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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. HyeonHye 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 SMALLSCALE PRESSURECONTROLLED 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 (SNAPAIV4).........................................................113 Voltage Input M odule (SNAPAITM 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 21 Descriptions and applications of Opto 22 I/O modules used in this research ..........20 22 Calibrated sensor accuracies .............................................................................. 21 23 Performance of pressure control algorithm.................................................26 24 Bell jar leakage rates .......... .. .... ......................... ................ ........ .... 27 25 Performance of CO2 control algorithm at 12 kPa with plants.............................29 26 Performance of the air temperature and relative humidity control algorithm at 12 kPa w ith plants .................. .... ... ................... ......... ............ .. 31 41 Controlled environment chamber conditions ................................. ............... 65 42 Evapotranspiration treatment structure. ...................................... ............... 67 43 Evapotranspiration and resistance results ..................................... .................73 44 Root mean square error of surface resistance model.....................................77 51 Parameter descriptions and reference values. .................................. .................79 52. Sensitivity analysis of the evapotranspiration model for Mars greenhouse c o n d itio n s ......................................................................... 8 2 53 Change in evapotranspiration rate and estimated error of parameters for overall error calcu lation ............................. .................................................. ............... 83 61 Comparison of temperature sensors for leaf temperature measurement ................89 62 Effects of pressure on evapotranspiration rate and leaf temperature ....................91 63 Leaf temperature model results for 12 and 101 kPa .................. ...... .............94 Ai Slope and intercept equations for carbon dioxide sensors. ............. ................111 A2 Slope equations for the oxygen sensors. ............................ ..... ...........112 LIST OF FIGURES Figure pge 11 Artist's conception of a future M ars colony.................................... ...... ............. ... 1 12 Leaf to air vapor pressure deficit approximation .................................. .............. .7 21 Schematic of pressure controlled plant chambers. ................................................ 15 22 Pressure controlled plant chambers..... .. .............................. ......... ................... 15 23 Schematic of one pressure controlled plant chamber ................ ....... ...........16 24 Picture of one of the three pressure controlled plant chambers ........................... 17 25 L eight level control ...................... .................... ... .... ........ ......... 25 26 CO2 control without plants at standard pressure. .............................................. 27 27 Effect of vacuum pump on CO2 control at low pressures................. ........... 28 28 CO2 control with plants at 12 kPa ............................ ... ............... 29 29 Air temperature and relative humidity control at 12 kPa with plants. ...................31 31 Velocity boundary layer over a horizontal flat plate............................................. 34 32 Thermal boundary layer over a horizontal flat plate that is warmer than the surrounding air. .......................................................................35 33 Thermal boundary layer over a horizontal flat plate that is cooler than the su rrou n d in g air ..................................................... ................ 3 5 34 L eaf replica .................................................................. ...........................40 35 Convection heat transfer experimental setup ................................. ............... 41 36 Temperature profile for leaf replica during heating and subsequent cooling phase at 101 kPa and an air velocity of 5.8 m s ....................... ...................42 37 Transformed cooling data for the leaf replica at 101 kPa and an air velocity of 5 .8 m s ..................................................................................4 5 38 Surface temperature of leaf replica during heating and subsequent cooling phase for four air velocity treatm ents at 12 kPa. ...................................... ..................47 39 Transformed surface temperature data for leaf replica at 12 kPa. .........................47 310 Surface temperature of leaf replica during heating and subsequent cooling phase at 33 kP a. .............................................................................4 8 311 Transformed surface temperature data for leaf replica at 33 kPa. .........................48 312 Surface temperature of leaf replica during heating and subsequent cooling phase at 66 kP a. .............................................................................49 313 Transformed surface temperature data for leaf replica at 66 kPa. .........................49 314 Surface temperature of leaf replica during heating and subsequent cooling phase at 10 1 kP a. ............................................................................50 315 Transformed surface temperature data for leaf replica at 101 kPa ........................50 316 Measured and predicted values for external resistance of leaf replica as a function of pressure and four levels of air velocity...............................................52 317 Rate of heat transfer from leaf replica as a function of pressure and air velocity ....52 318 External resistance model performance ....................................... ............... 53 319 External resistance m odel error ........................................ ........... ............... 54 320 Effect of atmospheric pressure on boundary layer thickness of a horizontal flat p late ................................................................................5 5 321. Effect of air velocity on boundary layer thickness of a horizontal flat plate............55 41 The effect of pressure on mass diffusivity of water in air................... ............61 42 Leaf temperature transient response to changes in total pressure............................66 43 Visual observations of water status at 101 and 12 kPa........................................74 44 Effects of pressure and CO2 on evapotranspiration ............. ..... ............... 75 45 Effect of CO2 on surface resistance...................................... ........................ 75 46 Effects of pressure and PAR on evapotranspiration ................. ..... .............76 47 Actual and predicted values of surface resistance at 40 Pa and 341 [[mol m2 s1. ..76 51 Predicted and measured evapotranspiration rate as a function of pressure .............81 52 Model performance at reference conditions...................................... ..............83 53 M odel performance in elevated CO2 ............................ .................................... 84 54 Model performance in low PAR conditions...................................... ...................84 61 Leaf temperature measurement at 25 kPa .......................................................90 62 Effect of pressure on leaftoair temperature difference ................................. 91 63 Effect of evapotranspiration rate on leaftoair temperature difference .................92 64 Effects of net radiation on leaftoair 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 C1 Top view of bell jar base ...................................................... ............ 118 C2 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 lifesupport systems as sources of food, oxygen, and waste treatment. Constraints of building a structure on the Martian surface to withstand Earthsimilar 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 lifesupport 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 smallscale 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 longterm 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 11. Artist's conception of a future Mars colony. The settlement includes an inflated greenhouse for food and production, oxygen production, and waste treatment. LowPressure, 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 onehundredth 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 Earthsimilar 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 onethird 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 PenmanMonteith 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 PenmanMonteith evapotranspiration model begins with a steady state energy balance of the plant canopy (equation 11). R HLE = (11) where: Rn = net radiation, W m2 H = sensible heat flux, W m2 LE = latent heat flux, W m2 Sensible heat flux, H, is estimated by equation 12. H Pacp(Tea Tar) (12) rh 3 where: pa = density of air, kg m3 Cp = specific heat of air at constant pressure, J kg1 oC1 Tieaf = leaf temperature, C Tair = air temperature, C rh = external resistance for sensible heat transfer by convection, s m1 Equation 13 gives the estimation for the latent heat flux, LE. LE = cVPDeafa (13) y( rh) where: VPDieafair = leaf to air vapor pressure deficit, kPa VPDleaf air =(eleaf e ) (14) esleaf = saturation vapor pressure at leaf temperature, kPa ea = vapor pressure, kPa y = psychrometric constant, Pa C1 Pc Y=O (15) 0.622k S= latent heat of vaporization, kJ kg1 P = pressure, Pa rs = surface resistance of canopy to water vapor transfer, s m1 Calculation of the sensible and latent heat fluxes of equations 12 and 13 requires surface temperature, a variable that is typically unknown. Penman (1948) incorporated a simplifying assumption to eliminate leaf temperature from the model. Equation 16 shows an approximation for VPDieafair 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 ) (16) An example is shown in Figure 12. 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 17. 7.5T e (T) = 0.61078 10 237.3+T (17) where: es(T) = saturation vapor pressure at temperature T, kPa T = temperature, C In Figure 12 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 VPDieafair and the estimation from equation 16 is only 0.08 kPa. 5 4.5 slope = A =0.18 S4 3.5 3 3 2. A Ta,,r Tlearf)= 0.18*(2420) =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 12. Leaf to air vapor pressure deficit approximation. To eliminate leaf surface temperature from the evapotranspiration model, Penman (1948) introduced an approximation for VPDieafair. 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 16 into 13 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 13. Substitution into the heat balance of equation 11 and rearranging gives a standard from of the PenmanMonteith equation (Monteith, 1965) that does not require knowledge of leaf temperature. E R, + p, c,, VPD ,, lr LE = (18) A+y(1r /rh) The PenmanMonteith 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 shortterm 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 shortduration 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 smallscale 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 SMALLSCALE PRESSURECONTROLLED 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 smallscale pressurecontrolled 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 lowpressure 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 lowpressure 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 smallscale 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 lowpressure 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 offtheshelf 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 orings and installed tightly to minimize leakage. To minimize costs, wire feedthroughs were constructed inhouse. Art clay was packed into the center of 1.905cm 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 typeT and one typeK thermocouples were made for each bell jar. I I I Vacuum PC based data acquisition Pump and control system Figure 21. Schematic of pressure controlled plant chambers. Experimental replication was achieved using three independently controlled bell jars. Figure 22. Pressure controlled plant chambers. The small chambers were placed inside a larger plant growth chamber for highquality external lighting. C02 and vacuum Figure 23. Schematic of one pressure controlled plant chamber. 17 o lilki  WEE ~i'"" Figure 24. 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 steadystate heat transfer rate required to condense water was calculated by equation 1. q = (ihH2 )(h ) (21) where: q = heat transfer by condensation, W m = mass rate of water condensed, kg s1 hfg = latent heat of vaporization, kJ kg1 At 10 kPa, the latent heat of vaporization is 2389 kJ kg1. 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 ) (22) where: q = rate of heat transfer, W h = convective heat transfer coefficient, W m2 K1 Acoil = coil surface area, m2 Tair = air temperature, K Tcoil = coil surface temperature, K h = 0.729 gp! (, )khsD (23) N (T(a, T,)D D where: h = convective heat transfer coefficient, W m2 K1 2 g = acceleration due to gravity, m s2 pi = density of liquid, kg m3 pv = density of vapor, kg m3 ki = thermal conductivity of liquid, W m1 K1 hfg = latent heat of vaporization, kJ kg1 N = number of horizontal tubes ti = viscosity of liquid, kg s1 m1 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 m3; pi = 0.997 kg m3; ki = 0.606 W m1 K1; 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 m2 K1 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 = (24) 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 PCbased 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 21. Descriptions and applications of Opto 22 I/O modules used in this research. Opto 22 module description Quantity Application Vacuum pump, solenoid SNAPOAC5, 412250 VAC input 1a m valve SNAPAOV25, 0 to +10 VDC analog output 1 Mass flow controller Solenoid valves, heaters, SNAPODC5SNK, 560 VDC output, sink 4 id, humidifiers, and fans SNAPAITM, mV or thermocouple input 2 Infrared thermocouples Oxygen sensors, typeT SNAPAITM2, mV or thermocouple input 5 thermocoules thermocouples Pressure, CO2, and SNAPAIV4, 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 typeT 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 (HIH3610003, Honeywell, Freeport, IL). The oxygen concentration was measured using a galvanic cell type oxygen sensor (MAX250, Maxtec, Salt Lake City, UT). A lowcost OEM ultrasonic sensor was used to measure carbon dioxide (6004 CO2 module, Telaire, Goleta, CA). Leaf temperature was measured with infrared thermocouples (OS36SMK140F, Omega, Stamford, CT). Load cells were used for measuring plant weight (LPS2kg, Celtron Technologies, Inc., Colvina, CA). Table 22. Calibrated sensor accuracies. All sensors were calibrated within one year of the start of experiments. Parameter Sensor description Accuracy Air temperature TypeT 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 (25) where P = power, W I = current, A V = voltage, V Each bell jar had two manually controlled fans (BM511504WB50LOO, NMB Technologies, Chatsworth, CA) to maintain air circulation. The specified air flow rate at standard pressure was 1.42 L s1 (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* (26) 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 (FMA3202C02, 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 threeway 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 m2 s1 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 m2 s1. 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 m2 s1 Figure 25. Light level control. Fine mesh screening material was used to reduce the PAR level inside the bell jars from an average of 341 pmol m2 s1 to 161 Lpmol m2 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 23. Since leakage increases at low pressure, data for a setpoint of 12 kPa are given as a worst case situation. Table 23. Performance of pressure 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 control algorithm was turned off. Pressure data were again recorded every minute for a onehour 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 24. 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 26 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 26. 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 27 shows the CO2 concentration and pressure for a onehour 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 27. 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 28 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 27 are given in Table 25. 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 28. 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 25. Performance of CO2 control algorithm at 12 kPa with plants. Descriptive statistics are given for data recorded at oneminute 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 29 shows the air temperature and relative humidity for the 50minute 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 26, which gives descriptive statistics for air temperature and relative humidity, the maximum standard deviation over the 50minute 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 cTair(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 29. 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 26. 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 50minute 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 smallscale 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 50W 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 12) 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 31 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 31. 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 32 and 33 show the thermal boundary layer over a horizontal flat plate with a surface temperature warmer (Figure 32) and cooler (Figure 33) 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 32. 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 33. 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, nondimensional 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 (31) v where: u, = free stream air velocity, m s1 L = characteristic length, m v = kinematic viscosity, m2 s1 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 32. Pr = (32) where: a = thermal diffusivity, m2 s1 Grashof number, ratio of buoyancy to viscous forces, is calculated by equation 33. Gr = gO3 )L (33) 2 where: g = gravitational constant, m s2 3 = 1/Ta =coefficient of thermal expansion, K1 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 s1 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 s1 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 (34) 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 (35) Equation 35 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 36 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 (36) In free convection conditions equation 37 for characteristic length, L, suggested by Incropera and DeWitt (1996) was applied to improve model accuracy. L (37) P Stanghellini (1987) developed equation 38 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 (38) From the Nusselt number, the external resistance to sensible heat transfer for a single leaf can be calculated by equation 39. L re (39) 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 310. This equation assumes that all leaves contribute equally to sensible heat transfer. rh r (310) 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 311 (Incropera and DeWitt, 1996). 5L 5L (311) 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 (312) 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 rectangularshaped replica (Figure 34) was made by wrapping a 12.7 cm x 2.54 cm (5 in x 1 in) flexible 10W Kapton heater (model BKL3005, Birk Manufacturing, Inc., East Lyme, CT) with standard grade aluminum foil (thickness = 0.16 mm). A small typeT 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 34. 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 (BM511504WB50LOO, NMB Technologies, Chatsworth, CA) was positioned about 2.5 cm in front of the leading edge of the heated sheet as shown in Figure 35. 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 35. 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 sl). 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 typeK thermocouple located about 5 cm above the sheet. Figure 36 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 36. 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 313. C =H + R, (313) where: C = rate of change of heat content of foil sheet, W m2 H = rate of sensible heat transfer, W m2 R = rate of radiation heat transfer, W m2 The rate of change in the heat content of the foil sheet is given by equation 314. dT, d(Ts T, C = ,cL d = p,cL d( (314) where: ps = density of leaf replica sheet, kg m3 cps= specific heat of leaf replica sheet, kJ kg1 K1 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 12. 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 315. Variables in bold denote absolute temperature. R, = o(T, T,,) (315) where: a = StefanBoltzmann constant = 5.670 x 10 W m2 K4 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 314 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) (316) where: hr = radiation heat transfer coefficient, W m2 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 (317) (T T) (T T) ((T, )T and simplifying h, = cy(T, + T )(T2 + Tf2) (318) 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 (319) T e=T S m (320) Combining equations 318, 319, and 320 and simplifying, hr 2Tm2T T _T )2 h, = os2T, 2T,2 + 2 (321) Assuming that the difference between the surface and air temperatures, TsTa, 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 322. hr = co4T3 Substituting equations 12, 314, 316, 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 325. d(T, T) P +ac h dt repScL p ps (322) 322 into the heat balance of equation 3 Ta) hr(T Ta) h L (T)T, pcsL T (T)T) (323) (324) (325) The solution to the differential equation 325 was 326. (T~ T a (T T = pa pr (, 1tl) (326) rePcpL p, c L_ Equation 326 was related to the cooling curves (as in Figure 36) to solve for the external resistance. Figure 37 shows a plot of the natural logarithm of TsTa of the same data as Figure 36 for time equal 50 to 110 seconds. Equating the slope, m, of a linear regression line through this data with equation 326 and rearranging gave equation 327 for external resistance, re. r = pa (327) 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 37. Transformed cooling data for the leaf replica at 101 kPa and an air velocity of 5.8 m s1. The slope of a linear regression line was related to Equation 326 to determine the external resistance to sensible heat transfer. The slope of the linear regression line for the transformed data of Figures 36 and 37 was 0.0617. This value and the following properties for air and the sheet were applied to Equation 327 to calculate the external resistance: pa=1.16 kJ kg1 K1; cpa=1.007 kJ kg1 K1; ps=1800 kJ kg1 K1; cps=0.98 kJ kg1 K1; 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 322 was 0.393 W m2 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 38, 310, 312, and 314 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 39, 311, 313, and 315 show the natural logarithm of TsTa during cooling. The slopes from linear regression analysis for each curve were used to determine the external resistance, re, in equation 327. 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 38. 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 39. 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 310. 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 311. 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 312. 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 313. 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 314. 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 315. 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 39. Figure 316 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 12 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 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 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 316. 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 317. 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 318 and 319 show two tests for model performance. In Figure 318 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 319. 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 m1 Figure 318. 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 S5.0 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 319. 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 320 and 321 show the effects of pressure and air velocity, respectively, on boundary layer thickness (equation 311). In Figure 320 the velocity boundary layer thickness was plotted as a function of pressure for an air velocity of 1.0 m s1. 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 321. At air velocities of 1.0 m s1 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 320. 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 321. 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 s1) tested. The average error between the predicted and empirical resistances was 2.6 s m1. 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 s1. 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 PenmanMonteith model (equation 18). 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 superelevated 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 shortterm 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 significant effect of longterm 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 m2 (400700 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 m2 s1 (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 41 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 (41) where Dw = mass diffusivity of water at pressure P, m2 s1 P0 = standard pressure= 101.3 kPa Do = mass diffusivity of water at standard pressure = 2.50 x 105 m2 s1 A plot of mass diffusivity as a function of pressure, calculated by equation 41, is shown in Figure 41. 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). 3.0E04 E 2.5E04 .E 2.0E04 . 1.5E04 0 'i 1.0E04 S5.0E05 O.OE+00 0 20 40 60 80 100 Pressure, kPa Figure 41. 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 42 to calculate stomatal conductance, the inverse of stomatal resistance. D 1 g, (42) Sr where gs = surface conductance, mm s1 D = mass diffusivity, mm2 s1 /= effective path length for diffusion through stomatal pore, mm rs = surface resistance, s mm1 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 42 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 43). The corresponding change in stomatal resistance would be a decrease by a factor of 10. D10 g 3 2.53x104 (43) Di101.3 2.5x10 5 where: gslo = stomatal conductance at 10 kPa, m s1 gso01.3 = stomatal conductance at 101 kPa, m s1 Dio = mass diffusivity of water at 10 kPa, m2 s1 D101.3 = mass diffusivity of water at 101.3 kPa, m2 s1 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 m2) had 30 stomata mm1 on the upper surface of the leaf compared to less than one stomata mm1 for those grown in low light (20 W m2). 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 0.21.6 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 shortterm exposure to different levels of pressure, CO2 concentration, and PAR inside the smallscale pressure controlled chambers described in chapter 2. Each of the three bell jarbased 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 18to24dayold radish plants (Raphanus sativa L. 'Cherry Bomb II') were available for each threehour measurement period. Seeds were pretreated for 1520 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 smallscale pressure controlled chambers. The chamber environmental conditions are given in Table 41. 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 18to24dayold 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 41. 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 m2 s1 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 wellwatered 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 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 steadystate. Leaf temperature was measured with an infrared thermocouple while plants were subjected to 12 kPa for three hours (see Figure 42). Plants reached steadystate, 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 ) >Steadystate 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 42. Leaf temperature transient response to changes in total pressure. Radish plants subjected to 12 kPa reached steadystate within one hour of initial pressure drop. Experimental Design Experiments were completely randomized with a 4x2x2 factorial treatment structure. Table 42 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 threehour measurement period was considered a replication. Table 42. 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 m2 s1 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 44 gives an example of a Jarvistype 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,) (44) 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 44 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 45 and 46, was calculated from evapotranspiration rates measured in the previously described experiments by inversion of a) the latent heat loss equation (13) and b) the PenmanMonteith evapotranspiration model (equation 18). Values of surface resistance estimated by these two equations were compared to determine the applicability of the PenmanMonteith model for lowpressure conditions. Inversion of equation 13 yielded the following equation for surface resistance. ParCa VPDleaf r, = L rh (45) LE where: pa = density of air, kg m3 Cp = specific heat of air at constant pressure, J kg1 oC1 VPDeafair = leaftoair vapor pressure deficit, kPa y = psychrometric constant, Pa C1 LE = latent heat flux, W m2 rh = canopy external resistance for sensible heat transfer, s m1 Equation 46 was obtained by inversion of the PenmanMonteith model. Pa= aVPDa.h lA(LE R,) yLE yLE where: VPDair = air vapor pressure deficit, kPa A = slope of saturation vapor pressure curve, Pa C1 Rn = net radiation, W m2 Equations 45and 46 required estimation of several heat fluxes and air properties. Latent heat flux, LE, was estimated by equation 47. The latent heat of vaporization, X, was assumed to be 2442 kJ kg1 for an air temperature of 24 C. ET (g m2 s1) was the measured evapotranspiration from the experiments described above. LE = ET (47) The procedure for estimating net radiation, Rn, was the same as used in Zolnier et al. (2004). Net radiation, equation 48, 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 shortwave radiation was 95 W m2 without shading and 48 W m2 with shading in place. Long wave radiation was calculated by the StefanBoltzmann 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,, T4) (48) where: p = reflectivity, dimensionless a = StefanBoltzmann constant, W m2 K4 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 310 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 (LI3000A, 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 45 are shown in Table 43. Values of surface resistance estimations made by the PenmanMonteith 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 43 and 43). At reference levels of CO2 and PAR (40 Pa and 341 [tmol m2 s1) average ET increased from 2.3 g m2 min1 at 101 kPa to 3.3 g m2 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 m2 min1 between 101 and 12 kPa. Likewise, ET increased from 1.4 to 3.1 g m2 min1 in a low PAR environment (161 [[mol m2 s1). Because the observed trend in evapotranspiration as a function of pressure was similar to that of mass diffusivity (Figure 41), 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 43), calculated by equation 45, decreased with pressure as predicted by equation 44. The lowest resistances were observed at 12 and 33 kPa (Figure 45). ET was also influenced by decreases in external resistance at low pressures (Chapter 3). Elevated CO2 concentrations decreased ET (data shown in Table 43). 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 44). At 12 kPa, however, ET decreased from 3.3 to 2.7 g m2 min1 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 m1 to 228.3 m1 (Figure 46). 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 43). In fact, there were no statistical differences between ET at 12 kPa and elevated CO2 (ET = 2.7 g m2 min1) and 101 kPa and 40 Pa of CO2 (ET = 2.3 g m2 min1). There was a slight decrease in ET, although not significant at all pressures, when PAR was reduced from 341 to 161 tpmol m2 s1 (Table 43 and Figure 46). 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 47. This equation was developed for incorporation in the surface resistance model of equation 44. This additional function (equation 47) accounted for the effect of pressure on rs in the multiplicative model. rs = rs01 (0.0066 P + 0.36) (47) To estimate surface resistance, a reference value was multiplied by an empirical linear function as in equation 47. 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 m2 s1), 518.7 (CO2 = 150 Pa; PAR = 341 [[mol m 2 S1), and 446.4 s m1 (CO2 = 40 Pa; PAR = 161 [Lmol m2 1). Table 43. 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 g2 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 S1 2.7 (0.06)B* 19.5 (3.1) 228.3 (7.8)B CO2 40Pa PAR 161 mol m2 3.1 (0.1)A* 16.3 (+5.5) 210.3 (24.5)B 33 kPa CO2 = 40 Pa A PAR 341 mol m2 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 m2 S1 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 m2 s 2.3 (0.3)A** 46.1 (10.6) 463.9 (+52.2)A*** CO2 = 150 Pa B ** PR = 31 m2 s1 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 m2 S1 Figure 43. 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 44. Effects of pressure and CO2 on evapotranspiration. Evapotranspiration rates increased with decreasing pressure and CO2 concentration. PAR was 341 tmol m2 s1 60 Pressure, kPa 100 120 Figure 45. 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 m2 S1 * * * S40 Pa *150Pa 0 * * 6 I* *1 0 a 3 E ) 3.25 0 E. 2.5 IA CL S1.75 341 pmols m2 s1 161 tmols m2 s1 0 20 40 60 80 100 Pressure, kPa Figure 46. 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 47. Actual and predicted values of surface resistance at 40 Pa and 341 [[mol m2 s 1 r= rs101(0.0066*P + 0.36) R2 = 0.91 The root mean square error (RMSE) of the model, calculated by equation 48, is shown in Table 44 for different environmental conditions. C 1 ^  RMSE= 7 (y, )2 (47) where: N = number of predictions y = ith actual value = ith predicted value Table 44. Root mean square error of surface resistance model. RMSE Environmental conditions m1 (sm ) C02= 150 Pa 92.7 PAR = 341 [tmol m2 s1 C02 = 40 Pa 77.3 PAR = 161 t[mol m2 sl 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 m2 s1 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 51. Evapotranspiration rate was calculated by equation 13 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 VPDieafair 90, 50, +50 % from their reference values. The percent change in evapotranspiration was calculated by equation 51 for each parameter perturbation. ET ETo % change = E (51) ET where ET = evapotranspiration rate with one parameter varied, g m2 s1 ET = evapotranspiration calculated at reference parameters, g m2 s1 Table 51. 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 m1 VPDieafair Leaftoair 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 52 (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, (52) 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 VPDleafair 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 51 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 51 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 51. Predicted and measured evapotranspiration rate as a function of pressure. Sensitivity Analysis The change in evapotranspiration rate for the parameters in Table 51 varied one at a time is given in Table 52. Predicted ET and the percent change from the ET at reference conditions calculated by equation 51 are shown. Predicted ET when all parameters were at reference values was 2.22 g m2 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 m1 decreased ET by 31%. Conversely, decreasing rs by 90% increased ET fourfold. At constant pressure, changes in surface resistance were caused by other environmental parameters such as CO2 concentration and PAR availability (see chapter 4). Table 52. 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 m2 min1 Parameter ET g m2 min1 % 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 m1 4.07 83 696 s m1 1.53 31 928 s m1 1.16 47.7 VPleafair 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 52. Table 53 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 m2 min1 83 Table 53. 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 s1) .1 Air velocity, m s1 0.46 ( 2.5 m 0.1 m 0.172 (> 2.5 m s1) Surface resistance, s m1 0.011 35 s m1 VPDleafair 0.84 0.1 kPa Performance of the evapotranspiration model was validated by comparison to independent data. Equation 47 was used to calculate the root mean square error of the model at 12, 33, 66, and 101 kPa. The model was validated (Figures 52, 53, and 54) for the reference conditions (CO2 = 40 Pa; PAR = 340 [tmol m2 s1), elevated CO2 (CO2 = 150 Pa; PAR = 340 mrnol m2 s1); and reduced PAR (CO2 = 40 Pa; PAR = 160 [tmol m 2 S1). The RMSE error was 0.2 g m2 min' in reference conditions, 0.4 g m2 min' in elevated CO2, and 0.3 g m2 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 52. Model performance at reference conditions. Carbon dioxide concentration was 40 Pa and PAR was 340 [[mol m2 S1 0 20 40 60 Pressure, kPa 80 100 120 Figure 53. Model performance in elevated CO2. Carbon dioxide concentration was 150 Pa and PAR was 340 [tmol m2 S1 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 54. Model performance in low PAR conditions. Carbon dioxide concentration was 40 Pa and PAR was 160 [mol m2 S1 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 m2 min1 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 11). 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 (VPDcropair) is the driving force for evapotranspiration (Zolnier et al., 2000). Accurate calculation of the VPDcropair 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 PenmanMonteith 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 12). The slope is evaluated at the air temperature and is assumed to provide a good 