high? (Id: 3) Operator Type: AND

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129 TRUE Exit to: Fans ON (Id: 2) FALSE Exit to: Fans OFF (Id: 7) Is bFans Variable True? Carbon Dioxide and Pressure Control Action Block: Delay 2 sec (Id: 0) Exit to: MFC control (Id: 4) Delay (Sec) 2.0 OptoScript Block: MFC control (Id: 4) Exit to: Pressure control logic (Id: 27) // If CO2 addition needed, turn on MFC for calculated time ////// Bell jar 1 ////// if (bJar1) then if (hasdowntimerexpired(dtdiffusion_0)) then if (CO2_set[0] CO2[0] > 40) then // Toggle flags for user interface bCO2[0] = 1; // Raise CO2 flag for bell jar 1 bMFC = 1; // Raise mass flow controller flag // Set MFC flow rate and timer Q = (Prsr[0]/10) 5; // If CO2 setpoint is 160 ppm or more > actual CO2, //only try to fill to 90% if (CO2_set[0] CO2[0] > 160) then

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130 MFCtime[0] = (CO2_set[0] CO2[0])*0.9/40; else MFCtime[0] = 1.0; endif // Open appropriate solenoids and start mass flow //controller and timer turnon(doBJsol_0); // Open bell jar solenoid setdowntimerpreset(MFCtime[0] dtMFC_0); // Set timer turnon(doCO2); // Open CO2 solenoid aoMFC = Q/10; // Turn on MFC at specified flow rate starttimer(dtMFC_0); // Start timer // Wait while timer counts down while (not hasdowntimerexpired(dtMFC_0)) delaymsec(100); wend // Close solenoids and turn off MFC after timer //expires aoMFC = -1.0; // Turn off MFC turnoff(doCO2); // Close CO2 solenoid turnoff(doBJsol_0); // Close bell jar solenoid bCO2[0] = 0; bMFC = 0; // Set down timer to allow for CO2 diffusion before //adding more setdowntimerpreset(60.0, dtdiffusion_0); starttimer(dtdiffusion_0); endif endif endif ////// Bell jar 2 ////// if (bJar2) then if (hasdowntimerexpired(dtdiffusion_1)) then if (CO2_set[1] CO2[1] > 40) then // Toggle flags for user interface bCO2[1] = 1; // Raise CO2 flag for bell jar 2 bMFC = 1; // Raise mass flow controller flag // Set MFC flow rate and timer Q = (Prsr[1]/10) 5; // If CO2 setpoint is 160 ppm or more > actual CO2, //only try to fill to 90% if (CO2_set[1] CO2[1] > 160) then MFCtime[1] = (C O2_set[1] CO2[1])*0.9/40; else MFCtime[1] = 1.0; endif

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131 // Open appropriate solenoids and start mass flow //controller and timer turnon(doBJsol_1); // Open bell jar solenoid setdowntimerpreset(MFCtime[1], dtMFC_1); // Set timer turnon(doCO2); // Open CO2 solenoid aoMFC = Q/10; // Turn on MFC at specified flow rate starttimer(dtMFC_1); // Start timer // Wait while timer counts down while (not hasdowntimerexpired(dtMFC_1)) delaymsec(100); wend // Close solenoids and turn off MFC after timer expires aoMFC = -1.0; // Turn off MFC turnoff(doCO2); // Close CO2 solenoid turnoff(doBJsol_1); // Close bell jar solenoid bCO2[1] = 0; bMFC = 0; // Set down timer to allow for CO2 diffusion before //adding more setdowntimerpreset(60.0, dtdiffusion_1); starttimer(dtdiffusion_1); endif endif endif ////// Bell jar 3 ////// if (bJar3) then if (hasdowntimerexpired(dtdiffusion_2)) then if (CO2_set[2] CO2[2] > 40) then // Toggle flags for user interface bCO2[2] = 1; // Raise CO2 flag for bell jar 3 bMFC = 1; // Raise mass flow controller flag // Set MFC flow rate and timer Q = (Prsr[2]/10) 5; // If CO2 setpoint is 160 ppm or more > actual CO2, //only try to fill to 90% if (CO2_set[2] CO2[2] > 160) then MFCtime[2] = (CO2_set[2] CO2[2])*0.9/40; else MFCtime[2] = 1.0; endif // Open appropriate solenoids and start mass flow //controller and timer turnon(doBJsol_2); // Open bell jar solenoid setdowntimerpreset(MFCtime[2], dtMFC_2); // Set timer turnon(doCO2); // Open CO2 solenoid

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132 aoMFC = Q/10; // Turn on MFC at specified flow rate starttimer(dtMFC_2); // Start timer // Wait while timer counts down while (not hasdowntimerexpired(dtMFC_2)) delaymsec(500); wend // Close solenoids and turn off MFC after timer expires aoMFC = 0; // Turn off MFC turnoff(doCO2); // Close CO2 solenoid turnoff(doBJsol_2); // Close bell jar solenoid bCO2[2] = 0; bMFC = 0; // Set down timer to allow for CO2 diffusion before //adding more setdowntimerpreset(60.0, dtdiffusion_2); starttimer(dtdiffusion_2); endif endif endif OptoScript Block: Pressure control logic (Id: 27) Exit to: Delay 2 sec (Id: 0) // Turn on vacuum pump if pressure greater than setp oint ////// Bell Jar 1 ////// if (bJar1) then repeat if (prsr[0] > prsr_set[0] + 3) then turnon(doBJsol_0); // Open solenoids for bell jars //if pressure too high bVac = 1; // Raise vacuum pump control bVacSol[0] = 1; // Raise vacuum flags for user //interface elseif (prsr[0] < prsr_set[0]) then turnoff(doBJsol_0); // Close solenoids for bell //jars if pressure too high bVacSol[0] = 0; bVac = 0; endif // Turn vacuum pump ON if needed if (bVac) then turnon(doVacSol); // Open vacuum pump solen oid turnon(doPump); // Vacuum pump

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133 endif until (not bVac); //If bell jar is offline, close solenoids elseif (not bJar1) then turnoff(doBJsol_0); bVacSol[0] = 0; endif // Turn OFF vacuum pump and lower flags when no longer //needed turnoff(doPump); // Vacuum pump bVacSol[0] = 0; // Vacuum solenoid flags for user //interface bVac = 0; // Vacuum pump control flag ////// Bell Jar 2 ////// if (bJar2)then repeat if (prsr[1] > prsr_set[1] + 3) then turnon(doBJsol_1); // Open solenoids for bell jars //if pressure too high bVac = 1; // Raise vacuum pump control bVacSol[1] = 1; // Raise vacuum flags for user //interface elseif (prsr[1] < prsr_set[1]) then turnoff(doBJsol_1); // Close solenoids for bell //jars if pressure too high bVacSol[1] = 0; bVac = 0; endif // Turn vacuum pump ON if needed if (bVac) then turnon(doVacSol); // Open vacuum pump solenoid turnon(doPump); // Vacuum pump endif until (not bVac); //If bell jar is offline, close solenoids elseif (not bJar2) then turnoff(doBJsol_1);

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134 bVacSol[1] = 0; endif // Turn OFF vacuum pump and lower flags when no longer //needed turnoff(doPump); // Vacuum pump bVacSol[1] = 0; // Vacuum solenoid flags for user //interface bVac = 0; // Vacuum pump control flag ////// Bell Jar 3 ////// if (bJar3)then repeat if (prsr[2] > prsr_set[2] + 3) then turnon(doBJsol_2); // Open solenoids for bell jars if pressure too high bVac = 1; // Raise vacuum pump control bVacSol[2] = 1; // Raise vacuum flags for user //interface elseif (prsr[2] < prsr_set[2]) then turnoff(doBJsol_2); // Close solenoids for bell //jars if pressure too high bVacSol[2] = 0; bVac = 0; endif // Turn vacuum pump ON if needed if (bVac) then turnon(doVacSol); // Open vacuum pump solenoid turnon(doPump); // Vacuum pump endif until (not bVac); //If bell jar is offline, close solenoids elseif (not bJar3) then turnoff(doBJsol_2); bVacSol[2] = 0; endif // Turn OFF vacuum pump and lower flags when no longer //needed

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135 turnoff(doPump); // Vacuum pump bVacSol[2] = 0; // Vacuum solenoid flags for user //interface bVac = 0; // Vacuum pump control flag turnoff(doVacSol); // Close vacuum pump solenoid Temperature and Relative Humidity Control Action Block: Delay 2 sec (Id: 0) Exit to: Air temp control (Id: 14) Control delay Delay (Sec) 2.0 OptoScript Block: Air temp control (Id: 14) Exit to: Humidity control (Id: 20) // If Tair greater than setpoint temp, turn cooling coil ON bCoil = 0; for j = 0 to 2 step 1 if (Ta[j] > T_set[j] + 0.5) then bCoil = 1; endif

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136 next // If Tair less than setpoint temp, turn heater ON for j = 0 to 2 step 1 if (Ta[j] < T_set[j] 0.5) then bHeater[j] = 1; elseif (Ta[j] > T_set[j]) then bHeater[j] = 0; endif next OptoScript Block: Humidity control (Id: 20) Exit to: Send output flags to control devices (Id: 21) // If RH greater than setpoint RH, turn cooling coil ON for j = 0 to 2 step 1 if (RH[j] > RH_set[j] + 4) then bCoil = 1; endif next // If RH less than setpoint RH, turn humidifier ON for j = 0 to 2 step 1 if (RH[j] < RH_set[j] 4) then bHumidifier[j]=1; else bHumidifier[j]=0; endif next OptoScript Block: Send output flags to control devices Exit to: Delay 2 sec (Id: 0) if (bManual == 0) then // Automatic cooling coil and heater control if (bJar1 or bJar2 or bJar3) then // Turn coil ON/OFF as needed

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137 if (bCoil) then turnon(doCoil); else turnoff(doCoil); endif // If bell jar is ON, turn heaters and humidifiers //ON/OFF as needed //// Bell Jar 1 //// // Heater control if (bJar1) then if (bHeater[0]) then turnon(doHeater_0); else turnoff(doHeater_0); endif // Humidifier control if (bHumidifier[0]) then turnon(doHumidifier_0); else turnoff(doHumidifier_0); endif endif //// Bell Jar 2 //// // Heater control if (bJar2) then if (bHeater[1] and not bHeater[0]) then turnon(doHeater_1); else turnoff(doHeater_1); endif // Humidifier control if (bHumidifier[1]) then turnon(doHumidifier_1); else turnoff(doHumidifier_1); endif endif //// Bell Jar 3 //// // Heater control

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138 if (bJar3) then if(bHeater[2]and not bHeater[0]and not bHeater[1]) then turnon(doHeater_2); else turnoff(doHeater_2); endif // Humidifier control if (bHumidifier[2]) then turnon(doHumidifier_2); else turnoff(doHumidifier_2); endif endif endif else // Manual override of cooling coil, humidifiers, and eaters if (bCoil_man) then turnon(doCoil); else turnoff(doCoil); endif if (bHumidifier_man[0]) then turnon(doHumidifier_0); else turnoff(doHumidifier_0); endif if (bHumidifier_man[1]) then turnon(doHumidifier_1); else turnoff(doHumidifier_1); endif if (bHumidifier_man[2]) then turnon(doHumidifier_2); else turnoff(doHumidifier_2); endif

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139 if (bHeater_man[0]) then turnon(doHeater_0); else turnoff(doHeater_0); endif if (bHeater_man[1]) then turnon(doHeater_1); else turnoff(doHeater_1); endif if (bHeater_man[2]) then turnon(doHeater_2); else turnoff(doHeater_2); endif endif // Turn off heater and humidifier if bell jar is offline if(not bJar1) then turnoff(doHeater_0); turnoff(doHumidifier_0); endif if(not bJar2) then turnoff(doHeater_1); turnoff(doHumidifier_1); endif if(not bJar3) then turnoff(doHeater_2); turnoff(doHumidifier_2); endif if (not bJar1 or not bJar2 or not bJar3) then turnoff(doCoil); endif

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140 APPENDIX E EVAPOTRANSPIRATION MODEL The evapotranspiration model, includ ing calculation of external and surface resistance, was implemented in Matlab (Release 13, Mathworks, Natick, MA). Following is the code for the evapotranspiration model. clc clear % Input variables LAI = 1.0; % Leaf area index L = 0.127; % Characteristic length of leaf, m Patm = 10:5:101; % Atmospheric pressure, kPa Ri = 95; % Incident radiation, W/m^2 Ta = 25 + 273.15; % Ambient temperature, K Tsur = 24 + 273.15; % Temperature of surroundings, K VPD = 0.75; % Air vapor pressure deficit, kPa u = 1.3; % Air velocity, m/s rsref = 28; % Reference rs at low PAR, s/m % Constant air properties mu = 184.6e-7; % Dynamic viscosity, N s/ m^2 k = 0.0263; % Thermal conductivity of air, W/m K Cp = 1.007; % Specific heat of air constant P, kJ/kg K R = 287.05; % Gas constant, J/kg K g = 9.81; % Gravitational constant, m/s^2 for i = 1:length(Patm) % Estimate leaf temperature Tl(i) = (0.0634.*Patm(i)+19.34) + 273.15; % Leaf temp, K %%%%% Calculate canopy external resistance %%%%% % Calculate pressure and te mperature dependent air

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141 % properties rho(i) = (Patm(i)*1000)/(R*Ta); % Air density, kg/m^3 v(i) = mu/rho(i); % Kinematic viscosity, m^2/s alpha(i) = k/(rho(i)*Cp*1000); % Thermal diffusivity, m^2/s beta = 1/Ta; % Coefficient of thermal expansion, K^-1 % Calculate dimensionless numbers Re(i) = rho(i)*u*L/mu; % Reynold's number Pr(i) = v(i)/alpha(i); % Prandtl number Gr(i) = g*beta*abs(Tl(i)-Ta)*L^3./(v(i)^2); %Grashof number Ra(i) = Gr(i)*Pr(i); % Rayleigh numb er % Does forced or free convection dominate? Free = 0; Forced % = 1; Mixed = 2 check(i) = Gr(i)/Re(i)^2; x(i) = abs(1-check(i)); if x(i) > 0.9 if check(i) > 1 conv(i) = 0; else conv(i) = 1; end else conv(i) = 2; end % Calculate Nusselt number based on dominate HT mode if conv(i) == 1 % Forced convection dominates % Average Nusselt number for laminar flow Nu(i) = 0.664*Re(i)^(1/2).*Pr(i)^(1/3); elseif conv(i) == 0 % Free (natural) convection dominates L = 0.0105; Nu(i) = 0.59*Ra(i)^0.25; % Nusselt number for % upper surface of a heated plate (from % Incropera and DeWitt, 1996) else % Mixed convection dominates Nu(i) = 0.37.*(Gr(i)+6.92.*Re(i).^2)^(0.25); % Stanghellini (1987) end % Calculate external resistance rh_leaf(i) = L/(alpha(i)*Nu(i)); rh(i) = rh_leaf(i)/(2*LAI);

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142 %%%%% Calculate surface resistance %% %%% rs(i) = rsref.*Patm(i)./101.3; %%%%% Calculate rate of ET %%%%% % Psychrometric parameters lambda = 2442; % Latent heat of vapo rization at 25 C, kJ/kg delta = 184; %Slope sat vapor pressure curve at 25 C, Pa/C gamma(i) = 1000*Patm(i).*Cp./(0.622.*lambda); % Psychrometric constant, Pa/C % Calculate net radiat ion Rn(i) = (1-0.27).*Ri + 5.67e-8.*0.9.*(Tsur.^4-Tl(i).^4); % Calculate LE, W/m^2 LE(i) = (delta.*Rn(i) + 1000^2.*rho(i).*Cp. *VPD./rh(i))./(delta + gamma(i).*(1 + rs(i)./rh(i))); % Calculate ET, g/m^2/min ET(i) = LE(i).*60./lambda; end % Plot model vs. actual data Pact = [12 12 12 33 33 33 66 66 66 101 101 101]; ETact = [3.37 2.81 2.89 2.78 2.75 2.45 2.41 2.53 2.55 2.64 2.57 2.41]; plot(Patm,ET, Pact, ETact, 'o'), xlabel('Pressure (kPa)'), ylabel('Evapotranspiration (g m^2 min^-1)') % Display results on screen

PAGE 157

143 BIOGRAPHICAL SKETCH Erin Georgette Wilkerson was born on March 15, 1977, in East Tennessee. She is the daughter of George and Lawana Wilkers on. Erin and her younger brother, Wesley, grew up on their familys beef and tobacco farm in Union County, Tennessee. Since 2004 the Wilkerson family has operated a 40-cow dairy farm near their home. Erin was valedictorian of the Class of 1995 at Horace Maynard High School. She earned a B.S. degree in agricultural engineer ing from the University of Tennessee in 1999 and a M.S. degree in biosystems and agricu ltural engineering from the University of Kentucky in 2002.


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Copyright Date: 2008

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Title: Plant Evapotranspiration in a Greenhouse on Mars
Physical Description: Mixed Material
Copyright Date: 2008

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PLANT EVAPOTRANSPIRATION IN A GREENHOUSE ON MARS


By

ERIN GEORGETTE WILKERSON
















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2005




























Copyright 2005

by

Erin Georgette Wilkerson























Dedicated to the memory of my grandmother, Elsie Bell Wilkerson, whose sweet spirit
and strong faith will always challenge and encourage me















ACKNOWLEDGMENTS

I thank the engineers and scientists who took time from their busy schedules to

invest in my professional development and my work. My major professor, Dr. Ray

Bucklin, was a patient advisor and source of wisdom. He gave me freedom to explore

my research topic, yet was readily available when problems arose. My committee, Dr.

Khe Chau, Dr. Dennis McConnell, Dr. Jim Jones, and Dr. Charles Beatty, very kindly

challenged me to be a better engineer and researcher. Dr. Ray Wheeler, Dr. Phil Fowler,

and Dr. John Sager welcomed me to the Space Life Sciences Lab and took me under their

wings while I learned the ropes at KSC. Dr. Hyeon-Hye Kim and the folks from

Dynamac taught me how to grow radishes and always had answers to my many

questions. The KSC Prototype Shop guys built some beautiful bases for me in exchange

for a few cookies.

I may have learned a lot of math, biology, and physics these past three years, but I

have learned so much more about myself and the wonderful people in my life. Dr.

Stephanie Reeder may have grown up in Florida, but she was destined to find her way to

the mountains and my life. The most beautiful engineers I know, Dr. Czarena Crofcheck,

Dr. Mari Chinn, and Dr. Grace Danao, are the best colleagues and friends a girl could ask

for. Jennifer DeFoe and Angela Archer have supported me for many years. I'm so

blessed to have two such amazing cheerleaders in my corer! My beautiful, awesome

"big sis" Kathy has enriched my life in so many ways. I always wanted a sister and I sure

picked a good one! Newman Webb has very patiently put up with my fussing and









complaining the past couple of years, all the while reminding me what I was here for and

all that I have to look forward to. And my wonderful family, Daddy, Momma, and

Wesley, have loved and supported me unconditionally. They have taught me how to

work hard and how to treat people right.

















TABLE OF CONTENTS

page

A C K N O W L E D G M E N T S ................................................................................................. iv

LIST OF TABLES ..................... .......... ........ ................ .........ix

LIST OF FIGURES ............................... ... ...... ... ................. .x

A B STR A C T ..................... ................................... ........... ... .............. xiii

CHAPTER

1 GENERAL INTRODUCTION ...................................................... .....................

Low -Pressure, Inflatable Greenhouse....................................... ......... ............... 2
Grow ing Plants in Reduced Pressures ........................................ ...................... 3
Evapotranspiration M odel .................................................. .............................. 5
R research O bjectives.......... ................................................................... ........ .... .8
D issertation O organization ................................................................... ......... ...........9

2 DEVELOPMENT OF SMALL-SCALE PRESSURE-CONTROLLED PLANT
C H A M B E R S .................................. ................................... ............... 11

L literature R review ..................................................................... .............. 11
Objectives .............. ........... ................. .......... 13
B ell Jar S y stem ...................................................................... 14
D ata A acquisition and Control .............................................................................. 20
Instrum entation .............................................................. ......................................20
Temperature and Humidity Control .............................. .................. 22
Pressure and Carbon Dioxide Concentration Control ......................................23
L ig h t C o n tro l .................................................................... 2 5
P perform an ce T estin g ............................... .......... .... ...... .................. ..................... 2 6
Pressure .......................................................26
Carbon dioxide ...................................................... 27
Air Temperature and Relative Humidity ........................ ..................29
Conclusions and Future Development ................ ........................................31

3 EFFECTS OF PRESSURE ON LEAF CONVECTIVE HEAT TRANSFER ...........33









Literature Review .................................... .. .... ..... .. ............33
C onvection H eat T ransfer....................................................................................34
External resistance.................. ............. .... .......... ............ 37
B oundary layer thickness ........................................ ......... ............... 38
O objectives ..............................................39.............................
M materials and M methods ....................................................................... ..................39
R results and D iscu ssion .............................. ........................ .. ...... .... ...... ...... 46
M odel P perform ance ......................... .......................... .. ......... .......... ..... 1
B boundary Layer Thickness.............................. .......................... ............... 54
C o n c lu sio n s........................................................................................................... 5 6

4 SURFACE RESISTANCE TO EVAPOTRANSPIRATION IN REDUCED
PRES SURE EN VIRONM EN TS ........................................ ......................................57

L literature R review ......................... .. .............. ..... .................. ............... 57
Effects of Environmental Variables on Stomatal Control...............................57
V apor pressure deficit ............................................................................ 58
Carbon dioxide ............................ ............. 59
Photosynthetically active radiation ................................... ............... ..60
Mass Diffusivity and Stomatal Resistance .....................................................60
Plant A adaptation and Surface Resistance ......................................... .................62
O objectives .................................63................................................
M materials and M methods ....................................................................... ..................64
Plant M material .............................................. ........ 64
Evapotranspiration M easurem ent .......................... .............. ... ... .............65
E x p erim ental D esign ........................................ ............................................66
M odel D evelopm ent ...................................... .... ................ .. ............ ......67
R results and D iscu ssion .............................. ........................ .. ...... .... ...... ...... 70
C o n c lu sio n s........................................................................................................... 7 7

5 EVAPOTRANSPIRATION MODEL PERFORMANCE IN MARS
GREENHOU SE CONDITION S ........................................ .......................... 78

O bj ectives .................................79................................................79
M materials and M methods ....................................................................... ..................79
R results and D iscu ssion .............................. ........................ .. ...... .... ...... ...... 80
Sensitivity A analysis ...... .. .... .................................................. ............... 8 1
E rro r A n a ly sis ................................................................................................ 8 2
C o n c lu sio n s........................................................................................................... 8 5

6 LEAF TEMPERATURE IN A MARS GREENHOUSE ..........................................86

L iteratu re R ev iew ............................................................................ .................... 8 6
O objectives .................................87................................................
M materials and M methods ....................................................................... ..................88
R results and D discussion ....................... ...... .......... ............... .... ....... 89
Infrared Thermocouple Performance .............................................. ........89









Effects of Evapotranspiration at Reduced Pressures on Leaf Temperature ........90
Leaf Temperature in a M ars Greenhouse .................................... .................92
C o n c lu sio n s..................................................... ................ 9 5

7 CONCLUSIONS AND FUTURE RESEARCH ................................. ...............96

L IST O F R E F E R E N C E S ...................................................................... ..................... 10 1

APPENDIX

A SEN SOR CALIBRA TION S......................................................... ............... 106

P re ssu re ........................................................................................................ 1 0 6
Leaf Temperature ............... ............................................. ................ 106
A ir T em perature ........................................ .. ....... ..........109
W eight ............................... ............................ .... ..... ........ 109
C arbon D ioxide C oncentration................................... .................................... 110
O xygen concentration .................................................................................. 112

B SEN SOR ERROR BUDGETS ....................................................... .... ........... 113

Voltage Input Module (SNAP-AIV-4).........................................................113
Voltage Input M odule (SNAP-AITM -2).......................................................113
P re s su re ........................................................................................................ 1 1 4
Relative H um idity ............................................. .... .. ................ 114
O x y g e n .....................................................................................................1 1 5
Carbon D dioxide .................................................................... ......... 115
L eaf tem perature .............................................................. .. ....... ....... 115
A ir tem perature .................. ............................ .. ..... ................ 116

C BELL JAR BASE DRAW INGS ......................................................... .... ........... 117

D BELL JAR CONTROL ALGORITHM ....................................... ............... 122

D ata B uffer R outine ................................................ .............................. 122
V ariable U pdate R outine ........................................................ ............. 126
Fan Control Routine .............................. ...... ...... ... ..............128
Carbon Dioxide and Pressure Control ............. .......................... .................129
Temperature and Relative Humidity Control ...................................................135

E EVAPOTRANSPIRATION MODEL ............................................. ...............140

BIOGRAPHICAL SKETCH ........................................................... ........143
















LIST OF TABLES


Table p

2-1 Descriptions and applications of Opto 22 I/O modules used in this research ..........20

2-2 Calibrated sensor accuracies .............................................................................. 21

2-3 Performance of pressure control algorithm.................................................26

2-4 Bell jar leakage rates .......... .. .... ......................... ................ ........ .... 27

2-5 Performance of CO2 control algorithm at 12 kPa with plants.............................29

2-6 Performance of the air temperature and relative humidity control algorithm at 12
kPa w ith plants .................. .... ... ................... ......... ............ .. 31

4-1 Controlled environment chamber conditions ................................. ............... 65

4-2 Evapotranspiration treatment structure. ...................................... ............... 67

4-3 Evapotranspiration and resistance results ..................................... .................73

4-4 Root mean square error of surface resistance model.....................................77

5-1 Parameter descriptions and reference values. .................................. .................79

5-2. Sensitivity analysis of the evapotranspiration model for Mars greenhouse
c o n d itio n s ......................................................................... 8 2

5-3 Change in evapotranspiration rate and estimated error of parameters for overall
error calcu lation ............................. .................................................. ............... 83

6-1 Comparison of temperature sensors for leaf temperature measurement ................89

6-2 Effects of pressure on evapotranspiration rate and leaf temperature ....................91

6-3 Leaf temperature model results for 12 and 101 kPa .................. ...... .............94

A-i Slope and intercept equations for carbon dioxide sensors. ............. ................111

A-2 Slope equations for the oxygen sensors. ............................ ..... ...........112
















LIST OF FIGURES


Figure pge

1-1 Artist's conception of a future M ars colony.................................... ...... ............. ... 1

1-2 Leaf to air vapor pressure deficit approximation .................................. .............. .7

2-1 Schematic of pressure controlled plant chambers. ................................................ 15

2-2 Pressure controlled plant chambers..... .. .............................. ......... ................... 15

2-3 Schematic of one pressure controlled plant chamber ................ ....... ...........16

2-4 Picture of one of the three pressure controlled plant chambers ........................... 17

2-5 L eight level control ...................... .................... ... .... ........ ......... 25

2-6 CO2 control without plants at standard pressure. .............................................. 27

2-7 Effect of vacuum pump on CO2 control at low pressures................. ........... 28

2-8 CO2 control with plants at 12 kPa ............................ ... ............... 29

2-9 Air temperature and relative humidity control at 12 kPa with plants. ...................31

3-1 Velocity boundary layer over a horizontal flat plate............................................. 34

3-2 Thermal boundary layer over a horizontal flat plate that is warmer than the
surrounding air. .......................................................................35

3-3 Thermal boundary layer over a horizontal flat plate that is cooler than the
su rrou n d in g air ..................................................... ................ 3 5

3-4 L eaf replica .................................................................. ...........................40

3-5 Convection heat transfer experimental setup ................................. ............... 41

3-6 Temperature profile for leaf replica during heating and subsequent cooling phase
at 101 kPa and an air velocity of 5.8 m s ....................... ...................42

3-7 Transformed cooling data for the leaf replica at 101 kPa and an air velocity of
5 .8 m s ..................................................................................4 5









3-8 Surface temperature of leaf replica during heating and subsequent cooling phase
for four air velocity treatm ents at 12 kPa. ...................................... ..................47

3-9 Transformed surface temperature data for leaf replica at 12 kPa. .........................47

3-10 Surface temperature of leaf replica during heating and subsequent cooling phase
at 33 kP a. .............................................................................4 8

3-11 Transformed surface temperature data for leaf replica at 33 kPa. .........................48

3-12 Surface temperature of leaf replica during heating and subsequent cooling phase
at 66 kP a. .............................................................................49

3-13 Transformed surface temperature data for leaf replica at 66 kPa. .........................49

3-14 Surface temperature of leaf replica during heating and subsequent cooling phase
at 10 1 kP a. ............................................................................50

3-15 Transformed surface temperature data for leaf replica at 101 kPa ........................50

3-16 Measured and predicted values for external resistance of leaf replica as a
function of pressure and four levels of air velocity...............................................52

3-17 Rate of heat transfer from leaf replica as a function of pressure and air velocity ....52

3-18 External resistance model performance ....................................... ............... 53

3-19 External resistance m odel error ........................................ ........... ............... 54

3-20 Effect of atmospheric pressure on boundary layer thickness of a horizontal flat
p late ................................................................................5 5

3-21. Effect of air velocity on boundary layer thickness of a horizontal flat plate............55

4-1 The effect of pressure on mass diffusivity of water in air................... ............61

4-2 Leaf temperature transient response to changes in total pressure............................66

4-3 Visual observations of water status at 101 and 12 kPa........................................74

4-4 Effects of pressure and CO2 on evapotranspiration ............. ..... ............... 75

4-5 Effect of CO2 on surface resistance...................................... ........................ 75

4-6 Effects of pressure and PAR on evapotranspiration ................. ..... .............76

4-7 Actual and predicted values of surface resistance at 40 Pa and 341 [[mol m-2 s-1. ..76

5-1 Predicted and measured evapotranspiration rate as a function of pressure .............81









5-2 Model performance at reference conditions...................................... ..............83

5-3 M odel performance in elevated CO2 ............................ .................................... 84

5-4 Model performance in low PAR conditions...................................... ...................84

6-1 Leaf temperature measurement at 25 kPa .......................................................90

6-2 Effect of pressure on leaf-to-air temperature difference ................................. 91

6-3 Effect of evapotranspiration rate on leaf-to-air temperature difference .................92

6-4 Effects of net radiation on leaf-to-air temperature difference............................ 94

A -i Pressure sensor calibration ......................................................... ............... 107

A -2 Infrared sensor calibration ......................................................... .............. 108

A -3 Therm ocouple calibration ............................................... ............ ............... 108

A -4 L oad cell calibration ....................................................................... ..................109

A -5 Carbon dioxide sensor calibration .................................. .................... ............... 111

C-1 Top view of bell jar base ...................................................... ............ 118

C-2 Bottom view of bell jar base .............................. ............ .. ......................... 119

C -3 B ell jar base top plate ..................................................................... ............. 120

C -4 C cooling coil. .........................................................................12 1















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

PLANT EVAPOTRANSPIRATION IN A GREENHOUSE ON MARS

By

Erin Georgette Wilkerson

December 2005

Chair: Ray A. Bucklin
Major Department: Agricultural and Biological Engineering

Successful crop production is vital to manned missions to Mars. Plants play integral

roles in conceptual life-support systems as sources of food, oxygen, and waste treatment.

Constraints of building a structure on the Martian surface to withstand Earth-similar

interior air pressures make it necessary to develop plant growth systems capable of

operating in air pressures as low as 0.1 to 0.3 atm (10 30 kPa). Research has shown

that plants are capable of surviving in such environments, but have increased rates of

water loss. The enormous costs associated with launching a manned mission to Mars

make it crucial that plants be not only capable of survival, but also of producing fruit and

seed. Plant growth and development, and thus, performance of a biological life-support

system are highly dependent on plant environmental responses. Therefore, it is important

that the interactions between plants and the environment of a Mars greenhouse are well

understood.









A model was used to predict the rate of evapotranspiration in response to changes

in pressure, C02, and light. The model was compared to empirical data obtained in

experiments performed in a system of three small-scale low pressure controlled

environment chambers built for this research. The system provided control of pressure,

CO2 concentration, air temperature, and relative humidity and measured plant weight and

leaf temperature.

The rate of evapotranspiration changed little when pressure was 33 kPa and greater,

but increased significantly at 12 kPa. Plants quickly wilted when pressure was 12 kPa

and CO2 was 40 Pa. Reduced pressure increased the rate of evapotranspiration by

decreasing resistances to sensible and latent heat loss as well as reducing the

effectiveness of convection. However, when CO2 concentration was increased from 40 to

150 Pa, stomata closed and evapotranspiration decreased even at the lowest pressure.

Thus, plants are capable of growing at extreme low pressures, but are more sensitive to

changes in other environmental parameters. In a low pressure Mars greenhouse, failure

of the control system will likely result in crop failure.














CHAPTER 1
GENERAL INTRODUCTION

For a long-term manned mission in space (- 3 years), the costs of transporting and

storing consumable resources (e.g. food, oxygen) are not feasible and resources must be

produced in situ. Preliminary strategies for a manned mission to Mars include a

greenhouse for the production of vascular plants. Growing plants provide essential life

support functions such as food production, oxygen production and waste treatment

(Drysdale et al., 1999) and psychological benefits associated with the sensory value of

fresh food and of nurturing plants (Corey et al., 2002).


Figure 1-1. Artist's conception of a future Mars colony. The settlement includes an
inflated greenhouse for food and production, oxygen production, and waste
treatment.









Low-Pressure, Inflatable Greenhouse

One possible concept, currently being developed by researchers at the University of

Florida and the Kennedy Space Center, is an inflatable greenhouse system. Such a

system would be autonomous and could be deployed during an unmanned mission 100 to

120 days prior to the crew's arrival (Fowler et al., 2001). The purpose of a greenhouse on

Mars is no different than on Earth to overcome "climatic adversity" (Hanan, 1998).

However, the Martian climate presents several new and interesting challenges.

Reductions in gravity, atmospheric pressure, light levels, and temperature all significantly

affect the design and control of a greenhouse (Bucklin et al., 2004). The climatic factor

of greatest concern for plant growth and development is pressure.

The atmospheric pressure on Mars varies greatly with location, but is always less

than one-hundredth that of Earth sea level (101.3 kPa) and for structural design purposes

can be considered equal to zero (Bucklin et al., 2004). It is possible to build a structure

capable of withstanding a pressure differential of 100 kPa as would result for a

greenhouse maintaining Earth-similar pressures on Mars. However, the costs associated

with such a massive structure are prohibitive. Also, it is desirable for the structure to be

transparent in order to make use of the sun's radiant energy for plant photosynthesis as

well as heating (Corey at al., 2002; Ferl et al., 2002). Consequently, it is important to

minimize the pressure differential across the structure surface by maintaining a low

atmospheric pressure within. No official decisions have been made regarding the internal

pressure of a Mars greenhouse. Present strategies call for less than one-third the

atmospheric pressure of Earth (Bucklin et al. 2004; Fowler et al., 2001).









Growing Plants in Reduced Pressures

Based on the results of previous studies, avoiding excessive water losses and

subsequent dehydration is likely to be a challenge in maintaining productivity of plants in

a low atmosphere Mars greenhouse (0.1 0.2 atm). Large reductions in atmospheric

pressure have been shown to significantly increase the rate of evapotranspiration (Andre

and Massimino, 1992; Corey at al., 1997; Daunicht and Brinkjans, 1992; Goto et al.,

1995; Goto et al., 1996; Goto et al., 2002; Massimino and Andre, 1999; Rule and Staby,

1981; Rygalov et al., 2002). The most likely explanation for these increases is the

inversely proportional relationship between pressure and mass diffusivity. As the mass

diffusivities of CO2 and water increase, so do the boundary layer and stomatal

conductances to CO2 and water exchange (Nobel, 1999; Monteith and Unsworth, 1990).

Because evapotranspiration is increased at low pressure, the health and productivity

of plants grown at low pressures depends on their ability to maintain turgidity in an

environment with a high transpirational load. In their studies on tomato plants, Daunicht

and Brinkjans (1992), showed slight decreases (<10%) in biomass and leaf area and a

slight increase (10%) in the dry weight of plants grown at 40 kPa versus 100 kPa (= Earth

atmospheric pressure). On the last day of their study, the photosynthesis and

transpiration rates were 12 and 39% higher, respectively, for the plants grown at the

lower pressure. They concluded that, in spite of having a higher photosynthesis rate,

plants grown at the lower pressure were most significantly affected by the increase in

transpiration rate, which they considered to be the cause of reduced growth. In

experiments by Goto et al. (2002) vegetative rice plants were grown in one of three total

pressure environments: 34, 50, and 100 kPa. Growth, as measured by plant height and









dry weight, were statistically similar for 50 and 100 kPa, but significantly reduced at 34

kPa. They also concluded that this growth inhibition at extreme low pressures was

caused by water stress. This is a reasonable conclusion based on earlier studies by the

same research group in which rates of transpiration for maize were approximately four

times higher at 10 kPa than at 100 kPa (Goto et al, 1996). Experiments to measure the

open water surface evaporation by Rygalov et al. (2002) showed marked increases at total

pressures less than 25 kPa. These low pressures (< 25 kPa) correspond to the design

internal pressure range currently being considered for the Mars greenhouse (Bucklin et

al., 2004).

Increases in mass diffusivity may not be the only reason for increases in

evapotranspiration at low pressures. Goto et al. (1996) incorporated a simple model for

the changes in stomatal and boundary layer resistances at low pressures to predict

transpiration rate as a function of vapor pressure deficit (VPD) and resistance to water

vapor transfer. In this model, the resistances were adjusted proportional to changes in

mass diffusivity as pressure decreased. In other words, it was assumed that the stomatal

opening remained the same at all pressures and changes in stomatal resistance were

caused only by an increase in the mass diffusivity of water vapor. With their assumptions

that stomatal and boundary layer resistances were affected only by pressure and VPD

remained constant, the measured transpiration rates showed smaller incremental increases

than simulated rates. Goto et al. (1996) hypothesized that stomatal control might also be

affected by pressure changes. Decreases in stomatal aperture at low pressures, but

constant VPD, seem likely considering the increases in evaporation rate and recent

research claiming that stomatal control is a function of the rate of water loss rather than









humidity (Monteith, 1995). It was also shown in work by Paul et al. (2004) that

Arabidopsis plants subjected to reduced pressures show gene expressions as if they are in

drought stress despite no visible signs of desiccation. Stomatal controls, and

consequently transpiration and photosynthesis rates, are also affected by CO2

concentration, VPD, and photosynthetically active radiation (PAR) (Jarvis, 1976). The

effects of interaction between pressure and these variables have not been explored.

Evapotranspiration Model

The Penman-Monteith evapotranspiration model (Monteith, 1965) has been used

extensively over the past several decades to predict plant water loss rates in field and

greenhouse conditions. Based on work by Penman (1948) and later modified by

Monteith, the model predicts the evapotranspiration of plants as driven by convective and

radiative forces and incorporates the resistances of the crop canopy to water vapor loss.

Derivation of the Penman-Monteith evapotranspiration model begins with a steady-

state energy balance of the plant canopy (equation 1-1).

R -H-LE = (1-1)
where: Rn = net radiation, W m-2
H = sensible heat flux, W m-2

LE = latent heat flux, W m-2

Sensible heat flux, H, is estimated by equation 1-2.


H Pacp(Tea Tar) (1-2)
rh
-3
where: pa = density of air, kg m-3
Cp = specific heat of air at constant pressure, J kg-1 oC-1

Tieaf = leaf temperature, C

Tair = air temperature, C

rh = external resistance for sensible heat transfer by convection, s m-1









Equation 1-3 gives the estimation for the latent heat flux, LE.


LE = cVPDeaf-a (1-3)
y(- rh)
where: VPDieaf-air = leaf to air vapor pressure deficit, kPa

VPDleaf air =(eleaf e ) (1-4)

esleaf = saturation vapor pressure at leaf temperature, kPa

ea = vapor pressure, kPa

y = psychrometric constant, Pa C-1

Pc
Y=O- (1-5)
0.622k

S= latent heat of vaporization, kJ kg-1

P = pressure, Pa

rs = surface resistance of canopy to water vapor transfer, s m-1

Calculation of the sensible and latent heat fluxes of equations 1-2 and 1-3 requires

surface temperature, a variable that is typically unknown. Penman (1948) incorporated a

simplifying assumption to eliminate leaf temperature from the model. Equation 1-6

shows an approximation for VPDieaf-air calculated from air vapor pressure deficit (VPDair),

the leaf to air temperature difference, and the slope of the saturation vapor pressure curve

(A).

VPDearr VPDor + A(Te TT ) (1-6)

An example is shown in Figure 1-2. Consider a leaf whose surface temperature is

20 C in a 24 C airstream. Saturation vapor pressure at a given temperature, T, is

calculated by equation 1-7.

7.5T


e (T) = 0.61078 10 237.3+T


(1-7)










where: es(T) = saturation vapor pressure at temperature T, kPa

T = temperature, C

In Figure 1-2 the dashed line is a straight line with slope equal to the saturation

vapor pressure curve at the air temperature, 24 C. The difference between the actual

VPDieaf-air and the estimation from equation 1-6 is only 0.08 kPa.

5

4.5
slope = A =0.18
S4

3.5

3 3
2. A Ta,,r -Tlearf)= 0.18*(24-20) =0.72



1.5 ea = 1.49 kPa
O 1

0.5

0
18 20 22 24 26 28 30 32 34
Temperature, C
Figure 1-2. Leaf to air vapor pressure deficit approximation. To eliminate leaf surface
temperature from the evapotranspiration model, Penman (1948) introduced an
approximation for VPDieaf-air. This approach assumes that the saturation vapor
pressure curve can be approximated by a straight line with slope calculated at
air temperature for small differences between leaf and air temperature (figure
adapted from Jones, 1992).


Substituting equation 1-6 into 1-3 yields an equation for latent heat flux as a

function of leaf to air temperature difference. The leaf temperature can be eliminated by

combining this new equation with 1-3. Substitution into the heat balance of equation 1-1

and rearranging gives a standard from of the Penman-Monteith equation (Monteith, 1965)

that does not require knowledge of leaf temperature.









E R, + p, c,, VPD ,, lr
LE =- (1-8)
A+y(1r /rh)

The Penman-Monteith model requires the measurement or estimation of five

variables to calculate the rate of evapotranspiration. The net radiation, Rn, and air vapor

pressure deficit, VPDair, are environmental parameters. The external and surface

resistances to evapotranspiration are estimated via heat transfer and biological models.

The external resistance, rh, is the resistance to sensible heat transfer from the leaf and is

calculated by convection heat transfer models. The surface resistance, rs, is the resistance

of water vapor transfer through the leaf cuticle layer and the stomata. Models for surface

resistance account for the effects of environmental conditions (e.g PAR, VPD, CO2) on

stomatal behavior. The remaining model parameters are physical constants for particular

environmental conditions.

Research Objectives

Several researchers have shown that, despite increases in transpiration rate, plants

are capable of surviving in low pressures and at moderate pressures may even experience

enhanced growth due to higher photosynthesis rates. However, it is important that plants

be not only capable of survival, but also of thriving to produce fruit and seed. To

optimize life support functions plant responses must be considered along with physical

constraints in the design of a greenhouse system for Mars.

There is a significant amount of research modeling the effects of environmental

factors on plant growth and development and applying these models to control systems in

order to optimize the plant environment. There is also an increasing amount of research

on the effects of reduced atmospheric pressure on short-term plant growth. This

proposed research would extend and complement this previous research in several ways.









Extreme low atmospheric pressure (< 20 kPa) is an environmental factor that has not yet

been fully explored with regard to its effect on plant response especially with regard to

interactions C02, PAR, and VPD. Furthermore, leaf temperature has not been measured

during reduced pressure experiments and should provide useful information with regard

to evapotranspiration rates and plant water status. The goal of this research is to improve

the current understanding of the effects of atmospheric pressure on plant

evapotranspiration via the use of short-duration experiments and mathematical modeling.

Using a modeling approach makes it possible to test current understanding of the effects

of pressure on plant evapotranspiration including stomatal conductance, which cannot be

measured during low pressure experiments using current technology.

The objectives of this research are to:

1. Quantify the effects of pressure on external and surface resistances to

canopy sensible and latent heat transfer.

2. Investigate the effects of changes in evapotranspiration rate at low pressures

on leaf temperature of mature radish plants.

3. Incorporate the effects of atmospheric pressure into an evapotranspiration

model and apply the model to predict water loss rates of plants growing in a

greenhouse on Mars.

Dissertation Organization

This dissertation is organized topically with chapters two through six each focusing

on a different component of the research objectives. The development and performance

of a small-scale low pressure system is described in chapter two. This system was used

to measure the effects of pressure on surface resistance (chapter three), external

resistance (chapter four), and leaf temperature (chapter five). Chapters three and four






10


include the development of mathematical models for surface and external resistances,

respectively. In chapter six, these models are incorporated into a model to simulate

evapotranspiration rate of radish plants as a function of pressure. Chapter seven

addresses the overall conclusions and future recommendations resulting from this body of

work. The references list for the entire dissertation is included following chapter 7.

Appendices include supplementary information such as sensor calibrations, engineering

drawings, and the control algorithm.














CHAPTER 2
DEVELOPMENT OF SMALL-SCALE
PRESSURE-CONTROLLED PLANT CHAMBERS

Simulation of a Mars greenhouse environment is complex. It requires a chamber

capable of maintaining low pressures for extended periods of time and a control system

for many linked environmental parameters. The objective of this chapter is to describe

the development of three small-scale pressure-controlled plant chambers used in this

research.

Literature Review

As interest in advanced life support systems for Mars exploration missions has

increased during the past several years, so has research activity regarding plant responses

to low pressure environments. Researchers at Kennedy Space Center, Texas A&M

University, University of Guelph, and University of Tokyo, as well as the University of

Florida have each developed their own unique low pressure growth systems for studying

the effects of Mars greenhouse conditions on plants.

The Mars Dome, developed by researchers at Kennedy Space Center and the

University of Florida, is a polycarbonate dome joined to a stainless steel base (Fowler at

al., 2002). It was originally designed to operate as a pressurized vessel inside a larger

vacuum chamber, but added reinforcement made it possible to grow plants at reduced

pressures (> 25 kPa) inside with Earth normal pressure outside. A microcontroller

system monitored and controlled temperature, pressure, humidity and plant irrigation.









The main component of the Mars Dome was a central tower that contained all

electronic components and temperature and humidity control devices. Nine scales

surrounded the tower. Plants were weighed throughout an experiment to quantify

evapotranspiration rates and activate irrigation events.

A group of engineers and plant scientists at Texas A&M University designed and

built small cylindrical low-pressure plant growth chambers (Brown, 2002; Purswell,

2002). Six clear acrylic cylinders each measuring 0.31 m in diameter and 0.91 m in

height were placed in a larger environment chamber to control light and temperature. A

distributed control system monitored and controlled pressure and concentrations of

oxygen and carbon dioxide. A cooling coil provided a condensing surface for

dehumidification.

The University of Guelph developed two different types of low-pressure growth

systems. They developed large vacuum chambers with hydroponics systems and some

smaller steel cylindrical growth chambers. Both types of growth chambers offered

control of critical environmental parameters pressure, light, temperature, relative

humidity, and carbon dioxide concentration.

Engineers at the University of Florida designed and built two new low pressure

systems. One was a large vacuum chamber placed inside a large freezer. The

environment inside the vacuum chamber closely resembled that of the Martian surface -

virtually no atmospheric pressure and temperatures below freezing. A polycarbonate

dome with steel base, similar to the Mars Dome described above, was placed inside the

vacuum chamber and pressurized to simulate a greenhouse on Mars. Experiments were

performed with this system to better understand heat transfer in a Martian greenhouse and









develop temperature and humidity control systems for reduced pressures. A small-scale

system for detailed plant experiments was also developed at UF and KSC and is

described in the remainder of this chapter.

Replication is necessary in plant experiments to perform statistical analysis, draw

sound conclusions, and extrapolate conclusions to other situations. Plant experiments

performed in the large low-pressure systems described above such as the Mars Dome and

the UF low temperature vacuum chamber must be replicated in time. To save time and

ensure identical treatments, it is desirable to perform replications simultaneously. Three

bell jars were used in this research for plant experiments (see Figures 1 and 2). An

aluminum base was designed and constructed to house the temperature and humidity

controls and wiring. A PC based data acquisition and control system was developed to

monitor and control pressure, temperature, humidity, and carbon dioxide concentration.

Plant weight and leaf temperature were also measured to evaluate evapotranspiration and

water stress.

Objectives

The objective of the work described in this chapter was to design and construct

plant growth chambers to meet the following design criteria:

Steadily maintain pressures as low as 10 kPa over long periods of time,

Allow exterior lighting to reach plant canopy,

Three simultaneous replications,

Control pressure, air temperature, humidity, CO2 concentration, and

Monitor environmental parameters, leaf temperature, and plant weight.









Bell Jar System

Bell jars were selected as the primary component of the plant growth chambers

because they were readily available and easy to replace. Glass bell jars, routinely used in

vacuum studies, are strong and relatively easy to seal. The inside and outside diameter of

each bell jar was 213 and 222 mm, respectively They were 381 mm tall.

New aluminum bases constructed by the Kennedy Space Center Design and

Development Integration Branch (prototype shop) were designed to house a cooling coil,

humidifier, two fans, sensors, wiring, and fittings. Preliminary plant experiments

performed in bell jars with off-the-shelf plastic bases emphasized their small volume. It

was difficult and awkward to accommodate all instrumentation, heating and cooling

equipment, scale, and the plant. The new bases were deep enough to house these

components below the plant as shown in Figures 3 and 4. Detailed engineering drawings

of the base are in appendix 3.

Ports for gases, water, and wiring were made in the bottom of the bell jar bases.

Fittings for water and gases were fitted with o-rings and installed tightly to minimize

leakage. To minimize costs, wire feedthroughs were constructed in-house. Art clay was

packed into the center of 1.905-cm bushings to hold wires in place. The thickness of the

clay was 1.25 cm. Solid wires cut to length were inserted through the clay. To minimize

air passing through the wire insulation, about 0.5 cm was stripped away before wires

were inserted. Epoxy was poured into both sides of the bushing so that the exposed

portion of each wire was completely covered. Three wire feedthroughs containing nine

wires and one with two type-T and one type-K thermocouples were made for each bell

jar.




















I I I
Vacuum PC based data acquisition
Pump and control system
Figure 2-1. Schematic of pressure controlled plant chambers. Experimental replication
was achieved using three independently controlled bell jars.


Figure 2-2. Pressure controlled plant chambers. The small chambers were placed inside a
larger plant growth chamber for high-quality external lighting.
























































C02 and vacuum


Figure 2-3. Schematic of one pressure controlled plant chamber.







17











o lilki -
WEE ~i'""


Figure 2-4. Picture of one of the three pressure controlled plant chambers.


rdl:d~ttl


** '"iitftwu *"s
r* *
L~ m rt


-".'. "









The cooling coil was designed for dehumidification. From preliminary

experiments (data not shown) the average evapotranspiration rate for a single mature

radish plant at 10 kPa was estimated to be approximately 0.075 g H20 min-'. Since the

lowest pressure treatment applied in this research was 12 kPa, the evapotranspiration rate

for 10 kPa was assumed to be a good approximation for the maximum expected in this

research. Thus, the coil was designed to condense water at a rate equal to the assumed

evapotranspiration rate for two mature radish plants at 10 kPa, 0.15 g H20 min.

The steady-state heat transfer rate required to condense water was calculated by

equation 1.

q = (ihH2 )(h ) (2-1)

where: q = heat transfer by condensation, W

m = mass rate of water condensed, kg s-1

hfg = latent heat of vaporization, kJ kg-1

At 10 kPa, the latent heat of vaporization is 2389 kJ kg-1. The rate of heat transfer

required to condense water at 0.15 gH20 min1 was 6 W.

The rate of heat transfer by water condensing on the coil was calculated by

equation 2 with the average convective heat transfer coefficient taken from Incropera and

DeWitt (1996) for water condensation on a horizontal tube (equation 3).

q = hAco, (Tar To ) (2-2)

where: q = rate of heat transfer, W

h = convective heat transfer coefficient, W m-2 K-1

Acoil = coil surface area, m2

Tair = air temperature, K









Tcoil = coil surface temperature, K


h = 0.729 gp! (-, )khsD (2-3)
N (T(a, T,)D D

where: h = convective heat transfer coefficient, W m-2 K-1

-2
g = acceleration due to gravity, m s-2

pi = density of liquid, kg m-3

pv = density of vapor, kg m-3

ki = thermal conductivity of liquid, W m-1 K-1

hfg = latent heat of vaporization, kJ kg-1

N = number of horizontal tubes

ti = viscosity of liquid, kg s-1 m-1

Tsat = saturation temperature, K

Ts = coil surface temperature, K

D = tubing diameter, m

The following values for properties of water vapor and saturated liquid at 10 kPa

were used: pv = 0.111 kg m-3; pi = 0.997 kg m-3; ki = 0.606 W m-1 K-1; and lti = 934 x 106.

The number of horizontal tubes, N, was assumed to be two for a coil and the tube

diameter, D, was 0.0635 m (0.25 in). The resulting heat transfer coefficient was 39.8 W

m-2 K-1

Equating the two expressions for the rate of heat transfer (equations 1 and 2) and

rearranging, yields an equation for calculating the coil surface area needed.


Acol = (2-4)
h(Tar, TO)









Assuming that the coil temperature was 3 C and air temperature was 24 C, the

coil surface area needed to condense 0.15 g H20 min1 was calculated to be 0.0075 m2

(11.6 in2). Designed with a factor of safety of 2.5, the coil surface area was

approximately 0.0187 m2 (29 in2).

Data Acquisition and Control

Environmental parameters within the bell jar were monitored and controlled by a

PC-based data acquisition and control system. Pressure, air temperature, and CO2

concentration of each bell jar were controlled independently.

Instrumentation

An Opto 22 system was used for data acquisition and control. An I/O and

communications processor (SNAP ultimate brain, Opto22, Temecula, CA) managed 16

digital and analog I/O modules. Table 1 lists the modules used in this research and their

application. The control program was written in ioControl 6.0 (Opto 22, Temecula, CA),

a flowchart based software designed for the Opto system. A user interface and display

program was written in ioDisplay 6.0 software (Opto 22, Temecula, CA).

Table 2-1. Descriptions and applications of Opto 22 I/O modules used in this research.
Opto 22 module description Quantity Application
Vacuum pump, solenoid
SNAP-OAC5, 412-250 VAC input 1a m
valve
SNAP-AOV-25, 0 to +10 VDC analog output 1 Mass flow controller
Solenoid valves, heaters,
SNAP-ODC5SNK, 5-60 VDC output, sink 4 id,
humidifiers, and fans
SNAP-AITM, mV or thermocouple input 2 Infrared thermocouples
Oxygen sensors, type-T
SNAP-AITM2, mV or thermocouple input 5 thermocoules
thermocouples
Pressure, CO2, and
SNAP-AIV-4, 0 to +10 VDC analog input 3 relative humidity sensors
and load cells









All sensors were calibrated within one year prior to the start of experiments. Table

2 lists the calibrated accuracy of each sensor. Calibration data and error budget

calculations for all sensors (excluding RH sensors which were factory calibrated) are

included in appendix A. Air temperature was measured by type-T thermocouples placed

just below the height of the plant canopy. They were shielded to reduce measurement

error caused by the high radiation environment of the outside growth chamber. The

thermocouples were calibrated using a two point calibration (10 C and 40 C) in a

thermometer calibrator (TCAL, Sun Electronic Systems, Inc., Titusville, FL). Small

integrated circuit sensors were used to monitor pressure (MPXH6115A6U, Freescale

Semiconductor, Inc., Austin, TX) and relative humidity (HIH-3610-003, Honeywell,

Freeport, IL). The oxygen concentration was measured using a galvanic cell type oxygen

sensor (MAX-250, Maxtec, Salt Lake City, UT). A low-cost OEM ultrasonic sensor was

used to measure carbon dioxide (6004 CO2 module, Telaire, Goleta, CA). Leaf

temperature was measured with infrared thermocouples (OS36SM-K-140F, Omega,

Stamford, CT). Load cells were used for measuring plant weight (LPS-2kg, Celtron

Technologies, Inc., Colvina, CA).

Table 2-2. Calibrated sensor accuracies. All sensors were calibrated within one year of
the start of experiments.
Parameter Sensor description Accuracy
Air temperature Type-T thermocouples + 0.5 C
Pressure Integrated circuit pressure sensor + 0.53 kPa
Relative humidity Integrated circuit RH sensor + 2.1 %
Oxygen Galvanic cell sensor + 1.0 %
Carbon dioxide Ultrasonic sensor + 100 ppm (at 2000 ppm)
Leaf temperature Mini infrared thermocouples + 0.8 C
Plant weight Load cell + 0.1 g









Temperature and Humidity Control

The air temperature of each bell jar was determined by the outside temperature of

the bell jar, the coil temperature, and a heater. At the beginning of the control loop, the

current air temperature of each jar was compared to the setpoint temperature. The heater

or cooling coil was activated as needed. Only one solenoid valve was available for

controlling the water flow through the cooling coils. Thus, cooling coil temperature was

not controlled independently and was similar in the three bell jars at all times.

Relative humidity was determined by the rate of plant evapotranspiration and the

cooling coil temperature. When the relative humidity of any one of the three bell jars

was higher than setpoint, the solenoid valve was opened to allow chilled water to flow

through the coils. On the other hand, if relative humidity was too low in a bell jar, the

humidifier for that bell jar was turned on until setpoint was achieved.

The surface temperature of the copper cooling coils was determined by the

temperature and flow rate of water flowing through them. Both of these factors were

controlled by a chilled water bath and were the same for all three bell jars. A solenoid

valve in the chilled water line was opened to allow water to pass through the cooling coil

if the air temperature or relative humidity of any one of the bell jars was too high.

A 50 W, 1 Q power resistor was used as the heating source in each bell jar. The

power output of the resistor was set by varying the voltage across it. The Opto modules

used to turn the heaters on/off were rated at 4 A. The resistors were 1 Q, so the

theoretical magnitude of the current draw (A) was equal to the magnitude of the voltage

drop (V). However, at 8 A the current draw was only 4 A, within the limit of the Opto

module. The power output of the heater was 28 W as calculated by equation 5.









P=IV (2-5)

where P = power, W

I = current, A

V = voltage, V

Each bell jar had two manually controlled fans (BM5115-04W-B50-LOO, NMB

Technologies, Chatsworth, CA) to maintain air circulation. The specified air flow rate at

standard pressure was 1.42 L s-1 (3 cfm) per fan. To reduce disturbance caused by high

air velocities within the plant canopy, a pulse width modulation routine was applied to

reduce the fan flow rate. Power to the fans (12 V) was cycled on/off every 500

milliseconds. The volumetric flow rate of a given fan is proportional to the fan speed and

diameter (Henderson et al., 1997). Therefore, although the mass flow rate of air

decreased at lower pressures due to decreased air density, air velocity was not affected by

pressure. Some leaf movement was observed at pressures as low as 12 kPa, leading to

the conclusion that the fan output was adequate for air mixing within the range of

pressures used in this research. All fans were turned on at the start and remained on

throughout the duration of each experiment.

Pressure and Carbon Dioxide Concentration Control

Internal pressure and carbon dioxide concentration control for all three bell jars

were carried out in the same ioControl chart to avoid timing conflicts. At the beginning

of the control loop, the current CO2 concentration (ppm) in each bell jar was compared to

the setpoint concentration (ppm) for that bell jar. The measured and setpoint

concentrations, given in units of parts per million, were converted to units of mass by

equation 6 derived from the ideal gas law.











CO2 mass =44* (2-6)
8.3144* T 7r

where CO2_mass = mass of carbon dioxide inside, g

[C02] = carbon dioxide concentration, ppm

p = bell jar pressure, Pa

Vbj = bell jar volume, m3

TairK = absolute temperature of air inside bell jar, K

The current mass of CO2 in each bell jar was compared to the setpoint mass for that

particular jar. If the current level was more than 120 ppm below setpoint, the mass of

CO2 required to reach the setpoint was calculated and CO2 was added by the mass flow

controller (FMA3202-C02, Omega, Stamford, CT). To avoid overshoot that sometimes

occurs when the mass flow controller (MFC)was first turned on, the MFC is turned on

and vented for 12 seconds before the three-way solenoid valve was switched to permit

CO2 flow into one of the three bell jars. One of three solenoids was opened to allow CO2

into the desired bell jar. The MFC flow rate was always set at 40 ml/min. After time

elapsed to add 70% of the calculated mass of CO2 needed to the bell jar the MFC was

turned off. The bell jar solenoid valve remained open for 30 seconds to allow CO2 in the

tubing to diffuse into the bell jar. With plants present, mixing within the bell jar was

allowed for 60 seconds before the next CO2 addition. Without plants, mixing was

allowed for ten minutes.

Pressure control logic occurred immediately following the carbon dioxide control.

As in the CO2 control logic, pressures of the three bell jars were independently controlled

one at a time. The pressure of each bell jar was compared to the setpoint pressure of that









jar. If pressure exceeded the setpoint by 1 kPa, the solenoid valve for that bell jar opened

and the vacuum pump was turned on. The vacuum pump remained on until the current

pressure was equal to the setpoint. After pressure control of the bell jar, the entire

CO2/pressure control loop began again.

Light Control

The light within the bell jars was controlled externally to the system. The light

level on the bases without the bell jars was 349.9, 372.8, 353.2 pmol m-2 s-1 for chambers

1, 2, and 3 respectively. With the bell jars in place the light level were 338.4, 351.4, and

333.3 tpmol m-2 s-1. Thus, the average transmissivity of the bell jars was 95%. It is

believed that the highly reflective surfaces of the external growth chamber contributed to

such a large amount of light transmitted through the bell jar.

A "sock" made of a lightweight screening material was configured for each bell jar

to reduce the internal light level for low light treatments (see Figure 5). With the socks in

place, the light levels inside the three bell jars were 158.5, 166.5, and 156.5 [pmol m-2 s-1















Figure 2-5. Light level control. Fine mesh screening material was used to reduce the
PAR level inside the bell jars from an average of 341 pmol m-2 s-1 to 161
Lpmol m-2 -1.









Performance Testing

Data from several experiments were used to quantify the performance of the small-

scale chambers. When applicable, environmental data are reported as described in

ANSI/ASAE Standard EP411.1 "Guidelines for Measuring and Reporting Environmental

Parameters for Plant Experiments in Growth Chambers".

Pressure

The system was operated for one hour at a pressure setpoint of 12 kPa for all three

bell jars. Pressure was recorded every minute during this time. The maximum,

minimum, average, and standard deviation of the pressure data for each bell jar are given

in Table 2-3. Since leakage increases at low pressure, data for a setpoint of 12 kPa are

given as a worst case situation.

Table 2-3. Performance of pressure control algorithm. Descriptive statistics are given
for data recorded at one-minute intervals for a one hour period. All values are
in kPa.
Bell Jar 1 Bell Jar 2 Bell Jar 3
Average 12.61 12.49 12.55
Maximum 13.05 13.06 13.07
Minimum 12.12 12.04 12.09
Standard deviation 0.26 0.03 0.30

To quantify the leakage rate of each bell jar, the pressure was reduced to 12, 33, or

66 kPa and the pressure control algorithm was turned off. Pressure data were again

recorded every minute for a one-hour period. The leakage rate was taken as the pressure

increase per minute as determined by slope of a linear regression line. Table 4 shows the

rate of pressure increase for each bell jar at 12, 33, and 66 kPa.












Table 2-4. Bell jar leakage rates. The rate of pressure increase is given for each bell jar
in kPa min1.
Initial pressure, kPa Bell Jar 1 Bell Jar 2 Bell Jar 3
12 0.07 0.15 0.12
33 0.03 0.14 0.08
66 0.02 0.08 0.06

Carbon dioxide

The CO2 control algorithm was tested with and without plants. Figure 2-6 shows

the CO2 concentration as a function of time without plants at standard pressure with the

setpoint equal to 1000 ppm. CO2 was added incrementally until the concentration was

within 120 ppm of the setpoint. Within 45 minutes, the CO2 concentration was within 60

ppm of the 1000 ppm setpoint. Achieving setpoint took much longer without plants

because ten minutes was allowed for mixing versus the one minute allowed when plants

were present. This longer mixing time was required to avoid overshoot that often

occurred when no plants were inside the bell jar to take up CO2.


1100

1000

E 900
e-*- Bell jar 1
.2 800
800 -- Bell jar 2
*-E / Bell jar 3
u 700

O 600

500

400
0 20 40 60 80 100
Time, min
Figure 2-6. CO2 control without plants at standard pressure. The CO2 concentration
within all three bell jars was within 60 ppm of the 1000 ppm setpoint
approximately 45 minutes from the activation of the CO2 algorithm.











The CO2 control algorithm was also tested at a reduced pressure. Figure 2-7 shows

the CO2 concentration and pressure for a one-hour period. Data were recorded at one-

minute intervals. The pressure setpoint was 12 kPa with a hysteresis of 1 kPa and the

CO2 setpoint was 9000 ppm. The CO2 concentration dropped by approximately 800 ppm

each time the pump was activated, a reduction of only about 8.2%. This corresponded

well to a 8.3% decrease in pressure in reducing it from 13 to 12 kPa, indicating that the

air within the bell jar was well mixed. At higher pressures, the vacuum pump activity

had less effect on CO2 concentration. For example, if the total pressure was 67 kPa and

the vacuum pump was turned on to reduce the pressure by 1 kPa, assuming the air inside

the bell jar is well mixed, the decrease in CO2 would be only 1.5%.


10500

10000

9500

9000

8500

8000 -*- Carbon dioxide
Pressure
7500

7000


15

-14.5

14

13.5

13 L

12.5 .

12

11.5

11

10.5

10


0 10 20 30 40 50 60
Time, min
Figure 2-7. Effect of vacuum pump on CO2 control at low pressures. At 12 kPa, with no
plants, the activity of the vacuum pump to maintain the pressure setpoint had a
considerable effect on the CO2 concentration.



Another test of the CO2 algorithm was performed with plants inside the bell jar.

With a total pressure setpoint of 12 kPa, the CO2 setpoint was 3367 ppm (0.04 kPa partial










pressure). Figure 2-8 shows the CO2 concentration over time for each of the three bell

jars with two mature radish plants inside. Summary statistics for the same data as in

Figure 2-7 are given in Table 2-5. The control system was successful in responding to

plant CO2 uptake and reductions caused by vacuum pump activity and maintained the

CO2 setpoint with a maximum standard deviation of 267 ppm.


4600

4100

3600

3100

2600

2100

1600

1100

600

100


-1





-*- Bell jar 1
Bell jar 2
Bell jar 3





0 20 40 60 80 100 120
Time. min


Figure 2-8. CO2 control with plants at 12 kPa. The CO2 control algorithm reached the
3367 ppm setpoint in less than 40 minutes from the start of the experiment.



Table 2-5. Performance of CO2 control algorithm at 12 kPa with plants. Descriptive
statistics are given for data recorded at one-minute intervals for a one hour
period. The CO2 setpoint was 3367 ppm. All values are in ppm.
Bell Jar 1 Bell Jar 2 Bell Jar 3
Average 3574 3383 3335
Maximum 3885 3656 3786
Minimum 3204 2935 2738
Standard deviation 181 157 267


Air Temperature and Relative Humidity

The air temperature and relative humidity control algorithm was also tested at 12

kPa. The setpoints, 24 C and 70%, were chosen to achieve a VPDair of 0.9 kPa. Figure









2-9 shows the air temperature and relative humidity for the 50-minute period beginning

one hour after the start of the experiment. The air temperature of bell jar 3 was the last to

reach its setpoint. As previously mentioned, the power resistors that served as the bell jar

heating elements could not be operated simultaneously to avoid exceeding the current

rating of the Opto output modules. The control algorithm placed priority numerically. In

other words, power was given to the resistor in bell jar 3 only if the air temperatures in

bell jars 1 and 2 were at or above setpoint. Furthermore, heating occurred slowly because

current was limited to only 4 A. From equation 5, the power output of the resistor was

calculated to be 28 W. Although it took some time to achieve the setpoint in bell jar 3,

once the air temperature reached 24 C, the heater was sufficient to maintain temperature

as demonstrated by a maximum air temperature standard deviation of 0.3 C (see Table 2-

6).

Relative humidity was maintained fairly constant throughout the duration of the

setpoint. From Table 2-6, which gives descriptive statistics for air temperature and

relative humidity, the maximum standard deviation over the 50-minute period was only

1.1%. The mean values for bell jars 1 and 2 were slightly below the 70% setpoint. This

occurred because chilled water flow to the three cooling coils was controlled together.

The coil remained on as long as the humidity in any one of the bell jars was above the

setpoint. However, it should be pointed out that humidity in all three bell jars was within

the 5% deviation from setpoint recommended by ASAE standard ANSI/ASAE Standard

EP411.1 during the entire experiment.











25

24.5

24

23.5

23

S22.5
E
_ 22 -c-Tair(1)
< -- Tair(2)
21.5
-- Tair (3)
21 -- RH(1)
RH (2)
20.5 -- RH (3)

20 ..
60 65 70 75 80 85
Time, min


85

80

75

70

65 y

60

55

50

S 45
90 95 100 105 110


Figure 2-9. Air temperature and relative humidity control at 12 kPa with plants. The
control algorithm successfully achieved and maintained the 24 C and 70%
setpoints one hour after the start of the experiment.



Table 2-6. Performance of the air temperature and relative humidity control algorithm at
12 kPa with plants. Descriptive statistics are given for data recorded at one-
minute intervals for a 50-minute period. The air temperature and relative
humidity setpoints were 24 C and 70% to achieve a VPDair of 0.9 kPa.
Bell Jar 1 Bell Jar 2 Bell Jar 3
Air temperature, C
Average 24.0 24.0 23.8
Maximum 24.2 24.2 24.1
Minimum 23.7 23.8 23.0
Standard deviation 0.1 0.1 0.3
RH, %
Average 66.4 68.2 70.6
Maximum 69.7 71.0 72.4
Minimum 65.0 66.0 68.4
Standard deviation 1.1 1.1 0.9



Conclusions and Future Development

The bell jar based small-scale controlled environment chambers described in this


chapter worked well for the purposes of this research to study short term effects of


pressure, C02, and light on plant evapotranspiration. The control algorithm successfully









maintained pressure, CO2 concentration, air temperature, and relative humidity while

measuring plant weight and leaf temperature.

There were a few limitations of the system. Leakage rates were higher than

desired. The wire feedthrough and water fittings built in the lab were adequate, but did

not perform as well as commercial vacuum fittings. For this research, maintaining

pressure and CO2 setpoints was a primary objective. The vacuum pump and CO2

algorithm were capable of overcoming leakage to sufficiently maintain the pressure and

CO2 setpoints. In other applications of this system, such as monitoring CO2 drawdown to

measure photosynthesis, high leakage rates may be of more concern.

Another limitation of this system was the heating power limitations. The current

rating of the output modules limited the power for heating to 28 W for a single bell jar at

a time. If more current could be applied to the 50-W resistors for heating, the air

temperature setpoints could be achieved more quickly. For the purposes of this research

the ambient environment was buffered by the external growth chamber and the heat

output of the power resistor was capable of overcoming the temperature decrease that

occurred when the cooling coil was turned on. However, in settings with a higher heating

load, more power may be needed to maintain the temperature setpoint.














CHAPTER 3
EFFECTS OF PRESSURE ON LEAF CONVECTIVE HEAT TRANSFER

The rate of water loss from leaves is governed by the leaf energy balance that

includes the effects of radiation, water evaporation, and convection. Heat transfer by

convection occurs when air passes over the leaf surface and is significantly affected by

the density of air, which is determined by total pressure. This chapter presents

convective heat transfer analysis for a leaf represented by a horizontal flat sheet as

affected by pressure and air velocity.

Literature Review

The rate of sensible heat transfer by convection (equation 1-2) has a significant

impact on the leaf energy balance. Convection determines the degree to which the leaf is

affected by the ambient aerial environment. When convective heat transfer is high, as for

a plant outdoors in windy conditions, leaf temperature approaches air temperature

regardless of the radiative load (Jarvis and McNaughton, 1986; Jones, 1992). On the

other hand, if the rate of convective heat transfer is low, radiation heat transfer dominates

the leaf energy balance.

Convective heat transfer analysis is also significant because it provides a way to

estimate the thickness of boundary layers. Knowledge of the thickness of the velocity

and thermal boundary layers that form over the surface of a leaf are important in order to

accurately quantify the ambient environment. Within the boundary layer there are

gradients of air velocity, gas concentration, and temperature. Sensors must be located

outside the boundary layer in the free stream to best measure the surrounding









environment. On the other hand, locating sensors within the boundary layer provides

information about the leaf microclimate.

Convection Heat Transfer

Resistance to convective heat transfer is caused by the boundary layer that forms

above the leaf as air passes over. Figure 3-1 shows a theoretical diagram of the velocity

boundary layer over a horizontal thin plate. The air above the plate surface can be

thought of as a series of infinitely thin horizontal layers of particles. The air particles

that come in contact with the surface of the plate have zero velocity and exert a shear

stress on the layer just above it, slowing it down. This second layer slows down the third

by exerting a shear force and so on until the effect is negligible and the local velocity

reaches the free stream velocity, u,. A horizontal velocity gradient exists between the

plate surface (u = 0) and the free stream (u = u,). The boundary layer thickness,6, is

defined as the vertical distance, y, at which u = 0.99 u, (Incropera and DeWitt, 1996).

u. Free stream
6(x)
U- L--* ----- 5(x}

y u' u Velocity
boundary layer


I
Figure 3-1. Velocity boundary layer over a horizontal flat plate (adapted from Incropera
and DeWitt, 1996).


A thermal boundary layer similar to the velocity boundary layer also develops

over the surface of a flat plate. Figures 3-2 and 3-3 show the thermal boundary layer over

a horizontal flat plate with a surface temperature warmer (Figure 3-2) and cooler (Figure

3-3) than the free stream air temperature. A horizontal temperature gradient develops









between the surface temperature, Ts, and the free stream temperature, To. The thickness

of the thermal boundary layer, 6t, is defined as the vertical distance at which the air

temperature, T, is equal to 0.99T, (Incropera and DeWitt, 1996).


TY Free stream
U, Nx}



y TT Thermal
T boundary layer




Figure 3-2. Thermal boundary layer over a horizontal flat plate that is warmer than the
surrounding air (adapted from Incropera and DeWitt, 1996).


T. Free stream
uc, -(x)


y T e -- nT Thermal
/. boundary layer


X
Figure 3-3. Thermal boundary layer over a horizontal flat plate that is cooler than the
surrounding air (adapted from Incropera and DeWitt, 1996).


The mathematical derivations involved in boundary layer analysis are beyond the

scope of this review and are not included. To simplify analysis, the following non-

dimensional groups Reynolds, Prandtl, Grashof, and Nusselt numbers are employed

in the solutions. The Reynolds and Grashof numbers are used to determine if forced,

free, or mixed convection is dominant. Then, based on the dominant mode of convection,

non-dimensional groups are used to calculate resistances and boundary layer thicknesses.









Forced convection occurs when the fluid movement across the surface is driven

externally by a pump, fan, or wind. Free convection is driven by buoyancy forces created

by temperature gradients in the fluid. Mixed convection occurs when the effects of

forced and free convection are similar in magnitude and neither can be neglected.

The Reynolds number, Re, is the ratio of inertia to viscous forces and is calculated

as:


Re uL (3-1)
v

where: u, = free stream air velocity, m s-1

L = characteristic length, m

v = kinematic viscosity, m2 s-1

Kinematic viscosity, a function of fluid density, is highly pressure dependent. As a

result, assuming all other parameters are held constant, Reynolds number will decrease as

pressure is dropped.

Prandtl number, ratio of viscosity to thermal conductivity, is calculated as follows

in equation 3-2.


Pr = (3-2)


where: a = thermal diffusivity, m2 s-1

Grashof number, ratio of buoyancy to viscous forces, is calculated by equation 3-3.


Gr = gO3 )L (3-3)
-2


where: g = gravitational constant, m s-2

3 = 1/Ta =coefficient of thermal expansion, K-1









Ts = surface temperature, K

Ta = air temperature, K

External resistance

The method of calculation of the rate of sensible heat transfer from the crop canopy

is determined by the dominant mode of convective heat transfer forced, free, or mixed.

In typical field conditions wind velocities are in the range of 1 to 5 m s-1 and forced

convection is the primary mode of sensible heat transfer (Hanan, 1998). In Earth

greenhouse applications typical air velocities of 0.5 to 0.7 m s-1 are considered acceptable

(ASHRAE, 2001). In these lower air velocities, free convection plays a larger role and a

mixed convection model is most accurate (Bailey and Meneses, 1995; Stanghellini, 1987;

Zhang and Lemeur, 1992).

The magnitude of the ratio Gr/Re2 determines the principal mode of convection. If

Gr/Re2 1, both free and forced convection must be considered (mixed convection). If

Gr/Re2 <<1, forced convection dominates and free convection may be neglected.

Likewise, if Gr/Re2 >>1, forced convection may be neglected

The Nusselt number is a measure of the magnitude of convection heat transfer

occurring at a surface. Calculation of the Nusselt number depends on the dominant mode

of convection heat transfer. In the case of forced convection, the Nusselt number for a

horizontal thin plate is (Incropera and DeWitt, 1996):

Nu = 0.664Rel/2 Pr1/3 (3-4)

For free convection of the upper surface of a horizontal, heated plate, the Nusselt

number is (Incropera and DeWitt, 1996):

Nu = 0.54(Gr Pr)1/4 (3-5)









Equation 3-5 for a heated upper surface was applied in this analysis because it is

most appropriate for the convection experiments performed in this research. In the case

of an actual leaf at reduced pressures equation 3-6 for a cooler than air surface may be

more appropriate considering evaporative cooling caused by high transpiration rates.

Nu = 0.27(Gr Pr)1/4 (3-6)

In free convection conditions equation 3-7 for characteristic length, L, suggested by

Incropera and DeWitt (1996) was applied to improve model accuracy.


L (3-7)
P

Stanghellini (1987) developed equation 3-8 for the Nusselt number in mixed

convection conditions that worked well for horizontal leaves in a greenhouse.

Nu = 0.37(Gr+ 6.92Re2 )1/4 (3-8)

From the Nusselt number, the external resistance to sensible heat transfer for a

single leaf can be calculated by equation 3-9.

L
re (3-9)
aoNu

The external resistance of a crop canopy, rh, was estimated by Zhang and Lemeur

(1992) from the re of a horizontal flat plate by equation 3-10. This equation assumes that

all leaves contribute equally to sensible heat transfer.


rh r (3-10)
2LAI

Boundary layer thickness

The average thickness of the velocity boundary layer for forced flow over a

horizontal, thin flat plate is given by equation 3-11 (Incropera and DeWitt, 1996).









5L
5L (3-11)
Re1/2

The Prandtl number, a measure of the ratio of the viscosity forces to diffusion, can

be used to estimate the thickness of the thermal boundary layer, 6t, based on 6.

SPr3 (3-12)
6t

Objectives

The objective of this chapter was to use classical convection heat transfer analysis

to determine the effects of pressure and air velocity on the external resistance and

boundary layer thickness of radish plants growing at atmospheric pressures as low as 12

kPa. The theoretical heat transfer model described above was compared with data from a

series of controlled lab experiments.

Materials and Methods

The sensible heat transfer from a leaf replica was measured to evaluate the effects

of pressure and air velocity on external resistance. The rectangular-shaped replica

(Figure 3-4) was made by wrapping a 12.7 cm x 2.54 cm (5 in x 1 in) flexible 10-W

Kapton heater (model BKL3005, Birk Manufacturing, Inc., East Lyme, CT) with

standard grade aluminum foil (thickness = 0.16 mm). A small type-T thermocouple was

sandwiched between the heater upper surface and the foil. It was assumed that there was

no temperature gradient along the thickness of the foil so that the temperature measured

by the thermocouple was equal to the upper surface temperature of the leaf replica.

Power to the heater was supplied by a DC power supply. The voltage input was 13.2 V

and the current draw was 0.82 A.










.5 Thermocouple -Aluminum foil
Heater
12.7 cm Aluminum foil

to DC power
supply

Figure 3-4. Leaf replica. A leaf replica made by wrapping a thin, flexible heater with
aluminum foil was used to measure the effects of pressure and air velocity on
convective heat transfer.


A fan (BM5115-04W-B50-LOO, NMB Technologies, Chatsworth, CA) was

positioned about 2.5 cm in front of the leading edge of the heated sheet as shown in

Figure 3-5. The fan output was varied by cycling power to the fan (1 second delay) and

positioning layers of screening material over the fan outlet. The volumetric flow rate of a

given fan is proportional to the fan speed and diameter (Henderson et al., 1997).

Therefore, although the mass flow rate of air decreased at lower pressures due to

decreased air density, air velocity was not affected by pressure. At standard pressure, air

velocity was measured about 5 cm above the sheet with a hot wire anemometer (model

407123, Extech Instruments, Waltham, MA). One of the bell jar chambers and the data

acquisition system described in chapter 2 was modified for these experiments to control

pressure.




























Figure 3-5. Convection heat transfer experimental setup. A fan was positioned in front of
a thin heated sheet inside one of the bell jar chambers.


External resistance was determined from cooling curves generated for the heated

foil sheet at four levels of pressure (12, 33, 66, and 101 kPa) and air velocity (0, 1.8, 2.9,

and 5.8 m s-l). Power was turned on to the heating element of the sheet until the surface

temperature approached 80 C. The power supply was then turned off and the sheet was

allowed to cool until the surface temperature approached the ambient air temperature

measured by a type-K thermocouple located about 5 cm above the sheet. Figure 3-6 is an

example of a cooling curve at 5.8 m s- and 101 kPa.












60

50


40 \
I--
S30--

201

10


0 20 40 60 80 100 120 140
Time, s
Figure 3-6. Temperature profile for leaf replica during heating and subsequent cooling
phase at 101 kPa and an air velocity of 5.8 m s1


The slope of the cooling curve was related to the rate of sensible heat loss as

determined by a mass balance of the foil sheet given by equation 3-13.

C =H + R, (3-13)


where: C = rate of change of heat content of foil sheet, W m-2

H = rate of sensible heat transfer, W m-2

R = rate of radiation heat transfer, W m-2

The rate of change in the heat content of the foil sheet is given by equation 3-14.

dT, d(Ts T,
C = ,cL d = p,cL d( (3-14)



where: ps = density of leaf replica sheet, kg m-3

cps= specific heat of leaf replica sheet, kJ kg-1 K-1

L = length of sheet, m

Ts = sheet surface temperature, C









Ta = air temperature, C

The rate of sensible heat transfer, H, is given by equation 1-2. Note that the canopy

resistance term, rh, was replaced by the resistance for a single flat plate, re, for this

analysis. Net radiation was calculated by the following equation 3-15. Variables in bold

denote absolute temperature.

R, = o(T, T,,) (3-15)

where: a = Stefan-Boltzmann constant = 5.670 x 10- W m-2 K-4

E = emissivity of sheet surface

Tsur = average temperature of surrounding surfaces, K

It was assumed that the system was in equilibrium and the temperature of the

surroundings could be well approximated by air temperature.

An approximation was employed to eliminate the fourth order terms of the

radiation equation 3-14 and simply the solution of the heat balance. A coefficient, hr, was

introduced to cast the net radiation equation in a form similar to the convection equation.

R, = -o(T4 T4) = h,(T, T) (3-16)

where: hr = radiation heat transfer coefficient, W m-2 K

Rearranging to solve for hr and expanding the fourth order polynomial

(T,4 T'4) T ~ T 2"T + T" (T T,)(T, + T, )(T + T2 2
h, = om = os = o7 (3-17)
(T -T) (T T) ((T, )T

and simplifying


h, = cy(T, + T )(T2 +- Tf2)


(3-18)









To further simplify the equation two more variables, Tm and e, were introduced.

Tm was the mean of the sheet surface temperature, Ts, and the air temperature, Ta. The

difference between Ts and Ta was 2e so that:

T +e = Tm (3-19)


T e=T
S m


(3-20)


Combining equations 3-18, 3-19, and 3-20 and simplifying,

hr 2Tm2T -T -_T )2
h, = os2T, 2T,2 +
2


(3-21)


Assuming that the difference between the surface and air temperatures, Ts-Ta, was

significantly less than the absolute temperature of either the surface or air, the last term

could be neglected. Therefore, the radiation heat transfer coefficient was given by

equation 3-22.


hr = co4T3

Substituting equations 1-2, 3-14, 3-16, and

13 gave the following differential equation.

d(T -T) _-P ,p(T -
SCPs dt


Dividing both sides by pscpsL

d(T, -TJ) -, Pc,(T, -Ta)
dt rePscpsL

and rearranging to simplify yielded equation 3-25.

d(T, -T) P +ac h
dt repScL p ps


(3-22)

3-22 into the heat balance of equation 3-


Ta)
hr(T Ta)


h
L (T)-T,
pcsL


T (T)-T)


(3-23)





(3-24)





(3-25)










The solution to the differential equation 3-25 was 3-26.


(T~ -T a (T T =- pa pr (, 1-tl) (3-26)
rePcpL p, c L_

Equation 3-26 was related to the cooling curves (as in Figure 3-6) to solve for the

external resistance. Figure 3-7 shows a plot of the natural logarithm of Ts-Ta of the same

data as Figure 3-6 for time equal 50 to 110 seconds. Equating the slope, m, of a linear

regression line through this data with equation 3-26 and rearranging gave equation 3-27

for external resistance, re.


r = pa (3-27)
m(PcpSL) +hr


5




y = -0.0617x + 7.1408
R2 = 0.9996
3-






1


0
45 55 65 75 85 95 105 115
Time, s

Figure 3-7. Transformed cooling data for the leaf replica at 101 kPa and an air velocity
of 5.8 m s-1. The slope of a linear regression line was related to Equation 3-26
to determine the external resistance to sensible heat transfer.


The slope of the linear regression line for the transformed data of Figures 3-6 and

3-7 was -0.0617. This value and the following properties for air and the sheet were









applied to Equation 3-27 to calculate the external resistance: pa=1.16 kJ kg-1 K-1;

cpa=1.007 kJ kg-1 K-1; ps=1800 kJ kg-1 K-1; cps=0.98 kJ kg-1 K-1; and L=0.22 mm. The

average air temperature during all testing was 25 C. Assuming an emissivity of bright

aluminum foil of 0.05 (McQuistan and Parker, 1994) and a maximum sheet surface

temperature of 80 C, the radiation heat transfer coefficient calculated by equation 3-22

was 0.393 W m-2 K. This gave an external resistance of 50.1 m s-.

Results and Discussion

The external resistance of a thin, heated sheet was empirically determined at four

levels of pressure and air velocity using temperature profiles during a cooling phase.

Figures 3-8, 3-10, 3-12, and 3-14 show the difference between surface temperature of the

sheet and air temperature during heating and subsequent cooling at 12, 33, 66, and 101

kPa, respectively. Figures 3-9, 3-11, 3-13, and 3-15 show the natural logarithm of Ts-Ta

during cooling. The slopes from linear regression analysis for each curve were used to

determine the external resistance, re, in equation 3-27. At each pressure, cooling occurred

at a faster rate with increasing air velocity. Decreasing pressure also decreased the rate of

cooling. As previously mentioned, volumetric flow rate and, therefore, air velocity was

not affected by pressure. However, air density and mass flow rate decrease with

pressure. Decreasing the air density reduced the cooling capacity of the air passing over

the sheet. Note that differences in maximum temperature were due to the time period that

the heating element was turned on, which was controlled manually.











ou


70

60 5.8 m/s
At \ m 2.9 m/s
50 R 1.8 m/s
SAL # still air

S40


30

20


10

0
0 20 40 60 80 100 120 140
Time, s

Figure 3-8. Surface temperature of leaf replica during heating and subsequent cooling
phase for four air velocity treatments at 12 kPa.


45 55 65 75 85 95 105
Time, s

Figure 3-9. Transformed surface temperature data for leaf replica at 12 kPa.














70

60- 5.8 m/s
60
/ 2.9 m/s
5 1.8 m/s
50
+ still air

40 -

30

20

10

0
0 20 40 60 80 100 120 140
Time, s

Figure 3-10. Surface temperature of leaf replica during heating and subsequent cooling
phase at 33 kPa.


m58 = -0.0495


A 5.8 m/s
* 2.9 m/s
1.8 m/s
* still air


m1 8= -0.0249

ms, = -0.0198


45 55 65 75 85 95 105
Time, s

Figure 3-11. Transformed surface temperature data for leaf replica at 33 kPa.


m2 9 =-0.0364


L




























0 20 40 60 80 100 120 140
Time, s
Figure 3-12. Surface temperature of leaf replica during heating and subsequent cooling
phase at 66 kPa.


3

2.5
S 2 A 5.8 m/s
I-


1.5
1.8 m/s
m2 9 = -0.0436
1 still air
mi a = -0.0328
0.5
mstll = -0.0235
0
45 55 65 75 85 95 105 1
Time, s
Figure 3-13. Transformed surface temperature data for leaf replica at 66 kPa.















70

6 5.8 m/s
60
0 2.9 m/s

502 e9 1.8 m/s
1 --* still air
S40 o2


30


20


10



0 20 40 60 80 100 120 140
Time, s

Figure 3-14. Surface temperature of leaf replica during heating and subsequent cooling
phase at 101 kPa.



4.5

4-

3.5




2.5

!- L 5.8 m/s
2 I
m 2.9 m/s
mS 8 = -0.0618
1.5 1.8 m/s
m2 9 = -0.0604
1 still air
mi 8 = -0.0375
0.5
msl, = -0.0255


45 55 65 75 85 95 105 115
Time, s

Figure 3-15. Transformed surface temperature data for leaf replica at 101 kPa.









Model Performance

The empirically determined values for external resistance were compared with the

classical heat transfer model of equation 3-9. Figure 3-16 shows the empirical values and

model predictions at each level of air velocity as a function of pressure. The model

accurately predicted the proportional effects of both pressure and air velocity on external

resistance. Resistance to heat transfer increased with increasing pressure and air velocity.

Equation 1-2 predicted that the rate of convective heat transfer was inversely proportional

to external resistance. That is, if air density, specific heat, and temperature difference

remained the same, convective heat transfer should increase as resistance decreases.

However, as previously mentioned, the significant decrease in air density at lower

pressures reduced the heat transfer capacity of air passing over the surface. This was

demonstrated by calculating the rate of sensible heat transfer, H, from the heated sheet for

the external resistance values determined experimentally. Figure 3-17 shows the rate of

heat transfer for the sheet with a surface area of 0.0032 m2 as a function of pressure and

air velocity. The rate of heat transfer was an average of 50% higher at standard pressure

than at 12 kPa. This increase was much less than the 88% decrease in air density from

101 to 12 kPa demonstrating the effect of external resistance. Higher values of re at

standard higher pressures reduced the magnitude of the effect on convection.














140


120


E 100
vc
U
S80
6i
m 60

w
su.


10 20 30 40 50 60 70 80 90 100
Pressure, kPa

Figure 3-16. Measured and predicted values for external resistance of leaf replica as a
function of pressure and four levels of air velocity.


0.4

0.2

0-
0 -------------------------------

0 20 40 60 80 100 120
Pressure, kPa

Figure 3-17. Rate of heat transfer from leaf replica as a function of pressure and air
velocity.










The ability of the theoretical model to predict external resistance was evaluated by

comparison to the experimentally determined values. Figure 3-18 and 3-19 show two

tests for model performance. In Figure 3-18 the predicted values were plotted against

empirical values. The 1:1 line represents perfect model fit. The points lined up nicely

along the 1:1 line which indicated that the predicted values closely matched the

experimental values for both free and forced convection conditions. Forced convection

dominated at air velocities above 1.8 m s- and free convection was dominant in still air.

None of the combinations of pressure and air velocity tested resulted in mixed

convection. The actual model error as given by the difference between predicted and

experimentally determined values was plotted as a function of pressure in Figure 3-19.

The maximum error was 21.1 s m- and the average error was only 2.6 s m- for all

conditions tested.

200

5.8 m/s 1:1
0 2.9 m/s
160--
A 1.8 m/s
0 m/s
E 120



S80



40

0
**



0 40 80 120 160 200
re (experimental), s m-1


Figure 3-18. External resistance model performance. Predicted values of re are shown
plotted against empirically determined values.











25.0

20.0

E 15.0

S10.0

.- 5.0 -
,.
X 0.0

S-5.0


Im 2.9 m/s
-15.0
e 1.8 m/s
-20.0 -- *still air

-25.0 -..
0 20 40 60 80 100 120
Pressure, kPa
Figure 3-19. External resistance model error. The difference between predicted and
experimental external resistance is plotted as a function of pressure.




Boundary Layer Thickness

Pressure and air velocity also play significant roles in the thickness of the boundary

layer, 6, that forms over the horizontal surface. Figure 3-20 and 3-21 show the effects of

pressure and air velocity, respectively, on boundary layer thickness (equation 3-11). In

Figure 3-20 the velocity boundary layer thickness was plotted as a function of pressure

for an air velocity of 1.0 m s-1. The thickness of the boundary layer increased

exponentially as pressure decreased so that it was greater than 2 cm as pressure

approached zero.

Boundary layer thickness at standard pressure was plotted as a function of air

velocity in Figure 3-21. At air velocities of 1.0 m s-1 and above, there was little change in

6. However, when the air velocity was low the boundary layer increased significantly.












Note that this predicted trend held true for all pressures. Changes in pressure only shift


the magnitude of these curves.



2.6

2.4

2.2

2

1.8
I-
1.6

1.4

1.2
m
1

0.8

0.10 20 30 40 50 60 70 80 90 100
Pressure (kPa)

Figure 3-20. Effect of atmospheric pressure on boundary layer thickness of a horizontal
flat plate. Air velocity was held constant at 1.0 m s-


1 2


3
Air velocity (m/s)


Figure 3-21. Effect of air velocity on boundary layer thickness of a horizontal flat plate.
Pressure was held constant at 101 kPa.









Conclusions

To predict the external resistance and boundary layer thickness for a mature radish

leaf, convection heat transfer analysis was performed both theoretically and

experimentally for a horizontal flat plate. A classical heat transfer model for both free

and forced convection regimes was compared with data from controlled experiments.

The model fit well for all levels of pressure (12, 33, 66, and 101 kPa) and air velocities

(still air, 1.9, 2.8, and 5.8 m s-1) tested. The average error between the predicted and

empirical resistances was 2.6 s m-1. As predicted by the model and observed in

experiments, external resistance was proportional to both pressure and air velocity.

Boundary layer thickness, however, increased significantly at low pressures and air

velocities less than 1 m s-1. The external resistance model developed here was a

necessary component of the evapotranspiration model that was the overall goal of this

research. This analysis also served as a mechanism for testing conventional convection

heat transfer equation in low pressure conditions. Predictions of boundary layer

thickness, although not tested experimentally, provided some guidance for choosing

appropriate locations to measure environmental conditions. Large boundary layers that

occurred at low pressures and low air velocities should be considered in the design of low

pressure systems.















CHAPTER 4

SURFACE RESISTANCE TO EVAPOTRANSPIRATION IN
REDUCED PRESSURE ENVIRONMENTS

Evapotranspiration, the total water lost by plant transpiration and evaporation from

the plant and surrounding ground surfaces, can be predicted by the Penman-Monteith

model (equation 1-8). Monteith (1965) modified an evaporation model developed by

Penman (1948) to account for resistances of the crop canopy to water vapor loss. In this

research, surface resistance is defined as the resistance to water vapor transfer through the

leaf cuticle layer and stomata. Changes in surface resistance are caused by the opening

and closing of stomata while the cuticle resistance remains relatively constant. This

chapter examines the effect of atmospheric pressure and other environmental variables on

the surface resistance to evapotranspiration.

Literature Review

The rate of water loss by evapotranspiration is determined by both physical and

biological parameters. Water vapor diffuses mostly through stomata, and to a lesser

extent through the leaf cuticle, from saturated air inside the leaf to the surrounding

environment. The rate of water diffusion through the leaf surface is limited by stomatal

aperture allowing the plant some control of transpiration rate.

Effects of Environmental Variables on Stomatal Control

Stomata reduce plant water loss while allowing CO2 diffusion into the leaf for

photosynthesis. Therefore, it is no surprise that stomatal control is significantly affected









by the ambient environment. Photosynthetically active radiation (PAR), CO2

concentration, vapor pressure deficit (VPD), and plant water status are all known to have

an effect on stomatal action.

Vapor pressure deficit

During the past two decades a considerable amount of research has been done to

investigate stomatal control with regard to ambient humidity. In question is whether

guard cells "sense" humidity or the rate of evapotranspiration. Most researchers have

concluded that plants use a "feedback" method of control in which they detect and

respond to changes in the rate of evapotranspiration and/or water status and not humidity

(Comstock, 2002; Lhomme, 2001; Monteith, 1995; Mott and Parkhurst, 1991; and

Outlaw, 2003). If the rate of water loss is greater than the rate of water uptake, the water

potential of the tissue surrounding the guard cells decreases. Although the exact

mechanism is not known, these desiccating cells are believed to send a signal to nearby

guard cells causing them to close and the rate of evapotranspiration to decrease

(Comstock, 2002). High rates of evapotranspiration may also have a direct affect on

guard cell action. According to Outlaw (2003), solutes accumulate in the guard cell

apoplast (dead tissue including cell walls, intracellular spaces, and xylem elements

through which water flows) as the transpiration stream evaporates. The solute

concentration increases at high rates of transpiration and, by osmosis, water flows into

the apoplast leaving the guard cells less turgid and causing them to close.

The relationship between stomatal resistance, evapotranspiration rate, VPD, and

mass diffusivity was cleverly demonstrated in experiments by Mott and Parkhurst (1991).

They compared stomatal resistance of several plant species in air and in helox (79%

helium and 21% oxygen). Water evaporates 2.33 times faster in helox than in air due to









the higher mass diffusivity of water in helox. Therefore, in cases of equal stomatal

aperture and VPD, evapotranspiration occurred faster for plants in the helox mixture.

Carbon dioxide

In normal and slightly above Earth ambient CO2 concentrations in the range of 400

to 1000 ppm (Po2 = 40.4 to 101 Pa) decreases in concentration cause stomatal opening

(Assmann, 1999; Wheeler et al., 1999) and thus, an increase in surface resistance. At

CO2 concentrations above approximately 1000 ppm there is little to no change in

stomatal resistance (Jarvis, 1976; Stanghellini and Bunce, 1993). However, in plants

exposed to super-elevated CO2 concentrations greater than 10,000 ppm (Pco2 = 1.01 kPa)

stomatal resistance was shown to decrease in potato and wheat plants leading to

decreased water use efficiency (Wheeler et al., 1999).

Some plants may acclimate to higher CO2 concentrations as shown by Stanghellini

and Bunce (1993). Stomatal resistance increased less as CO2 concentration was

increased from 500 to 2000 ppm for tomato plants grown at 700 ppm versus plants grown

at 350 ppm. The decreased sensitivity to changes in CO2 may mean that plants grown at

higher concentrations have increased water use. Soybeans grown at 800 ppm of CO2 had

similar values of canopy surface resistance during short-term exposure to 330 ppm as

plants grown at 330 ppm (Jones et al., 1985). Likewise, the surface resistance of plants

grown at 330 ppm was similar during short-term exposure to 800 ppm as the plants

grown at the higher CO2 concentration. A more significant effect of long-term exposure

to higher CO2 concentrations was the increase in leaf area. The leaf area of soybeans

grown at 800 ppm was 1.8 times greater than those grown at 330 ppm. Increased leaf

area led to higher transpiration rates for plants grown at 800 ppm when the surface

resistance decreased during exposure to an ambient CO2 concentration.









Photosynthetically active radiation

Stomata respond to light both directly and indirectly. As the intracellular CO2

concentration decreases due to photosynthesis, stomata open to take in more CO2

(Outlaw, 2003). Stomatal resistance of poinsettia cuttings decreased significantly when

incident radiation was increased from 50 to 300 W m-2 (400-700 nm) in work by Zolnier

et al. (2001). There is less of an effect of the magnitude of PAR on stomatal resistance

at levels above 500 [tmol m-2 s-1 (Jarvis, 1976).

Mass Diffusivity and Stomatal Resistance

Because mass diffusivity is pressure dependent, growing plants in reduced pressure

environments can be expected to yield results similar to those of Mott and Parkhurst's

(1991) helox experiments. Equation 4-1 gives the relationship derived from the ideal gas

law to quantify the effect of pressure on mass diffusivity (Incropera and DeWitt, 1996).

It is assumed that the ideal gas law is valid for the range of pressures used in this research

( 10 kPa).


D =Do P0

21
(4-1)

where Dw = mass diffusivity of water at pressure P, m2 s-1

P0 = standard pressure= 101.3 kPa

Do = mass diffusivity of water at standard pressure = 2.50 x 10-5 m2 s-1

A plot of mass diffusivity as a function of pressure, calculated by equation 4-1, is

shown in Figure 4-1. Note that the rate of water diffusion increases significantly at

pressures less than 25 kPa. A sharp increase in mass diffusivity at pressures below 25

kPa was verified in experiments by Rygalov et al. (2002).










3.0E-04


E 2.5E-04


.E 2.0E-04


.- 1.5E-04
0

'i 1.0E-04


S5.0E-05


O.OE+00
0 20 40 60 80 100
Pressure, kPa
Figure 4-1. The effect of pressure on mass diffusivity of water in air. At pressures lower
than 30 kPa, such as those being considered for a greenhouse on Mars, water
diffusion occurs much faster than at standard pressure.


Nobel (1999) gives equation 4-2 to calculate stomatal conductance, the inverse of

stomatal resistance.

D 1
g, (4-2)
Sr


where gs = surface conductance, mm s-1

D = mass diffusivity, mm2 s-1

/= effective path length for diffusion through stomatal pore, mm

rs = surface resistance, s mm-1

If stomatal density and pore depth does not change the effect path length, S, is a

function of stomatal aperture only (Mott and Parkhurst, 1991).

Note from equation 4-2 that surface resistance is negatively proportional to mass

diffusivity. As an example, consider a plant at 10 kPa and one at standard earth pressure









(101.3 kPa). If all other conditions remain the same and stomatal opening does not

change, stomatal conductance will increase by the ratio of the mass diffusivity at 10 kPa

to the mass diffusivity at 101.3 kPa. The result is an increase in stomatal conductance by

approximately a factor of 10 (see equation 4-3). The corresponding change in stomatal

resistance would be a decrease by a factor of 10.


D10 g 3 2.53x10-4 (43)
Di101.3 2.5x10 5

where: gslo = stomatal conductance at 10 kPa, m s-1

gso01.3 = stomatal conductance at 101 kPa, m s-1

Dio = mass diffusivity of water at 10 kPa, m2 s-1

D101.3 = mass diffusivity of water at 101.3 kPa, m2 s-1

Plant Adaptation and Surface Resistance

This research focused on short term response of surface resistance to changing

environmental conditions and did not consider effects of adaptations of plants grown at

high CO2 concentrations or low pressures. Adaptation of plants to Mars greenhouse

conditions may affect surface resistance. For example, stomatal density has been shown

to be significantly affected by environmental conditions during development.

In a study by Schoch et al. (1980), a decrease in the stomatal index (ratio of

stomatal cells to total number of cells) of new, developing leaves of Vigna sinensis plants

growing in high light conditions was observed following exposure to only one day of

shade. Gay and Hurd (1975) found that tomatoes grown under high light conditions (100

W m-2) had 30 stomata mm-1 on the upper surface of the leaf compared to less than one

stomata mm-1 for those grown in low light (20 W m-2).









Humidity and carbon dioxide concentrations have also been shown to impact

stomatal frequency. A study by Bakker (1991) compared the stomatal density and

average size of stomata for cucumber, tomato, and sweet pepper grown in a range of air

vapor pressure deficit (VPDair) treatments from 0.2-1.6 kPa. Their results showed that

both stomatal density and size, and, consequently, total pore area, increased with lower

VPDair (high humidity). Woodward (1987) found that stomatal frequencies have

decreased by about 40% since before the industrial revolution when atmospheric CO2

concentration was about 60 ppm lower than current levels. Similarly, during exposure to

the same VPDair and PAR levels tomato plants grown at 700 ppm experienced higher

rates of water loss than plants grown at 350 ppm (Stanghellini and Bunce, 1993). It

should be noted that there is significant variation between species with regard to the

effect of carbon dioxide concentration on stomatal density.

Environmental conditions may also affect the leaf area and/or size of stomata so

that changes in stomatal density do not necessarily denote changes in total pore area.

Bakker (1991) showed that statistical changes in stomatal pore area may not necessarily

result in significant changes in stomatal conductance. In a study by Jones et al. (1985)

leaf area was a factor of 1.8 greater for soybeans grown at 800 ppm than plants grown at

330 ppm. Surface resistance was similar for both sets of plants at the same CO2

concentration leading the authors to conclude that increased water loss rates of plants

acclimated to higher CO2 conditions was caused by enhanced leaf area and not surface

resistance adaptations.

Objectives

The objective of this chapter is to quantify the effects of atmospheric pressure,

CO2, and PAR on evapotranspiration and surface resistance. These effects will be









incorporated into an empirical model of surface resistance for mature radish plants

acclimated to standard pressure.

Materials and Methods

Experiments to collect data for calculation of surface resistance were performed

in controlled environment conditions as suggested by Jarvis (1976). Evapotranspiration

rates of radish plants were measured during short-term exposure to different levels of

pressure, CO2 concentration, and PAR inside the small-scale pressure controlled

chambers described in chapter 2. Each of the three bell jar-based chambers was

considered a replication as it offered independent control of pressure, CO2 concentration,

air temperature, and relative humidity. Maximum PAR was determined by the external

growth chamber and screens were added to reduce the light level.

Plant Material

A group of twelve pots each containing two 18-to-24-day-old radish plants

(Raphanus sativa L. 'Cherry Bomb II') were available for each three-hour measurement

period. Seeds were pretreated for 15-20 minutes in a 10% trisodium phosphate solution

prior to planting. Three or four pretreated seeds were planted per pot containing in metro

mix media. All plants were grown in the same controlled environment chamber as the

small-scale pressure controlled chambers. The chamber environmental conditions are

given in Table 4-1. Plants were culled after one week to leave two similar sized

seedlings per pot. Plants were watered daily with a 1 X Hoagland's solution. Planting

dates were staggered so that 12 pots of 18-to-24-day-old radish plants were available for

each week of experimentation. One pot per chamber was randomly selected for each

measurement period. Each pot was never used more than once per day to allow for

complete recovery following stress event.









Table 4-1. Controlled environment chamber conditions. The radish plants used in this
research were grown in the following conditions for 24 days.
Parameter Setpoint
Air temperature 24 C
Relative humidity 70%
PAR 360 [tmol m-2 s-1
Photoperiod 16/8

Evapotranspiration Measurement

To measure evapotranspiration, a randomly selected pot of radish plants was

centered on the load cell of the bell jar chamber. Before the start of each run, 20 mL of

nutrient solution was added to a small tray placed underneath the pot of radishes to make

certain that plants were well-watered throughout the measurement period. The bell jar

was then placed on top of the base and, if necessary, the shading material was slipped

over the bell jar to reduce the light level. Environment setpoints were added to the

control program and data logging was activated. One hour was allowed for the system

and plants to stabilize. The rate of evapotranspiration was taken as the slope of a linear

regression line fit to the weight data for the subsequent two-hour period. Each run of

three replications lasted a total of three hours.

A preliminary experiment was performed to determine the amount of time needed

for plants to reach steady-state. Leaf temperature was measured with an infrared

thermocouple while plants were subjected to 12 kPa for three hours (see Figure 4-2).

Plants reached steady-state, as indicated by stabilization of leaf temperature,

approximately 45 minutes after the pressure was reduced to 12 kPa.










27 120


25 Leaf temperature 100
-Pressure

23 -80
) --->Steady-state
2 21 60 ,
0 U
E 2)
19 40


17 20


15 0
0 0.5 1 1.5 2 2.5 3
Time from start, hr
Figure 4-2. Leaf temperature transient response to changes in total pressure. Radish
plants subjected to 12 kPa reached steady-state within one hour of initial
pressure drop.


Experimental Design

Experiments were completely randomized with a 4x2x2 factorial treatment

structure. Table 4-2 gives the levels of pressure, C02, and PAR treatments applied. Data

not used in the development of the surface resistance model were used for validation of

the evapotranspiration model (chapter 6). As previously mentioned, a pot containing two

radish plants inside each of the bell jars for the three-hour measurement period was

considered a replication.









Table 4-2. Evapotranspiration treatment structure. A 4x2x2 factorial treatment structure
was used in this research to determine the effects of pressure, CO2, and PAR
on evapotranspiration and surface resistance of radish plants.
Treatment Levels
Pressure 12, 33, 66, and 101 kPa
C02 40 and 150 Pa
PAR 340 and 160 [[mol m-2 s-1

Model Development

Empirical models for surface resistance based on the work of Jarvis (1976) have

been widely used in greenhouse applications (Baille et al., 1994; Stanghellini, 1987;

Zolnier et al., 2001) to predict the effects of environmental conditions on surface

resistance, rs. These models predict surface resistance as a reference value multiplied by

a dimensionless function that accounts for the change in surface resistance caused by

changes in environmental conditions. Equation 4-4 gives an example of a Jarvis-type

model for surface resistance that accounts for the effects of solar radiation (PAR), air

vapor pressure deficit (VPDair), and carbon dioxide concentration (C02). Note that the

functions for environmental factors are not necessarily of the same mathematical form.

r = r f, (PAR)f2(VPD)f3(CO,) (4-4)

The reference resistance, rsref, is a physiological value and can be determined

from experimentation or from literature (Stanghellini, 1987). This model assumes that

there are no interactions among environmental variables. The nature of the functions for

environmental factors is best determined by regression analysis from controlled

environment data (Jarvis, 1976).

The simple, empirical model of equation 4-4 is often chosen over more complex,

mechanistic models for predicting surface resistance. Stomatal control is complicated

and likely involves signals from a number of sources throughout the plant. The level of









detail required for development and application of a mechanistic model of stomatal action

is often not feasible or necessary. Aubinet et al. (1991) found that when considering a

crop grown in protected culture, external resistances caused by leaf boundary layers were

typically much larger than the surface resistances. Their data suggest that stomatal

opening and closing has little effect on evapotranspiration rate compared to the external

resistance on a canopy scale.

Surface resistance, equations 4-5 and 4-6, was calculated from evapotranspiration

rates measured in the previously described experiments by inversion of a) the latent heat

loss equation (1-3) and b) the Penman-Monteith evapotranspiration model (equation 1-8).

Values of surface resistance estimated by these two equations were compared to

determine the applicability of the Penman-Monteith model for low-pressure conditions.

Inversion of equation 1-3 yielded the following equation for surface resistance.

ParCa VPDleaf

r, = L rh (4-5)
LE

where: pa = density of air, kg m-3

Cp = specific heat of air at constant pressure, J kg-1 oC-1

VPDeaf-air = leaf-to-air vapor pressure deficit, kPa

y = psychrometric constant, Pa C-1

LE = latent heat flux, W m-2

rh = canopy external resistance for sensible heat transfer, s m-1

Equation 4-6 was obtained by inversion of the Penman-Monteith model.

Pa= aVPDa.h lA(LE- R,)
yLE yLE









where: VPDair = air vapor pressure deficit, kPa

A = slope of saturation vapor pressure curve, Pa C-1

Rn = net radiation, W m-2

Equations 4-5and 4-6 required estimation of several heat fluxes and air properties.

Latent heat flux, LE, was estimated by equation 4-7. The latent heat of vaporization, X,

was assumed to be 2442 kJ kg-1 for an air temperature of 24 C. ET (g m-2 s-1) was the

measured evapotranspiration from the experiments described above.

LE = ET (4-7)

The procedure for estimating net radiation, Rn, was the same as used in Zolnier et

al. (2004). Net radiation, equation 4-8, was the sum of the effects of long- and short-

wave radiation. Incoming shortwave radiation, Rsw, was measured at canopy height

beneath the bell jar with and without shading material by an Eppley pyranometer (Model

PSP, The Eppley Laboratory, Inc, Newport, RI). The average incoming short-wave

radiation was 95 W m-2 without shading and 48 W m-2 with shading in place. Long wave

radiation was calculated by the Stefan-Boltzmann equation. The reflectance and

emissivity of the canopy was assumed to be 0.27 and 0.90 respectively (Zolnier et al.,

2004).

R, = (1- p)R. + o(T,4,, T-4) (4-8)

where: p = reflectivity, dimensionless

a = Stefan-Boltzmann constant, W m-2 K-4

E = emissivity, dimensionless

Tsur = average absolute temperature of surroundings, K

Ts = average absolute temperature of canopy, K









It was assumed that the bell jar was in equilibrium with the external chamber and

that Tsur could be well estimated by the chamber temperature of 24 C.

The canopy external resistance, rh, was calculated by equation 3-10 from values of

re predicted by the model described in chapter 3 for air velocity equal to 1.3 m s1. Leaf

area of each plant was measured on day 24 by a leaf area meter (LI-3000A, Licor

Biosciences, Lincoln, NE). A preliminary experiment was performed to determine the

change in leaf area from day 18 to day 24. There were no statistical differences between

total leaf area of radish plants on days 18, 20, 22, and 24 (a = 0.05). From this, it was

concluded that measuring leaf area each day during experimentation was not necessary.

Functional relationships for the effects of many environmental factors including

PAR, C02, VPD, and leaf temperature have been developed for a variety of crops. In this

research, data from short duration controlled environment experiments with mature

radish plants were used to determine the effect of pressure on rs. Effects of CO2 and

PAR were incorporated in rsref. Although it is recognized that there may be adaptations,

such as changes in stomatal density, that occur during long term exposure to different

environmental conditions, only the short term responses were considered in the scope of

this research.

Results and Discussion

Mean values of evapotranspiration, canopy external resistance (rh), and surface

resistance (rs) calculated by equation 4-5 are shown in Table 4-3. Values of surface

resistance estimations made by the Penman-Monteith model at the lowest pressures were

negative. Negative values of surface resistance are not physically possible and this

estimation error was attributed to the lower leaf temperatures that occurred at 12 kPa (see

chapter 6). Thus, the remaining results and conclusions are based on surface resistance









calculated by the latent heat equation. Reference conditions were at 101 kPa. The

effects CO2 and PAR on evapotranspiration and surface resistance were evaluated by

comparison to these reference conditions.

Evapotranspiration (ET) was negatively proportional to pressure (Figures 4-3 and

4-3). At reference levels of CO2 and PAR (40 Pa and 341 [tmol m-2 s-1) average ET

increased from 2.3 g m-2 min1 at 101 kPa to 3.3 g m-2 min1 at 12 kPa. The same trend in

ET as a function of pressure was observed in different levels of CO2 and PAR. In

elevated CO2 conditions (150 Pa) ET increased from 2.0 to 2.7 g m-2 min-1 between 101

and 12 kPa. Likewise, ET increased from 1.4 to 3.1 g m-2 min-1 in a low PAR

environment (161 [[mol m-2 s-1). Because the observed trend in evapotranspiration as a

function of pressure was similar to that of mass diffusivity (Figure 4-1), it is hypothesized

that increases in ET were direct results of increases in stomatal conductance at reduced

pressures. This agreed with the relationship given by Mott and Parkhurst (1991) for

stomatal conductance. Surface resistance (Table 4-3), calculated by equation 4-5,

decreased with pressure as predicted by equation 4-4. The lowest resistances were

observed at 12 and 33 kPa (Figure 4-5). ET was also influenced by decreases in external

resistance at low pressures (Chapter 3).

Elevated CO2 concentrations decreased ET (data shown in Table 4-3). When the

concentration of CO2 was increased from 40 to 150 Pa, ET decreased some, although not

significantly, at 33, 66, and 101 kPa (Figure 4-4). At 12 kPa, however, ET decreased

from 3.3 to 2.7 g m-2 min-1 which was statistically significant (a=0.05). This decrease in

ET at elevated CO2 corresponded to an increase in rs from at 12 kPa from 178.6 s m-1 to

228.3 m-1 (Figure 4-6). The mass diffusivity of water vapor, a function of pressure, was









the same for these two treatments. Therefore, the increase in rs in elevated CO2

conditions could only have been a physiological response. As in research by Assmann

(1999) and Wheeler et al. (1999), stomata closed when CO2 levels rose from 40 to 150 Pa

causing an increase in rs. The increase in rs was enough to protect the plants from the

severe water stress observed at 12 kPa and 40 Pa of CO2 (see photo in Figure 4-3). In

fact, there were no statistical differences between ET at 12 kPa and elevated CO2 (ET =

2.7 g m-2 min1) and 101 kPa and 40 Pa of CO2 (ET = 2.3 g m-2 min1). There was a slight

decrease in ET, although not significant at all pressures, when PAR was reduced from

341 to 161 tpmol m-2 s-1 (Table 4-3 and Figure 4-6). The decrease in incident radiant

energy reduced the energy available for water evaporation.

An empirical equation for surface resistance as a function of pressure was

determined by linear regression in Figure 4-7. This equation was developed for

incorporation in the surface resistance model of equation 4-4. This additional function

(equation 4-7) accounted for the effect of pressure on rs in the multiplicative model.

rs = rs01 (0.0066 P + 0.36) (4-7)

To estimate surface resistance, a reference value was multiplied by an empirical

linear function as in equation 4-7. The reference value, rsioi, was the surface resistance

determined at a particular set of environmental conditions. In this research, reference

values were taken as the average surface resistance at 101 kPa for a particular CO2and

PAR setpoint. No functions were developed to account for changes in CO2 and PAR.

463.9 (CO2= 40 Pa; PAR = 341 mrnol m-2 s-1), 518.7 (CO2 = 150 Pa; PAR = 341 [[mol m

2 S-1), and 446.4 s m1 (CO2 = 40 Pa; PAR = 161 [Lmol m-2 -1).









Table 4-3. Evapotranspiration and resistance results. Shown below are mean values (
standard deviation) of evapotranspiration, canopy external resistance (rh), and
surface resistance (r,) for three replications. Letter superscripts indicate
statistical differences among values in a column per pressure treatment and
symbolic superscripts indicate differences between pressures for each
treatment (a = 0.05).
Evapotranspiration rh rs
Treatment g-2 m ) ( ( 1
(g i mm ) (sm ) (s m )
12 kPa
CO2 40Pa
PAR 341 ol -2 -1 3.3 (0.1)A 15.0 (0.68) 178.6 (5.9)A
PAR = 341 |jmol m 2 s __
CO2 =150 Pa
R 341 tmol m2 S-1 2.7 (0.06)B* 19.5 (3.1) 228.3 (7.8)B
CO2 40Pa
PAR 161 mol m-2 3.1 (0.1)A* 16.3 (+5.5) 210.3 (24.5)B
33 kPa
CO2 = 40 Pa A
PAR 341 mol m-2 1 2.9 (+0.2)A 23.0 (+2.6) 293.9 (23.5)A
CO2 = 150 Pa
PAR = 341 tmol m- s- 2.8 (0.1)A 24.7 (+0.9) 296.2 (16.0)
CO2 =40 Pa B*
PAR= 161 tmol m2 -1 2.3 (+0.2)B 31.0 (8.8) 378.8 (+40.0)
66 kPa
CO2 = 40 Pa
P = 34 mol ms 2.4 (+0.2) 34.0 (+6.6) 369.8 (27.1)***
PAR = 341 Lmol m-2 S-1
CO2 = 150 Pa
PAR =341 mol m2 s1 2.0 (+0.3) 35.6 (+0.9) 477.6 (82.3)A
CO2 = 40 Pa**
PAR 161 tmol -2 -1 2.0 (+0.2)* 40.6 (+14.4) 436.8 (66.9)
PAR = 161 |jmol m 2 s __
101 kPa
CO2 = 40 Pa
PAR 341 tmol m-2 s 2.3 (0.3)A** 46.1 (10.6) 463.9 (+52.2)A***
CO2 = 150 Pa B **
PR = 31 m-2 s-1 2.0 (0.2)A** 49.4 (+9.5) 518.7 (68.3)A**
PAR =341 tmol m 2 S *( )
CO2 = 40 Pa B ***
PAR 161 mol m s 1.4 (0.4)B*** 62.6 (+11.2)B 664.1 (+84.0)B
PAR= 161 tmol m-2 S-1















































Figure 4-3. Visual observations of water status at 101 and 12 kPa. Photo A shows a
turgid radish plant at 101 kPa inside the bell jar system. Photo B shows a
radish plant 45 minutes after pressure was reduced to 12 kPa. The CO2
concentration for the plants in both photos is 40 Pa.































1.5 I i
0 20 40 60 80 100
Pressure, kPa

Figure 4-4. Effects of pressure and CO2 on evapotranspiration. Evapotranspiration rates
increased with decreasing pressure and CO2 concentration. PAR was 341
tmol m-2 s-1


60
Pressure, kPa


100 120


Figure 4-5. Effect of CO2 on surface resistance. At 12 kPa, surface resistance increased
somewhat when the CO2 concentration was increased from 40 to 150 Pa.
PAR was 341 [jmol m-2 S-1


*
*
*
S40 Pa
*150Pa 0
*

*
|6
I*
*1


0
a

3















E


) 3.25

0

E. 2.5
IA


CL
S1.75


341 pmols m-2 s-1
161 tmols m-2 s-1











0 20 40 60 80 100
Pressure, kPa


Figure 4-6. Effects of pressure and PAR on evapotranspiration. Evapotranspiration rates
increased with decreasing pressure. There were no statistical differences
between light levels at the lowest pressure treatment. CO2 was 40 Pa.


Pressure, kPa

Figure 4-7. Actual and predicted values of surface resistance at 40 Pa and 341 [[mol m-2 s
1


r= rs101(0.0066*P + 0.36)
R2 = 0.91









The root mean square error (RMSE) of the model, calculated by equation 4-8, is

shown in Table 4-4 for different environmental conditions.


C 1 --^ --
RMSE= 7 (y, )2 (4-7)


where: N = number of predictions

y = ith actual value

= ith predicted value


Table 4-4. Root mean square error of surface resistance model.
RMSE
Environmental conditions m1
(sm )
C02= 150 Pa
92.7
PAR = 341 [tmol m-2 s-1
C02 = 40 Pa
77.3
PAR = 161 t[mol m-2 s-l


Conclusions

Surface resistance is the resistance of the leaf surface to water vapor loss. It

accounts for the effects of stomata and the leaf cuticle. Since cuticle resistance is

constant, changes in surface resistance can be used to understand stomatal control in

response to environmental conditions. Surface resistance for mature radish plants,

calculated from measured values of evapotranspiration, increased significantly with

increasing pressure while evapotranspiration decreased. An empirical model developed

to predict rs as a function of pressure and a reference value determined at standard

pressure performed well. There was also a significant effect of CO2 on stomata. Surface

resistance increased and ET decreased when CO2 rose from 40 to 150 Pa for all pressure

treatments. Decreasing PAR from 340 to 160 [tmol m-2 s-1 had little effect on rs or ET.














CHAPTER 5
EVAPOTRANSPIRATION MODEL PERFORMANCE IN
MARS GREENHOUSE CONDITIONS

The evapotranspiration models described in Chapter 1 provides a way to calculate

the water loss rate of a crop of plants. It accounts for the physical environment as well as

physiological control of plant stomata to limit water loss. Because water stress is

anticipated to be a limiting factor in growing plants in a low pressure Mars greenhouse,

understanding the effects of environmental parameters on evapotranspiration rate is

important in designing the structure and control system.

Thorough analysis of a mathematical model provides a great deal of information.

The sensitivity of the prediction to each parameter identifies the parameters with the most

influence. To reduce water stress of plants in a Mars greenhouse, more attention should

be focused on those parameters that have the strongest affect on the rate of water loss.

Design decisions regarding parameters with little influence on ET can be based solely on

other factors besides plant water stress.

Error analysis quantifies the performance of the model. One method to quality

error is to calculate the anticipated error of the prediction resulting from error in the

estimation or measurement of parameters. Another method of error analysis is validation

of the prediction in comparison with actual data. Strong correlation of the model with

actual data establishes confidence in the model predictions.









Objectives

The objective of this chapter is to evaluate the performance of the Penman-

Monteith model including the resistance models of Chapters 3 and 4 to predict

evapotranspiration rate of radish plants in Mars greenhouse conditions.

Materials and Methods

The sensitivity of evapotranspiration rate predictions to pressure, air velocity,

surface resistance, temperature of surroundings, and incident radiation was determined by

varying one parameter at a time with remaining parameters held constant. The

parameters evaluated and their reference values are listed in Table 5-1.

Evapotranspiration rate was calculated by equation 1-3 for air velocity, surface

resistance, and incident radiation varied by -90, -50, +50, and +100% of the reference

value. Pressure was varied -90, -25, -50, and -75% and VPDieaf-air -90, -50, +50 % from

their reference values. The percent change in evapotranspiration was calculated by

equation 5-1 for each parameter perturbation.

ET- ETo
% change = E (5-1)
ET

where ET = evapotranspiration rate with one parameter varied, g m-2 s-1

ET = evapotranspiration calculated at reference parameters, g m-2 s-1

Table 5-1. Parameter descriptions and reference values.
Parameter Description Reference value
P Atmospheric pressure 101 kPa
u. Air velocity 1.3 m s1
rs Surface resistance 464 s m-1
VPDieaf-air Leaf-to-air vapor pressure deficit 2.65 kPa


The error of the evapotranspiration model was evaluated in two ways. First, the

propagation of error from environmental measurements to predicted evapotranspiration









was calculated by equation 5-2 (Dally et al., 1993). Errors associated with measurement

of pressure, air velocity, incident radiation, temperature of surroundings and estimation of

surface resistance were included in the calculation of evapotranspiration error.


E (ET (ET )2 ET d
dET = p + P2 +---+\ dp, (5-2)


SET
where =change in ET per unit change in parameter pi
ap,

dpi = error in estimation of pi

The unit change in ET per unit of each parameter was determined by sensitivity analysis.

The errors associated with P, uo, and VPDleaf-air were estimated as typical errors for that

particular type of sensor. Surface resistance error was estimated as the standard error of

the regression model in Chapter 4.

The second method for evaluating the error of the evapotranspiration model was by

validation using independent data. Two sets of the evapotranspiration experiments

described in Chapter 4 were performed with three replications each. One set was used to

develop the surface resistance model and the other was for validation of the

evapotranspiration model. The model was validated by computing the RMSE of the

model compared to the actual data for different environmental conditions.

Results and Discussion

Evapotranspiration rate was predicted as a function of atmospheric pressure above

10 kPa in Figure 5-1 for the reference conditions. The model predicted a gradual increase

in ET as pressure dropped from 101 to approximately 35 kPa and a more significant

increase in ET at pressures below 35 kPa. The actual data shown in Figure 5-1 were also

used to develop surface resistance model in Chapter 4.







81


4.0

Model
3.5 Measured

E
0 3.0


2.5



S2.5
"W 2.0



1.5
0 20 40 60 80 100
Pressure, kPa


Figure 5-1. Predicted and measured evapotranspiration rate as a function of pressure.




Sensitivity Analysis

The change in evapotranspiration rate for the parameters in Table 5-1 varied one at

a time is given in Table 5-2. Predicted ET and the percent change from the ET at

reference conditions calculated by equation 5-1 are shown. Predicted ET when all

parameters were at reference values was 2.22 g m-2 min1

Air velocity was negatively proportional to the external resistance to sensible heat

transfer. Increasing air velocity decreased the resistance to heat transfer. When air

velocity was increased by 50%, ET increased to 2.26 g m2 min 1.8% of the reference

ET. Surface resistance was also negatively proportional to ET. With pressure held

constant, increasing the surface resistance by 50% from 464 to 696 s m-1 decreased ET by

31%. Conversely, decreasing rs by 90% increased ET four-fold. At constant pressure,









changes in surface resistance were caused by other environmental parameters such as

CO2 concentration and PAR availability (see chapter 4).

Table 5-2. Sensitivity analysis of the evapotranspiration model for Mars greenhouse
conditions. Given are the evapotranspiration rate and percent change from
reference conditions when only one parameter is varied. The
evapotranspiration rate at the reference conditions was 2.47 g m-2 min-1
Parameter ET g m-2 min-1 % change
Pressure
10.1 kPa 3.02 36
50 kPa 2.60 17
Air velocity
0.13 m s (rh = 146.2 s m-) 1.87 -16
0.65 m s (rh = 66.8 s m-) 2.14 -4
1.95 m s1(rh = 38.6 s m) 2.26 1.8
2.60 m s (rh = 33.4 s m-) 2.28 2.7
Surface resistance
46.4 s m1 12.23 451
232 s m-1 4.07 83
696 s m1 1.53 -31
928 s m1 1.16 -47.7
VPleaf-air
0.27 kPa 0.23 -90
1.3 kPa 1.09 -51
4.0 kPa 4.00 81


Error Analysis

The expected error in predicted evapotranspiration rate caused by error in

parameter estimation was calculated by equation 5-2. Table 5-3 lists the change in ET

per unit change in each parameter and error for estimation of each parameter. Error in

the estimation of pressure, air velocity, incident radiation, and surrounding temperature

are typical errors for sensors for that particular parameter. The estimation error for

surface resistance is the RMSE error of the model in Chapter 4 for reference conditions.

The expected error in prediction of evapotranspiration rate was 0.36 g m-2 min1







83


Table 5-3. Change in evapotranspiration rate and estimated error of parameters for
overall error calculation.
Parameter aET/ppi dpi
Pressure, kPa -0.009 0.5 kPa
.1 0.46 (< 2.5 m s-1) .1
Air velocity, m s1 0.46 ( 2.5 m 0.1 m
0.172 (> 2.5 m s1)
Surface resistance, s m-1 -0.011 35 s m-1
VPDleaf-air 0.84 0.1 kPa



Performance of the evapotranspiration model was validated by comparison to

independent data. Equation 4-7 was used to calculate the root mean square error of the

model at 12, 33, 66, and 101 kPa. The model was validated (Figures 5-2, 5-3, and 5-4)

for the reference conditions (CO2 = 40 Pa; PAR = 340 [tmol m-2 s-1), elevated CO2 (CO2

= 150 Pa; PAR = 340 mrnol m-2 s-1); and reduced PAR (CO2 = 40 Pa; PAR = 160 [tmol m

2 S-1). The RMSE error was 0.2 g m-2 min' in reference conditions, 0.4 g m-2 min' in


elevated CO2, and 0.3 g m-2 min' in reduced PAR.


4
7 3.8
E 3.6

E 3.4
c 3.2
.o *
2 3
Q.
S2.8 *
0
5 2.6
> 2.4
2.2

0 20 40 60 80 100 120
Pressure, kPa

Figure 5-2. Model performance at reference conditions. Carbon dioxide concentration
was 40 Pa and PAR was 340 [[mol m-2 S-1


































0 20 40 60
Pressure, kPa


80 100 120


Figure 5-3. Model performance in elevated CO2. Carbon dioxide concentration was 150
Pa and PAR was 340 [tmol m-2 S-1



4

S 3.8

E 3.6


(N
E 3.4

c 3.2
0
> 3

C 2.8

o 2.6
0.
> 2.4
W


* N
S


0 20 40 60 80 100 120
Pressure (kPa)


Figure 5-4. Model performance in low PAR conditions. Carbon dioxide concentration
was 40 Pa and PAR was 160 [mol m-2 S-1


r 2.5


cn

0
0 2

1.
> 1.5
W






85


Conclusions

The evapotranspiration model incorporating the external and surface resistance

models developed in this research performed well to predict evapotranspiration rate of

mature radish plants in Mars greenhouse conditions. The value of the predicted

evapotranspiration was close to the independent evapotranspiration rate measurements.

The root mean square error of the model compared to independent data was less than 0.5

g m-2 min-1 for all conditions tested.














CHAPTER 6
LEAF TEMPERATURE IN A MARS GREENHOUSE

Leaf temperature is an important component of the leaf energy balance. Leaf

temperature influences the rate of the evapotranspiration, convection and radiation heat

fluxes. High rates of evapotranspiration at low pressures and the extremely cold

environment in a Mars greenhouse may cause leaf temperatures below typical values on

Earth. This chapter examines the impacts of reduced pressures on leaf temperature and

how this affects evapotranspiration.

Literature Review

The temperature of a leaf is determined by the leaf heat balance (equation 1-1). If

the rate of heat gain is greater than the rate of heat loss leaf temperature will rise.

Conversely, if the rate of heat loss exceeds heat gains, the leaf temperature will decrease.

The primary modes of heat transfer for a crop canopy are radiation, convection, and latent

heat loss by evapotranspiration.

The vapor pressure deficit between the crop canopy and ambient air (VPDcrop-air) is

the driving force for evapotranspiration (Zolnier et al., 2000). Accurate calculation of the

VPDcrop-air requires that the temperature of the leaf is known to calculate the vapor

pressure of the saturated surface of the leaf. A simplification in the derivation of the

Penman-Monteith model described in chapter 1 assumes that the leaf temperature is

approximately equal to the air temperature. This simplification introduces a new

variable, A, which is the slope of the saturation vapor pressure curve (see Figure 1-2).

The slope is evaluated at the air temperature and is assumed to provide a good