Physical Principles of Meteorology and fnvironmental Physics

Global. Synoptic and Micro Scales

David Blake Thp llnivP((J"Y nfQIIPpn(lnnli Au(trnlifl

Robert Robson James Cook University, Townsville and

The Australian Notional University, (anberra, Australia

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: ' \l\'~rld 'SciEimtific I ," " " .' ,(" ~,::,;'{<',. , 1,~,:, · , ; , , - , " , ' 'NEW JERSEY · LO NDON ' . SING AP ORE · BEIJING · SilANG HAl • HONG KONG · TAIPEI· CHENNAI

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PHYSICAL PRI NCIPLES OF METEOROLOGY AND ENVIRONMENTAl, PHYSICS t;lobal, Synoptic a nd Micro Scales

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About the Authors

David Blake (PhD, University of Queensland) is a physics researcher at the Umversity of ~ueensland , and ma.na.ging director of Solar Sells Pty. Ltd. ; a renewable energy consultancy. Robert Robson (PhD, ANU; Fellow, Royal Meteorological Society; Fellow, America.n Physical Society) is a physics and meteorology researcher nnd lecturer at the Australian Na.tional University and James Cook UniversitYl and a fanner forecaster with the Australian Bureau of Meteorology.

v jj

Preface

Meteorology is generally regarded as a discipline in its own right and is nor-mally taught at universities (if at all) separately from mainstream physics.In general the research literature is divided along similar lines, with someoutstanding exceptions to this rule, e.g., Lorenz’s 1963 paper in the Jour-nal of the Atmospheric Sciences, which has provided a springboard for theburgeoning field of chaos and nonlinear dynamics. One of the goals of ourbook is to bring the two fields a little closer, for there has never been abetter time to do so.

At the time of writing, the public debate over the global climate hasreached a frenzied pitch with the release of the 4th Report of the Intergov-ernmental Panel on Climate Change (http://www.ipcc.ch/). Moreover, awidespread perception is that water, rather than oil or even terrorism, willbe the other main global political issue of the century. Never has it beenmore important for the scientific community to provide the decision makerswith objective and accurate information. Unfortunately the global climatemodels upon which the IPCC, economists, politicians and others rely tomake their decisions, are by their very nature complex and opaque to allbut the specialist few. This provides fertile ground for the global warm-ing skeptics, and there is by no means general acceptance of anthropogenicwarming, even among meteorologists and climatologists.

This book provides both theoretical and practical grounding in meteo-rology, with an emphasis on phenomena in the boundary layer, and aims atfurnishing either a stand alone course or a firm platform for the reader toproceed with further study in one of the specialist areas, including globalclimate modeling. The theory component derives from a course of about 40lectures given at the senior undergraduate and graduate level, and is of a

ix

x Physical Principles of Meteorology and Environmental Physics

standard comparable with the Australian Bureau of Meteorology’s graduatetraining course for weather forecasters.

The main practical component concerns a research project measuringCO2 exchange between the atmosphere and (a) native tropical rainforestand (b) introduced sugar cane in tropical north-eastern Australia. The aimhere is to introduce the reader to experimental techniques and procedures,but there is a particularly important lesson to be learned from the results:during the peak growth phase, it is observed that sugar cane sequestratesmore than three times as much carbon dioxide as does rainforest on an av-erage daily basis! This result seems to contradict the widespread belief thatclearing rainforest and replacing it with crops is self-evidently a bad thing,but of course one has to take many other factors into account. Whateverits implications for climate modeling might be, it only serves to reinforceour belief that unsubstantiated assumption is never a substitute for hardphysics. That, in a nutshell spells out what this book is all about.

David BlakeThe University of Queensland, Australia

Robert RobsonJames Cook University, Townsville andThe Australian National University, Canberra, Australia

January, 2008

A cknowledgments

The authors would li ke to thank Professor Steve Turton and Dr Michael Liddell of James Cvok U UiV c.:! l:;i l..y whu lJ l u v id~u. t.h~ equipl1Hmt ll sed iu the experimental component of this work. The authors are also very grateful to Dr. Hank de Wit, of the Australian Bureau of Meteorology, for help wI th t he aeralogical diagram which accompanies this book. The support of the Queensland Sugar Research and Development Corporation is gratefully acknowledged .

xi

Contents

About the Authors vii

Preface ix

Acknowledgments xi

List of Figures xix

List of Tables xxv

Theoretical Foundations 1

1. The Big Picture 3

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 The Atmospheric Environment . . . . . . . . . . . . . . . 5

1.2.1 Composition of the Atmosphere . . . . . . . . . . 51.2.2 Vertical Structure of the Atmosphere . . . . . . . 71.2.3 The Horizontal Picture . . . . . . . . . . . . . . . 91.2.4 Water in the Atmosphere . . . . . . . . . . . . . . 9

1.3 Solar Radiation . . . . . . . . . . . . . . . . . . . . . . . . 111.3.1 Solar Constant . . . . . . . . . . . . . . . . . . . . 111.3.2 Radiative Equilibrium, Atmospheric Solar Energy

Budget . . . . . . . . . . . . . . . . . . . . . . . . 121.4 Estimation of Average Terrestrial Temperatures . . . . . . 121.5 Enhanced Greenhouse Effect . . . . . . . . . . . . . . . . 151.6 Problems for Chapter 1 . . . . . . . . . . . . . . . . . . . 16Problems for Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . 16

xiii

xiv Physical Principles of Meteorology and Environmental Physics

2. Atmospheric Thermodynamics and Stability 21

2.1 Equation of State of the Atmosphere . . . . . . . . . . . . 212.2 Atmospheric Thermodynamics . . . . . . . . . . . . . . . 232.3 Hydrostatic Equilibrium, Height Computations . . . . . . 282.4 Thermodynamic Diagrams . . . . . . . . . . . . . . . . . . 312.5 Examples on the Use of the F160 Diagram . . . . . . . . . 332.6 Lapse Rate and Stability, Adiabatic Lapse Rate . . . . . . 362.7 Saturated Adiabatic Lapse Rate . . . . . . . . . . . . . . 392.8 Stable Atmosphere, Brunt-Vaisala Frequency . . . . . . . 412.9 Model Atmospheres . . . . . . . . . . . . . . . . . . . . . 41

2.9.1 Homogeneous Atmosphere . . . . . . . . . . . . . 412.9.2 Isothermal Atmosphere . . . . . . . . . . . . . . . 422.9.3 Constant Lapse Rate Atmosphere . . . . . . . . . 42

Problems for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . 43

3. Air Flow on a Rotating Earth 47

3.1 Introduction, Equation of Motion . . . . . . . . . . . . . . 473.2 Decoupling of Vertical and Horizontal Motion . . . . . . . 513.3 Geostrophic Approximation . . . . . . . . . . . . . . . . . 523.4 Balanced Curved Flow: Natural Coordinates . . . . . . . 53

3.4.1 Acceleration in Natural Coordinates . . . . . . . . 533.4.2 Equation of Motion in Natural Coordinates . . . . 55

3.5 Inertial, Cyclostrophic and Gradient Flow . . . . . . . . . 563.5.1 Inertial Flow . . . . . . . . . . . . . . . . . . . . . 563.5.2 Cyclostrophic Flow . . . . . . . . . . . . . . . . . 573.5.3 Geostrophic Flow . . . . . . . . . . . . . . . . . . 583.5.4 Gradient Flow . . . . . . . . . . . . . . . . . . . . 583.5.5 Trajectories and Streamlines . . . . . . . . . . . . 60

3.6 Frictional Effects . . . . . . . . . . . . . . . . . . . . . . . 603.7 Vertical Variation of the Geostrophic Wind . . . . . . . . 62

3.7.1 Isobaric Coordinates . . . . . . . . . . . . . . . . 623.7.2 Wind Shear and Thermal Wind Equation . . . . . 643.7.3 Implications of the Equations . . . . . . . . . . . 65

Problems for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . 69

4. Divergence, Vorticity and Circulation 73

4.1 Equation of Continuity . . . . . . . . . . . . . . . . . . . . 734.2 Mechanism of Pressure Change . . . . . . . . . . . . . . . 75

Contents xv

4.3 Vorticity and Circulation Theorems . . . . . . . . . . . . 774.4 The Vorticity Equation and its Implications . . . . . . . . 794.5 Potential Vorticity . . . . . . . . . . . . . . . . . . . . . . 834.6 Further Comments on Vorticity . . . . . . . . . . . . . . . 844.7 Rossby Waves . . . . . . . . . . . . . . . . . . . . . . . . . 85Problems for Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . 87

5. Boundary Layer Meteorology 91

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 915.2 Turbulence in the Atmosphere . . . . . . . . . . . . . . . 915.3 Turbulent Balance Equation . . . . . . . . . . . . . . . . . 94

5.3.1 Momentum Balance (Equation of Motion) . . . . 965.3.2 Energy Balance . . . . . . . . . . . . . . . . . . . 965.3.3 Moisture Balance Equation . . . . . . . . . . . . . 96

5.4 Calculation of Vertical Flux; Flux-GradientRelationships . . . . . . . . . . . . . . . . . . . . . . . . . 97

5.5 Turbulent Transport Equations . . . . . . . . . . . . . . . 985.6 Surface Boundary Layer . . . . . . . . . . . . . . . . . . . 985.7 Momentum Flux, Vertical Wind Profile . . . . . . . . . . 995.8 Energy Fluxes at the Earth’s Surface . . . . . . . . . . . . 1035.9 Planetary Boundary Layer . . . . . . . . . . . . . . . . . . 107

5.9.1 Heat Transfer in the Planetary Boundary Layer . 1085.9.2 Wind in the Planetary Boundary Layer . . . . . . 1115.9.3 Dispersion of Pollutants from an Elevated Source 113

5.10 Richardson Number, Obukhov Length . . . . . . . . . . . 116Problems for Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . 118

6. Biometeorology, Environmental Biophysics 123

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1236.2 Metabolism, Maintenance of Body Temperature . . . . . . 1246.3 Molecular Versus Turbulent Transport . . . . . . . . . . . 1256.4 Modes of Heat Transfer . . . . . . . . . . . . . . . . . . . 128

6.4.1 Radiation . . . . . . . . . . . . . . . . . . . . . . . 1286.4.2 Convective Heat Transfer . . . . . . . . . . . . . . 1306.4.3 Evaporation, Latent Heat Exchange . . . . . . . . 1306.4.4 Heat Conduction . . . . . . . . . . . . . . . . . . 131

6.5 Summary of Formulae and Expression for Total Heat Loss 1336.6 The Importance of Latent Heat: Some Examples . . . . . 133

xvi Physical Principles of Meteorology and Environmental Physics

6.6.1 Energy Expended in Respiration . . . . . . . . . . 1346.6.2 Heat Loss from a New-Born Infant . . . . . . . . 136

6.7 Inside the Organism: When Heat Conductionis Important . . . . . . . . . . . . . . . . . . . . . . . . . . 1376.7.1 Temperature Rise in a Working Muscle . . . . . . 1376.7.2 Conduction and Convection . . . . . . . . . . . . 139

6.8 Transpiration in Plants . . . . . . . . . . . . . . . . . . . 1416.8.1 Resistance to Diffusion . . . . . . . . . . . . . . . 1416.8.2 Leaf Structure . . . . . . . . . . . . . . . . . . . . 1426.8.3 Diffusion from a Circular Orifice, Perforated Screen 1426.8.4 Transpiration from Leaves . . . . . . . . . . . . . 145

6.9 Flux Versus Temperature, Fact Versus Fiction . . . . . . . 146Problems for Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . 148

Experiments in the Tropical Boundary Layer 155

7. Introduction to the Experiments 157

7.1 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 1577.2 A Brief Survey of Eddy Correlation Measurements . . . . 161

7.2.1 Instrumentation . . . . . . . . . . . . . . . . . . . 1627.2.2 Topography, Vegetation and Geophysical

Variability . . . . . . . . . . . . . . . . . . . . . . 1647.3 Practical Considerations . . . . . . . . . . . . . . . . . . . 167

8. Approaches to Measurement of Net Ecosystem Exchange 169

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1698.2 Comparison of Flux Measurement Techniques . . . . . . . 170

8.2.1 Flux Gradient Methods . . . . . . . . . . . . . . . 1708.2.2 Eddy Correlation Methods . . . . . . . . . . . . . 170

8.3 Approaches to NEE Measurement . . . . . . . . . . . . . 1718.3.1 The Balance Equation . . . . . . . . . . . . . . . 1718.3.2 The Reynolds Approach . . . . . . . . . . . . . . 1728.3.3 The WPL Approach . . . . . . . . . . . . . . . . . 1738.3.4 The Lee Approach . . . . . . . . . . . . . . . . . . 1768.3.5 Reconciling the WPL and Lee Approaches . . . . 178

8.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

Contents xvii

9. Application of the WPL Method 183

9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1839.2 Coordinate Frames . . . . . . . . . . . . . . . . . . . . . . 183

9.2.1 General . . . . . . . . . . . . . . . . . . . . . . . . 1839.2.2 Coordinate Rotations . . . . . . . . . . . . . . . . 184

9.3 Fourier Analysis . . . . . . . . . . . . . . . . . . . . . . . 1869.4 Averaging Periods . . . . . . . . . . . . . . . . . . . . . . 1889.5 Sampling Rates . . . . . . . . . . . . . . . . . . . . . . . . 1909.6 Sensor Placement . . . . . . . . . . . . . . . . . . . . . . . 192

9.6.1 Sensor Height . . . . . . . . . . . . . . . . . . . . 1929.6.2 Sensor Separation, Flow Distortion and Path

Length Averaging . . . . . . . . . . . . . . . . . . 1929.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

10. Experimental Methods 195

10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 19510.2 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . 196

10.2.1 Sonic Anemometer . . . . . . . . . . . . . . . . . 19610.2.2 Infrared Gas Analyser (IRGA) . . . . . . . . . . . 19710.2.3 Datalogger . . . . . . . . . . . . . . . . . . . . . . 19710.2.4 Flux Measurement System . . . . . . . . . . . . . 197

10.3 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 19810.3.1 Sonic Anemometer . . . . . . . . . . . . . . . . . 19810.3.2 Infrared Gas Analyser . . . . . . . . . . . . . . . . 199

10.4 Processing Software . . . . . . . . . . . . . . . . . . . . . 20110.4.1 Fourier Analysis . . . . . . . . . . . . . . . . . . . 20110.4.2 Logger Program . . . . . . . . . . . . . . . . . . . 20310.4.3 Analysis Program . . . . . . . . . . . . . . . . . . 203

10.5 Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . 20610.6 Experimental Sites . . . . . . . . . . . . . . . . . . . . . . 20810.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

11. Results and Analysis 211

11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 21111.2 Time Series Analysis . . . . . . . . . . . . . . . . . . . . . 212

11.2.1 Rainforest . . . . . . . . . . . . . . . . . . . . . . 21211.2.2 Sugar Cane . . . . . . . . . . . . . . . . . . . . . . 21911.2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . 223

xviii Physical Principles of Meteorology and Environmental Physics

11.3 Effects of Averaging Period and Sampling RateVariations on Flux Measurements . . . . . . . . . . . . . . 22811.3.1 Averaging Periods . . . . . . . . . . . . . . . . . . 22811.3.2 Sampling Rates . . . . . . . . . . . . . . . . . . . 229

11.4 Fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23111.5 Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . 23911.6 Summary of Experimental Issues . . . . . . . . . . . . . . 23911.7 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . 24111.8 Recommendations for Further Study . . . . . . . . . . . . 242

11.8.1 Allowance for Convergence in the Horizontal Wind 24211.8.2 Energy Balance Closure . . . . . . . . . . . . . . . 24211.8.3 Transfer Functions . . . . . . . . . . . . . . . . . . 24211.8.4 Equipment Mounting . . . . . . . . . . . . . . . . 24311.8.5 Detrending . . . . . . . . . . . . . . . . . . . . . . 24311.8.6 Software . . . . . . . . . . . . . . . . . . . . . . . 243

Appendix A Some Useful Numerical Values 245

Appendix B Saturated Vapour Density and Pressure of H2O 247

Appendix C Vector Identities 249

Bibliography 251

References 255

Index 257

1.1

1.2

List of Figures

Schematic representation of the vertical temperature structure in the lowest 100 km of the atmosphere.

Schematic rcpl'c3cnto.tion of radia.tive cquil ibl'iUl'n in the Earth-atmosphere system .

1.3 Average solar radiation budget in the Earth-atmosphere system

1.4 Simplified model of radiative transfer processes in the J!1t. m ofi;phf;'l 'r,>

1.5 Schematic representation of the three possible radiative

8

12

13

1.3

equilibrium points for a model absorption coefficient a(T) 19

2.1 Schematic representation of adiabats and isotherms on a p - a diagram

2.2

2.3

Cartesian coordinate systems used in meteorology ..

Vertical column of air, showing forces acting on a slab

2.4 Graphical Il1Cthocl of determlOation of mean temperature of a layer from observed radioson de temperature trace

26 28

28

30

2.5 Acl iabats, isotherms and isobaric surface on an cmagram 32

2.6 rvlethod of calculation of thermodynamic parameters . 34

2.7 Method of calculation of lifting condensation level (LCL) and cloud hmghts for data shown in Table ~.1 ;)5

2.8 Schematic illustration of stabil ity in a simple mechanical system 36

2.9 Illustration of a rising air parcel and environmental lapse rate referred to in the text . . . . . . . 37

xix

xx Phystcal PrtnC1.ples of Meteorology and Envinmm,ental Physics

2.10 Four types of plume behaviour under various conditions of stability and instability. At left: broken lines, dry adiabatic lapse rate; full lines) existing lapse rates

2.11

3.1 3.2

Schematic representation of a turbulent eddy in the boundary layer .

Schematic illustration of Buys-Ballots law. Model of the Earth showing latitude measured positive in the northern hemisphere, and negative in the southern

45

46

48

hemi::iphcrc 40

3.3 Horizontal forces (x-di rection only shown) acting on an air pa.rcel 50

::iA 'file coord mate system describmg curved flow. 54 3.5 Calculation of 6.s . . 54 3.6 Inertial flow in both hemispheres 56 3.7 (i)R,>O,~<() (ii )R,<O. 57 3.8 Force balance in the four types of gradient flow: (a) regular

low, (h) rpgllbr hie;h, ((~) ::..nnm~.loll ~ low, (cl) nnon1::lJom; high 59

3.9 Balanced flow in the prcsence o[ friction . 61 3.10 Schematic representation of two isobaric surfaces in the

3.11

3.12

3.13

3.14

315 3.16 3.17 3.18

4. 1

4.2

4.3 4.4

verl.ica.l p la.ue .

Schematic representation of geostrophic fl ow in relation to height contours on an isoba,ric surface . . Vertical section of the atmosphere showing a layer of air bounded by two isobaric surfaces. Global mean "onal temperature distribution and vertical wind shear in the southern hemisphere . ... Horizontal cold a.ir advection and backing of wind with height

Diagrams for Worked Example Problem 3.1 Problem 3.4 Problem 3.6

A fluid element with horizontal cross section 6A Schematic representation of vertical columns of air showing successive zones of surface convergence and divergence . Frictional convergence in a northern hemisphere cyclone. Circulation around an arbitrary loop L

63

63

66

67

R7 68 69 70

71

73

76 77 77

4.5

4.6 4.7

4.8

4.9

5.1

List oJ Pigu'res

Solid body circulation at angular velocity w .

Spin of an element of the Earth's surface of area JA Anticyclonic circulation resulting from divergence Vertical cross section showing motion of a flu id e lement over a north-south. mountain ra.nge .

Clockwise rotation of a ::paddle wheel" in a shear flow

au/ay > a ..

Schematic representation of average wind flow near the surface

5.2 Schematic representation of turbulent eddy motIOn nea.r the

xxi

79 81 82

81

85

92

surface 93 5.3 Simple model of an eddy of dimension I . 93 5.4 Schematic representa.tion of the way in which Zo and u. are

determined from empirieal data (+) 101

5.5 r..1easurement of mean wincl versus height for yOll11g S1lgar cane. 102

5.6 Parti tioning of radiative energy fluxes for day and night 103 5.7 Sudace enerb,}r fl uxe~, da.y and night, with the energy balance

represented by RN = If + LE + G 104 5.8 Schematic representation of the (potential) temperature

variations in the atmospheric boundary layer over the course of a day . 109

5.9 The Ekrnan spiral, as given by (5.72), showing winds at tlu·ee heights . 113

5.10 Dispersion of pollutants from an elevated source in the pre<er",,, of o.n Aievet.en inver.ion At height. l . "1"14

5.11 Normalized concentration calculated from (5.76) for a low-level inversion 117

6.1 A living '(organism)) and S0111e forms of energy and matter exchange with its environment 124

6.2 Schernatic diagHWll showing how the body reacts to ovedH~at,-

ing in order to maintain body temperature at normal values 126

6.3 Linear temperature profile in slab geometry. 132 6.4 Simplified physieal model of the breathing process 134

6.5 Cylindrical model of a muscle. 137

6.6 Temperature as a function of radial distance in the cylindrical muscle . . . . . . . . . . 139

6.7 Heat fluxes before and after putting on clothing 140 (j.~ Equivalent circuit dia.gra.m for the situat ion shown in

Figure 6.7 . 141 6.9 Evaporation from a tube . . . . . . . . . . . 143 6.10 (a) As for Fig. G.9, with a perforated screen over the mouth

of the tube; and (b) details of the pores in the screen. 14<1 6.11 The equivalent circuit diagram for F igure 6.10 (see also

Problem 6.5) . . . . 144 6.12 Temperature profile in a two sub-layer system 149 6.13 Model of heat transfer botween a human and the environm ent 150

6. 14 Model of beat transfer in 1\ human limb . . . 151 6.15 Model of heat transfer through a layer of soil 152

7,1 The traditional method of obtaining data in the surface boundary layer is to attach in.struments at various heights UIl a. Luwer 158

7.2 Tethered balloon in fl ight 159 7.3 Tethered balloon at launch, showing instrument package 160 7.4 Acoustic sounder, located at Townsville on the north-cast

coast of tropical Austr!! li " (lati tude 190 13', South, longitude 1460 48', East) . ...... ......... 160

7.5 A typical acoustic sounder recording of the transition period from night to day (from Potts [14]) 161

9.1 Polar coordinate system . . . 185 9.2 ScI,ematic representation of aliasing of frequencies above the

NYfJ.lI i~t. frp.flll p.nr.y . 191

1.0.1 Campbell Scienti fi c CSAT3 sonic anemometer (head only) , phot.ogmph courtesy CA.mpbell Scientific Jnc. . . . . . . 195

10.2 LiCor LI7500 open path CO2 / H20 analyser (head and electronics box), photograph courtesy LiCor Inc. J 96

10.3 f..jxperimento.J setup s llgo.r cane . 198

10.4 Experimental setup - rainforest 199 10.5 Power system - Canopy Crane (note calibration gas visible in

background) . . . 200 10.6 Experimental sites 209

11.1 Vertical velocity amplitude spectnun for rainforest, 12am, day 78, 1hr @ 20Hz. 213

xxiii

11.2 Vertical velocity amplitude spectrum for rainforest , 12pm, day '(8, Ihr IQJ 20Hz . :11:;

11.3 Horizontal velocity amplitude spectrum for rainforest, 12am, day 78, 1 hr @ 20Hz . 214

11.4 Horizontal velocity amplitude spectrum for rainforest, 12pJ11,

day 78, Ihr @ 20Hz . 214 11.5 Vertical power spectrum for rainforest , 113m , day 75 , 3.8 days

@ Q.2Hz . 216

11.6 Horizontal velocity power spectrum for rainforest , 1 hun, day 75 , 3.8 days ~ 0.2Hz . 216

11.7 Vertical velocity weighted energy density spectrum for rain-forest, llam, day 75 , 3.8 days @ 0.2Hz 217

11.8 Horizontal velocity weighted energy density spectrum for rain-forest, lIaIn, day 75 , 3.8 days @ 0.2Hz 217

11.9 iVfp.an tp.mpp.n1tnrp. Anc! mp.f1n VariAn(~p. of 1IIT time serif'S ( five

minute means) , rainforest, day 78 . 218

11.10 I\'l ean temperature and mean variance of wPv time series (five miuut.e ulei:lusL J(;I.iufuJe:sL, t..lCl~ 78 . 218

11. 1.1 Mean tempora.ture and mean variance of WPc time series (five minute means) ) rainforest, day 78 220

11.12 [vlean variance of vertical wind and mean variance of wT time

series (five minute means), rainforest, day 78 . 220 11.13 Vert ical velocity amplitude spectrum for sugar cane, 12am ,

day 23, 1111' @ 20Hz . . . 221

11.14 Vertical velocity amplitude spectrum for sugar cane , 12pm, day 23, 1111' @ 20Hz 221

U .15 Horizontal velocity amplitude spectrum for sugar cane, 12alTl 1

day 23, Ihr @ 20Hz . . . . . 222 11. 16 Horizontal vclocitya.mplitude spectruIl1 for sugar cane, 12pm,

d,W 23, 1111' @ 20Hz 222

11.17 Vertical velocity power spectrum for sugar cane, 7am , day 21, 3.8 days @ 0.2Hz . . 224

11.18 Horizontal velocity power spectrum for sugar cane, 7am , day 21, 3.8 days @ Q.2Hz . . . . . . . . . . . . . 221

11.1 9 V/eighted vertical velocity energy density spectrum for sugar cane, ll am , day 21, 3.8 days @ Q.2Hz . 225

11.20 Weighted horizontal velocity energy density spectrum for sugar cane, Ilmn, day 21, 3.8 clays @ O.2Hz . 225

:-odv PhY~1cal Principlt!~ of Meteorology and E'I'11"jronmentcd PhY~1C~

11.21

11.22

11.23

11.24

11.25 11.26

11.27 1128 11.29 11.30 11.31 11.32 11 33 11.34 11.35 11 .36

Nlean temperature and mean variance of wT time series (five minute means) , sugar cane, day :lJ 220 :Mean temperature and mean variance of WPv time series (five minute means), sugar cane, da.y 23 . 226 JVlean temperature and mean variance of WPv time series (five minute means), sugar cane, day 23 227 :Mean variance of vertical wind and mean variance of wT time series (five minute means), sugar cane, day 23 227 CO2 Flux for various averaging periods (as marked) 228 CO2 Flux fOl" variouG n.vcro.oing poriod6 (as mtuked) 230 CO2 ["lux for various sampling rates (as marked) . 230 Eight clay mean sensible heat flux - rainforest 232 EIght clay mean uncorrected latent heat flux - rainforest 232 Eight day mean corrected latent heat flux - rainforest 233 Eight day mean uncorrected CO2 flux - rainforest 233 Eight day mean corrected CO2 flux - rainforest 234 Eight day mean WPL correction to the CO2 flux - rainforest 234 Eight day lIlean sensible heat flux - sugar cane 235 Eight day mean uncorrected latent heat flux - sugar cane 235 Eight day mean corrected latent heat flux - sugar cane 236

11.37 Eight day mean Ul1con'f:'ctf-Jri CO2 A.ux - ~ugar ('.l:1t1e 2:1fi

11.38 Eight day lIlean corrected CO2 fl ux - sugar cane 237 11.39 Eight day mean WPL correction to the CO2 flux - sugar cane 237

B.I Saturated vapour density (p,) and saturated vapour pressure (e,) for water. 247

List of Tables

1.1 Various length scales encountered in physical systems 4 1'. 2 Ivlru:;~ aud energy in the Earth-atmosphere system 4 1.3 Composition of dry air below ~80 km 6

2.1 Rudiu::;uLHJe data. at Town~ville on 20.4 ,74 at 0900 34

2.2 Stability cri teria for saturated and unsaturated air 39

3.1 The varluu~ alluwecl t)ulutions of (3.34) fo J' the northern henlt-

sphere f > 0 59

::i . 1 'I'ypit..:<d VttlUeiS ur ruuglllleiSs length and friction velocity 101

6.1 Representative values for emissivity 129

11.1 Peak CO2 f1tLX value for varying averaging periods (polyno-mial fit to data, day 23) . . 229

11.2 S Ul111Ui:tlY vJ' n;iSul~iS uf uigll L-da,y lIleaIl flux 1llI;;l:;I.:ju re11leut.s uver

rainforest and sugar cane . . 231

D.l StLtLU at.eci vupo ur ul:;:u:;iLy (Ps) awl tii::l.LuraLetl vtl(Juur pre.s.sun:l

(e s ) for water 247

xxv