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Suburban evapotranspiration estimates in Vancouver from energy balance measurements Kalanda, Brian Douglas 1979

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SUBURBAN EVAPOTRANSPIRATION ESTIMATES IN VANCOUVER FROM ENERGY BALANCE MEASUREMENTS by BRIAN DOUGLAS KALANDA B. Sc., McMaster U n i v e r s i t y , 1976 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Dept. of Geography) We accept t h i s t h e s i s as conforming to the req u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA J u l y , 1979 (c) B r i a n Douglas Kalanda I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 W e s b r o o k P l a c e V a n c o u v e r , C a n a d a V6T 1W5 • E - 6 B P 7 5 - 5 1 1 E ABSTRACT This study i s concerned w i t h the energy balance of a suburban area of south c e n t r a l Vancouver and i n p a r t i c u l a r w i t h the r o l e of evapo-t r a n s p i r a t i o n i n t h i s balance. In the l a t e summer - e a r l y f a l l of 1977 a measurement program was conducted to determine the energy balance components us i n g the Bowen r a t i o - energy balance approach. The Bowen r a t i o was obtained from d i f f e r e n t i a l psychrometric measurements taken above mean r o o f - l e v e l . Net r a d i a t i o n was measured d i r e c t l y and the vo l u m e t r i c heat storage was parameterized i n terms of net r a d i a t i o n . The r e s u l t s i n d i c a t e that the Bowen r a t i o - energy balance approach i s a p p l i c a b l e to suburban environments. An e r r o r a n a l y s i s developed f o r the r e v e r s i n g psychrometer system i n d i c a t e s that the e r r o r s i n the tu r b u l e n t f l u x e s were t y p i c a l l y 10 - 20%. The t u r b u l e n t l a t e n t heat f l u x was always a s i g n i f i c a n t and o f t e n the dominant energy s i n k f o r t h i s ' s u r f a c e 1 . This i s shown to be l a r g e l y due to s o i l moisture replenishment by p r e c i p i t a t i o n and i r r i g a t i o n ( e s p e c i a l l y lawn s p r i n k l i n g ) . The tu r b u l e n t f l u x e s tended to be in-phase w i t h net r a d i a t i o n during the day. This appears to be a r e s u l t of the decreasing importance of n o n - r a d i a t i v e c o n t r o l s ( e s p e c i a l l y the vapour pressure d e f i c i t ) on e v a p o t r a n s p i r a t i o n as the land use changes from r u r a l to h e a v i l y urbanized. Sustained periods of p o s i t i v e t u r b u l e n t f l u x e s were recorded at n i g h t , however the Bowen r a t i o was predominantly negative i n d i c a t i n g that only one tu r b u l e n t f l u x was p o s i t i v e . The data do not r e v e a l any dependence on wind d i r e c t i o n . The i n f l u e n c e ( i f any) of the i i i sea breeze could not be i s o l a t e d . The e q u i l i b r i u m e v a p o t r a n s p i r a t i o n r a t e o f t e n c l o s e l y approximated the measured e v a p o t r a n s p i r a t i o n . i v ACKNOWLEDGEMENTS I would l i k e to express my most s i n c e r e a p p r e c i a t i o n to my supervisor Dr. T.R. Oke f o r h i s support i n a l l f a c e t s of t h i s study. H i s encouragement and advice c o n t r i b u t e d g r e a t l y to t h i s research. I would a l s o l i k e to thank the other members of my committee Dr. T.A. Black and Dr. J.E. Hay f o r t h e i r h e l p f u l advice. My g r a t i t u d e a l s o extends to my f r i e n d s and collegues who have f r e e l y given me t h e i r time on many occasions. I am deeply indebted to Dr. T.A. Black, Mr. D. S p i t t l e h o u s e and Mr. P. Wong f o r the c o n s t r u c t i o n of the r e v e r s i n g psychrometer system. S p e c i a l thanks to the B.C. Hydro and Power A u t h o r i t y f o r the use of the Mainwaring Substation as the urban s i t e and Mr. B. E t t i n g e r f o r p r o v i d i n g the r u r a l s i t e . I am very g r a t e f u l to Mr. D. Steyn f o r h i s e x c e l l e n t a s s i s t a n c e i n the pre p a r a t i o n of t h i s study. F i n a l l y I would l i k e to thank my f a m i l y f o r the opportunity to pursue my education. V TABLE OF CONTENTS Page ABSTRACT i i ACKNOWLEDGEMENTS i v TABLE OF CONTENTS v LIST OF ILLUSTRATIONS v i i i LIST OF TABLES X CHAPTER ONE - INTRODUCTION 1 1.1 Review of Energy Balance Framework 4 1.2 Present State of Knowledge 7 1.3 Approaches Toward E v a l u a t i n g E v a p o t r a n s p i r a t i o n 12 1.4 S i t e C onsideration and S e l e c t i o n 18 1.5 Objectives 20 CHAPTER TWO - DETAILS OF IMPLEMENTATION - SITES AND 21 INSTRUMENTATION 2.1 Suburban S i t e and Surroundings 21 2.2 Instrumentation and Data Processing 25 .1 Net all-wave r a d i a t i o n f l u x d e n s i t y 25 .2 A i r temperature and humidity d i f f e r e n c e s 27 .3 A d d i t i o n a l measurements 33 2.3 R u r a l S i t e 34 2.4 Instrumentation and Data Processing 34 .1 Net all-wave r a d i a t i o n f l u x d e n s i t y 34 .2 Change i n v o l u m e t r i c heat storage 36 v i Page .3 Sensible heat f l u x d e n s i t y 36 .4 Temperature and humidity d i f f e r e n c e s 37 CHAPTER THREE - EVALUATION OF THE BOWEN RATIO - ENERGY BALANCE APPROACH IN AN URBAN ENVIRONMENT 38 3.1 Rur a l Intercomparison Experiment 39 3.2 Determination of Volumetric Heat Storage 40 3.3 Bowen Ra t i o - Energy Balance E r r o r A n a l y s i s 48 CHAPTER FOUR - BOWEN RATIO - ENERGY BALANCE RESULTS 57 4.1 General Energy Balance R e s u l t s 57 4.2 V a r i a b i l i t y i n the Turbulent Energy P a r t i t i o n i n g due to S e c t o r a l D i f f e r e n c e s and N o n - S t a t i o n a r i t y 64 .1 E f f e c t s of changes i n wind d i r e c t i o n 64 .2 E f f e c t s of land-sea breeze c i r c u l a t i o n 67 4.3 Magnitude and D i u r n a l P a t t e r n of the Sensible and Latent Heat Flu x D e n s i t i e s 70 .1 Daytime patterns i n the s e n s i b l e and l a t e n t heat f l u x d e n s i t i e s 70 .2 Magnitude and d i r e c t i o n of n o c t u r n a l s e n s i b l e and l a t e n t heat f l u x d e n s i t i e s 77 4.4 E v a p o t r a n s p i r a t i o n and Suburban Water Use 80 CHAPTER FIVE - MODELLING DAYTIME EVAPOTRANSPIRATION 88 5.1 I n t r o d u c t i o n 88 .1 E q u i l i b r i u m e v a p o t r a n s p i r a t i o n 89 .2 P o t e n t i a l e v a p o t r a n s p i r a t i o n 90 5.2 Results 92 .1 E q u i l i b r i u m and measured e v a p o t r a n s p i r a t i o n 92 .2 P o t e n t i a l e v a p o t r a n s p i r a t i o n 102 CHAPTER SIX - CONCLUSIONS 105 v i i Page REFERENCES 107 APPENDIX ONE - NOTATION 114 APPENDIX TWO - BOWEN RATIO - ENERGY BALANCE ERROR ANALYSIS 118 v i i i LIST OF ILLUSTRATIONS Page 1.1 Schematic d e p i c t i o n of the f l u x e s i n v o l v e d i n the water balance of an urban b u i l d i n g - a i r volume. 2 1.2 Schematic d e p i c t i o n of the f l u x e s i n v o l v e d i n the energy balance of an urban - b u i l d i n g a i r volume. 5 1.3 The greater Vancouver area. 10 2.1 Plan-view of the Sunset s i t e 22 2.2 View l o o k i n g west from top of tower. 23 2.3 West - east c r o s s - s e c t i o n of s i t e . 26 2.4 Side- and plan-views of instrumentation l e v e l s . 28 2.5 C r o s s - s e c t i o n through long a x i s of sensing head. 30 2.6 Photograph of Thermometer Interchange System. 30 2.7 A s p i r a t i o n pathway. 31 2.8 Plan-view of r u r a l s i t e . 35 3.1 Comparison of hourly average Q using yaw sphere -thermometer (YST) and Bowen r a t i o (3) approaches. 41 3.2 Bowen r a t i o - energy balance e r r o r a n a l y s i s (T = 288 K). 51 3.3 Bowen r a t i o - energy balance e r r o r a n a l y s i s (T = 283 K). 52 3.4 Example of suburban energy balance showing t y p i c a l e r r o r s i n t u r b u l e n t f l u x e s . 55 4.1 Examples of d i u r n a l p a t t e r n of suburban energy balance. 59 4.2 D i u r n a l v a r i a t i o n of $ f o r Sunset s i t e . 63 4.3 Daytime p a t t e r n i n energy balance components on days w i t h f a i r l y constant wind d i r e c t i o n . 66 4.4 Comparison of daytime p a t t e r n i n energy balance components on sea breeze (a - c) and non-sea breeze (d - f ) days. 69 IX Page 4.5 Example energy balances where lagged behind the decrease i n Q* i n the afternoon i n Vancouver (Fairview) (Yap and Oke, 1974) and St. L o u i s , Mo. (Ching, et a l . , 1978). 71 4.6 Daytime patterns of w i t h aysmmetry (a, b ) ; without aysmmetry (c, d). 73 4.7 Daytime p a t t e r n of Q„ and vapour pressure d e f i c i t . 74 Ej 4.8 An example where lags behind the decrease i n Q* a f t e r mid-day over a f o r e s t . 75 4.9 Examples of suburban n o c t u r n a l energy balances. 79 4.10 Energy balance components during a suburban Drying p e r i o d . 81 4.11 Water demand hydrographs f o r a r e s i d e n t i a l area of Vancouver, 1971. 84 4.12 Greater Vancouver Water D i s t r i c t water use, 1977. 85 5.1 Suburban Drying P e r i o d 1 (August 28 - September 1, September 5, 1977). 95 5.2 Hourly v a r i a t i o n of a' during Drying P e r i o d 1. 96 5.3 Suburban Drying P e r i o d 2 (September 8 - September 14, 1977). 98 5.4 P r e c i p i t a t i o n and a' r e l a t e d to Drying Periods 1 and 2. 99 5.5 Hourly v a r i a t i o n of a' during Drying Period 2. 100 5.6 Daytime comparison of measured and e q u i l i b r i u m (Q and Qg-, r e s p e c t i v e l y ) e v a p o t r a n s p i r a t i o n r a t e s and the hourly trend i n a' at the Sunset s i t e during p o t e n t i a l c o n d i t i o n s . 103 LIST OF TABLES Page 2.1 Aerodynamic Displacement Height (d) and Roughness Length ( Z Q ) Estimates Using Three Approaches. 24 3.1 D e s c r i p t i o n of M e t r o p o l i t a n Land Use Categories. 44 3.2 Percentage A r e a l Land Use Coverage f o r 16 Sectors Centred on the Sunset Experimental S i t e . 45 3.3 Derived R e l a t i o n s h i p s Between Net all-wave R a d i a t i o n (Q*) and Volumetric Heat Storage (AQ ). 46 4.1 Turbulent Energy P a r t i t i o n i n g - Daytime T o t a l s . 61 5.1 Comparison of Measured (CO and E q u i l i b r i u m (Q^ f-,) Model Daytime T o t a l E v a p o t r a n s p i r a t i o n . 93 CHAPTER ONE INTRODUCTION I t i s recognized that u r b a n i z a t i o n modifies the surface energy and water balance. However, there remains only a rudimentary under-standing of the energetic and c l i m a t i c i m p l i c a t i o n s of these changes. The need f o r such i n f o r m a t i o n a r i s e s from a d e s i r e to gain i n s i g h t i n t o the complex exchange processes present and t h e i r r o l e i n generating urban c l i m a t e s , and to provide input data f o r numerical models of the urban atmosphere. This study i s c e n t r a l l y concerned w i t h an examination of the r o l e of e v a p o t r a n s p i r a t i o n i n an urban area. To date, the changes i n evapo-t r a n s p i r a t i o n induced by u r b a n i z a t i o n remain e s s e n t i a l l y unresolved. E v a p o t r a n s p i r a t i o n can be discussed i n both a water balance and an energy balance framework. The water balance of an urban area i s the balance between i t s water inputs ( p r e c i p i t a t i o n ( P ) , water re l e a s e d by combustion ( F ) , and water piped i n ( I ) ) and outputs (runoff (Ar) , evapo-t r a n s p i r a t i o n ( E ) , net ground storage (AS) and net moisture advected t o / from the urban system (AA)) ( F i g . 1.1). The two anthropogenic sources (water released by combustion and water piped in) may have many p o s s i b l e i n f l a e n c e s on the a i r and surface moisture balances. For example, the water released by combustion has been shown to be r e s p o n s i b l e f o r i c e -fog development when temperatures are below -30 °C (e.g. Hage, 1972). This source may a l s o p a r t l y be r e s p o n s i b l e f o r the night-time humidity excess i n the c i t y (e.g. Hage, 1975). In urban areas where i r r i g a t i o n 1 2 Figure 1.1 : Schematic d e p i c t i o n of the f l u x e s i n v o l v e d i n the water balance of an urban b u i l d i n g - a i r volume, ( a f t e r Oke, 1978a) 3 ( s p r i n k l i n g ) i s important, one may f i n d higher s o i l moisture l e v e l s compared to r u r a l counterparts. The i n t r o d u c t i o n of impervious surfaces leads to two changes i n the output terms. F i r s t l y , the amount of runoff i s increased by the low i n f i l t r a t i o n c a p a c i t y of urban m a t e r i a l s . Secondly, si n c e these urban m a t e r i a l s p a r t i a l l y or competely replace v e g e t a t i o n one can expect e v a p o t r a n s p i r a t i o n to be reduced or even e l i m i n a t e d at these l o c a t i o n s . The few e v a p o t r a n s p i r a t i o n measurements a v a i l a b l e tend to support t h i s view (Oke, 1978a). One of the p r i n c i p a l problems i n implementing the water balance approach i s how to a c c u r a t e l y measure/estimate the components, e s p e c i a l l y e v a p o t r a n s p i r a t i o n . L'vovich and Chernogayeva (1977) used t h i s approach to approximate annual e v a p o t r a n s p i r a t i o n i n Moscow as the d i f f e r e n c e between p r e c i p i t a t i o n and r u n o f f . Greenland (1977) a l s o used t h i s approximation f o r h i s study of southern Ontario. The e r r o r s a s s o c i a t e d w i t h t h i s approach even on an annual b a s i s are probably l a r g e . On s h o r t e r time s c a l e s the e r r o r s could exceed the magnitude of the components them-s e l v e s . In f a c t , none of the components can be a c c u r a t e l y estimated on a short-time b a s i s . Problems i n c l u d e the s p a t i a l and temporal v a r i a t i o n i n p r e c i p i t a t i o n , ungauged leakage from storm sewers and water p i p e s , u n c e r t a i n t i e s i n e s t i m a t i n g ground water residence times, e t c . To date a complete urban water balance has not been assessed, nor i s there any i n d i c a t i o n that t h i s can be accomplished i n the near f u t u r e . The surface energy balance can be considered as the p a r t i t i o n i n g of the net r a d i a n t energy at the surface i n t o conductive and conve^ctive ( s e n s i b l e and l a t e n t ) flows of energy. The l a t e n t heat f l u x i s the energy equivalent of e v a p o t r a n s p i r a t i o n . This framework has been s u c e s s f u l l y used to provide both short - ( h a l f hour or l e s s ) and l o n g - term q u a n t i t a t i v e 4 data i n both n a t u r a l and urban environments (Yap and Oke, 1974; Ching, et a l . , 1978) and can provide the informa t i o n necessary to s a t i s f y the needs o u t l i n e d above. Thus the energy balance framework was s e l e c t e d f o r t h i s i n v e s t i g a t i o n . 1.1) Review of Energy Balance Framework The complexity of the urban/atmosphere i n t e r f a c e poses some problems i n formulating and c l o s i n g a 'surface' energy balance. For the purposes of t h i s study the urban 'surface' w i l l be defined as a datum l o c a t e d at about mean r o o f - l e v e l (plane ABCD i n F i g . 1.2). Borrowing terminology used i n n a t u r a l v e g e t a t i o n s t u d i e s the l a y e r s above and below the plane ABCD are r e f e r r e d to as the urban boundary l a y e r and urban canopy l a y e r r e s p e c t i v e l y (Oke, 1976). The energy budget f o r the volume below the plane ABCD extending to a depth where s i g n i f i c a n t v e r t i c a l exchanges are absent, can be expressed as an equivalent surface balance by: Q* + Q p = Q E + A Q S + A Q A (W m"2) (1.1) where Q* - net all-wave r a d i a t i o n f l u x d e n s i t y ; Q - anthropogenic heat r f l u x d e n s i t y ; Q and Q - turbu l e n t s e n s i b l e and l a t e n t heat f l u x d e n s i t i e s , H E r e s p e c t i v e l y ; A Q - change i n heat stored i n the volume per u n i t surface area and A Q ^ - net energy ( s e n s i b l e and l a t e n t ) advected i n t o or out of the volume per u n i t surface area. Non-radiative f l u x e s d i r e c t e d away from the 'surface' are considered p o s i t i v e . Anthropogenic heat (Q„) i s an energy source unique to the urban F environment, being that released by the combustion processes a s s o c i a t e d w i t h domestic, i n d u s t r i a l and t r a n s p o r t a t i o n a c t i v i t i e s . Yap (1973) 4 data i n both n a t u r a l and urban environments (Yap and Oke, 1974; Ching, et a l . , 1978) and can provide the in f o r m a t i o n necessary to s a t i s f y the needs o u t l i n e d above. Thus the energy balance framework was s e l e c t e d f o r t h i s i n v e s t i g a t i o n . 1.1) Review of Energy Balance Framework The complexity of the urban/atmosphere i n t e r f a c e poses some problems i n for m u l a t i n g and c l o s i n g a 'surface' energy balance. For the purposes of t h i s study the urban 'surface' w i l l be defined as a datum lo c a t e d at about mean r o o f - l e v e l (plane ABCD i n F i g . 1.2). Borrowing terminology used i n n a t u r a l v e g e t a t i o n s t u d i e s the l a y e r s above and below the plane ABCD are r e f e r r e d to as the urban boundary l a y e r and urban canopy l a y e r r e s p e c t i v e l y (Oke, 1976). The energy budget f o r the volume below the plane ABCD extending to a depth where s i g n i f i c a n t v e r t i c a l exchanges are absent, can be expressed as an equivalent surface balance by: Q* + Q p = Q £ + AQ S + AQ A (W m"2) (1.1) where Q* - net all-wave r a d i a t i o n f l u x d e n s i t y ; Q - anthropogenic heat F f l u x d e n s i t y ; Q u and Q - turbu l e n t s e n s i b l e and l a t e n t heat f l u x d e n s i t i e s , rl E r e s p e c t i v e l y ; AQ - change i n heat stored i n the volume per u n i t surface area and AQ - net energy ( s e n s i b l e and l a t e n t ) advected i n t o or out of the volume per u n i t surface area. Non-radiative f l u x e s d i r e c t e d away from the 'surface' are considered p o s i t i v e . Anthropogenic heat (Q ) i s an energy source unique to the urban F environment, being that r e l e a s e d by the combustion processes a s s o c i a t e d w i t h domestic, i n d u s t r i a l and t r a n s p o r t a t i o n a c t i v i t i e s . Yap (1973) 5 Figure 1.2 : Schematic d e p i c t i o n of the f l u x e s i n v o l v e d i n the energy balance of an urban b u i l d i n g - a i r volume. The e f f e c t i v e surface i s shown by plane ABCD. ( a f t e r Oke, 1978a) 6 c a l c u l a t e d Q f o r the C i t y of Vancouver using the procedure o u t l i n e d by r Bach (1970). Using a 1970 f u e l i n v e n t o r y , the aggregate values were -2 -2 15 W m and 23 W m f o r summer and w i n t e r , r e s p e c t i v e l y . As the present study was conducted i n l a t e summer - e a r l y f a l l , a value between the above r e s u l t s should be r e p r e s e n t a t i v e of the whole c i t y . Such a value i s s u f f i c i e n t l y s m a l l r e l a t i v e to the magnitudes of the other terms i n (1.1) that i t may be tempting to ignore i t . However i t must be remembered that l a r g e r Q values may be found i n l o c a l i z e d areas, or over sh o r t e r time r periods and that Yap's r e s u l t s may not be r e p r e s e n t a t i v e of c o n d i t i o n s i n 1977. On the other hand i t can be argued that i f a l l other terms i n (1.1) are evaluated by measurement the anthropogenic heat inputs to the atmosphere w i l l be in c l u d e d . F o l l o w i n g t h i s argument e x p l i c i t treatment of Q i s neglected i n t h i s study, but i t should be appreciated that t h i s r r e s u l t s i n an urban energy budget which cannot be broken down i n t o a l l of the components of (1.1) because a l l terms may i n c l u d e some heat flow due to QF. The change i n heat storage (AQ ) of n a t u r a l v e g e t a t i o n systems i s normally d i v i d e d i n t o two components: the heat f l u x d e n s i t y at the s o i l surface and the heat stored i n the l a y e r of biomass and a i r l y i n g between the ground and the measuring height. Since the l a t t e r term i s o f t e n very s m a l l , AQg can be approximated by the s o i l surface heat f l u x d e n s i t y alone. In the urban environment, the a d d i t i o n a l heat exchanges w i t h i n and between b u i l d i n g s ( w a l l s and r o o f s ) , t r e e s , roads, e t c . , must a l s o be considered. This r e q u i r e s a c o n s i d e r a t i o n of energy flows i n t o and/or out of v e r t i c a l , h o r i z o n t a l and i n c l i n e d s u r f a c e s , any combination of which may be i r r a d i a t e d d i r e c t l y by the sun w h i l e others are i n shade. S i m i l a r l y because of the complex mosaic of urban surface m a t e r i a l s and 7 t h e i r geometric c o n f i g u r a t i o n , the number of surfaces r e q u i r i n g consider-a t i o n becomes very l a r g e . These complications make d i r e c t measurement of A Q very d i f f i c u l t . A d i s c u s s i o n of the approach taken to determine A Q O b i n t h i s study i s presented i n Chapter 3. Advection ( A Q ) i s the h o r i z o n t a l t r a n s f e r of heat which occurs when a i r moves across h o r i z o n t a l g r adients of temperature and humidity. The s p a t i a l v a r i a b i l i t y i n the r a d i a t i v e , thermal, moisture and aero-dynamic p r o p e r t i e s of the urban 'surface' d i c t a t e s that micro-scale and probably l a r g e r s c a l e advection i s an important feature of urban areas, e s p e c i a l l y below the plane ABCD ( F i g . 1.2). However t h i s study i s concerned w i t h a r e a l f l u x estimates obtained i n the urban boundary l a y e r and theref o r e w i t h advection above the canopy zone ( i . e . the plane ABCD). The measures taken to minimize the e f f e c t s of advection upon f l u x e v a l u -a t i o n i n t h i s study are discussed l a t e r i n t h i s chapter. 1.2) Present State of Knowledge Each element of the complex urban surface mosaic w i l l create i t s own three-dimensional envelope. When energy balance measurements are attempted i n such an envelope (see f o r example Landsberg and M a i s e l , 1972; Nunez and Oke, 1977) i t must be recognized that the r e s u l t s are r e s t r i c t e d to the s c a l e of the phenomena of i n t e r e s t (Ching, et a l . , 1978). Ignoring t h i s r e s t r i c t i o n can r e s u l t i n dubious conclusions. For example, Landsberg and M a i s e l (1972) attempted to use t h e i r r u r a l vs. tarmacadam parking l o t energy balance r e s u l t s to describe the processes c r e a t i n g meso-scale c l i m a t i c f e a t u r e s , notably the urban heat i s l a n d , by the l a c k of evapo-t r a n s p i r a t i o n and r e s u l t i n g increased s e n s i b l e heat f l u x over the parking l o t . Although i t may be reasonable to argue that l a r g e areas of 8 waterproofed surface cover, l i k e c i t y c entres, would have n e g l i g i b l e evapo-t r a n s p i r a t i o n , the importance of t h i s m o d i f i c a t i o n has yet to be assessed. U n c r i t i c a l acceptance of such comparisons has co n t r i b u t e d to the 'hot', 'rough', and 'dry' c l a s s i f i c a t i o n s o c c a s i o n a l l y a p p l i e d to urban areas (e.g. Hanna, 1969; Munn, 1972).-The i n f l u e n c e of the 'hot' and 'dry' viewpoint i s p a r t i c u l a r l y evident i n numerical models of the urban atmosphere. Because of the dearth of energy balance i n f o r m a t i o n modellers have been forced to a r b i t r a r i l y estimate c e r t a i n energy balance r e l a t e d parameters, e s p e c i a l l y w i t h respect to e v a p o t r a n s p i r a t i o n . For example, Myrup (1969) assumed the r e l a t i v e humidity of the a i r l a y e r near the ground could be represented by the f r a c t i o n of the t o t a l area occupied by evaporating surfaces. Another modelling approach i s to use a surface moisture a v a i l a b i l i t y parameter (Atwater, 1972; Carlson and Boland, 1978). The values f o r t h i s parameter range from zero f o r a dry surface to u n i t y f o r a saturated surface and can be adjusted to account f o r s o i l moisture i n vegetated areas or the pr o p o r t i o n of impervious surfaces. Both Atwater (1972) and Carlson and Boland (1978) found t h i s to be the most s e n s i t i v e parameter i n t h e i r models. I t should be c l e a r that t h i s parameter w i l l vary c o n s i d e r a b l y , depending on land use and s o i l moisture. Despite t h i s t y p i c a l urban values have been s e l e c t e d as being between 0.1 and 0.2. The a p p l i c a b i l i t y of such low values i s questionable. For example, Marotz and Coiner (1973) found the p r o p o r t i o n of green spaces i n eastern Kansas c i t i e s to be q u i t e l a r g e (50 to 80%) and Auer (1978) found the corresponding value i n St. Louis to be 65%. Although c e r t a i n i n t r a - u r b a n areas (e.g. i n d u s t r i a l and commercial centres) w i l l have much lower proportions i n green space, these r e s u l t s i n d i c a t e that the moisture parameter values s e l e c t e d to date are 9 probably not r e p r e s e n t a t i v e of l a r g e areas of many c i t i e s . Ackerman (1977) used the Bowen r a t i o , g ( r a t i o of s e n s i b l e to l a t e n t heat f l u x , 8 - Q T J/Q T 7) 5 to describe the moisture a v a i l a b i l i t y i n urban areas ri E ( t y p i c a l r u r a l values range between 0.3 and 0.8). Ackerman chose an urban value of 2.0 but emphasised that the s e l e c t i o n was r a t h e r a r b i t r a r y , as l i t t l e i s known about t h i s q u a n t i t y i n urban areas. His model output was a l s o found to be very s e n s i t i v e to the value of 3 chosen. In summary, numerical models of the urban atmosphere have developed methods f o r approximating the r o l e of e v a p o t r a n s p i r a t i o n but there i s reason to c a l l i n t o question t h e i r p h y s i c a l bases. I t a l s o appears as i f the values s e l e c t e d are not r e p r e s e n t a t i v e of many c i t i e s . Since almost a l l models are found to be s e n s i t i v e to e v a p o t r a n s p i r a t i o n the development of greater i n s i g h t i n t o the r o l e of t h i s term should provide v a l u a b l e i n f o r m a t i o n . Chandler (1965) was one of the f i r s t to attempt to q u a n t i f y evapo-t r a n s p i r a t i o n by comparing measurements from evaporation pans l o c a t e d i n London, U.K. and i t s r u r a l surroundings. However, i n a d d i t i o n to design and exposure problems the a p p l i c a b i l i t y of such estimates to a c t u a l a r e a l urban e v a p o t r a n s p i r a t i o n i s questionable. Oke, et a l . (1972) were the f i r s t to determine r e l i a b l e urban Bowen r a t i o s . T h e i r Montreal, P.Q. i n v e s t i g a t i o n was ex p l o r a t o r y i n nature and used f a i r l y u n s o p h i s t i c a t e d equipment, but was s u f f i c i e n t to show that the l a t e n t heat f l u x (Q„) was a s i g n i f i c a n t term i n the energy balance. Another h i advance i n the understanding of urban ene r g e t i c s was made by Yap and Oke (1974). They d i r e c t l y measured net r a d i a t i o n (Q*), s e n s i b l e heat f l u x (Q u) and change i n heat storage (AQ ) over a 3 - 4 storey commercial/ rl b r e s i d e n t i a l area (70 to 80% impervious surface cover) of Vancouver, B.C. (Fa i r v i e w s i t e , F i g . 1.3). P r i o r to we t t i n g by a severe storm, Q was the 10 Figure 1.3 : The greater Vancouver area. dominant energy s i n k . A f t e r the event Q dominated, i n f a c t , Q„ was s t i l l E E as l a r g e as Q ( i . e . g = 1) f i v e days a f t e r the storm. The d i u r n a l p a t t e r n of Q revealed two features unique to the urban environment. F i r s t , some-n times Q was found to remain r e l a t i v e l y l a r g e during the afternoon and H second, Q o f t e n d i d not reverse i t s d i r e c t i o n of flow at n i g h t , n Ching et a l . (1978) conducted a s i m i l a r study i n St. L o u i s , Mo. i n mid-summer. D i r e c t measurements of Q were conducted at 3 s i t e s : H i n d u s t r i a l / c o m m e r c i a l (90% impervious surface c o v e r ) , r e s i d e n t i a l (<50% impervious surface c o v e r ) , and r u r a l . On a l i m i t e d number of occasions d i r e c t Q measurements were a l s o made at the i n d u s t r i a l / c o m m e r c i a l and E r u r a l s i t e s . The s e n s i b l e heat f l u x r e s u l t s at the i n d u s t r i a l / c o m m e r c i a l s i t e s u b s t a n t i a t e d many of the r e s u l t s of Yap and Oke (1974) : Q„ was the H dominant energy s i n k , d i d not reverse i t s d i r e c t i o n of flow at nig h t and became a p r o p o r t i o n a t e l y l a r g e r component of the energy balance i n the l a t e afternoon. At the r e s i d e n t i a l s i t e , Q was l e s s than h a l f that recorded H at the i n d u s t r i a l / c o m m e r c i a l s i t e . This decrease was a t t r i b u t e d to more a c t i v e e v a p o t r a n s p i r a t i o n . The n o c t u r n a l f l u x d i d reverse i t s d i r e c t i o n of flow ( i . e . i t was s i m i l a r to that normally expected i n a r u r a l e n v i r o n -ment) . Sens i b l e heat f l u x estimates at the r u r a l s i t e were only m a r g i n a l l y smaller than those recorded f o r the r e s i d e n t i a l s i t e . T his may seem s u r p r i s i n g as i t i n d i c a t e s that the almost 50% impervious surface cover at the r e s i d e n t i a l s i t e only m a r g i n a l l y a f f e c t e d the a r e a l energy balance. Bowen r a t i o s were c a l c u l a t e d from simultaneous measurements of the s e n s i b l e and l a t e n t heat f l u x e s . As expected, g was c o n s i s t e n t l y l a r g e r (approx-imately 2.0) at the i n d u s t r i a l / c o m m e r c i a l s i t e than at the r u r a l s i t e (approximately 0.7). Nocturnal Q f l u x e s were not reported. E Dabberdt and Davis (1978) were able to compute s p a t i a l l y - a v e r a g e d 12 g values i n St. Louis as a r e s i d u a l using a i r c r a f t measurements i n a climatonomical framework. Bowen r a t i o s ranged from 0.4 i n r u r a l areas to 1.3 i n a c o m m e r c i a l / i n d u s t r i a l / o l d r e s i d e n t i a l area (showers the day p r i o r to the study probably account f o r the low magnitudes). Coppin (1978 - pers. comm. T. Oke) found by d i r e c t measurement of Q and Q that g was between 0.8 and 2.5 f o r a suburban area i n Adelaide, E H A u s t r a l i a w i t h well-watered gardens. This occurred at the end of a hot, dry summer and so most of the a v a i l a b l e moisture was a t t r i b u t e d to human a c t i v i t i e s . Nocturnal Q values were o c c a s i o n a l l y p o s i t i v e , though more H o f t e n near zero or s l i g h t l y negative. I t i s c l e a r from t h i s review that d e s p i t e some advances many d i s -crepancies and questions remain. The apparent d i f f e r e n c e s i n the St. Louis s t u d i e s (Ching et a l . and Dabberdt and Davis) may be the r e s u l t of i n a c c u r -a c i e s w i t h i n the methods themselves or may i n d i c a t e a c t u a l s p a t i a l and/or temporal v a r i a b i l i t y . The r e s u l t s i n d i c a t e that there can be s i g n i f i c a n t d i f f e r e n c e s i n the energy balance of d i f f e r e n t urban land uses and there i s l i t t l e evidence that the r e s u l t s of one c i t y are r e p r e s e n t a t i v e of another. C e r t a i n l y the f i n d i n g most r e l e v a n t to t h i s study i s the i n d i c a t i o n that the urban environment may not be 'hot' and 'dry' as has o f t e n been assumed. 1.3) Approaches Toward E v a l u a t i n g E v a p o t r a n s p i r a t i o n There are a number of approaches f o r e v a l u a t i n g e v a p o t r a n s p i r a t i o n v i a the surface energy balance ( f o r reviews see - Webb, 1975; Thorn, 1975; Oke, 1978a). However only a few are a p p l i c a b l e to a r e a l f l u x e s t i m a t i o n and these are o u t l i n e d below. a) Climatonomic approach - This i s an a n a l y t i c a l approach o r i g i n a l l y derived by L e t t a u and L e t t a u (1972) where a 'primary response f u n c t i o n ' (temperature) and secondary response f u n c t i o n s (energy f l u x e s ) are r e l a t e d i n terms of a s i n g l e ' f o r c i n g f u n c t i o n ' ( i n c i d e n t s o l a r r a d i a t i o n ) . The evaporative f l u x and the inverse Bowen r a t i o are obtained by r e s i d u a l a f t e r p a r a m e t e r i z a t i o n of the r a d i a t i v e f l u x e s and the s e n s i b l e heat f l u x . Dabberdt and Davis (1978) used t h i s approach to o b t a i n s p a t i a l l y -averaged estimates of the inv e r s e Bowen r a t i o using a i r c r a f t measurements over St. L o u i s , Mo. The r e s u l t s were considered to be r e a l i s t i c and the approach worthy of f u t u r e c o n s i d e r a t i o n . Some of the drawbacks w i t h t h i s approach i n c l u d e : operation r e s t r i c t i o n s associated w i t h weather and f l i g h t r e g u l a t i o n s ; p r a c t i c a l l i m i t a t i o n s on measurement c o n t i n u i t y created by f u e l l i m i t a t i o n s and c o s t ; and the v a l i d i t y of the inverse Bowen r a t i o and evaporative f l u x when gained by r e s i d u a l . (b) O p t i c a l approach - In t h i s approach the path-averaged s e n s i b l e heat f l u x i s determined from the s c i n t i l l a t i o n s of a received l a s e r beam. The r e s u l t s are f e l t to be more r e p r e s e n t a t i v e and re q u i r e l e s s averaging time than po i n t measurements. Although promising the system i s at present only i n the experimental stage. Futhermore, to obt a i n estimates of Q one would s t i l l need to determine Q* and AQ and then solve f o r Q by r e s i d u a l . b E (c) Eddy c o r r e l a t i o n approach - In t h i s approach d i r e c t measurements of the tu r b u l e n t f l u x e s are obtained from f a s t response sensors ( f o r reviews see Webb, 1975; McNeil and Shuttleworth, 1975; Oke, 1978a). Yap and Oke (1974), Ching, et a l . (1978) and Coppin (1978 - pers. comm. T. Oke) used t h i s approach to determine Q u i n c i t i e s , the l a t t e r two stu d i e s a l s o obtained n d i r e c t estimates of Q . The approach has a number of advantages: i t E provides d i r e c t measurements; r e q u i r e s r e l a t i v e l y simple theory and can be used without any s p e c i f i c a t i o n of the surface c o n d i t i o n s or atmospheric s t a b i l i t y . U n f o r t u n a t e l y p r a c t i c a l l i m i t a t i o n s , e s p e c i a l l y i n s t r u m e n t a l 14 requirements and c o s t , keep i t from being widely used. This i s p a r t i c u l a r l y true of the Q £ sensors. For example, Ching, et a l . (1978) found s i g n i f i c a n t d e t e r i o r a t i o n of t h e i r sensor a f t e r only 8 days of use. As a r e s u l t many s t u d i e s that have used t h i s approach solve f o r Q„ by r e s i d u a l a f t e r d i r e c t measurement of Q„, Q* and AQ . Some eddy c o r r e l a t i o n sensors are a l s o r e s t r i c t e d by weather c o n d i t i o n s . For example, the Q^ system used by Yap and Oke (1974) cannot be used during heavy r a i n . These features make long term s t u d i e s d i f f i c u l t , (d) P r o f i l e approach - Under t h i s heading there are two b a s i c approaches: the aerodynamic method and the Bowen r a t i o - energy balance method. i ) Aerodynamic approach - In t h i s approach the turbu l e n t f l u x e s are evaluated from measured i n t e r - h e i g h t d i f f e r e n c e s of mean wind, temperature and humidity. This approach has two major drawbacks. F i r s t l y , the assumed e q u a l i t y of the eddy d i f f u s i v i t i e s f o r heat, water vapour and momentum i s only v a l i d under n e u t r a l c o n d i t i o n s . Although semi-emperic formulae have been developed to extend t h i s assumption to non-neutral c o n d i t i o n s none are wholly s a t i s f a c t o r y . Secondly, i t i s a l s o assumed that there i s a balance between the production and d i s s i p a t i o n of turbu-l e n t k i n e t i c energy, a c o n d i t i o n u n l i k e l y to be f u l f i l l e d i n the c i t y . In t h i s study continuous e v a p o t r a n s p i r a t i o n and energy balance r e s u l t s were r e q u i r e d . For t h i s purpose the Bowen r a t i o - energy balance approach was s e l e c t e d as being the most appropriate and w i l l be discussed i n more d e t a i l . i i ) Bowen r a t i o - energy balance approach - In t h i s approach the sum of the t u r b u l e n t terms (Q_ and Q u) are evaluated by r e s i d u a l a f t e r measurement of the other terms i n the energy balance and t h e i r r a t i o i s determined by d i f f e r e n t i a l psychrometry. Bowen's r a t i o (3) can be 15 estimated using e i t h e r a f i x e d m u l t i - l e v e l sensor array or a two -l e v e l sensor array where the sensors are p e r i o d i c a l l y interchanged. Both systems are capable of p r o v i d i n g almost continuous r e s u l t s f o r extended periods and can be used (w i t h some l o s s of accuracy) during r a i n f a l l . These c a p a b i l i t i e s a l l o w a wide range of synoptic c o n d i t i o n s to be examined. Assuming that advection (AQ.) i s n e g l i g i b l e and that Q ( i f A r a p p l i c a b l e ) i s i n c l u d e d i n a l l other f l u x e s (1.1) can be r e - w r i t t e n : Q* = Q H + Q E + AQ S (1.2) Bowen's r a t i o (g) i s found by t a k i n g the r a t i o of the f l u x - gradient equations f o r Q_ and QU: EJ n Q = I ^ P - K^-S. (1.3) if (1-A) -3 where p - a i r d e n s i t y (kg m ); c - s p e c i f i c heat of a i r at constant pressure ( J kg 1 K ; y - psychrometric constant*; and - eddy 2 - 1 — d i f f u s i v i t i e s f o r water vapour and heat, r e s p e c t i v e l y (m s ) ; 0 -mean a i r temperature (K); e - mean vapour pressure (kPa); and z -height (m). Thus: 1 y = c P/XE where - P - a i r pressure (Pa); X - l a t e n t heat of vapor-i z a t i o n ( J k g - 1 ) ; and e - r a t i o of the molecular weights of water and dry a i r . When P = 100 kPa and G = 293 K y = 66 Pa K" 1. 16 90 T~KW 9 z Equation (1.5) can be s i m p l i f i e d i f 80 and 8e are measured over the same height i n t e r v a l and i f e q u a l i t y of the d i f f u s i o n c o e f f i c i e n t s i s assumed ( i . e . = K^) (Swinbank and Dyer, 1967; Webb, 1970; Dyer, 1974), then using f i n i t e d i f f e r e n c e s and c a n c e l l i n g common terms: = (1.6) Equation (1.2) can then be rearranged using (1.6) to solve f o r Q £ and QR: Q* " AQc Q F = ^ (1.7) E 1 + 3 3(Q* - AQ ) Q H = — (1-8) H 1 + 3 Thus w i t h estimates of Q*, AQ , A0 and Ae one can determine a l l energy balance components. In comparison w i t h short v e g e t a t i o n , the c i t y represents a very rough aerodynamic surface. Thus f o r s i m i l a r Q and Q i n the two environ-E H ments, the v e r t i c a l gradients of temperature and humidity w i l l be much smaller i n the c i t y because the eddy d i f f u s i o n c o e f f i c i e n t s w i l l be much l a r g e r . This places considerable demand on instrumentation. Two e a r l y attempts at e s t i m a t i n g 3 i n the urban environment (Bach, 1970; Myrup and Morgan, 1972) f a i l e d because of instrumental l i m i t a t i o n s . 17 The question then becomes which instrumental array i s capable of pro p e r l y determining AO and Ae. Forest micrometeorologists a l s o f r e q u e n t l y encounter very small temperature (0.03 K m * ) and s p e c i f i c humidity (0.01 g kg *m *) gradients (Black and McNaughton, 1971; Gash and Stewart, 1975) and as a r e s u l t they have devoted considerable research to t h i s question. Gash and Stewart (1975) employed a nine - l e v e l array w i t h seven of the l e v e l s above mean t r e e height. This array was considered to y i e l d more i n s i g h t i n t o the aerodynamic p r o p e r t i e s of the surface than an interchanging (reversing) array and to make i t p o s s i b l e to consider whether or not s u f f i c i e n t f e t c h e x i s t s . I t was a l s o hoped that the l a r g e array would reduce the e f f e c t of the systematic and p e r s i s t e n t e r r o r s present i n any given sensor p a i r upon the o v e r a l l p r o f i l e . McNeil and Shuttleworth (1975) compared the Gash and Stewart (1975) nine - l e v e l a r r a y w i t h a two - l e v e l r e v e r s i n g a r r a y and a prototype eddy c o r r e l a t i o n device. I d e n t i c a l high q u a l i t y sensors were used i n both the two - l e v e l and nine - l e v e l systems. The nine - l e v e l array f r e q u e n t l y produced r e s u l t s that were s i g n i f i c a n t l y d i f f e r e n t from those of the r e v e r s i n g a r r a y and the eddy c o r r e l a t i o n device. This was a t t i b u t e d to the i n f e r i o r handling of the systematic e r r o r by the m u l t i -l e v e l system compared to the r e v e r s i n g system. By interchanging the sensors on a short and r e g u l a r b a s i s a mean gradient can be c a l c u l a t e d as the average of the gradients i n the two c o n f i g u r a t i o n s . Assuming the systematic e r r o r s are independent of h e i g h t , the e r r o r a s s o c i a t e d w i t h the mean gradient should be s i g n i f i c a n t l y reduced. McNeil and S h u t t l e -worth (1975) recommended th a t a study p r i m a r i l y concerned w i t h the measurement of the energy f l u x e s should use the two - l e v e l r e v e r s i n g 18 array. Using a s l i g h t l y d i f f e r e n t r e v e r s i n g system Black and McNaughton (1971) were able to determine the d a i l y t o t a l evaporation over a Douglas f i r f o r e s t at Haney, B.C. w i t h an e r r o r of l e s s than 10%. Given t h i s experience over rough f o r e s t e d surfaces i t was decided to attempt to use a two - l e v e l r e v e r s i n g system i n the c i t y to measure the temperature and humididty gradients necessary to evaluate 3 v i a (1.6). D e t a i l s of the system are given i n Chapter 2 and i t s performance i s evaluated i n Chapter 3. I t i s worth p o i n t i n g out here that the methods and instrumentation used i n t h i s study have been developed f o r micro - s c a l e i n v e s t i g a t i o n s . By applying them i n the urban boundary l a y e r they are being t e s t e d under l o c a l - s c a l e c o n s t r a i n t s f o r which they were not o r i g i n a l l y intended. Although t h i s may introduce c e r t a i n shortcomings i n the i n v e s t i g a t i o n they are considered to be amongst the best approaches a v a i l a b l e and worth experimenting w i t h to see i f they are capable of advancing our knowledge of urban e n e r g e t i c s . 1.4) S i t e C o n s i d e r a t i o n and S e l e c t i o n Over a f l a t surface w i t h s p a t i a l l y uniform r a d i a t i v e , thermal, moisture and aerodynamic p r o p e r t i e s , i t i s customary to consider the surface boundary l a y e r as being the near - surface atmospheric l a y e r w i t h i n which tu r b u l e n t f l u x e s are constant w i t h height. The depth of t h i s l a y e r i n c r e a s e s w i t h : i n c r e a s i n g d i s t a n c e from the nearest upwind d i s c o n t i n u i t y i n surface p r o p e r t i e s ; i n c r e a s i n g atmospheric i n s t a b i l i t y ; and i n c r e a s i n g surface roughness. Far from any major d i s c o n t i n u i t i e s the surface l a y e r reaches an e q u i l i b r i u m depth of t y p i c a l l y about 50 m. S p a t i a l changes i n surface p r o p e r t i e s l e a d to h o r i z o n t a l gradients and the p r o b a b i l i t y of 19 advective t r a n s p o r t . Advective f l u x e s d i s r u p t the surface energy balance and l e a d to v a r i a t i o n of f l u x e s w i t h height so that measurements conducted above the surface are no longer r e p r e s e n t a t i v e of the underlying surface. In the urban canopy l a y e r s p a t i a l v a r i a b i l i t y i s the norm and t h e r e f o r e so i s micro - advection. In t h i s study f l u x measurements were conducted i n the lower p o r t i o n of the urban boundary l a y e r ( i . e . above the canopy) i n an area dominated by suburban land uses and were averaged over a one - hour p e r i o d . This arrangement was chosen to minimize advection i n the f o l l o w i n g three ways. F i r s t , an hourly averaging period takes advantage of the n a t u r a l v a r i a b i l i t y i n wind d i r e c t i o n which a i d s i n s p a t i a l averaging and a l s o samples a l l eddy s i z e s l i k e l y to c o n t r i b u t e to t u r b u l e n t heat f l u x e s i n the c i t y (Yap, 1973). Second, being above the urban canopy l a y e r , micro - s c a l e i n f l u e n c e s were assumed to be suppressed by the e f f e c t i v e mixing produced by atmospheric turbulence over the rough c i t y surface. T h i r d , the observation s i t e was purposely l o c a t e d i n an area of r e l a t i v e l y homogeneous land use so as to f u r t h e r minimize anomalous i n f l u e n c e s . Through these measures the experimental design sought to r e l e g a t e advective f l u x e s ( A Q ^ ) to a minor ( h o p e f u l l y n e g l i g i b l e ) r o l e . I t i s also necessary to invoke t h i s assumption i f point ( s i n g l e s i t e ) measurements are to be used to approximate a r e a l values. The observation s i t e i s l o c a t e d i n south - c e n t r a l Vancouver, B.C. at a l o c a t i o n h e r e i n a f t e r r e f e r r e d to as Sunset ( F i g . 1.3); otherwise known as the Mainwaring Substation of B.C. Hydro (49°13'37" N, 123°4'37" W -90 m a.m.s.l.). W i t h i n a 2 km r a d i u s of the s i t e t e r r a i n i s g e n e r a l l y f l a t or gently u n d u l a t i n g w i t h slopes t y p i c a l l y l e s s than 6°. Small i s o l a t e d areas of steeper slopes do however e x i s t . Urban development i n the area 20 i s predominantly s i n g l e - f a m i l y suburban housing. No c l e a r l y anomalous heat and/or water vapour sources were apparent. The s i t e a l s o provided e x c e l l e n t s e c u r i t y and could be e a s i l y s u p p l i e d w i t h e l e c t r i c a l power. 1.5) Objectives The primary o b j e c t i v e of the i n v e s t i g a t i o n i s to o b t a i n suburban energy balance estimates w i t h s p e c i a l emphasis upon the magnitude and d i u r n a l p a t t e r n of e v a p o t r a n s p i r a t i o n (Q_). In d e t a i l the o b j e c t i v e s are to: a) evaluate the a p p l i c a b i l i t y of the Bowen r a t i o - energy balance approach i n an urban environment. b) examine d i u r n a l and longer p e r i o d p a t t e r n s i n the Bowen r a t i o ( 3 ) , e v a p o t r a n s p i r a t i o n (Q„) and the tu r b u l e n t s e n s i b l e heat f l u x (Q u) and i l ri to attempt to r e l a t e them to environmental and surface parameters. c) examine the p o s s i b i l i t y of modelling the daytime urban e v a p o t r a n s p i r a t i o n regime i n terms of simple environmental parameters. CHAPTER TWO DETAILS OF IMPLEMENTATION - SITES AND INSTRUMENTATION This chapter o u t l i n e s the experiments conducted i n t h i s i n v e s t -i g a t i o n . The p r i n c i p a l experiment was conducted at the Sunset suburban 30 m tower s i t e ( F i g . 2.1) during the period from l a t e August to e a r l y October, 1977. The d e t a i l s of t h i s experiment are o u t l i n e d i n Se c t i o n 2.1. A secondary experiment was conducted at a r u r a l s i t e i n J u l y , 1977. I t was designed to provide both f a m i l i a r i z a t i o n w i t h , and i n i t i a l check o f , the instruments i n v o l v e d , d e t a i l s of t h i s experiment are presented i n Sectio n 2.3. 2.1) Suburban S i t e and Surroundings Suburban land uses dominate the area surrounding the Sunset s i t e to at l e a s t 2 km i n a l l d i r e c t i o n s (see F i g . 2.2). R a d i a t i o n measurements from the tower suggest the area has a short-wave albedo of 0.12 -0.14. Employing the r e s u l t s of a survey of b u i l d i n g dimensions the mean aero-dynamic displacement height (d) and roughness l e n g t h (Z q ) f o r the area were found by employing the equations of Kutzbach (1961), L e t t a u (1969) and Counihan (1971) (Table 2.1). In the n e u t r a l atmosphere t y p i c a l of urban areas (Oke, 1978a) and given the Z q values l i s t e d i n Table 2.1, one can expect h e i g h t : f e t c h r a t i o s of 1:50 or more (Munro and Oke, 1975). Given a f e t c h of 2 km or more t h i s should r e s u l t i n a constant f l u x l a y e r 2 40 m i n depth. I d e a l l y to maximize the magnitude of v e r t i c a l temperature and humidity gradients i t i s necessary to conduct measurements i n the lower N i Waverly East 4 8 t h Ave. CD CO OJ C u > a East 4 7 t h Ave pledge Mainwaring Substation Tower T r a i l e r  Grass /nth East 49 Ave. Scale 9 3 9 60 9,0 m Figure 2.1 : Plan-view of Sunset s i t e . Figure 2.2 : View l o o k i n g west from top of tower. M 24 TABLE 2.1 Aerodynamic Displacement Height (d) and Roughness Length ( Z Q ) Estimates Using Three Approaches Author of Approach d Z Q (m) (m) Kutzbach (1961) 3.1 0.9 Le t t a u (1969) 2.5 0.5 Counihan (1971) 1.0 1.0 25 p o r t i o n of t h i s l a y e r , on the other hand the lowest sensor height should be at l e a s t f i v e times the roughness length above the roughness elements (Tanner, 1963). Assuming a mean element height of 5 - 6 m and a 5 m d i f f e r e n c e between the surrounding land surface and the base of the 30 m tower ( F i g . 2.3) t h i s means that the lowest sensor height should not be lo c a t e d lower than about 12 - 15 m above the tower base. The s i t e layout and dimensions are given i n Figures 2.1 and 2.3. The t r a i l e r l o c a t e d near the tower base provided a c o n t r o l l e d environment f o r measurement r e c o r d i n g . 2.2) Instrumentation and Data Processing (Suburban s i t e ) Of the terms i n the energy balance equation (1.2) only the net a l l -wave r a d i a t i o n f l u x d e n s i t y (Q*) was measured d i r e c t l y . The turbu l e n t terms (Q and Q ) were c a l c u l a t e d w i t h the a i d of hour l y Bowen r a t i o (3) estimates i . H determined using t w o - l e v e l d i f f e r e n t i a l psychrometry and the change i n the heat storage (AQ ) was parameterized i n terms of Q* ( f o r a more d e t a i l e d d i s c u s s i o n see Ch. 3). 2.2.1) Net all-wave r a d i a t i o n f l u x d e n s i t y The net all-wave r a d i a t i o n f l u x d e n s i t y (Q*) was measured w i t h a net pyrradiometer (Swissteco Pty. L t d . , Model S I ) . The sensor c o n s i s t s of a wire-wound, p l a t e d (copper-constantan) thermopile. Thin, molded polyethy-lene domes cover both of the blackened thermopile s u r f a c e s . The domes are kept r i g i d and f r e e of i n t e r n a l condensation by a c o n t r o l l e d flow of dry a i r produced by a r e c i r c u l a t i n g system f o l l o w i n g the design of Stevens and Wright (1977). A i r i s forced through a des s i c a n t ( S i l i c a gel) by an aquarium pump and l e d to and from the domes v i a f l e x i b l e tubing. The Figure 2.3 : West - East c r o s s - s e c t i o n of s i t e . 27 r e c y c l i n g feature s i g n i f i c a n t l y reduces the frequency w i t h which the dessicant needs replacement. The instrument was mounted on the south side of the tower, 22 m above i t s base ( l e v e l 2 - F i g . 2.4). The height insured a view f a c t o r so that 95% of the upwelling r a d i a t i o n emanated from a c i r c l e of about 100 m r a d i u s . The s o u t h e r l y exposure and the sep a r a t i o n from the tower minimized tower 'shadow' e f f e c t s . The net pyrradiometer s i g n a l was recorded on a multi-channel data logger (Doric S c i e n t i f i c L t d . , Model 210) housed i n the t r a i l e r . The s i g n a l was a u t o m a t i c a l l y scanned and p r i n t e d every 5 min. Hourly means were c a l c u l a t e d and converted to energy f l u x d ensity e q u i v a l e n t s by a p p l i -c a t i o n of the appropriate c a l i b r a t i o n c o e f f i c i e n t . 2.2.2) A i r temperature and humidity d i f f e r e n c e s V e r t i c a l d i f f e r e n c e s of temperature and humidity were measured by wet- and dry-bulb psychrometry. The system was a modified v e r s i o n of that presented by Black and McNaughton (1971) and Black, et a l . (1973). The f o l l o w i n g d i s c u s s i o n gives a summary d e s c r i p t i o n of the general system and the m o d i f i c a t i o n s incorporated f o r the present study. For a more general d i s c u s s i o n the reader i s r e f e r r e d to the aforementioned s t u d i e s . Simply s t a t e d the system c o n s i s t s of two v e r t i c a l l y - s e p a r a t e d psychrometers ( a s p i r a t e d and sh i e l d e d against r a d i a t i o n ) , a r e v e r s i n g mechanism and a data logger i n c o r p o r a t i n g c o n t r o l l o g i c f o r system opera-t i o n . The temperature sensors are s i l i c o n diodes ( F a i r c h i l d FD 300, see Sargeant, 1965). S i l i c o n diodes were chosen ( i n the o r i g i n a l system Black and McNaughton used germanium diodes) because of t h e i r l i n e a r v o l t a g e vs. temperature c h a r a c t e r i s t i c , l a r g e temperature s e n s i t i v i t y (^  2 mV K ^ ) , low 28 Figure 2.4 : Side - and plan (diagrams not to scale) - views of instrumentation l e v e l s . 29 cost and easy a v a i l a b i l i t y . Two p a i r s were s e l e c t e d such that the i n d i v i d u a l temperature s e n s i t i v i t i e s of a given p a i r matched to w i t h i n 0.1%. One p a i r was used f o r the dry-bulb and the other f o r the wet-bulb sensors, w i t h one of each p a i r i n each head. Two other system m o d i f i c a t i o n s were incorporated. F i r s t , because s i l i c o n diodes are smaller than germanium diodes i t was p o s s i b l e to use a sensor housing w i t h a smaller i n t e r n a l diameter ( F i g s . 2.5 and 2.6), thereby reducing a s p i r a t i o n requirements. Furthermore by using a c r y l i c tubing ( i n s t e a d of s t a i n l e s s s t e e l ) a l i g h t e r yet s t i l l durable sensor housing was r e a l i z e d . To reduce s o l a r heating the tubes were wrapped i n a l a y e r of polyurethane i n s u l a t i o n which i n turn was wrapped i n h i g h l y r e l f e c t i v e , aluminized Mylar tape. Second, a l a r g e r perspex r e s e r v o i r , capable of h o l d i n g a 4 - 5 day supply of d i s t i l l e d water f o r the wet-bulb wick was employed. The r e s e r v o i r s were wrapped i n aluminized Mylar tape and mounted p a r a l l e l to the sensor housing. A short perspex tube (6 mm ID) connected the r e s e r v o i r to the sensor housing and served as a pathway f o r the wet-bulb w i c k i n g ( F i g . 2.5). In a n t i c i p a t i o n of small v e r t i c a l gradients of wet- and dry-bulb temperature (< 0.1 K m *) the v e r t i c a l separation between the sensing heads was set at 4.0 m. Each sensing head was attached to a 2.0 m l o n g , t h i n -w a l l e d , s t a i n l e s s s t e e l tube which i n turn was coupled i n t o a machined T-j u n c t i o n ( F i g . 2.7). Angled support arms increased r i g i d i t y . The T-junc-t i o n o u t l e t was connected to a s t a i n l e s s s t e e l tube i n a sealed b a l l - b e a r i n g housing. Thus the sensing heads were capable of 180° r o t a t i o n by means of a r e v e r s i n g motor (Hurst Model DA, 4 rpm) connected to the back end of the tube. Cushioned r o t a t i o n stops were p o s i t i o n e d such that r o t a t i o n was term-inated once the heads were v e r t i c a l l y a l i g n e d . A f l e x i b l e c o u p l i n g was used Figure 2.6 : Photograph of Thermometer Interchange System. Polyurethane A c r y l i c Aluminized Mylar \ A c r y l i c Tube S t a i n l e s s S t e e l Connector F a i r c h i l d FD 300 Diodes Epoxy Support For Diode Scale 2 i x x x x y x y x x y w w x x y y . Perspex Reservoir cm Re s e r v o i r / F i l l i n g Hole Diode Leads J (wrapped i n aluminized Mylar) Figure 2.5 : Cr o s s - s e c t i o n through long a x i s of sensing head. > Sensor Head (see F i g . 2.4) 4.0 m c Head Assembly on Tower Housing f o r Reversing Motor 1.6 m Scale > 0 10 20 i i i • • cm Tubing to Vacuum Pump on Ground Figure 2.7 : A s p i r a t i o n pathway. 32 f o r the connection to prevent motor damage when r o t a t i o n was terminated. The a s p i r a t i o n pathway i s shown i n Figure 2.7. A vacuum pump (Gast Manuf. Corp.) l o c a t e d on the ground near the base of the tower provided v e n t i l a t i o n through the sensing heads at a r a t e of about 3.5 m s *. The r e v e r s i n g system was mounted on a 3.7 m long s l i d i n g cross-arm such that the upper and lower sensors were p o s i t i o n e d at 22.5 and 18.5 m above the tower base r e s p e c t i v e l y , at 2 m out from the tower. The sensing heads were a l i g n e d w i t h t h e i r p o r t s f a c i n g WNW ( l e v e l 1 - F i g . 2.4). This o r i e n t a t i o n avoided d i r e c t s o l a r i r r a d i a t i o n of the sensors, even at low s o l a r a l t i t u d e s . The wet- and dry-bulb s i g n a l s were monitored by a data logger (designed and b u i l t under the s u p e r v i s i o n of Dr. T. A. Black, S o i l Science Dept., UBC). The logger i n c l u d e d two vo l t a g e i n t e g r a t o r s (1000 counts mV * h * ) , a two-channel paper-tape p r i n t e r , c o n t r o l l o g i c and a r e l a y to c o n t r o l the r o t a t i o n d i r e c t i o n of the r e v e r s i n g motor. The logger i n t e g r a t e d and p r i n t e d the wet- and dry-bulb temperature d i f f e r e n c e s . P r o v i s i o n was a l s o made to al l o w access to the output s i g n a l of each i n d i v i d u a l sensors. An e x t e r n a l electro-mechanical timer c o n t r o l l e d the le n g t h of i n t e g r a t i o n p e r i o d s , p r i n t e r o p e r a t i o n and sensing head r e v e r s a l through the r e l a y and c o n t r o l l o g i c . This allowed the system to be operated e s s e n t i a l l y unattended f o r a number of days. Each run c o n s i s t e d of a 5 min e q u i l i b r a t i o n p eriod (to a l l o w the sensors to adju s t to the ambient c o n d i t i o n s ) followed by a 10 min pe r i o d of i n t e g r a t i o n . At the end of each run the i n t e g r a t e d wet- and dry-bulb temperature d i f f e r e n c e s (AT^ and AT, r e s p e c t i v e l y ) were p r i n t e d , the i n t e g r a t o r s r e s e t to zero and the sensing heads reversed. This sequence was a u t o m a t i c a l l y repeated on a continuous b a s i s . Four such i n t e g r a t e d AT^ 33 and AT s i g n a l s were used to compute mean hourly temperature d i f e r e n c e s a f t e r a p p l i c a t i o n of the appropriate c a l i b r a t i o n c o e f f i c i e n t s . The wet- and dry-bulb temperature s i g n a l s (T^ and T, r e s p e c t i v e l y ) from one sensing head were continuously recorded on s t r i p - c h a r t recorders E s t e r l i n e Angus, Model MS401). Hourly mean voltage values were c a l c u l a t e d and converted to absolute temperatures by a p p l i c a t i o n of the appropriate sensor c a l i b r a t i o n c o e f f i c i e n t . The mean hour l y T and T^ values were used to estimate a c t u a l vapour pressure ( e ) : e = e s ( T „ ) - ^ ( T " V ( 2 ' 1 } W where: ^ ~ s a t u r a t i o n vapour pressure at the mean wet-bulb temperature W (T ). Values of e , > were c a l c u l a t e d f o l l o w i n g Lowe (1977): W s U V T e s ( T T 7 ) " a o + V a l + V a 2 + V a 3 + V a 4 + V a 5 + T W A 6 ) ) ) ) ) ( 2 ' 2 ) w Values f o r the polynomial c o e f f i c i e n t s are given i n Lowe (1977). 2.2.3) A d d i t i o n a l measurements Wind speed and d i r e c t i o n were measured using a G i l l cup anemometer and microvane (R. M. Young Co.) mounted at the 30 m l e v e l ( l e v e l 3 - F i g . 2.4) on a 2.5 m long s l i d i n g cross-arm. The s i g n a l s were recorded on a two-channel s t r i p chart recorder (Rustrak I n c . ) . Mean ho u r l y values were estimated from the chart record. Upward - and downward - f a c i n g pyranometers (Kipp and Zonen, Model CM5) were used to measure the incoming (K4-) and r e f l e c t e d (K+) short-wave r a d i a t i o n f l u x d e n s i t i e s , r e s p e c t i v e l y . The instruments were p o s i t i o n e d at l e v e l 2, 2 m from the tower ( F i g . 2.4). Both s i g n a l s were recorded on the 34 Doric data logger and h o u r l y mean values obtained as f o r Q * . S o i l water p o t e n t i a l was measured at three suburban l o c a t i o n s using a P e l t i e r - c o o l e d thermocouple dewpoint hygrometer system (Neumann and T h u r t e l l , 1971) (Wescor, I n c . ) . D a i l y observations at a depth of 0.01 m were obtained f o r an i r r i g a t e d lawn, n o n - i r r i g a t e d short grass and a mixed deciduous - coni f e r o u s treed area. Standard hourly m e t e o r o l o g i c a l observations were obtained from the Vancouver I n t e r n a t i o n a l Weather O f f i c e (7.8 km SW of the Sunset s i t e ) . 2.3) Rural S i t e Experiments were a l s o conducted at a r u r a l s i t e (0.5 km north of the Trans Canada Highway on 2 3 2 n d S t . , F t . Langley, B.C.). The s i t e , i t s surroundings and the l o c a t i o n of the t r a i l e r are shown i n Figure 2.8. The f i e l d c o n s i s t e d of 0.1 m t a l l lodged grass p a r t i a l l y covered by a dry grass l i t t e r . The s o i l water content during the study period was found to be approximately 15% by weight by g r a v i m e t r i c a n a l y s i s . 2.4) Instrumentation and Data Processing At the r u r a l s i t e the only term i n the energy balance equation (1.2) not d i r e c t l y measured was the l a t e n t heat f l u x d e n s i t y ( Q „ ) . I t was E estimated using two approaches: f i r s t l y , by r e s i d u a l a f t e r measuring a l l other energy balance terms ( Q * , Q „ and A Q C ) d i r e c t l y ; and secondly, using n o the Bowen r a t i o - energy balance approach as described : i n Chapter 1.4. Sensor l o c a t i o n s are shown i n Figure 2.8. 2.4.1) Net all-wave r a d i a t i o n f l u x d e n s i t y A net pyrradiometer and purging system s i m i l a r to that described i n Barn Scale 0 3 0 60 i i 1 ' 1 m 1 Figure 2.8 : Plan-view of r u r a l s i t e . Ln 36 S e c t i o n 2.2.1 was mounted 1 m above the surface. This ensured that 95% of the r a d i a t i o n sensed by the lower face of the pyrradiometer was emanating from a c i r c l e w i t h a 5 m r a d i u s which was considered to provide adequate s p a t i a l sampling. The f i e l d of view of the upper face was e s s e n t i a l l y f r e e of o b s t r u c t i o n . To e l i m i n a t e p o s s i b l e shadow e f f e c t s from the supporting mast the instrument was o r i e n t a t e d toward the south. The net pyrradiometer s i g n a l was recorded on a v o l t - t i m e i n t e g r a t o r ( L i n t r o n i c L t d . , Model Mark V, 100 counts mV ^ h . Integrated values were a u t o m a t i c a l l y p r i n t e d every hour. Energy f l u x e q u i v a l e n t s were found by a p p l i c a t i o n of the appropriate c a l i b r a t i o n c o e f f i c i e n t . 2.4.2) Change i n v o l u m e t r i c heat storage A s o i l heat f l u x p l a t e (Middleton Pty. Ltd.) was placed j u s t below the s o i l surface (< 10 mm) at a p o i n t w i t h i n the f i e l d of view of the net pyrradiometer. I t was assumed that v e r t i c a l heat f l u x divergence i n the s o i l l a y e r above the sensor was n e g l i g i b l e . Heat storage i n the v e g e t a t i v e canopy was a l s o neglected. The v o l t a g e s i g n a l was recorded on a L i n t r o n i c v o l t - t i m e i n t e g r a t o r . Energy f l u x e q u i v a l e n t s were found by a p p l i c a t i o n of the appropriate c a l i b r a t i o n c o e f f i c i e n t . 2.4.3) Sen s i b l e heat f l u x d e n s i t y The s e n s i b l e heat f l u x d e n s i t y (Q ) was d i r e c t l y measured using a yaw H sphere - thermometer system. D e t a i l e d d i s c u s s i o n of the theory and oper-a t i o n of t h i s eddy c o r r e l a t i o n instrument are presented i n Tanner and T h u r t e l l (1970) and Yap, et a l (1974). The instrument was i n s t a l l e d w i t h the sensor at a height of approximately 1 m at the l o c a t i o n shown i n Figure 2.8. 37 2.4.4) Temperature and humidity d i f f e r e n c e s The r e v e r s i n g psychrometer system as described i n S e c t i o n 2.2.2 was a l s o employed here. However, v e r t i c a l separation of the sensors was reduced to 1 m. The instrument was mounted with the sensors at the 0.5 and 1.5 m l e v e l s . The sensors faced east and the a s p i r a t i o n r a t e was maintained at 3.5 m s *. CHAPTER THREE EVALUATION OF THE BOWEN RATIO - ENERGY BALANCE APPROACH IN AN URBAN ENVIRONMENT This chapter i s concerned w i t h an e v a l u a t i o n of the Bowen r a t i o -energy balance approach ( e s p e c i a l l y i n an urban environment) and i s d i v i d e d i n t o three main s e c t i o n s . F i r s t , the r e s u l t s of a r u r a l experiment are presented. The main o b j e c t i v e of t h i s was to compare s e n s i b l e heat f l u x estimates using both the eddy c o r r e l a t i o n and Bowen r a t i o - energy balance approaches. In a d d i t i o n to e s t a b l i s h i n g the agreement between the two methods i t was hoped that the r e s u l t s would be of use i n the determin-a t i o n of the vol u m e t r i c heat storage (AQg) i n the urban experiment. The second s e c t i o n i s devoted to a c o n s i d e r a t i o n of the ways i n which AQg may be determined i n the urban environment. This i s probably the most awkward term i n the urban energy balance to evaluate. The d i s c u s s i o n reviews p o t e n t i a l approaches to solve the problem and o u t l i n e s the method s e l e c t e d . The t h i r d s e c t i o n presents an e r r o r a n a l y s i s of the Bowen r a t i o - energy balance approach. In view of the small v e r t i c a l gradients of temperature and humidity t y p i c a l l y encountered over the aerodynamically-rough urban surface t h i s a n a l y s i s i s c r u c i a l to e s t a b l i s h the v a l i d i t y of the turb u l e n t f l u x estimates. 38 39 3.1) R u r a l Intercomparison Experiment As an i n i t i a l t e s t of the newly constructed Thermometer Interchange System (TIS) s e n s i b l e heat f l u x (Q ) estimates using the TIS i n the H Bowen r a t i o - energy balance framework were compared w i t h independent estimates from an eddy c o r r e l a t i o n system at a r u r a l s i t e where the inherent assumptions necessary to each system might be expected to be met. The eddy c o r r e l a t i o n instrument was a yaw sphere - thermometer (YST) system (Ch. 2). The data set c o n s i s t s of 22 hourly averaged estimates of Q using H both the eddy c o r r e l a t i o n (Q^yST)^ a n c* ^ o w e n r a t i ° ~ energy balance (Qu/o\) approaches. Observations were l i m i t e d to the daytime during 4 days i n l a t e J u l y , 1977. Throughout the period s k i e s were c l e a r and winds were c o n s i s t e n t l y l i g h t (< 2 m s ^) and predominantly from w e s t e r l y or e a s t e r l y d i r e c t i o n s . The Q„, 0s estimates were c o n s i s t e n t l y s l i g h t l y greater than Q , . . H(.p; n ( , i b l , j L i n e a r r e g r e s s i o n of the estimates from the two approaches y i e l d s : QH(YST) °* 7 9 QH(3) - 13.6 2 c o e f f i c i e n t of determination (r ) = 0.86 and standard e r r o r of Q^ysT) -2 (S_ ) = ± 15 W m . This i n d i c a t e s that the estimates are w e l l Si (YST) c o r r e l a t e d but that there i s systematic d i f f e r e n c e ( Q ^ y g j ) < ^H(3)^ between them. The d i f f e r e n c e could be the r e s u l t of many f a c t o r s i n c l u d i n g i nstrumental e r r o r s , d i f f e r e n t i a l s e n s i t i v i t y to advective i n f l u e n c e s between the systems, the s p a t i a l separation of the systems, neglect of s o i l heat f l u x divergence/convergence i n the Bowen r a t i o - energy balance c a l c u l a t i o n s , e t c . However, the r e s u l t s l i e w i t h i n the s c a t t e r found i n 40 previous intercomparison i n v e s t i g a t i o n s using s i m i l a r systems ( F i g . 3.1). More recent work using the same TIS used i n t h i s study but at a d i f f e r e n t s i t e shows very much b e t t e r absolute agreement (D. Steyn, pers. comm.). Sp i t t l e h o u s e and Black (1978) compared a s i m i l a r TIS w i t h an eddy c o r r e l a t i o n system (Q H, •>) which uses a fast-response thermistor and G i l l p r o p e l l e r anemometers. Li n e a r r e g r e s s i o n of the estimates from the two systems i n d i c a t e d QT1/ . to be s l i g h t l y l a r g e r than Q„, n S However the J H(e) b J e H ( B ) . sample s i z e was q u i t e small (10 po i n t s ) and e x h i b i t s a f a i r l y l a r g e s c a t t e r ( S n - 44 W m ). Wind speeds that were of the same order of magnitude gH(e) as the s t a l l i n g speeds of the anemometers made i t d i f f i c u l t to increase t h e i r sample s i z e . I t i s concluded that i n ge n e r a l , there i s a reasonable and f a i r l y c o n s i s t e n t agreement between the two measuring systems. Therefore the r e s u l t s of the r u r a l comparison were considered s u f f i c i e n t to support the use of the TIS i n the urban environment. 3.2) Determination of Volumetric Heat Storage As p r e v i o u s l y mentioned the vo l u m e t r i c heat storage (AQg) f o r a b u i l d i n g - a i r - s o i l volume i s the most d i f f i c u l t energy balance term to determine. D i r e c t measurement of AQ would r e q u i r e a c o n s i d e r a t i o n of the c o n t r i b u t i o n of a l l components comprising the urban 'surface' ( w a l l s , r o o f s , a s p h a l t , grass, etc.) and th e r e f o r e as a p r a c t i c a l procedure was considered to be beyond the scope of t h i s study. Because the heat stored or released by the 'surface'must a l s o be considered, methods developed f o r e s t i m a t i n g the heat storage i n the l a y e r between the ground and some reference height are i n a p p l i c a b l e (e.g. as used i n f o r e s t s , see Stewart and Thorn, 1973). Figure 3.1 : Comparison of hou r l y average Q using yaw sphere - thermometer (YST) and Bowen r a t i o Xg) approaches. Ladner (moist, t a l l grass, Yap, et a l . , 1974) and White Lake (short dry scrub, Brown, Oke and Williams - unpubl.) data included f o r comparison. One approach might be to solve (1.2) f o r AQg. This was attempted using d i r e c t measurement of Q* and Q (the l a t t e r using the YST) and using H the TIS to estimate g and thereby Q E (= ^(YST)^ H o w e v e r > instrume n t a l problems allowed only a small amount .of data to be c o l l e c t e d and rendered the r e s u l t s i n c o n c l u s i v e . The approach remains a p o s s i b l e a l t e r n a t i v e to d i r e c t measurement of AQg. However, AQg i s then the s i n k f o r a l l e r r o r s i n determining the other terms and since i t i s l i k e l y to be the smallest term the percentage e r r o r i s l i k e l y to be l a r g e e s p e c i a l l y on an ho u r l y b a s i s . Ching, et a l . (1978) conducted a s i m i l a r experiment i n both a r u r a l area and an i n d u s t r i a l / c o m m e r c i a l area of St. L o u i s . Using d i r e c t measurements of Q*, Q and Q they found three hour averaged AQ values H E S to be 16% and 24% of Q* i n the r u r a l and urban areas, r e s p e c t i v e l y . The f i n a l approach to be discussed here i s to parameterize AQg i n terms of Q* ( i . e . to represent the storage term as a f r a c t i o n of the r a d i a t i o n f o r c i n g f u n c t i o n ) . Such a procedure i s suggested on the b a s i s of experiments i n d i f f e r e n t surface regimes. Heat storage has been found to be an approximately l i n e a r f u n c t i o n of net all-wave r a d i a t i o n i n the cases of bare s o i l (Fuchs and Hadas, 1972), grass (Oke - unpublished), tarmacadam (Terjung, et a l . , 1971) and r o o f s (Nunez, 1974). The e x i s t e n c e of such a r e l a t i o n s h i p i m p l i e s that the p a r t i t i o n i n g of energy between the storage (AQ ) and t u r b u l e n t terms (Q , Q ) f o l l o w s some reco g n i z a b l e o H E p a t t e r n . In the case of storage heat uptake and l o s s i s l a r g e l y c o n t r o l l e d by r e l a t i v e l y constant thermal p r o p e r t i e s (e.g. thermal admittance) whereas the tur b u l e n t terms are r e l a t e d to the very much more v a r i a b l e nature of the atmosphere, e s p e c i a l l y i t s d i f f u s i v i t y . There i s some evidence that such p a r t i t i o n i n g i s d i f f e r e n t i n the day-time from that at n i g h t , probably because of the d i u r n a l v a r i a t i o n of s t a b i l i t y and wind speed ( P r i e s t l e y , 43 1959; Nickerson and Smiley, 1975; Nunez, 1974). T y p i c a l values of heat stored or released range from 0.1 to 0.35 Q*. Noting these r e l a t i o n s h i p s the f o l l o w i n g scheme of para m e t e r i z a t i o n was used to c h a r a c t e r i z e AQ i n suburban t e r r a i n . Four broad c a t e g o r i e s of suburban land use i n the area surrounding the s i t e were i d e n t i f i e d : m e t r o p o l i t a n n a t u r a l (Mn), i n d u s t r i a l / c o m m e r c i a l ( I C ) , pavement ( P ) , and r e s i d e n t i a l housing (Rh). Expanded d e s c r i p t i o n s of these c a t e g o r i e s are given i n Table 3.1 and the percentage a r e a l coverage of each i n the study area i s given i n Table 3.2. In the l a t t e r t a b l e the data are arranged i n t o the 16 equal area s e c t o r s of a c i r c l e of 2 km radi u s centred on the s i t e . U t i l i z i n g data given by Mather (1967), Terjung, et a l . (1971), Yap (1973), Nunez (1974), Nickerson and Smiley (1975), and Oke (1978 - unpublished) r e l a t i o n s h i p s between Q* and AQ^ f o r each land-use category were derived by l i n e a r r e g r e s s i o n as given i n Table 3.3. The appropriate AQg value f o r each sector was determined by weighting each equation i n Table 3.3 i n p r o p o r t i o n to the a r e a l coverage of each land-use category. A l l equations were then solved f o r a given Q*. The r e s u l t s were summed and the aggregate d i v i d e d by Q* to determine the p r o p o r t i o n of Q* a t t r i b u t e d to AQ . A mean p a r t i t i o n i n g of 0.23 Q* was found f o r a l l s e c t o r s . This i s i n e x c e l l e n t agreement w i t h the r e s u l t s of Ching, et a l . (1978) who found 0.24 Q* f o r an i n d u s t r i a l / c o m m e r c i a l area of St. L o u i s . This value a l s o l i e s between dry surface values of 0.31 to 0.65 Q* and vegetated surface values of 0.05 to 0.1 Q* reported by Monteith (1973). Nocturnal data are not as r e a d i l y a v a i l a b l e i n the l i t e r a t u r e , t h e r e f o r e the simpler weighting system o u t l i n e d below was necessary. For each of the four land-use c a t e g o r i e s l i s t e d i n Table 3.2 an average t o t a l a r e a l coverage value was c a l c u l a t e d . These were then combined i n t o a 44 TABLE 3.1 D e s c r i p t i o n of M e t r o p o l i t a n Land Use Categories .1 CATEGORY Me t r o p o l i t a n n a t u r a l (Mn) I n d u s t r i a l - Commercial (I-C) Pavement (P) R e s i d e n t i a l housing (Rh) DESCRIPTION inc l u d e s parks, f o r e s t e d areas, cemeteries, r e s i d e n t i a l lawns, boulevards and i s o l a t e d t r e e s and hedges. Although garages and a l l e y s were included here they represent a combined t o t a l of l e s s than 3% of a given s e c t o r area. i n c l u d e s b u i l t up areas along roads and l a r g e r b u i l d i n g s s c a t t e r e d throughout r e s i d e n t i a l areas (commercial, e d u c a t i o n a l , e t c . ) . T y p i c a l l y 1 - 3 s t o r i e s and f l a t r o o f s . The main s t r e e t of commer-c i a l areas was a l s o included i n t h i s category. r e s i d e n t i a l s t r e e t s , sidewalks and parking l o t s . s i n g l e f a m i l y d w e l l i n g s , 1 - 2 s t o r i e s t a l l w i t h p i t c h e d r o o f s and m u l t i p l e f a m i l y d w e l l i n g s were a l s o i n c l u d e d . 1 The c a t e g o r i e s chosen here were based on p r e - e x i s t i n g knowledge of the surface types present. In other areas other c a t e g o r i e s w i l l l i k e l y be r e q u i r e d , f o r example, heavy i n d u s t r i a l or compact commercial (> 10 storey) (e.g. Auer, 1978). 45 TABLE 3.2 Percentage A r e a l Land Use Coverage f o r 16 Sectors Centred on the Sunset Experimental S i t e SECTOR Mn I-C P Rh N 68 4 12 16 NNE 65 6 12 17 NE 64 12 11 15 ENE 61 13 11 15 E 60 12 12 16 ESE 68 6 11 15 SE 63 13 10 14 SSE 61 13 11 15 S 54 27 8 11 SSW 57 21 9 13 SW 67 4 12 17 WSW 63 11 11 15 W 62 10 12 16 WNW 66 10 10 14 NW 78 8 6 8 NNW 71 4 11 14 Suburban 64 11 11 14 Average 46 TABLE 3.3 Derived R e l a t i o n s h i p s Between Net All-wave R a d i a t i o n (Q*) and Volumetric Heat Storage (AQ g) LAND USE DAYTIME (Q* > 0) DERIVED RELATIONSHIPS SOURCES Me t r o p o l i t a n n a t u r a l (Mn) I n d u s t r i a l -Commercial (I-C) Pavement (P) R e s i d e n t i a l Housing (Rh) Nat u r a l Impervious AQg = 0.20Q* + 3 r = 0.91 n = 53 S A O = 9.2 W m~2 AQg AQ = 0.30Q* - 16 AQg = 0.39Q* - 14 r 2 = 0.99 n = 10 SAQ S - 7'° W m " 2 AQg = 0.27Q* - 17 3 NOCTURNAL (Q* < 0) AQ = 0.54Q* AQ = 0.90Q* Oke (unpublished) Terjung, et a l . (1971) , Yap (1973), Nunez (1974) Terjung, et a l . (1971) Yap (1973), Nunez(1974) Nickerson and Smiley (1975) 2, Mather (1967) 3 Nunez (1974) 3 1 These equations have been obtained by the combination of a number of r e l a t i o n s h i p s derived from d i f f e r e n t s u r f a c e s . Therefore i t was not p o s s i b l e to i n c l u d e any r e g r e s s i o n s t a t i s t i c s f o r the combined equations l i s t e d above. However, a l l of the i n d i v i d u a l r e l a t i o n s h i p s used here except Terjung, et a l . (1971) where n = 10, had r 2 > 0.8 and n > 20. 2 S t a t i s t i c s not given. 3 Not c a l c u l a t e d by r e g r e s s i o n , estimate only 47 simple urban or n a t u r a l c l a s s i f i c a t i o n . These values were then used as weighting f a c t o r s f o r the equations l i s t e d i n Table 3.3 r e s u l t i n g i n a 0.70 Q* suburban n o c t u r n a l p a r a m e t e r i z a t i o n . -2 -1 D a i l y t o t a l s were c o n s i s t e n t l y p o s i t i v e (0.1 to 0.8 MJ m day ) p r i o r to September 14, 1977 and c o n s i s t e n t l y negative t h e r a f t e r (-0.1 to -2 -1 -0.9 MJ m day ). This p o s i t i o n of the seasonal change-over i s i n approximate agreement w i t h that found f o r a n a t u r a l surface at A s t o r i a , Oregon (46° 12' N; S e l l e r s , 1965). There are a number of assumptions i n v o l v e d i n the scheme o u t l i n e d above: • i t ignores moisture, wind and geometry d i f f e r e n c e s f o r impervious surfaces. • i t assumes a s i n g l e suburban Q* value i s s u f f i c i e n t . Support f o r t h i s approach i s provided by Nunez (1974) and Oke (1974, 1978a) who show r e l a t i v e l y small i n t r a - u r b a n d i f f e r e n c e s . • i t ignores h y s t e r e s i s and other asymmetric f a c t o r s of heating and c o o l i n g . Urban s t u d i e s seem to show l e s s asymmetry than other surfaces (Terjung, et a l . , 1971; Nunez and Oke, 1977; Yap, 1973; Nunez, 1974). • there i s the danger that bulk s t a t i s t i c a l r e l a t i o n s h i p s , even though w e l l c o r r e l a t e d o v e r a l l , may give l a r g e and/or systematic e r r o r s f o r shorter time p e r i o d s , e.g. 1 h. Comparisons of time s e r i e s of c a l c u l a t e d and measured values shows the scheme does tend to overestimate measured values around midday f o r i n d i v i d u a l s u r f a c e s . However when combined i n t o the weighted suburban equation t h i s e f f e c t was of the order of 10 - 15 _2 W m r e p r e s e n t i n g only 2 to 4% of Q* at midday. • the changeover from the daytime (Q* > 0) to the n o c t u r n a l (Q* < 0) scheme produces an abnormal 'step' i n the course of AQ but s i n c e energy amounts 48 are small t h i s anomaly i s l i k e l y to be minor. In summary t h i s study uses the f o l l o w i n g constant parameterizations of AQg: Daytime (Q* > 0 ) : AQg = 0.23Q* Night (Q* < 0 ) : AQ = 0.70Q* 3.3) Bowen Ratio - Energy Balance E r r o r A n a l y s i s The e r r o r a n a l y s i s o u t l i n e d below f o l l o w s those of Cook and Rabinowicz (1963), Fuchs and Tanner (1970) and B a i l e y ( 1 9 7 7 ) . For a given r e s u l t Y determined from a combination of measurements (x^, x 2 , x^, •••> x^) which have as s o c i a t e d e r r o r s (6x,, 6x„, 6x~, 6x ) i t can be shown t h a t : 1 2 3 n Y = f ( x x + 6x 1, x 2 + 6 x 2 , x n +.5x n). (3.1) The t o t a l or maximum e r r o r i n Y can be found by d i f f e r e n t i a t i n g (3.1): 6Y = f ^ S x , + f ^ x 0 + . . . + j X s x . (3.2) 9x, 1 9x„ 2 9x n 1 2 n However there i s only a small p r o b a b i l i t y that a l l e r r o r s are i n the same d i r e c t i o n . The probable e r r o r i s found by squaring each term on the r.h.s. of (3.2) and t a k i n g the square root of t h e i r sum: ^ p r o b (3.3) The equivalent equations used to evaluate the probable e r r o r i n T, T , 3 , Q„ and Q u are given i n Appendix 2. The absolute and r e l a t i v e e r r o r s E H i n c u r r e d i n making temperature measurements w i t h the TIS were found using 49 informat i o n presented by Black, et a l . (1973), Tang, et a l . (1976), S p i t t l e h o u s e (pers. comm.) and l a b o r a t o r y t e s t i n g . 3.3.1) E r r o r s i n absolute temperature P o t e n t i a l e r r o r s i n c u r r e d i n o b t a i n i n g wet- and dry-bulb temper-atures were assessed using the diode c a l i b r a t i o n e r r o r s , the recorder accuracy and e r r o r s due to hand-scaling of the recorder c h a r t s . E r r o r s due to r a d i a t i v e heating of the sensors, v a r i a b i l i t y of the wet-bulb feed and v a r i a t i o n of T^ along the wick (Lourence and P r u i t t , 1969) were not evaluated. An e r r o r of approximately ±1.0 K was found to be t y p i c a l over the temperature range 273 to 293 K. 3.3.2) E r r o r i n temperature d i f f e r e n c e s P o s s i b l e e r r o r sources i n v o l v e d i n measuring temperature d i f f e r e n c e s i n c l u d e those a s s o c i a t e d w i t h matching and c a l i b r a t i n g the diodes, i n t e g r a t o r absolute c a l i b r a t i o n e r r o r , i n t e g r a t o r accuracy and the e f f e c t s of s i g n a l t r u n c a t i o n at the beginning and end of an i n t e g r a t i o n p e r i o d * . The e f f e c t s of e r r o r s due to the timer ( i . e . to d i s s i m i i l a r i t i e s of i n t e g r a t i o n period) were assumed n e g l i g i b l e . For hour l y averaged temper-ature d i f f e r e n c e s of 0.04 K to 0.20 K e r r o r s were ±2.5% to ±1.5%, r e s p e c t --3 i v e l y . I f a constant absolute e r r o r of ±1 x 10 i s assumed (1.5% of 1 The i n t e g r a t o r s i n t h i s logger f u n c t i o n continuously. However, the i n t e g r a t o r counts are only recorded during the 10 min run. Should the timer s t a r t or f i n i s h the i n t e g r a t i o n period when the i n t e g r a t o r i s b u i l d i n g towards another count the t o t a l could gain or l o s e 1 count. Since there are four such periods i n each hou r l y temperature gradient c a l c u l a t i o n the r e s u l t could t h e o r e t i c a l l y be out by ±4 counts, however t h i s i s h i g h l y u n l i k e l y . The random e r r o r i s expected to be much l e s s . 50 0.20 K) the r e l a t i v e e r r o r f o r a temperature d i f f e r e n c e of 0.04 K increases to 7.5%. The l a t t e r i s more conservative and i s used i n a l l f u t u r e c a l c u l a t i o n s . 3.3.3) E r r o r i n the Bowen r a t i o Assuming the psychrometer ' c o n s t a n t ' ( Y ) to be a true constant, the e r r o r s i n the Bowen r a t i o (6) were considered to r e s u l t from the dermin-a t i o n of At (AT or A T ) and the slope of the s a t u r a t i o n vapour pressure vs. W temperature curve (S). The former i s given i n Section 3.3.2 above and the e r r o r i n S was evaluated using the e r r o r s of the o p e r a t i o n a l equation (Lowe, 1977) and of T (Section 3.3.1). A constant r e l a t i v e e r r o r i n S W of 5.5% was found. 3.3.4) E r r o r i n net r a d i a t i o n and volume heat storage The sources considered to c o n t r i b u t e to an e r r o r i n the determin-a t i o n of net r a d i a t i o n (Q*) were the c a l i b r a t i o n e r r o r of the sensor and the r e s o l u t i o n of the recorder. A constant r e l a t i v e e r r o r of ±5% of Q* was assumed to apply at a l l times (Latimer, 1972). The e r r o r i n the volume heat storage (AQg) could not be o b j e c t i v e l y determined because of the method of c a l c u l a t i o n . The e r r o r i n AQ was set at ±5% of the corresponding Q* value used i n i t s computation. 3.3.5) E r r o r i n l a t e n t and s e n s i b l e heat f l u x d e n s i t i e s The e r r o r i n the l a t e n t (Q„) and s e n s i b l e (Q u) heat f l u x d e n s i t i e s are a f u n c t i o n of the e r r o r s i n Q*, AQg and 3. R e s u l t s are summarized i n Figures 3.2 and 3.3. The graphic form used here was p r i m a r i l y chosen over the t a b u l a r format because of the more compact form of the graph. I t a l s o / 53 demonstrates q u i t e r e a d i l y how the e r r o r i n a given term changes over the temperature gradient range used and how the e r r o r a l t e r s as the value of that term changes (e.g. changes i n 6 3 f o r 3 = 1.0 and 3 = 2.0). I t a l s o has the advantage of showing these changes continuously r a t h e r than the s t e p - l i k e form of a t a b l e , however i t i s l i k e l y to be slower to use than a t a b l e . There i s a d i f f e r e n t f a m i l y of curves f o r each value of T and thus S. Comparison of Figures 3.2 and 3.3 r e v e a l s that the r e l a t i v e e r r o r s i n 3, Q„ and Q are smaller f o r given values of AT and AT when T (and thus E H W W S) i n c r e a s e s . This i s due to a r e d u c t i o n i n the e r r o r a s s ociated w i t h determining r e l a t i v e l y l a r g e r vapour pressure d i f f e r e n c e s (Ae), s i n c e S = Ae/AT^. Because SQ* and 6AQg have been defined as being l i n e a r ( i . e . 6Q* = 6AQg = 0.05Q* f o r a l l Q* values) the graphs can be used f o r any Q* value. However, the absolute magnitude of Q„ and Q T must be determined (e.g. 1.7 E. H and 1.8) se p a r a t e l y . A summary of the procedure used to determine the values (assuming T w = 288 K) i s as f o l l o w s : 1) Locate the AT and AT^ values i n the upper r i g h t hand panel of Figure 3.2 f o r which the e r r o r s are to be found ( i n the example p l o t t e d i n F i g . 3.2 AT = -0.16 K and AT^ = -0.084 K) . The appropriate 3 value i s found at the point of i n t e r s e c t i o n of the chosen AT and AT^ values ( i n t h i s case 3 = 2.0). 2) The e r r o r i n 3 (63) c a n then be found by moving from the poi n t of the AT and AT i n t e r s e c t i o n h o r i z o n t a l l y across to the appropriate 3 curve i n w the upper l e f t hand panel ( i . e . i n our example 3 = 2.0 curve) and then moving d i r e c t l y down to the h o r i z o n t a l a x i s ( i n our example 63 = 0.45 or about 23%). 3) To f i n d the r e l a t i v e e r r o r i n Q p (^ Q^ ) continue v e r t i c a l l y downward to 54 the appropriate curve ( B = 2.0) i n the lower l e f t hand panel and read o f f 6Qg on the v e r t i c a l a x i s ( i n our example 60^, = 17.6%). F i n a l l y moving across to the next appropriate curve ( B = 2.0) i n the lower r i g h t hand panel to the lowest h o r i z o n t a l a x i s the r e l a t i v e e r r o r i n Q (SQ U) can be found ( i n our example 6Q U = 11.8%). I f Q* = 300 W m~2 then AQq, Q and Q u H E n -2 -2 would be 69.0, 77.0 and 154.0 W m , r e s p e c t i v e l y . Thus 6Q = 13.6 W m E -2 and 6Q = 18.2 W m . As one would expect from (1.5) and the constant n r e l a t i v e e r r o r s i n Q* and AQ the r e l a t i v e e r r o r s i n Q and QT7 p a r a l l e l o E H those i n B . However, note that increases i n the r e l a t i v e e r r o r s i n Q and E Q u tend to be smaller than the increase i n the r e l a t i v e e r r o r i n B . Note rl a l s o that the e r r o r s i n B , Q u and Q can increase q u i t e r a p i d l y w i t h only H E a small change i n the temperature d i f f e r e n c e s . This s e n s i t i v i t y i s a d i r e c t r e s u l t of the small magnitude of the temperature d i f f e r e n c e s . In the suburban tower study AT and AT^ were t y p i c a l l y l e s s than 0.05 K m * ( i . e . < ±0.2 K over the 4 m separation) w i t h AT u s u a l l y being w smaller i n magnitude than AT. In general the temperature d i f f e r e n c e s i n d i c a t e lapse c o n d i t i o n s (temperature decreasing w i t h height and AT and AT negative) during the day and weak lapse to i n v e r s i o n c o n d i t i o n s at w n i g h t . The absence of e i t h e r strong s t a b i l i t y or i n s t a b i l i t y i s t y p i c a l of urban climates (Oke, 1978a). An example of the e r r o r s i n the t u r b u l e n t f l u x e s t y p i c a l l y found i n t h i s study i s shown i n Figure 3.4. The e r r o r s (10 - 20% during the day and somewhat l a r g e r at n i g h t ) are l a r g e r than those u s u a l l y found w i t h t h i s approach over non-urban surfaces (e.g. Davies and A l l e n , 1973). This has obvious i m p l i c a t i o n s regarding the a p p l i c -a b i l i t y of t h i s approach (with the system at present) i n d r i e r and/or aerodynamically rougher urban areas. (Note a l s o the l a r g e r s c a t t e r f o r White Lake i n F i g . 3.1. At t h i s semi-arid s i t e humidity d i f f e r e n c e s were 600 r C N I 500 400 B 13 PN 300 4-1 •H CO C OJ o g 200 h 60 c w September 11, 1977 Sunset S i t e o — o / \ + q* o o x 0 -a—-© . • • — • /— • — • / o — o — o — o — o - 1 0 0 6 2 4 6 8 10 12 14 16 18 20 22 24 Time (PST) Figure 3.4 : Example of suburban energy balance showing t y p i c a l e r r o r s i n turbulent f l u x e s . 56 very s l i g h t and there i s some reason to suspect that the eddy c o r r e l a t i o n approach which only senses dry-bulb temperature f l u c t u a t i o n s i s b e t t e r s u i t e d than the Bowen r a t i o - energy balance approach.) However, given the c o n s t r a i n t s on t h i s system i n t h i s enviornment (see Ch. 2) e r r o r s of t h i s magnitude were considered acceptable and thus the Bowen r a t i o - energy balance approach was deemed a p p l i c a b l e to t h i s environment. CHAPTER FOUR BOWEN RATIO - ENERGY BALANCE RESULTS This chapter i s c e n t r a l l y concerned w i t h the i n f o r m a t i o n obtained using the Bowen r a t i o - energy balance approach at the Sunset suburban s i t e . The f i r s t s e c t i o n presents an overview of t h i s i n f o r m a t i o n . The f o l l o w i n g s e c t i o n s focus on p a r t i c u l a r f e a t u r e s . S p e c i a l a t t e n t i o n w i l l be drawn to the r o l e of e v a p o t r a n s p i r a t i o n i n the energy balance, i n c l u d i n g the magnitude and d i u r n a l v a r i a t i o n of the Bowen r a t i o and the response of the suburban area to a period of d r y i n g f o l l o w i n g p r e c i p i t a t i o n . 4.1) General Energy Balance Results By way of i n t r o d u c t i o n the m e t e o r o l o g i c a l c o n d i t i o n s during the study p e r i o d (August 19 - October 4, 1977) w i l l be summarized. P r i o r to the mid-August s t a r t of t h i s study Vancouver had been subjected to a prolonged dry s p e l l of about 5 weeks during which < 1 mm of p r e c i p i t a t i o n had been recorded. The ensuing 6 weeks were c h a r a c t e r i z e d by frequent p r e c i p i t a t i o n u s u a l l y w i t h only 2 - 3 days between events. I t was over t h i s 6 week pe r i o d that the bulk of the measurements were conducted. Although the p r e c i p i t a t i o n could be expected to keep s o i l moisture l e v e l s q u i t e high there were two d r y i n g periods of 6 - 7 days d u r a t i o n which should have allowed the s o i l to at l e a s t p a r t i a l l y dry. Thus i t w i l l be p o s s i b l e to examine the t u r b u l e n t energy p a r t i t i o n i n g over a f a i r l y broad spectrum of s o i l moisture c o n d i t i o n s . The a p p l i c a b i l i t y of the i n f o r m a t i o n obtained here depends l a r g e l y 57 58 on the e r r o r s a s s o c i a t e d w i t h the tu r b u l e n t f l u x e s (see Ch. 3.3). Shown i n Figure 4.1 are s e l e c t e d examples of the d i u r n a l energy balances found i n t h i s study. During the day the r e l a t i v e e r r o r s i n the tu r b u l e n t f l u x e s are g e n e r a l l y between 10% and 20%. I n d i v i d u a l cases of r e l a t i v e e r r o r s much l a r g e r than t h i s can be found. In many cases these e r r o r s occurred i n the morning or l a t e afternoon when the temperature gradients were very s m a l l . However, si n c e these times are a l s o c h a r a c t e r i z e d by l i t t l e a v a i l a b l e energy the absolute e r r o r s i n the tu r b u l e n t terms are s m a l l . In general the e r r o r s are l a r g e r than those encountered i n most n a t u r a l surface s t u d i e s , f o r example Davies and A l l e n (1973) report r e l a t i v e e r r o r s of l e s s than 5% i n the c a l c u l a t i o n of hour l y e v a p o t r a n s p i r a t i o n f o r p e r e n n i a l r y e -grass. On the other hand they are not out of l i n e w i t h the f o r e s t r e s u l t s of McNaughton and Black (1973) who found maximum r e l a t i v e e r r o r s i n h a l f -hourly e v a p o t r a n s p i r a t i o n estimates to be t y p i c a l l y about 20%. However, they f e l t the consistency of t h e i r r e s u l t s i n d i c a t e d that the random e r r o r s were somewhat sm a l l e r . The r e l a t i v e e r r o r s i n the suburban n o c t u r n a l t u r b u l e n t f l u x e s are o f t e n greater than 20%. However, the low energy a v a i l a b i l i t y tended to keep the absolute e r r o r s f a i r l y s m a l l . The probable e r r o r s i n both daytime t o t a l and 24 h t o t a l s of Q„ (and Q„) are about 7 - 10% w i t h the 24 h t o t a l e r r o r being s l i g h t l y l a r g e r . This i s i n good agreement w i t h McNaughton and Black (1973) who rep o r t maximum r e l a t i v e e r r o r s of 15% f o r 24 h t o t a l s of e v a p o t r a n s p i r a t i o n . I t should be c l e a r from t h i s d i s c u s s i o n that the Bowen r a t i o - energy approach i s a p p l i c a b l e to suburban energy balance s t u d i e s on a d a i l y , day-time t o t a l and even hour l y b a s i s . In Figure 4.1 i t i s very evident that the magnitude of Q was 500 400 300 200 100 0 -200 500 400 300 200 100 0 -100 -200 August 30, 1977 o - o O * ' V o Y -100 - o - o - o - o - c r E » \ • /  o ! 1 • - i 1 i _ September 10, 1977 o - o / \ / I * ^ J :V ^8=8=8-8=1 12 16 20 0 1 i 1 ' • § i 8 12 16 2 0 2 4 September 13, 1977 Time (PST) September 16, 1977 o ' \ 7 / r w \ \ 0 % t £ o-O - o - o m - J - 1 1 -L 1 ' 12 16 20 0 Time (PST) ~i 1 i\ 1 1 1 ' 4 8 12 16 20 24 Figure 4.1 : Examples of d i u r n a l p a t t e r n of suburban energy balance. Where p o s s i b l e estimates on s e n s i b l e heat f l u x and l a t e n t heat f l u x are included. e r r o r Ln 60 always a s i g n i f i c a n t , and o f t e n the dominant, energy s i n k . This was true throughout t h i s study. This d i r e c t l y opposes the 'hot' and 'dry' l a b e l o c c a s i o n a l l y a p p l i e d to urban climates (see Ch. 1.2). The p a r t i t i o n i n g between the s e n s i b l e (Q ) and l a t e n t (Q ) heat f l u x d e n s i t i e s on a daytime t o t a l b a s i s (g) i s given i n Table 4.1. Use of these s t a t i s t i c s dampens the hour-to-hour v a r i a b i l i t y i n the Bowen r a t i o (g) and provides a p i c t u r e of the o v e r a l l t u r b u l e n t energy p a r t i t i o n i n g . The a n a l y s i s was r e s t r i c t e d to periods of p o s i t i v e net r a d i a t i o n (Q*) as t h i s i s the p e r i o d of dominant energy exchange. I n d i v i d u a l hours were e l i m i n a t e d i f the e r r o r i n e i t h e r t u r b u l e n t f l u x was greater than 100% and values were r e s t r i c t e d to days having 7 or more hours of usable data. The e r r o r (Sg) a s s o c i a t e d w i t h a given g was determined: where 6QTT and 6Q_ are the probable e r r o r s a s s o c i a t e d w i t h Q„ and Q , n r . n t r e s p e c t i v e l y and n i s the number of hours used. Of the 24 days s u i t a b l e f o r a n a l y s i s g was <1.0 on 14 days and <2.0 on 22 days (Table 4.1). However, considerable day-to-day v a r i a b i l i t y i n g e x i s t s . This can be e x p l a i n e d , at l e a s t i n p a r t , by the i n f l u e n c e of p r e c i p i t a t i o n (e.g. low g values are a s s o c i a t e d w i t h p r e c i p i t a t i o n occurrences (Table 4.1). However, there are some low g v a l u e s , notably September 1, September 13 and September 14 which occur d e s p i t e the absence of p r e c i p i t a t i o n . I t i s hypothesized that some of t h i s type of day-to-day v a r i a b i l i t y i n g can be explained i n terms of lawn i r r i g a t i o n TABLE 4.1 Turbulent Energy P a r t i t i o n i n g - Daytime T o t a l s DATE AUGUST SEPTEMBER OCTOBER 19 1.07 0.11 21 2.08 0.33 27 1.33 0.10 28 0.39 0.05 29 0.98 0.09 30 1.06 0.09 31 1.63 0.15 1 0.46 0.07 5 0.63 0.05 8 0.65 0.06 9 0.71 0.06 10 2.39 0.25 11 2.15 0.23 13 0.47 0.05 14 0.65 0.07 15 0.74 0.08 16 0.56 0.06 17 0.72 0.07 21 0.51 0.07 22 1.98 0.23 25 0.79 0.07 28 0.30 0.08 1 0.92 0.08 3 1.65 0.19 ±6g PRECIPITATION (TJ 0.4 56.5 6.7 30.4 10.6 2.0 39.6 17.0 14.2 1 As recorded at VANCOUVER INTERNATIONAL AIRPORT 62 ( s p r i n k l i n g ) . This i s discussed i n more d e t a i l i n S e c t i o n 4.4. The r e s u l t s of Table 4.1 are a l s o i n good agreement w i t h previous research (see Chapter 1.2). For example Oke, et a l . (1972) found that hourly 3 values were u s u a l l y l e s s than u n i t y i n Montreal. There i s a l s o good agreement w i t h the energy balance s t u d i e s of Yap and Oke (1974) and Oke (1978b) who report 6 values of <2.0 f o r the F a i r v i e w r e s i d e n t i a l / commercial area of Vancouver and <1.0 f o r the Burnaby suburban area ( F i g . 1.2). Oke (1978b) a l s o shows 3 < 2.0 f o r a suburban area of Uppsala, Sweden which adds f u r t h e r support to the f i n d i n g s of t h i s study. The r e s u l t s of Table 4.1 a l s o compare favourably w i t h those of Ching, et a l . (1978) who report mid-day Bowen r a t i o s of 2.0 (3 h average values) f o r an i n d u s t r i a l / c o m m e r c i a l s i t e i n St. Louis Mo. and 0.7 f o r a nearby r u r a l s i t e . In summary i t i s apparent that the evaporative f l u x at the Sunset s i t e can be q u i t e l a r g e d e s p i t e the 35% r e d u c t i o n i n t r a n s p i r i n g surface area (see Table 3.2), i n f a c t the daytime trend i n the hourly 3 values i s not u n l i k e those found over non-urban surfaces such, as grass or f o r e s t s ( F i g . 4.2). However the trend i n 3 i s somewhat more v a r i a b l e than that u s u a l l y found over non-urban surfaces. By d e f i n i t i o n (1.7, 1.8), the v a r i a b i l i t y i n 3 w i l l r e s u l t i n d i s t i n c t hour-to-hour v a r i a b i l i t y i n the t u r b u l e n t f l u x e s (see F i g . 4.1). This v a r i a b i l i t y may be the r e s u l t of a number of f a c t o r s i n c l u d i n g n o n - s t a t i o n a r i t y i n the m e t e o r o l o g i c a l f i e l d s , i n s u f f i c i e n t averaging times, surface roughness, e t c . The i n f l u e n c e of these f a c t o r s on the turbulent energy p a r t i t i o n i n g i s discussed i n more d e t a i l i n Sections 4.2 and 4.3. Another fea t u r e of the daytime trend i n g i s the general symmetry around noon. This i s d i s t i n c t l y d i f f e r e n t from energy balance s t u d i e s conducted i n more h e a v i l y urbanized areas (Yap and Oke, 1974; Ching, et a l . , 1978) where Q H and thus g l a g s o •rH U rt u a OJ o ca o - September 8, 1977 D - September 11, 1977 1 1 o - September 17, 1977 V - August 29, 1977 0 -2 -A • -0 J t_ T7ii—r V ^ . ° - 0 - ° - 0 - 0 - n ^ O .T Cl \. 10 14 18 1 1— 1 i i i i i i i O-O' <. • - \ ,.v. V : v ; Z 1 -J-. . 0 -« -u-o->,--o 0^_o i i i i i i i 1 1 22 2 Time (PST) 10 14 18 22 o •H 4-1 rt M C cu o m -4 •T •• i r i i i o - Grass - September 1 r 26, i r - i — - • • 1957 V - Forest - July 14, 1970 \"*-\ o i l \ U \ \ » ' i i 27 i i i 10 14 Time (h) 18 22 Figure 4.2 : Diurnal v a r i a t i o n of B for Sunset s i t e . Grass (alphalfa brome) and forest ( f i r ) data from Tanner and Pelton (1960) and Black and McNaughton (1971) included for comparison. as 64 behind the afternoon r a t e of decrease of Q*, and f u l l y vegetated-surface s t u d i e s (McNaughton and Black, 1973; Black and G o l d s t e i n , 1977) where Q_ and thus 3 * l a g s behind the decrease i n Q*. This w i l l be discussed i n more d e t a i l i n S e c t i o n 4.3. The n o c t u r n a l 3 values were t y p i c a l l y negative at the Sunset suburban s i t e . Although t h i s opposes the r e s u l t s of Oke, et a l . (1972) and the i n d u s t r i a l / c o m m e r c i a l s i t e r e s u l t s of Ching, et a l . (1978) s i m i l a r r e s u l t s have been reported by Coppin (1978 - pers. comm. T. Oke). Assuming the a v a i l a b l e energy at n i g h t i s negative ( i . e . Q* - AQ < 0) the negative 3 values found at the Sunset s i t e i n d i c a t e that e i t h e r Q„ or Q (but not r. n both) w i l l be p o s i t i v e (see 1.7, 1.8). The occurrence of p o s i t i v e s e n s i b l e heat f l u x e s at n i g h t i s unique to the urban environment and i s discussed i n more d e t a i l i n S e c t i o n 4.3. 4.2) V a r i a b i l i t y i n the Turbulent Energy P a r t i t i o n i n g Due to S e c t o r a l D i f f e r e n c e s and N o n - S t a t i o n a r i t y In t h i s s e c t i o n aspects of the v a r i a b i l i t y i n the t u r b u l e n t energy p a r t i t i o n i n g due to s e c t o r a l d i f f e r e n c e s i n land use and n o n - s t a t i o n a r i t y i n the m e t e o r o l o g i c a l f i e l d s are discussed. This i n v o l v e s c o n s i d e r a t i o n of the v a r i a t i o n s i n the p a r t i t i o n i n g i n response to changes I n wind d i r e c t i o n and t o the e f f e c t s of land-sea breezes. 4.2.1) E f f e c t s of changes i n wind d i r e c t i o n Despite the general homogeneity of the suburban t e r r a i n surrounding t h i s s i t e there are d i f f e r e n c e s i n the p r o p o r t i o n of n a t u r a l and impervious surface cover i n d i f f e r e n t compass s e c t o r s (Table 3.2). This may be expected to l e a d to d i f f e r e n c e s i n the energy p a r t i t i o n i n g and t h e r e f o r e 65 the t u r b u l e n t f l u x e s measured at a f i x e d point as a r e s u l t of d i f f e r e n t d i r e c t i o n s of a i r f l o w . The data were c l a s s i f i e d according to the mean wind d i r e c t i o n during the hour of observation (and thus to a c e r t a i n p r o p o r t i o n of impervious surface cover; Table 3.2). Turbulent f l u x estimates were normalized by net r a d i a t i o n (Q*) to remove the d i u r n a l v a r i a t i o n i n t h i s term. The data were a l s o analyzed w i t h and without l a n d -sea breeze i n f l u e n c e s since t h i s phenomenon could a l s o lead to v a r i a b i l i t y i n the tu r b u l e n t f l u x e s . Neither p o p u l a t i o n i n d i c a t e d any r e l a t i o n s h i p between the tu r b u l e n t f l u x e s and the p r o p o r t i o n of impervious surface cover over which the a i r had t r a v e r s e d . A number of f a c t o r s may have i n f l u e n c e d t h i s outcome: the t u r b u l e n t f l u x e s were of t e n q u i t e v a r i a b l e even when the wind d i r e c t i o n was constant ( F i g . 4.3). This made i t d i f f i c u l t to a t t r i b u t e any given f l u c t u a t i o n to a change i n wind d i r e c t i o n , the n a t u r a l v a r i a b i l i t y i n wind d i r e c t i o n over the per i o d of one hour may lead to a f l u x estimate that i s not r e p r e s e n t a t i v e of any 1, 2 or even more of the 16 sect o r s used. This makes i t d i f f i c u l t to p r o p e r l y c a t e g o r i z e the turbu l e n t f l u x e s , the d i f f e r e n c e i n the p r o p o r t i o n of n a t u r a l and impervious surface cover between adjacent s e c t o r s i s t y p i c a l l y < 10% (Table 3.2) and t h i s may be too small a d i f f e r e n c e to detect w i t h the approach used i n t h i s i n v e s t i g a t i o n , changes i n the surface p r o p e r t i e s w i t h time, e s p e c i a l l y s o i l moisture, made i t d i f f i c u l t to compare days or even the morning and afternoon periods of one day, s o i l moisture may vary s p a t i a l l y depending on the n a t u r a l v a r i a b i l i t y i n p r e c i p i t a t i o n and p o s s i b l y the preponderence of lawn s p r i n k l i n g so that the a c t u a l s p a t i a l v a r i a b i l i t y i s not s o l e l y a f u n c t i o n of the p r o p o r t i o n Wind Direction I 0 13, •U •H c n U 500 400 300 200 100 SE - i 1 1 1 i Aug. 2 7 ( Q * y A Q c ) \ 7 \ \ O L /9/K\ \ o V QE B \ NNE I I 1 1 1 — — I r Aug. 29 / \ / ° M O d/ v • \ NW -i 1 1 n Sept. 10 />-o \ o , v. \ ••A of v o // . w 0/ , ° • v NW SE i 1 1 1 1 1 r Sept. 11 IT \ . , \ IJ O _ i i t — i — , i . '<•>'] i—i—i—i—i—i—n Sept. 22 o-o-°,*-A 12 16 H 16 : 8 1 2 1 6 Time (PST) 12 Figure 4.3 : Daytime pattern i n energy balance components on days with f a i r l y constant wind d i r e c t i o n . 67 of natural surface cover. Thus the surface mosaic was too complex for the analysis used. Nonetheless one can conclude that i f a systematic v a r i a t i o n existed i t appears to be r e l a t i v e l y small. A.2.2) E f f e c t of land-sea breeze c i r c u l a t i o n Because of Vancouver's coastal l o c a t i o n the meso-scale flow pattern i s often dominated by land-sea breezes, p a r t i c u l a r l y i n summer. Land-sea breeze occurrences were distinguished from synoptic wind patterns by applying the c r i t e r i o n that the d i u r n a l pattern of the wind d i r e c t i o n had to s h i f t from a north-easterly to a westerly d i r e c t i o n i n the morning or early afternoon and back to a north-easterly d i r e c t i o n a f t e r sunset. Four-teen days met t h i s requirement. However, on these days changes i n a i r temperature and humidity were small or absent. This may have been due to the tower s i t e being located about 12 km inland and/or the effectiveness of the mixing produced by atmospheric turbulence over the rough c i t y surface. This l i m i t e d the c r i t e r i a by which land-sea breezes could be i d e n t i f i e d . However, the sea breeze wind-shift and the s e t t i n g up of the return land flow occurred at about 9:00 to 11:00 PST and 20:00 to 21:00 PST, r e s p e c t i v e l y , which i s i n good agreement with the findings of Emslie (1968) at the F i r s t Narrows Bridge over Burrard Inlet ( F ig. 3.1). Although 14 days met the land-sea breeze c r i t e r i o n a number of other days may have been at l e a s t p a r t i a l l y influenced by these l o c a l winds. Recent work with mini-temperature-sondes and an acoustic radar at the Sunset s i t e i n d i c a t e that on occasion the sea breeze front passes the s i t e but remains undetected i n the surface boundary layer (D. Steyn, pers. comm.). I t therefore appears possible that the mixing produced by the rough 68 c i t y surface may g r e a t l y modify the near-surface sea breeze. This makes i t d i f f i c u l t to t y p i f y the phenomenon and to determine i f or how i t i n f l u e n c e s the t u r b u l e n t f l u x e s found i n t h i s study. I t a l s o means that- previous research on the behaviour and c h a r a c t e r i s t i c s of the surface and the near-surface atmospheric l a y e r s i n response to the sea breeze at non-urban l o c a t i o n s (e.g. Johnson and O'Brien, 1973; Neumann and Mahrer, 1975; Mahrer and P i e l k e , 1977; Simpson, et a l . , 1977) are not e a s i l y compared w i t h the r e s u l t s of t h i s study. For example, a recent study by Barbato (1978) shows that the moisture content of the sea breeze i n Boston, Mass. i s d i r e c t l y r e l a t e d to the r e g i o n a l wind speed and d i r e c t i o n p r i o r to the morning wind-s h i f t . To i l l u s t r a t e the d i f f i c u l t i e s encountered the energy balance components f o r s e l e c t e d 'sea breeze' and 'non-sea breeze' days are shown i n Figure 4.4. As shown on September 9 and 26 ( F i g . 4.4a,'b) and on other 'sea breeze' days there was a prolonged dip i n Q f o l l o w i n g the passage of H the sea breeze f r o n t . However, not a l l 'sea breeze' days demonstrated t h i s c o r r e l a t i o n ( F i g . 4.4c). According to the mean wind d i r e c t i o n the sea breeze f r o n t appeared to pass the s i t e on August 31 at about 9:00 PST, however Q increased q u i t e r e g u l a r l y u n t i l about 12:00 PST. The dip at n 12:00 PST could a l s o be i n t e r p r e t e d as the dips noted on the other 'sea breeze' days. S i m i l a r l y the tur b u l e n t f l u x p a t t e r n s shown i n Figure 4.4d, e and f a l s o c o n t a i n breaks or dips that could be i n t e r p r e t e d as an i n d i c a t o r or a r e s u l t of the passage of the sea breeze f r o n t , however the wind d i r e c t i o n s are d e f i n t e l y not sea breeze i n o r i g i n . In c o n c l u s i o n i t i s apparent that the inform a t i o n a v a i l a b l e i n t h i s i n v e s t i g a t i o n i s not capable of a c c u r a t e l y d e s c r i b i n g sea breeze charact-e r i s t i c s nor t h e i r p o t e n t i a l e f f e c t s on the surface l a y e r t u r b u l e n t f l u x e s . 500-400-300 200 100 0 — i 1 1 1 r (a) September 9 (Q* - AQ ) / ° / s V \ / ° 0 \ n Q F X J L. 12 16 ~~\ 1 1 1 r (b) September 26 A-a a / • t i V i \ ° 8 ' 12 Time (PST) 16 500 400 300 200 100 0 T 1 1 1— (d) August 27 o-°~o^Q* - AQg) -j ///A \ \ / V / r j _ a - D o O O .2/ ^ L : i L 8 12 16 12 Time (PST) Figure 4.4 : Comparison of daytime p a t t e r n i n energy balance components on sea breeze (a - c) and non-sea breeze (d - f ) days. Arrow ( t ) i n d i c a t e s time of sea breeze passage. 70 4.3) Magnitude and D i u r n a l P a t t e r n of the Sensible and Latent Heat Flux D e n s i t i e s I t i s the purpose of t h i s s e c t i o n to d i s c u s s the magnitude and d i u r n a l patterns of the s e n s i b l e (Q u) and l a t e n t (Q_) heat f l u x d e n s i t i e s found at the Sunset s i t e . I t i s d i v i d e d i n t o two subsections which d e a l w i t h the daytime and n o c t u r n a l p a t t e r n s , r e s p e c t i v e l y . Compared to most non-urban surfaces the t u r b u l e n t f l u x p a t t e r n over urban areas d i s p l a y s some unique f e a t u r e s . These i n c l u d e a l a g i n the decrease of the s e n s i b l e heat f l u x compared to the decrease i n net r a d i a t i o n (Q*) i n the l a t e a f t e r -noon, d i s t i n c t o s c i l l a t i o n s i n the daytime t u r b u l e n t f l u x p a t t e r n and the occurrence of p o s i t i v e t u r b u l e n t f l u x e s at n i g h t . 4.3.1) Daytime patte r n s i n the s e n s i b l e and l a t e n t heat f l u x d e n s i t i e s The f i r s t f e a t u r e of the t u r b u l e n t heat f l u x p a t t e r n to be discussed here i s that the s e n s i b l e heat f l u x d e n s i t y (Q„) of c i t i e s o f t e n , but not n always, lags behind the decrease i n net r a d i a t i o n (Q*) a f t e r mid-day ( F i g . 4.5; Yap and Oke, 1974; Ackerman and Hildebrand, 1977; Ching, et a l . , 1978). Evidence of such an e f f e c t was sought i n the Sunset data. Days w i t h heavy cloud cover were e l i m i n a t e d from a n a l y s i s because the v a r i a t i o n i n Q was H too small to evaluate. To s i m p l i f y the a n a l y s i s 3 or 4 h Q u and Q* energy t o t a l s (depending on the number of usable hours of data) were c a l c u l a t e d f o r both afternoon and morning periods and expressed as Q^ /Q* r a t i o s thereby n o r m a l i z i n g f o r r a d i a n t energy a v a i l a b i l i t y . This allowed days w i t h i n t e r -m i t t e n t or v a r i a b l e cloud cover to be examined. Days e x h i b i t i n g asymmetry i n the Q regime should then possess l a r g e r values of t h i s r a t i o i n the H afternoon. Only two days i n d i c a t e d c l e a r l y l a r g e r afternoon Q„/Q* r a t i o s . The Sensible Heat Flux S i t e s : (a) I n d u s t r i a l - commercial (b) R e s i d e n t i a l (c) Rural T — i — i — i — r - r — i — i — i i r Time (PST) Time (CST) Figure 4.5 : Example energy balances where Q H lagged behind the decrease i n Q* i n the afternoon i n Vancouver (Fairview) (Yap and Oke, 1974) and St. Lou i s , Mo. (Ching, et a l . , 1978). 72 daytime course of a v a i l a b l e energy (Q* - AQ ) and Q f o r these days are b H shown i n Figure 4.6. For comparison Figure 4.6 a l s o contains two examples when t h i s asymmetry was not present. Generally speaking, these days (September 10, 11) show an in-phase, f a i r l y symmetrical r e l a t i o n s h i p between Q and the a v a i l a b l e energy. H By d e f i n i t i o n Q„ must a l s o show a s i m i l a r r e l a t i o n s h i p w i t h the a v a i l a b l e energy ( F i g . 4.7). Over a well-watered n a t u r a l s i t e Q„ tends to remain high i n the afternoon, l a r g e l y i n response to the peak i n the atmos-ph e r i c vapour pressure d e f i c i t which t y p i c a l l y e x i s t s at t h i s time (McNaughton and Black, 1973; Black and G o l d s t e i n , 1977), an example i s given i n Figure 4.8. At the Sunset s i t e the atmospheric vapour pressure d e f i c i t a l s o peaked i n the l a t e afternoon at about 600 - 1000 Pa ( F i g . 4.7) but f o r some reason the e v a p o t r a n s p i r a t i o n p o t e n t i a l that t h i s created was not r e a l i z e d . The suburban r e s u l t s are t h e r e f o r e , not i n agreement w i t h those t y p i f y i n g e i t h e r other urban or many non-urban sur f a c e s . The f o l l o w i n g e x p l a n a t i o n i s o f f e r e d . At the Sunset s i t e approximately 35% of the surrounding surface cover i s impervious (Table 3.2) which t h e r e f o r e presents an almost i n f i n i t e r e s i s t a n c e to water vapour t r a n s p o r t . The s t a t e of atmospheric moisture demand th e r e f o r e has no relevance to these surfaces. The t r a n s p i r i n g s u r f a c e s , on the other hand, may be responding to the vapour pressure d e f i c i t during the day (assuming n o n - l i m i t i n g s o i l moisture) and e x h i b i t i n g the p a t t e r n commonly found over n a t u r a l surfaces. The amalgamation of the f l u x e s from these two surface regimes i n t o an a r e a l f l u x appears to e f f e c t i v e l y e l i m i n a t e asymmetry. When one views the e n t i r e spectrum of land use from r u r a l to h i g h l y impervious i t becomes apparent that as the percentage of impervious surface cover increases the i n f l u e n c e of the vapour Energy Flu x Density (W i—• CO UJ -O o o o o o o o o -2 Energy Flu x Density (W m ) OO H -2 Energy Flu x Density (W m ) Energy Flux Density (W m -2 o o o o o o o o o o o • — \ 1 a. o v ' OS }—* * t—» i CO (D t> X) o rt c o (T> 3 D " (D H 3 ft) OO H ^ 500 27 August " 30 August - 8 September - 11 September - 13 September - 16 September • i B S 400 *—' (Q* -AQ„) ,ox b ° o. • A • i /V- \ J cr o c r , i I I I (Q* - AQg) o-o - (Q* o AQS) / o (Q* - AQ S) /0-ov » (Q* " AQ ) o-r» S -Energy Flux Density h-1  N3 CO o o o o o o o • A 0 o / ) n \ II i i I I i : M 1 aa \o - II \ o o / \ 0 o . 1 \ 1 X \ // - \4 o o ffisw II '\ - o • \ IJ If i i i i i n (Q* " AQg) - ^ E \ y A , , , ,a\ 12 16 12 16 12 16 8 Time (PST) 12 16 12 16 12 16 l.Or 0.8 0.6 0.4 0.2h ct) PM 4-1 •H O •H U-1 0) O cu u 3 CO CO CU S4 PM u 3 0! > -• - - A / • • . / /V • • / / - \ • • / \ / • /v. • • •-• M • • • • • / • / - t / • . . ,1 1 1 1 1 • / • - / • / • .. 1 1 1. L. 1 1 I 1 1 1 • / • • / i i i i i . / • / • i i i i i l i I 1 1 12 16 12 16 12 16 8 Time (PST) 12 16 12 16 8 12 16 Figure 4.7 : Daytime patterns of Q and vapour pressure d e f i c i t . E I cn C o X 3 .H En 0) c w -100 10 12 14 Time (PST) 3 r ex, cu u-i ca >-i ai > P M Q l h 10 12 14 Time (PST) Figure 4.8 : An example where Q E l a g s behind the decrease i n Q* a f t e r mid-day over a f o r e s t , ( a f t e r McNaughton and Black, 1973) 76 pressure d e f i c i t w i l l decrease a l l o w i n g a l a r g e r p r o p o r t i o n of the a v a i l a b l e energy i n the afternoon to go to Q„. Thus i t seems reasonable to expect Q u to be low i n the afternoon at a r u r a l s i t e , i n between and in-phase w i t h the a v a i l a b l e energy at a suburban s i t e and high i n the afternoon at a h i g h l y impervious s i t e (e.g. Yap and Oke, 1974). This hypothesis i s w e l l supported by the r e s u l t s of Ching, et a l . (1978) where the aysmmetry i n 0-, was smaller at a r e s i d e n t i a l s i t e than at t h e i r h i g h l y impervious i n d u s t r i a l / c o m m e r c i a l s i t e and non-existent or even reversed (Q peak i n the morning) at t h e i r r l r u r a l s i t e ( F i g . 4.5). Further support i s a l s o given by Oke (1979) who found that the evaporative f l u x from an i r r i g a t e d lawn not only f o l l o w s the p a t t e r n of an ' i d e a l ' surface but that the evaporative f l u x i s f u r t h e r enhanced by m i c r o - s c a l e advection. The symmetry found here w i l l depend on the a v a i l a b i l i t y of s o i l moisture. When s o i l moisture i s a l i m i t i n g f a c t o r on the e v a p o t r a n s p i r a t i o n r a t e the increased surface r e s i s t a n c e may at l e a s t p a r t i a l l y o f f s e t the p o t e n t i a l created by the atmospheric vapour pressure d e f i c i t . At these times suburban areas could have Q patterns which more c l o s e l y resemble H those found i n more impervious areas. Another p o s s i b i l i t y e x i s t s and should be mentioned. The method used to determine the t u r b u l e n t f l u x e s may have masked the a c t u a l d i u r n a l p a t t e r n s . The Bowen r a t i o - energy balance approach used here included a p a r a m e t e r i z a t i o n of the volumetric heat storage (AQg) which forced the t o t a l t u r b u l e n t t r a n s p o r t (Q u + Q„) to be in-phase w i t h Q*. However, i f rl b there was a genuine aysmmetry i t should have appeared as p r o g r e s s i v e l y l a r g e r Bowen r a t i o s i n the afternoon which, g e n e r a l l y speaking, was not the case (e.g. F i g . 4.2). A second fea t u r e of the daytime p a t t e r n i n the t u r b u l e n t energy 77 f l u x e s i s the presence of s h o r t - p e r i o d f l u c t u a t i o n s that appear to be independent of Q* (e.g. F i g . 4.7 - August 27, September 11, 13). S i m i l a r f l u c t u a t i o n s have been reported by McNaughton and Black (1973) f o r a young Douglas f i r f o r e s t . They i n t e r p r e t the f l u c t u a t i o n s as being a consequence of the l a r g e f o r e s t roughness. This r e s u l t s i n a very low aerodynamic r e s i s t a n c e to vapour t r a n s p o r t and enhances the r o l e of m e t e o r o l o g i c a l c o n t r o l s on e v a p o t r a n s p i r a t i o n ( e s p e c i a l l y the vapour pressure d e f i c i t ) compared to a short crop. Thus one expects changes i n Q (and Q ) that are i n response to the m e t e o r o l o g i c a l wind and humidity c o n t r o l s and not the r a d i a n t energy a v a i l a b i l i t y . However, an examination of Figure 4.7 i n d i c a t e s that the f l u c t u a t i o n s are not simply a r e s u l t of the vapour pressure d e f i c i t . An a d d i t i o n a l or a l t e r n a t i v e explanation i s that the f l u c t u a t i o n s are a r e s u l t of i n s u f f i c i e n t observation averaging times. Yap and Oke (1974) found that a 2 h averaging p e r i o d was required to smooth f l u c t u a t i o n s i n urban s e n s i b l e heat f l u x e s over Vancouver. However, the v a r i a b i l i t y i n Q*, wind d i r e c t i o n , wind speed, e t c . that can occur over a 2 h p e r i o d n e c e s s i t a t e d the use of 1 h averaging periods. Given the a v a i l a b l e i n f o r -mation i t i s impossible to e l i m i n a t e t h i s type of problem i n the Sunset data. A study s p e c i f i c a l l y designed to d i s c o v e r the eddy spectrum and the nature of turbulence at t h i s s i t e i s c u r r e n t l y underway. 4.3.2) Magnitude and d i r e c t i o n of n o c t u r n a l s e n s i b l e and l a t e n t heat f l u x d e n s i t i e s Previous research i n h i g h l y impervious urban areas (Oke, et a l . , 1972; Yap and Oke, 1974; Ching, et a l . , 1978) have i n d i c a t e d that u n l i k e most non-urban surfaces the s e n s i b l e heat f l u x (Cv,) i s o f t e n d i r e c t e d away from the surface ( p o s i t i v e ) at n i g h t . Results from a r a t h e r l i m i t e d data 78 set (4 days) by Ching, et a l . (1978) i n d i c a t e that the l a t e n t heat f l u x (Q_) E i s a l s o p o s i t i v e throughout the night at a h i g h l y impervious s i t e . At a r e s i d e n t i a l s i t e Ching, et a l . (1978) found Q to be negative at n i g h t , n l i k e many non-urban su r f a c e s . On the other hand, Coppin (1978 - pers. comm. T. Oke) has found p o s i t i v e t u r b u l e n t f l u x e s at n i g h t , though more o f t e n they were near-zero or s l i g h t l y n e g a t i v e , i n a suburban area of A d e l a i d e , A u s t r a l i a . Evidence of such features was sought i n the Sunset data. In the f o l l o w i n g a n a l y s i s i t has been assumed that the net a v a i l a b l e energy (_Q* - AQ ) i s always negative at n i g h t . This i m p l i e s that AQ i s l e s s than the measured Q* and that the p a r a m e t e r i z a t i o n of AQ (0.7Q*) provides a reasonable approximation of the a c t u a l value. In keeping w i t h these assumptions the signs of the t u r b u l e n t f l u x e s w i l l be s t r e s s e d more than t h e i r magnitudes. I t should a l s o be noted that the i n d u s t r i a l / commercial r e s u l t s of Ching, et a l . (1978) i n d i c a t e that (Q* - AQ g) i s p o s i t i v e at night i n h i g h l y impervious areas. Thus i t appears as i f the assumptions used here cannot be a p p l i e d u n i v e r s a l l y . To be considered i n t h i s a n a l y s i s a given n i g h t had to have at l e a s t 10 h of data. Bowen r a t i o s at the Sunset s i t e were t y p i c a l l y negative but were o c c a s i o n a l l y p o s i t i v e . Because the s i g n of (Q* - AQg) i s n e g a t i v e , p o s i t i v e Q E (Q H negative) values occur when 8 < -1 and p o s i t i v e Q H (Q E negative) values when -1 £ B < 0 (see 1.7, 1.8). Both f l u x e s w i l l be negative i f -2 B i s p o s i t i v e . F l u x magnitudes were u s u a l l y l e s s than 20 W m but were -2 o c c a s i o n a l l y as l a r g e as 100 W m Nocturnal patterns of the energy balance components are shown i n Figure 4.9. P o s i t i v e values of Q u and/or Q„ (but never simultaneously) were recorded i n 21 of the 29 n i g h t s s u i t a b l e f o r i n v e s t i g a t i o n . Of the other 8 n i g h t s only one had c o n s i s t e n t l y negative Q F and Q H ( i . e . 6 > 0 ) . CM I e •H W a CU o 00 u cu c w lOOr 50 0 -50 -100 August 28 - 29 ' J\/T 1 100 r September 15 - 16 50 0 -50 -100 • I 1 1— L 18 20 22 24 100 50 0 -50 -100 September 17 -18 8 17 19 21 23 1 3 Time (PST) September 26 - 27 to -V--V-.-y.-V, , °\ D:S:o:S:D;8:g:9A ° (Q* - AQ S) ° \ V i • _J 1 1 — — 1 a n - n — 1 T3..S3 ' \ O - O „ o ,g_o-o-o-o-o-o-o-o-o • I 1 — - — 1 ' — / 3 5 7 Time (PST) 17 19 21 23 1 17 19 21 23 1 Figure 4.9 : Examples of suburban nocturnal energy balances, 80 The other 7 n i g h t s had hours w i t h p o s i t i v e t u r b u l e n t f l u x e s however the e r r o r a s s o c i a t e d w i t h the appropriate f l u x was > 100% and hence the s i g n could not be c o n f i d e n t l y s t a t e d . Of the 21 n i g h t s w i t h p o s i t i v e t u r b u l e n t f l u x e s , 7 had 5 h or more of p o s i t i v e Q values and 8 had 5 h or more of n p o s i t i v e Q_ values. Yap and Oke (1974) were the f i r s t to report the occurrence of p o s i t i v e Q values at n i g h t . This f e a t u r e was dominant 1.2 m above the F a i r v i e w r o o f -H top s i t e and common 20 m above the roof (70 - 80% of surrounding area covered by impervious s u r f a c e s ) . The frequent but not dominant occurrence of upward heat flow (Q„ or QIT) at night i n the present study i s i n good hi n agreement w i t h t h e i r r e s u l t s . The d i f f e r e n c e between the r e s i d e n t i a l s i t e r e s u l t s of Ching, et a l . (1978) and those of the present study may be explained i n terms of the height of measurement i n v o l v e d . As Yap and Oke (1974) show t h i s f e a t u r e i s l i k e l y to decrease w i t h height away from the urban/air i n t e r f a c e . The r e s u l t s of Ching, et a l . (1978) r e f e r to c o n d i t i o n s about 22 m above r o o f - l e v e l whereas those of t h i s study are f o r about 10 m above mean r o o f - l e v e l . The r e s u l t s of the present study are i n good agree-ment w i t h those of Coppin (1978 - pers. comm. T. Oke) who re p o r t s o c c a s i o n a l p o s i t i v e n o c t u r n a l t u r b u l e n t f l u x e s i n a suburb of Adelaide: 4.4) E v a p o t r a n s p i r a t i o n and Surburban Water Use As an i n t r o d u c t i o n to t h i s s e c t i o n the course of the energy balance components during a 'drying p e r i o d ' (a pe r i o d devoid of p r e c i p i t a t i o n input to the surface water balance) i s examined. Daytime values of the energy balance components f o r the period September 8 - 1 4 are shown i n Figure 4.10. Daytime t o t a l Bowen r a t i o values (B) are a l s o i n c l u d e d . The d r y i n g p e r i o d began a f t e r a thunderstorm on September 7. The CNl I 6 >. 4-1 •H CO c cu o r H Pn >. 60 M CD C Pd 500 400 300 200 100 0 Day 1 - September 8 (Q* " AQ ) • A s \ • o A ' / V D \ v - : v \ \o J 2_L . - f t 8 12 16 500p Day 4 - September 11 400 300 200 100 0 (Q* " AQ ) / / • _ l l I I I Q Day 2 - September 9 c> ° N^ \ o / ,D / " ^ A JL i i 1 1 — J I f i 8 12 16 Time (PST) Day 6 September 13 ^0-0 o o / A D / \ \ o • h o.. • o / v - ' \ A/ V. a&Sj L \ o \ _i a Day 3 - September 10 / - v - \ si--o / V o w IK i £ i o j 8 12 16 r Day 7 September 14 /A' x o 8 12 16 16 8 8 12 Time (PST) Figure 4.10 : Energy balance components during a suburban drying period. 12 16 82 storm l a s t e d f o r about 1 - 2 h and was r a t h e r l o c a l i z e d ('vll mm at Vancouver I n t e r n a t i o n a l A i r p o r t but only 1 - 4 mm at other s t a t i o n s i n Vancouver). During the ensuing 4 days the t u r b u l e n t energy p a r t i t i o n i n g reversed: i n i t i a l l y the l a t e n t heat f l u x was dominant, then the s e n s i b l e heat f l u x replaced i t as the main energy s i n k . The speed of t h i s r e v e r s a l might be expected to r e f l e c t the change i n the amount of s o i l moisture a v a i l a b l e f o r e v a p o t r a n s p i r a t i o n . The l a t e n t heat f l u x from the t o t a l suburban area during Days 1 and 2 of the d r y i n g period i s equivalent to a 4 mm depth of water. Assuming that impervious surfaces c o n t r i b u t e a n e g l i g i b l e amount, and c o n s i d e r i n g the percentage of the area covered by such surfaces (about 35% - Table 3.2) i t f o l l o w s that the remaining vegetated areas c o n t r i b u t e d the equivalent of 5 - 6 mm of water. This probably r e s u l t e d i n s u f f i c i e n t s o i l moisture d e p l e t i o n to cause the r e d u c t i o n i n Q noted on Days 3 and 4. No data were a v a i l a b l e f o r Day 5 h i but on the f o l l o w i n g two days 6 had decreased to values s i m i l a r to that of Day 1 of the d r y i n g p e r i o d , d e s p i t e the absence of p r e c i p i t a t i o n . The 'drying' ended w i t h p r e c i p i t a t i o n during the evening of September 14 - 15 ( i . e . Day 7). I t i s g e n e r a l l y accepted that e v a p o t r a n s p i r a t i o n i s c l o s e l y r e l a t e d to the a v a i l a b l e s o i l moisture ( P r i e s t l e y and T a y l o r , 1972; Davies and A l l e n , 1974; Barton, 1979). (Unfortunately problems w i t h the s o i l moisture measurements i n t h i s study rendered the r e s u l t s useless.) Assuming the decrease i n 6 on Days 6 and 7 i s not i n e r r o r the r e q u i r e d increase i n s o i l moisture may have been brought about by urban i r r i g a t i o n ( e s p e c i a l l y lawn s p r i n k l i n g ) . To give an i n d i c a t i o n of the amount of water s u p p l i e d by s p r i n k l i n g the r e s u l t s of an independent study w i l l be discussed. The d i u r n a l 83 2 p a t t e r n of water use f o r a 0.21 km area i n South Vancouver i s given i n Figure 4.11*. Hydrograph 1 represents t y p i c a l water use by t h i s area i n the w i n t e r / s p r i n g / f a l l seasons whereas hydrograph 2 i s t y p i c a l of the much greater summer use. Therefore the area between the two curves gives an approximation of the t o t a l amount of water used i n s p r i n k l i n g i n one day. Taking t h i s amount and assuming i t i s uniformly d i s t r i b u t e d over the 0.12 2 km of lawn present i n t h i s area corresponds to an a p p l i c a t i o n of about 10 mm of water ( i . e . equivalent to the p r e c i p i t a t i o n event on September 7). Thus i t seems c e r t a i n that urban lawns possess s i g n i f i c a n t l y greater s o i l moisture than n a t u r a l r u r a l areas, e s p e c i a l l y during prolonged dry s p e l l s . Considering that d a i l y t o t a l s of e v a p o t r a n s p i r a t i o n are about 3 mm or l e s s at t h i s time of year, the independent study i n d i c a t e s that s p r i n k l i n g amounts are c e r t a i n l y i n excess of the amounts r e q u i r e d to e x p l a i n the recovery of i n the suburban energy balance a few days a f t e r r a i n . P r i o r to August 19, 1977 (the s t a r t of t h i s study) there had been no p r e c i p i t a t i o n f o r about 3 weeks and l e s s * t h a n 0.7 mm f o r about 5 weeks. N o n - i r r i g a t e d grass areas at and around the s i t e were completely brown. However, daytime t o t a l Bowen r a t i o values were <2.1 (see Table 4.1 -August 19, 21). At t h i s time the water use by the Greater Vancouver Water D i s t r i c t (GVWD) was at i t s highest l e v e l of the year w i t h a demand 2 approximately 2.5 times that found i n the w i n t e r months ( F i g . 4.12) . Thus we hypothesize that lawn s p r i n k l i n g probably plays an important r o l e i n keeping 8 r e l a t i v e l y low i n the suburbs. In an attempt to prove that the decrease i n 8 on Days 6 and 7 of the 'drying p e r i o d ' was a r e s u l t of s p r i n k l i n g , the GVWD d a i l y records were 1 Dafa c o l l e c t e d and s u p p l i e d by Vancouver C i t y Engineering Dept. 2 Data c o l l e c t e d and supplied by Greater Vancouver Water D i s t r i c t . 84 T 1 1 1 1 1 1 1 1 1 r Time (h) Figure 4.11 : Water demand hydrographs f o r a r e s i d e n t i a l area of Vancouver, 1971. 1 - F a l l - winter - s p r i n g day 2 - Hot summer day w i t h s p r i n k l i n g (data c o l l e c t e d and supplied by Vancouver C i t y Engineering Dept.) 85 T 1 1— r Frequent P r e c i p i t a t i o n A f t e r August 21 i i \ i i i i 1 1 1 1  J F M A M J J A S O N D Figure 4.12 : Greater Vancouver Water D i s t r i c t water use, 1977. (data c o l l e c t e d and s u p p l i e d by Greater Vancouver Water D i s t r i c t ) 86 examined. I t was f e l t that the hypothesis would be proven i f these records showed a d i s t i n c t increase i n water use during the l a t t e r part of t h i s d r y i n g p e r i o d . U n f o r t u n a t e l y i n d i v i d u a l water consumption i s not monitored i n Vancouver, so a n a l y s i s was r e s t r i c t e d to the flow r a t e i n two p i p e l i n e s (Stanley Park p i p e l i n e and U n i v e r s i t y Endowment Lands -U n i v e r s i t y of B r i t i s h Columbia (UEL-UBC) p i p e l i n e ) . The Stanley Park p i p e l i n e serves much of the west end of Vancouver and through r e s e r v o i r s connects to parts of Richmond and Tsawwassen ( m u n i c i p a l i t i e s to the south of Vancouver). Therefore, i t serves a wide v a r i e t y of consumers ( i n d u s t -r i a l , commercial, r e s i d e n t i a l , etc.) and has a f a i r l y l a r g e flow r a t e 9 -1 ( i 1.59 x 10 1 day ). Winter flow r a t e s were examined to determine a t y p i c a l ' n o n - s p r i n k l i n g ' r a t e . This was f e l t to represent a base flow against which the flow f o r summer days could be compared. The d i f f e r e n c e was expected to be a good approximation of the water used f o r s p r i n k l i n g . Although i t was p o s s i b l e to i s o l a t e the s p r i n k l i n g component f a i r l y 9 c o n f i d e n t l y when the water use i n summer was high (maximum about 4.8 * 10 1 day ^ - see a l s o J u l y and August i n F i g . 4.12) the f l o w r a t e s i n September were not s t a t i s t i c a l l y d i f f e r e n t from the base flow. Thus the decrease i n g i n the l a t t e r part of the d r y i n g period can not be c o n f i d e n t l y s t a t e d as being a r e s u l t of s p r i n k l i n g . This outcome may have been a consequence of the l a r g e flow r a t e , the complex network and the v a r i e t y of consumers. A second t e s t was conducted using the smaller UEL-UBC p i p e l i n e . This l i n e does not feed any r e s e r v o i r s and serves i n s t i t u t i o n a l , r e s i d e n t i a l and r e c r e a t i o n a l users ( i n no s p e c i f i c o r d e r ) . T y p i c a l w i n t e r flow r a t e s 8 —1 are about 1.6 x 10 1 day . Again i t was p o s s i b l e to i s o l a t e the s p r i n k l i n g term when the demand was high but not during the study p e r i o d . 87 In c o n c l u s i o n the p a t t e r n i n 3 during the l a t t e r part of t h i s d r y i n g period could not be explained and i s t h e r e f o r e open to at l e a s t two i n t e r p r e t a t i o n s . F i r s t , the decrease i n 3 on Days 6 and 7 i s f i c t i t i o u s and the r e s u l t s are due t o , say advection or meso-scale/synoptic changes. Second, t h i s decrease i n 3 i s due to s p r i n k l i n g but the a n a l y s i s was not capable of proving i t s r o l e . C e r t a i n l y the South Vancouver study, the GVWD annual c y c l e of water use and the low 3 values that occurred at the s t a r t of t h i s study p o i n t to the importance of s p r i n k l i n g as a water source i n g e n e r a l , but they do not prove that the decrease i n 3 on these s p e c i f i c days was a r e s u l t of s p r i n k l i n g . This could be r e s o l v e d by repeating the experiment i n an area where the water use i s monitored more c l o s e l y ( i . e . i n areas where i n d i v i d u a l houses are monitored) or by observation of the frequency of s p r i n k l i n g i n the area studied and a l a r g e array of s o i l moisture measurements. CHAPTER FIVE MODELLING DAYTIME EVAPOTRANSPIRATION 5.1) I n t r o d u c t i o n The purpose of t h i s chapter i s to examine the f e a s i b i l i t y of modelling suburban e v a p o t r a n s p i r a t i o n . E v a p o t r a n s p i r a t i o n modelling techniques are u s u a l l y employed so as to e l i m i n a t e or reduce the need to make f i e l d o bservations, e s p e c i a l l y s i n c e measurement can be c o s t l y , but al s o because the data gained may only have l i m i t e d s p a t i a l v a l i d i t y . Model s e l e c t i o n depends on the nature and d e s i r e d accuracy of output, and the nature of the input parameters a v a i l a b l e or r e q u i r i n g measurement and t h e i r accuracy. In t h i s study the modified v e r s i o n of the P r i e s t l e y and Taylor (1972) model developed by Davies and A l l e n (1973) w i l l be used and i s w r i t t e n : d where a ' can be estimated: S d + Y 1 S^ - slope of the s a t u r a t i o n vapour pressure versus temperature curve; y -psychrometric 'constant'; Q* - net all-wave r a d i a t i o n ; AQg - net volumetric heat storage and 6 - sum of the s e n s i b l e heat f l u x (Q u) d i v i d e d by the l a t e n t heat f l u x (Q,,) over the daytime p e r i o d . This expression has been E s u c c e s s f u l l y used by Davies and A l l e n (1973), B a i l e y (1977) and Barton (1979) to show that a' i s d i r e c t l y r e l a t e d to s o i l moisture. The absence 88 of any u s e f u l s o i l moisture data i n the present study l i m i t s the scope of t h i s i n v e s t i g a t i o n but a' was experimentally determined to assess i t s value i n the suburban environment. Two s p e c i a l cases of (5.1), namely the e q u i l i b r i u m and p o t e n t i a l r a t e s , are discussed below. 5.1.1) E q u i l i b r i u m e v a p o t r a n s p i r a t i o n The e q u i l i b r i u m e v a p o t r a n s p i r a t i o n r a t e (Q„~) was o r i g i n a l l y EQ developed by S l a t y e r and M c l l r o y (1961) and can be w r i t t e n : This form i s i d e n t i c a l to (5.1) when a' = 1.0 and thus: a' = Q /Q E EQ • T h e o r e t i c a l l y (5.2) i s only a p p l i c a b l e when the surface and the atmosphere are both saturated or i n the case of a d r i e r environment where the s a t u r a t i o n d e f i c i t s at the surface and at some height are greater than zero, but i d e n t i c a l . The existence of e i t h e r c o n d i t i o n i n Nature i s u n l i k e l y . This l e d S l a t y e r and M c l l r o y (1961) and Monteith (1965) to b e l i e v e that (5.2) would have l i m i t e d a p p l i c a b i l i t y . However, t h i s has not proven to be the case as Denmead and M c l l r o y (1970), Davies (1972), Wilson and Rouse (1972), Rouse and Stewart (1972) and Stewart and Rouse (1976a) have obtained s a t i s f a c t o r y e v a p o t r a n s p i r a t i o n estimates from f a i r l y dry surfaces w i t h (5.2). This appears to be l a r g e l y a r e s u l t of the mid-range p o s i t i o n of a' = 1.0 during n o n - p o t e n t i a l c o n d i t i o n s ( B a i l e y , 1977). 90 5.1.2) P o t e n t i a l e v a p o t r a n s p i r a t i o n P o t e n t i a l e v a p o t r a n s p i r a t i o n CO.™) can be defined as the r a t e of r t water l o s s from a 'wet' surface r e s t r i c t e d only by the a v a i l a b l e energy and not by the water supply (Tanner, 1967). N P r i e s t l e y and Taylor (1972) suggest that when a i r t r a v e l s a long d i s t a n c e over a moist surface: QpE = a ( ^ 7 ) ( Q * - A V ( 5 - 3 ) where: a - e m p i r i c a l l y d e r i v e d constant. For p o t e n t i a l e v a p o t r a n s p i r a t i o n they found a to be about 1.26 f o r a wide v a r i e t y of su r f a c e s . S i m i l a r values have been obtained by Davies and A l l e n (1973) and Stewart and Rouse (1976b, 1977). However, f o r some n a t u r a l surfaces a appears to take a value nearer u n i t y , i n c l u d i n g l i c h e n mat (Rouse and Stewart, 1972; Stewart and Rouse, 1976a), Douglas f i r (McNaughton and Bl a c k , 1973) and a bare and p a r t i a l l y blackened s o i l surface (Barton, 1979). These values represent the upper l i m i t to a' f o r that p a r t i c u l a r s u r f ace. I t i s d i f f i c u l t to d e f i n e the ' p o t e n t i a l r a t e ' i n a c i t y . There may i n f a c t be more than one ' p o t e n t i a l r a t e ' . For example, one when the e n t i r e suburban surface i s wet, one when the impervious surfaces are dry but the vegetated areas are s t i l l s aturated and p o s s i b l y one when the only t r a n s p i r i n g surfaces are those a f f e c t e d by s p r i n k l i n g . By examining periods immediately f o l l o w i n g p r e c i p i t a t i o n ( e n t i r e surface wet) i t may be p o s s i b l e to assess a' under c o n d i t i o n s c l o s e to those d e f i n i n g ' p o t e n t i a l e v a p o t r a n s p i r a t i o n ' . I t should a l s o be noted that (5.1 to 5.3) were o r i g i n a l l y developed f o r use over extensive homogeneous surfaces and thus are l i m i t e d to advection f r e e s i t u a t i o n s . However, an urban 'surface' i s composed of a 91 wide array of c l i m a t o l o g i c a l l y d i s s i m i l a r elements i n c l u d i n g pavement, b u i l d i n g s , moist or even saturated lawns and t r e e s . Therefore the equations are being examined under c o n d i t i o n s f o r which they were not intended, but they seemed the most appropriate because of t h e i r proven a p p l i c a b i l i t y over a wide range of surfaces i n c l u d i n g b a r l e y and t a l l grass ( S z e i c z and Long, 1969), f i e l d beans (Davies, 1972), pasture, beans, bare s o i l , l a k e s and oceans ( P r i e s t l e y and T a y l o r , 1972), corn (Wilson and Rouse, 1972), l i c h e n mat (Rouse and Stewart, 1972), p e r r e n i a l ryegrass (Davies and A l l e n , 1973) Douglas f i r (McNaughton and Black, 1973) and soybean ( B a i l e y , 1977) and because of the r e l a t i v e l y simple array of input v a r i a b l e s they r e q u i r e . Barton (1979) presents an a l t e r n a t i v e way to-assess the evapotrans-p i r a t i o n from non-saturated surfaces using the P r i e s t l e y and Taylor (1972) model. In t h i s scheme a i s defined as a constant whose value depends on the nature of the surface. A v a r i a b l e i s introduced which i s d i r e c t l y r e l a t e d to s o i l moisture. This scheme i s shown to perform very w e l l over both bare and grass covered s u r f a c e s . However, without s o i l moisture data t h i s approach does not provide any more in f o r m a t i o n than the a' approach. I t a l s o r e q u i r e s a knowledge of a, and as w i l l be shown a cannot be e a s i l y defined i n t h i s suburban environment. I f these shortcomings can be over-come i n f u t u r e s t u d i e s t h i s approach i s worthy of f u t u r e research. Estimates of a' can be obtained using e i t h e r 24h or daytime ( p o s i t i v e net r a d i a t i o n ) t o t a l s . The l a t t e r were chosen f o r three reasons: 1) The dominant p e r i o d of evaporation c o i n c i d e s w i t h that of p o s i t i v e net r a d i a t i o n . 2) The number of days w i t h a f u l l 24 h of usable data were l i m i t e d because of the frequency of r a i n , m issing data (maintenance, etc.) and data 92 discarded because of the s i z e of the e r r o r s a s s o c i a t e d w i t h the t u r b u l e n t f l u x estimates. 3) Daytime t o t a l s have been s u c c e s s f u l l y used by a number of researchers to evaluate the performance of the e q u i l i b r i u m model and/or to evaluate a' (Davies, 1972; Davies and A l l e n , 1973; Wilson and Rouse, 1972; B a i l e y , I t should a l s o be pointed out that daytime t o t a l s of a v a i l a b l e energy (Q* - AQ ) are greater than 24 h t o t a l s and that daytime t o t a l Q i s b E s l i g h t l y smaller than 24 h t o t a l Q„ unless there i s heavy d e w f a l l . As a E r e s u l t a' (see 5.1) i s g e n e r a l l y l e s s on a daytime r a t h e r than 24 h b a s i s w i t h the d i f f e r e n c e depending on the magnitude of (Q* - AQg) on a daytime t o t a l and 24 h t o t a l b a s i s and the amount of e v a p o t r a n s p i r a t i o n / d e w f a l l at n i g h t (e.g. Tanner and Jury, 1975). Daytime t o t a l a' (a') were c a l c u l a t e d i f 7 h or more of usable data e x i s t e d . I n d i v i d u a l hours were el i m i n a t e d i f g was negative or i f the e r r o r i n Q was greater than 75%. E 5.2) R e s u l t s 5.2.1) E q u i l i b r i u m and measured e v a p o t r a n s p i r a t i o n The r e s u l t s of the comparison of measured, e q u i l i b r i u m evapotrans-p i r a t i o n and the r e s u l t i n g a' values are given i n Table 5.1. The e r r o r (6a') i s c a l c u l a t e d : 1977) . where: 6EQ E = ( Z ( 6 Q E ) 2 ) J S TABLE 5.1 Comparison of Measured (Q_) and E q u i l i b r i u m E Model (Q^r,) Daytime T o t a l E v a p o t r a n s p i r a t i o n 1 DATE n ^EQ a' ±6a' 1977 (h) (MJ AUGUST 19 7 3.6 5.1 0.70 0.06 27 10 4.0 6.0 0.67 0.05 28 7 1.4 1.2 1.13 0.08 29 9 3.1 4.0 0.79 0.06 30 9 3.9 3.5 0.81 0.06 31 9 3.3 4.8 0.60 0.05 SEPTEMBER 1 9 3.1 5.5 0.92 0.07 5 8 4.6 4.9 0.95 0.06 8 11 4.5 4.6 0.98 0.06 9 11 5.3 5.6 0.94 0.06 10 10 2.4 5.3 0.46 0.05 11 10 3.0 5.9 0.50 0.05 13 8 5.4 5.4 1.00 0.06 14 9 2.5 2.6 0.96 0.07 15 7 1.1 1.2 0.96 0.08 16 9 3.2 2.9 1.10 0.08 17 8 1.9 2.1 0.89 0.06 21 10 2.7 2.4 1.13 0.10 22 9 1.2 • 2.2 0.57 0.06 25 8 3.5 4.0 0.89 0.05 OCTOBER 1 7 2.9 3.3 0.87 0.06 3 7 2.0 3.0 0.65 0.05 1 n - number of hours used 94 6 Z% • ( E ( 6 V 2 ^ 2 and SQgQ i s c a l c u l a t e d as a f u n c t i o n of the e r r o r s i n Q * , AQg and (see 5.2). The s c a t t e r i n the a' values (0.49 to 1.27) can i n p a r t , be explained by examining the response of the suburban t e r r a i n to periods of d r y i n g f o l l o w i n g p r e c i p i t a t i o n . Two such periods w i l l be discussed v i z : P e r i o d 1 (August 28 - September 5) and P e r i o d 2 (September 8 - 14). Daytime comparisons of Q and Q during Drying P e r i o d 1 are E EQ shown i n Figure 5.1. Approximately 64 mm of p r e c i p i t a t i o n was recorded at Vancouver I n t e r n a t i o n a l A i r p o r t i n the week p r i o r to t h i s d r y i n g p e r i o d w i t h almost 90% of the p r e c i p i t a t i o n o c c u r r i n g from August 2 3 - 2 5 . Rain-f a l l ended at about 10:15 PST on August 28 and energy balance measurements were undertaken immediately. Thus measurements were conducted w h i l e a l l suburban surfaces ( n a t u r a l and impervious) were s t i l l wet. To the f i r s t order Q on August 28 would appear to c l o s e l y approximate Q ( F i g . 5.1) EQ E w i t h a s l i g h t tendency to underestimate (see F i g . 5.2 and Table 5.1). The daytime t o t a l a' (1.13) f o r t h i s day may be i n t e r p r e t e d as an i n d i c a t i o n of the s i z e of t h i s term when the surface i s t r u l y 'wet' (a more d e t a i l e d d i s c u s s i o n of t h i s term i s presented l a t e r i n t h i s c h a pter). The over-e s t i m a t i o n of Q,, by Q_,_ on a daytime t o t a l b a s i s on the ensuing three days E EQ probably r e l a t e s to the d r y i n g of the impervious surfaces followed by p a r t i a l d r y i n g of the n a t u r a l s u r f a c e s . This i s a l s o shown i n the hourly patterns of a' ( F i g . 5.2) and the increase i n the vapour pressure d e f i c i t ( F i g . 5.1). On the f i f t h day of d r y i n g (September 1) the p r o p o r t i o n of a v a i l a b l e energy used by Q„ again increased to the extent that the e q u i l i b r i u m value provides a good estimate of measured e v a p o t r a n s p i r a t i o n 300-200 100 0-August 28 a' = 1.13 'P cr 1 J L August 29 a' = 0.79 itJ la 3 ^ August 30 a' = 0.81 (QVs AQ g) p fa; ^ August 31 a' = 0.60 A / \ i • September 1 a' = 0.92 / 0 I) r September 5 a' = 0.95 o, -> o \ « \ y \ o - o o • »-£A o a-a ^ O -I I I L_ Iff If _J I I I L_ X 8 12 16 8 12 16 8 12 16 8 12 16 8 12 16 Time (PST) 8 12 16 * r © - I A 1000 - o .A • J \ O - / V o A 0 / o / \ / * o - / -500 -o / o - o / - / \ / - 0 0 / 0 / 0 / o - / - / • O 0 / o o " J v 0 / o / o / o - / 0 0 / o - o 1 1 1 i I I i i / o 1 1 1 1 1 1 1 1 1 1 i i i i i o - o 1 1 1 1 i 8 12 16 8 12 16 8 12 16 8 12 16 8 12 16 8 12 16 Time (PST) Figure 5.1 : Suburban Drying P e r i o d 1 (August 28 - September 1, September 5, 1977. August 28 r August 29 2.0 1.0 kM r August 30 r August 31 j i — i -i t i i — i — i 8 ' 12 16 8 12 T6 8 12 fe j i — i — i September 1 r September 5 n ' T O " • i i I I I i i 16 8 12 16 8 12 16 8 12 16 • • I L. Time (PST) Figure 5.2 : Hourly v a r i a t i o n of a ' during Drying P e r i o d 1. M 3 97 on both a hourly and daytime t o t a l b a s i s ( F i g s . 5.1, 5.2). Approximately 30 mm of p r e c i p i t a t i o n was recorded at the A i r p o r t between September 2 and 4. On the f o l l o w i n g day (September 5) Q_„ was a EQ good approximation of Q on both an hourly and a daytime t o t a l b a s i s . E Instrumental maintenance prevented any measurements on September 6 and 7. Drying P e r i o d 2 began on September 8 ( F i g . 5.3) f o l l o w i n g a p p r o x i -mately 11 mm of p r e c i p i t a t i o n on September '7. S i m i l a r to Drying P e r i o d 1 a' f o l l o w s a U-shaped p a t t e r n ( F i g . 5.4). On the f i r s t two days (September 8, 9) and the l a s t two days (September 13, 14) Q i s i n good EQ agreement w i t h Q on a daytime t o t a l b a s i s , but on an h o u r l y b a s i s a' i s E q u i t e v a r i a b l e ( F i g . 5.5) p r i m a r i l y due to tthe v a r i a b i l i t y i n Q (see E d i s c u s s i o n Ch. 4) and the s e n s i t i v i t y of a' to the d i f f e r e n c e between Q„ and Q _ during low energy p e r i o d s . Drying P e r i o d 2 concluded w i t h r a i n EQ during the l a t e evening of September 14 and the morning of September 15. The observations from Drying Periods 1 and 2 prompts suggestion of the f o l l o w i n g g e n e r a l i z a t i o n s : 1) The e q u i l i b r i u m r a t e o f t e n c l o s e l y approximates measured evapotrans-p i r a t i o n on both an hourly and/or daytime t o t a l b a s i s i n a suburban area comprised of approximately 35% impervious surface cover types. 2) The response of the suburban area to d r y i n g appears to be q u i t e r a p i d w i t h marked decreases i n a' g e n e r a l l y o c c u r r i n g two to three days a f t e r p r e c i p i t a t i o n . However, t h i s decrease then seems to be l i m i t e d so that a' increases again t h e r e a f t e r . This recovery may not remain such that a' = 1.0 as found i n the two d r y i n g periods discussed above. For example, a' was l e s s than 1.0 at the end of the more prolonged d r y i n g p e r i o d immediately p r i o r to the beginning of t h i s study (up to August 20). 500f September 8 a* = 0.98 I 400 300 200 100 0 September 9 a' = 0.94 o \ i i • ' ' September 10 a' = 0.46 ( Q * - A Q ) o-ox S o o 0 A 1 f J I 1 L . September 11 September 13 September 14 a' = 0.50 o o / \ / ti A * 9 l - o j &1 '. o 1 • r a ' = 1.00 o-o ° K • o \ 0.96 W Vo ^ X If8 I a I I 12 16 8 12 16 8 12 16 8 12 16 8 12 16 8 12 16 Time (PST) 1000r 500h -• A / o-o » 1 1,. 1 1—1— o / • o / 0 / o - / / o-o o o'° V " / 0 / _ o-o 1 1 1 1 1 _ o /V o / - o jo / o ~o / o / o Ol 1 1 1 1 o-o O / 0 • .w - / 0 / 0 1 1 1 1 1 0 • r-o / -O O / o °* ° 1 1 1 1— 12 16 8 Time (PST) Figure 5.3 : Suburban Drying Period 2 (September 8 - September 14, 1977). vo 00 P r e c i p i t a t i o n (mm day *) c i - i ft) Ln -> TJ ri ft) o Xi o 3 Cu 3 cu s I fD fD C L 3 OQ TJ ft! i-l H-O Cu cn CO 3 Cu N) •O > c OQ NJ C CJ> CD NJ OO o CO fD XI rt a> s-ft) 1-1 o " T - -\— NJ O T -NJ - r -o •o O I— oo o NJ ft) 1-1 1 ^ H- H-O 3 Cu OQ NJ 66 r September 8 r September 9 r September 10 2.0 l « 1.0 . y r- September 11 • • • • i I September 13 r September 14l J I I L _ l L l _ J 1 1 8 12 16 8 12 16 8 12 16 8 12 16 8 12 16 Time (PST) Figure 5.5 : Hourly v a r i a t i o n of a' during Drying Period 2. 8 12 16 101 P r i o r to August 20 there had been no measurable p r e c i p i t a t i o n f o r about 5 weeks. The grass at a n o n - i r r i g a t e d s i t e (about 1.5 km NW of the Sunset s i t e ) was completely brown and the s o i l water p o t e n t i a l measurements gave values between 1500 and 1700 Pa; approximately the w i l t i n g - p o i n t of many p l a n t s (Rose, 1966). On the other hand s o i l water p o t e n t i a l values f o r an i r r i g a t e d lawn were about 10 Pa, which i s near to f i e l d c a p a c i t y . Therefore even during extremely dry c o n d i t i o n s i r r i g a t e d surfaces can be expected to f r e e l y t r a n s p i r e . Oke (1979) suggests that they do so at an enhanced r a t e due to advection of heat from the surrounding dry areas. The value of a' f o r August 19 was 0.70. A s i m i l a r value was found f o r August 20, however t h i s was based on only 6 h of data but i t does lend support to the previous day's r e s u l t . Such a f i g u r e i s i n t e r e s t i n g i n i t s own r i g h t . I t i n d i c a t e s that i n an area c o n s i s t i n g of 35% impervious surface cover and where p r e c i p i t a t i o n had not occurred f o r about 5 weeks e v a p o t r a n s p i r a t i o n was s t i l l proceeding at about three quarters of the e q u i l i b r i u m r a t e . There can be l i t t l e question that these r e s u l t s are the outcome of a h i g h l y complex set of near-surface processes and any attempt to speculate on the a p p l i c a b i l i t y of t h i s model i n other areas w i t h d i f f e r e n t land uses would be questionable. Nontheless, t h i s model may provide a b a s i s f o r estimates of e v a p o t r a n s p i r a t i o n i n other suburban areas. The most d i f f i c u l t d e c i s i o n w i l l be the s e l e c t i o n of a' (or a'). Further research i n t o the value of a' (and a ' ) , e s p e c i a l l y i n r e l a t i o n to s o i l moisture a v a i l a b i l i t y , may prove most b e n e f i c i a l . A l t e r n a t i v e l y i t may be p o s s i b l e to determine, or at l e a s t approximate a' from more d e t a i l e d s t u d i e s of p r e c i p i t a t i o n , s p r i n k l i n g and land use. 102 5.2.2) P o t e n t i a l e v a p o t r a n s p i r a t i o n As o u t l i n e d at the outset of t h i s chapt er i t i s d i f f i c u l t to define ' p o t e n t i a l ' e v a p o t r a n s p i r a t i o n i n the c i t y . For example, one may d e f i n e the ' p o t e n t i a l ' r a t e as the evaporative r a t e when the e n t i r e surface i s wet. However, the impervious surfaces are l i k e l y to dry c o n s i d e r a b l y f a s t e r than the n a t u r a l surfaces w i t h the a c t u a l r a t e depending on the amount of standing water, wind speed, net r a d i a t i o n , e t c . , f o l l o w i n g the event. C l e a r l y t h i s i s a complex problem w i t h numerous f a c t o r s a l s o i n f l u e n c i n g the evaporative r a t e from the vegetated s u r f a c e s . U n f o r t u n a t e l y no records were kept as to when the impervious surfaces d r i e d out. This plus the l a c k of s o i l moisture data l i m i t s the d i s c u s s i o n i n the f o l l o w i n g examples. However, i f Q„ i s proceeding at some ' p o t e n t i a l r a t e ' i n the b c i t y i t may be i d e n t i f i e d by examining the evaporative f l u x a f t e r p r e c i p i t a t i o n occurs. Three days were examined, August 28, September 16 and September 21. On August 28 and September 16 energy balance measurements were s t a r t e d l e s s than 2 h a f t e r p r e c i p i t a t i o n had ended, however the measurements on September 21 were not s t a r t e d u n t i l about 12 h a f t e r the p r e c i p i t a t i o n ended. On the morning of August 28 approximatey 7 mm of p r e c i p i t a t i o n was recorded at the the A i r p o r t . On September 15 2 mm were recorded and a th t r a c e occurred on the morning of the 16 . P r i o r to September 21 a p p r o x i -mately 40 mm of p r e c i p i t a t i o n was recorded at the A i r p o r t . About 65% of t h i s t o t a l was recorded on September 19 w i t h another 30% coming from i n t e r m i t t e n t showers on September 20. The showers ended by about 1700 PST at the A i r p o r t . P l o t t e d i n Figure 5.6 are evaporative f l u x e s and hourly a' values f o r these days. The e q u i l i b r i u m r a t e and daytime t o t a l a' values are a l s o i n c l u d e d . I t i s apparent that a' and a' values tend to be r 2. 1. Time (PST) Figure 5.6 : Daytime comparison of measured and e q u i l i b r i u m ( Q E and Q E Q» r e s p e c t i v e l y ) e v a p o t r a n s p i r a t i o n r a t e s and the hourly trend i n a' at the Sunset s i t e during ' p o t e n t i a l c o n d i t i o n s . 104 s i g n i f i c a n t l y greater than 1.0 f o l l o w i n g p r e c i p i t a t i o n . However, there was not enough i n f o r m a t i o n to s t a t e how these values r e l a t e to the ' p o t e n t i a l r a t e ' i n a suburban area. Future research i s warranted e s p e c i a l l y i f more d e t a i l e d s t u d i e s of lawn s p r i n k l i n g , s o i l moisture and the time r e q u i r e d f o r impervious surfaces to dry out can be undertaken. CHAPTER SIX CONCLUSIONS This study sought to examine e v a p o t r a n s p i r a t i o n i n the context of the a r e a l energy balance of a suburban area i n Vancouver, B.C. using the Bowen r a t i o - energy balance approach. The Bowen r a t i o was obtained from d i f f e r e n t i a l psychrometric measurements conducted above mean r o o f - l e v e l . The f o l l o w i n g i s a summary of the f i n d i n g s of t h i s study. 1) The Bowen r a t i o - energy balance approach can be used i n the suburban environment. E r r o r s i n the turbulent f l u x e s were t y p i c a l l y about 10 -20% ( o c c a s i o n a l l y l a r g e r ) . Greater and p o s s i b l y unacceptably l a r g e e r r o r s could occur i n d r i e r and/or aerodynamically rougher urban areas. 2) The most d i f f i c u l t problem i n implementing the Bowen r a t i o - energy balance approach i s the determination of the v o l u m e t r i c heat storage. In t h i s study the vo l u m e t r i c heat storage was parameterized i n terms of the net r a d i a t i o n . The l i m i t a t i o n s of t h i s s o l u t i o n were documented. A q u a n t i t a t i v e assessment of t h i s term i s g r e a t l y d e s i r e d . 3) A s i g n i f i c a n t and o f t e n dominant p r o p o r t i o n of the net r a d i a t i o n at the suburban s i t e was u t i l i z e d i n l a t e n t heat t r a n s f e r . I t was shown that under c e r t a i n c o n d i t i o n s urban i r r i g a t i o n ( e s p e c i a l l y lawn s p r i n k l i n g ) can s u b s t a n t i a l l y increase s o i l moisture and thereby the a v a i l a b i l i t y of water f o r evaporation. The t u r b u l e n t f l u x e s i n t h i s study tended to show an in-phase r e l a t i o n s h i p w i t h net r a d i a t i o n . This appears to be a r e s u l t of the decreasing r o l e of the vapour pressure 105 106 d e f i c i t as an evaporative c o n t r o l as the land use changes from r u r a l to h e a v i l y urbanized. 4) Sustained periods of p o s i t i v e t u r b u l e n t f l u x e s o f t e n occurred at n i g h t at t h i s suburban s i t e . However, the Bowen r a t i o was predominantly negative i n d i c a t i n g that only one t u r b u l e n t f l u x was p o s i t i v e . The growing data base on t h i s f e a t u r e i n d i c a t e that the s i g n of the Bowen r a t i o may depend on the measurement height and the degree of u r b a n i z a t i o n . 5) The energy balance data d i d not r e v e a l any s e c t o r a l dependency. Although t h i s may serve as a f i r s t approximation i n f u t u r e s t u d i e s of suburban areas, i t would be of value to examine t h i s dependency i n areas where a more d i s t i n c t v a r i a t i o n i n land use e x i s t s . 6) The data i n t h i s study were incapable of i s o l a t i n g the i n f l u e n c e ( i f any) of the sea breeze oh t u r b u l e n t energy p a r t i t i o n i n g at the surface. This was p r i m a r i l y a problem of i d e n t i f i c a t i o n . The urban surface can apparently modify the sea breeze to the extent that i t can pass the s i t e but remain undetected i n the near-surface atmospheric l a y e r s . 7) Daytime t o t a l s of e v a p o t r a n s p i r a t i o n normalized by the e q u i l i b r i u m r a t e o f t e n showed c o n s i d e r a b l e , but c o n s i s t e n t , v a r i a t i o n . U n f o r t u n a t e l y i t was not p o s s i b l e to develop a r e l a t i o n s h i p between t h i s r a t i o and s o i l moisture (which could then be t e s t e d as an estimate of daytime water l o s s from other suburban areas) as the l a t t e r were not a v a i l a b l e . However, t h i s r a t i o was o f t e n near u n i t y ( l a r g e l y due to s o i l moisture r e p l e n i s h -ment by p r e c i p i t a t i o n and lawn s p r i n k l i n g ) during the study p e r i o d and thus the e q u i l i b r i u m r a t e may provide an i n d i c a t i o n of the s i z e of the evaporative f l u x i n other well-watered suburban areas. Further research on the value of t h i s r a t i o , e s p e c i a l l y i n r e l a t i o n to s o i l moisture a v a i l a b i l i t y , could prove to be b e n e f i c i a l . 107 REFERENCES Ackerman, B. and P.H. Hildebrand, 1977: Turbulent e n e r g e t i c s of urban and r u r a l p l a n e t a r y boundary l a y e r s . Proc. f a l l meeting of A. G.U., Pullman, Wash. Abs t r a c t i n EOS, 58, 1146. Ackerman, T.P., 1977: A model of the e f f e c t of aeroso l s on urban cl i m a t e s w i t h p a r t i c u l a r a p p l i c a t i o n to the Los Angeles b a s i n . J . Atmos. S c i . , 34, 531 - 547. Auer, A.H. 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Meteorol., 13, 880 - 890. 114 APPENDIX ONE NOTATION A B C D I-C K+ *H L v Mn <EQ ^H(e) QH(YST) UPPER CASE ROMAN temperature d i f f e r e n c e equivalent temperature d i f f e r e n c e equivalent temperature d i f f e r e n c e equivalent temperature d i f f e r e n c e equivalent i n d u s t r i a l - commercial land use incoming g l o b a l s o l a r r a d i a t i o n f l u x d e n s i t y r e f l e c t e d g l o b a l s o l a r r a d i a t i o n f l u x d e n s i t y eddy d i f f u s i v i t y f o r heat exchange eddy d i f f u s i v i t y f o r water vapour exchange l a t e n t heat of v a p o r i z a t i o n m e t r o p o l i t a n n a t u r a l land use atmospheric pressure (Chapter 2) pavement (Chapter 3) l a t e n t heat f l u x d e n s i t y e q u i l i b r i u m e v a p o t r a n s p i r a t i o n r a t e anthropogenic heat f l u x d e n s i t y s o i l heat f l u x d e n s i t y s e n s i b l e heat f l u x d e n s i t y s e n s i b l e heat f l u x d e n s i t y as measured by eddy c o r r e l a t i o n system s e n s i b l e heat f l u x d e n s i t y as measured by yaw sphere -thermometer system mV mV mV mV dimensionless -2 W m W m 2 2 -1 m s 2 -1 m s J k g " 1 dimensionless kPa dimensionless W m -2 W m W m -2 W m -2 W m -2 W m -2 W m -2 115 -2 Q J J / D \ s e n s i b l e heat f l u x d e n s i t y as measured by Bowen W m r a t i o - energy balance approach -2 Q p o t e n t i a l e v a p o t r a n s p i r a t i o n W m PE Rh r e s i d e n t i a l housing land use dimensionless S, slope of the s a t u r a t i o n vapour pressure versus Pa K ^  temperature curve at T w and T r e s p e c t i v e l y T dry-bulb a i r temperature K TTT wet-bulb a i r temperature K w Y dependent v a r i a b l e b b' c P c' C i n t d d' 8<V m t x LOWER CASE ROMAN c a l i b r a t i o n constant (Chapter 2) i n t e r c e p t of l i n e a r r e g r e s s i o n equation (Appendix 2) i n t e g r a t o r output slope of l i n e a r r e g r e s s i o n equation i n t e g r a t o r output s p e c i f i c heat of a i r at constant pressure i n t e g r a t o r output sensor c a l i b r a t i o n zero-plane displacement height i n t e g r a t o r output vapour pressure s a t u r a t i o n vapour pressure at wet-bulb temperature recorder output s i g n a l wet- or dry-bulb temperature independent v a r i a b l e height surface roughness l e n g t h dimensionless K counts 10 mm K mV _ 1 counts 10 min 1 J k g " 1 K _ 1 counts 10 min 1 K mV _ 1 m counts 10 min 1 Pa Pa mV K dimensionless m m 116 UPPER CASE GREEK dry a d i a b a t i c lapse r a t e net moisture advection; r a t e per u n i t volume (per u n i t h o r i z o n t a l surface area) net energy ( l a t e n t and s e n s i b l e ) advection; r a t e per u n i t volume (per u n i t h o r i z o n t a l surface area) net energy storage; r a t e per u n i t volume (per u n i t h o r i z o n t a l surface area) net moisture storage; r a t e per u n i t volume (per u n i t h o r i z o n t a l surface area) dry-bulb temperature d i f f e r e n c e wet-bulb temperature d i f f e r e n c e mean vapour pressure d i f f e r e n c e net r u n o f f wet- or dry-bulb temperature d i f f e r e n c e height d i f f e r e n c e p o t e n t i a l temperature d i f f e r e n c e p o t e n t i a l wet-bulb temperature d i f f e r e n c e K n f 1 kg m s W m -2 -2 W m i ~ 3 " ! kg m s K K Pa mm, kg m s K m K K LOWER CASE GREEK constant i n equation 5.3 v a r i a b l e i n equation 5.1 v a r i a b l e i n equation 5.1 used on a daytime t o t a l b a s i s Bowen r a t i o daytime t o t a l Bowen r a t i o psychrometric constant r a t i o of molecular weight of water to mean molecular weight of dry a i r dimensionless dimensionless dimensionless dimensionless dimensionless Pa K - 1 dimensionless l a t e n t heat of v a p o r i z a t i o n d e n s i t y of a i r temperature d i f f e r e n c e equiva 118 APPENDIX TWO BOWEN RATIO - ENERGY BALANCE ERROR ANALYSIS The probable absolute e r r o r i n a given r e s u l t Y as a f u n c t i o n of '1' 2' , x measurements i s : n 6Y = 9Y « x , f + ^ x Y + ^ - 1 J 'V 9 x2 2 (A2.1) A2.1) E r r o r i n Absolute Temperature In general wet- and dry-bulb temperatures are determined from a c a l i b r a t i o n equation of the form: t = a + bm where: t = T or T ; a, b - i n t e r c e p t and slo p e , r e s p e c t i v e l y determined from w r e g r e s s i o n a n a l y s i s and m - recorder input s i g n a l . Therefore the probable e r r o r (<5t) i s : fit 3t (A2.2) Since 3t/3a = 1, 3t/3b = m and 3t/3m = b (A2.2) becomes: 6t = ( 6 a ) 2 + (m6b) 2 + (b6m) 2 (A2.3) The e r r o r i n the i n t e r c e p t (a) and the slope (b) of a t y p i c a l sensor used i n the TIS are 0.06 K and 0.0015 K mV \ r e s p e c t i v e l y . The e r r o r s a s s o c i -ated w i t h the recorder and hand-scaling of the charts r e s u l t e d i n an e r r o r (6m) of ±2 mV. Over the temperature range 273 - 293 K the absolute e r r o r i s ther e f o r e ±1.0 K. A2.2) E r r o r i n Temperature D i f f e r e n c e Hourly averaged wet- and dry-bulb temperature d i f f e r e n c e s are c a l c u l a t e d as: , (a' - b') + (c« - d ' ) x _6_ x c a l ( A 2 . 4 ) 4 c. . i n t where: At = AT or AT W; a', b', c', d' - i n t e g r a t o r outputs f o r the four 10 min i n t e g r a i o n periods occuring i n each hour (counts/10 min); c ^ n t - . i n t e g r a t o r c a l i b r a t i o n (1000 counts mV 1 h *) and c a l - sensor c a l i b r a t i o n (K mV * ) . The net r e s u l t was m u l t i p l i e d by 6 to convert the counts/10 min to counts per hour. This can be r e s t a t e d : A t = (A - B) + (C - D) x M l ( A 2 > 5 ) 4 where; A, B, C, D - temperature d i f f e r e n c e e q u i v a l e n t s (mV) f o r the four i n t e g r a t i o n p e r i o d s . Therefore: 6At = 3At^V + •• • '3 A t » ) 2 + ( ^ ) : (A2.6) As a working assumption i t i s assumed A ^ B ^ C - D ^ x a n < ^ : 1 2 0 6At = + &4 (A2.7) 1 The e r r o r i n x i - s a f u n c t i o n of i n t e g r a t o r accuracy ( 0 . 5 % - Tang, et a l . 2 1 9 7 6 ) , i n t e g r a t o r c a l i b r a t i o n e r r o r ( 0 . 2 % ) and a s i g n a l t r u n c a t i o n e r r o r ( ± 1 count). The e r r o r i n the slope of the c a l i b r a t i o n equation of a t y p i c a l - 3 - 1 sensor i s 1 . 5 x 1 0 K mV . S o l u t i o n of the p a r t i a l s g i v e s : 3At 3A = 0 . 2 5 x c a l (K mV l) 3At •3 X = ± 0 . 2 5 x c a l 3At 3B = - 0 . 2 5 x c a l (K-mV l) 3At = ( A - B ) + ( C - D ) 3 c a l 4 Over the At range of 0 . 2 K to 0 . 0 4 K the absolute e r r o r (6At) decreased - 3 - 3 from ± 3 x 1 0 K to ± 1 x 1 0 K corresponding to r e l a t i v e e r r o r s of ± 1 . 5 % to ± 2 . 5 % . In a l l c a l c u l a t i o n s a constant 6At of ± 0 . 0 0 3 K i s used. This corresponds to r e l a t i v e e r r o r s ranging from ± 1 . 5 % to ± 7 . 5 % over the At range 0 . 2 K to 0 . 0 4 K. 1 For h a l f hour averages: 6 A t = A t r u n c a t i o n e r r o r of ± 1 count f o r a hour p e r i o d i s assumed (maximum e r r o r i s ±2 counts). For At values of 0 . 2 , 0 . 1 , and 0 . 0 5 K the r e s u l t a n t e r r o r s i n At ( A 2 . 7 ) are ± 0 . 0 0 3 , ± 0 . 0 0 2 a n d ± 0 . 0 0 1 5 K, r e s p e c t i v e l y . A2.3) E r r o r i n the Bowen Ratio The Bowen r a t i o (3) i s c a l c u l a t e d : Y(AT - r ) (s + Y)AT w - yAT (A2.8) -1, Assuming y and V ( a d i a b a t i c lapse r a t e c o r r e c t i o n , 0.0098 K m ) to be constant and 6At = <5ATTT = 6AT: w 63 = 2 W (A2.9) The e r r o r i n S i s determined from the c a l i b r a t i o n e r r o r (0.01% - Lowe,1977) and the e r r o r i n TTT (±1.0 K) , which r e s u l t s i n 5.5% change i n S over the W temperature range 278 K to 288 K. Thus: 6S = ((1 x 10 4 ) 2 + (5.5 x 10 2 ) 2 ) 2 = ±5.5% S o l u t i o n of the p a r t i a l s i n (A2.9) g i v e s : 33 3AT S + Y ATI7 - 2AT + Y W ( Y V T 2 Is + V A T W 93 3 AT, W AT. n-1 W AT 2 A Tw + s ^ f ^ 1 33 9S w -1 A summary of r e l a t i v e e r r o r s i n 3 i s presented i n Figur e s 3.2 and 3.3. 122 A2.4) E r r o r s i n Net R a d i a t i o n and Volumetric Heat Storage Net r a d i a t i o n (Q*) i s determined: Q* = cm where: c - sensor c a l i b r a t i o n ; and m - recorder input s i g n a l . Therefore: The e r r o r i n the sensor c a l i b r a t i o n (6c) was set at ±5%, a f i g u r e i n The r e s o l u t i o n of the r e c o r d i n g system (6m) was ±5 x 10 mV. These values r e s u l t e d i n an e r r o r of about ±5% f o r Q*. No attempt was made to evaluate the e r r o r due to the non-continuous p e r i o d i c sampling scheme used i n gathering observations. The e r r o r i n AQ^ (parameterized i n terms of Q*) was set at ±5% of Q*. A f u l l y q u a n t i t a t i v e assessment of e r r o r s was not p o s s i b l e . A2.5) E r r o r i n Latent Heat Flux Density 6Q* = ((m6c) 2 + (c6m) 2) (A2.10) excess of that a n t i c i p a t e d f o r a w e l l - maintained sensor (Latimer, 1972). -3 Latent heat f l u x d e n s i t y (Q ) i s determined: Q* -1 + 6 ( A 2 . l l ) Therefore: (A2.12) 123 where the s o l u t i o n of the p a r t i a l s are: 3Q E 1 3Q* 1 + 3Qx 3Q* 1 + 3QE Q* - AQg 9Q* (1 + 6 ) 2 T y p i c a l r e l a t i v e e r r o r s f o r Q are summarized i n Figures 3.2 and 3.3. E A2.6) E r r o r i n Sen s i b l e Heat F l u x Density Sensible heat f l u x d e n s i t y (Q ) i s determined: H Q* - AQC QH = e x - r r y Therefore: 6QR = 1% dq* 3QH > (A2.13) where the s o l u t i o n of the p a r t i a l s are: 30, H 3 3Q* 1 + 3Q H 3AQC 1 + 3QH Q* - AQS ~ ~ = (1 + g)2 T y p i c a l r e l a t i v e e r r o r s f o r Q are summarized i n Figures 3.2 and 3.3. 

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