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Download The A STUDY OF.THE ENERGY BALANCE OF A DOUGLAS-FIR FOREST by KEITH G. McNAUGHTON B.Sc. (Hons.)} Monash University, 1966 B.A., Monash University, 1969 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of SOIL SCIENCE We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA February 1974 In presenting this thesis in partial fulfilment of the require• ments for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. KEITH G. McNAUGHTON Department of Soil Science The University of British Columbia Vancouver 8, Canada Date ABSTRACT This thesis is in the form of four self contained papers that report aspects of a study of the energy balance of a young Douglas-fir forest growing at the University of British Columbia Research Forest at Haney, B.C. The chapters discuss the experimen• tal methods used and special instrumentation developed, the data analysis, and some attempts to understand the relationships observed by employing simple forest models and ideas on boundary layer equilibration processes. Chapter 1. The psychrometric apparatus design for Bowen ratio determination reported by Sargeant and Tanner was modified and a new apparatus built. Modification of the intake design improved the symmetry and rigidity of the sensor mounting. Wet and dry bulb differences were measured with an error less than 0.01°C over a vertical distance of 1 meter. Continuous measurements of the Bowen ratio over a 7.8-meter Douglas-fir forest were made for 6 weeks. An example of the energy balance for the forest for 1 day using this equipment is reported. Chapter 2. Daily evapotranspiration from a Douglas-fir forest was calculated using Webb's average Bowen ratio method. Webb's method is generalized to include the effects of the diabatic wind profile. Over a 17-day period characterized by light winds, the modified Webb iii method agreed with the daily totals of half-hour energy balance calculations to within 1 1/2% on the average, while Webb's method overestimated by 26% on the average. Chapter 3. Energy balance measurements of evapotranspiration from a young Douglas-fir forest are reported for a period of 18 days in July 1970 when soil water was not limiting. Peak daily evapotranspir• ation rates characteristically occurred two to three hours after solar noon and evaoptranspiration showed a short-term independence from net radiation. This behaviour is interpreted as being a consequence of the large forest roughness. Daily evapotranspiration and net radiation were, however, well correlated. Values of surface diffusion resistance calculated from Monteith's combination formula are presented. Daytime values showed significant day-to-day differences and an attempt to define a potential evapotranspiration rate assuming a constant daytime surface resistance was not successful. Comparison of evapotranspiration measurements with a potential evaporation formula for wet surfaces developed by Priestley and Taylor suggests that evaporation of intercepted water proceeds 20% more rapidly than evapotranspiration from the non-wetted canopy. Chapter 4. The process of modification of the Bowen ratio, with distance downwind of a change in surface wetness, is considered with the view to establishing the final equilibrium ratio of the fluxes of sensible and latent heat after advective effects become negligible. A method of generating, from the coupled equations for heat and vapour diffusion, two new diffusion equations in composite variables, iv which may be solved independently, is developed. The method leads to the conclusions that there is a basic difference between equilibration over land and over water. Also the rate of equilibration depends strongly on atmospheric mixing and hence surface roughness and atmospheric stability. It is concluded that, for terrestial surfaces, the equilibrium evaporation rate is approximated by LE = (r^r)(Rn - G) for 24 hour periods. This result is in accord with some recent experimental findings. V TABLE OF CONTENTS Page ABSTRACT 11 LIST OF TABLES vii LIST OF FIGURES viii ACKNOWLEDGEMENTS x INTRODUCTION 1 CHAPTER 1 - PSYCHROMETRIC APPARATUS FOR BOWEN RATIO DETERMINATION OVER FORESTS 4 Abstract 5 1. Introduction 5 2. Sensors and Measurement Circuit 6 3. Sensing Heads 7 4. Performance and Evaluation 11 References 20 CHAPTER 2 - AVERAGE BOWEN-RATIO METHODS OF CALCULATING EVAPOTRANSPI RATION APPLIED TO A DOUGLAS- FIR FOREST 21 Abstract 22 1. Introduction 22 2. Symbols and Units 23 3. Theory 24 4. Methods and Results 30 4.1 Method for Calculating 30 4.2 Comparison of Evapotranspiration Estimates. 32 vi Page 5. Discussion 36 6. Conclusion 38 References 39 CHAPTER 3 - A STUDY OF EVAPOTRANSPIRATION FROM A DOUGLAS- FIR FOREST USING THE ENERGY BALANCE APPROACH ... 41 Abstract 42 1. Introduction 43 2. Symbols and Units 43 3. Monteith's Equation . 45 4. Surface and Aerodynamic Resistances 46 5. Experimental Site 50 6. Results and Discussion 51 6.1 Energy Balance 51 6.2 Surface Resistance 59 6.3 Potential Evapotranspiration Estimates ... 62 7. Conclusions 70 References 72 CHAPTER 4 - EQUILIBRIUM EVAPORATION 76 Abstract 77 1. Introduction 78 2. Symbols and Units 80 3. Theory 81 4. Discussion 93 References 96 LIST OF TABLES Table Page CHAPTER II 1. Dependence of the Integrated Diabatic Influence Function $ on the Richardson Number, Ri (From Lettau, 1962) 29 2. Daily Estimates of Evapotranspiration (mm) from an 11-Year Old, 7.8-Meter High Douglas Fir Plantation at U.B.C. Research Forest, Haney, B.C. in the Summer of 1970. G5/(l+3) Must be Sub• tracted from the Modified Webb Method Estimates to Correct for Net Daily Soil Heat Flux at the 5-cm Depth 34 CHAPTER III 1. Summary of Daily Evapotranspiration Data from a Douglas Fir Forest at the U.B.C. Research Forest, Haney B.C 64 vii i LIST OF FIGURES Figure Page CHAPTER I 1. Measurement circuit used in the psychrometric apparatus for Bowen ratio determination. All fixed resistors are low temperature coefficient metal film type. The IK resistors are matched to 0.2% . 8 2. Sensing head design. The second head is a mirror image of the head illustrated 9 3. Sensing head with the trapdoor displayed to show the mounting of the diode sensors and wicking system 10 4. Apparatus in position above the Douglas-fir forest. Reversing motor and air tube for aspiration can be seen 12 5. Typical traces of dry bulb and wet bulb differ• ences over 1 meter (AT,_ and ATW) obtained with the psychrometric apparatus. Diode sensitivity is 2.25 mv C-l 14 6. Example of the measured dry and wet bulb differ• ences and the calculated Bowen ratios 15 7. Daytime Bowen ratios on an expanded scale. The vapour pressure differences over 1 meter are calculated from the wet and dry bulb differences shown in Figure 6 and measured absolute wet bulb temperatures 16 8. Energy balance diagram for July 14,1970. The anomalous behaviour of the calculated sensible and latent heat flux densities of 2030 h is due to a Bowen ratio near -1 17 Figure Page CHAPTER II 1. Daily evapotranspiration from a Douglas-fir forest calculated by the Webb, modified Webb and aerodynamic methods compared with half- hour energy balance/Bowen ratio measurements 35 CHAPTER III 1. Energy balance diagram for a day with variable net radiation. The latent heat flux density is largely independent of the short term changes in net radiation. The Bowen ratio at 1900 PST was -0.97 54 2. Daytime trends of meteorological parameters and (A-D) the derived surface diffusion resistance of a 7.8-m high Douglas-fir forest at Haney, B.C. The free evaporation rate is shown as the equiva• lent latent heat flux density. Erratic values of the sensible and latent heat flux and consequently the surface resistance near 1800 PST are due to Bowen ratios near -1 at those times 55-58 3. Comparison of calculated 24-hour evapotranspiration values assuming constant daytime surface resistance of 75 s m"l with measured values. Broken lines represent 10% deviation from the 1:1 line 66 4. Measured daily values of evapotranspiration 1 s compared with j- ($ + y)(Rn - G). Data for July 21 and July 25, when rain fell, are shown as triangles and have not been used to determine the line of best fit. The available energy, Rn - G,is expressed as an equivalent depth of water evaporated 69 X ACKNOWLEDGEMENTS I am greatly indebted to my supervisor, Dr. T.A. Black, for whatever success I have achieved in this study. The value of his guidance, assistance and friendship throughout the period of my doctoral studies cannot be underestimated. I am also indebted to Drs. T.M. Ballard, T.R. Oke, C.A. Rowles and J. DeVries, who served on my doctoral committee, and who have given advice and encouragement at all stages of this work. The assistance of Mr. John Walters, Director of the U.B.C. Research Forest, and his staff during the experimental phase of this work is gratefully acknowledged. A particular debt of gratitude is owed to President Walter H. Gage,who, in his capacity as Director of Inter-Faculty and Student Affairs, provided financial assistance for my wife and son to travel to Australia and visit my mother before she died. Finally I wish to thank my fellow graduate students and faculty members of the department of Soil Science who have helped me in countless ways and provided a pleasant and stimulating environment in which to work.
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