Copyright is owned by the Author of the thesis. Permission is given for a copy to be downloaded by an individual for the purpose of research and private study only. The thesis may not be reproduced elsewhere without the permission of the Author.

MODELLING THE GREENHOUSE ENVIRONMENT

AND THE

GROWTH OF CUCUMBERS

( Cucumis sativus L.)

A thes i s

submitted i n partial fulfilment of the requirements for the degree

of

Doctor of Philosophy

in

Agricultural Engineering

at

Mas s ey University

Col in Mark Well s

1992

Massey University Library Thesis Copyright Form

Title: MODELLING THE GREENHOUSE ENVIRONMENT AND THE GROWTH OF CUCUMBERS (Cucumis sativus L.)

(1) I give permission for my thesis to be made available to readers in the Massey University Library under conditions determined by the Librarian.

(2) I do not wish my thesis, or a copy, to be sent to another institution without my written consent for 12 months.

(3) I agree that my thesis may be copied for Library use.

Signed:

Date:

The copyright of this thesis belongs to the author. Readers must sign their name in the space below to show that they recognise this. They are asked to add their permanent address.

NAME AND ADDRESS DATE

ii

ABSTRACT

Mathematical model s which describe the greenhouse environment , and the

growth of a crop of cucumbers , in that environment , have been devel oped and

tested . The models have been used to predict : the response of the

greenhouse to varying weather conditions , the growth of the crop l eaf

canopy , and the weight and number of fruit harvested .

The greenhouse environment has been modell ed using a system of non- l inear

differential equations , derived from a consideration of the energy and mas s

balance s of the glazing , internal structure , crop canopy , root media , fl oor , deep s oil layers , and the greenhouse air spac e . The equations have been s olved for five minute time steps , us ing measured value s of outs ide weather c onditions and c ontrol inputs as boundary value s .

Entry of s olar radiation into the greenhouse , and abs orption by various

surfaces , has been determined us ing transmission tabl e s generated us ing a " ray- trac ing " l ight transmi ssion model . The l ight transmis s i on model has

been c al ibrated in a separate experiment . The incoming s olar radiation has been partitioned between diffus e , dire c t , photosynthetically active and

near infra - red radiati on , for use in the crop model .

Val idation experiments have been performed to test the greenhouse environment simulation model . The results of the val idation exerc i s e showed

that the model was capable of predicting the temperatures in the greenhouse , within a few degrees . The mean errors were smaller for the crop

canopy , root medium , and fl oor , than for the glazing or air temperature . Prediction errors for relative humidity and carbon dioxide c oncentration

were more variabl e .

An exi s ting model of cucumber devel opment rate , and l eaf expans i on , has been modified and val idated . This gave good results when adequate account

was taken of l eaf s enes cense , and initiation of lateral growths .

Sub-model s for photosynthes i s , respiration , and assimilate partitioning have been developed , and c ombined with the greenhouse environment and leaf

expans ion model s . The c ombined model has been used to predict the c ourse of growth of a cucumber crop over one growing s eason , and the number and

weight of fruit harvested . The predictions have been c ompared to r esults from a test crop . Thi s revealed that while the total number of fruit

harvested was accurately predicted , the total we ight of harvested fruit was not .

The model s are intended to be used in the study of optimal c ontrol o f the

greenhouse environment .

iii

ACKNOWLEDGEMENTS

I would l ike to thank my chief supervisor , Dr . Cliff Studman (Agricultural Engineering Department ) and my e o - supervisors , Drs . Paul Austin , Bob

Chapl in , and Tim Hesketh ( Department of Production Technol ogy ) , for their as sistance during the cours e of this project .

I would al so l ike to expres s my appreciation to all the technical staff

(Agricultural Engineering Department ) , e specially Mr . Leo Bolter , and his family , who assi sted with much of the data collection .

Many thanks to all tho s e who helped in s ome way , particularly staff at the

Plant Growth Unit , and at Fruit and Tree Division , DSIR .

Funding for the purchase of the data collection system was provid e d by grants from the C . Alma Baker Trust , Univers ity Grants Committee , and the

Mas s ey University Res earch Fund .

And finally I would l ike to expres s my gratitude to David , Denise , Daniel , Jeremy , Joshua , and Jame s , for their l ove and support in times of

desperation !

This the s i s is dedicated to Karen , Amy-Lee , and Adam , who will at last have the ir husband and father to themselves again !

iv

The Grand Academy of Lagado

The first man I saw was of meagre aspect , with sooty hands and face , hi s hair and beard long , ragged and singed in several place s . His clothes,

shirt and skin were all of the same colour . He had been eight years upon a pro ject for extracting sunbeams out of cucumbers , which were to be put into

vial s hermetically sealed , and let out to warm the air in raw inclement summers . He told me he did not doubt that in eight years more he should be

abl e to supply the Governor's gardens with sunshine at a reasonabl e rate .

from Guill iver ' s Travel s

by Jonathon Swift

TABLE OF CONTENTS

PAGE

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii ACKNOWLEDGEMENTS iii LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X LIST OF PLATES LIST OF SYMBOLS

xii xiii

1 INTR.ODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . 1 HISTORICAL DEVELOPMENT OF THE GREENHOUSE . . . . . . . . . . . . . . . . . . . . . . . 1 1 . 2 JUSTIFICAT I ON AND OUTLINE OF RESEARCH . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 . 3 ORGANIZATION OF THE THESIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 OPTIMIZATION OF GREENHOUSE PRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2 . 1 THE NATURE OF THE GREENHOUSE ENVIRONMENT . . . . . . . . . . . . . . . . . . . . . . . 7 2 . 2 THE NATURE OF GREENHOUSE CROP PRODUCTION . . . . . . . . . . . . . . . . . . . . . . . 8

2 . 2 . 1 Greenhouse Vegetable Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 . 2 . 1 . 1 Once-A-Year Mono-Cultures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 . 2 . 1 . 2 Rotational Multi-cultures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2 . 2 . 1 . 3 Rotational Mono-cultures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 . 2 . 2 Greenhouse Gut-Flower Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2 . 2 . 3 Greenhouse Ornamental and Nursery Production . . . . . . . . . . . . . . . . 12 2 . 2 . 4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2 . 3 MODELS AS TOOLS FOR OPTIMIZATION AND CONTROL . . . . . . . . . . . . . . . . . . . 13 2 . 3 . 1 Of Axioms, Empiricism and Analytical Models . . . . . . . . . . . . . . . . . 14 2 . 3 . 2 Dynamic and Steady State Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2 . 3 . 3 Deterministic and Stochastic models . . . . . . . . . . . . . . . . . . . . . . . . . 15 2 . 3 . 4 Continuous and Discrete Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2 . 4 IDENTIFICATION OF THE GREENHOUSE SYSTEM . . . . . . . . . . . . . . . . . . . . . . . . 15

3 EXPERIMENTAL PROCEDURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3 . 1 MEASUREMENT OF THE GREENHOUSE ENVIRONMENT . . . . . . . . . . . . . . . . . . . . . . 17

3 . 1 . 1 Description of the Greenhouse and Site . . . . . . . . . . . . . . . . . . . . . . 19 3 . 1 . 2 Data-Logging System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3 . 1 . 3 Measured Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3 . 1 . 3 . 1 Boundary Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3 . 1 . 3 . 2 Internal Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3 . 2 DETERMINING NATURAL VENTI LATION OF THE GREENHOUSE . . . . . . . . . . . . . . 34 3 . 3 DETERMINING LIGHT TRANSMISSION OF THE GREENHOUSE . . . . . . . . . . . .. . . 35 3 . 4 MEASUREMENT OF THE CUCUMBER CROP

3 . 4 . 1 The 1987 Crop and Experiments 3 . 4 . 2 The 1988 Crop and Experiments 3 . 4 . 3 The 1989 Crop and Experiments

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 36

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 37

4 SOLAR RADIATION ENTR.Y INTO A GREENHOUSE . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4 . 1 MODELLING INCIDENT SOLAR RADIATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4 . 1 . 1 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4 . 1 . 2 Separation of Diffuse Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4 . 1 . 3 Gircumsolar Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4 . 1 . 4 Separation of PAR and N I R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4 . 2 MODELLING LIGHT TRANSMI SSION BY THE GREENHOUSE . . . . . . . . . . . . . . . . . 46 4 . 2 . 1 Transmission of Full Size Greenhouses . . . . . . . . . . . . . . . . . . . . . . . 47 4 . 2 . 2 Transmission of Scale Models of Greenhouses . . . . . . . . . . . . . . . . . 48

V

4 . 2 . 3 Mathematical Models of Greenhouse Light Transmission ....... . 4 . 3 DEVELOPMENT AND VALIDATION OF A LIGHT TRANSMI SSION MODEL ...... .

4 . 3 . 1 Choice of Basic Model ...................................... . 4 . 3 . 2 Division of Sky Vault ...................................... . 4 . 3 . 3 Modifications to Existing Transmission Model ............... . 4 . 3 . 4 Trial 1 . Absorption by the Greenhouse Elements ............. .

4 . 3 . 4 . 1 Results ................................................... .

4 . 3 . 5 Trial 2 . Effect of Reference Plane Height .................. .

4 . 3 . 5 . 1 Results 4 . 3 . 6 Trial 3 . Evaluation of Diffuse Sky Distributions

4 . 3 . 6 . 1 Results 4 . 3 . 7 Trail 4 . Validation of the Modified Model 4 . 3 . 8 Discussion ................................................. .

4 . 4 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 THE GREENHOUSE MODEL 5 . 1 REVIEW OF EXISTING MODELS ..................................... .

5 . 1 . 1 Time Series Models ......................................... . 5 . 1 . 2 Steady state Single Component Models ....................... .

5 . 1 . 3 Steady State Multiple Component Models ..................... .

5 . 1 . 4 Dynamic Models ............................................. .

5 . 1 . 5 Models Including the Carbon Dioxide Balance ................ . 5 . 1 . 6 Summary of Existing Models ................................. .

5 . 2 RATIONALE FOR A NEW GREENHOUSE MODEL .......................... . 5 . 3 ENERGY AND MASS BALANCES ...................................... .

5 . 3 . 1 Preliminaries .............................................. . 5 . 3 . 2 Greenhouse Glazing ......................................... .

5 . 3 . 3 Greenhouse Structure ....................................... .

5 . 3 . 4 Crop Canopy ................................................ .

5 . 3 . 5 Root Medium ................................................ . 5 . 3 . 6 Floor ...................................................... . 5 . 3 . 7 Soil Layers ................................................ . 5 . 3 . 8 I nside Air Space ........................................... . 5 . 3 . 9 Energy Balance Equations ................................... . 5 . 3 . 10 Mass Balance Equations .................................... .

5 . 3 . 11 Solar Radiation Gains ..................................... .

5 . 3 . 12 Convective Exchanges ...................................... .

5 . 3 . 13 Radiative Exchanges ....................................... . 5 . 3 . 14 Conductive Exchanges ...................................... . 5 . 3 . 15 Evaporati ve Exchanges ..................................... . 5 . 3 . 16 Advecti ve Exchanges ....................................... .

5 . 3 . 17 Carbon Dioxide Exchanges .................................. . 5 . 4 DETERMINATI ON OF ANCILLARY PARAMETERS ......................... .

5 . 4 . 1 Greenhouse Dimensions ...................................... . 5 . 4 . 2 Densities and Specific Heat Capacities ..................... . 5 . 4 . 3 Composition of the Floor and Soil Layers ................... . 5 . 4 . 4 Composition of the Root Media .............................. . 5 . 4 . 5 Thermal Capacities of the Greenhouse Components ............ .

5 . 4 . 6 Solar Radiation Parameters ................................. .

5 . 4 . 7 Convective Heat Transfer Coefficients ...................... . 5 . 4 . 8 Radiation Heat Transfer Coefficients ....................... .

5 . 4 . 8 . 1 Thermal Radiation Transmission of the Crop .............. . 5 . 4 . 8 . 2 Self View Factor of the Crop ............................ . 5 . 4 . 8 . 3 Self View Factor of the Root Medium ..................... .

5 . 4 . 8 . 4 View Factor Root Medium to Floor ........................ . 5 . 4 . 8 . 5 View Factor Root Medium to Crop ......................... .

vi

48 52 52 53 53 5 5 5 5 5 7 5 7 58 58 59 74 74

76 76 80 81 83 85 88 88 90 91 92 96 97 98 99 100 101 102 105 106 107 109 109 113 113 115 117 117 117 119 120 12 1 122 122 123 126 127 128 129 130 130

5 . 4 . 8 . 6 View Factor Root Medium to Heating System ............... . 5 . 4 . 8 . 7 View Factor Root Medium to Structure .................... . 5 . 4 . 8 . 8 View Factor Root Medium to Glazing ...................... . 5 . 4 . 8 . 9 View Factors for the Floor .............................. . 5 . 4 . 8 . 10 View Factors for the Crop .............................. . 5 . 4 . 8 . 11 View Factors for the Heating System .................... . 5 . 4 . 8 . 12 View Factors for the Structure ......................... . 5 . 4 . 8 . 13 View Factors for the Glazing ........................... . 5 . 4 . 8 . 14 Combined Emissivity View Factors ....................... .

5 . 4 . 9 Determination of the Effective Sky Temperature ............. . 5 . 4 . 10 Conductive Heat Transfer Coefficients ..................... . 5 . 4 . 11 Evaporative Mass Transfer Resistances ..................... . 5 . 4 . 12 Advective Heat and Mass Transfer Coefficients ............. .

5 . 5 IMPLEMENTATION OF THE MODEL ................................... . 5 . 5 . 1 Integration Technique ...................................... . 5 . 5 . 2 Discontinuities ............................................ .

5 . 6 RESULTS OF THE SIMULATION ..................................... . 5 . 6 . 1 Sample Results of the Greenhouse Simulation with Static Crop 5 . 6 . 2 Long Term Correlations ..................................... .

5 . 7 DISCUSSION ..................................................... . 5 . 8 SUMMARY . . . . . . . . . . . . . . . • • . • . . . . . . . . . . . . • • . • . . . . . . • . . . . . . . . . . . . . .

6 THE CROP MODEL 6 . 1 SHORT REVIEW OF EXISTING CROP MODELS

6 . 1 . 1 Empirical Models of Greenhouse Crops ....................... . 6 . 1 . 2 Analytical Models of Greenhouse Crops ...................... .

6 . 2 A CROP MODEL FOR GREENHOUSE CUCUMBER .......................... .

6 . 2 . 1 Development of the Plant and Expansion of the Leaf Surface 6 . 2 . 1 . 1 Allometric Relationships ................................ . 6 . 2 . 1 . 2 Plastochron Index ....................................... . 6 . 2 . 1 . 3 Leaf Production Rate .................................... . 6 . 2 . 1 . 4 Growth of Successive Leaves ............................. . 6 . 2 . 1 . 5 Leaf Senescense ......................................... .

6 . 2 . 1 . 6 Validation of Leaf Growth and Development ............... . 6 . 2 . 2 Radiation in the Crop Canopy ............................... .

6 . 2 . 2 . 1 Radiative Properties of Leaves .......................... . 6 . 2 . 2 . 2 Leaf Angle Distribution ................................. . 6 . 2 . 2 . 3 Extinction Coefficient for Direct Radiation ............. . 6 . 2 . 2 . 4 Extinction Coefficient for Diffuse Radiation ............ . 6 . 2 . 2 . 5 Reflectance of the Plant Canopy ......................... . 6 . 2 . 2 . 6 Transmission of Radiation ............................... . 6 . 2 . 2 . 7 Absorption of Photosynthetically Active Radiation ....... . 6 . 2 . 2 . 8 Sunlit and Shaded Leaves ................................ .

6 . 2 . 3 Photosynthesis ............................................. . 6 . 2 . 3 . 1 Maximum Rate of Gross Photosynthesis .................... . 6 . 2 . 3:2 Light Use Efficiency Factor ............................. . 6 . 2 . 3 . 3 Gross Photosynthesis .................................... . 6 . 2 . 3 . 4 Canopy Photosynthesis ................................... .

6 . 2 . 4 Respiration ................................................ . 6 . 2 . 4 . 1 Maintenance Respiration ................................. . 6 . 2 . 4 . 2 Growth Respiration ...................................... .

6 . 2 . 5 Carbohydrate and Starch Reserves ........................... . 6 . 2 . 6 Partitioning ............................................... .

6 . 3 IMPLEMENTATION OF THE MODELS .................................. . 6 . 4 RESULTS OF THE COMBINED MODEL 6 . 5 DISCUSSION

vii

130 131 131 131 132 132 133 133 134 135 136 137 138 140 140 141 142 142 157 16 1 163

165 165 166 166 168 170 171 172 172 174 181 181 183 183 184 185 187 188 190 190 191 192 192 194 195 195 196 196 197 199 200 202 203 204

viii

6.6 SUMMARY 206

7 OVERVIEW AND CONCLUSIONS .......................................... 207 7.1 SUMMARY AND RECOMMENDATIONS .................................... 207 7.2 I MPLICATIONS FOR THE INDUSTRY .................................. 210 7. 3 CONCLUSI ON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

8 REFERENCES 213

Al NATURAL VENTILATION OF THE TEST GREENHOUSE 241 Al.l REVIEW OF EXISTING MODELS ..................................... 241 Al.2 AN EMPIRICAL MODEL FOR THE TEST GREENHOUSE .................... 242

A2 INTERNAL RESISTANCE OF CUCUMBER LEAVES A2.1 INTRODUCTION A2.2 RESULTS

A3 PROGRAM LISTINGS AND DATA FILES

245 245 246

251 A3.1 GREENHOUSE SIMULATION MODEL ................................... 251

A3.1.1 Main Simulation Model ...................................... 251 A3 .1. 2 Global Variables ........................................... 257 A3.1.3 Function Interpolator ...................................... 263 A3.1.4 Soil Thermal Properties Routine ............................ 265 A3.1.5 Convective Heat Transfer Coefficient Routine ............... 266 A3.1.6 Data I nput and Initialization Routine ...................... 269 A3.1.7 Daily Variable Parameter Routine ........................... 274 A3.1.8 Solar Radiation Partitioning Routine ....................... 276 A3.1.9 Crop Development Model ..................................... 278 A3.1.10 Photosynthesis Routine .................................... 284 A3.1.11 Crop Growth and Respiration Routine ....................... 287 A3.1.12 Greenhouse Energy and Mass Balance Model .................. 291 A3.1.13 Simulation I nput File ..................................... 299 A3 .1.14 I nitial Plant Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300

A3.2 LIGHT TRANSMISSION MODEL ...................................... 302 A3.2.1 Main Light Transmission Program GST2.F ..................... 302 A3.2.2 Ray Tracing Subroutine RAY.F ............................... 309 A3.2.3 Transmission Subroutine TRANS.F ............................ 311 A3.2.4 Direct Light Transmission And Absorption Data .............. 313 A3.2.5 Diffuse Light Transmission Program D IFF2.F ................. 317 A3.2.6 Diffuse Light Transmission And Absorption Data ............. 319

TABLE

3 .1. 3.2. 4.1. 5 .1. 5.2. 5.3. 5.4. 5.5. 5.6. 5.7. 5.8. 5.9. 5.10. 6.1. 6.2. 6.3. 6.4.

LIST OF TABLES

PAGE

Schedule of Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Data-Logging Instrumentation ................................. 24 Mathematical Models of Greenhouse Light Transmission ........ . Models of the Greenhouse Environment ........................ . Greenhouse Dimensions ....................................... . Calculated Surface Areas .................................... . Density of Greenhouse Components ............................ . Specific Heat Capacity of Greenhouse Components ............. . Composition of the Floor and Soil by Volume Fraction ........ . Thermal Capacity of Greenhouse Components ................... . Parameters for Forced Convection Correlations ............... . Parameters for Free Convection Correlations

49 77 118 118 119 120 120 122 124 125

Emissivity of Greenhouse Surfaces ............................ 127 Average Radiative Properties of Green Leaves ................. 184 Maintenance Respiration Coefficients ......................... 197 Growth Respiration Coefficients for Organic Compounds ........ 198 Growth Respiration Coefficients used in Model ................ 199

ix

LIST OF FIGURES

FIGURE PAGE

2.1. Three Level Representation of the Greenhouse System .......... 16 3.1. Plan of No. 23 Greenhouse, Plant Growth Unit ................. 21 3.2. Position of Pyranometers for Light Transmission Tests ........ 35 4.1. Correlations of Diffuse Fraction vs Clearness I ndex ..... · ' · .. 42 4.2. Effect of Greenhouse Components and Dust on Light ............ 55 4.3. Increased Transmission due to I nternal Reflection ............ 56 4.4. Effect of Greenhouse Components and Dust on Absorption ....... 57 4.5. Effect of Reference Plane Height on Light Transmission ....... 58 4.6. Components of Global Radiation 14/7/89 ....................... 60 4.7. Predicted & Measured Light Levels Point 2B 14/7/89 ........... 60 4.8. Predicted & Measured Transmissivity Point lA 14/7/89 ......... 61 4.9. Components of Global Radiation on 9/7/89 ..................... 62 4.10. Predicted & Measured Light Levels Point lA 9j7j89 ............ 62 4.11. Predicted & Measured Transmissivity Point lA 9j7j89 .......... 63 4.12. Components of Global Radiation on 23j7j89 .................... 64 4.13. Predicted & Measured Light Levels Point 4B 23/7/89 ........... 64 4.14. Predicted & Measured Transmissivity Point 4B 23/7/89 ......... 65 4.15. Components of Global Radiation on 7/7/89 ..................... 66 4.16. Predicted & Measured Light Levels Point lA 7j7j89 ............ 66 4.17. Predicted & Measured Transmissivity Point lA 7/7/89 .......... 67 4.18. Predicted vs Measured Radiation Levels Point lA .............. 67 4.19. lB .............. 68 Predicted vs Measured Radiation Levels Point 4.20. 2A .............. 68 Predicted vs Measured Radiation Levels Point 4.21. 2B .............. 69 Predicted vs Measured Radiation Levels Point 4.22. 3A .............. 69 Predicted vs Measured Radiaiton Levels Point 4.23. 3B .............. 70 Predicted vs Measured Radiation Levels Point 4.24. 4A .............. 70 Predicted vs Measured Radiation Levels Point 4.25. Predicted vs Measured Radiation Levels Point 4B .............. 71 4.26. Predicted vs Measured Hourly Light Excluding Perimeter ....... 72 4.27. Predicted vs Measured Hourly Light for Perimeter ............. 72 4.28. Predicted vs Measured Daily Light Excluding Perimeter ........ 73 4.29. Predicted vs Measured Daily Light for Perimeter .............. 73 5.1. Sensible Heat Flows in a Greenhouse .......................... 92 5. 2. Mass Flows in a Greenhouse ................................... 93 5.3. Prevailing Weather Conditions 8jllj89 ........................ 143 5.4. Measured and Simulated Air Temperature 8jllj89 ............... 143 5.5. Measured and Simulated Wet Bulb Temperature 8jllj89 .......... 144 5.6. Measured and Simulated Relative Humidity 8jllj89 ............. 144 5.7. Measured and Simulated Leaf Temperature 8/11/89 .............. 145 5.8. Measured and Simulated Glazing Temperature 8/11/89 ........... 145 5.9. Measured and Simulated Root Medium Temperature 8jllj89 ....... 146 5.10. Measured and Simulated Soil Temperature (5 cm) 8jllj89 ....... 146 5.11. Measured and Simulated Water Uptake Rate 8jllj89 ............. 147 5.12. Measured and Simulated Transpiration Rate 8jllj89 ............ 147 5.13. Measured and Simulated COz concentration 8/11/89 ............. 148 5.14. Prevailing Weather Conditions 29/11/89 ....................... 150 5.15. Measured and Simulated Air Temperature 29jllj89 .............. 151 5.16. Measured and Simulated Wet Bulb Temperature 29jllj89 ......... 151 5.17. Measured and Simulated Glazing Temperature 29jllj89 .......... 152 5.18. Measured and Simulated Leaf Temperature 29/11/89 ............. 152 5.19. Measured and Simulated Root Medium Temperature 29/11/8 ....... 153 5.20. Prevailing Weather Conditons 20j9j89 ......................... 154

X

5.21. Measured and Simulated Air Temperature 20/9/89 .............. . 5.22. Measured and Simulated Wet Bulb Temperature 20/9/89 ......... . 5.23. Measured and Simulated Relative Humidity 20/9/89 ............ . 5.24. Measured and Simulated Glazing Temperature 20j9j89 .......... . 5.25. Measured and Simulated Root Medium Temperature 20/9/89 ...... . 5.26. Daily Mean Error of Air Temperature Prediction .............. . 5.27. Daily RMS Error of Air Temperature Prediction ............... . 5.28. Daily Correlation Coefficient of Air Temperature ............ . 5.29. Daily Mean Error of Leaf Temperature Prediction ............. . 5.30. Daily RMS Error of Leaf Temperature Prediction .............. . 5.31. Daily Correlation Coefficient of Leaf Temperature ........... . 6.1. Schematic of a Crop Model for Greenhouse Cucumber ........... . 6.2. Leaf Pattern Curves for Leaf Length ......................... . 6.3. A Typical Leaf Pattern Curve ................................ . 6.4. Function f (i) for Leaf Expansion vs Leaf Number ............. . 6.5. Predicted vs Measured Leaf Area ............................. . 6.6. Predicted vs Measured Number of Leaves ...................... . 6.7. Endogenous Photosynthetic Capacity of a Leaf ................ . 6.8. Mesophyll Conductance of a Leaf ............................. . 6.9. Predicted vs Measured Number of Fruit Picked per Plant ...... . 6.10. Predicted vs Measured Weight of Fruit Picked per Plant ...... . Al.l. Predicted vs Measured Ventilation Rate of Greenhouse ........ . Al.2. Predicted vs Measured Infiltration Rate of Greenhouse ....... .

A2.1. Internal Leaf Resistance vs Vapour Pressure Deficit ......... . A2.2. Internal Leaf Resistance vs Solar Radiation ................. . A2.3. Internal Leaf Resistance vs Leaf Temperature ................ . A2.4. Internal Leaf Resistance vs Carbon Dioxide .................. . A2.5. Measured vs Simulated Internal Leaf Resistance .............. .

xi

154 155 155 156 156 158 158 159 160 160 161 168 175 176 179 182 182 193 194 203 204 243 244 246 247 248 249 250

PLATE

I. II. III. IV. V. VI. VII. VIII.

xii

LIST OF PLATES

PAGE

No 23 Greenhouse, Plant Growth Unit, Massey University . . ... . . 20 Cucumbers soon after Transplanting ... . ....... . . ... . . . . .. . . .. . 23 The Data-Logging System ... . ... . .. . .. . . . . . . ... . . . . . .. . ... . . . . . 24 Wind Vane and Anemometer on 10 m Mast ..... . . . .............. . . 26 Window opening Measurement System .... . .. . . . . .. . .......... . . . . 29 Leaf Temperature Measurement and Hot Bulb Anemometer . . .. . . .. . 30 Linear Pyranometers and Linear Net Radiometer .. . . . .. . . . . .. . . . 31 The Lysimeter Platform during Construction . .............. . . . . 34

SYMBOL IN TEXT

A

As

Atop

Age(i)

As si m a

Bs

b

LIST OF SYMBOLS

SYMBOL DESCRIPTION UNITS IN MODEL

ARM( I ) or area of a leaf cm2 ARL (I)

Abot open area of bottom ventilators m2 and doors

Ac surface area of the crop canopy m2 (one side only)

Af area of the greenhouse floor m2

Ag surface area of the greenhouse m2 glazing

Ah surface area of the greenhouse m2 heating system

Am

As

Atop

exposed surface area of the root m2 medium bags

surface area of the greenhouse structure

open area of top ventilator windows

AgeFruM (I) age of the i-th fruit or

day

AgeFruL (I)

Assim

A

Ad

As

Be

Bcave

Bf

Bg

Bm

Bpar

Bs

B

Bd

assimilation rate of the crop mgC02.plant-1.s-1

slope of the leaf pattern curve cm.cm-1.day-1 during the primordial phase of leaf development

delay value of parameter a cm.cm_1.day_1 stationary (normal) value of cm.cm-1.day-1 parameter a

solar radiation absorbed by the W.m-2 crop per unit floor area

average daily solar radiation W.m-2 intensity at the top of the crop

solar radiation absorbed by the W.m-2 floor per unit floor area

solar radiation absorbed by the W.m-2 glazing per unit floor area

solar radiation absorbed by the W.m-2 root medium per unit floor area

average daily photosynthetically MJ.m-2 active radiation at top of crop

solar radiation absorbed by the W.m-2 greenhouse structure per unit floor area

slope of the leaf pattern curve cm.cm-1.day-1 during the expanding phase of leaf development

delay value of parameter b cm.cm-1.day-1

xiii

Bs

Cloud Cloud

Cao

Cc a

Cfa

Cga

Cgo

Cha

Cma

Cpa

C pcl Cpcl

Cpgb Cpgb

c pgl Cpgl

Cpa

C porn Cpom

C ps Cps

Cpq

Cpv

Cpw Cpw

Cpl

stationary (normal) value of parameter b cloud cover fraction

cm.cm-�.day-�

rate of sensible heat loss from W.m2 greenhouse due to ventilation

rate of convection from the crop W.m-2 to the inside air per unit floor area

rate of convection from the W.m-2 floor to the inside air per unit floor area

rate of convection from the W.m-2 glazing to the inside air per unit floor area

rate of convection from the W.m-2 glazing to the outside air per unit floor area

rate of convection from the W.m-2 heating system to the inside air per unit floor area

rate of convection from the root W.m-2 medium to the inside air per unit floor area

specific heat capacity of inside J.g-�.0c-� dry air

specific heat capacity of the crop

specific heat capacity of clay J.g-�. oc-� minerals

specific heat capacity of the J.g-�. oc-� dry fraction of the floor layer

specific heat capacity of the J.g-�. oc-� glazing bars

specific heat capacity of the J.g-�. oc-� greenhouse glazing material

specific heat capacity of the J.g-�. oc-� dry fraction of the root medium

specific heat capacity of J.g-�. oc-� outside dry air

specific heat capacity of J.g-�. oc-� organic matter

specific heat capacity of the J.g-�. oc-� greenhouse structure

specific heat capacity of quartz J.g-�. oc-� minerals

specific heat capacity of water J.g-�. oc-� vapour

specific heat capacity of liquid J.g-�. oc-� water

specific heat capacity of the dry fraction of the 1st soil layer

xiv

c

d

E ao

E dra in

E drip

Elrr

E up

EOT

F

F cc

Gp2

Gp3

Gp4

GpS

Gsa

C02 a

G02o

G

Gd

Gs

BagD

DMc

D

Eao

Edrn

Edrip

Eirr

Eup

EOT

ea

esat

eo

FDG

Fee

specific heat capacity of the J.g-�.0c-� dry fraction of the 2nd soil layer

specific heat capacity of the J.g-�. oc-� dry fraction of the 3rd soil layer

specific heat capacity of the J.g-�. oc-� dry fraction of the 4th soil layer

specific heat capacity of the J.g-�. oc-� dry fraction of the 5th soil layer

rate of convection from the W.m-2 greenhouse structure to the inside air per unit floor area

carbon dioxide concentration of �1.1-� the inside air

carbon dioxide concentration of �1.1-� the outside air

logarithm of the relative length -of the unfolding leaf

delay value of parameter c

stationary (normal) value of parameter c

diameter of the root medium bags m

total dry matter of the crop

characteristic dimension

gDM

m

latent heat loss from the inside W.m-2 air due to ventilation per unit floor area

advective energy loss from the W.m-2 root medium due to drainage per unit floor area

advective energy loss from the W.m-2 glazing due to dripping per unit floor area

advective energy addition to the W.m-2 root medium due to irrigation per unit floor area

advective energy exchange W.m-2 between the root medium and the crop due to water uptake per unit floor area

equation of time minute

vapour pressure of inside air Pa

saturated vapour pressure of Pa inside air

vapour pressure of outside air Pa

fraction of dividing cells in a leaf

self view factor of the crop

Fcg

F eh

F ern

F CS

F gsky

-F he

F hh

F hs

F m e

F mf

F mg

F mm

F ms

F se F sf F sg

Fcf

Fcg

Fch

Fern

Fcs

Ffc

Ffg

Ffh

Ffm

Ffs

Fgsky

Fhc

Fhf

Fhg

Fhh

Fhm

Fhs

Fmc

Fmf

Frog

Fmh

From

Fms

Fsc

Fsf

Fsg

view factor of the crop to the floor

view factor of the crop to the glazing

view factor of the crop to the heating system

view factor of the crop to the root medium

view factor of the crop to the structure

view factor of the floor to the crop

view factor of the floor to the glazing

view factor of the floor to the heating system

view factor of the floor to the root medium

view factor of the floor to the structure

view factor of the glazing to the sky

view factor of the heating system to the crop

view factor of the heating system to the floor

view factor of the heating system to the glazing

self view factor of the heating system

view factor of the heating system to the root medium

view factor of the heating system to the structure

view factor root medium to crop

view factor root medium to floor -

view factor root medium to glazing

view factor root medium to heating system

self view factor of the root medium

view factor root medium to structure

view factor of the structure to the crop

view factor of the structure to the floor

view factor of the structure to the glazing

xvi

F sh

F sm

F ss F sun

FA/ 'f eg

'f eh

'fes

'f f e

'f !m

'frs

'f gsky

'f me

'f mg

'f mh

'f ms

'f sg

fao

Fsh

Fsm

Fss

FracSun

FAI

SFcg

SFch

SFcs

SFfc

SFfg

SFfh

SFfm

SFfs

SFgsky

SFhg

SFhg

SFmc

SFmg

SFmh

SFms

SFsg

fao

view factor of the structure to the heating system

view factor of the structure to the root medium

self view factor of the structure

fraction sunlit leaf area

exposed floor area index

combined emissivity view factor from the crop to the glazing

combined emissivity view factor from the crop to the heating system

combined emissivity view factor from the crop to the structure

combined emissivity view factor from the floor to the crop

combined emissivity view factor from the floor to the glazing

combined emissivity view factor from the floor to the heating system

combined emissivity view factor from the floor to the root medium

combined emissivity view factor from the floor to the structure

combined emissivity view factor from the glazing to the sky

combined emissivity view factor from the heating system to the glazing

combined emissivity view factor from the heating system to the structure

combined emissivity view factor from the root medium to the crop

combined emissivity view factor from the root medium to the glazing

combined emissivity view factor from the root medium to the heating system

combined emissivity view factor from the root medium to the structure

combined emissivity view factor from the structure to the glazing

rate of water vapour exchange between the inside and outside air per unit floor area

xvii

f ea fca

f drain fdrn

f drip fdrip

f fru it ffruit

fga

firr firr

fma fma

} up fup

f gross FGross

f growth FGrowth

f resp FResp

f vent Fvent

Field Field

Gr Gr

Gfl

Gfm

Gl2

G23

G34

rate of water vapour exchange g.m-2.s-1 between the crop and the inside air per unit floor area

rate of water loss from the root g.m-2.s-1 medium by drainage per unit floor area

rate of water loss from the underside of the glazing by dripping per unit floor area

rate of water loss from the crop g.m-2.s-1 by removal of fruit

rate of water vapour exchange between the glazing and the inside air per unit floor area

rate of water addition to the root medium by irrigation per unit floor area

rate of water vapour exchange g.m-2.s-1 between the root medium and the inside air per unit floor area

rate of water uptake by the crop g.m-2.s-1 from the root medium per unit floor area

rate of carbon dioxide removal mgG02.m-2.s-1 from inside air by photosynthesis per unit floor area

rate of carbon dioxide addition mgG02.m-2.s-1 to inside air by growth respiration per unit floor area

rate of carbon dioxide addition mgG02.m-2.s-1 to inside air by maintenance respiration per unit floor area

rate of carbon dioxide removal from inside air by ventilation per unit floor area

field capacity of the root medium

Grashof number

rate of conduction between the W.m-2 floor and the first soil layer per unit floor area

rate of conduction between the W.m-2 floor and the root medium per unit floor area

rate of conduction between the W.m-2 1st and 2nd soil layers per unit floor area

rate of conduction between the W.m-2 2nd and 3rd soil layers per unit floor area

rate of conduction between the W.m-2 3rd and 4th soil layers per unit floor area

xviii

GAl

g

HA!

hcca

het a

G45

G5d

Gsg

GAI

g

HAI

Ha

He

Hf

Hg

Hm

Hs

Hl

H2

H3

H4

H5

hao

hGca

hGfa

hGga

hGgo

hcha

rate of conduction between the W.m-2 4th and 5th soil layer per unit floor area

rate of conduction between the W.m-2 5th soil layer and the deep ground per unit floor area

rate of conduction between the W.m-2 greenhouse structure and the glazing per unit floor area

glazing area index

gravitational constant

surface area of the heating system relative to the floor area

enthalpy of the inside air per J.m-2 unit floor area

enthalpy of the crop canopy per J.m-2 unit floor area

enthalpy of the greenhouse floor J.m-2 layer per unit floor area

enthalpy of the greenhouse J.m-2 glazing per unit floor area

enthalpy of the root medium bags J.m-2 per unit floor area

enthalpy of the greenhouse J.m-2 structure per unit floor area

enthalpy of the 1st soil layer J.m-2 per unit floor area

enthalpy of the 2nd soil layer J.m-2 per unit floor area

enthalpy of the 3rd soil layer J.m-2 per unit floor area

enthalpy of the 4th soil layer J.m-2 per unit floor area

enthalpy of the 5th soil layer J.m-2 per unit floor area

advective heat transfer W.m-2• 0G-1 coefficient for ventilation heat loss

convective heat transfer W.m-2. oc-1 coefficient of the crop

convective heat transfer W.m-2. oc-1 coefficient of the floor

convective heat transfer W.m-2. oG-1 coefficient of the inside of the glazing

convective heat transfer W.m-2• 0G-1 coefficient of the outside of the glazing

convective heat transfer W.m-2. oc-1 coefficient of the heating system

xix

hem a hCma

hcsa hCsa

her m hGfm

hGfl

hG12

hG23

hG34

hG45

hcsd hG5d

hGsg

hRcg hRcg

hRch

hRcs

hRrc hRfc

hRfg

hRfh hRfh

hRfm

hRfs

hRgsky hRgsky

hRhg

hRhg

convective heat transfer coefficient of the root medium

convective heat transfer coefficient of the greenhouse structure

conductance between the floor W.m-2. oC_1 and the root medium

conductance between the floor W.m-2. oC_1 and the 1st soil layer

conductance between the 1st and W.m-2. oc-1 2nd soil layers

conductance between the 2nd and W.m-2. oC_1 3rd soil layers

conductance between the 3rd and W.m-2.°C-1 4th soil layers

conductance between the 4th and W.m-2. oc-1 5th soil layers

conductance between the 5th soil W.m-2.°C-1 layer and the deep ground

conductance between the greenhouse structure and the glazing

radiative heat transfer W.m-2.°C-1 coefficient from the crop to the glazing

radiative heat transfer W.m-2. oc-1 coefficient from the crop to the heating system

radiative heat transfer W.m-2. oc-1 coefficient from the crop to the structure

radiative heat transfer W.m-2. oc-1 coefficient from the floor to the crop

radiative heat transfer W.m-2. oc-1 coefficient from the floor to the glazing

radiative heat transfer W.m-2.°C-1 coefficient from the floor to the heating system

radiative heat transfer W.m-2. oc-1 coefficient from the floor to the root medium

radiative heat transfer W.m-2• oc-1 coefficient from the floor to the structure

radiative heat transfer W.m-2.°C-1 coefficient from the glazing to the sky

radiative heat transfer W.m-2. oc-1 coefficient from the heating system to the glazing

radiative heat transfer W.m-2. oc-1 coefficient from the heating system to the structure

XX

hRmc hRmc

hRmg

hRmh

hRms

hRsg hRsg

I opdr

I pbeam I beam

Idf

I p d r Idr

I psc

I sh d Ishd

I sun I sun

I

J K bdt Kbdf

K bdr Kbdf

Kd

K ndf Kndf

K ndr Kndr

K pdt Kpdf

radiative heat transfer coefficient from the root medium to the crop

radiative heat transfer W.m-2• oC-1 coefficient from the root medium to the glazing

radiative heat transfer W.m-2.°C-1 coefficient from the root medium to the heating system

radiative heat transfer W.m-2. °C-1 coefficient from the root medium to the structure

radiative heat transfer W.m-2.°C-1 coefficient from the structure to the glazing

intensity of direct PAR radiation above the crop

intensity of the direct PAR W.m-2 radiation beam absorbed in a lqyer of the crop

intensity of diffuse PAR W.m-2 radiation absorbed in a layer of the crop

intensity of direct PAR W.m-2 radiation absorbed in a layer of the crop

intensity of scattered PAR W.m-2 radiation absorbed in a layer of the crop

intensity of PAR radiation absorbed by shaded leaves in a layer of the crop

intensity of PAR radiation absorbed by sunlit leaves in a layer of the crop

leaf number

Julian day number

extinction coefficient for diffuse radiation in a stand of "black" leaves

extinction coefficient for direct radiation in a stand of "black" leaves

diffuse fraction index

extinction coefficient for diffuse radiation in real leaves

extinction coefficient for direct radiation in real leaves

extinction coefficient for NIR diffuse radiation in real leaves

extinction coefficient for NIR direct radiation in real leaves

extinction coefficient for PAR diffuse radiation in real leaves

day

xxi

K pdr

Le L

LA/

LCT

L E ea

L E ga

L E ma

L S T

M A !

Nu

Nu forced

Nur ree

N p lant

N v

Kpdr

Kt

kf

km

kl

k2

k3

k4

kS

Le

LM or LL

LM ( I ) or LL (I)

LAI

LEca

LEg a

LEma

M a

Mw

MAI

Nu

Nufor

Nufre

Nplant

Nv

extinction coefficient for PAR direct radiation in real leaves

sky clearness index

thermal conductivity of the floor

thermal conductivity of the root W.m-l. oc-l medium

thermal conductivity of the 1st W.m-l. oc-l soil layer

thermal conductivity of the 2nd W.m-l. oc-l soil layer

thermal conductivity of the 3rd W.m-l. oc-l soil layer

thermal conductivity of the 4th W.m-l. oc-l soil layer

thermal conductivity of the 5th W.m-l. oc-l soil layer

Lewis number

length of a leaf

length of the i-th leaf

length of the i+l-th leaf

reference length for a primordial leaf

length of the unfolding leaf

leaf area index

local civil time

rate of evaporative heat loss from the crop per unit floor area

cm

cm

cm

cm

cm

hrs

rate of evaporative heat loss W.m-2 from the glazing per unit floor area

rate of evaporative heat loss from the root medium per unit floor area

local solar time

molecular mass of dry air

hrs

gDA.mol-l

molecular mass of carbon dioxide gC02.mol-l

molecular mass of water

root medium surface area index

Nusselt number

Nusselt number for forced convection

Nusselt number for free convection

number of plants in the greenhouse

airchange rate

gH20.mol-l

plant

hr-l

xxii

NC;

n

p

pen

p gmax

P nmax

P shd

P sun

PGR1'

PGR(i)1

q

Re

R

R dzo

R gsky

NGM(I) or NGL(I)

N

Po

PG02

Fend

PGmax

PNmax

PGshd

PG sun

Pt

PGRFmax

relative number of cells along the mid-rib of the i-th leaf

number of leaves below the unfolding leaf in which cell division is occurring

barometric pressure

plastochron index of plant

cell.cell-1

Pa

carbon dioxide limited rate of mgG02.m-2.s-1 photosynthesis for a single leaf

endogenous rate of mgG02.m-2.s-1 photosynthesis for a single leaf

rate of gross photosynthesis for mgG02.m-2.s-1 a single leaf

maximum rate of gross mgG02.m-2.s-1 photosynthesis for a single leaf

maximum rate of net mgG02.m-2.s-1 photosynthesis for a single leaf

rate of gross photosynthesis for mgG02.m-2.s-1 a single shaded leaf

rate of gross photosynthesis for mgG02.m-2.s-1 a single sunlit leaf

rate of gross photosynthesis for mgG02.m-2.s-1 a layer of sunlit and shaded leaves

maximum potential growth rate of mgDM.s-1 a fruit

PGRFruM(I) potential growth rate of the mgDM.s-1 or i-th fruit PGRFruL(I)

Q rate of leaf initiation in the apex of a stem

leaves.d-1

Qs

Re

R

Rcg

Rch

Res

Rd

Rd20

Rgsky

stationary rate of leaf leaves.d-1 initiation in the apex of a stem

Reynolds number

universal gas constant J.mol-1.K-4

rate of net radiation exchange W.m-2 between the crop and the glazing per unit floor area

rate of net radiation exchange W.m-2 between the crop and the heating system per unit floor area

rate of net radiation exchange W.m-2 between the crop and the greenhouse structure per unit floor area

dark respiration rate for a mgG02.m-2.s-1 single leaf

dark respiration rate for a mgG02.m-2.s-1 single leaf at 20°G

rate of net radiation exchange W.m-2 between the glazing and the sky per unit floor area

xxiii

Rfc

Rfg

Rfm

Rfs

Rhf

R hg Rhg

Rhs

R mc Rmc

Rmg

Rmh

R ms Rms

Rsg

RGR c;

R G R p;

RGRt

RGR t; RGR

RH RH

rate of net radiation exchange W.m-2 between the floor and the crop per unit floor area

rate of net radiation exchange W.m-2 between the floor and the glazing per unit floor area

rate of net radiation exchange W.m-2 between the floor and the root medium per unit floor area

rate of net radiation exchange W.m-2 between the floor and the greenhouse structure per unit floor area

rate of net radiation exchange W.m-2 between the heating system and the floor per unit floor area

rate of net radiation exchange W.m-2 between the heating system and the glazing per unit floor area

rate of net radiation exchange W.m-2 between the heating system and the structure per unit floor area

rate of net radiation exchange W.m-2 between the root medium and the crop per unit floor area

rate of net radiation exchange W.m-2 between the root medium and the glazing per unit floor area

rate of net radiation exchange W.m-2 between the root medium and the heating system per unit floor area

rate of net radiation exchange W.m-2 between the root medium and the structure per unit floor area

rate of net radiation exchange W.m-2 between the greenhouse structure and the glazing per unit floor area

relative growth rate of cells along the mid-rib of the i-th leaf

relative growth rate of the cm.cm-2.plast-1 plant per plastochron

relative growth rate of the i-th cm.cm-2.plast-1 leaf per plastochron

relative growth rate of the plant per unit time

cm.cm-2.day-1

relative growth rate of the i-th cm.cm-2.day-1 leaf per unit time

relative humidity of inside air %

relative water content of the crop

relative water content of the root medium

xxiv

r ao

r V ea

rvma

sdr '

S dr '

s ndf

S ndr

s pdf

s pd r

SAl

SLA

s

T.

rao

rm

rVca

rVci

rVga

rVma

Se

Sdf

Sdr

Sdf

Sdr

Sg

Sn

Sndf

Sndr

So

Sp

Light

Spdf

Spdr

Ssc

SAI

SLA

Ta

advective mass transfer resistance between inside and outside of the greenhouse

mesophyll resistance

boundary layer resistance of the s.m-� crop for water vapour transfer

internal leaf resistance for s.m-� water vapour transfer

boundary layer resistance of the s.m-� glazing for water vapour transfer

boundary layer resistance of the s.m-� root medium for water vapour transfer

circumsolar component of global W.m-2 solar radiation

diffuse component of global W.m-2 solar radiation

direct component of global solar W.m-2 radiation

diffuse component of global solar radiation corrected for circumsolar radiation

direct component of global solar W.m-2 radiation corrected for circumsolar radiation

global solar radiation on the horizontal at the ground

near infra-red solar radiation

diffuse component of near infra-red solar radiation

direct component of near infra-red solar radiation

extra-terrestrial radiation on a W.m-2 horizontal surface

photosynthetically active solar W.m-2 radiation

average daily photosynthetically J.m-2.d-� active radiation at the top of the crop

diffuse component of W.m-2 photosynthetically active solar radiation

direct component of W.m-2 photosynthetically active solar radiation

solar constant W.m-2

greenhouse structure area index

specific leaf area of the crop m2.kgDM-�

slope of the saturation vapour Pa. oc-� pressure curve

temperature of the inside air °C

T ad

T aw

T cloud

T ow

T s

T sky

T4

t

V gb

V m

vs w

w

Temp

Tad

Taw

Tc

Td

Tf

Tg

Th

Tm

To

Tod

Tow

Ts

Tsky

Tl

T2

T3

T4

TS

T

Ua

Uo

Vgb

Vs

WHCc

WHCm

average daily crop temperature

dew-point temperature of the inside air

wet-bulb temperature of the inside air

temperature of the crop canopy

temperature of the cloud base

temperature of the deep ground

temperature of the floor layer

temperature of the greenhouse glazing

logarithmic mean temperature of °C the heating system

temperature of the root medium °C

temperature of the outside air °C

dew point temperature of the °C outside air

wet bulb temperature of the °C outside air

temperature of the greenhouse °C structure

apparent radiant temperature of °C the sky

temperature of the 1st soil °C layer

temperature of the 2nd soil °C layer

temperature of the 3rd soil °C layer

temperature of the 4th soil °C layer

temperature of the 5th soil °C layer

time s

inside air velocity m.s-1

outside wind speed at lOm above m.s-1 ground

volume of glazing bars m3

volume of root medium

volume of structure

width of a leaf

water holding capacity of the crop

water holding capacity of the root medium humidity ratio

cm

gHzO.gDM-1

gHzO.gDA-1

xxvi

X

X ci rc

Xomm

Xqm

y

a

amp

f3 r

y

X

Fbark

xomm

xqm

y

SAzi

Acndf

Acndr

Acpdf

Acpdr

Afn

Afp

Agdf

Agdr

Afn

Afp

Asdf

Asdr

StrucAF

SAlt

Compoint

Comp25

Gamma

da

eccentricity of the leaf angle distribution

circumsolar radiation correction -factor

fraction of bark in the root medium

fraction of organic matter in the root medium

fraction of quartz minerals in the root medium

parameter of the leaf angle distribution function

azimuth of the solar beam

absorptivity of the crop for diffuse near infra-red radiation

absorptivity of the crop for direct hear infra-red radiation

absorptivity of the crop for diffuse photosynthetically active radiation

absorptivity of the crop for direct photosynthetically active radiation

absorptivity of the floor for near infra-red radiation

absorptivity of the floor for photosynthetically active radiation

absorptivity of the glazing for diffuse radiation

absorptivity of the glazing for direct radiation

absorptivity of the root medium for near infra-red radiation

absorptivity of the root medium for photosynthetically active radiation

absorptivity of the structure for diffuse radiation

absorptivity of the structure for direct radiation

light absorption factor of structure

solar altitude

compensation point carbon dioxide concentration

compensation point carbon dioxide concentration at 25°C

the psychrometric constant

average depth (height) of the greenhouse inside airspace

0

f,Ll.l-1

Pa.°C-1

m

XXV'ii

ll.gl

Ei

TJ

TJ pot

L

df

dgl

BagH

delT

dl

d2

d3

d4

dS

ec

ef

eg

eh

em

es

esky

HBlock

SBlock

Eff

EffO

La

Lb

Le

Lp

Kmc

K

thickness of the floor layer m

thickness of the glazing m

depth of the root medium bags m

temperature difference between °C inlet and outlet of heater

thickness of the 1st soil layer m

thickness of the 2nd soil layer m

thickness of the 3rd soil layer m

thickness of the 4th soil layer m

thickness of the 5th soil layer m

solar declination angle

emissivity of the crop

emissivity of the floor

0

emissivity of the glazing

emissivity of the heating system -

emissivity of the root medium

emissivity of the structure

emissivity of a clear sky

emissivity of a cloudy sky

radiation interception coefficient of the heating system

radiation interception coefficient of the greenhouse structure

actual light use efficiency factor

potential light use efficiency factor

exponential decay constant for the parameter a during primordial phase of leaf development

plast

exponential decay constant for plast the parameter b during expanding phase of leaf development

exponential decay constant for the parameter c used to determine the unfolding leaf

plastochron constant of adaptation

angle of incidence between a leaf and the solar beam

hydraulic conductivity of the crop

thermal diffusivity of air

latitude of the greenhouse

plast

0

0

xxviii

P a

P c

P cndf

P cndr

P cpdf

P cpdr

P ct r

P r

P nd r

P nhor

P ph or

Lamb

V

XC02a

XiC02a

XiC02o

rho a

Rhocndf

Rhocndr

Rhocpdf

Rhocpdr

Rhondr

Rhonhor

Rhopdr

Rhophor

Sigma

Sign

Sigp

latent heat of vapourization of J.g-1 water at reference temperature of 0°C

kinematic viscosity of air m2.s-1

carbon dioxide content of inside mgC02.m-2 air per unit floor area

carbon dioxide concentration of mgC02.m-3 inside air

carbon dioxide concentration of mgCOz.m-3 outside air

density of dry air inside the gDA.m-3 greenhouse

density of carbon dioxide in the gC02.m-3 greenhouse

reflectivity of a canopy of non - horizontal leaves and underlying floor for diffuse NIR radiation

reflectivity of a canopy of non - horizontal leaves and underlying floor for direct NIR radiation

reflectivity of a canopy of non - horizontal leaves and underlying floor for diffuse PAR radiation

reflectivity of a canopy of non - horizontal leaves and underlying floor for direct PAR radiation

reflectivity of a canopy of non- horizontal leaves for direct radiation

reflectivity of the floor

reflectivity of a canopy of horizontal leaves for direct radiation

reflectivity of a canopy of non- horizontal leaves for direct NIR radiation

reflectivity of a canopy of horizontal leaves for direct NIR radiation

reflectivity of a canopy of non - horizontal leaves for direct PAR radiation

reflectivity of a canopy of horizontal leaves for direct PAR radiation

the Stephan - Boltzmann constant

scattering coefficient for NIR radiation

scattering coefficient for PAR radiation

xxix

Taucb

Taucndf

L cn dr Taucndr

L cpdf Taucpdf

Taucpdr

Taugdf

L gd r Taugdr

TauRF

Phi a

Phic

Ph if

Phig

Phi m

Phis

Phil

Phi2

Phi3

Phi4

PhiS

X a

Xc

transmis s ivity of a canopy of "black " l eaves for far infra - red radiati on

transmis sivity of the crop for diffuse near infra - red radiation

transmis s ivity of the crop for direct near infra- red radiation

transmis sivity of the crop for diffuse photosynthetically active radiati on

transmis s ivity of the crop for direct photosynthetically active radiation

transmi s s ivity of the glazing for diffus e radiation

transmi s s ivity of the glazing for direct radiati on

greenhouse l ight transmis si on correction factor

thermal capacity of the dry air J . m- 2 fraction of the ins ide air per unit fl oor area

thermal capacity of the dry J . m- 2 fraction of the crop per unit fl oor area

thermal capacity of the dry J . m- 2 fraction of the fl oor layer per unit floor area

thermal capacity of the glazing J . m- 2 per unit fl oor area

thermal capacity of the dry J . m- 2 fraction of the root medium per unit fl oor area

thermal capacity of the dry J . m- 2 fraction of the greenhouse structure per unit floor area

thermal capacity of the dry J . m- 2 fraction of the 1st soil layer per unit fl oor area

thermal capacity of the dry J . m- 2 fraction of the 2nd soil layer per unit fl oor area

thermal capacity of the dry J . m- 2 fraction of the 3rd soil layer per unit floor area

thermal capacity of the dry J . m- 2 fraction of the 4th s oil layer per unit floor area

thermal c apacity of the dry J . m- 2 fraction of the 5th s oil layer per uni t floor area

moisture c oncentration of the g . m- 2 inside air per unit fl oor area

moisture c oncentrati on of the g . m- 2 crop per unit fl oor area

XXX

X , c Xc

Xf

Xg

Xm

X , m Xm

Ghil

Ghi 2

Ghi 3

Ghi4

Ghi5

X a Chi a

Xo Ghio

Psic

Ps im

Gape

Gapm

w

maximum moisture concentrati on g . m- 2 of the crop per unit floor area

moisture c oncentrati on of the g . m- 2 fl oor layer per unit fl oor area

concentration of mois ture on the g . m- 2 unders ide of the glazing per unit fl oor area

moisture concentration of the g . m- 2 root medium per unit fl oor area

maximum moisture c oncentrati on of the root medium per unit fl oor area

moisture concentrati on of the 1st s oil layer per unit floor area

moisture c oncentrati on of the 2nd soil layer per unit floor area

moisture concentration of the 3rd s o il layer per unit floor area

moisture concentrati on of the 4th soil layer per unit floor area

moisture concentration of the 5th soil layer per unit floor area

absolute humidity of the inside g . m- 3 air

absolute humidity of the outs ide g . m- 3 air

water potential of the crop

water potential of the root medium

hydraul ic capacitance of the crop

hydraul ic capacitance of the root medium

hour angl e of the sun

bar

bars

bars - 1

bars - 1

0

xxxi