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UBC Theses and Dissertations

Sensible heat fluxes measured in and near Vancouver, B.C. Yap, David Hamilton 1973

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SENSIBLE HEAT FLUXES MEASURED IN AND NEAR VANCOUVER, B.C. by DAVID HAMILTON YAP B . S c , M c G i l l U n i v e r s i t y , 1966 M . S c , M c G i l l U n i v e r s i t y , 1969 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department o f Geography We a c c e p t t h i s t h e s i s as c o n f o r m i n g to t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA March, 1973 In presenting 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 of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the 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 reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. Department of Geography The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date A p r i l 24, 1973 ABSTRACT A yaw s p h e r e - t h e r m o m e t e r assembly ( Y S T ) , t o measure s e n s i b l e h e a t f l u x d e n s i t y by the eddy c o r r e l a t i o n method, was b u i l t f o l l o w i n g t h e d e s i g n o f Tanner and T h u r t e l l ( 1 9 7 0 ) . Wind t u n n e l e x p e r i m e n t s i n d i c a t e t h a t the s p h e r e c o n s t a n t s h o u l d be 1.57, which i s s i g n i f i c a n t l y l e s s than t h e p r e -v i o u s l y used t h e o r e t i c a l v a l u e o f 2.25. The e f f e c t s o f t i l t i n d i c a t e t h a t heat f l u x e s may be i n e r r o r by 5 per c e n t per d e g r e e o f t i l t i n u n s t a b l e , and up t o 11 p e r c e n t per d e g r e e i n s t a b l e c o n d i t i o n s . A m o d i f i e d thermometer assembly was found n e c e s s a r y to p r o v i d e d u r a b i l i t y . F i e l d c o m p a r i s o n s o f the heat f l u x e s measured by the yaw s p h e r e -thermometer system and a Bowen r a t i o a p p a r a t u s p r o d u c e d s a t i s f a c t o r y agreement. D i r e c t measurements o f s e n s i b l e h e a t f l u x e s o v e r a g r a s s s u r f a c e a t L a d n e r , B.C. i n d i c a t e a d i u r n a l c o u r s e v e r y s i m i l a r to t h a t o f the n e t r a d i a t i o n . In g e n e r a l , h a l f - h o u r a v e r a g i n g p e r i o d s showed no phase l a g between s e n -s i b l e h e a t and net r a d i a t i o n . F i e l d c o m p a r i s o n o f two YST systems gave good and c o n s i s t e n t agreement. A t a h e i g h t of 2 m above ground and a h o r i z o n t a l c r o s s w i n d s e p a r a t i o n i i o f 1.5 m, l e s s t h a n 5 per c e n t v a r i a b i l i t y was n o t e d i n t h e h e a t f l u x measurements from the two s y s t e m s . F o r a 19 m h o r i z o n t a l s e p a r a t i o n , the v a r i a b i l i t y was f o u n d to be l e s s t h a n 20 per c e n t . I t i s shown t h a t the p a r a m e t e r ( a ) , advanced by P r i e s t l e y and T a y l o r ( 1 9 7 2 ) , can be a u s e f u l c l i m a t i c i n d i c a t o r . The a p p l i c a b i l i t y o f t h e eddy c o r r e l a t i o n t e c h n i q u e t o t h e measurement o f s e n s i b l e h e a t t r a n s f e r between the atmosphere and the urban i n t e r f a c e i s demon-s t r a t e d f o r a l i m i t e d a r e a o f t h e c i t y o f V a n c o u v e r , B.C. D e s p i t e t h e enormous c o m p l e x i t i e s o f the t u r b u l e n t heat exchange p r o c e s s e s , t h e urban s e n s i b l e h e a t f l u x p a t t e r n , o b t a i n e d d i r e c t l y a t h e i g h t s o f 1.2, 2, 4 and 20 m above r o o f - t o p l e v e l , l a r g e l y r e f l e c t e d time and magnitude changes i n the net r a d i a t i o n f i e l d , d u r i n g t h e d a y t i m e . N o c t u r n a l urban s e n s i b l e heat f l u x e s , near r o o f - t o p l e v e l , were f o u n d to be d i r e c t e d away from the a c t i v e s u r f a c e . T h i s i s t h e r e v e r s e o f the normal r u r a l c a s e . W i t h i n the l o c a l r o o f - t o p boundary l a y e r , t h e s e n s i b l e heat f l u x was f o u n d to be a p p r o x i m a t e l y c o n s t a n t w i t h h e i g h t and s p a c e (20% v a r i a t i o n ) d u r i n g the d a y t i m e . A t n i g h t , the e x i s t e n c e o f f l u x d i v e r g e n c e and hence, n o n - c o n s t a n c y o f the h e a t f l u x , i s s u g g e s t e d . Daytime r o o f - t o p e n e r g y b a l a n c e s i n d i c a t e t h a t a s i g n i f i c a n t p o r t i o n o f th e net r a d i a t i o n i s u t i l i z e d i n s e n s i b l e h e a t t r a n s f e r and i n h e a t s t o r a g e i n the r o o f . The g r e a t e s t e n e r g y i s used i n s e n s i b l e h e a t t r a n s f e r , which i s abo u t t h r e e t i m e s t h e h e a t s t o r a g e a t noon. With t y p i c a l v a l u e s o f ne t r a d i a t i o n o f 60 mWcm"2, the s e n s i b l e heat f l u x i s a b o u t 30 mWcm"2 and the heat s t o r a g e 10 mWcm"2. The r e s i d u a l term ( e q u a t e d t o l a t e n t h e a t t r a n s f e r ) i s q u i t e a p p r e c i a b l e . I t i s p o s s i b l e t h a t t h e r o l e o f l a t e n t h e a t t r a n s f e r i s i m p o r t a n t f o r urban e n e r g y b a l a n c e c o n s i d e r a t i o n s . The n o c t u r n a l r o o f - t o p e n e r g y b a l a n c e r e q u i r e d a l a t e n t h e a t term o f abo u t 15 mWcm"2 d i r e c t e d towards t he a c t i v e s u r f a c e . The e n e r g y b a l a n c e o f the s u r r o u n d i n g urban a r e a was deduced from measurements o f s e n s i b l e h e a t f l u x and net r a d i a t i o n a t h e i g h t s above the r o o f - t o p boundary l a y e r . On t h e a s s u m p t i o n t h a t t h e s e p o i n t measurements a p p r o x i -m a t e l y r e f l e c t a r e a l l y i n t e g r a t e d a v e r a g e s , p a r t i t i o n i n g o f t h e h e a t between s e n s i b l e and l a t e n t heat y e i l d s a Bowen r a t i o o f ~ 1 a t midday. TABLE OF CONTENTS Page ABSTRACT . . . . . . . . . i i LIST OF TABLES. . .' v i i i L IST OF FIGURES i x LIST OF SYMBOLS x i i i ACKNOWLEDGEMENTS x v i C h a p t e r 1 INTRODUCTION 1 Ge n e r a l Background 1 Review. . . . . . . . . . . . . . 3 O b j e c t i v e s 15 2 SITE AND INSTRUMENTATION . . . . . . . 16 E x p e r i m e n t a l S i t e s 16 Ge n e r a l I n s t r u m e n t a t i o n and E x p e r i m e n t a l P r o c e d u r e s . . . . . . . . . . 35 Measurement Programme 39 3 THE YAW SPHERE-THERMOMETER SYSTEM. . . . . . . . 41 I n t r o d u c t i o n 41 Equipment D e s c r i p t i o n 42 v C h a p t e r Page Review o f the Yaw S p h e r e - T h e r -mometer T h e o r y 44 D e t e r m i n a t i o n o f the Sphere C o n s t a n t . . . . 50 E f f e c t o f Yaw Sphere A x i s T i l t 55 Thermometer System and F r e q u e n c y Response 60 F i e l d T e s t s R e s u l t s . . 66 4 SENSIBLE HEAT FLUX MEASUREMENTS OVER A RURAL SURFACE 72 I n t r o d u c t i o n . 72 E x p e r i m e n t a l S i t e and P r o c e d u r e s 74 D i u r n a l B e h a v i o u r o f the S e n s i b l e Heat F l u x 75 Measurements o f S p a t i a l V a r i a t i o n o f the S e n s i b l e Heat F l u x 83 P a r a m e t e r i z a t i o n o f the S e n s i b l e Heat F l u x and E v a p o r a t i o n . . . . . . . 92 5 SENSIBLE HEAT FLUXES OVER AN URBAN AREA 98 I n t r o d u c t i o n . 98 Boundary L a y e r C o n s i d e r a t i o n s . . . . . . .100 Mean V e r t i c a l V e l o c i t y C o n s i d e r a t i o n s . . .105 Samp l i n g C o n s i d e r a t i o n s 106 D i u r n a l Urban S e n s i b l e Heat F l u x P a t t e r n 115 S p a t i a l S a m p l i n g 124 6 URBAN ENERGY BALANCE 131 I n t r o d u c t i o n . . . . 131 v iC h a p t e r Page A r t i f i c i a l Heat and M o i s t u r e P r o d u c t i o n 132 R o o f - t o p Energy B a l a n c e 136 Energy B a l a n c e o f an Urban A r e a 152 7 SUMMARY OF CONCLUSIONS . 159 S u g g e s t i o n s f o r F u t u r e Work . . . . . . . . 163 REFERENCES . 1 6 6 APPENDIX A SAMPLE CALCULATION OF THE SENSIBLE HEAT FLUX 174 v i i LIST OF TABLES Tab! e Page T. Comparison o f a r t i f i c i a l e n e r g y f l u x d e n s i t y and a v e r a g e net r a d i a t i o n f o r s e l e c t e d urban a r e a s ( c . f . (SMIC, 1 9 7 1 ) ) . . . . . 10 2. Comparison o f day t i m e c u m u l a t i v e s e n s i b l e h e a t f l u x d e n s i t i e s from t h e yaw s p h e r e -thermometer (HYST) and Bowen r a t i o (H„) systems 71 3. Comparison o f a v e r a g e f l u x e s ( c . f . Dyer and H i c k s , 1972) 86 4. Comparison o f c u m u l a t i v e s e n s i b l e h e a t f l u x d e n s i t i e s from t h e yaw s p h e r e -thermometer systems (H YST/I an(^ H Y S T 2 a t 2 m above ground f o r an h o r i z o n t a l c r o s s w i n d s e p a r a t i o n o f 1.5 m . . . . . 89 5. Comparison o f c u m u l a t i v e s e n s i b l e heat f l u x d e n s i t i e s from t h e yaw s p h e r e -thermometer systems ( H y s T i a n c l H Y S T z ) a t 2 m above ground f o r an h o r i z o n t a l c r o s s w i n d s e p a r a t i o n o f 19 m . . . . . . . . . . . 91 6. Comparison o f day t i m e c u m u l a t i v e s e n s i b l e h e a t f l u x d e n s i t i e s from the yaw s p h e r e -thermometer systems ( H y s T i and H Y S T 2 ) above the urban r o o f 129 v i i i LIST OF FIGURES F i g u r e Page 1. S c h e m a t i c heat b a l a n c e o f a volume, one f a c e o f which i s the E a r t h ' s s u r f a c e ( a f t e r Suomi, 1 957) 4 2. S c h e m a t i c h e a t b a l a n c e o f urban b u i l d i n g -a i r volume . . . . . 6 3. The G r e a t e r Vancouver a r e a . 17 4. P e r c e n t a g e o f days w i t h m e a s u r e a b l e p r e c i p i -t a t i o n - Vancou v e r C i t y (1906-1955) - 7 day r u n n i n g mean ( c . f . H a r r y and W r i g h t , 1967). . . 20 5. Map o f Ladner e x p e r i m e n t a l s i t e 27 6. S k e t c h o f Lad n e r s i t e showing minimum f e t c h d i s t a n c e s 28 7. S i t e p l a n o f the urban a r e a ( V a n c o u v e r S c h o o l Board B u i l d i n g and i t s immediate e n v i r o n s ) . . . . . . . . . 31 8. The Vanc o u v e r S c h o o l Board B u i l d i n g ( p l a n view) 32 9. An example o f the l o c a t i o n o f the he a t i s l a n d c o r e s i n V a n c o u v e r , B.C . . . . 34 10. S c h e m a t i c d i a g r a m o f the r e c o r d i n g system . . . 43 11. The yaw sp h e r e - t h e r m o m e t e r a s s e m b l y . . . . . . 45 i x F i g u r e Page 12. S c h e m a t i c r e p r e s e n t a t i o n o f the a n g l e s , ty, a, 0 and the wind v e c t o r W on the yaw s p h e r e 48 13. G r a p h i c a l d e t e r m i n a t i o n o f the s p h e r e c o n s t a n t (b) and a l i g n m e n t e r r o r ( 6 ) . . 53 14. The e f f e c t o f t i l t on the geometry o f the s p h e r e 56 15. The r e s i s t a n c e thermometer . 61 16. The m o d i f i e d r e s i s t a n c e thermometer . 63 17. Comparison o f the two yaw sp h e r e - t h e r m o m e t e r systems f o r s e n s i b l e heat f l u x measurements (a) w i t h o r i g i n a l r e s i s t a n c e thermometer, (b) w i t h m o d i f i e d thermometer d e s i g n i n Y S T 1 . . . 64 18. F r e q u e n c y r e s p o n s e o f the yaw s p h e r e t u b i n g and B a r o c e l 65 19. Comparison o f s e n s i b l e h e a t f l u x d e n s i t i e s from the yaw sp h e r e - t h e r m o m e t e r system ( H Y s i O and the Bowen r a t i o system (Ho) o v e r g r a s s a t L a d n e r , B.C 67 20. Comparison o f HysT and H R a t L a d n e r , B.C. on Aug. 27, 1971. . . . . . . . . . . . . . . . . 68 21. D i u r n a l v a r i a t i o n o f H and c o m p a r i s o n o f the two YST systems 76 22. D i u r n a l v a r i a t i o n o f H and c o m p a r i s o n o f the two YST systems 77 23. D i u r n a l v a r i a t i o n o f H and c o m p a r i s o n o f the two YST systems 78 24. D i u r n a l energy b a l a n c e and s p a t i a l v a r i a t i o n o f H 79 x F i g u r e Page 25. D i u r n a l e n e r g y b a l a n c e and s p a t i a l v a r i a -t i o n o f H 80 26. An example o f l a r g e f l u c t u a t i o n s i n H w i t h 30 min a v e r a g i n g p e r i o d s 82 27. D i u r n a l v a r i a t i o n o f a (examples o f e a r l y and l a t e summer o b s e r v a t i o n s ) 94 28. R a t i o o f H/LE v s . t e m p e r a t u r e 96 29. (a) Boundary l a y e r development o v e r an a b r u p t change i n s u r f a c e r o u g h n e s s , (b) Boundary l a y e r d e v e l o p m e n t f o l l o w i n g a change from smooth t o a rough s u r f a c e where the r o u g h n e s s e l e m e n t s a r e above the s u r f a c e 101 30. S c h e m a t i c d i a g r a m o f the l o c a l boundary above a b u i l d i n g f o r a c o n s t a n t a n g l e o f a t t a c k o f the wind f l o w 103 31. Urban s e n s i b l e h e a t f l u x e s f o r h a l f - h o u r and one hour a v e r a g i n g p e r i o d s 109 32. Urban s e n s i b l e heat f l u x e s f o r h a l f - h o u r and one hour a v e r a g i n g p e r i o d s 110 33. Urban s e n s i b l e h e a t f l u x e s f o r h a l f - h o u r , one hour and two hour a v e r a g i n g p e r i o d s 113 34. Urban s e n s i b l e heat f l u x e s f o r h a l f - h o u r a v e r a g i n g p e r i o d s 114 35. D i u r n a l v a r i a t i o n o f t h e urban s e n s i b l e h e a t f l u x e s a t 1.2 m above r o o f 117a 36. D i u r n a l v a r i a t i o n o f t h e urban s e n s i b l e h e a t f l u x e s a t 1.2 m above r o o f 117b x i F i g u r e Page 37. D i u r n a l v a r i a t i o n o f t h e urban s e n s i b l e heat f l u x a t 20 m above r o o f 117c 38. E f f e c t o f shadow on the d i u r n a l b e h a v i o u r o f urban heat s t o r a g e 118 39. Urban e n e r g y b a l a n c e s (a) J u l y 7, 1972 w i t h d r y c o n d i t i o n s , (b) J u l y 13, 1972 f o l l o w i n g wet p e r i o d , ( c ) J u l y 17, 1972 5 days a f t e r wet p e r i o d . . . . . . 122 40. H o r i z o n t a l s p a t i a l v a r i a t i o n o f the urban s e n s i b l e h e a t f l u x e s 126 41. V e r t i c a l s p a t i a l v a r i a t i o n o f t h e urban s e n s i b l e h e a t f l u x e s 128 42. Daytime r o o f - t o p e n e r g y b a l a n c e 139 43. Daytime r o o f - t o p e n e r g y b a l a n c e . . 140 44. N o c t u r n a l r o o f - t o p e n e r g y b a l a n c e 151 45. N o c t u r n a l r o o f - t o p e n e r g y b a l a n c e 151 46. D i u r n a l b e h a v i o u r o f G i n v a r i o u s urban f a b r i c s . 156 47. Urban s e n s i b l e heat f l u x e s and p o i n t measurements o f Rn and G 157 48. The b r i d g e c i r c u i t 176 x i i LIST OF SYMBOLS a a n g l e between the wind v e c t o r and t h e b i s e c t o r o f the p o r t s ( C h a p t e r 3) a P r i e s t l e y and T a y l o r p a r a m e t e r ( C h a p t e r 4) b s p h e r e c o n s t a n t B b r i d g e c o n s t a n t B Bowen r a t i o (H/LE) Cp s p e c i f i c heat a t c o n s t a n t p r e s s u r e ^pb t h e r m a l c a p a c i t y o f c i t y s t r u c t u r e s d d i a m e t e r o f t h e s p h e r e D d i v e r g e n c e terms 6 t i l t e r r o r e vapour p r e s s u r e E water vapour f l u x E0 b r i d g e o u t p u t e r a t i o o f the mole w e i g h t o f water vapour to t h a t o f dr y a i r ( C h a p t e r 1) e r a t i o o f meter c o n d u c t i v i t y to medium c o n d u c t i v i t y ( C h a p t e r 6) x i i i f r a t i o o f mean f l u x d e n s i t y t h r o u g h the meter to t h e mean f l u x d e n s i t y t h r o u g h the medium F a r t i f i c i a l g e n e r a t i o n o f heat and water vapour $ c o s p e c t r u m between t h e v e r t i c a l v e l o c i t y (w) and w the a i r t e m p e r a t u r e (T) G a m p l i f i e r g a i n ( C h a p t e r 3) G s o i l h eat s t o r a g e H s e n s i b l e heat f l u x I g t r u e e f f e c t i v e o u t g o i n g r a d i a t i o n from the s u r f a c e L l a t e n t h e a t o f v a p o u r i z a t i o n LE l a t e n t h e a t f l u x M p r e s s u r e t r a n s d u c e r c o n s t a n t v k i n e m a t i c v i s c o s i t y n f r e q u e n c y p p r e s s u r e P g s t a t i c p r e s s u r e q s p e c i f i c h u m i d i t y R s p e c i f i c gas c o n s t a n t Re R e y n o l d s no. Rn net r a d i a t i o n p a i r d e n s i t y x i v a S t e f a n - B o l t z m a n n c o n s t a n t s l o p e o f the s a t u r a t i o n vapour c u r v e a t the a p p r o p r i a t e t e m p e r a t u r e T a i r t e m p e r a t u r e t e m p e r a t u r e o f c i t y s t r u c t u r e s T s s u r f a c e t e m p e r a t u r e 9 i n c l u d e d a n g l e between t h e p o r t s x n e g a t i v e momentum f l u x u h o r i z o n t a l wind v e l o c i t y component a l o n g d i r e c t i o n o f the wind IT mean wind speed V a i r speed ( C h a p t e r 3) V s t o r a g e terms i n volume ( C h a p t e r 1) V v e l o c i t y v e c t o r v c r o s s w i n d h o r i z o n t a l component o f the wind v e l o c i t y w v e r t i c a l v e l o c i t y component X J . Z J t i l t a x i s p l a n e ( — ) time a v e r a g e a t a g i v e n p o i n t ( )' f l u c t u a t i o n a bout t h e mean V 8/8x + 8/3y XV ACKNOWLEDGEMENTS T h i s s t u d y was s u p e r v i s e d by Dr. T.R. Oke. To him I am d e e p l y i n d e b t e d f o r the encouragement, a s s i s t a n c e and c o n s t r u c t i v e i d e a s d u r i n g a l l s t a g e s o f my t h e s i s work. The a u t h o r a l s o w i s h e s to e x p r e s s h i s t h a n k s t o Dr. T.A. B l a c k and M e s s r s . K. McNaughton and R. W i l s o n o f t h e S o i l S c i e n c e Department f o r t h e i r h e l p i n t h e c o n -s t r u c t i o n and t e s t i n g o f the yaw s p h e r e - t h e r m o m e t e r s y s t e m . The main e x p e r i m e n t s were c o n d u c t e d a t C a n a d i a n F o r c e s S t a t i o n L a d n e r and the V a n c o u v e r S c h o o l Board b u i l d -i n g . P e r m i s s i o n t o use t h e s e f a c i l i t i e s a r e g r a t e f u l l y a c k n o wledged. I g r a t e f u l l y acknowledge the s u p p o r t from t h e N a t i o n a l R e s e a r c h C o u n c i l t h r o u g h a s c h o l a r s h i p d u r i n g t h e • p e r i o d 1970-73. x v i C h a p t e r 1 INTRODUCTION G e n e r a l Background The r e c e i p t , t r a n s f o r m a t i o n and t r a n s f e r o f e n e r g y a t t h e e a r t h - a t m o s p h e r e i n t e r f a c e i s b a s i c t o a r a t i o n a l u n d e r s t a n d i n g o f c l i m a t e s . E s t i m a t i o n o f the v e r t i c a l eddy f l u x e s o f p h y s i c a l e n t i t i e s , such as s e n s i b l e h e a t , water v a p o u r and momentum i n the a t m o s p h e r i c boundary l a y e r r e m ains a t t h e c o r e o f m i c r o m e t e o r o l o g i c a l r e s e a r c h . Knowledge o f t h e s e f l u x e s i s a l s o i m p o r t a n t i n the s t u d y o f the g e n e r a l c i r c u l a t i o n o f t h e atmosphere s i n c e t h e y d e f i n e the l o w e r boundary c o n d i t i o n s o f the l a r g e r s c a l e a t m o s p h e r i c dynamics. U n t i l v e r y r e c e n t l y , t h e f i e l d o f urban m i c r o -m e t e o r o l o g y was a l m o s t n o n - e x i s t e n t . A l t h o u g h a l a r g e body o f urban c l i m a t e l i t e r a t u r e e x i s t s ( see t h e summaries g i v e n by Brooks ( 1 9 5 2 ) , K r a t z e r ( 1 9 5 6 ) , L a n d s b e r g ( 1 9 6 1 ) , C h a n d l e r (1968) and P e t e r s o n ( 1 9 6 9 ) ) , a t t e n t i o n has been p r i m a r i l y c o n f i n e d t o t h e d e s c r i p t i o n o f t h e b a s i c n a t u r e o f c l i m a t i c e f f e c t s p r o d u c e d by urban a r e a s . The p r o c e s s e s g i v i n g r i s e 1 2 to urban c l i m a t e s remained l a r g e l y s p e c u l a t i v e . T h i s l a c k o f i n f o r m a t i o n c o n c e r n i n g the u n d e r l y i n g mechanisms g o v e r n i n g urban c l i m a t e has a t t r a c t e d many r e s e a r c h e r s , e s p e c i a l l y s i n c e t h e r e c e n t WMO Symposium on Urban C l i m a t e s (WMO, 1970). Most o f t h e work, however, seems t o be c e n t r e d on m o d e l l i n g the urban e n v i r o n m e n t ( s e e f o r example, t h e C o n f e r e n c e on Urban E n v i r o n m e n t , 1972). E x p e r i m e n t a l r e s e a r c h t o probe t h e p h y s i c a l b a s i s o f urban c l i m a t e i s s t i l l l a r g e l y d e f i c i e n t , due t o t h e enormous c o m p l e x i t y o f t h e c i t y / a t m o s p h e r e i n t e r -f a c e and t h e need f o r s o p h i s t i c a t e d measurement t e c h n i q u e s . T h i s s t u d y seeks t o a c h i e v e some i n s i g h t i n t o t h e manner i n w hich h e a t i s u t i l i z e d i n t h e urban atmosphere and i n t o t h e e n e r g e t i c s o f urban m i c r o m e t e o r o l o g y t h r o u g h d i r e c t measurements. F o r most n a t u r a l s u r f a c e s , the n a t u r e o f t h e i r e n e r g e t i c b a s i s has been e l u c i d a t e d t h r o u g h h e a t budget s t u d i e s . S i m i l a r s t u d i e s f o r c i t i e s a r e f r a g m e n t a r y o r a b s e n t . T h i s d e a r t h o f knowledge c o n c e r n i n g the e n e r g y f l u x e s i n urban a r e a s has been m e n t i o n e d by many a u t h o r s i n r e c e n t y e a r s ( e . g . Munn ( 1 9 6 6 ) , M i l l e r ( 1 9 6 8 ) , Lowry (1969) and Oke ( 1 9 6 9 ) ) . I t i s to be e x p e c t e d t h a t u r b a n i z a t i o n w i l l m a r k e d l y m o d i f y the s u r f a c e h e a t b a l a n c e . D e t e r m i n a t i o n o f t h i s a l t e r e d h e a t b a l a n c e i s one o f t he t a s k s o f urban c l i m a t o l o g y ( L a n d s b e r g , 1970). T h r o u g h o u t t h i s s t u d y , the h e a t b a l a n c e a p p r o a c h has been u t i l i z e d , and t h e r e f o r e i t i s u s e f u l to r e v i e w t h e framework h e r e . 3 Review The c o n c e p t o f heat b a l a n c e i s embodied i n the p r i n c i p l e o f c o n s e r v a t i o n o f e n e r g y : the d i f f e r e n c e between he a t i n f l o w and o u t f l o w i s the h e a t s t o r e d o r used w i t h i n the system o f c o n c e r n . The heat b a l a n c e o f a volume, one f a c e o f which i s the E a r t h ' s s u r f a c e , i s s c h e m a t i c a l l y shown i n F i g . 1. U s i n g the c o n s e r v a t i o n p r i n c i p l e , i t can be e x p r e s s e d as a g e n e r a l e q u a t i o n a t any i n s t a n t i n t i m e as f o l 1 o w s : + R n = ± H ± L E ± G ± V ± D (1.1) where Rn, H, LE and G r e p r e s e n t the v e r t i c a l f l u x e s o f n e t r a d i a t i o n , s e n s i b l e h e a t , l a t e n t heat and s o i l h eat r e s p e c -t i v e l y . V i s the s t o r a g e o f h e a t i n the volume and D i s the h o r i z o n t a l d i v e r g e n c e o f s e n s i b l e and l a t e n t h e a t . F o r a f l a t , s o l i d s u r f a c e o r a homogeneous vege-t a t e d s u r f a c e w i t h a d e q u a t e f e t c h , the d i v e r g e n c e and volume s t o r a g e terms a r e u s u a l l y s m a l l compared w i t h the v e r t i c a l f l u x e s ( e . g . Begg et al.s 1964; Brown and Covey, 1967; Lemon, 1967), and a c c o r d i n g l y , the h e a t b a l a n c e e x p r e s -s i o n r e d u c e s t o : ± R n = ± H ± LE ± G (1.2) 4 NET RADIATION (Rn) ^ SENSIBLE HEAT TRANSFER (H) LATENT HEAT TRANSFER (LE) LATENT HEAT f±3 SENSIBLE HEAT t I I I / /6y ' STORAGE TERMS IN VOLUME (V) SOIL HEAT CONDUCTION (G) DIVERGENCE TERMS (D) LATENT HEAT SENSIBLE HEAT i F i g . 1. Sc h e m a t i c heat b a l a n c e o f a volume, one f a c e o f which i s the E a r t h ' s s u r f a c e ( a f t e r Suomi, ( 1 9 5 7 ) . 5 The n e g l e c t o f o t h e r terms u s u a l l y i n v o l v e s an e r r o r o f l e s s than 10 per c e n t o f the net r a d i a t i o n ( D a v i e s et al.3 1969). Numerous examples o f heat b a l a n c e s t u d i e s o f t y p i c a l r u r a l s u r f a c e s ( g r a s s , c r o p s and f o r e s t ) can be c i t e d ( f o r example: L e t t a u and D a v i d s o n , 1957; W r i g h t and Lemon, 1962). Through volume c o n s i d e r a t i o n s , i t i s a l s o p o s s i b l e to f o r m u l a t e the heat b a l a n c e o f an urban a r e a . A s c h e m a t i c r e p r e s e n t a t i o n o f t h e heat b a l a n c e o f an u r b a n - b u i l d i n g a i r volume i s shown i n F i g . 2. I t may be r e p r e s e n t e d by the f o l l o w i n g e q u a t i o n ,z ± R n ± F = ± H ± L E ± G ± Le 3e ,_ RT 9t 6 z 9 T h b 'pb a t Sz 9T 3t Sz V H ( p u T ) 6 z Le R ue] IT J Sz (1.3) where the meaning o f the symbols i s : Cp, s p e c i f i c h eat o f a i r a t c o n s t a n t p r e s s u r e ; p, a i r d e n s i t y ; u, h o r i z o n t a l wind v e l o c i t y ; T, a i r t e m p e r a t u r e ; L, l a t e n t heat o f v a p o u r i z a -t i o n ; E, water vapour f l u x ; e, t h e r a t i o o f the mole w e i g h t NET RADIATION (Rn) SENSIBLE HEAT TRANSFER (H) LATENT HEAT TRANSFER (LE) LATENT HEAT SENSIBLE HEAT • C n l l D T F T F R M S IN VOI U M F f I I SOURCE E  I  L E 1. ART IF IC IAL H E A T G E N E R A T I O N (F„) 2. ART IF IC IAL W A T E R V A P O U R S O U R C E ( F W ) STORAGE TERMS IN VOLUME 1. H E A T S T O R A G E IN AIR" -2. H E A T S T O R A G E IN BUILDINGS: 3. L A T E N T H E A T S T O R A G E : f*Z.C dC Jo AT 5F LATENT HEAT loo ooj SENSIBLE HEAT SOIL HEAT CONDUCTION (G) DIVERGENCE: j * L* 7H Sz DIVERGENCE, f* Cp ?H(fuT) %l F i g . 2. S c h e m a t i c heat b a l a n c e o f urban b u i l d i n g - a i r volume. 7 o f water vapour to t h a t o f d r y a i r ; R, the s p e c i f i c gas c o n s t a n t ; e, vapour p r e s s u r e ; C ^ , t h e r m a l c a p a c i t y and t e m p e r a t u r e o f c i t y s t r u c t u r e s , r e s p e c t i v e l y ; F, a r t i f i c i a l g e n e r a t i o n o f heat and water vapour and , 9/9x + 8/3y . O t h e r symbols have t h e i r meaning as b e f o r e . A l t h o u g h the g o v e r n i n g e n e r g y budget e q u a t i o n s may be r e a d i l y s p e c i f i e d f o r the urban s i t u a t i o n , the t h r e e -d i m e n s i o n a l n a t u r e o f the prob l e m i s most f o r m i d a b l e . The complex c i t y system r a i s e s s e r i o u s d i f f i c u l t i e s . In p a r -t i c u l a r , i t becomes a l m o s t i m p o s s i b l e to d e f i n e such b a s i c c o n c e p t s as the l o c a t i o n o f the ' s u r f a c e ' i t s e l f . The many b u i l d i n g s and m u l t i p l e - l e v e l s u r f a c e s p r e s e n t a complex geometry to t h e atmosphere. F u r t h e r c o m p l i c a t i o n s a r i s e from man-made p r o d u c t i o n o f h e a t and water vapour i n c i t i e s . Each e l e m e n t o f the mosaic which forms a c i t y ( t h e home, b u i l d i n g , pavement, r o a d , g a r d e n , e t c . ) c r e a t e s i t s own d i s t i n c t i v e m i c r o c l i m a t i c e n v e l o p e . One s h o u l d t h e r e f o r e e x p e c t t h a t t h e i n h o m o g e n e i t i e s ( h o r i z o n t a l l y and v e r t i c a l l y ) p r o d u c e d by t h e s e e l e m e n t s would r e s u l t i n s i g n i f i c a n t m i c r o -c l i m a t i c v a r i a b i l i t y . I t may not however be u n r e a s o n a b l e to s u g g e s t t h a t a f i r s t o r d e r u n i t y o f b u i l d i n g d e v e l o p m e n t s h o u l d g i v e a r e g i o n a l c o n t i n u i t y to t h e b a s i c urban c l i m a t e ( C h a n d l e r , 1965). Indeed, e v i d e n c e from s t u d i e s o f t h e hea t i s l a n d ( t h e c h a r a c t e r i s t i c warmth o f the c i t y ) s u p p o r t s t h i s view s i n c e t h e h o r i z o n t a l t e m p e r a t u r e p a t t e r n near s t r e e t 8 l e v e l o f t e n c l o s e l y p a r a l l e l s the urban m o r p h o l o g y , e.g. Maxwell ( 1 9 7 1 ) . Hence, by c o n f i n i n g our i n v e s t i g a t i o n i n the complex c i t y system to a l i m i t e d u r b a n - b u i l d i n g - a i r volume where b u i l d i n g s a r e o f u n i f o r m t y p e , h e i g h t , d e n s i t y and f u n c t i o n , some de g r e e o f c l i m a t i c c o n t i n u i t y may be e x p e c t e d . In d o i n g s o , we n e c e s s a r i l y r e s t r i c t t h e scope o f the r e s e a r c h to a s m a l l p o r t i o n o f the d i v e r s i f i e d urban l a n d s c a p e . A t the same time however, i t o f f e r s a r a t i o n a l a p p r o a c h towards p r o b i n g the urban atmosphere and s h o u l d e n a b l e an e l u c i d a t i o n o f t h e e n e r g e t i c b a s i s o f c i t y c l i m a t e . The c o m p l e x i t y o f the t h r e e - d i m e n s i o n a l n a t u r e o f t h e prob l e m i s e v i d e n t . I t i s not however p r o p o s e d to e v a l u a t e a l l the en e r g y terms i n d i c a t e d f o r such a volume, but r a t h e r to use t h i s framework, and t o f o c u s a t t e n t i o n p r i m a r i l y on t h e v e r t i c a l e n e r g y e x c h a n g e s . In r e c e n t y e a r s , urban heat budget s t u d i e s have a t t r a c t e d the a t t e n t i o n o f a number o f r e s e a r c h e r s . Even so i t i s not s u r p r i s i n g t h a t we know so l i t t l e a b o ut t h e components o f the he a t budget i n urban a r e a s i n view o f t h e c o m p l e x i t i e s o f the e n v i r o n m e n t and out l a c k o f a p p r o p r i a t e m e a s u r i n g t e c h n i q u e s to a s s e s s q u a n t i t a t i v e l y t h e s e e n e r g e t i c e x c h a n g e s . E x p e r i m e n t a l e v i d e n c e o f t h e urban e n e r g y com-ponents i s s t i l l f r a g m e n t a r y . The r a d i a t i o n a l a s p e c t s have now been i n v e s t i g a t e d to some e x t e n t ( e . g . Tag, 1968; Hawkins, 1969; T e r j u n g , 1970; Bach, 1970 and Oke and F u g g l e , 9 1972). The e f f e c t o f r a d i a t i v e exchanges between b u i l d i n g e l e m e n t s , and shadow a r e a s remain o u t s t a n d i n g problem a r e a s f o r i n v e s t i g a t i o n . The few a t t e m p t s made to measure the h e a t s t o r e d i n the c i t y b u i l d i n g m a t e r i a l s ( e . g . D a v i s , 1968 and T e r j u n g , 1970) o n l y p r o v i d e g r o s s e s t i m a t e s o f t h i s e n e r g y b a l a n c e component. A s p a t i a l a v e r a g i n g p r o c e d u r e t h a t i n c l u d e s g e o m e t r i c a l c o n s i d e r a t i o n s might y i e l d r e a s o n -a b l e h e a t s t o r a g e e s t i m a t e s , but has not y e t been a t t e m p t e d . E s t i m a t i o n o f the a r t i f i c i a l h eat p r o d u c e d i n c i t i e s can be f o u n d i n the l i t e r a t u r e ( e . g . Oke, 1969; SMIC, 1971). The a r t i f i c i a l e n e r g y f l u x d e n s i t y f o r v a r i o u s c i t i e s i s g i v e n i n T a b l e 1. D e t e r m i n a t i o n o f the v e r t i c a l f l u x e s o f s e n s i b l e and l a t e n t h e a t o v e r urban a r e a s remains an o u t s t a n d i n g p r o b l e m . A t t e m p t s have been made to a s s e s s t h e s e f l u x e s i n d i r e c t l y v i a t h e Bowen r a t i o / e n e r g y b a l a n c e method w i t h l i t t l e s u c c e s s ( e . g . Bach, 1970; Myrup and Morgan, 1972). F u g g l e (1971) and T e r j u n g (1971) have o b t a i n e d s t a b l e measure-ments i n t h i s r e g a r d , but o f a l i m i t e d n a t u r e . T h e r e have been no a t t e m p t s a t d i r e c t measurements o f t h e s e e n e r g y f l u x e s . I t i s thus o b v i o u s t h a t much r e s e a r c h i s s t i l l needed i n t h i s a r e a o f urban heat b a l a n c e c l i m a t o l o g y . A c c o r d i n g l y , the p r i n c i p a l aim o f t h i s r e s e a r c h w i l l be d i r e c t e d towards d i r e c t a s s e s s m e n t o f the eddy f l u x e s i n T a b l e I C o m p a r i s o n o f a r t i f i c i a l e n e r g y f l u x d e n s i t y and a v e r a g e n e t r a d i a t i o n f o r s e l e c t e d u r b a n a r e a s ( c . f . (SMIC, 1971)) C i t y A r e a ( k m 2) Popu1 a t i on I 0 6 A r t i f i c i a 1 e n e r g y f l u x d e n s i t y (mWcm - 2) A v e r a g e n e t r a d i a t i on (mWcm" 2) A v e r a g i n g P e r i od West Ber1 i n * 234 2.3 .2.1 5.7 Y e a r Hamburg 747 1 .8 1 .3 5.5 Y e a r Moscow 878 6.4 12.7 4.2 Y e a r C i n c i n n a t i 200 0.54 2.6 Summer Los A n g e l e s 3500* 7.0 2. 1 10.8 Y e a r M a n h a t t a n , New Y o r k 59 1 .7 4.0 19.8 Summer W i n t e r F a i r b a n k s , A 1 a s k a * 37 0.03 1 .9 1 .8 Y e a r M o n t r e a 1 * 78 9.8. Y e a r B u i l d i n g a r e a o n l y . - J o B a s e d on m o d i f i e d SMIC ( 1 9 7 1 ) , Summers ( 1 9 6 4 ) and Oke ( 1 9 6 9 ) . 11 the urban c o n t e x t , and i n p a r t i c u l a r , s e n s i b l e h e a t . I t i s t h e r e f o r e u s e f u l to r e v i e w the m e a s u r i n g t e c h n i q u e . Most o f m i c r o m e t e o r o l o g i c a l r e s e a r c h has been c e n t r e d on means o f d e r i v i n g t h e f l u x e s o f h e a t , w a t e r vapour and momentum t h r o u g h i n d i r e c t methods, based on t e m p e r a t u r e , w ater vapour and wind p r o f i l e s , which n e c e s -s a r i l y i n v o l v e a s s u m p t i o n s about the c h a r a c t e r o f t h e atmo s p h e r e . A c o n s i d e r a b l e l i t e r a t u r e on p r o f i l e f o r m u l a s t o a c c o m p l i s h t h i s has been d e v e l o p e d . D i r e c t measurement o f t h e s e f l u x e s has r e c e i v e d much impetus i n r e c e n t y e a r s , as s u i t a b l e m e a s u r i n g t e c h n i q u e s have been d e v e l o p e d t o u t i l i z e such an a p p r o a c h . E x c e p t f o r the few m i l l i m e t e r o f a i r above t h e ground ( t h e l a m i n a r boundary l a y e r ) , where e n t i t i e s a r e t r a n s f e r r e d by m o l e c u l a r p r o c e s s e s , t u r b u l e n c e i s t h e p r i n c i p a l mechanism f o r a t m o s p h e r i c t r a n s p o r t near t h e E a r t h ' s s u r f a c e . The d i r e c t measurement o f e d d y - f l u x e s i s based on f l u c t u a t i o n t h e o r y . By c o n s i d e r i n g t h e v e r t i c a l t r a n s p o r t o f a p h y s i c a l e n t i t y ( s ) a c r o s s u n i t h o r i z o n t a l a r e a , i t can be shown ( e . g . Swinbank, 1951, P r i e s t l e y , 1959) t h a t the v e r t i c a l f l u x ( F g ) under c o n d i t i o n s o f s t e a d y - s t a t e and h o r i z o n t a l u n i f o r m i t y i s g i v e n by F s = (pw)s (1.4) 12 where p i s the a i r d e n s i t y ; w i s t h e v e r t i c a l wind component and t h e bar i n d i c a t e s a tim e a v e r a g e a t a g i v e n p o i n t . T h us, f o r example, t h e t u r b u l e n t heat f l u x may be w r i t t e n H = C p TpwJT (1.5) where T i s t h e a i r t e m p e r a t u r e and C p i s the s p e c i f i c h e a t a t c o n s t a n t p r e s s u r e . The v a r i a b l e s p, w and T may f u r t h e r -more be e x p r e s s e d i n terms o f a mean q u a n t i t y p l u s a f l u c -t u a t i o n a b o u t t h a t mean so t h a t H = C p [ ( p + p ' ) ( w + w')(T + T ' ) ] and i f t h e r e i s no s i g n i f i c a n t c o n v e r g e n c e o r d i v e r g e n c e ( i . e . pw - 0) the s e n s i b l e h e a t f l u x e x p r e s s i o n can be expanded to g i v e H = C p [ p w'T' + w p'T' + p'w'T'] (1.6) 13 I f the mean v e r t i c a l wind i s c l o s e to z e r o , the second term i n t h e b r a c k e t can be n e g l e c t e d . The magnitude o f t h e t h i r d term ( t h e t r i p l e moment), compared to the f i r s t term i n t h e b r a c k e t , has been shown by B u s i n g e r and Miyake (1968) e x p e r i m e n t a l l y to be a r a t i o o f about 0.0014 and t h e r e f o r e the s e n s i b l e h e a t f l u x e x p r e s s i o n r e d u c e s to H = C p p wT 7" (1.7) In a s i m i l a r manner, t h e v e r t i c a l f l u x e s o f l a t e n t h e a t and momentum can be o b t a i n e d d i r e c t l y from t h e c o v a r i a n c e s o f w and q ( s p e c i f i c h u m i d i t y ) f l u c t u a t i o n s and w and u f l u c t u a t i o n s , r e s p e c t i v e l y . Hence LE = p L w'q' (1.8) T = -p w'u' ( T : n e g a t i v e momentum f l u x ) T h i s a p p r o a c h ( t h e eddy c o r r e l a t i o n t e c h n i q u e ) i s a f u n -damental method f o r m e a s u r i n g t u r b u l e n t t r a n s f e r , and i t p o s s e s s e s t h e adv a n t a g e o f d i r e c t l y m e a s u r i n g eddy f l u x e s . The d i r e c t m e a s u r i n g t e c h n i q u e s , however, a r e not e a s i l y a c c o m p l i s h e d s i n c e t h e y r e q u i r e v e r y f a s t - r e s p o n s e s e n s o r s t h a t must measure the p u l s a t i o n s o f t h e wind and t h e 14 a p p r o p r i a t e p h y s i c a l e n t i t y o v e r the e n t i r e f r e q u e n c y range c o n t r i b u t i n g to the f l u x . In t h i s s t u d y , a t t e n t i o n i s l i m i t e d to the use o f t h i s t e c h n i q u e i n the measurement o f s e n s i b l e h e a t . For the measurement o f H, the s t r i n g e n t r e q u i r e -ments o f the wind s e n s o r a r e h a r d e s t to meet. Two o f the most p r o m i s i n g a p p r o a c h e s a r e the s o n i c anemometer ( M i t s u t a , 1966, 1968; Kaimal et al.3 1968) and the p r e s s u r e - s p h e r e anemometer ( T h u r t e l l et al.3 1970; Wesely et al.3 1972). Comparisons o f H d e t e r m i n e d by i n s t r u m e n t s i n c o r p o r a t i n g t h e s e wind s e n s o r s have been most e n c o u r a g i n g ( e . g . Wesely et al.3 1970). R e c e n t l y Tanner and T h u r t e l l (1970) d e v e l o p e d a r e l a t i v e l y s i m p l e yaw s p h e r e - t h e r m o m e t e r (YST) system f o r the measurement o f s e n s i b l e heat f l u x i n c o r p o r a t i n g the p r e s s u r e - s p h e r e p r i n c i p l e . The yaw s p h e r e when d i r e c t e d i n t o the wind f l o w g e n e r a t e s a p r e s s u r e d i f f e r e n c e between two p o r t s t h a t i s p r o p o r t i o n a l t o the p r o d u c t o f the h o r i z o n t a l and v e r t i c a l w i n d s . The a n a l o g p r e s s u r e s i g n a l i s used to d r i v e a r e s i s t a n c e - t h e r m o m e t e r b r i d g e . The b r i d g e o u t p u t i s then d i r e c t l y r e l a t e d to the s e n s i b l e h e a t f l u x . T h i s system was chosen f o r the p u r p o s e o f our i n v e s t i g a t i o n . A s i g n i f i c a n t a s p e c t o f t h i s r e s e a r c h i n c l u d e s i n s t r u m e n t a l development and improvement, and f i e l d c o m p a r i s o n t e s t s o v e r a s i m p l e r u r a l s u r f a c e . 15 O b j e c t i ves In summary, the p r i m a r y o b j e c t i v e s o f t h i s t h e s i s can be s t a t e d as f o l l o w s : 1) t o c o n s t r u c t , c a l i b r a t e and t e s t a yaw-s p h e r e - t h e r m o m e t e r s y s t e m f o r d i r e c t m e a s u r e m e n t s o f s e n s i b l e h e a t f l u x dens i t y , 2) t o e x a m i n e t h e s p a t i a l v a r i a b i l i t y o f t h e eddy f l u x i n t h e a t m o s p h e r i c b o u n d a r y l a y e r , 3) t o d e t e r m i n e t h e m a g n i t u d e and s i g n o f t h e s e n s i b l e h e a t f l u x e s o v e r an u r b a n a r e a , 4) t o i n v e s t i g a t e t h e r o l e o f t h i s p a r a m e t e r i n t h e u r b a n e n e r g y b a l a n c e f r a m e w o r k . I t s h o u l d be emphasized t h a t some o f t h e s e o b j e c -t i v e s a r e v e r y d i f f i c u l t to a c h i e v e , and c o u p l e d w i t h l i m i t a t i o n s i n o b s e r v a t i o n must n e c e s s a r i l y c r e a t e s h o r t -comings. T h i s s t u d y i s however e x p e c t e d t o c o n t r i b u t e to our knowledge o f eddy f l u x measurement i n the a t m o s p h e r i c boundary l a y e r , and i n p a r t i c u l a r , to heat exchange p r o -c e s s e s i n the urban e n v i r o n m e n t . C h a p t e r 2 SITE AND INSTRUMENTATION E x p e r i m e n t a l S i t e s G e n e r a l a s p e c t s . For the p u r p o s e o f t h i s i n v e s t i g a t i o n , two e x p e r i -mental s i t e s were chosen i n and near V a n c o u v e r , B.C. G r e a t e r V a n c o u v e r , w i t h a p o p u l a t i o n e x c e e d i n g one m i l l i o n , c o v e r s t h e w e s t e r n m o s t p o r t i o n o f the Lower M a i n l a n d a r e a o f B r i t i s h C o l u m b i a . A map o f the r e g i o n d e p i c t i n g g e o g r a p h i c a l and p o l i t i c a l l a n d m a r k s , l a n d use and the l o c a t i o n o f the e x p e r i m e n t a l s i t e s i s shown i n F i g . 3. Dense, h i g h - r i s e b u i l d i n g s a r e c o n f i n e d p r i m a r i l y t o t h e C e n t r a l B u s i n e s s D i s t r i c t (CBD) on th e B u r r a r d P e n i n s u l a . The t o p o g r a p h y i s v a r i e d . The l a n d o v e r t h e a r e a s l o p e s g r a d u a l l y from s o u t h t o n o r t h , r i s i n g r a p i d l y from B u r r a r d I n l e t to the mountain r i d g e s a l o n g i t s n o r t h s h o r e . These mountain peaks r i s e t o h e i g h t s i n e x c e s s o f 1000 m. In the s o u t h w e s t e r n a r e a s o f Richmond and D e l t a , the l a n d i s f l a t and i s used p r i m a r i l y f o r a g r i c u l t u r e , 16 1 7 & # # & W H I T E ROCK T S A W W A S S E N U R B A N SITE (V.S.B.) •Jf R U R A L SITE (LADNER) BUILT UP A R E A C O N T O U R I N T E R V A L 300M 10 KM J F i g . 3. The G r e a t e r V a n c o u v e r a r e a . 18 a l t h o u g h r a p i d u r b a n i z a t i o n i s becoming e v i d e n t . The S u r r e y a r e a i s one o f r o l l i n g f a r m l a n d s w i t h o c c a s i o n a l h i l l s r e a c h i n g to e l e v a t i o n s o f 100 m. In the c i t y p r o p e r , the ground s l o p e s g r a d u a l l y from the F r a s e r upwards to form a s l i g h t r i d g e between t h i s r i v e r and B u r r a r d I n l e t . Here l a n d e l e v a t i o n s r e a c h 100-150 m and c o n t a i n s e v e r a l c r e s t s . The v a r i e d t o p o g r a p h y , the c l o s e p r o x i m i t y o f the l a n d t o w a t e r b o d i e s , and the d e g r e e o f u r b a n i z a t i o n e x e r t marked i n f l u e n c e s on the l o c a l c l i m a t e . The c l i m a t e o f the r e g i o n i s b e s t d e s c r i b e d as m o d i f i e d m a r i t i m e , c h a r a c t e r i z e d by wet m i l d autumn and w i n t e r , and r e l a t i v e l y d r y c o o l summers. T e m p e r a t u r e . T e m p e r a t u r e s a r e m o d i f i e d by p r o x i m i t y to G e o r g i a S t r a i t . Mean d a i l y t e m p e r a t u r e s range from about 2-5°C d u r i n g the months o f J a n u a r y and F e b r u a r y t o about 17-18°C d u r i n g the months o f J u l y and A u g u s t . The t e m p e r a t u r e p a t t e r n o f the G r e a t e r V a n c o u v e r a r e a has r e c e n t l y been r e p o r t e d by E m s l i e ( 1 9 7 2 ) . L a r g e v a r i a t i o n s i n t h e s u r f a c e t e m p e r a t u r e f i e l d e x i s t . The c ause o f t h e s e v a r i a t i o n s i s a t t r i b u t e d to the f o l l o w i n g f a c t o r s : 19 a) The d i s t a n c e f r o m t h e o c e a n and i t s m o d i f y i n g e f f e c t on a i r t e m p e r a t u r e , b) s e a b r e e z e s , c ) c o l d a i r d r a i n a g e t o low a r e a s a t n i g h t , d) t h e n o r m a l d e c r e a s e o f t e m p e r a t u r e w i t h h e i g h t , e) h e a t i s l a n d e f f e c t , f ) s o u t h e r l y a s p e c t , g) s y s t e m a t i c v a r i a t i o n s i n c l o u d i n e s s , h) a t m o s p h e r i c p o l l u t i o n i n t h e downtown a r e a . P r e c i p i t a t i on. E x t r e m e l y v a r i e d p r e c i p i t a t i o n p a t t e r n s o c c u r i n th e G r e a t e r V a n c o u v e r r e g i o n as a r e s u l t o f w e s t e r l y w i n d s , c o u p l e d w i t h t h e a b r u p t t e r r a i n l e v e l changes i n t h e n o r t h e r n s e c t i o n s ( W r i g h t and T r e n h o l m , 1969). Annual p r e c i p i t a t i o n v a r i e s from < 100 cm i n the Tsawassen a r e a to > 250 cm i n p a r t s o f No r t h V a n c o u v e r . A s i m i l a r t r e n d i n c l o u d c o v e r may be i n f e r r e d from t h e p r e c i p i t a t i o n p a t t e r n . The s e a s o n a l v a r i a t i o n o f p r e c i p i t a t i o n i n Vancouver i s shown i n F i g . 4. The summer i s g e n e r a l l y d r y w i t h o n l y a few days o f r a i n , whereas the w i n t e r i s c h a r a c t e r i z e d by many days o f r a i n i n each month. F i g . 4. P e r c e n t a g e o f days w i t h m e a s u r a b l e p r e c i p i t a t i o n - Vancouver C i t y (1906-1955) - 7 day r u n n i n g mean ( c . f . H a r r y and W r i g h t , 1967). o 21 Wi nds. The p r e v a i l i n g wind d i r e c t i o n s a r e e a s t e r l y and w e s t e r l y a l o n g the a x i s o f the F r a s e r V a l l e y . E a s t e r l y winds a r e a s s o c i a t e d w i t h the development o f n i g h t time l a n d b r e e z e s and w i t h the g e n e r a l f l o w ahead o f any f r o n t a l s y s t e m . W e s t e r l i e s o c c u r as a f t e r n o o n sea b r e e z e s o r f o l l o w i n g f r o n t a l p a s s a g e s and a r e g e n e r a l l y much s t r o n g e r than the e a s t e r l y w i n d s . E a s t e r l i e s a r e p r e d o m i n a n t t h r o u g h -o u t t h e y e a r , d i m i n i s h i n g g r a d u a l l y from w i n t e r to summer. W e s t e r l i e s show an i n c r e a s e i n f r e q u e n c y o f o c c u r r e n c e from w i n t e r to summer. Mean wind speeds do n o t show much v a r i a t i o n from month t o month. The p r e s e n c e o f a l o c a l sea b r e e z e - l a n d b r e e z e c i r c u l a t i o n and v a l l e y c o n s t r i c t i o n o f t e n combine t o i n h i b i t t h e t r a n s p o r t o f a t m o s p h e r i c p o l l u t a n t s away from t h e a r e a i n p r o l o n g e d p e r i o d o f a n t i -c y c l o n i c w eather c o n d i t i o n s . V i s u a l o b s e r v a t i o n s i n d i c a t e t h a t t h e p o l l u t a n t s i n such s i t u a t i o n s a r e c a r r i e d up t h e v a l l e y d u r i n g the d a y t i m e w i t h the o n s h o r e b r e e z e , o n l y to r e t u r n to the c i t y a t n i g h t w i t h t h e l a n d b r e e z e c i r c u l a t i o n . H e a t i n g s e a s o n . H e a t i n g r e q u i r e m e n t to p r o v i d e r e a s o n a b l e c o m f o r t t h r o u g h o u t t h e y e a r i s g e n e r a l l y e x p r e s s e d i n terms o f 22 "degree d a y s " ( t h e number o f d e g r e e s F t h a t the mean d a i l y t e m p e r a t u r e i s below 6 5 ° F ) . For V a n c o u v e r , on the a v e r a g e , 90 per c e n t o f the h e a t i n g s e a s o n ( h e a t i n g d e g r e e - d a y s ) o c c u r s between September and A p r i l , w i t h J a n u a r y and F e b r u a r y b e i n g the two g r e a t e s t h e a t i n g months. In c o n -t r a s t , J u l y and A u g u s t may be c o n s i d e r e d to be n o n - h e a t i n g months ( H a r r y and W r i g h t , 1967). T h i s g e n e r a l p i c t u r e p r o v i d e s the b a s i c c l i m a t e c o n t e x t w i t h i n which the m i c r o c l i m a t i c i n v e s t i g a t i o n s o f t h i s s t u d y took p l a c e . A more d e t a i l e d d e s c r i p t i o n o f the g e n e r a l c l i m a t e o f the V a n c o u v e r a r e a i s g i v e n by H a r r y and W r i g h t ( 1 9 6 7 ) . S i t e c o n s i d e r a t i o n s . E x p e r i m e n t a l s t u d i e s i n the a t m o s p h e r i c boundary l a y e r a r e s t r o n g l y i n f l u e n c e d by the s p a t i a l v a r i a b i l i t y o f m e t e o r o l o g i c a l phenomena i n both the h o r i z o n t a l and v e r t i c a l d i r e c t i o n s . To some e x t e n t , o b s e r v a t i o n s i n such an e n v i r o n m e n t can o n l y be c o n d u c t e d i m p e r f e c t l y . F o r w h i l e s p a t i a l s a m p l i n g i s h i g h l y d e s i r a b l e , e s p e c i a l l y o v e r rugged t e r r a i n , t h i s i s o f t e n d i f f i c u l t to a c h i e v e because o f p r a c t i c a l l i m i t a t i o n s . One i s then l e d to c o n s i d e r p o i n t measurements w i t h t h e i r i n h e r e n t l i m i t a t i o n s , and t o 23 l i m i t s t u d y o f the p r o c e s s e s to the time domain. P a r t i c u l a r a t t e n t i o n then must be g i v e n to the i m p o r t a n t and o f t e n d i f f i c u l t problem o f s i t e s e l e c t i o n . In c h o o s i n g the s i t e , o b j e c t i v e c r i t e r i a s h o u l d be s p e c i f i e d . P r i m a r y c o n s i d e r a t i o n s h o u l d be g i v e n t o : a) t h e p u r p o s e o f t h e i n v e s t i g a t i o n , b) t h e n a t u r e o f t h e u n d e r l y i n g s u r f a c e , c ) p r a c t i c a l l i m i t a t i o n s . In t h i s s t u d y the f o l l o w i n g g e n e r a l s i t e s e l e c t i o n c r i t e r i a were employed. a) t h e s i t e and i t s i m m e d i a t e e n v i r o n s s h o u l d be as n e a r l y as p o s s i b l e c h a r a c t e r i s t i c o f t h e a r e a , t h e c l i m a t e o f w h i c h i s t o be e x p l o r e d , b) i t s h o u l d be w i t h i n an a r e a t h a t i s f a i r l y u n i f o r m and e x t e n s i v e so a s t o m i n i m i z e s m a l l s e a I e - a d v e c t i v e i n f l u e n c e s and t o e n s u r e a d e q u a t e f e t c h , c ) p r o p e r a l l o w a n c e s h o u l d be made w i t h r e f e r e n c e t o t h e e x p o s u r e o f t h e s i t e f o r t h e e n t i t i e s t o be m e a s u r e d , d) t h e s i t e s h o u l d be a c c e s s i b l e , w i t h a d e q u a t e power and p r o t e c t i o n f r o m v a n d a l i s m . A p a r t from p r a c t i c a l l i m i t a t i o n s (see (d) a b o v e ) , an e x p e r i m e n t a l s i t e t h a t s a t i s f i e s t h e s e g e n e r a l c r i t e r i a can u s u a l l y be f o u n d i n r u r a l a r e a s . T hus, an e x t e n s i v e , u n i f o r m f l a t a r e a o r a homogeneous v e g e t a t e d s u r f a c e w i t h 24 adeq u a t e f e t c h would be a p p r o p r i a t e f o r the r u r a l e x p e r i -mental s i t e . A f i x e d s a m p l i n g p o i n t may then be c o n s i d e r e d s u f f i c i e n t l y r e p r e s e n t a t i v e o f the a r e a . S i t e s e l e c t i o n i n t h e urban e n v i r o n m e n t , to meet the above c r i t e r i a , i s e x t r e m e l y d i f f i c u l t . I n deed, i t i s i m p o s s i b l e t o d e f i n e a s a m p l i n g s i t e which c o u l d be c o n -s i d e r e d ' r e p r e s e n t a t i v e ' o f t h e c i t y as a whole, b e c a u s e t h e urban ' t o p o g r a p h y ' and the s o u r c e and s i n k d i s t r i b u -t i o n s o f h e a t , w a t er vapour and momentum i s h i g h l y i r r e g u l a r . By c o n s i d e r i n g o n l y a v e r y s m a l l p o r t i o n o f t h e urban l a n d -s c a p e (a l i m i t e d u r b a n - b u i l d i n g - a i r v o l u m e ) , i t may be p o s s i b l e t o o b t a i n a s i t e and i t s immediate e n v i r o n s t h a t i s a p p r o x i m a t e l y c h a r a c t e r i s t i c o f an urban a r e a . I f t h e a r e a p o s s e s s e s a b a s i c c o n t i n u i t y o f f o r m , c r i t e r i o n (b) may be a d e q u a t e l y s a t i s f i e d . I t s h o u l d be p o i n t e d o u t , however, t h a t where d i s t i n c t changes i n the p r o p e r t i e s o f the u n d e r l y i n g s u r f a c e o c c u r , i n t e r n a l boundary l a y e r s d e v e l o p and deepen downwind. In urban a r e a s , many changes o c c u r due t o t h e v a r i e t y o f s u r f a c e t y p e s and the n a t u r e o f the s u r f a c e geometry. S u r f a c e d i s c o n t i n u i t i e s may a l s o be c r e a t e d by t e m p e r a t u r e a n o m a l i e s ( f o r example, c o n t r a s t i n g a r e a s i n shadow and d i r e c t s u n l i g h t ) . The problem o f a c h i e v i n g s u i t a b l e h e i g h t / f e t c h r a t i o to e n s u r e r e p r e s e n t a -t i v e n e s s would become f o r m i d a b l e i f t h e s e changes r e s u l t e d 25 i n d i s t i n c t l o c a l i z e d boundary l a y e r s . Dyer (1963) i n d i c a t e s a h e i g h t / f e t c h r a t i o 1:200-300 f o r 90 per c e n t a d j u s t m e n t to a new s u r f a c e c o n d i t i o n . S u f f i c i e n t f e t c h would thus o n l y be r e a l i z e d f o r c o n d i t i o n s v e r y c l o s e t o the p a r t i c u l a r s u r f a c e o v e r which measurements were made. Such l o c a l i z e d e f f e c t s may not be v e r y s i g n i f i c a n t o v e r a r e l a t i v e l y dense u n i f o r m urban a r e a s i n c e the i n t e r n a l b o u n d a r i e s a r e l i k e l y to become d i f f u s e d t h r o u g h t u r b u l e n t m o t i o n o f t h e a i r as i t t r a v e r s e s o v e r t h e b u i l d i n g e l e m e n t s . The c h o i c e o f s i t e may thus m i n i m i z e t h i s e f f e c t . To a l l o w f o r p r o p e r e x p o s u r e a t the s i t e and to e n s u r e a r e l a t i v e l y u n i f o r m m e t e o r o l o g i c a l f i e l d , measurements i n the urban c o n t e x t s h o u l d be c o n d u c t e d above r o o f l e v e l . In c h o o s i n g t h e urban e x p e r i m e n t a l s i t e , t h e f o l l o w i n g c r i t e r i a were s p e c i f i e d : a) t h e s i t e s h o u l d be l o c a t e d i n an a r e a o f b u i l d i n g c o n t i n u i t y ( u n i f o r m t y p e , h e i g h t , d e n s i t y and f u n c t i o n ) and m e a s u r e m e n t s s h o u l d be made a b o v e r o o f -l e v e l , so as t o e n s u r e some u n i f o r m i t y i n t h e m e t e o r o l o g i c a l f i e l d s , b) t h e s i t e s h o u l d have s u i t a b l e f e t c h f r o m n o n - u r b a n s u r f a c e s so as t o a v o i d l a r g e s c a l e a d v e c t i v e i n f l u e n c e s , c ) t h e a r e a o f c o n c e r n s h o u l d be n e a r t h e c e n t r e o f t h e u r b a n h e a t i s l a n d , b u t h o r i z o n t a l t e m p e r a t u r e g r a d i e n t s s h o u l d be r e I a t i v e I y smaI I , d) t h e r e s h o u l d be no m a j o r a n o m a l y n e a r b y t h a t m i g h t s p o r a d i c a l l y a f f e c t r e s u l t s ( e x . i n d u s t r i a l p l a n t w i t h h i g h w a s t e h e a t and w a t e r v a p o u r e m i s s i o n s ) . 26 The f o l l o w i n g two s e c t i o n s d e s c r i b e the s i t e s chosen i n l i g h t o f t h e s e c r i t e r i a . The r u r a l s i t e . The r u r a l o b s e r v a t i o n a l s i t e was l o c a t e d on t h e f l a t d e l t a r e g i o n o f the F r a s e r , about 28 km s o u t h o f V a n c o u v e r ( c . f . F i g . 3 ) . The s i t e chosen was an e x t e n s i v e , f l a t g r a s s e d s u r f a c e on the abandoned a i r p o r t a t C a n a d i a n F o r c e s S t a t i o n , L a d n e r . The g e n e r a l l o c a t i o n o f the s i t e i s shown on F i g s . 5 and 6. I n t e r r u p t i o n s i n t h e g r a s s s u r f a c e p r o p e r t i e s were c r e a t e d by the a i r p o r t runways, Boundary Bay and by a s t e p change i n the g r a s s h e i g h t i n the NNE-SSE s e c t o r d u r i n g the f i e l d programme o f 1971. The g r a s s o v e r the e x p e r i m e n t a l s i t e was ~ 90 cm t a l l , g i v i n g a r o u g h n e s s l e n g t h o f ~ 10 cm based on a n a l y s i s o f n e u t r a l wind p r o f i l e s . R a d i a t i o n measurements gave a s h o r t - w a v e a l b e d o o f 0.23 and a long-wave e m i s s i v i t y o f 0.98 f o r the g r a s s s u r f a c e . H e i g h t / f e t c h r a t i o s (1:165 to 1:200) were fo u n d to be s u f f i c i e n t t o e n s u r e r e p r e s e n t a t i v e o b s e r v a t i o n s i n most i n s t a n c e s . Minimum f e t c h d i s t a n c e s , and the g e n e r a l l o c a t i o n o f t h e i n s t r u m e n t s a r e shown i n F i g . 6. The s i t e was c o n s i d e r e d s a t i s f a c t o r y i n r e s p e c t o f the g e n e r a l c r i t e r i a p r e v i o u s l y s t a t e d ( e . g . u n i f o r m i t y i n t e r r a i n F i g . 5. Map o f L a d n e r e x p e r i m e n t a l s i t e . S k e t c h o f L a d n e r s i t e showing minimum f e t c h d i s t a n c e s . 29 and v e g e t a t i o n c o v e r , freedom from v e r t i c a l o b s t r u c t i o n s , a c c e s s i b i l i t y , a v a i l a b l e power and s e c u r i t y ) . A p o s i t i v e f e a t u r e o f t h i s s i t e was the f a c t t h a t i t had been p r e -v i o u s l y used f o r e x t e n s i v e s t u d i e s o f the t u r b u l e n t t r a n s f e r mechanisms i n the a t m o s p h e r i c boundary l a y e r ( e . g . McBean and M i y a k e , 1972). The urban s i t e . The urban e x p e r i m e n t a l s i t e , c hosen f o r t h i s s t u d y was l o c a t e d i n a mixed commercial and m e d i u m - r i s e r e s i d e n t i a l d i s t r i c t . O b s e r v a t i o n s were c o n d u c t e d o v e r t h e f l a t - t o p r o o f o f a f o u r - s t o r e y b u i l d i n g ( t h e Van c o u v e r S c h o o l Board B u i l d -i n g ) i n t h e midtown a r e a ( F i g . 3 ) . The minimum f e t c h t o non-urban s u r f a c e s was a p p r o x i m a t e l y 1.5 km (N. t o F a l s e C r e e k , and NW t o E n g l i s h B a y ) . O t h e r w i s e t h e b u i l d i n g s w i t h i n a 2 km r a d i u s o f the s i t e were f a i r l y u n i f o r m i n • h e i g h t , d e n s i t y and f u n c t i o n ( e x c e p t i n t h e e a s t e r l y s e c t o r , where i r r e g u l a r i t i e s i n t h e s u r f a c e due t o t h e d i f f e r e n t shape and h e i g h t s o f b u i l d i n g s were n o t i c e a b l e ) . A v e r a g e b u i l d i n g h e i g h t s were ~ 10-13 m. W i t h i n a 2 km r a d i u s o f t h e e x p e r i m e n t a l s i t e , b u i l d i n g s o c c u p i e d ~ 70-80 per c e n t o f each b l o c k , e x c e p t near the p e r i p h e r y i n the n o r t h e a s t and s o u t h e r l y s e c t o r s . A p p r o x i m a t e l y 70 per c e n t o f t h e s e 30 b u i l d i n g s c o n s i s t e d o f m e d i u m - r i s e r e s i d e n t i a l d w e l l i n g s , p r i m a r i l y o f f l a t - t o p r o o f s c o v e r e d w i t h g r a v e l and t a r . A s i t e p l a n showing t h e l o c a t i o n o f the V a n c o u v e r S c h o o l Board B u i l d i n g (VSB) and i t s immediate e n v i r o n s i s shown i n F i g . 7. A s u r v e y based on l a n d uses w i t h i n the 2 km c i r c l e gave e s t i m a t e s o f i m p e r v i o u s h o r i z o n t a l s u r f a c e a r e a o f a p p r o x i -m a t e l y 70 per c e n t . C l o s e r t o the a c t u a l s i t e , t h e i m p e r v i o u s l a n d a r e a was about 80 per c e n t . The a r e a s l o p e s g r a d u a l l y downwards from s o u t h to n o r t h , d r o p p i n g a p p r o x i m a t e l y 50 m o v e r the 4 km d i s t a n c e ( i . e . s l o p e ~ 1 i n 8 0 ) . The i n f l u e n c e o f w a ter s u r f a c e s to the n o r t h ( m a i n l y E n g l i s h B a y ) , c o u l d not always to a v o i d e d a t the VSB s i t e . A i r f l o w sometimes o c c u r r e d from t h i s d i r e c t i o n . Measurements c o n d u c t e d c l o s e t o the VSB r o o f - t o p s u r f a c e would not be a f f e c t e d by t h i s i n f l u e n c e . A t g r e a t e r h e i g h t s , however, i t was r e c o g n i z e d t h a t measurements would p r o b a b l y be a f f e c t e d by the c o n t r a s t s i n w a t e r / l a n d t e m p e r a t u r e s and h u m i d i t i e s . T h i s n e c e s s i t a t e d c o n s i d e r a t i o n o f the p r e v a i l -i n g wind d i r e c t i o n d u r i n g o b s e r v a t i o n p e r i o d s . A p l a n view o f the r o o f - t o p s u r f a c e o f t h e VSB b u i l d i n g i s shown i n F i g . 8. The r o o f m a t e r i a l s c o n s i s t e d o f t a r w i t h a c o v e r i n g l a y e r o f f i n e g r a v e l which had a s h o r t - w a v e a l b e d o o f 0.21 and a long-wave e m i s s i v i t y o f 0.92. The r e s t o f t h e b u i l d i n g was c o n s t r u c t e d o f r e d b r i c k and c o n c r e t e . T h e r e were no major v e n t i l a t i o n o u t l e t s a t r o o f 31 F i g . 7. S i t e p l a n o f the urban a r e a ( V a n c o u v e r S c h o o l Board B u i l d i n g and i t s immediate e n v i r o n s ) . 1 L O C A T I O N O F RN, Y S T (20M) O N M A S T , 20M A B O V E POSITION 4 2 G R O O F < O N SUPER S T R U C T U R E ) 3 L O C A T I O N O F T A R A N D C O N C R E T E S L A B S 4 Y S T L O C A T I O N F O R M E A S U R E M E N T S A T .1.2, 2.0 A N D 4.0M MAIN EXPERIMENTAL AREA (GRAVEL AND TAR ROOF) PATIO (WOOD OVER TAR & GRAVEL) J B R O A D W A Y h L l o t h A V E ^ ~ii ir L © V-S.B BLDG. N " (GRAVEL AND TAR ROOF) 4M A B O V E POSITION 4 XL T E L E S C O P I N G M A S T S U P E R -S T R U C T U R E 10M A B O V E POSITION 4 G R A V E L A N D T A R R O O F • I N C I N E R A T O R 10 M F i g . 8, The Vancouver S c h o o l Board B u i l d i n g ( P l a n view) 33 l e v e l e x c e p t f o r the i n c i n e r a t i o n chimney on the s u p e r s t r u c -t u r e . In g e n e r a l , d a y t i m e wind d i r e c t i o n s were p r e d o m i n a n t l y from the n o r t h , west and s o u t h e r l y s e c t o r s . A t n i g h t , t h e r e was a t e n d e n c y sometimes f o r the development o f e a s t e r l y w i n d s . The e x a c t l o c a t i o n s o f the i n s t r u m e n t s on t h e r o o f a r e shown i n F i g . 8. D u r i n g the o b s e r v a t i o n programme o f 1972, a s u r v e y o f V a n c o u v e r ' s h e a t i s l a n d was u n d e r t a k e n . I t was f o u n d t h a t the a r e a o f the e x p e r i m e n t a l s i t e was c l o s e t o one o f the c o r e s o f the h e a t i s l a n d a t n i g h t (see F i g . 9 ) . R e l a -t i v e l y s m a l l t e m p e r a t u r e g r a d i e n t s o c c u r w i t h i n t h e a r e a . A few d a y t i m e s u r v e y s i n d i c a t e d even s m a l l e r h o r i z o n t a l tem-p e r a t u r e g r a d i e n t s . I t must however be n o t e d t h a t c o n t r a s t -i n g a r e a s i n shadow and s u n l i g h t would be l i k e l y to produce l o c a l i z e d t e m p e r a t u r e g r a d i e n t s . In our a r e a , t h e s e c o u l d h a r d l y be a v o i d e d . I t w i l l be assumed t h a t t h e s e e f f e c t s a r e s m a l l , on t h e b a s i s t h a t t u r b u l e n t m i x i n g o f t h e a i r t e n d s to produce u n i f o r m i t y i n the t e m p e r a t u r e f i e l d . A l t h o u g h t h i s s i t e p o s s e s s e s o b v i o u s l i m i t a t i o n s , i t was c o n s i d e r e d a c c e p t a b l e f o r the s t u d y , based on the c r i t e r i a s p e c i f i e d p r e v i o u s l y . F i g . 9. An example of the l o c a t i o n o f the heat i s l a n d c o r e s i n V a n c o u v e r , B.C. CO 35 G e n e r a l I n s t r u m e n t a t i o n and E x p e r i m e n t a l P r o c e d u r e s The s i n g l e most i m p o r t a n t i n s t r u m e n t f o r t h i s s t u d y was the yaw s p h e r e - t h e r m o m e t e r eddy c o r r e l a t i o n s y stem t o measure s e n s i b l e heat f l u x d i r e c t l y . S i n c e the d e v e l o p m e n t , c a l i b r a t i o n and t e s t i n g o f t h i s a p p a r a t u s forms an i n t e g r a l p a r t o f the r e s e a r c h , i t w i l l be p r e s e n t e d s e p a r a t e l y i n the n e x t c h a p t e r . Here a t t e n t i o n i s l i m i t e d to o t h e r r e l e -v a n t i n s t r u m e n t a t i o n used i n the c o u r s e o f the i n v e s t i g a t i o n . Radi a t i on. Net r a d i o m e t e r s ( S w i s s t e c o P t y . L t d . , Model S I ) were used t o measure the n e t s u r f a c e a l l - w a v e r a d i a t i o n . The r a d i a t i o n s e n s o r c o n s i s t s o f a c r o s s - s h a p e d t h e r m o p i l e c o n -s t r u c t e d o f c o p p e r - p l a t e d c o n s t a n t a n w i r e . The t h e r m o p i l e s u r f a c e s a r e e n c l o s e d w i t h i n a p a i r o f molded p o l y e t h y l e n e domes, 0.5 mm i n t h i c k n e s s , which a r e t r a n s p a r e n t t o r a d i a -t i o n i n t h e w a v e l e n g t h s between 0.3 y and 100 u. The domes were kept r i g i d and f r e e o f i n t e r i o r c o n d e n s a t i o n by a c o n t r o l l e d f l o w o f d r y n i t r o g e n . A more p r a c t i c a l way t o keep the domes purged by means o f d r y a i r ( D a v i e s et al.3 1970) was a d o p t e d d u r i n g the m e a s u r i n g programme i n 1972. The r a d i o m e t e r time c o n s t a n t was 23 s, and the t h e r m o p i l e s e n s i t i v i t y was a p p r o x i m a t e l y 0.39 mv/mWcm"2 ( c a l i b r a t i o n s 36 s u p p l i e d by N a t i o n a l R a d i a t i o n L a b o r a t o r y , Canada A E S ) . E x c e p t where n o t e d i n the t e x t , the o u t p u t s o f the r a d i o -meters were r e c o r d e d c o n t i n u o u s l y on v o l t - t i m e i n t e g r a t o r s ( L i n t r o n i c , L t d . ) , u s i n g a 30 min i n t e g r a t i o n p e r i o d . In a l l s t u d i e s c o n c e r n e d w i t h the measurement o f s u r f a c e r a d i a t i o n f l u x e s , i t i s i m p o r t a n t t h a t the r a d i a t i o n r e c e i v e d by the s e n s o r i s r e p r e s e n t a t i v e o f the s u r f a c e under s t u d y . A t the r u r a l s i t e , t h i s was not d i f f i c u l t to a c h i e v e s i n c e the s u r f a c e was r e l a t i v e l y homogeneous, and n e t r a d i a -t i o n was m o n i t o r e d a t a c o n v e n t i o n a l h e i g h t o f 1 m. A t the urban s i t e , c o r r e c t l o c a t i o n o f the s e n s o r i s i m p o r t a n t f o r view f a c t o r c o n s i d e r a t i o n s . To e n s u r e a good h o r i z o n t a l f i e l d o f view, t h e r a d i o m e t e r was mounted a p p r o x i m a t e l y 20 m above the p r i n c i p a l r o o f - t o p s u r f a c e on a f i x e d t e l e -s c o p i n g mast a t t h e p o s i t i o n shown i n F i g . 8. A t e s t o f the h e i g h t v a r i a b i l i t y i n t h e n e t r a d i a n t f l u x o v e r t h e h e i g h t range 11 to 20 m showed l e s s t h a n 5 per c e n t v a r i a t i o n d u r i n g the d a y t i m e . H o r i z o n t a l v a r i a b i l i t y o f t h e urban n e t r a d i a t i o n f i e l d was not examined. Some v a r i a t i o n s a r e to be e x p e c t e d i n measurements o v e r a r o o f as opposed t o t h o s e o v e r a canyon (between b u i l d i n g e l e m e n t s ) , p a r t i c u l a r l y when shadow a r e a s a r e e x t e n s i v e ( e . g . C r a i g and Lowry, 1972). View f a c t o r c o n s i d e r a t i o n s and the e f f e c t o f the i n t e r v e n i n g a i r l a y e r between the r a d i a t i o n s e n s o r and the r o o f - t o p s u r f a c e w i l l be examined i n C h a p t e r 6. 37 S o i l h eat s t o r a g e . S o i l h eat s t o r a g e was measured u s i n g h e a t f l u x p l a t e s ( M i d d l e t o n and C o . ) . The heat f l u x p l a t e c o n s i s t s o f two m e t a l l i c s u r f a c e p l a t e s s e p a r a t e d by a s u b s t a n c e o f known c o n d u c t i v i t y . A t h e r m o p i l e w i t h a l t e r n a t e j u n c t i o n s i n good t h e r m a l c o n t a c t w i t h one o f the s u r f a c e p l a t e s measures the t e m p e r a t u r e d i f f e r e n t i a l between the s u r f a c e s , and hence can be c a l i b r a t e d to p r o v i d e the heat f l u x d e n s i t y . A t the r u r a l l o c a t i o n , t h r e e such p l a t e s ( o f a p p r o x i m a t e l y equal c a l i b r a t i o n : 0.28 mv/mWcm"2) were c o n n e c t e d i n s e r i e s and p l a c e d about 2.5 cm below the s o i l s u r f a c e . T h i s a r r a n g e m e n t p r o v i d e d a l a r g e r s i g n a l f o r measurements, and gave a b e t t e r s p a t i a l s a m p l i n g . S o i l f l u x d i v e r g e n c e between the 2.5 cm d e p t h and the s u r f a c e was computed v i a the c a l o r i m e t r i c ( t e m p e r a t u r e i n t e g r a l ) method (Fuchs and T a n n e r , 1968). T h i s was f o u n d t o be v e r y s m a l l i n magnitude and was s u b s e q u e n t l y n e g l e c t e d i n t h i s s t u d y . A t the urban s i t e , a heat f l u x p l a t e was embedded i n the g r a v e l and t a r r o o f , c a r e b e i n g t a k e n to e n s u r e no e x p o s u r e to s o l a r r a d i a t i o n . The p l a t e was l o c a t e d about 0.5 cm below the s u r f a c e . The measured heat f l u x p r o v i d e d an e s t i m a t e o f the amount o f heat p a s s i n g i n t o o r o u t o f the r o o f . Heat f l u x p l a t e s were a l s o embedded i n s l a b s o f t a r and c o n c r e t e and p l a c e d on the VSB r o o f i n o r d e r t o 38 p r o v i d e some u n d e r s t a n d i n g o f the way i n w hich o t h e r urban m a t e r i a l s may d i f f e r from the r o o f v a l u e . No a t t e m p t was made to e s t i m a t e the s t o r a g e by the v e r t i c a l w a l l s o f t h e b u i l d i n g . E r r o r s a s s o c i a t e d w i t h the use o f the f l u x p l a t e i n t h e r o o f w i l l be d i s c u s s e d i n C h a p t e r 6. The r o o f f l u x p l a t e o u t p u t s i g n a l was a l s o r e c o r d e d on a v o l t - t i m e i n t e g r a t o r , u s i n g a 30 min i n t e g r a t i o n p e r i o d . The p l a t e s i n t h e s l a b s o f t a r and c o n c r e t e were c o n t i n u o u s l y m o n i t o r e d on a p o t e n t i o m e t r i c r e c o r d e r (Honeywell, E l e c t r o n i k 1 9 4 ) . O t h e r i n s t r u m e n t s . The f o l l o w i n g a d d i t i o n a l equipment was u s e d : 1. F o r t h e f i e l d t e s t s o f the yaw s p h e r e - t h e r -mometer s y s t e m , c o m p a r i s o n was made a g a i n s t the Bowen r a t i o / e n e r g y b a l a n c e method. The Bowen r a t i o a p p a r a t u s used i s d e s c r i b e d i n d e t a i l i n the p a p e r by B l a c k and McNaughton ( 1 9 7 1 ) . I t i s a p s y c h r o m e t r i c a p p a r a t u s d e s i g n . f o r Bowen r a t i o d e t e r m i n a t i o n t h a t measures the wet- and d r y - b u l b d i f f e r e n c e s o v e r a v e r t i c a l d i s t a n c e o f 0.6 o r 1 m w i t h an e r r o r l e s s t h a n 0.01°C. The t e m p e r a t u r e s e n s o r s c o n s i s t o f two matched p a i r s o f 1N2356 germanium d i o d e s . The germanium d i o d e has a l i n e a r v o l t a g e - t e m p e r a t u r e c h a r a c t e r i s t i c and 39 l a r g e s e n s i t i v i t y o f a b o u t 2.3 m v ° C _ 1 . The time c o n s t a n t o f the s e n s i n g heads i s a p p r o x i m a t e l y 1 min. A c c o r d i n g l y , o n l y d a t a r e c o r d e d f o r t h e l a s t 10 min o f each 15-min p e r i o d i s used i n th e Bowen r a t i o c a l c u l a t i o n s . H a l f - h o u r l y Bowen r a t i o s a r e computed from the d i f f e r e n c e s between v o l t a g e a v e r a g e s from two c o n s e c u t i v e 10-min p e r i o d s . The o u t p u t s i g n a l s were c o n t i n u o u s l y m o n i t o r e d on a p o t e n t i o m e t r i c r e c o r d e r ( H o n e y w e l l , E l e c t r o n i k 1 9 4 ) . 2. S u r f a c e r o u g h n e s s c h a r a c t e r i s t i c s a t the L a d n e r s i t e were d e t e r m i n e d from p r o f i l e measurements w i t h a s i x -l e v e l s e n s i t i v e wind p r o f i l e system (C.W. T h o r n t h w a i t e A s s o c i a t e s ) . Wind speeds were measured a t 1.13, 2.00, 1.43, 1.73, 2.33 and 2.93 m above ground l e v e l . 3. Short-wave a l b e d o measurements were o c c a s i o n a l l y m o n i t o r e d w i t h dome s o l a r i m e t e r s ( L i n t r o n i c , L t d . ) ( M o n t e i t h , 1 959). These i n s t r u m e n t s c o n s i s t o f an e i g h t y - j u n c t i o n t h e r m o p i l e , e n c l o s e d by a t h i n - w a l l e d f r o s t e d g l a s s dome ( t r a n s p a r e n t t o r a d i a t i o n i n the w a v e l e n g t h range 0.3y t o 3.3u. Measurement Programme The o b s e r v a t i o n programme was i n i t i a l l y s t a r t e d i n t h e l a t e summer o f 1970 i n M o n t r e a l as a p r e l i m i n a r y r e s e a r c h 40 p r o j e c t . C I i m a t o l o g i c a l a p p r o a c h e s to the d e t e r m i n a t i o n o f the urban s e n s i b l e heat f l u x e s were i n v e s t i g a t e d (Oke et al.3 1972). The eddy c o r r e l a t i o n method a p p e a r e d most l i k e l y to a c h i e v e s u c c e s s i n the c o n t e x t o f the c i t y and a c c o r d i n g l y was a d o p t e d . O n l y s u b s e q u e n t work i s r e p o r t e d i n t h i s t h e s i s. The yaw s p h e r e - t h e r m o m e t e r system was c o n s t r u c t e d and c a l i b r a t e d i n 1971. L a t e r t h a t summer the f i e l d com-p a r i s o n t e s t s were c o n d u c t e d a t the r u r a l s i t e i n L a d n e r , B.C. D u r i n g the f o l l o w i n g w i n t e r , a second YST system was c o n -s t r u c t e d . The main f i e l d programme was c a r r i e d o u t a t L a d n e r and i n Vanc o u v e r d u r i n g the summer o f 1972. O b s e r v a t i o n s were c o n d u c t e d under v a r i o u s weather c o n d i t i o n s t h r o u g h o u t t h i s p e r i o d and were o n l y o m i t t e d d u r i n g s p e l l s o f wet w e a t h e r . In g e n e r a l , d u r i n g an o b s e r -v a t i o n a l s e q u e n c e , c o n t i n u o u s measurements were made t h r o u g h -out t h e day and i n the c i t y o f t e n t h r o u g h o u t t h e n i g h t as w e l l . In t h i s manner, i t was p o s s i b l e to i n v e s t i g a t e t h e d i u r n a l b e h a v i o u r o f the en e r g y f l u x e s under most weather c o n d i t i o n s t h a t t y p i c a l l y o c c u r i n Vancouver d u r i n g t h e summer. The normal s a m p l i n g i n t e r v a l was s e t a t 30 min f o r each system i n e v a l u a t i n g the heat f l u x e s . C h a p t e r 3 THE YAW SPHERE-THERMOMETER SYSTEM I n t r o d u c t i o n The p r i n c i p l e o f the yaw s p h e r e - t h e r m o m e t e r system f o r d i r e c t measurements o f s e n s i b l e h e a t f l u x d e n s i t y was b r i e f l y m e n t i o n e d i n t h e f i r s t c h a p t e r . The s p h e r e , when d i r e c t e d i n t o the f l o w , g e n e r a t e s a p r e s s u r e d i f f e r e n c e between two p o r t s t h a t i s p r o p o r t i o n a l to the p r o d u c t o f the h o r i z o n t a l and v e r t i c a l w i n d s . T h i s p r e s s u r e d i f f e r e n c e , c o n v e r t e d t o an a n a l o g s i g n a l and e l e c t r i c a l l y f i l t e r e d , i s then used t o d r i v e a r e s i s t a n c e - t h e r m o m e t e r b r i d g e . I n t e -g r a t i o n o f the o u t p u t , d i v i d e d by the mean h o r i z o n t a l wind speed y i e l d s H. F u l l d e t a i l s o f t h e c o n s t r u c t i o n and t h e o r y o f o p e r a t i o n o f the system a r e g i v e n i n Ta n n e r and T h u r t e l l (1970) and our system c l o s e l y f o l l o w e d t h e i r o r i g i n a l d e s i g n . Here, we s h a l l be p r i m a r i l y c o n c e r n e d w i t h f o u r i m p o r t a n t a s p e c t s . F i r s t l y , c e r t a i n a e r o d y n a m i c c h a r a c t e r i s t i c s on t h e b a s i s o f wind t u n n e l e x p e r i m e n t s a r e i n v e s t i g a t e d . S e c o n d l y , the e f f e c t s o f t i l t i n g the 41 42 s p h e r e a r e a n a l y s e d . T h i r d l y , the t e m p e r a t u r e s e n s o r p e r -formance i s e v a l u a t e d f o r d i f f e r e n t c o n f i g u r a t i o n s . F i n a l l y , the r e s u l t s o f a f i e l d c o m p a r i s o n between the YST system and a Bowen r a t i o a p p a r a t u s a r e p r e s e n t e d . We s h a l l p r o c e e d f i r s t w i t h a b r i e f d e s c r i p t i o n o f the i n s t r u m e n t and a r e v i e w o f the yaw s p h e r e - t h e r m o m e t e r t h e o r y . Equipment D e s c r i p t i o n The yaw s p h e r e c o n s i s t s o f two 1.59 mm d i a m e t e r h o l e s , d r i l l e d o f f - c e n t r e , t h r o u g h a 5-cm p l a s t i c s p h e r e so t h a t t h e i n c l u d e d a n g l e between the p o r t h o l e s and the c e n t r e o f t h e s p h e r e i s 4 5 ° . A G i l l p r o p e l l e r vane (R.M. Young Co.) was m o d i f i e d so t h a t the s p h e r e c o u l d be mounted i n t h e p o s i t i o n where the p r o p e l l e r i s n o r m a l l y s i t u a t e d . Two 1.59 mm O.D. p o l y e t h y l e n e tubes were b r o u g h t t h r o u g h the stem and base o f the vane h o u s i n g and a t t a c h e d t o a c a p a c i t i v e p r e s s u r e t r a n s d u c e r ( D a t a m e t r i c s I n c . , Model 511-8 B a r o c e l ) . The p r e s s u r e t r a n s d u c e r was l o c a t e d below the vane h o u s i n g i n a t h e r m a l l y r e g u l a t e d box. A s c h e m a t i c d i a g r a m o f the r e c o r d i n g system i s shown i n F i g . 10. The e l e c t r i c a l a n a l o g o f the p r e s s u r e g e n e r a t e d between the yaw s p h e r e p o r t s (AP) i s o b t a i n e d from the B a r o c e l and i t s s i g n a l c o n d i t i o n e r . I t i s then p a s s e d t h r o u g h an a c t i v e h i - p a s s f i l t e r ( a p p r o x i m a t e l y 43 POLYETHYLENE TUBES (1.59 mm O.D.) YAW SPHERE (5 CM DIA.) BAROCEL AND ELECTRONICS ACTIVE HI-PASS FILTER (GAIN«»1, T = 8 MIN) 40.2 K F I / V 4 0 2 K Ql * - — -L - V BRIDGE FAST RESPONSE RESISTANCE THERMOMETER •w 1800 a LO-PASS FILTER DIFF \ AMP T=5 SEC INTEGRATOR / VARIABLE GAIN F i g . 10 S c h e m a t i c d i a g r a m o f the r e c o r d i n g s y s t e m . 44 u n i t y g a i n , and a time c o n s t a n t o f 8 min) t o p r o v i d e the s i g n a l o f (AP - A P ) . T h i s s i g n a l i s used to d r i v e the r e s i s t a n c e - t h e r m o m e t e r b r i d g e so t h a t the o u t p u t becomes p r o p o r t i o n a l t o AT(AP - AP), where AT i s the b r i d g e im-b a l a n c e . By p e r i o d i c a l l y b a l a n c i n g the b r i d g e , i t i s p o s s i b l e to p r e v e n t undue s a t u r a t i o n o f the o u t p u t f l u c t u -a t i o n s i n the n e x t s t a g e s o f the c i r c u i t . A d i f f e r e n t i a l a m p l i f i e r i s used to i n c r e a s e the o u t p u t s i g n a l from t h e b r i d g e . T h i s i s f o l l o w e d by a 5 sec l o - p a s s f i l t e r t o d e c r e a s e t r a n s i e n t r e s p o n s e and dynamic range r e q u i r e m e n t s b e f o r e i n t e g r a t i o n on a r e c o r d e r w i t h a b a l l and d i s c i n t e g r a t o r ( H o n e y w e l l , E l e c t r o n i k 194 and D i s c I n t e g r a t o r ) . A nearby s e n s i t i v e anemometer (C.W. T h o r n t h w a i t e A s s o c i a t e s ) wind system i s used to o b t a i n the mean h o r i z o n t a l wind speed a t the h e i g h t o f the s p h e r e . A p h o t o g r a p h o f t h e c o m p l e t e yaw s p h e r e - t h e r m o m e t e r assembly i s shown i n F i g . 11. Review of the Yaw Sphere-Thermometer T h e o r y In r e a l f l u i d f l o w , the p r e s s u r e d i s t r i b u t i o n a t p o i n t s on a s p h e r e can be w r i t t e n ( a f t e r M a r t i n o t - L a g a r d e et at., 1952) F i g . 11. The yaw s p h e r e - t h e r m o m e t e r a s s e m b l y . 45 46 P = P s + ( p / 2 ) V 2 [ l - b s i n 2 ^ ] ; if; < 60° (3.1) where P s i s the s t a t i c p r e s s u r e , p t h e a i r d e n s i t y , V the a i r speed and i|i i s the a n g l e between \V and the r a d i u s v e c t o r o f the p o i n t . The 'sphere c o n s t a n t ' (b) i s to be d e t e r m i n e d e x p e r i m e n t a l l y . I t i s a f u n c t i o n o f the R e y n o l d s number Re = Vd/v ( d , the d i a m e t e r o f t h e s p h e r e and v , the k i n e m a t i c v i s c o s i t y o f the f l u i d ) but i s r e l a -t i v e l y c o n s t a n t f o r 2000 < Re < 200,000. In i d e a l , i r r o t a -t i o n a l f l u i d f l o w , t h e t h e o r e t i c a l v a l u e o f b i s 2.25. On d i r e c t i n g the s p h e r e a z i m u t h l y i n t o t h e wind, the components o f the wind v e c t o r w i t h r e s p e c t to the x, z p l a n e (formed by the yaw s p h e r e p o r t s and i t s b i s e c t o r ) a r e u = |\V | cos a , v = 0 and w = |\V | s i n a where a i s the a n g l e between the wind v e c t o r and the b i -s e c t o r o f the p o r t s . The p r e s s u r e d i f f e r e n c e between the p o r t s o f the yaw s p h e r e i s then g i v e n by A P = p b ( s i n 9) u w (3.2) 47 where 6 i s the i n c l u d e d a n g l e between the p o r t s . A s c h e m a t i c d i a g r a m t o i l l u s t r a t e the a n g l e s , a and 9, and the wind v e c t o r W, i s g i v e n i n F i g . 12. The p r e s s u r e d i f f e r e n c e (AP) i s c o n v e r t e d to an a n a l o g s i g n a l and p a s s e d t h r o u g h a h i g h - p a s s f i l t e r which i s s u b s e q u e n t l y used to d r i v e a r e s i s t a n c e - t h e r m o m e t e r b r i d g e . A m p l i f i c a t i o n and i n t e g r a t i o n o f t h i s b r i d g e o u t -p u t , e x p r e s s e d i n R e y n o l d s ' n o t a t i o n , g i v e s E 0 = p b ( s i n e ) GBM (u w'T' + w u'T' + u'w'T') (3.3) where, G i s the a m p l i f i e r g a i n , B i s the b r i d g e c o n s t a n t and M, the p r e s s u r e t r a n s d u c e r c o n s t a n t . The n a t u r e o f t h i s o u t p u t s i g n a l needs c a r e f u l c o n s i d e r a t i o n . In e q u a t i o n (3.1) the moment u'T' c h a r a c -t e r i z e s the t u r b u l e n t h e a t f l o w i n t h e d i r e c t i o n o f the mean wind v e l o c i t y . One would e x p e c t t h i s q u a n t i t y t o be n e g a t i v e f o r u n s t a b l e , and p o s i t i v e f o r s t a b l e s t r a t i f i c a -t i o n (Monin and Yaglom, 1971). D i r e c t measurements show t h a t on the a v e r a g e , the r a t i o u'T'/w'T' grows w i t h i n -c r e a s i n g s t a b i l i t y ( e . g . Z u b k o v s k i i and T s v a n g , 1966; Wesely et al.3 1970; S h e p p a r d , see Monin and Yaglom, 1971) and i n d i c a t e s t h a t |u'T'| i s l a r g e r than w'T' o v e r a range 48 F i g . 12. S c h e m a t i c r e p r e s e n t a t i o n o f the a n g l e s a, 8 and the wind v e c t o r W on the yaw s p h e r e . 49 o f s t a b i l i t y . However, s i n c e w i s t y p i c a l l y v e r y s m a l l compared to u~, the term w u'T' w i l l be s m a l l compared to u w'T', and w i l l be assumed n e g l i g i b l e . I f we can assume the t r i p l e moment u'w'T' to be s m a l l when compared to the term IT w'T', t h e n , as shown by Tanner and T h u r t e l l ( 1 9 7 0 ) , the e x p r e s s i o n f o r E"0 r e d u c e s t o E f l * p b ( s i n e) GBM u w'T (3.4) and s i n c e t h e s e n s i b l e heat f l u x can be w r i t t e n as H = pC vTV t h e n (3.5) Thus the s e n s i b l e h e a t f l u x can be d e t e r m i n e d from the •yaw s p h e r e - t h e r m o m e t e r system o u t p u t i f u i s measured nearby a t the same h e i g h t . Kondo et al. (1970) s u g g e s t t h a t measurements w i t h cup anemometers o v e r e s t i m a t e the mean wind speed by about 4-7 per c e n t f o r the wind o v e r l a n d by day, and by about 1-3 per c e n t a t n i g h t , but more r e c e n t work by Hyson (1972) shows the o v e r e s t i m a t i o n t o be o f the o r d e r o f 1 per c e n t . S l i g h t u n d e r e s t i m a t i o n o f 50 H may t h e r e f o r e be e x p e c t e d i f u i s measured w i t h a cup anemometer. A sample c a l c u l a t i o n o f the s e n s i b l e h e a t f l u x , w i t h the a p p r o p r i a t e c o n s t a n t s i n v o l v e d , i s g i v e n i n Appe n d i x A. D e t e r m i n a t i o n o f the Sphere C o n s t a n t The s p h e r e c o n s t a n t was d e r i v e d from d a t a c o l l e c t e d i n a s e r i e s o f wind t u n n e l e x p e r i m e n t s w i t h the yaw s p h e r e . The s p h e r e p o r t s were a l i g n e d a z i m u t h l y i n t o the d i r e c t i o n o f t h e mean f l o w thus a l l o w i n g a ( t h e a n g l e o f a t t a c k o f the f l o w to the yaw s p h e r e a x i s ) , to be measured d i r e c t l y . E q u a t i o n (3.2) can be r e w r i t t e n b = 2 AP/(p|\V| 2 s i n 2a s i n e ) (3.6) For o u r s p h e r e 6, the i n c l u d e d a n g l e between the p o r t s , was 4 5 ° . An e l e c t r i c a l a n a l o g o f the p r e s s u r e d i f f e r e n c e between the yaw s p h e r e p o r t s (AP) was m o n i t o r e d on a c h a r t r e c o r d e r . The p a r a m e t e r s p and W were known f o r each wind t u n n e l e x p e r i m e n t . T hus, knowing a l l the terms on the r i g h t hand s i d e o f e q u a t i o n (3.6) the s p h e r e c o n s t a n t c o u l d be e v a l u a t e d . F i r s t l y , f o r a c o n s t a n t a n g l e o f a t t a c k 51 o f t h e f l o w (a) , a s e r i e s o f measurements were made a t v a r i o u s wind speeds (V) w i t h 6000 < Re < 20,000. Then the a x i s o f the yaw s p h e r e probe was t i l t e d t h r o u g h a s e r i e s o f a n g l e s , | a | < 1 0 ° . I n h e r e n t l i m i t a t i o n s o f the wind t u n n e l d i d not a l l o w l a r g e r a n g l e s o f a t t a c k , nor t o c a l i -b r a t e the s p h e r e f o r Re < 6000. The s p h e r e c o n s t a n t was o b t a i n e d from measurements i n both l a m i n a r f l o w and i n g r i d t u r b u l e n c e ( p r o d u c e d by i n t r o d u c i n g a g r i d i n t o a u n i f o r m f l o w ) . T h i s g r i d a l l o w e d g e n e r a t i o n o f a 9 per c e n t t u r -b u l e n c e l e v e l a t the yaw s p h e r e p o r t s . In the wind t u n n e l , the a n g l e o f a t t a c k (a) was measured as t h a t between the h o r i z o n t a l and the a p p a r e n t a x i s o f the yaw s p h e r e probe ( i . e . the s p h e r e and i t s s u p p o r t i n g s t e m ) . Any i n h e r e n t m i s a l i g n m e n t i n the yaw s p h e r e a x i s and s u p p o r t i n g stem would m a n i f e s t i t s e l f as a c o n s t a n t e r r o r i n the measurement o f a i n the wind t u n n e l . L e t t h i s t i l t e r r o r be 6. With the a s s u m p t i o n t h a t 26 i s s m a l l sin ( 2 a + 26) « s i n 2a + 26 cos 2a and e q u a t i o n (3.6) becomes 52 2 b = 2 AP/- p |\V | ( s i n 2 a + 2 6 cos 2 a ) s i n 9 (3.7) The above e x p r e s s i o n w i l l be w r i t t e n t a n 2a + 26 = 1/b 2 A P/(p |\V | cos 2a s i n e (3.8) so t h a t a p l o t o f t a n 2a v e r s u s 2AP/p |\V | 2 c o s a s i ne y i e l d s a s l o p e o f 1/b, i n t e r c e p t v a l u e s o f -26 on the a b s c i s s a and 2bS on t h e o r d i n a t e . F i g . 13 r e p r e s e n t s such a g r a p h f o r V = 4 m s " 1 and 6 m s " 1 i n l a m i n a r f l o w . The s p h e r e c o n s t a n t o b t a i n e d was 1.57 w i t h a t i l t e r r o r o f ~ 1 ° . T h i s v a l u e f o r b i s s i g n i f i c a n t l y l e s s than the t h e o r e t i c a l v a l u e o f 2.25. Data from the 9 per c e n t t u r b u l e n c e l e v e l e x p e r i m e n t s y i e l d e d a b e s t i m a t e w i t h i n 6 per c e n t o f t h e 1.57 v a l u e . L i t t l e emphasis i s p l a c e d on t h i s v a r i a t i o n s i n c e t h e AP t r a c e on the c h a r t r e c o r d e r c o u l d not be r e s o l v e d to b e t t e r than ±10 per c e n t f o r the g r i d t u r b u l e n c e e x p e r i m e n t . F i g . 13 a l s o r e v e a l s the c o n s t a n c y o f the b v a l u e f o r v a r y i n g R e y n o l d s number. In a n o t h e r s e r i e s o f e x p e r i m e n t s i n the wind t u n n e l , the f a s t - r e s p o n s e r e s i s t a n c e thermometer (used w i t h the yaw s p h e r e to measure the s e n s i b l e h e a t f l u x ) was mounted a t the s i d e o f the s p h e r e i n i t s u s u a l p o s i t i o n f o r f i e l d 53 T A N 2 a (RADIANS) F i g . 13. G r a p h i c a l d e t e r m i n a t i o n o f the s p h e r e c o n s t a n t (b) and a l i g n m e n t e r r o r ( 6 ) . The e q u a t i o n o f t h e l i n e i s : t a n 2a = -26 + 1/b(2AP/p |\V | 2 cos 2a s i n e ) The s l o p e = 1/b = 0.638, t h e r e f o r e b = 1.57; the i n t e r c e p t = -26 = -0.023, t h e r e f o r e 5= 0 . 0 1 7 5 r a d = l 0 A l s o s i n c e 2b6 - 0.055 a g a i n b = 1.57. 54 measurements. T h i s c o n f i g u r a t i o n had no n o t i c e a b l e e f f e c t on the p r e s s u r e g e n e r a t e d a t the p o r t s , o r on the s p h e r e c o n s t a n t . A c c o r d i n g l y , a v a l u e o f b = 1.57 was c h o s e n . I t i s i n t e r e s t i n g t o note t h a t a v a l u e o f b = 1.79 has r e c e n t l y been e s t a b l i s h e d f o r the o r i g i n a l yaw s p h e r e used by Tanner and T h u r t e l l ( T a n n e r , 1971, p r i v a t e c o m m u n i c a t i o n ) . V a l u e s o f b l e s s than 2.25 have a l s o been r e p o r t e d by M a r t i n o t - L a g a r d e et al. (1952) and Wesely et al. (1972) f o r o t h e r s p h e r e s w i t h d i f f e r e n t p o r t - h o l e c o n f i g u r a t i o n s . The r e a s o n f o r t h e s e lower v a l u e s may be due t o s l i p p a g e o f the f l o w around the smooth s u r f a c e o f th e s p h e r e . T h u r t e l l ( p r i v a t e c o m m u n i c a t i o n , 1972) i n d i c a t e s t h a t r o u g h e n i n g t h e s p h e r e s u r f a c e g i v e s a b v a l u e c l o s e r t o t h a t p r e d i c t e d by t h e o r y . W h i l e i t was not p o s s i b l e t o i n v e s t i g a t e the n a t u r e o f b below Re = 6000 , we s h a l l assume ( a f t e r M a r t i n o t - L a g a r d e et al., 1952) t h a t i t behaves a p p r o x i m a t e l y c o n s t a n t down to Re = 2000. F o r our 5-cm yaw s p h e r e t h i s i m p l i e s t h a t the e x p e r i m e n t a l l y d e t e r m i n e d s p h e r e c o n s t a n t s h o u l d be used o n l y when the mean wind speed i s > 60 cm s " 1 . In view o f t h i s , g r e a t c a u t i o n must be used i n i n t e r p r e t i n g r e s u l t s from t h e yaw s p h e r e under v e r y l i g h t wind c o n d i t i o n s , f o r i n s t a n c e a t n i g h t . 55 E f f e c t o f Yaw Sphere A x i s T i l t In s e c t i o n " D e t e r m i n a t i o n o f the Sphere C o n s t a n t , " i t was shown t h a t any i n h e r e n t m i s a l i g n m e n t i n the yaw s p h e r e a x i s c o u l d be d e t e r m i n e d from g e n e r a l c o n s i d e r a t i o n s of the a n g l e o f a t t a c k o f the f l o w i n c i d e n t on the s p h e r e i n a wind t u n n e l . Knowledge of t h i s c o u l d then be a p p l i e d i n a c c u r a t e l y a l i g n i n g the a x i s o f the s p h e r e h o r i z o n t a l l y i n f i e l d measurements. In p r a c t i c e , h o r i z o n t a l l e v e l l i n g o f the yaw s p h e r e a x i s may not always be a s s u r e d . Conse-q u e n t l y some e s t i m a t e o f l i k e l y e r r o r i n s e n s i b l e h e a t f l u x measurements due to a t i l t o f f - a x i s (due t o c o n s t r u c -t i o n m i s a l i g n m e n t or i n a c c u r a t e l e v e l l i n g i n the f i e l d ) i s g i v e n h e r e . L e t us assume t h a t the s p h e r e i s t i l t e d o f f - a x i s so t h a t t h e t i l t a n g l e (6) i s p o s i t i v e ( i . e . upwards, see F i g . 1 4 ) . The components o f the wind v e c t o r w i t h r e s p e c t to the x T , z T p l a n e (formed by the p o r t s and the t i l t - a x i s ) a r e u T = (u cos 6 - w s i n 6), v T = 0 and w T = (u s i n 6 + w cos 6) 56 F i g . 14. The e f f e c t o f t i l t on the geometry o f the s p h e r e . 57 I f we assume 6 to be s m a l l , then u T (u - 6w) and w T - (u6 + w). S u b s t i t u t i n g t h e s e a p p r o x i m a t i o n s o f u T and w T f o r the u and w components i n e q u a t i o n (3.1) y i e l d s E ° ( T I L T ) ~ P b ( s i n 6 ) G B M J ( u w'T' + w u'T' + u'w'T') + 6(2u ITT7" - 2w w^ T1" + u' *T' - w' Z T ' ) j (3.9) S i n c e w i s t y p i c a l l y v e r y s m a l l when compared t o u , the above e x p r e s s i o n r e d u c e s to E ° ( T I L T ) 85 P b ( s i n 9 ) G B M ( u w'T' + 26 u u'T') (3.10) i f we assume the t r i p l e moment terms t o be n e g l i g i b l e . Then ( T I L T ) = E o + E" 6 0 ' where E 6 0 = p b ( s i n e ) G B M 26 u u T T r 58 i s t h e e r r o r c a u s e d by the t i l t . T h i s e f f e c t i v e l y p r o d u c e s an e r r o r i n the he a t f l u x 6H = C p|T>(sine)GBMJ ' E ^ / U = p C p 2 6 u'T' (3.11) For a s m a l l p o s i t i v e t i l t o f f - a x i s the YST system w i l l t h e r e f o r e p r o d u c e a he a t f l u x measurement H ( T I L T ) ^ H + 6 H = p C p | w , T ' + 2 6 u'TJ (3.12) Thus, f o r 6 = 1° , H 1 C = S C p j ^ T ^ + 0.035 u~T^j . From p r e v i o u s s t u d i e s c o n c e r n i n g the dependence o f u' T '/WT 1 on R i c h a r d s o n number, we note t h a t the r a t i o i n c r e a s e s from -1.4 i n u n s t a b l e t o -3.2 i n s l i g h t l y s t a b l e c o n d i t i o n s . U s i n g t h e s e r e s u l t s , we can make some e s t i m a t e o f the e r r o r 6H under d i f f e r e n t s t a b i l i t y c o n -d i t i o n s . D u r i n g the d a y t i m e w i t h m o d e r a t e l y n e g a t i v e Ri , - u'T' - 1.4 wT 1" so t h a t H ] 0 would then e f f e c t i v e l y i n c l u d e an e r r o r o f ~ 5 per c e n t . On the o t h e r hand, under n i g h t - t i m e c o n d i t i o n s w i t h weak s t a b i l i t y , 59 u'T' = -3.2 w'T' i n the l i m i t . In t h i s c a s e would i n c l u d e an e r r o r o f ~ 11 per c e n t . I t can thus be s e e n , as an a p p r o x i m a t i o n , t h a t the e r r o r c a u s e d by a 1° t i l t o f f - a x i s i n the yaw s p h e r e would r e s u l t i n an e r r o r o f ~ 5 per c e n t i n the d a y t i m e , and t h a t the e r r o r would grow w i t h i n c r e a s i n g s t a b i l i t y to a p p r o a c h a v a l u e o f ~ 11 per c e n t a t n i g h t . A l t h o u g h l a r g e t i l t e r r o r s ( o f the o r d e r o f 5°) s h o u l d not o c c u r i n p r a c t i c e , we s h a l l c o n s i d e r such an e f f e c t on o u r system to h e l p d e l i n e a t e the e r r o r magnitude a t s m a l l a n g l e s o f t i l t . F o r a 5° o f f - a x i s t i l t o f the s p h e r e , the e r r o r i n m e a s u r i n g the s e n s i b l e heat f l u x would be ~ 25 per c e n t i n m o d e r a t e l y u n s t a b l e s t r a t i f i c a t i o n . The above a n a l y s i s a g a i n s u g g e s t s t h a t the YST system needs c a r e f u l c o n s i d e r a -t i o n i f used a t n i g h t , when l i g h t winds and s t a b l e s t r a t i -f i c a t i o n g e n e r a l l y p r e v a i l . L a r g e t i l t s i n the yaw s p h e r e a x i s would l e a d to c o n s i d e r a b l e e r r o r s i n the measurements of the s e n s i b l e h e a t f l u x . With c o n v e n t i o n a l l e v e l i n g d e v i c e s , i t s h o u l d be p o s s i b l e to m i n i m i z e t h i s o f f - a x i s t i l t so t h a t t h i s s o u r c e o f e r r o r i n the s e n s i b l e heat f l u x measurements i s w i t h i n the range o f g e n e r a l h e a t f l u x s p a t i a l v a r i a b i l i t y . F i e l d measurements o f the t i l t e f f e c t on heat f l u x measurements w i t h the F l u x a t r o n (an eddy c o r r e l a t i o n 60 i n s t r u m e n t ) a r e r e p o r t e d i n the r e c e n t paper o f Dyer and H i c k s ( 1 9 7 2 ) . An e r r o r o f a p p r o x i m a t e l y 4 per c e n t per d e g r e e was f o u n d . I t would seem from our a n a l y s i s t h a t the YST system i s s l i g h t l y more s e n s i t i v e to l e v e l l i n g e r r o r s than the F l u x a t r o n . Thermometer System and F r e q u e n c y Response The f a s t - r e s p o n s e thermometer was i n i t i a l l y b u i l t f o l l o w i n g the d e s i g n o f Wesely et al. ( 1 9 7 0 ) . The t h e r -mometer elem e n t c o n s i s t e d o f about 65 cm o f p l a t i n u m - c o a t e d t u n g s t e n w i r e w i t h a d i a m e t e r o f 5.6y. T h i s w i r e was welded to i t s s t a i n l e s s s t e e l s i d e s u p p o r t w i t h the a i d o f a D i s a h o t - w i r e anemometer w e l d i n g a s s e m b l y . A p h o t o -g r a p h o f the r e s i s t a n c e thermometer i s shown i n F i g . 15. The t e m p e r a t u r e c o e f f i c i e n t o f r e s i s t a n c e o f the tempera-t u r e e l e m e n t was o b t a i n e d from measurements o f the t h e r -mometer r e s i s t a n c e i n a t e m p e r a t u r e - c o n t r o l l e d o i l bath o v e r the range 15°C to 30°C. I t was f o u n d to be 0.0033 ± 0 . 0 0 0 0 5 ° C _ 1 . C a l c u l a t i o n s by Wesely et al. (1970) i n d i c a t e t h a t f o r the r e s i s t a n c e w i r e used i n the thermometer, the time c o n s t a n t i s a p p r o x i m a t e l y 1.5 m i l l i s e c i n " s t i l l a i r " and about 0.6 m i l l i s e c i n 10 m s - 1 w i n d s . Up to a F i g . 15. The r e s i s t a n c e thermometer. 62 f r e q u e n c y o f 20 Hz, r e d u c t i o n i n a m p l i t u d e s h o u l d be l e s s than 2 per c e n t and phase s h i f t about 1 0 ° . S o l a r h e a t i n g o f the f i n e r e s i s t a n c e w i r e was shown to be n e g l i g i b l e f o r eddy f l u x c a l c u l a t i o n s . Under f i e l d c o n d i t i o n s our thermometer r e s p o n d e d w e l l , but i t s d u r a b i l i t y was n o t always s a t i s f a c t o r y . As a r e s u l t , a s l i g h t l y m o d i f i e d d e s i g n was d e v e l o p e d . The thermometer el e m e n t and s u p p o r t t e r m i n a l s remained the same. The t r i a n g u l a r frame however was e l i m i n a t e d by w i n d i n g the e l e m e n t d i r e c t l y around the s i d e s u p p o r t s which were c o v e r e d w i t h an i n s u l a t i n g l a y e r o f epoxy r e s i n . The r i g i d i t y o f the thermometer was m a i n t a i n e d by i n s e r t i n g two t h i n c e r a m i c s p a c e r s ( F i g . 1 6 ) . F i e l d t e s t s o f the two thermometer d e s i g n s i n two YST systems p l a c e d 2 m a p a r t p r o d u c e d a l m o s t i d e n t i c a l r e s u l t s (see F i g . 17) under a v a r i e t y o f wind and c l o u d c o n d i t i o n s . The new d e s i g n has p r o v e d to be more d u r a b l e . F r e q u e n c y r e s p o n s e and phase s h i f t o f t h e yaw s p h e r e t u b i n g and B a r o c e l c l o s e l y f o l l o w e d t h a t r e p o r t e d by T anner and T h u r t e l l (1970, F i g . 1 8 ) . The i n c r e a s e i n l e n g t h o f t u b i n g i n our system r e s u l t e d i n s 1 i g h t l y .more a t t e n u a t i o n . In the f r e q u e n c y domain the t u r b u l e n t h e a t f l u x c o u l d be measured to an upper f r e q u e n c y l i m i t o f ~ 8 Hz w i t h o u t s i g n i f i c a n t a t t e n u a t i o n . F i g . 16. The m o d i f i e d r e s i s t a n c e thermometer. 63 I I I I L_ 1 I I 08 10 12 14 16 18 20 22 TIME (PST) 06 08 10 12 14 16 18 20 1 I I I I I 1 I F i g . 17. Comparison o f the two yaw s p h e r e - t h e r m o m e t e r systems f o r s e n s i b l e heat f l u x measurements (a) w i t h o r i g i n a l r e s i s t a n c e thermometers (b) w i t h m o d i f i e d r e s i s t a n c e thermometer d e s i g n i n Y S T i . 65 LEGEND x RELATIVE AMPLITUDE • PHASE SHIFT 0 8 16 24 FREQUENCY (Hz) F i g . 18. F r e q u e n c y r e s p o n s e o f the yaw s p h e r e t u b i n g and B a r o c e l . Data p o i n t s from t h i s s t u d y ; l i n e s from r e s u l t s o f Tanner and T h u r t e l l ( 1 9 7 0 ) . 66 F i e l d T e s t s R e s u l t s T h e r e i s no s t a n d a r d t o c a l i b r a t e an i n s t r u m e n t which measures s e n s i b l e h e a t f l u x d e n s i t y . To g a i n c o n f i -dence i n the YST system however, we compared the measure-ments a g a i n s t i n d e p e n d e n t e v a l u a t i o n s o f H from a Bowen r a t i o a p p a r a t u s . The s i t e used was the e x t e n s i v e g r a s s s u r f a c e a t L a d n e r , B.C. The g r a s s was d r y , and the ground s u r f a c e c o n s i s t e d o f a dense o l d - g r a s s l i t t e r l a y e r . The i n s t r u m e n t h e i g h t s and mast l o c a t i o n s e n s u r e d adequate f e t c h / h e i g h t r a t i o s from a l l wind d i r e c t i o n s e x c e p t from the NNE-SSE s e c t o r . Winds were p r e d o m i n a n t l y SW-NW d u r i n g t h e t e s t r u n s . The c o m p l e t e YST system was mounted a p p r o x i m a t e l y 1.5 m above ground l e v e l w i t h the Bowen r a t i o a p p a r a t u s mounted a t the same h e i g h t , and 4 m from the YST s y s t e m . Net r a d i a t i o n and s o i l h eat f l u x d e n s i t y were a l s o r e c o r d e d c o n t i n u o u s l y d u r i n g d a y l i g h t hours f o r a p e r i o d o f f o u r d a y s . The r e s u l t s o f the c o m p a r i s o n e x p e r i m e n t s a r e p r e s e n t e d i n F i g s . 19 ( a - c ) and 20. C l e a r l y , w i t h the p o s s i b l e e x c e p t i o n o f Aug u s t 24, 1971 ( F i g . 1 9 ( a ) ) , the agreement between the i n d e p e n d e n t s e n s i b l e h e a t f l u x measurements (H Y<j T and H^) i s v e r y p r o m i s i n g . T h e r e a r e two p o s s i b l e e x p l a n a t i o n s f o r the poor agreement on Aug u s t 24. F i g . 19 ( a - c ) . Comparison o f s e n s i b l e heat f l u x d e n s i t i e s from the yaw s p h e r e - t h e r m o m e t e r system ( H Y S T ) and the Bowen r a t i o system (Hp) o v e r g r a s s a t L a d n e r , B.C. f o r (a) August 24, (b) August 25 and. ( c ) August 26, 1971 . 68 TIME (PST) F i g . 20. Comparison o f H Y S T an<^ 3^ a* L a d n e r , B.C. o.n August 27, 1971. Net r a d i a t i o n (Rn) and s o i l h eat f l u x d e n s i t y (G) a r e i n c l u d e d . 69 F i r s t l y , wind d i r e c t i o n was v a r i a b l e on t h i s day, and i n a d d i t i o n f l o w from the E s e c t o r was not uncommon. S e c o n d l y , net r a d i a t i o n was v e r y v a r i a b l e i n the a f t e r n o o n c o n t r i b u t -i n g to a n o n - s t e a d y s t a t e atmosphere. T h i s makes i t d i f f i c u l t to i n t e g r a t e the r e c o r d e r t r a c e and c o u l d l e a d to e r r o r s i n Bowen r a t i o c o m p u t a t i o n s . In g e n e r a l , the en e r g y p a r t i -t i o n i n g r e s u l t e d i n H - 0.5 Rn a t noon on most d a y s . The s o i l heat f l u x d e n s i t y was s m a l l , p r o b a b l y as a r e s u l t o f the i n s u l a t i n g e f f e c t o f the g r a s s canopy and l i t t e r l a y e r . T a b l e 2 g i v e s the c u m u l a t i v e s e n s i b l e h e a t f l u x d e n s i t i e s f o r each day f o r each method, e x p r e s s e d as a r a t i o . S a m p l i n g p e r i o d s have been a d j u s t e d to conform t o t h o s e o f the YST s y s t e m . E x c e p t f o r A u g u s t 24 the d i f f e r -ence between the two methods i s l e s s than 10 per c e n t . We may c o n c l u d e t h a t , i n g e n e r a l , t h e r e i s good and c o n s i s t e n t d i u r n a l agreement between t h e YST and Bowen r a t i o a p p r o a c h e s to e v a l u a t i n g H. Dyer and H i c k s (1972) i n d i c a t e t h a t H may show a 10 per c e n t s p a t i a l v a r i a b i l i t y o v e r u n i f o r m t e r r a i n , and t h i s may a c c o u n t f o r a p a r t o f the d i f f e r e n c e s between the H t r a c e s i n F i g s . 1 9 ( a - c ) and 20. O t h e r p o s s i b l e e r r o r s i n the YST system i n c l u d e t i l t e r r o r , o v e r e s t i m a t e s o f u" by the cup anemometer, f r e -quency r e s p o n s e l i m i t a t i o n and s m a l l z e r o d r i f t s i n the e l e c t r o n i c s . S i m i l a r l y , the Bowen r a t i o method r e l i e s upon the a s s u m p t i o n o f e q u a l i t y between.the t r a n s f e r c o e f f i c i e n t s f o r h e a t and water v a p o u r . 71 T a b l e 2 C o m p a r i s o n o f d a y t i m e c u m u l a t i v e s e n s i b l e h e a t f l u x d e n s i t i e s f r o m t h e yaw s p h e r e -t h e r m o m e t e r ( H Y g j ) and Bowen r a t i o (H f t) s y s t e m s D a t e D u r a t i o n ( m i n ) H Y S T / H 8 24 A u g u s t 1 971 476 1 .23 25 A u g u s t 1 97 1 458 0.99 26 A u g u s t 1971 549 0.92 27 A u g u s t 1 97 1 582 0.98 I C h a p t e r 4 SENSIBLE HEAT FLUX MEASUREMENTS OVER A RURAL SURFACE I n t r o d u c t i on I t was shown i n the p r e v i o u s c h a p t e r t h a t t h e p r o m i s e o f the yaw s p h e r e - t h e r m o m e t e r system a p p e a r s t o have been s u b s t a n t i a t e d . As no s t a n d a r d e x i s t s a g a i n s t which our i n s t r u m e n t can be c a l i b r a t e d , i t was n e c e s s a r y t o make com-p a r a t i v e but i n d e p e n d e n t e v a l u a t i o n o f H. Good agreement was o b t a i n e d between t h e measurements o f s e n s i b l e heat f l u x by t h i s d i r e c t t e c h n i q u e and the Bowen r a t i o / e n e r g y b a l a n c e method. T h i s r e l a t i v e l y s i m p l e eddy c o r r e l a t i o n d e v i c e e n a b l e d measurement o f s e n s i b l e h e a t f l u x e s c l o s e t o t h e s u r f a c e , and a t t h e same t i m e , to make r e a l time a n a l y s i s a l m o s t i m m e d i a t e l y i n t h e f i e l d . The l a t t e r a d v a n t a g e needs l i t t l e emphasis f o r most o t h e r d i r e c t m e a s u r i n g t e c h -n i q u e s r e q u i r e an e x t e n s i v e l a b o u r o f d a t a p r o c e s s i n g and c o m p u t a t i o n . T h i s problem has tend e d to l i m i t the body o f d i r e c t heat f l u x measurements which c o v e r s u b s t a n t i a l time p e r i o d s . The YST system overcomes t h i s p roblem and hence p e r m i t s t h e a c q u i s i t i o n o f s i g n i f i c a n t l e n g t h s o f heat f l u x d a t a . 72 73 T h i s c h a p t e r d e a l s m a i n l y w i t h measurements made a t t h e Ladne r s i t e d u r i n g the months o f June and e a r l y J u l y 1972, and i s c o n f i n e d p r i m a r i l y to a c o n s i d e r a t i o n o f t h e f o l l o w i n g t h r e e a s p e c t s . F i r s t l y , the d i u r n a l b e h a v i o u r o f t h e s e n s i b l e h e a t f l u x and o t h e r e n e r g y budget p a r a m e t e r s i s d i s c u s s e d . S e c o n d l y , a l i m i t e d i n v e s t i g a t i o n o f t h e s p a t i a l v a r i a b i l i t y o f H and the problems a s s o c i a t e d w i t h s a m p l i n g i n t h e time domain i s p r e s e n t e d . The s u c c e s s a c h i e v e d w i t h the i n i t i a l YST system l e d to t h e c o n s t r u c t i o n o f a secon d system w i t h i d e n t i c a l d e s i g n f e a t u r e s . The a v a i l a b i l i t y o f two such i n s t r u m e n t s a l l o w e d e x a m i n a t i o n o f t h e s p a t i a l v a r i a b i l i t y o f t h e s e n s i b l e h e a t f l u x i n the a t m o s p h e r i c boundary l a y e r . The fu n d a m e n t a l p r e m i s e i n much m i c r o m e t e o r o l o g i c a l r e s e a r c h , t h a t the f l u x e s o f h e a t , water vapour and momentum a r e r e l a t i v e l y c o n s t a n t i n t h e h o r i z o n t a l and v e r t i c a l w i t h i n the a t m o s p h e r i c boundary l a y e r , r e q u i r e s f u r t h e r t e s t i n g . A l i m i t e d i n v e s -t i g a t i o n o f t h e v a l i d i t y o f assuming a ' c o n s t a n t f l u x l a y e r ' near the s u r f a c e i s p r e s e n t e d h e r e . T h i r d l y , e x t e n s i v e measurements o f H and o t h e r e n e r g y b a l a n c e components, p r o -v i d e d the n e c e s s a r y d a t a to a t t e m p t an a s s e s s m e n t o f t h e ener g y p a r t i t i o n i n g between the s e n s i b l e and l a t e n t heat f l u x e s . The v a l u e o f u s i n g l a r g e - s c a l e p a r a m e t e r i z a t i o n o f heat f l u x e s (as advanced by P r i e s t l e y and T a y l o r , 1972) was i n v e s t i g a t e d . 74 E x p e r i m e n t a l S i t e and P r o c e d u r e s D u r i n g t h i s p e r i o d o f o b s e r v a t i o n , the g r a s s s u r f a c e was a p p r o x i m a t e l y 90 cm t a l l , as i n the p r e v i o u s summer, and had a r o u g h n e s s l e n g t h o f a p p r o x i m a t e l y 10 cm. No a t t e m p t was made to measure s o i l w e t n e s s . E x t e n s i v e r a i n t h r o u g h o u t the p r e v i o u s w i n t e r and s p r i n g and as w e l l , between days on which our measurements were made, e n s u r e d t h a t the s u r f a c e had ample m o i s t u r e s u p p l y . The water t a b l e was o n l y about 30 cm below the s u r f a c e o f the s i t e . Two YST systems ( d e s i g n a t e d YST X and Y S T 2 ) were mounted 2 m above ground l e v e l w i t h t h e i r s e n s i t i v e cup anemometers a t the same h e i g h t about 1 m away. Net r a d i a t i o n a t 1 m and s o i l h eat f l u x d e n s i t y a t a dep t h o f 2.5 cm were c o n t i n u o u s l y m o n i t o r e d n e a r b y . The f r e q u e n t s p e l l s o f r a i n t h r o u g h o u t t h i s o b s e r -v a t i o n p e r i o d r e s u l t e d i n a d i s c o n t i n u o u s s e t o f d a t a i n -v o l v i n g t w e l v e days o f r e c o r d . C o n t i n u o u s r e c o r d l e n g t h s v a r i e d from t h r e e hours to 14 hours on a g i v e n day. E x p e r i -ments were t e r m i n a t e d a t t h e o n s e t o f r a i n o r d e w f a l l s i n c e the YST i n s t r u m e n t s a r e u n a b l e to o p e r a t e under such c o n d i -t i o n s w i t h o u t r i s k o f damage. The b a s i c a v e r a g i n g p e r i o d used was 30 min, based on c o n s i d e r a t i o n o f s t e a d y - s t a t e con-d i t i o n s . Problems a s s o c i a t e d w i t h t h i s c h o i c e o f s a m p l i n g i n t e r v a l w i l l be examined. 75 D i u r n a l B e h a v i o u r o f the S e n s i b l e Heat F l u x Some example r e s u l t s o f d i r e c t measurements of the s e n s i b l e h e a t f l u x , a l o n g w i t h o t h e r measured e n e r g y f l u x e s , f o r v a r i o u s w eather c o n d i t i o n s a r e shown i n F i g s . 21-25. Heat f l u x e s from b o t h YST systems a r e shown ( t h e s e w i l l be d i s c u s s e d i n the n e x t s e c t i o n ) . The i l l u s t r a t e d examples c o n s i s t o n l y o f o b s e r v a t i o n days on which f a i r l y l o n g r e c o r d s o f c o n t i n u o u s measurements were o b t a i n e d . The d i u r n a l changes i n H a r e c l e a r l y e v i d e n t . By day, the s e n s i b l e heat f l u x i s d i r e c t e d away from the a c t i v e s u r f a c e , whereas a t n i g h t a r e v e r s e f l o w i s g e n e r a l l y i n d i -c a t e d . I t i s p a r t i c u l a r l y s i g n i f i c a n t t o n o t e the c l o s e r e l a t i o n s h i p i n the d i u r n a l c o u r s e o f the heat f l u x w i t h t h a t o f the n e t r a d i a t i o n . T h i s i s w e l l e x e m p l i f i e d on days when t h e r e a r e f l u c t u a t i o n s i n the net r a d i a t i o n f i e l d ( i . e . on days when v a r i a b l e c l o u d i n e s s o c c u r r e d ) . A s i m i l a r phase agreement has been f o u n d by Hanafusa ( 1 9 7 1 ) . W h i l e no a t t e m p t was made to q u a n t i f y the phase d i f f e r e n c e t h r o u g h harmonic a n a l y s i s , i t i s a p p a r e n t t h a t t h e r e i s v i r t u a l l y no l a g between Rn and H when a v e r a g e s a r e t a k e n f o r h a l f - h o u r i n t e r v a l s . Maxima and minima i n the d i u r n a l c o u r s e o f Rn g e n e r a l l y r e s u l t e d i n a c o r r e s p o n d i n g b e h a v i o u r o f H. Under c l e a r s k i e s , the peak s e n s i b l e heat f l u x i s a t t a i n e d around noon. Thus, the s e n s i b l e heat f l u x i n the 76 LADNER, B.C. JUNE 15, 1972 -A H Y S T 2 HEIGHT : 2m HOR. SEPARATION: 1.5m 2.4 2.7 3.1 3.0 3.0 2.5 2.6 2.5 1.9 1.6 0.8 WIND U 2 (M/S) 2.4 ™ t f t t t t f I I I I t t t t t I ' J 08 10 12 14 16 18 20 22 TIME (PST) F i g . 21. D i u r n a l v a r i a t i o n o f H and c o m p a r i s o n o f the two YST s y s t e m s . LADNER, B.C. JUNE 21, 1972 ' H vsr 2 HEIGHT : 2m WIND U (M/S) 2.7 3.0 3.1 2.8 1.8 2.1 3.1 2.8 2.9 2.9 2.4 1.7 1.1 I J I I I I I I 06 08 10 12 14 16 18 20 TIME (PST) F i g . 22. D i u r n a l v a r i a t i o n o f H and c o m p a r i s o n o f the two YST s y s t e m s . - 1 0 L WIND U 2 < M / S ) 2.3 2.8 2.3 2.4 2.7 2.6 2.4 2.2 1.8 1.0 1.2 1.3 1.3 1.0 DIR X X / / / / / - • - > - * y y f 4 I I I 1 I I I I 06 08 10 12 14 16 18 20 TIME (PST) F i g . 23. D i u r n a l v a r i a t i o n o f H and c o m p a r i s o n o f the two YST s y s t e m s . U (M/S) 4.1 4.4 5.1 5.1 4.9 5.4 5.1 5.0 4.9 5.1 4.5 3.9 2.7 1.9 2 • I R — * —»- — ^ — ^ — V - > —*" — - > I I J I I I I I 06 08 10 12 14 16 18 20 TIME (PST) F i g . 24. D i u r n a l energy b a l a n c e and s p a t i a l v a r i a t i o n o f H. 70 r LADNER, B.C. JULY 2, 1972 ~* H Y S T * H HEIGHT : 2m HOR. SEPARATION 80 19m WIND U (M/S) 2.8 3.8 3.6 2 DIR N V \ 3.8 4.1 3.8 4.0 4.2 4.5 4.1 3.7 2.7 2.0 \ \ \ \ \ v \ \ \ \ ± _L ± J 06 08 10 12 14 16 18 20 TIME (PST) F i g . 25. D i u r n a l e n e r g y b a l a n c e and s p a t i a l v a r i a t i o n o f H. 81 p l a n e t a r y boundary l a y e r shows an immediate r e s p o n s e to the change o f n e t r a d i a n t energy s u p p l y a t the s u r f a c e . E x c e p t i o n s to t h i s d i s t i n c t phase r e l a t i o n s h i p were noted on two d a y s , one o f which i s shown i n F i g . 22. A f t e r 1300 PST on June 21, 1972, the net r a d i a t i o n p r o g r e s -s i v e l y d e c r e a s e d w h i l e the s e n s i b l e h e a t f l u x r e m ained c o n s i s t e n t l y h i g h f o r s e v e r a l h o u r s . The maximum v a l u e o f H o c c u r r e d a few hours a f t e r the r a d i a t i o n maximum. In a d d i t i o n , the s e n s i b l e h e a t f l u x e s do not a p p e a r to d e c l i n e as r a p i d l y w i t h the a p p r o a c h o f s u n s e t and the a n t i c i p a t e d ' t u r n o v e r ' to a downward f l u x i s c l e a r l y d e l a y e d . A s i m i l a r t r e n d was o b s e r v e d on June 30 (see F i g . 2 6 ) , a day on which sunny s k i e s p r e v a i l e d . T h i s o b s e r v e d f e a t u r e was not e v i d e n t i n t h e measurements t a k e n on the day p r e c e d i n g o r f o l l o w i n g June 30 when s i m i l a r weather c o n d i t i o n s p r e v a i l e d . The r e a s o n f o r t h e s e two e x c e p t i o n s i s not c l e a r . I t i s s u g g e s t e d t h a t t h i s b e h a v i o u r was c a u s e d by a d v e c t i v e i n f l u e n c e s from t h e runway as w e s t e r l y winds p r e v a i l e d on both o c c a s i o n s ( F i g s . 22 & 2 6 ) . While much c a r e was t a k e n i n our c h o i c e o f m e a s u r i n g h e i g h t f o r the YST systems to e n s u r e s u i t a b l e f e t c h from a l l wind d i r e c t i o n s , i t may have been p o s s i b l e t h a t t h e measurements a t the 2 m h e i g h t on t h e s e p a r t i c u l a r a f t e r n o o n s d i d n o t r e f l e c t t h e p r o c e s s e s o f t h e u n d e r l y i n g s u r f a c e . LADNER, B.C. JUNE 30, 1972 82 H H Y S T Y S T 2 HEIGHT : 2m HOR. SEPARATION 19 m - 1 0 L WIND U 2 (M/S) 4.8 4.7 4.6 3.8 DIR ± 4.1 4.3 4.6 4.8 X N> X *x I I ± J 06 08 10 12 14 16 18 20 TIME (PST) F i g . 26. An example o f l a r g e f l u c t u a t i o n s i n H w i t h 30 min a v e r a g i n g p e r i o d s . 83 D u r i n g a s u c c e s s i o n o f days ( J u l y 1-5), c l e a r s k i e s p e r s i s t e d . The heat u t i l i z e d to warm the a i r v i a s e n s i b l e h e a t f l u x showed a p r o g r e s s i v e d e c r e a s e from J u l y 1 to J u l y 5. One would have e x p e c t e d the o p p o s i t e t r e n d i f d r y i n g out o f t h e s o i l was o c c u r r i n g , but on the c o n t r a r y , the s u r f a c e seemed to have had ample s u p p l y o f w a t e r . An e x a m i n a t i o n o f t h i s b e h a v i o u r w i l l be d i s c u s s e d i n t h e s e c t i o n " P a r a m e t e r i z a t i o n o f the S e n s i b l e Heat F l u x and E v a p o r a t i o n . " I t s h o u l d be n o t e d t h a t the heat s t o r a g e i n the ground i s u n u s u a l l y low d u r i n g a l l t h e s e measurements. T h i s was p r o b a b l y c r e a t e d by the t a l l g r a s s c o v e r and i t s i n s u l a t -i n g e f f e c t . In g e n e r a l , t h e r e e x i s t e d a d i u r n a l c o u r s e o f G. I t d i d not however show c l o s e s i m i l a r i t y to t h e Rn p a t t e r n on days w i t h v a r i a b l e n e t r a d i a n t e n e r g y i n p u t . Under c l e a r s k i e s a t noon, maximum v a l u e s o f G were o n l y a bout 5 per c e n t o f Rn. Measurements o f S p a t i a l V a r i a t i o n o f the S e n s i b l e Heat F l u x G e n e r a l a s p e c t s . The b a s i c a s s u m p t i o n o f much m i c r o m e t e o r o l o g i c a l r e s e a r c h i s t h a t H i s r e l a t i v e l y c o n s t a n t i n the s u r f a c e boundary l a y e r o v e r a homogeneous s u r f a c e . The j u s t i f i c a t i o n o f t h i s a s s u m p t i o n can be seen from an a n a l y s i s o f the R e y n o l d s e q u a t i o n f o r t e m p e r a t u r e . The d e v e l o p m e n t i s g i v e n 84 i n M o r d u k h o v i c h and Tsvang (1966) and i s b r i e f l y summarized below. The R e y n o l d s e q u a t i o n f o r t e m p e r a t u r e may be w r i t t e n 3T 3_uT 3v_T 3wT = 3Rni 1 (A i\ 8 t 3x 3y 3 z 3z pC where the n o t a t i o n s a r e s i m i l a r to t h o s e p r e v i o u s l y d e f i n e d . On a p p l i c a t i o n o f t h e e q u a t i o n o f c o n t i n u i t y and the assump-t i o n t h a t v~ = w = 0, e q u a t i o n (4.1) can be e x p r e s s e d as f o l l o w s 3T - 3T Su^T 1" dV7!^ dvPTr _ dRn _]_ /. 9> 3t U 3x 3x 3y 3z 3z pC K*' d ) p F o r s t e a d y - s t a t e c o n d i t i o n s and i n the absence o f r a d i a t i v e f l u x d i v e r g e n c e , the terms ( 3 T / 3 t , 3R~n/3z) equal z e r o . Symmetry w i t h r e s p e c t t o the a v e r a g e t r a n s p o r t s u g g e s t s t h a t 3v'T'/3y s h o u l d a l s o be z e r o . A c o m p a r i s o n o f the r e m a i n i n g terms i n d i c a t e t h a t the p r i m a r y c a u s e o f a change i n H w i t h h e i g h t would be due to the a d v e c t i o n term s i n c e 3u'T'/3x << u 3T/3x . Thus, i n the a b s e n c e o f a d v e c t i o n , 85 one would e x p e c t H to be r e l a t i v e l y c o n s t a n t w i t h h e i g h t i n t h e a t m o s p h e r i c boundary l a y e r . In a s i m i l a r way, o n l y s l i g h t v a r i a t i o n i n H s h o u l d be e x p e c t e d i n the h o r i z o n t a l o v e r an e x t e n s i v e homogeneous s u r f a c e . E x p e r i m e n t a l e v i d e n c e to t e s t t h i s a s s u m p t i o n has been g a t h e r e d i n r e c e n t y e a r s t h r o u g h d i r e c t measurements o f H v i a the eddy c o r r e l a t i o n t e c h n i q u e . The r e c e n t work o f Dyer and H i c k s (1972) i n d i c a t e s a v a r i a t i o n i n H o f l e s s than 10 per c e n t f o r v e r t i c a l h e i g h t s o f 4-14 m, and h o r i z o n t a l s e p a r a t i o n o f 1-150 m, o v e r an e x t e n s i v e u n i f o r m p l a n t s u r f a c e . T h e i r r e s u l t s a r e g i v e n i n T a b l e 3. T h i s p r o v i d e s some v a l i d i t y f o r t h e t r a d i t i o n a l a s s u m p t i o n o f the c o n s t a n t f l u x l a y e r . On the o t h e r hand, the e a r l i e r works o f M o r d u k h o v i c h and Tsvang (1966) and B u s i n g e r et al. (1967) i n d i c a t e l a r g e s p a t i a l v a r i a b i l i t y i n t h e heat f l u x e s o f t h e o r d e r o f a f a c t o r o f 2. Measurements were made between the 1 and 4 m h e i g h t by M o r d u k h o v i c h and Tsvang w h i l e the r e s u l t s o f B u s i n g e r et al. were f o r a h o r i z o n t a l s e p a r a -t i o n o f 5 m. These r e s u l t s a r e most d i s t u r b i n g f o r t h e y s u g g e s t t h a t E u l e r i a n p o i n t o b s e r v a t i o n s may y i e l d ques-t i o n a b l e samples even o v e r a u n i f o r m s u r f a c e w i t h a d e q u a t e f e t c h . To e x p l a i n t h e i r d i s c r e p a n c y , B u s i n g e r et al. advanced t h e f o l l o w i n g p o s t u l a t i o n . The c o n v e c t i v e e l e m e n t s c o n t r i b u t i n g to the heat f l u x may c o n s i s t o f h o r i z o n t a l 86 T a b l e 3 C o m p a r i s o n o f a v e r a g e f l u x e s a. C o m p a r i s o n o f a v e r a g e f l u x e s (H i ^ ) a t 14 m h e i g h t w i t h a v e r a g e f l u x e s (hU) a t 4 m h e i g h t a t T s i m l y a n s k , U.S.S.R. ( c . f . D y e r and H i c k s , 1972) D a t e Du r a t i on (m i n) Hit/H 11* 16 J u l y 1970 17 J u l y 1970 300 390 0.92 1 .00 b. C o m p a r i s o n o f a v e r a g e f l u x e s ( H i and H2) t a k e n a t a n o m i n a l h e i g h t o f 4 m a t v a r i o u s c r o s s - w i n d s e p a r a t i o n s a t T s i m l y a n s k , U.S.S.R. ( c . f . D y e r and H i c k s , 1 9 7 2 ) . D a t e D u r a t i o n (mi n) S e p a r a t i o n (m) H2/H1 21 J u n e 1 970 570 1 1 .05 25 J u n e 1 970 313 1 0.98 1 2 J u l y 1 970 420 1 0 1.13 1 4 J u l y 1 970 360 1 0 0.94 3 J u l y 1 970 622 30 1 .03 5 J u l y 1 970 513 30 1.12 29 J u n e 1 970 207 60 1 .08 9 J u l y 1 970 268 60 1.14 18 J u l y 1 970 470 1 50 1 .07 87 r o l l s w i t h t h e i r l e n g t h a x i s i n the d i r e c t i o n o f t h e mean win d . These r o l l s r o t a t e s l o w l y i n o p p o s i t e d i r e c t i o n , t h e r e b y c r e a t i n g zones o f c o n v e r g e n c e and d i v e r g e n c e . Measurements i n two c o n t r a s t i n g z o n e s , even o v e r c o n s i d e r -a b l e time p e r i o d s , would thus y i e l d the no t e d v a r i a t i o n i n H. E v i d e n c e o f the o r g a n i z e d b e h a v i o u r o f t h e s e c o n -v e c t i v e e l e m e n t s has r e c e n t l y been r e p o r t e d by D a v i s o n and Miyake (1972) f o r h e i g h t s g r e a t e r than 50 m. I t i s a p p a r e n t t h a t much r e s e a r c h remains around t h i s f u n d a m e n t a l h y p o t h e s i s . The measurements r e p o r t e d h e r e , though l i m i t e d i n s c o p e , s h o u l d c o n t r i b u t e to t h e s m a l l body o f p e r t i n e n t d a t a t h a t p r e s e n t l y e x i s t s . S p a t i a l v a r i a b i l i t y e x p e r i m e n t s . In o r d e r to p r e s e r v e an adeq u a t e h e i g h t / f e t c h r a t i o a t the L a d n e r s i t e , no a t t e m p t was made to examine t h e v e r t i c a l v a r i a t i o n o f heat f l u x . O n l y measurements above the g r o u n d , a t h e i g h t s o f 2 m o r l e s s c o u l d e n s u r e s u i t a b l e f e t c h from a l l wind d i r e c t i o n s . W h i l e i t might have been p o s s i b l e to i n v e s t i g a t e v a r i a t i o n o f H between t h e 1 and 2 m h e i g h t s , the f r e q u e n c y r e s p o n s e o f t h e YST system d i d not f a v o u r such measurements. A c c o r d i n g l y , o n l y the h o r i z o n t a l v a r i a t i o n o f the s e n s i b l e heat f l u x a t a f i x e d h e i g h t o f 88 2 m above the ground was i n v e s t i g a t e d . Comparison o f the two YST systems were f i r s t made f o r a h o r i z o n t a l c r o s s w i n d s e p a r a t i o n o f 1.5 m. The two i n s t r u m e n t s were then p l a c e d 19 m a p a r t to i n v e s t i g a t e the s p a t i a l v a r i a t i o n . The 1.5 m s e p a r a t i o n p r o v i d e d a b a s i c c o m p a r i s o n between the two i n s t r u m e n t s . The s m a l l s e p a r a t i o n between i n s t r u m e n t s was to e n s u r e t h a t s a m p l i n g o c c u r r e d i n the same a i r s t r e a m . The c l o s e agreement between heat f l u x e s o b t a i n e d from the two i n s t r u m e n t s can be seen i n F i g s . 21-23. O n l y a few per c e n t v a r i a t i o n can be n o t e d . In g e n e r a l , s l i g h t l y h i g h e r v a l u e s were o b t a i n e d w i t h the Y S T 2 i n s t r u m e n t . T h i s d i f f e r e n c e a p p e a r s to be s y s t e m a t i c and may have been c a u s e d by s l i g h t d i f f e r e n c e s i n c a l i b r a t i o n c o n s t a n t s which were not t a k e n i n t o a c c o u n t . The d i f f e r e n c e i s however s m a l l enough to be c o n s i d e r e d i n s i g n i f i c a n t . C u m u l a t i v e s e n s i b l e heat f l u x e s f o r each i n s t r u m e n t , e x p r e s s e d as a r a t i o , f o r the 1.5 m h o r i z o n t a l c r o s s w i n d s e p a r a t i o n a r e g i v e n i n T a b l e 4. S a m p l i n g p e r i o d s have been a d j u s t e d to o n l y t h o s e f o r which c o m p a r i s o n i s p o s s i b l e . The d i f f e r e n c e i s g e n e r a l l y l e s s than 5 per c e n t i n the heat f l u x measurements f o r the two i n s t r u m e n t s . I n d i r e c t l y , t h i s r e s u l t a l s o s u g g e s t s s m a l l s p a t i a l v a r i a b i l i t y . F o r t h e 19 m c r o s s w i n d s e p a r a t i o n , r e l a t i v e l y good agreement was f o u n d i n the H measurements ( F i g s . 2 4 - 2 6). 89 T a b l e 4 C o m p a r i s o n o f c u m u l a t i v e s e n s i b l e h e a t f l u x d e n s i t i e s f r o m t h e yaw s p h e r e - t h e r m o m e t e r s y s t e m s ( h Y S T 1 A N D H Y S T 2 ^ a t 2 m a b o v e g r o u n d f o r an h o r i z o n t a l c r o s s w i n d s e p a r a t i o n o f 1.5 m D a t e D u r a t i o n ( m i n ) H Y S T i / H Y S T 2 1 5 J u n e 1 972 593 0.97 1 6 J u n e 1 972 170 1 .09 21 J u n e 1 972 712 1 .01 22 J u n e 1 972 274 0.99 24 J u n e 1 972 704 0.96 29 J u n e 1 972 1 1 4 0.99 90 A t t h i s l a r g e s e p a r a t i o n d i s t a n c e , the two YST systems c o u l d be p o s s i b l y s a m p l i n g i n d i f f e r e n t a i r s t r e a m s . The d e g r e e of f l u x v a r i a t i o n i s more pronounced than a t the 1.5 m s e p a r a -t i o n . T h i s i s a l s o e v i d e n t from the c u m u l a t i v e s e n s i b l e heat f l u x e s , e x p r e s s e d as a r a t i o , g i v e n i n T a b l e 5. The h o r i z o n t a l v a r i a b i l i t y i s l e s s than 20 per c e n t . a n d i s c o n s i s t e n t w i t h the h y p o t h e s i s o f the r e l a t i v e c o n s t a n c y o f the heat f l u x e s i n the s u r f a c e boundary l a y e r . These r e s u l t s t e n d to s u g g e s t t h a t r e p r e s e n t a t i v e heat f l u x e s may be a c h i e v e d by E u l e r i a n p o i n t s a m p l i n g to w i t h i n twenty per c e n t . On a few o c c a s i o n s , s h o r t - t e r m time v a r i a t i o n ( l e s s than 30 min) i n the heat f l u x measurements was n o t e d . T h i s was p a r t i c u l a r l y e v i d e n t on June 30 ( F i g . 2 6 ) . The cause o f t h e s e l a r g e f l u c t u a t i o n s i n H a r e c l e a r l y not r e l a t e d to t h e changes i n the net r a d i a t i o n f i e l d . R a t h e r , i t may be a s s o c i a t e d w i t h the c h o i c e o f an adequate s a m p l i n g i n t e r v a l . J h e use o f one-hour s a m p l i n g i n t e r v a l s would have e l m i n a t e d t h e s e s h o r t term f l u c t u a t i o n s . Smoothing o f the d a t a c a n n o t however be e a s i l y j u s t i f i e d s i n c e t h e s e f l u c t u a t i o n s may c o n t a i n p h y s i c a l s i g n i f i c a n c e . On t h i s p a r t i c u l a r day, t h e measured H f l u c t u a t i o n s o c c u r r e d a t the two s i t e s 19 m a p a r t . A f t e r n o o n , the c o u r s e o f H a t the two s i t e s i s out o f phase, a l t h o u g h the c u m u l a t i v e heat f l u x e s f o r t h a t p e r i o d remain a p p r o x i m a t e l y equal a t the two l o c a t i o n s . 91 T a b l e 5 C o m p a r i s o n o f c u m u l a t i v e s e n s i b l e h e a t f l u x d e n s i t i e s f r o m t h e yaw s p h e r e - t h e r m o m e t e r s y s t e m s (H and H ) I b l l i b i 2 a t 2 m a b o v e g r o u n d f o r an h o r i z o n t a l c r o s s w i n d s e p a r a t i o n o f 19 m D a t e D u r a t i o n (m i n ) H Y S T i / H Y S T 2 29 J u n e 1 972 60 0.98 30 J u n e 1 972 450 0.94 1 J u l y 1 972 728 0.94 2 J u l y 1 972 728 0.85 3 J u l y 1 972 331 0.83 92 Thus, i n a s t a t i s t i c a l s e n s e , t h e r e i s l i t t l e s p a t i a l v a r i -a b i l i t y f o r a l o n g - t e r m a v e r a g e . The e x i s t e n c e o f c o n v e c -t i v e r o l l s c o u l d a l s o e x p l a i n t h e s e s h o r t - t e r m f l u c t u a t i o n s . P a r a m e t e r i z a t i o n o f the S e n s i b l e Heat F l u x and E v a p o r a t i o n In i n v e s t i g a t i n g the p a r t i t i o n i n g o f energy between t h e s e n s i b l e heat f l u x and e v a p o r a t i o n , the g e n e r a l frame-work s u g g e s t e d by P r i e s t l e y and T a y l o r (1972) has been employed. The d a t a i s a n a l y z e d i n terms o f the q u a n t i t y a, d e f i n e d by a = LE/^^CH+LE)] = L E / j ^ R n - G ) ] (4.3) where y t h e p s y c h r o m e t r i c c o n s t a n t s d e f i n e d as 3 q s/3T a t the a p p r o p r i a t e t e m p e r a t u r e . The p a r a m e t e r a p r o v i d e s some measure o f the a r i d i t y o f the of the s u r f a c e . A p r i o r i , one would e x p e c t i t to be s m a l l e r f o r u n s a t u r a t e d s u r f a c e s than f o r s a t u r a t e d s u r f a c e s . The d i u r n a l b e h a v i o u r o f a a t the Ladner s i t e was examined u s i n g d a t a f o r l a t e A ugust 1971 and June 1972. The p e r i o d i n Aug u s t was p r e c e d e d by two months o f f a i r l y d r y w e a t h e r , w h i l s t i n June the a r e a had been under the 93 i n f l u e n c e o f wet weather c o n d i t i o n s f o r some t i m e . Examples f o r A u g u s t 26, 1971 and June 24, 1972 a r e shown i n F i g . 27. The v a l u e s o f LE i n e q u a t i o n 4.3 were o b t a i n e d as r e s i d u a l s from the energy b a l a n c e e q u a t i o n s i n c e the f l u x e s Rn, H and G were known. I t can be seen from the graph t h a t a was lower i n the l a t e summer o f 1971 than a t the s t a r t o f t h e summer o f 1972. E s t i m a t e s o f a f o r the days shown gave a mean v a l u e o f 0.73 on A u g u s t 26, 1971 and 1.09 on June 24, 1972 f o r the p e r i o d 1000-1600 PST. The s p r e a d o f t h e s e v a l u e s may be e x p e c t e d to r e f l e c t the n a t u r e o f the s o i l - p l a n t system water a v a i l a b i l i t y . Data from a number o f s a t u r a t e d l a n d and open water s i t e s were examined by P r i e s t l e y and T a y l o r ( 1 9 7 2 ) . From t h e s e d a t a , the b e s t e s t i m a t e o f a was f o u n d to be 1.26. I f we may use a = 1.26 f o r s a t u r a t e d s u r f a c e s (as o b t a i n e d by P r i e s t l e y and T a y l o r from mean d a i l y q u a n t i t i e s ) , a r i d i t y i n d e x e s may be computed f o r t h e s e two d a y s . The a r i d i t y i n d e x ( t h e r a t i o o f t h e a l p h a f o r n o n - s a t u r a t e d to t h a t f o r a s a t u r a t e d s u r f a c e ) would be 0.58 f o r A u g u s t 26 , 1971 and 0.87 f o r June 2.4, 1972. The u s e f u l n e s s o f the p a r a m e t e r a i n a c l i m a t o -l o g i c a l s ense a p p e a r s most e n c o u r a g i n g . I t may p r o v e a p p r o p r i a t e i n a c l a s s i f i c a t i o n scheme f o r v a r i o u s c l i m a t e s when d e t e r m i n e d on a monthly b a s i s . 94 2.0 Od= LE / { ( S / s + 7 ) ( R n - G ) } LADNER, B.C. • AUGUST 26, 1971 K JUNE 24, 1972 06 1.5 k 0.0 I I I I I I I 06 08 10 12 14 16 18 TIME (PST) F i g . 27. D i u r n a l v a r i a t i o n o f a (examples o f e a r l y and l a t e summer o b s e r v a t i o n s ) . 95 I t can be seen from e q u a t i o n 4.3 t h a t a i s r e l a t e d to t h e Bowen r a t i o t h r o u g h the f o l l o w i n g e q u a t i o n I t i s thus p o s s i b l e to examine the p a r t i t i o n i n g o f t h e s e n s i b l e and l a t e n t heat f l u x e s t h r o u g h the above e x p r e s s i o n . For a s a t u r a t e d s u r f a c e , a b e i n g a p p r o x i m a t e l y c o n s t a n t , one would e x p e c t 3 to show a dependence on s u r f a c e tempera-t u r e . The p r e d i c t e d p a r t i t i o n i n g o f e n e r g y between H and LE as a f u n c t i o n o f t e m p e r a t u r e i s shown i n F i g . 28 ( u s i n g a = 1.26 i n e q u a t i o n 4 . 4 ) . C u r v e s f o r a c o n s t a n t a o f 1.10 and 1.00 a r e a l s o shown. U s i n g the e n e r g y b a l a n c e measurements f o r L a d n e r , a p p r o x i m a t e Bowen r a t i o s were computed f o r a l l o b s e r v a t i o n days d u r i n g June and e a r l y J u l y 1972. These d a t a a r e p l o t t e d a g a i n s t mean d a i l y s c r e e n -l e v e l a i r t e m p e r a t u r e f o r the c o r r e s p o n d i n g days i n F i g . 28. ( I t s h o u l d be n o t e d t h a t our v a l u e s a r e o n l y a p p r o x i m a t e s i n c e the l e n g t h o f the h e a t f l u x r e c o r d s do not p r o v i d e 24 hour t o t a l s . A c c o r d i n g l y the t e m p e r a t u r e r e c o r d has been a d j u s t e d to c o n s i d e r o n l y the p e r i o d s o f f l u x measurements.) With the e x c e p t i o n o f two p o i n t s , the 3 d a t a c l e a r l y show a t e m p e r a t u r e dependence s i m i l a r to t h a t o f a 3 + 1 _H_ LE (4.4) 96 H / L E LADNER, B.C. 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 J U N E - J U L Y 1972 7 • 1 JUNE 15 3 D 2 JUNE 16 3 JUNE 21 4 JUNE 22 5 JUNE 24 \ 6 JUNE 29 N \ 7 JUNE 30 Nx 8 JULY 1 \ 9 JULY 2 N 10 JULY 3 4<n 1 1 J U L Y 5 N \ N !2 JULY 12 N \ X 5 h s X ^ a = 1.00 N X Nx ^ ot= 1.10 X 10 x ^ 11 a n 06 = 1.26 J_ 10 15 20 25 TEMPERATURE (°C) F i g . 28. R a t i o o f H/LE v s . t e m p e r a t u r e . 97 s a t u r a t e d s u r f a c e w i t h an a l p h a v a l u e between a p p r o x i m a t e l y 1.00 and 1.10. The two anomalous d a t a p o i n t s a r e f o r the days d i s c u s s e d i n the s e c t i o n on " D i u r n a l B e h a v i o u r o f the S e n s i b l e Heat F l u x , " when the d i u r n a l b e h a v i o u r o f H d i d not r e f l e c t t h e net r a d i a t i o n p a t t e r n . The e x c e p t i o n s on F i g . 28 a r e t h e r e f o r e p o s s i b l y a l s o due to a d v e c t i v e i n f l u -e n c e s . These r e s u l t s i n d i c a t e t h a t t h e p a r t i t i o n i n g o f H and LE d u r i n g the o b s e r v a t i o n p e r i o d a t t h e Ladn e r s i t e was s t r o n g l y r e l a t e d to t e m p e r a t u r e . I t i s to be e x p e c t e d t h a t t h i s r e l a t i o n s h i p would not c o n t i n u e t h r o u g h the summer when m o i s t u r e i s not as f r e e l y 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 on . C h a p t e r 5 SENSIBLE HEAT FLUXES OVER AN URBAN AREA I n t r o d u c t i o n The r e s u l t s o f d i r e c t measurements o f urban s e n -s i b l e h eat f l u x e s have not been p r e v i o u s l y r e p o r t e d . T h i s has l a r g e l y been due to the need f o r complex i n s t r u m e n t a t i o n to d e t e r m i n e t h i s eddy f l u x and, i n a d d i t i o n , the h i g h l y i r r e g u l a r urban s u r f a c e imposes s e v e r e l i m i t a t i o n on any i n s t r u m e n t a l t e c h n i q u e . As a r e s u l t , t h e r e i s v e r y l i t t l e e x p e r i m e n t a l e v i d e n c e to v e r i f y o r r e f u t e the commonly h e l d a s s u m p t i o n s on the n a t u r e o f the s e n s i b l e h e a t f l u x i n an urban a r e a . The magnitude and b e h a v i o u r o f t h i s e n e r g y component has remained l a r g e l y s p e c u l a t i v e . The s u c c e s s and c o n f i d e n c e d e r i v e d from the YST eddy c o r r e l a t i o n system o v e r the r e l a t i v e l y simple g r a s s s u r f a c e , s u g g e s t e d i t s use o v e r the c i t y s u r f a c e to i n v e s t i -g a t e the b e h a v i o u r o f the s e n s i b l e h e a t f l u x . T h e r e f o r e , such measurements were c o n d u c t e d o v e r a l i m i t e d p o r t i o n o f the urban a r e a i n V a n c o u v e r , B.C. I t must be emphasized t h a t t h e scope o f t h i s s t u d y i s v e r y l i m i t e d . S p a t i a l 98 99 s a m p l i n g , both h o r i z o n t a l l y and v e r t i c a l l y , i s c o n f i n e d to a l i m i t e d urban b u i l d i n g - a i r volume. Due to p r a c t i c a l l i m i t a t i o n s , measurements were o n l y a t t e m p t e d above an i n d i v i d u a l b u i l d i n g r o o f . The c h o i c e of m e a s u r i n g a t r o o f - t o p l e v e l and above, r a t h e r than between the b u i l d i n g e l e m e n t s , was g o v e r n e d p r i m a r i l y by i n s t r u m e n t a l c o n s i d e r a t i o n s . The s u c c e s s f u l i m p l e m e n t a t i o n o f the ,eddy c o r r e l a t i o n t e c h n i q u e , e m p l o y i n g E u l e r i a n p o i n t measurements of h e a t f l u x e s , r e q u i r e s s u f f i c i e n t s p a t i a l homogeneity i n the m e t e o r o l o g i c a l f i e l d s to e n s u r e n e g l i g i b l y s m a l l mean v e r t i c a l a i r movement. W i t h i n the canyon (between b u i l d i n g e l e m e n t s ) t h i s r e q u i r e m e n t would be u n l i k e l y t o be s a t i s f i e d . Hence i t would be n e c e s s a r y to d e v i s e a means o f s p a t i a l l y i n t e g r a t i n g the f l u x e s i n the h o r i z o n t a l to a c h i e v e t r u l y m e a n i n g f u l r e s u l t s . Above the b u i l d i n g e l e m e n t s , however, the p o s s i b i l i t y o f s u c c e s s w i t h t h i s t e c h n i q u e i s enhanced, p a r t i c u l a r l y i f the urban a r e a under s t u d y p o s s e s s e s a de g r e e o f b u i l d i n g c o n t i n u i t y ( u n i f o r m i t y o f t y p e , h e i g h t , d e n s i t y and f u n c t i o n ) . C o n v e r g e n c e o r d i v e r g e n c e i n t h e mean a i r m o t i o n would then tend to be m i n i m i z e d above r o o f -top l e v e l . I t may then be p o s s i b l e to make r e a s o n a b l e e s t i m a t e s o f t h e s e n s i b l e heat f l u x from p o i n t measurements t h a t a r e o f more g e n e r a l a p p l i c a b i l i t y f o r t h e s t u d y a r e a . A d e s c r i p t i o n o f our urban e x p e r i m e n t a l s i t e was g i v e n i n C h a p t e r 2. The e x t e n t t o which t h e s u r r o u n d i n g a r e a p o s s e s s e s 100 the d e s i r e d b u i l d i n g c o n t i n u i t y w i l l u n d o u b t e d l y a f f e c t t h e degree o f g e n e r a l i z a t i o n t h a t i s p o s s i b l e from our measure-ments. Boundary L a y e r C o n s i d e r a t i o n s In the p r e s e n c e o f an a b r u p t change i n s u r f a c e r o u g h n e s s , the development o f a boundary l a y e r can be a n t i c i -p a t e d . As the a i r f l o w s downstream from t h i s change, t h r e e r e g i o n s i n the boundary l a y e r f l o w can be e n v i s a g e d ( F i g . 2 9 ( a ) ) . Region I c o n s i s t s o f t h e upstream f l o w , and a l s o forms t h e downstream f l o w above the boundary l a y e r o f t h e new s u r f a c e c o n d i t i o n . Region II i s the i n t e r n a l l a y e r where the f l o w has re s p o n d e d and i s a d j u s t i n g to t h e new s u r f a c e . T h i s merges f u r t h e r downstream i n t o R e g i o n I I I , the a s y m p t o t i c s e l f - p r e s e r v i n g s t a t e o f the new s u r f a c e . E x p e r i m e n t a l e v i d e n c e based on wind t u n n e l work by L u x t o n (1970) s u g g e s t s t h a t the growth o f the i n t e r n a l boundary l a y e r f o l l o w i n g an a b r u p t change i n r o u g h n e s s , where the new s u r f a c e c o n s i s t s o f e l e m e n t s t h a t s t a n d proud from the s u r f a c e , c . f . F i g . 2 9 ( b ) , may be dominated by the wake from the l e a d i n g r o u g h n e s s e l e m e n t . I t may be u s e f u l t o use t h i s c a s e as an a n a l o g y when c o n s i d e r i n g the a i r f l o w from t h e c o u n t r y to the c i t y and the s u b s e q u e n t development o f an 101 REGION I NEW SURFACE ROUGHNESS F i g . 29. (a) Boundary l a y e r development o v e r an a b r u p t change i n s u r f a c e r o u g h n e s s . (b) Boundary l a y e r development f o l l o w i n g a change from smooth t o a rough s u r f a c e where the r o u g h n e s s e l e m e n t s a r e above the s u r f a c e . 102 i n t e r n a l urban boundary l a y e r . F u r t h e r m o r e , we s h a l l make the common a s s u m p t i o n t h a t any boundary l a y e r growth a s s o c i a t e d w i t h the i n d i v i d u a l b u i l d i n g e l e m e n t s i n the urban a r e a w i l l be s t r i c t l y l o c a l i z e d . S i n c e the i n v e s t i g a t i o n o f the urban s e n s i b l e h e a t f l u x e s was c o n f i n e d to measurements above the r o o f o f an i n d i v i d u a l b u i l d i n g i n the c i t y , c a r e f u l c o n s i d e r a t i o n to the t y p e o f f l o w p a t t e r n around the b u i l d i n g i s n e c e s s a r y . A s c h e m a t i c r e p r e s e n t a t i o n o f the t y p i c a l wind f l o w p a t t e r n a round a b u i l d i n g i s shown i n F i g . 30 ( c . f . H a l i t s k y , 1962). W h i l e the s i t u a t i o n i n t h e atmosphere i s more complex, and p a r t i c u l a r l y so i n the urban c o n t e x t , t h i s f l o w v i s u a l i z a -t i o n around a b u i l d i n g i n an i d e a l f l u i d s i t u a t i o n does p r o v i d e some i n s i g h t i n t o t h e n a t u r e o f the problem t h a t i s l i k e l y to o c c u r i n t h e ca s e o f measurements made above the r o o f o f a b u i l d i n g . F o r example, we might e x p e c t d i s -s i m i l a r i t i e s i n the measurements c l o s e to the r o o f s u r f a c e ( w i t h i n t h e t u r b u l e n t zone) as compared w i t h t h o s e made above the s u r f a c e o f s e p a r a t i o n . For t h i s s t u d y , i t . w i l l be assumed t h a t measurements o f s e n s i b l e heat f l u x e s above the l o c a l boundary o f the r o o f a r e r e p r e s e n t a t i v e o f a r e a l urban h e a t f l u x e s , w h i l e t h o s e c o n d u c t e d i n the t u r b u l e n t zone r e f l e c t to a l a r g e e x t e n t v a l u e s a s s o c i a t e d w i t h t h e r o o f - t o p i t s e l f . T h us, a t h e i g h t s above t h e s u r f a c e o f s e p a r a t i o n , t h e a s s u m p t i o n i s made t h a t l o c a l i n h o m o g e n e i t i e s 10 CONSTANT WIND DIRECTION 30. S c h e m a t i c o f the l o c a l boundary above a b u i l d i n g f o r a c o n s t a n t a n g l e o f a t t a c k o f the wind f l o w . 104 i n the s e n s i b l e h e a t f l u x e s become i n s i g n i f i c a n t i n c o m p a r i s o n w i t h t h e m e s o - s c a l e urban f l u x e s . The e x i s t e n c e o f a r e t u r n f l o w (as shown i n F i g . 30) might be e x p e c t e d to c o m p l i c a t e the measurements near the s u r f a c e . Munn (1966) i n d i c a t e d t h a t t h e f l u x e s o f h e a t , momentum and water vapour i n t h i s t u r b u l e n t zone o f t h e r o o f had not been s t u d i e d , i n d e t a i l . The p r e s e n t work s h o u l d t h e r e f o r e h e l p e l u c i d a t e t h e b e h a v i o u r o f H i n t h i s zone. The p r i n c i p a l l e v e l s , a t which heat f l u x measure-ments were c o n d u c t e d , were 1.2, 4.0 and 20 m above the r o o f -top s u r f a c e . Measurements a t the 1.2 m l e v e l were p r o b a b l y w i t h i n t h e l o c a l boundary l a y e r o f the r o o f , w h i l e t h o s e a t 4.0 m a p p e a r e d to be above the s u r f a c e o f s e p a r a t i o n . T h i s c l a s s i f i c a t i o n i s based on the f a c t t h a t t h e wind d i r e c t i o n a t t h e 1.2 m l e v e l was q u i t e v a r i a b l e , whereas t h o s e a t 4.0 m a p p e a r e d g e n e r a l l y more c o n s t a n t , and co n -s i s t e n t w i t h t h e wind d i r e c t i o n r e c o r d e d a t 20 m above t h e r o o f s u r f a c e . V a r i a t i o n s i n the h e i g h t o f the boundary l a y e r above the r o o f seem to have a f f e c t e d the 4.0 m l e v e l measurements o c c a s i o n a l l y and were p r o b a b l y c a u s e d by t h e change i n a n g l e o f a t t a c k o f the wind f l o w to the b u i l d i n g . In g e n e r a l , however, the s e n s i b l e heat f l u x measurements a t 4.0 m and above, may be c o n s i d e r e d a r e f l e c t i o n o f v a l u e s above the r o o f - t o p t u r b u l e n t zone. 105 In p r e s e n t i n g t h e s e r e s u l t s , we s h a l l l i m i t our a t t e n t i o n i n t h i s c h a p t e r p r i m a r i l y t o a s p e c t s o f s a m p l i n g c o n s i d e r a t i o n s , the d i u r n a l b e h a v i o u r and the s p a t i a l v a r i -a b i l i t y o f H a t t h i s urban s i t e . D i s c u s s i o n s i n terms o f the e n e r g y b a l a n c e framework w i l l be l i m i t e d s i n c e i t w i l l be t r e a t e d more e x t e n s i v e l y i n the f o l l o w i n g c h a p t e r . Mean V e r t i c a l V e l o c i t y C o n s i d e r a t i o n s The complex n a t u r e o f t h e a t m o s p h e r e - u r b a n i n t e r -f a c e p r e s e n t s a s e r i o u s d i f f i c u l t y i n o b t a i n i n g an e x p e r i -mental s i t e above which t h e v e r t i c a l c o n v e r g e n c e o r d i v e r -gence i n the mean a i r mo t i o n i s v e r y s m a l l . I t may be p o s s i b l e , however, t h r o u g h c a r e f u l s i t e s e l e c t i o n , t o m i n i -mize t h i s e f f e c t a p p r e c i a b l y so t h a t s e n s i b l e h e a t f l u x measurements by t h e eddy c o r r e l a t i o n t e c h n i q u e can be employed s u c c e s s f u l l y . For our urban s i t e , i n v e s t i g a t i o n o f t h e w f i e l d was o n l y o f an e x p l o r a t o r y n a t u r e . No s u i t a b l e means o f a c c u r a t e l y m e a s u r i n g the mean v e r t i c a l a i r movement was a v a i l a b l e . Some a t t e m p t s , however, were made to d e t e r m i n e w w i t h a v e r t i c a l G i l l anemometer a t v a r i o u s p o s i t i o n s and h e i g h t s above the r o o f - s u r f a c e . Near t h e s u r f a c e , t y p i c a l v a l u e s o f w (30 min a v e r a g e s ) were w i t h i n ± 10 cm s " 1 . L i t t l e c o n f i d e n c e c o u l d be p l a c e d 106 on t h e s e magnitudes as they were w i t h i n the r e s o l u t i o n c a p a b i l i t y o f the i n s t r u m e n t and the p r e c i s i o n to which w c o u l d be measured. In g e n e r a l , s m a l l n e g a t i v e v a l u e s o f w ( d o w n d r a f t s i t u a t i o n ) were found near the s u r f a c e , whereas a t 20 m, a t e n d e n c y f o r p o s i t i v e v a l u e s ( u p d r a f t s i t u a t i o n ) seemed to p r e v a i l . While u n c e r t a i n t i e s i n the measurements p r e c l u d e any d e f i n i t i v e s t a t e m e n t on the n a t u r e o f the w f i e l d above the r o o f s u r f a c e , the r e l a t i v e l y s m a l l v a l u e s measured may p e r m i t us to assume t h a t w ( a v e r a g e d o v e r a s u f f i c i e n t t i m e p e r i o d ) i s g e n e r a l l y i n s i g n i f i c a n t . S a m p l i n g C o n s i d e r a t i o n s The optimum a v e r a g i n g p e r i o d f o r s e n s i b l e heat f l u x measurements was i n v e s t i g a t e d by Chou ( 1 9 6 6 ) . F o r s a m p l i n g i n t e r v a l s g r e a t e r than 20 min, he found s t a b l e a v e r a g e v a l u e s o f H were a c h i e v e d i n the l o w e s t 10 m o f the atmosphere. T h i s was based on e x t e n s i v e measurements c o n d u c t e d o v e r a u n i f o r m r u r a l s u r f a c e under d i f f e r e n t s t a b i l i t y c o n d i t i o n s . Based on t h e s e r e s u l t s , 30 min s a m p l i n g i n t e r v a l was a d o p t e d f o r heat f l u x measurements a t the r u r a l e x p e r i m e n t a l s i t e . In g e n e r a l , t h i s c h o i c e a p p e a r s to have been a d e q u a t e . A few e x c e p t i o n s were noted where a l o n g e r a v e r a g i n g p e r i o d m i g h t have been more a p p r o p r i a t e , as d i s c u s s e d i n C h a p t e r 4. The s u i t a b i l i t y o f a p p l y i n g the 107 same s a m p l i n g i n t e r v a l to the H measurements o v e r the urban s u r f a c e r e q u i r e s c a r e f u l c o n s i d e r a t i o n . S h o r t p e r i o d o s c i l l a t i o n s i n the h e a t f l u x f i e l d a r e d i r e c t l y r e l a t e d to the s c a l e s o f t u r b u l e n c e o v e r the s p a t i a l domain. To a v o i d t h e s e s t a t i s t i c a l f l u c t u a t i o n s , i t i s n e c e s s a r y to use a s u i t a b l e s a m p l i n g i n t e r v a l . T h i s i s g o v e r n e d by the c o s p e c t r u m o f H o v e r the f r e q u e n c y domain. H = P C p n h $ w T ( n ) dn (5.1) where p a i r d e n s i t y Cp s p e c i f i c h eat o f a i r a t c o n s t a n t p r e s s u r e $ , c o s p e c t r u m between the v e r t i c a l v e l o c i t y (w) and t h e a i r t e m p e r a t u r e (T) n f r e q u e n c y ( s u b s c r i p t s I and h r e f e r t o the lower and upper l i m i t s o f n, r e s p e c t i v e l y ) The l i m i t s o f the i n t e g r a l s h o u l d c o n t a i n a l l f r e q u e n c i e s t h a t c o n t r i b u t e to the heat f l u x . In p r a c t i c e the l o w e r l i m i t o f the i n t e g r a l i s d e t e r m i n e d by a s a m p l i n g p e r i o d s u f f i c i e n t l y l o n g to c o n t a i n the i m p o r t a n t low f r e q u e n c y c o n t r i b u t i o n s t o the f l u x . The work o f B u s i n g e r et al. (1967) o v e r g r a s s shows s i g n i f i c a n t c o n t r i b u t i o n s t o the 108 f l u x i n t h e c o s p e c t r u m o f w and T ( $ w j ) down to 0.003 Hz. A c c o r d i n g l y , the c h o i c e o f a 30 min s a m p l i n g p e r i o d f o r our r u r a l heat f l u x measurements i s f u r t h e r s u p p o r t e d . In c o n t r a s t , t h e r e i s no e x p e r i m e n t a l e v i d e n c e a v a i l a b l e to s u g g e s t t h e s i g n i f i c a n t f r e q u e n c y domain f o r urban s e n s i b l e h e a t f l u x e s . However, the r e c e n t work.of S t e e n b e r g e n (1971) s u g g e s t s a s h i f t o f energy i n the v e r t i c a l v e l o c i t y s p e c t r u m towards l o n g e r w a v e l e n g t h s ( i . e . lower f r e q u e n c i e s ) c l o s e to the s u r f a c e i n the c i t y , as compared to the c o u n t r y . T h i s s h i f t may be a s c r i b e d to m e c h a n i c a l t u r b u l e n c e . The t e m p e r a t u r e s p e c t r u m o v e r the c i t y i s not known, but i t would seem r e a s o n a b l e to e x p e c t a s h i f t i n the h e a t f l u x c o s p e c t r u m toward lower f r e q u e n c i e s i n the c i t y . C o n s e q u e n t l y , the need f o r l o n g e r s a m p l i n g i n t e r v a l s to a c h i e v e s t a b l e urban s e n s i b l e h e a t f l u x v a l u e s may be a n t i c i p a t e d ( i . e . l o n g e r than 30 m i n ) . As s e n s i b l e heat f l u x measurements were m o n i t o r e d . c o n t i n u o u s l y ( e x c e p t f o r p e r i o d i c i n t e r r u p t i o n s f o r i n s t r u -m e n t a t i o n c h e c k s ) , heat f l u x v a l u e s f o r v a r i o u s a v e r a g i n g p e r i o d s c o u l d be o b t a i n e d by s u b d i v i d i n g the r e c o r d a p p r o -p r i a t e l y . Two examples of urban h e a t f l u x v a r i a t i o n s , 4.0 m above the r o o f , u s i n g both h a l f - h o u r and one hour a v e r a g i n g p e r i o d s , a r e shown i n F i g s . 31 and 32. (The c o r r e s p o n d i n g n e t r a d i a t i o n f i e l d a t 20 m above the r o o f i s a l s o i n d i c a t e d on t h e s e g r a p h s (n.b. a l l n e t r a d i a t i o n measurements i n the 70 VANCOUVER, B.C. 109 V.S.B. BLDG. JULY 5, 1972 F i g . 31. Urban sensib le heat f luxes for ha l f -hour and one hour averaging per iods . 70 VANCOUVER, B.C. 1 1 0 V.S.B. BLDG. JULY 6, 1972 ROOF U 4 ( M / S ) 3 . 6 4.1 3.8 3.9 3.5 3.7 OIR 4 i f f t • I 1 1 1 1 I I I 06 08 70 12 14 16 18 20 TIME (PST) F i g . 32. Urban s e n s i b l e heat f l u x e s f o r h a l f - h o u r and one hour a v e r a g i n g p e r i o d s . c i t y w i l l r e f e r to t h i s l e v e l ) . . ) The use o f h a l f - h o u r a v e r a g e s shows c o n s i d e r a b l e f l u c t u a t i o n s i n the d i u r n a l c o u r s e o f H t h a t a r e c l e a r l y not r e l a t e d to time changes i n the net r a d i a t i o n f i e l d . I t may t h e r e f o r e not be u n r e a s o n -a b l e to s u g g e s t t h a t t h e y a r e p r i m a r i l y a m a n i f e s t a t i o n o f the s c a l e s o f t u r b u l e n c e o v e r the s p a t i a l domain t h a t a r e g e n e r a t e d by the urban s u r f a c e s . These o s c i l l a t i o n s can be a v o i d e d by the use o f a l o n g e r a v e r a g i n g i n t e r v a l . By the use o f one hour heat f l u x a v e r a g e s , the f l u c t u a t i o n s a r e smoothed ou t and the r e s u l t a n t heat f l u x f i e l d can then be seen to be a more d i r e c t r e s p o n s e to the time chang i n t h e net r a d i a t i o n p a t t e r n . Thus, i f we can assume t h a t the low f r e q u e n c y c o n t r i b u t i o n s to the h e a t f l u x i n the c i t y a r e a p p r e c i a b l e , the o s c i l l a t i o n s may s i m p l y a r i s e from the c h o i c e o f s a m p l i n g i n t e r v a l . F u r t h e r m o r e , i n o r d e r to a c h i e v e s t a b l e H v a l u e s and to c o n t a i n a l l f r e -q u e n c i e s t h a t c o n t r i b u t e to the heat f l u x , an a v e r a g i n g p e r i o d l o n g e r than h a l f - h o u r s h o u l d be a d o p t e d . C l o s e r to the r o o f - t o p s u r f a c e , w i t h i n the t u r b u -l e n t zone, the a p p l i c a t i o n o f a one hour s a m p l i n g i n t e r v a l was not always s a t i s f a c t o r y . L a r g e o s c i l l a t i o n s seem to o c c u r , e s p e c i a l l y around mid-day, t h a t were not a s s o c i a t e d w i t h changes i n the net r a d i a t i o n f i e l d and t h a t c o u l d not be e l i m i n a t e d by one hour a v e r a g e s . These c o u l d have been the r e s u l t o f i n h o m o g e n e i t i e s i n the m e t e o r o l o g i c a l f i e l d , 112 c r e a t e d p a r t l y by r e t u r n f l o w unto the r o o f from n e i g h b o u r i n g s t r e e t c a n y o n s , t h a t a f f e c t the E u l e r i a n p o i n t measurements. F i g . 33 i l l u s t r a t e s t h i s f e a t u r e u s i n g heat f l u x v a r i a t i o n s a t the 1.2 m l e v e l . Between 1000 and 1400 PST, we note t h a t two hour a v e r a g i n g i n t e r v a l s would smooth the f l u c t u a t i o n s and p r o d u c e a d i u r n a l b e h a v i o u r i n H t h a t i s more c o n s i s t e n t w i t h the net r a d i a t i o n c h a n g e s . T h e r e i s , however, some danger i n u s i n g such l o n g s a m p l i n g i n t e r v a l s as n o n - s t e a d y s t a t e c o n d i t i o n s a r e l i k e to o c c u r . W h i l e the above examples seem to s u g g e s t the need f o r s a m p l i n g i n t e r v a l s beyond 30 min, t h e r e were o c c a s i o n s when the use o f 30 min a v e r a g e s a p p e a r e d to be a d e q u a t e . T h i s o c c u r r e d c o n s i s t e n t l y under c o n d i t i o n s o f low n e t r a d i a t i o n i n p u t . The heat f l u x v a l u e s were s t a b l e and c o r r e s p o n d e d to changes i n the r a d i a t i o n p a t t e r n . An example i s shown i n F i g . 34. Thus, w i t h a r e d u c t i o n i n t h e r m a l c o n v e c t i o n , the a p p a r e n t low f r e q u e n c y c o n t r i b u t i o n to t h e c i t y becomes l e s s i m p o r t a n t . The r e s u l t s p r e s e n t e d above i n d i c a t e the d i f f i -c u l t i e s e n c o u n t e r e d i n d e t e r m i n i n g s u i t a b l e a v e r a g i n g p e r i o d s f o r urban heat f l u x measurements. The i m p o r t a n t s c a l e s o f t u r b u l e n c e o v e r the s p a t i a l domain f o r c i t y s u r f a c e s a r e p r o b a b l y q u i t e v a r i a b l e and a r e u n d o u b t e d l y c o n t r o l l e d by t h e complex n a t u r e o f the r o u g h n e s s and t h e r m a l p r o p e r t i e s o f t h e u n d e r l y i n g s u r f a c e . As a r e s u l t , the use o f a f i x e d 70 VANCOUVER, B.C. V.S.B. BLDG. JULY 28, 1972 113 F i g . 33. Urban s e n s i b l e heat f l u x e s f o r h a l f hour, one hour and two hour a v e r a g i n g p e r i o d s . 114 WIND Tj 4 (M/S) 2.8 3.3 3.4 2.8 3.5 t t t t t I I I » I 06 08 10 12 14 TIME (PST) F i g . 34. Urban s e n s i b l e heat f l u x e s f o r h a l f - h o u r a v e r a g i n g p e r i o d s . 115 a v e r a g i n g p e r i o d i s o f t e n u n s a t i s f a c t o r y . For the p u r p o s e s o f t h i s s t u d y , a s a m p l i n g p e r i o d between o n e - h a l f hour and one hour i s a d o p t e d f o r a l l s u b s e q u e n t d i s c u s s i o n s o f t h e urban heat f l u x , u n l e s s o t h e r w i s e n o t e d . D i u r n a l Urban S e n s i b l e Heat F l u x P a t t e r n From the c o n t i n u o u s s e r i e s o f urban H measurements, an a s s e s s m e n t o f the d i u r n a l p a t t e r n can be made. Some o f the c h a r a c t e r i s t i c f e a t u r e s a r e i n d i c a t e d i n F i g s . 31-34. D u r i n g the d a y t i m e , the f l u x e s a r e d i r e c t e d away from the urban s u r f a c e . Peak v a l u e s o f H a r e a t t a i n e d a r o u n d noon under c l e a r s k i e s when net r a d i a t i o n v a l u e s r e a c h a maximum. In a d d i t i o n , t h e s e examples e x h i b i t a d i u r n a l c o u r s e t h a t c l o s e l y p a r a l l e l s the time changes i n the net r a d i a t i o n f i e l d . In g e n e r a l , t h e s e f e a t u r e s were c o n s i s t e n t on a l l o b s e r v a t i o n days and f o r the measurements a t 1.2, 4.0 and 20 m above the r o o f . The a c t u a l magnitude o f the s e n s i b l e h e a t f l u x e s show a d e c r e a s e w i t h h e i g h t ( f r o m 1.2 to 4.0 m). T h i s i s not s u r p r i s i n g s i n c e we might a n t i c i p a t e t h a t measurements c o n d u c t e d w i t h i n the t u r b u l e n t zone o f the r o o f p r i m a r i l y r e f l e c t t h e r o o f - t o p s u r f a c e c o n d i t i o n s whereas t h o s e a t 4.0 m a r e a m a n i f e s t a t i o n o f a s p a t i a l l y a v e r a g e d heat f l u x o f the r o o f and s u r r o u n d i n g a r e a s which s h o u l d i n c l u d e a l a r g e r p r o p o r t i o n o f e v a p o r a t i n g s u r f a c e s . 116 On many a f t e r n o o n s and e v e n i n g s , the urban s e n s i b l e h e a t v a l u e s r e m ained c o n s i s t e n t l y h i g h f o r s e v e r a l h o u r s . T h i s was f o u n d i n the measurements a t a l l o b s e r v a t i o n h e i g h t s . A few examples a r e g i v e n i n F i g s . 35-37. The c ause o f t h i s b e h a v i o u r i s not known, but the f o l l o w i n g e x p l a n a t i o n i s p o s t u l a t e d . D u r i n g a g r e a t p o r t i o n o f the d a y t i m e , a p p r e -c i a b l e amounts o f h e a t a r e s t o r e d w i t h i n the c i t y ' s f a b r i c . T h i s s o u r c e o f e n e r g y i s t h e n e x p e c t e d to become a v a i l a b l e f o r r e l e a s e to t h e a i r a t n i g h t . Heat r e l e a s e s from the urban s t r u c t u r e s , however, a r e l i k e l y t o o c c u r somewhat e a r l i e r t h a n s u n s e t s i n c e the g e o m e t r i c a l c o n f i g u r a t i o n o f b u i l d i n g a r r a y s i s c o n d u c i v e to the g e n e r a t i o n o f e x t e n s i v e shadow a r e a s when the sun i s a t low z e n i t h a n g l e s ( e x t e n s i v e shadow a r e a s i n the e a r l y morning would p r e s u m a b l y c a u s e a r e t a r d a t i o n i n the s e n s i b l e heat f l o w t o warm the urban a i r ) . An example o f t h i s b e h a v i o u r can be seen i n F i g . 38, f o r a t a r s l a b on the urban r o o f . Around 1600 PST, the s l a b was i n f l u e n c e d by the shadow c a s t by the s u p e r s t r u c t u r e on the r o o f . S h o r t l y t h e r e a f t e r , the heat f l u x (G) i n the s l a b r e v e r s e d i t s d i r e c t i o n o f f l o w . T h e r e o c c u r r e d a l a r g e f l o w o f heat out o f the t a r s l a b i n t o the a i r . In c o n t r a s t , the p o i n t measurements o f G i n the unshaded r o o f - t o p i t s e l f showed a f l o w i nwards t h r o u g h o u t t h i s p e r i o d . T h i s t y p e of b e h a v i o u r ( c r e a t e d by shadow a r e a s ) can be e x p e c t e d to enhance the urban s e n s i b l e heat F i g . 35. D i u r n a l v a r i a t i o n o f the urban s e n s i b l e heat f l u x a t 1.2 m above r o o f . F i g . 37. D i u r n a l v a r i a t i o n o f the urban s e n s i b l e heat f l u x a t 20 m above r o o f . 118 V A N C O U V E R , B.C. V. S. B. B L D G . J U L Y 25, 1972 15 h 10 I E u > i / i Z LU a x => 5 _ i u. > O O i LU z LU 0 - 5 -10 -15 GTAR SLAB r I 1 1 1 1 1 1 06 08 10 12 14 1 16 1 8 ^ 20 1 1 T I M E (PST) 1 1 T A R S L A B IN S H A D O W F i g . 38. E f f e c t o f shadow on the d i u r n a l b e h a v i o u r o f urban r o o f heat s t o r a g e . 119 f l u x e s by drawing upon s t o r a g e . Thus, w h i l e the g a i n o f net r a d i a t i o n p r o g r e s s i v e l y d e c r e a s e s w i t h the a p p r o a c h o f s u n s e t , a r e l a t i v e enhancement o f s e n s i b l e h e a t f l o w may d e v e l o p . T h i s would f a v o u r the slow d e c l i n e i n H towards s u n s e t as has been n o t e d on many o c c a s i o n s . W h i l e t h i s e x p l a n a t i o n may be a p p l i c a b l e to c o n d i t i o n s above the boundary l a y e r o f the r o o f , i t would seem l e s s s a t i s f y i n g f o r c o n d i t i o n s w i t h i n the t u r b u l e n t zone. Perhaps heat r e l e a s e s from urban s t r u c t u r e s towards s u n s e t i n t o the n e i g h b o u r i n g s t r e e t canyons a r e c o u p l e d w i t h the r e t u r n f l o w onto the r o o f to p r o v i d e the n e c e s s a r y enhancement o f H as we have o b s e r v e d i n the measurements a t the 1.2 m l e v e l . I t i s i n t e r e s t i n g to note t h a t t h e s t a r t o f r a p i d growth o f the urban h e a t i s l a n d , AT ( u r b a n - r u r a l ) i s o b s e r v e d to o c c u r d u r i n g the p e r i o d near s u n s e t (Oke and E a s t , 1971; Hage, 1971; and Oke et al. , ( 1 9 7 2 ) . N i g h t - t i m e v a l u e s o f H a r e a l s o shown i n F i g s . 35-37. Wh i l e t h e r e i s l e s s c o n f i d e n c e i n the a b s o l u t e m agnitudes o f the n o c t u r n a l v a l u e s , the o b s e r v e d p a t t e r n a p p e a r s c o n s i s t e n t and i s most i n t e r e s t i n g . Near t h e r o o f s u r f a c e (1.2 m), t h e r e i s c o n s i s t e n t l y a f l o w o f h e a t away from the s u r f a c e a t n i g h t . At 4.0 m, the n o c t u r n a l v a l u e s a r e more v a r i a b l e g i v i n g f l o w s t o w a r d s , and away from the s u r f a c e d u r i n g the same n i g h t . The few n o c t u r n a l measure-ments a t 20 m show a s i m i l a r p a t t e r n to t h a t o b s e r v e d a t 120 the 4 m l e v e l ( F i g . 3 7 ) . The a p p a r e n t l a c k o f r e v e r s a l o f s e n s i b l e heat f l o w near the s u r f a c e i n the c i t y a t n i g h t (as compared to a r u r a l s i t e ) must t h e r e f o r e be c o n s i d e r e d as one o f the s o u r c e terms f o r the o b s e r v e d heat i s l a n d . The few s e n s i b l e h e a t f l u x measurements a t 20 m above the r o o f were g e n e r a l l y s m a l l e r i n magnitude than t h o s e f o u n d a t the 4 m l e v e l , both by day and by n i g h t . T h i s a p p a r e n t d i v e r g e n c e i n the heat f l u x above t h e boundary l a y e r o f t h e r o o f seems to s u g g e s t t h a t e i t h e r a d v e c t i v e i n f l u e n c e s a r e i m p o r t a n t o r e l s e c o n v e r g e n c e w i l l have warmed the a i r l a y e r . T h i s however does not p r e c l u d e the e x i s t e n c e o f a c o n s t a n t f l u x l a y e r above the r o o f - t o p boundary l a y e r s i n c e i n a d e q u a t e f e t c h / h e i g h t r a t i o may have a f f e c t e d the measurements a t 20 m, p a r t i c u l a r l y d u r i n g the d a y t i m e w i t h the p r e v a i l i n g wind from the n o r t h w e s t . I t was m e n t i o n e d e a r l i e r t h a t t h e minimum f e t c h i s a p p r o x i -m a t e l y 1.5 km from non-urban s u r f a c e s (water b o d i e s ) f o r • t h i s e x p e r i m e n t a l s i t e . T h i s o c c u r s f o r winds from the n o r t h w e s t . As a r e s u l t , the p r i n c i p a l boundary l a y e r d e velopment o v e r the a r e a s t u d i e d d u r i n g the daytime may be r e l a t i v e l y s h a l l o w . The measurements a t 20 m may thus be o n l y p a r t i a l l y r e p r e s e n t a t i v e o f the u n d e r l y i n g c o n d i t i o n s . U n f o r t u n a t e l y , we do not have any H d a t a f o r i n t e r m e d i a t e l e v e l s between 4 and 20 m to c o n f i r m o r r e f u t e the c o n s t a n c y o f f l u x i n the i n t e r n a l boundary l a y e r o f the c i t y . 121 A n o t h e r i n t e r e s t i n g example o f the b e h a v i o u r o f urban s e n s i b l e heat f l u x e s i s shown i n F i g . 39. F i g . 39(a) shows the d i u r n a l c o u r s e o f H on J u l y 7, 1972 f o r d r y c o n -d i t i o n s . The v a l u e s o f G shown a r e t h o s e o b t a i n e d f o r the r o o f - t o p s u r f a c e . For the d i s c u s s i o n to f o l l o w , we s h a l l assume t h a t the r e s i d u a l ( o b t a i n e d as the r e s i d u a l o f the v e r t i c a l h e a t b a l a n c e e x p r e s s i o n , e q u a t i o n 1.2 ) may be a p p r o x i m a t e l y e q u a t e d to the l a t e n t heat f l u x . F o l l o w i n g t h i s o b s e r v a t i o n day, t h e r e was a p e r i o d o f heavy r a i n which c e a s e d on J u l y 12. The r e s u l t s f o r J u l y 13 ( F i g . 39 ( b ) ) , when r o o f - t o p a r e a s were s a t u r a t e d show a r e m a r k a b l e drop i n the s e n s i b l e h e a t f l u x , which s u g g e s t s t h a t most o f the a v a i l a b l e energy was u t i l i z e d f o r e v a p o r a t i o n . In the days f o l l o w i n g , t h e r e was a p e r i o d o f d r y w e a t h e r c o n d i t i o n s . The s e n s i b l e h e a t f l u x showed a p r o g r e s s i v e i n c r e a s e so t h a t by J u l y 17 ( F i g . 3 9 ( c ) ) , i t had r e g a i n e d v a l u e s s i m i l a r to t h o s e o b s e r v e d p r i o r to the r a i n f a l l . The r e s i d u a l term, however, was s t i l l a p p r e c i a b l e , the i m p l i c a t i o n s o f which w i l l be d i s c u s s e d i n the next c h a p t e r i n the c o n t e x t o f urban energy b a l a n c e . I t i s i n t e r e s t i n g , however, to note t h a t s i g n i f i c a n t amounts o f r a i n f a l l a r e i n t e r c e p t e d by f l a t - t o p r o o f s u r f a c e s d u r i n g wet s p e l l s . An a p p r e c i a b l e q u a n t i t y does not run o f f but remains as p u d d l e s on the s u r f a c e , o r i s a b s o r b e d i n the uppermost l a y e r o f the r o o f . T h i s water th e n becomes a v a i l a b l e f o r VANCOUVER, B.C. V.S.B. BLDG. JULY 7, 1972 H : 4m ABOVE ROOF WIND U _ (M/S) 2.8 3.3 3.4 4 2.8 3.5 DIR t t t I 06 08 10 12 14 TIME (PST) I E u 3: E^ >• H to Z LU Q X > LU z F i g . 39. Urban energy b a l a n c e s (a) J u l y 7 1972 f o l l o w i n g wet p e r i o d . u4 0 n / S N . 9 2.0 2.0 2.8 2.5 3.9 °>« t f T t f t i 1 —I I I 06 08 10 12 14 TIME (PST) 1972 w i t h dry c o n d i t i o n s ; (b) J u l y 13, r o F i g . 39. Urban e n e r g y b a l a n c e ( c ) J u l y 17, 1972, 5 days a f t e r wet p e r i o d . 124 e v a p o r a t i o n i n t o the urban a tmosphere. Under such c o n d i t i o n s , energy u t i l i z a t i o n to warm the urban a i r v i a s e n s i b l e h e a t t r a n s f e r i s c l e a r l y r e t a r d e d a t the expense o f l a t e n t h e a t t r a n s f e r . T h i s b r i e f s t u d y o f the d i u r n a l p a t t e r n o f urban H v a l u e s i n d i c a t e s t h a t the eddy c o r r e l a t i o n t e c h n i q u e can be used w i t h r e l a t i v e s u c c e s s i n the urban c o n t e x t , and t h a t a number o f u n i q u e l y urban f e a t u r e s a r e e v i d e n t . S p a t i a l S a m p l i n g A l i m i t e d s t u d y o f the s p a t i a l v a r i a b i l i t y o f t h e s e n s i b l e h e a t f l u x e s o v e r a u n i f o r m g r a s s s u r f a c e was p r e -s e n t e d i n C h a p t e r 4. The r e s u l t s s u p p o r t e d the b a s i c a s s u m p t i o n o f a c o n s t a n t f l u x l a y e r , assuming l e s s than 20 per c e n t v a r i a b i l i t y to be a c c e p t a b l e . The a p p l i c a b i l i t y o f t h i s p r e m i s e i n the c o n t e x t o f the c i t y i s v e r y ques-t i o n a b l e s i n c e the mosaic o f urban s t r u c t u r e s may i n d u c e a d v e c t i v e i n f l u e n c e s t h a t r e s u l t i n the f o r m a t i o n o f a n o n - c o n s t a n t f l u x l a y e r . Where t h e r e e x i s t s a measure o f b u i l d i n g c o n t i n u i t y , some u n i f o r m 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 can be a n t i c i p a t e d . A c c o r d i n g l y , s m a l l s p a t i a l v a r i a b i l i t y i n the H measurements above l o c a l r o o f - t o p boundary l a y e r s may be t a k e n to r e f l e c t the e x t e n t to which the urban a r e a s t u d i e d p o s s e s s e s b u i l d i n g c o n t i n u i t y 125 ( o u t l i n e d i n the f i r s t s e c t i o n ) . Here, we assume t h a t the measurements a r e made w i t h i n a l a r g e r s c a l e urban boundary l a y e r ( i . e . f r e e o f non-urban i n f l u e n c e s ) . A l t h o u g h i t was not p o s s i b l e to s t u d y l a r g e s c a l e a r e a l v a r i a t i o n s , a l i m i t e d s t u d y o f the s p a t i a l v a r i a b i l i t y o f H i n the immediate v i c i n i t y o f the r o o f - t o p s u r f a c e was c o n d u c t e d . As a p a r a l l e l , we might e x p e c t t h a t s p a t i a l measurements c o n d u c t e d s i m u l t a n e o u s l y w i t h i n t h e t u r b u l e n t zone o f t h e r o o f s h o u l d y i e l d c o n s i s t e n c y i f the f l o w i s p r i m a r i l y r e s p o n d i n g to the u n d e r l y i n g s u r f a c e . Measure-ments beneath and above the s u r f a c e o f s e p a r a t i o n o v e r t h e r o o f would not be e x p e c t e d t o show t h i s c o n s i s t e n c y . S i m u l t a n e o u s measurements d u r i n g t h e da y t i m e w i t h two YST systems were made f o r v e r t i c a l s e p a r a t i o n s o f 0.8 m (between 1.2 and 2.0 m), o f 2.8 m (between 1.2 and 4.0 m) and f o r h o r i z o n t a l s e p a r a t i o n s o f 2.5 and 7.0 m, a t a v e r t i c a l h e i g h t o f ~ 1.5 m. Onl y measurements a t t h e 4.0 m l e v e l can be e x p e c t e d t o be above the l o c a l r o o f - t o p boundary l a y e r . Examples o f H measurements ~ 1.5 m above the r o o f f o r a h o r i z o n t a l s e p a r a t i o n between the two YST systems o f 2.5 m a r e shown i n F i g . 4 0 ( a ) . The d i u r n a l b e h a v i o u r o f t h e two H v a l u e s e x h i b i t s c l o s e s i m i l a r i t y w i t h t h i s s m a l l s e p a r a t i o n d i s t a n c e . T h e r e i s , however, some v a r i a b i l i t y i n the i n d i v i d u a l one hour a v e r a g e s o f H from the two i n s t r u m e n t s . C u m u l a t i v e t o t a l s o f the heat 30 CN I E u 1 20 >-H t/I 2 io X Z3 >• o (JJ z LU - 1 0 L 06 401 CN I E | 301 >• | 20| X 3 >• 10 (b) VANCOUVER, B.C. V.S.B. BLDG AUG. 24, 1972 HEIGHT ABOVE ROOF : 1.5m HOR. SEPARATION : 2.5m 126 WIND U I - 5 (M /S ) J.4 1.6 I.6 V A R I A B L E WIND D IRECTION 1.8 1.6 2.0 1.6 1.2 0.9 0.6 J_ _L J 08 10 12 14 16 Y S T 18 20 T I M E (PST) VANCOUVER, B.C. V.S.B. BLDG. AUGUST 28, 1972 HEIGHT ABOVE ROOF . 1.5m HOR. SEPARATION 7.0m WIND U J 5 (M /S) 1.0 1-2 1.6 1.7 1.6 1.4 1.6 1.7 V A R I A B L E WIND DIRECTION i . ± J 06 08 10 12 14 16 18 20 TIME (PST) F i g . 40. H o r i z o n t a l s p a t i a l v a r i a t i o n o f the urban s e n s i b l e h eat f l u x e s . 127 f l u x e s from both i n s t r u m e n t s , e x p r e s s e d as a r a t i o ( H V C T / Y 5 T i H ) i n d i c a t e ~ 20 per c e n t v a r i a t i o n . S i m i l a r r e s u l t s were o b t a i n e d i n the H c o m p a r i s o n f o r a h o r i z o n t a l s e p a r a -t i o n o f 7.0 m ( F i g . 4 0 ( b ) ) . These r e s u l t s a r e c o n s i s t e n t f o r o t h e r o b s e r v a t i o n days on which h o r i z o n t a l c o m p a r i s o n s were made (s e e T a b l e 6 ) . While t h e y i n d i c a t e r e l a t i v e l y l a r g e h o r i z o n t a l v a r i a t i o n when compared to t h a t f o r the r u r a l g r a s s s u r f a c e , they do s u p p o r t the p r e m i s e o f a p p r o x i m a t e h o r i z o n t a l f l u x c o n s t a n c y i n the t u r b u l e n t zone of the r o o f . S i m i l a r l y , the h e i g h t v a r i a t i o n w i t h i n the boundary l a y e r o f the r o o f ( o b s e r v e d from the 1.2 and 2.0 m l e v e l s ) a p p e a r e d c o n s i s t e n t ( F i g . 4 1 ( a ) ) . L e s s than 20 per c e n t v a r i a t i o n was n o t e d . The two o b s e r v a t i o n days on which H c o m p a r i s o n s between the 1.2 and 4.0 m l e v e l s were made, showed more v a r i a b i l i t y . Good agreement was f o u n d on A u g u s t 30, 1972 ( F i g . 4 1 ( b ) ) , whereas on September 1, 1972, a 50 per c e n t r e d u c t i o n was noted i n the 4.0 m v a l u e s . T a b l e 6 g i v e s a summary o f the s p a t i a l e x p e r i m e n t a l days and the c u m u l a t i v e t o t a l s from the two YST i n s t r u m e n t s , e x p r e s s e d as a r a t i o . They s u p p o r t the p r e m i s e o f c o n s t a n c y w i t h i n the boundary l a y e r o f the r o o f , i f we c o n s i d e r 20 per c e n t v a r i a t i o n to be a c c e p t a b l e . While no measurements o f the s p a t i a l v a r i a b i l i t y o f the n o c t u r n a l f l u x e s were a t t e m p t e d , i t may be p o s s i b l e 1 28 VANCOUVER, B.C. V.S.B. BLDG. AUG. 25, 1972 H YST HYST 2 VERT. SEP. 0.8m I E u E z LU Q X > LU z LU V A R I A B L E WIND D IRECTION I 1 I _L J 06 08 2 0 r ( b ) 10 12 14 16 10 U 0 18 20 TIME (PST) VANCOUVER, B.C. V.S.B. BLDG. AUG. 30, 1972 H Y S T I (1.2m) H Y S T 2 (4.0m) VERT. SEP. 2.8m WIND 0 1 2 ( M / S ) 2.0 2.3 3.1 3.1 2.8 3.6 3.4 4.2 4.0 2.7 V A R I A B L E WIND D IRECTION 0. (M/S) 2.3 3.3 3.7 3.4 3.2 3.9 3.9 4.9 4.4 4.0 I I I I I I 3.1 06 08 10 12 14 -L J 16 18 20 TIME (PST) F i g . 41. V e r t i c a l s p a t i a l v a r i a t i o n o f the urban s e n s i b l e h eat f l u x e s . T a b l e 6 C o m p a r i s o n o f d a y t i m e c u m u l a t i v e s e n s i b l e h e a t f l u x d e n s i t i e s f r o m t h e yaw s p h e r e - t h e r m o m e t e r s y s t e m s (Hys^! and H YgT2^ above t h e u r b a n r o o f D a t e D u r a t i o n ( m i n ) u / u Y S T l YST2 Rema r k s 24 A u g u s t 1 972 584 0.79 H o r i z o n t a l s e p a r a t i o n 2.5 m a t 1.5 m 1 eve 1 a b o v e r o o f - t o p 28 29 A u g u s t A u g u s t 1 972 1 972 420 332 i .09 0.98 H o r i z o n t a l s e p a r a t i o n 7.0 m a t 1.5 m 1 eve 1 a b o v e r o o f - t o p 25 A u g u s t 1 972 682 0.88 V e r t i c a l s e p a r a t i o n 0.8 m, a t 1.2 m and 2 . 0 m I e ve 1s a bove r o o f - t o p 30 1 A u g u s t 1972 S e p t e m b e r 1972 525 426 0.88 1 .48 * V e r t t c a l s e p a r a t i o n 2.8 m, a t 1.2 m and 4.0 m l e v e l s a bove r o o f - t o p * H v c,_ a t t h e 1.2 m l e v e l and H v o _ a t t h e 2.0 and 4.0 m l e v e l s . l o l l I b l 2 130 to make some i n f e r e n c e s from the d i u r n a l b e h a v i o u r o f H p r e v i o u s l y d i s c u s s e d . C o n s i s t e n t l y , i t was f o u n d t h a t the H v a l u e s a t t h e 1.2 m l e v e l were d i r e c t e d away from the s u r f a c e a t n i g h t ( s e e F i g s . 35 and 3 6 ) . At the 4 and 20 m l e v e l s , n o c t u r n a l f l u x e s were more v a r i a b l e but s m a l l e r t h a n t h o s e a t the 1.2 m l e v e l . With the p r e s i s t e n c e o f l i g h t winds a t n i g h t , the boundary l a y e r d e velopment o v e r the r o o f - t o p s u r f a c e would not be e x p e c t e d to be as marked. As a r e s u l t , n o n - c o n s t a n c y i n the urban s e n s i b l e h e a t f l u x may be i n f e r r e d from our n i g h t - t i m e o b s e r v a t i o n s . F u g g l e (1971) a r r i v e d a t a s i m i l a r c o n c l u s i o n from s t u d i e s o f r a d i a t i v e f l u x d i v e r g e n c e i n the a i r l a y e r i m m e d i a t e l y above c i t y s t r u c t u r e s a t n i g h t . An i n c r e a s e i n r a d i a t i v e d i v e r g e n c e ( c o o l i n g ) a p p e a r e d to be p a r t i a l l y o f f s e t by a c o r r e s p o n d i n g i n c r e a s e i n s e n s i b l e h e a t c o n v e r g e n c e (warm-ing)-. The r e s u l t s from t h i s s t u d y a l s o i n d i c a t e s e n s i b l e h e a t f l u x c o n v e r g e n c e i n the l ower a t m o s p h e r e . Thus, the i n t e r a c t i o n o f f l u x d i v e r g e n c e i n the net r a d i a t i o n f i e l d , w i t h t h a t o f t h e v e r t i c a l t e m p e r a t u r e s t r u c t u r e c o u l d have p r o d u c e d the s e n s i b l e heat c o n v e r g e n c e . In the a bsence o f a d v e c t i v e i n f l u e n c e s , t h i s i s o f f e r e d as a p o s s i b l e e x p l a n a -t i o n f o r the n i g h t - t i m e b e h a v i o u r o f urban H v a l u e s c l o s e to the r o o f s u r f a c e . C h a p t e r 6 URBAN ENERGY BALANCE I n t r o d u c t i o n The a p p l i c a b i l i t y o f the eddy c o r r e l a t i o n t e c h n i q u e to t h e measurement o f s e n s i b l e heat t r a n s f e r between the atmosphere and the urban i n t e r f a c e was d e m o n s t r a t e d i n the p r e v i o u s c h a p t e r . D e s p i t e the enormous c o m p l e x i t i e s o f th e t u r b u l e n t heat exchange p r o c e s s e s i n the c i t y , i t was shown t h a t the urban s e n s i b l e h e a t f l u x p a t t e r n , o b t a i n e d d i r e c t l y from E u l e r i a n p o i n t measurements, l a r g e l y r e f l e c t s t ime changes i n th e net r a d i a t i o n f i e l d . Even the magnitudes o f t h e heat f l u x e s do not appear i n c o n s i s t e n t w i t h t h o s e o f the net r a d i a t i o n d u r i n g t h e d a y t i m e . In the a b s e n c e of a r t i f i c i a l l y g e n e r a t e d heat a t the s u r f a c e and a d v e c -t i o n e f f e c t s , i t s h o u l d be e x p e c t e d t h a t the amount o f heat used to warm the a i r v i a s e n s i b l e heat t r a n s f e r w i l l not exceed the net r a d i a n t heat g a i n e d a t the s u r f a c e . The i n d e p e n d e n t measurements o f urban H s u p p o r t t h i s . I t s h o u l d be emphasized t h a t t h i s r e s u l t has been d e r i v e d from c o m p l e t e l y i n d e p e n d e n t measurements o f net r a d i a t i o n 131 132 and s e n s i b l e heat f l u x . In a d d i t i o n , i t was p o s s i b l e t o make a l i m i t e d a s s e s s m e n t o f the d i u r n a l b e h a v i o u r , and s p a t i a l v a r i a b i l i t y o f H o v e r a r e s t r i c t e d urban a r e a . These r e s u l t s a r e now c o n s i d e r e d i n t h e c o n t e x t o f the ener g y b a l a n c e framework. Measurements o f H c o n c u r r e n t l y w i t h o t h e r e n e r g y components ( n e t r a d i a t i o n and s o i l h eat s t o r a g e ) p r o v i d e the b a s i s f o r a d i s c u s s i o n o f t h e urban h e a t b a l a n c e . S i n c e both Rn and G a r e o b t a i n e d from p o i n t measurements, do u b t s as t o t h e i r u s e f u l n e s s and v a l i d i t y must a r i s e when t h e y a r e used to c h a r a c t e r i z e an urban a r e a . F u r t h e r m o r e , i t i s n e c e s s a r y t o make a s s u m p t i o n s i n o r d e r t o s i m p l i f y t h e t h r e e - d i m e n s i o n a l n a t u r e o f t h e problem and the e x i s t e n c e o f a n t h r o p o g e n i c s o u r c e s o f heat and m o i s t u r e . R e c o g n i z i n g t h e s e s h o r t c o m i n g s , i t i s s t i l l p o s s i b l e to g a i n some g e n e r a l i n s i g h t s i n t o t h e e n e r g e t i c exchanges i n t h e urban e n v i r o n m e n t v i a the ene r g y b a l a n c e framework. A r t i f i c i a l Heat and M o i s t u r e P r o d u c t i o n In c i t i e s , a r t i f i c i a l h eat and m o i s t u r e a r e r e l e a s e d i n t o the atmosphere p r i m a r i l y from i n d u s t r i a l , t r a n s p o r t a t i o n and d o m e s t i c s o u r c e s . These s o u r c e s g e n e r a t e heat by com-b u s t i o n p r o c e s s e s , which then e n t e r s the atmosphere e i t h e r d i r e c t l y o r i n d i r e c t l y i n the form o f s e n s i b l e h e a t . A 133 r e l a t i v e l y s m a l l f r a c t i o n o f t h i s a r t i f i c i a l heat g e n e r a t e d w i l l be u t i l i z e d i n the e v a p o r a t i o n o f l i q u i d w a t e r and t h e r e f o r e e n t e r s t h e atmosphere i n the form o f l a t e n t h e a t . The a r t i f i c i a l heat g e n e r a t i o n can thus be e x p e c t e d to pro d u c e p r i m a r i l y a m o d i f i c a t i o n o f the n a t u r a l s e n s i b l e h e a t exchange. F o r many m e t r o p o l i t a n a r e a s , t h e magnitude o f t h i s a r t i f i c i a l e n e r g y f l u x d e n s i t y has been e s t i m a t e d ( s e e f o r example, Oke ( 1 9 6 9 ) , SMIC ( 1 9 7 1 ) ) . They i n d i c a t e t h a t man-made he a t p r o d u c t i o n has a t t a i n e d v a l u e s which a r e a s i g n i f i c a n t f r a c t i o n o f t h e n a t u r a l net r a d i a t i o n f o r many m i d - l a t i t u d e c i t i e s . In some i n s t a n c e s ( e . g . c i t i e s w i t h a c o l d w i n t e r c l i m a t e ) , t h i s term may even be l a r g e r t h a n Rn. T h i s e n e r g y , e m i t t e d d i r e c t l y o r i n d i r e c t l y i n t o t h e urban atmosphere i n t h e form o f s e n s i b l e h e a t , i s g e n e r a l l y a c c e p t e d as the prime cause f o r t h e t h r e e -d i m e n s i o n a l urban heat i s l a n d s o b s e r v e d d u r i n g the w i n t e r i n m i d - l a t i t u d e s . A r t i f i c i a l heat g e n e r a t i o n i s d i r e c t l y r e l a t e d to e n e r g y consumption and t h e r e f o r e shows a s t r o n g s e a s o n a l p a t t e r n w i t h summer v a l u e s c o n s i d e r a b l y l o w e r than t h o s e f o r the w i n t e r h e a t i n g s e a s o n . B o r n s t e i n (1968) has r e p o r t e d summer v a l u e s o f a r t i f i c i a l e n ergy f l u x d e n s i t y f o r M a n h a t t a n , New York, t h a t a r e about 1/6 o f the w i n t e r v a l u e s . S i m i l a r l y , Oke (1969) showed the summer a r t i f i c i a l h e a t p r o d u c t i o n t o be about 1/3 o f w i n t e r v a l u e s i n M o n t r e a l . T h i s p o i n t i s emphasized s i n c e the s t u d y p e r i o d here r e f e r s 134 to a summer-time s i t u a t i o n i n Va n c o u v e r . We thus a n t i c i p a t e t h a t the e f f e c t o f t h i s term w i l l d i m i n i s h from w i n t e r t o summer i n our e n e r g y b a l a n c e c o n s i d e r a t i o n s . U s i n g the p r o c e d u r e o u t l i n e d by Bach (1970) t h e av e r a g e annual a r t i f i c i a l heat p r o d u c t i o n f o r V a n c o u v e r i n 1970 was c a l c u l a t e d . The e s t i m a t e was based on u n p u b l i s h e d d a t a o f e l e c t r i c i t y , g a s , f u e l o i l , g a s o l i n e and c o a l c o n s u m p t i o n and m e t a b o l i c heat g e n e r a t i o n f o r the V a n c o u v e r a r e a i n 1970. The p r i m a r y s o u r c e s o f a r t i f i c i a l h e a t , i n d e s c e n d i n g o r d e r o f i m p o r t a n c e , were f u e l o i l , g a s , g a s o l i n e and e l e c t r i c i t y . The e s t i m a t e was found to be a p p r o x i m a t e l y 1.9 mWcm"2 and i s somewhat s m a l l e r than t h o s e o f o t h e r mid-l a t i t u d e N o r t h A m e r i c a n c i t i e s . F o r example, Bach (1970) r e p o r t e d an a v e r a g e summer v a l u e o f 2.6 mWcm"2 f o r C i n c i n n a t i , whi1e Summers (1964) e s t i m a t e d an a v e r a g e annual v a l u e o f 9.8 mWcm"2 f o r M o n t r e a l ( s e e T a b l e 1 ) . The v a l u e f o r V a n c o u v e r , however, does not a p p e a r u n r e a s o n a b l e s i n c e h e a t i n g degree days here a r e l o w e r than t h o s e o f c o n t i n e n t a l m i d - l a t i t u d e c i t i e s , and c o n s e q u e n t l y may be e x p e c t e d to pro d u c e lower energy consumption demand. The s e a s o n a l v a r i a t i o n o f the a r t i f i c i a l h eat f l u x d e n s i t y f o r V a n c o u v e r showed t h a t 60 per c e n t o f the a r t i f i c i a l h e a t was p r o d u c e d i n the w i n t e r months ( O c t o b e r - M a r c h ) . For 1970, the w i n t e r and summer v a l u e s were found to be 2.3 and 1.5 mWcm-2 r e s p e c t i v e l y . 135 W h i l e t h e e x a c t p a r t i t i o n i n g o f t h i s a v a i l a b l e e n e r g y i n t o s e n s i b l e and l a t e n t heat i s not known, i t i s not u n r e a s o n a b l e to s u g g e s t t h a t l e s s than 10 per c e n t e n t e r s the urban atmosphere as l a t e n t h e a t . I t i s n o t e d , f o r example, t h a t Oke and H a n n e l l (1970) e s t i m a t e d t h a t l e s s than 10 per c e n t o f the energy o u t p u t o f a s t e e l m i l l a t H a m i l t o n , O n t a r i o , e n t e r e d the atmosphere as l a t e n t h e a t . C o n s e q u e n t l y , we s h a l l i g n o r e the a r t i f i c i a l h eat c o n t r i b u t i o n to l a t e n t heat p r o c e s s e s f o r t h e Va n c o u v e r summertime s i t u a t i o n . A l t h o u g h the o v e r a l l a r t i f i c i a l h eat g e n e r a t i o n f o r summer i n Vanco u v e r i s r e l a t i v e l y s m a l l , i t s h o u l d be p o i n t e d o u t t h a t a l l e s t i m a t e s o f man-made heat p r o d u c t i o n ( i n c l u d i n g our e s t i m a t e ) r e p r e s e n t an a v e r a g e v a l u e o v e r the h o r i z o n t a l a r e a ! d i m e n s i o n s o f the c i t y . We thus e x p e c t h i g h e r v a l u e s i n the more d e n s e l y u r b a n i z e d a r e a o f t h e c i t y . F u r t h e r m o r e , the t h r e e - d i m e n s i o n a l a s p e c t o f t h e s u r f a c e and the n a t u r e o f b u i l d i n g heat exchange may cause l o c a l i z a t i o n o f t h i s heat as i t e n t e r s t h e urban a t m o s p h e r e . F o r a l i m i t e d urban b u i l d i n g - a i r volume i n the absence o f i n d u s t r i a l s o u r c e s , the p r i m a r y a r t i f i c i a l h e a t i s g e n e r a t e d by t r a n s p o r t a t i o n and d o m e s t i c s o u r c e s . Heat g e n e r a t e d by t r a n s p o r t a t i o n e n t e r s the a i r volume a t s t r e e t l e v e l , w i t h i n t h e canyon between b u i l d i n g e l e m e n t s , whereas d o m e s t i c a l l y g e n e r a t e d heat may p a r t l y e n t e r the 136 atmosphere d i r e c t l y a t r o o f - l e v e l o r t h r o u g h v e n t s on the s i d e s o f a b u i l d i n g . Some o f the heat w i l l a l s o pass i n d i r e c t l y to the atmosphere t h r o u g h the w a l l s and windows o f the i m p e r f e c t l y i n s u l a t e d b u i l d i n g . The net e f f e c t c o u l d a c c e n t u a t e th e warming between dense b u i l d i n g e l e m e n t s , p a r t i c u l a r l y a t n i g h t , when the n a t u r a l e n e r g y components a r e smal1. As an a p p r o x i m a t i o n , we s h a l l assume t h a t the v a l u e o f 1.5 mWcm"2 can be a p p l i e d to the s t u d y a r e a . C o n s e q u e n t l y , t h e e r r o r c r e a t e d by n e g l e c t i n g t h i s e n e r g y s o u r c e term s h o u l d be i n s i g n i f i c a n t d u r i n g t h e d a y t i m e s i n c e the v a l u e i s a t l e a s t an o r d e r o f magnitude s m a l l e r than the n a t u r a l e n e r g y components. O m i s s i o n o f t h i s h eat term a t n i g h t , however, may be u n r e a s o n a b l e as the a r t i f i c i a l e n e r g y f l u x d e n s i t y i s then l i k e l y t o be an a p p r e c i a b l e f r a c t i o n o f the n a t u r a l e n e r g y components. Roof-Top Energy B a l a n c e To b e g i n d i s c u s s i o n o f the urban heat b a l a n c e , we f i r s t c o n s i d e r the s i t u a t i o n c l o s e to t he s u r f a c e , w i t h i n the l o c a l r o o f - t o p boundary l a y e r (see F i g . 3 0 ) . In d o i n g s o , we a v o i d most o f the t h r e e - d i m e n s i o n a l a s p e c t s and a t t e m p t t o view the heat b a l a n c e as b a s i c a l l y a one-dimen-s i o n a l p r o b l e m . F o r the r o o f - t o p s u r f a c e i t s e l f , we can use t h e f o l l o w i n g s i m p l e heat b a l a n c e e x p r e s s i o n 137 Rn = H + LE + G (6.1 ) S i n c e t h e n e t r a d i a t i o n ( R n ) , t h e r o o f h e a t f l u x (G) and t h e s e n s i b l e heat f l u x (H) were known v i a d i r e c t measurements, the l a t e n t h e a t f l u x (LE) i n t h e above e x p r e s -s i o n r e m a i n e d as t h e r e s i d u a l . (We s h o u l d n o t e t h a t t h i s p r o c e d u r e e n a b l e s us t o use t h e e n e r g y b a l a n c e framework b u t does not p r o v i d e a b u d g e t a r y check on t h e i n d e p e n d e n t l y measured e n e r g y p a r a m e t e r s . A h e a t b a l a n c e c h e c k i s o n l y p o s s i b l e i f we assume the r o o f - t o p s u r f a c e t o be c o m p l e t e l y d r y ( i . e . LE i s z e r o ) . ) L e t us now examine the a p p l i c a b i l i t y o f t h e e n e r g y f l u x measurements f o r the r o o f s u r f a c e . As n e t r a d i a t i o n was o n l y m o n i t o r e d c o n t i n u o u s l y a t 20 m above t h e main r o o f s u r f a c e , t h e measurements o b t a i n e d a t t h i s l e v e l w i l l be used i n t h e r o o f - t o p e n e r g y b a l a n c e c o n s i d e r a -t i o n . T h i s s h o u l d n o t be u n r e a s o n a b l e d u r i n g t h e d a y t i m e s i n c e i t was p r e v i o u s l y n o t e d t h a t the h e i g h t - v a r i a t i o n i n Rn between 11 and 20 m above the r o o f was l e s s than 5 per c e n t . The measurement o f G was made i n the uppermost g r a v e l and t a r l a y e r o f t h e r o o f . T h i s p r o v i d e d a measure o f t h e h e a t f l o w i n g i n t o o r out o f t h e r o o f s u r f a c e . I f we assume t h a t some a r t i f i c i a l h e a t p a s s e s i n d i r e c t l y to t h e atmosphere t h r o u g h t h e i m p e r f e c t l y i n s u l a t e d r o o f , t h e n t h e r o o f - t o p G measurements a l s o c o n t a i n a measure o f t h i s 138 term. D u r i n g the d a y t i m e , t h i s a r t i f i c i a l heat w i l l r e d u c e the n a t u r a l G o f the r o o f and by n i g h t , w i l l augment the n a t u r a l G. D i r e c t H measurements a t the 1.2 m l e v e l above the r o o f o n l y w i l l be used f o r the r o o f - t o p e n e r g y b a l a n c e c o n s i d e r a t i o n s . They r e p r e s e n t v a l u e s w i t h i n t h e l o c a l t u r b u l e n c e zone o f the r o o f and s h o u l d l a r g e l y r e f l e c t t h e u n d e r l y i n g s u r f a c e c o n d i t i o n s . Daytime b a l a n c e . Two examples o f t y p i c a l d a y t i m e v a r i a t i o n o f the measured e n e r g y b a l a n c e components near r o o f - l e v e l a r e g i v e n i n F i g s . 42 and 43. These r e s u l t s i n d i c a t e t h a t a s i g n i f i -c a n t p o r t i o n o f the n e t r a d i a n t e n e r g y g a i n e d a t the r o o f s u r f a c e i s u t i l i z e d i n s e n s i b l e heat t r a n s f e r and i n h e a t s t o r a g e i n t h e r o o f . Of t h e s e two t r a n s f e r p r o c e s s e s , the g r e a t e s t amount o f e n e r g y i s used i n s e n s i b l e heat t o warm the a i r ( f o r example, a t midday H i s t y p i c a l l y ~ 3 G ) . Even s o , the r e s i d u a l term ( e q u a t e d t o LE) i s q u i t e a p p r e c i -a b l e . I t s h o u l d be n o t e d t h a t the d i u r n a l c y c l e o f the r e s i d u a l term shows a morning peak on J u l y 27 ( F i g . 42) whereas on the f o l l o w i n g day ( F i g . 4 3 ) , the peak o c c u r s i n t h e l a t e e v e n i n g . The c ause o f t h i s b e h a v i o u r i s not known but i t may be r e l a t e d t o the p r e s e n c e o f a d v e c t i o n even a t the 1.2 m l e v e l above the r o o f . I f the r e s i d u a l 139 VANCOUVER, B.C. V.S.B. BLDG JULY 27, 1972 H : 1.2m ABOVE ROOF 1.9 1.9 1.5 1.4 0.8 V A R I A B L E WIND DIRECTION 06 _ J _ 08 10 12 14 16 JL J 18 20 TIME (PST) F i g . 42. Daytime r o o f - t o p e n e r g y b a l a n c e . 140 VANCOUVER, B.C. V.S.B. BLDG JULY 28, 1972 H : 1.2m ABOVE ROOF 18 20 TIME (PST) F i g . 43. Daytime r o o f - t o p e n e r g y b a l a n c e . 141 term, e q u a t e d to L E , i s r e a l , we must c o n c l u d e t h a t the r o o f - t o p s u r f a c e i s not t h o r o u g h l y d r y but t h a t i t c o n t a i n s a v a i l a b l e w a ter which i s s u b s e q u e n t l y r e l e a s e d as m o i s t u r e to the urban atmosphere and consumes l a t e n t heat o f v a p o u r i -z a t i o n . On the o t h e r hand, the r e l a t i v e l y l a r g e r e s i d u a l term may a r i s e from c o n s i s t e n t u n d e r e s t i m a t i o n o f the s u r f a c e s n e s i b l e h e a t f l u x by the eddy c o r r e l a t i o n i n s t r u -ment, as w e l l as from u n d e r e s t i m a t i o n o f the s u r f a c e n e t r a d i a t i o n and s o i l h e a t s t o r a g e t e r m s . These p o s s i b i l i t i e s a r e examined f u r t h e r below. T h e o r e t i c a l c o n s i d e r a t i o n s i n d i c a t e t h a t n e t r a d i a t i o n measurements become i n c r e a s i n g l y l e s s r e p r e s e n t a -t i v e o f s u r f a c e c o n d i t i o n s w i t h i n c r e a s i n g h e i g h t above the s u r f a c e when s u r f a c e t e m p e r a t u r e s a r e s i g n i f i c a n t l y d i f f e r e n t from t h a t o f t he ambient a i r . E x p e r i m e n t a l l y , t h i s e f f e c t was f o u n d to c r e a t e a 7 per c e n t d i s c r e p a n c y between net r a d i a t i o n measured a t 50 cm above a d r y , bare s o i l and t h a t measured a t 215 cm f o r d a y l i g h t hours ( I d s o and C o o l e y , 1971). A s i m i l a r e f f e c t can be a n t i c i p a t e d i n t h e n e t r a d i a t i o n measurements above the urban r o o f s u r f a c e , when s u r f a c e t e m p e r a t u r e s a r e s i g n i f i c a n t l y warmer than t h e ambient a i r t e m p e r a t u r e s . Measurements o f t r u e r o o f - t o p s u r f a c e t e m p e r a t u r e were made w i t h a Barnes s e n s o r d u r i n g the d a y t i m e by i s o l a t i n g the s u r f a c e from sky r a d i a t i o n and a l l o w i n g i t to r a d i a t e as an a p p a r e n t b l a c k b o d y . The 142 method used i s d e s c r i b e d by Fuchs and Ta n n e r ( 1 9 6 6 ) . The r o o f - s u r f a c e t e m p e r a t u r e s t h u s o b t a i n e d were f o u n d to be l a r g e r t h a n 40°C, w h i l e s c r e e n h e i g h t a i r t e m p e r a t u r e s were ~ 20°C. The maximum e f f e c t o f a i r - r o o f s u r f a c e t e m p e r a t u r e d i f f e r e n c e s on t h e e f f e c t i v e o u t g o i n g r a d i a t i o n c o u l d then be d e t e r m i n e d a p p r o x i m a t e l y from the e m p i r i c a l r e l a t i o n s h i p ( b a s e d on t h e d a t a o f R i d e r and Ro b i n s o n (1951)) when s c r e e n h e i g h t i s 1 m and the s u r f a c e e m i s s i v i t y i s assumed e q u a l t o one. ! s " 1 s = 0.205 (upper l i m i t ) (6.2) a T * - T* where a S t e f a n - B o l t z m a n n c o n s t a n t I i s the t r u e e f f e c t i v e o u t g o i n g r a d i a t i o n from t h e s u r f a c e I i s t h e t r u e e f f e c t i v e o u t g o i n g r a d i a t i o n a t s c r e e n h e i g h t T s t e m p e r a t u r e o f the s u r f a c e T ambient t e m p e r a t u r e a t s c r e e n h e i g h t I f we assume a maximum a i r - r o o f s u r f a c e t e m p e r a t u r e d i f f e r e n c e o f 30°C and an ambient t e m p e r a t u r e o f 20°C, i t can be seen t h a t I i s a p p r o x i m a t e l y 4 mWcm"2 g r e a t e r than I. The e f f e c t o f such l a r g e a i r - r o o f s u r f a c e t e m p e r a t u r e d i f f e r e n c e s can then be e x p e c t e d t o produce an o v e r e s t i m a t i o n o f t h e 143 s u r f a c e net r a d i a t i o n o f 4 mWcm"2 when net r a d i a t i o n measure-ments a t the 1 m l e v e l a r e e x t r a p o l a t e d t o the r o o f s u r f a c e . F u r t h e r m o r e , i f we assume t h a t Rn measurements a t the 20 m l e v e l a r e g r e a t e r than t h o s e a t 1 m by 5 per c e n t , t h e net e f f e c t would y i e l d a maximum o v e r e s t i m a t i o n o f r o o f -s u r f a c e Rn o f ~ 7 mWcm"2 when Rn measurements a t 20 m a r e used to r e p r e s e n t s u r f a c e c o n d i t i o n s . Thus, the r e l a t i v e l y l a r g e r e s i d u a l term, d e r i v e d from the heat b a l a n c e e x p r e s -s i o n , can be p a r t l y a t t r i b u t e d t o the e x t r a p o l a t i o n o f Rn a t 20 m to the r o o f s u r f a c e . In t h e r o o f - t o p s u r f a c e e n e r g y b a l a n c e , G v a l u e s were o b t a i n e d from a f l u x p l a t e embedded i n the uppermost g r a v e l and t a r l a y e r o f the r o o f , a p p r o x i m a t e l y 0.5 cm below the s u r f a c e . A c c o r d i n g l y , an u n d e r e s t i m a t i o n o f s u r f a c e G w i l l a r i s e from d i v e r g e n c e e f f e c t s i n the 0.5 cm l a y e r between the p l a t e and the s u r f a c e , d u r i n g t h e da y t i m e . The r o o f s u r f a c e G can be e x p r e s s e d i n the f o l l o w -i n g manner roof s u r f a c e 0-0.5 cm (6.3) + G heat f l u x p l a t e at 0.5 cm where AG i s the change i n heat s t o r a g e i n the top 0.5 cm. No a t t e m p t was made to measure AG. I t s c o n t r i b u t i o n to the 144 r o o f - s u r f a c e v a l u e , however, i s u n l i k e l y to be s i g n i f i c a n t . I t i s n o t e d , f o r i n s t a n c e , t h a t T u r n e r (1969) o b t a i n e d AG v a l u e s f o r the top 0.5 cm i n a c o n c r e t e s l a b t h a t were ~ 10 per c e n t o f the f l u x p l a t e G v a l u e s a t the 0.5 cm de p t h , d u r i n g the d a y t i m e . Thus, i f we assume a s i m i l a r o r d e r o f magnitude e f f e c t f o r the top 0.5 cm o f the r o o f , the use o f G measurements a t the 0.5 cm depth t o r e p r e s e n t s u r f a c e v a l u e s would produce a maximum u n d e r e s t i m a t i o n o f ~ 1 mWcm-2 d u r i n g the d a y t i m e . In a d d i t i o n to d i v e r g e n c e e f f e c t s , e r r o r s o f G may a r i s e from d i f f e r e n c e s i n t h e r m a l c o n d u c t i v i t i e s o f the f l u x p l a t e and the g r a v e l and t a r r o o f medium. The magnitude o f t h i s e f f e c t can be d e t e r m i n e d a p p r o x i m a t e l y from the f o r m u l a g i v e n by P h i l l i p (1961) f = 1/[1 - a r ( l - e " 1 ) ] (6 where f r a t i o o f mean f l u x d e n s i t y t h r o u g h t h e m e t e r t o t h e f l u x d e n s i t y t h r o u g h t h e med i urn e r a t i o o f m e t e r c o n d u c t i v i t y t o medium c o n d u c t i v i t y r r a t i o o f t h e mean m e t e r t h i c k n e s s i n t h e g e n e r a l d i r e c t i o n o f t h e h e a t f l o w t o t h e s q u a r e r o o t o f t h e mean c r o s s -s e c t i o n t h e m e t e r p r e s e n t s n o r m a l t o t h e d i r e c t i o n a a c o n s t a n t , e q u a l t o 1.70 145 For t h e heat f l u x p l a t e , the th e r m a l c o n d u c t i v i t y i s ~ 84.0 mWcm" l 0K - 1 and the v a l u e o f r i s 0.13. I f we assume a ther m a l c o n d u c t i v i t y o f the g r a v e l and t a r medium o f ~ 25.2 mWcnr^K"" 1, the above e q u a t i o n y i e l d s a v a l u e o f f = 1.18. Thus, the heat f l u x measured by the meter i s 18 per c e n t l a r g e r than t h a t t h r o u g h the g r a v e l and t a r medium. S i n c e peak f l u x p l a t e G v a l u e s measured d u r i n g the d a y t i m e were ~ 10 mWcm-2, maximum o v e r e s t i m a t i o n o f G f o r the r o o f - t a r and g r a v e l medium would be ~ 2 mWcm - 2. I t can thu s be seen t h a t e r r o r s o f the r o o f - s u r f a c e G from the use o f the h e a t f l u x p l a t e embedded a t 0.5 cm i n the g r a v e l and t a r medium a r e l i k e l y to be n e g l i g i b l e . The p o s s i b i l i t y o f c o n s i s t e n t u n d e r e s t i m a t i o n o f s u r f a c e s e n s i b l e h e a t f l u x e s by the eddy c o r r e l a t i o n i n s t r u -ment a t 1.2 m above t h e r o o f s u r f a c e d u r i n g t h e d a y t i m e c o u l d n ot be r e a d i l y a s s e s s e d . Some u n c e r t a i n t i e s must e x i s t i n the use o f H v a l u e s a t the 1.2 m l e v e l t o r e p r e -s e n t s u r f a c e c o n d i t i o n s . The complex n a t u r e o f the f l o w i n t h e t u r b u l e n t zone o f the r o o f , i n c l u d i n g a r e t u r n f l o w onto t h e r o o f from n e i g h b o u r i n g s t r e e t canyons may c r e a t e d i f f i c u l t i e s i n the a c t u a l measurement o f the s e n s i b l e h e a t f l o w o f f the r o o f . I t i s not known, however, i f t h i s e f f e c t would produce a s y s t e m a t i c u n d e r e s t i m a t i o n o f H d u r i n g the d a y t i m e . In u s i n g the eddy c o r r e l a t i o n t e c h -n q i u e , i t i s n e c e s s a r y to assume t h a t the v e r t i c a l v e l o c i t y , 146 a v e r a g e d f o r a s u f f i c i e n t time p e r i o d , i s c l o s e to z e r o o v e r the r o o f s u r f a c e . A l t h o u g h some a t t e m p t s were made to d e t e r m i n e w w i t h a v e r t i c a l anemometer, l i t t l e c o n f i d e n c e can be p l a c e d on the a c t u a l m a g nitudes as t h e s e v a l u e s (± 10 c m s - 1 ) were w i t h i n the r e s o l u t i o n c a p a b i l i t y o f the i n s t r u m e n t . I t a p p e a r e d , however, t h a t t h e r e was a t e n d e n c y towards s l i g h t d o w n d r a f t c o n d i t i o n s d u r i n g the d a y t i m e near the r o o f s u r f a c e . A c c o r d i n g l y eddy f l u x measurements o f s e n s i b l e heat would be u n d e r e s t i m a t i n g the s e n s i b l e heat t r a n s p o r t from the r o o f . On the o t h e r hand, the n a t u r e o f t h e o u t p u t from th e yaw s p h e r e - t h e r m o m e t e r a s s e m b l y s u g g e s t s a s l i g h t o v e r e s t i m a t i o n o f the eddy f l u x o f s e n s i b l e h e a t d u r i n g t h e d a y t i m e w i t h s m a l l n e g a t i v e mean v e r t i c a l v e l o c i t i e s . Thus, the e x i s t e n c e o f s m a l l n e g a t i v e w may not have a f f e c t e d the s e n s i b l e heat f l u x measurements to any a p p r e c i a b l e e x t e n t . As an a p p r o x i m a t i o n , i t may thus n o t be u n r e a s o n a b l e to assume no s y s t e m a t i c u n d e r e s t i m a t i o n o f H f o r t h e r o o f s u r f a c e d u r i n g the d a y t i m e . The p r e c e d i n g a n a l y s i s o f e r r o r s a s s o c i a t e d w i t h the use o f Rn, G and H measurements to r e p r e s e n t r o o f s u r f a c e c o n d i t i o n s d u r i n g the d a y t i m e can thus e x p l a i n o n l y p a r t o f the l a r g e r e s i d u a l term n o t e d from the heat b a l a n c e c o n s i d e r a t i o n s . A maximum p o s s i b l e c o n t r i b u t i o n t o t h e r e s i d u a l term from t h e s e e r r o r s i s l i k e l y to be ~ 7 mWcm-2. The r e m a i n i n g p o r t i o n o f the r e s i d u a l term ( e q u a t i o n to LE) 147 would s t i l l be a p p r e c i a b l e . A c c o r d i n g l y , the p o s s i b i l i t y o f l a t e n t heat t r a n s f e r from the r o o f - t o p s u r f a c e i s examined f u r t h e r below. I t i s o f t e n s t a t e d i n t h e l i t e r a t u r e t h a t t h e c i t y has l i t t l e a v a i l a b l e water f o r e v a p o r a t i o n ( f o r example, C h a n d l e r , ( 1 9 6 5 ) , P e t e r s o n ( 1 9 6 9 ) ) . T h i s a s s e s s m e n t i s o f f e r e d on t h e b a s i s t h a t the r e p l a c e m e n t o f n a t u r a l spongy r u r a l s u r f a c e by urban m a t e r i a l s r e n d e r s the s u r f a c e more i m p e r v i o u s to w a t e r . I t i s s u g g e s t e d t h a t p r e c i p i t a t i o n then l e a d s p r i m a r i l y to more r a p i d r u n - o f f . Lacy (1972, p r i v a t e c o m m u n i c a t i o n ) , however, i n d i c a t e s t h a t q u a n t i t a t i v e measurements do not s u p p o r t t h i s . He c i t e s examples from the r e s u l t s o f measurements i n a number o f E n g l i s h towns which show t h a t , on the a v e r a g e , r u n - o f f i s o n l y 40 per c e n t o f the t o t a l r a i n f a l l . Over a t e s t d i s t r i c t , 95 p e r c e n t paved, the r u n - o f f was a bout 50 per c e n t o f t h e r a i n -f a l l . T hese r e s u l t s s u g g e s t t h a t a l a r g e f r a c t i o n o f t h e r a i n f a l l i s a b s o r b e d by unpaved g r o u n d s , by porous m a t e r i a l s o r r e m a i n s as p u d d l e s . T h i s water would s u b s e q u e n t l y be a v a i l a b l e as a s o u r c e f o r e v a p o r a t i o n . I t would th u s seem t h a t the w i d e l y h e l d a s s u m p t i o n t h a t LE << H o v e r an urban a r e a i s u n f o u n d e d . The r e c e n t work o f Oke et al. (1972) i n M o n t r e a l s h o u l d a l s o be n o t e d i n t h i s r e g a r d . The p a r t i t i o n i n g o f e n e r g y between H and LE o v e r a r o o f - t o p s u r f a c e was d e r i v e d 148 from the Bowen r a t i o method, u s i n g t e m p e r a t u r e and wet-b u l b g r a d i e n t s between 2, 4 and 6 m above the r o o f s u r f a c e , and assuming s i m i l a r i t y i n the t r a n s f e r c o e f f i c i e n t s f o r h e a t and water v a p o u r . T h e i r r e s u l t s i n d i c a t e t h a t a g r e a t e r p o r t i o n o f e n e r g y i s used f o r l a t e n t h e a t t r a n s f e r than f o r s e n s i b l e h e a t ( i . e . B < 1) d u r i n g most o f the day-t i m e , and hence LE was found to be an i m p o r t a n t term i n the urban e n e r g y b a l a n c e . . In view o f t h e s e e x p e r i m e n t a l f i n d i n g s , i t i s a p p a r e n t t h a t one may not be j u s t i f i e d i n assuming t h a t the r o l e o f l a t e n t heat t r a n s f e r i n the c i t y i s i n s i g n i f i c a n t . The e x t e n t to which one can g e n e r a l i z e urban a r e a l a t e n t h e a t t r a n s f e r to i n d i v i d u a l r o o f - t o p s u r f a c e s must remain somewhat s p e c u l a t i v e . A l t h o u g h t h e r e were no q u a n t i t a t i v e measurements o f the m o i s t u r e s t a t e o f the r o o f s u r f a c e , i t seems d u b i o u s i f not u n r e a s o n a b l e to e x p e c t such l a r g e l a t e n t h e a t f l o w s d u r i n g the d a y t i m e as shown i n F i g s . 42 and 43. A t the same t i m e , we must e x p e c t some l a t e n t heat t r a n s f e r from the r o o f i f i t i s not t h o r o u g h l y d r y . The l a r g e r e s i d u a l term o b t a i n e d from our r o o f -top e n e r g y b a l a n c e c o n s i d e r a t i o n s may t h e r e f o r e p a r t l y a r i s e from t h e p r e s e n c e o f l a t e n t heat t r a n s f e r and p a r t l y from e r r o r s a s s o c i a t e d w i t h the use o f Rn, 6 and H measurements a t a f i n i t e d i s t a n c e from the a c t u a l r o o f s u r f a c e . 149 In g e n e r a l , t h e r o o f - t o p e n e r g y b a l a n c e showed t h a t t h e major p a r t i t i o n i n g o f the a v a i l a b l e n e t r a d i a t i o n a t midday was i n t o s e n s i b l e h e a t t r a n s f e r . F o r a net r a d i a n t i n p u t o f 60 mWcm"2, G was t y p i c a l l y 10 mWcm"2 and H about 30 mWcm"2. I f the r e s i d u a l e n e r g y was c o n v e r t e d t o l a t e n t h e a t , we o b t a i n a Bowen r a t i o o f 1.5. T h i s v a l u e i s a p p r o x i m a t e l y t w i c e t h a t o f the maximum v a l u e o b t a i n e d f o r the L a d n e r g r a s s s u r f a c e , a t midday. On the o t h e r hand, o v e r e s t i m a t i o n o f s u r f a c e Rn by 7 mWcm"2 would y i e l d midday v a l u e f o r t h e r e s i d u a l term o f 13 mWcm"2. T y p i c a l Bowen r a t i o s f o r the r o o f s u r f a c e would th e n be 2.3, i f t h i s r e s i d u a l e n e r g y was c o n v e r t e d t o l a t e n t h e a t . N o c t u r n a l b a l a n c e . The a p p l i c a b i l i t y o f the n o c t u r n a l e n e r g y f l u x measurements f o r t h e r o o f s u r f a c e needs c a r e f u l c o n s i d e r a -t i o n s . The e x i s t e n c e o f r a d i a t i v e f l u x d i v e r g e n c e a t n i g h t ( e . g . F u g g l e , 1971) p r e s e n t s a d i f f i c u l t y i n e x t r a p o l a t i n g Rn measurements a t 20 m above t h e r o o f t o t h a t o f the r o o f -s u r f a c e . S i m i l a r l y , s e n s i b l e h e a t f l u x d i v e r g e n c e would i n v a l i d a t e a t t e m p t s t o use the H measurements a t the 1.2 m l e v e l as r e p r e s e n t a t i v e o f the u n d e r l y i n g s u r f a c e . I t s h o u l d be no t e d t h a t t h e YST i n s t r u m e n t i s l e s s r e l i a b l e a t 150 n i g h t i f l i g h t winds p r e v a i l . With t h e s e l i m i t a t i o n s i n mind, a b r i e f a s s e s s m e n t o f the n o c t u r n a l s i t u a t i o n i s p r e s e n t e d below. Two examples o f t y p i c a l n o c t u r n a l v a r i a t i o n o f the measured he a t b a l a n c e components a r e shown i n F i g s . 44 and 45. As p r e v i o u s l y n o t e d i n C h a p t e r 5, the n o c t u r n a l s e n s i b l e h e a t f l u x e s remain d i r e c t e d away from the a c t i v e r o o f s u r f a c e t h r o u g h o u t the c o u r s e o f the n i g h t . The mag-n i t u d e s were t y p i c a l l y 5 to 10 mWcm"2. I f we assume t h a t a l l the measured e n e r g y components a r e a p p l i c a b l e t o the r o o f s u r f a c e , i t i s n e c e s s a r y t o s u g g e s t a l a r g e f l o w o f l a t e n t heat to the a c t i v e s u r f a c e a t n i g h t (~ 10 to 15 mWcm"2). T h i s would p r e s u m a b l y r e s u l t i n s i g n i f i c a n t dew f o r m a t i o n on the r o o f s u r f a c e . W h i l e the o c c u r r e n c e o f e x t e n s i v e dew f o r m a t i o n on the r o o f s u r f a c e was o b s e r v e d d u r i n g the l a t t e r p a r t o f Augu s t 1972, t h e r e was no v i s i b l e e v i d e n c e d u r i n g the o b s e r v a t i o n program i n J u l y . The a p p a r e n t l y l a r g e l a t e n t heat t r a n s f e r t o the s u r f a c e a t n i g h t may have a r i s e n from the i n a p p l i c a b i l i t y o f our measurements o f Rn and H f o r s u r f a c e c o n d i t i o n s . However based on the r e s u l t s o f F u g g l e (1971) the Rn d i v e r g e n c e and H c o n v e r g e n c e would te n d to be c o m p l i m e n t a r y . I t i s i n t e r e s t i n g to note t h a t the heat f l o w towards the r o o f s u r f a c e (6) was nev e r g r e a t e r than 3 mWcm"2. T h i s v a l u e i n c l u d e s a measure o f the a r t i f i c i a l h eat f l o w towards 151 20 CN I E u E 10 to LLl Q X 0 >-ai. ULi - 1 0 VANCOUVER, B.C. V.S.B. BLDG. JULY 24-25, 1972 H: 1.2m ABOVE ROOF / RESIDUAL (LE) | WIND U 1 - 2 (m/s) -201-1.5 1.1 1-2 1.1 1.2 1.1 1.1 1.1 1.3 1-5 DIR MISSING L 20 22 J U L Y 24 24 02 04 06 J U L Y 25 J F i g . 44 CN I E o E^ > to z X Z3 > LU 20 10 - 1 0 08 10 TIME (PST) N o c t u r n a l r o o f - t o p e n e r g y b a l a n c e . VANCOUVER, B.C. V.S.B. BLDG. JULY 27-28, 1972 H : 1.2 m ABOVE ROOF _ S RESIDUAL (LE) WIND -20 L 1 2 0.5 0.5 0.8 0.6 0.5 0.5 0.5 0.5 0.8 0.5 DIR MISSING I 1 1 1 I L 20 22 24 J U L Y 27 02 04 J U L Y 28 06 ± J 08 10 TIME (PST) F i g . 45. N o c t u r n a l r o o f - t o p e n e r g y b a l a n c e . 152 the r o o f s u r f a c e , and hence i t can be c o n c l u d e d t h a t a r t i -f i c i a l h eat t h r o u g h t he r o o f does not s i g n i f i c a n t l y c o n -t r i b u t e to t h e r o o f - t o p e n e r g y b a l a n c e a t n i g h t . Energy B a l a n c e o f an Urban A r e a A l t h o u g h we may r e a d i l y s p e c i f y the g o v e r n i n g e n e r g y b a l a n c e e x p r e s s i o n f o r a l i m i t e d u r b a n - b u i l d i n g a i r volume, the t h r e e - d i m e n s i o n a l n a t u r e o f the p r o b l e m remains most f o r m i d a b l e ( s e e F i g . 2 ) . Some o f t h e s e c o m p l e x i t i e s may be a v o i d e d i f we can assume t h a t h o r i z o n t a l a d v e c t i o n and a r t i f i c i a l h eat g e n e r a t i o n a r e s m a l l w i t h i n the a r e a o f c o n c e r n . As an a p p r o x i m a t i o n , t h e s e a s s u m p t i o n s do not a p p e a r u n r e a s o n a b l e based on the s i t e c h a r a c t e r i s t i c s and a r t i f i c i a l h e a t c o m p u t a t i o n s . E x p e r i m e n t a l measurements of the e n e r g y b a l a n c e components o v e r a l i m i t e d urban a r e a t h e n become b a s i c a l l y a s p a t i a l p r o b l e m and a l l terms i n the h e a t b a l a n c e e x p r e s s i o n must r e f e r t o s p a t i a l l y i n t e g r a t e d a v e r a g e s . T h i s , however, i s s t i l l e x t r e m e l y d i f f i c u l t t o a c h i e v e , p a r t i c u l a r l y i n the measurement o f Rn and 6. M e a n i n g f u l e s t i m a t e s o f Rn s h o u l d i n c l u d e measurements above the s t r e e t canyons and r o o f s u r f a c e s . S i m i l a r l y , the measurement o f G must r e p r e s e n t an i n t e g r a t e d v a l u e f o r the v a r i o u s c i t y f a b r i c s o v e r the t h r e e - d i m e n s i o n a l s o l i d s u r f a c e a r e a . On the o t h e r hand, measurement o f LE 1 o r H o v e r the l i m i t e d urban a r e a may be a c h i e v e d from p o i n t measurements, p r o v i d e d t h a t t h e s e a r e made a t a h e i g h t above the l o c a l r o o f - t o p boundary l a y e r . At t h i s h e i g h t , we assume t h a t l o c a l i n h o m o g e n e i t i e s i n t h e s e n s i b l e and l a t e n t heat f l u x e s become i n s i g n i f i c a n t i n c o m p a r i s o n to t h e m e s o - s c a l e urban boundary l a y e r f l u x e s . The t u r b u l e n t eddy f l u x e s s h o u l d then be r e p r e s e n t a t i v e o f s p a t i a l l y i n t e g r a t e d v a l u e s . We s h a l l now examine our measurements i n t h i s c o n t e x t . In t h i s s t u d y , both Rn and G were d e r i v e d from p o i n t measurements. A c c o r d i n g l y , t h e i r u s e f u l n e s s i n t h e e n e r g y b a l a n c e e x p r e s s i o n f o r an urban a r e a a p p e a r s some-what d o u b t f u l . The measurement o f Rn a t 20 m above the urban r o o f s u r f a c e does p r o v i d e a good h o r i z o n t a l f i e l d -o f - v i e w t h a t i n c l u d e s the urban r o o f s u r f a c e , as w e l l as s t r e e t c a n y o n s , but the r a d i a n t e n e r g y r e c e i v e d by the s e n s o r from below r e f l e c t s p r i m a r i l y t h a t f r a c t i o n e m i t t e d by the immediate u n d e r l y i n g s u r f a c e , namely, the r o o f - t o p . The h o r i z o n t a l a r e a c o n t r i b u t i n g to 90 per c e n t o f the f l u x measured by the net r a d i o m e t e r a t 20 m above the r o o f en-compasses a c i r c l e o f r a d i u s equal to 60 m. G e n e r a l i z a t i o n o f t h e s e Rn r e s u l t s to t h a t o v e r the s t r e e t canyons may not be j u s t i f i e d , e s p e c i a l l y i n s i t u a t i o n s where l a r g e shadow a r e a s o c c u r a t s t r e e t l e v e l . As the net r a d i a t i o n f i e l d above s t r e e t canyons has not been p r e v i o u s l y i n v e s t i g a t e d i n any d e p t h , i t s c o n t r i -b u t i o n to the s p a t i a l l y i n t e g r a t e d Rn v a l u e o v e r an urban a r e a can o n l y be t r e a t e d q u a l i t a t i v e l y . The r e c e n t model o f the e f f e c t o f the t r a p p i n g o f s o l a r r a d i a t i o n by the c a nyon, advanced by C r a i g and Lowry ( 1 9 7 2 ) , s u g g e s t s t h a t the canyon l o w e r s the urban a l b e d o . Hence, we m i g ht e x p e c t an i n c r e a s e i n the e f f e c t i v e net s o l a r r a d i a t i o n above the s t r e e t canyon compared w i t h t h a t o v e r an open h o r i z o n t a l r o o f s u r f a c e . S i m i l a r l y , the e f f e c t i v e o u t g o i n g long-wave r a d i a t i o n from the canyon can be e x p e c t e d to be somewhat r e d u c e d i n c o m p a r i s o n w i t h t h a t o f an open h o r i z o n t a l s u r f a c e b ecause o f the v e r t i c a l w a l l s (Munn, 1966). These two p r o c e s s e s a r e l i k e l y to enhance the net r a d i a t i o n above the s t r e e t c a n y o n . In the a bsence o f q u a n t i f i a b l e e s t i m a t e s o f t h e s e e f f e c t s , we can o n l y s u g g e s t t h a t our p o i n t - m e a s u r e -ment o f Rn above the r o o f s u r f a c e i s l i k e l y to be some-what lower than t h a t o f a s p a t i a l l y i n t e g r a t e d a v e r a g e Rn f o r t h e s u r r o u n d i n g urban a r e a . The r o o f - t o p G measurements a r e o n l y i n d i c a t i v e o f one urban f a b r i c i n a h o r i z o n t a l p o s i t i o n , and c a n n o t be used s o l e l y to a r r i v e a t an e s t i m a t e o f s p a t i a l l y i n t e -g r a t e d v a l u e s o f G f o r the t h r e e - d i m e n s i o n a l s y s t e m . A s p a t i a l l y i n t e g r a t e d a v e r a g e o f G i s t h e r e f o r e v e r y d i f f i c u l t to a c h i e v e , but s i n c e we do have s i m u l t a n e o u s measurements 155 o f G i n t a r and c o n c r e t e s l a b s , p l a c e d h o r i z o n t a l l y on t h e urban r o o f s u r f a c e , we may be a b l e to i n d i c a t e upper l i m i t s to an a v e r a g e G v a l u e f o r the urban a r e a . An example o f the d i u r n a l b e h a v i o u r o f G i n v a r i o u s u rban f a b r i c s i s shown i n F i g . 46. The v a l u e s f o r c o n c r e t e and t a r were o b t a i n e d from s o i l heat f l u x p l a t e s embedded i n s l a b s o f the r e s p e c t i v e m a t e r i a l s p l a c e d on the urban r o o f s u r f a c e . I t can be seen t h a t the heat s t o r e d i n the t a r b l o c k i s q u i t e a p p r e c i a b l e ( a p p r o x i m a t e l y 70 per c e n t h i g h e r than t h a t o f the urban r o o f s u r f a c e ) . On t h i s p a r t i c u l a r day, G i n t h e t a r b l o c k was about 25 per c e n t o f the n e t r a d i a t i o n a t midday. I t i s n o t u n r e a s o n a b l e to s u g g e s t t h a t the G v a l u e f o r the t a r b l o c k p r o v i d e s an upper l i m i t to the amount o f e n e r g y t h a t can be s t o r e d o v e r the t h r e e - d i m e n s i o n a l s o l i d s u r f a c e d u r i n g the d a y t i m e . The a c t u a l s p a t i a l l y a v e r a g e d G w i l l be s i g n i f i c a n t l y l ower than t h i s upper l i m i t when the urban f a b r i c s o f v a r y i n g t h e r m a l c a p a c i t i e s a r e a l l t a k e n i n t o a c c o u n t . The s e n s i b l e heat f l u x v a r i a t i o n a t h e i g h t s o f 4 and 20 m above the urban r o o f s u r f a c e was p r e s e n t e d i n the p r e v i o u s c h a p t e r . As t h e s e measurements were c o n d u c t e d above the l o c a l r o o f - t o p boundary l a y e r , t h e y may be assumed i n d i c a t i v e o f s p a t i a l l y i n t e g r a t e d a v e r a g e s . A n o t h e r example o f the H measurements f o r the 4 m l e v e l above the r o o f i s g i v e n i n F i g . 47, a l o n g w i t h the p o i n t measurements F i g . 46. D i u r n a l b e h a v i o u r urban f a b r i c s . o f G i n v a r i o u s VANCOUVER, B.C. V.S.B. BLDG. JULY 5, 1972 Rn H : 4m ABOVE ROOF U R B A N A -I R O O F -10*- WIND U 4 (M/S) 2.1 2.7 3.2 3.1 2 . 2 2.9 2.5 1.9 2.1 1.8 1.4 I 1 1 1 1 I I I 06 08 10 12 14 16 18 20 TIME (PST) F i g . 47. Urban s e n s i b l e heat f l u x e s and p o i n t measurements o f Rn and G. 158 o f Rn and o f the r o o f - t o p G. In g e n e r a l , midday v a l u e s o f urban H were ~ 20 to 25 mWcm-2, when Rn was 60 mWcm"2. I f we c o n s i d e r t h i s p o i n t measurement o f Rn t o be the lo w e r l i m i t o f an a r e a l l y i n t e g r a t e d a v e r a g e , we can p e r f o r m t h e f o l l o w i n g a n a l y s i s f o r the ene r g y b a l a n c e o f the urban a r e a . As an extreme c a s e , l e t us assume the upper l i m i t o f an av e r a g e G i d e n t i c a l to t h a t t y p i c a l l y i n the t a r b l o c k a t midday ( i . e . ~ 15 mWcm - 2). The urban e n e r g y b a l a n c e then y i e l d s a r e s i d u a l term ( t a k e n to be LE) o f - 20 t o 25 mWcm-2. Thus, the r e s u l t would i n d i c a t e a p p r o x i m a t e l y equal p a r t i t i o n i n g o f the heat u t i l i z a t i o n between s e n s i b l e and l a t e n t h e a t t r a n s f e r ( i . e . B ~ 1) aroun d noon. These v a l u e s o f Rn and G a r e c o n s i d e r e d extreme l i m i t s . A c c o r d -i n g l y * i f we assume H to be c o r r e c t , we can a n t i c i p a t e LE to be s l i g h t l y l a r g e r than H i n the r e a l s i t u a t i o n f o r the urban a r e a a t midday. T h i s b r i e f a n a l y s i s p r o v i d e s some i n s i g h t i n t o t h e energy p a r t i t i o n i n g o v e r an urban a r e a . The r e s u l t s a r e c o n s i s t e n t w i t h s i m i l a r f i n d i n g s from the ene r g y b a l a n c e e s t i m a t i o n s o v e r M o n t r e a l (Oke et al. 3 1 97 2 ) . C h a p t e r 7 SUMMARY OF CONCLUSIONS A yaw s p h e r e - t h e r m o m e t e r assembly ( Y S T ) , to measure s e n s i b l e h e a t f l u x d e n s i t y by the eddy c o r r e l a t i o n method, was b u i l t f o l l o w i n g t h e d e s i g n o f T a n n e r and T h u r t e l l ( 1 9 7 0 ) . From wind t u n n e l e x p e r i m e n t s the 'sphere c o n s t a n t ' was d e t e r m i n e d to be 1.57. T h i s v a l u e i s s i g n i f i c a n t l y l e s s than t h a t p r e d i c t e d t h e o r e t i c a l l y , namely, 2.25. I t i s i m p o r t a n t t h a t the yaw s p h e r e a p p r o a c h be m o d i f i e d to i n c l u d e an e x p e r i m e n t a l l y d e t e r m i n e d 'sphere c o n s t a n t . ' A n a l y s i s o f t h e e f f e c t s o f t i l t i n g t h e yaw s p h e r e a x i s i n d i c a t e s t h a t an e r r o r f o a p p r o x i m a t e l y 5 per c e n t per d e g r e e o f t i l t i s l i k e l y w i t h m o d e r a t e l y u n s t a b l e c o n d i t i o n s . T h i s e r r o r may a t t a i n 11 per c e n t per d e g r e e i n v e r y s t a b l e c o n d i t i o n s . A m o d i f i e d thermometer assembly was f o u n d n e c e s s a r y to p r o v i d e d u r a b i l i t y i n the f i e l d . In the f r e -quency domain the t u r b u l e n t heat f l u x c o u l d be measured t o an upper f r e q u e n c y l i m i t o f 8 Hz w i t h o u t s i g n i f i c a n t a t t e n u -a t i o n . F i e l d c o m p a r i s o n s o f the heat f l u x e s measured by the yaw s p h e r e - t h e r m o m e t e r system and a Bowen r a t i o a p p a r a t u s 159 160 p r o d u c e d s a t i s f a c t o r y agreement. Daytime c u m u l a t i v e s e n s i b l e h e a t f l u x d e n s i t i e s i n d i c a t e t h a t the d i f f e r e n c e between the two methods i s g e n e r a l l y l e s s than 10 per c e n t . D i r e c t measurements o f s e n s i b l e heat f l u x e s o v e r a g r a s s s u r f a c e a t L a d n e r , B.C. i n d i c a t e a d i u r n a l c o u r s e v e r y s i m i l a r to t h a t o f the net r a d i a t i o n . In g e n e r a l , h a l f - h o u r a v e r a g i n g p e r i o d s showed no phase l a g between s e n s i b l e heat and net r a d i a t i o n . F i e l d c o m p a r i s o n o f two YST systems gave good and c o n s i s t e n t agreement. A t a h e i g h t o f 2 m above ground and a h o r i z o n t a l c r o s s w i n d s e p a r a -t i o n o f 1.5 m, l e s s than 5 per c e n t v a r i a b i l i t y was n o t e d i n the heat f l u x measurements from the two systems. F o r a 19 m h o r i z o n t a l s e p a r a t i o n , the v a r i a b i l i t y was f o u n d t o be l e s s t h a n 20 per c e n t . These r e s u l t s g i v e s u p p o r t t o the b a s i c a s s u m p t i o n t h a t the s e n s i b l e heat f l u x i s r e l a -t i v e l y c o n s t a n t i n t he a t m o s p h e r i c boundary l a y e r . I t i s shown t h a t the p a r a m e t e r (a), advanced by P r i e s t l e y and T a y l o r ( 1 9 7 2 ) , can be a u s e f u l c l i m a t i c i n d i c a t o r , and hence l a r g e s c a l e p a r a m e t e r i z a t i o n o f s u r f a c e heat f l u x e s a p p e a r s e n c o u r a g i n g . The p a r t i t i o n i n g o f e n e r g y between s e n s i b l e and l a t e n t heat ( i . e . the Bowen r a t i o ) d u r i n g June and e a r l y J u l y 1972 shows a t e m p e r a t u r e dependence s i m i l a r to t h a t o f a s a t u r a t e d s u r f a c e w i t h an a l p h a v a l u e between a p p r o x i m a t e l y 1.00 and 1.10. 161 The a p p l i c a b i l i t y o f the eddy c o r r e l a t i o n t e c h n i q u e to the measurement o f s e n s i b l e heat t r a n s f e r between the atmosphere and the urban i n t e r f a c e i s d e m o n s t r a t e d f o r a l i m i t e d a r e a o f the c i t y o f V a n c o u v e r , B.C. D e s p i t e t h e enormous c o m p l e x i t i e s o f the t u r b u l e n t heat exchange p r o -c e s s e s , the urban s e n s i b l e heat f l u x p a t t e r n , o b t a i n e d d i r e c t l y a t h e i g h t s o f 1.2, 2, 4 and 20 m above r o o f - t o p l e v e l , l a r g e l y r e f l e c t e d time and magnitude changes i n the net r a d i a t i o n f i e l d d u r i n g the d a y t i m e . N o c t u r n a l urban s e n s i b l e heat f l u x e s , near r o o f - t o p l e v e l , were f o u n d t o be d i r e c t e d away from the a c t i v e s u r f a c e . T h i s i s r e v e r s e of t h e normal r u r a l c a s e . W i t h i n the l o c a l r o o f - t o p boundary l a y e r , t h e s e n s i b l e heat f l u x was f o u n d t o be a p p r o x i m a t e l y c o n s t a n t w i t h h e i g h t and space (20 per c e n t v a r i a t i o n ) d u r i n g t h e d a y t i m e . A t n i g h t , the e x i s t e n c e of f l u x d i v e r g e n c e and hence, n o n - c o n s t a n c y o f the heat f l u x , i s s u g g e s t e d . Daytime r o o f - t o p e n e r g y b a l a n c e i n d i c a t e s t h a t a s i g n i f i c a n t p o r t i o n o f the net r a d i a t i o n i s u t i l i z e d i n s e n s i b l e h e a t t r a n s f e r and i n hea t s t o r a g e i n the r o o f . The g r e a t e s t e n e r g y i s used i n s e n s i b l e heat t r a n s f e r , which i s about t h r e e times the heat s t o r a g e a t noon. A r t i f i c i a l e n e r g y f l u x d e n s i t y a p p e a r s to be i n s i g n i f i c a n t . With t y p i c a l v a l u e s o f net r a d i a t i o n o f 60 mWcm"2, the s e n s i b l e heat f l u x i s about 30 mWcm-2 and the heat s t o r a g e 162 10 mWcm"2. The r e s i d u a l term ( e q u a t e d t o l a t e n t h e a t ) i s a p p r e c i a b l e . On t h e o t h e r hand, t h e e r r o r s a s s o c i a t e d w i t h t h e use o f ne t r a d i a t i o n measurements to r e p r e s e n t a c t u a l s u r f a c e c o n d i t i o n s c o u l d have r e s u l t e d i n an o v e r e s t i m a t i o n o f t h e r e s i d u a l term up t o 7 mWcm-2. A c c o r d i n g l y , i f the s e n s i b l e h e a t f l u x measurements a r e n o t s y s t e m a t i c a l l y b i a s e d and the s t o r a g e term e r r o r s a r e s m a l l , the r e s i d u a l e n e r g y , c o n v e r t e d t o l a t e n t h e a t , would be 13 mWcm"2 a t midday. T h i s would the n y i e l d a Bowen r a t i o f o r t h e r o o f -top s u r f a c e o f 2.3. I t would seem t h a t t h e r o l e o f l a t e n t h e a t t r a n s f e r f o r t h e r o o f - s u r f a c e needs f u r t h e r i n v e s t i -g a t i o n . The n o c t u r n a l r o o f - t o p e n e r g y b a l a n c e r e q u i r e d a l a t e n t h e a t term o f about 15 mWcm"2 d i r e c t e d towards the a c t i v e s u r f a c e . The e n e r g y b a l a n c e o f the s u r r o u n d i n g a r e a was deduced from measurements o f s e n s i b l e h e a t f l u x and net r a d i a t i o n a t h e i g h t s above the r o o f - t o p boundary l a y e r . On t h e a s s u m p t i o n t h a t t h e s e p o i n t measurements a p p r o x i -m a t e l y r e f l e c t a r e a l l y i n t e g r a t e d a v e r a g e s , p a r t i t i o n i n g o f t h e heat between s e n s i b l e and l a t e n t heat y i e l d s a Bowen r a t i o o f ~ 1 a t midday. The c i t y does not app e a r to a c t as a " d e s e r t " as has sometimes been s u g g e s t e d . I t would seem t h a t t h e r o l e o f l a t e n t h e a t t r a n s f e r i s impor-t a n t f o r urban e n e r g y b a l a n c e c o n s i d e r a t i o n s . The a c c u r a t e d e t e r m i n a t i o n o f the e n e r g y b a l a n c e f o r an urban a r e a 163 remains o u t s t a n d i n g . T h i s t a s k can o n l y be a c c o m p l i s h e d by some means o f o b t a i n i n g s p a t i a l l y i n t e g r a t e d a v e r a g e s o f a l l the ene r g y b a l a n c e components. Such a f o r m i d a b l e and e s s e n t i a l t a s k was beyond the scope o f t h i s r e s e a r c h u n d e r t a k i ng. S u g g e s t i o n s f o r F u t u r e Work From t h i s r e s e a r c h , many q u e s t i o n s have been r a i s e d which w a r r a n t more a t t e n t i o n . Some o f t h e s e a r e o f f e r e d here as s u g g e s t i o n s f o r f u t u r e work. 1. The s p a t i a l v a r i a b i l i t y o f s e n s i b l e h e a t f l u x e s i n the a t m o s p h e r i c boundary l a y e r o v e r a f l a t u n i f o r m s u r f a c e s h o u l d be f u l l y examined. E x t e n s i v e and r e l i a b l e d a t a a r e r e q u i r e d to t e s t t h e f u n d a m e n t a l h y p o t h e s i s o f t h e c o n s t a n t f l u x l a y e r . 2. The pa r a m e t e r ( a ) , advanced by P r i e s t l e y and T a y l o r (1972) s h o u l d be i n v e s t i g a t e d f u r t h e r , to d e t e r m i n e i t s u s e f u l n e s s as a c l i m a t i c i n d i c a t o r and i n l a r g e s c a l e p a r a m e t e r i z a t i o n o f s u r f a c e h e a t f l u x e s o v e r v a r i o u s s u r f a c e s . T h i s c o u l d p r o v e most u s e f u l i n n u m e r i c a l m o d e l i n g o f t h e l a r g e r s c a l e a t m o s p h e r i c d y n a m i c s . 164 3. The s i g n i f i c a n t f r e q u e n c y domain f o r urban s e n s i b l e h e a t f l u x e s remains o u t s t a n d i n g . A d e t a i l e d s t u d y of the urban s e n s i b l e heat f l u x c o s p e c t r u m v i a o t h e r eddy c o r r e l a t i o n i n s t r u m e n t s ( e . g . a c o u s t i c anemometer-thermometer) i s s u g g e s t e d . F u r t h e r m o r e , the i n t e g r a t e d urban c o s p e c t r u m c o u l d then be compared w i t h s i m u l t a n e o u s measurements from the yaw s p h e r e - t h e r m o m e t e r s y s t e m . 4. The e f f e c t o f r a d i a t i v e exchanges between b u i l d i n g e l e m e n t s , and shadow a r e a s remain a r e a s f o r i n -v e s t i g a t i o n . E x t e n s i v e r a d i a t i o n measurements, w i t h i n an urban c a n y o n , may p r o v i d e i n s i g h t i n t o t h i s f o r m i d a b l e p r o b l e m . 5. Heat s t o r a g e o r r e l e a s e i n the v a r i o u s c i t y b u i l d i n g m a t e r i a l s ( i n c l u d i n g shadow a r e a s ) d e s e r v e s much a t t e n t i o n . A s p a t i a l a v e r a g i n g p r o c e d u r e , o v e r t h e t h r e e -d i m e n s i o n a l s u r f a c e o f an urban c a n y o n , i s s u g g e s t e d as an i n i t i a l a p p r o a c h t o t h i s t a s k . 6. S t u d i e s o f t h e c o u p l i n g between the e n e r g e t i c p r o c e s s e s a t s t r e e t l e v e l and t h o s e a t r o o f - l e v e l and above, a r e r e q u i r e d . 165 7. In t h i s s t u d y , the m agnitudes o f d i v e r g e n c e t e r m s , h e a t s t o r a g e i n the a i r and l a t e n t heat s t o r a g e f o r the l i m i t e d urban b u i l d i n g - a i r volume were c o n s i d e r e d n e g l i g i b l e . The v a l i d i t y o f t h e s e a s s u m p t i o n s needs to be e x p l o r e d . 8. The r o l e o f l a t e n t heat t r a n s f e r i n urban e n e r g y b a l a n c e s t u d i e s w a r r a n t s more a t t e n t i o n . 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APPENDIX A SAMPLE CALCULATION OF THE SENSIBLE HEAT FLUX The s e n s i b l e heat f l u x e x p r e s s i o n f o r t h e yaw s p h e r e - t h e r m o m e t e r system i s g i v e n by e q u a t i o n 3.5. H * C p C b C s i n e j G B M ] " 1 E 0 / u where C : the s p e c i f i c heat a t c o n s t a n t p r e s s u r e p (1 .01 J g - l 0 K - M b : sp h e r e c o n s t a n t (1.57) 6 : the i n c l u d e d a n g l e between t h e p o r t s (45°) G : a m p l i f i e r g a i n B : b r i d g e c o n s t a n t M : t r a n s d u c e r c o n s t a n t E"0 : i n t e g r a t e d o u t p u t v o l t a g e from the b r i d g e u : mean h o r i z o n t a l wind speed T r a n s d u c e r C o n s t a n t (M) T h i s c o n s t a n t i s o b t a i n e d from t h e s p e c i f i c a t i o n s o f the B a r o c e l and i t s e l e c t r o n i c s . I t i s g i v e n by the f o l l o w i n g e x p r e s s i o n 174 175 f u l l s c a l e M = ( r a n g e s w i t c h p o s i t i o n ) ( p r e s s u r e r a n g e ) where f u l l s c a l e = 10 v o l t s p r e s s u r e range = 10 mb = 101* dyne cm" range s w i t c h p o s i t i o n ( e . g . 0.03, 0.01, 0.003, 0.001) Thus, f o r a range s w i t c h p o s i t i o n o f 0.003 B r i d g e C o n s t a n t (B) The b r i d g e c i r c u i t i s shown i n F i g . 48. i s the v o l t a g e a p p l i e d to the b r i d g e ( i . e . the h i - p a s s f i l t e r e d a n a l o g p r e s s u r e s i g n a l ) and E 0 i s t h e b r i d g e o u t p u t ( t h e i m b a l a n c e ) . A c c o r d i n g l y , M = 1/3 v o l t s cm 2dyne -1 AT E. Ri + Ri» + R 3 where a To = c o e f f i c i e n t o f r e s i s t a n c e o f the thermometer at T 0 (0.0033 ° K " 1 ) 176 177 B _ Ri, + R 3 (where R r e f e r s to t h e Ri + Ri* + R 3 a p p r o p r i a t e r e s i s t a n c e s shown i n F i g . 48) Thus, f o r a b r i d g e b a l a n c e o f Ri» = 650ft ( i . e . the thermometer r e s i s t a n c e o f 1950ft) B = 1.53 x 10"" ° K - 1 Example U s i n g the v a l u e s o f M and B above and an a m p l i f i c a t i o n g a i n (G) o f 290 H * 614 x 1 0 2 % u E 0 i n v o l t s fu" i n cms" 1 H i n mWcm"2 Thus, w i t h a 30 min a v e r a g e E 0 v a l u e o f 0.0901 v o l t s and a mean wind speed (u) o f 296 cms" 1 a t noon H = 18.6 mWcnr 2 

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