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The energy balance of an urban canyon Nunez, Manuel 1974

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THE ENERGY BALANCE OF AN URBAN CANYON by MANUEL NUNEZ B . S c , U n i v e r s i t y o f M o n t r e a l , 1963 M.Sc , McMaster U n i v e r s i t y , 1971 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Geography We ac c e p t t h i s t h e s i s as conforming t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA December, 1974 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shal make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shal not be alowed without my written permission. Department of The University of British Columbia Vancouver 8, Canada Date A B S T R A C T A review of the l i t e r a t u r e i n d i c a t e s t h a t t h e r e a r e d e f i c i e n c i e s i n n u m e r i c a l models which d e s c r i b e the s e n s i b l e heat f l u x a t the complex urban i n t e r f a c e . S i m i l a r l y , e x p e r i -mental t e c h n i q u e s a r e not a p p l i c a b l e t o the urban a r e a (e.g., Bowen's r a t i o , aerodynamic methods) or can o n l y be a p p l i e d a t a s u f f i c i e n t h e i g h t above the roughness elements (eddy c o r r e -l a t i o n ) . T h i s study i n v e s t i g a t e s an e x p e r i m e n t a l approach t o c a l c u l a t i n g the s e n s i b l e heat f l u x f o r c l o u d l e s s s k i e s and l i g h t winds. Using the energy balance a t the s u r f a c e , t h i s term i s o b t a i n e d as a r e s i d u a l i f t h e o t h e r terms a r e measured. The experiment was conducted i n what was c o n s i d e r e d to be the e s s e n t i a l u n i t o f the urban s t r u c t u r e : the 'urban canyon 1 c o n s i s t i n g of .the combination o f w a l l s and ground ( s t r e e t ) , and the a i r volume c o n t a i n e d between two a d j a c e n t b u i l d i n g s . I f the f l u x e s o f s e n s i b l e heat a r e known a t the t h r e e canyon s u r f a c e s , then the s e n s i b l e heat r e l e a s e d t o or from the atmos-phere i s o b t a i n e d i f proper c o n s i d e r a t i o n i s g i v e n t o a d v e c t i o n and heat s t o r a g e change i n the c a n y o n - a i r volume. The canyon chosen was l o c a t e d i n c e n t r a l Vancouver, B.C., was a l i g n e d North-South and c o n s i s t e d o f two c o n c r e t e food p r o c e s s i n g p l a n t s , p a i n t e d white and se p a r a t e d by a c l a y -base f l o o r covered by g r a v e l . The canyon was approximately 8 m i n width, 6 m i n h e i g h t and 79 m i n l e n g t h . A boom was i n -s t a l l e d a c r o s s the canyon top and served as a trackway f o r a movable c a r r i a g e and a v e r t i c a l mast. E i g h t net r a d i o -meters and thermocouple a i r temperature sensors were mounted on the mast, and seventeen subsurface f l u x p l a t e s were i n -s t a l l e d on the canyon w a l l s and ground. A l y s i m e t e r measured the s u r f a c e water l o s s . In a d d i t i o n to these measurements, s p e c i a l experiments were conducted t o i n v e s t i g a t e the i n d i v i -d u a l r o l e s o f a d v e c t i o n , s o l a r r a d i a t i o n and su b s u r f a c e heat st o r a g e i n the canyon. R e s u l t s i n d i c a t e t h a t the s o l a r r a d i a t i o n r e -c e i v e d along the w a l l s i s a f u n c t i o n o f the s o l a r z e n i t h and azimuth a n g l e . The average s o l a r f l u x r e c e i v e d by each can-yon s u r f a c e i s c h a r a c t e r i z e d by a peak; w i t h added secondary maxima on each w a l l c o r r e s p o n d i n g to p e r i o d s o f maximum i r r a -d i ance on the o p p o s i t e w a l l . The albedo o f the canyon system shows two d i s t i n c t peaks a t the times o f maximum i r r a d i a n c e o f the white w a l l s . A t noon the albedo o f the canyon system approximates t h a t o f the canyon f l o o r . Both the net r a d i a t i o n and s u b s u r f a c e heat f l u x respond to s o l a r r a d i a t i o n d u r i n g the day and thus a s i m i l a r dependence on s o l a r z e n i t h and azimuth angle i s observed f o r these q u a n t i t i e s . At n i g h t the net long-wave r a d i a t i o n a t l o c a t i o n s i n the canyon v a r i e s l i n e a r l y v/ith the sky view f a c t o r . The t r a n s p o r t of heat by a d v e c t i o n i n t o o r out of the canyon a i r volume depends t o a l a r g e e x t e n t on the i v wind f i e l d . With winds ^2 m s on c l o u d l e s s days, the net a d v e c t i o n g i v e s r i s e to an upward f l u x o f approximately 7 0 -2 -1 W m . With winds o f 1 m s the co r r e s p o n d i n g a d v e c t i o n -2 i s 15 W m . In the absence o f s t r o n g a d v e c t i v e f l u x e s , the p a r t i t i o n i n g o f the r a d i a n t energy, a c r o s s the canyon top, and a t s o l a r noon on a c l e a r summer day i s as f o l l o w s : n e t _2 a l l wave r a d i a t i o n f l u x : 510 W m , s e n s i b l e heat f l u x : 320 -2 -2 W m , l a t e n t heat f l u x : 50 W m , s u b s u r f a c e heat f l u x ; 140 W m ^. At n i g h t the wind f i e l d drops below 1 m s ^ and a balance i s e s t a b l i s h e d between the net r a d i a t i o n d e f i c i t and the s u b s u r f a c e heat f l u x which flows towards the c a n y o n - a i r — 2 volume. 'Typical v a l u e s f o r both are 60 W m a t the canyon top. Both the s e n s i b l e and l a t e n t heat f l u x e s a r e c l o s e t o zero. Measurements i n d i c a t e t h a t under these n o c t u r n a l con-d i t i o n s , the volume d i v e r g e n c e of net r a d i a t i o n i s the main c o o l i n g mechanism f o r the can y o n - a i r volume. The c o o l i n g may a l s o be approximated by the Brunt formula curve which employs a mean canyon s u r f a c e admittance and a net r a d i a t i o n a c r o s s the canyon top. A m o d e l l i n g scheme i s d e v i s e d which c a l c u l a t e s s o l a r r a d i a t i o n as the main energy source d u r i n g p e r i o d s o f sunny s k i e s and l i g h t winds. Linkages are then sought, v i a canyon measurements, between the net s o l a r r a d i a t i o n , the net a l l - w a v e r a d i a t i o n and the subsurface heat f l u x . The s e n s i b l e heat f l u x i s the end r e s u l t . The r e s u l t s appear V promising, although more measurements are needed over a v a r i e t y of urban s u r f a c e s . TABLE OF CONTENTS Page ABSTRACT . . . . i i LIST OF TABLES , , . . . i x LIST OF FIGURES . . . „ „ . . * LIST OF SYMBOLS x i v ACKNOWLEDGEMENTS x x v CHAPTER 1 INTRODUCTION . . . . . . . . . . . . . 1 A. APPROACHES TO FLUX ESTIMATION IN URBAN AREAS . . 1 B. RESEARCH APPROACH 7 C. OBJECTIVES . . . . . . 13 2 SITE, INSTRUMENTATION AND DATA ACQUISITION 15 A. GEOGRAPHIC SITUATION . . . . . . . . 15 1. Vancouver Region and Climate . . . . . . . . 15 2. Urban Canyon Experimental S i t e . . . . . . . 17 B. INSTRUMENTATION. . . . . . . . . . . . . . , o . . . 24 1. Solar Radiation 24 2. Net All-wave Radiation . . . . . . . . . . . 25 3. A i r Temperature 26 4. Subsurface Heat Storage 27 5. Experimental Arrangement i n the Canyon . . . 30 C. DATA ACQUISITION 31 D. OBSERVATION PERIOD . . . . . . . . 33 3 SOLAR RADIATION EXCHANGES IN THE CANYON. . . . . . . 35 A. INTRODUCTION . . . . . . 35 1. General. . . . . . . . . . . . . . . . . . . 35 2. Experimental Arrangement . . . . . . . . . . 36 j (a) Component surface fluxes . . . . . . . . 36 (b) Canyon top and roof fluxes . . . . . . . 37 v i v i i CHAPTER P a 9 e B. SOLAR RADIATION RESULTS. 3 8 1. Solar Radiation Input (K4-) ,to Component Surfaces 3 8 2. Albedos of the Component Surfaces. . . . . . 40 3. Albedo of the Canyon System 43 4. Absorption by the Canyon System . 47 4 NET RADIATION IN THE CANYON 52 A. INTRODUCTION . 52 B. SURFACE NET RADIATION IN THE CANYON. . . . . . . 53 1. Net Radiation of the Component Surfaces. . . 53 2. Net Radiation of the Canyon System . . . . . 56 3. Net Long-wave Radiation i n the Canyon at Night 61 C. LONG-WAVE FLUX DIVERGENCE IN THE CANYON-AIR VOLUME G6 1. Introduction 66 2. Horizontal Flux Divergence in the Canyon. . 67 3. Flux Divergence in the Canyon Cross-Section. 7 0 D. RADIATIVE AND ACTUAL COOLING IN THE CANYON-AIR VOLUME 73 5 SUBSURFACE HEAT FLUX IN THE CANYON . . . . . . . . . 82 A. INTRODUCTION 82 B. CALIBRATION . . . . . . . . . 83 C. CALIBRATION IN CONCRETE . . . . . . . . . . . . . . 87 D. SUBSURFACE FLUX DIVERGENCE 91 E. SUBSURFACE HEAT FLUX IN THE CANYON. . . . . . . . 94 6 ENERGY BALANCE OF THE CANYON .100 A. INTRODUCTION 100 B. ADVECTION - HORIZONTAL AND VERTICAL TRANSPORT OF HEAT BY MEAN MOTION .101 1. Flow P a r a l l e l to the Canyon . . . . . . . . .103 2. Flow Across the Canyon. 110 C. ENERGY BALANCE OF THE CANYON. 113 1. Instrumentation 113 v i i i CHAPTER Page 2. Surface Energy Balance of the Component Surfaces „ » „ „ . . H 5 3. Energy Balance at the Canyon Top. . . . . . 117 4 . Canyon A i r Cooling/Warming Rates 120 7 MODELLING CONSIDERATIONS. . . . . . . . . 123 A. INTRODUCTION „ . „ „ . 123 B. STAGE I - CALCULATION OF K+ 126 C. STAGE II - CALCULATION OF K* IN THE CANYON. . . 129 D. STAGE III - THE RELATION BETWEEN K* AND Q*. . . 134 E. STAGE IV - THE RELATION BETWEEN Q. AND Q_.. . . 136 t Cat F. CONCLUSION . . . . . . . . . . 141 8 SUMMARY OF CONCLUSIONS. . . . . . . . . . I 4 3 REFERENCES 146 APPENDIX A: HEAT FLUX PLATE CALIBRATION . . . . . . . 155 APPENDIX B: CALCULATION OF THE SOLAR ANGLE OF INCIDENCE ON THE VERTICAL WALLS OF THE CANYON . . . . . . . . . . . . 157 APPENDIX C: CALCULATION OF SUNLIT PORTION OF CANYON . 159 LIST OF TABLES TABLE Page 2.1 Schedule of f i e l d a c t i v i t i e s i n 1973. . . . . . . 33 4.1 R e g r e s s i o n a n a l y s i s between L* and V F g . . . . . . 65 4.2 Values o f thermal c o n d u c t i v i t y , v o l u m e t r i c heat c a p a c i t y and admittance s e l e c t e d t o r e p r e s e n t the canyon 79 5.1 Comparison o f heat f l u x p l a t e c a l i b r a t i o n s . . . . 84 5.2 Comparison of r o o f , w a l l and f l o o r maximum,. heat f l u x d i v e r g e n c e s . . . . . . 94 i x LIST OF FIGURES Page Box model d e s c r i b i n g the flow o f energy i n the urban canyon . « . . » o . o 9 The G r e a t e r Vancouver a r e a a , , . . 16 T y p i c a l heat i s l a n d c o n f i g u r a t i o n and a i r p o l l u t i o n d i s t r i b u t i o n . . . . . . . . . . 18 S i t e p l a n of the e x p e r i m e n t a l a r e a . . . . . . . . 20 S u r f a c e lan d use i n the immediate canyon surroundings , . . . . . . 22 Canyon c r o s s - s e c t i o n : (a) dimensions, (b) e x p e r i m e n t a l arrangement, , . 23 Canyon c r o s s - s e c t i o n viewed from the south end i n the e a r l y a f t e r n o o n . . . . . . . . . . . . . . 28 The temperature and r a d i a t i o n mast and a l s o the l o c a t i o n o f t h e heat f l u x p l a t e s on the w a l l , 29 C l i m a t o l o g i c a l t r e n d s f o r May-October 1973, Vancouver I n t e r n a t i o n a l A i r p o r t . . . . . . . . . 34 Incoming s o l a r r a d i a t i o n on the i n d i v i d u a l canyon s u r f a c e s . . . . . 3 9 Albedo of the i n d i v i d u a l canyon s u r f a c e s . . . . . 41 x i FIGURE Page 3.3 Albedo of the canyon system and the roof 44 3.4 Solar r a d i a t i o n fluxes averaged across the canyon cross-section. . . . . . . . . . . . . 46 3.5 Ratio of absorbed solar r a d i a t i o n i n canyon system to an equivalent h o r i z o n t a l area vs. zenith angle . . . . . . . . 48 3.6 Solar r a d i a t i o n absorption by the canyon. . . . . 51 4.1 Net- all-wave r a d i a t i o n incident on the west w a l l . (Q*) . September 10, 1973 5 5 4.2 Net all-wave r a d i a t i o n incident on the ground. (Q*) . September 10, 1973 57 4.3 Net all-wave radiation incident on the east w a l l . (Q|) . September 10, 1973 58 4.4 Net all-wave r a d i a t i o n averaged over three canyon surfaces. (Q*). September 10, 1973 . . . 60 4.5 The r e l a t i o n s h i p between sky view factor (VF ) and net long-wave ra d i a t i o n (L*) at night. September 9, 10, 1973. A l l data c o l l e c t e d at 2030 PST 64 4.6 Radiative energy storage i n canyon volume due to lengthwise divergence [Q*]„ , . 69 rl 4.7 Radiative energy storage i n canyon volume due to cross-sectional divergence [Q*] . . . . . . .72 c 4.8 Radiative vs. measured temperature change for a l l data 75 x i i FIGURE Page 4.9 R a d i a t i v e v s . measured temperature change f o r data c o l l e c t e d a f t e r 2030 PST 76 4.10 Temperature decrease a f t e r sunset i n the canyon u s i n g average data f o r September 9, 10, 11 and 13: (a) compared w i t h t o t a l r a d i a t i v e c o o l -i n g i n the canyon averaged over the same p e r i o d ; (b) compared w i t h the Brunt c o o l i n g r a t e . . . . . . 80 5.1 Comparison o f s o i l heat f l u x p l a t e v/ith g r a d i e n t measurements (sand) . June 27, 28, 1973 . » 86 5.2 D e t e r m i n a t i o n o f the thermal c o n d u c t i v i t y o f c o n c r e t e 89 5.3 Comparison o f s o i l heat f l u x p l a t e w i t h g r a d i e n t measurements ( c o n c r e t e ) . May 30, 31 and a June 4, 1973 . . . 90 5.4 Divergence experiment i n Geography B u i l d i n g r o o f , U.B.C. September 5, 6, 1974. . . , . . . . . . . . . 93 5.5 Subsurface heat f l u x a t f i x e d p o i n t s i n the canyon. J u l y 27, 1973 <• . , » 96 5.6 S p a t i a l average of the subsurface heat f l u x f o r J u l y 27, 1973: (a) averaged a l o n g each canyon s u r f a c e ; (b) averaged over the th r e e canyon s u r f a c e s 98 6.1 Schematized a i r flow i n the canyon. . . . . . . . 102 6.2 Ad v e c t i o n o f heat i n t o or out of the canyon pc A f Q ( u o - A U q ) A 1 / A 2 . . . . . . . . . . 1 0 7 x i i i FIGURE 6.3 6.4 6.5 6.6 6.7 6.8 7.1 7.2 7.3 7.4 7.5 C l Page R e l a t i o n between h o r i z o n t a l a d v e c t i o n i n the canyon [pc A T Q ( U - A U Q ) A ^ / A _ ] and mean canyon wind speed? J u l y 10, 11, 12, 13, 1973 109 F r i c t i o n a l l o s s o f h o r i z o n t a l v e l o c i t y i n the canyon between two l o c a t i o n s 28 m a p a r t . J u l y 10, 11, 12, 13, 1973 109 V e r t i c a l wind v e l o c i t i e s a t t h r e e canyon l o c a t i o n s . October 6, 1973. 15 minute averages. Wind from the west 112 3-day average energy balance components f o r i n d i v i d u a l canyon s u r f a c e s . September 9, 10, 11, 1973 116 3-day average energy balance components i n the canyon. September 9, 10, 11, 1973. . 118 C o o l i n g r a t e s i n the canyon. September 9, 1973 . 121 M o d e l l i n g scheme t o o b t a i n s e n s i b l e heat f l u x s (a) day; (b) n i g h t . . . . . . . . . . . . . . . . 125 Comparison o f c a l c u l a t e d and measured net s o l a r r a d i a t i o n (K*) f o r the Geography B u i l d i n g r o o f , U.B.C. 128 * Net s o l a r f l u x (Xfc) f o r the canyon system . . . . 133 R e l a t i o n between K* and Q* from canyon and r o o f measurements. June 17, 18, 1974 137 * R e l a t i o n between h o u r l y Q and Q f o r canyon and r o o f measurements. September 1-5, 7, 9-11, 1973. . . . . . . . . . . 140 Shadow le n g t h s i n the canyon. . . . . . . . . . . 160 LIST OF SYMBOLS O TDESCRIPTION Cross-sectional area i n canyon (=W.H) Cross-sectional area i n canyon (=L.H) i t h surface of the canyon-air volume Y-intercept obtained from a l i n e a r regression of Q vs * * Slope of the regression of Q vs L Heat capacity of a s o l i d Heat capacity averaged over the three canyon surfaces Constant i n turbulent transfer equation S p e c i f i c heat of a surface S p e c i f i c heat of a i r at constant pressure SYMBOL DESCRIPTION D D i f f u s e incoming s o l a r r a d i a t i o n i n c i d e n t on canyon top De' Dw' Da D i f f u s e s o l a r r a d i a t i o n i n c i d e n t on the e a s t , west and " ground s u r f a c e s of the canyon F 1 ' F 2 F r a c t i o n o f the incoming d i f f u s e r a d i a t i o n D t h a t i s i n -c i d e n t on e i t h e r o f the two canyon w a l l s , and ground r e s p e c t i v e l y H' V e r t i c a l d i s t a n c e between the top o f the e a s t e r n w a l l and the shadow h e i g h t o f the i r r a d i a t e d w a l l H Canyon h e i g h t H e Height of e a s t w a l l i n canyon h S u r f a c e h e a t i n g c o e f f i c i e n t I E x t r a - t e r r e s t r i a l s o l a r r a d i a t i o n i n t e n s i t y o J I' Incoming d i r e c t r a d i a t i o n a f t e r d e p l e t i o n by R a y l e i g h s c a t t e r i n g , water vapour and a e r o s o l s J i » j o D i r e c t i o n c o s i n e s o f two vectors, m c a l c u l a t i o n of i> SYMBOL DESCRIPTION K + t » K t t Incoming and outgoing s o l a r f l u x on the canyon system (averaged a c r o s s the canyon t o p ) r e s p e c t i v e l y K+.,K+. I n d i v i d u a l measurements of incoming and outgoing r a d i -a t i o n a t canyon top K+ ,K+T7,K+^ Incoming s o l a r r a d i a t i o n averaged over the e a s t , e' w g e' w g west and ground s u r f a c e s of the canyon r e s p e c t i v e l y * * * K e,K u,K n Net s o l a r r a d i a t i o n averaged over the ea s t , west and ground s u r f a c e s o f the canyon r e s p e c t i v e l y K. Net s o l a r f l u x o f the canyon system (averaged across the canyon top) ' K4.' Mean s o l a r r a d i a t i o n r e c e i v e d on a canyon s u r f a c e from an i r r a d i a t e d second canyon s u r f a c e K Eddy d i f f u s i v i t y f o r heat o r water vapour K R Eddy d i f f u s i v i t y o f heat K* Eddy d i f f u s i v i t y o f heat f o r the canyon system H k Thermal c o n d u c t i v i t y DESCRIPTION Thermal c o n d u c t i v i t y averaged over the t h r e e canyon s u r f a c e s Thermal c o n d u c t i v i t y of. sand and concrete r e s p e c t i v e l y A r b i t r a r y canyon l e n g t h Incoming and outgqirig long-wave r a d i a t i o n f l u x r e s p e c t i v e l y Net long-wave r a d i a t i o n f l u x Mean n e t long-wave r a d i a t i o n a l o n g t h e canyon ground S o l a r a i r mass Per c e n t o f the canyon w a l l s i n s u n l i g h t D i r e c t i o n c o s i n e s o f two v e c t o r s i n c a l c u l a t i o n o f i|» Net all-wave r a d i a t i o n f l u x Net all-wave r a d i a t i o n averaged over the e a s t , west and ground s u r f a c e s o f the canyon r e s p e c t i v e l y SYMBOL DESCRIPTION TYPICAL UNITS Net a l l wave r a d i a t i o n averaged over the i t h s u r f a c e of the canyon W m -2 Net a l l - w a v e . ^ r a d i a t i o n f l u x of the canyon system (averaged a c r o s s the canyon top) W m -2 _* Q Net all-wave r a d i a t i o n averaged over the three canyon s u r f a c e s W m -2 QN' QS Net all-wave r a d i a t i o n i n the v e r t i c a l plane and averaged over the n o r t h and south c r o s s - s e c t i o n of t h e canyon r e s p e c t i v e l y W m -2 * [Q ] Net s t o r a g e of Q i n the canyon-air volume J s -1 * [Q 1 Net s t o r a g e o f r a d i a n t energy i n the canyon-air volume due t o d i v e r g e n c e i n the n e t all-wave r a d i a t i o n normal t o the canyon c r o s s - s e c t i o n J s -1 * [Q 1 H Net s t o r a g e o f r a d i a n t energy i n the canyon-air volume due t o d i v e r g e n c e i n the all-wave r a d i a t i o n i n a plane normal t o the canyon c r o s s - s e c t i o n J s -1 Advected heat i n the canyon-air volume due t o h o r i z o n t a l mass t r a n s p o r t J s -1 x < I-1-SYMBOL DESCRIPTION TYPICAL UNITS <E La t e n t heat f l u x W m - 2 L a t e n t heat f l u x o f the canyon system (averaged a c r o s s the canyon top) W m - 2 Anthropogenic heat f l u x r e l e a s e d from b u i l d i n g s W m - 2 Subsurface heat f l u x W m - 2 'G(o) Q, G(z) Conductive heat f l u x a t the i n t e r f a c e Subsurface heat f l u x a t depth z W m - 2 W m - 2 Q R ,Qr ,Qr S p a t i a l l y averaged subsurface heat .flux g f o r the e a s t , west and ground s u r f a c e s r e s p e c t i v e l y W m - 2 Q Subsurface heat f l u x o f the canyon system Gt W m - 2 Q Subsurface heat f l u x averaged over the three canyon s u r f a c e s W m G - 2 'H S e n s i b l e heat f l u x Q H / Q H '^H S e n s i b l e heat f l u x t o o r from the e a s t , west and e w 9 ground s u r f a c e s r e s p e c t i v e l y W m - 2 W m - 2 x TYPICAL SYMBOL DESCRIPTION UNITS Q H t S e n s i b l e heat f l u x o f the canyon system (averaged a c r o s s the canyon top) W m~ ^ l ' ^ 2 D i r e c t i o n c o s i n e s o f two v e c t o r s i n c a l c u l a t i o n o f ip deg R R e l a t i v e e f f i c i e n c y o f the canyon system i n t r a p p i n g s o l a r r a d i a t i o n when compared t o a h o r i z o n t a l area r Radius v e c t o r o f t h e sun S r R a y l e i g h s c a t t e r i n g c o e f f i c i e n t S^ S c a t t e r i n g c o e f f i c i e n t f o r water vapour S C l i m a t o l o g i c a l v a r i a b l e i n the t u r b u l e n t t r a n s f e r (Equation 1 . 2 ) T Q,T^ Instantaneous a i r temperatures i n the canyon, averaged over the canyon c r o s s - s e c t i o n and separated by a d i s t a n c e L K T 2 Instantaneous a i r temperature averaged over the canyon top K T ,T.,T 0 Time-average o f ins t a n t a n e o u s temperatures T ,T., and T„ r e s p e c t i v e l y u J . ^ K X K TYPICAL DESCRIPTION UNITS Instantaneous temperature departures o f T ,>T.. ,T 2 from T Q f T ^ , T 2 r e s p e c t i v e l y , ° K Mean a i r temperature K Mean s u r f a c e temperature i n the canyon K Subsurface temperature S u r f a c e temperatures o f the canyon w a l l s and ground r e s p e c t i v e l y K U n i t o f time s Instantaneous wind v e l o c i t i e s i n the canyon, averaged over _^ the canyon c r o s s - s e c t i o n and separated by a d i s t a n c e L m s Time-average o f in s t a n t a n e o u s h o r i z o n t a l v e l o c i t i e s _^ U q and u^, r e s p e c t i v e l y ^ m s Instantaneous v e l o c i t y d e p a r t u r e s o f u and u^ from u Q and u^ r e s p e c t i v e l y ° Canyon-air volume View f a c t o r f o r a s u r f a c e - 3 m TYPICAL SYMBOL DESCRIPTION UNITS VF e,VF w,VF E a s t w a l l , west w a l l and sky v i e w - f a c t o r s f o r p o i n t s a l o n g the canyon s u r f a c e s VF. View f a c t o r f o r the i r r a d i a t e d i t h s u r f a c e as seen 1 _ by the j t h s u r f a c e m W Canyon width m Instantaneous v e r t i c a l v e l o c i t y averaged over the canyon top (A2) m s w w Time-average o f v e r t i c a l v e l o c i t y w m s w' Instantaneous d e p a r t u r e of w from w m s X D i s t a n c e between s e n s i n g element and base of the v e r t i c a l s u r f a c e i n view f a c t o r c a l c u l a t i o n m X m,X F r a c t i o n o f the canyon ground t h a t i s i n shadow i n the morning and a f t e r n o o n , r e s p e c t i v e l y Y Height o f v e r t i c a l s u r f a c e i n view f a c t o r c a l c u l a t i o n m Z' Z e n i t h angle o f the Sun deg TYPICAL SYMBOL DESCRIPTION UNITS z U n i t o f h e i g h t o r depth m a Albedo o f a s u r f a c e a , a , a I n d i v i d u a l albedos f o r the e a s t , west and ground e w 9 s u r f a c e s o f the canyon r e s p e c t i v e l y c t t Albedo o f the canyon system (averaged a c r o s s the canyon top) a' R e f l e c t i v i t y f o r long-wave r a d i a t i o n 6' Bowen's r a t i o i S f c Bowen's r a t i o f o r the canyon top A F i n i t e d i f f e r e n c e approximation e E m i s s i v i t y o f a s u r f a c e 0 P o t e n t i a l temperature K 0' A r c t a n (Y/X) deg x x H-H-TYPICAL SYMBOL DESCRIPTION UNITS 2 -1 < Thermal d i f f u s i v i t y of a surface m s * * X Slope of L vs K r e l a t i o n - _2 - i -i< u Mean thermal admittance of the three canyon surfaces J m K S —3 p A i r density kg m — 3 p ' Density of a surface kq m a Stefan-Boltzmann constant W m-^ 0 Absorption c o e f f i c i e n t for water vapour <(>' Azimuth angle between the solar beam and canyon longitudinal d i r e c t i o n deg Transmission c o e f f i c i e n t for aerosol absorption and scattering , Transmission c o e f f i c i e n t for aerosol scattering or absorption Solar angle of incidence f o r the canyon walls deg x x < °. ft.Solar irradiance from secondary r e f l e c t i o n s on the _ «= / w y —2 east, west and ground surfaces of the canyon respectively W m ACKNOWLEDGEMENTS I would l i k e to g r a t e f u l l y acknowledge the encourage-ment, a s s i s t a n c e and s u g g e s t i o n s g i v e n t o me by my s u p e r v i s o r , Dr. T. R. Oke. I am a l s o i n d e b t e d t o members o f my committee and e s p e c i a l l y t o Mr. M. Church of the Department of Geography, to Dr. S. Pond o f the I n s t i t u t e of Oceanography, U.B.C., f o r t h e i r many h e l p f u l d i s c u s s i o n s , and to Dr. T. A. B l a c k o f the S o i l S c i e n c e Department, who p r o v i d e d l a b o r a t o r y c a l i b r a t i o n f a c i l i t i e s . The author i s g r a t e f u l t o Mr. K. N i c o l , and my br o t h e r , Mr. J . Nunez, who helped i n the data c o l l e c t i o n ; to Mr. A. Ramirez who d i d the d r a f t i n g and to Miss S. A i z e n -man who typed the t h e s i s . T h i s p r o j e c t was conducted i n the grounds o f K r a f t Co. and Pi n e Tree Nut Co. and to them I am g r a t e f u l f o r the use o f t h e i r f a c i l i t i e s . T h i s p r o j e c t was funded through N a t i o n a l Research C o u n c i l , and Atmospheric Environment S e r v i c e g r a n t s to Dr. T. R. Oke. | XXV CHAPTER 1 INTRODUCTION A. APPROACHES TO FLUX ESTIMATION IN URBAN AREAS M o s t work i n u r b a n c l i m a t o l o g y h a s b e e n d i r e c t e d t o w a r d s d e s c r i b i n g t h e t i m e and s p a c e d i s t r i b u t i o n s o f c l i m a t o l o g i c a l p a r a -m e t e r s s u c h as a i r t e m p e r a t u r e , w a t e r v a p o u r , w i n d s p e e d , a n d a i r p o l l u t a n t s ( f o r r e v i e w s o f t h i s work see K r a t z e r , 1956; P e t e r s o n , 1969; and Oke, 1 9 7 4 ) . A l t h o u g h t h i s has i n c r e a s e d o u r k n o w l e d g e o f t h e c l i m a t i c e f f e c t s o f u r b a n i z a t i o n , i t h a s n o t r e s u l t e d i n a c l e a r u n d e r s t a n d i n g o f t h e mechanisms l y i n g a t t h e r o o t o f u r b a n c l i m a t o l o g y . I n p a r t i c u l a r i t i s n e c e s s a r y t o f u r t h e r u n d e r s t a n d t h e b e h a v i o u r o f t h e f l u x e s t r a n s f e r r i n g e n e r g y , mass and momentum b e t w e e n t h e a t m o s p h e r e and t h e u r b a n i n t e r f a c e . T h i s s t u d y i s c e n t r a l l y c o n c e r n e d w i t h t h e u r b a n i n t e r -f a c e e n e r g y b a l a n c e , b u t i t i s i m p o r t a n t t o p o i n t o u t t h a t t h e e n e r g y f l u x e s c a n n o t be d i v o r c e d f r o m i n t e r a c t i o n s w i t h t h e f l u x e s o f mass and momentum. F o r e x a m p l e , t h e e x c h a n g e o f b o t h s h o r t and lo n g - w a v e r a d i a t i o n b etween t h e a t m o s p h e r e and t h e s u r f a c e i s m o d i f i e d b y t h e p r e s e n c e o f p o l l u t a n t s ; t h e p a r t i t i o n -i n g o f a v a i l a b l e e n e r g y i s s t r o n g l y i n f l u e n c e d by t h e a v a i l a b i l i t y o f e v a p o r a b l e w a t e r ; and t h e e f f i c i e n c y o f t u r b u l e n t t r a n s p o r t i s p a r t i a l l y c o n t r o l l e d b y t h e g e n e r a t i o n o f f o r c e d c o n v e c t i o n . I n p a r t i c u l a r t h i s s t u d y i s c o n c e r n e d w i t h t h e means whereby t h e s e n s i b l e h e a t f l u x by t u r b u l e n t t r a n s f e r may be 1 2 determined. I t s importance i n a l t e r i n g the thermal s t r u c t u r e o f the urban boundary l a y e r i s a n t i c i p a t e d t o be s u b s t a n t i a l (e.g., i n c o n t r o l l i n g l apse r a t e s and hence s t a b i l i t y and p o l l u t i o n d i s -p e r s i o n ; i n c r e a t i o n of the urban heat i s l a n d ; i n e s t i m a t i n g b u i l d -i n g and community h e a t i n g requirements, etc.) but l i t t l e d e t a i l e d work i s a v a i l a b l e . Three c l a s s e s o f approach have been undertaken p r e v i o u s -l y i n attempting t o e s t i m a t e the magnitude o f the urban s e n s i b l e heat f l u x , namely num e r i c a l models, m i x i n g depth models and measurement. The t h e o r e t i c a l models are u s u a l l y based upon the f o l l o w i n g e q u a t i o n s : Q* + Q E + Q H + Q G = 0 (1.1) 9 S 3 S TT = Cxl7 ( Kx TT) + Advecticm (1.2) 3T 3 2T T T T ~ = k — ^ (1.3) 8 t 3 z 2 where. * Q = net all-wave r a d i a t i o n , Q E = l a t e n t heat f l u x , Q H = s e n s i b l e heat f l u x , Q G = sub s u r f a c e heat f l u x , S x = c l i m a t o l o g i c a l v a r i a b l e (temperature, water vapour, e t c . ) , C = c o n s t a n t , 3 K x = eddy d i f f u s i v i t y f o r p r o p e r t y (heat, water vapour) , T 2 = subsurface temperature, k = subsurface thermal c o n d u c t i v i t y , t = time, z = h e i g h t . E q u a t i o n s 1 . 1 , 1.2 and 1.3 are the two-dimensional forms of the s u r f a c e energy b a l a n c e , atmospheric t u r b u l e n t t r a n s f e r and sub-surface heat f l u x e q u a t i o n s r e s p e c t i v e l y . As a f i r s t approximation the a d v e c t i v e term i s i g n o r e d . E q u a t i o n s 1 . 1 , 1.2 g i v e a c l o s e d s e t i f K k and the s u r f a c e boundary c o n d i t i o n s are x, known, whence t h e s e n s i b l e heat f l u x (Q„) i s o b t a i n e d from: tx Q H = - P C P K H H ' d ' 4 where p = a i r d e n s i t y , c = s p e c i f i c heat o f a i r a t c o n s t a n t ^ p r e s s u r e , T = mean a i r temperature. T h i s approach was taken by Myrup (1969) i n h i s p i o n e e r i n g numeri-c a l model o f the urban heat i s l a n d . The model was not i n t e n d e d f o r r e s e a r c h purposes, and f o r s i m p l i f i c a t i o n avoided i n c l u s i o n of a d v e c t i o n , s t a b i l i t y c o r r e c t i o n of K„, and i n i t i a l l y assumed r l Qg = 0 i n the c i t y . Furthermore, a constant f l u x l a y e r was i assumed so t h a t the model was n o t time-dependent. N e v e r t h e l e s s , some i n t e r e s t i n g r e s u l t s were o b t a i n e d which i l l u s t r a t e d the 4 character of the urban energy balance. In his model surface e f f e c t s are p a r t i c u l a r l y s i g n i f i c a n t . The model r e s u l t s showed a i r and surface temperatures to be strongly related to the amount of t r a n s p i r i n g surface. The model was l a t e r applied to Sacramento, C a l i f . (Myrup and Morgan, 1972) by d i v i d i n g the c i t y into small c e l l s and using representative values of albedo, emissivity, thermal conductivity, f r a c t i o n of trans-p i r i n g surface and heat capacity f o r each c e l l . Roughness lengths were employed using the method of Lettau (1969). Following t h i s analysis, the authors were able to calculate the s p a t i a l d i s t r i b u t i o n of the d i f f e r e n t surface energy b a l -ance components i n Sacramento. Unfortunately independent mea-surements of these terms were not available probably because of experimental d i f f i c u l t i e s to be discussed l a t e r on i n t h i s chapter. I t i s reasonable to assume that more r e a l i s t i c des-c r i p t i o n s of the energy transfers could be had by incorporating J (a) stability-dependent eddy d i f f u s i v i t i e s , (b) r a d i a t i v e flux divergence, (c) the momentum transfer equation, (d) advection and the equation of continuity, (e) r e a l i s t i c surface boundary fluxes. Some early boundary layer models e x i s t which incorporate some of these features. Estoque (1963) used (a), (b) and (c) i n his work which also included a constant f l u x layer followed by a t r a n s i t i o n layer. The model was meant to apply over a r u r a l surface. Similar models have been developed by Pandolfo et al. 5 (1963) and Wu (1965) among o t h e r s . Tag (1969) a p p l i e d the Estoque model t o an urban a r e a and c a l c u l a t e d s u r f a c e temper-a t u r e warming. Term (d) can be used t o study the urban c i r -c u l a t i o n system i n the absence of e x t e r n a l winds (Delage and T a y l o r , 1970; Vukovich, 1971) as w e l l as t o study the m o d i f i -c a t i o n o f r u r a l a i r as i t c r o s s e s the urban a r e a . These l a t e r models r e p r e s e n t the most advanced approach t o d a t e , and i n most cases i n c o r p o r a t e terms (a) to (d) (Estoque and Bhumral-kar , 1970; P a n d o l f o et al. , 1971; Wagner and Yu, 1972). Although most o f t h e s e models r e c r e a t e i n some form the observed f e a t u r e s of the urban heat i s l a n d , t h e r e i s need o f e x p e r i m e n t a l programmes t o v e r i f y t h e i r r e s u l t s (see, f o r example, Tag, 1969; B o r n s t e i n , 1972; McElroy, 1972a, 1972b). In many r e a l s i t u a t i o n s , the inhomogeneity o f the s u r f a c e may render the c a l c u l a t i o n s o f the eddy d i f f u s i v i t i e s based on e s t a b l i s h e d wind p r o f i l e t heory, i n v a l i d . Furthermore, a l -though the urban boundary l a y e r has been shown t o e x i s t as a mean p r o p e r t y ( C l a r k e , 1969; Oke and E a s t , 1971; Tyson et al,s 1972) i t must i n c o r p o r a t e l a r g e i n h o m o g e n e i t i e s a t the s u r -face due t o the complex n a t u r e o f the urban atmosphere i n t e r -face i n space. Thus even though the heat f l u x a t any p o i n t on the s u r f a c e may be w e l l behaved, i t s e s t i m a t i o n from boundary l a y e r t h e o r y may be i n c o r r e c t . S urface inhomogeneities may a l s o cause d i f f i c u l t i e s i n t h e j c a l c u l a t i o n of r e a l i s t i c f l u x e s a t or near the i n t e r -6 f a c e because c u r r e n t t u r b u l e n t t r a n s f e r t h e o r y i s not a p p l i -c a b l e . T h e r e f o r e i t seems t h a t ca t e g o r y (e) i s a t p r e s e n t n e g l e c t e d i n these models, and t h e r e i s need f o r c o n t r i b u t i o n s i n t h i s a r e a . However, due to the complexity o f the flow, i t i s d o u b t f u l i f p u r e l y t h e o r e t i c a l approaches c o u l d be u s e f u l , even i n r e g u l a r i d e a l i z e d b l o c k - a r r a y s . I n s t e a d , the i n p u t must come from e x p e r i m e n t a l programmes to study the energy flow i n t h i s complex environment. The mixing depth models on the o t h e r hand assume t h a t a t some c r i t i c a l h e i g h t the i r r e g u l a r i t i e s i n the s u r f a c e f l u x e s have been smoothed t o p r o v i d e an i n t e g r a t e d s p a t i a l average. T h i s concept i s used by Summers (1965) and Leahey and F r i e n d (1971) equate the development of a thermal- boundary l a y e r to the s u r f a c e heat f l u x w i t h assumptions r e g a r d i n g the form of the wind and temperature p r o f i l e s . Such an approach might appear a t t r a c t i v e i n e s t i m a t i n g g r o s s urban s u r f a c e f l u x e s g i v e n the a p p r o p r i a t e i n p u t i n f o r m a t i o n . However, some of the t h e o r e t i c a l o b j e c t i o n s r a i s e d p r e v i o u s l y , p l u s the expense of p r o v i d i n g the necessary data, make t h i s approach i m p r a c t i c a l . The measurement approach to the e v a l u a t i o n o f Q H i n urban areas u s u a l l y i n v o l v e s the use o f m i c r o m e t e o r o l o g i c a l t e c h -niques such as the Bowen r a t i o , aerodynamic or eddy c o r r e l a t i o n methods. Oke et al. (1972) have p o i n t e d out the r e l a t i v e m e r i t s and d e f i c i e n c i e s o f these approaches i n the urban environment. They conclude t h a t the f i r s t two approaches i n v o l v e assumptions 7 u n l i k e l y t o be r e a l i z e d i n the urban s i t u a t i o n , but t h a t the eddy c o r r e l a t i o n approach h o l d s promise. I n i t i a l work w i t h such a system has v e r i f i e d t h i s (Yap and Oke, 1974), but a l s o suggests t h a t i t should be employed a t a s u f f i c i e n t h e i g h t t h a t l o c a l s p a t i a l v a r i a b i l i t y i s smoothed out. I f the s u r f a c e energy balance i s r e q u i r e d , t h i s i n t r o d u c e s the p o s s i b i l i t y o f e r r o r s a s s o c i a t e d w i t h any h e i g h t v a r i a t i o n i n QH< Given these d i f f i c u l t i e s i n d e t e r m i n i n g Q„ i n the n s u r f a c e energy balance o f the c i t y , a new approach i s attempted here. B. RESEARCH APPROACH The essence of the approach employed i n t h i s study i§ t h a t Q H may be o b t a i n e d as a r e s i d u a l i n the simple s u r f a c e energy balance e q u a t i o n (Equation 1.1) i f a l l o t h e r terms are a c c u r a t e l y measured o r otherwise determined. Much of the v a l u e o f such an approach r e s t s on the c a r e f u l i d e n t i f i c a t i o n o f what c o n s t i t u t e d a s i g n i f i c a n t urban s u r f a c e . There are p r o b a b l y no t r u l y r e p r e -s e n t a t i v e urban surfaces such as those i d e n t i f i e d as c h a r a c t e r -i s t i c o f r u r a l and other h o r i z o n t a l n a t u r a l t e r r a i n f o r e x p e r i -mental purposes. However, t h e r e may be some t y p i c a l urban s u r -f a c e units c o n s i s t i n g of a combination o f s u r f a c e s (both h o r i z o n -t a l and v e r t i c a l ) whose b a s i c form i s repeated throuqhout the urban a r e a . Here we s p e c i f i c a l l y i d e n t i f y the 'urban canyon' as 8 an important b a s i c u n i t o f the urban s t r u c t u r e . I t c o n s i s t s of the combination o f w a l l s , and ground ( s t r e e t ) and the a i r volume c o n t a i n e d between two a d j a c e n t b u i l d i n g s ( F i g u r e 1.1). Such a p h y s i c a l arrangement r e p r e s e n t s a t h r e e -dimensional d i s t o r t i o n o f the h o r i z o n t a l s u r f a c e case, and i s c h a r a c t e r i z e d by complex r a d i a t i v e and aerodynamic exchanges below r o o f - l e v e l . The urban canyon t o g e t h e r w i t h s i m p l e r r o o f s u r f a c e s forms the lower boundary f o r most of the urban boundary l a y e r , a t l e a s t i n the c e n t r a l p o r t i o n of most c i t i e s . Such a concept i s s i m i l a r t o , but independent o f , t h a t employed by T e r -jung and L o u i e (1973, 1974) where they i d e n t i f y a " r a d i a t i o n n e i g h -borhood" as a t y p i c a l u n i t capable o f i n t e g r a t i o n t o p r o v i d e a s y n t h e t i c c i t y system. The canyon donsidered i n t h i s t h e s i s i s e s s e n t i a l l y a two-dimensional example i n which the t r a n s f e r of energy between the atmosphere and the canyon c r o s s - s e c t i o n i s not dependent on the l o n g i t u d i n a l d i s t a n c e along the canyon. Thus a r e a l canyon s i t u a t i o n was found which was o f s u f f i c i e n t l e n g t h and which was c h a r a c t e r i z e d by homogeneity i n i t s l o n g i t u d i n a l a x i s . T h i s c h a r a c t e r i s t i c does not exclude the presence o f a d v e c t i o n but o n l y a s s u r e s t h a t the energy exchanges a r e s i m i l a r i n the g r e a t e r p a r t of the canyon. The s u i t a b i l i t y o f a p p l y i n g the u n i t canyon r e s u l t s to a l a r g e r urban area (and o t h e r canyons) w i l l , of course, depend on the c h a r a c t e r o f the energy balance terms a t the i n t e r f a c e . F i g . 1.1 Box model d e s c r i b i n g the flow of e n e r g y - i n the urban canyon. VO 10 I f the r a d i a t i o n f l u x e s behave as w e l l - d e f i n e d f u n c t i o n s of the p h y s i c a l p r o p e r t i e s o f the canyon(e.g., dimensions, albedo, s u r f a c e f a b r i c ) then these terms can be modelled i n o t h e r can-yon s i t u a t i o n s . S i m i l a r l y i f the h o r i z o n t a l t r a n s p o r t of heat i n t o , o r out o f , the canyon i s s m a l l , then the i m p l i c a t i o n i s t h a t the v e r t i c a l exchange of heat i s governed by p r o c e s s e s o c c u r r i n g i n s i d e the canyon. Thus Q H may be modelled i n o t h e r canyon s i t u a t i o n s i f i t i s shown t o be a well-behaved f u n c t i o n o f the o t h e r energy balance terms. T h i s attempt a t g e n e r a l i z i n g the canyon measurements i m p l i e s t h a t t h e r e must be some form o f c o n t r o l on the e x t e r n a l energy i n p u t s to the canyon system ( s o l a r r a d i a t i o n and s y n o p t i c winds), o t h e r w i s e the r e s u l t s w i l l be b i a s e d and t h e i r a p p l i c a -b i l i t y to o t h e r s i t u a t i o n s would be q u e s t i o n a b l e . I t was d e c i d e d i n t h i s study t o look a t c o n d i t i o n s which were as c l o s e t o steady-s t a t e as p o s s i b l e : g e n e r a l l a r g e - s c a l e subsidence weather c h a r a c -t e r i z e d by c l e a r s k i e s , l i g h t winds and dry s p e l l s , These con-d i t i o n s are i n themselves important s i n c e i t i s d u r i n g these s p e l l s t h a t a i r p o l l u t i o n and heat i s l a n d anomalies have maximum e f f e c t (Summers, 1965). Although the p o s s i b i l i t y o f u s i n g the urban canyon as a m o d e l l i n g u n i t i s c o n s i d e r e d here a l s o , the c e n t r a l emphasis i s upon examining the nature of the p h y s i c a l exchanges i n t e r a c t i n g w i t h i n such a geometric c o n f i g u r a t i o n . The study o f the urban canyon i s important a l s o f o r what i t t e l l s us about the c l i m a t i c c o n d i t i o n s w i t h i n s t r e e t s . F o r i t i s here t h a t much o f the b i o -11 logical activity of c i t i e s takes place (both animal and vege-tative) , and wherein some of the pollutants (particulate, gaseous, thermal and acoustic) are released. Equally i t is where most of the studies of the climatic effects of urbanization have been conducted (e.g., automobile traverses of air temperature) but where the energetic basis for climatic interpretation i s almost entirely lacking. Assuming no phase changes of water in the air volume, the energy balance for the air volume contained in an urban can-yon such as that in Figure 1.1 is given: t QAdv ] + ( QHe + <W H ' L + QHg * W ' L " QHt ' W - L - . * ( 1 5 ) P V at P c p where [QTVJ.. ] = advected heat due to horizontal Adv , transport, Q H e, Q H w Q = sensible heat flux to, or from, ' g the east, west and ground surfaces respectively, H, L, W = canyon height, length and width respectively, Q H t = sensible heat flux through the canyon top, 8 T pc / — dV = rate of change of energy storage V in the canyon-air volume V, * /div Q dV = rate of change of energy storage V due to net radiative divergence in the canyon-air volume. 12 The l e f t - h a n d s i d e o f E q u a t i o n 1.5 d e f i n e s the net s e n s i b l e heat i n p u t to the c a n y o n - a i r volume. These terms t h e r e -f o r e must be balanced on the r i g h t - h a n d s i d e by the r e s u l t i n g change i n the s e n s i b l e energy st o r a g e (temperature) i n the a i r volume p l u s (or minus) the net energy change due to r a d i a t i v e f l u x d i v e r g e n c e . Under near calm c o n d i t i o n s (commonly a t n i g h t ) the terms on the l e f t - h a n d s i d e w i l l become s m a l l and the two terms on the r i g h t - h a n d s i d e w i l l p r o v i d e the dominant i n t e r -a c t i o n . The d i v e r g e n c e of net r a d i a t i o n i n the c a n y o n - a i r volume can be r e - w r i t t e n as * " * / d i v Q dV = I Q.A. V i = l 1 1 (1.6) * where, d e f i n e s the net r a d i a n t energy normal to the i t h s u r f a c e (A^) of the c a n y o n - a i r volume. The Q H f l u x e s f o r the canyon w a l l s , i f assumed to be impervious and d r y , are g i v e n as: Q„ = Q (1.7) and f o r the canyon f l o o r : * Q G " Q E (1.8) i f some' sm a l l amount of water i s assumed to be a v a i l a b l e . 13 Given an a p p r o p r i a t e sampling scheme over the canyon surfaces, a l l the terms i n E q u a t i o n 1.5 can thus be measured u t i l i z i n g f a i r l y s t a n d a r d m e t e o r o l o g i c a l i n s t r u m e n t a t i o n (e.g., f l u x p l a t e s , radiometers, a l y s i m e t e r and thermometers) w i t h the e x c e p t i o n of Q„.. T h i s term then becomes s o l v a b l e as the r l t r e s i d u a l , and r e p r e s e n t s the f l u x o f s e n s i b l e heat t o (or from) the urban boundary l a y e r above the b u i l d i n g s . In combination w i t h the s e n s i b l e heat f l u x from the r o o f - t o p s t h i s term i s a fundamental lower boundary c o n d i t i o n i n the meso-scale energy balance o f the c i t y and i t s atmosphere. The knowledge g a i n e d i n e v a l u a t i n g the energy balance o f the c a n y o n - a i r volume v i a measurement p r o v i d e s h e l p i n e s t a b l i s h i n g e m p i r i c a l r e l a t i o n s h i p s , and i n t e s t i n g t h e o r e t i -c a l models, which may then be a p p l i e d to o t h e r canyon systems e x i s t i n g under s i m i l a r c o n s t r a i n t s . C. OBJECTIVES The s p e c i f i c o b j e c t i v e s of t h i s study may be summar-i z e d as the f o l l o w i n g : ( i ) to measure and i n t e r p r e t the nature of the energy balance terms ( r a d i a t i v e , c o n d u c t i v e and c o n v e c t i v e ) a t the i n t e r -f a c e of the component s u r f a c e s o f an urban canyon, I 1 4 ( i i ) t o measure, compute and i n t e r p r e t the nature of heat f l u x e s ( r a d i -a t i v e and c o n v e c t i v e ) i n v o l v e d i n the energy balance of a c a n y o n - a i r volume, ( i i i ) t o g e n e r a l i z e the r e s u l t s of ( i) and ( i i ) towards t h e i r f u t u r e i n -c o r p o r a t i o n i n t o a m o d e l l i n g scheme d e s c r i b i n g the behaviour of Q H a t the urban/atmosphere i n t e r f a c e . i CHAPTER 2 SITE, INSTRUMENTATION AND DATA ACQUISITION A. GEOGRAPHIC SITUATION 1. Vancouver Region and C l i m a t e The e x p e r i m e n t a l s t u d i e s were conducted i n Vancouver, B. C. (49°N l a t i t u d e , 123° W l o n g i t u d e ) which i s l o c a t e d a t the mouth o f the F r a s e r R i v e r on the Lower Mainland of B r i t i s h Columbia ( F i g u r e 2.1). The C i t y o f Vancouver i s m a i n l y r e s i -d e n t i a l except f o r commercial c e n t r e s , and pockets o f main l y l i g h t i n d u s t r y . The t o t a l p o p u l a t i o n o f the G r e a t e r Vancouver r e g i o n i s a p p r o x i m a t e l y one m i l l i o n , w i t h the h i g h e s t d e n s i t y l o c a t e d near the C e n t r a l Business D i s t r i c t (C.B.D.). The m a c r o - c l i m a t o l o g y o f the Vancouver Region i s c h a r a c t e r i z e d by wet, m i l d w i n t e r s and d r y , warm summers. The w i n t e r i s dominated by the passage of P a c i f i c d i s t u r b a n c e s caught up i n the flow of the W e s t e r l i e s . In the summer the northward e x t e n s i o n o f the P a c i f i c S u b - T r o p i c a l High P r e s s u r e area b r i n g s g e n e r a l l y c l o u d l e s s s k i e s and l i g h t e r winds, and the tendency f o r the development of important meso-scale c l i m a t e s . D e t a i l e d accounts o f the c l i m a t e o f the r e g i o n a re g i v e n by Harry (1955), Harry and Wright (1967) and Hare and Thomas (1974). The o b s e r v a t i o n s i n t h i s study were r e s t r i c t e d t o the summer months, and to days wi t h c l o u d l e s s s k i e s and l i g h t winds, 15 16 /1 • ; i II ' •' ' i « * \ / • i \\' \\r"7 Grouse; / OHollyburn, ^ S V N \ \ - ; ; , i i , ; Mt • .' R idge /' V A t a p i l a n o ', ', v'/ ' S e y m o Georgia Tsawwa^sen O Experimental site Built up area Contours White Rock \ Contour 'interval 3 0 0 m 0 5 10 Km I I I F i g . 2.1 The G r e a t e r Vancouver a r e a . 17 Under such conditions the experimental s i t e l o c a t i o n (Figure 2.1) i s l i k e l y to encounter a number of meso-scale phenomena. In p a r t i c u l a r , the wind regime i s characterized by east-west oriented l o c a l winds generated by land/sea thermal differences and probably augmented by a mountain/valley c i r c u l a t i o n (Emslie;, 1971). The diurnal wind-shift i s very marked during t h i s period. The meso-scale heat i s l a n d of Vancouver i s also well developed under a n t i c y c l o n i c weather, commonly r e s u l t i n g i n urban/rural temperature differences of 5 degrees C e l s i u s , and maximum differences of greater than 11 degrees Celsius on espe-c i a l l y calm and clear nights (Oke, 1972). The heat i s l a n d also shows a diurnal cycle with the maximum magnitude occurring 3-4h a f t e r sunset (Oke and Maxwell, 1974). An example of the heat i s l a n d configuration i s given i n Figure 2.2 (Oke, 1974, personal communication). This shows the experimental s i t e to be well within the heat i s l a n d , but i s not located i n an area of sharp temperature gradient. Note also that the d i s t r i b u t i o n of p a r t i c u l a t e matter from a study by Emslie and Salterthwaite (1966) shows some s i m i l a r i t y with the heat i s l a n d pattern (Figure 2.2). Spa t i a l sampling of other pollutants i s not s u f f i c i e n t to make sim i l a r comparisons, but discussion of ava i l a b l e information i s contained i n B.C. Research Council (1970) and Lynch and Emslie (1972) . 2. Urban Canyon Experimental S i t e To f u l f i l l the requirements of an urban canyon as out-o F i g . 2.2 T y p i c a l heat i s l a n d c o n f i g u r a t i o n and a i r p o l l u t i o n d i s t r i b u t i o n . 19 l i n e d i n Chapter 1, the following set of s i t e c r i t e r i a were deemed desirable on t h e o r e t i c a l or purely p r a c t i c a l grounds: (a) canyon length >^ 50 m, (b) width: height r a t i o between 1:0.5 and 1:6, (c) homogeneity of canyon surface materials, (d) uniformity of surrounding structures, (e) no windows or obstructions along canyon sides, (f) no shadows i n the canyon cast by external objects, (g) impermeable canyon surfaces, (h) freedom from t r a f f i c , (i) easy access. The s e l e c t i o n of a s i t e which f u l f i l l e d a l l of these nine c r i t e r i a proved very d i f f i c u l t . The s i t e selected d i d not f u l l y conform with c r i t e r i a (e), (f) and (g) but was s a t i s f a c t o r y i n a l l other respects. The experimental canyon i s located i n a r e s i d e n t i a l / l i g h t i n d u s t r i a l zone, 3.5 km south of Burrard I n l e t , and 6 km south-east of the C.B.D. (Figure 2.1). I t i s located i n a s l i g h t topographic depression, with a 1 i n 12.5 slope to the north, and a 1 i n 19 slope to the south. The neighbourhood l o c a t i o n of the s i t e i s shown i n Figure 2.3 which also includes the percentage of each block area which i s composed of impervious materials. The area to the north of the s i t e i s composed mainly of i n d u s t r i a l buildings (food processing and warehousing), whereas to the south 20 7th 4 0 2 4 5 45 40 40 39 1 95 | - - - - « 95 9 5J 40 10 th 2 0 95 3 0 B r o a d w a y 70 i o 1 <D 8 0 ' 8 0 O o l — o 2 I I 90 1 9 0 I I 80 70 • Experimental site _xj Impervious surface (% of block) +m++ Railroad track L 0 J 0.25 0.5 Km F i g . 2 .3 S i t e p l a n o f the exp e r i m e n t a l a r e a . i 21 the area i s m a i n l y r e s i d e n t i a l . In the immediate surroundings most b u i l d i n g s were 7-8 m i n h e i g h t . The canyon i t s e l f ( F i g u r e 2.4) i s a l i g n e d n o r t h / s o u t h and i s l o c a t e d between two l a r g e food p a c k i n g and s t o r a g e p l a n t s . They do not r e p r e s e n t s i g n i f i c a n t sources f o r anthropogenic heat (Qp). The canyon dimensions a r e approximately 8 m i n width, 6 m i n h e i g h t , and 79 m i n l e n g t h . The two w a l l s were, however, o f d i f f e r e n t h e i g h t s [see F i g u r e 2 . 5 ( a ) ] , and t h i s may be ex-pected to cause r e s u l t s t o d e p a r t i n magnitude somewhat from those i n a symmetrical canyon, but should not s i g n i f i c a n t l y a f f e c t the n a t u r e o f the p r o c e s s e s . Here i t w i l l be assumed t h a t the r e s u l t s a r e the same as those o c c u r r i n g i n a canyon w i t h equal s i d e s , but the magnitude o f the expected d i f f e r e n c e s w i l l be d i s c u s s e d . The canyon w a l l s are c o n c r e t e , covered w i t h s e v e r a l c o a t s o f f l a t , white p a i n t . They a r e smooth except f o r some narrow s t r u c t u r a l columns (9 cm x 60 cm) which occur every 3 m a l o n g the e a s t w a l l , and extend t o w i t h i n 50 cm o f the t o p o f the w a l l [ F i g u r e 2.5(a)]. The canyon f l o o r c o n s i s t s o f a 3 t o 5 cm l a y e r o f g r a v e l c h i p s on a c l a y base. U n l i k e the w a l l s t h e r e f o r e i t does not s t r i c t l y conform to c r i t e r i o n (g), and t h i s was accounted f o r i n the i n s t r u m e n t a l d e s i g n . The r o o f s o f both b u i l d i n g s are g r a v e l - o v e r - t a r . There a r e some s m a l l areas o f g r a s s to the south, and bare ground and bushes to the n o r t h o f the canyon b u i l d i n g s ( F i g u r e 2.4). Approximately 80-95 per c e n t o f the h o r i -z o n t a l area o c c u p i e d by the two p l a n t s i s covered by impervious s u r f a c e s . S co le G r o n v i e w H i g h w a y E3 A spha l t • T a r - G r a v e l Roof Fine Gravel p i T r a i l e r EH Coarse Gravel |3 Gra s s H Bare So i l Ra i l r ood 0 Canyon cross-section c£^ 2s B a s h e s F i g . 2.4 S u r f a c e l a n d use i n the immediate canyon s u r r o u n d i n g s . 7 ' > A Pine Tree / Nut Co./ / (West / wall) / / / /• / / A _ L ' 0.5 m TV I E IT) io I E ro r-' I I I • I 9 cm-1 h I m — - • 7 i 0.6 m T 7 / / • Kraft Foods (East wall) / / / / / / / / / (a) r-Mast / / / \ Ta -lr^» /-Boom / >ine / / A Z i A Z j Z y 0 ; A A A A A /y. / Kraft ^ Foods (East wall) Pine Tree Nutco. Q ( !/: 7 6 m / 7fi " (West Qfij/1 W Q , I ) „ y-7B • /.76 « /.76 • Qtf. -7 1.06m / T, T, Ts T+-Tj Qs .61 " P S " / 0.3 m 1.73 m 1.73™ 1.73 m 1.73m 0.3m Q j i , Soil heat flux plates on canyon walls £ ground Net radiometers to measure a vert ica l -flux" Q> Net radiometers to measure a horizontal f lux Tt Ventilated thermocouples to measure air temperature 2.5 Canyon c r o s s - s e c t i o n : (a) Dimensions (b) E x p e rimental Arrangement 24 There are v e n t i l a t i o n ports on the roofs of both buildings, and a v e n t i l a t o r o u t l e t on the south end of the east wall. None of these i s anticipated to provide s i g n i f i c a n t ther-mal e f f e c t s i n the canyon-air volume. Two superstructures on the west bu i l d i n g did, however, cast shadows on the east wall during the l a t e afternoon (1430-1700 PST) giving a disturbed shadow out-l i n e . Data during t h i s period were omitted from analyses (see Chapter 3). B. INSTRUMENTATION 1. Solar Radiation Two types of pyranometers were used i n the experimental work. For c o l l e c t i n g data on a continuous basis a Kipp and Zonen solarimeter was used. This pyranometer i s of the Moll-Gorczynski type, consisting of 14 constantan-manganin thermocouples joined in s e r i e s to a blackened surface, and t h i s i s referenced to the body temperature of the instrument. The sensing surface i s covered with two concentric hemispheric glass domes 2 mm thick designed to reduce the transfer of heat by convection between the s e n s i t i v e surface and the outer dome. The glass domes have an e f f e c t i v e wave length transparency i n the range 0.3 to 2.0 microns. The instrument i s f i t t e d with a d e s s i c a n t - f i l l e d c a r t -ridge which prevents moisture build-up i n the instrument i n t e r i o r . The approximate output of the instrument i s 1 mv f o r an incoming -2 solar r a d i a t i o n of 93 W m . The response-time of the instrument 25 (represented by ninety-eight per cent of complete response to a step change) i s achieved i n 3 0 s. A l l pyranometers were ca l i b r a t e d at the Canadian National Radiation Laboratory. Where spot readings were desired, the Kipp s o l a r i -meter proved impractical because of i t s bulkiness and weight (4.5 kg), and dome solarimeters (Lintronic Ltd., U.K.) were employed. These solarimeters are r e l a t i v e l y l i g h t (80 g) and construction d e t a i l s are described by Monteith (1959) . They consist of an eight-junction thermopile enclosed by a fr o s t e d glass dome, with an e f f e c t i v e transparency range of 0.3 to 3.3 microns. The nominal c a l i b r a t i o n of the instrument i s 1 mv f o r -2 an incoming solar r a d i a t i o n of 28 W m 2. Net All-wave Radiation Net radiometers used were of the Funk type (Model S i , Swissteco Pty. Ltd., A u s t r a l i a ) . The thermopile consists of copper-plated constantan wires joined i n - s e r i e s between the upper and lower sensing elements. The domes are transparent to r a d i a t i o n with wavelengths i n the range 0.3 to 100 microns, and thus the instrument i s s e n s i t i v e to both short-wave and long-wave r a d i a t i o n . In c e r t a i n cases t h i s presents a problem, since the c a l i b r a t i o n constant of the instrument might be d i f f e r e n t for short-wave and long-wave r a d i a t i o n . To minimize the d i f f e r -ence i t i s customary to paint t h i n white s t r i p s across the blackened surface so as to increase the solar reflectance with-out changing the long-wave a b s o r p t i v i t y . Because of t h i s tech-26 nique, the difference between the short and long-wave c a l i b r a -tions f o r a l l the instruments employed was <_ 1.5 per cent. Dur-ing the daytime, the c a l i b r a t i o n constants for short- and long-wave ra d i a t i o n were averaged and the resultant value applied to the data. The long-wave c a l i b r a t i o n was used for a l l night-time data. A l l net radiometers were c a l i b r a t e d at the Canadian National Radiation Laboratory. A t y p i c a l c a l i b r a t i o n gives 1 mv _2 for a net r a d i a t i o n f l u x of 28 W m . The time constant of the instrument i s 23 s. The t h i n polyethylene domes were kept i n f l a t e d by dry a i r pumped into the instrument. The a i r was dr i e d by f o r c i n g i t with a 4W 115V aquarium pump through an a c r y l i c tube f i l l e d with s i l i c a g e l . The radiometers are f i t t e d with small port-holes concentric with the domes to allow v e n t i l a t i o n of the outer part of the domes and thus prevent dew formation at night. This feature was not used i n t h i s study since i t was noticed that no dew formed either on the instruments, or i n the canyon during the night. 3. A i r Temperature The a i r temperature element used i n t h i s study was a copper-constantan thermocouple [Ceramocouple, Thermo-Electric (Canada) Ltd.] with a time constant of 0.25 s. These sensors are matched pairs of ISA T c a l i b r a t i o n , 24 AWG conductors, sealed i n a 0.315 cm O.D. s t a i n l e s s s t e e l sheath, and insulated with magnesium oxide. The sensor was housed i n a 13 cm long s h i e l d made from p o l y v i n y l chloride (PVC) tubing with an I.D. 27 o f 3 cm. The o u t e r w a l l s o f the tube were covered w i t h alum-i n i z e d Mylar t o prevent r a d i a t i o n h e a t i n g . A i r was a s p i r a t e d through the PVC tube by means o f a 7W 115V f a n . A 60 cm cross-arm o f PVC t u b i n g connected the f a n t o the thermocouple housing ( F i g u r e 2.7). The thermocouple r e f e r e n c e temperature i s i n c o r p o r a t e d i n t o the data a c q u i s i t i o n system ( S e c t i o n C ) . 4. Heat Storage S o i l heat f l u x p l a t e s (Science A s s o c i a t e s Inc.) were used t o measure the f l o w o f heat i n t o , and out o f , the canyon s u r f a c e s . The sensor i s a d i s c t h a t measures 1.3 cm i n d i a -meter, and 1 mm i n t h i c k n e s s . The upper and lower f a c e s have a copper s c r e e n c o a t i n g , and the f i l l i n g m a t e r i a l i s a t e l l u r -i u m - s i l v e r a l l o y . A s i g n a l i s generated by a t h e r m o p i l e which has a l t e r n a t e j u n c t i o n s on each m e t a l l i c s u r f a c e . The heat flow through the instrument (QQ) i s g i v e n by the c o n d u c t i v i t y o f the instrument (k) m u l t i p l i e d by the temperature g r a d i e n t a c r o s s the f a c e s (AT/Az). Q G = -k(AT/Az) (2.1) The p l a t e output was t y p i c a l l y about 0.1 mv f o r a heat f l u x of 120 W m~2. The measurement of canyon w a l l and f l o o r heat f l u x e s i s o f c e n t r a l importance i n t h i s study, t h e r e f o r e c o n s i d e r a b l e e f f o r t was spent i n t e s t i n g t h i s i nstrument. The t e s t r e s u l t s are g i v e n i n the s u b - s u r f a c e heat f l u x c h a p t e r (Chapter 5 ) . F i g . 2. C Canyon c r o s s - s e c t i o n viewed from t h e s o u t h end i n the e a r l y a f t e r n o o n . Ilote the boon and the mast arranf-enent b e i n g t r a v e r s e d , a l s o the s u p e r s t r u c t u r e shadov; on the e a s t w a l l . IV) 00 Fin.. 2.7 The temperature and r a d i a t i o n mast and also the location of the heat flux plates on the v/all. .'!ote the difference i n orientation of the lowest radiometer com-pared to the others. 30 5. Experimental Arrangement i n the Canyon Most o f the e x p e r i m e n t a l work was conducted a t a canyon c r o s s - s e c t i o n which was l o c a t e d 35 m from the n o r t h end o f the canyon ( F i g u r e 2.4). A t t h i s p o s i t i o n an aluminum boom was c o n s t r u c t e d a c r o s s the canyon top [ F i g u r e s 2.5(b) and 2.6). The boom formed a r i g i d trackway f o r a c a r r i a g e w i t h wheels which c o u l d be moved t o any p o s i t i o n a c r o s s the canyon. A v e r t i c a l mast was a t t a c h e d to the c a r r i a g e , and i t supported cross-arms a t e i g h t l e v e l s spaced a t 0.7 6 m i n t e r v a l s upwards from the ground [ F i g u r e 2.5(b), 2.6 and 2.7], To sample the c r o s s - s e c t i o n the mast was moved to f i v e p o s i t i o n s a c r o s s the canyon width [ F i g u r e 2 . 5 ( b ) ] . Thus, w i t h instruments mounted on the cross-arms, one t r a v e r s e a c r o s s the canyon y i e l d e d a 5 x 8 m a t r i x o f data p o i n t s . The net r a d i o m e t e r s and a i r temperature sensors were mounted on the e i g h t cross-arms ( F i g u r e 2.7). The lowest, and h i g h e s t r a d i o m e t e r s were mounted i n the u s u a l h o r i z o n t a l p o s i -t i o n so as to measure the net r a d i a n t f l u x on a h o r i z o n t a l s u r -f a c e . The remaining s i x were arranged w i t h t h e i r s e n s i n g elements p a r a l l e l to the v e r t i c a l w a l l s , measuring the net r a d i a n t f l u x on a v e r t i c a l s u r f a c e . Thus f o l l o w i n g a t r a v e r s e i t was p o s s i b l e t o determine the net r a d i a n t f l o w a c r o s s the p e r i m e t e r of the c r o s s -s e c t i o n . The a i r temperature sensor s h i e l d s f a c e d downwards to minimize r a d i a t i o n e r r o r s . 31 Seventeen heat f l u x plates were embedded i n the walls and f l o o r of the canyon cross-section; s i x i n each wa l l , and f i v e across the f l o o r [Figure 2.5(b)].' Holes 1 cm deep, and 1.5 cm i n diameter, were d r i l l e d i n the walls. The hole was f i l l e d to 0.5 cm with wet concrete, the plate i n s t a l l e d , and the hole f i l l e d so as to be f l u s h with the wall surface. A f t e r drying the area was sprayed l i g h t l y with white paint. The f l o o r plates were i n s t a l l e d 5 cm deep i n the gravel (to avoid d i r e c t r e c e i p t of solar r a d i a t i o n ) , and at distances of 0.3, 1.8, 3.6, 5.5 and 7.3 m from the east w a l l . During one measurement phase each i n d i v i d u a l plate was monitored separately, but during the main energy balance runs the plates from each of the three com-ponent canyon surfaces (east w a l l , west wall and floor) were joined i n - s e r i e s . An a d d i t i o n a l heat flux plate was embedded at a depth of 0.5 cm i n the tar-over-gravel roof of the west bu i l d i n g . The preceding instruments and experimental arrange-ment represent the main measurement array. On occasion, d i f f e r -ent instruments, or arrangements were employed. Where t h i s occurred, i t i s mentioned within the r e s u l t s sections which follow i n Chapters 3 to 6. C. DATA ACQUISITION A t r a i l e r (2.4 x 2.4 x 6.2 m) was located at the north end of the canyon (Figure 2.4) and housed a l l data acqui-32 s i t i o n equipment. The c a b l e s f o r the r a d i a t i o n and heat f l u x s i g n a l s were 18 gauge copper arranged i n 9 conductor p a i r s . Each p a i r and i t s d r a i n w i r e were s h i e l d e d w i t h p o l y e s t e r , and a chrome-vinyl j a c k e t p r o v i d e d o v e r a l l p r o t e c t i o n . The temper-a t u r e s i g n a l s were c a r r i e d by 20 gauge copper-constantan exten-s i o n c a b l e , s h i e l d e d w i t h a l u m i n i z e d mylar, and covered w i t h v i n y l . The 8 temperature, 8 r a d i a t i o n and 4 s o i l heat f l u x p l a t e s i g n a l s were monitored on a data l o g g i n g system ( D i g i t r e n d 210, D o r i c S c i e n t i f i c ) . I t i s c a p a b l e o f a c c e p t i n g t e n s i g n a l s o f range 0-10 mv, ten o f range 0-100 mv, and 20 copper-constantan thermocouple o u t p u t s . The s i g n a l s are measured u s i n g a d u a l -s l o p e i n t e g r a t i o n method. A r e f e r e n c e temperature o f 0°C f o r the copper-constantan thermocouples i s an i n t e g r a l p a r t o f the system. A c o n s t a n t v o l t a g e check on the a c c u r a c y and r e l i a b i l -i t y o f the data l o g g i n g system i s a l s o b u i l t - i n . A h i g h p r e -c i s i o n o p t i o n was i n s t a l l e d which allowed measurements to a temp-e r a t u r e r e s o l u t i o n o f 0.1°C, and an a c c u r a c y o f 1 uV. A b s o l u t e temperatures c o u l d be o b t a i n e d to w i t h i n ±0,3°C. During the main p a r t of t h e d a t a c o l l e c t i o n , a l l chan-n e l s from each location were monitored every t h r e e minutes d u r i n g the day, and the d a t a p r i n t e d on paper tape. The data was t r a n s -f e r r e d t o computer c a r d s ; two c a r d s r e p r e s e n t i n g one 3 min scan-n i n g sequence. During n i g h t t i m e measurements the data from each (ocdrion was monitored once every s i x minutes. A l l d a t a were subsequently reduced to h o u r l y averages. 33 D. OBSERVATION PERIOD As mentioned previously, the study i s confined to cloudless sky, l i g h t wind conditions, and i n Vancouver t h i s i s consistently achieved only i n the summer. The observation period was between May and October, 1973, and the d a i l y sequence of some weather elements for t h i s period i s given i n Figure 2.8. Temperatures were cooler than normal (except f o r September), but r a i n f a l l was s u b s t a n t i a l l y less than normal throughout. The sche-dule of f i e l d a c t i v i t i e s i s given i n Table 2.1, TABLE 2.1 SCHEDULE OF FIELD ACTIVITIES IN 1973 P E R I O D A C T I V I T Y A p r i l 29 - June 28 C a l i b r a t i o n of s o i l heat f l u x plates at University of B.C. July 9 - July 14 Canyon advection July 16 - July 20 Net r a d i a t i o n f l u x divergence along canyon axis July 26 - August 1 Canyon subsurface heat f l u x August 8 - August 14 Canyon solar r a d i a t i o n September 1 - October 12 Canyon energy balance F i g . 2.8 C l i m a t e - l o g i c a l trends f o r May-October, 1973, Vancouver I n t e r n a t i o n a l A i r p o r t U ) CHAPTER 3 SOLAR RADIATION EXCHANGES IN THE CANYON A. INTRODUCTION 1. Gen e r a l Most r e s e a r c h on s o l a r r a d i a t i o n i n urban areas has been concerned w i t h the a t t e n u a t i o n due t o i n c r e a s e d , or changed, a e r o s o l . T h i s study, on the o t h e r hand, c o n s i d e r s the incoming s o l a r r a d i a t i o n a t r o o f - t o p l e v e l and w i t h i n the s t r u c t u r e o f the urban canyon. Thus there i s no attempt t o analyze the mod-i f i c a t i o n of the s o l a r beam d u r i n g i t s passage through the urban atmosphere, the emphasis here i s upon i t s r e c e i p t , r e f l e c t i o n , a b s o r p t i o n and t r a n s f o r m a t i o n i n the canyon environment. I t i s t h e r e f o r e viewed as the most important i n p u t f o r c i n g f u n c t i o n i n the s u r f a c e energy balance of the t o t a l canyon system v i a i t s component s u r f a c e s (walls and f l o o r ) , P r e v i o u s work on the r o l e o f the s u r f a c e i n the ex-change o f s o l a r r a d i a t i o n a t the urban s u r f a c e has been r e s t r i c -ted t o o n l y a few o b s e r v a t i o n a l s t u d i e s , and fewer m o d e l l i n g attempts. O b s e r v a t i o n s o f the s o l a r f l u x e s or the s u r f a c e a l -bedo have been undertaken from a e r i a l p l a t f o r m s (Kung et al.t 1964; B a r r y and Chambers, 1966); from s i n g l e urban s u r f a c e s such as a r o o f , p a r k i n g l o t , e t c . (Bach and P a t t e r s o n , 1969; Oguntoy-inbo, 1970; Fuggle, 1971); and i n o n l y one case w i t h i n the urban canyon ( T u l l e r , 1973). These s t u d i e s g e n e r a l l y r e f e r t o gross 36 a e r i a l estimates of surface albedo, or very li m i t e d spot values, and therefore do not contribute s i g n i f i c a n t l y to an understand-ing of the d e t a i l s of r a d i a t i v e exchange at the complex urban surface. The modelling studies (Craig and Lowry, 1972; Terjung and Louie, 1973, 1974) involve c a l c u l a t i n g s o l a r fluxes and albedos from t h e o r e t i c a l solar d i s t r i b u t i o n s and assumed sur-face dimensions and r a d i a t i v e properties. They predict a canyon system albedo which i s dependent upon the zenith angle of the Sun, and increased absorption i n the canyon compared to a f l a t surface. These r e s u l t s are capable of t e s t i n g by obser-vation and w i l l be referred to l a t e r . This chapter describes the r e s u l t s of solar r a d i a t i o n measurements i n the experimental canyon (Chapter 2). It con-siders the time dependent input of solar r a d i a t i o n to the i n d i -vidual canyon surfaces, the albedo of the surfaces and the t o t a l system, and the resultant absorption by the t o t a l canyon system. Such information i s important i n understanding the r o l e of such a three-dimensional configuration i n r e f l e c t i n g or trapping solar r a d i a t i o n , and i n evaluating the performance of t h e o r e t i c a l models i n the prediction of s o l a r exchanges under non-ideal conditions. The b i o l o g i c a l and a r c h i t e c t u r a l value of such information should also not be overlooked. 2. Experimental Arrangement (a) Component surface fluxes. To measure the s o l a r 37 r a d i a t i o n normal to each component canyon surface the light-* weight dome solarimeters (Chapter 2) were employed. Two so l a r -imeters (back-to-back) were attached to the end of an aluminum pole. Spot measurements of the incoming and outgoing s o l a r fluxes were made by holding the solarimeter sensing surface p a r a l l e l to and about 0.5 m above the surface being investigated. The surface albedo (a) i s then defined by: where K+, K+ = outgoing and incoming s o l a r r a d i a t i o n fluxes, res p e c t i v e l y . Observations were made at heights of 1 and 3,3 m above ground f o r the east and west walls, at distances of 0,68 3.8 and 7 m from the east wall for the canyon f l o o r . The so l a r -imeter outputs were measured on a portable IDC microvoltmeter (Comark E l e c t r o n i c s Ltd.) once every hour a (b) Canyon top and f l o o r fluxes. To measure the r a d i -ation fluxes at the top of the canyon3upward, and downward faeiRf Kipp and Zonen solarimeters (Chapter 2) were mounted at a height of 5.5 m on an arm extending h o r i z o n t a l l y from the movable car= riage on the cross-canyon boom. Measurements were made at di§= tances of 0.6, 1.8, 3.8, 5.6 and 7 m from the east w a l l . Assum-ing the albedo to be constant along the length of the canyon, which seems reasonable, the integrated albedo of the canyon system averaged across the top (a t) i s given by? i • 38 5 i = l 1 K + t at = ~ = K77 0.2) E K+ . 1=1 1 where K+. , K+. = i n d i v i d u a l measurements o f K + and K+, a t 1 1 the f i v e l o c a t i o n s a c r o s s the canyon top, K+., K+ t = o u t g o i n g and incoming s o l a r r a d i a t i o n of the canyon system averaged a c r o s s the canyon to p . Another s o l a r i m e t e r was l o c a t e d over the r o o f of the west b u i l d -i n g to c o n t i n u o u s l y monitor the s o l a r r a d i a t i o n r e f l e c t e d . The r o o f albedo was c a l c u l a t e d from E q u a t i o n 3.1 u s i n g K-K from the boom r e s u l t s . In September both K + and K-h were measured over the r o o f . A l l s i g n a l s were recorded on a p o t e n t i o m e t r i c s t r i p - c h a r t r e c o r d e r (Model 194, Honeywell). To s i m p l i f y comparisons, t h e d a t a f o r most o f the r e s u l t s presented i n t h i s c h a p t e r a r e f o r the same f o u r c l o u d -l e s s days (August 8, 9, 13 and 14,1973). B. SOLAR RADIATION RESULTS 1. S o l a r R a d i a t i o n Input (K4-) to Component S u r f a c e s The incoming s o l a r r a d i a t i o n f l u x f o r each component s u r f a c e i s shown i n F i g u r e 3.1. T h i s shows t h a t t h e regime f o r each canyon s u r f a c e i s c h a r a c t e r i z e d by one p e r i o d o f s t r o n g s o l a r i r r a d i a n c e . The p o s i t i o n and magnitude o f the peak i n p u t August 8,9,13,14,1973 Solar irradiance on individual canyon component surfaces ,1 E a < ct < 600 i SOO I 400 300 West wall Ground . East wall a I I 4 I I o z o u z 200 100 \ V _ l L . _J I \ J L. _1 L . 10 12 14 16 18 7 TIME (PST) 11 IJ 15 17 19 6 TIME (PST) 8 10 12 14 16 18 TIME (PST) F i g . 3.1 Incoming solar r a d i a t i o n on the in d i v i d u a l canyon surfaces. vo 40 f o r each s u r f a c e i s governed by the l o c a l angle o f i n c i d e n c e of t h e d i r e c t s o l a r beam f o r t h a t s u r f a c e o r i e n t a t i o n , and the i n t e n s i t y of t h e s o l a r beam. Thus the maximum K4- o c c u r s a t approximately 0930, 1330 and 1500 PST f o r t h e west w a l l , f l o o r ane e a s t w a l l l o c a t i o n s r e s p e c t i v e l y . The f l o o r r e c e i v e s the h i g h e s t i n p u t (=75 0 W m ) near the time of s o l a r noon, and the _2 two w a l l s r e c e i v e approximately 150 W m l e s s a t the time of t h e i r maximum r e c e i p t . The two w a l l s a l s o e x h i b i t an i n t e r e s t i n g secondary peak (1500 PST f o r t h e west w a l l , and 0930 PST f o r the e a s t w a l l ) . These are p r o b a b l y a r e s u l t of the i n c r e a s e d d i f f u s e r e f l e c t i o n i n the canyon s i n c e the t i m i n g o f these secondary peaks corresponds t o the times o f maximum s o l a r i r r a d i a n c e of the o p p o s i t e w a l l . Note a l s o t h a t the e f f e c t i v e day l e n g t h f o r s o l a r r a d i a t i o n i s s h o r t f o r a l l s u r f a c e s (=10 h) but t h a t f o r approximately 4 h t h e r e i s a r e l a t i v e l y i n t e n s e r a d i a t i o n c l i m a t e . Each s u r f a c e i s a c t i v e f o r a s h o r t time w h i l s t the o t h e r s are r e l a t i v e l y p a s s i v e . The form of the s o l a r r a d i a t i o n r e c e i p t f o r each component s u r f a c e i n F i g u r e 3.1 i s v e r y b a s i c to the energy * balance of the canyon. I t w i l l be shown t h a t the c o u r s e o f Q , Q G and Q H are i n t i m a t e l y l i n k e d t o the form o f the s o l a r i n p u t . 2. Albedos o f t h e Canyon Component S u r f a c e s and Roof. The albedos of the component s u r f a c e s are g i v e n i n F i g u r e 3.2 as a f u n c t i o n of the s o l a r angle o f i n c i d e n c e , d e f i n e d r e l a t i v e t o the i n d i v i d u a l s u r f a c e ' s l o c a l o r i e n t a t i o n . 41 0.80i 0.70 0.60 I 0.50 O £ 0.40] 0.301 0.20 * WEST WALL O EAST WALL O GROUND • ROOF August 8, 9, 13, 14; 1973 0.10 ° Q ° o DO o 4 * * ' {III 0.00 1 20 30 40 SO 60 i 70 80 — i 90 ANGLE OF INCIDENCE (DEGREES) F i g . 3.2 Albedo of the i n d i v i d u a l canyon surfaces and roof. 42 Thus for the horizontal surfaces (ground and roof) t h i s i s syn-onymous with the Sun's zenith angle, but f o r the v e r t i c a l sur-faces (walls) i t i s a complicated function of the Sun's zenith angle and the azimuth angles of both the Sun and the surface. The component surface albedos are grouped i n t o two gross classes. The roof and f l o o r albedos are generally low in comparison with most natural surfaces (0.10 - 0.20), whereas those of the walls are r e l a t i v e l y high (0.45 - 0.75). Ignoring any dependence of the albedos on zenith angle (see below) the data i n Figure 3.2 were averaged and the mean surface albedos were 0.62, 0.52, 0.13, and 0.13 f o r the west w a l l , east wall canyon f l o o r and roof surfaces respectively. C l e a r l y the con-fidence to be placed on these mean values i s d i f f e r e n t for each surface. Some natural surfaces e x h i b i t a dependence of t h e i r albedo on the zenith angle of the Sun (e.g., f o r crops see Monteith and Szeicz, 1961; Davies and Buttimor, 1969; Nkemdirim, 1972; for water see Nunez et al.t 1972), but there i s l i t t l e i n -formation for bu i l d i n g materials. Craig and Lowry (1972) assumed such a dependence for the materials i n t h e i r t h e o r e t i c a l canyon albedo model and therefore i t i s i n t e r e s t i n g to see i f the data here confirm t h i s . The r e s u l t s i n Figure 3.2 do not c l e a r l y demonstrate that the surface albedos are dependent on zenith angle. V i s u a l l y , there i s some suggestion of the wall and roof albedos s l i g h t l y 43 increasing at greater l o c a l zenith angles, but s t a t i s t i c a l l y these trends proved to possess l i t t l e s i g n i f i c a n c e . The small range of canyon f l o o r zenith angles allows l i t t l e i n t e r p r e t a t i o n to be made. In summary therefore the data do not allow firm con-clusions to be drawn. This i s i n part probably due to the spot measurement technique adopted. In the absence of t h i s i n f o r -mation i t w i l l be assumed that . there i s no zenith angle de-pendence, and the mean albedos w i l l be used i n c a l c u l a t i o n s . 3. Albedo of the Canyon System Although the component surface albedos do not show an obvious solar angle (or time) dependence, the albedo of the canyon system, a (as calculated from Equation 3.2) does show a marked variation,(Figure 3.3). The v a r i a t i o n shows a f c to peak at 0930 and 1500 PST, and to be a minimum at 1230 PST. The d i -urnal range being approximately 0.18. The time-dependent changes of a f c are e a s i l y explained in terms of the roles of the component surfaces already discussed. The system albedo peaks correspond exactly with those of the two walls. Some of the d i f f u s e r e f l e c t i o n from the high albedo walls, at these times of t h e i r maximum irradiance, w i l l be l o s t to the atmosphere thus increasing a^.. The time of minimum a f c corresponds to maximum irradiance of the f l o o r whose albedo i s the lowest of a l l the canyon component surfaces. By contrast the albedo of the e s s e n t i a l l y h o r i z o n t a l roof i s also included i n Figure 3.3 (sha-44 0.30 0.26 o o o o C a n y o n - A u g u s t 8 , 9 , 13, 14j I S 7 3 • Roof - August 8, 9, 13,14, September 4 , 9 , 1 0 « 1 9 7 3 0.22 i O a Ui ca 0,18 0.14 0.10; o o o o o 0 o o v o o o _o O Q ° •• o o • • t : o 0.06 0.02! 10 11 12 13 14 15 16 17 18 19 TIME (PST) F i g . 3.3 Albedo of the canyon system and the r o o f . Open c i r c l e s r e f e r to mean f l u x e s measured across the canyon top. 45 dows p r i o r t o 1000 PST p r e c l u d e d e a r l y morning r e s u l t s ) and sug-g e s t s a much more r e g u l a r d i u r n a l p a t t e r n . E x p l a n a t i o n o f the d i f f e r e n t magnitudes o f t h e two a^ . peaks i s l e s s simple, but the f o l l o w i n g three e x p l a n a t i o n s are suggested. F i r s t l y , the higher morning peak compared to t h a t i n the afterrton must i n p a r t be due to the h i g h e r albedo of the west w a l l (see F i g u r e 3.2). Secondly, the c o m p l i c a t i o n of s u p e r - s t r u c t u r e shadows i n the a f t e r n o o n on the e a s t w a l l may reduce i t s r e f l e c t i v i t y , but t h i s should o n l y d ecrease the v a l u e o f by a s m a l l amount (=0.01). T h i r d l y , t h e d i f f e r e n c e s i n h e i g h t between the two w a l l s (Chapter 2) w i l l r e s u l t i n asym-metry i n K+ t between the morning and a f t e r n o o n . T h i s w i l l de-c r e a s e the i n p u t of d i r e c t beam and d i f f u s e sky r a d i a t i o n i n the morning, and i n c r e a s e t h e d i f f u s e i n t h e a f t e r n o o n due t o the r e f l e c t i o n i n t o the canyon from the p o r t i o n o f the e a s t w a l l w h i c h i s above the t h e o r e t i c a l l y d e f i n e d canyon-top ( i . e . , above the boom). I t i s p o s s i b l e t h a t the morning/afternoon change i n the r a t i o of d i r e c t t o d i f f u s e beam s o l a r r a d i a t i o n has an e f f e c t on the system albedo. The asymmetry of K i ^ i s i l l u s -t r a t e d i n F i g u r e 3.4, where measured K l t i s compared t o the t h e o r e t i c a l K+ t o b t a i n e d from the Houghton (1954) model as used by Nunez et al. (1971). Note, however, t h a t because o f the asymmetric a f c d i s t r i b u t i o n the measured K+ does appear t o be roughly symmetric about s o l a r noon O1200 PST) . The time-dependence of i m p l i e s t h a t a e r i a l s u r -46 August 8,9,13,14,1973 < ai < O 900 r 800 h 700 600 I E Z 2 500 400 300 .200 100 « ° o © o o ° o Incoming solar radiation • Outgoing solar radiation — — Theoretical incoming solar radiation o o o o \ o 0 \ o ° 0 / / / o \ / o "o / O o / o \ \ / / / 0 / °o / o / ° \ o \° o \ o \ o \ \o \ \ / / o o o oo Y J L 10 11 12 13 14 15 16 17 18 19 TIME (PST) F i g . 3.4 Solar r a d i a t i o n fluxes averaged across the canyon cross-section. 47 veys of urban albedo must integrate t h e i r r e s u l t s over time as well as space. Equally i t w i l l be important to ascertain the roles of str e e t o r i e n t a t i o n , and geometry, 4. Absorption by the Canyon System The r o l e of geometry i n trapping solar r a d i a t i o n can be i s o l a t e d by comparing the a b s o r p t i v i t y of the canyon system (1 - a f c), with that of an equivalent horizontal area with the. same percentage composition of surface albedos ( i . e . , t h i s i s equivalent to removing the canyon geometry by l a y i n g the walls f l a t but maintaining the areas and albedos of the component surfaces). Using the mean albedos of the f l o o r and walls, and the canyon dimensions, we can define the albedo of an equivalent horizontal area (a) by: 0.13 W + 0.52 H + 0.62 H a = 2H-TT1 " ( 3 ' 3 ) Since a l l the quantities are constant f o r the canyon a i s con-stant and equal to 0.3 93 f o r the experimental canyon, giv i n g (1 - a) = 0.607. The factor which defines the r e l a t i v e trapping e f f i c i e n c y of the canyon geometry i s the r a t i o of a b s o r p t i v i t i e s (R) given by: (1 - o. ) R = E_ (3.4) (1 - a) Figure 3.5 shows how R varies with the zenith angle of the|Sun. Cl e a r l y the geometry increases the absorption 48 F i g . 3.5 R a t i o of absorbed s o l a r r a d i a t i o n i n canyon system to an e q u i v a l e n t h o r i z o n t a l area vs. z e n i t h angle. 49 e f f i c i e n c y by a minimum of 2 0 per cent to a maximum of 50 per cent at solar noon. The un-weighted mean d a i l y value of R i s 1.36, i n d i c a t i n g that t h i s canyon i s about a t h i r d more e f f i -cient in trapping solar radiation than an equivalent h o r i z o n t a l surface. The behaviour of R with zenith angle was considered by Terjung and Louie (1973) for the case of t h e o r e t i c a l can-yons having d i f f e r e n t height to width r a t i o s , and a uniform albedo f o r a l l component surfaces. Their c a l c u l a t i o n s show an increase i n R with a decrease in zenith angle. The experi-mental r e s u l t s show a much more complex pattern which i s a t t r i -butable to the changing r o l e s of the component surfaces and roof with time, and t h e i r very d i f f e r e n t albedos. F i n a l l y , i n t h i s chapter we consider whether the two sets of experimental data (i n d i v i d u a l surface fluxes, and fluxes across the canyon top) are consistent i n accounting for the sol a r radiation i n the system. Thus we require that a l l the s o l a r r a d i a t i o n entering the canyon volume balance with that leaving: K+. .L.W. + a K4- .L.H + a K+ .L.W.+ a K + .L.H. t e e g g w w a.K+. .W.L. + K4- .L.H. + K+...L.H. + K+ .L.W. t t e w g or, K* = (H/W)(K* + K*) + K* t e w g (3.5) 50 * where K = net s o l a r r a d i a t i o n , and the s u b s c r i p t s * e , w, and g r e f e r t o the e a s t w a l l , west w a l l and ground (canyon f l o o r ) s u r f a c e s r e s p e c t i v e l y . The r e s u l t s o f s u b s t i t u t i n g the ex p e r i m e n t a l r e s u l t s i n E q u a t i o n 3.5 are shown w i t h F i g u r e 3.6. Apart from the d i s -crepancy between 1400 and 1600 PST the agreement i s good. I g -n o r i n g the d a t a f o r t h i s p e r i o d , the d a i l y mean s o l a r absorp-t i o n from the i n d i v i d u a l s u r f a c e s was 363 W m , and t h a t from -2 the canyon top was 3 89 W m . T h i s agreement to w i t h i n 7% i s encouraging and h e l p s t o support the c h o i c e o f i n s t r u m e n t a l techniques employed. The d i s c r e p a n c y between 1400 and 1600 PST i s pr o b a b l y a r e s u l t o f an i n s t r u m e n t a l view f a c t o r prob-lem d u r i n g t h i s time when the e a s t w a l l has s u p e r - s t r u c t u r e shadows upon i t (Figure 2.6). Thus the spot measurement s o l a r -imeter c l o s e t o the w a l l would r e g i s t e r a much reduced f l u x , but t h e overhead s o l a r i m e t e r would 'see* a much l a r g e r a r e a ( i n c l u d i n g the non-shadowed w a l l f u r t h e r down canyon) and would r e g i s t e r a much s m a l l e r e f f e c t . The shadow w i l l a l s o * a f f e c t the f l u x e s o f Q and Q G measured on the e a s t w a l l . Thus measurements f o r the e a s t w a l l i n t h i s p e r i o d are om i t t e d i n the c h a p t e r s which f o l l o w . 51 /August 8, 9,13, 14, 1973 900 i o Sum of individual wall absorptions • Absorption of canyon - system 800 700 600 500 400 300 200 100 • • o o • o • o J L o • O ° O • o o o 8 9 10 11 12 13 14 15 16 17 18 19 TIME (PST) F i g . 3.6 S o l a r r a d i a t i o n a b s o r p t i o n by t h e c a n y o n . 52 CHAPTER 4 NET RADIATION IN THE CANYON A. INTRODUCTION * The net all-wave r a d i a t i o n (Q ) r e p r e s e n t s the e f f e c t i v e energy source (or sink) d r i v i n g the exchange o f heat and water vapour between the s u r f a c e and the atmosphere (Equation 1.1). The net r a d i a t i o n balance may be w r i t t e n : * * * Q = K + L = K4- - K+ + L.+ - Lt (4.1) = K>(1 - a) + L + ( l - a') - eaT* O a where ' * L , L t , Lt = net,incoming and o u t g o i n g long-wave r a d i a t i o n , r e s p e c t i v e l y , a' = s u r f a c e r e f l e c t i v i t y f o r long-wave r a d i a t i o n , e = s u r f a c e e m i s s i v i t y , a = Stefan-Boltzmann c o n s t a n t ( 5 . 6 7 x 10-8 w m - 2 K - 4 ) , Ts = s u r f a c e temperature. By day the s o l a r r a d i a t i o n terms dominate i n d e c i d i n g the course 4c o f Q , and these have been d e s c r i b e d f o r the canyon s i t u a t i o n i n Chapter 3. In the absence o f o b s t r u c t i o n s L4- i s a f u n c t i o n o f the atmospheric e m i s s i v i t y and temperature s t r u c t u r e , and L+ 53 depends on the s u r f a c e p r o p e r t i e s e, a' and T . By n i g h t the s balance i s r e s t r i c t e d to these long-wave exchanges. There are few e x p e r i m e n t a l s t u d i e s o f Q i n c i t i e s . A v a i l a b l e u r b a n / r u r a l daytime comparisons (Bach and P a t t e r s o n , * 1969, P r o b a l d , 1972) i n d i c a t e t h a t Q i s s l i g h t l y decreased i n the c i t y . By n i g h t , r e s u l t s (Oke and F u g g l e , 1972; Rouse * and McCutcheon, 1972) show the L l o s s t o be s l i g h t l y g r e a t e r from c i t i e s because even though L4- i s i n c r e a s e d , Lt i s even more enhanced. T h i s chapter f i r s t l y i n v e s t i g a t e s t h e magnitude, and * time and space v a r i a t i o n s o f Q r e c e i v e d by the component s u r -f a c e s . Secondly, i t c o n s i d e r s the r o l e of r a d i a t i v e f l u x d i v e r -gence i n the canyon-air volume, and t h i r d l y , i t s r e l a t i o n t o canyon c o o l i n g r a t e s . B. SURFACE NET RADIATION IN THE CANYON 1. Net R a d i a t i o n o f the Component S u r f a c e 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 canyon d i c t a t e s t h a t Q f o r i t s component s u r f a c e s w i l l be a complex f u n c t i o n o f many f a c t o r s . The v a r i a b i l i t y of the s o l a r terms has been d i s -cussed, but the long-wave terms are e q u a l l y c o m p l i c a t e d . In p a r -t i c u l a r , the long-wave exchange w i l l depend upon the temperature and e m i s s i v i t y o f a l l media i n i t s f i e l d o f view, and f o r a can-yon s u r f a c e t h a t w i l l i n v o l v e o t h e r canyon s u r f a c e s i n a d d i t i o n 54 to the sky. A l l p o i n t s i n the canyon w i l l p ossess t h e i r own view f a c t o r (VF) w i t h r e s p e c t t o a l l o t h e r r a d i a t i n g o b j e c t s . * The form of the Q d i s t r i b u t i o n s i n the canyon r e -mained s i m i l a r throughout the p e r i o d o f measurement and hence here we w i l l c o n f i n e a n a l y s i s to the data from one day (Sept-ember 10, 1973). Measurements were taken 0.3 m from each s u r -f a c e , these were a t 1.06, 2.58 and 4.12 m above the f l o o r f o r the w a l l d a t a , and a t t h r e e l o c a t i o n s a c r o s s the canyon f o r the f l o o r d a t a (0.30 m from each w a l l and i n the c e n t r e ) . The d i u r n a l course o f Q f o r p o s i t i o n s on the canyon west w a l l a re g i v e n i n F i g u r e 4.1. During the daytime the p a t t e r n i s s t r o n g l y r e l a t e d t o K4- [ F i g u r e 3 . 1 ( a ) ] . As the d i f f u s e beam i n p u t s t r e n g t h e n s a f t e r 053 0 PST the Q l o s s i s decreased u n t i l the d i r e c t beam suddenly e n t e r s the canyon. A t * the time o f maximum K4- a t each l o c a t i o n Q i s a l s o maximum. The peak i n p u t o c c u r s a t the h i g h e s t l o c a t i o n on the w a l l f i r s t , and with the g r e a t e s t magnitude s i n c e the l o c a l angle o f i n c i d e n c e i s c l o s e s t t o the normal then and t h e r e . As the day p r o g r e s s e s the l o c a l angle o f i n c i d e n c e on the w a l l i n c r e a s e s so t h a t the magnitude of the peaks a t lower l e v e l s i s l e s s , and the r a d i a n t i n p u t decreases towards noon. A t approximately the time of maximum s o l a r i r r a d i a n c e o f the e a s t w a l l [ F i g u r e 3.1(c)] t h e r e * i s a weak secondary peak Q on the west w a l l ( F i g u r e 4.1). The n o c t u r n a l s i t u a t i o n i s c h a r a c t e r i z e d by a net r a d i a n t l o s s a t a l l l o c a t i o n s . The l o s s i s g r e a t e s t a t the h i g h e s t l e v e l s which possess the l a r g e s t sky view f a c t o r [see s e c t i o n B ( 3 ) ] . The l o s s 400| F i g . 4.1 Net a l l wave radiation incident on the°west wall. (Q ). September 10, 1973. w Ln 0 56 i s g r e a t e s t i n the e a r l y evening when s u r f a c e temperatures a r e a t t h e i r warmest f o r the n i g h t . The daytime p a t t e r n f o r the canyon f l o o r i s d e t e r -mined by i t s n o r t h - s o u t h o r i e n t a t i o n ( F i g u r e 4.2). As d i f f u s e * r a d i a t i o n f i l l s the canyon Q i n c r e a s e s s l i g h t l y , but w i t h d i r e c t i r r a d i a t i o n ( f i r s t a t the west l o c a t i o n , then a t the c e n t r e and east) i t r i s e s s h a r p l y , and f a l l s a g a i n e q u a l l y s h a r p l y w i t h the p r o g r e s s i o n o f the shadows. A t n i g h t the r e l a t i v e long-wave l o s s e s a t each l o c a t i o n are i n ac c o r d w i t h t h e i r sky view f a c t o r s , being g r e a t e s t a t the canyon c e n t r e , and l e a s t f o r base of the west w a l l [see S e c t i o n B ( 3 ) ] . The Q c y c l e f o r the e a s t w a l l ( F i g u r e 4.3) i s almost a mirror-image o f t h a t f o r the west w a l l , except t h a t d a t a a re omitted a t the time o f the s u p e r s t r u c t u r e shadows i n the a f t e r -noon. Note, however, t h a t c o n t r a r y t o the west w a l l the magni-* tude o f the Q peaks decreases w i t h h e i g h t . T h i s i s because i n the a f t e r n o o n the whole w a l l i s i r r a d i a t e d by d i r e c t beam and then the shadow moves up the w a l l , whereas i n the morning the shadow moves down the w a l l as deeper p o s i t i o n s a r e i r r a d i a t e d . For the a f t e r n o o n case the topmost l e v e l on the e a s t w a l l has been warmed f o r many hours b e f o r e i t r e c e i v e s i t s maximum K l . Thus i t w i l l have warmed-up and be e m i t t i n g L+more s t r o n g l y , * r e s u l t i n g i n a lower Q . 2. ' Net R a d i a t i o n o f the Canyon System The average net r a d i a t i o n over the canyon s u r f a c e s 57 560-520-480-440-400-360-320-280-240-1 e =5 200-K iZ 160 -o 120 -•5 o oe 80-+ *\ Or 40-0 -•10--20--30--40-•50--60-fay P o s i t i o n o c r o s s C a n y o n _ 80 cm. away from west wal l — C a n y o n c e n t r e \ 80 cm. away f rom east wal l hloh Ma QtptnJaJ Scofo 8a/aw Xaro 22 24 . T i m e (PST) F i g . 4.2 Net all - w a v e r a d i a t i o n i n c i d e n t on the ground. ( Q g ) • September 10, 1973 59 _* (Q ) i s c a l c u l a t e d u s i n g the canyon dimensions as w e i g h t i n g f a c t o r s so t h a t : * (Q* • H + Q* • H + Q* • W)L 0 = _§ " g ( 4 2) g (2H + W)L { q " L ) where * * * Qg/ Q w/ Q = net all- w a v e r a d i a t i o n averaged ^ over the e a s t , west and f l o o r 1 s u r f a c e s o f the canyon r e s p e c t i v e l y , and the dummy l e n g t h L i s i n c l u d e d f o r c l a r i t y , thus u n i t s i n the numerator a r e e n e r g y / u n i t time, and i n the denominator are _* area. F i g u r e 4.4 g i v e s Q f o r the same day as F i g u r e s 4.1, 4.2 * and 4.3. Note t h a t u n l i k e the Q regimes o f the component s u r -_* f a c e s , Q f o r the canyon system i s a smooth b e l l - c u r v e s i m i l a r i n form t o t h a t f o r an u n o b s t r u c t e d h o r i z o n t a l s u r f a c e . I t i s important t o r e a l i z e t h a t Q i s the average surface v a l u e f o r the canyon and i s not synonymous w i t h the net * r a d i a t i o n measured a c r o s s the top o f the canyon (Q f c), which i s a s p a t i a l l y averaged v a l u e as seen from above the canyon. The two q u a n t i t i e s a re r e l a t e d : Q*(W.L) = Q*(2H + W)L + [Q*] (4.3) * where [Q ] = the net r a d i a n t energy s t o r a g e i n the can y o n - a i r volume. The f i r s t term on the r i g h t has u n i t s o f e n e r g y / u n i t time, and when added t o the volume st o r a g e g i v e s the energy / u n i t time a c r o s s 60 280-240-I 61 the canyon top. If there is no storage (or divergence) in the air volume, Equation 4.3 reduces to: * _ zr* (2H + W) Q t - Q ' W~ (4.4)  _* Thus Qt and Q are related by a constant factor governed by the canyon dimensions. As a f i r s t approximation in overall energy flux con-siderations i t is probably acceptable to ignore [Q ] as in Equa-tion 4.4. However, although small this term w i l l be shown in Section C to be of central importance in explaining nocturnal air temperature cooling rates. 3. Net Long-wave Radiation in the Canyon at Night * The net long-wave radiation (L ) measured anywhere in an urban area is complicated by the range of radiating surfaces which contribute to the balance at any one point. This i s espe-c i a l l y important when t a l l structures enter the field-of-view of a pyrradiometer at night. Under such circumstances LI w i l l be enhanced compared to an unobstructed sky because z (and commonly T ) are larger than for the atmosphere. The effective-ness of the night sky as a radiation sink for any location i s therefore intimately connected to the sky view factor (VFg) of that point. 62 The c a l c u l a t i o n of the view factor (VF) for locations i n the canyon followed the method of Davies et al. (1970). The ca l c u l a t i o n s r e f e r to an i n f i n i t e s i m a l surface element j u s t above, and p a r a l l e l to, a canyon surface. For a v e r t i c a l wall of i n f i n i t e length (—««to + °°) , with the sensing element horizontal and i n a place which includes the base of the w a l l : • 2 , , ™ _ , s i n 0' +• cos 0' - 1 ,AC\ coi-e 1 ( 4' 5 ) where : G = arctan (Y/X), Y = wall height, X = distance between sensing element and the base of the w a l l . Equation 4.5 can be applied to obtain the sky view factor for surface elements along the two walls i f we assume the walls to be of s u f f i c i e n t length that they approximate i n f i n i t y . For a point on the east wall, at a height h above the ground Y = W and X = (H - h). For a point on the west wall the greater height of the east wall (He) must be considered, so that Y = W, but X = (H e - h). Equation 4.5 does not apply to points along the ground, but the sky view factor for the ground can be obtained as the r e s i d u a l *after c a l c u l a t i n g the view factors f o r the east and west walls (VF , VF ) since: e w VF^ + VF + VF = 1.0 (4.6) s e w 63 T h i s s t a t e s t h a t the e n t i r e f i e l d of view f o r a sens i n g element along the canyon f l o o r i s determined by the ea s t and west w a l l s , and the sky. T h i s i s o n l y s t r i c t l y t r u e i f the w a l l s a r e o f i n f i n i t e l e n g t h ( i . e . , the canyon ends do not c o n t r i b u t e r a d i a t i o n t o the s e n s i n g element near the ground), but w i l l be taken as an approximation here. the w a l l s , and canyon ground and a c r o s s the canyon top a r e r e -l a t e d t o the sky view f a c t o r f o r each l o c a t i o n i n F i g u r e 4 . 5 . The data a re f o r two n i g h t s . Two r e l a t i o n s h i p s appear t o be e v i d e n t . The f i r s t c o v e r s the r e s u l t s f o r the w a l l s and canyon top. The r e l a t i o n i s approximately l i n e a r , w i t h i n c r e a s i n g L a t h i g h e r VF . The second a p p l i e s t o the canyon f l o o r r e s u l t s s which a l s o e x h i b i t a l i n e a r r e l a t i o n , w i t h about the same s l o p e , _2 but d i s p l a c e d = 12 W m below the f i r s t l i n e f o r the same view f a c t o r . T h i s i s e x p l a i n e d by the f a c t t h a t the canyon w a l l s are warmer than the f l o o r . An es t i m a t e o f t h i s d i f f e r e n c e may be made by assuming the f l o o r r e l a t i o n can be e x t r a p o l a t e d to zero view f a c t o r a t which time a l l the r a d i a t i o n must come from the w a l l s . Then: V a l u e s o f L measured a t d i f f e r e n t l o c a t i o n s near L (4.7) where L r e g r e s s i o n i n t e r c e p t = 3.4 W m -2 (Table 4.1) , 9 e s u r f a c e e m i s s i v i t y o f w a l l s and ground (assumed = 0 . 9 5 ) , 80r -70 -60r O West wait e East wall a Ground B Canyon Top I -50h a •5 -40h o o I 9 C O _ l -30 r 2 -20r O ~ o • • o°''° o • • • • -10 .4 .5 6 View factor for sXy ( VF $ ) .7 1.0 F i g . 4.5 The r e l a t i o n s h i p between sky view factor (VF ) and net long-wave ra d i a t i o n (L*) at night. s September 9, 10, 1973. A l l data c o l l e c t e d at 2030 PST„ 65 Tw'' T g ~ m e a n w a l l and canyon f l o o r temperatures r e s p e c t i v e l y . Assuming T w i s approximated'by the mean a i r temper-a t u r e i n the canyon on these n i g h t s (2 89 K), the temperature d i f f e r e n c e between the w a l l s and the f l o o r i s ; T , - T n = 7 — 3 - = 2 ' 6 0 ° C < 4 w* > 4eaT , R e s u l t s from 0300 PST i n d i c a t e t h a t the l i n e a r r e -* l a t i o n between L and V F s i s maintained through the n i g h t w i t h minor changes i n s l o p e and i n t e r c e p t (Table 4 . 1 ) . TABLE 4.1 RESULTS OF REGRESSION ANALYSIS BETWEEN L* AND VF * (L = a + b.VF ) DATA SET TIME a b r 2 S ' E * L * (PST) (W m"2) ( W m - 2 } ALL DATA 2030 -4.9 -71.2 -0.86 7.3 0300 -7.2 -64.0 -0.85 6.7 ALL DATA (Less F l o o r ) 2030 -8.8 -70.7 -0.98 3.4 0300 -10.8 -63.5 -0.98 2.6 FLOOR ONLY 2 030 3.4 -63.6 -0.61 2.3 0300 7.9 -73.3 -0.79 1.7 I t i s l i k e l y t h a t t h i s type of r e l a t i o n s h i p holds on most o c c a s i o n s w i t h c l o u d l e s s s k i e s , l i g h t winds and a dry sur-66 face. This s i t u a t i o n occurrs when the processes are l a r g e l y governed by such properties as the surface thermal conductivity and the r a d i a t i o n geometry which remain e s s e n t i a l l y constant. C. LONG-WAVE FLUX DIVERGENCE IN THE CANYON-AIR VOLUME 1. Introduction I n i t i a l work i n r a d i a t i v e flux divergence was by use of r a d i a t i o n charts or complex numerical methods (Elsasser, 1942; Elsasser and Culbertson, 1960; Brooks, 1950). These tech-niques were further refined f o r the case of the boundary layer (Deacon, 1950; Funk, 1960) and computer technology has allowed * f l u x divergence (div Q ) to be incorporated into boundary layer models (Zdunkowski and Track, 1971; Atwater, 1972). Funk (1960) made the f i r s t d i r e c t measurement of * div Q at a r u r a l s i t e using accurate radiometry. Funk's r e -s u l t s , l a t e r v e r i f i e d by Gaevskaya et al. (1973) show that with l i g h t winds and cloudless skies the r a d i a t i v e cooling rate con-siderably exceeds the actual measured cooling rate. Fuggle (1971) shows s i m i l a r r e s u l t s for an above-roof urban s i t e . The discrepancy i s a t t r i b u t e d to the f a c t that the r a d i a t i v e cooling i s i n f a c t o f f s e t by turbulent warming. Gaevskaya et al. (1973) point out that the r a d i a t i v e and turbulent processes are simul-taneous, non-linear and cannot be simply added to achieve t o t a l cooling. This i s further supported by the r e s u l t s of Timanov-skaya and Farapanova (1967) who independently measured the r a d i a t i v e and sensible heat divergences. 67 Under calm conditions we might expect that the r a d i a -t i v e divergence w i l l dominate, and may approximate the actual cooling rate. Rider and Robinson (1951) found that on calm cle a r nights, the r a d i a t i o n divergence approached zero i n the mean. The urban canyon i s l i k e l y to be a good lo c a t i o n since airflows sometimes almost becomes stagnant between the r a d i a t i n g * elements. Thus div Q was studied i n the canyon at night to ob-serve i t s magnitude and d i r e c t i o n , and to compare the r a d i a t i v e cooling rates (AT/At) with the actual cooling (AT/At) . In r mea s * studying div Q i t must be remembered that the canyon i s not homogeneous i n the lengthwise d i r e c t i o n . Thus i t i s necessary to investigate both t h i s horizontal divergence, and that i n the canyon cross-section, r e s u l t i n g i n canyon-air volume divergence. 2.Longitudinal Flux Divergence i n the Canyon Longitudinal f l u x divergence along the canyon length was investigated with the aid of two net radiometers whose long-wave c a l i b r a t i o n s agreed to within 1 per cent. They were mounted at 3 m above the f l o o r on two masts separated by a horizontal distance of 7.6m and were located on eit h e r side of the main experimental cross-section. The radiometer receiving surfaces were oriented normal to the lengthwise d i r e c t i o n , and t h e i r difference was taken to be the horizontal divergence. The radiometer signals were monitored every 10 min, and the data averaged over a 1 h period during the period from 1600 PST on July 17, to 0700 PST on July 20, 1973. Only the nocturnal data are considered here. 68 The o v e r a l l l o n g i t u d i n a l r a d i a t i o n d i v e r g e n c e i n the H * canyon-air volume [Q ] i s g i v e n by [Q'*1H = (Q* - Q*)W.H. (4.9) where Q s, Q N = the net all- w a v e r a d i a t i o n a t the south and n o r t h ends o f the canyon, r e s p e c t i v e l y , and the square b r a c k e t s i n d i c a t e volume averages. I t i s * * * assumed t h a t Q g and Q N a r e average v a l u e s o f Q f o r the south and n o r t h v e r t i c a l c r o s s - s e c t i o n s . G e n e r a l l y the r a d i o m e t e r s i n d i c a t e d a net r a d i a n t c o o l i n g i n the canyon. The p o s s i b i l i t y e x i s t s t h a t t h i s a r i s e s from d i f f e r e n t view f a c t o r s f o r the two r a d i o m e t e r s , but t h i s i s d i s c o u n t e d on the grounds t h a t the canyon has a u n i f o r m c r o s s - s e c t i o n , and the d i s t a n c e t o * the canyon ends i s c o n s i d e r a b l e . The v a l u e o f [Q ]„ o b t a i n e d n i s i n t e r p r e t e d t o be due to the d i f f e r e n c e i n thermal e n v i r o n -ment between the canyon and i t s s u r r o u n d i n g s . The r a d i a t i v e temperature change per u n i t time i n the canyon-air volume c o r r e s p o n d i n g t o the net change i n * storage [Q ] H i s g i v e n by: A T t Q * ] H (££> = - — 4 (4.10) A t r p v P-The r e s u l t i n g r a d i a t i v e c o o l i n g i n the c a n y o n - a i r volume f o r the three o b s e r v a t i o n n i g h t s i s g i v e n i n F i g u r e 4.6. Most of the c o o l i n g r a t e s are i n the range 0 t o 1.0°C h " 1 w i t h a mean 69 o o oT I I o > E ? » o tt c > — o> r; o» .E c •o o o -c oc u 3 ~-2 4-1 A, -e e-o A o e o f Q July 17/18 • July 18/19 • July 19/20 18 19 2 20 2 2 23 2 4 01 02 0 3 0 4 0 5 0 6 TimelPST) F i g . 4 . 6 R a d i a t i v e energy s t o r age i n canyon volume due to l eng thw i se d i v e r g e n c e •[Q*] H. • 70 of 0.6°C h x . A regression l i n e f i t t e d to the data i n -dicated a s l i g h t decrease i n r a d i a t i v e cooling with time, but the slope was not highly s i g n i f i c a n t . The r e s u l t s c l e a r l y * show the existence of [Q ]„ i n the urban canyon and therefore n i t must be considered i n canyon-air cooling at night. 3. Flux Divergence i n the Canyon Cross-Section The r a d i a t i v e f l u x divergence for the canyon cross-section ( i . e . , the experimental section normal to the canyon axis) can be expressed i n terms of a net storage i n the a i r -volume: [Q*] c = (W.Q* + H(Q* + Q*) - W.Q*}L (4.11) Equation 4.11 can be evaluated using the mast and boom arrange-* ment of radiometers described i n Chapter 2. A l l of the Q terms on the right-hand side represent measurements around the perimeter of the cross-section. During nocturnal observations each of the f i v e positions across the canyon cross-section was sampled once every 3 min before midnight and once every 6 min. * a f t e r . The data were averaged over a 1 h period and [Q ] c calcu-lated. The sampling frequency i s adequate to account for storage changes with time based on the work of Lee and G i l l e (1972) . They show that a i r temperature changes i n the atmosphere due to an o s c i l l a -tory r a d i a t i o n f i e l d i s a function of height so that high frequency fl u c t u a t i o n s are damped within a few centimeters of the sur-face, leaving longer period waves to contribute at greater 71 h e i g h t s . A l s o Fuggle (1971) showed t h a t h i g h frequency f l u c t u -* a t i o n s o f d i v Q are an o r d e r o f magnitude l e s s than the steady-s t a t e v a l u e . F i g u r e 4.7 shows the v a r i a t i o n o f the r a d i a t i v e temper-* a t u r e change (using [Q ] c i n E q u a t i o n 4.10) w i t h time on f o u r c l o u d l e s s n i g h t s w i t h l i g h t winds, 2 of which are incomplete data s e t s . In the e a r l y evening t h e r e i s c o n s i d e r a b l e s c a t t e r , probably as a r e s u l t of temperature f l u c t u a t i o n s a s s o c i a t e d w i t h i n t e r m i t t e n t t u r b u l e n c e as the daytime winds subside t o the n o c t u r n a l calm. F o l l o w i n g sunset a t a p p r o x i m a t e l y 1730 PST r a d i a t i v e c o o l i n g i s s t r o n g (1.5 - 3.0°C h "*") , but as the n i g h t p r o g r e s s e s t h i s g r a d u a l l y decreases u n t i l about midnight f o l l o w -i n g which r a d i a t i v e warming o c c u r s . T h i s i s a v e r y i n t e r e s t i n g p a t t e r n q u i t e u n l i k e most o t h e r environments r e p o r t e d , but i t s e x p l a n a t i o n i s not c l e a r . The p o s s i b i l i t y o f measurement e r r o r due to dew d e p o s i t i o n ( i n c r e a s i n g L+) i s v e r y u n l i k e l y because the instruments were checked v i s u a l l y w h i l s t i n o p e r a t i o n and no dew was observed, and as the r e s u l t s i n Chapter 6 w i l l show, the canyon i s c h a r a c t e r i z e d by e v a p o r a t i o n throughout these n i g h t s . Assuming the warming i s r e a l i t s e x p l a n a t i o n must be r e l a t e d t o the temperature s t r u c t u r e . In g e n e r a l most theory and measurements f i n d r a d i a -t i v e warming c l o s e to the ground by day ( l a p s e c o n d i t i o n s ) , and r a d i a t i v e c o o l i n g by n i g h t ( i n v e r s i o n ) , but i t i s p o s s i b l e to f i n d accounts of warming c l o s e to the ground a t n i g h t . F l e a g l e I J&T /At )y *1 u3 f r O H-0) rr O H O CO CO t CO CD CD CD 3 CD O rr P-•O iQ 3 ^< 0) t- 1 CO rr fli O H- tl < 0» CD u3 h CD CD 3 o CD O * o ' - J 3 3 O < o CD Qi C CD ( Radiative Temperature Change in Canyon volume / "Ch-1) 1 ro 1 00 ro O to ro ro 3 3 O ro o OJ 2 o 01 o • o •o I —I • > o • * o o 1* o • 6 > • • o CO CO CO CO (D (H (D (D •O -O X) x> —* cTZ. 73 (1965) and Kondo (1971) both note t h i s close to the ground from t h e o r e t i c a l considerations, and Lieske and Stroschein (1967) * corroborate t h i s from div Q measurements over an a r c t i c snow surface. In the three-dimensional canyon s i t u a t i o n r a d i a t i v e * warming occurs when the sum Q entering the volume i s greater * than the sum Q leaving the canyon top. This might occur i f the canyon-air volume were warmer than the a i r above the canyon top and surrounding roofs. Unfortunately, no temperature data l i n k i n g the canyon and the a i r layer above were observed i n t h i s study. I t does seem r e a l i s t i c , however, to postulate that the roofs cool more than the canyon from view factor consider-ations (Figure 4.5). D. RADIATIVE AND ACTUAL COOLING IN THE CANYON-AIR VOLUME As mentioned i t i s not normal to expect actual measured cooling rates to agree with computed r a d i a t i v e rates, because the procedure neglects turbulent heat transfer as a process i n producing a i r temperature change. However, for the case of stagnant a i r i n a canyon i t may not be unreasonable to expect agreement, and t h i s . p o s s i b i l i t y i s tested here. Measured temperature change (AT/At) meas was obtained by s p a t i a l l y averaging the mean hourly a i r tempera-tures across the canyon cross-section, and r a d i a t i v e change was * computed using [Q ] ^ i n Equation 4.10. Data was a v a i l a b l e for the nights of September 9-11 and 13, 1973. 74 F i g u r e 4.8(a) shows the agreement between (AT/At) and (AT/At) . Large s c a t t e r i s o b t a i n e d a t h i g h c o o l i n g ' meas ^ 3 ^ r a t e s which tend to occur i n the e a r l y evening and may be r e l a t e d t o u n s e t t l e d winds a t t h i s time (see a l s o F i g u r e 4.7). Because the v a r i a n c e i s not evenly d i s t r i b u t e d a r e -g r e s s i o n a n a l y s i s was not attempted. However, when the d a t a p r i o r t o 203 0 PST are e l i m i n a t e d a more d e f i n e d r e l a t i o n i s o b t a i n e d [ F i g u r e 4 . 9 ( a ) ] . The l e a s t squares f i t to the d a t a i n d i c a t e s t h a t (AT/At) i s approximately twice as l a r g e as (AT/At)____ f and the r e l a t i o n s h i p i s s i g n i f i c a n t a t the 1% l e v e l . * These r e l a t i o n s do not, however, account f o r [Q ] . I f we assume the r a t e s g i v e n i n F i g u r e 4.6 are a p p l i c a b l e to the September d a t a then an o v e r a l l c a n y o n - a i r volume f l u x d i v e r -* * * gence [Q ] = [Q ] + [Q ] i s o b t a i n e d . Although t h i s approach H C o v e r s i m p l i f i e s the s i t u a t i o n i t i s the o n l y p r a c t i c a l means a v a i l a b l e here. F i g u r e s 4.8(b) and 4.9(b) show how the t o t a l r a d i a t i v e temperature change (using [Q ] i n E q u a t i o n 4.10). agrees w i t h the measured c o o l i n g f o r a l l the d a t a , and f o r d a t a a f t e r 2030 PST r e s p e c t i v e l y . Again the l a t t e r r e l a t i o n i s b e s t and s i g n i f i c a n t a t the 1% l e v e l . The s l o p e of the r e l a t i o n i n F i g u r e 4.9(b) i s 2.27 and t h i s i s c o n s i d e r a b l y smaller than the 3.5 r e p o r t e d by Funk (1960) f o r a r u r a l s i t e , and 3.0 g i v e n by Fuggle (1971) f o r an above-roof urban s i t e . These d i f f e r e n c e s are p r o b a b l y r e l a t e d t o such s i t e p h y s i c a l p r o p e r t i e s as atmos-o)Excluding Horizontol Divergence M Including Horizontol Divergence o September 9/10 • September 10/11 A. September 11 (evej & September 13 leva) o y o O S • • ' A o • • © • / o • o , e ^ o ^ o • • _ • _or> o -.5 -10 -15 -20 10 -.5 * -10 -'-5 -2;° ^ -• . . . Meosured Temperature Chcmge.(O/^tHX Measured Temperature Change^T/AtfaeaS F i g - 4.8 R a d i a t i v e vs. measured temperature change f o r a l l data. ( j a) Excluding Horizontal Divergence o September 9 / i0 • September 10/11 A September II (evej A September 13 (eve) 3.0 1.0 IP b) Including Horizontal Divergence r f = o.56 STD. error inf^ -V=a50°ch" -1.0 -1.5 -2.0 Measured Temperoture Change^AT/A-^hjeaS (^ Ch-<) Measured Temperature Change. Car') ' F i g . 4.9 Radiative vs. measured temperature change for data c o l l e c t e d a f t e r 2030 PST„ 77 p h e r i c e m i s s i v i t y , sky view f a c t o r , aerodynamic roughness and v e r t i c a l temperature s t r u c t u r e . The r e s u l t s bear out the hypothesis t h a t i n a s h e l t e r e d urban canyon the agreement between (AT/At) and (AT/At) i s improved. T h i s i s f u r t h e r r meas supported by F i g u r e 4.10(a) which compares the r a d i a t i v e , and a c t u a l c o o l i n g f o l l o w i n g sunset. I n i t i a l l y r a d i a t i v e c o o l i n g i s s t r o n g e r than the measured, but 5h a f t e r sunset the t r e n d r e v e r s e s due t o the f l u x convergence noted i n F i g u r e 4.7. The c u m u l a t i v e agreement i s e x c e l l e n t s i n c e by 9h a f t e r sun-s e t the d i f f e r e n c e i s o n l y 0.5°C. A t any time d u r i n g the c o o l -i n g p e r i o d the maximum d i s c r e p a n c y i s app r o x i m a t e l y 1.2°C. Alth o u g h r a d i a t i v e f l u x d i v e r g e n c e g i v e s u s e f u l i n s i g h t s i n t o the p h y s i c a l p r o c e s s e s c o n t r o l l i n g n o c t u r n a l c o o l i n g , i t s u s e f u l n e s s as a p r e d i c t i v e or f o r e c a s t i n g t o o l i s l i m i t e d , e s p e c i a l l y i n an urban canyon where a t h e o r e t i c a l framework has y e t to be fo r m u l a t e d . A much more common approach i s t o r e l a t e a i r c o o l i n g to s u r f a c e c o o l i n g v i a an a n a l y s i s pre-sented by Brunt (1941). The Brunt formula i s a s o l u t i o n o f the s u r f a c e energy balance e q u a t i o n f o r c o n d i t i o n s when advec-t i o n , and a p p r e c i a b l e s e n s i b l e or l a t e n t heat t r a n s f e r may be n e g l e c t e d . T h i s o c c u r s under c l o u d l e s s , l i g h t wind c o n d i t i o n s * and then the L l o s s must be balanced by an upward f l o w o f heat * from the u n d e r l y i n g medium. F u r t h e r , i f L i s assumed to be con s t a n t w i t h time ( f o r the canyon see F i g u r e s 4.1 to 4.4 a t night) and the i n i t i a l s u b s u r f a c e temperature p r o f i l e i s assumed 78 i s o t h e r m a l , then the s u r f a c e temperature decrease from sun-s e t (AT ) i s g i v e n by: s * AT = - j 2 L t • t h (4.12) where t = time from sunset, C = heat c a p a c i t y of the u n d e r l y i n g medium. S i m i l a r but more complex formulae have been developed by F l e a g l e (1950), and H a l t i n e r and M a r t i n (1957) but they i n v o l v e d too many i n p u t parameters f o r use here. Kawamura (1965) showed t h a t i n t r a -urban a i r temperature d i f f e r e n c e s were c o r r e l a t e d w i t h s u r f a c e c o n d u c t i v i t y and heat c a p a c i t y . Oke and Maxwell (1975) show t h a t although E q u a t i o n 4.12 f i t s r u r a l d a t a w e l l , i t i s not as u s e f u l i n d e s c r i b i n g the urban c o o l i n g i n M o n t r e a l and Vancouver whose c o o l i n g appears to be l i n e a r l y r e l a t e d t o time. Although E q u a t i o n 4.12 was intended f o r h o r i z o n t a l s u r f a c e s i t was t e s t e d here f o r use i n d e s c r i b i n g c o o l i n g i n the canyon, w i t h a p p r o p r i a t e m o d i f i c a t i o n . F i r s t l y , the v a l u e s f o r k and C were s e l e c t e d (Table 4.2). The canyon f l o o r was assumed to be composed of 80% g r a v e l ( g r a n i t e + a i r ) and 20% sandy c l a y , and the g r a v e l was found to c o n t a i n 37% a i r by volume. * Secondly, i t i s not c l e a r where L r e f e r s t o i n the case o f the canyon. Two d i f f e r e n t v a l u e s were used i n E q u a t i o n 79 * 4.12, one was an average L f o r the th r e e canyon s u r f a c e s _* computed i n the same manner as Q (Equation 4.2), the o t h e r was L f o r the canyon top computed as_Q (Equation 4.4). TABLE 4.2 VALUES OF THERMAL CONDUCTIVITY (k) , HEAT CAPACITY (C), THERMAL ADMITTANCE (y) FOR CANYON MATERIALS MATERIAL -1 -1 -3 -1 -2 -1 -1 (W m K ) (J m K ) (J m * K SOURCE s 2) CONCRETE GRANITE SANDY CLAY A I R CANYON AVERAGE 1.60 2. 80 0.92 0.02 1.60 2.09 x 10 6 1.83 x 10 3 2.15 x 1 0 6 2.45 x 10 3 2.47 x 10 6 1.51 x 10 3 1.20 x 10- 4.89 1.88 x 10 6 1.73 x 10 3 I.H.V.E. (1969) L i s t (1965) L i s t (1965) L i s t (1965) C a l c u l a t e d + u = (kC)^ The r e s u l t s o f the Brunt c a l c u l a t i o n s a re compared w i t h the average measured canyon c o o l i n g [ c a l c u l a t e d as i n F i g u r e 4.10 (a)] i n F i g u r e 4.10(b). C l e a r l y the Brunt curve u s i n g the a v e r -* * age s u r f a c e L v a l u e i s u n s a t i s f a c t o r y but t h a t u s i n g L f o r the canyon top i s a good d e a l c l o s e r t o the measured r e s u l t s , such t h a t a s l i g h t adjustment i n the y v a l u e would produce good 80 O r i • Measured temperature cooling o Radiative cooling o 2 3-4 5 6 7 8 9 O • O 4 5 6 Time from sunset (hrs) 10 \ (W-\ 2 3 4 5 6 7-o e Measured temperature cooling AVoncouver dota (Ofee et al . ,1972) O Brunt formula ( L*, av. 3 components) Brunt- form ula, (Cy canjroh fop) E c »-8 -9 • io!- 4 5 6 Time from sunsel (hrs) 10 F i g . 4.10 Temperature decrease a f t e r sunse't i n the canyon u s i n g data f o r September 9, 10, 11 and 13: (a) compared w i t h t o t a l r a d i a t i v e c o o l i n g i n the canyon averaged over the same p e r i o d ; (b) compared w i t h the Brunt c o o l i n g r a t e . 81 agreement. In the f i r s t few hours a f t e r sunset the Brunt curve r e p r e s e n t s too h i g h a c o o l i n g r a t e but l a t e r i t almost p a r a l l e l s the measurements. I t may be t h a t i n c r e a s e d t u r b u l e n c e i n the e a r l y evening r e t a r d s the canyon c o o l i n g , or i t may be t h a t i n i t i a l l y the s u r f a c e c o o l s more r a p i d l y than the a i r . A l t e r n a t i v e l y i t may be t h a t the s e n s i b l e heat l o s s from the top o f the canyon i s r e s t r i c t e d i n the e a r l y evening u n t i l the warmer canyon a i r possesses enough buoyancy t o i n t e r a c t w i t h the a i r l a y e r above. R e s u l t s from Oke and Maxwell (197 5) are a l s o i n -clu d e d i n F i g u r e 4.10(b)-. These data a r e s p a t i a l l y averaged temperatures observed d u r i n g automobile t r a v e r s e s i n c e n t r a l Vancouver on c l o u d l e s s n i g h t s w i t h v e r y l i g h t winds. The r e s u l t s , t h e r e f o r e , a l s o r e f e r t o in-canyon c o n d i t i o n s and the agreement w i t h the data here i s remarkably good e s p e c i a l l y a f t e r about 3h a f t e r s u n s e t . The Brunt a n a l y s i s p r o v i d e s a r e l a t i v e l y simple way t o model the heat i s l a n d u s i n g a p p r o p r i a t e s u r f a c e p r o p e r -t i e s f o r urban and r u r a l a r e a s , but i t i s r e s t r i c t e d t o the m e t e o r o l o g i c a l c o n d i t i o n s o u t l i n e d . CHAPTER 5 SUBSURFACE HEAT FLUX IN THE CANYON A. INTRODUCTION The s u b s u r f a c e heat f l u x (Q G) i s c o n s i d e r e d to be an important term i n urban c l i m a t e s . I t i s commonly regarded as a c r i t i c a l f a c t o r i n the development of the n o c t u r n a l heat i s l a n d ( i . e . , r e l e a s e o f s t o r e d daytime heat from b u i l d i n g m a t e r i a l s ) , but t h e r e are no d i r e c t s t u d i e s t o v e r i f y such an a s s e r t i o n . In a d d i t i o n i n the case o f a 'dry' canyon an a b i l -* i t y t o a p p o r t i o n the a p p r o p r i a t e amount of Q t h a t i s used or p r o v i d e d by Q_ a u t o m a t i c a l l y g i v e s Q„ as a r e s i d u a l . Given the thermal p r o p e r t i e s of the m a t e r i a l (espe-c i a l l y k and C), and the s u r f a c e boundary c o n d i t i o n s the sub-s u r f a c e heat f l u x c o u l d be d e r i v e d t h e o r e t i c a l l y (e.g., Carslaw and Jaeger, 1959). For the canyon, however, the s u r f a c e bound-ar y c o n d i t i o n s are not a l l known and d i r e c t measurement of Q„ Cj was undertaken. T h i s chapter examines the problems of measurement o f Q G i n the canyon ( i n c l u d i n g the c a l i b r a t i o n , behaviour and e r r o r s a s s o c i a t e d w i t h heat f l u x p l a t e s ) , a n d the t y p i c a l p a t t e r n of heat cond u c t i o n i n the canyon. In p a r t i c u l a r the p a t t e r n s of Q_ are r e l a t e d t o the complex i n p u t (or l o s s ) o f r a d i a n t energy i n the canyon (as shown i n Chapters 3 and 4 ) . i 82 83 B. CALIBRATION The heat f l u x p l a t e s ( d e s c r i b e d i n Chapter 2) were s u p p l i e d w i t h f a c t o r y c a l i b r a t i o n s . A check on t h i s c a l i b r a t i o n was f i r s t conducted f o l l o w i n g the technique of Idso (1971, 1972). D e t a i l s a re p r o v i d e d i n Appendix A. In o u t l i n e the method i n -v o l v e s the heat f l u x sensor b e i n g p l a c e d i n f r o n t o f a hot p l a t e the heat output o f which i s c o n t i n u o u s l y a d j u s t e d . Both s i d e s o f the sensor, and the hot p l a t e a re p a i n t e d f l a t b l a c k , and the experiment i s conducted i n a c o n t r o l l e d l i g h t and temperature environment. A p l o t o f sensor output a t known hot p l a t e temp-e r a t u r e s s h o u l d y i e l d a s t r a i g h t l i n e , the s l o p e o f which i s r e l a t e d to the sensor c a l i b r a t i o n . A comparison between s i x o f these l a b o r a t o r y c a l i -b r a t i o n s and those s u p p l i e d by the f a c t o r y i s g i v e n i n T a b l e 5.1. C l e a r l y the l a b o r a t o r y t echnique g i v e s lower sensor o u t -put c a l i b r a t i o n s , but the range o f d i f f e r e n c e s (6 - 25%) i s unacceptably l a r g e . The r e p e a t a b i l i t y o f the l a b o r a t o r y c a l i -b r a t i o n was found to be approximately 10% f o r a g i v e n p l a t e . Random e r r o r s are u n l i k e l y to e x p l a i n the observed f a c t o r y / l a b o r a t o r y c a l i b r a t i o n d i f f e r e n c e s which are t h e r e f o r e p r o b a b l y r e l a t e d to an e r r o r i n one of the procedures. A second independent check on the f a c t o r y c a l i b r a t i o n was conducted f o l l o w i n g the scheme o f Fuchs and Tanner (1968). T h i s i n v o l v e s immersing the sensor i n a substance of known t h e r -mal c o n d u c t i v i t y , and measuring the v e r t i c a l temperature g r a d i e n t 84 ac r o s s i t . By employing a m o d i f i c a t i o n of Eq u a t i o n 2.1, the sensor output a t known heat f l u x r a t e s i s o b t a i n e d . TABLE 5.1 COMPARISON OF HEAT FLUX PLATE CALIBRATIONS PLATE FACTORY LABORATORY . LAB./FACT. % NO. CALIBRATION CALIBRATION RATIO DIFFERENCE (yV/Wm - 2) (yV/Wm - 2) FROM FACTO 1 0.71 0.63 0.89 11 2 0.86 0.65 0.75 24 3 0.71 0.67 0.94 6 4 0. 69 0.57 0.83 17 5 0.75 0.64 0.86 13 6 0.79 0.59 0.74 25 Mean 0.84 16 F o l l o w i n g Fuchs and Tanner a p l a t e was p l a c e d i n a box (0. 53 x 0.53 x 0.18m) of d r y beach sand. The p l a t e was l o c a t e d a t a depth o f 5 cm and thermocouples were used to mea-sure the v e r t i c a l temperature d i f f e r e n c e s between the 3 and 5 cm, and 5 and 7 cm depths. The sand heat f l u x (CO was G then assumed to be g i v e n by: AT AT Q G = k s < ( A Z Z ) 3 - 5 + ( A z Z ) 5 - 7 > / 2 (5.1) where k g = thermal c o n d u c t i v i t y o f sand (assumed v a l u e o f 0.25 Wm ±K 1 a f t e r Fuchs and Tanner, 1968); 85 AT (^ z z) = v e r t i c a l temperature g r a d i e n t x ^ between depths x and F i g u r e 5.1 g i v e s the r e s u l t s o f comparison between Qn o b t a i n e d from the g r a d i e n t method (Equation 5;1) and from the heat f l u x p l a t e (using both the f a c t o r y and l a b o r a t o r y c a l i b r a t i o n s ) , f o r an experiment conducted o u t - o f - d o o r s ; Some o f the data s c a t t e r i s p r o b a b l y a t t r i b u t a b l e t o the combined e f f e c t s o f the n a t u r a l v a r i a b i l i t y i n the r a d i a n t i n p u t and eon= v e c t i v e a c t i v i t y , and the d i f f e r e n t response times of the thermocouples v i s - a - v i s the heat f l u x p l a t e . The f a c t o r y c a l i b r a t i o n u n d e r p r e d i c t s the f l u x ( r e g r e s s i o n s l o p e = G;85)j whereas the l a b o r a t o r y c a l i b r a t i o n s l i g h t l y o v e r p r e d i c t s ( r e -g r e s s i o n s l o p e = 1.14). There i s l i t t l e to choose between tfi§ two approaches, but the f a c t o r y v a l u e s would appear b e t t e r f o r the f o l l o w i n g reason. P r e l i m i n a r y measurements up to 10 days p r i o r €6 €H§ r e s u l t s i n F i g u r e 5.1 suggest t h a t the o r i g i n a l sand was n©€ e n t i r e l y d r y and thus the assumed v a l u e o f k g was i n c o r r e c t i T h i s d r y i n g appears to be almost complete by June 28 but any f u r t h e r s l i g h t changes would b r i n g the f a c t o r y r e s u l t s c l o s e r t o the 1:1 l i n e , but move the l a b o r a t o r y v a l u e s f u r t h e r away. Knowing the p l a t e s were t o be used i n c o n c r e t e i n the canyon/ i t was d e c i d e d to r e p e a t the g r a d i e n t approach experiment u s i n g a c o n c r e t e b l o c k . 86 F i g . 5.1 Comparison of s o i l heat f l u x plate with gradient measurements (sand). June 27, 28, 1973. 87 C. CALIBRATION IN CONCRETE To r e p e a t the sand experiment u s i n g c o n c r e t e r e -q u i r e s a knowledge of the thermal c o n d u c t i v i t y of c o n c r e t e (k ). c The value o f k , however, shows a wide range o f v a l u e s (see I.H.V.E., 1969 ) t h e r e f o r e experimental d e t e r m i n a t i o n was deemed n e c e s s a r y . The v a l u e o f fc f o r the c o n c r e t e b l o c k was d e t e r -c mined u s i n g a thermal comparator (Powell, 195 7; A n s o r i and I q b a l , 1 9 7 1 ) . The comparator c o n s i s t s of two phosphor-bronze spheres (0.4 cm diameter) mounted i n b a l s a wood. One sphere p r o t r u d e s s l i g h t l y from the wood, the o t h e r remains s l i g h t l y i n s e t , and the d i f f e r e n t i a l temperature between them i s measured by 36 AWG i r o n - c o n s t a n t a n thermocouples. The pro-cedure i s t o heat these u n i t s t o approximately 70°C i n an oven and a l l o w the d i f f e r e n t i a l temperature t o s e t t l e t o zero. The comparator i s removed and p l a c e d i n c o n t a c t w i t h the sample which i s at room temperature. A n s o r i and I q b a l (1971) then show t h a t the spheres c o o l a t d i f f e r e n t r a t e s , and by conduc-t i o n a l one, and t h a t the c o o l i n g i s p r o p o r t i o n a l t o the r o o t of t h e sample's c o n d u c t i v i t y . The c o n d u c t i v i t y of the sample can be measured i f samples o f o t h e r m a t e r i a l s o f known conduc-t i v i t y are a v a i l a b l e f o r comparison. In t h i s case samples of e b o n i t e , pyrex and q u a r t z (thermal c o n d u c t i v i t i e s 0.19, 1.15 and 1.40 Wm "^ K \ r e s p e c t i v e l y ) were compared w i t h a s l a b o f i c o n c r e t e (18 x 13 x 2.5 cm) cut from the b l o c k used i n the ex-88 periment. F i g u r e 5.2 shows an example of the k- vs c o o l i n g p l o t s . T h i s experiment y i e l d e d k c = 0.85 Wm~1k~1, and on the b a s i s o f other runs a mean v a l u e o f k =0.90 Wm"^"^ was c s e l e c t e d f o r use. I t i s i m p l i c i t i n the t h e o r y of the heat f l u x p l a t e t h a t the p l a t e c o n d u c t i v i t y be r o u g h l y e q u i v a l e n t t o t h a t o o f the medium i n which i t i s immersed. S o i l heat f l u x p l a t e s o f the type used here n o r m a l l y have thermal c o n d u c t i v i t i e s w i t h -i n the range o f most s o i l s , 0.3 t o 3 0.0 Wm"^"1 (Fuchs and Tanner, 1968), and t h e c o n c r e t e v a l u e l i e s w i t h i n t h i s range. Because the a c t u a l thermal c o n d u c t i v i t y o f the p l a t e s v/ere not a v a i l a b l e . ( e i t h e r from the manufacturer, o r from experiment) the heat f l u x output o f the p l a t e s was d i r e c t l y compared w i t h t h a t from the g r a d i e n t method o u t l i n e d i n the p r e v i o u s sec-t i o n . Concrete was poured t o form a blo c k (0.42 x 0.42 x 0.15 m),. T h i s e n c l o s e d a heat f l u x p l a t e a t a depth o f 5 cm and two temperature d i f f e r e n c e thermocouple p a i r s between 3 and 5 cm, and 5 and 7 cm as i n the sand experiment. A f t e r a l l o w -i n g the c o n c r e t e t o d r y , measurements were conducted o u t - o f - d o o r s t o g i v e simultaneous heat f l u x e s from the p l a t e and the g r a d i e n t s u s i n g E q u a t i o n 5.1, and k c d e r i v e d from the comparator e x p e r i -ment. The r e s u l t s of t h i s experiment are g i v e n i n F i g u r e 5.3. C l e a r l y the comparison u s i n g the f a c t o r y c a l i b r a t i o n i s O Ebonite SO 60 70 80 90 10,0 Ng '20 Oifferentiol cooling. (jJv in 10 secoVvts) co vo F i g . 5.2 Qetermination of the thermal c o n d u c t i v i t y of concrete. E o Q. 100 80 60 40 20 -60 . -4P , -2p / / / / / / A* / ° ' 08 o f\ o • °°. * y o / _ l I JL. 20 40 6 0 8 0 0 e Gradient method (Wm-») r--20 - 4 0 -60 O Laboratory • Factory k e=O.90 Wm - ' K 100 5.3 Comparison of s o i l heat flux plate with gradient measurements (concrete). May 30, 31, and June 4 1973. 91 s u p e r i o r , and t h i s v e r i f i e s the t e n t a t i v e c o n c l u s i o n reached i n the p r e c e d i n g s e c t i o n . The agreement u s i n g the f a c t o r y c a l i b r a t i o n i s w i t h i n 5 % , and on t h i s b a s i s f a c t o r y v a l u e s were a p p l i e d t o a l l the canyon s u b s u r f a c e d a t a . D.- SUBSURFACE FLUX DIVERGENCE Heat f l u x p l a t e s i n s e r t e d beneath the s u r f a c e r e -f e r t o heat f l u x e s a t t h a t depth and not those a t the s u r f a c e / atmosphere i n t e r f a c e which are needed i n the s u r f a c e energy balance. I t i s t h e r e f o r e n e c e s s a r y t o e s t i m a t e t h i s d i v e r -gence to assess i t s importance. The v e r t i c a l d i vergence i n the heat f l u x Q Q i s g i v e n by: 9 Q r 9 T vr-onr ( 5 - 2 ) I n t e g r a t i o n between the s u r f a c e and a depth z g i v e s : Q G(o ) " . Q G ( z ) + V * ^ d Z • < 5 - 3 ' where Q_, . = co n d u c t i v e heat f l u x a t the i n t e r f a c e ; G (o) Q_, x = subsurface heat f l u x a t depth z. G(z) The second term on the r i g h t hand s i d e o f E q u a t i o n 5 . 3 may be approximated: ! 92 8T AT V z TT d z - c r r A z ( 5- 4 ) Flux divergence i n bu i l d i n g materials was f i r s t evaluated i n the tar and gravel roof of the U.B.C. Geography Building. Equations 5.3 and 5.4 were used to estimate t h i s divergence by measuring Q_ at 0.5 cm with a flux plate, AT /At 6 — 3 — i at 0.25 cm with a thermocouple, and using C = 3.17 x 10 Jm K (Saal, Heukelom and Blokker, 1940; I.H.V.E. Guide, 19 69). The re s u l t s i n Figure 5.4 show divergence to be lea s t at night with a s l i g h t tendency for underestimation of the nocturnal upward flux using the plate alone. In the_late morning there i s an underestimation by the pla t e of the flux i n t o the roof, reach-mg a maximum of 40 Wm , or about 35% of Q G( 0) > a t about 1000 PST. The divergence changes sign i n the afternoon so that the plate alone w i l l overestimate the flux when Q G( 0) becomes neg-ati v e . This hysteresis behaviour i s consistent with s o i l re-s u l t s (Fuchs and Tanner, 1968; Fuchs and Hadas, 1972). Table 5.2 presents a comparison of the maximum flux divergences for the roof, the canyon concrete walls, and the canyon f l o o r . The canyon AT /At values are surface values mea-sured with a Barnes Infra-red Thermometer (Model PRT 10, Barnes Engineering L t d . ) , and are therefore larger than a layer aver-age. Equally they were taken i n extreme conditions when shading of a s u n l i t wall causes sudden cooling and therefore provide safe overestimates. The divergences i n Table 5.2 refer to the layer from the surface to 0.5 cm (the depth of the p l a t e s ) . F i g . 5.4 Divergence experiment i n Geography Building roof, U.B.C. September 5, 6, 1974. 94 TABLE 5.2 COMPARISON OF ROOF, WALL AND FLOOR MAXIMUM HEAT FLUX DIVERGENCES C AT /At d l v QG(0-0.5) " C(AT z/At)Az SURFACE (jrrfV1) (°C s"1) ( W n f 2 ) Roof 3.17 x 10 6 25.2 x 10 4 40 Canyon Walls 2.09 x 10 6 5.5 x 10~ 4 6 Canyon F l o o r 1.57 x 10 6 44.6 x 10~ 4 35 * From Table 4.2 In more un i f o r m c o n d i t i o n s the canyon AT /At measure-z ments i n d i c a t e t h a t d i v QG(g-o 5) w i l l o n l y be 12-20% o f these maximum v a l u e s and i n energy terms can be c o n s i d e r e d s m a l l ( i . e . , -2 -2 w a l l s 0.75 - 1.2 W m ; f l o o r 4.4 - 7.0 W m ). Consequently, no c o r r e c t i o n s f o r f l u x d i v e r g e n c e were a p p l i e d to the canyon d a t a . 0) E. SUBSURFACE HEAT FLUX IN THE CANYON The n a t u r e o f Q G i n the canyon was i n t e n s i v e l y s t u d i e d i n the p e r i o d J u l y 26 to August 1, 197 3. T h i s p e r i o d was c h a r a c t e r i z e d by c l o u d - f r e e c o n d i t i o n s and l i g h t winds. O b s e r v a t i o n s were made eve r y 10 min from each o f the 17 heat f l u x p l a t e s i n t h e canyon c r o s s - s e c t i o n [ F i g u r e 2 . 5 ( b ) ] , The d a t a were averaged t o g i v e h a l f - h o u r l y means. The d i u r n a l p a t t e r n was c o n s i s t e n t from day t o day and t h e r e f o r e the r e s u l t s f o r one day ( J u l y 27) may be assumed t y p i c a l • , F i g u r e 5.5 shows the daytime v a r i a t i o n o f Q_ a t two p o s i t i o n s , f o r each o f t h e t h r e e canyon s u r f a c e s on J u l y 27. O b v i o u s l y , t h e s t o r a g e p a t t e r n i n each component * s u r f a c e i s s t r o n g l y r e l a t e d to the p a t t e r n o f Q' , as com-p a r i s o n o f F i g u r e s 4.1 - 4.3 and 5.5 w i l l show. Common f e a t u r e s * o f the daytime Q and. Q_ regimes i n c l u d e the. r e l a t i v e t i m i n g . and. magnitude o f t h e peak f l u x e s a t each l o c a t i o n ; the secondary peaks r e l a t e d t o r e f l e c t i o n o f s o l a r r a d i a t i o n from the two w a l l s ; and t h e r e l a t i v e l a c k o f d i f f e r e n t i a t i o n i n f l u x magni-tude when the s u r f a c e i s not i n r e c e i p t o f d i r e c t beam s h o r t -wave r a d i a t i o n . The n o c t u r n a l r e s u l t s a l s o show agreement w i t h the * * Q (or L ) p a t t e r n . In p a r t i c u l a r i n the e a r l y e v e n i n g the g r e a t -e s t s t o r a g e r e l e a s e from both w a l l s i s from the l o c a t i o n s w i t h the l a r g e s t sky view f a c t o r ( i . e . , the h i g h e s t sensor l e v e l ) , The d i f f e r e n c e i s much s m a l l e r i n the l a t e n i g h t p e r i o d , p r e -* sumably because t h e L l o s s e s are l e s s when the heat r e s e r v o i r i s somewhat d e p l e t e d . A l l l o c a t i o n s i n t h e canyon e x h i b i t nega-t i v e Q v a l u e s a t n i g h t ( i . e . , heat flow out o f the b u i l d i n g s and ground). The upper l e v e l on the west w a l l a l s o shows nega-96 (a) West wall 5m height -1.2m height - A — 5 m height 1.2 m height 10 II 12 13 14 15 Time IPST) F i g . 5.5 S u b s u r f a c e heat f l u x a t f i x e d p o i n t s i n the canyon. J u l y 27, 1?73. 97 t i v e Q G a t midday, j u s t a f t e r i t becomes shaded. T h i s be-haviour i s s i m i l a r to t h a t d e s c r i b e d by Yap and Oke (1974)„ T h e i r q u a l i t a t i v e e x p l a n a t i o n suggests t h a t i f a s t r o n g l y heated s u r f a c e i s plunged i n t o shade i t s r a p i d s u r f a c e c o o l -i n g r e v e r s e s the temperature g r a d i e n t i n the topmost l a y e r * and r e s u l t s i n an upward heat f l u x , even though Q may not be n e g a t i v e . The same e x p l a n a t i o n may e x p l a i n the sharp r e v e r -s a l i n the d i r e c t i o n of Q Q a t the upper sensor l e v e l on the e a s t w a l l a t about 173 0 PST. I t i s a l s o c l e a r t h a t Q_ f o r the G ground a t n i g h t i s l e s s than f o r the w a l l s . T h i s i s o p p o s i t e to e x p e c t a t i o n s based on view f a c t o r c o n s i d e r a t i o n s . I t i s p o s s i b l e t h a t t h i s i s due t o the f a c t t h a t Q Q from the w a l l s i s enhanced by the r e l e a s e o f anthropogenic heat (Q ) from the F b u i l d i n g s . The s p a t i a l l y averaged f l u x e s f o r each s u r f a c e (Qn„r Q_ and Q_ ) are g i v e n i n F i g u r e 5.6(a). T h i s c l e a r l y uw o»g Ge demonstrates t h a t the importance o f the i n d i v i d u a l components i s r e s t r i c t e d t o s e p a r a t e times of the day, and a l s o the domi-nant r o l e p l a y e d by the ground heat s t o r a g e i n a b s o l u t e terms. In a manner analogous to E q u a t i o n s 3.3 and 4.2, a s p a t i a l l y averaged Q„ over the t h r e e canyon s u r f a c e s i s d e f i n e d ? G Q C W ' H + Q • W + O • H G 2H + W { ' ; The r e s u l t i s given i n F i g u r e 5.6(b), which i s c h a r a c t e r i z e d by a smooth d i u r n a l course, approximately symme-98 d) SPATIAL AVERAGE ALONG EACH SURFACE -401 ' i <• » i i c i i i i—_-s b) SPATIAL AVERAGE OVER THREE SURFACES T i m e (PST ) F i g . 5.6 S p a t i a l average o f the s u b s u r f a c e heat f l u x f o r J u l y 27, 1973: (a) averaged along each canyon s u r f a c e ; (b) averaged over the three canyon s u r f a c e s . 99 t r i c a l about noon, even though the component s u r f a c e r o l e s are -2 not. A l s o i t i s noted t h a t the peak Q„ of 53 W m i s a t t a i n e d l a at about 1245 PST, c l o s e t o s o l a r noon (1315 PST). I t i s n o r -* mal f o r Q G t o peak about 2h ahead of Q f o r most un o b s t r u c t e d h o r i z o n t a l s u r f a c e s ( S e l l e r s , 1965). Although d a i l y t o t a l c a l -c u l a t i o n s f o r the w a l l s showed s l i g h t d e f i c i t s , t h i s was l a r g e -l y o f f s e t by a net g a i n i n the f l o o r and the ground. Thus f o r the whole system the d a i l y t o t a l s torage approximates z e r o . r CHAPTER 6 ENERGY BALANCE OF THE CANYON A. INTRODUCTION As noted i n Chapter 1, solution of the energy balance of the canyon i s an important objective of t h i s study. The complexity of the urban/atmosphere interface has discour-aged d i r e c t measurement of the energy balance u n t i l recently. There are a few p i l o t studies of the urban energy balance above roofs (e.g., Oke et al., 1972; Yap, 1973; Yap and Oke, 1974) and over paved urban surfaces (Landsberg and Maisel, 1972), but none for the canyon environment. The energy balance f o r most surfaces may be written as i n Equation 1.1: Q* + Q H + Q E + Q G = 0 (6.1) We observe the sign convention that p o s i t i v e q u antities con-tribu t e to interface warming, and negative ones to cooling. In t h i s study Equation 6.1 was used f o r the energy balance of the * canyon f l o o r where Q , Q_ and Q_ were available from meaSUre-Jj (a ment, and Q H was obtained as a r e s i d u a l . For the painted-concrete canyon walls was again determined as a resi d u a l , i n Equation 6.1 but Q_ was assumed to be zero. Anthropogenic heat terms w i l l modify Q_ but w i l l not introduce errors i n the surface energy balance. The energy balance for each of the com-100 101 ponent s u r f a c e s i s g i v e n i n S e c t i o n C o f t h i s c h a p t e r . Whenever measurements remote from a f i n i t e s u r f a c e are used t o c h a r a c t e r i z e the energy balances at t h e i n t e r f a c e the p o s s i b i l i t y o f energy a d v e c t i o n from s u r r o u n d i n g e n v i r o n -ments must be c o n s i d e r e d . Convergence o r divergence o f heat w i t h i n the canyon from o u t s i d e w i l l mean t h a t E q u a t i o n 6.1 does not r e p r e s e n t the s u r f a c e balance c o r r e c t l y . E q u a l l y the energy balance o f the canyon system d e f i n e d a c r o s s the top: Q t + Q H t + Q E t + Q G t " ° ( 6 « w i l l n ot agree w i t h measurement i f energy i s added t o the ca n y o n - a i r volume by a d v e c t i o n from o u t s i d e . To e v a l u a t e the r o l e o f a d v e c t i o n i n t h e canyon an experiment was conducted, and i s r e p o r t e d i n S e c t i o n B ahead o f the energy balance r e -s u l t s . F i n a l l y , t h i s chapter d e a l s w i t h the a i r cooling/warm-i n g r a t e s i n t h e canyon because these are t h e thermal c l i m a t i c e x p r e s s i o n of t h e energy exchanges, and because they p r o v i d e some i n d i r e c t v e r i f i c a t i o n o f the canyon a i r c i r c u l a t i o n . B. ADVECTION - HORIZONTAL AND VERTICAL TRANSPORT OF HEAT o BY MEAN MOTION Here we w i l l c o n s i d e r the problem o f a d v e c t i v e heat t r a n s p o r t i n t o (or out of) the canyon under two types o f a i r flow. I n i t i a l l y we w i l l c o n s i d e r the s i m p l e s t c o n d i t i o n where the wind i s f l o w i n g p a r a l l e l t o the canyon s i d e s ( i . e . , lengthwise) as i l l u s t r a t e d i n F i g u r e 6.1(a). L a t e r we w i l l 102 F i g . 6.1 Schematized a i r flow i n the canyon. 103 consider the case of Figure 6.1(b) where the external wind s t r i k e s the canyon at some angle to the lengthwise axis. The dimensions and areas i n the analysis which follows are given in Figure 6.1(c). 1• Flow P a r a l l e l to Canyon Let U q be the instantaneous wind v e l o c i t y , averaged over the cross-sectional area A^, for the p a r a l l e l -flow case. Then the mean-horizontal heat transport through A^ can be approximated by: P C P U o T o A l = p c p ( u c + u o } ( T o + T o ) A l = pc (u T + u ' T' ) A, ,(• P O O O O l V o • J / where u Q = time-averaged horizontal v e l o c i t y , u' = instantaneous v e l o c i t y departure from ° the mean, T Q = instantaneous a i r temperature, T Q = time-averaged a i r temperature, = instantaneous temperature departure from the mean . and these r e s u l t s are assumed representative over the cross-section A^. The f i r s t and second terms i n Equation 6.3 represent the mean, and turbulent heat transport r e s p e c t i v e l y . S i m i l a r l y at some distance L downstream the mean transport through the canyon cross-section 104 w i l l be: and the mean heat flow through the canyon top (Q H t) iss Q H t = P C P ( W T 2 ) A 2 = pc (wT + w*T')A_ (6,5) P 2 2 / where w = instantaneous v e r t i c a l v e l o c i t y averaged over the area A 2 = W,L, w = time-averaged v e r t i c a l v e l o c i t y , w' = instantaneous v e r t i c a l v e l o c i t y departure from the mean, T 2 = time-averaged a i r temperature, and space-averaged over the canyon top area A 2 , T^ = instantaneous departure from T^o Denoting p o s i t i v e changes by the d e l t a symbols, we have u^ = u Q - A U q since any change i n u inside the canyon must be due to f r i c t i o n with the walls. The sign of the change i n T Q i s not c e r t a i n so that T. = T ± AT . Substituting these r e -l o o ^ la t i o n s i n the energy balance of the canyon-air volume gives: 105 p C p [ u o T o A l ~ u l T i A i " W T 2 A 2 ] + S o u r c e terms + Storage te = p C p [ ± A T o ( u o - A 5 0 ) A l + T 0A{I OA 1 4- u ^ F A 1 - - w^ A , , rms - v/'T^A^ + Source terms + Storage terms = 0 (6.6) The signs of the turbulent t r a n s f e r terms are a r b i -trary since the c o r r e l a t i o n between u" and T' i s not known. o o The other terms are p o s i t i v e i f they contribute to canyon-a i r warming. We w i l l now consider the r o l e of the terms i n Equation 6.6. Observations of the a i r temperature change i n the canyon show that the heat storage term i s n e g l i g i b l e . We w i l l also assume that the horizontal divergence of the turbu-lent transport terms u'T 1 i s small and may be neglected. This o o assumption, however, remains untested f o r a canyon environment. With these assumptions Equations 6.6 reduces to: pc p[(+AT o(u o - Au Q) + T Q A u O ) A 1 - (wT2 + W T T J ) A 2 I + Source terms = 0 (6.7) Under v i r t u a l l y calm conditions the mean flow terms are n e g l i -gible, and the energy of the source terms i s transported out of the canyon by v e r t i c a l turbulence pc p(w'T^)A 2 alone. This would be the i d e a l case where advection would be zero. Although the energy balance measurements i n t h i s study were r e s t r i c t e d to very l i g h t winds, i t was f e l t necessary to ascertain the magni-106 tude of the f i r s t four terms in Equation 6.7 under the experi-mental conditions. To begin with, we w i l l investigate the size of the f i r s t two terms, ± p c A T (u - A u )A n ; and then p o o o 1 the t h i r d and fourth terms i n combination, p c (T A u A.. - w T „ A 0 ) , The terms ± p c A T (u - A u )A, represent the heat p o o o 1 transport by the mean wind i n combination with the mean h o r i -zontal temperature gradient. To evaluate th i s two instrumen-ted masts were located at the mid-width of the canyon, separated ° by the length-wise distance L = 28 m, and with the most souther-ly mast 40 m from the canyon's south end. Sensitive anemometers (C. W. Thornthwaite Assoc.) and thermometers were exposed at 1,8 and 3.7 m.above the canyon f l o o r . The thermometers were shielded,, and aspirated 26 AWG copper-constantan thermocouples joined to provide temperature differences between the two masts at the two heights. A G i l l wind vane (R. M. Young Co.) was also i n -s t a l l e d between the two masts to measure the wind d i r e c t i o n . A l l signals were monitored every two minutes on the data acquisition, system (Chapter 2) and hourly averages calculated. The experi-ment was conducted during portions of four cloudless days. Figure 6.2 presents the r e s u l t s f o r along-canyon winds (from d i f f e r e n t d i r e c t i o n s at d i f f e r e n t speeds). The value of u i s the mean of two l e v e l s , and A T i s the mean of o ' o the two horizontal gradients. Thus i t i s assumed that these point measurements approximate the mean cross-section conditions. From what at f i r s t appears to be a confused scene, two conclusions 107 21 22 23 I50r IOO • Wind A Advection E •o <u a> a . W •o c c o >» c o o c o <u -100 Time (PST) F i g . 6.2 Advection of heat i n t o or out of the canyon p ' c p A T 0 ( u Q - AU Q) A^yA^. ; [Arrows' I n d i c a t e wind d i r e c t i o n - -up i n d i c a t e s wind from s o u t h ] . 108 emerge. F i r s t l y , w i t h winds c o n s i s t e n t l y from one d i r e c t i o n along the canyon, the advected energy term i s a f u n c t i o n o f windspeed (e.g., J u l y 10). Secondly,' t h e s i g n o f the advec-t i o n term i s d i r e c t l y r e l a t e d t o the wind d i r e c t i o n , s o uther-l y winds r e s u l t i n a n e t a d d i t i o n o f energy t o the c a n y o n - a i r volume (warming) and n o r t h e r l y winds a n e t d e p l e t i o n ( c o o l i n g ) . T h i s means t h a t the a r e a t o the south o f t h e canyon (Grandview Highway) i s g e n e r a l l y warmer than the canyon, whereas the area to t h e n o r t h ( r a i l r o a d right-of-way) i s c o o l e r (see F i g u r e 2.4). I g n o r i n g t h e s i g n o f the a d v e c t i o n i t becomes c l e a r that the a b s o l u t e v a l u e o f the n e t t r a n s p o r t i s r e l a t e d t o the canyon wind speed ( F i g u r e 6.3). The form o f the r e l a t i o n i s not c e r t a i n b u t an average t r e n d i s g i v e n by the e y e - f i t l i n e . T h i s i n d i c a t e s t h a t on average f o r along-canyon winds o f 2 m s ^ -2 on c l o u d l e s s summer days t h e net a d v e c t i o n i s about 70 W m ; -1 -2 and a t 1 m s the t r a n s p o r t i s approximately 15 W m The term o f pc (T Au A, - wT 0A_) a r i s e s from t h e f r i c -p o o 1 2 2 t i o n a l r e t a r d a t i o n o f a i r f l o w a l o n g the canyon s u r f a c e s r e s u l t i n g i n u p l i f t . Components A U q and w are r e l a t e d by t h e equ a t i o n of c o n t i n u i t y f o r i n c o m p r e s s i b l e flow: Q A. w = i u r i (6.8) oA 2 and s u b s t i t u t i o n g i v e s the e x p r e s s i o n f o r the mean heat t r a n s p o r t as a r e s u l t o f f r i c t i o n a l r e t a r d a t i o n : pc A-Au (T - T_) (6.9) p 1 O O 2 109 > £ ~ o o O > < 150 100 50 s A A ' t' A' *AA/A A A A • A*A I Canyon wind speed ( ms'1) Fi g . 6.3 Relation between horizontal advection i n the canyon [pc^AT^u^ - A u ^ A ^ A ^ ] and mean canyon wind speed. July 10, 11, 12, 13, 1973. E e 13 U _o > OJ c o u 2.0 1.5 0.5 A -~A-A A A V V A A • northerly coihds v southerly o>indS ' 2 3 4 Ve lo ci ty Tj0 ims"') Fi g . 6.4 F r i c t i o n a l loss of h o r i z o n t a l . v e l o c i t y i n the canyon between two locations 28 m apart.' July 10, 11, 12, 13, 1973. 110 If T > T_ there w i l l be advective warming, i f T < c o o l -O 2 O 2. ing, and i f A U q = 0 advective transport i s zero. The observed f r i c t i o n a l loss A U q as a function of U q i s given i n Figure 6.4, using the average data from the two masts and winds from both the north and south. From Equation 6.8 the maximum u value of 4.75 m s corresponds to a v e r t i c a l v e l o c i t y , w of 1.28 m s No simultaneous (T - T^) measurements were observed. However, using the r e s u l t s from September with the f u l l moveable mast temperature matrix, maximum (T Q - T^) values of 0.2°C were ob-served i n the canyon. This would produce an i n f l a t e d maximum -2 advective warming of approximately 100 W m „ More t y p i c a l _2 values reduce t h i s to about 25 W m I t i s concluded that under l i g h t wind^conditions the t o t a l advective transport with along-canyon winds i s <100 -2 W m . This term w i l l not be accounted for i n the energy balances to follow, and must therefore be considered to be an error f a c t o r . 2. Flow Across the Canyon In the case where the mean wind d i r e c t i o n i s at some angle to the canyon axis, a c i r c u l a t i o n s i m i l a r to that shown i n Figure 6.1(b) (e.g., Georgii, 1969; Wise 1971) may be expected. In t h i s s i t u a t i o n the mean v e r t i c a l flow may be im-portant i n transporting the heat from the canyon into the over-l y i n g 'urban boundary layer. The mean fl u x across the canyon I l l top w i l l then conform to the following modification of Equation 6.5s Q H t = P°p + w^T 1- 2)dA 2)/A 2 (6.10) The existence of such a c i r c u l a t i o n was v i s u a l l y noted by obser-ving tracers, and by measuring the sign and size of the v e r t i c a l v e l o c i t y with a G i l l p r opeller anemometer (R. M. Young Co.). The r e s u l t s i n Figure 6.5 are 15 min averages for three locations across the top of a canyon on a day with strong WNW winds. The r e s u l t s confirm that w ^ 0 with downdrafts over the east w a l l , and updrafts over the west wall and centre, and thus we must expect the mean c i r c u l a t i o n term (wT2) i n Equation 6.10 to be operative. There i s no reason to believe that under these circumstances the turbulent term w'T ' 2 i s absent e i t h e r , and therefore both measurements may operate to remove (or add) heat from the canyon volume. When the meso-scale wind d i r e c t i o n i s normal to the along-canyon axis the horizontal advection i l l u s t r a t e d i n Figures 6.2 and 6.3 may be assumed to be absent, and the mean v e r t i c a l c i r c u l a t i o n exchange expressed by Equation 6.10 w i l l be the domi-nant non-radiative mode of heat exchange with the canyon surround-ings. This form of 'advection' i s not expected to be of net im-portance to the energy balance of the canyon-air volume. This i s because unlike the horizontal advection case the a i r i s not free to pass through the canyon, i t can only enter and e x i t the 0.3 m from W. wall » Canyon centre o - c 0.3 m from E. wall F i g . 6.5 V e r t i c a l wind v e l o c i t i e s at three canyon locations, October 6, 1 9 7 3 . 15 minute averages. Wind from the west. ro 113 canyon v i a the ar e a A 2 (canyon t o p ) . Any n e t i n p u t o f energy ( i . e . , from t h e heated upwind ro o f ) must r e s u l t i n e i t h e r a net change i n energy s t o r a g e i n the a i r volume, o r a n e t change i n the canyon s u r f a c e energy b a l a n c e . The former i s not observed i n our o b s e r v a t i o n s , and the l a t t e r a l t h o u g h un-* l i k e l y would be accounted f o r i n the Q and 0_ measurements near the i n t e r f a c e . T h e r e f o r e E q u a t i o n 6.10 w i l l r e p r e s e n t the t o t a l energy f l u x from t h e c a n y o n - a i r volume t h a t i s escap i n g i n t o the atmosphere d u r i n g t h e day. A n e g a t i v e q u a n t i t y i m p l i e s a l o s s o f energy w h i l e a p o s i t i v e v a l u e r e p r e s e n t s an energy g a i n by the a i r volume. In the absence o f h o r i z o n t a l a d v e c t i o n and r a d i a t i v e f l u x d i v e r g e n c e , the above term equals the t o t a l s e n s i b l e heat incoming or ou t g o i n g from the three canyon s u r f a c e s . F o r the more g e n e r a l case o f meso-scale winds a t other angles o f a t t a c k t o the canyon t h e n e t heat exchange w i t h the surroundings w i l l i n v o l v e some h o r i z o n t a l a d v e c t i o n and some mean v e r t i c a l c i r c u l a t i o n t r a n s p o r t . T h i s should r e s u l t i n a t o t a l ' a d v e c t i v e ' t r a n s p o r t which w i l l be approximately r e p r e s e n t e d by t h e h o r i z o n t a l a d v e c t i o n r e l a t i o n o f F i g u r e 6.3. C. ENERGY BALANCE OF THE CANYON 1. I n s t r u m e n t a t i o n  1 The energy balance i n s t r u m e n t a t i o n f o r Q and Qn 114 at the canyon wall and f l o o r surfaces was as i n Chapters 4 and 5. Assuming the walls to be 'dry' during the observation period t h e i r balance i s completed by assuming Q H to be the balance r e s i d u a l . The gravel over clay f l o o r , however, could be assumed to possess evaporable water even though the surface appeared r e l a t i v e l y a r i d . Correspondingly a miniature weigh-able lysimeter was i n s t a l l e d i n the canyon. 0 The simple design p r i n c i p l e followed that of Pas-q u i l l (1950). The lysimeter consists of two a c r y l i c tubes (thickness 0.4 cm, length 16 cm), one able to f i t i n s i d e the other (diameters 10 and 11 cm). The inner tube contains the undisturbed s o i l sample (closed at the base v/ith a p l a s t i c bag cover), and the other tube i s sunk i n the ground to pro-vide a neat housing and moisture s h i e l d . The inner tube i s f i l l e d with s o i l by i n s e r t i n g i t inside a standard g o l f hole-cutter, which i s then used to core out the undisturbed sample, The lysimeter was located i n the centre of the canyon--, and 0.5 m south of the flux plate l i n e . Measurements were made every hour during the energy balance experiment, The inner tube and s o i l were removed and quickly weighed on a t r i p l e -beam balance (Fisher S c i e n t i f i c Co. Ltd.) and then replaced. The balance had a capacity of 2.61 kg, and a resolution of 0.1 g; t h i s gave a resolution of about 10 W m i n the hourly Q E estimates (excluding observer and other e r r o r s ) . The sample needed replacement following r a i n , and a f t e r a few days' use. 115 2. Surface Energy Balance of Component Surfaces The intensive observation period for energy balance measurement' was September 9-11, 1973. The weather was characterized by continuously cloudless skies, and weak winds (usually <2 m s ^ by day, and <1 m s ^ by night i n the canyon). Figure 6.6 shows the three-day average hourly energy balance components f o r both walls and the canyon f l o o r . Simi-* l a r d i u r n a l patterns of Q and Q „ for each surface have been described and analyzed i n Chapters 4 and 5, thus here we w i l l focus on the turbulent terms Q„ and Q_, and the r e l a t i v e mag-nitude of the component.terms. For a l l three surfaces Q R represents the dominant energy d i s s i p a t i o n mode during the daytime. Thus at midday Q H * * represents 0.70 - 0.80 Q for the dry walls, and 0.6 0 Q for the canyon f l o o r . At night Q H i s very small f o r a l l surfaces, and thus f o r the two walls the nocturnal balance i s approxi-* -2 mately Q = Q Q 3 50 W m . In general Q H i s p o s i t i v e at night ( i . e . , the canyon a i r i s warmer than the walls and floor) but s l i g h t l y negative values are evident for the west wall at times. This may be r e a l , but i s also probably within instrumental accuracy. The pattern of Q E for the f l o o r i s reasonable giving s l i g h t evaporation through the night [again within the i n s t r u -mental accuracy given in Section C ( l ) ] , and peak values (=50 W m at midday. This would produce a Bowen r a t i o ( 6 ' = QH/QE) °f approximately 5.5. C l e a r l y i n absolute energy terms the f l o o r Fig. 6 . 6 3-day average energy balance components f o r i n d i v i d u a l canyon surfaces. September 9, 10, 11, 1973. 117 i s by far the most important exchange surface i n the canyon. 3. Energy Balance at the Canyon Top The d i u r n a l v a r i a t i o n of the average energy balance components f o r the complete canyon system (as i n Equa= tion 6.2), are shown i n Figure 6.7. Considering the windspeeds during the experimental period i t i s assumed that the maximum error involved i n ignoring the advective terms i s approximately -2 -2 70 W m by day,and 15 W m by night (Figure 6,3). On most occasions they w i l l be less than these values. I t i s also im-* portant to remember that Q t i s obtained from the three surfaces (see Equations 4.3 and 4.4) and i s not a measured value, D i f f e r -ences between t h i s quantity and measurement would be important i n r a d i a t i v e cooling/warming c a l c u l a t i o n s , but do not s i g n i f i -cantly a f f e c t the r e s i d u a l , Q„.. The course of the composite balance components i s remarkably smooth considering the d i f f e r i n g phase r e l a t i o n s f o r the i n d i v i d u a l surfaces (Figure 6.6). I t i s i n t e r e s t i n g to note * -2 that the peak Q value i s 500 W m , which i s very s i m i l a r to -2 the 460 W m measured over a f l a t gravel-over-tar roof i n central Vancouver at the same time (Brown, personal communi-* catio n ) . Equally the nocturnal Q l o s s values agree very close--2 l y at both s i t e s , being approximately 70 W m . The only s i g -n i f i c a n t difference between the two s i t e s i s that the times of * Q = 0 occur about one hour l a t e r i n the morning, and probably 118 2 4 6 8 10 12 14 16 18 20 22 24 T i m e (ps.T) F i g . 6.7 3-day average energy balance compo-nents i n the canyon. September 9, 10, 11, 1973. 119 one hour e a r l i e r i n the evening, at the canyon s i t e . This agreement between roof and canyon values may indicate that * the s p a t i a l v a r i a b i l i t y of Q i n an urban area i s not large when viewed from an a e r i a l platform. The r e l a t i v e r o l e s of Q„,, Q and Q show that Cat H t E t by day the most important mechanism for heat loss from the canyon i s that of sensible heat, and at the peak Q = 0.66 Q . H t By comparison the latent heat transfer i s small, so that = 6.5 at midday. The role of C- i s c e r t a i n l y important in the * o v e r a l l balance so that at the peak Q = 0.30 Q . The po s i -V j t tion of t h i s peak storage i s i n phase with the net ra d i a t i o n , as noted f o r Q „ e a r l i e r i n the summer [Figure 5.6(b)], and t h i s i s l a t e r than f o r horizontal surfaces (e.g., for f l a t roof values see Yap and Oke, 1974). At night the turbulent terms Q„. and Q_. are small n t Cit -2 (<25 W m ) and of opposite sign, thus t h e i r net e f f e c t i s close to zero in the balance. The net loss of long-wave r a d i -ation i s therefore balanced by drawing upon the subsurface heat storage. The absence of convective a c t i v i t y therefore high-l i g h t s the conclusion drawn i n Chapter 4 that ra d i a t i v e flux divergence i s the main a i r cooling mechanism at night i n the canyon under a n t i c y c l o n i c conditions. There are no energy balance measurements for a canyon with which these r e s u l t s can be compared. To put them in the urban context, however, there are energy balance data for 120 other parts of Vancouver. Yap (personal communication) pro-vides data from above a f l a t gravel-over-tar roof i n c e n t r a l * -2 Vancouver. With Q = 5 00 W m at midday on September 1, 1972, -2 Q„ from eddy c o r r e l a t i o n measurements was about 25 0 W m near H -2 the roof, and 2 00 W m at higher l e v e l s which were interpreted as representing areal values rather than just f o r the roof. Perhaps more pertinent to t h i s study, are measurements conducted at 50 m on a tower 4 km downwind of the canyon at the same time as the r e s u l t s i n Figure 6.7. The eddy c o r r e l a t i o n measurements are expected to represent integrated urban Q R fluxes. Although somewhat v a r i a b l e , the peak Q„ values were approximately 25 0 W m r l during the period of the canyon experiment. (Brown, personal communication). Thus the canyon r e s u l t s probably represent close to an upper l i m i t f o r Q H values i n the urban area as we might expect, since water i s very r e s t r i c t e d there compared to the t o t a l urban surface. 4. Canyon A i r Cooling/Warming Rates Canyon a i r cooling/warming rates were calculated as i n Chapter 4, Section E from the hourly mean temperatures i n the 7 x 5 matrix. The r e s u l t s for September 9, 1973 are given i n Figure 6.8. At 0800 PST the top of the west wall i s i n d i r e c t i l l u m i n a t i o n and the strongest heating of the a i r occurs at the same l o c a t i o n . Note, however, that the rates of change of F i g . 6.8 Warming r a t e s i n the canyon. September 9, 1973. 122 a i r temperature have t h e i r h i g h e s t n u m e r i c a l v a l u e o f any time of t h e day i n the morning. T h i s may be because the canyon a i r i s s t a b l e and i s not r e a d i l y exchanging heat w i t h the e x t e r i o r , By 1200 PST a ve r y d i f f e r e n t s i t u a t i o n has developed now t h a t the sun i s s h i n i n g d i r e c t l y down the canyon. The s t r o n g changes of warming r a t e i n the h o r i z o n t a l may be r e l a t e d t o a mean v e r t i c a l c i r c u l a t i o n . Such a c i r c u l a t i o n c o u l d a r i s e •J from e x t e r n a l wind e f f e c t s , i n t e r n a l buoyancy e f f e c t s , o r a combination of these dynamic and thermal causes. By 1600 PST the whole canyon i s c o o l i n g as i t becomes shaded. The s t r o n g -e s t c o o l i n g occurs on the e a s t w a l l which has j u s t changed from str o n g Q ga i n t o a l o s s . The i s o - l i n e s of temperature change are s t i l l a l i g n e d v e r t i c a l l y . At 2100 PST the canyon c o o l i n g appears t o o r i g i n a t e from the w a l l s i n agreement w i t h t h e o r y . The s m a l l e r c o o l i n g near t h e f l o o r i s somewhat s u r p r i s i n g on view f a c t o r grounds (see F i g u r e 4.5). A f u l l e x p l a n a t i o n i s not apparent but may be r e l a t e d to the d i f f e r i n g heat c a p a c i -t i e s o f the w a l l s and f l o o r (see Table 5.2)„ CHAPTER 7 MODELLING CONSIDERATIONS A. INTRODUCTION The p r e c e d i n g c h a p t e r s p r e s e n t and i n t e r p r e t measure-ments of the energy exchanges and balances i n the environment of one s p e c i f i c urban canyon. The purpose was to i l l u m i n a t e the nature o f the p h y s i c a l p r o c e s s e s o p e r a t i n g i n such a s t r u c -t u r e , and t h e i r r o l e i n e s t a b l i s h i n g the thermal environment o f the canyon. In the l a r g e r c o n t e x t of urban c l i m a t o l o g y the can-yon i s seen as a b a s i c g e o m e t r i c a l u n i t o f the urban-atmosphere i n t e r f a c e , so t h a t these data may h e l p t o e s t a b l i s h t h e o r e t i c a l and e m p i r i c a l r e l a t i o n s h i p s o f use i n m o d e l l i n g o t h e r urban c o n -f i g u r a t i o n s , and p o s s i b l y an i n t e g r a t e d urban s u r f a c e . Because the m o d e l l i n g scheme must i n c o r p o r a t e some of these e m p i r i c a l r e l a t i o n s , the g e n e r a l i t y o f the model i s l i m i t e d by the c o n s t r a i n t s o f the exp e r i m e n t a l c o n d i t i o n s . I n p a r t i c u l a r the model which f o l l o w s can r e f e r o n l y s t r i c t l y to s u r f a c e c o n d i t i o n s i n the m i d - l a t i t u d e s i n summer w i t h c l o u d -l e s s s k i e s , weak a i r f l o w and l o c a t i o n s where e v a p o r a t i n g s u r -f a c e s a re absent. Although such l i m i t a t i o n s may appear v e r y r e s t r i c t i v e , i n f a c t they l a r g e l y r e p r e s e n t c o n d i t i o n s under which maximum heat i s l a n d s and a i r p o l l u t i o n c o n c e n t r a t i o n s are observed, and under which many oth e r models break down. The 123 124 m o d e l l i n g scheme i s d i r e c t e d towards the s e n s i b l e heat f l u x which i s important i n the urban atmosphere because i t d i r e c t l y a l t e r s the s t a b i l i t y . F i g u r e 7.1 s c h e m a t i c a l l y d e p i c t s the sequence of steps i n v o l v e d i n o p e r a t i o n a l i z i n g the model proposed here. The t h e o r e t i c a l , c l o u d l e s s sky v a l u e o f K l above the s u r f a c e i s c a l c u l a t e d i n STAGE I . Given the b u i l d i n g dimensions and * the albedos o f the component s u r f a c e s the v a l u e o f K i s ob-* t a i n e d i n STAGE I I . U s i n g an e m p i r i c a l r e l a t i o n s h i p between K and Q (developed here) the r a d i a t i o n balance i s determined i n STAGE I I I . A s i m i l a r r e l a t i o n s h i p i s employed to o b t a i n Q Q from Q* i n STAGE IV, and thus f i n a l l y by assuming l a t e n t (Q_) and anthropogenic heat (Q F) t o be n e g l i g i b l e , Q H i s o b t a i n e d as a r e s i d u a l i n the s u r f a c e energy balance (Equation 6.1) i n STAGE V. The need t o r e s o r t t o e m p i r i c a l r e l a t i o n s h i p s between * * * K and Q , and Q and Q G i s r o o t e d i n fundamental t h e o r e t i c a l d i f f i c u l t i e s which are o u t l i n e d l a t e r i n t h i s c h a pter. The assumption r e g a r d i n g Q p i s v a l i d a t e d f o r the e x p e r i m e n t a l s i t e i n summer by the work o f Yap (1973) on the urban s c a l e , and by t h e . b u i l d i n g c h a r a c t e r i s t i c s (Chapter 2) on the m i c r o - s c a l e . Given r e a s o n a b l e adherence t o the c o n s t r a i n t s on t h i s model, i t may be p o s s i b l e to apply i t not j u s t t o a s i n g l e can-yon, but to an a r r a y of b l o c k - l i k e s t r u c t u r e s w i t h dimensions and (a) DAY THEORETICAL INCOMING SOLAR RADIATION (KA) NET SOLAR RADIATION (K*) ALBEDO BUILDING DIMENSIONS NET ALL-WAVE RADIATION (Q ) BUILDING DIMENSIONS SUBSURFACE HEAT FLUX (QG) SENSIBLE HEAT FLUX IQH) ( b ) N I G H T NET LONG-WAVE SUBSURFACE RADIATION HEAT FLUX ( L*) (Q G ) SENSIBLE HEAT FLUX I Q H ) F i g v 7 o i „ M o d e l l i n g scheme to o b t a i n s e n s i b l e heat f l u x : (a) day? (b) n i g h t * 126 o r i e n t a t i o n approaching an urban s i t u a t i o n . For example, the model may p r o v i d e a f i r s t approximation to the s u r f a c e energy balance i n an urban area c h a r a c t e r i z e d by l a c k of n a t u r a l s u r -f a c e s and u n i f o r m i t y i n b u i l d i n g type. In p a r t i c u l a r i t may p r o v i d e more r e a l i s t i c s u r f a c e boundary c o n d i t i o n s f o r dynamic models of the urban boundary l a y e r . to the sequence of STAGES i n v o l v e d i n the model ( i . e . , F i g u r e 7.1) . B. STAGE I - CALCULATION OF K4; The Houghton (1954) model f o r c l e a r s k i e s , as o u t -l i n e d i n Nunez et al. (1971), was used to p r e d i c t incoming s o l a r r a d i a t i o n . In the model the e x t r a - t e r r e s t r i a l r a d i a t i o n i s de-p l e t e d by water vapour a b s o r p t i o n and s c a t t e r i n g , atmospheric R a y l e i g h s c a t t e r i n g , a e r o s o l s c a t t e r i n g and a b s o r p t i o n . Hough-ton assumed t h a t a b s o r p t i o n occurs b e f o r e s c a t t e r i n g , and t h a t o n e - h a l f o f the s c a t t e r e d r a d i a t i o n reaches the s u r f a c e as the d i f f u s e component. The f i n a l e x p r e s s i o n i s : The remainder of t h i s chapter i s o r g a n i z e d a c c o r d i n g I o I (r ) cos Z ' [ ( 1 - 0 ) < l - S r ) T d + I I 0.5 T d , ( l - 0 w ) ( l - ( l - S w ) • (1-S r) x d,>] (7.1) 127 where I = e x t r a - t e r r e s t r i a l s o l a r r a d i a t i o n o • o i n t e n s i t y = 1355 W m~z, r = r a d i u s v e c t o r o f the Sun, Z* = z e n i t h angle of the Sun, 0 w = a b s o r p t i o n c o e f f i c i e n t f o r water vapour, S w = s c a t t e r i n g c o e f f i c i e n t f o r water vapour, . S r = R a y l e i g h s c a t t e r i n g c o e f f i c i e n t , = t r a n s m i s s i o n c o e f f i c i e n t f o r a e r o s o l absorp-t i o n and s c a t t e r i n g = (.95) m, where m i s the s o l a r a i r mass, T d , = t r a n s m i s s i o n c o e f f i c i e n t f o r a e r o s o l s c a t t e r -i n g o r a b s o r p t i o n = (.975) m„ Term I r e p r e s e n t s the d i r e c t r a d i a t i o n r e c e i v e d a t the s u r f a c e , and Term I I the d i f f u s e component. The a e r o s o l t r a n s m i s s i o n c o e f f i c i e n t i s a g l o b a l average c a l c u l a t e d by Houghton, Values f o r 0 , S , S were a l s o o b t a i n e d from curves g i v e n by W w JT Houghton (1954). Nunez et al. (1971) assumed t h a t h a l f o f t h e a e r o s o l d e p l e t i o n was due t o a e r o s o l s c a t t e r i n g . T h e r e f o r e 2 T d ^ ^ Td'^ * N u n e z e * a1" (1971) c o n f i r m t h a t t h i s t e c h n i q u e p r o v i d e s a good method f o r o b t a i n i n g K l f o r a h o r i z o n t a l s u r f a c e i n d i f f e r e n t a e r o s o l environments. A mean monthly p r e c i p i t a b l e water vapour o f 1.80 cm was used i n the c a l c u l a t i o n o f 0 w . T h i s v a l u e was o b t a i n e d from Hay (1971). F i g u r e 7.2 shows the agree-* ment between c a c u l a t e d K v a l u e s (using K l from the Houghton model, and a mean measured albedo o f 0.124), and those measured 128 F i g . 7.2 Comparison of c a l c u l a t e d and measured net s o l a r r a d i a t i o n (K*) f o r the Geography B u i l d i n g r o o f , U.B.C. 129 over the r o o f o f the Geography Department b u i l d i n g a t U.B.C. on June 17, 18, 1974. I t i s now r e q u i r e d to d e v i s e a m o d e l l i n g scheme which a l l o w s s i m i l a r p r e d i c t i o n s w i t h i n a canyon geo-metry . * o C. STAGE I I - CALCULATION OF K IN THE 'CANYON The approach u t i l i z e d here f i r s t i n v o l v e s c a l c u l a t i n g the s o l a r r a d i a t i o n i n c i d e n t on each o f the canyon s u r f a c e s (both w a l l s , and the f l o o r ) . G iven the albedo o f these s u r f a c e s and * the canyon dimensions i t i s then p o s s i b l e to c a l c u l a t e f r o m E q u a t i o n 3.5: K* = (H/W)(K* + K*) + K* (7.2) and a l s o the albedo o f the canyon system (<*t) from: K * t " K t 't K+ t (7,3) where, K+ t i s the i n p u t from the Houghton c a l c u l a t i o n s averaged a c r o s s the canyon t o p . S i n c e t h i s p a r t i c u l a r e x p e r i m e n t a l can-yon has w a l l s o f uneven h e i g h t , K+ t w i l l d i f f e r s l i g h t l y from the Houghton c a l c u l a t i o n . * The Kfc model g i v e n i n E q u a t i o n 7.2 i n v o l v e s the f o l l o w -i n g assumptions: (i) d i f f u s e r a d i a t i o n from the sky i s d i s t r i b u t e d over the canyon s u r f a c e s a c c o r d i n g 130 to t h e i r s u r f a c e a r e a s , ( i i ) the canyon s u r f a c e s a r e Lambertian and t h e r e f o r e r e f l e c t the s o l a r r a d i a t i o n i n a d i f f u s e f a s h i o n , ( i i i ) the canyon i s of s u f f i c i e n t l e n g t h such t h a t the s u r f a c e s may be c o n s i d e r e d of i n -f i n i t e e x t e n t i n view f a c t o r c a l c u l a t i o n s , (iv) t h e r e i s no l o s s o f s o l a r energy lengthwise from the canyon, 0 (v) t h e r e i s no a b s o r p t i o n o f s o l a r energy i n the c a n y o n - a i r volume. As an example, the s o l a r r a d i a t i o n i n c i d e n t on each o f the th r e e canyon s u r f a c e s (K4-w, K4-g and K+ e) f o r the e a r l y morning i s g i v e n by: K4- = ( I ' • cos <J0P + D + n W W W K+ g = D g + a w • ( I ' cos 4-) • VF^_ g ( ? K * e = D e + aw ' ( I ' C O S * } " V Fw-e + Q e where I' = incoming d i r e c t r a d i a t i o n a f t e r d e p l e t i o n by R a y l e i g h s c a t t e r i n g , water vapour and a e r o s o l s , (Houghton model), <J> = angle o f i n c i d e n c e f o r the canyon w a l l s , P = per c e n t o f the canyon w a l l s i n s u n l i g h t , ^e' w^' fi = s ° l a r i r r a d i a n c e from secondary r e f l e c t i o n s ^ on the e a s t , west and ground s u r f a c e s , D , D , D = d i f f u s e r a d i a t i o n i n c i d e n t on the e a s t , e w cr ^ west and ground s u r f a c e s , VF^_. = view f a c t o r f o r the i r r a d i a t e d i t h s u r -^ f a c e as seen by the j t h s u r f a c e . 131 The d i f f u s e r a d i a t i o n from the sky (D) i n c i d e n t on each w a l l i s c a l c u l a t e d u s i n g the p r i n c i p l e of c o n s e r v a t i o n o f r a d i a n t energy. Denoting and as the f r a c t i o n of the incoming d i f f u s e r a d i -a t i o n i n c i d e n t on the w a l l s and ground r e s p e c t i v e l y , we o b t a i n : D * W • L = (D • F1 • H • L) + (D • F± • H - L) + (D • F 2 • W • L) ' (7.5) The f i r s t and second terms on the r i g h t - h a n d s i d e r e f e r t o t h e d i f f u s e r a d i a t i o n i n c i d e n t on the two canyon w a l l s (F^ i s assumed by symmetry t o be e q u a l on the two canyon walls)» The t h i r d term r e f e r s t o D on the canyon ground. S i m p l i f y i n g , F 1(2H/W) + F 2 = 1 (7.6) and thus an i n f i n i t e number o f s o l u t i o n s e x i s t f o r F^ and F^* The i s o t r o p y of the d i f f u s e r a d i a t i o n would b e s t be r e p r e s e n t e d i f F 1 = F 2 , I f t h i s i s the case F 1 would e q u a l 1/(1 + 2H/W) which equals 0.403. T h e r e f o r e D_ = D = D = 0.403D. e w g The view f a c t o r f o r each i r r a d i a t e d canyon s u r f a c e as seen by an o p p o s i t e canyon s u r f a c e i s c a l c u l a t e d as f o l l o w s . For each p o i n t (i) along the r e c e i v i n g s u r f a c e , the view f a c t o r i s o b t a i n e d u s i n g Equations 4.5 or 4.6 depending on whether the s u r f a c e s a r e p e r p e n d i c u l a r or p a r a l l e l . The mean r a d i a t i o n r e -c e i v e d on the f i r s t s u r f a c e from the i r r a d i a t e d second s u r f a c e K+1 i s : 1 3 2 n •I V F 2 - i K l ' = I 1 cos t|) • a 1 1 = I ' cos i}> • a V F 2 _ 1 ( 7 , 7 ) and the sum i s performed over the n r e c e i v i n g p o i n t s along s u r f a c e 1. The view f a c t o r s change w i t h the i r r a d i a n c e o f the w a l l . I t i s important t o r e a l i z e t h a t t h i s a n a l y s i s o n l y a p p l i e s t o the i r r a d i a t e d p o r t i o n o f the canyon s u r f a c e . Other s u r f a c e s do not r e f l e c t s o l a r energy o t h e r than t h a t from t h e i r r a d i a t e d w a l l s . The outg o i n g r a d i a t i o n from the s u n l i t w a l l was allowed to be r e f l e c t e d a maximum o f t h r e e times i n the can-yon s i n c e the t h i r d o r d e r term c a l c u l a t i o n s were s m a l l . T h i s term i s c a l c u l a t e d from E q u a t i o n 7 . 7 , and i s denoted by the symbol ft i n Eq u a t i o n 7 . 4 . The c a l c u l a t i o n o f <ji and P a r e d e s c r i b e d i n Appendices B and C. F i g u r e 7 . 3 shows the net s o l a r a b s o r p t i o n by the * experimental canyon system (K^) f o r August 1 3 . Albedos o f 0 . 6 2 , 0 . 5 2 and 0 . 1 3 were used f o r the west w a l l , e a s t w a l l and ground r e s p e c t i v e l y (see Chapter 3 ) . The comparable e x p e r i m e n t a l d a t a i n F i g u r e 7 . 3 a r e based on 4 days of o b s e r v a t i o n (August 8 , 9 7 13 and 1 4 , 1 9 7 3 ) and r e p r e s e n t i n s t a n t a n e o u s r e a d i n g s a t the g i v e n times. In the morning experimental-model d i f f e r e n c e s - 2 are <50 W m . In the a f t e r n o o n , however, the model c o n s i s t e n t l y underestimates the f l u x e s . The maximum underestimate i s =50 - 2 W m a t 1 4 0 0 PST. Reasons f o r these d i f f e r e n c e s a re u n e x p l a i n e d , but c o u l d i n c l u d e the f o l l o w i n g : (i) temporal changes i n the a t t e n u a t i o n o f K+ t due to the d i u r n a l t r a n s p o r t o f p o l l u t a n t s by the sea breeze c i r c u l a t i o n , 133 * F i g . 7.3 Net s o l a r f l u x (K \ f o r the canyon system. 134 ( i i ) improper assumptions r e g a r d i n g the r a d i a t i v e p r o p e r t i e s of the w a l l s and t h e i r p a i n t , i n c l u d i n g the p o s s i b i l i t y t h a t the s u r -f a c e s are non-Lambertian, ( i i i ) measurement e r r o r s . On a mean d a i l y b a s i s the d i s c r e p a n c y between the model and measurements K above the canyon i s about 7% (389 W -2 -2 m measured, 365 W m c a l c u l a t e d ) . However, the d i s c r e p a n c y between the model and measurements from the i n d i v i d u a l canyon s u r f a c e s i s <1% (363 W m measured; 365 c a l c u l a t e d ) . T h i s r a i s e s the p o s s i b i l i t y t h a t the measurements above the canyon are i n e r r o r but t h i s c o u l d hot be f u r t h e r proven. Thus f o r d a i l y t o t a l s the model i s pro b a b l y adequate, but r e q u i r e s f u r -t h e r work t o g a i n c o n f i d e n c e i n p r e d i c t i n g h o u r l y v a l u e s . D. STAGE I I I •= THE RELATION BETWEEN K AND Q Prompted by d i f f i c u l t i e s i n measuring Q , and the low d e n s i t y o f standard networks, s e v e r a l s t u d i e s have attempted * * to d e f i n e r e l a t i o n s between K and Q , M o n t e i t h and Szeiez (1961) and Davies and Buttimor (1969), among o t h e r s , have i n v e s t i g a t e d the u s e f u l n e s s p f a s u r f a c e h e a t i n g c o e f f i c i e n t (h) which re= l a t e s the thermal response of the s u r f a c e t o the net r a d i a n t in-= Ci * * put, and i s d e f i n e d by h = -dL /dQ . A c c o r d i n g t o t h i s approach * * the r e l a t i o n between Q and K has the form; Q* = K * / ( l + h) + a (7,8) 135 where a i s a co n s t a n t o b t a i n e d from a l i n e a r r e g r e s s i o n of Q * and K . Idso (1968) has c r i t i c i z e d the h e a t i n g c o e f f i c i e n t concept on the grounds t h a t i t i s i n a p p r o p r i a t e t o expect a s i n g l e c o n s t a n t to r e p r e s e n t the i n t e r a c t i o n o f a l l the exchange.3 c o n t r i b u t i n g t o the thermal balance (and t h e r e f o r e h ) a t a s u r f a c e . S i m i l a r l y , on s t a t i s t i c a l grounds Gay (1971) argued * * a g a i n s t p l o t t i n g K vs Q , and proposed t h a t the long^wave * response would be b e t t e r g i v e n by a p l o t of K vs L , The * * slope o f t h i s r e l a t i o n (X = dL /dK ) w i l l then be n e g a t i v e , zero or p o s i t i v e depending on whether f o r a g i v e n 6K , <SL + i§ g r e a t e r , equal o r l e s s than <5L+, U n f o r t u n a t e l y , measurement l i m i t a t i o n s JLn t h i s Study p r e c l u d e d the implementation o f the Gay (1971) approach* In * order to o b t a i n Q i t was t h e r e f o r e n e c e s s a r y t o r e s o r t t o the * * p h y s i c a l l y l e s s s a t i s f a c t o r y r e l a t i o n between K and Q (Equa= t i o n 7 . 8 ) . Such an a n a l y s i s i s t h e r e f o r e o n l y defended. <§R th§ grounds o f p r a c t i c a l i t y , and no d e t a i l e d p h y s i c a l i n t e r p r e t a t i o n s , (e.g., h e a t i n g c o e f f i c i e n t s ) w i l l be pursued. C l e a r l y f u r t h e r work should attempt t o f o l l o w the p h y s i c a l l i n k a g e s between K , L and Q . * Hourly Q measurements f o r the i n d i v i d u a l canyon s u r f a c e s on September 1-5, 7, and 9-11 were averaged t o o b t a i n _* * a mean Q day, and Q was o b t a i n e d by use of E q u a t i o n 4,4, Cor= i36 r esponding Kfc v a l u e s were computed f o r September iO , as i n * * STAGE I I . The r e l a t i o n between K and Q i s g i v e n i n Figur§ 7.4. The canyon r e s u l t s (walls, f l o o r and canyon top) form a 2 _ - • -w e l l d e f i n e d r e l a t i o n s h i p f o r m o d e l l i n g purposes (r = Qi96f -2 _ * S.E.Q^ = 28.0 W m ). T h i s i s t o be expected s i n c e Q c o n t a i n s * K as i t s dominant term. E q u a l l y the r o o f - t o p measurements from the U.B.C. Geography Department b u i l d i n g show a s t r o n f 2 ~ 2 c o r r e l a t i o n (r = 0.98; S.E.^* = 16.7 W m ) 4 The d i f f e r e n c e Q* between the two c o u l d be r e l a t e d to the e r r o r i n computing K f o r the canyon (Stage I I ) , o r measurement e r r o r s i n K f o r the r o o f , or i t may be r e a l ( d i f f e r e n c e i n canyon/roof warmiftf/ c o o l i n g r a t e s ) . E. STAGE IV - THE RELATION BETWgEN_Q*. ANP_Q^ P a r t i t i o n i n g the net r a d i a n t energy intt§ i t s c3c3mp©™ nent t u r b u l e n t and s t o r a g e energy f l u x e s i s o f c e n t r a l iffifG£%&m@ i n any m o d e l l i n g scheme Of the urban energy balance.. Givefi §h§ t h e o r e t i c a l d i f f i c u l t i e s i n v o l v e d i n o b t a i n i n g Q^ - (see Chapter" i j y t h i s s e c t i o n d i s c u s s e s another approach. F o l l o w i n g P r i e s t l e y (1959) the ra t i o * o f s e n s i b l e t<§ s u b s u rface heat f l u x i n the absence o f e v a p o r a t i o n can be deserig§§' by: -|00 l i i i i i i 1 i 0 100 200 300 400 500 600 700 800 K*(Wm-1) F i g . .7.4 Relation between K* and Q* from canyon and roof measurements. Note that canyon values of Q* are measured hourly average fluxes for September 1-5, 7, 9-11., 1973. K* values for the canyon are corresponding t h e o r e t i c a l calculations for September 10, 1973. A l l roof data are measured hourly averages obtained on June 17, 18, 1974. 138 where K„ = t u r b u l e n t d i f f u s i v i t y f o r heat, H 0 = p o t e n t i a l temperature* Furthermore the thermal c o n d u c t i v i t y k can be w r i t t e n i n terms o f a thermal d i f f u s i v i t y 14: K = k / p ' c ' (7<i0) and p ' = d e n s i t y o f the s u r f a c e m a t e r i a l t c' = s p e c i f i c heat o f the s u r f a c e m a t e r i a l * Schmidt (1918) d e r i v e s the f o l l o w i n g r e l a t i o n s Q H P C /K P C O / K H - -J3. = P , H = P—-& (7*11) QQ P 'C VK y Thus the r a t i o o f the two f l u x e s i s r e l a t e d t o the p h y s i c a l p r o p e r t i e s o f the two media, and to the aerodynamic p r o p e r t i e s of the l o c a t i o n . T h e r e f o r e under v a r y i n g s y n o p t i c c o n d i t i o n s and i n the absence of l a t e n t heat t r a n s f e r t i s the o n l y term t o n change i n the r i g h t hand s i d e o f E q u a t i o n 7.11,. *. Hourly averaged v a l u e s of Q and are a v a i l a b l e f o r t Cat the canyon. N e g l e c t i n g the s m a l l l a t e n t heat term, Q„./Q^. can f i t o>t * be o b t a i n e d from Q„./C> = (Q./C> )-"!, and t h e r e f o r e K„ can be n t Cat t (jt n obtained f o r the l i g h t wind c o n d i t i o n of the e x p e r i m e n t a l p e r -i o d . However, i t must remembered t h a t K„ n o r m a l l y r e f e r s to a rl 139 h o r i z o n t a l s u r f a c e . The r e s u l t a n t K„ o b t a i n e d i n t h i s a n a l y -s i s r e f e r s to a canyon c o n f i g u r a t i o n . To p reven t c o n f u s i o n the canyon d i f f u s i v i t y w i l l be l a b e l l e d K^. 1 * F i g u r e 7.5 shows h o u r l y Q and Q f o r the canyon t O t d u r i n g the ca lm, c l o u d l e s s s p e l l i n the f i r s t h a l f o f September. The r e l a t i o n s h i p i s w e l l d e f i n e d . F u r t h e r m o r e , two d i f f e r e n t reg imes a r e n o t i c e d . The l a t e e v e n i n g , e a r l y morning and n i g h t -t ime da ta ( Q G t <50 W m ) have a lower s l o p e than the r e s t . T h i s i s p r o b a b l y due to the lower l e v e l o f t u r b u l e n t a c t i v i t y a t -2 n i g h t . The g r e a t e r s c a t t e r i n the >50 W m da ta r e f l e c t s the v a r i a b i l i t y o f the dayt ime t u r b u l e n t hea t f l u x . On t h i s b a s i s two d i s t i n c t reg imes i n p a r t i t i o n i n g a r e r e c o g n i z e d , and r e f e r r e d to as the ' n i g h t ' and ' d a y ' c o n d i t i o n reg imes . 3 Us ing a mean therma l admi t t ance (y) o f 1.73 x 10 -2 -1 -h -J m K s , f o r the t h r e e canyon s u r f a c e s (Chapter 4 ) , and a 3 - 3 - 1 v a l u e o f 1.20 x 10 J m K f o r the heat c a p a c i t y o f a i r , the -1 i - 1 s o l u t i o n t o E q u a t i o n 7.11 i s Q t T ./Q_, = 0.69 m s 2 / K „ . S i n c e H t G t rl * Q H t / Q G t = Q t ^ G t - 1 v a l u e s o f Qgt c a n b e o b t a i n e d u s i n g t h e s l o p e s * o f the Q G t vs Q r e l a t i o n s h i p s (n ight-weak t u r b u l e n c e ; d a y - s t r o n g tu rbu lence ) shown i n F i g u r e 7.5. The s l o p e s a r e 2.22 and 4.70 f o r the n i g h t and day cases r e s p e c t i v e l y . These y i e l d v a l u e s ' 2 - 1 2 - 1 o f K R o f 3.13 m s a t n i g h t and 28.7 m s by day. The l a t t e r agrees to w i t h i n an o r d e r o f magnitude w i t h dayt ime v a l u e s o f K R ( S e l l e r s , 1965; P r i e s t l e y , 1959). 140 640 f 560 4 8 0 4 0 0 r A A A A A A ^ - A A A A A A A A A A A A A A A A A A 320r 240r 160 A A A A A A * A A A A 8 Or A A A A A A A A A A A •80 A A A AA A A A A -80 - 4 0 A AA . A 4 0 Oct A Canyon Site A Geography Roof (U.B.C) 80 ( W r r f 2 ) 120 160 200 F i g . 7.5 R a d i a t i o n between h o u r l y Q and Q f o r canyon and r o o f measurements. G t September 1-5, 7, 9-11, 1973. (Canyon) June 17, 18, 1974 (Geography B u i l d i n g r o o f ) 141 Future work should investigate the r e l a t i o n between * Q and Q_ f o r a v a r i e t y of urban surfaces and configurations under the same synoptic conditions. As a f i r s t step i n such * an analysis, Q and Q„ values from the Geography Department roof are included i n Figure 7.5. The data represent mean hourly values c o l l e c t e d during r e l a t i v e l y calm c l e a r conditions on June 17, 18, 1974. The data give i n d i c a t i o n s of a hystere-s i s loop between the morning and afternoon r e s u l t s . This i s s i m i l a r to the r e s u l t s of Fuchs and Hadas (1972) working over dry l o e s s i a l s o i l . If t h i s phenomenon i s c h a r a c t e r i s t i c of dry, horizontal surfaces, future work must incorporate i t into modelling schemes. F. CONCLUSION In reviewing the model STAGES i t i s c l e a r that the solar terms K+ and K* can be calculated i n an urban canyon. In the case of K* t h i s assumes an accurate knowledge of the albedo of the component surfaces. The daytime model was, how-ever, unable to incorporate long-wave exchange i n the canyon. At night the s i t u a t i o n i s s i m p l i f i e d , and the r e l a t i o n between L and the sky view factor (Chapter 4) i s well defined, and i n conjunction with a Brunt-type cooling analysis allows c a l c u l a -t i o n of canyon cooling rates (Chapter 4). The r e l a t i o n be-* tween Q and Q^ , i s promising, but requires t e s t i n g i n other geometric c o n f i g u r a t i o n s and f o r o t h e r s u r f a c e m a t e r i a l s . S i n c e the model i s d i r e c t e d towards p r e d i c t i o n o f Q H r e l a t i v e l y l a r g e e r r o r s i n such i n t e r m e d i a t e terms as Qn may be a c c e p t a b l e i f the r e s u l t a n t Q„ e r r o r i s ij ri s m a l l . CHAPTER 8 SUMMARY OF CONCLUSIONS The following major conclusions may be drawn from the preceding study: [1] In agreement with t h e o r e t i c a l models, the d i u r n a l s p a t i a l l y integrated albedo of the canyon system shows three d i s t i n c t periods. The f i r s t and l a s t periods are dominated by a large solar r e f l e c t i o n of the east and west walls. The middle period has a low albedo and represents the contribution of the canyon ground. Thus two d i s t i n c t albedo peaks occur which support the Lambertian assumption for the canyon surfaces. The absorption e f f i c i e n c y of the canyon r e l a t i v e to a h o r i z o n t a l surface varies from a minimum of 1.2. when one of the walls i s f u l l y i r r a d i a t e d to a maximum of 1.5 at noon. [2] The net all-wave r a d i a t i o n i s dominated by the solar term during the day. The actual amount of radiant energy r e -ceived depends on the solar zenith and azimuth angles. Thus * the Q trace f o r each wall i s characterized by a peak. At night the net long-wave r a d i a t i o n d e f i c i t (L ) i n the canyon increases l i n e a r l y with sky view factor. Divergence of net long-wave r a d i a t i o n i s found to e x i s t along the l o n g i t u d i n a l 143 144 l e n g t h o f the canyon, and t o t a l d i v e r g e n c e i n the c a n y o n - a i r volume i s the main a i r c o o l i n g mechanism a t n i g h t . V a l u e s o f * Q t and s p a t i a l l y averaged v a l u e s o f k and C gave good e s t i -mates o f the can y o n - a i r c o o l i n g when used i n the Brunt equa-t i o n . [3] The sub s u r f a c e heat f l u x i n each canyon w a l l responds to s o l a r r a d i a t i o n d u r i n g the day. T h e r e f o r e a d i s t i n c t peak i n Q_ occurs f o r each w a l l as i t i s i r r a d i a t e d . Divergence of Q G was found to i n t r o d u c e o n l y a s m a l l e r r o r i n the measure-ments . [4] The t r a n s p o r t o f heat by a d v e c t i o n i s s t r o n g l y dependent on the wind f i e l d . The hot and c o l d sources seemed t o be l o c a l i z e d to the south and n o r t h end o f the canyon r e s p e c t i v e l y . With winds 2^ m s ^ on c l o u d l e s s summer days, the net a d v e c t i o n i s a p p r o x i --2 -1 -2 mately 70 W m . With winds o f 1 m s the v a l u e drops t o 15 W m A mean c i r c u l a t i o n develops a l o n g the canyon c r o s s - s e c t i o n i f the e x t e r n a l wind i s a t r i g h t a n g l e s t o the canyon l e n g t h . T h i s mean flo w may a l s o be an important mechanism i n t r a n s p o r t i n g heat t o , * or from, the canyon-air volume. Maximum v a l u e s f o r Q. and Q„, t Gt -2 a t s o l a r noon d u r i n g a c l e a r summer p e r i o d a r e 510 and 140 W m -2 r e s p e c t i v e l y . S i m i l a r l y maximum Q i s 50 W m , w h i l e maximum £it -2 Q H t i s approximately 320 W m . At n i g h t both and QU4_ are 145 c l o s e to zero, and a balance seems to be e s t a b l i s h e d between * - 2 C" and the net r a d i a t i o n d e f i c i t Q. (^60 W m ) . [5] The s o l a r r a d i a t i o n model p r e d i c t s d a i l y v a l u e s o f * K t which agree to w i t h i n 7% w i t h measured v a l u e s . However, t h e r e seems to be c o n s i s t e n t l y b e t t e r p r e d i c t i o n i n the morning than i n the a f t e r n o o n . The r e l a t i o n between computed * * K and measured Q i s w e l l d e f i n e d a l t h o u g h c o n s i d e r a b l e s c a t t e r e x i s t s . T h i s r e l a t i o n may p o s s i b l y be improved by * * t a k i n g simultaneous measurements o f Q and K . S i m i l a r l y , * the r e l a t i o n between Q and QG" i s p r o m i s i n g , but more measure-ments are needed over a v a r i e t y o f s u r f a c e s . R E F E R E N C E S Ansori, S. A. and M. 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B l o k k e r , 1940: P h y s i c a l Constants and A s p h a l t i c Bitumens, J. Inst. Petroleum, 26, 29-38. Schmidt, W., 1918: Wirkungen des l u f t a u s t a u s c h e s auf das k l i m a und den t a g l i c h e n gang der l u f t t e m p e r a t u r i n der hoke, Sits-ber. Akad. Wissensch. Wien, 127, 1942-1957. S e l l e r s , W. D., 1965: Physical Climatology, The Univ. o f Chicago P r e s s , Chicago and London, 272 pp. Summers, P. W., 1965: An urban heat i s l a n d model: ' i t s r o l e i n a i r p o l l u t i o n w i t h a p p l i c a t i o n t o M o n t r e a l , First Cdn. Conf. on Micrometeor. , Toronto. Tag, P. M., 1969: Surface Temperatures in an Urban Environment, Unpub. M.Sc. T h e s i s , Dept. o f Meteor., Penn. S t a t e Univ., 69 pp. Terju n g , W. H. and S. F. L o u i e , 1973: S o l a r r a d i a t i o n and urban heat i s l a n d s , Annals of the Assoc. Amer. Geog., 63, No. 2, 181-207. Terjung, W. H. and S. F. L o u i e , 1974: A c l i m a t i c model of urban energy budgets, Geog. Annalysis,. 6, 341-367. Timanovskaya, R. G. and G. P. Faraponova, 1967: Measurements of r a d i a t i v e heat i n f l u x i n the atmospheric ground l a y e r , Izvestia Atm. Ocean Phys., 3, No. 12, 742-748. T u l l e r , S. E., 1973: M i c r o c l i m a t i c v a r i a t i o n s i n a downtown urban environment, Geog. Annaler, 54, Ser. A., 123-135. 154 Tyson, P. D., W. J . F. du T o i t and R. F. Fuggle, 1972: Temper-a t u r e s t r u c t u r e above c i t i e s : review and p r e l i m i n a r y f i n d -i n g s from the Johannesburg Urban Heat I s l a n d P r o j e c t , Atmos. Env., 6, 533-542. Vukovich, F. M., 1971: T h e o r e t i c a l a n a l y s i s of the e f f e c t o f mean wind and s t a b i l i t y on a heat i s l a n d c i r c u l a t i o n c h a r a c -t e r i s t i c o f an urban complex, Month. Rev., 99, 919-926. Wagner, N. K. and T. W. Yu, 1972: Heat i s l a n d f o r m a t i o n : a num e r i c a l experiment, Conf. on Urban Env. and Second Conf. on Biometeor., Amer. Meteor. S o c , P h i l . , Penn. , 83-88. Wise, A. F. E., 1971: E f f e c t s due to groups o f b u i l d i n g s , Intnl. Conf. on Architect. Aerodyn. , Phil. Trans. Roy. Soc, London, A269, 469-485. Wu, S. S., 1965: A study o f heat t r a n s f e r c o e f f i c i e n t s i n the lowest 400 metres o f the atmosphere, J. Geophys. Res., 70, 1801-1807. Yap, D. H., 1973: Sensible Heat Fluxes in and near Vancouver, Unpub. Ph.D. T h e s i s , Univ. o f B.C., 177 pp. Yap, D. H. and T. R. Oke, 1974: S e n s i b l e heat f l u x e s over an urban a r e a - Vancouver, B.C., J. Appl. Meteor., ( i n p r e s s ) . Zdunkowski, W. G. and D. C. Track, 1971: A p p l i c a t i o n of a r a d i a t i v e - c o n d u c t i v e model to the s i m u l a t i o n o f n o c t u r n a l temperature changes over d i f f e r e n t s o i l t y p e s , J. Atm. Sci, 10, 937-948. APPENDIX A HEAT FLUX PLATE CALIBRATION [IDSO (1971, 1972) TECHNIQUE] The Idso (1972) technique o f heat f l u x p l a t e c a l i b r a -t i o n i n v o l v e s exposing the f l u x p l a t e t o the heat output of a hot p l a t e under c o n t r o l l e d c o n d i t i o n s . The hot p l a t e used was made of aluminum (15 x 20 x 1 cm) and the output c o u l d be v a r i e d from 0 t o 20 W. An FD 300 d i o d e was i n s e r t e d a t a depth o f 0.5 cm under the c e n t r e of the p l a t e . T h i s was a c h i e v e d by d r i l l i n g a h o l e i n from one s i d e and p a r a -l l e l t o the f a c e o f the p l a t e . The diode was s e a l e d i n w i t h s i l -i c o n e rubber cement. The temperature g i v e n by the diode was assumed to be t h a t o f the s u r f a c e , T s . The diode output was c o n t i n u o u s l y monitored on a p o t e n t i o m e t r i c s t r i p - c h a r t r e c o r d e r . The s u r f a c e s o f the hot p l a t e and the heat f l u x p l a t e were sprayed w i t h b l a c k p a i n t . The experiment was conducted i n a c o n t r o l l e d l i g h t and temperature environment, w i t h the hot p l a t e p l a c e d w i t h i t s f a c e i n a v e r t i c a l p l a n e , and the heat f l u x p l a t e suspended p a r a l l e l t o i t and 10 cm from i t s c e n t r e . The hot p l a t e was heated to a high, temperature ( = 50°C), and then allowed t o c o o l to room temp-e r a t u r e by a l t e r i n g the power output. During the c o o l i n g phase both T and the heat f l u x p l a t e output were monitored, s 155 156 Under these c o n d i t i o n s the t o t a l r a d i a t i o n r e c e i v e d by the heat f l u x p l a t e from the blackened hot p l a t e i s g i v e n as: L+ = e.VF.aT 4 (A.l) s where VF i s the view f a c t o r of the hot p l a t e as seen from the h e a t f l u x p l a t e . The v a l u e o f VF was c a l c u l a t e d t o be 0.495 f o l l o w i n g the method o f Davies et al. (1970) and e was assumed to be 0.95. The f l u x p l a t e output (yV) w i l l depend upon L4- and t h e r e f o r e T . A p l o t o f t h i s output vs L+ y i e l d s a s t r a i g h t s l i n e whose s l o p e d e f i n e s a c a l i b r a t i o n f a c t o r (CF) f o r the f l u x -2 p l a t e response t o a n e t r a d i a t i o n change (yV/W m ). F u r t h e r Idso (1972) shows t h a t the net r a d i a t i o n o f the v e r t i c a l f l u x p l a t e (Q ) i s r e l a t e d t o the heat conducted through the p l a t e (QG) by: EQ* = 2 Q G (A.2) Thus, the c a l i b r a t i o n o f the sample heat f l u x p l a t e (CF 1) i s found t o be: C F X = h > z CF (A.3) APPENDIX B CALCULATION OF THE SOLAR ANGLE OF INCIDENCE ON THE VERTICAL WALLS OF THE CANYON (\}>) By d e f i n i t i o n , the angle of i n c i d e n c e i s the angle between the normal t o the s u r f a c e (vector 1) and the d i r e c t s o l a r r a d i a t i o n (vector 2). T h i s a n g l e can be c a l c u l a t e d i f the d i r e c t i o n c o s i n e s o f the two l i n e s are known w i t h r e s p e c t to an a r b i t r a r y a x i s . Denoting the angle o f i n c i d e n c e as ^ we haves cos ^ = cos cos j 2 + cos p^ cos p 2 + cos cos q 2 (B.l) where j, p and q are the d i r e c t i o n c o s i n e s o f v e c t o r s 1 and 2 a g a i n s t the x, y and z axes r e s p e c t i v e l y . Choosing c o - o r d i n a t e s w i t h the x - a x i s normal t o the w a l l ; the y a x i s running h o r i z o n t a l and on the w a l l ; and the z a x i s v e r t i c a l and on the w a l l , we have: cos j1 = 1, cos j = S i n z' sin(180 - 4•), cos = cos q^ = 0 and <j>' i s the azimuth angle between the s o l a r beam and the canyon l o n g i t u d i n a l d i r e c t i o n . 157 158 T h e r e f o r e : cos i\> = s i n Z' s i n <j»1 and 4> = cos ''"(sin Z' s i n <j>') . (B.2) APPENDIX C CALCULATION OF SUNLIT PORTION OF CANYON (P) Figure C.l(a) i l l u s t r a t e s the azimuthal geometry of the canyon s i t u a t i o n . In C. 1(b), a ray grazing the top of the eastern wall s t r i k e s the opposite wall at some unknown depth H* measured from the top of the canyon w a l l . From geometry i t can be deduced that: H 1 = [7.54/sin 4 • ] /tan Z' ( C l ) and therefore the s u n l i t portion of the wall (P) i s given as: e ~ 5.59m ( ^ - Z } In the l a t e morning sunlight s t r i k e s the ground d i r e c t l y and the portion of the ground that i s i n shadow X m i s : „ _ 7.31(7.54) . m iP so that 7.54 m - X m P = m (C 4) e 7.54 m C j S i m i l a r l y , i n the early afternoon [Figure C.l(d)] the length of shadow i s : y - 5.59 (7.54) A A - g l ( C D ) 159 F i g . C l Shadow lengths i n the canyon. 161 and 7.54 m - X P = 7.54 m A ( C ' 6 ) In the l a t e a f t e r n o o n [ F i g u r e C.l(a)] the t o t a l s u n l i t p o r t i o n i s simply g i v e n by: P = 1-72 m + H' . . e 7.31 m vu./; 0 

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