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An evaporatranspiration-interception model for urban areas Grimmond, Christine Susan 1988

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AN EVAPORATRANSPIRATION-INTERCEPTION MODEL FOR URBAN AREAS By CHRISTINE SUSAN BETHAM GRIMMOND BSc. (Hons.) U n i v e r s i t y o f Otago, 1980 MSc. U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1984 A THESIS SUBMITTED IN THE REQUIREMENTS DOCTOR OF PARTIAL FULFILLMENT OF FOR THE DEGREE OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (Department o f Geography) We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA November 1988 © CHRISTINE SUSAN BETHAM GRIMMOND, 1988 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 shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia Vancouver, Canada Date 4 NcVlMAbOT I 1 DE-6 (2/88) ABSTRACT T h i s s t u d y p r e s e n t s a model t o c a l c u l a t e e v a p o t r a n s p i r a t i o n f r o m u r b a n a r e a s f o r use o v e r a wide range o f m e t e o r o l o g i c a l c o n d i t i o n s . The e v a p o t r a n s p i r a t i o n - i n t e r c e p t i o n model i s a m o d i f i e d v e r s i o n o f t h o s e a t t r i b u t a b l e t o Penman-Monteith ( 1 9 6 5 ) , R u t t e r e t a l . (1971). and S h u t t l e w o r t h ( 1 9 7 8 ) . Sub-models t o c a l c u l a t e a n t h r o p o g e n i c h e a t f l u x , s t o r a g e h e a t f l u x , a e r o d y n a m i c r e s i s t a n c e , s u r f a c e r e s i s t a n c e and d r a i n a g e a r e d e v e l o p e d . The model and i t s sub-components, where p o s s i b l e , a r e t e s t e d a g a i n s t measured d a t a f r o m a s u b u r b a n s i t e i n V a n c o u v e r , B.C. T h i s i s t h e f i r s t e x t e n d e d s e t o f w i n t e r / s p r i n g t i m e e n e r g y b a l a n c e measurements f o r a c i t y . I t shows t h a t t h e l a t e n t h e a t f l u x c a n be t h e most i m p o r t a n t o u t p u t f l u x o f t h e e n e r g y b a l a n c e i n w i n t e r t i m e . The s p r i n g e n e r g y b a l a n c e i s s i m i l a r i n form t o t h a t i n summer. C o n s t r u c t i o n o f v a l i d e n e r g y b a l a n c e s f o r s p a t i a l l y - n o n - u n i f o r m s u r f a c e s s u c h as c i t i e s r e q u i r e s t h a t a l l component f l u x e s r e p r e s e n t i d e n t i c a l s o u r c e a r e a s . G i v e n t h a t t h e r a d i a t i v e f i e l d i s r e l a t i v e l y u n i f o r m i n space i t i s a p p r o p r i a t e t o match a l l f l u x e s t o t h e s o u r c e a r e a s f o r t h e t u r b u l e n t f l u x e s s i n c e t h e s e a r e v e r y v a r i a b l e . A scheme t o match a r e a s i s d e v e l o p e d u s i n g t h e Schmid (1988) model f o r t h e t u r b u l e n t s o u r c e a r e a s and a g e o g r a p h i c i n f o r m a t i o n s y s t e m c o n t a i n i n g t h e s u r f a c e c h a r a c t e r i s t i c s n e c e s s a r y t o c a l c u l a t e t h e s p a t i a l l y - c o r r e s p o n d i n g a n t h r o p o g e n i c and s t o r a g e f l u x e s . The a n t h r o p o g e n i c h e a t f l u x a t a p o i n t i s more v a r i a b l e i n space t h a n t i m e . T h e r e f o r e t h e c a l c u l a t e d f l u x i s s t r o n g l y i n f l u e n c e d by t h e method u s e d t o i d e n t i f y t h e s o u r c e a r e a . A t e s t o f s t o r a g e h e a t f l u x models c o n c l u d e s t h a t t h e o b j e c t i v e h y s t e r e s i s model o f C l e u g h (1988) p e r f o r m s w e l l , e s p e c i a l l y d u r i n g t h e d a y t i m e . The model i n t r o d u c e s an a p p r o p r i a t e t e m p o r a l asymmetry i n the storage f l u x . The surface resistance model developed for the c i t y i s a modified version of that suggested by J a r v i s (1976) . The performance of the model i s good and resembles that obtained for s i m i l a r models applied to f o r e s t s . Comparison of modelled and measured evapotranspiration using the complete model shows t h i s to be a promising method which i s capable of providing r e a l i s t i c hourly and d a i l y estimates of the areally-averaged l a t e n t heat f l u x and surface water state i n urban areas. TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS i v _ LIST OF TABLES v i i i LIST OF FIGURES x i LIST OF SYMBOLS & ABBREVIATIONS x i v ACKNOWLEDGEMENTS x x i PART I INTRODUCTION CHAPTER 1 INTRODUCTION 1.1 R a t i o n a l e 1 1.2 The a p p r o a c h t a k e n t o model s e a s o n a l e v a p o t r a n s p i r a t i o n 5 1.3 P e n m a n - M o n t e i t h - R u t t e r e v a p o t r a n s p i r a t i o n - i n t e r c e p t i o n model 6 1.4 A p p r o a c h t o p r o b l e m s o l u t i o n and s t r u c t u r e o f t h e t h e s i s 10 CHAPTER 2 OBSERVATION PROGRAMME 2.1 P h y s i c a l s e t t i n g 11 2.2 G e n e r a l c l i m a t o l o g y o f Vanco u v e r and t h e measurement p e r i o d 11 2.3 Measurement c o n s i d e r a t i o n s 14 2.4 The i n s t r u m e n t s 17 PART II DEVELOPMENT AND TESTING OF SUBMODELS CHAPTER 3 SURFACE DESCRIPTION 3.1 I n t r o d u c t i o n 26 3.2 Boundary s e l e c t i o n f o r s u r f a c e d e s c r i p t i o n 31 3.2.1 R a d i a n t f l u x e s 33 3.2.2 T u r b u l e n t f l u x e s 35 3.3 Surface database 3.4 Summary CHAPTER 4 ANTHROPOGENIC HEAT FLUX 4.1 Introduction 4.2 Methods of c a l c u l a t i o n 4.2.1 Anthropogenic heat produced by combustion of vehicle f u e l s 4.2.2 Anthropogenic heat produced by combustion from stationary sources 4.2.3 Anthropogenic heat produced by metabolism 4.3 Modelled values of anthropogenic heat f l u x 4.5 Incorporation of anthropogenic heat f l u x into the energy balance CHAPTER 5 STORAGE HEAT FLUX 5.1 Introduction 5.2 Methods of c a l c u l a t i o n 5.2.1 Objective l i n e a r regression model 5.2.2 Hysteresis model 5.2.3 Objective hysteresis model 5.3 'Measured' storage heat f l u x 1987 5.4 Comparison of storage heat f l u x models with 'measured' storage heat f l u x 5.4.1 The d i f f e r e n t models 5.4.2 Influence of landuse d e s c r i p t i o n 5.5 Discussion CHAPTER 6 ENERGY BALANCE 6.1 Introduction 6.2 Determination of hourly energy balances v i 6.3 Measured hourly energy balance, 1987 88 CHAPTER 7 RESISTANCES, DRAINAGE AND STORAGE CAPACITY 7.1 Introduction 99 7.2 ' Aerodynamic resistance 99 7.3 Surface resistance 104 7.4 Drainage 112 7.5 Storage capacity 116 PART III MODEL PERFORMANCE AND CONCLUSIONS CHAPTER 8 PERFORMANCE OF THE EVAPOTRANSPIRATION-INTERCEPTION MODEL 8.1 Introduction 120 8.2 Structure of the model 120 8.3 Performance of the model 126 8.3.1 Methods used to compare the performance of the model 126 8.3.2 Base run of the model 128 8.4 S e n s i t i v i t y analysis of the model 141 8.4.1 Rutter 142 8.4.2 Time step 142 8.4.3 Aerodynamic resistance 147 8.4.4 Surface resistance 151 8.4.5 Storage capacities 156 8.4.6 Drainage functions 167 8.5 Discussion 174 CHAPTER 9 CONCLUSIONS 9.1 Summary of conclusions 179 9.2 Future research 182 v i i REFERENCES CITED 183 APPENDIX I J u l i a n day calender for the measurement period, 1987 193 APPENDIX II Equations used i n ca l c u l a t i o n s 11.1 Temperature difference 194 11.2 Slope of the saturation vapour pressure curve 194 11.3 Psychrometric constant 194 11.4 Latent heat of vaporization 195 11.5 Mixing Ratio 195 11.6 Vapour pressure 195 11.7 Saturation vapour pressure 195 11.8 S p e c i f i c heat of a i r at constant pressure 195 11.9 Density of moist a i r 196 11.10 Adjusted v i r t u a l temperature 196 11.11 Relative humidity 196 11.12 Vapour pressure d e f i c i t 196 11.13 S p e c i f i c humidity d e f i c i t 196 APPENDIX III Error analysis for the RTDMS and fluxes 197 calculated from i t APPENDIX IV Cal c u l a t i o n of s t a b i l i t y and f r i c t i o n v e l o c i t y 199 APPENDIX V Procedure for accessing d i f f e r e n t geometries from the database V . l C i r c l e s and quadrants 204 V.2 E l l i p s e s 204 V.3 Sectors 205 V.4 Discussion 206 v i i i LIST OF TABLES T a b l e Page 2 . 1 Normal ( 1 9 5 1 - 1 9 8 0 ) and 1 9 8 7 measurements o f c l i m a t i c v a r i a b l e s f o r Van c o u v e r I n t e r n a t i o n a l A i r p o r t 1 5 2 . 2 I n s t r u m e n t a t i o n 2 1 3 . 1 1 Framework f o r u r b a n c l i m a t e c l a s s i f i c a t i o n p r o p o s e d by Oke ( 1 9 8 4 ) 2 8 3 . 2 Mean l e n g t h o f plumes f o r use w i t h t h e s e c t o r s model 4 2 3 . 3 I n f o r m a t i o n c o n t a i n e d w i t h i n t h e s u r f a c e d a t a b a s e f o r each g r i d s q u are 4 6 4 . 1 F u e l c o n s u m p t i o n , d e n s i t y and n e t h e a t c o m b u s t i o n 5 4 5 . 1 P e r c e n t a g e o f s u r f a c e t y p e i n t h e S u n s e t s t u d y a r e a f o r use w i t h t h e o b j e c t i v e h y s t e r e s i s model f o r s t o r a g e h e a t f l u x d e n s i t y 7 0 5 . 2 S u r f a c e c o e f f i c i e n t s f o r t h e o b j e c t i v e h y s t e r e s i s s t o r a g e h e a t f l u x d e n s i t y model 7 1 5 . 3 C o e f f i c i e n t s r e s u l t i n g f r o m a f i t o f t h e measured 1 9 8 7 AQs and Q* d a t a t o t h e h y s t e r e s i s AQg model 7 5 5 . 4 M o n t h l y v a r i a t i o n i n h y s t e r e s i s e q u a t i o n c o e f f i c i e n t s 7 7 5 . 5 S t a t i s t i c a l r e s u l t s o f c o m p a r i s o n between measured and m o d e l l e d AQ S 7 8 6 . 1 C o m p a r i s o n o f Q^g and Q ^ J J w i t h v a r y i n g e r r o r s i n fl 9 0 6 . 2 Mean d a i l y e n e r g y budget components f o r 1 9 8 7 9 1 6 . 3 Daytime e n e r g y b a l a n c e f l u x e s and r a t i o s f o r measurement p e r i o d and by month, 1 9 8 7 9 3 6 . 4 Mean d a i l y Q* and AQg by month f o r K e r r i s d a l e , Vancouver 9 6 7 . 1 S u r f a c e r e s i s t a n c e model f i t t e d p a r a m e t e r s and t e s t s t a t i s t i c s 1 1 0 7 . 2 V a l u e s o f d r a i n a g e f u n c t i o n p a r a m e t e r s 1 1 5 7 . 3 V a l u e s o f s t o r a g e c a p a c i t i e s f o r paved s u r f a c e s & r o o f s 1 1 8 7 . 4 V a l u e s o f s t o r a g e c a p a c i t i e s f o r v e g e t a t i o n 1 1 9 I X 8.1 I n i t i a l data requirements f o r the model 123 8.2 Hourly data requirements f o r the model 125 8.3 Output from the evapotranspiration-interception model 127 8.4 Values assigned to parameters f o r base run of the model 129 8.5 S t a t i s t i c s f o r base model values of Qg 131 8.6 S t a t i s t i c s of model performance f o r Qg when Rutter t r a n s i t i o n equations are used 143 8.7 S t a t i s t i c s of model performance f o r Qg when computational time step changed " 146 8.8 S t a t i s t i c s of model performance f o r Qg when the r a equation i s changed 149 8.9 S t a t i s t i c s of model performance f o r Qg when rg maximum i s changed 152 8.10 S t a t i s t i c s of model performance f o r Qg when rg parameters are changed 154 8.11 S t a t i s t i c s of model performance f o r Qg when the value of S i s changed f o r pavement 157 8.12 S t a t i s t i c s of model performance for Qg when the value of S i s changed for buildings 159 8.13 S t a t i s t i c s of model performance f o r Qg when the value of S i s changed f o r coniferous vegetation 160 8.14 S t a t i s t i c s of model performance f o r Qg when S i s changed for deciduous vegetation and the timing of the t r a n s i t i o n period i s al t e r e d 161 8.15 S t a t i s t i c s of model performance f o r Qg when S i s changed for i r r i g a t e d and un i r r i g a t e d grass 162 8.16 S t a t i s t i c s of model performance f o r Qg when S capacity i s changed f o r a l l surface types 165 8.17 S t a t i s t i c s of model performance f o r Qg when drainage functions are changed and S = 0.5 mm 168 8.18 S t a t i s t i c s of model performance f o r Qg when drainage functions are changed and S = 1.0 mm 169 8.19 S t a t i s t i c s of model performance f o r Qg when drainage functions are changed and S = 2.0 mm 170 X 8.20 Comparison of the performance of two models to ca l c u l a t e evapotranspiration i n urbanized t e r r a i n 177 II. 1 C o e f f i c i e n t s f o r use with the Lowe (1977) polynomials 194 II I . l RTDMS thermopile c a l i b r a t i o n values 197 IV. 1 Comparison between measured and modelled values of u* and z/L 203 x i LIST OF FIGURES F i g u r e Page 1.1 Urb a n e n e r g y and w a t e r b a l a n c e s 2 1.2 C o n c e p t u a l framework o f t h e m o d i f i e d P e n m a n - M o n t e i t h - R u t t e r S h u t t l e w o r t h e v a p o t r a n s p i r a t i o n - i n t e r c e p t i o n model 2 2.1 The l o c a t i o n o f t h e Suns e t s i t e i n t h e Vancouver a r e a and s u r r o u n d i n g l a n d use 12 2.2 Vi e w l o o k i n g s o u t h w e s t f r o m t h e t o w e r 13 2.3 I d e a l i s e d arrangement o f bo u n d a r y l a y e r s t r u c t u r e s o v e r a c i t y ( a f t e r Oke, 1984) 16 2.4 S c h e m a t i c o f t h e Suns e t t o w e r and i n s t r u m e n t l o c a t i o n s 19 2.5 P h o t o g r a p h i c v i e w o f t h e t o p p a r t o f Sun s e t tower 20 3.1 A e r i a l p h o t o g r a p h o f a r e a t o t h e n o r t h w e s t o f t h e tower 29 3.2 S c h e m a t i c o f t h e i n f l u e n c e o f t h e l o c a t i o n o f t h e b o u n d a r i e s f o r s u r f a c e d e s c r i p t i o n 30 3.3 Wind d i r e c t i o n f r e q u e n c y (%) f o r t h e Suns e t s i t e JD 21-179, 1987 32 3.4 D i m e n s i o n s o f t h e s o u r c e a r e a f o r t u r b u l e n t f l u x measurements 36 3.5 Source a r e a f o r one ho u r w i t h t h e 9 w e i g h t e d bands u s i n g t h e plume model , . 3 9 3.6 Examples o f d i f f e r e n t s o u r c e a r e a s w i t h c h a n g i n g m e t e o r o l o g i c a l c o n d i t i o n s 41 3.7 Examples o f ' s e c t o r s ' 43 3.8 Map o f g r i d s q u a r e s w h i c h c o n t a i n m a j o r r o a d s i n t h e a r e a c o v e r e d by t h e d a t a b a s e 45 3.9 Maps o f s u r f a c e t y p e 48 3.10 I n f l u e n c e o f c h a n g i n g s o u r c e a r e a on p e r c e n t a g e o f l a n d use c h a r a c t e r i s t i c s i n f l u e n c i n g measurements 51 4.1 Mean p r o f i l e s o f t r a f f i c c o u n t s f o r major and minor r o a d s 54 4.2 A n t h r o p o g e n i c h e a t f l u x f o r JD 22, 1987 57 x i i 4.3 Map o f a n t h r o p o g e n i c h e a t f l u x f o r 900 LAT, JD 22, 1987 c e n t r e d on t h e Suns e t s i t e 58 4.4 A n t h r o p o g e n i c h e a t f l u x w i t h i n c r e a s i n g r a d i u s f r o m t h e tower f o r JD 22, 1987 59 4.5 H o u r l y a n t h r o p o g e n i c h e a t f l u x m o d e l l e d u s i n g plumes & a 2 km r a d i u s c i r c l e as t h e b a s i s f o r a s s i g n i n g v a l u e s f o r s u r f a c e p a r a m e t e r s 61 4.6 Wind d i r e c t i o n f r e q u e n c y p l o t f o r : a) a l l h o u r s b) h o u r s when Qp plumes > Qp 2 km r a d i u s c i r c l e c ) h o u r s when Qp plumes < Qp 2 km r a d i u s c i r c l e 62 4.7 P l o t o f h o u r l y Qp c a l c u l a t e d u s i n g plumes & s e c t o r s f o r a s s i g n i n g v a l u e s f o r s u r f a c e p a r a m e t e r s 64 5.1 P l o t s o f h o u r l y ensemble a v e r a g e s o f s t o r a g e h e a t f l u x r e s i d u a l f o r h o u r s w i t h v a r y i n g e r r o r s i n fl 73 5.2 R e s i d u a l s v e r s u s m o d e l l e d s t o r a g e h e a t f l u x d e n s i t i e s u s i n g t h e o b j e c t i v e h y s t e r e s i s model 80 5.3 M o d e l l e d v e r s u s measured s t o r a g e h e a t f l u x d e n s i t i e s w i t h e r r o r i n fl < 20% 81 5.4 Maps o f s t o r a g e h e a t f l u x f o r : (a) ensemble 800 LAT (b) ensemble 1200 LAT 84 6.1 Comparison o f QJJ d e t e r m i n e d u s i n g eddy c o r r e l a t i o n (SAT) & c a l c u l a t e d f r o m fi - e n e r g y b a l a n c e method 89 6.2 Ensemble a v e r a g e e n e r g y b a l a n c e p l o t s 92 7.1 Aerodynamic r e s i s t a n c e c a l c u l a t e d f o r h o u r s when i t was p o s s i b l e t o c a l c u l a t e s t a b i l i t y w i t h d i r e c t measurements o f s e n s i b l e h e a t f l u x 101 7.2 D i u r n a l t r e n d o f ensemble mean and s t a n d a r d d e v i a t i o n o f measured s u r f a c e c o n d u c t a n c e 107 7.3 Compa r i s o n between h o u r l y measured and m o d e l l e d s u r f a c e c o n d u c t a n c e 111 7.4 Ensemble mean o f h o u r l y measured and m o d e l l e d s u r f a c e c o n d u c t a n c e 113 8.1 B a s i c s t r u c t u r e o f t h e e v a p o t r a n s p i r a t i o n - i n t e r c e p t i o n model f o r u r b a n a r e a s 121 x i i i 8.2 Comparison o f h o u r l y measured and m o d e l l e d QE f o r t h e 'base' model r u n 132 8.3 Comparison o f d a i l y measured and m o d e l l e d QE f o r t h e 'base' model r u n 133 8.4 C u m u l a t i v e p l o t o f measured and m o d e l l e d 'base' r u n E 134 8.5 Time s e r i e s o f h o u r l y measured and m o d e l l e d Qg ('base') 135 8.6 Ensemble p l o t s o f measured and m o d e l l e d 'base' r u n Qg 137 8.7 P l o t s o f p r e c i p i t a t i o n , w a t e r u s e , s u r f a c e wetness and m o d e l l e d s u r f a c e w a t e r s t a t e 139 8.8 I n f l u e n c e o f u s i n g t h e R u t t e r and S h u t t l e w o r t h t r a n s i t i o n e q u a t i o n s on t h e c u m u l a t e d E 144 8.9 . I n f l u e n c e o f c h a n g i n g t h e t i m e s t e p on c u m u l a t e d E 145 8.10 I n f l u e n c e o f u s i n g a 3600 s t i m e s t e p on c u m u l a t e d E 148 8.11 I n f l u e n c e o f e q u a t i o n u s e d t o c a l c u l a t e aerodynamic r e s i s t a n c e on c u m u l a t e d E 150 8.12 I n f l u e n c e o f t h e maximum v a l u e a s s i g n e d t o r g on c u m u l a t e d E 153 8.13 I n f l u e n c e o f p a r a m e t e r s u s e d f o r c a l c u l a t i n g r g on c u m u l a t e d E 155 8.14 I n f l u e n c e o f t h e v a l u e a s s i g n e d t o s u r f a c e s t o r a g e c a p a c i t y o f g r a s s on c u m u l a t e d E 163 8.15 I n f l u e n c e o f c h a n g i n g a l l t h e s u r f a c e s t o r a g e c a p a c i t i e s on c u m u l a t e d E 166 8.16 I n f l u e n c e of. c h a n g i n g d r a i n a g e f u n c t i o n s and c o e f f i c i e n t s on c u m u l a t e d E when S = 0.5 mm f o r a l l s u r f a c e s 171 8.17 I n f l u e n c e o f c h a n g i n g d r a i n a g e f u n c t i o n s and c o e f f i c i e n t s on c u m u l a t e d E when S = 1.0 mm f o r a l l s u r f a c e s 172 8.18 I n f l u e n c e o f c h a n g i n g d r a i n a g e f u n c t i o n s and c o e f f i c i e n t s on c u m u l a t e d E when S = 0.5 mm f o r a l l s u r f a c e s 173 8.19 C o m p a r i s o n o f d a i l y measured and m o d e l l e d e v a p o r a t i o n u s i n g t h e Grimmond e t a l . (1986) a d v e c t i o n - a r i d i t y model and t h e 1987 S u n s e t d a t a 178 IV.1 Measured v e r s u s m o d e l l e d u * 201 IV.2 Measured v e r s u s m o d e l l e d z/L 202 x i v LIST OF SYMBOLS AND ABBREVIATIONS Some symbols are relevant f o r one equation and are not l i s t e d here A source area (m^) Aj area i r r i g a t e d Ay area u n i r r i g a t e d AE a v a i l a b l e energy (W m"^ ) a plume model dimension - distance to upwind edge of plume (m) a^ empirical c o e f f i c i e n t used i n objective l i n e a r storage heat f l u x density parameterization. a l a2 a3 empirical c o e f f i c i e n t s used i n hysteresis type storage heat f l u x density determination ag - ag c o e f f i c i e n t s used to calculate s and eg b empirical c o e f f i c i e n t i n drainage function b + c plume model dimension - length of plume (m) b^ empirical c o e f f i c i e n t used i n objective l i n e a r storage heat f l u x density parameterization C state of surface water store (mm) compressibility factor of moist a i r C-L mean consumption (of e l e c t r i c i t y Watts; gas Joules) f o r an in d i v i d u a l consumer by premise class ( i ) A C change i n surface water status (mm) Cf intercept of l i n e a r functional r e l a t i o n s h i p cp s p e c i f i c heat of a i r at constant pressure (J Kg'/- K x) D drainage (mm h"l) DQ drainage rate when C = S (mm h"l) d zero-plane displacement length (m) d Wilmott & Wicks (1980) index of agreement d plume model dimension - h a l f width of plume (m) X V E evapotranspiration (ram) EPM evapotranspiration determined from Penman-Monteith equation (mm) EV energy used by vehicles (J nT^) e a vapour pressure (Pa) eS saturation vapour pressure (Pa) F water released due to anthropogenic a c t i v i t i e s (mm) GEF gas e f f i c i e n c y (0.675) GR g r i d consumption (E e l e c t r i c i t y (W), G gas(J)) g a c c e l e r a t i o n due to g r a v i t y (m s"^) Sa aerodynamic conductance (mm s"-'-) SS surface conductance (mm s~^) §ST stomatal conductance (mm s"^) I piped water supply (mm) JD J u l i a n day K* net shortwave r a d i a t i o n (W m"^ ) k von Karman's constant L, LAI l e a f area index (m m"-*-) L Monin-Obukhov s t a b i l i t y length (m) Lt long-wave r a d i a t i o n emitted from the surface (W m"z) LI long-wave r a d i a t i o n received at the surface (W m~2) Lm maximum l e a f area index (mm"-'-) L V l a t e n t heat of vaporization (J kg"-'-) M metabolic rate (subscript a animals, p humans) (W) MAE mean absolute error mf slope of l i n e a r functional r e l a t i o n s h i p m0 slope of l i n e a r regression forced through the o r i g i n X V I N&S Nash & S u t c l i f f e (1970) 'goodness o f f i t ' NHC n e t h e a t c o n s u m p t i o n by f u e l t y p e ( J Kg'^) n number o f h o u r s o r d a t a p o i n t s nv^ number o f v e h i c l e s i n c o n t r i b u t i n g a r e a by r o a d t y p e ( i ) P p r e c i p i t a t i o n (mm) PX w a t e r a r r i v i n g a t the s u r f a c e (mm) ?1 f i t t e d p a r a m e t e r f o r s u r f a c e r e s i s t a n c e model (mm s"-1) P2 f i t t e d p a r a m eter f o r s u r f a c e r e s i s t a n c e model (W m~2) P3 f i t t e d p a r a m e t e r f o r s u r f a c e r e s i s t a n c e model (kg m~l) P4 f i t t e d p a r a m eter f o r s u r f a c e r e s i s t a n c e model (g kg"-*-) P5 f i t t e d p arameter f o r surfa c e - r e s i s t a n c e model (°C) Pg f i t t e d p a r a m e t e r f o r s u r f a c e r e s i s t a n c e model (mm"-'-) p a t m o s p h e r i c p r e s s u r e (Pa) Q* n e t a l l - w a v e r a d i a t i o n (W m~2) AQA n e t h e a t a d v e c t i o n (W m"2) Qg l a t e n t h e a t f l u x (W m"2) QER QE c a l c u l a t e d as a r e s i d u a l f r o m t h e e n e r g y b a l a n c e (W m~2) QES QE c a l c u l a t e d u s i n g s o n i c anemometer thermometer - s e n s i b l e h e a t f l u x & Bowen r a t i o (W m"2) QEfi QE c a l c u l a t e d u s i n g the Bowen r a t i o - e n e r g y b a l a n c e (W m"2) Qp a n t h r o p o g e n i c h e a t f l u x (W m"2) QpH a n t h r o p o g e n i c h e a t produced by c o m b u s t i o n from s t a t i o n a r y s o u r c e s (W m"2) Qpj/j a n t h r o p o g e n i c h e a t produced by human/animal m e t a b o l i s m (W m"2) Qpy a n t h r o p o g e n i c h e a t produced by c o m b u s t i o n o f v e h i c l e f u e l s (W m - 2) QH s e n s i b l e h e a t f l u x (W m"2) Qf^jj s e n s i b l e h e a t f l u x d e t e r m i n e d f r o m Bowen r a t i o (W m"2) X V I 1 Q M AQ S AQSR R R RH RMSE RMSEg RMSEu RTDMS Ar r b ^H rS rSS rST rV S SAT s d s s d s t maximum h o u r l y n e t a l l - w a v e r a d i a t i o n (W m~2) s t o r a g e h e a t f l u x (W m"2) s t o r a g e h e a t f l u x d e t e r m i n e d as a r e s i d u a l (W m"2) gas c o n s t a n t f o r d r y a i r ( J kg"-*- K"-1) parameter i n S h u t t l e w o r t h (1988) s u r f a c e r e s i s t a n c e e q u a t i o n r e l a t i v e h u m i d i t y (%) r o o t mean square e r r o r s y s t e m a t i c r o o t mean square e r r o r u n s y s t e m a t i c r o o t mean square e r r o r r e v e r s i n g t e m p e r a t u r e d i f f e r e n c e m e a s u r i n g system r u n o f f (mm) m i x i n g r a t i o ( k g kg"- 1) c o e f f i c i e n t o f d e t e r m i n a t i o n aerodynamic r e s i s t a n c e (s m'^) boundary l a y e r r e s i s t a n c e (s m""-*-) s e n s i b l e h e a t f l u x r e s i s t a n c e (s m'^) s u r f a c e r e s i s t a n c e (s m'^) S h u t t l e w o r t h s u r f a c e r e s i s t a n c e used i n t r a n s i t i o n between wet and d r y s u r f a c e w a t e r s t a t e (s m'^) s t o m a t a l r e s i s t a n c e (s m'^) l a t e n t h e a t f l u x r e s i s t a n c e (s m'-1) s u r f a c e w a t e r c a p a c i t y (mm) s o n i c anemometer-thermometer system summer w a t e r s t o r a g e c a p a c i t y f o r d e c i d u o u s t r e e s (mm) d a i l y i n c r e m e n t i n s t o r a g e c a p a c i t y f o r d e c i d u o u s t r e e s d u r i n g g r o w i n g s e a s o n (mm) Jws w i n t e r w a t e r s t o r a g e c a p a c i t y f o r d e c i d u o u s t r e e s (mm) X V I 1 1 S]_, S2 f i t t e d p a r a m e t e r s i n s u r f a c e c o n d u c t a n c e model (mm) AS change i n w a t e r s t o r a g e (mm) s s l o p e o f t h e s a t u r a t i o n vapour p r e s s u r e v e r s u s t e m p e r a t u r e c u r v e (Pa C' 1) sd s t a n d a r d d e v i a t i o n S.E. s t a n d a r d e r r o r T t e m p e r a t u r e (°C) Tp t h r o u g h f a l l (mm) T(j d r y b u l b t e m p e r a t u r e (°C) Tt^ minimum t e m p e r a t u r e l i m i t i n s u r f a c e c o n d u c t a n c e model (°C) maximum t e m p e r a t u r e l i m i t i n s u r f a c e c o n d u c t a n c e model (°C) T§ s t e m f l o w (mm) ( C h a p t e r 1) Tg s u r f a c e t e m p e r a t u r e (°C) ( C h a p t e r 4) T'y a d j u s t e d v i r t u a l t e m p e r a t u r e (K) wet b u l b t e m p e r a t u r e (°C) AT t e m p e r a t u r e d i f f e r e n c e (°C) t t i m e t D J u l i a n day t h a t the w i n t e r t o summer t r a n s i t i o n f o r d e c i d u o u s v e g e t a t i o n s t o r a g e c a p a c i t y b e g i n s t e J u l i a n day the summer s t o r a g e c a p a c i t y f o r d e c i d u o u s v e g e t a t i o n i s r e a c h e d u mean wi n d speed (m s'^) u,v f r i c t i o n v e l o c i t y (m s'^-) V vapour p r e s s u r e d e f i c i t (Pa) W parameter i n S h u t t l e w o r t h (1978) s u r f a c e r e s i s t a n c e e q u a t i o n WFS^ w e i g h t i n g o f f u e l s a l e s by f u e l t y p e ( i ) w s s u r f a c e wetness wu e x t e r n a l w a t e r use (mm) x i x w'T' k i n e m a t i c s e n s i b l e h e a t f l u x d e n s i t y (W m"^) X f r a c t i o n o f w a t e r on the canopy Xp sen s e d c o n c e n t r a t i o n o r e f f e c t l e v e l i n s o u r c e a r e a model z measurement h e i g h t (m) z^ mixed l a y e r d e p t h (m) zg h e i g h t o f s e n s o r (m) ZQ momentum roughness l e n g t h (m) ZQV w a t e r vapour roughness l e n g t h (m) z-y measurement h e i g h t o f bottom c a r t o f RTDMS (m) Z 2 measurement h e i g h t o f t o p c a r t o f RTDMS (m) Z 3 measurement h e i g h t o f wind speed (m) a a l b e d o f r a c t i o n o f a r e a c o v e r e d by i t h s u r f a c e t y p e u s e d i n the l i n e a r o b j e c t i v e s t o r a g e h e a t f l u x d e n s i t y p a r a m e t e r i z a t i o n . fi Bowen r a t i o (Qj^/Qg) 5q s p e c i f i c h u m i d i t y d e f i c i t (g kg~^) 66 s o i l m o i s t u r e d e f i c i t (mm) e r a t i o o f t h e m o l e c u l a r w e i g h t o f w a t e r vapour t o d r y a i r ( A p p e n d i x I I ) e e r a i s s i v i t y ( C h a p t e r s 3 & 4) 7 p s y c h r o m e t r i c c o n s t a n t (Pa C"^) F d r y a d i a b a t i c l a p s e r a t e (K m"-'-) p d e n s i t y o f a i r ( k g m"^) Pi_ d e n s i t y o f f u e l t y p e s ( i ) (kg nT^) r a v e r a g i n g t i m e ( s ) 6* t e m p e r a t u r e s c a l e f o r t u r b u l e n t h e a t t r a n s f e r (K) Ad p o t e n t i a l t e m p e r a t u r e d i f f e r e n c e (K) XX a<p s t a n d a r d d e v i a t i o n o f the w i n d d i r e c t i o n ( o r r a d ) a S t e f a n - B o l t z m a n c o n s t a n t (W n T 2 K"^) <p mean w i n d d i r e c t i o n (° or r a d ) V>H s t a b i l i t y f u n c t i o n f o r h e a t V>M s t a b i l i t y f u n c t i o n f o r momentum exchange V>v s t a b i l i t y f u n c t i o n f o r water vapour exchange x x i ACKNOWLEDGEMENTS Dr. Tim Oke, my s u p e r v i s o r , p r o v i d e d academic s t i m u l a t i o n and g u i d a n c e t h r o u g h o u t my g r a d u a t e s t u d i e s . H i s a d v i c e , encouragement and humour have been much a p p r e c i a t e d . I w o u l d l i k e t o e x p r e s s my a p p r e c i a t i o n o f my s u p e r v i s o r y committee: Dr. M. C h u r c h , Dr. D.G. S t e y n and Dr. S.O. R u s s e l l , f o r t h e i r comments a t a l l s t a g e s o f my s t u d i e s and t h e i r prompt r e a d i n g o f my t h e s i s . J e f f J o y c e , Gabor F r i s k a , Rene K o n d r a t s k y and Joh n B u t c h e r p r o v i d e d h e l p i n th e f i e l d . My f e l l o w c l i m a t o l o g y g r a d u a t e s t u d e n t s Jamie V o o g t , M a t t h i a s R o t h and P e t e r J a c k s o n p r o v i d e d u s e f u l d i s c u s s i o n . HaPe Schmid c o n t r i b u t e d t h r o u g h many h o u r s o f d i s c u s s i o n and a s s i s t a n c e i n t h e f i e l d . The f o l l o w i n g o r g a n i z a t i o n s g e n e r o u s l y p r o v i d e d d a t a : B.C.Hydro, C i t y o f Vancouver Water Works and T r a f f i c D epartments, V a n c o u v e r S c h o o l B o a r d , and Vancou v e r P a r k s B o a r d . B.C. Hydro p r o v i d e d t h e s i t e f o r t h e to w e r i n t h e i r M a i n w a r i n g s u b s t a t i o n . F u n d i n g f o r t h i s r e s e a r c h has been p r o v i d e d t o Dr. T.R. Oke by N a t u r a l S c i e n c e s E n g i n e e r i n g R e s e a r c h C o u n c i l o f Canada and A t m o s p h e r i c E n v i r o n m e n t S e r v i c e o f E n v i r o n m e n t Canada. P e r s o n a l f u n d i n g was p r o v i d e d t h r o u g h U n i v e r s i t y o f B r i t i s h C o l u m b i a G r a d u a t e F e l l o w s h i p s and T e a c h i n g and R e s e a r c h A s s i s t a n t s h i p s i n t h e Department o f Geography. I n p a r t i c u l a r I w o u l d l i k e t o th a n k H e l e n C l e u g h f o r many h o u r s o f d i s c u s s i o n on a l l t o p i c s and i n v a l u a b l e h e l p i n t h e f i e l d , no m a t t e r what t h e weat h e r ; and C a t h e r i n e Souch f o r h e r a s s i s t a n c e i n a l l a s p e c t s o f t h i s work and above a l l f o r h e r s u p p o r t and encouragement. PART I INTRODUCTION ' CHAPTER 1 INTRODUCTION 1.1 Rationale E v a p o r a t i o n ( E ) , t h e mass e q u i v a l e n t o f t h e l a t e n t h e a t e n e r g y f l u x (Qg), i s the term t h a t l i n k s t h e e n e r g y and t h e w a t e r b a l a n c e s . I n t h e u r b a n e n v i r o n m e n t t h e w a t e r b a l a n c e i s w r i t t e n : P + I + F = E + A r + A S + A A (1.1) where P - p r e c i p i t a t i o n (mm); I - p i p e d w a t e r s u p p l y (mm); F - w a t e r r e l e a s e d due t o a n t h r o p o g e n i c a c t i v i t i e s (mm); A r - r u n o f f (mm); AS - change i n w a t e r s t o r a g e (mm) f o r t h e p e r i o d o f i n t e r e s t ; and AA - n e t m o i s t u r e a d v e c t i o n (mm) and t h e u r b a n e n e r g y b a l a n c e a s : Q* + Q F = Q E + Q H + AQ S + AQ A (1.2) where Q* - n e t a l l - w a v e r a d i a t i o n (W m" 2); Qp - e n e r g y r e l e a s e d due t o a n t h r o p o g e n i c a c t i v i t i e s (W ra"2); Q H - s e n s i b l e h e a t f l u x (W m" 2); AQg - s t o r a g e h e a t f l u x (W n T 2 ) ; and AQ.A - n e t h e a t a d v e c t i o n (W m" 2). These b a l a n c e s a p p l y t o t h e t o p o f a volume w h i c h e x t e n d s t o s u f f i c i e n t d e p t h t h a t v e r t i c a l h e a t and w a t e r exchange i s n e g l i g i b l e ( F i g . 1.1). F l u x e s a r e d e t e r m i n e d p e r u n i t a r e a o f t h e t o p o f t h e volume. A f u l l e r e x p l a n a t i o n o f t h i s c o n c e p t i s g i v e n by Oke ( 1 9 8 8 ) . T r a d i t i o n a l l y e v a p o r a t i o n i n an u r b a n e n v i r o n m e n t has been assumed t o be c o n s i d e r a b l y l e s s t h a n t h a t f r o m n e i g h b o u r i n g r u r a l a r e a s because o f t h e supposed c o n t r a s t between t h e h y d r o l o g i c p r o p e r t i e s o f b u i l d i n g m a t e r i a l s and v e g e t a t i o n - c o v e r e d s o i l s ( C h a n d l e r , 1 9 7 6 ) . However t h i s e x p e c t a t i o n has n o t been w i d e l y t e s t e d and u r b a n e v a p o r a t i o n has r e c e i v e d l i t t l e a t t e n t i o n i n t h e f i e l d s o f b o t h u r b a n c l i m a t o l o g y and u r b a n h y d r o l o g y . V e r y few, i f any c o m p r e h e n s i v e , r e l i a b l e o b s e r v a t i o n s o f n a t u r a l w a t e r l o s s t o t h e a i r by e v a p o r a t i o n and e v a p o t r a n s p i r a t i o n i n u r b a n a r e a s e x i s t ( A t k i n s o n , 1 9 8 5 ) . I n d e e d i t h a r d l y Figure 1.1 Urban energy and water balances (after Oke, 1988). Figure 1.2 Conceptual framework of the Penman-Monteith-Rutter-Shuttleworth evapotranspiration-interception model adapted for urban areas. 'Floating plane' is equivalent to ABCD in Fig. 1.1. Q* - net all-wave radiation density Q„ - sensible heat flux density QE - latent heat flux density - anthropogenic heat flux density AQg - storage heat flux density r - aerodynamic resistance Tg - surface resistance r - surface resistance (Shuttleworth, 1978) P - rain f a l l E - evapotranspiration D - drainage I - external water use 3 rates mention in textbooks on the subject (e.g. Lazaro, 1979; Landsberg, 1981; Hall, 1984). Interestingly, recent work by Kalanda et a l . (1980) and Grimmond and Oke (1986) shows that evaporation has a larger magnitude than originally thought, for example, i n a temperate city (Vancouver, B.C.) i t has been shown to constitute 37% of the losses of the annual external water balance. A recent trend i n urban runoff work is towards continuous simulation, rather than modelling the runoff from individual r a i n f a l l events. Between-event simulation makes i t necessary to account not only for the runoff but also for the other components of the water balance. Currently evapotranspiration i s either ignored or dealt with via evaporation pan data (e.g. Alley et a l . . 1980; Wenzell and Voorhees, 1980; Sman et a l . . 1988) so that van den Ven (1988) concludes that the weakest point in the urban water balance remains the estimation of evapotranspiration. A model for use in conjunction with available runoff models to determine continuous hourly evapotranspiration would be useful for the modelling of water quantity, water quality and urban climate. In the water quantity modelling i t is of interest to be able to predict the surface water storage status, and for water quality modelling i t is valuable to know the volumes of water present both during and between storms (low flows) in order to calculate pollutant concentrations. In the f i e l d of urban climatology there is a more ready awareness of the evaporative terra. However there has s t i l l only been a limited number of urban energy balance studies, and their emphasis has been to study dry summertime conditions. This is largely due to the d i f f i c u l t y of conducting micrometeorological measurements at the local scale (see Chapter 3 for discussion of scales) i n urban areas, and especially i n non-dry conditions. The few studies conducted under non-summertime conditions have not separated the turbulent terms (QJJ, Qg) of the energy balance (e.g. Kerschgens and Drauschke, 4 1986). Models t o d e t e r m i n e t h e e v a p o t r a n s p i r a t i o n f r o m u r b a n a r e a s c a n be d i v i d e d i n t o two g r o u p s (Oke e t a l . . 1988). F i r s t l y , t h e r e a r e t h o s e w h i c h c o n s i d e r e v a p o t r a n s p i r a t i o n as one f l u x i n t h e t o t a l s u r f a c e e n e r g y b a l a n c e These a r e one-, two- and q u a s i - t h r e e - d i m e n s i o n a l n u m e r i c a l b o u n d a r y l a y e r models. The c o n v e c t i v e f l u x e s a r e o f t e n p a r t i t i o n e d u s i n g a s t a t i c m o i s t u r e a v a i l a b i l i t y f a c t o r o r an assumed Bowen r a t i o . Ross and Oke (1988) c o n c l u d e t h a t t h e l a t e n t h e a t f l u x i s t h e p o o r e s t p a r t o f t h r e e u r b a n c l i m a t e models t h e y v a l i d a t e d a g a i n s t measured e n e r g y b a l a n c e f l u x e s ( d r y summertime). The s e c o n d g r o u p i n c l u d e s s i m p l e s t a t i s t i c a l a l g o r i t h m s and p h y s i c a l l y - b a s e d models u t i l i s i n g h y d r o - m e t e o r o l o g i c a l d a t a as i n p u t . C u r r e n t l y none i s c a p a b l e o f m o d e l l i n g e v a p o t r a n s p i r a t i o n f o r u r b a n a r e a s o v e r a range o f s e a s o n a l c o n d i t i o n s . The o b j e c t i v e o f t h i s t h e s i s i s t o d e v e l o p a model t o e s t i m a t e h o u r l y , and l o n g e r - t i m e p e r i o d , e v a p o t r a n s p i r a t i o n f o r u r b a n a r e a s , t h a t i s u s e f u l a c r o s s a wide range o f m e t e r o l o g i c a l c o n d i t i o n s . I t s h o u l d be n o t e d t h a t t h e c a s e o f snow on t h e s u r f a c e i s n o t i n c l u d e d . W i t h i n t h e Oke (1984) framework o f u r b a n c l i m a t e c l a s s i f i c a t i o n t h e model t o be d e v e l o p e d i s r e l e v a n t t o t h e " l o c a l " s c a l e . T h i s means t h a t t h e model s h o u l d s i m u l a t e t h e p r o c e s s e s a s s o c i a t e d w i t h u r b a n u n i t s o f t h e s i z e o f c i t y - b l o c k s t o l a n d use z o n e s . 1.2 The approach taken to aodel seasonal evapotranspiration I f e v a p o t r a n s p i r a t i o n i s t o be c a l c u l a t e d u n d e r d i v e r s e m e t e o r o l o g i c a l c o n d i t i o n s i t i s n e c e s s a r y t o have a model t h a t c a n cope w i t h c h a n g i n g w a t e r a v a i l a b i l i t y on t h e s u r f a c e d u r i n g and f o l l o w i n g r a i n f a l l . I t i s t h e r e f o r e deemed a p p r o p r i a t e t o t a k e an e v a p o t r a n s p i r a t i o n - i n t e r c e p t i o n a p p r o a c h . The p h y s i c a l s t r u c t u r e o f t h e c i t y has been compared i n f o r m t o t h a t o f a f o r e s t (Oke, 1976, 1989) t h r o u g h t h e e x i s t e n c e o f an u r b a n canopy l a y e r below 5 t h e u r b a n boundary l a y e r . The u r b a n canopy l a y e r c o n s i s t s o f t h e a i r c o n t a i n e d between t h e roug h n e s s e l e m e n t s ( b u i l d i n g s and t r e e s ) w h i c h a r e e q u i v a l e n t t o t h e t r e e s i n a f o r e s t . I t i s t h e r e f o r e p r o p o s e d t h a t a n a p p r o p r i a t e model framework i s t h e P e n m a n - M o n t e i t h - R u t t e r - S h u t t l e w o r t h e v a p o t r a n s p i r a t i o n -i n t e r c e p t i o n model ( M o n t e i t h , 1965; R u t t e r e t a l . . 1971) o r i g i n a l l y d e v e l o p e d f o r f o r e s t s . The c o n c e p t u a l framework o f t h i s model a d a p t e d f o r u r b a n a r e a s i s shown d i a g r a m m a t i c a l l y i n F i g u r e 1.2. T h i s model i s t h e most s u c c e s s f u l , r i g o r o u s , r o b u s t p h y s i c a l l y - b a s e d e v a p o t r a n s p i r a t i o n - i n t e r c e p t i o n model c u r r e n t l y a v a i l a b l e (Gash, 1979; S h u t t l e w o r t h , 1983, 1988a). I n e s s e n c e t h e model i s u s e d t o c a l c u l a t e a r u n n i n g w a t e r b a l a n c e o f t h e 'canopy' and ' t r u n k s ' . I t r e q u i r e s i n p u t s o f h o u r l y r a i n f a l l and t h e m e t e o r o l o g i c a l p a r a m e t e r s n e c e s s a r y t o e s t i m a t e e v a p o r a t i o n , and p r o v i d e s o u t p u t s o f t h r o u g h f a l l , s t e m f l o w and e v a p o r a t i o n o f i n t e r c e p t e d w a t e r . The e v a p o r a t i o n i s c a l c u l a t e d f r o m t h e Penman-Monteith e q u a t i o n . The model a l l o w s f o r a c o n t i n u o u s t r e a t m e n t o f s u r f a c e r e s i s t a n c e f o r t h e t r a n s i t i o n between wet and d r y s u r f a c e s . The f o l l o w i n g s e c t i o n o u t l i n e s t h e P e n m a n - M o n t e i t h - R u t t e r -S h u t t l e w o r t h e v a p o t r a n s p i r a t i o n - i n t e r c e p t i o n model and t h e a d a p t a t i o n s i n c o r p o r a t e d so t h a t i t c a n be a p p l i e d t o u r b a n a r e a s . 1.3 Pennan-Monteith-Rutter-Shuttlevorth evapotranspiration-interception model The p r o c e s s o f e v a p o t r a n s p i r a t i o n f r o m s u r f a c e s w h i c h have some v e g e t a t i v e c o v e r c a n be c o n s i d e r e d t o c o n s i s t o f t h r e e p h a s e s : 1) e v a p o r a t i o n f r o m a t o t a l l y wet s u r f a c e ; 2) e v a p o t r a n s p i r a t i o n f r o m a p a r t i a l l y wet s u r f a c e ; and 3) t r a n s p i r a t i o n f r o m a d r y s u r f a c e ( w a t e r l o s s f r o m v e g e t a t i o n whose o u t e r s u r f a c e s a r e d r y ) . I n t h e f i r s t phase, t h e w a t e r t h a t i s e v a p o r a t e d i s i n t e r c e p t e d w a t e r . The 6 amount of intercepted water at any particular time i s controlled not only by evaporation but also by the amount of precipitation, and the 'canopy' morphology which influences surface storage and drainage. In an urban area an array of surfaces (buildings, roads, vegetation) create the 'canopy'. If i t i s assumed that the components of the 'canopy' are exposed to the same local scale climate then a single-source (layer) model can be used to determine the latent heat flux (Qg) • The best tested approach i s the physically-based Monteith (1965) version of the Penman equation (Stewart, 1984; Dolman et a l . . 1988): Q E - s(Q* - AQg) + (p c D V)/r H (1.3) s + 7 ( r v + r s ) / r H where s - slope of the saturation vapour pressure versus temperature curve (Pa C-l); Q* - net a l l wave radiation (W m"z); AQg - storage heat flux (W m"^); 7 - psychrometric 'constant'(Pa °C " 1 ) ; p - density of a i r (kg m"^); cp - specific heat of a i r (J kg"^ - °C"^); V - vapour pressure d e f i c i t of the ai r (Pa); rfl - sensible heat flux resistance (s m"l); Ty - latent heat flux resistance (s m"^ -); and rg - surface resistance (s m'^). A l l of the terms in this equation are influenced by the urban environment and i t i s also necessary to include an additional term, the anthropogenic heat flux ( Q F ) . SO: Q E - s(Q* + Q F - AQg) + (p c p V)/r H (1.4) s + 7 ( r v + r g ) / r H Equation 1.4 i s applicable to dry surfaces (phase 3 outlined above). In applying 1.4 i t i s commonly assumed that rjj and ry are equal and related to rjj, the equivalent resistance for momentum (this i s often called the aerodynamic resistance, r a ) . Equation 1.4 can thus be re-written: Q E - s (Q* + Q F - AQg) + (p c p V ) / r a (1.5) s + 7 (1 + r s / r a ) When the surface i s completely wet (phase 1) the rg term of equation 1.5 i s zero. Therefore equation 1.5 becomes: Q E - s (Q*-KjF-AQs) + (p c p V)/r a (1.6) The transition between evaporation of intercepted water (phase 1) and transpiration (phase 3) for forested areas has been modelled by Rutter et a l . (1971, 1975). The Rutter model calculates evaporation using equation 1.6 when the surface i s wet (phases 1 & 2) adjusted by a function (X) of current canopy water storage (C) and canopy storage capacity (S): X-l when C>S X-C/S when C<S. (1.7) S i s defined as the amount of water l e f t on the canopy when r a i n f a l l and throughfall have ceased. It corresponds to the storage capacity of Zinke (1967) following Horton (1919), or canopy saturation value of Leyton et a l . (1967). It is comparable to f i e l d capacity of a so i l (Rutter et a l . . 1971). The overlap between the evaporation of intercepted water and transpiration is poorly defined i n the Rutter model (Shuttleworth, 1983). To unify the two processes correctly, a physically continuous transition between wet and dry canopies i s required. Equation 1.3 forms the basis of the unified model proposed by Shuttleworth (1978), i n which rg i s replaced by a redefined surface resistance, rgg, equal to rg in dry conditions and to zero i n wet conditions, with a smooth transition between the two depending on the fractional surface wetness. Shuttleworth's theoretical analysis has been tested over t a l l vegetation (Shuttleworth, 1978) and takes the form: r S S " f H W CLJii V 1 - r b ( s / 7 + 1) (1.8) | r b ( s / 7 + 1)J [r s + rb(s/7 + 1)J where W - 1 when C>S (1.9) W - R-l when C<S (1.10) R-S/C R - ( r s / r a ) ( r a - r b ) (1.11) r s + (s/7 + 1) r b 8 where r D - mean boundary layer resistance (s m"1), defined by Shuttleworth (1983) as: r b - l . l u * - 1 + 5 . 6 M * 1 / 3 (1.12) where u* - f r i c t i o n velocity (m s ' l ) . Both Rutter and Shuttleworth use equation 1.5 when the surface i s completely dry (phase 3). The Rutter model can be used to calculate a continuous or running water balance, summarised by the continuity equation: d£ - P(1-T F-T S) - D - E P M (1.13) dt where t - time (h); P - precipitation (mm); Tp - throughfall or proportion of rain f a l l i n g directly to the ground through the gaps in the canopy; Tg - proportion of rain diverted to the 'trunks'; D - drainage (mm h'^); and EpM " evapotranspiration (mm). This model represents the canopy as a single-layer store of moisture which is f i l l e d by incoming r a i n f a l l ; i s capable of holding a pre-set amount of water, S; and drains at a rate, D, expressed as an empirical function i n proportion to the amount of water i n the store. The throughfall (Tp) represents water not available for evaporation from the canopy. Subsidiary evaporation may arise from trunks wetted by stemflow (Tg). Rutter et a l . (1971) estimate this via a sub-model involving a secondary water store whose mathematical behaviour mimics that of the canopy. Multi-layer models also have been developed (e.g. Sellers and Lockwood, 1981). Shuttleworth (1988a) considers, the treatment of the whole canopy as a single moisture store the simplest, and therefore the most robust and general model of evapotranspiration-interception. In this study, which is a f i r s t attempt to use the evapotranspiration-interception approach i n the urban environment, the canopy i s treated as a single-layer moisture store, but with 9 p a r a l l e l s t o r e s w h i c h a l l o w c o n s i d e r a t i o n o f t h e d i f f e r e n t s u r f a c e t y p e s w i t h i n t h e u r b a n a r e a . A s a f i r s t a p p r o x i m a t i o n t h e u r b a n s y s t e m c o n s i s t s o f t w o s u r f a c e t y p e s : b u i l t / i m p e r v i o u s a n d v e g e t a t e d . T h e c a n o p y c a n b e c o n s i d e r e d s p a r s e w i t h n o c l o s e d , e l e v a t e d l a y e r a b o v e t h e g r o u n d , u n l i k e a f o r e s t . T h e t r e e s u s u a l l y h a v e v e g e t a t i o n ( g r a s s ) b e l o w , t h e r e f o r e w h e n w a t e r f a l l s b e t w e e n t h e m i t m a y b e c a u g h t b y t h e v e g e t a t i o n b e l o w . T h e n e a r s u r f a c e v e g e t a t i o n h a s t h e s a m e l o c a l c l i m a t e a s t h e l a r g e v e g e t a t i o n . T h e r e i s l i t t l e r e l e v a n c e t o t h e c o n c e p t o f t h r o u g h f a l l f r o m i m p e r v i o u s s u r f a c e s ( b u i l d i n g s ; p a v e d r o a d , p a t h s ) t h e r e f o r e t h i s t e r m c a n b e s e t t o z e r o o r a v e r y s m a l l n u m b e r f o r b o t h t h e v e g e t a t e d a n d b u i l t s u r f a c e t y p e s . I n u r b a n a r e a s t h e s u b s i d i a r y l o s s , d u e t o ' s t e m f l o w ' , f r o m w e t t e d ' t r u n k s ' c a n b e i n t e r p r e t e d a s t h a t f r o m w a l l s o f b u i l d i n g s a n d f r o m t r u n k s o f t h e t a l l v e g e t a t i o n . I t i s g e n e r a l l y n o t p o s s i b l e f o r w a l l s t o b e w e t t e d b y ' s t e m f l o w ' f r o m t h e r o o f d u e t o r o o f g u t t e r i n g , a l t h o u g h i t i s p o s s i b l e f o r t h e w a l l s t o b e w e t t e d d i r e c t l y d u r i n g r a i n f a l l . H o w e v e r w a l l s t e n d n o t t o b e e x t e n s i v e l y w e t t e d u n d e r n o r m a l r a i n ( L a c y , 1 9 7 7 ) . T h e s u r f a c e a r e a o f t r u n k s i n t h e u r b a n s y s t e m i s n o t l a r g e ( s e e C h a p t e r 3 ) , h e n c e t h e a m o u n t o f w a t e r b e i n g s t o r e d c a n b e r e g a r d e d a s n e g l i g i b l e . I t i s t h e r e f o r e p r o p o s e d t h a t u r b a n s t e m f l o w a l s o b e s e t t o z e r o . I n u r b a n a r e a s t h e r e i s a n a d d i t i o n a l s o u r c e o f w a t e r f o r w e t t i n g t h e c a n o p y , t h e p i p e d w a t e r s u p p l y ( I ) . T h u s , n e g l e c t i n g t h r o u g h f a l l a n d s t e m f l o w a n d a d d i n g i r r i g a t i o n t h e m o d e l c a n b e r e - f o r m u l a t e d f o r u r b a n a r e a s a s : dfi - ( P + I ) - D - E P M ( 1 . 1 4 ) d t C c a n now b e c o n s i d e r e d t o b e t h e s u r f a c e s t o r a g e s t a t e . T h e s p e c i f i c n a t u r e o f t h e u r b a n s u r f a c e r e s i s t a n c e a n d d r a i n a g e f u n c t i o n s a r e 1 0 presented in Chapter 7. 1.4 Approach to problem solution and structure of the thesis To develop and test the model outlined above measurements were conducted over a wide range of meteorological conditions. They were conducted from January to June, 1987 i n a suburb of Vancouver, B.C. The evaporative flux was determined using the energy balance framework and micrometeorological measurements. A description of the methods and measurements is contained in Chapter 2. Although the energy balance i t s e l f i s not the focus of this study these are amongst the f i r s t energy balance measurements conducted in winter and spring, so discussion of the fluxes i s included i n Chapter 6. Development of the urban evapotranspiration-interception model involved the need for other sub-models to calculate anthropogenic heat flux, storage heat flux, aerodynamic resistance, surface resistance and drainage. A common requirement of these sub-models and the overall model is knowledge of the 'surface'. There is no clear cut methodology to determine what the 'surface' i s or what area should be considered for description. This issue i s addressed in Chapter 3. The results of this are used i n the development of the models of anthropogenic heat flux (Chapter 4); storage heat flux (Chapter 5); and surface resistance and drainage (Chapter 7). The f u l l evapotranspiration-interception model is tested against the measured latent heat fluxes in Chapter 8 together with sensitivity analyses of the model. CHAPTER 2 OBSERVATION PROGRAMME 1 2.1 Physical Setting Vancouver, B.C. (49° 15'N, 123° 18'W) i s l o c a t e d on t h e west c o a s t o f N o r t h A m e r i c a , b u t i s c l i m a t i c a l l y i s o l a t e d from the c o n t i n e n t a l i n t e r i o r by a s e r i e s o f mountain c h a i n s p a r a l l e l l i n g t he c o a s t l i n e . The c i t y i s s h e l t e r e d f r o m the P a c i f i c Ocean by Vancouver I s l a n d . The c i t y i s s i t u a t e d a t the west end o f t h e Lower F r a s e r V a l l e y and has low t o moderate r e l i e f . O b s e r v a t i o n s f o r t h i s s t u d y were c o n d u c t e d i n t h e Sunset s u b u r b , Vancouver ( F i g . 2.1). T h i s s i t e has been used f o r a number o f c l i m a t o l o g i c a l s t u d i e s . Sunset has p r e d o m i n a n t l y one- and t w o - s t o r e y s i n g l e f a m i l y d w e l l i n g s ( F i g . 2.2). The a r e a has a s l i g h t s outhwestward s l o p e t o w a r d s t h e F r a s e r R i v e r . 2.2 General climatology of Vancouver and the measurement period The g e n e r a l c l i m a t o l o g y o f Vancouver i s d e s c r i b e d i n Hay and Oke ( 1 9 7 6 ) , the f o l l o w i n g i s a b r i e f d e s c r i p t i o n . The l a r g e s c a l e upper l e v e l f l o w i s g e n e r a l l y from the w e s t e r l y q u a r t e r , from t h e P a c i f i c . Embedded i n t h i s f l o w a r e d i s t u r b a n c e s ( c y c l o n e s ) w h i c h a r e b e s t d e v e l o p e d and most f r e q u e n t i n w i n t e r . H i g h - p r e s s u r e ( a n t i - c y c l o n i c ) r egimes have a r e l a t i v e l y l o w f r e q u e n c y i n t he w i n t e r months, n o r m a l l y b e i n g u n a b l e t o w i t h s t a n d t h e i n v a s i o n o f a v i g o r o u s c y c l o n i c d i s t u r b a n c e . Summer b r i n g s an e x t e n s i o n o f t h e P a c i f i c a n t i c y c l o n e regime i n t o t he m i d - l a t i t u d e s , r e s u l t i n g i n the predominance o f h i g h - p r e s s u r e c o n d i t i o n s and g e n e r a l l y c l e a r , warm wea t h e r . S e v e r a l p h y s i c a l f e a t u r e s o f t h e l a n d s c a p e combine t o produce l o c a l c l i m a t e v a r i a t i o n s . C h i e f among t h e s e a r e the i n f l u e n c e s o f top o g r a p h y , p r o x i m i t y t o the ocean, and u r b a n i z a t i o n . The s e t t i n g o f Vancouver l e a d s t o the o c c u r r e n c e o f l a n d / s e a and moun-t a i n / v a l l e y c i r c u l a t i o n s . The e f f e c t o f the l a n d / s e a b r e e z e i s t o cause 1 2 Figure 2.1 The location of the Sunset site in the Vancouver area and surrounding landuses. Sunset - site of tower for present study Kerrisdale - site of tower for Grimmond 0.983) study Oakridge - site of water use meter Airport - AES climate station Figure 2 . 2 View lo o k i n g southwest from the t owe 1 4 p r e d o m i n a n t l y w e s t e r l y winds d u r i n g daytime and weaker e a s t e r l y f l o w d u r i n g the n i g h t . The l a n d / s e a b r e e z e has a h i g h e r f r e q u e n c y d u r i n g t h e summertime ( S t e y n and F a u l k n e r , 1986). Due t o the sea b r e e z e and t h e a s s o c i a t e d a d v e c t i o n o f marine a i r , the h e i g h t o f t h e p l a n e t a r y boundary l a y e r i s t y p i c a l l y r e d u c e d t o o n l y 500 m ( S t e y n and Oke, 1982; C l e u g h , 1988; S t e y n and McKendry, 1988). I n t h i s s t u d y measurements were c o n d u c t e d from J u l i a n Day (JD) 21 ( J a n u a r y 21) t o 179 (June 28) 1987 (see Appendix I f o r JD c a l e n d a r ) . T a b l e 2.1 p r o v i d e s m o n t h l y a v e r a g e c l i m a t e s t a t i s t i c s t o e n a b l e a c o m p a r i s o n o f the c l i m a t i c s t a t u s o f 1987 w i t h t h e 'normal'. I t i s based on d a t a c o l l e c t e d by the A t m o s p h e r i c Environment S e r v i c e (AES) a t t h e Vancouver I n t e r n a t i o n a l A i r p o r t C l i m a t e S t a t i o n ( F i g . 2.1). I n g e n e r a l , t h e measurement p e r i o d was warmer t h a n n o r m a l , had a g r e a t e r number o f s u n s h i n e h o u r s , b u t had a l m o s t normal p r e c i p i t a t i o n (more as r a i n and l e s s as snow t h a n n o r m a l ) . 2.3 Measurement considerations The o b j e c t i v e o f t h i s r e s e a r c h was t o d e t e r m i n e f l u x e s f r o m an a r e a o f suburban l a n d use; i . e . a t t h e l o c a l s c a l e (Oke, 1984), r a t h e r t h a n f r o m i n d i v i d u a l s u r f a c e s s u c h as lawn o r pavement. T h e r e f o r e measurements must be made w e l l above t h e h e i g h t o f the roughness e l e m e n t s t o en s u r e o b s e r v a t i o n s a r e c o n d u c t e d i n the s u r f a c e l a y e r ( F i g . 2 .3), so t h a t t h e y r e p r e s e n t t h e i n t e g r a t e d e f f e c t s o f the s u r f a c e t y p e s w h i c h c h a r a c t e r i s e t h e l a n d u se. C l e u g h and Oke (1986) n o t e t h a t "due t o the p r e s e n c e o f r e l a t i v e l y t a l l r oughness elements and t h e g r e a t s p a t i a l v a r i a b i l i t y o f s u r f a c e m a t e r i a l s w h i c h c h a r a c t e r i s e suburban t e r r a i n , t he c h o i c e o f t h e s e n s o r h e i g h t and a v e r a g i n g time ( T ) , i s n o t a s i m p l e t a s k " . R o t h (1988) r e p o r t s a s t u d y o f the t u r b u l e n c e s p e c t r a o f t e m p e r a t u r e , the v e r t i c a l and l o n g i t u d i n a l wind components as w e l l as t h e c o s p e c t r a o f the 1 5 T a b l e 2.1 Normal (N) (1951-1980) and 1987 measurements o f c l i m a t i c v a r i a b l e s f o r Vancouver I n t e r n a t i o n a l A i r p o r t (Canada, Dept. o f Env i r o n m e n t , A.E.S., 1987; Hay & Oke, 1976) Month P r e c i p i t a t i o n Mean A i r B r i g h t Mean Mean Wind Temperature Sunsh i n e R e l a t i v e Speed H u m i d i t y (mm) (°C) ( h o u r s ) (%) (km h " 1 ) N 1987 N 1987 N 1987 N 1987 N 1987 JANUARY 146. .8 130, .7 2, .5 4. .4 53. .5 59, .5 87 83 12, .2 12. .3 FEBRUARY 114. .7 78. .0 4. .6 6. ,5 87, .2 80. .1 85 77 12. .4 10. .7 MARCH 101. .0 142. .9 5. .8 8, .0 129. .3 126. ,1 82 80 13. .5 11. .6 APRIL 59. .3 63, .2 8. .8 10. .4 180. .5 174. ,7 75 73 13, .3 12 .6 MAY 51. .6 85, .8 12. .2 13, .0 246, .1 267, ,3 74 73 11, .8 13, .7 JUNE 45. .2 17, .8 15. .1 16, .0 238. ,4 296, .7 76 73 11. .5 12, ,1 JAN-JUNE 525. .9 534. .7 8. .2 9, ,7 935, .0 1004. ,4 NOTES: J a n u a r y - M i l d t e m p e r a t u r e s p r e v a i l e d d u r i n g the month w i t h l ow s n o w f a l l t o t a l s , w h i l e i n o t h e r r e s p e c t s t h e month'was v e r y n e a r normal F e b r u a r y - I n g e n e r a l the month was d u l l , warmer t h a n e x p e c t e d , w i t h r a i n f a l l f a l l i n g f r e q u e n t l y but below t h e normal t o t a l f o r t h e month March - Warm and wet. Mean t e m p e r a t u r e f o r t h e month was more t h a n 2 de g r e e s above normal and p r e c i p i t a t i o n was more t h a n 50% h i g h e r t h a n normal A p r i l - M i l d c o n d i t i o n s dominated the month w i t h p r e c i p i t a t i o n n e a r normal and p r e d o m i n a n t l y f a l l i n g i n the f i r s t h a l f o f t h e month May - C o n s i d e r a b l y s u n n i e r and warmer t h a n n o r m a l , b u t r a i n f e l l on more t h a n the normal number o f days and the amount was more t h a n 60% g r e a t e r t h a n normal June - W e l l below normal p r e c i p i t a t i o n amounts and much h i g h e r t h a n normal s u n s h i n e 1 6 F i g u r e 2.3 I d e a l i s e d arrangement o f boundary l a y e r s t r u c t u r e s o v e r a c i t y ( a f t e r Oke, 1984) . 1 7 fluxes of sensible heat and momentum at the Sunset s i t e , i n c l u d i n g an assessment of whether the measurement height used i s above the 'roughness sub-la y e r ' (Raupach, 1979) or ' t r a n s i t i o n layer' (Garratt, 1980). Roth concluded that, although the sensor height of 20-21 m above zero plane displacement, i s at, or below, recommended values for the top of the roughness sub-layer, the height i s suitable f o r turbulence measurements. Cleugh and Oke (1986) use Wyngaard's (1973) analysis to y i e l d r f or t h i s measurement height at the Sunset s i t e . In unstable conditions (z/L = -1) they f i n d r between 80 and 130 minutes for a sensible heat f l u x measured with 10% uncertainty, and 36 to 60 mins for 15% uncertainty. In neutral s t a b i l i t y r should be about 67% greater. Roth (1988) compared averaging times for heat f l u x covariances computed over 60 min with the mean of those over four 15 min periods and found no s i g n i f i c a n t under- or over-estimation over the range 5 to 300 W m"2. Similar conclusions a r i s e from q u a l i t a t i v e assessment of the spectra; i.e the averaging time f o r turbulent fluxes can be relaxed. In accord with these findings a sensor height of >20 m above zero plane displacement, and an averaging time of 60 minutes were selected f o r the present study. The displacement length was determined, f o r the Sunset s i t e by Steyn (1980), using the techniques of Kutzbach (1961) and Nicholson (1975), to be 3.5 m. Steyn (1980) calculated the roughness length, v i a Lettau's (1969) method, to be 0.52 m. 2.4 The Instruments The instruments were mounted on a 29 m tri a n g u l a r section s t e e l l a t t i c e free standing tower located within the Mainwaring substation of B.C. Hydro. The base of the tower i s 5 m below the l e v e l of the surrounding embankment. The maximum e f f e c t i v e height of the tower i s 20.5 ra (height of instrument 1 8 minus z e r o p l a n e d i s p l a c e m e n t and embankment). The e n v i r o n m e n t a l v a r i a b l e s measured were: n e t r a d i a t i o n f l u x d e n s i t y ( Q * ) , s e n s i b l e h e a t f l u x d e n s i t y (QJJ,) , wi n d speed (u) and d i r e c t i o n (<p) , wet (Ty) and d r y (T^) b u l b a i r t e m p e r a t u r e , r e l a t i v e h u m i d i t y (RH), s u r f a c e wetness (wg), p r e c i p i t a t i o n (P) and s o i l m o i s t u r e d e f i c i t (59). D e t a i l s o f t h e i n s t r u m e n t a t i o n and t h e i r p o s i t i o n s on the tower a r e p r o v i d e d i n F i g u r e s 2.4 and 2.5 and T a b l e 2.2. The s i g n a l s were l o g g e d on two Campbell S c i e n t i f i c I n c CR21X d a t a l o g g e r s . The d a t a were w r i t t e n t o c a s s e t t e t a p e s and r e a d on t o the UBC mainframe computer u s i n g a Campbell S c i e n t i f i c I n c C20 A u d i o s p h e r e I n t e r f a c e . A l l t i m e s r e f e r r e d t o a r e l o c a l a p p a r e n t t i m e ( L A T ) . The s o n i c anemometer-thermometer system (SAT) us e d f o r m e a s u r i n g s e n s i b l e h e a t f l u x d e n s i t y (QH). u t i l i s e s t h e eddy c o r r e l a t i o n a p p r o a c h . The v e r t i c a l v e l o c i t y i s sensed as a phase s h i f t i n the sound wave, and t h e a i r t e m p e r a t u r e by a f i n e w i r e t h e r m o c o u p l e ( d i a m e t e r 12.7/xm). The w i n d speed and t e m p e r a t u r e were sampled a t 10 Hz and c o v a r i a n c e s d e t e r m i n e d f o r 15 min p e r i o d s . The h o u r l y QH was o b t a i n e d from the average o f t h e f o u r 15 min v a l u e s . I t i s d i f f i c u l t t o a s s e s s t h e a c t u a l measurement e r r o r a s s o c i a t e d w i t h eddy c o r r e l a t i o n e s t i m a t e s o f Q ^ ( C l e u g h , 1988). The r e s u l t s o f R o t h (1988) i n d i c a t e t h a t t he s o n i c anemometer-thermometer measures w'T' c o s p e c t r a " a d e q u a t e l y " . An i n t e r c o m p a r i s o n o f h o u r l y f l u x e s f r o m two i n s t r u m e n t s o b t a i n e d a RMSE o f 12 W m"2 ( C l e u g h , 1988; Schmid, 1988). Tanner ( C a m p b e l l S c i e n t i f i c , p e r s . comm., 1987) s u g g e s t s t h a t t he measurement e r r o r i s l e s s t h a n 10%. The r e v e r s i n g t e m p e r a t u r e d i f f e r e n c e measurement system (RTDMS), u s e d t o d e t e r m i n e Bowen r a t i o s (IS—QH/QE), was s i m i l a r t o t h a t d e s c r i b e d by McCaughey e t a l . ( 1 9 8 7 ) . The wet and d r y b u l b t h e r m o c o u p l e s (10 j u n c t i o n c o p p e r / c o n s t a n t a n t h e r m o p i l e s ) were mounted w i t h i n s h i e l d s on two c a r t s w h i c h move up 19 Figure 2.4 Schematic of the Sunset tower and instrument locations. Instruments include: net pyrradiometer, sonic anemometer/ thermometer (level 4, SW); relative humidity probe, Met-101 wind vane, Met-101 cup anemometer (level 3, NE) ; Bowen Ratio system (levels 1 and 2). (Adapted from Cleugh, 1988; Roth, 1988"). <u > e 4> > 01 NE SW CJ rH 0) <D 4-1 > 4-1 0) 01 1-1 01 > O o cd w .e c 00 3 •H O 01 M ,C 00 4 3 2 20.5 19.0 17.2 29.0 27.5 25.7 10.1 18.6 0.0 8.5 21 T a b l e 2.2 I n s t r u m e n t a t i o n V a r i a b l e I n s t r u m e n t s E f f e c t i v e 3 S a m p l i n g R e c o r d i n g ( M a n u f a c t u r e r H e i g h t Time I n t e r v a l model) (m) ( s ) (min) Q * Net p y r r a d i o m e t e r 20.5 1 5 ( S w i s s t e c o S I ) QH S o n i c anemometers 20.5 0.1 15 thermometer (Campb e l l S c i e n t i f i c CA27) u Cup anemometer 19 1 5 (Met-One 012A) <p Wind vane 19 1 5 (Met-One 024A) RH & T H u m i d i t y & 19 1 5 t e m p e r a t u r e probe ( R o t r o n i c s I n s t r u m e n t Corp MP-100) T d & T w McCaughey RTDMS upper c a r t 17.2 1 10 l o w e r c a r t 10.1 w s S u r f a c e wetness - 1 5 s e n s o r Weiss P Raingauge - 1 5 ( M e t e o r o l o g i c a l R e s e a r c h I n c 382B) a H e i g h t above ground minus embankment h e i g h t and z e r o p l a n e d i s p l a c e m e n t 2 2 and down on a t r a c k w a y . The c a r t s , s e p a r a t e d by 7.1 ra, a r e r e v e r s e d t w i c e each hour. A t e n minute p e r i o d a l l o w s f o r t r a v e l l i n g ( l e s s t h a n 4 mins) and e q u i l -i b r a t i o n a t t h e new l e v e l . The r e m a i n i n g 20 mi n u t e s a t each l e v e l a l l o w e d f o r two 10 minute a v e r a g e s . B was c a l c u l a t e d : i i = 7 ( A T H + T Az) (2.1) (s + 7 ) A T W - 7 A T d where A T d - d r y b u l b t e m p e r a t u r e d i f f e r e n c e (°C); ATy - wet b u l b t e m p e r a t u r e d i f f e r e n c e (°G); T - d r y a d i a b a t i c l a p s e r a t e (°C m"!); s - s l o p e o f t h e s a t u r a t i o n vapour p r e s s u r e c u r v e a t Ty (Pa °C"1); 7 - p s y c h o m e t r i c c o n s t a n t (Pa °C " 1 ) ; and Az - s e n s o r s e p a r a t i o n (m). See A p p e n d i x I I f o r t h e methods used t o d e t e r m i n e . t h e i n d i v i d u a l terms. Qpj can be d e t e r m i n e d f r o m fl u s i n g the energy b a l a n c e : Q H f i = [B (Q* + Q F - A Q S ) ] / ( 1 + B) (2.2) where Qp - a n t h r o p o g e n i c h e a t f l u x (see C h a p t e r 4 ) ; and AQg - s t o r a g e h e a t f l u x (see Chap t e r 5 ) . S i m i l a r l y t he l a t e n t h e a t f l u x (Qg) can be d e t e r m i n e d : QE B - (Q* + Q F - AQ S) / ( 1 + A) (2.3) A l t e r n a t i v e l y , Qg c a n be c a l c u l a t e d u s i n g fi and the QJJ measured w i t h t h e SAT: Q E S=Q H/B (2.4) See C h a p t e r 6 f o r d i s c u s s i o n o f the methods u s e d t o d e t e r m i n e energy b a l a n c e f l u x e s . The e r r o r a n a l y s i s used t o d e t e r m i n e the p r e c i s i o n o f the r e v e r s i n g t e m p e r a t u r e d i f f e r e n c e measurement system (RTDMS) f o l l o w s t h e p r o c e d u r e o f K a l a n d a (1979) who c o n d u c t e d an e r r o r a n a l y s i s o f a r e v e r s i n g t e m p e r a t u r e system f o l l o w i n g the method o f Cook and R a b i n o w i c z (1963) ( A p p e n d i x I I I ) . U s i n g t h i s method e r r o r s were d e t e r m i n e d f o r t h e t e m p e r a t u r e d i f f e r e n c e s , a b s o l u t e t e m p e r a t u r e s , fl, Qpjjj and Qgjj. The e r r o r s c a l c u l a t e d f o r each hour were used t o s t r a t i f y t he d a t a t o d e c i d e whether i t was o f use t o t e s t the submodels (see C h a p t e r 5) and f o r the d e t e r m i n a t i o n o f 'measured' Qg (see 2 3 C h a p t e r 6 ) . Net a l l - w a v e r a d i a t i o n was measured w i t h a n e t p y r r a d i o m e t e r . The p o l y t h e n e domes were k e p t i n f l a t e d and f r e e o f i n t e r n a l c o n d e n s a t i o n by a i r pumped t h r o u g h g r a n u l a t e d s i l i c a d e s i c c a n t . T y p i c a l measurement e r r o r s f o r n e t p y r r a d i o m e t e r s a r e 3-4% on i n s t a n t a n e o u s measurements ( L a t i m e r , 1972). F o r h o u r l y v a l u e s an e r r o r o f 5% i s g e n e r a l l y u s e d ( C l e u g h and Oke, 1986). The r e l a t i v e h u m i d i t y and t e m p e r a t u r e probe was housed i n a r e f l e c t i v e s h i e l d w h i c h a l l o w e d a i r f l o w around the s e n s o r but p r o t e c t e d the s e n s o r f r o m s o l a r r a d i a t i o n and p r e c i p i t a t i o n . The r e l a t i v e h u m i d i t y i s measured w i t h a C-80 HYGROMER s e n s o r w h i c h i s c o n n e c t e d t o a c a p a c i t i v e b r i d g e . The u n i t senses t e m p e r a t u r e w i t h a p r e c i s i o n P t 100 RTD w h i c h forms p a r t o f a m e a s u r i n g b r i d g e . The o u t p u t f r o m the b r i d g e f e e d s an a m p l i f i c a t i o n and l i n e a r i z a t i o n c i r c u i t . The i n s t r u m e n t has a n o m i n a l a c c u r a c y o f + 1.5% RH a t 25°C and + 2 . 5 % over the t e m p e r a t u r e range o f -50 t o +150°C ( m a n u f a c t u r e r ' s s p e c i f i c a t i o n s ) . The n o m i n a l a c c u r a c y o f the t e m p e r a t u r e o v e r the range -20 t o + 50°C i s + 0.35°C ( m a n u f a c t u r e r ' s s p e c i f i c a t i o n s ) . The i n s t r u m e n t r e p e a t a b i l i t y i s 0.5% f p r RH and 0.1°C f o r t e m p e r a t u r e , o r b e t t e r ( m a n u f a c t u r e r ) . An u n s h i e l d e d t i p p i n g b u c k e t r a i n gauge was mounted w i t h the 200 mm o r i f i c e a p p r o x i m a t e l y l e v e l w i t h the t o p of the embankment. I t t i p p e d w i t h t h e a c c u m u l a t i o n of" 0.2 mm i n a c o l l e c t i o n b u c k e t . A r e e d s w i t c h i s a c t u a t e d by a magnet on the t i p p i n g b u c k e t . The t i p p i n g b u c k e t mechanism has a n o m i n a l a c c u r a c y o f + 1% f o r up t o 76.2 mm h'^ and + 5% up t o 254 mm h"^ ( m a n u f a c t u r e r s p e c i f i c a t i o n s ) . There i s no means of m e a s u r i n g the ' t r u e ' p r e c i p i t a t i o n ( i . e . the amount o f w a t e r w h i c h would have r e a c h e d the ground had the gauge n o t been p r e s e n t , hence a l l measurements are r e l a t i v e ) . Measurement e r r o r s f o r d a i l y t o t a l s can be assumed t o be ± 7% based on r e s e a r c h c o n d u c t e d by H u t c h i n s o n ( 1 9 6 9 ) , M a n d e v i l l e and Rodda ( 1 9 7 0 ) , F i n k e l s t e i n ( 1 9 7 1 ) , R a p i e r and Gr a n t 2 4 ( 1 9 7 1 ) , Waugh (1971) and A l d r i d g e ( 1 9 7 6 ) . The random e r r o r s f o r s h o r t e r t i m e p e r i o d s w i l l be g r e a t e r . H u t c h i n s o n (1969) r e p o r t s e r r o r s o f 12.5%, a t t h e 95% c o n f i d e n c e l i m i t s , f o r i n d i v i d u a l s t o r m s . The w i n d speed s e n s o r was a 3-cup anemometer w i t h a m a g n e t i c - r e e d s w i t c h assembly w h i c h p r o d u c e d a s e r i e s of c o n t a c t c l o s u r e s , t h e f r e q u e n c y o f w h i c h was p r o p o r t i o n a l t o t h e wind speed. The s t a r t i n g speed o f t h e anemometer i s 0.5 m and the n o m i n a l a c c u r a c y o v e r the c a l i b r a t e d range o f 0 t o 50 m s'^ i s +1.5% ( m a n u f a c t u r e r s p e c i f i c a t i o n s ) . The w i n d d i r e c t i o n s e n s o r uses a l i g h t w e i g h t , a i r - f o i l vane and a p o t e n t i o m e t e r t o produce an o u t p u t t h a t v a r i e s i n p r o p o r t i o n t o w i n d d i r e c t i o n . The vane has a 0.5 m s~^ t h r e s h o l d and a +5° n o m i n a l a c c u r a c y ( m a n u f a c t u r e r s p e c i f i c a t i o n s ) . The a t m o s p h e r i c p r e s s u r e d a t a used i n t h i s s t u d y were c o l l e c t e d a t the Vancouver I n t e r n a t i o n a l A i r p o r t C l i m a t e S t a t i o n (see F i g . 2.1). Three s u r f a c e wetness s e n s o r s were b u i l t f o l l o w i n g the g e n e r a l d e s i g n o f Weiss and Lukens (1981) ( W e i s s , p e r s . comm.). The s e n s o r s c o n s i s t o f a frame (0.1 m x 0.1 m) w i t h 30 AWG w i r e t h r e a d e d a c r o s s t h e c e n t r e w i t h m u s l i n m a t e r i a l weaved t h r o u g h the w i r e . The w i r e has a 2 V AC v o l t a g e p a s s i n g t h r o u g h i t and t h e o u t p u t v o l t a g e , w h i c h v a r i e s d e p e n d i n g on t h e wetness o f the m a t e r i a l ( a s u r r o g a t e f o r the s u r f a c e ) , i s l o g g e d on t h e CR21X. The o u t p u t does n o t g i v e a n u m e r i c a l v a l u e of degree of wetness but an i n d i c a t i o n of whether t h e s u r f a c e i s wet o r d r y . Two s e n s o r s were l o c a t e d on g r a s s and a t h i r d i n a c o n i f e r o u s hedge j u s t o u t s i d e the M a i n w a r i n g s u b s t a t i o n s i t e . V a n d a l i s m p r e v e n t e d more e x t e n s i v e use o f t h i s t y p e o f i n s t r u m e n t a t i o n . V i s u a l o b s e r v a t i o n s of the d r y i n g of d i f f e r e n t s u r f a c e t y p e s were made on numerous o c c a s i o n s t h r o u g h the measurement p e r i o d . G r a v i m e t r i c s o i l m o i s t u r e samples were t a k e n a p p r o x i m a t e l y t h r e e t i m e s a week from two s i t e s n e a r the tower. From mid May (JD 133) samples were 2 5 g a t h e r e d a t an a d d i t i o n a l t h r e e s i t e s , b o t h i r r i g a t e d and n o n - i r r i g a t e d , a round t h e tower a r e a . The average d r y w e i g h t m o i s t u r e c o n t e n t ( G a r d n e r , 1965) f o r t he p r o f i l e f r o m the s u r f a c e t o a d e p t h o f 200 mm was d e t e r m i n e d . These d a t a were u s e d w i t h d r y b u l k d e n s i t y measurements ( H i l l e l , 1971) t o d e t e r m i n e s o i l m o i s t u r e d e f i c i t (88). Water use was m o n i t o r e d by the E n g i n e e r i n g Department, C i t y o f Vancouver from May 19, 1987 (JD 139) i n the r e s i d e n t i a l a r e a o f O a k r i d g e ( F i g . 2.1). The w a t e r use f o r t h e 21 ha catchment was r e c o r d e d a t 15 min i n t e r v a l s w i t h a r e s o l u t i o n o f 2.832 m^. The volume used e x t e r n a l l y f o r i r r i g a t i o n was s e p a r a t e d f r o m t h e t o t a l based on p r e v i o u s work i n the same catchment (Grimmond, 1983). I t was assumed t h a t the same d e p t h o f w a t e r was a p p l i e d t o the i r r i g a t e d a r e a i n the Sunset suburb as was a p p l i e d i n t h e O a k r i d g e catchment. From v i s u a l s u r v e y s a t b o t h s i t e s i t was d e t e r m i n e d t h a t d i f f e r e n t p r o p o r t i o n s o f t h e r e s i d e n t i a l v e g e t a t i o n were i r r i g a t e d ( O a k r i d g e 95%; Sunset 60 % ) . The e x t e r n a l w a t e r use d a t a s e t was e x t e n d e d back t o JD 121, s e l e c t e d as the day o f the o n s e t o f i r r i g a t i o n ( based on o b s e r v a t i o n s and Grimmond, 1983), u s i n g a m u l t i p l e r e g r e s s i o n e q u a t i o n d e v e l o p e d f r o m t h e h o u r l y 1987 d a t a s e t i n c o r p o r a t i n g t i m e o f day, h o u r s s i n c e r a i n , a v a i l a b l e e n e r g y , t e m p e r a t u r e and vapour p r e s s u r e d e f i c i t . 26 PART II DEVELOPMENT AND TESTING OF SUBMODELS CHAPTER 3 SURFACE DESCRIPTION 3.1 Introduction A f u n d a m e n t a l m e t h o d o l o g i c a l problem i n u r b a n h y d r o c l i m a t o l o g i c a l r e s e a r c h i s t h e d e f i n i t i o n o f t h e l o c a t i o n , and o t h e r c h a r a c t e r i s t i c s , o f the u r b a n ' s u r f a c e ' . The a c t i v e s u r f a c e o f any system i s one o f i t s most i m p o r t a n t c l i m a t i c d e t e r m i n a n t s because i t i s the p r i m a r y s i t e o f ener g y , mass and momentum t r a n s f e r and t r a n s f o r m a t i o n . The urban-atmosphere i n t e r f a c e i s e x t r e m e l y complex t h e r e b y d e f y i n g s i m p l e d e s c r i p t i o n (Oke, 1984). Measurement and m o d e l l i n g b o t h r e q u i r e the s u r f a c e datum t o be d e f i n e d and d e s c r i b e d : t o c h a r a c t e r i s e t h e s i t e where measurements have been c o n d u c t e d ; and i f t h e o b j e c t i v e o f a s t u d y i s t o v a l i d a t e a model i t i s o b v i o u s l y i m p o r t a n t t h a t the model s u r f a c e d e s c r i p t i o n / i n p u t s and o u t p u t s a r e f o r t h e same s u r f a c e as t h a t f o r w h i c h the measurements were c o n d u c t e d . The s u r f a c e d e f i n i t i o n u t i l i z e d i s dependent upon t h e p r o c e s s ( e s ) b e i n g s t u d i e d and the s p a t i a l and t e m p o r a l s c a l e o f the s t u d y . D i f f e r e n t h y d r o -c l i m a t i c f l u x e s a r e i n f l u e n c e d by d i f f e r e n t c h a r a c t e r i s t i c s o f t h e s u r f a c e . T h e r e f o r e t h e f i r s t s t e p i n any i n v e s t i g a t i o n i s t o i d e n t i f y t he c h a r a c t e r i s -t i c s o f i m p o r t a n c e t o t h e p r o c e s s ( e s ) . F o r example, s t u d i e s o f n e t r a d i a t i o n r e q u i r e a l b e d o and e m i s s i v i t y t o d e s c r i b e t h e s u r f a c e ; t u r b u l e n c e work may need the roughness l e n g t h , d i s p l a c e m e n t l e n g t h , roughness element s e p a r a t i o n , h e i g h t o f roughness e l e m e n t s ; and s t o r a g e h e a t f l u x s t u d i e s need t h e r m a l a d m i t t a n c e , p e r c e n t a g e o f g r e e n and b u i l t space. The s c a l e o f the s t u d y d e t e r m i n e s what i s r e g a r d e d as b e i n g homogeneous and what i s h e t e r o g e n e o u s . A t any s c a l e , t e m p o r a l o r s p a t i a l , w h i c h i s r e g a r d e d as homogeneous f o r the e n t i t y under s t u d y t h e r e i s s u b - s c a l e h e t e r o g e n e i t y . T h i s s t u d y i s c o n c e r n e d w i t h d e t e r m i n a t i o n o f f l u x e s a t the l o c a l s c a l e , as d e f i n e d 27 by Oke ( 1 9 8 4 ) , i n an u r b a n a r e a ( T a b l e 3.1); i . e . s c a l e I I - 4 w i t h s u b - s c a l e s 1-1 t o 1-4. The suburban s u r f a c e i s e x t r e m e l y non-homogeneous a t t h e s u b s c a l e . F o r example, ar o u n d t h e measurement s i t e t h e r e a r e p a r k s , s m a l l a r e a s o f c o m m e r c i a l b u i l d i n g s , s c h o o l s , c h u r c h e s e t c i n a d d i t i o n t o h o u s i n g a r e a s (see F i g . 3.1). W i t h i n e a c h o f t h e s e t y p e s o f p r o p e r t i e s t h e r e a r e s u b - s c a l e h e t e r o g e n e i t i e s : c o n c r e t e , g r a s s , d e c i d u o u s and c o n i f e r o u s t r e e s e t c . Once t h e s c a l e and t h e a p p r o p r i a t e p a r a m e t e r s f o r t h e s u r f a c e d e s c r i p t i o n have been i d e n t i f i e d , t h e r e r e m a i n s the p r a c t i c a l d e c i s i o n o f where t o draw b o u n d a r i e s . Because o f s u b - s c a l e h e t e r o g e n e i t y the c h o i c e o f b o u n d a r i e s may u n k n o w i n g l y o r p u r p o s e f u l l y change the a p p a r e n t s i t e d e s c r i p t i o n . T h i s c a n be d e m o n s t r a t e d w i t h a v e r y s i m p l e example. I f c i r c l e 'a' ( F i g . 3.2) i n d i c a t e s t h e s i t e d e s c r i p t i o n b o u n d a r i e s r a t h e r t h a n c i r c l e 'b', t h e n t h e v a l u e a s s i g n e d t o the s u r f a c e parameter "number o f t r e e s " changes f r o m 0 t o 21. I f t h i s i s an i m p o r t a n t parameter ( e . g . m o d e l l i n g s u r f a c e r e s i s t a n c e f o r evapo-t r a n s p i r a t i o n ) t h e n t h e s i t e d e s c r i p t i o n o b v i o u s l y i s v e r y d i f f e r e n t d e p e n d i n g on t h e l o c a t i o n o f t h e b o u n d a r i e s . O f t e n t h e s i t e has been d e s c r i b e d i n a s t a t i c s e n s e . One d e s c r i p t i o n o f the s u r f a c e has been u s e d f o r a l l p e r i o d s o f measurements o r m o d e l l i n g , and does no t v a r y w i t h wind d i r e c t i o n o r m e t e o r o l o g i c a l c o n d i t i o n s ( e . g . s t a b i l i t y ) . T y p i c a l l y t h i s d e s c r i p t i o n i s based on a mean pa r a m e t e r f o r a c i r c l e a r o u n d the measurement s i t e . A c i r c l e has been used by a number o f r e s e a r c h e r s w o r k i n g a t the Sunset s i t e ( K a l a n d a , 1979; S t e y n , 1980; Oke e t a l . . 1981; Loudon, 1984), e l s e w h e r e i n Vancouver (Yap,1973), i n St L o u i s ( C h i n g e t a l . . 1983), and W o r c e s t e r ( Y e r s e l and Goble, 1986). A l t h o u g h some o f t h e s e r e s e a r c h e r s have d i v i d e d the c i r c l e up i n t o e q u a l s i z e s e c t o r s ( e . g . 16 -22.5° s e c t o r s ) . The c h o i c e o f r a d i u s f o r t h e c i r c l e i s o f t e n based on c a l c u l a t e d f e t c h 28 T a b l e 3.1 Framework f o r u r b a n c l i m a t e c l a s s i f i c a t i o n p r o p o s e d by Oke (1984) a) Turbulent Boundary Layers L a y e r F l o w c h a r a c t e r i s t i c s D i m e n s i o n s 3 S c a l e I . Urban canopy H i g h l y t u r b u l e n t , Same as H b M i c r o b u i l d i n g s (UCL) c o n t r o l l e d by t y p i c a l l y 10 m roughness elements Roughness sub H i g h l y t u r b u l e n t 2D - 3D b M i c r o l a y e r wakes and plumes, t y p i c a l l y 20-40 m t r a n s i t i o n zone I I . U r b a n boundary T u r b u l e n t , i n c l u d e s Depends on s u r f a c e L o c a l & l a y e r (UBL) s u r f a c e & mixed f l u x e s o f h e a t and Meso l a y e r s momentum, t y p i c a l l y day 1 km, n i g h t 0.2 km b) Urban Morphology Urban u n i t s Urban f e a t u r e s Urban c l i m a t e D i m e n s i o n s S c a l e phenomena H W L 1. B u i l d i n g 2. Canyon 3. B l o c k S i n g l e b u i l d i n g , t r e e o r g a r d e n Urban s t r e e t & b o r d e r i n g b u i l d i n g s o r t r e e s C i t y b l o c k , p a r k , f a c t o r y complex 4. Land-use R e s i d e n t i a l zones c o m m e r c i a l i n d u s t r i a l e t c . C i t y Urban a r e a Wake, plume o r 10m shadow Canyon s h e l t e r , c i r c u l a t i o n , shade, b i o c l i m a t e C l i m a t e s o f p a r k s , b u i l d i n g c l u s t e r s , cumulus m i n i - b r e e z e s L o c a l c l i m a t e s i n c l . w i n d s , c l o u d modi-f i c a t i o n Heat i s l a n d , u r b a n c i r c u l a t i o n u r b a n e f f e c t s i n g e n e r a l 10m 10m 10m 30m 300m M i c r o 0.5km 0.5km 5km 5km L o c a l 25km 25km Meso a Dimensions of boundary l a y e r s a r e d e p t h s of a f f e c t e d atmosphere; d i m e n s i o n s o f m o r p h o l o g i c a l u n i t s a r e t h o s e of u r b a n s t r u c t u r e s o r p l a n a r e a , b H - b u i l d i n g h e i g h t , D - b u i l d i n g s p a c i n g 30 Figure 3.2 Schematic of the influence of the location of the boundaries for surface description. See text for further explanation. r e q u i r e m e n t s . F o r example, S t e y n (1980) c a l c u l a t e d t h e f e t c h r e q u i r e m e n t s f o r the Sunset s i t e t o be 1485 m u s i n g the r e l a t i o n p r e s e n t e d by Munro and Oke (19 7 5 ) . The 2 km r a d i u s u s e d p r o v i d e s an e x t r a 500 m t o ensure adequate f e t c h . Yap (1973) w o r k i n g e l s e w h e r e i n Vancouver, a l s o c a l c u l a t e d t h e r e q u i r e d f e t c h t o be a p p r o x i m a t e l y 1.5 km, and chose a c i r c l e o f 2 km r a d i u s . There does n o t appear t o be an o b j e c t i v e means t o d e c i d e on the s i z e o f t h e r a d i u s . The c i r c l e a p p r o a c h assumes e i t h e r t h a t t h e s u r f a c e i s s p a t i a l l y homogeneous and/or, t h a t o v e r time the v a r i a t i o n o f w i n d d i r e c t i o n w i l l c r e a t e s p a t i a l a v e r a g i n g . I n r e a l i t y t h e r e a r e p r e f e r r e d w i n d d i r e c t i o n s . T h i s can be seen f r o m t h e w i n d f r e q u e n c y r o s e f o r t h e measurement p e r i o d JD 22-179, 1987 ( F i g . 3.3). The s u r f a c e c o n t r i b u t i n g t o a t u r b u l e n t f l u x a t a p o i n t i s c o n s t a n t l y c h a n g i n g . T h i s s u g g e s t s t h a t a dynamic a p p r o a c h may be more a p p r o p r i a t e ( i . e . where t h e s u r f a c e c h a r a c t e r i s t i c s and c h a n g i n g m e t e o r o l o g i c a l c o n d i t i o n s , i n c l u d i n g wind d i r e c t i o n , a r e t a k e n i n t o a c c o u n t ) . T h i s c h a p t e r i s c o n c e r n e d w i t h methods t o d e s c r i b e t h e s u r f a c e w h i c h a r e dynamic and the development o f a d a t a b a s e o f s u r f a c e c h a r a c t e r i s t i c s f o r use w i t h t h e s e methods. The methods and d a t a b a s e o u t l i n e d i n t h i s c h a p t e r a r e used s u b s e q u e n t l y t o c a l c u l a t e a n t h r o p o g e n i c and s t o r a g e h e a t f l u x so as t o a r r i v e a t a s p a t i a l l y - c o n s i s t e n t e nergy b a l a n c e when c o m b i n i n g measured and c a l c u l a t e d t erms. They a r e a l s o used t o model l a t e n t h e a t f l u x d e n s i t i e s w h i c h a r e c o n s i s t e n t w i t h measured v a l u e s . 3.2 Boundary Selection for Surface Description As s t a t e d i n C h a p t e r 1, the o b j e c t i v e o f t h i s r e s e a r c h i s t o d e v e l o p and t e s t an e v a p o t r a n s p i r a t i o n model a t the l o c a l s c a l e . To t e s t t h e model i t i s n e c e s s a r y t o have l a t e n t h e a t f l u x (Qg) measurements. These were d e t e r m i n e d w i t h i n an energy b a l a n c e framework, i n w h i c h i t i s n e c e s s a r y t o have v a l u e s o f 32 Figure 3.3 Wind d i r e c t i o n frequency (%) f o r the Sunset s i t e (JD 21-179, 1987) Wind Direction Frequency (%) JD 21 - 179, 1987 n=3779 hours t h e a n t h r o p o g e n i c h e a t f l u x ( Q F ) and s t o r a g e h e a t f l u x (AQg). To model t h e s e f l u x e s (Qg, Qp, AQg) i t i s n e c e s s a r y t o i n p u t c e r t a i n s u r f a c e c h a r a c t e r i s t i c s (see C h a p t e r s 7 , 4 , a n d 5 r e s p e c t i v e l y f o r d e t a i l s ) . T h e r e f o r e t h e r e needs t o be a b a s i s f o r l o c a t i n g t h e b o u n d a r i e s f o r t h e a r e a s used t o d e t e r m i n e s u r f a c e p a r a m e t e r s . I n t h i s s e c t i o n i t i s i n t e n d e d t o c o n s i d e r what shapes ( a r e a s ) s h o u l d be use d t o d e s c r i b e t h e s i t e f o r m o d e l l i n g p u r p o s e s so t h a t i t w i l l be c o n s i s t e n t w i t h the s o u r c e a r e a s o f the measurements, and t h e r e f o r e a s p a t i a l l y c o n s i s t e n t e n e r g y b a l a n c e computed. I n t h i s s t u d y , n e t r a d i a t i o n ( Q * ) , s e n s i b l e h e a t f l u x ( Q H ) . and t h e Bowen r a t i o ( B = Q H / Q E ) were measured d i r e c t l y ( s e e C h a p t e r 2 ) . I n o r d e r t o c o n s i d e r t h e a r e a s t h a t c o n t r i b u t e t o t h e i r measurement, a t a p o i n t on the tower, t h e s e c a n be d i v i d e d i n t o measurements o f r a d i a n t (Q*) and t u r b u l e n t (Qpj and Qg) energy f l u x d e n s i t i e s . 3.2.1 Radiant Fluxes A l b e d o , e m i s s i v i t y and s u r f a c e t e m p e r a t u r e a r e the s u r f a c e p a r a m e t e r s n o r m a l l y u s e d t o d e s c r i b e a s i t e when c o n s i d e r i n g r a d i a n t f l u x e s . A l b e d o i n f l u e n c e s t h e n e t short-wave r a d i a t i o n ; and e m i s s i v i t y and s u r f a c e t e m p e r a t u r e i n f l u e n c e t h e n e t long-wave r a d i a t i o n . Oke ( 1 9 8 7 ) r e v i e w e d t h e " a v a i l a b l e e v i d e n c e r e g a r d i n g s p a t i a l l y r e p r e s e n t a t i v e v a l u e s o f the s u r f a c e a l b e d o o f c i t i e s " . He n o t e d " r e m a r k a b l e convergence o f o p i n i o n , c o n s i d e r i n g t h e g e o g r a p h i c a l d i v e r s i t y o f the c i t i e s r e p r e s e n t e d " and s u g g e s t e d a v a l u e o f 0 . 1 4 f o r u r b a n c e n t r e s and 0 . 1 5 f o r s u b u r b s . I t i s n o t p o s s i b l e t o measure an a r e a l average f o r e m i s s i v i t y . A r n f i e l d ( 1 9 8 2 ) t a b u l a t e d e m i s s i v i t i e s f o r a range o f s u r f a c e s t o use w i t h h i s g e o m e t r i c u r b a n r a d i a t i o n model. The v a l u e s he c a l c u l a t e d f o r e i g h t u r b a n l a n d use zones i n Columbus, Ohio show a r e l a t i v e l y s m a l l range f r o m 0 . 9 3 7 t o 0 . 9 6 1 i n snow-free c o n d i t i o n s . Schmid 3 4 (1988) c o n d u c t e d a s t u d y on t h e s p a t i a l v a r i a n c e o f r e m o t e l y - s e n s e d s u r f a c e t e m p e r a t u r e f o r an a r e a a r o u n d the Sunset tower. He showed t h a t t h e s p a t i a l d i s t r i b u t i o n o f s u r f a c e t e m p e r a t u r e has a dominant component o f a h i g h l y r e g u l a r p a t t e r n and a minor component o f b r e a k s i n t h i s r e g u l a r i t y c a u s e d by p a r k s , s c h o o l grounds e t c . He c o n c l u d e d , based on s t r o n g c o n s i s t e n c y o f s p e c t r a l v a r i a n c e d i s t r i b u t i o n s between d i f f e r e n t a r e a s and domain s i z e s t h a t t h e r e i s an o v e r a l l homogeneity t o the s p a t i a l s u r f a c e t e m p e r a t u r e d i s t r i b u t i o n . Q*, when measured w i t h a n e t p y r r a d i o m e t e r , i s bas e d upon a c i r c u l a r v i e w from the tower. The r a d i u s o f t h e "seen a r e a " w i t h a v i e w f a c t o r o f 0.95, c a l c u l a t e d u s i n g R e i f s n y d e r ( 1 9 6 7 ) , i s 108 m when the n e t p y r r a d i o m e t e r i s mounted a t a h e i g h t o f 24 m. T h i s i s c o n s i d e r a b l y s m a l l e r t h a n t h e 2 km r a d i u s c i r c l e u s e d f o r s u r f a c e d e s c r i p t i o n i n p r e v i o u s s t u d i e s . However, Grimmond (1983) and C l e u g h (1988) have d e m o n s t r a t e d t h a t w i t h i n a 5 km r a d i u s c i r c l e o f the Sunset tower t h e r e i s v e r y l i t t l e v a r i a b i l i t y o f Q* under c l e a r c o n d i t i o n s . The measured v a r i a b i l i t y o f 0.5-4.5% i s o f the same o r d e r as t y p i c a l measurement e r r o r s ( L a t i m e r , 1972). Under c l o u d y c o n d i t i o n s t h e r e i s a s l i g h t l y g r e a t e r v a r i a b i l i t y ( 6 %) between s i t e s (Grimmond, 1983). I t i s g r e a t e s t under p a r t l y c l o u d y c o n d i t i o n s when i t i s p o s s i b l e f o r c l o u d t o a f f e c t one s i t e but n o t a n o t h e r . I t i s c o n c l u d e d t h a t n e t r a d i a t i o n i s c o n s e r v a t i v e w i t h r e s p e c t t o v a r i a b i l i t y o f s u r f a c e t y p e s w i t h i n u r b a n l a n d u s e s , and t h e r e f o r e an a r e a l a r g e r t h a n the v i e w o f the n e t p y r r a d i o m e t e r i s a l l o w a b l e f o r s u r f a c e d e s c r i p t i o n . The a r e a p r o b a b l y s h o u l d n o t be s m a l l e r o t h e r w i s e i t may n o t sample a s u f f i c i e n t l y r e p r e s e n t a t i v e range o f s u r f a c e t y p e s . 3 5 3.2.2 Turbulent fluxes The a r e a i n f l u e n c i n g t h e measurement o f t u r b u l e n t f l u x e s a t a p o i n t i s upwind i n t h e p r e v a i l i n g w i n d d i r e c t i o n . The c o l l e c t i o n o f s u r f a c e e l e m e n t s w h i c h i n f l u e n c e t h e a i r p a r c e l s t h a t a r e sampled as t h e y pass the s e n s o r i s termed t h e 'source a r e a ' . The upwind, downwind and l a t e r a l b o u n d a r i e s o f t h e so u r c e a r e a a r e dependent on t h e c h a r a c t e r i s t i c s o f t h e f l o w and on t h e boundary l a y e r development i n the a t m o s p h e r i c l a y e r between t h e s u r f a c e and the s e n s o r l e v e l (Schmid, 1988). P a s q u i l l (1972) d e v e l o p e d a model t o d e t e r m i n e t h e d i m e n s i o n s o f t h e s o u r c e a r e a s d o r a i n a n t l y a f f e c t i n g p o i n t measurements. The d i m e n s i o n s o f the e l l i p t i c a l l y - s h a p e d s o u r c e a r e a s ( F i g . 3.4a) a r e a f a i r l y s e n s i t i v e f u n c t i o n o f s e n s o r h e i g h t , and a r e f u r t h e r a f f e c t e d by s t a b i l i t y and r o u g h n e s s , i n t h a t o r d e r o f i m p o r t a n c e . P a s q u i l l d e m o n s t r a t e d t h a t a l l o f t h e d i m e n s i o n s o f the so u r c e a r e a i n c r e a s e as t h e s t a b i l i t y changes f r o m u n s t a b l e t o n e u t r a l t o s t a b l e c o n d i t i o n s . The model a l l o w s f o r the p a t c h i n e s s o f the s u r f a c e a t a v a r i e t y o f s c a l e s w h i c h a f f e c t t he boundary l a y e r s t r u c t u r e . The s u r f a c e i s r e g a r d e d as an a r r a y o f e l e m e n t a r y ' s o u r c e s ' from w h i c h a p r o p e r t y i s e m i t t e d , o r ' s i n k s ' i n t h e case o f momentum. The s c a l a r ( h e a t , water vapour e t c . ) p r o d u c e d by any g i v e n s o u r c e , and sampled a t a g i v e n h e i g h t , r i s e s t o a maximum a t a d i s t a n c e downwind and t h e n d e c l i n e s c o n t i n u o u s l y a t g r e a t e r d i s t a n c e s . P a s q u i l l u s e d Smith's (1957) r e c i p r o c a l theorem, w h i c h s t a t e s t h a t t h e c o n c e n t r a t i o n a t ground l e v e l downwind o f a p o i n t - o r l i n e - s o u r c e a t s e n s o r h e i g h t zg i s i d e n t i c a l t o the c o n c e n t r a t i o n a t the x and y but a t t h e h e i g h t z g , due t o an e x a c t l y s i m i l a r s o u r c e a t t h e ground. T h i s can be v i s u a l i s e d u s i n g F i g u r e 3.4b. I n s t e a d o f c a l c u l a t i n g t he d i s p e r s i o n from a p o i n t ( e . g . a smoke s t a c k ) t o an a r e a , t h e ' r e c i p r o c a l ' i s c a l c u l a t e d , i . e . the a r e a i n f l u e n c i n g t h a t 36 F i g u r e 3.4 D i m e n s i o n s o f t h e s o u r c e a r e a f o r t u r b u l e n t f l u x m e a s u r e m e n t s : ( a ) p l a n v i e w ( b ) s i d e v i e w ( a ) M e a s u r e m e n t / ' p o i n t / a ' W i n d D i r e c t i o n ( b ) a - d i s t a n c e t o u p w i n d e d g e o f s o u r c e a r e a b + c - l e n g t h o f s o u r c e a r e a d - h a l f t h e w i d t h o f s o u r c e a r e a \ a \ b + c T o w e r W i n d D i r e c t i o n p o i n t . The f u n c t i o n a l f o r m o f t h e s o u r c e a r e a s i s p r e c i s e l y t h a t c o n t a i n e d i n the t h e o r e t i c a l g r o u n d - l e v e l d i s t r i b u t i o n f r o m an e l e v a t e d s o u r c e i f the r e c i p r o c a l r e l a t i o n between the d i s t r i b u t i o n s from ground and e l e v a t e d s o u r c e s i s a d o p t ed. P a s q u i l l u s e d a G a u s s i a n form o f v e r t i c a l d i s t r i b u t i o n and assumed complete r e f l e c t i o n o f the plume. From the r e c i p r o c a l r e l a t i o n t h e c o n t o u r d e f i n i n g t h e s o u r c e o r s i n k a r e a w i l l be i d e n t i c a l w i t h t h e i s o p l e t h f o r a g i v e n c o n c e n t r a t i o n . He chose the a r e a bounded by t h e X m a x / 2 i . e . the a r e a i n w h i c h the c o n c e n t r a t i o n from an e l e m e n t a r y u n i t p o i n t s o u r c e i s g r e a t e r t h a n one h a l f o f the maximum c o n c e n t r a t i o n from s u c h a s o u r c e , as sens e d a t t h e same h e i g h t . Schmid (1988) has u p d a t e d P a s q u i l l ' s a p p r o a c h i n v i e w o f some r e c e n t developments i n d i f f u s i o n t h e o r y . The model was d e v e l o p e d t o i d e n t i f y t he so u r c e a r e a o f measured t u r b u l e n t f l u x e s and t h e i r r e p r e s e n t a t i v e n e s s . Schmid uses h i s model i n u r b a n and non-urban a r e a s t o i d e n t i f y t he s o u r c e a r e a s o f t u r b u l e n t s e n s i b l e h e a t f l u x measurements and t o a s s e s s the r e p r e s e n t a t i v e n e s s of o b s e r v a t i o n s i t e s . A s h o r t range plume model forms the c o r e o f the Schmid s o u r c e a r e a model. Schmid f o l l o w s W e i l ' s (1985) a p p l i e d d i f f u s i o n m o d e l l i n g recommendations and u t i l i z e s t h e p r o b a b i l i t y d e n s i t y f u n c t i o n ( p . d . f . ) plume d i s p e r s i o n model d e v e l o p e d by G r y n i n g e t a l . ( 1 9 8 7 ) . Whereas P a s q u i l l assumed G a u s s i a n d i f f u s i o n f o r b o t h t h e h o r i z o n t a l and v e r t i c a l d i s t r i b u t i o n s . Schmid i n c o r p o r a t e s W e i l ' s (1985) c o n c l u s i o n t h a t w h i l e plume d i f f u s i o n i s G a u s s i a n i n t h e h o r i z o n t a l , i t i s n o t so i n the v e r t i c a l . The i m p l i c a t i o n i s t h a t , w i t h skewed v e r t i c a l d i f f u s i o n , the symmetry a s s u m p t i o n i n S m i t h (1957) i s i n v a l i d and t h e c o n c e p t o f r e c i p r o c i t y s h o u l d be m o d i f i e d o r r e p l a c e d . Schmid u s e d a s l i g h t l y d i f f e r e n t c o n c e p t o f r e c i p r o c i t y w h i c h i s n o t c o n s t r a i n e d by any 38 p a r t i c u l a r form o f v e r t i c a l o r h o r i z o n t a l d i f f u s i o n . The t o t a l e f f e c t ex-p e r i e n c e d by t h e s e n s o r i s d e t e r m i n e d by t h e w e i g h t e d c o n t r i b u t i o n s o f a l l s o u r c e s upwind, and t h e r e s u l t i n g t w o - d i m e n s i o n a l s o u r c e w e i g h t d i s t r i b u t i o n f u n c t i o n has i t s maximum a t t h e maximum s o u r c e l o c a t i o n . The g e o m e t r i c l o c a t i o n o f a l l p o i n t s o u r c e s , whose e f f e c t l e v e l a t t h e s e n s o r l o c a t i o n e q u a l s an a r b i t r a r y c r i t e r i o n 'P', w h i c h d e f i n e s a s e n s e d c o n c e n t r a t i o n o r e f f e c t l e v e l ( X p ) , forms a c l o s e d c u r v e , w h i c h i s the boundary o f t h e P-source a r e a . Schmid uses t h e f r a c t i o n o f the t o t a l e f f e c t w h i c h i s c o n t r i b u t e d by the P-source a r e a as the c r i t e r i o n f o r The P-source a r e a i s d e f i n e d i n a s i m i l a r f a s h i o n t o t h e F - p e r c e n t a g e e f f e c t i v e f e t c h by Gash ( 1 9 8 6 ) . The model i d e n t i f i e s n i n e w e i g h t e d s o u r c e a r e a l e v e l s . Schmid's model was d e v e l o p e d f o r u n s t a b l e c o n d i t i o n s . I n t h e c u r r e n t work i t was e x t e n d e d , u s i n g G r y n i n g e t a l . ( 1 9 8 7 ) , t o i n c o r p o r a t e s t a b l e c o n d i t i o n s . F o r u n s t a b l e c o n d i t i o n s , t h e s t a b i l i t y f u n c t i o n s u s e d i n t h e model were changed i n t h i s s t u d y from t h o s e o f Dyer and B r a d l e y (1982) t o t h o s e o f Dyer (1974) based on t h e c o m p a r i s o n w i t h measured u * and z/L (see App e n d i x I V ) . F o r s t a b l e c o n d i t i o n s the r e l a t i o n s o f Dyer (1974) and van U l d e n and H o l t s l a g (1985) were u s e d (see App e n d i x I V ) . The i n p u t s n e c e s s a r y t o d e t e r m i n e the w e i g h t e d s o u r c e a r e a s f r o m t h e model a r e : t h e s i t e c o n d i t i o n s ( roughness ( Z Q ) and z e r o - p l a n e d i s p l a c e m e n t ( d ) ) ; and m e t e o r o l o g i c a l s c a l i n g p a r a m e t e r s (Monin-Obukhov s t a b i l i t y l e n g t h ( L ) , f r i c t i o n v e l o c i t y ( u * ) , and e i t h e r t h e s t a n d a r d d e v i a t i o n o f w i n d d i r e c t i o n (c7(p) and mean wi n d speed ( u ) , or the mixed l a y e r d e p t h ( z ^ ) ) . The o u t p u t o f the model c o n s i s t s o f n i n e s o u r c e a r e a e l l i p s e s f o r each hour ( F i g . 3.5). The a r e a between each e l l i p s e has e q u a l w e i g h t ; i . e . the a r e a l a b e l l e d 'a' c o n t r i b u t e s the same amount t o the measured f l u x as t h a t l a b e l l e d 'b'. I t i s p r o p o s e d h e r e t h a t the w e i g h t e d s o u r c e a r e a s , i d e n t i f i e d v i a t h e Schmid model, a r e t h e most a p p r o p r i a t e means f o r a s s i g n i n g b o u n d a r i e s t o 39 F i g u r e 3.5 Source a r e a f o r one hour w i t h t h e n i n e w e i g h t e d bands. The a r e a l a b e l l e d 'a' c o n t r i b u t e s t h e same amount t o the measured f l u x as t h a t l a b e l l e d 'b'. I n n e r c i r c l e 2 km r a d i u s , o u t e r 5 km. JD 22, 1987: 900 LAT Wind d i r e c t i o n - 303 N d e t e r m i n e v a l u e s o f s u r f a c e p a r a m e t e r s , f o r m o d e l l i n g e n e r g y b a l a n c e f l u x e s , t o o b t a i n a c o n s i s t e n t e nergy b a l a n c e w i t h t h e measured terms. Use o f t h e Schmid s o u r c e a r e a model l e a d s t o a dynamic assessment o f s u r f a c e p a r a m e t e r s because, u n l i k e the f i x e d c i r c l e o f i n f l u e n c e a p p r o a c h , t h e l o c a t i o n o f t h e b o u n d a r i e s change w i t h m e t e r o l o g i c a l c o n d i t i o n s . F i g u r e 3.6 shows th e l o c a t i o n and shape o f t h e s o u r c e a r e a f o r f o u r d i f f e r e n t h o u r s d u r i n g a 24 h p e r i o d . The f i r s t t h r e e ( F i g . 3.6a,b,c) a r e c o n s e c u t i v e h o u r s w h i c h have i n c r e a s i n g c o n v e c t i v e a c t i v i t y , and the f o u r t h ( F i g . 3.6d) i s under s t a b l e c o n d i t i o n s . I t can be seen t h a t the s o u r c e a r e a s i z e d e c r e a s e s as c o n d i t i o n s become more u n s t a b l e . T a b l e 3.2 g i v e s t h e mean, s t a n d a r d d e v i a t i o n , minimum, and maximum o f t h e plume d i m e n s i o n s by s t a b i l i t y c l a s s f o r a l l h o u r s u s e d i n t h i s s t u d y . C a l c u l a t i o n o f t h e h o u r l y s o u r c e a r e a s r e q u i r e s h o u r l y v a l u e s o f L and u*, w h i c h i n t u r n r e q u i r e measured v a l u e s o f t h e s e n s i b l e h e a t f l u x d e n s i t y (see A p p e n d i x I V ) . T h i s i s n o t a l w a y s a v a i l a b l e so a v e r y s i m p l e scheme, termed h e r e ' s e c t o r s ' , i s a l s o p r o p o s e d f o r c o m p a r i s o n . T h i s scheme t a k e s i n t o a c c o u n t s e v e r a l f e a t u r e s : the s o u r c e a r e a i s a l i g n e d a l o n g t h e mean w i n d d i r e c t i o n (<p) , the l a t e r a l d i s p e r s i o n i s i n f l u e n c e d by a^, and a r e a s c l o s e r t o the measurement p o i n t c o n t r i b u t e more t h a n a r e a s f u r t h e r away. The ' s e c t o r s ' a r e a l i g n e d a l o n g <p and have a w i d t h o f 2(7^, ( F i g . 3.7). The l e n g t h of t h e ' s e c t o r s ' and the l o c a t i o n of the w e i g h t e d b o u n d a r i e s were d e t e r m i n e d f r o m the mean d i m e n s i o n s f o r s t a b l e and u n s t a b l e 'plumes' f o r t h e h o u r s when QIJ- d a t a were a v a i l a b l e ( T a b l e 3.2a,b). F o r the u n s t a b l e case the mean b+c d i m e n s i o n s were used f o r t h e s e c t o r s ( T a b l e 3.2a). F o r the s t a b l e case the T a b l e 3.2b v a l u e s were i n c r e a s e d so t h a t c o n c e n t r a t i o n l e v e l 9 was e q u a l t o 5000 m and the o t h e r l e v e l s were i n c r e a s e d by the same p e r c e n t a g e (101.9%) ( T a b l e 3.2c). The r e a s o n i s t h a t t h e Schmid model c u t s o f f a t 5000 m and t h e r e f o r e b i a s e s 4 1 Figure 3.6 Examples of different source area with changing meteorological conditions. Inner cir c l e 2 km radius, outer 5 km. JD 22, 1987: 900 LAT Wind direction - 303 L - -1433 u* - 0.19 JD 22, 1987: 1000 LAT Wind direction - 246 L - -44 u* - 0.17 4 2 T a b l e 3.2 Mean l e n g t h o f plumes ( c a l c u l a t e d f r o m t h e m o d i f i e d Schmid (1988) model) f o r use w i t h t h e s e c t o r s . C a l c u l a t e d f r o m 1476 u n s t a b l e h o u r s and 241 s t a b l e h o u r s . A l l d i m e n s i o n s a r e i n me t r e s . F i g u r e 3.3 shows t h e p o s i t i o n o f the a, b+c and d d i m e n s i o n s . Cone. a b+c d L e v e l Mean s.d. Max M i n Mean s.d. Max M i n Mean s.d. Max M i n (a) U n s t a b l e 1 42. .4 14. .0 60. ,8 6. .5 113. .2 47. .5 200. ,0 14. .0 32, .4 14, .2 188, .3 4. .0 2 35, .8 11. .7 50. .8 5 .6 178 .5 75, .8 320. .2 21, .8 47 .9 21 .2 282, .0 5 .8 3 31. ,8 10. .3 44. ,9 5. .1 247. .8 106. ,5 451. ,7 29. .7 62. .7 28, .1 370. .3 7, .5 4 28, .9 9, .3 40. .7 4. .7 330, .2 142. .6 607, .2 39, .0 79, .0 35, .7 470. .3 9, .3 5 26, .7 8. .5 37. .6 4. .4 427, .6 183. .5 784. .6 50. .1 97. .0 44, .0 579. .7 11, .3 6 25, .0 8, .0 35. .2 4. .1 538, .7 229, .2 985. ,4 62, .5 116. .3 52, .9 696. .9 13 .5 7 23. .5 7. .4 33. ,1 3. ,9 681, .8 288. .7 1251, ,1 76. .6 139. .8 63, .9 840. .6 16, .4 8 22, .0 6. .9 30, ,8 3, .7 909, .0 382, .7 1676. .6 95, .0 175. .0 80, .3 1053. .1 20, .6 9 20. .1 6. ,2 28. ,0 3. ,6 1405, .0 591. ,8 2610. ,0 118, .9 247, .5 112, .9 1481. .3 29, .8 W I S t a b l e 1 87, .4 1, ,7 91. ,0 83. .8 319. .7 16, ,4 350, ,9 286. .0 39. ,6 21. .4 197. ,7 11. .1 2 72 .3 1. .3 75. .1 69. .6 512, .1 27. .8 565. .1 454, .9 60, .6 32, .8 302. .3 17, .0 3 63. .4 1. .1 65. ,7 61. .1 723, .9 41. .4 802, ,8 638, .9 82, .3 44, ,5 407. .8 22. .9 4 57, .1 1. .0 59. ,2 55, .0 972, .5 56. .9 1080, ,8 858. .2 106. .2 57. .5 526. ,6 29. .8 5 52. .6 0. .9 54. ,6 50, ,5 1252. .2 73. ,7 1392, ,2 1106. .0 131, ,9 71. ,3 653. .1 36. .8 6. 49. .1 0. .9 51, .0 47, .2 1569. .1 93. .6 1746. ,6 1381. .6 159, .8 86, .3 790. .6 44, .7 7 45. .9 0. ,8 47. 6 44. ,1 1999. .4 124. ,5 2234. .8 1747. ,4 196, ,0 106. .1 971. ,9 54. .9 8 42. .5 0. .8 44. .1 40, .9 2702. .3 179. .6 3041, ,0 2335. .4 252. .5 136. .6 1246. ,9 70, .1 9 38, .2 0. .7 39. ,6 36. .8 4301, ,9 322. .4 4906. ,6 3636. .1 371, ,5 201. .0 1818. .8 102, .7 ( c ) S t a b l e / N e u t r a l - v a l u e s u s e d f o r ' s e c t o r s ' l e n g t h . 1 372 2 595 3 841 4 1130 5 1455 6 1824 7 2324 8 3141 9 5000 43 Figure 3.7 Examples of 'sectors'. Inner c i r c l e 2 km radius, outer 5 km. (a) JD 22, 1987: 1000 LAT Unstable Wind direction - 246 s.d. - 36 « (b) JD 21, 1987: 600 LAT Stable Wind direction - 298 4 4 the mean to le s s than 5000 m. From P a s q u i l l (1972) i t seems appropriate to increase them and put a l l non-unstable hours into one set. 3.3 Surface Database To c a l c u l a t e the surface parameter values i t was necessary to create a computerised database and accessing system which would allow a parameter to be assessed i n response to d i f f e r e n t source area shapes as conditions and scenarios changed. The requirements of the database were that the i n d i v i d u a l g r i d squares of information would allow the influence of small d i f f e r e n c e s i n l o c a t i o n of the area boundaries to be i d e n t i f i e d , but not so small that the e f f o r t required to gather the necessary information was u n r e a l i s t i c . These requirements were deemed met using 100 ra x 100 m squares, and data were c o l l e c t e d f o r a 5 km radius c i r c l e centred on the tower ( i . e . approximately 8000 squares). The choice of a 5 km c i r c l e was based on the areal l i m i t s permitted by the Schmid (1988) model. Each square was assigned an X and Y co-ordinate between -50 and +50 (no zero). As an example, Figure 3.8, i s a map of the g r i d squares which contain a major road. The Greater Vancouver Regional D i s t r i c t (GVRD) 1:2500 land use maps, which have the land use f o r i n d i v i d u a l properties, for M u n i c i p a l i t i e s of Burnaby (1980) and Richmond (1980) and the City of Vancouver (1983) were used as the i n i t i a l data source. For each g r i d square the data l i s t e d i n Table 3.3 were obtained. Additional information was gathered from S t a t i s t i c s Canada (1987) for the 1986 census, a e r i a l photographs (Vancouver C i t y Planning Dept., 1985, scale 1:2500), and v i s u a l inspection. The areal extent of surface types within a property were determined from Ci t y of Vancouver By-Laws (1987); f a c i l i t i e s within each park from Vancouver Board of Parks and Recreation (1986) and 4 5 Figure 3.8 Map of grid squares which contain major roads in the area covered by the database. Each point is a 100 x 100 m square. The grid extends from -50 to -1 and 1 to 50 along the longest axes (N - S and E - W). Inner c i r c l e 2 km radius, outer 5 km 4 6 T a b l e 3.3 I n f o r m a t i o n c o n t a i n e d w i t h i n t he s u r f a c e d a t a b a s e f o r each g r i d s quare I n f o r m a t i o n Source 1 X c o - o r d i n a t e 2 Y c o - o r d i n a t e S i n g l e f a m i l y d w e l l i n g s 3 Number 4 A r e a Apartments 5 Number o f l o t s 6 Number o f u n i t s 7 A r e a Apartments above c o m m e r c i a l 8 Number o f l o t s 9 Number o f u n i t s 10 A r e a Commercial 11 Number 12 A r e a I n d u s t r i a l 13 Number 14 A r e a " I n s t i t u t i o n a l " 5 15 Number 16 A r e a 17 Code P a r k s b 18 A r e a 19 Code R o a d s 0 20 Back a l l e y l e n g t h 21 M i n o r l e n g t h 22 Major l e n g t h P o p u l a t i o n 23 P o p u l a t i o n / d w e l l i n g 24 P o p u l a t i o n GVRD l a n d u s e maps GVRD l a n d u s e maps GVRD l a n d u s e maps GVRD l a n d u s e maps GVRD l a n d u s e maps GVRD l a n d u s e maps GVRD l a n d u s e maps GVRD l a n d u s e maps GVRD l a n d u s e maps GVRD l a n d u s e maps GVRD l a n d u s e maps GVRD l a n d u s e maps GVRD l a n d u s e maps GVRD l a n d u s e maps GVRD l a n d u s e maps GVRD l a n d u s e maps GVRD l a n d u s e maps GVRD l a n d u s e maps GVRD l a n d u s e maps GVRD l a n d u s e maps S t a t Canada 1986 Census by census t r a c t From d a t a b a s e a " I n s t i t u t i o n a l " - f o r example s c h o o l s , c h u r c h , h o s p i t a l r a i l w a y y a r d s - t h r e e " b l o c k s " o f space were a s s i g n e d t o t h i s - Code r e f e r s t o t h e typ e o f i n s t i t u t i o n b P a r k s - Code r e f e r s t o i n d i v i d u a l p a r k c Roads - w i d t h s a s s i g n e d based on GVRD l a n d use maps and v i s u a l i n s p e c t i o n 4 7 H i c k o k ( 1 9 7 7 ) ; d a t a f o r s c h o o l s from Vancouver S c h o o l B o a r d ( 1 9 8 2 ) ; and a e r i a l p h o t o g r a p h s (Vancouver C i t y P l a n n i n g Department, 1985). F u r t h e r i n f o r m a t i o n was c a l c u l a t e d and added f o r t h e m o d e l l i n g o f i n d i v i d u a l f l u x e s ; i . e . sub-d a t a b a s e s were g e n e r a t e d f o r the c a l c u l a t i o n o f s p e c i f i c f l u x e s ( s ee subsequent c h a p t e r s ) . The d a t a b a s e was compared w i t h a p r e v i o u s d e t a i l e d s u r f a c e d e s c r i p t i o n c o n d u c t e d by Grimmond (1983) f o r the Hudson Catchment; a 21 ha a r e a ap-p r o x i m a t e l y 4.5 km west o f the Sunset Tower. The s u r f a c e c h a r a c t e r i s t i c s were f o u n d t o a g r e e v e r y c l o s e l y . The p o p u l a t i o n c a l c u l a t e d f r o m t h e d a t a b a s e a l s o c o r r e s p o n d e d v e r y c l o s e l y t o t h a t f o r i n d i v i d u a l c e n s u s t r a c t s . A second more d e t a i l e d s u r f a c e s u r v e y was c o n d u c t e d o f 10 b l o c k s n e a r the tower. F o r each 1 m x 1 m square the s u r f a c e t y p e and h e i g h t were d e t e r m i n e d . The i n f o r m a t i o n i n c l u d e d : v e g e t a t i o n t y p e ; v e g e t a t i o n t y p e b e n e a t h ; shape o f v e g e t a t i o n ; b u i l d i n g t y p e ; r o o f t y p e ; and paved s u r f a c e m a t e r i a l s . The i n f o r m a t i o n was g a t h e r e d f r o m v i s u a l s u r v e y s and a e r i a l p h o t o g r a p h s (Vancouver C i t y P l a n n i n g Dept., 1985, s c a l e 1:2500). To c o n d u c t t h e c o m p a r i s o n between d i f f e r e n t boundary l o c a t i o n s c e n a r i o s d i f f e r e n t g e o m e t r i c shapes ( c i r c l e s , q u a d r a n t s , e l l i p s e s and s e c t o r s ) had t o be a c c e s s e d f r o m t h e d a t a b a s e . Appendix V o u t l i n e s t h e p r o c e d u r e s used t o d e t e r m i n e w h i c h c o - o r d i n a t e s s h o u l d be a c c e s s e d f o r t h e d i f f e r e n t g e o m e t r i e s . Once t h e g r i d c o - o r d i n a t e s a r e i d e n t i f i e d t h e r e q u i r e d i n f o r m a t i o n from the d a t a b a s e c a n be a c c e s s e d and the v a l u e o f the s u r f a c e p a r a m e t e r c a l c u l a t e d . W i t h the use o f t h e d a t a b a s e i t i s p o s s i b l e t o produce maps o f s u r f a c e t y p e s c o n t a i n e d w i t h i n e a c h g r i d s q u a r e . F i g u r e 3.9a-h shows t h e p l a n a r e a o f p a r t i c u l a r s u r f a c e t y p e s i n 1000 m 2 c l a s s e s w i t h i n e ach g r i d s q u are (a square c o n t a i n s 10000 ra2). I f a p a r t i c u l a r s u r f a c e t y p e does n o t o c c u r i n a square t h e n i t w i l l appear b l a n k ( e . g . much of F i g . 3.9d). I n o r d e r t o i l l u s t r a t e the F i g u r e 3.9 Maps o f s u r f a c e t y p e : 4 8 • < WOO m2 , < 2000 1 < 3 0 0 0 Y < 4 0 0 0 + < 5 0 0 0 X < 6 0 0 0 7 < 7000 < 8000 = < 9000 • < OOOO * 10000 ( a ) B u i l d i n g s (b) Pavement ( c ) G r a v e l (d) Water 49 Figure 3.9 Maps of surface types (cont.): (e) Grass j I (f) Coniferous trees N • < WOO m2 , < 2000 I < 3000 Y < 4000 + < 5000 X < 6000 X < 7000 a < 8000 - < 9000 • < XJOOO X 10000 l l i l i i i l i i l i i l i i i l M _ .;:::::::::::::::::::::::::::::::::::::: :H::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::: :::.:i;:::::M:'ie ; :""'ii'SlSb. :=;::;::?^ :|S::::::":::::'p5 t e m p o r a l v a r i a b i l i t y i n t r o d u c e d by t h i s dynamic m o d e l l i n g a p p r o a c h F i g u r e 3.10a,b,c shows t h e v a r i a t i o n i n p r o p o r t i o n o f t h r e e o f t h e more i m p o r t a n t s u r f a c e t y p e s t h r o u g h t i m e , f o r t h o s e h ours o f the s t u d y p e r i o d when t h e s o u r c e a r e a c o u l d be c a l c u l a t e d u s i n g plumes. The s i g n i f i c a n c e o f t h e s e changes a r e d i s c u s s e d i n subsequent c h a p t e r s . 3 . 4 Sunmary I n t h i s c h a p t e r an o b j e c t i v e means o f l o c a t i n g t h e b o u n d a r i e s t o a s s i g n v a l u e s t o s u r f a c e p a r a m e t e r s has been p r o p o s e d , termed 'plumes'. T h i s t a k e s i n t o a c c o u n t t h e a r e a a c t u a l l y c o n t r i b u t i n g t o a t u r b u l e n t f l u x measurement , a p o i n t and how t h i s changes w i t h m e t e o r o l o g i c a l c o n d i t i o n s . I t i s assumed t h a t f l u x e s m o d e l l e d u s i n g plumes f o r the a s s i g n m e n t o f b o u n d a r i e s and d e r i v a t i o n o f s u r f a c e p a r a m e t e r s a r e c l o s e s t t o t h e ' t r u e ' v a l u e s . I n subsequent c h a p t e r s f l u x e s m o d e l l e d u s i n g the plume method a r e compared w i t h the o t h e r methods o u t l i n e d i n t h i s c h a p t e r . T h i s i s a c h i e v e d w i t h t h e a i d o f the 100 m x 100 m g r i d s q u a r e s d a t a b a s e d e s c r i b e d h e r e . F i g u r e 3.10 I n f l u e n c e o f t h e c h a n g i n g s o u r c e a r e a s on p e r c e n t a g e o f l a n d u s e c h a r a c t e r i s t i c s i n f l u e n c i n g measurements. S o u r c e a r e a s a r e plumes. Note v e r t i c a l s c a l e s a r e d i f f e r e n t . 51 0 500 1000 1500 2000 2500 3000 3500 Time s i n c e JD 22 (h) 52 CHAPTER 4 ANTHROPOGENIC HEAT FLUX 4.1 Introduction A n t h r o p o g e n i c h e a t f l u x (Qp), t h e energy r e l e a s e d due t o human a c t i v i t i e s , i s o f t e n r e g a r d e d as n e g l i g i b l e o r i s i g n o r e d i n u r b a n energy b a l a n c e s t u d i e s . T h i s i s due t o two f a c t o r s , b o t h o f w h i c h a r e r e l a t e d t o t h e f a c t t h a t most o f t h e s e s t u d i e s have been c o n d u c t e d under summer c o n d i t i o n s . F i r s t l y , i n many u r b a n a r e a s t h e a b s o l u t e s i z e o f Qp i s s m a l l e r i n summer t h a n i n w i n t e r . S e c o n d l y , even i f t h i s was n o t the case i n t h e summertime t h e magnitude o f the o t h e r f l u x e s a r e l a r g e r and t h e r e f o r e t h e r e l a t i v e i m p o r t a n c e o f Qp i s s m a l l e r . I t s magnitude may o n l y be o f t h e o r d e r o f t h e e r r o r o f measurement. Thus n o t o n l y i t s p r o p o r t i o n a l s i g n i f i c a n c e , but a l s o i t s a b s o l u t e magnitude i s l a r g e r under non-summer t i m e c o n d i t i o n s i n a te m p e r a t e c i t y s u c h as Vancouver. T h e r e f o r e Qp must be c o n s i d e r e d i n s e a s o n a l e n e r g y b u d g e t s . Qp can be s u b d i v i d e d i n t o t h r e e components: Q F - Q F V + Q F H + Q F M where Qpy - h e a t p r o d u c e d by co m b u s t i o n o f v e h i c l e f u e l s (W m~ 2); QpH - fr o m " s t a t i o n a r y s o u r c e s " ( p r i m a r i l y w i t h i n b u i l d i n g s ) ( W ra"2); and QpM - h e a t r e l e a s e d by m e t a b o l i s m (W m~ 2), g e n e r a l l y t h i s i s n e g l i g i b l e compared t o the o t h e r two components b u t f o r c o m p l e t e n e s s was i n c o r p o r a t e d i n t h i s s t u d y . Qp can n o t be measured d i r e c t l y . T h i s c h a p t e r o u t l i n e s t h e methods used t o de t e r m i n e Qp on an h o u r l y b a s i s ; and c o n s i d e r s t he i n f l u e n c e o f s u r f a c e d e s c r i p t i o n on i t s e s t i m a t i o n . 4.2 Methods of calculation 4.2.1 Anthropogenic heat produced by combustion of vehicle fuels Qpy i s d e f i n e d as the energy produced by the c o m b u s t i o n o f v e h i c l e f u e l s w i t h i n t h e s o u r c e a r e a . T h i s i s a f u n c t i o n o f the amount o f g a s o l i n e used and i t s energy c o n t e n t , w h i c h can be r e l a t e d t o t h e number o f v e h i c l e s t r a v e l l i n g 5 3 w i t h i n the s o u r c e a r e a , t h e d i s t a n c e t h e y t r a v e l , t h e t y p e o f g a s o l i n e u s e d , and t h e i r f u e l e f f i c i e n c y ( d i s t a n c e t r a v e l l e d p er u n i t o f g a s o l i n e ) . Qpv was c a l c u l a t e d f o r each hour ( t ) u s i n g the* s o u r c e a r e a (A) s u r f a c e d e s c r i p t i o n : QFV - t ( n V i ( t ) D V i) EV]/[A 3600] (4.2) where nyy - number o f v e h i c l e s by r o a d t y p e (major o r m i n o r ) i n the s o u r c e a r e a ; Dvi - d i s t a n c e o f r o a d w i t h i n the c o n t r i b u t i n g a r e a by r o a d t y p e (m) ; EV - energy used by a v e h i c l e ( J m"-'-): EV - (NHCi P i WFSi)/FE (4.3) where NrlC^ - n e t h e a t c o m b u s t i o n by f u e l t y p e ( J kg"-*-); PI - d e n s i t y o f f u e l by f u e l t y p e (kg 1'-*-); WFS-L - w e i g h t i n g o f f u e l s a l e s by f u e l t y p e ; and FE - average f u e l economy (m l ' ^ ) . I n B r i t i s h C o lumbia t h r e e t y p e s o f f u e l a r e commonly used. T a b l e 4.1 l i s t s t he v a l u e s used f o r NHC and py f o r t h e s e f u e l t y p e s . The f u e l s a l e s , WFS, were used t o w e i g h t the r e l a t i v e p r o p o r t i o n s o f t h e s e f u e l t y p e s f o r t h e Qp-y c a l c u l a t i o n s . An av e r a g e v a l u e of 11.2531 x 10^ m 1"^ was u s e d f o r t h e f u e l economy ( W h i t f o r d , 1984). T h i s r e p r e s e n t s an ave r a g e f o r a l l v e h i c l e t y p e s d r i v i n g i n a c i t y , t o a c c o u n t f o r the v a r i e t y w h i c h t r a v e l w i t h i n the s t u d y a r e a . F i g u r e 4.1 i l l u s t r a t e s t he ny p r o f i l e s f o r t h e s t u d y a r e a f o r the major and minor r o a d s . The d a t a were o b t a i n e d from t r a f f i c c o u n t s c o n d u c t e d by Vancouver C i t y T r a f f i c Department. Dy was d e t e r m i n e d based on t h e a r e a o f ro a d s w i t h i n the s o u r c e a r e a each hour f r o m the s u r f a c e d a t a b a s e (see C h a p t e r 3). 4.2.2 Anthropogenic heat flux produced by combustion from stationary sources I n the s t u d y a r e a , t h e two f u e l s w h i c h c o n t r i b u t e t o Qp^ a r e e l e c t r i c i t y and gas; o t h e r f u e l s were r e g a r d e d as b e i n g n e g l i g i b l e and were i g n o r e d . Two s c a l e s o f d a t a were a v a i l a b l e t o e n a b l e the c a l c u l a t i o n o f QpH- F i r s t l y , d a t a 5 4 Table 4.1 Fuel consumption, density and net heat combustion (sources: Oilweek. Sept 21, 1987; Shell Canada Ltd. personal communication, 1988) Fuel Consumption in BC Consumption Density Rangea Net Heat Combustion Type Jan-June, 1987 (Ml) (%) (kg m'3) (J kg' 1) Premium 185.8 11.03 740-770 (755) 44,332,985 unleaded Regular 621.1 36.86 720-740 (730) 44,862,959 unleaded Regular 878.1 52.11 710-730 (720) 45,072,159 leaded a Gasoline density varies with fuel mix and season - the midpoint value (in brackets) was used Figure 4.1 Mean profiles of t r a f f i c counts for major and minor roads in the study area Time (hour) 5 5 a t t h e i n d i v i d u a l p r o p e r t y (consumer) s c a l e were a v a i l a b l e f o r 600 consumers w i t h i n c l o s e p r o x i m i t y o f the measurement tower. The d a t a were s t r a t i f i e d by p remise c l a s s : s i n g l e f a m i l y d w e l l i n g , a p a r t m e n t s , i n s t i t u t i o n a l ( f u r t h e r s u b d i v i d e d i n t o s c h o o l s , c h u r c h e s , h o s p i t a l s e t c ) , i n d u s t r i a l e t c . These d a t a were a v a i l a b l e i n v a r i a b l e two monthly b i l l i n g p e r i o d i n t e r v a l s w i t h no i n d i c a t i o n o f h o u r l y v a r i a b i l i t y o f use. S e c o n d l y , t h e o n l y a v a i l a b l e i n f o r m a t i o n showing h o u r l y d i f f e r e n c e s i n c o n s u m p t i o n , was a t the s c a l e o f the " I n t e g r a t e d System f o r BC" f o r e l e c t r i c i t y , and t h e "Lower M a i n l a n d " f o r gas. The a p p r o a c h t a k e n was t o a p p o r t i o n the l o c a l s c a l e p r e m i s e c l a s s d a t a u s i n g the g r i d f l u c t u a t i o n s . Fo r e a ch hour Qpjj was c a l c u l a t e d u s i n g : Q F H - [ ( G R E ( t ) S ( n E i C E i ) ) + ( ( G R G ( t ) S ( n G i C G i ) G E F ) / 3 6 0 0 ) ] / A (4.4) where G R ( t ) - hour ( t ) g r i d c o n s u m p t i o n ( g r ( t ) ) as a p r o p o r t i o n o f the t o t a l g r i d c o n s u m p t i o n f o r the s t u d y time p e r i o d ( S g r ( t ) ) : G R ( t ) = g r ( t ) / S g r ( t ) (4.5) s u b s c r i p t E and G - e l e c t r i c i t y and gas r e s p e c t i v e l y ; n - number o f consumers by premise c l a s s ( i ) ; C - t o t a l mean co n s u m p t i o n f o r an i n d i v i d u a l consumer by p r e m i s e c l a s s (Watts e l e c t r i c i t y , J o u l e s g a s ) ; GEF - gas e f f i c i e n c y ( 0 . 6 7 5 ) ; n o t e e l e c t r i c i t y = 1.00; and A - s o u r c e a r e a ( m 2 ) . BC Hydro p r o v i d e d t h e gas and e l e c t r i c i t y d a t a a t t h e two s c a l e s ( g r i d and consumer). The number o f consumers f o r each hour f o r e a c h p r e m i s e c l a s s was d e t e r m i n e d from the s u r f a c e d a t a b a s e (see C h a p t e r 3 ) . 4.2.3 Anthropogenic heat produced by metabolism QpM i s c a l c u l a t e d u s i n g : QFM ( t ) = t ( n p % ( t ) ) + ( n A M A ( t ) ) ] / A (4.6) where n - number o f p e o p l e ( s u b s c r i p t P) o r a n i m a l s ( s u b s c r i p t A ) ; M ( t ) - m e t a b o l i c r a t e (W) a t time t ; and A - c o n t r i b u t i n g a r e a ( m 2 ) . The day was s u b d i v i d e d i n t o two time p e r i o d s : " a c t i v e " (0700 - 2300 h o u r s ) and 5 6 "sleep" (2300 - 0700 hours). Metabolic rates from Oke (1978) were used for the people, and the number of people contributing f o r each hour estimated using the database. Following Bach (1970) MA was set to approximately 25% of Mp. The number of animals was assumed to be 10% of the people. 4.3 Modelled values of anthropogenic heat flux Figure 4.2 shows the temporal trend of the three Qp components and t h e i r combined t o t a l f o r JD 22, 1987, using the 2 km radius c i r c l e to determine the required mean surface parameters. The influence of the morning and afternoon rush hours are apparent i n the Qpy and Qp p r o f i l e s , and the s l i g h t l y out of phase peaks i n Qpn- Q F M I s r e l a t i v e l y small and shows a step t r a n s i t i o n between the 'sleep' and 'active' periods of the day. In the summer time Qp^ i s reduced but Qpy remains approximately the same. Using the database i t i s possible to c a l c u l a t e the siz e of the anthropogenic heat f l u x density f or each g r i d square f o r any hour. F i g . 4.3 i s a map of Qp for the hour 900 LAT, JD 22, 1987. Qp ranged from 0 W m"2, f o r the Fraser r i v e r and some farm land i n Richmond (see F i g . 2.1), to approximately 80 W m , where two major roads and high density housing occur i n one square. Comparison of t h i s map with that of major roads ( F i g . 3.8) reveals the importance of Qpy because the general g r i d nature of the streets i s evident i n the Qp map. The e f f e c t of changing the area used to determine the surface parameters can be seen from Figure 4.4. In t h i s example the influence of changing the radius of a c i r c l e or a quadrant i s considered. In Figure 4.4 the radius was increased from 100 m to 4.9 km i n 100 m increments. Surface parameters are determined f o r the area of the quadrant or c i r c l e from the tower out to that radius. If increasing the radius had no e f f e c t one would see the same temporal F i g u r e 4.2 A n t h r o p o g e n i c h e a t f l u x f o r JD 22, 1987. P l o t s shows t h e t h r e e components o f the f l u x and t h e t o t a l h o u r l y f l u x . 5 8 Figure 4.3 Map of anthropogenic heat flux for 900 LAT, JD 22, 1987 centred on the Sunset site. Inner circle has a radius of 2 km. F i g u r e 4.4 A n t h r o p o g e n i c h e a t f l u x (W m Z ) w i t h i n c r e a s i n g r a d i u s from t h e tower f o r JD 22, 1987: (a) c i r c l e ( b ) NW q u a d r a n t ( c ) NE q u a d r a n t (d) SW q u a d r a n t (e) SE q u a d r a n t . 6 0 t r e n d t h r o u g h t h e day e x t e n d i n g a l o n g t h e r a d i u s a x i s ( y - a x i s ) . As c a n be seen t h e r e i s c o n s i d e r a b l e v a r i a b i l i t y . The g r e a t e s t v a r i a b i l i t y o c c u r s c l o s e t o the tower. T h i s i s i n p a r t a consequence o f t h e f a c t t h a t as t h e r a d i u s i s ext e n d e d the s u r f a c e c h a r a c t e r i s t i c s a r e a v e r a g e d o v e r a l a r g e r a r e a and t h e r e f o r e any s m a l l change i s l e s s s i g n i f i c a n t . F u r t h e r , i f t h e a r e a used t o a s s i g n v a l u e s t o s u r f a c e p a r a m e t e r s e x e r t s no i n f l u e n c e i t would be e x p e c t e d t h a t h o u r l y Qp f l u x e s , c a l c u l a t e d u s i n g d i f f e r e n t s o u r c e a r e a s schemes, would p l o t on a one-to-one l i n e . F i g u r e 4.5 i s a p l o t o f Qp m o d e l l e d f o r 1708 h o u r s u s i n g two d i f f e r e n t schemes: ( i ) plumes as c a l c u l a t e d f r o m t h e Schmid (1988) model ( h e r e assumed t o be t h e b e s t method t o d e s c r i b e t h e s o u r c e a r e a f o r a t u r b u l e n t f l u x , see s e c t i o n 3.2); and ( i i ) 2 km r a d i u s c i r c l e . The s u r f a c e p a r a m e t e r i s a t i o n i s s t a t i c w i t h the c i r c l e , b u t w i t h t h e plumes i t changes w i t h the c h a n g i n g m e t e o r o l o g i c a l c o n d i t i o n s . I t can be seen t h a t t h e two Qp v a l u e s do n o t p l o t a l o n g a one-to-one l i n e . The mean f o r t h e plume v a l u e s was 9.51 W m~2 (s.d.=3.08 W m" 2), and t h a t f o r t h e 2 km c i r c l e was 8.63 W m"2 (s.d.=2.34 W m" 2). The RMSE f o r t h e r e l a t i o n was 2.35 W m"2. T h i s can be e x p l a i n e d by t h e l o c a t i o n o f the s o u r c e a r e a s . F i g u r e 4.6 shows t h e wind d i r e c t i o n f r e q u e n c i e s f o r the 1708 h o u r s t h a t have been compared. F i g u r e 4.6a shows the wind d i r e c t i o n f o r a l l 1708 h o u r s ; F i g u r e 4.6b shows the w i n d d i r e c t i o n f o r t h o s e hours when the plumes were g r e a t e r t h a n the 2 km r a d i u s c i r c l e ; and, F i g u r e 4.6c when t h e c i r c l e Qp were g r e a t e r . The plumes a r e g e n e r a l l y g r e a t e r when the wind d i r e c t i o n i s f r o m the two s o u t h e r l y q u a d r a n t s and g e n e r a l l y l e s s when from the two n o r t h e r l y q u a d r a n t s . T h i s can be e x p l a i n e d by the s u r f a c e t y p e s and t h e r e f o r e a n t h r o p o g e n i c e n e r g y s o u r c e s f o und w i t h i n the a r e a ( s e e F i g . 3.9). As s t a t e d i n C h a p t e r 3 s i n c e the plumes r e q u i r e Q^ d a t a , w h i c h i s n o t always a v a i l a b l e the s i m p l e r ' s e c t o r s ' w h i c h i n c o r p o r a t e some o f the dynamic 61 F i g u r e 4.5 H o u r l y a n t h r o p o g e n i c heat f l u x m o d e l l e d u s i n g plumes and 2 km r a d i u s c i r c l e as the b a s i s f o r a s s i g n i n g v a l u e s t o s u r f a c e p a r a m e t e r s . F i g u r e 4.6 Wind d i r e c t i o n f r e q u e n c y p l o t f o r : Ca) a l l h o u r s (b) h o u r s when Q^ , plumes g r e a t e r t h e n 2 km r a d i u s c i r c l e C c ) h o u r s when plumes l e s s t h a n 2 km r a d i u s c i r c l e . 62 ( a ) n = 1708 (b) n = 1113 ( c ) 6 3 nature of source areas are proposed (section 3.2.2). Figure 4.7 i s a plot of 1708 hourly Qp values modelled using plumes and sectors as the basis f o r assigning values to surface parameters. The mean f o r the sectors i s 9.08 W m"2 (s.d.=3.17 W m" 2)(see above f or plumes), and the RMSE i s 1.18 W m"2. The sectors simulate the source area of the plumes reasonably w e l l . Therefore i t i s proposed that i n the absence of Qji, sectors be used f o r assigning surface parameter values. This allows for continuous c a l c u l a t i o n of Qp. 4.4 Incorporation of anthropogenic heat flux into the energy balance Consideration needs to be given to the i n c l u s i o n of the Qp term i n the energy balance. It i s dependent upon how the other terras of the energy balance have been assessed. In t h i s study some portion of Qp i s already incorporated i n measurements of the output fluxes: Q^ (using the SAT) and RTDMS temperatures. Measurements of Q*, also, p a r t i a l l y include Qp because i t af f e c t s the long-wave exchange portion of Q* v i a the surface temperature (Tg): Lt = eaTg 4 (4.7) Q* = K* + ( L l - L t ) (4.8) where Lt - long-wave r a d i a t i o n emitted from the surface (W m" 2); e - emis s i v i t y of the surface materials: and a - Stefan-Boltzmann constant (W m"2 K " 4 ) ; K* - net shortwave r a d i a t i o n (W m"2); and LI - long-wave r a d i a t i o n received at the surface (W m" 2). Qp causes an increase i n Tg which leads to an increase i n Lt. Within a 0 -40°C range a one degree r i s e i n Tg res u l t s i n a 5 to 6 W m"2 increase i n Lt, Therefore the measured Q* f l u x includes a reduction due to the Qp fl u x . The increase i n Tg, and therefore the e f f e c t on Q*, i s a function of the heat capacity of the b u i l d i n g f a b r i c , the 3-D surface area of the b u i l d i n g and the amount of energy released within the bu i l d i n g . The e f f e c t on the temperature can be cal c u l a t e d approximately through the following steps: F i g u r e 4.7 P l o t o f h o u r l y Q F c a l c u l a t e d u s i n g plumes and s e c t o r s f o r a s s i g n i n g v a l u e s f o r s u r f a c e p a r a m e t e r s . 6 5 1) The average maximum hourly Qp^ and Qpn are calculated for a time period (units of Joules) for an individual 'average' premise. 2) The summed Qp^ and Qpjj are reduced by 30% because of air leakage heat losses from buildings (Canadian General Standards Board, 1980). 3) The surface area of the buildings is calculated and used to determine a mean flux density (W m"2) loss from within the buildings. 4) Using values assigned for the heat capacity of the building fabrics and building thicknesses the change in external surface temperature can be calculated. 5) The effect on Lt is calculated and the net effect on Q* determined. Such calculations indicate that the increase in Tg will be less than one Celsius degree. The effect on Q* is very small under most conditions. Therefore in this study Qp was directly added to the energy balance. The significance of Qp in the seasonal energy balance is discussed in Chapter 6. 6 6 CHAPTER S: STORAGE HEAT FLUX 5.1 Introduction I n u r b a n a r e a s , t h e s u b - s u r f a c e o r s t o r a g e h e a t f l u x (AQg) i s t h e n e t upta k e o r r e l e a s e o f en e r g y f r o m the u r b a n system. I t i n c l u d e s l a t e n t and s e n s i b l e h e a t changes i n the a i r , b u i l d i n g s , v e g e t a t i o n , and ground e x t e n d i n g from above r o o f - l e v e l t o a d e p t h i n the ground where n e t h e a t exchange o v e r the p e r i o d o f s t u d y i s n e g l i g i b l e (Oke & C l e u g h , 1987). One r e a s o n t o de t e r m i n e the s i z e o f t h i s f l u x i s t o a s c e r t a i n t h e amount o f a v a i l a b l e e nergy (Q*+Qp-AQg) f o r the t u r b u l e n t s e n s i b l e (Q^) and l a t e n t (Qg) h e a t f l u x e s . I t i s not p o s s i b l e t o d i r e c t l y measure the i n t e g r a t e d h e a t s t o r a g e o f t h e u r b a n system. There a r e two i n d i r e c t methods t o o b t a i n 'measured' v a l u e s o f AQg. F i r s t l y , one c o u l d measure AQg f o r a l l t he component s u r f a c e s w i t h i n t h e s t u d y a r e a and combine them w i t h an a p p r o p r i a t e w e i g h t i n g scheme. I n an u r b a n a r e a t h i s r e q u i r e s a l a r g e s a m p l i n g e f f o r t because o f t h e m u l t i - f a c e t t e d s u r f a c e w i t h i t s wide range o f s u r f a c e m a t e r i a l s . There have been s t u d i e s f o r i n d i v i d u a l s u r f a c e t y p e s , f o r example c o n c r e t e by D o l l e t a l . ( 1 9 8 5 ) ; and r o o f s by Yap (1972) and T a e s l e r ( 1 9 7 8 ) . S e c o n d l y , i f a l l o t h e r terras o f the ene r g y b a l a n c e a r e measured AQg can be d e t e r m i n e d as t h e r e s i d u a l : AQg = Q* + Q F - Q H - QE ( 5 . D T h i s method has the d i s a d v a n t a g e s t h a t : (1) a l l t h e o t h e r f l u x e s have t o be measured and by methods n o t r e q u i r i n g the s t o r a g e h e a t f l u x t o be d e t e r m i n e d ; and (2) because AQg i s a r e s i d u a l t he c a l c u l a t e d f l u x c o n t a i n s t he net c u m u l a t i v e e r r o r s o f t h e o t h e r measurements. I n t h i s s t u d y AQg i s needed, n o t o n l y t o model Qg, but a l s o t o d e t e r m i n e the 'measured' Qg f o r t h e e v a l u a t i o n o f model p e r f o r m a n c e . T h i s c h a p t e r o u t l i n e s t h e methods used t o d e t e r m i n e AQg on an h o u r l y b a s i s and compares the 6 7 values obtained with those 'measured' by the residual method. 5.2 Methods of Calculation There are curr e n t l y two types of models to ca l c u l a t e urban AQg. F i r s t l y , there are those that use heat conduction equations incorporated i n surface energy balance models. Most boundary layer models use values of thermal properties f o r b u i l d i n g materials and a one-dimensional heat conduction equation based at some assumed urban 'surface' plane (Oke and Cleugh, 1987). Some come close to portraying 3-dimensional urban surface geometry (e.g. Terjung and O'Rourke, 1980; Sievers and Zdunkowski, 1986). Unfortunately none have been v e r i f i e d using measured heat f l u x d e n s i t i e s (Oke and Cleugh, 1987). Peikorz (1987) attempted to measure and model t h i s f l u x f o r i n d i v i d u a l surfaces and to combine them into an urban model. Unfortunately he d i d not have AQs r e s i d u a l s against which to compare the fluxes. He was forced to r e l y on measurements i n a concrete path and a lawn. F u l l determination requires an extensive array of temperature measurements which sample a l l facets and surface types. Secondly, there are models which estimate storage as a function of Q* and the surface cover types present i n the study area. This i s the type of model used here. This kind of model has the advantage' of not re q u i r i n g extensive temperature measurements and requires r e l a t i v e l y l i t t l e computational resources. Three such models are outlined below and t h e i r performance assessed. 5.2.1 Objective linear regression model (Oke, Kalanda and Steyn, 1981) The model proposed by Oke et a l . (1981), to estimate s p a t i a l l y averaged urban heat storage, combines empirical l i n e a r regression equations between net 6 8 r a d i a t i o n (Q*) and AQg, f o r a number of urban surfaces and weights t h e i r role i n proportion to the plan area of greenspace and b u i l t surface present i n the study area: n AQg = 2 a i ( a i Q* + bi) (5.2) i-1 where - the f r a c t i o n of the area covered by the i t h surface type; and a i - b i - c o e f f i c i e n t s i n the parameterization f o r the i t h surface type. Oke et a l . (1981) present equations determined from measured data f o r a roof, an urban canyon, and pavement. These are combined to assign the c o e f f i c i e n t s for the daytime (Q*>0) b u i l t surface type. The daytime and nocturnal (Q*<0) greenspace c o e f f i c i e n t s are based on data c o l l e c t e d from s i t e s with short grass. At night the b u i l t c o e f f i c i e n t s are based on data f o r an urban canyon. Oke et a l . (1981) present the following equations f o r Sunset: AQg = (Q*-27) x 0.25 Q*>0 (5.3) AQg = Q* x 0.67 Q*<0 (5.4) The f r a c t i o n s of greenspace and b u i l t covers were based on a 2 km radius c i r c l e . 5.2.2 Hysteresis model (Camuffo and Bernardi, 1982; Oke and Cleugh, 1987) Observations i n bare s o i l have shown that there i s a d i f f e r e n t r e l a t i o n s h i p between the r i s i n g and f a l l i n g limb of the d a i l y cycle between Q* and AQg, and that AQg peaks one to two hours before Q*. Camuffo and Bernardi (1982) suggested a r e l a t i o n s h i p between AQg and Q* which takes into account t h i s hysteresis pattern. The general form of the equation has three terms: Q s = a]Q* + a 2dQ* + a 3 (5.5) dt where aj_, a2, a 3 - empirical c o e f f i c i e n t s ; and dQ*= Q*(t) - [Q*(t+1) + Q*(t - l ) ] / 2 (5.6) dt 69 The second term g i v e s t h e h y s t e r e s i s l o o p d e p a r t u r e s f r o m t h e l i n e a r r e l a t i o n s h i p . Oke and C l e u g h (1987) o b s e r v e d t h i s h y s t e r e s i s p a t t e r n i n measurements o f Q* and AQg ( d e t e r m i n e d by r e s i d u a l ) c o n d u c t e d i n J u l y / A u g u s t 1978 a t S u n s e t , Vancouver. They u s e d t h e h o u r l y ensemble a v e r a g e s t o d e t e r m i n e t h e f o l l o w i n g c o e f f i c i e n t s f o r a l l h o u r s : a^=0.35, a2=0.28 and a3=-40; and, when Q* i s p o s i t i v e : a^=0.30, a2=0.25 and a3=-22. The h y s t e r e s i s f o r m seems c a p a b l e of r e p r e s e n t i n g most f e a t u r e s o f the s t o r a g e regime: t h e magnitude by day and by n i g h t , t h e d a y t i m e phase s h i f t r e l a t i v e t o t h e n e t r a d i a t i o n , and t h e t i m e s of t r a n s i t i o n between h e a t r e l e a s e and uptake (Oke and C l e u g h , 1987). 5.2.3 Objective hysteresis model (Cleugh, 1988) The d i s a d v a n t a g e o f t h e Oke and C l e u g h (1987) models a r e , as t h e y n o t e , t h a t t h e c o e f f i c i e n t s o n l y r e l a t e t o the s p e c i f i c s i t e and w e a t h e r c o n d i t i o n s o f t h e 1978 s t u d y . F u r t h e r d e v e l o p i n g the h y s t e r e s i s i d e a f o r u r b a n a r e a s C l e u g h (1988) combines Camuffo and B e r n a r d i (1982) t y p e h y s t e r e s i s e q u a t i o n s d e r i v e d f r o m d a t a f o r i n d i v i d u a l s u r f a c e t y p e s w i t h an Oke e t a l . (1981) t y p e o f a r e a l w e i g h t i n g scheme t o c r e a t e an o b j e c t i v e method a p p l i c a b l e t o any u r b a n s i t e . The s u r f a c e d e s c r i p t i o n r e q u i r e d i n v o l v e s d e t e r m i n a t i o n o f t h e p l a n a r e a o f g r e e n s p a c e , t h e 3 - d i m e n s i o n a l a r e a o f r o o f s , t h e p l a n a r e a o f paved s u r f a c e s , and t h e 3 - d i m e n s i o n a l a r e a of w a l l s ( T a b l e 5.1). The f o u r a r e a s a r e d e t e r m i n e d as a p e r c e n t a g e of t h e p l a n a r e a p l u s the a r e a of w a l l s and r o o f ( i . e . the t o t a l i s g r e a t e r t h a n the p l a n a r e a ) . These p e r c e n t a g e v a l u e s a r e used w i t h c o e f f i c i e n t s f o r each of t h e s u r f a c e t y p e s (see T a b l e 5.2). 70 Table 5.1 Percentage of surface type in the Sunset study area for use with the objective hysteresis model for storage heat flux density. Total area - 2D greenspace + 3D roof + 2D impervious + 3D walls Surface Type (%) Greenspace Roof Impervious Walls 2 km radius Circle 31 23 20 26 Quadrant NE 28 24 20 28 SE 27 25 21 27 SW 32 21 23 24 NW 36 21 18 25 Cleugh (1988) a: c i r c l e 43 13 11 33 Plumes Mean (n-1715) 30 23 20 27 sd 5 2 2 2 max 66 27 34 30 min 23 9 14 10 Error i n fl <20% A l l hours: mean 31 23 20 27 Q*+Qp positive: mean 31 23 20 28 Sectors Mean (n-3779) 32 22 20 26 sd 6 2 2 3 max 52 26 25 30 min 24 16 14 19 Error in fi <20% A l l hours: mean 32 22 20 25 Q*+Qp positive: mean 29 23 20 28 Mean when model applied to a l l hours in study period when Q*+Qp positive Plumes & Sectors 30 23 20 27 a Cleugh (1988) calculated the proportion of each surface type using a different method to that used in this study. She used the data for a 2 km radius c i r c l e presented by Kalanda (1979) and Steyn (1980) which was based on samples from aerial photographs. She used the two-dimensional percent landuse, the number of buildings and their mean dimensions to calculate the proportions. She assumed that the roofs were f l a t , which i s probably reasonable i n this case as the average 3D area i s not much greater than the 2D area. The major difference between the two studies i s in the vegetation percentages. 71 T a b l e 5.2 I n d i v i d u a l s u r f a c e c o e f f i c i e n t s f o r t h e o b j e c t i v e h y s t e r e s i s s t o r a g e h e a t f l u x model and the mean c o e f f i c i e n t s a r i s i n g f r o m i t s a p p l i c a t i o n t o Sun s e t , Vancouver. ai &2 a 3 (a) Surface Type ( C l e u g h , 1988) Surfaces, No. of data sets Greenspace 0.34 0.38 -21.9 S h o r t g r a s s , b a r e s o i l (3) R o o f t o p 0.30 0.34 -23.0 Van c o u v e r , U p p s a l a (2) Impe r v i o u s 0.59 0.36 -49.6 C o n c r e t e , a s p h a l t (2) Canyon 0.32 0.01 -27.7 Vancouver (1) (b) Application of objective hysteresis model: Sunset, Vancouver 2 km radius circle C l e u g h (1988) 0.35 0.25 -29.4 P r e s e n t s t u d y 0.38 0.27 -29.3 Source areas - mean c o e f f i c i e n t s f o r h o u r s when 'measured' AQg D a v a i l a b l e A l l h o u r s Plumes 0.37 0.27 -29.1 S e c t o r s 0.37 0.27 -29.1 Q*+Qp p o s i t i v e : Plumes 0.37 0.26 -29.4 S e c t o r s 0.37 0.26 -29.2 - a p p l i c a t i o n t o whole s t u d y p e r i o d 1987 when Q*+Qp i s p o s i t i v e : Plumes & S e c t o r s 0.38 0.27 -29.3 b 'Measured' as a r e s i d u a l i n the energy b a l a n c e 7 2 5.3 'Measured' storage heat flux 1987 Most t e s t s o f u r b a n AQg models have been c o n d u c t e d w i t h summertime d a t a . F o r t h i s s t u d y and t o h e l p e s t a b l i s h t h e i r g e n e r a l i t y i t was n e c e s s a r y t o t e s t t h e s e models under o t h e r c o n d i t i o n s t o a s s e s s t h e i r p e r f o r m a n c e i n non-summertime c o n d i t i o n s . I n t h i s s t u d y i t i s p o s s i b l e t o d e t e r m i n e AQg as a r e s i d u a l (AQg^) when: 1) Q* i s measured d i r e c t l y ; 2) Qp i s c a l c u l a t e d as o u t l i n e d i n Ch a p t e r 4; 3) Q H i s measured d i r e c t l y u s i n g the SAT system ( Q H S ) ; A N & 4) fl i s measured u s i n g t h e RTDMS system. Qg i s c a l c u l a t e d u s i n g : QES - QHS / A (5.7) AQsR c a n b e c a l c u l a t e d u s i n g e q u a t i o n 5.1. As was n o t e d above, t h i s method i n c o r p o r a t e s t h e n e t e r r o r s from the o t h e r f l u x e s i n t h e AQg term. I n o r d e r t o o b t a i n t h e b e s t e s t i m a t e o f AQg^ i t i s n e c e s s a r y t o pay a t t e n t i o n t o t h e e r r o r s i n t h e measurements t h a t c o n t r i b u t e t o the 'measured' v a l u e s . The e r r o r i n Q* was t a k e n t o be ±5% ( L a t i m e r , 1972), and i n Q H S t o be ±10% (Tanner, p e r s . comm.). The e r r o r s i n fi v a r y w i t h t h e s i z e o f t h e a b s o l u t e t e m p e r a t u r e g r a d i e n t s and the t e m p e r a t u r e (see Appendix I I I ) . The r e j e c t i o n o f d a t a w i t h l a r g e e r r o r s i n fi mean t h a t t he d a t a s e t i s r e d u c e d c o n s i d e r a b l y . There were 1586 h o u r s when a l l terms were measured and the r e s u l t i n g f l u x e s (Qgg, AQg^) were r e a s o n a b l e . Of t h e s e h o u r s , 23% (362 h o u r s ) had an e r r o r i n B of <10%. The m a j o r i t y o f t h e s e h o u r s (97%) were when Q*+Qp was l e s s t h a n z e r o ( s e e T a b l e 5.3). Of the 1586 h o u r s , 66% had an e r r o r i n B o f <60%. P l o t s o f the ensemble a v e r a g e s o f AQg and Q* show t h a t t he h y s t e r e s i s p a t t e r n r e p o r t e d by Oke and C l e u g h (1987) i n u r b a n a r e a s d u r i n g summer a l s o o c c u r s i n w i n t e r and s p r i n g ( F i g . 5.1). The c o e f f i c i e n t s f o r t h e Camuffo and 7 3 Figure 5.1 Plots of hourly ensemble averages of storage heat flux residual and net radiation for hours when error in Bowen Ratio i s : (a) < 20% (21-59 n-101, 60-120 n=250, 151-179 n=243) (b) < 30% (.21-59 n-122, 60-120 n=313, 151-179 n=362) (c) < 40% (.21-59 n-138, 60-120 n=313, 151-179 n=369) (a) § 300 0* (W n-^) 1 I I 1 1 1 1 -100 0 100 200 300 400 500 600 700 0* (W nT2) Numbers on plots indicate time (LAT) 74 B e r n a r d i (1982) t y p e o f e q u a t i o n were d e t e r m i n e d f o r d i f f e r e n t s i z e s o f e r r o r s i n B f o r : a l l h o u r s ; when Q*+Qp was < 0; and when Q*+Qp was p o s i t i v e ( T a b l e 5.3). I t s h o u l d be n o t e d t h a t t h e s e f i t t e d c o e f f i c i e n t s were u s e d o n l y f o r d e s c r i p t i v e p u r p o s e s . The model u s e d f o r c a l c u l a t i n g AQg i n t h e en e r g y b a l a n c e i n t h i s s t u d y u s e s t h e o b j e c t i v e l y d e t e r m i n e d c o e f f i c i e n t s ( s e e s e c t i o n s 5.4, 5.5). The p a r a m e t e r s o b t a i n e d when Q*+Qp i s n e g a t i v e s u g g e s t t h a t v i r t u a l l y a l l t h e e n e r g y i s b e i n g removed f r o m s t o r a g e , and t h e h y s t e r e s i s t e r m (a2) i s n o t s i g n i f i c a n t . S i n c e t h e r e i s a b i a s i n t h e d a t a t o w a r d s h o u r s when Q*+Qp i s <0, the p a r a m e t e r s f o r t h e c o m p l e t e s e t ( a l l h o u r s ) a r e b i a s e d t o w a r d s t h e s e h o u r s . T h e r e f o r e , when h o u r s w i t h Q*+Qp p o s i t i v e a r e f i t t e d as a s e p a r a t e s e t , t h e v a l u e s a s s i g n e d t o a.\ and a 3 a r e r e d u c e d , and a2 i s i n c r e a s e d ( s e e T a b l e 5.3). There i s more s c a t t e r ( r 2 i s s m a l l e r ) and a l a r g e r s t a n d a r d e r r o r f o r t h e h o u r s when Q*+Qp i s p o s i t i v e . Hours w i t h <10% e r r o r i n B have a h i g h v a l u e o f a.\ because Q*+Qp f o r t h e s e h o u r s i s o n l y j u s t g r e a t e r t h a n z e r o . From t h e f o r e g o i n g i t a p p e a r s t h a t t h e a p p r o p r i a t e t y p e o f e q u a t i o n t o model AQg s h o u l d a l l o w f o r AQg t o e q u a l Q*+Qp when t h e l a t t e r i s n e g a t i v e , and when Q*+Qp- i s p o s i t i v e t h e v a l u e s o f t h e p a r a m e t e r s be s i m i l a r t o t h o s e d e t e r m i n e d when t h e e r r o r i n B i s between <12% and <20% ( s e e T a b l e 5.3). I t s h o u l d be n o t e d t h a t i f i t i s n e c e s s a r y d u r i n g c a l c u l a t i o n s t o s u b t r a c t AQg f r o m Q*+Qp the r e s u l t w i l l a l w a y s be z e r o i f AQg e q u a l s Q*+Qp when t h e l a t t e r i s n e g a t i v e . F o r example, t h i s o c c u r s when c a l c u l a t i n g t h e s e n s i b l e h e a t (Qnfl) and l a t e n t h e a t (QEB) f l u x e s f r o m B. T h i s r e s u l t s i n a l l n o c t u r n a l QJJJJ and Q Eg b e i n g e q u a l t o z e r o . T h e r e f o r e f o r some p u r p o s e s t h e e q u a l i t y AQg - Q*+Qp i s i n a p p r o p r i a t e . I n t h i s s t u d y f o r t h e h o u r s when Q*+Qp i s n e g a t i v e t h e f o l l o w i n g were u s e d : ai=0.98, a2=0.004 and a 3~2.5 ( T a b l e 5.3 A e r r o r s <16% and <17%). 7 5 Table 5.5 Statistical results of comparison between 'measured' and modelled AQg. The 'measured' AQg uses B values with errors of <20X. Equation mf r 2 RMSE MAE d N&S W m-2 W m-2 n A l l hours Objective linear-^ 0. .64 0. ,87 36, .6 25. .1 0. ,91 0. .77 595 HysteresisS 0. ,76 0. ,87 30. ,4 18. ,3 0. ,95 0. ,84 595 Objective hysteresis": Cleugh coeff. 0. .76 0. .87 30. .7 21. .7 0. .95 0. .84 595 Plumes 0. .83 0. 87 36, .8 25. .1 0. .96 0. ,86 285 Sectors 0. ,81 0. ,87 29. ,3 20. .5 0. ,95 0. ,85 595 Q*+Qp (positive) Objective linear-^ 0. ,54 0. ,48 88. .0 66. .8 0. ,69 0. ,25 72 HysteresisS; Q* positive 0. ,62 0. ,61 76. ,1 57. .2 0. ,78 0. ,44 72 Objective hysteresis 0: Cleugh coeff. 0. ,72 0, ,60 70. .2 53, .2 0. .83 0. .52 72 Plumes 0. .69 0. ,50 69, .9 52. .8 0. ,80 0. .47 61 Sectors 0. ,77 0. ,59 66. .8 50. .3 0. .56 0. .56 72 A l l hours: If Q*+Qp negative AQg modelled - Q*+Qp Objective hysteresis": Cleugh coeff. 0. .85 0, .90 26, ,3 11. ,0 0. ,96 0. .88 595 2 km cir c l e 0. .90 0. .90 25, .2 10. .8 0. ,97 0. .89 595 Plumes 0. .85 0. .89 35. .4 25. .1 0. ,96 0. .87 285 Sectors 0. .85 0. ,90 26. .4 11. .1 0. ,96 0. .88 595 A l l hours: If Q*+QF ^ 0 A Q S modelled - 0 . 9 8 ( 0 * 4 % ) + 0 . 0 0 4 dC^ +Qp/dt + 2.5 Objective hysteresis* 1: Cleugh coeff. 0.83 0.90 26.0 10.9 0.96 0.88 595 2 km circl e 0.89 0.90 24.9 10.6 0.97 0.89 595 Plumes 0.88 0.89 33.8 15.9 0.97 0.88 285 Sectors 0.87 0.90 25.1 10.8 0.97 0.89 595 m slope of linear functional relationship between 'measured' & modelled AQg RMSE - root mean square error MAE - mean absolute error d - index of agreement Wilmott and Wicks (1980) N&S - goodness of f i t Nash and Sutcliffe (1970) f - Oke et al, (1981) g - Camuffo and Bernardi - type using Oke & Cleugh (1987) coefficients h - Cleugh (1988) 76 To o b t a i n enough d a t a t o l o o k a t t h e monthly v a r i a t i o n i n t h e h y s t e r e s i s e q u a t i o n c o e f f i c i e n t s i t i s n e c e s s a r y t o use d a t a w i t h <30% and <40% e r r o r i n JJ ( T a b l e 5.4). T h i s means t h a t t h e v a l u e s o f i n d i v i d u a l c o e f f i c i e n t s a r e g r e a t e r t h a n i f d a t a w i t h l e s s e r r o r had been us e d . The c o e f f i c i e n t s f o r Q*+Qp n e g a t i v e a r e v e r y c o n s i s t e n t between months and f o r most p u r p o s e s AQg c o u l d be s e t e q u a l t o Q*+Qp under a l l c o n d i t i o n s . The c o e f f i c i e n t s f o r the h o u r s when Q*+Qp i s p o s i t i v e a r e l e s s c o n s i s t e n t . F o r the J a n u a r y - F e b r u a r y p e r i o d (JD 21-59) t h e r e a r e so few d a t a p o i n t s t h a t the t h r e e p o i n t s added when t h e t h r e s h o l d i s r e l a x e d t o <40% e r r o r change t h e e q u a t i o n q u i t e s u b s t a n t i a l l y . The &\ c o e f f i c i e n t s f o r A p r i l (91-120) and June (152-179) a r e l a r g e r t h a n f o r t h e o t h e r months. There i s no c l e a r t r e n d towards a g r e a t e r p e r c e n t a g e o f Q*+Qp g o i n g i n t o AQg as t h e seasons p r o c e e d towards summer. 5.4 Comparison of Storage heat flux models with 'measured' AQS 5.4.1 The different models AQg was c a l c u l a t e d u s i n g the models o u t l i n e d i n s e c t i o n 5.2 ( o b j e c t i v e l i n e a r ; h y s t e r e s i s ; o b j e c t i v e h y s t e r e s i s ) . The m o d e l l e d f l u x e s were compared w i t h 'measured' AQg (see 5.3) when the e r r o r i n fl was <20%. T a b l e 5.5 summarises the s t a t i s t i c s f o r the v a r i o u s methods when compared a g a i n s t t h e 'measured' AQg. As was n o t e d above, the d a t a s e t i s b i a s e d towards the ho u r s when Q*+Qp i s n e g a t i v e . As was e x p e c t e d t h e performance o f the o b j e c t i v e l i n e a r model was t h e p o o r e s t . Measures o f goodness o f f i t such as the s l o p e o f the l i n e a r f u n c t i o n a l r e l a t i o n s h i p (mf) between the r e s i d u a l s and the m o d e l l e d f l u x (Mark and Church, 1977), the c o r r e l a t i o n c o e f f i c i e n t ( r 2 ) , W i l m o t t and Wicks ' (1980) i n d e x o f agreement ( d ) , and Nash and S u t c l i f f e ' s (1970) "goodness o f f i t " Table 5.4 Monthly v a r i a t i o n i n hysteresis equation c o e f f i c e n t s . a l a2 a3. S.E. n^ -Error in fl < 3 Q » Q*+Qp negative ( l i n e a r ) JD 21-59 0, .81 -2, .9 0. ,72 16. ,1 107 60-90 1. .00 5. .6 0. ,84 10. .2 107 91-120 0. .98 1. ,7 0. ,93 5. ,4 141 121-151 1. .09 8. .6 0. .85 6. .4 136 152-179 1. .06 5. .4 0. ,95 3. .2 89 Q*+Qp negative JD 21-59 0, .80 0. .26 -3. ,8 0. ,74 15. .6 107 60-90 0, .97 0. .17 3, .2 0. ,86 9. .7 107 91-120 141 121-151 1. .15 -0, .14 13, .7 0. .88 5. .7 136 152-179 89 Q*+Ojp positive JD 21-59 0, .39 0, .76 -20, .2 0. ,58 60. .1 15 60-90 0, .31 0, .31 -7, .7 0. .51 47. .6 19 91-120 0. .45 0. .34 -44. ,0 0. .52 76. ,6 46 121-151 0 .39 0. .33 -23, .2 0. .55 68, .5 47 152-179 0. .54 0. .46 -43. .0 0. ,84 51. ,6 41 Error in fl <40X Q*+Qp (all hours) JD 21-59 0. .42 0, .59 -22. .9 0. ,73 27, ,5 138 60-90 0. .41 0, .39 -30, .6 0. ,87 25. .4 147 91-120 0. .46 0, .33 -33, .2 0. .47 41, .4 215 121-151 0, .44 0, .18 -39, .7 0. ,88 38, .8 208 152-179 0. .55 0. .43 -34, .2 0. ,55 32. .6 161 0*+Qp (negative) JD 21-59 0, .81 0. .27 -3, ,7 0. ,76 14. .8 120 60-90 1. .00 0, .18 5. .2 0. ,85 10. .7 119 91-120 0. .98 -0. .01 1. ,7 0. .93 5. .3 146 121-151 1. .14 -0, .13 12, .7 0. ,88 5. ,6 142 152-179 0. .86 0. .16 -10. ,1 0. ,94 3. ,4 96 Q*+Qp (positive) JD 21-59 0. .32 0, .65 -5. ,2 0. ,60 56. ,7 18 60-90 0. .34 0. .37 -7. .8 0. ,58 46. .3 28 91-120 0, .48 0. .35 -40. ,7 0. 57 72. 2 69 121-151 0 .41 0. .19 -25. .9 0. .54 67. ,5 66 152-179 0, .56 0, .44 -38. ,4 0. 85 51. .3 65 b S.E. - standard error (W ra"^) c n - number of data points 7 8 T a b l e 5.5 S t a t i s t i c a l r e s u l t s o f co m p a r i s o n between 'measured' and m o d e l l e d AQg. The 'measured' AQg uses B v a l u e s w i t h e r r o r s o f <20%. E q u a t i o n mf r 2 RMSE W m"2 MAE W nf •2 d N&S n A l l hours O b j e c t i v e l i n e a r - ^ 0. ,64 0.87 36.6 25. .1 0. ,91 0. .77 595 H y s t e r e s i s S 0. ,76 0.87 30.4 18. ,3 0. ,95 0. ,84 595 O b j e c t i v e h y s t e r e s i s " : C l e u g h c o e f f . 0. ,76 0.87 30.7 21. .7 0. ,95 0. ,84 595 Plumes 0, .83 0.87 36.8 25. .1 0, ,96 0, .86 285 S e c t o r s 0. .81 0.87 29.3 20. ,5 0. ,95 0. ,85 595 Q * + Q F (positive) O b j e c t i v e l i n e a r ^ 0. ,54 0.48 88.0 66. ,8 0. ,69 0. .25 72 H y s t e r e s i s S : Q* p o s i t i v e 0, .62 0.61 76.1 57. ,2 0. ,78 0, .44 72 O b j e c t i v e h y s t e r e s i s " : C l e u g h c o e f f . 0. .72 0.60 70.2 53. .2 0. .83 0, .52 72 Plumes 0, .69 0.50 69.9 52. ,8 0. .80 0. .47 61 S e c t o r s 0, .77 0.59 66.8 50. .3 0, .56 0, .56 72 All hours: If Q*+Qp negative AQg modelled - Q * + Q F O b j e c t i v e h y s t e r e s i s * 1 : C l e u g h c o e f f . 0, .85 0.90 26.3 11. ,0 0. ,96 0. .88 595 2 km c i r c l e 0. .90 0.90 25.2 10. .8 0, .97 0, .89 595 Plumes 0. .85 0.89 35.4 25. ,1 0. ,96 0. .87 285 S e c t o r s 0. .85 0.90 26.4 11. .1 0, .96 0, .88 595 A l l hours: If Q*+Qp < 0 AQg modelled - 0 . 9 8 ( 0 * 4 % ) + 0 . 0 0 4 dQ*+Qp/dt + 2.5 O b j e c t i v e h y s t e r e s i s * 1 : C l e u g h c o e f f . 0. .83 0.90 26.0 10. ,9 0. ,96 0. .88 595 2 km c i r c l e 0, .89 0.90 24.9 10. .6 0. .97 0, .89 595 Plumes 0. .88 0.89 33.8 15. ,9 0. .97 0, .88 285 S e c t o r s 0, .87 0.90 25.1 10, .8 0. .97 0, .89 595 m s l o p e o f l i n e a r f u n c t i o n a l r e l a t i o n s h i p between 'measured' & m o d e l l e d AQg RMSE - r o o t mean square e r r o r MAE - mean a b s o l u t e e r r o r d - i n d e x o f agreement W i l m o t t and Wicks (1980) N&S - goodness o f f i t Nash and S u t c l i f f e (1970) f - Oke e t a l . (1981) g - Camuffo and B e r n a r d i - typ e u s i n g Oke & C l e u g h (1987) c o e f f i c i e n t s h - C l e u g h (1988) 79 (N&S) a r e f u r t h e s t f r o m 1.0 o f a l l t h r e e models. A l s o t h e r o o t mean s q u a r e e r r o r (RMSE) and t h e mean a b s o l u t e e r r o r (MAE) a r e t h e l a r g e s t . The h y s t e r e s i s - t y p e models p e r f o r m e d b e t t e r . Of t h e two h y s t e r e s i s m odels, t h e o b j e c t i v e one, where c o e f f i c i e n t s a r e d e t e r m i n e d by t h e p r o p o r t i o n s o f s u r f a c e t y p e s p r e s e n t , p e r f o r m e d b e t t e r t h a n t h e e m p i r i c a l f i t s t o t h e J u l y / A u g u s t 1978 d a t a o f Oke and C l e u g h ( 1 9 8 7 ) . The i n c l u s i o n o f a s e p a r a t e e q u a t i o n f o r t h e h o u r s when Q*+Qp i s n e g a t i v e l e a d s t o an even b e t t e r p e r f o r m a n c e o f t h e o b j e c t i v e h y s t e r e s i s model ( T a b l e 5.5) ( F i g . 5.2a,b). The e q u a l i t y AQg - Q*+Qp i s s a t i s f a c t o r y b u t , as e x p e c t e d , t h e use o f a b e s t f i t e q u a t i o n t o t h e 1987 d a t a l e a d s t o t h e b e s t p e r f o r m a n c e . F o r t h e r e a s o n s o u t l i n e d i n t h e p r e c e d i n g s e c t i o n t h i s f o r m o f e q u a t i o n was u t i l i s e d f o r c a l c u l a t i n g t h e h o u r l y AQg, when Q*+Qp i s l e s s t h a n z e r o , u s e d i n th e r e m a i n d e r o f t h i s r e s e a r c h . F o r t h e h o u r s when Q*+Qp was g r e a t e r t h a n z e r o t h e o b j e c t i v e c o e f f i c i e n t s ( T a b l e 5.2a, n o t e c o e f f i c i e n t s i n T a b l e 5.2b a r e th e mean c o e f f i c i e n t s , see s e c t i o n 5.4.2) w i t h c h a n g i n g l a n d u s e p r o p o r t i o n s were use d . The l a r g e s t AQg f l u x d e n s i t i e s a r e u n d e r e s t i m a t e d by a l l o f t h e models ( F i g . 5.2a,b, 5.3a,b). T h e r e a p p e a r s t o be a ' c a p p i n g ' on t h e m o d e l l e d AQg. The maximum 'measured' AQg « 370 W m"2, whereas t h e maximum m o d e l l e d AQg = 290 W m"2 ( F i g . 5.2b, F i g . 5.3b). Even when t h e f l u x d e n s i t y i s m o d e l l e d w i t h t h e two e q u a t i o n s f i t t e d t o t h e 1987 d a t a ( i . e . c o e f f i c i e n t s f o r when Q*+Qp p o s i t i v e and Q*+Qp i s n e g a t i v e see T a b l e 5.3) t h e m o d e l l e d v a l u e s a r e r e l a t i v e l y l o w ( F i g . 5.3b). T h i s was a l s o s e e n i n t h e r e s u l t s r e p o r t e d by C l e u g h (1988) f o r J u l y - S e p t e m b e r 1986 ( s e e h e r F i g . A 3 . 3 ) . Her maximum 'measured' f l u x i s « 290 W m"2, whereas t h e maximum m o d e l l e d f l u x « 190 W m"2. 8 0 F i g u r e 5.2 R e s i d u a l s v e r s u s m o d e l l e d s t o r a g e h e a t f l u x d e n s i t i e s u s i n g t h e o b j e c t i v e h y s t e r e s i s model and i n c l u d i n g c h a n g i n g s o u r c e a r e a s f o r h o u r s when plumes c o u l d be i d e n t i f i e d : ( a ) a l l h o u r s e q u a t i o n (b) e q u a t i o n u s i n g AQg = Q* + Qp when Q* + Qp i s n e g a t i v e . ( a ) -100 0 100 200 300 400 AQg (W mr2) Residuals -100 0 100 200 300 400 AQg (W m"2) Residuals 81 F i g u r e 5.3 M o d e l l e d v e r s u s 'measured' s t o r a g e h e a t f l u x d e n s i t y w i t h B < 20% e r r o r : ( a ) u s i n g C l e u g h (1988) c o e f f i c i e n t s (b) u s i n g b e s t - f i t c o e f f i c i e n t s f o r 1987 d a t a and s e p a r a t e e q u a t i o n s f o r Q* + Qp n e g a t i v e o r p o s i t i v e . ( a ) 4 0 0 3 0 0 oo 3 •O o s e 3 < - 1 0 0 1 0 0 2 0 0 AQS (W m"2) Residuals - 1 0 0 1 0 0 2 0 0 3 0 0 AQg (W m"2) Residuals 4 0 0 8 2 5.4.2 Influence of land use description I n t h i s s e c t i o n t h e i n f l u e n c e o f u s i n g a s t a t i c o r dynamic s u r f a c e d e s c r i p t i o n i n the o b j e c t i v e h y s t e r e s i s model i s d i s c u s s e d . T a b l e 5.1 g i v e s the mean and range o f t h e l a n d use p r o p o r t i o n s d u r i n g t h e s t u d y p e r i o d . The 'measured' AQg h o u r s have s i m i l a r mean p r o p o r t i o n s t o t h e whole s t u d y p e r i o d . The p r o p o r t i o n s o f t h e s u r f a c e l a n d use w h i c h a r e p r e s e n t i n t he 2 km r a d i u s c i r c l e a r e a l s o v e r y s i m i l a r t o the mean when t h e s o u r c e a r e a s a r e t a k e n i n t o a c c o u n t . The maximum p e r c e n t a g e d i f f e r e n c e between the mean o f t h e v a r i o u s t e c h n i q u e s i s 2% f o r any p a r t i c u l a r l a n d use t y p e . T a b l e 5.2 a l s o i n c l u d e s t h e maximum and minimum f o r a l l the h o u r s i n t h e s t u d y p e r i o d f o r each s u r f a c e t y p e . The maximum v a r i a b i l i t y o c c u r s i n the gr e e n s p a c e s u r f a c e t y p e , w i t h a range ~ 40% ( p l u r a e s ) ( s e e F i g . 3.10). The range o f t h e o t h e r t h r e e s u r f a c e t y p e s i s a p p r o x i m a t e l y 20% ( p l u m e s ) . The maximum and minimum v a l u e s o f t h e c o e f f i c i e n t s o f the AQg model a r e a s s o c i a t e d w i t h the extremes i n l a n d u s e s , as would be e x p e c t e d (see T a b l e 5.2). The a^ and a 3 c o e f f i c i e n t s a r e s i m i l a r f o r g r e e n s p a c e , r o o f s , and canyon. The a 2 a r e s i m i l a r f o r g r e e n s p a c e , r o o f s and i m p e r v i o u s s u r f a c e t y p e s . The maximum (0.41) and minimum (0.36) v a l u e s o f a^ o c c u r when t h e pavement p r o p o r t i o n i s a t i t s maximum and minimum r e s p e c t i v e l y . The maximum a 2 (0.33) and the minimum a b s o l u t e v a l u e o f a 3 (26.9) a r e a s s o c i a t e d w i t h the maximum v e g e t a t i o n and minimum w a l l a r e a . The minimum a 2 (0.25) i s a s s o c i a t e d w i t h the maximum w a l l a r e a . The maximum a b s o l u t e v a l u e o f a 3 (32.1) o c c u r s when the pavement i s a t the maximum. The o b j e c t i v e model i s c o n s e r v a t i v e w i t h r e s p e c t t o changes i n p r o p o r t i o n s o f s u r f a c e s p r e s e n t . T a b l e 5.2 p r e s e n t s the mean e q u a t i o n s when t h e t u r b u l e n t s o u r c e a r e a s a r e u s e d t o d e t e r m i n e the s u r f a c e p r o p o r t i o n s f o r the models. The e q u a t i o n s v a r y v e r y l i t t l e , and as was n o t e d above, the extremes a r e a l s o n o t 8 3 v e r y l a r g e when t h e v a r y i n g s o u r c e a r e a s a r e t a k e n i n t o a c c o u n t . The mean e q u a t i o n s f o r t h e s o u r c e a r e a s and t h e e q u a t i o n f o r t h e f i x e d 2 km r a d i u s c i r c l e a r e a l l v i r t u a l l y t h e same. The c o e f f i c i e n t s a r e v e r y s i m i l a r t o t h o s e d e t e r m i n e d as t h e b e s t f i t when Q*+QF i s p o s i t i v e and fl has an e r r o r of 12-20% ( T a b l e 5.3). When the s u r f a c e d e s c r i b e d by t h e mean f o r the 2 km c i r c l e ( t h i s s t u d y ) and d e s c r i p t i o n i s a l l o w e d t o v a r y due t o change i n s o u r c e a r e a t h e r e i s some v a r i a b i l i t y b u t on the whole v e r y c l o s e agreement between t h e m o d e l l e d f l u x e s . The v a r i a t i o n i s p r o b a b l y s m a l l e r t h a n t h e d e v i a t i o n f r o m the ' t r u e ' AQg. T h e r e f o r e i f one i s n o t i n t e r e s t e d i n h o u r - t o - h o u r v a r i a b i l i t y t h e use o f a mean s u r f a c e d e s c r i p t i o n s h o u l d be s a t i s f a c t o r y . U s i n g the d a t a b a s e i t i s p o s s i b l e t o c a l c u l a t e the s i z e o f the s t o r a g e h e a t f l u x d e n s i t y f o r each g r i d square f o r any hour o r any energy c o n d i t i o n s . F i g u r e s 5.4a,b a r e maps o f AQg when the e r r o r i n B <16 % f o r the ensemble h o u r s 0800 (Q*+Q F=30 W m'2, d(Q*+Q F)/dt=107 W m - 2) and 1200 LAT (Q*+Q F=550 W m"2, d(Q*+Q F)/dt=55 W m" 2), r e s p e c t i v e l y . AQg ranged from -9 W m"2 t o 29 W m"2 a t 0800 LAT and from 151 t o 292 W m - 2 a t 1200 LAT. The p a r k s have the h i g h e s t AQg (compare F i g . 5.4a w i t h F i g . 3.9) a t 0800 LAT. A t midday the r o a d p a t t e r n i s e v i d e n t (compare F i g . 5.4b w i t h F i g . 3.8). T h i s f i g u r e d e m o n s t r a t e s the i n f l u e n c e o f b o t h the l a n d use and the t h r e e c o e f f i c i e n t s . The g r i d s q u a r e s w h i c h have the l a r g e s t f l u x a r e not the same a t b o t h t i m e s , a l t h o u g h t h o s e w i t h the s m a l l e s t f l u x e s a r e s i m i l a r . T h i s i n d i c a t e s t h a t c o n s i d e r a t i o n o f the s o u r c e a r e a f o r some s i t e s may be more c r i t i c a l t h a n would appear t o be t h e case a t the p r e s e n t s t u d y s i t e . Changing the s u r f a c e t y p e s i n f l u e n c e s the c a l c u l a t e d AQg i n a d i f f e r e n t manner t h r o u g h the day because o f the c h a n g i n g w e i g h t i n g of the a^ and a 2 c o e f f i c i e n t s . F i g u r e 5.4 Map o f s t o r a g e heat f l u x f o r : (a) ensemble 800 LAT (b) ensemble 1200 LAT (see t e x t f o r f u l l d e t a i l s ) 8 5 5 . 4 Discussion This study i s one of the f i r s t to consider storage heat f l u x during non summertime conditions. It i s encouraging that the objective hysteresis AQg model, previously only used i n the summer, performs so well. A p p l i c a t i o n of the model taking into account the varying source areas suggests that (unless the surrounding s i t e i s extremely heterogeneous) the model can be applied using only a mean areal determination of the surface d e s c r i p t i o n . The parameterization i s conservative with respect to changes i n the proportions of land use. In t h i s study the changing source areas were taken into account. The objective hysteresis model does not include the 3-dimensional character of vegetation. Since the model i s performing s a t i s f a c t o r i l y i t seems that t h i s can continued to be ignored. The area of vegetation, excluding grass, i s small compared to the proportions of other surface types i n the Sunset study area (Chapter 3). There have been d e t a i l e d studies of the storage heat f l u x f or a young eucalyptus f o r e s t (Aston, 1985), mixed f o r e s t (McCaughey, 1985) and Amazonian t r o p i c a l f o r e s t (Moore and Fisch, 1986) but there are no data av a i l a b l e f or the storage heat f l u x of i n d i v i d u a l trees and bushes. Determination of the hysteresis equation c o e f f i c i e n t s from the data presented i n these publications suggest extremely small proportions of net r a d i a t i o n going into storage. From the Aston (1985) data a^=0.0004, a2=0.18 and a3=3.9; for the McCaughey (1985) data a]_=0.11, a2=0.11 and a3=-12.3 ( i t i s not possible to use the Moore and F i s c h (1986) data). These equations are probably not appropriate for i n c l u s i o n i n the objective model because i n an urban area i n d i v i d u a l trees/bushes have a greater solar r a d i a t i o n load over the whole plant; i n p a r t i c u l a r the trunk, stem and branches rather than just the crown. The s i g n i f i c a n c e of heat storage i n the seasonal energy balance i s discussed i n Chapter 6. 8 6 CHAPTER 6 URBAN ENERGY BALANCE 6.1 Introduction The s u r f a c e e n e r g y b a l a n c e o f an e x t e n s i v e u r b a n i s e d s u r f a c e may be w r i t t e n : Q* + Q F = Q H + Q E + AQg + AQ A ( 6 . 1 ) where Q* - n e t a l l - w a v e r a d i a t i o n f l u x d e n s i t y (W m" 2); Qp - a n t h r o p o g e n i c h e a t f l u x d e n s i t y (W m" 2); Q H - s e n s i b l e h e a t f l u x d e n s i t y (W m" 2); Qp - l a t e n t h e a t f l u x d e n s i t y (W m" 2); AQg - n e t h e a t s t o r a g e (W m" 2)' and AQ A - n e t h e a t a d v e c t i o n (W m" 2). The p r e c e d i n g c h a p t e r s have o u t l i n e d t h e measurement programme and t h e methods t o c a l c u l a t e i n d i v i d u a l f l u x e s , e x c l u d i n g l a t e n t h e a t . I n t h i s c h a p t e r t h e r e s u l t s o f t h e p r e v i o u s c h a p t e r s a r e us e d t o o b t a i n h o u r l y l a t e n t h e a t f l u x e s and e n e r g y b a l a n c e s . These r e s u l t s a r e t h e f i r s t e x t e n d e d (more t h a n one o r two d a y s ) measured u r b a n b a l a n c e s f o r w i n t e r and s p r i n g c o n d i t i o n s . 6.2 Determination of hourly energy balances When models, r a t h e r t h a n measurements, were u s e d t o d e t e r m i n e a f l u x t h e so u r c e a r e a o f t h e a s s o c i a t e d t u r b u l e n t f l u x e s were t a k e n i n t o a c c o u n t , u s i n g t h e method o u t l i n e d i n C h a p t e r 3, t o e n s u r e t h a t t h e ene r g y b a l a n c e was c o n s i s t e n t f o r t h e h o u r . As was n o t e d i n C h a p t e r 3, i t was n o t p o s s i b l e t o c a l c u l a t e t h e s o u r c e a r e a u s i n g t h e Schmid model f o r a l l h o u r s o f t h e s t u d y p e r i o d , due t o t h e absence o f Q^ measurements. On t h o s e o c c a s i o n s ' s e c t o r s ' r a t h e r t h a n 'plumes' were u s e d t o d e s c r i b e t h e s o u r c e a r e a l o c a t i o n s and t o a c c e s s t h e s u r f a c e d a t a b a s e t o o b t a i n t h e a p p r o p r i a t e s u r f a c e d e s c r i p t i o n . The methods u s e d t o d e t e r m i n e e a c h o f t h e f l u x e s a r e as f o l l o w s : 1) Q* - d i r e c t l y measured as d e s c r i b e d i n C h a p t e r 2. 2) Qp - c a l c u l a t e d u s i n g t h e method d e s c r i b e d i n C h a p t e r 4. 3) AQg - c a l c u l a t e d u s i n g t h e o b j e c t i v e h y s t e r e s i s model o u t l i n e d i n C h a p t e r 8 7 5. The model used was the version with a separate equation f o r the hours when Q*+Qp i s le s s than zero (a^=0.98, a2=0.004, a3=2.5), and which took into account varying source areas. 4) Qpj - determined using one of two methods. If Q^s was ava i l a b l e from the eddy c o r r e l a t i o n measurement (see Chapter 2) i t was used. Otherwise, the measured Bowen r a t i o (B) was used to cal c u l a t e Q^ B : Q H f l - B (Q* + Q F - AQs) (6.2) 1 + fl If the r e s u l t i n g Q^g and late n t heat fluxes (Q E B) were r e a l i s t i c and the error i n Qpjjj and Qg B were l e s s than 30%; or i f the absolute size of both fluxes were le s s than 20 W m-2, then the calculated fluxes were used. 5) Qg - t h i s was dependent on the method used to determine Qpj. If Q^g was ava i l a b l e then Qg was determined as a re s i d u a l ( Q E R ) : Q E R " Q * + Q F " AQS - Q H S (6.3) When Q H S was not ava i l a b l e then QEJJ was calculated: QEB - (Q* + Q F - AQs) (6.4) 1 + fl The hours when t h i s was used are the same as those f o r Qnfl-6) AQ A - omitted on the basis of Steyn's (1985) analysis of data from the same tower. He showed that energy residuals from over-determined balances are zero i n the mean, and are unrelated to wind speed or d i r e c t i o n . This strongly suggests that the s i t e i s not characterised by systematic l o c a l scale advec-t i o n . This conclusion i s further supported by the small s p a t i a l v a r i a b i l i t y found by Schmid (1988) when comparing eddy c o r r e l a t i o n measurements of Qpj measured on the Sunset tower with those from a mobile tower operated at several s i t e s within a 2 km radius. The reason f o r choosing to accept Q^s f i r s t rather than following a procedure of determining an optimum energy balance, such as that suggested by 88 Steyn (1985), i s based on the expectation that t h i s procedure w i l l produce the smallest error i n the turbulent fluxes (see Chapter 2 and Appendix I I I ) . A comparison was conducted between the turbulent sensible heat f l u x d e n s i t i e s determined from the SAT (Q H S) a n c * t n e RTDMS ( Q H B ) • There were only 8 hours when Qpjg was measured and the error i n Q ^ J J was l e s s than 10% (Table. 6.1, Fi g . 6.1) but these, except for one point, p l o t on the one-to-one l i n e . Figures 6.1b-d show that as the error i n Q^fi increases the number of extreme o u t l i e r s does not increase; i . e . they are present at <20% error. At <100% error there i s noticeable i n c l u s i o n of values close to zero; i n p a r t i c u l a r are c a l c u l a t e d as almost equal to zero, whereas for the same hours Q^ s have a greater range. These r e s u l t s are s i m i l a r to those reported by Cleugh and Oke (1986) f o r a r u r a l s i t e . They f i n d a best f i t l i n e of Q H J J = 0.96Q H S +24.8 with an r 2 of 0.74 and a RMSE of 34.1 W m"2 (n=69). There were 2324 hours with Q^g data and an a d d i t i o n a l 788 hours when A was measured and the fluxes met the conditions outlined above. Therefore i t was possible to determine the energy balance for 3112 of the 3795 hours during the period JD 21-179, 1987. AQg was calculated f or most of the 3779 hours with Q* data. For these hours i t i s possible to c a l c u l a t e the t o t a l turbulent energy ( Q H + Q E) by d i f f e r e n c e . 6.3 Measured hourly energy balance, 1987 The ensemble hourly energy balances were calculated for each month and for the en t i r e measurement period (Table 6.2, 6.3, Figure 6.2). The hours included are only those for which a l l fluxes of the budget were determined. For p r a c t i c a l reasons t h i s means the data set i s biased s l i g h t l y towards conditions with high r a d i a t i v e input ( d r i e r weather). This can be seen by comparing Table 6.2a (energy balance hours-only) with Table 6.2c ( a l l hours T a b l e 6 . 1 Comparison o f Q^g and Q ^ J J (W m"^) w i t h v a r y i n g e r r o r s i n l i . % e r r o r n Q H J J Q H S RMSE MAE mf r i n Ji Mean sd Mean sd <10% 8 3 2 , . 2 3 5 , . 9 3 5 , . 4 5 2 , . 6 2 3 . 4 1 3 . . 7 0 , . 6 9 0 . . 8 7 <20% 4 9 9 1 7 0 , . 2 9 3 . . 7 1 3 9 , . 9 8 8 , . 9 6 8 , . 1 5 2 . . 0 1 . . 3 4 0 . , 5 8 <30% 6 8 3 1 4 9 , . 3 9 4 , . 8 1 2 2 . 9 7 2 , . 1 6 7 . . 0 7 2 . . 1 1 . . 3 1 0 . , 5 8 <40% 7 7 7 1 3 6 , , 8 9 6 . , 5 1 1 4 , . 2 7 4 . . 0 6 4 . . 9 4 7 , . 5 1 . . 3 0 0 . , 6 0 <50% 8 4 6 1 2 8 , . 8 9 7 , . 4 1 0 7 , . 6 7 5 , . 2 6 3 . 1 4 5 . . 7 1 . . 3 0 0 . , 6 3 <60% 8 9 0 1 2 3 . , 5 9 8 . , 2 1 0 3 . . 7 7 6 , . 0 6 2 , . 2 4 4 . . 6 1 . . 2 9 0 . , 6 4 <70% 9 4 8 1 1 7 , . 2 9 9 . . 3 9 8 , . 5 7 6 . . 8 6 1 , . 0 4 3 . . 2 1 . . 2 9 0 . . 6 6 <80% 9 9 1 1 1 2 . , 8 9 9 . , 5 9 5 . .2 7 7 . . 1 6 0 , . 0 4 2 , . 2 1 . , 2 8 0 . 6 7 <90% 1 0 3 3 1 0 8 . . 6 9 9 . , 7 9 2 . . 3 7 7 . , 5 5 9 , . 6 4 1 , . 7 1 . . 2 8 0 . 6 7 <100% 1 0 7 9 ' 1 0 4 . , 1 9 9 . 9 8 8 . , 9 7 7 . . 9 5 9 . . 0 4 0 . . 9 1 . , 2 7 0 . 6 8 n - number o f ho u r s sd - s t a n d a r d d e v i a t i o n RMSE - r o o t mean square e r r o r MAE - mean a b s o l u t e e r r o r mf - s l o p e o f l i n e a r f u n c t i o n a l r e l a t i o n s h i p (Mark and Church, 1 9 7 7 ) 9 0 F i g u r e 6.1 C o m p a r i s o n o f QJJ d e t e r m i n e d u s i n g eddy c o r r e l a t i o n ( S A T ) and Bowen R a t i o - e n e r g y b a l a n c e methods: (a) < 10% e r r o r i n B (b) < 20% e r r o r i n B ( c ) < 30% e r r o r i n fl (d) < 100% e r r o r i n fl (a) (b) 500 400 C N 300 I S3 200 100 (c) 1:1/ 100 200 300 100 200 300 Q H S ( W M _ 2 ) Q H S (W m-2) Cd) 500 -400 300 6 I3 m Si 200 100 "•ft*- * a. 0 100 200 300 Q H S ( W m-2) 0 100 200 300 Q H S (W m-2) 9 1 Table 6.2 Mean d a i l y (24 hours) energy balance components for the whole measurement period and by month, 1987. Ensemble averages f o r : (a) mean fluxes (W m"2) for energy balance hours (b) r a t i o s of f l u x to av a i l a b l e energy f o r energy balance hours (c) mean fluxes (W m"2) and r a t i o s f o r a l l hours with net r a d i a t i o n data. (a) Q * Q F A Q S Q H Q E * of hours usable JD 21-179 94.3 8.3 12.4 48.1 42.2 82.0 21-59 22.1 9.0 -9.6 15.9 24.8 75.5 60-90 77.0 8.9 7.1 42.5 36.4 74.1 91-120 89.0 8.3 9.8 40.6 46.9 91.5 121-151 133.3 7.6 23.8 66.7 50.4 82.8 152-179 139.6 7.6 25.7 72.3 49.2 92.9 (b) Q* 9F AQs Q H Q E fl Q * + Q F Q * + Q F Q * + Q F Q * + Q F Q * + Q F JD 21-179 .92 .08 .12 .47 .41 1.14 21-59 .71 .29 - .31 .51 .80 0.64 60-90 .90 .10 .08 .49 .42 1.17 91-120 .91 .09 .11 .42 .48 0.87 121-151 .95 .05 ••17 .47 .36 1.32 152-179 .95 .05 .17 .49 .33 1.47 (c) Q * Q F A Q s Q* Q F AQs Q * + Q F Q * + Q F Q * + Q F JD 21-179 76.0 8.4 6.0 0.90 0.10 0.07 21-31 1.3 9.4 -13.2 0.12 0.88 -1.23 32-59 14.8 9.1 -13.4 0.62 0.38 -0.56 21-59 10.9 9.2 -13.5 0.54 0.46 -0.67 60-90 51.0 8.9 -2.1 0.85 0.15 -0.04 90-120 86.4 8.3 8.8 0.91 0.09 0.09 121-151 121.3 7.7 20.2 0.94 0.06 0.16 152-179 134. 3 7.6 24.0 0.95 0.05 0.17 Figure 6.2 Ensemble average energy balance plots. 92 (a) JD 21-179, 1987 (b) JD 21-59, 1987 600 = 1 I : - A Of (c) JD 60-90. 1987 (d) JD 91-120, 1987 9 3 T a b l e 6.3 Daytime (Q*>0) energy b a l a n c e f l u x e s and r a t i o s o f f l u x e s t o a v a i l a b l e e nergy f o r t h e whole measurement p e r i o d and by month, 1987. The f l u x e s a r e c a l c u l a t e d from h o u r l y ensemble a v e r a g e s f o r each time p e r i o d , (a) Energy b a l a n c e f l u x e s (MJ m"~ d'^) (b) r a t i o s A l s o i n c l u d e d a r e r e s u l t s f r o m t h e same s i t e f o r two summer p e r i o d s i n 1980 and 1983 (see t e x t ) . (a) Q* Q F AQs Q H Q E n JD 21-179 10.18 0.48 2.79 4.19 3.68 12 21-59 3.98 0.52 1.14 2.29 3.07 8 60-90 8.91 0.43 2 . 39 3.86 3.10 10 91-120 9.84 0.48 2.61 3.62 4.10 12 121-151 13.81 0.47 4.04 5.65 4. 59 13 152-179 14.25 0.48 4. 24 6.09 4.40 13 1983 a 199-265 13.81 3.04 6.04 4.73 13 1980 b J u l y - m i d Aug. 13.86 1.99 1.23 3.86 (b) Q * Q F AQs Q H Q E li Q * + Q F Q * + Q F Q * + Q F Q * + Q F Q * + Q F JD 21-179 .96 .04 .26 . 39 .34 1.14 21-59 .92 .08 .17 .35 .47 0.74 60-90 .95 .05 .26 .41 .33 1.24 ' 91-120 .95 .05 .25 .35 .40 0.88 121-151 .97 .03 .28 .40 .32 1.23 152-179 .97 .03 .29 .41 .30 1.38 1983 a 199-265 .22 .44 .34 1.28 1980 b J u l y - m i d Aug. . 23 .11 .67 0.16 a C l e u g h and Oke (1986) - 30 days d u r i n g t h i s t ime p e r i o d - Qp n o t i n c l u d e d i n energy budget - daytime h o u r s assumed t o be 13 b Oke and McCaughey (1983) - 19 days d u r i n g t h i s t ime p e r i o d - Qp n o t i n c l u d e d i n energy budget n - number o f da y t i m e hours 9 4 with r a d i a t i o n data). The r a t i o s reported i n Table 6.2b ( d a i l y - 24 hours) and Table 6.3b (daytime - Q*>0) allow a comparison of the r e l a t i v e importance of i n d i v i d u a l fluxes i n the energy balance between months. Included i n Table 6.3 are the r e s u l t s of measurements conducted at the same s i t e as t h i s study by Oke and McCaughey (1983), and Cleugh and Oke (1986) i n the summers of 1980 and 1983, resp e c t i v e l y . In both studies Q* was measured i n the same manner as here but Qp was not included i n the energy balance. (Note therefore that r a t i o s include only Q*). Oke and McCaughey (1983) measured fl using a reversing d i f f e r e n t i a l psychrometer system d i f f e r e n t to that used i n t h i s study, see Kalanda et a l . (1980) f o r f u l l d e t a i l s . They used the objective l i n e a r storage heat f l u x parameterization (see section 5.2.1) to obtain AQg together with fl to cal c u l a t e Q^ and Qg. Cleugh and Oke (1986) also used the objective l i n e a r storage scheme and Qj^  was measured using a SAT leaving Qg as a residual i n the energy balance. The difference i n methods, e s p e c i a l l y considering t h e i r dependence on AQg and the r e s u l t s i n Chapter 5, suggest that the r e s u l t s should be compared with caution. The only fluxes d i r e c t l y comparable with the present r e s u l t s are Q*, and Qp^  f o r 1983. As expected, Qp decreases i n s i g n i f i c a n c e and size as Q* increases from winter to summer (Table 6.2, 6.3). The r e l a t i v e importance i s greater f or the whole day (Table 6.2) than f or the daytime hours (Table 6.3). In the daytime hours i t i s les s than 10% of the energy input (Q*+Qp) for a l l months. When the whole day i s considered Qp makes a larger than 10% contribution to the energy balance up u n t i l A p r i l . Therefore i t probably can be considered n e g l i g i b l e or can be ignored only i f research i s being conducted for daytime hours, or i f the whole day i s under consideration i n a non-wintertime study. It i s probably only necessary to pay close attention to the diurnal v a r i a b i l i t y i f a winter-9 5 time s t u d y i s b e i n g c o n d u c t e d . The 1 9 8 7 d a y t i m e AQ S/(Q*+Qp) r a t i o i n c r e a s e s from 0 . 1 7 t o 0 . 2 9 as Q* i n c r e a s e s ( T a b l e 6 . 3 ) . The 1 9 8 7 r a t i o s a r e h i g h e r t h a n f o r the two summertime s t u d i e s , e x c e p t f o r J a n u a r y / F e b r u a r y , b u t o f c o u r s e a d i f f e r e n t method was used i n 1 9 8 7 . There i s a n e t g a i n i n AQg f o r each month e x c e p t J a n u a r y -F e b r u a r y . I t i s r e l e v a n t t o e n q u i r e whether t h i s p a t t e r n makes sense i n r e l a t i o n , t o the a n n u a l s t o r a g e i n p u t / o u t p u t regime. T h i s was checked u s i n g Q* d a t a c o l l e c t e d a t a suburban s i t e ( K e r r i s d a l e ) 8 km t o t h e west of the Sunset s i t e i n 1 9 8 2 (Grimmond, 1 9 8 3 ) and t h e o b j e c t i v e h y s t e r e s i s s t o r a g e h e a t f l u x model ( w i t h s e p a r a t e e q u a t i o n s f o r d a y t i m e and n i g h t t i m e ) . T a b l e 6 . 4 shows t h a t a t K e r r i s d a l e t h e r e a r e 5 months o f n e t s t o r a g e h e a t l o s s ; March and O c t o b e r a r e the t r a n s i t i o n months between n e t g a i n and n e t l o s s ; and the peak g a i n o c c u r s i n June. U s i n g t h i s model i t i s c a l c u l a t e d t h a t i n 1 9 8 2 t h e r e was a s m a l l n e t g a i n i n AQg. I d e a l l y t h e r e s h o u l d be z e r o n e t h e a t s t o r a g e o v e r the a n n u a l p e r i o d , but the r e s u l t i s c o n s i d e r e d s a t i s f a c t o r y . The d a i l y ( T a b l e 6 . 2 ) and d a y t i m e ( T a b l e 6 . 3 ) f l u x i n c r e a s e s w i t h i n c r e a s i n g Q*. The monthly mean d a i l y r a t i o v a r i e s between 0 . 4 2 and 0 . 5 1 but does n o t show a d i s t i n c t s e a s o n a l t r e n d . The d a y t i m e r a t i o s v a r y between 0 . 3 5 and 0 . 4 1 . When Qp i s e x c l u d e d from the r a t i o the June r a t i o o f 0 . 4 3 i s v e r y s i m i l a r t o t h e 1 9 8 3 summertime r a t i o o f 0 . 4 4 . The May 1 9 8 7 d a t a had the same mean day t i m e Q* as the 1 9 8 3 d a t a . The Q H / Q * r a t i o f o r 1 9 8 3 was 0 . 4 4 and f o r May 1 9 8 7 was 0 . 4 1 . The 1 9 8 7 d a t a seem t o be more l i k e t h e 1 9 8 3 d a t a s e t t h a n t h a t f o r 1 9 8 0 . Qg, g e n e r a l l y , i n c r e a s e s w i t h i n c r e a s i n g Q*. However, the d a y t i m e and d a i l y Qg i n June 1 9 8 7 was l e s s t h a n f o r May. T h i s r e s u l t e d i n a s l i g h t l y l o w e r p r o p o r t i o n o f Q*+Qp g o i n g i n t o Qp. The t r e n d o f the mean monthly d a i l y Q E / ( Q * + Q F ) r a t i o shows a d e c r e a s e from 0 . 8 0 i n J a n u a r y / F e b r u a r y t o 0 . 3 3 i n 96 T a b l e 6.4 Mean d a i l y Q* and AQg by month f o r K e r r i s d a l e , Vancouver 1982 Q* W m" W m" W m~ 1982 JD 22-31+ b -0. .7 9 .4 -18, .9 31-59 20 .2 9 .1 -12, .2 60-90 54, .2 8 .9 0. .9 91-120 102, .9 8 .3 18, .1 121-151 134, .1 7 .7 28, .7 152-181 144, .3 7 .6 32, .7 182-212 123, .6 7. .6 26, .2 213-243 103, .6 7 .7 17. .7 244-273 66. .6 8, .3 4. ,4 274-304 30, .6 8, .9 -5. .2 305-334 3. ,7 9, .1 -18. ,2 335-365 -7. ,3 9, .4 -20. ,2 Year 64. 9 8. ,5 4. ,6 a Qp mean v a l u e s f r o m 1987 d a t a (see T a b l e 6.3). Assuming t h a t the f l u x i s s i m i l a r f o r the two a r e a s and y e a r s ; and t h a t the f l u x i s s y m m e t r i c a l i n t h e y e a r around June. b The J a n u a r y p e r i o d was measured i n two p a r t s : JD 22-31, 1982 and 1-21, 1983. 9 7 June. I n the w i n t e r t i m e t h i s may be due t o t h e c o m b i n a t i o n o f f r e q u e n t r a i n e v e n t s and s m a l l r a d i a t i o n i n p u t . Under s u c h c o n d i t i o n s the energy goes i n t o d r y i n g t h e s u r f a c e f i r s t . The d a y t i m e Qg/Q* r a t i o s do n o t show as pronounced a t r e n d . The 1983 r a t i o was 0.34 and t h o s e f o r May and June 1987 a r e 0.33 and 0.31 r e s p e c t i v e l y . June 1987 had low r a i n f a l l (see T a b l e 2.2), w i t h r a i n b e i n g r e c o r d e d on o n l y 6 days. The mean d a i l y Ji ( c a l c u l a t e d f r o m ensemble Qpj and Qg f l u x e s ) v a r i e s between 0.64 and 1.47 w i t h a mean f o r the measurement p e r i o d of 1.14. The daytime mean f o r t h e measurement p e r i o d i s the same w i t h a range o f 0.74 t o 1.38. There i s no d i s t i n c t t r e n d w i t h season. J a n u a r y / F e b r u a r y and A p r i l fl v a l u e s a r e l e s s t h a n 1.00. The 1983 summertime fl f a l l s between the May and June 1987 d a t a . The 1987 mean o f 1.14 i s c l o s e t o the t y p i c a l v a l u e o f 1.00 g i v e n by Oke (1982) f o r s u b u r b a n a r e a s . The d a i l y t r e n d s f o r the mean monthly f l u x e s a r e shown i n F i g u r e 6.2. The d a t a f o r t h e whole measurement p e r i o d ( F i g . 6.2a) show t h a t Qpj, Qg, and AQg f o l l o w a v e r y s i m i l a r p a t h u n t i l about 1200 LAT. I n t h e a f t e r n o o n Q^ i s g r e a t e r t h a n Qg w h i c h i n t u r n i s g r e a t e r t h a n AQg. Qp[ goes t h r o u g h z e r o a f t e r Q*, Qg a t a p p r o x i m a t e l y the same time as Q*, and AQg about an hour e a r l i e r . From F i g u r e 6.2 i t can be seen t h a t Qg i s an i m p o r t a n t term i n the energy b a l a n c e i n a l l months. I n p a r t i c u l a r , i t i s the dominant o u t p u t f l u x i n the J a n u a r y / F e b r u a r y p e r i o d . The d i u r n a l t r e n d o f the ensemble energy b a l a n c e s f o r March t o June a r e r e m a r k a b l y s i m i l a r i n form. The t h r e e o u t p u t f l u x e s a r e v e r y s i m i l a r b e f o r e s o l a r noon. T h i s i s d i f f e r e n t t h a n the summertime energy b a l a n c e s r e p o r t e d by C l e u g h and Oke (1986) and i s p r o b a b l y i n l a r g e p a r t due t o the i n c l u s i o n o f the h y s t e r e s i s t y p e s t o r a g e heat f l u x f u n c t i o n compared t o the l i n e a r one t h e y used. T h i s d e m o n s t r a t e s t h e i m p o r t a n c e o f the s t o r a g e p a r a m e t e r i z a t i o n , as i t i n f l u e n c e s the a p p a r e n t s i z e o f Qg u n l e s s Qg i s 9 8 d e t e r m i n e d i n d e p e n d e n t l y . The ensemble p l o t s , e x c e p t f o r J a n u a r y / F e b r u a r y , a r e g e n e r a l l y s i m i l a r t o t h o s e o f t h e C l e u g h and Oke s t u d y i n t h e a f t e r n o o n w i t h QH t h e l a r g e s t f l u x , t h e n Qg and t h e n AQg. T h i s s u g g e s t s t h a t t h e r e l a t i v e i m p o r t a n c e o f the f l u x e s remains s i m i l a r t h r o u g h the s p r i n g and summer. However, t h e w i n t e r may show the g r e a t e s t d i f f e r e n c e as n o t e d above. F u r t h e r w i n t e r measurements a r e needed t o document t h i s . The e v a p o r a t i v e f l u x e s c a l c u l a t e d h e r e a r e used i n C h a p t e r 8 f o r c o m p a r i s o n w i t h m o d e l l e d f l u x e s . 9 9 CHAPTER 7 RESISTANCES, DRAINAGE AND STORAGE CAPACITY 7.1 Introduction I n t h i s c h a p t e r t h e t h r e e r e m a i n i n g sub-models o f t h e m o d i f i e d Penman-M o n t e i t h - R u t t e r - S h u t t l e w o r t h e v a p o t r a n s p i r a t i o n - i n t e r c e p t i o n model a r e p r e s e n t e d . The models a r e f o r aerodynamic r e s i s t a n c e ( r a ) , s u r f a c e r e s i s t a n c e ( r g ) , and d r a i n a g e ( D ) . The f i r s t two a r e u s e d w i t h t h e Penman-Monteith e v a p o t r a n s p i r a t i o n e q u a t i o n , and t h e t h i r d i s us e d i n t h e c a l c u l a t i o n o f t h e r u n n i n g w a t e r b a l a n c e o f t h e s u r f a c e w a t e r s t o r e ( s e e C h a p t e r 1 ) . 7.2 Aerodynamic resistance A f t e r t h e i n p u t o f e n e r g y , t h e most i m p o r t a n t f a c t o r g o v e r n i n g t h e r a t e o f e v a p o r a t i o n i s t h e e f f i c i e n c y o f re m o v a l o f w a t e r v a p o u r f r o m t h e s u r f a c e ( S t e w a r t , 1984). F o r a g i v e n w i n d speed and vap o u r p r e s s u r e t h e r a t e o f removal o f w a t e r v a p o u r depends on t h e a t m o s p h e r i c t u r b u l e n c e c r e a t e d by t h e win d b l o w i n g o v e r t h e s u r f a c e r o u g h n e s s e l e m e n t s . The i n t e g r a t e d t r a n s f e r c o e f f i c i e n t f o r w a t e r v a p o u r between t h e e v a p o r a t i n g s u r f a c e and some r e f e r -ence h e i g h t i n t h e f r e e atmosphere i s termed t h e aerodynamic r e s i s t a n c e ( r a ) , o r i t s r e c i p r o c a l t h e ae r o d y n a m i c c o n d u c t a n c e ( g a ) . I t c a n be e s t i m a t e d u s i n g t h e f o l l o w i n g e q u a t i o n s . Under n e u t r a l a t m o s p h e r i c c o n d i t i o n s r a c a n be d e t e r m i n e d u s i n g t h e l o g a r i t h m i c w i n d p r o f i l e ( M o n t e i t h , 1965): r a = ( l / g a ) = { l n [ ( z - d ) / z 0 ] ) 2 / ( k 2 u ) (7.1) where z - w i n d speed measurement h e i g h t (m); d - d i s p l a c e m e n t l e n g t h (m); zg - momentum r o u g h n e s s l e n g t h (m); k - v o n Karman's c o n s t a n t ; and u - h o r i z o n t a l w i n d speed (m s"*-). I n n o n - n e u t r a l c o n d i t i o n s , and f o r w a t e r vapour exchange, t h e f o l l o w i n g e x p r e s s i o n a p p l i e s (Thorn, 1 9 7 2 ) : 10 0 r a = (ln[(z - d)/z 0] - tf){ln[(z - d ) / z 0 v ] - Vv)/(k2u) (7.2) where i/> - s t a b i l i t y function f o r momentum exchange; V>V - s t a b i l i t y function f o r water vapour exchange; and ZQv - water vapour roughness length. In t h i s study, f o r unstable conditions the s t a b i l i t y functions are those of Dyer (1974) based on a comparison with measured z/L (see Appendix IV). For stable conditions the r e l a t i o n s of Dyer (1974) and van Ulden and Holtslag (1985) are used (see Appendix IV). The water vapour roughness length was taken to be 10% of the momentum roughness length (Brutsaert, 1983). Thorn & O l i v e r (1977) proposed a semi-empirical formula based on Penman's (1948) o r i g i n a l formula f o r r a for crops: r a = 4.72 {ln[(z - d ) / z 0 ] ) / ( l + 0.5u) (7.3) Cal c u l a t i o n of r a using equations 7.1 or 7.3 only requires hourly wind speed whereas the non-neutral version requires s t a b i l i t y data (see Appendix IV). It i s assumed that the r a obtained when the boundary layer s t a b i l i t y i s taken into account i s closest to the 'true' value, but i n many f o r e s t evapora-t i o n - i n t e r c e p t i o n studies the neutral method has been used alone and^ found to be s a t i s f a c t o r y (Shuttleworth, 1988a). Figure 7.1 i s a comparison between the re s u l t s from the three equations using those hours when s t a b i l i t y could be estimated from a d i r e c t l y measured sensible heat f l u x ('sonic' method, Appendix IV). It shows r a calculated by each method plotted against the measured wind speed. The e f f e c t i v e height (z-d) of the anemometer was 19 m and ZQ=0.52 m (Chapter 2). Under c e r t a i n conditions the s t a b i l i t y corrected r a becomes extremely large: f i r s t l y , when the atmosphere i s unstable (-0-.4< z/L < 0) and wind speed i s less than 0.5 m s " l ; and secondly, when the atmosphere i s s l i g h t l y stable (z/L > 0) with low wind speed. In th i s study under these conditions r a was set to 175 s m"-*, the maximum value obtained by the neutral method. When the atmosphere i s more stable there i s a wider range of r a for 101 F i g u r e 7.1 Aerodynamic r e s i s t a n c e c a l c u l a t e d f o r h o u r s when i t was p o s s i b l e t o d e t e r m i n e s t a b i l i t y w i t h d i r e c t measurements o f Q^: n e u t r a l atmosphere e q u a t i o n (;—) ; Thorn & O l i v e r (1977) e q u a t i o n (—) ; and, n o n - n e u t r a l e q u a t i o n (x) . 180 160 140 120 100 i-H I s . co 80 v ' 60 40 20 8 10 12 14 w i n d speed (m s 1 0 2 low w i n d speeds. The n e u t r a l r e s u l t s p l o t a p p r o x i m a t e l y i n the m i d d l e o f the s t a b i l i t y c o r r e c t e d r a . The Thorn and O l i v e r e q u a t i o n does n o t show as much v a r i a b i l i t y . I t w ould appear t h a t i n u r b a n a r e a s , as i n f o r e s t e d e n v i r o n m e n t s , t h a t t h e n e u t r a l f o r m u l a i s a r e a s o n a b l e a p p r o x i m a t i o n . S t e w a r t ( 1 9 8 4 ) , f o r a f o r e s t , u s i n g t h e n e u t r a l e q u a t i o n c a l c u l a t e d r a t o be 5 s m"! (ZQ=1.3 m, z-d=5 m, u= 2 m s ' l ) . T h i s v a l u e i s o b v i o u s l y i n f l u e n c e d n o t o n l y by ZQ and d, c h a r a c -t e r i s t i c s o f t h e s u r f a c e , b u t a l s o by z. When z-d i s i n c r e a s e d t o 19 m ( t h e same as f o r t h i s s t u d y ) r a=21.4 s ra"-'-. F o r a c r o p he c a l c u l a t e d r a t o be 29 s m"l (ZQ=0.13 m, z-d=3 m, u=2 m s"-*). I f z-d i s changed t o 19 m, r a=74 s m"*-. When z-d i s s t a n d a r d i z e d i t c a n be seen t h a t t h e u r b a n v a l u e ( r a = 3 8 . 5 s m"-*-) i s a p p r o x i m a t e l y h a l f t h a t above a c r o p and t w i c e t h a t above a f o r e s t . The i m p l i c a t i o n s a s s o c i a t e d w i t h the use o f the i n d i v i d u a l r a models a r e d i s c u s s e d i n c o n j u n c t i o n w i t h the s e n s i t i v i t y a n a l y s e s o f the whole evapo-t r a n s p i r a t i o n - i n t e r c e p t i o n model i n C h a p t e r 8. 7.3 Surface resistance When t h e r e i s no r a i n o r dew on v e g e t a t i o n , w a t e r l o s s o c c u r s t h r o u g h the f o l i a g e s t o mata. T h i s p r o c e s s i s b i o l o g i c a l l y c o n t r o l l e d and changes w i t h m i c r o m e t e o r o l o g i c a l c o n d i t i o n s . The b i o p h y s i c a l and b i o c h e m i c a l mechanisms o f s t o m a t a l r e s i s t a n c e ( r g ^ ) a r e p o o r l y u n d e r s t o o d ( S h u t t l e w o r t h , 1988a). The form of s t o m a t a l r e s p o n s e o f t e n i s q u a l i t a t i v e l y s i m i l a r from one s p e c i e s t o the n e x t , but i t e x h i b i t s marked v a r i a t i o n s i n q u a n t i t a t i v e terms b o t h between and w i t h i n s p e c i e s ( J a r v i s e t a l . . 1976). A t the whole canopy s c a l e S h u t t l e w o r t h (1976, 1978, 1979) has shown t h a t the b u l k s t o m a t a l r e s i s t a n c e i s c l o s e l y r e l a t e d t o the s u r f a c e r e s i s t a n c e ( r g ) as d e f i n e d by M o n t e i t h ( 1 9 6 5 ) . I n t h i s a p p r o a c h the complex a r r a y o f v<$j f o r the i n d i v i d u a l l e a v e s i s 1 0 3 r e p l a c e d by an e q u i v a l e n t s y s t e m c o n t a i n i n g a s i n g l e h y p o t h e t i c a l l e a f w i t h a s i n g l e r g . Thorn (1972) showed t h a t i f t h e s o u r c e o f w a t e r v a p o u r e v a p o r a t e d i s th e canopy o f a f o r e s t , and t h e aerodynamic r e s i s t a n c e u s e d c o r r e c t l y d e s c r i -bes t h e t r a n s f e r o f w a t e r , t h e n r g i s e q u i v a l e n t t o t h e b u l k rgx- I n t h e more g e n e r a l c a s e where some o f t h e w a t e r v a p o u r comes f r o m o t h e r l a y e r s ( e . g . l i t t e r l a y e r and u n d e r s t o r e y ) , changes i n r g a l s o r e f l e c t changes i n t h e i r r a t e s o f e v a p o r a t i o n as w e l l as changes i n t h e canopy ( S t e w a r t , 1988). I n u r b a n a r e a s t h e d i v e r s i t y o f v e g e t a t i o n makes t h e d e t e r m i n a t i o n o f a b u l k s t o m a t a l r e s i s t a n c e v i r t u a l l y i m p o s s i b l e due t o s a m p l i n g p r o b l e m s and t h e added c o m p l i c a t i o n posed by t h e n o n - v e g e t a t e d a r e a s . T h e r e f o r e i t i s n e c e s s a r y t o model r g as a s i n g l e i n t e g r a t e d r e s i s t a n c e f o r t h e whole system. A t p r e s e n t t h e r e i s i n s u f f i c i e n t knowledge t o i n t e r p r e t t h e e f f e c t s o f e n v i r o n m e n t a l v a r i a b l e s on rg-p u s i n g a m e c h a n i s t i c model ( S t e w a r t , 1988). However, as p r o p o s e d by J a r v i s (1976) a p h y s i c a l l y - b a s e d model t o p r e d i c t rgx can be d e t e r m i n e d f r o m e m p i r i c a l r e l a t i o n s h i p s between r g j and c o n t r o l l i n g e n v i r o n m e n t a l v a r i a b l e s . R e s u l t s f r o m p l a n t p h y s i o l o g i c a l s t u d i e s have shown t h a t r g j , o r i t s i n v e r s e c o n d u c t a n c e ( g g j ) , depends p r i m a r i l y on t h e f o l l o w i n g e n v i r o n m e n t a l v a r i a b l e s : p h o t o n f l u x d e n s i t y , ambient c a r b o n d i o x i d e con-c e n t r a t i o n , l e a f - a i r s p e c i f i c h u m i d i t y d i f f e r e n c e , l e a f t e m p e r a t u r e and l e a f w a t e r s t a t u s ( J a r v i s , 1 9 7 6 ) . I n an a t t e m p t t o d e v e l o p a model o f r g f o r t h e whole canopy f o r use w i t h t h e Penman-Monteith model r e s e a r c h e r s have u t i l i s e d t h e r e s u l t s o f p l a n t p h y s i o l o g i c a l s t u d i e s o f r g j . E m p i r i c a l f o r m u l a e t h a t d e s c r i b e whole-canopy r g o f f o r e s t s i n terms o f t h e same o r s i m i l a r v a r i a b l e s i d e n t i f i e d t o c o n t r o l rg-p, have been c a l i b r a t e d a g a i n s t m i c r o m e t e o r o l o g i c a l d a t a (Gash e t a l . . 1988; L i n d r o t h , 1985; S e l l e r s e t a l . . 1 9 8 6 / S h u t t l e w o r t h , 1988a; S h u t t l e w o r t h , 1988b; S t e w a r t , 1988). The g e n e r a l f o r m f o r t h e canopy model i s e x p r e s s e d i n s i m i l a r 1 0 4 m a t h e m a t i c a l f o r m t o t h a t p r o p o s e d by J a r v i s (1976) f o r s t o m a t a l r e s p o n s e o f i n d i v i d u a l l e a v e s t o t h e e n v i r o n m e n t a l v a r i a b l e s i d e n t i f i e d above. I n a d d i t i o n r g has been shown t o be dependent on s e a s o n a l changes i n l e a f a r e a i n d e x ( L A I ) ( C a l d e r , 1 9 7 7 ) . The g e n e r a l f o r m o f t h e s e models ( e x p r e s s e d as a c o n d u c t a n c e (gg) i s : gg - P i L g ( v a r i a b l e s ) (7.4) where ~P\ - maximum v a l u e o f t h e s u r f a c e c o n d u c t a n c e (m s"*-); L - l e a f a r e a i n d e x ( L A I ) ; and g ( v a r i a b l e s ) - f u n c t i o n s o f t h e e n v i r o n m e n t a l v a r i a b l e s w h i c h have v a l u e s between z e r o and u n i t y . T h i s g e n e r a l f o r m was us e d t o d e v e l o p a model f o r t h e Sunse t s t u d y s i t e . I t assumes t h a t s u r f a c e c o n d u c t a n c e i s a f u n c t i o n o f t h e n o n - s y n e r g i s t i c i n t e r a c -t i o n between s t o m a t a l a p e r t u r e , l e a f a r e a i n d e x and e n v i r o n m e n t a l v a r i a b l e s . I t o p e r a t e s on an h o u r l y t i m e s c a l e . The e n v i r o n m e n t a l v a r i a b l e s i d e n t i f i e d by J a r v i s (1976) as d i r e c t l y i n f l u e n c i n g s t o m a t a l r e s i s t a n c e were n o t a v a i l a b l e b u t were r e p l a c e d by c l o s e l y r e l a t e d ones. S t e w a r t (1988) r e p l a c e d quantum f l u x d e n s i t y w i t h measurements o f t o t a l s o l a r r a d i a t i o n . I n t h i s s t u d y i t was r e p l a c e d by n e t r a d i a t i o n ( Q * ) . F o l l o w i n g S t e w a r t (1988) l e a f - a i r s p e c i f i c h u m i d i t y was r e p l a c e d w i t h s p e c i f i c h u m i d i t y d e f i c i t ( S q ) ; l e a f t e m p e r a t u r e by a i r t e m p e r a t u r e ( T ) ; and l e a f w a t e r s t a t u s by s o i l m o i s t u r e . d e f i c i t (69). The for m o f t h e model i s : gg = P l g ( Q * ) g ( 5 q ) g ( T ) g ( 5 e ) g ( L ) (7.5) The dependence on Q* i s e x p r e s s e d u s i n g t h e same m a t h e m a t i c a l f o r m o f e q u a t i o n as has been u s e d f o r s o l a r r a d i a t i o n ( s e e e.g. S h u t t l e w o r t h , 1988a): g(Q*) = (Qm/(P 2 + Q*)/[Qm/(Qm + P 2 ) ] ' (7.6) where Qm - maximum h o u r l y n e t r a d i a t i o n a n n u a l l y (W m"?); and ?2 - f i t t e d p a r a m e t e r (W m" 2). The dependence on 5q i s e x p r e s s e d as (Gash e t a l . . 1988; S t e w a r t , 1988): g ( 6 q ) = 1 - P 3 5q 0 < 5q < P 4 (7.7) 1 0 5 = 1 - P 3 P 4 Sq > P4 (7.8) The dependence on T i s d e f i n e d by ( S t e w a r t , 1988): g(T) = (T - T L ) ( T H - T ) i c / [ ( T - T L ) ( T H - T ) i c ] (7.9) where: T c = ( T H " P 5 ) / ( p 5 " T L ) (7.10) where Tj^, T^ - minimum and maximum t e m p e r a t u r e l i m i t s ( C) . The dependence on 86 i s d e s c r i b e d by ( S t e w a r t , 1988): g(86) = 1 - e x p ( P 6 (86 - (S1/?e + S 2 ) ) ) (7.11) where Si_, S 2 - f i t t e d p a r a m e t e r s w h i c h r e l a t e t o t h e maximum 86. The dependence on LAI f o l l o w s Dolman e t a l . ( 1 9 8 8 ) , but a l l o w s f o r the g r e a t e r d i v e r s i t y o f v e g e t a t i o n f o u n d i n the suburban a r e a compared t o a temperate f o r e s t : where ATJ - a r e a u n i r r i g a t e d ( m z ) ; Lm - maximum LAI i n ATJ- and A j - a r e a i r r i g a t e d ( m 2 ) . To o p t i m i s e the v a l u e s o f the par a m e t e r s (P]_, . . . .Pg) f o r the s t u d y a r e a 1986) was used w i t h 'measured' v a l u e s o f r g and the e n v i r o n m e n t a l v a r i a b l e s i d e n t i f i e d above. When the s u r f a c e i s d r y i t i s p o s s i b l e t o d e t e r m i n e a 'measured' s u r f a c e r e s i s t a n c e ( r g ) by r e a r r a n g i n g the Penman-Monteith equa-t i o n , and w i t h measured l a t e n t h e a t f l u x (Qg) ( M o n t e i t h , 1965) t o g i v e : The h o u r s used t o d e v e l o p and t e s t t he model were tho s e d a y l i g h t h o u r s f o r w h i c h aerodynamic r e s i s t a n c e c o u l d be c a l c u l a t e d w i t h the s t a b i l i t y c o r r e c t i o n t h a t was d e t e r m i n e d u s i n g d i r e c t l y measured (see eqn. 7.2), and when the s u r f a c e was d r y . F o r the s u r f a c e t o be c l a s s e d as d r y i t had t o meet the f o l l o w i n g c r i t e r i a : r a i n was n o t r e c o r d e d i n the c u r r e n t o r p r e v i o u s t h r e e g ( L ) - [ ( L ATJ) / Lm) + A I ] / ( A U + AT- ) (7.12) n o n - l i n e a r l e a s t s q u a r e s r e g r e s s i o n ( D e n i s e t a l . . 1981; Gay, 1983; Moore (7.13) . 10 6 hours; three hours with p o s i t i v e Q* had occurred since r a i n f a l l ; the hour preceding recorded r a i n was regarded as not dry; to account f o r dew the surface was not dry u n t i l two hours a f t e r Q* was greater than zero; the wetness sensors record the surface as dry; and that the surface was observed not to have puddles or received traces of r a i n . These l a t t e r times were based on v i s u a l observations of the surface wetness. The c r i t e r i a are s i m i l a r to those used by Shuttleworth (1988b). 543 hours of measured r$ met these c r i t e r i a . Figure 7.2 shows the ensemble mean and standard deviation of gg for these hours. The diurnal trend i s s i m i l a r to that reported for forests (e.g. Shuttleworth, 1988b). The values tend to be smaller than those reported for forests (approximately 75%) and to have a greater hourly standard deviation (approximately double)(see e.g. Stewart and de Bruin, 1984; Shuttleworth, 1988b; Stewart, 1988). The data were s p l i t i n two by putting alternate a v a i l a b l e days into two data sets: one of 300 and the other of 243 hours. This was done because no independent data set e x i s t s f or a suburban area which covers as wide a range of conditions as c o l l e c t e d i n t h i s study. The two data sets were used independently to develop and test the model. The data used to develop and test the model were 'measured' at the Sunset tower (see Chapter 2). Q* and T were measured d i r e c t l y , Sq was calculated from the measured T, and pressure, p. S o i l moisture d e f i c i t was determined for u n i r r i g a t e d areas using p r o f i l e s of gravimetric s o i l moisture and the dry bulk density of the s o i l . I r r i g a t e d areas were found to have no s o i l moisture d e f i c i t at any time. The surface d e s c r i p t i o n database and the source area model (see Chapter 3) enabled the area with coniferous, deciduous and grass vegetation, and the area i r r i g a t e d and u n i r r i g a t e d to be i d e n t i f i e d for each hour. Thus an areally-weighted 59 was determined for each hour. It was assumed 1 0 7 F i g u r e 7.2 D i u r n a l t r e n d o f ensemble mean and s t a n d a r d d e v i a t i o n o f measured s u r f a c e c o n d u c t a n c e f o r h o u r s w h i c h met t h e c r i t e r i a o u t l i n e d i n th e t e x t . 1 0 8 t h a t the a r e a i r r i g a t e d i s g r a s s and t h a t because o f lawn-mowing t h e LAI of the g r a s s remains c o n s t a n t s e a s o n a l l y a t 1.6 ( R i p l e y and Redmann, 1975). LAI f o r the u n i r r i g a t e d a r e a was d e t e r m i n e d as an a r e a l l y w e i g h t e d a v e r a g e o f the c o n i f e r o u s L A I , d e c i d u o u s LAI and the g r a s s v a l u e o f 1.6 f o r the s o u r c e a r e a f o r each hour. LAI f o r c o n i f e r o u s and d e c i d u o u s v e g e t a t i o n was s e t t o a maxima of 6 and 4 r e s p e c t i v e l y and minima o f 4 and 0 r e s p e c t i v e l y (Kramer and K o z l o w s k i , 1979). 360° panorama ph o t o g r a p h s were t a k e n from the tower ap-p r o x i m a t e l y w e e k l y t o i d e n t i f y the s t a g e s o f the g r o w i n g season. They were used t o model LAI f o r each day of the s t u d y p e r i o d f o r the two v e g e t a t i o n t y p e s u s i n g ( S t r e e t and Opik, 1984): l o g L + 1 = k [ ( d - d 0 ) - ( d 1 - d 0 ) ] (7.14) a - (L + 1) where a - maximum LAI minus t h e w i n t e r minimum ( 1 ) ; k - f i t t e d p arameter ( 0 . 0 5 ) ; d - J u l i a n day o f i n t e r e s t ; d o - s t a r t i n g day o f c u r v e from w i n t e r minimum o f LAI (JD 4 5 ) ; and di_ - day o f i n f l e c t i o n o f S c u r v e (JD 9 5 ) . T h e r e f o r e i t was p o s s i b l e t o a s s i g n a d a i l y v a l u e o f LAI f o r each v e g e t a t i o n type and, d e p e n d i n g on the s o u r c e a r e a b e i n g sampled d e t e r m i n e the w e i g h t e d average o f LAI f o r each hour. The a r e a i r r i g a t e d was d e t e r m i n e d based on v i s u a l s u r v e y s and w a t e r use d a t a ( C h a p t e r 2) i n c o n j u n c t i o n w i t h the d a t a base and the s o u r c e a r e a model t o d e t e r m i n e the s u r f a c e t y p e s sampled each hour. The model pa r a m e t e r s Lm, Qm, Tj^, T L , SI_ and S 2 must be a s s i g n e d b e f o r e the model can be f i t t e d t o the measured d a t a . From the c a l c u l a t e d L A I , the maximum-areally w e i g h t e d Lm i s 3.1. From measured Q* d u r i n g June ( w h i c h has the h i g h e s t v a l u e s f o r the y e a r ) Qm was s e t t o 725 W m"2. F o l l o w i n g S t e w a r t (1988) and Gash e t a l . (1988) T H was s e t t o 40°C and T L t o 0°C. Si_ and S 2 were d e t e r m i n e d by t r i a l and e r r o r (Dolman e t a l . . 1988) t o be 0.45 mm and 15 mm r e s p e c t i v e l y . 1 0 9 T a b l e 7.1 l i s t s t h e f i t t e d p a r a m e t e r s and t h e t e s t s t a t i s t i c s . The v a l u e s o f t h e model p a r a m e t e r s ( T a b l e 7.1a) P3 t o Pg a r e s i m i l a r t o t h o s e r e p o r t e d by S t e w a r t (1988) and Gash e t a l . (1988) f o r t e m p e r a t e f o r e s t s ( T h e t f o r d , U.K. and Les Landes, F r a n c e r e s p e c t i v e l y ) . The f i r s t two p a r a m e t e r s ( P i , P 2 ) a r e somewhat d i s s i m i l a r from t h o s e o f S t e w a r t (1988) and Gash e t a l . ( 1 9 8 8 ) . T h i s i s e x p e c t e d due t o two r e a s o n s . F i r s t l y t h e l a n d use o f t h i s s t u d y i s d i f -f e r e n t . The canopy v e g e t a t i o n i s more h e t e r o g e n e o u s and t h e r e a r e a r e a s t h a t a r e n o n - v e g e t a t e d . T h i s w i l l i n f l u e n c e P i . S e c o n d l y , P 2 i s a s s o c i a t e d w i t h n e t a l l - w a v e r a d i a t i o n i n t h i s s t u d y r a t h e r t h a n n e t s o l a r r a d i a t i o n as i n the o t h e r two s t u d i e s . S e v e r a l d i f f e r e n t forms o f t h e model were t r i e d t a k i n g i n t o a c c o u n t f e a t u r e s t h a t a r e d i s t i n c t l y u r b a n . The model p r e s e n t e d gave t h e b e s t e x p l a n a t i o n o f v a r i a n c e . The s t a t i s t i c s p e r t a i n i n g t o model development and performance t e s t s a r e p r e s e n t e d i n T a b l e s 7.1b and 7.1c r e s p e c t i v e l y . The model was f i r s t d e v e l o p e d u s i n g d a t a s e t AD2 and t e s t e d a g a i n s t AD1. I n d e p e n d e n t l y the p r o c e s s was r e v e r s e d and t h e AD1 d a t a s e t was used t o d e v e l o p t h e model and AD2 t o t e s t . The r 2 o f 0.71 f o r model AD2 i s s i m i l a r t o t h a t r e p o r t e d by S t e w a r t ( 1 9 8 8 ) . The l o w e r degree o f e x p l a n a t i o n w i t h d a t a s e t AD1 i s c o n s i s t e n t r e g a r d l e s s whether the d a t a were used t o d e v e l o p o r t e s t the model. T h i s may be a t -t r i b u t e d t o the g r e a t e r number o f o u t l i e r s i n t h i s d a t a s e t as e v i d e n t i n F i g u r e 7.3a. I n s p e c t i o n r e v e a l s t h e s e t o be h o u r s c h a r a c t e r i s e d by c l o u d y and p a r t l y c l o u d y c o n d i t i o n s , s u g g e s t i n g t h a t t h e n e t r a d i a t i o n f u n c t i o n i s i n a d e q u a t e f o r t h e s e c o n d i t i o n s . A l l t h r e e models show l a r g e r u n s y s t e m a t i c t h a n s y s t e m a t i c e r r o r s , w h i c h i n d i c a t e s t h e r e i s o n l y a s m a l l c o n s i s t e n t b i a s i n t h e model e s t i m a t e s . The s l o p e of t h e b e s t f i t l i n e i n d i c a t e s an under-p r e d i c t i o n f o r low gg ( h i g h r g ) and an u n d e r - p r e d i c t i o n f o r h i g h gg ( l o w r g ) . The s l o p e s f o r c e d t h r o u g h the o r i g i n f o r t h e t e s t s ( T a b l e 7.1c) a r e s i m i l a r t o 1 1 0 T a b l e 7.1 S u r f a c e r e s i s t a n c e model f i t t e d p a r a m e t e r s and t e s t s t a t i s t i c s (a) Model p a r a m e t e r s Model n P i mm s-1 ?2 W m" •2 ? 3 1 kg g'L P4 g k g -p 5 • i °C ? 6 - l mm -L A l t e r n a t e Days 1 (AD1) 300 56, .35 694. 9 0.0857 9.44 20.07 0.0105 A l t e r n a t e Days 2 (AD2) 243 53. ,95 634. 0 0.0821 8.91 18.88 0.0107 A l l days ( A l l ) 543 55. .20 669. 6 0.0840 9.02 19.56 0.0106 (b) Model development s t a t i s t i c s Data s e t u s e d f o r Model T e s t r 2 mg mf C f RMSE RMSE S RMSEy mm s " l mm s'^ mm s"-* mm s " l AD 1 AD 1 0.61 0.90 0.79 1.29 2.35 1.45 1.85 0.87 AD 2 AD 2 0.71 0.93 0.87 0.69 1.75 0.88 1.52 0.91 A l l A l l 0.65 0.91 0.82 1.05 2.11 1.21 1.73 0.89 (c ) Model t e s t s t a t i s t i c s AD 1 AD 2 0.71 0.89 0.87 0.44 1.79 0.91 1.54 0.91 AD 2 AD 1 0.61 0.92 0.78 1.57 2.36 1.47 1.85 0.87 May-June AD 1 AD 2 0.72 0.89 0.74 1.14 1.75 0.89 1.50 0.91 n=184 AD 2 AD 1 0.65 0.92 0.65 2.49 2.26 1.38 1.79 0.88 n=202 n - number o f hours mg - s l o p e f o r c e d t h r o u g h the o r i g i n mf & c f - s l o p e ( p r i n c i p a l a x i s ) and i n t e r c e p t f o r l i n e a r f u n c t i o n a l r e l a t i o n (Mark and Church, 1977) RMSE - r o o t mean square e r r o r RMSEg - s y s t e m a t i c e r r o r RMSEy - u n s y s t e m a t i c e r r o r d - i n d e x o f agreement ( W i l m o t t and Wicks, 1980) 11 1 F i g u r e 7.3 Comparison between h o u r l y measured and m o d e l l e d s u r f a c e c o n d u c t a n c e : (a) model AD1 d a t a AD2 (b) model AD2 d a t a AD1 (a) 1 4 • 2r T3 0J O J O a 10 1 1 2 t h o s e o b t a i n e d by S t e w a r t ( 1 9 8 8 ) . F i g u r e 7.4a,b show t h e d i u r n a l t r e n d o f t h e ensemble mean measured and m o d e l l e d ( u s i n g t h e o p p o s i t e model) gg. The m o d e l l e d and measured d a t a e x h i b i t t h e same t r e n d u s i n g e i t h e r model. I n b o t h c a s e s t h e model u n d e r - p r e d i c t s i n t h e m o r n i n g . The AD1 model was s e l e c t e d f o r c a l c u l a t i o n o f r g i n t h e e v a p o t r a n s p i r a t i o n -i n t e r c e p t i o n model. T h i s model, when t e s t e d , has t h e l o w e s t RMSE and t h e s l o p e o f t h e l i n e ( m f ) , d e r i v e d f r o m f u n c t i o n a l a n a l y s i s (Mark and C h u r c h , 1977) i s . t h e c l o s e s t t o u n i t y . The o t h e r two models a r e u s e d i n t h e s e n s i t i v i t y a n a l y s e s ( s e e C h a p t e r 8 ) . The r e s u l t s s u g g e s t t h a t t h i s f o r m o f model i s p r o m i s i n g f o r use i n u r b a n a r e a s . I t has t h e a d v a n t a g e o f b e i n g d y n a m i c a l l y r e s p o n s i v e t o b o t h m e t e o r o l o g i c a l and s e a s o n a l c o n d i t i o n s . 7.4 Drainage Most o f t h e t h e s i s t o t h i s p o i n t has been c o n c e r n e d w i t h t h e e v a p o t r a n s -p i r a t i o n p o r t i o n o f t h e P e n m a n - M o n t e i t h - R u t t e r e v a p o t r a n s p i r a t i o n - i n t e r c e p t i o n model. As n o t e d i n C h a p t e r 1 t h e model c a l c u l a t e s a r u n n i n g w a t e r b a l a n c e (eqn 1.14). The d e t e r m i n a t i o n o f t h e d r a i n a g e r a t e f o r u r b a n a r e a s i s p r o b l e m a t i c . T h i s t e r m does n o t c o r r e l a t e d i r e c t l y w i t h u r b a n r u n o f f . I t has t o be en-v i s a g e d as t h a t l o s s f r o m t h e ' s t o r a g e l a y e r ' w h i c h i s no l o n g e r a v a i l a b l e f o r e v a p o r a t i o n ; e.g. t h e w a t e r may e n t e r a p i p e s y s t e m o r i n f i l t r a t e i n t o t h e s o i l . G i v e n t h e range o f v e g e t a t i o n and o t h e r s u r f a c e s i n u r b a n a r e a s t h e measurement o f t h e d r a i n a g e r a t e i n v o l v e s a v a s t s a m p l i n g p r o b l e m . Added t o t h i s i s t h e d i f f i c u l t y o f making a c t u a l o b s e r v a t i o n s . Even i n f o r e s t a r e a s , t h e r e i s a l w a y s a s i g n i f i c a n t e r r o r i n v o l v e d i n t h e measurement o f t h i s t e r m ( S h u t t l e w o r t h , 1 9 8 8 a ) . To overcome t h e s e d i f f i c u l t i e s w i t h t h e u r b a n e n v i r o n m e n t i t was d e c i d e d t o use v a l u e s f o r t h e p a r a m e t e r s o f t h e d r a i n a g e f u n c t i o n s t a k e n f r o m t h e F i g u r e 7.4 E n s e m b l e m e a n o f m e a s u r e d a n d m o d e l l e d s u r f a c e c o n d u c t a n c e (a) d a t a AD2 ( - ) m o d e l l e d AD1 (A) ( b ) d a t a AD1 ( - ) m o d e l l e d AD2 (A) 8 10 12 14 16 18 T i m e 1 1 4 l i t e r a t u r e . The a p p r o a c h f o r c a l c u l a t i n g t h e d r a i n a g e r a t e i s o u t l i n e d below. The model d e v e l o p e d i n t h i s s t u d y , f o r u r b a n a r e a s , has a s i n g l e l a y e r m o i s t u r e s t o r e ( F i g . 1 . 2 ) . The d r a i n a g e f u n c t i o n d e s c r i b e s t h e r a t e a t w h i c h w a t e r d r a i n s f r o m t h i s m o i s t u r e s t o r e . I t i s s e t p r o p o r t i o n a l t o t h e c u r r e n t w a t e r s t a t u s o f t h i s s t o r e . I n t h e o r i g i n a l p a p e r s o f R u t t e r e t a l . ( 1 9 7 1 , 1 9 7 5 ) t h e y p r o p o s e d : D = D Q e x p { b ( C - S ) } . ( 7 . 1 5 ) where D Q - d r a i n a g e r a t e when C=S; b - e m p i r i c a l c o e f f i c i e n t ; and S - amount o f w a t e r t h e canopy s t o r e s / r e t a i n s a f t e r t h e r a i n f a l l and t h r o u g h f a l l c e a s e . However, t h i s f o r m u l a t i o n has an i n h e r e n t d i f f i c u l t y i n p r e d i c t i n g a f i n i t e d r a i n a g e when t h e canopy i s d r y ( C a l d e r , 1 9 7 7 ) . I t has been r e w r i t t e n ( e . g . H a l l d i n e t a l . . 1 9 7 9 ) t o r e c t i f y t h i s so t h a t i t r e a d s : D - D 0 e x p [ ( b C ) - l ] ( 7 . 1 6 ) T h i s d r a i n a g e f u n c t i o n has been u s e d by H a l l d i n e t a l . ( 1 9 7 9 ) , C a l d e r e t a l . ( 1 9 8 4 ) , C a l d e r and W r i g h t ( 1 9 8 5 ) and H a l l ( 1 9 8 5 ) . O t h e r p r o p o s a l s i n c l u d e C a l d e r ' s ( 1 9 7 7 ) l i n e a r t h r e s h o l d model, and Massman's ( 1 9 8 3 ) model w h i c h e x p l i c i t l y i n c l u d e s t h e r a i n f a l l r a t e i n a d d i t i o n t o t h e s t o r e d w a t e r . Thus f a r Massman's ( 1 9 8 3 ) model has o n l y been t e s t e d i n o l d growth Douglas f i r f o r e s t s and one o f t h e d r i p p a r a m e t e r s i n h i s dynamic model v a r i e s f r o m s t o r m t o s t o r m . C a l d e r and W r i g h t ( 1 9 8 5 ) compared t h e C a l d e r ( 1 9 7 7 ) t h r e s h o l d model and e q u a t i o n 7 . 1 6 b o t h o f w h i c h had been o p t i m i s e d a t a d i f f e r e n t s i t e i n t h e same f o r e s t . E q u a t i o n 7 . 1 6 w h i c h has been w i d e l y u s e d , gave s l i g h t l y b e t t e r p e r f o r m a n c e . Here e q u a t i o n 7 . 1 6 i s u s e d f o r t h e p r o p o r t i o n o f t h e s o u r c e a r e a w h i c h i s v e g e t a t e d b u t n o t i r r i g a t e d . T a b l e 7 . 2 l i s t s v a l u e s f o r t h e e q u a t i o n p a r a -m e t e r s w h i c h have been t a k e n f r o m t h e l i t e r a t u r e . F o r t h e a r e a w h i c h i s i m p e r v i o u s t h e u r b a n r u n o f f l i t e r a t u r e i s use d . There 1 1 5 T a b l e 7.2 V a l u e s o f d r a i n a g e f u n c t i o n p a r a m e t e r s (see t e x t f o r e x p l a n a t i o n ) A l l e q u a t i o n s mm h " 1 e x c e p t S h u t t l e w o r t h (1988b) mm min"!. Note t h a t when c a l c u l a t i o n i s c o n d u c t e d w i t h i n the e v a p o t r a n s p i r a t i o n -i n t e r c e p t i o n model the r e s u l t i n g d r a i n a g e i s a d j u s t e d f o r the t i m e s t e p o f the c a l c u l a t i o n . A u t h o r S u r f a c e E q u a t i o n DO b •pa C a l d e r (1977) Norway & S i t k a DQ exp(bC) 0.18 1. .76 _ s p r u c e D 0 C C<T 0.21 1.9 D 0 C -b O T 3.2 5, .6 1.9 C a l d e r & W r i g h t Norway & S i t k a 7. 16 0.013 1. .71 -(1985) s p r u c e D 0 C C<T 0.21 2.5 D 0 C -b O T 3.4 7. .9 2.5 H a l l (1985) H e a t h e r 7. 16 0.00085 5. .13 -Wax base & t r a y 7. 16 0.21 27, .09 -S h u t t l e w o r t h T r o p i c a l f o r e s t 7. 15 0.0014 5 , 25 -(1988b) (Amazonian) F a l k & Car p a r k 7. 17 32.0 . 1. 5 -Niemczynowicz Car p a r k , r o a d 7. 17 5.7 1. .5 -(1978) B i c y c l e p a r k 7 . 17 28.0 1, .5 -7. 18 10.0 3, .0 -Car p a r k 7. 17 15 ;o 1, .5 -Car p a r k 7 . 17 12.0 1. .5 -Car p a r k , r o a d 7. 17 17.0 1. .5 -B i c y c l e p a r k 7. 17 27.0 1. .5 -Car p a r k 7. 17 22.0 1. . 5 -Bar p a r k 7. 17 21.7 1. .5 a T - t h r e s h o l d v a l u e 1 16 have been a s m a l l number o f s t u d i e s w h i c h have d e t e r m i n e d the r u n o f f from a s i n g l e s u r f a c e t y p e r a t h e r t h a n f o r a l a n d use a r e a . F a l k and Niemczynowicz ( 1 9 7 8 ) p r o p o s e d the f o l l o w i n g e q u a t i o n s f o r t h e r e l a t i o n s h i p between d r a i n a g e and s t o r a g e ( u s i n g t h e same n o t a t i o n as ab o v e ) : D = D Q ( C t . i - S ) 1 3 ( 7 . 1 7 ) D - D 0 ( C t . i _ ) b ( 7 . 1 8 ) They r e p o r t v a l u e s o f t h e o p t i m i s e d c o e f f i c i e n t s from measurements c o n d u c t e d i n n i n e s m a l l ( 7 8 - 4 1 3 m 2) c o m p l e t e l y paved catchments ( T a b l e 7 . 2 ) . E q u a t i o n 7 . 1 7 a l l o w s f o r no d r a i n a g e when C < S . T h i s a s s u m p t i o n has a l s o been u s e d by r e s e a r c h e r s i n f o r e s t e d a r e a s , f o r example Gash and Morton ( 1 9 7 8 ) and Mu l d e r ( 1 9 8 5 ) . P r a t t e t a l . ( 1 9 8 4 ) s u g g e s t t h a t t h e r a t e o f d r a i n a g e f r o m f l a t r o o f s can be assumed t o be th e same as paved s u r f a c e s o f 1% s l o p e . E q u a t i o n 7 . 1 8 was used f o r the paved, b u i l t s u r f a c e s and f o r i r r i g a t e d g r a s s . I n t h i s s t u d y i t was no t p o s s i b l e t o d i r e c t l y t e s t the performance o f any i n d i v i d u a l d r a i n a g e e q u a t i o n . They can be a s s e s s e d by the performance o f the whole e v a p o t r a n s p i r a t i o n - i n t e r c e p t i o n model a g a i n s t the measured l a t e n t h e a t f l u x and by comparing the m o d e l l e d s u r f a c e s t a t e (C) w i t h t h e wetness s e n s o r s (see C h a p t e r 8 ) . The e f f e c t o f t h e c h o i c e o f e q u a t i o n and p a r a m e t e r s i s compared i n the s e n s i t i v i t y a n a l y s i s o f the whole e v a p o t r a n s p i r a t i o n - i n t e r c e p -t i o n model i n C h a p t e r 8 . 7.5 Storage capacity The v a l u e s o f the s u r f a c e s t o r a g e c a p a c i t y , l i k e the d r a i n a g e f u n c t i o n s , were based on v a l u e s t a k e n from the l i t e r a t u r e . The c a p a c i t y f o r a s u r f a c e t y p e i s assumed t o be c o n s t a n t t h r o u g h time f o r a l l t y p e s e x c e p t d e c i d u o u s v e g e t a t i o n , where a l l o w a n c e i s made f o r the change between w i n t e r and summer. T h i s i s done by the a d d i t i o n t o the w i n t e r s t o r a g e c a p a c i t y (S^y) o f an 1 1 7 i n c r e m e n t ( S d s t ) : S d s t = ( S d S - S d w ) / ( t e - t b ) (7.19) where S d g - summer d e c i d u o u s s t o r a g e c a p a c i t y (mm); t e - J u l i a n day on w h i c h the t r a n s i t i o n ends; and t ^ - J u l i a n day on w h i c h the t r a n s i t i o n b e g i n s f o r e ach day o f the t r a n s i t i o n p e r i o d . T a b l e s 7.3 and 7.4 l i s t v a l u e s t a k e n f r o m the l i t e r a t u r e f o r a n t h r o p o g e n i c and v e g e t a t e d s u r f a c e t y p e s . The v a l u e s used i n t h i s s t u d y a r e a a r e : f o r paved s u r f a c e s 0.48 mm ( F a l k and Ni e m c z y n o w i c z , 1978); f o r r o o f s 0.25 mm ( D a v i e s and H o l l i s , 1982); f o r c o n i f e r o u s t r e e s 1.2 mm ( S h u t t l e w o r t h , 1988a); f o r d e c i d u o u s t r e e s when l e a f l e s s 0.3 mm and when i n l e a f 0.8 mm ( S h u t t l e w o r t h , 1988a); and f o r g r a s s 1.3 mm ( Z i n k e , 1967). The i n f l u e n c e o f c h a n g i n g the v a l u e s a s s i g n e d t o s u r f a c e t y p e s a r e d i s c u s s e d i n the s e n s i t i v i t y a n a l y s i s o f the model i n C h a p t e r 8. 1 1 8 T a b l e 7.3 V a l u e s o f s t o r a g e c a p a c i t y f o r paved s u r f a c e s / r o o f s t a k e n f r o m t h e l i t e r a t u r e Source S u r f a c e Type S t o r a g e c a p a c i t y (mm) B r a t e r (1968) Pavement 1. .6 S m a l l paved a r e a 1. .0-2. . 5 W r i g h t - L a r g e paved a r e a s 1. .3-3. .8 (2. • 5) M c L a u g h l i n Roof - f l a t 2. .5-7 .6 (2. .5) E n g i n e e r s (1969) - s l o p e d 1. .3-2. .5 ( 1 . .3) M a r s a l e k (1977) I m p e r v i o u s 1. .57 SWMM M e c h l e r & I m p e r v i o u s 1. .6 R i e c k e n (1977) F a l k & P a r k i n g l o t 0, .13 Niemczynowicz P a r k i n g l o t & r o a d 1, .05 (1978) B i c y . & p a r k i n g 0. 48, 0. 33 P a r k i n g 0. • 52, 0. 56, , o .56, P a r k i n g & r o a d 0. .51 K i d d (1978) Urban 0. .67 S I.E. . 0 .11 0. .53 0 .10 0. .49 0 .12 0. .50 0 .18 0 .45 0 .10 0. .50 0 .29 0. .32 0 .12 0. .41 0 .29 D a v i e s & Roof ( p i t c h e d ) 0 .25 H o l l i s (1982) Road 1. .00 P r a t t e t a l . Roof ( p i t c h e d ) 1 .08 (1984) B u l f i l l Highway 1. .30 (1984) 1 .38 Niemczynomicz Urban 0 .7 (1986) Nouh(1986) R e s i d e n t i a l -imperv 1. .5 1 19 T a b l e 7.4 V a l u e s o f s t o r a g e c a p a c i t y f o r v e g e t a t i o n t a k e n from l i t e r a t u r e Source S u r f a c e t y p e S t o r a g e c a p a c i t y (mm) B r a t e r (1968) G r a s s l a n d 6.4 W r i g h t - Lawn g r a s s 5.1-12.7 (7.6) M c L a u g h l i n Wooded a r e a s & E n g i n e e r s g r a s s f i e l d s 5.1-15.2 (10.2) (1969) R u t t e r e t C o r s i c a n p i n e 1.05 a l . (1985) Douglas f i r 1.2 Norway s p r u c e 1.5 Hornbeam - l e a f y 1.0 - l e a f l e s s 0.65 Oak - l e a f y 0.875 - l e a f l e s s 0.275 - d e f o l i a t e d 0.175 M a r s a l e k (1977) Urban - p e r v i o u s 4.67 M e c h l e r & P e r v i o u s 6.4 R i e c k e n (1977) Nouh (1986) R e s i d e n t i a l - p e r v . 6.4 S h u t t l e w o r t h C o n i f e r o u s t r e e s 1.2 ±0.3 (1988a) Deciduous - i n l e a f 0.8 - l e a f l e s s 0.3 Z i n k e (1967) G r a s s 1.3 1 2 0 PART III MODEL PERFORMANCE AND CONCLUSIONS CHAPTER 8 PERFORMANCE OF THE EVAPOTRANSPIRATION-INTERCEPTION MODEL 8.1 Introduction The P e n m a n - M o n t e i t h - R u t t e r - S h u t t l e w o r t h e v a p o t r a n s p i r a t i o n - i n t e r c e p t i o n model and m o d i f i c a t i o n s f o r i t s use i n the u r b a n e n v i r o n m e n t were d e s c r i b e d i n Ch a p t e r 1. I n subsequent c h a p t e r s sub-models r e q u i r e d f o r the model have been d e v e l o p e d and where p o s s i b l e t e s t e d . I n t h i s c h a p t e r the performance o f the complete model i s e v a l u a t e d by c o m p a r i s o n w i t h measured l a t e n t h e a t f l u x d e n s i t i e s a t t h e Sunset suburban s i t e . The r e s u l t s o f s e n s i t i v i t y a n a l y s e s o f the model a r e a l s o p r e s e n t e d . 8.2 Structure of the model The computer v e r s i o n o f the model was w r i t t e n i n FORTRAN-77 and r u n on an Amdahl 5860 mainframe computer a t UBC. The code has a l s o been r u n on an IBM-c o m p a t i b l e p e r s o n a l computer u s i n g t h e WATF0R-77 c o m p i l e r . The c omplete model c o n s i s t s o f t h e f o l l o w i n g components: 1) a m o d i f i e d v e r s i o n o f the Schmid (1988) s o u r c e a r e a model ( C h a p t e r 3 ) ; 2) the s u r f a c e d a t a b a s e and a c q u i s i t i o n s u b r o u t i n e s ( C h a p t e r 3, App e n d i x V ) ; 3) the a n t h r o p o g e n i c h e a t f l u x model ( C h a p t e r 4 ) ; 4) the s t o r a g e h e a t f l u x model ( C h a p t e r 5 ) ; and 5) the e v a p o t r a n s p i r a t i o n model ( C h a p t e r s 1, 7, 8 ) . The sub-models can be r u n t o g e t h e r as one model o r each o f the sub-model components can be r u n as s t a n d - a l o n e models. The model i s d e s c r i b e d here assuming t h a t r e s u l t s o f the s o u r c e a r e a model and da t a b a s e a c q u i s i t i o n sub-models have a l r e a d y been o b t a i n e d and a r e r e a d i n as h o u r l y d a t a . The b a s i c s t r u c t u r e o f the e v a p o t r a n s p i r a t i o n - i n t e r c e p t i o n model i s p r e s e n t e d i n F i g u r e 8.1. The f i r s t s t e p i n a model r u n i s t o r e a d the i n i t i a l F i g u r e 8.1 B a s i c s t r u c t u r e o f e v a p o t r a n s p i r a t i o n - i n t e r c e p t i o n model f o r u r b a n i z e d a r e a s . READ - t i t l e , r u n number, t y p e o f r u n - s i t e c h a r a c t e r i s t i c s - s u r f a c e c h a r a c t e r i s t i c s - s u r f a c e r e s i s t a n c e / c o n d u c t a n c e p a r a m e t e r s - s t o r a g e h e a t f l u x p a r a m e t e r s - a n t h r o p o g e n i c h e a t f l u x p a r a m e t e r s h o u r l y c a l c u l a t i o n READ - h o u r l y d a t a ( T a b l e 8.2) I INITIAL CALCULATIONS - a v a i l a b l e e n e r g y (Qp eqn 4.1...4.6, AQg eqn 5.5) - s l o p e o f s a t u r a t i o n v a p o u r p r e s s u r e v s t e m p e r a t u r e c u r v e (eqn. I I . 2 ) - p s y c h r o m e t r i c ' c o n s t a n t ' (eqn. I I . 3 ) - l a t e n t h e a t o f v a p o r i z a t i o n (eqn. I I . 4 ) - s p e c i f i c h e a t o f a i r a t c o n s t a n t p r e s s u r e (eqn. I I . 8 ) - d e n s i t y o f m o i s t a i r (eqn. I I . 9 ) - v a p o u r p r e s s u r e d e f i c i t (eqn. 11.12) - s p e c i f i c h u m i d i t y d e f i c i t (eqn. 11.13) - f r i c t i o n v e l o c i t y (eqn. I V . 5 a ) - Monin Obukhov s t a b i l i t y l e n g t h ( e q n s . I V . l a o r IV.2) - s t o r a g e c a p a c i t y o f d e c i d u o u s v e g e t a t i o n (eqn. 7.19) RESISTANCES * | - aer o d y n a m i c r e s i s t a n c e (eqn. 7.1 , 7 . 2 a o r 7.3) | - s u r f a c e r e s i s t a n c e (eqns. 7.5...7.12) | - bou n d a r y l a y e r r e s i s t a n c e (eqn. 1.12) I | Number of Steps per Hour c a l c u l a t i o n _ | Number of Surfaces c a l c u l a t i o n . | i ^ r i DRAINAGE I I | - u s i n g s u r f a c e s t a t e o f p r e v i o u s t i m e s t e p and e q u a t i o n c hosen as | f | i n p u t f o r t h e i n d i v i d u a l s u r f a c e s ( e q n s . 7.15...7.18) | | 4 I I EVAPORATION | | | - S u r f a c e d r y (eqn. 1.5) ^ | | - S u r f a c e wet - e i t h e r R u t t e r (eqns. 1.6 and 1.7) | | j • - o r S h u t t l e w o r t h (eqn. 1.5 w i t h eqns. 1.8...1.11) j | I I I STORAGE CHANGE (eqn. 8.1) I I STORAGE STATE (eqn. 8.4) | | SUMMATION j j - W - l l f: WRITE - h o u r l y r e s u l t s ( o r r e s u l t s f o r e a c h t i m e s t e p ) I — : : = > a c a l c u l a t e d w i t h eqns IV.6, IV.7, I V . 9 , IV.1 3 , IV.14 1 2 2 d a t a r e q u i r e m e n t s . These a r e l i s t e d i n T a b l e 8.1. A t t h i s s t a g e a number of c h o i c e s a r e made about the ty p e o f r u n t o be c o n d u c t e d : 1) The e q u a t i o n t o be u s e d f o r the c a l c u l a t i o n o f e v a p o r a t i o n d u r i n g the t r a n s i t i o n between wet and d r y s u r f a c e s has t o be s p e c i f i e d . The o r i g i n a l R u t t e r e t a l . (1971) model uses a r a t i o o f t h e amount of wa t e r on the canopy t o t h e s t o r a g e c a p a c i t y (eqn. 1.7) w i t h t h e Penman-Monteith e q u a t i o n when the s u r f a c e i s wet (eqn. 1.6). T h i s means t h e r e i s a change t o e q u a t i o n 1.5 when the s u r f a c e i s d r y . S h u t t l e w o r t h (1978) p r o p o s e d a p h y s i c a l l y c o n t i n u o u s t r e a t m e n t o f the t r a n s i t i o n between the wet and d r y c a n o p i e s (eqns. 1.8...1.11 w i t h 1.5). T h i s second form i s the 'base' method o f c a l c u l a t i o n i n t h i s s t u d y . 2) The method used t o c a l c u l a t e t he aerodynamic r e s i s t a n c e has t o be i d e n t i f i e d . The 'base' method i s the n o n - n e u t r a l e q u a t i o n (7.2) w h i c h t a k e s i n t o a c c o u n t c h a n g i n g a t m o s p h e r i c s t a b i l i t y . I t s h o u l d be n o t e d t h a t when a l l the d a t a r e q u i r e m e n t s a r e n o t met f o r t h i s method (see s e c t i o n 7.2) the c a l c u l a t i o n d e f a u l t s t o the n e u t r a l method (eqn. 7.1). A comment i s w r i t t e n i n t o t he o u t p u t when t h i s o c c u r s . 3) The l e n g t h o f the sub-hour time s t e p f o r t h e c a l c u l a t i o n s , and t h e r e f o r e the number o f s t e p s per hour, i s s t a t e d . When t h i s t y p e o f model has been u s e d i n f o r e s t e n v i r o n m e n t s time s t e p s o f 120 ( S h u t t l e w o r t h , 1988b), 300 ( R u t t e r e t  a l . . 1971) and 720 seconds ( S e l l e r s and Lockwood, 1981) have been used. The sub-hour time s t e p a l l o w s f o r changes i n the d r a i n a g e r a t e , s u r f a c e s t a t e (amount of w a t e r on the s u r f a c e a t any t i m e ) and t h e r e f o r e e v a p o t r a n s p i r a t i o n r a t e w i t h i n an hour. The 'base' time s t e p used i n t h i s s t u d y i s 300 seconds, i . e . 12 s t e p s per hour ( F i g . 8.1). 4) The fo r m i n w h i c h the h o u r l y d a t a a r e t o be r e a d has t o be s e l e c t e d . S i n c e many o f the c a l c u l a t i o n s a r e i d e n t i c a l f o r r e p e a t e d r u n s o f t h e model, and r e q u i r e l a r g e amounts o f i n p u t d a t a i t i s p o s s i b l e t o do some o f the i n i t i a l 1 2 3 T a b l e 8.1 I n i t i a l d a t a r e q u i r e m e n t s f o r the model. T i t l e T i t l e o r comment Run number Type o f r u n T r a n s i t i o n between wet and d r y s u r f a c e - R u t t e r (eqn. 1.7) o r S h u t t l e w o r t h (eqn A e r o d y n a m i c • r e s i s t a n c e t y p e - n e u t r a l (eqn. 7.1), n o n - n e u t r a l Thorn & O l i v e r (1977) (eqn. 7.3) Time s t e p i n seconds Form i n w h i c h h o u r l y d a t a t o be r e a d i n i . e 1.8) (eqn. 7.2) o r i f some of t h e i n i t i a l c a l c u l a t i o n s have been done or n o t S i t e c h a r a c t e r i s t i c s S u r f a c e c h a r a c t e r i s t i c s S u r f a c e r e s i s t a n c e / c o n ductance p a r a m e t e r s A n t h r o p o g e n i c h e a t f l u x p a r a m e t e r s H e i g h t o f wind speed measurements Z e r o - p l a n e d i s p l a c e m e n t l e n g t h Roughness l e n g t h f o r momentum Number o f s u r f a c e t y p e s S u r f a c e w h i c h i s i r r i g a t e d f o r e a ch s u r f a c e : - s t o r a g e c a p a c i t y - d r a i n a g e f u n c t i o n t y p e - F a l k & Niemczynowicz (eqn. 7.17) - F a l k & Niemczynowicz (eqn. 7.18) - R u t t e r c o r r e c t e d (eqn. 7.16) - R u t t e r u n c o r r e c t e d (eqn. 7.15) - d r a i n a g e c o e f f i c i e n t s ( s e c t i o n 7.4): DQ, b - i n i t i a l s u r f a c e s t o r a g e s t a t u s S t o r a g e c a p a c i t y t r a n s i t i o n d e c i d u o u s winter-summer - day t r a n s i t i o n b e g i n s , ends - summer s t o r a g e c a p a c i t y Maximum l e a f a r e a i n d e x Maximum a i r t e m p e r a t u r e Minimum a i r t e m p e r a t u r e Si, S 2 r e l a t e d t o s o i l m o i s t u r e d e f i c i t (eqn 7.11) Maximum n e t r a d i a t i o n .P]_...Pg p a r a m e t e r s (eqns 7. 5... 7.12) Maximum/night-time s u r f a c e r e s i s t a n c e Energy used by a v e h i c l e (eqn. 4.3) T o t a l mean c o n s u m p t i o n by an i n d i v i d u a l consumer f o r the time p e r i o d o f s t u d y - by premise c l a s s f o r e l e c t r i c i t y & gas Gas e f f i c i e n c y (eqn. 4.5) M e t a b o l i c r a t e f o r p e o p l e and a n i m a l s by time o f day S t o r a g e h e a t f l u x p a r a m e t e r s a~i, a 2 , a 3 p a r a m e t e r s by s u r f a c e t y p e : T a b l e 5.2 12 4 c a l c u l a t i o n s b e f o r e - h a n d and r e a d t h e s e r e s u l t s i n . An example o f t h i s i s t h e c a l c u l a t i o n o f a v a i l a b l e e n e r g y (AE=Q*+Qp-AQg)• To c a l c u l a t e a l l t h e components f r o m s c r a t c h ( i . e . t o c a l c u l a t e b o t h Qp and AQg and t h e n AE) f o r e a c h h o u r r e q u i r e s a l a r g e amount o f a d d i t i o n a l i n i t i a l ( T a b l e 8.1) and h o u r l y i n p u t ( T a b l e 8.2). 5) The number o f s u r f a c e t y p e s needed t o c h a r a c t e r i z e t h e s t u d y a r e a has t o be s p e c i f i e d . I n t h i s s t u d y t h e 'base' number was s i x , namely: paved, b u i l t , c o n i f e r o u s , d e c i d u o u s , g r a s s u n i r r i g a t e d and g r a s s i r r i g a t e d . Note t h a t t h i s s p e c i f i c a l l y r e f e r s t o t h e e v a p o r a t i o n c a l c u l a t i o n whereas o t h e r c a l c u l a t i o n s r e q u i r e d i f f e r e n t a s p e c t s o f t h e s u r f a c e t o be i d e n t i f i e d ( e . g . C h a p t e r 4 ) . I n a d d i t i o n t o t h e s e c h o i c e s v a l u e s a r e a s s i g n e d t o t h e s i t e and s u r f a c e c h a r a c t e r i s t i c s ( T a b l e 8.1) i n c l u d i n g v a l u e s f o r t h e p a r a m e t e r s f o r c a l c u l a t i o n o f s u r f a c e r e s i s t a n c e , s t o r a g e and a n t h r o p o g e n i c h e a t f l u x e s and f o r d e t e r m i n a t i o n o f t h e s o u r c e a r e a o f t h e f l u x . The r e m a i n d e r o f t h e model i s i n a l o o p i n v o l v i n g r e a d i n g i n t h e d a t a ( T a b l e 8.2) and p e r f o r m i n g t h e c a l c u l a t i o n s f o r each h o u r . The i n i t i a l c a l c u l a t i o n s a r e l i s t e d i n F i g u r e 8.1 t o g e t h e r w i t h t h e a p p r o p r i a t e e q u a t i o n numbers. A l l o w a n c e i s made f o r change i n t h e s t o r a g e c a p a c i t y o f d e c i d u o u s v e g e t a t i o n as t h e l e a v e s grow between w i n t e r and summer (eqn. 7.19). The n e x t s t e p i s t h e c a l c u l a t i o n f o r t h e h o u r o f t h e aerodynamic (eqn. 7.1, 7.2 o r 7.3), boundary l a y e r (eqn. 1.12) and s u r f a c e r e s i s t a n c e s (eqns. 7.5 ... 7.12). The r e m a i n i n g s t e p s o f t h e model a r e c o n d u c t e d f o r t h e number o f s t e p s p e r h o u r f o r t h e number o f s u r f a c e t y p e s ( F i g . 8.1). A f t e r d r a i n a g e and e v a p o t r a n s p i r a t i o n have been c a l c u l a t e d t h e s u r f a c e s t o r a g e change (AC) i s c a l c u l a t e d f o r e a c h s u r f a c e : AC = PX - D - E (8.1) where PX - w a t e r a r r i v i n g a t t h e s u r f a c e (mm); D - d r a i n a g e (mm); and T a b l e 8.2 H o u r l y d a t a r e q u i r e m e n t s f o r t h e model 1 25 U n i t s Symbol Comments Day Hour R a i n f a l l mm P Net r a d i a t i o n W m - 2 Q* Wind spe e d m s _ 1 U Wind d i r e c t i o n * , r a d <P S t a n d a r d d e v i a t i o n o f <p ° , r a d <v A i r t e m p e r a t u r e °C Td Wet b u l b t e m p e r a t u r e °C T W o r r e l a t i v e h u m i d i t y % RH P r e s s u r e Pa P S e n s i b l e h e a t f l u x o r W m - 2 OH t e m p e r a t u r e d i f f e r e n c e °C E x t e r n a l w a t e r use mm wu L e a f a r e a i n d e x - L A I S o i l m o i s t u r e d e f i c i t mm SB 2-D f r a c t i o n o f : o p t i o n a l o p t i o n a l pavement -b u i l t -g r a s s -d e c i d u o u s c o n i f e r o u s i r r i g a t e d -u n i r r i g a t e d A n t h r o p o g e n i c h e a t f l u x W n T 2 Qp o r L e n g t h o f r o a d - ma j o r m - m i n o r m Number o f v e h i c l e s - major r o a d - mi n o r r o a d G r i d c o n s u m p t i o n - e l e c t r i c i t y W - gas J Number o f consumers \ by p r e m i s e t y p e Number o f p e o p l e Number o f a n i m a l s S t o r a g e h e a t f l u x W m"2 AQg o r P r o p o r t i o n o f Note: t o t a l a r e a e q u a l s t h e sum - 2D g r e e n s p a c e - o f t h e s e f o u r ( s e e T a b l e 5.1) - 3D w a l l s - 3D r o o f - 2D i m p e r v i o u s 1 2 6 E - evapotranspiration (mm). For a non-irrigated surface: PX = P (8.2) where P - r a i n (mm); and for an i r r i g a t e d surface: PX = P + wu (8.3) where wu - external water use (mm). The state of each surface store (C) i s then updated: Ct_i - AC (8.4) i f C t < 0 then for c a l c u l a t i o n purposes C t = 0 where t - time. When C t i s set to zero vegetation can continue to transpire as the plants have access to s o i l water. A running water balance i s maintained for each surface type. The f l u x c a l culated f o r an i n d i v i d u a l hour i s weighted for the surface types occurring i n the source area of the measurements (Chapter 3). At the end of each hour these fluxes are written out (Table 8.3). 8.3 Performance of the Model 8.3.1 Methods used to compare the performance of the model The performance of the model was compared with the measured lat e n t heat f l u x d e n s i t i e s c o l l e c t e d at the Sunset s i t e , Vancouver (see Chapters 2 & 6). The model was i n i t i a l i z e d with the surface dry, on JD 33 at 0000 LAT, and terminated on JD 179 at 0800 LAT, when f i e l d measurements ceased. In t h i s 3513 hour period, when Qg was modelled continuously, there are 2944 hours of measured Qg (see Chapter 6) available f o r comparison. The model's performance i s evaluated at a number of temporal scales: 1) Hourly - each hour with measured f l u x data are compared to the corresponding modelled value. T a b l e 8.3 Output from t h e e v a p o t r a n s p i r a t i o n - i n t e r c e p t i o n model 1 2 7 U n i t s Comments Day Hour L a t e n t h e a t f l u x W m"2 E v a p o t r a n s p i r a t i o n mm C u m u l a t i v e e v a p o t r a n s p i r a t i o n ram D r a i n a g e mm S u r f a c e s t a t e mm Change mm Comment Aerodynamic r e s i s t a n c e s m"l S u r f a c e r e s i s t a n c e s m"l whole & each s u r f a c e t y p e i f n o t p o s s i b l e t o c a l c u l a t e s t a b i l i t y 1 2 8 2) D a i l y - f l u x e s f o r a l l measured h o u r s a v a i l a b l e on a day a r e a v e r a g e d and compared w i t h t h e a v e r a g e m o d e l l e d f l u x f o r t h o s e h o u r s . Because o f m i s s i n g d a t a t h i s may mean t h a t a 'day' does n o t n e c e s s a r i l y c o n s i s t o f 24 h o u r s . 3) C u m u l a t i v e h o u r l y - h o u r s f o r w h i c h t h e r e a r e measurements a r e a c c u m u l a t e d and compared w i t h t h e c u m u l a t e d m o d e l l e d f l u x f o r t h e same h o u r s . A g a i n because o f m i s s i n g d a t a t h e v a l u e s a r e l e s s t h a n t h e ' t r u e ' t o t a l E f o r t h e t i m e p e r i o d (JD 33-179). 4) Ensemble h o u r l y - f o r e a c h month and f o r t h e whole t i m e p e r i o d (JD 33-179) t h e v a l u e s f o r a p a r t i c u l a r h o u r a r e a v e r a g e d . The p e r f o r m a n c e o f t h e model, i n p a r t i c u l a r t h e s u r f a c e w a t e r s t a t e , was a l s o compared w i t h t h e w e t n e s s s e n s o r s ( C h a p t e r 2 ) . The two wetness s e n s o r s , w h i c h were s i t u a t e d on u n i r r i g a t e d g r a s s and on a c o n i f e r o u s t r e e / h e d g e , gave an i n d i c a t i o n o f when t h e s e p a r t s o f t h e s u r f a c e were wet o r d r y . They were n o t i n s t a l l e d u n t i l JD 38. 8.3.2 'Base' run of the model F o r t h e 'base' r u n o f t h e model t h e v a l u e s a s s i g n e d t o t h e v a r i o u s p a r a m e t e r s were c h o s e n f r o m e x p e r i e n c e t o be t h o s e c o n s i d e r e d t o be t h e most p h y s i c a l l y r e a l i s t i c ( T a b l e 8.4) and a r e n o t a b e s t - f i t t o the model. D r a i n a g e c o e f f i c i e n t s ( T a b l e 7.2) and s u r f a c e s t o r a g e c a p a c i t i e s ( T a b l e 7.3, 7.4) were c h o s e n f r o m v a l u e s g i v e n i n t h e l i t e r a t u r e . The t r a n s i t i o n between summer and w i n t e r v a l u e s f o r t h e d e c i d u o u s v e g e t a t i o n s t o r a g e c a p a c i t y were b a s e d on panorama p h o t o g r a p h s t a k e n a p p r o x i m a t e l y w e e k l y f r o m t h e tower. The model was r u n w i t h t h e a v a i l a b l e e n e r g y a l r e a d y c a l c u l a t e d u s i n g t h e models d e s c r i b e d i n C h a p t e r 4 and C h a p t e r 5. The v a l u e o f r g max was s e t t o 9999 s m"1 ( f o l l o w i n g S h u t t l e w o r t h , 1988b) when t h e c a l c u l a t e d v a l u e s o f gg approached z e r o o r were n e g a t i v e . 1 2 9 T a b l e 8.4 V a l u e s a s s i g n e d t o par a m e t e r s f o r the 'base' r u n of the model Parameter V a l u e a s s i g n e d T i t l e Run number Su n s e t , V ancouver, 1987 1 Type o f r u n t r a n s i t i o n w e t / d r y r a t y p e Time s t e p of c a l c u l a t i o n s ( s ) S i t e c h a r a c t e r i s t i c s zy (m) d (m) z 0 (m) Number o f s u r f a c e t y p e s S h u t t l e w o r t h (eqn. 1.8) N o n - n e u t r a l (eqn. 7.2) 300 22.50 3.50 0.52 6 S u r f a c e S u r f a c e c h a r a c t e r i s t i c s S (mm) D f u n c t i o n (eqn. #) c o e f f i c i e n t - DQ - b C(t=0) 1 2 3 4 5 6 Pavement B u i l d i n g C o n i f e r o u s D eciduous G r a s s G r a s s u n i r r i g i r r i g 0.48 0.25 1.2 0.3 1.3 1.3 7.18 7.18 7.17 7.17 7.17 7.18 10 10 0.013 0.013 0.013 10 3 3 1.71 1.71 1. 71 3 0.0 0.0 0.0 0.0 0.0 0.0 Deciduous t r a n s i t i o n T b ( J D ) T E ( JD) s d s ( m m ) S u r f a c e i r r i g a t e d ( s u r f a c e //) S u r f a c e c o n d u c t a n c e Lm T h <;c) T L ( C) 51 (ram) 52 (mm) Qmax (W m~2) P^ (mm s--*-) P 2 (W m - 2) ?3 ( k S g ' J ) P4 (g k g " 1 ) P5 < ° c ) l P 6 (m m"1) r g max (s m""-'-) 65 115 0.80 6 3.10 40.00 0.00 0.45 15.00 725.00 53.95 633.95 0.0821 8.91 18.88 0.0107 9999.00 1 3 0 The s t a t i s t i c s f o r t h e model's performance as compared t o the measured Qg ar e p r e s e n t e d on an h o u r l y and d a i l y b a s i s i n T a b l e 8.5. The s t a t i s t i c s f o r the model a r e b e t t e r on an h o u r l y t h a n a d a i l y b a s i s p r i m a r i l y because o f t h e l a r g e number o f h o u r l y d a t a p o i n t s . F i g u r e s 8.2 and 8.3 a r e s c a t t e r p l o t s o f the h o u r l y and d a i l y measured v e r s u s m o d e l l e d d a t a p o i n t s , r e s p e c t i v e l y . I n b o t h f i g u r e s t h e d a t a a r e d i s t r i b u t e d a r o u n d the one t o one l i n e . The h o u r l y RMSE o f 27.7 W m"z can be c o n s i d e r e d t o be of t h e same o r d e r as the e r r o r o f the measurements. F i g u r e 8.4 shows the c u m u l a t i v e E f o r the measurement p e r i o d . From t h i s i t can be seen t h a t the model g e n e r a l l y u n d e r - p r e d i c t s u n t i l JD 130. Towards the end o f the s t u d y p e r i o d t h e c u m u l a t i v e t o t a l s a r e a l m o s t i d e n t i c a l . F i g u r e 8.5 shows t h e time s e r i e s o f measured and m o d e l l e d Qg. I n the e a r l y p a r t o f t h e y e a r t h e model u n d e r - p r e d i c t s d u r i n g the m i d d l e o f the day. From mid-March onwards the model mimics the measured d a t a e x t r e m e l y w e l l under a l l c o n d i t i o n s e x c e p t f o r d e w f a l l . P l o t s o f ensemble mean v a l u e s o f Qg f o r the whole s t u d y p e r i o d and f o r each month ( F i g . 8.6a-f) i l l u s t r a t e model p e r f o r m ance a t the d i u r n a l t i m e s c a l e , and changes i n t h i s s e a s o n a l l y . F i g u r e 8.6a, f o r the e n t i r e s t u d y p e r i o d , s u g g e s t s t h a t on average the model u n d e r - p r e d i c t s i n mid- t o l a t e - m o r n i n g and s l i g h t l y o v e r - p r e d i c t s i n the l a t e a f t e r n o o n . The maximum ensemble mean d i f f e r e n c e o f 17.6 W m"2 o c c u r s a t 1200 LAT when the measured f l u x i s 137.7 W m . From the monthly p l o t s i t can be seen t h a t i n the e a r l i e r months on average t h e model u n d e r - p r e d i c t s ( F i g . 8.6b,c,d) and l a t e r i n the y e a r o v e r -p r e d i c t s i n the a f t e r n o o n s ( F i g . 8 . 6 e , f ) . I n F e b r u a r y ( F i g . 8.6b) t h e model u n d e r - p r e d i c t s a l l day. A t 1200 LAT the mean m o d e l l e d Qg (50 W m"2) i s a p p r o x i m a t e l y h a l f t h e mean measured v a l u e (99 W m" 2). I n March and A p r i l ( F i g . 8.6c,d) the model p e r f o r m s v e r y w e l l i n the a f t e r n o o n but u n d e r - p r e d i c t s T a b l e 8.5 S t a t i s t i c s f o r the 'base' model v a l u e s o f Qg S t a t i s t i c H o u r l y D a i l y Number o f p o i n t s (n) 2944 125 Mean Measured (W m~2) 40 .10 40. 49 M o d e l l e d (W m"2) 40. .38 41. 87 S t a n d a r d d e v i a t i o n ( s d ) Measured (W m - 2) 63, .03 21. 80 M o d e l l e d (W m"2) 58. .20 23. 87 S l o p e - f u n c t i o n a l a n a l y s i s ( m f ) a 0, .92 1. 10 C o e f f i c i e n t o f d e t e r m i n a t i o n ( r 2 ) 0. .81 0. 71 Root mean square e r r o r (RMSE ) ( W m"2) 27, .65 13. 00 RMSE s y s t e m a t i c ( R M S E S ) ( W m"2) 10. .72 2. 17 R M S E u n s y s t e m a t i c (R M S E T J)(W m"2) 25. .49 12. 82 Index of. agreement ( d ) b 0. ,95 0. 91 Goodness of f i t ( N & S ) C 0. ,81 0. 64 a Mark and Church (1977) b W i l m o t t and Wicks (1980) c Nash and S u t c l i f f e (1970) F i g u r e 8.2 Comparison o f h o u r l y measured and m o d e l l e d Q E f o r t h e 'base model r u n -3-00 0 100 200 300 Q E (W m - 2) - measured i g u r e 8.3 Comparison o f d a i l y measured and m o d e l l e d Q E f o r t h e 'bas model r u n 1 3 4 Figure 8.4 Cumulative plot of measured and modelled (.'base1 rUn) evaporation (see text f o r d e t a i l s ) . meosur ed base Time (JD) 135 Figure 8.5 Time s e r i e s of hourly measured (—) and modelled (--) Qg (base). Note that the measured data are not continuous. 300. 250. 200 . 3 3 3 4 3 5 3 5 3 7 3 8 3 9 4 0 4 1 4 2 5 3 4 4 3 3 4 6 4 7 4 8 4 9 5 5 5 1 5 1 5 3 5 4 5 5 5 6 — 5 7 300. 250. 200 . 58 59 60 61 62 63 64 65 66 67 gg 69 70 71 72 73 74 75 76. 77 78 79 80 Si 8T I ; I \ I ( I II hi k il \ I I Jul 1 y A 1 M i l I 1 - V 11 pi' ' 1 1 Y K* (Ivy1 83 84 85 86 87 88 89 90 91 52 §3 94 95 96 97 98 99 100 101 102 16J 104 105 106 10 7 Time (JD) F i g u r e 8.5 (cont.) 136 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 133 134 135 136 137 138 139 MO 141 142 H3 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 Time (JD) 1 3 7 F i g u r e 8,6 Ensemble p l o t s o f measured and m o d e l l e d C'base' run) (a) (b) ( c ) (d) (e) Cf) 2 0 0 l — - M e a s u r e d i " M o d e l l e d 0 200 - M e a s u r e d M o d e l l e d 200 200 - M e a s u r e d Mode l i e d - M e a s u r e d " M o d e l l e d JD 3 3 - 1 7 9 , 1987 JD 3 3 - 5 9 , 1907 JD 6 0 - 9 0 , 1987 JD 1 2 1 - 1 5 1 , 19.17 JD 1 5 2 - 1 7 9 , 1987 T ime (LAT) 10 11 ]• 1 3 8 i n t h e m o r n i n g . I n May and June ( F i g . 8.6e,f) t h e o p p o s i t e o c c u r s ; t h a t i s t h e model p e r f o r m s e x t r e m e l y w e l l i n t h e morning but o v e r - p r e d i c t s i n t h e a f t e r n o o n . From t h i s i t i s c o n c l u d e d t h a t t h e model does w e l l on t h e a v e r a g e but f o r i n d i v i d u a l t i m e p e r i o d s t h e p e r f o r m a n c e i s - n o t so good. F i g u r e 8.7 p r o v i d e s a means t o compare t h e m o d e l l e d s u r f a c e s t a t e w i t h t h a t r e c o r d e d by t h e w e t n e s s s e n s o r s . I n e a c h box o f f i v e t r a c e s t h e u p p e r two p l o t s show th e w a t e r a r r i v i n g a t t h e s u r f a c e ; a t t h e t o p i s t h e r a i n f a l l r e c e i v e d by a l l s u r f a c e s , and t h e s e c o n d i s t h e e x t e r n a l w a t e r use (wu) w h i c h i s o n l y r e c e i v e d by t h e i r r i g a t e d g r a s s p o r t i o n o f t h e s u r f a c e . E x t e r n a l w a t e r use d i d n o t b e g i n u n t i l JD 121 ( C h a p t e r 2 ) . The t h i r d p l o t shows t h e s t a t u s o f t h e wetness s e n s o r s ( i . e . w h e t h e r wet o r d r y ) . The s e n s o r l o c a t e d on t h e g r a s s ( dashed l i n e ) has a s m a l l e r r ange t h a n t h a t l o c a t e d on t h e c o n i f e r o u s v e g e t a t i o n ( s o l i d l i n e ) . The g r a s s s e n s o r range i s f r o m h a l f way between wet and d r y and t h e wet end. The f o u r t h t r a c e i s t h e m o d e l l e d s u r f a c e w a t e r s t a t u s o f t h e whole s u r f a c e and t h e f i f t h o r l o w e s t p l o t shows th e m o d e l l e d w e t n e s s s t a t u s o f t h e i n d i v i d u a l s u r f a c e t y p e s . The s i x i n d i v i d u a l s u r f a c e s a r e n o t s e p a r a t e l y l a b e l l e d b u t t h e v e g e t a t e d s u r f a c e s a r e t h o s e w h i c h h o l d more w a t e r on t h e s u r f a c e and t h e l e s s e r v a l u e s a r e t h e b u i l t and paved s u r f a c e s . Once i r r i g a t i o n b e g i n s t h e s t a t e o f t h e i r r i g a t e d g r a s s s u r f a c e ( F i g . 8.7c,d t h e dashed l i n e i n t h e l o w e s t p l o t ) becomes d i s t i n g u i s h a b l e f r o m t h e o t h e r s u r f a c e s . . L o o k i n g a t t h i s s e t o f f i g u r e s (8.7a,b,c,d) i t c a n be s e e n t h a t t h e model does an e x t r e m e l y good j o b o f i n d i c a t i n g when th e s u r f a c e i s d r y . The m o d e l l e d s u r f a c e s t a t e f o l l o w s a v e r y s i m i l a r p a t h t o t h e s e n s o r s . V i s u a l o b s e r v a t i o n s o f d r y i n g i n d i c a t e t h a t t h e paved and b u i l t s u r f a c e s d r y more q u i c k l y t h a n t h e v e g e t a t e d s u r f a c e s and i t c a n be seen i n F i g u r e 8.7 t h a t t h e m o d e l l e d paved and b u i l t s u r f a c e s mimic t h i s p a t t e r n . T h i s s u g g e s t s t h a t t h e d r a i n a g e f u n c t i o n s i n t h e e v a p o r a t i o n model a r e s i m u l a t i n g t h e s u r f a c e w a t e r 1 39 F i g u r e 8.7 P l o t s o f p r e c i p i t a t i o n , w a t e r u s e , s u r f a c e w etness and m o d e l l e d s u r f a c e w a t e r s t a t e (.see t e x t f o r d e t a i l s ) . (a) JD 3A-74 l l JUic ll 'V. A . A ^ _ /A. >A\U<!u\ . I A V I X - J S  KfAP\ i* ib ja- *o * : -6 48 50 52 54 56 58 60 62 64 66 68 70 72 74 DAY (b) JD 75-116 Wet Ws IT A. I i 1 u IA k i . 76 78 80 82 8« 86 88 90 82 9« 96 98 CO 02 »» C6 108 IK) 11! i n IW DAY F i g u r e 8.7 ( c o n t . ) (c) JD 117-157 ill 11. . ... , i II . i _ A. *k A^ALA. A A „ A A. A A. A - ... .*! 1^ . A A ^ _A >. _ A - i .A - *» Ax 1 i 6 \ ........ IVU . J ' f\ A " A A/V ft/ 1 * J i • - - - - -. 1 ' 1 it » - . . 118 120 112 12* 126 128 130 132 13* 136 138 1*0 - 1*2 1** i«6 1*8 i i O ttl 15* ft* DAY (d) JD 158-179 1 . i . i. •L fU-,— L 1.;,.. 159 '61 163 '67 169 171 173 175 177 179 DAY 1 4 1 s t a t e a p p r o p r i a t e l y . The o n l y f e a t u r e n o t w e l l r e p r e s e n t e d i s t h e o c c u r r e n c e of d e w f a l l . T h i s was v i s u a l l y e v i d e n t on the g r a s s but n o t s i m u l a t e d . I n summary i t appears t h a t a l t h o u g h t h e model does w e l l on av e r a g e i t g e n e r a l l y u n d e r - p r e d i c t s i n t h e e a r l y p a r t o f t h e y e a r and p e r f o r m s b e t t e r i n th e s p r i n g / e a r l y summer, a l t h o u g h i t may t e n d t o o v e r - p r e d i c t . The m o d e l l e d Qg i s a l w a y s g r e a t e r t h a n z e r o . D e w f a l l i s n o t p r e d i c t e d b u t was o b s e r v e d t o o c c u r on g r a s s on some n i g h t s . D e w f a l l i s t h o u g h t t o be one of the r e a s o n s why the model under p r e d i c t s i n t h e morning. The e v a p o r a t i o n o f dew and the d r y i n g of t h e s u r f a c e i n the morning w i l l r e s u l t i n a l a r g e r measured e v a p o r a t i o n r a t e . The o v e r p r e d i c t i o n o f the model a p p e a r s t o c o i n c i d e w i t h the b e g i n n i n g o f e x t e r n a l w a t e r u s e . The o v e r p r e d i c t i o n may i n p a r t be due t o t h e w a t e r use i n p u t b e i n g t o o l a r g e . The w a t e r use d a t a used as h o u r l y i n p u t were c o l l e c t e d i n a n o t h e r more a f f l u e n t a r e a o f Vancouver ( C h a p t e r 2) and p r o - r a t e d f o r the a r e a i n t h e p r e s e n t s t u d y a r e a . 8.4 Sensitivity analysis of the model I n o r d e r t o a s s e s s the r o b u s t n e s s o f t h e model and i t s s e n s i t i v i t y t o v a r i o u s i n p u t p a r a m e t e r s and e q u a t i o n s the performance of the model was i n v e s t i g a t e d when v a r i o u s o f the i n i t i a l i n p u t s ( T a b l e 8.1) were changed o v e r a range o f v a l u e s . The e f f e c t o f making such changes i s r e p o r t e d i n c o m p a r i s o n t o b o t h the measured r e s u l t s and the 'base' r u n . I n each case o n l y the v a r i a b l e o f i n t e r e s t was changed from the 'base' r u n ( T a b l e 8.4), u n l e s s o t h e r w i s e s p e c i f i e d . C u m u l a t i v e p l o t s a r e used t o show the i n f l u e n c e o f the changes on the m o d e l l e d e v a p o r a t i o n (E) because t h e y a l l o w the s e a s o n a l e f f e c t s t o be gauged. 1 4 2 8.4.1 Rutter The model was r u n a f t e r c h a n g i n g t h e way i n w h i c h t h e t r a n s i t i o n between wet and d r y was r e p r e s e n t e d f r o m t h e S h u t t l e w o r t h a p p r o a c h (1.5 w i t h 1.8, 1.9, 1.10, 1.11) t o t h e t w o - s t e p R u t t e r e q u a t i o n s ( 1 . 5 , 1.6, 1.7). The p e r f o r m a n c e o f t h e model u s i n g t h e R u t t e r i n s t e a d o f t h e S h u t t l e w o r t h e q u a t i o n s i s s i g n i f i c a n t l y p o o r e r ( T a b l e 8.6, F i g . 8.8). The model was r u n u s i n g t h r e e d i f f e r e n t c o n d i t i o n s : f i r s t l y , ( t e r m e d R u t t e r i n T a b l e 8.6) t h e o n l y t h i n g changed was t h e s e t o f t r a n s i t i o n e q u a t i o n s ; s e c o n d l y , ( t e r m e d R u t t e r - d r a i n 1) t h e model was r u n w i t h a change o f t h e d r a i n a g e c o e f f i c i e n t b f o r s u r f a c e s 1, 2,and 6 f r o m 3 t o 1.5 ( s e e T a b l e 8.4); and t h i r d l y , ( t e r m e d R u t t e r - d r a i n 2) . t h e d r a i n a g e f u n c t i o n s f o r a l l s u r f a c e s were s e t t o e q u a t i o n 7.17 w i t h Dn=0.0014 and b=5.25 ( S h u t t l e w o r t h , 1988b). F o r t h e f i r s t two r u n s , t h e model u n d e r - p r e d i c t s c o n s i s t e n t l y f o r a l l months w h i c h means t h e c u m u l a t i v e t o t a l E i s c o n s i d e r a b l y l e s s t h a n t h a t measured ( F i g . 8.8). P a r t o f t h e p r o b l e m i s t h a t t h e e v a p o r a t i o n r a t e s do n o t appear t o be l a r g e enough t o d r y t h e s u r f a c e c o m p l e t e l y . T h i s may be overcome by u s i n g s t e e p e r d r a i n a g e f u n c t i o n s ( i . e . more d r a i n a g e p e r t i m e s t e p ) . The R u t t e r model a p p e a r s t o be v e r y s e n s i t i v e t o the d r a i n a g e f u n c t i o n s . I n v i e w o f t h i s r e s u l t and t h e r e l a t i v e l y good p e r f o r m a n c e o f t h e S h u t t l e w o r t h u n i f i e d a p p r o a c h no f u r t h e r s e n s i t i v i t y r u n s were made w i t h t h i s f o r m o f t h e model. 8.4.2 Time step of calculations As n o t e d above t h i s t y p e o f model has been r u n w i t h 120, 300, and 720 s ti m e s t e p s . I n t h e s e n s i t i v i t y a n a l y s i s t h e model i s r u n w i t h a 3600 s i n t e r v a l i n a d d i t i o n t o t h e s e 3 t i m e s t e p s ( F i g . 8.9, T a b l e 8.7). A p a r t f r o m t h e o b v i o u s i n c r e a s e i n c o m p u t a t i o n a l t i m e , t h e e f f e c t o f d e c r e a s i n g t h e 14 3 T a b l e 8.6 S t a t i s t i c s o f model p e r f o r m a n c e f o r Qg when t h e R u t t e r t r a n s i t i o n e q u a t i o n s a r e u s e d ( s e e t e x t f o r f u r t h e r e x p l a n a t i o n ) . S t a t i s t i c 3 'Base' R u t t e r R u t t e r R u t t e r d r a i n 1 d r a i n 2 (a) H o u r l v Mean (W ra~2) 40, .38 10 .07 5, .80 43, .82 sd (W n T 2 ) 58, .20 19 .36 14, .64 59, .18 mf 0, .92 0, .31 0, .23 0. .94 r 2 0, .81 0, .19 0, .13 0. .71 RMSE (W m"2) 27, .65 • 64, .78 68, .62 34. .56 RMSE S (W m"2) 10, .72 62, .38 67, .24 13. .61 R M S E T J (W m"2) 25. .49 17, .46 13, .69 31. .76 d 0, .95 0. .51 0. .48 0. .91 N&S 0, .81 -0, .06 -0. .19 0. .70 (b) D a i l y Mean (W m"2) 41. ,87 10. .56 6. ,05 45. ,15 sd (W n T 2 ) 23. ,87 11. .61 9. .03 28. ,60 mf 1. ,10 0. .53 0, .41 1. ,31 r 2 0. ,71 0. .07 0. ,04 0. ,57 RMSE (W m"2) 13. 00 37. ,06 40. ,85 19. 32 RMSE S (W m - 2) 2. ,17 35. ,33 39. .88 4. 66 RMSEn (W m - 2) 12. 82 11. .21 8. ,86 18. 75 d 0. 91 0. ,47 0. ,43. 0. 84 N&S 0. ,64 -1, ,89 -2. ,51 0. 21 a see T a b l e 8.5 f o r e x p l a n a t i o n o f s t a t i s t i c s F i g u r e 8.8 I n f l u e n c e o f u s i n g t h e R u t t e r and S h u t t l e w o r t h t r a n s i t i o n e q u a t i o n s on t h e c u m u l a t e d E. baas _ R u t l i r - b o x . _ Rutt tr - dram 1 . . . Ruttar - drain 2 43 107 Time (JD) 171 F i g u r e 8. 9 I n f l u e n c e o f c h a n g i n g t h e t i m e s t e p o f t h e c a l c u l a t i o n on t h e cumulated E. — w — X — x measured 120 s Time (JD) 1 46 T a b l e 8.7 S t a t i s t i c s o f model performance f o r Qg when the c o m p u t a t i o n a l t i m e s t e p changed. Note base c a l c u l a t i o n s have a 300 s ti m e s t e p b u t a d i f f e r e n t method o f c a l c u l a t i n g r<j max (see s e c t i o n 8.4.4). C o m p u t a t i o n a l time s t e p ( s ) S t a t i s t i c 3 'Base ' 120 300 720 3600 (a) H o u r l v Mean (W m"2) 40 .38 41 .26 41 .24 41 .20 40 .26 sd (W m~2) 58 .20 57 .67 57 .67 57 .68 57 .86 m f 0 .92 0 .91 0 .91 0 .92 0 .92 r 2 0 .81 0 .80 0 .80 0 .80 0 .81 RMSE (W n T 2 ) 27 .65 27 .96 27 .95 27 .90 27 .80 RMSE S (W n T 2 ) 10 .72 11 .39 11 .38 11 .35 11 .09 RMSEu (W m"2) 25. .49 25, .54 25. .53 25. .49 25 .49 d 0. .95 0, .94 0 .94 0 .94 0 .94 N&S 0 .81 0, .80 0, .80 0. .80 0 .81 (b) D a i l v Mean (W m"2) 41. ,87 42. ,72 42. ,71 42. ,65 41. ,66 sd (W m'2) 23. ,87 24. ,19 24. .19 24. ,23 24. ,60 mf 1. ,10 1. ,11 1. ,11 1. ,11 1. ,13 r 2 0. 71 0. 71 0. ,71 0. .71 0. ,72 RMSE (W n T 2 ) 13. ,00 .13. ,21 13. ,20 13. .18 12. ,99 RMSE S (W m"2) 2. 17 2. 62 2. 60 2. 53 1. 45 RMSEu < w m " 2 ) 12. ,82 12. 95 12. ,95 12. 94 12. 91 d 0. 91 0. 91 0. 91 0. 91 0. 92 N&S 0. 64 0. 63 0. 63 0. 63 0. 65 a See T a b l e 8.5 f o r e x p l a n a t i o n o f s t a t i s t i c s 1 4 7 c o m p u t a t i o n a l i n t e r v a l t o 120 s (number o f s t e p s p e r hour=30) i s n o t t o improve t h e performance of the model ( T a b l e 8.7). E x t e n d i n g t h e i n t e r v a l t o 720 s (number of s t e p s p e r hour=5) shows s l i g h t improvement i n the s t a t i s t i c a l p e r f o r m a n c e o f the model but o t h e r w i s e no s i g n i f i c a n t change i n the r e s u l t s . The e f f e c t o f c h a n g i n g t o 3600 s i s t o have the s u r f a c e d r y t o o q u i c k l y . P l o t s o f t h e s t a t e o f the s u r f a c e show a s e r i e s o f s p i k e s ( F i g . 8.10) r a t h e r t h a n t h e more r e a l i s t i c g r a d u a l d r y i n g ( F i g . 8.7). There i s s l i g h t improvement i n the s t a t i s t i c s f o r the performance o f the model compared t o t h e 720 s t i m e s t e p . The ensemble p l o t s f o r each month do n o t change a p p r e c i a b l y . I t would appear from t h e s e r e s u l t s t h a t t h e model can be r u n a t the l o n g e r 720 s t i m e s t e p r a t h e r t h a n 300 s, and m a i n t a i n a r e a l i s t i c s u r f a c e - s t a t e . E x t e n d i n g the time s t e p t o one h o u r , however, r e s u l t s i n l e s s r e a l i s t i c s u r f a c e s t a t e p r e d i c t i o n s . 8.4.3 Aerodynanic resistance The 'base' v e r s i o n o f the model used the n o n - n e u t r a l r a e q u a t i o n ( 7 . 2 ) . Runs were made u s i n g the n e u t r a l and the Thorn and O l i v e r (1977) e q u a t i o n s f o r c a l c u l a t i n g r a (eqns 7.1, 7.3 r e s p e c t i v e l y ) . These l e a d t o a s l i g h t l y p o o r e r s e t of s t a t i s t i c s f o r model performance but the model does work s l i g h t l y b e t t e r i n the e a r l i e r months ( T a b l e 8.8, F i g . 8.11). The model i s n o t p a r t i c u l a r l y s e n s i t i v e t o w h i c h e q u a t i o n i s used and t h e r e f o r e i t i s n o t e s s e n t i a l t o have the i n p u t n e c e s s a r y t o c a l c u l a t e the s t a b i l i t y f u n c t i o n s f o r the d e t e r m i n a t i o n of r a , . There i s v e r y l i t t l e d i f f e r e n c e between the m o d e l l e d Qg u s i n g the n e u t r a l and Thorn and O l i v e r e q u a t i o n s . The n e u t r a l e q u a t i o n g e n e r a t e s s l i g h t l y h i g h e r v a l u e s f o r Qg ( F i g . 8.11). 14 8 F i g u r e 8.10 I n f l u e n c e o f u s i n g a 3600 s t i m e s t e p on t h e m o d e l l e d w a t e r s u r f a c e s t a t e . Note t h e s p i k e s i n t h e l o w e r p o r t i o n o f t h e p l o t compared t o F i g . 8.6. 1 i l ,i tl 1, : . i 11, I1J1..1 j . .i.llL. d l L A 1 '/ i _ il v n i f j i i 'Tri* T l •\ -11, tai ll .11 i 1 A L Li i l .L J . i All Ilk ^ hi ilV J L 1(4 34 36 38 40 4 ! 44 4« 48 50 52 54 56 58 60 62 64 66 68 70 72 7* DAY 1 49 T a b l e 8.8 S t a t i s t i c s o f model performance f o r Qg when t h e r a e q u a t i o n i s changed r a e q u a t i o n S t a t i s t i c 3 Non- N e u t r a l Thorn & n e u t r a l * 3 O l i v e r Ca) H o u r l v Mean (W m"2) 40 .38 42 .13 41 .64 sd (W n T 2 ) 58 .20 59 .74 58 .14 mf 0 .92 0. .95 0 .92 r 5 0. .81 0, .79 0 .79 RMSE (W m" 2V 27 .65 29 .07 29 .00 RMSE S (W m"2) 10. .72 10. .09 11, .47 RMSEu (W n T 2 ) 25. .49 27. .26 26. .64 d 0. .95 0. .94 0. .94 N&S 0. .81 0. .79 0, .78 ( b ) D a i l v Mean (W m"2) 41. .87 43. .71 43. .25 sd (W n T 2 ) 23. ,87 24. ,54 24. .13 mf 1. .10 1. ,13 1. ,11 r 2 0. 71 0. .68 0. ,67 RMSE (W n T 2 ) 13. ,00 14. ,39 14. .27 RMSE S (W n T 2 ) 2. 17 3. 59 3. 43 RMSEu (W n T 2 ) 12. 82 13. 94 13. 85 d 0. 91 0. 90 0. 90 N&S 0. 64 0. .56 0. 57 a See T a b l e 8.5 f o r e x p l a n a t i o n o f s t a t i s t i c s b Base e q u a t i o n 150 F i g u r e 8.11 I n f l u e n c e o f e q u a t i o n used t o c a l c u l a t e a erodynamic r e s i s t a n c e on cumulated E. 1 51 8.4.4 Surface resistance The changes made to the model r e l a t i n g to rg can be s p l i t into two types: f i r s t l y those concerning the rg maximum; and, secondly those changing the values of the parameters used within the rg sub-model (see section 7.3). The model was run with f i v e d i f f e r e n t methods to deal with large rg (or gg approaching zero) and when Q* i s negative. In the 'base' run when gg approaches zero or becomes negative rg i s set to 9999 s m'^-. In the other four cases rg was set to 9999, 2500, 1250 or 750 s m"-'- when Q* i s negative. Table 8.9 contains the hourly and d a i l y s t a t i s t i c s f o r the comparison with these changes. It can be seen that there i s very l i t t l e difference between the 'base' run and those when rg max was set to 9999 s nT^. As the value of rg max i s decreased the performance deteriorates s l i g h t l y . Figure 8.12 shows a systematic influence on the cumulative p l o t s . This i s primarily due to the fact that as rg max i s reduced night-time values of Qg increase, and therefore accumulated Qg becomes larger. However, the daytime performance i s not improved. The values of the rg parameters (P]_...Pg) were changed between the three sets of model parameters presented i n Table 7.1 (AD2 were the 'base' parameters). Table 8.10 presents the s t a t i s t i c s f o r the hourly and d a i l y comparisons. The 'base' r e s u l t s are generally s l i g h t l y better than when the other two sets of parameters were used. Figure 8.13 shows the cumulative plot for the three sets of rg parameters and the measured values. Using AD1 and A l l parameters the calculated day-time fluxes are s l i g h t l y l e s s than f o r the 'base' case. The values obtained using AD1 are smaller than those using the A l l parameters. The AD1 and A l l versions of the runs remain closer to p a r a l l e l with the measured cumulative E during the l a t e r months, suggesting that they are better at pred i c t i n g Qg than the AD2 ('base') parameters which are over-1 5 2 Table 8.9 S t a t i s t i c s of model performance f or Qg when rg max i s changed rg max (s m"1) S t a t i s t i c 3 9999 2500 ' 1250 750 'Base' (a) Hourly Mean (W m~2) sd (W nT 2) mf r 2 RMSE (W nT 2) RMSES (W m"2) R M S E T J (W m'2) d N&S (b) Da i l y Mean (W m"2) sd (W nT 2) mf r 2 RMSE (W nT 2 RMSEg (W m" R M S E T J (W m'2) d N&S 40. .38 41. .24 42 . 28 43. , 51 40, .38 58. .20 57. .67 57. .07 56, .42 58. .20 0. .92 0, .91 0, .91 0. .90 0. .92 0, .81 0. ,80 0. .80 0. .79 0. .81 27. .65 27. .95 28. ,43 29. ,16 27. .65 10. .72 11. ,38 12. .24 13. 37 10. .72 25. ,49 25. ,53 25. ,65 25. ,91 25. ,49 0. ,95 0. 94 0. 94 0. 94 0. 95 0. .81 0. .80 0. ,80 0. ,79 0. .81 41. .88 42, .71 43 .71 44 .91 41 .87 23. .87 24. • 19 24. .56 24 .99 23, .87 1 .10 1, .11 1 .13 1, .15 1 .10 0. , 71 0. .71 0, .72 0, .72 0, . 71 13. .01 13. .20 13 . 52 14, .01 13 .00 2. ,17 2. ,60 3, .38 4, .47 2, .17 12. ,83 12. .95 13 , .09 13, .28 12. .82 0. ,91 0. ,91 0, .•91 0. ,91 0. ,91 0. ,64 0. ,63 0, .62 0. ,59 0. .64 a See Table 8.5 for explanation of s t a t i s t i c s F i g u r e 8.12 I n f l u e n c e o f t h e maximum v a l u e a s s i g n e d t o r g on cum u l a t e d E. meosured Time (JD) 1 5 4 Table 8.10 S t a t i s t i c s of model performance f o r Qg when rg parameters are changed rg parameters S t a t i s t i c 3 AD1 A l l 'base' (a) Hourly Mean (W m~2) sd (W nT 2) mf r 2 RMSE (W m"2) RMSEg (W ra"2) RMSEn (W nT2') d N&S (b) Daily Mean (W m"2) sd (W m"2) mf r 2 RMSE (W ra-2) RMSEg (W m"2) R M S E T J (W nT 2) d N&S 39, .20 39 .84 40 .38 56 .31 57 .43 58 .20 0, .89 0 .91 0 .92 0. .81 0 .81 0. .81 27. .64 27 .65 27 .65 12. ,45 11. .42 10. .72 24. ,68 25, .53 25, .49 0. .94 0, .95 0 .95 0. .81 0, .81 0, .81 4.0. 68 41. . 32 41. .87 "22. 85 23. ,52 23. .87 1. ,05 1, .08 1. .10 0. 70 0. .71 0. ,71 12. 81 12. .93 13. ,00 2. ,70 2. ,20 2. ,17 12. 52 12. .74 12. ,82 0. 91 0. ,91 0. .91 0. 65 0. .65 0. ,64 a See Table 8.5 f o r explanation of s t a t i s t i c s F i g u r e 8.13 I n f l u e n c e o f t h e pa r a m e t e r s u s e d f o r c a l c u l a t i n g r<, on cumulated E. m e a s u r e d b a s e - AD2 AD1 A l l 1501 V Jli W cu •H i O I O O H 50" 0 43 107 Time (.JD) 171 156 predicting. The model responds to reasonably small changes i n rg (as w i l l be produced by changing rg model parameters) but i t i s not so s e n s i t i v e as to make the use of any of the models i n section 7.3 unwise. 8.4.5 Storage capacities Three types of changes were made to the model r e l a t i n g to the storage capacity (S): f i r s t l y , changing the value of S for an i n d i v i d u a l surface and keeping the remainder of the surfaces at the base value; secondly changing a l l surface values on a single run; and t h i r d l y , changing the storage capacity i n conjunction with the drainage functions. The r e s u l t s of the l a t t e r a l t e r a t i o n s are discussed i n the drainage section which follows. The storage capacity of each of the surface types was changed over a range of values determined from previous studies (Tables 7.3, 7.4). It should be appreciated that the magnitude of the response of the model depends not only on the change i n the value of S but also on the r e l a t i v e abundance of the surface type within the study area (see Chapter 3). A p r i o r i i t i s to be expected that changes to the deciduous and coniferous vegetation have the lea s t e f f e c t because they occupy the two smallest areas within the current study s i t e , whereas' changes i n the grass capacity w i l l have the most e f f e c t . For paved surfaces S was changed from 0.30 to 2.50 mm (Table 8.11). The ef f e c t of t h i s i s to decrease the mean modelled value of Qg and the R M S E , RMSEg and R M S E i j . The systematic error for the MSE of the d a i l y Qg shows an improvement from 3.4% to 1.6%. This suggests that model performance would be improved by increasing the size of S for the paved surfaces, although there i s less than 1 W m"^  change i n the ensemble values f o r each of the months. However, the o v e r a l l r e s u l t s show that the model i s not p a r t i c u l a r l y s e n s i t i v e 15 7 Table 8.11 S t a t i s t i c s of model performance f o r Qg when S the value of S i s changed for the pavement S t a t i s t i c 3 0.3 S capacity (mm) - pavement 0.48 b 0.56 1.00 2.50 (a) Hourly Mean (W nT 2) sd (W m - 2) mf r 2 RMSE (W ra"2) RMSEg (W ra"2) RMSEu (W ra"2) d N&S (b) Daily Mean (W m"2) sd (W nT 2) r z RMSE (W nT 2) RMSES (W m"2) RMSEu (W nT 2) d N&S 40. . 55 40, ,38 40, ,32 40. .13 39, .96 58, .19 58, .20 58, .21 58. .23 58. .25 0. .92 0. ,92 0, .92 0. .92 0. .92 0. .81 0. .81 0, .81 0. .81 0, .81 27. .72 27. ,65 27. ,63 27. ,56 27. .52 10. .76 10. .72 10, .70 10. .64 10. .60 25. .54 25. ,49 25. ,47 25. .42 25, .40 0. .95 0, .95 0. .95 0. ,95 0, ,95 0. .81 0, .81 0. .81 0. .81 0, .81 42. .07 41. .87 41. ,81 41. ,57 41. ,39 23. ,76 23. .87 23. ,90 24. ,03 24. ,14 1. .09 1. .10 1, .10 1, ,10 1. .11 0. ,71 0. ,71 0. ,71 0. 72 0. ,72 13. ,04 13. ,00 12. ,99 12. ,94- 12. ,91 2. ,40 2. ,17 2 , 09 1. ,83 1. ,62 12. ,82 12. ,82 12. ,82 12. .81 12. ,81 0. ,91 0. ,91 0, ,91 0. ,92 0. ,92 0. ,64 0. ,64 0. ,65 0. .65 0. ,65 a See Table 8.5 f o r explanation of s t a t i s t i c s b 'Base' value 1 5 8 t o changes i n the s i z e o f S w i t h i n t h e range o f v a l u e s r e p o r t e d i n t h e l i t e r a t u r e . The i n f l u e n c e o f c h a n g i n g S f o r b u i l d i n g s f r o m 0.25 t o 2.50 mm ( T a b l e 8.12) r e s u l t s i n a v e r y s i m i l a r r e s p o n s e i n the c a l c u l a t e d Qg as f o r the changes i n 5 o f t h e pavement. T h i s i s q u i t e r e a s s u r i n g g i v e n t h a t i t i s d i f f i c u l t t o measure and/or a s s i g n a b s o l u t e v a l u e s t o t h i s p arameter (see f o r example F a l k 6 N i e m c z y n o w i c z , 1978). The r e s p o n s e t o changes i n the s i z e o f S f o r c o n i f e r o u s v e g e t a t i o n from 0.75 t o 2.5 mm ( T a b l e 8.13), t h e s i z e o f t h e w i n t e r and summer v a l u e s o f S f o r d e c i d u o u s v e g e t a t i o n , and t h e t i m i n g o f t h e t r a n s i t i o n between t h e s e ( T a b l e 8.14) a r e v i r t u a l l y u n d e t e c t a b l e . T h i s i s i n l a r g e p a r t due t o t h e i r r e l a t i v e i n s i g n i f i c a n c e i n t h e Sunset s t u d y a r e a i n terms o f p r o p o r t i o n s o f s u r f a c e c o v e r ( F i g . 3.9). The v a l u e s a s s i g n e d t o S f o r g r a s s were v a r i e d o v e r . t h e l a r g e range quoted i n t h e l i t e r a t u r e ( T a b l e 7.4) from 0.5 t o 10.2 mm ( T a b l e 8.15, F i g . 8.14). The i r r i g a t e d and u n i r r i g a t e d g r a s s were a s s i g n e d the same v a l u e e x c e p t f o r the one case where the u n i r r i g a t e d g r a s s was a s s i g n e d a l a r g e r v a l u e o f 10.2 mm compared t o the i r r i g a t e d v a l u e o f 7.6 mm. The model showed a d i s t i n c t r e s p o n s e t o the i n c r e a s e i n the s i z e o f S f o r g r a s s f o r two r e a s o n s . F i r s t l y , t he s i z e o f the changes t o S a r e much l a r g e r t h a n f o r o t h e r s u r f a c e t y p e s because a w i d e r range o f v a l u e s have been r e p o r t e d i n the l i t e r a t u r e (see T a b l e s 7.3, 7.4); and s e c o n d l y , because g r a s s i s the most e x t e n s i v e i n d i v i d u a l s u r f a c e t y p e i n the s t u d y a r e a . Three t h i n g s a r e a p p a r e n t from F i g u r e 8.13: f i r s t l y , f o r g r a s s the s m a l l e r the v a l u e o f S the l a r g e r the m o d e l l e d E; s e c o n d l y , i n c r e a s i n g the s i z e o f S beyond a c e r t a i n p o i n t ( s m a l l e r t h a n 6.4 mm) has no f u r t h e r i n f l u e n c e on c a l c u l a t e d E; and t h i r d l y , once e x t e r n a l w a t e r use b e g i n s (JD 121), w h i c h o c c u r s on a p o r t i o n of- the g r a s s , t h e r e i s a 1 59 Table 8.12 S t a t i s t i c s of model performance f o r Qg when the value of S i s changed f o r buildings S capacity (mm) - buildings S t a t i s t i c 3 0.25 b 0.48 1.00 2.50 (a) Hourlv Mean (W nT 2) 40 .38 40 .18 39 .94 39 .77 sd (W nT 2) 58 .20 58 .23 58 .26 58 .29 mf 0 .92 0 .92 0 .92 0 .93 r 2 0. .81 0 .81 0 .81 0 .81 RMSE (W nT 2) 27. .65 27 .61 27 .54 27 .52 RMSEg (W nT 2) 10, .72 10, .67 10. .61 10 .57 RMSEij (W nT 2) 25, .49 25, .46 25, .42 25. .40 d 0. .95 0, .95 0. .95 0. .95 N&S 0, .81 0, .81 0 .81 0 .81 (b) Daily Mean (W m"2) 41. ,87 41. ,64 41, .37 41, .18 sd (W m'2) 23. .87 24. ,01 24, .17 24, . 28 mf 1. , 10 . 1. .10 1, .11 1, .11 r 2 0. .71 0. ,71 ' 0. 72 0. ,72 RMSE (W nT 2) 13. ,00 12. .98 12 . 93 12. .91 RMSES (W m - 2) 2. .17 1. ,91 1. .58 1. ,38 RMSEij (W m"2) 12 . ,82 12. ,84 12. .83 12. ,84 d 0. 91 0. ,91 0. ,92 0. ,92 N&S 0. ,64 0. ,65 0. .65 - 0. ,65 a See Table 8.5 for explanation of s t a t i s t i c s b 'Base' value 160 T a b l e 8.13 S t a t i s t i c s o f model performance f o r Qg when the v a l u e o f S i s changed f o r c o n i f e r o u s v e g e t a t i o n S t a t i s t i c 3 0.75 S c a p a c i t y (mm) - c o n i f e r o u s v e g e t a t i o n 0.90 1.20 b 1.50 2.0 2.5 (a) H o u r l y Mean (W n T 2 ) sd (W n T 2 ) mf RMSE (W rrT 2 RMSES (W m" RMSEu (W m"2) d N&S (b) D a i l y Mean (W n T 2 ) sd (W n T 2 ) m£ r 5 RMSE (W n T 2 RMSE S (W nT RMSEu (W m-^) d N&S 40 .39 40 .39 40 .38 40 .37 40 .36 40 .35 58 .20 58 .20 58 .20 58 .20 58 .20 58 .19 0 .92 0 .92 0 .92 0. .92 0 .92 0 .92 0. .81 0 .81 0. .81 0, .81 0 .81 0 .81 27 .65 27 .65 27 .65 27 .65 27 .65 27 .65 10 .72 10 . 72 10. .72 10, .72 10. .72 10 .72 25 .49 25 .49 25. .49 25. .49 25, .49 25. .49 0, .95 0. .95 0. .95 0. .95 0. .95 0. .95 0. .81 0, .81 0. .81 0, .81 0. .81 0, .81 41. .88 41. .88 41. .87 41. ,86 41. 85 41. ,84 23. .86 23. .86 23. .87 23. .88 23. .88 23. .88 1. .09 1. .09 1. 10 1. .09 1. .09 1. ,10 0. .71 0. .71 0. .71 0. .71 0. .71 0. ,71 13. .00 13. ,00 13. 00 13. 00 13. 00 13. 00 2. ,18 2. .18 2. .17 2. 16 . 2. .15 2. .13 12. ,82 12. ,82 12. 82 12. 82 12. 82 12. 82 0. 91 0. 91 0. 91 0. 91 0. 91 0. .91 0. ,65 0. ,64 0. 64 0. 64 0. 64 0. 64 a See T a b l e 8.5 f o r e x p l a n a t i o n o f s t a t i s t i c s b 'Base' v a l u e 1 6 1 Table 8 . 1 4 S t a t i s t i c s of model performance f o r QJT when the value of S and the timing of the t r a n s i t i o n period i s changed f or deciduous vegetation Winter: Summer: T b (JD): T e (JD): 0 . 2 0 0 . 8 0 6 5 1 1 5 S capacity (mm) - deciduous vegetation 0 . 3 0 B 0 . 4 0 0 . 8 0 0 . 8 0 6 5 6 5 1 1 5 1 1 5 0 . 3 0 0 . 6 0 6 5 1 1 5 0 . 2 0 0 . 6 0 6 5 1 1 5 0 . 3 0 0 . 4 0 0 . 9 0 0 . 9 0 6 5 6 5 1 1 5 1 1 5 0 . 3 0 0 . 8 0 8 5 9 5 0 . 3 0 0 . 8 0 4 5 1 3 5 S t a t i s t i c 3 (a) Hourly Mean (W m"z) sd (W nT 2) mf r 2 R M S E (W nT ? R M S E S (W nT RMSETJ (W m" d N&S (b) Daily Mean (W m"i sd (W nT 2) mf r 2 RMSE (W m"2 R M S E S (W m-RMSETJ (W m" d ' N&S 4 0 . . 3 8 4 0 . . 3 8 4 0 . 3 9 4 0 . . 4 0 4 0 . 4 0 4 0 . 3 8 4 0 . 3 9 4 0 , . 3 8 4 0 . 3 9 5 8 . . 2 0 5 8 , . 2 0 5 8 . 2 1 5 8 . . 2 1 5 8 . . 2 1 5 8 . . 2 0 5 8 . . 2 0 5 8 . . 2 0 5 8 . 2 1 0 . 9 2 0 . . 9 2 0 . 9 2 0 . . 9 2 0 . 9 2 0 . 9 2 0 . . 9 2 0 . . 9 2 0 . 9 2 0 , . 8 1 0 , . 8 1 0 . . 8 1 0 , . 8 1 0 . . 8 1 0 . . 8 1 0 , . 8 1 0 , . 8 1 • 0 . . 8 1 2 7 , . 6 5 2 7 , . 6 5 2 7 . . 6 6 2 7 . . 6 6 2 7 . . 6 5 2 7 . . 6 5 2 7 , . 6 6 2 7 . . 6 6 2 7 . . 6 4 1 0 , . 7 2 1 0 . . 7 2 1 0 . . 7 1 1 0 . . 7 1 1 0 . . 7 1 1 0 . . 7 2 1 0 , . 7 2 1 0 . . 7 2 1 0 . . 7 1 2 5 . . 4 8 2 5 , . 4 9 2 5 . . 5 0 2 5 . . 5 0 2 5 . . 5 0 2 5 . . 4 9 2 5 . . 5 0 2 5 . . 5 0 2 5 , . 4 9 0 , . 9 5 0 . . 9 5 0 . . 9 5 0 . . 9 5 0 , . 9 5 0 . . 9 5 0 . , 9 5 0 . , 9 5 0 . . 9 5 0 . . 8 1 0 , . 8 1 0 , . 8 1 0 , . 8 1 0 , . 8 1 0 . . 8 1 0 , . 8 1 0 . , 8 1 0 . . 8 1 4 1 . , 8 7 4 1 . , 8 7 4 1 , . 8 9 4 1 , , 9 0 4 1 . . 8 9 4 1 . . 8 7 4 1 . . 8 8 4 1 . , 8 7 4 1 . . 8 8 2 3 . . 8 7 2 3 . . 8 7 2 3 , . 8 6 2 3 . . 8 6 2 3 , . 8 6 2 3 . . 8 7 2 3 . . 8 6 2 3 . . 8 7 2 3 , . 8 6 1 , . 0 9 1 . . 1 0 1 . . 0 9 1 . . 0 9 1 . . 0 9 1 . . 0 9 1 . , 0 9 1 . , 0 9 1 . . 0 9 0 . • 7 1 . 0 . , 7 1 0 , . 7 1 0 , . 7 1 0 , . 7 1 0 , . 7 1 0. . 7 1 0 . , 7 1 0 . . 7 1 1 3 . . 0 0 1 3 . . 0 0 1 3 , . 0 1 1 3 . . 0 1 1 3 . . 0 1 1 3 , , 0 0 1 3 . , 0 0 1 3 . , 0 1 1 3 . . 0 0 2 . . 1 7 2 . , 1 7 2 , . 1 9 2 . , 2 0 2 . . 1 9 2: , 1 7 2 . , 1 8 2 . , 1 7 2 , . 1 8 1 2 . . 8 2 1 2 . . 8 2 1 2 . . 8 2 1 2 , . 8 2 1 2 . . 8 2 1 2 , . 8 2 1 2 . , 8 2 1 2 . , 8 3 1 2 . . 8 2 0 . , 9 1 0 . , 9 1 0 , . 9 1 0 . , 9 1 0 . . 9 1 0 . , 9 1 0 . , 9 1 0 . , 9 1 0 . , 9 1 0 . . 6 4 0 . . 6 4 0 , . 6 4 0 , . 6 4 0 , . 6 4 0 , . 6 4 0 . , 6 4 0 . , 6 4 0 , . 6 4 a See Table 8 . 5 for explanation of s t a t i s t i c s b 'Base' value 1 6 2 Table 8.15 S t a t i s t i c s of model performance f o r Qg when the value of S i s changed f o r i r r i g a t e d and u n i r r i g a t e d grass S capacity (mm) grass I r r i g a t e d 0.5 1. 3 b 6.4 7.6 7.6 Unirrigated 0.5 1.3 6.4 7.6 10.2 S t a t i s t i c 3 (a) Hourly Mean (W nT 2) sd (W nT 2) mf r 5 RMSE (W n r 2 ) RMSES (W nT 2) RMSEu (W nT 2) d N&S (b) Daily Mean (W m - 2) sd (W nT 2) mf r 2 RMSE (W m'2) RMSES (W nT 2) RMSEu (W m'2) d N&S 43. .08 40, .38 38, .03 37 .91 37, .87 59. .91 58. .20 56. .72 56, .65 56 , 65 0, .95 0, .92 0, .90 0 .90 0, .90 0, ,78 0. .81 0. ,83 0, .83 0, .83 30, .07 27, .65 26, .42 26. . 39 26. ,40 10. ,58 10. .72 11. ,69 11 .75 11, .76 28. .15 25. .49 23. .70 23. .63 23. ,63 0. ,94 0, .95 0, .95 0 .95 0, .95 0, .77 0. .81 0, .82 0. .82 0, .82 44. ,66 41. ,87 39. ,44 39, .31 39. ,25 26, .09 23. .87 22, .45 22. .39 22, .42 1. .20 1. .10 1, .13 1, .03 1. ,03 0, .67 0. .71 0. .75 0. .75 0, .75 15. . 6 0 13. ,00 11. , 58 11. .53 11. ,52 4. .20 2. ,17 2. .61 2 .69 2 , .68 15. ,02 12. ,82 11. ,28 11, .21 11. ,21 0, .89 0. ,91 0, ,93 0 .93 0. .93 0. ,49 0. .64 0. .72 0, .72 0. ,72 a See Table 8.5 for explanation of s t a t i s t i c s b 'Base' value 163 Figure 8.14 Influence of the value assigned to the surface storage capacity of grass on cumulated E. 164 d i s t i n c t increase i n the modelled values of E ( i . e . a steeper slope i n F i g . 8.14). The s t a t i s t i c s show s l i g h t l y c o n t r a d i c t i n g e f f e c t s of changing the size of S at the hourly and d a i l y scales. With increasing S the hourly s t a t i s t i c s show a decreased mf, an increased r 2 , a decreased RMSE and RMSEu but an increased RMSEg. On a d a i l y basis however increasing S i s associated with a decrease i n RMSE, and i n both the RMSEg and RMSEu- The hourly ensemble data show that the la r g e s t difference from the 'base' r e s u l t s occurs at 1800 hours LAT. In the winter the difference at t h i s time was <7 W m"2 for S=0.5 mm. During June the difference was <20 W nT 2. With large values of S the modelled Qg was reduced by 2-3 W m"2 during the winter, and i n June the maximum differen c e i n the morning i s approximately 6 W m - 2 and i n the l a t e afternoon approximately 15 W ra-2. It would appear from t h i s s e n s i t i v i t y analysis the size which influences the modelled Qg i s around the value of 1.3 ram suggested by Zinke (1967). The larger values although c a l l e d depression storage capacity i n the l i t e r a t u r e (see section 7.4) may represent a 'lumped f i t ' to other parts of la r g e r runoff models rather than p h y s i c a l l y r e a l i s t i c values. The second type of changes to the storage capacities involved a l t e r i n g a l l the values of S for the d i f f e r e n t surfaces at one time. Four runs of t h i s type were conducted (see Table 8.16 for d e t a i l s ) : f i r s t l y , a l l values of S were decreased to small values f o r each of the respective surface types (see Tables 7.3, 7.4); secondly, a l l surfaces were assigned large values; t h i r d l y , a l l storage c a p a c i t i e s were set to 0.5 mm; and fourthly, a l l were set to 1.0 mm. Figure 8.15 shows the e f f e c t of these changes on cumulated E. A l l of the runs under-predict Qg u n t i l the onset of i r r i g a t i o n , as does the base run. After that time the slope of the cumulative curve steepens considerably f o r a l l runs except f o r the curve f o r the case where S was assigned a large value for each surface. For a l l curves, except f o r the base run, a f t e r about JD 145 the 1 6 5 Table 8.16 S t a t i s t i c s of model performance f o r Qg when S capacity changed f o r a l l surface types S capacity (mm) - a l l surfaces small base large a l l a l l s pavement 0.30 0.48 2.50 0.5 1.0 s b u i l d i n g 0.25 0.25 2.50 0.5 1.0 s coniferous 0.75 1.20 2.50 0.5 1.0 s deciduous^ 0.20 0.30 0.40 0.495 0.995 s grass 0.50 1.30 7.60 0.5 1.0 S t a t i s t i c 3 (a) Hourly Mean (W m"2) sd (W m"2) mf mf r 5 RMSE (W m'2) RMSES (W nT 2) R M S E T J (W m"2) d N&S (b) Da i l y Mean (W m"2) sd (W nT 2) mf r 2 RMSE (W nT 2) RMSEg (W nT 2) R M S E T J (W m"2) d N&S 43 .26 40. .38 36. .85 47, .39 45, .72 59 .92 58. .20 56. .92 63, .03 62. .33 0 .95 0, .92 0. .90 1. .00 . 0, .99 0 .78 0. .81 0, .83 0, .75 0. .77 '30. .16 27. .65 26. .48 33, .40 31. .71 10, .66 10. .72 11. .75 11. .15 10. .13 28, .21 25. .49 23. .73 31. .49 30. .05 0, .94 0. .95 0. .95 0. .93 0. .93 0, .77 0. .81 0. .82 0. .72 0. .75 44, .87 41. .87 38. .09 49. .20 47. ,39 25. .99 2.3. .87 23. .21 29. .27 28. .77 1. .19 1. 10 1. .06 1. .34 1. ,32 0. .66 0. .71 0. ,76 0. .60 0. .63 15. .66 . 13. .00 11. ,76 20. ,46 18. ,90 4. .42 2. .17 2. .87 8. .76 6. .97 15. .03 12. .82 11. ,40 18. .49 17. .57 ' 0. 88 0. .91 0. ,93 0. ,83 0. .85 0. .48 0. .64 0. ,71 0. .12 0. ,25 a See Table 8.5 f o r explanati b Deciduous value f o r winter Deciduous values f o r summer fo r summer 0.60 0 on of s t a t i s t i c s using the same headings as above .80 0.90 0.5 1.0 Figure 8.15 Influence of changing a l l the surface storage c a p a c i t i e s on the cumulated E C s e e text and Table 8.16 for further d e t a i l s ) . 166 Time (JD) 1 6 7 performing well on a hour to hour basis. The s t a t i s t i c s f o r the runs compared with the measured data suggest that when the surface storage c a p a c i t i e s are set to l a r g e r values the model performs better (Table 8.16). 8.4.6 Drainage functions The drainage functions were varied over a range of c o e f f i c i e n t s and equation types (see Table 8.17 f o r d e t a i l s ) with the storage c a p a c i t i e s f o r a l l surfaces being set to one value then changed to 0.5 mm (Table 8.17), 1.0 mm (Table 8.18), and 2.0 mm (Table 8.19). The e f f e c t s of changing the drainage functions can be seen more c l e a r l y from the cumulative p l o t s (Figs. 8.16, 8.17, 8.18). The l a r g e s t values are obtained when S=0.5 mm. With a l l of the models the beginning of external water use i s associated with a steep r i s e i n the slope of the cumulative curves. When S=0.5 mm a l l of the cumulative curves cross the measured E curve ( F i g . 8.16). When S=1.0 mm and equation 7.20 i s used the cumulative E i s l e s s than the measured E, but by the end of the study period they are converging, i n d i c a t i n g over-prediction i n the l a t t e r period. The same equation under pr e d i c t s the cumulative E when S=2.0 mm ( F i g . 8.18) but maintains a more s i m i l a r slope to that of the measured E. These runs show the Shuttleworth form of t r a n s i t i o n i s s e n s i t i v e to the drainage functions used, but not to the same extent as when the Rutter t r a n s i t i o n i s used. This indicates care must be taken i n assigning drainage functions and c o e f f i c i e n t s . I t appears that those selected i n t h i s study f o r the Sunset s i t e simulate the drainage and surface water state well (see F i g . 1 6 8 Table 8.17 S t a t i s t i c s of model performance f o r Qg when the drainage functions are changed and S = 0.5 mm Drainage functions - S = 0.5 mm a l l surfaces v b v c 7 20 7.18 7.18 7.20 7.20 7.17 v v 10 0.013 0.018 32 12 0.0014 v v 3 1.71 1.76 1.5 1.5 5.25 Eqn no.: Coeff D Q : Coeff b: S t a t i s t i c 3 (a) Hourly Mean (W nT 2) sd (W m - 2) mf r 2 RMSE (W nT 2) RMSEg (W m - 2) RMSEn (W m - 2) d N&S (b) Da i l y Mean (W m"2) sd (W nT 2) " f RMSE (W nT 2 RMSEg (W m" R M S E T J (W m'z) d N&S 40. .38 47. .39 41. .88 49. .92 48. .82 46. .77 46. .90 45, .11 58. .20 63. .03 59. .77 65. .65 64. .09 61. .26 61. .32 60. .67 0. .92 1, .00 0. .95 1. .04 1. .02 0. .97 0. .97 0, .96 0. .81 0. .75 0. .77 0. .72 0. ,73 0. .75 0. .75 0. .76 27. .65 33. .40 30. .26 36. .78 35. ,32 32. .83 32. .88 32. .13 10. 72 11. .15 10. .58 12. .23 11. ,99 11. ,98 12. .01 11. .47 25. ,49 31. .49 28. .35 34. .69 33. ,22 30. ,57 30. ,61 30. .02 0. .95 0, .93 0, .94 0. .91 0. .92 0. .93 0. .93 0. .93 0. .81 .0, .72 0. .77 0. .66 0. .69 0. .73 0. .73 0, .74 41. .87 49. .20 43. .41 51. .94 50. ,71 48. .31 48. .44 46. .75 23. .87 29, .27 26. .77 28. .96 28. ,49 28. .56 28. .54 27. .95 1. .10 1. .34 1. .23 1. .32 1. ,31 1. .31 1. .31 1. .28 0. .71 0. .60 0. .68 0. .54 0. ,57 0. .62 0. ,62 0. .64 13. .00 20. .46 15. .37 22. .72 21. ,35 19. ,24 19. .30 17. .99 2. .17 8. .76 2. ,93 11. .46 10. ,23 7. .85 7. ,98 6. .28 12. .82 18, .49 15. .09 19. .61 18. .74 17. .56 17. .57 16. .86 0. .91 0. .83 0. .89 0. .79 0. .81 0. .84 0. .84 0. .86 0. .64 0, .12 0. .50 -0. .09 0. .04 0. .22 0, .22 0. .32 a See Table 8.5 f o r explanation of s t a t i s t i c s b 'Base' equations with base S c a p a c i t i e s c 'Base' equations but S = 0.5 f o r a l l surfaces 1 6 9 Table 8.18 S t a t i s t i c s of model performance f o r Qg when the drainage functions are changed and S = 1.0 mm Drainage functions - S = 1.0 mm a l l surfaces Eqn no.: v b v c 7.20 7.18 7.18 7.20 7.20 7.17 Coeff D Q : V V 10 0 .013 0 .018 32 12 0 .0014 Coeff b: V V 3 1 .71 1 .76 1, .5 1 .5 5 .25 S t a t i s t i c 3 (a) Hourlv Mean (W m~2) 40 .38 45, .72 39 .34 48, .20 46, .97 48. .24 48, .35 47 .26 sd (W m'2) 58 .20 62, .33 58 .64 64, .20 62, .89 53. .23 63, .31 62 .57 m f 0 .92 0, .99 0 .93 1 .02 1, .00 1. .00 1. .00 0 .99 r 2 0 .81 0, .77 0 .80 0, .75 0, .76 0. .76 0, .76 0, .76 RMSE (W nT 2) 27 .65 31, .71 28 .33 34, .17 32, .85 32. .90 32. .97 32 .35 RMSES (W nT 2) 10 .72 10, .13 10 .63 11, .08 10, .80 11. ,32 11. .36 11, .01 RMSEu ( w m " 2 ) 25 .49 30, .05 26 .26 32, .32 31. .02 30. ,89 30. .96 30, .42 d 0 .95 0. .93 0 .94 0, .92 0. .93 0. ,93 0. .93 0, .93 N&S 0 .81 0. .75 0 .80 0. .71 0. •73 0. ,73 . 0. 73 0. .74 (b) D a i l v Mean (W m"2) 41, .87 47. ,39 40 .71 50. .12 48. ,82 49. ,81 49. ,91 48. .89 sd (W nT 2) 23, .87 18. .77 25 .44 28. .22 27. .79 28. 49 28. ,48 28. .13 mf 1, .10 1. ,32 1 .17 1. .29 1. .27 1. 31 1. ,31 1. .29 r 2 0, .71 0. ,63 0, .72 0. ,57 0. .60 0. 61 0. .60 0. .61 RMSE (W m"2) 13, .00 18. ,90 13 .44 20. ,79 19. ,49 20. 22 20. ,30 19. .39 R M S E S (W m - 2) 2, .17 6. ,97 0, .29 9. ,64 8. ,34 9. 32 9. ,43 8. .41 RMSEu ( w m " 2 ) 12, .82 17. ,57 13, .43 18. ,42 17. ,62 17. 95 17. ,98 17. .47 d 0, .91 0. ,85 0, .91 0. ,82 0. ,84 0. 83 0. 83 0. ,84 N&S 0, .64 0. ,25 0, .62 0. ,09 0. ,20 0. 14 0. 13 0. ,21 a See Table 8.5 f o r explanation of s t a t i s t i c s b 'Base' equations with base S c a p a c i t i e s c 'Base' equations but S = 1.0 f o r a l l surfaces 1 7 0 Table 8.19 S t a t i s t i c s of model performance f o r Qg when the drainage functions are changed and S = 2.0 mm Drainage functions - S =2.0 mm a l l surfaces Eqn no.: v b 7.20 7.18 7.18 7.20 7.20 7.17 Coeff D 0: v 10 0.013 0.018 32 12 0.0014 Coeff b: v 3 1.71. 1.76 1.5 1.5 5.25 S t a t i s t i c 3 (a) Hourly Mean (W m"2) 40.38 sd (WHT 2) 58.20 mf 0.92 r 2 0.81 RMSE (W m"2) 27.65 RMSES (W nT 2) 10.72 R M S E T J (W nT 2) 25.49 d 0.95 N&S 0.81 (b) Da i l y Mean (W m"2) 41.87 sd (W nT 2) 23.87 mf 1.10 r2 0.71 RMSE (W nT 2) 13.00 RMSES (W nT 2) 2.17 R M S E T J (W m'2) 12.82 d 0.91 N&S 0.64 37, .64 45, .28 44, .01 57. .74 62, .52 61, .41 0, .92 ,0, .99 0, .97 0. .81 0. .78 ' 0, .79 27. .41 30. .86 29, .93 11. .25 9. .41 9, .44 24. .99 29. .39 28, .40 0. .95 0. .94 0, .97 0. .81 0. .76 0, .79 38. ,92 47. ,18 45. .83 .24. ,51 26. ,98 26. .51 1. ,12 1. ,24 1. .22 0. ,74 0. ,63 0. .65 12. ,52 17. ,81 16. .61 1. ,71 6. ,70 '5. ,36 12. ,41 16. ,50 15. .72 0. 92 0. 86 0. ,87 0. ,67 0. ,33 0. .42 50, .94 51, .02 50, .38 67, .60 67, .69 67, .16 1 .07 1, .07 1, .07 0, .75 0, .75 0, .75 35, .64 35, .75 35, .24 11, .70 11, .76 11, .33 33, .67 33. .76 33, .37 0, .92 0, .92 0, .92 0, .68 0. .68 0, .69 52. .68 52. .77 52. .19 29. .47 29. .49 29. .27 1. .35 1. .35 1. .34 0. .54 ' 0. .54 0. ,55 23. .32 23. ,42 22. ,81 12. .19 12. .28 11. ,70 19. ,88 19. ,94 19. ,58 0. ,79 0. .79 0. ,79 -0. ,15 -0. ,15 -0. ,09 a See Table 8.5 f o r explanation of s t a t i s t i c s b 'Base' equations with base S ca p a c i t i e s 1 71 Figure 8.16 Influence of changing drainage functions and c o e f f i c i e n t s on the cumulated E when S = 0.5 mm f o r a l l surfaces. N » >. K measured base various 7.20. 10, 3 7.18. 0.013. 1.71 7.18. 0.018, 1.76 43 107 Time ( JD) 171 Figure 8.17 Influence of changing drainage functions and c o e f f i c i e n t s on the cumulated E when S = 1.0 mm f o r a l l surfaces. 1 7 2 n n i i it measured base various 43 107 Time (JD) 171 Figure 8.18 Influence of changing drainage functions and c o e f f i c i e n t s on the cumulated E when S = 2.0 mm f o r a l l surfaces. 1 73 i , I, » n measured base 7.20. 10, 3 7.18, 0.013, 1.71 j 7.18, 0.018, 1.76 $ 7.20, 32. 1.5 / 7.20. 12, 1.5 I1. 43 107 171 Time (JD) 8.7) 1 7 4 8.5 Discussion One portion of the model req u i r i n g more attention i n the future i s the under p r e d i c t i o n i n the e a r l i e r part of the year. The measured Qg suggest that i t i s an important part of the urban energy and water balances (see Chapter 6 ) i n these months and should not be ignored. The f i r s t l i n e of pursuit should be with regard to the surface resistance. The model developed i n Chapter 7 i s based on very l i t t l e winter data with a dry surface and therefore may not be f u l l y representative. Further, for the summer months ca r e f u l thought needs to be given to the hourly input of external water use. It i s probable that the water use calculated for input i n t h i s study was too large. For the reasons stated below t h i s hourly input was not adjusted to f i t the measured data. From the s e n s i t i v i t y analyses i t can be concluded that i f the model i s to be applied to other areas close a t t e n t i o n needs to be paid to the drainage and storage c a p a c i t i e s of the dominant surface types and the r e s u l t s of these s e n s i t i v i t y analyses be kept i n mind with regards to the e f f e c t s of s e t t i n g appropriate values. Wetness sensors, located on a number of representative surfaces, appear to be a simple of way of assessing the performance of the model i f measurements of Qg are not a v a i l a b l e (as i s frequently the case). The model developed i n t h i s thesis, the performance of which i s discussed i n t h i s chapter, shows d e f i n i t e promise for use i n urban areas. The objective of t h i s thesis was not to model the evapotranspiration for a p a r t i c u l a r time and place but to consider a methodology for modelling evapotranspiration continuously over a range of meteorological conditions i n urbanized t e r r a i n . Therefore there has been no e x p l i c i t attempt to f i t / c a l i b r a t e the model to the measured data. The performance of the model, using p h y s i c a l l y r e a l i s t i c values 1 7 5 obtained from the l i t e r a t u r e f or the drainage functions and storage capacities with the other sub-models developed e a r l i e r i n the t h e s i s , suggests that t h i s type of approach to modelling i s d e f i n i t e l y useful for p r e d i c t i n g urban evapotranspiration and state of the surface. If t h i s model i s to be applied at other l o c a t i o n s the changes required for a p p l i c a t i o n of the model pr i m a r i l y r e l a t e to the assignment of parameter values. For example i f a t r o p i c a l c i t y i s under consideration i t would be advisable to conduct Qg measurements so that the surface resistance sub-model had appropriate parameters. For the t r o p i c a l case, and other locations where intense r a i n f a l l events occur further i n v e s t i g a t i o n of the Massman (1985) drainage functions, which allow for the i n c l u s i o n of the i n t e n s i t y of r a i n f a l l , may be worthwhile. In t h i s study the case of snow has been e x p l i c i t l y ignored. The incorporation of t h i s as an a d d i t i o n a l sub-model should be reasonably easy with the appropriate melt equations. The model would have to keep a record not only of the depth of water within a store but also whether i t was i n a l i q u i d or a s o l i d state. Discussion of s i m p l i f i c a t i o n s to the model which would allow i t s more ready a p p l i c a t i o n have already been mentioned (e.g. the use of sectors instead of plumes, and the use of the neutral equation for rg instead of the non-neutral version). There i s merit i n further research into the influence of s i m p l i f i c a t i o n s , i n p a r t i c u l a r to adapt the model so that i t requires only r o u t i n e l y - c o l l e c t e d meteorological data. P r i o r to t h i s work there i s no other model to compute hourly evapotranspiration for urban t e r r a i n . However, there are models at the d a i l y time scale (e.g. Grimmond et a l . . 1986; Cleugh, 1988). The Cleugh (1988) model, which uses a coupled surface and mixed layer approach, was not a v a i l a b l e at the time of writing but i n any case requires atmospheric 17 6 soundings that were not a v a i l a b l e . The Grimmond et a l . (1986) model i s a combination a d v e c t i o n - a r i d i t y model developed from that of Brutsaert and Strieker (1979). It has been applied elsewhere i n Vancouver (Grimmond and Oke, 1986) as part of an urban water balance study. Here t h i s model was run.using the 'base' data so that i t s performance could be compared with the evapotranspiration-interception model (Table 8.20, F i g . 8.19). In the comparison the Grimmond et a l . (1986) evaporation sub-model was run independently using the empirical c o e f f i c i e n t s reported i n t h e i r study. The surface database and source area sub-models were used to determine the a v a i l a b l e energy and the sizes of the i r r i g a t e d and u n i r r i g a t e d areas. Comparison of these r e s u l t s with those obtained f o r the 'base' run of the evapotranspiration-interception model at the d a i l y time scale (Table 8.5, F i g . 8:3) shows that whilst both perform acceptably the model developed i n t h i s study performs better; with a better slope, l e s s s c a t t e r around the one to one l i n e and improved s t a t i s t i c s . In p a r t i c u l a r the RMSE i s halved and the r 2 and d are considerably improved. Table 8.20 Comparison of the performance of two models to ca l c u l a t e d a i l y evapotranspiration i n urbanized t e r r a i n S t a t i s t i c Grimmond Present et a l . (1986) Study Number of points (n) 125 125 Mean Measured (W m"2) 40. 49 40.49 Modelled (W m"2) 37. 49 41.87 Standard deviation (sd) Measured (W ra"2) 21. 80 21.80 Modelled (W m"2) 34. 36 23.87 Slope - functional analysis (mf) a 1. 56 1.10 C o e f f i c i e n t of determination ( r 2 ) 0. 41 0.71 Root mean square error (RMSE)(W m"2) 26. 53 13.00 RMSE systematic (RMSEg)(W m"2) 2. 94 2.17 RMSE unsystematic (RMSEn)(W m"2) 26. 37 12.82 Index of agreement ( d ) b 0. 75 0.91 Goodness of f i t (N&S) C -0. 50 0.64 a Mark and Church (1977) b Wilmott and Wicks (1980) c Nash and S u t c l i f f e (1970) Figure 8.19 Comparison of d a i l y measured and modelled evaporation using the Grimmond et a l . (.1986) ad v e c t i o n - a r i d i t y model and the 1987 Sunset data set 1 7 8 Q measured (W m_2) 1 7 9 CHAPTER 9 CONCLUSIONS 9.1 Summary of conclusions The objective of t h i s thesis was to develop a model to calculate evapotranspiration from urban areas for use over a wide range of meteorological conditions. This d i c t a t e s the need for a model which can cope with changing water a v a i l a b i l i t y at the surface both during and following r a i n f a l l . Considering t h i s i t was deemed appropriate to adopt an evapotranspiration-interception approach. Development of the evapotranspiration-interception model created the need fo r sub-models to calculate anthropogenic heat f l u x , storage heat f l u x , aerodynamic resistance, surface resistance and drainage. Knowledge of the nature of the 'surface' i s a common requirement of these sub-models and the o v e r a l l model, so a scheme to archive surface information was also developed. The main conclusions which can be drawn from t h i s study are: • To determine the value for a surface parameter (e.g. amount of greenspace) i t i s necessary to locate the area which i s to be described. The l o c a t i o n of the boundaries for t h i s area may a f f e c t the value assigned to the surface parameters and therefore any subsequent f l u x c a l c u l a t i o n s . In an area, such as suburban t e r r a i n , i t i s possible at the l o c a l scale to i d e n t i f y an area which i s homogeneous (e.g. a r e s i d e n t i a l area) but within t h i s homogeneous unit there i s a large degree of sub-scale heterogeneity (e.g. vegetation, buildings, roads). The influence of t h i s sub-scale heterogeneity i s demonstrated through the c a l c u l a t i o n of anthropogenic heat flux, storage heat flux, and l a t e n t heat f l u x with the a i d of a database which stores surface c h a r a c t e r i s t i c s (e.g. greenspace, bu i l d i n g type e t c . ) . • An objective means for l o c a t i n g the boundaries of the source area contributing to turbulent and radiant heat f l u x measurements at a point i s 1 8 0 presented. It uses a modified version of the source area model developed by Schmid (1988). A s i m p l i f i e d version, termed 'sectors', was developed. It requires more e a s i l y obtained input data than the f u l l source area model and les s computation time yet i t maintains most of the physics. Combining the source area c a l c u l a t i o n s with the surface d e s c r i p t i o n database i t i s possible to obtain a s p a t i a l l y consistent energy balance even when some terms are measured and others are calculated. This method also has applications when comparing modelled and measured fluxes to ensure t h e i r s p a t i a l consistency. • The anthropogenic heat f l u x i s s p a t i a l l y very variable therefore the l o c a t i o n of the boundaries of the area used to calculate the anthropogenic heat f l u x contributing to the energy balance at a point strongly influences the si z e of the f l u x obtained. Seasonally the anthropogenic heat f l u x i s not so v a r i a b l e . For the Sunset s i t e i t only varies from a mean d a i l y value of 9.5 W m"2 (winter) to 7.5 W m~2 (summer). • The objective hysteresis model proposed by Cleugh (1988) to calculate urban heat storage performs well i n a l l seasons during the daytime. At night the storage heat f l u x i s approximately equal to the sum of the net r a d i a t i o n and anthropogenic heat f l u x . At the Sunset s i t e the influence of the changing surface type (due to changing source area locations) on the storage heat f l u x was minimal. Nevertheless there i s evidence to suggest that i n areas where the surface i s le s s homogeneous t h i s may not 'be the case. • The winter/spring urban energy balances observed i n t h i s study are d i f f e r e n t to.those reported for summertime conditions at the same s i t e . The fluxes are not symmetrical about solar noon. This i s p r i m a r i l y due to the storage heat f l u x being determined by the more r e a l i s t i c objective hysteresis equation rather than the objective l i n e a r equation. Hence e a r l i e r interpretations should be modified. Apart from t h i s feature the spring season balances are 181 s i m i l a r to those reported f o r the summertime i n terms of the r e l a t i v e importance of the i n d i v i d u a l fluxes. • The wintertime energy balance appears to be d i f f e r e n t to that i n spring and summer. The most noticeable feature i s the increased importance of the l a t e n t heat f l u x . On average i t i s the l a r g e s t output f l u x i n the balance. A secondary, more expected feature, i s the increased importance of anthropogenic heat f l u x as an input. • The aerodynamic resistance of an urban area can be reasonably approximated by a simple neutral s t a b i l i t y wind equation. Such s i m p l i f i c a t i o n has the l i m i t a t i o n of showing no v a r i a b i l i t y f o r a given wind speed. • The use of modified J a r v i s (1976) functions to c a l c u l a t e surface resistance f o r urban areas proved encouraging. The s t a t i s t i c s f o r the performance of the optimised suburban surface resistance sub-model are s i m i l a r to those obtained f o r f o r e s t e d areas (e.g. Stewart, 1988). • The Penman-Monteith-Rutter-Shuttleworth evapotranspiration i n t e r c e p t i o n model developed i n t h i s thesis f o r urban areas performed very w e l l . It i s an improvement over a v a i l a b l e methods. Incl u s i o n of the Shuttleworth (1978) u n i f i e d t r a n s i t i o n between wet and dry surfaces was found to be superior to the Rutter et a l . (1971, 1975) t r a n s i t i o n scheme. This i s i n large part due to the increased s e n s i t i v i t y of the evaporation to the drainage functions when the Rutter t r a n s i t i o n i s used. • It i s po s s i b l e to use the evaporation-interception model with values of storage capacity, drainage function and other hydrologic parameters taken from the l i t e r a t u r e to obtain r e a l i s t i c hourly and d a i l y estimates of l a t e n t heat f l u x and surface water state. 182 9.2 Future research Throughout the thesi s , where appropriate, s p e c i f i c recommendations f o r future research have been made and are not repeated here. The o v e r a l l conclusion i s that the Penman-Monteith-Rutter-Shuttleworth model i s very-useful i n the urban environment but so f a r i t has only been tested at one suburban s i t e . Further fieldwork i n other c i t i e s and climates to test the model would be h e l p f u l i n demonstrating i t s robustness. 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APPENDIX I JULIAN DAY CALENDAR FOR MEASUREMENT PERIOD 1987 Day JAN FEB MAR APRIL MAY JUNE 1 32 60 91 121 152 2 33 61 92 122 153 3 34 62 93 123 154 4 35 63 94 124 155 5 36 64 95 125 156 6 37 65 96 126 157 7 38 66 97 127 158 8 39 67 98 128 159 9 40 68 99 129 160 10 41 69 100 130 161 11 42 70 101 131 162 12 43 71 102 132 163 13 44 72 103 133 164 14 45 73 104 134 165 15 46 74 105 135 166 16 47 . 75 106 136 167 17 . 48 76 107 137 168 18 49 77 108 138 169 19 50 78 109 139 170 20 5.1 79 110 140 171 21 21 52 80 111 141 172 22 22 53 • 81 112 142 173 23 23 54 82 113 143 174 24 24 55 83 114 144 175 25 25 56 84 115 145 176 26 26 57 85 116 146 177 27 27 58 86 117 147 178 28 28 59 87 118 148 179 29 29 88 119 149 30 30 89 120 150 31 31 90 151 1 9 4 APPENDIX II EQUATIONS USED IN CALCULATIONS 11.1 Temperature Difference (AT) The same method i s used f o r both the dry bulb and the wet bulb temperature di f f e r e n c e s from the RTDMS: AT - (AT! - AT 2)/2 ( I I . l ) where AT^ - mean of the temperature d i f f e r e n c e f o r the two. 10 minute periods which during the daytime are negative ( C); and AT 2 - mean of the two 10 minute temperature d i f f e r e n c e s when the carts ..are reversed (°C). 11.2 Slope of the saturation vapour pressure curve (s) From Lowe (1977): s = a 0 + T ( a x + T ( a 2 + T ( a 3 + T ( a 4 + T ( a 5 + a 6 T ) ) ) ) ) (II.2) where ag - ag - c o e f f i c i e n t s (Table I I . l ) ; and T - temperature (°C). Table I I . l : C o e f f i c i e n t s f o r use with Lowe (1977) polynomials (temperature C) e S(> 0 ) (J>a> e S(< 0 ) " (Pa) s(>0 ) (Pa "C' 1) 0 6.10779961 1 4.436518521X10"1 2 1.428945805xl0" 2 3 2.650648471xl0" 4 4 3.031240396xl0" 6 5 2.034080948xl0- 8 6 6.136820929X10" 11 6.109177959 5.03469897X10" 1 1.886013408xl0- 2 4.176223716X10"4 5.824720280xl0" 6 4.838803174xl0" 8 1.838826904X10"10 4.438099984X10-1 2.857002636x10-2 7.938054040xl0" A 1.215215065xl0" 5 1.036561403xl0" 7 3.532421810X10"10 -7.090244804X10"13 s(<0°) (Pa "c1) 5.030305237X10-1 3.773255020xl0" 2 1.267995369xl0" 3 2.477563108X10'5 3.005693132xl0" 7 2.158542548xl0" 9 7.131097725xl0- 1 2 II.3 Psychrometric constant ( 7 ) From Frits c h e n and Gay (1979): 7 - ( c P p)/(eL v) (II.3) where cp - s p e c i f i c heat of a i r at constant pressure (J kg'^ K'^), see below p - atmospheric pressure (Pa); 1 - r a t i o of the molecular weight of water vapour to that of dry a i r (0.62197 L i s t , 1966); and Ly - l a t e n t heat of vapo r i z a t i o n c a l c u l a t e d using the wet bulb 195 temperature Ty (J kg'^). 11.4 Latent Heat of Vaporization (Ly) From Henderson-Sellers (1984): L v = 1.91846 x 10 6 (T/ (T-33.91)) 2 (II.4) where T - temperature (K). 11.5 Mixing Ratio (r) From Frits c h e n and Gay (1979): r = (e e a ) / ( p - e a) (II.5) where e a - vapour pressure (Pa). 11.6 Vapour Pressure (e a) From Fr i t s c h e n and Gay (1979): e a - eS - i " ! c P p ( T d - T w) (II.6) m2 eLy where eg - saturation vapour pressure (Pa) at Ty; Ly- - determined at Ty; I'd _ dry bulb temperature ( C) ; and Ty - wet bulb temperature ( C). The r a t i o m^ /m2 approaches unity when v e n t i l a t i o n v e l o c i t i e s exceed about 3 m s'^-. For t h i s study the r a t i o was assumed to be unity. 11.7 Saturation Vapour Pressure (eg) From Lowe (1977): e s = a 0 + T ( a x + T ( a 2 + T ( a 3 + T ( a 4 + T ( a 5 + a 6 T ) ) ) ) ) (II.7) where ag - ag - c o e f f i c i e n t s (Table I I . l ) . 11.8 Specific Heat of Air at Constant Pressure (cp) From L i s t (1966): c P - (0.2403 + 0.4409 r) x 4186.7456 (II. 8 ) Note that c P i s dependent on r, which i s dependent on e a, which i s dependent on cp. Therefore i t i s necessary to calculate these i t e r a t i v e l y . In t h i s study cp was i n i t i a l l y set to 1010 J kg--*- then equations II. 5, II. 8 and II. 6 196 were solved u n t i l the difference between the old and new cp was acceptable (<0.0001 d i f f e r e n c e ) . 1 1 . 9 Density of moist a i r (p) From L i s t (1966) p i n kg m"^  i s : p «= _p_ 0.34838 (II.9) T'V where T'y - adjusted v i r t u a l temperature, see below. 11.10 Adjusted virtual temperature (T'y) From L i s t (1966): T'V = CA T d (1 + r / e ) / ( l + r) (11.10) where c^ - compr e s s i b i l i t y f a c t o r of moist a i r (0.9995). 11.11 Relative Humidity (RH) RH was ca l c u l a t e d from the RTDMS data using (Mcintosh & Thorn, 1972): RH - 100 e a / e s (11.11) where eg - calculated using T d. 11.12 Vapour pressure d e f i c i t (V) V (Pa) i s calculated using the dry bulb temperature to calculate both e a and V = e s ( T d ) - e a ( T d ) (II.12) 11.13 Specific humidity d e f i c i t (Sq) Sq (g kg"-'-) i s calculated from V using (Dolman et a l . . 1988): Sq - e V/p (11.13) 197 APPENDIX III: ERROR ANALYSIS FOR THE RTDMS AND FLUXES CALCULATED FROM IT This discussion of errors follows Kalanda (1979), who used the method of Cook and Rabinowicz (1963). The probable absolute error i n a given r e s u l t Y, where Y = F(x;[,x 2), may be expressed as: 6Y = [(dY/dxx 6 X 1 ) 2 + (3Y/3x 2 5 x 2 ) 2 ] 0 - 5 ( I I I . l ) The wet- (ATy) and dry-bulb (AT d) temperatures differences are determined from a c a l i b r a t i o n equation of the form: AT = mx + c (111. 2) where m - slope; x - signal (mV); and c - intercept. The probable error (6AT) i s : 5AT = [(3AT/3c 6 c ) 2 + (3AT/3m 6m) 2 + (3AT/3x 6 x) 2 ] 0 - 5 (III.3) Since 3AT/3c=l, 3AT/3m=x and 3AT/3x=m III.3 becomes: 5T - [ ( 6 c ) 2 + (x5m) 2 '+ (m6x) 2 ] 0 - 5 (III.4) The c a l i b r a t i o n equations for the thermopiles and t h e i r errors are l i s t e d i n Table I I I . l . 5x i s determined from the data logger (CR21X). The f u l l scale range (FSR) error i s 0.05% of the 5.0 mV FSR used; i . e . 2.5 x 10" 3 mV. The error i n AT W i s approximately 0.007°C (Cleugh, 1988). This leads to a 5-15% error i n the range of temperature differences measured. Table I I I . l RTDMS thermopile c a l i b r a t i o n values (McCaughey, pers. comm., 1986) Sensor m 6m c 5c AT W 0 .00248 0, ,000003 -0, .003617 0. .003478 ATd 0, .00249 0, .000002 -0, .013774 0, .002310 The error i n fl i s computed from: 5fl = [(36/3AT w 6 A T W ) 2 + (3fl/3AT d 6 A T d ) 2 + (3B/3s 5 s ) 2 ] 0 - 5 (III.5) where s - slope of the saturation vapour pressure curve versus temperature 198 curve (Pa °C" 1) Kalanda (1979) solved the p a r t i a l d i f f e r e n t i a l equations f o r III.5: 3B/3ATd = [ ( s + 7 ) / 7 AT W) - 2AT d + 7 / ( s + 7 ) ( A T d 2 / A T w ) ] " X (III.6) 3fl/3AT w = [(s+ 7 / 7 AT w 2/AT d - 2AT W + 7 / ( s + 7 ) A T d ] - 1 (III.7) 3fi/3s = [ - ( s + 7 ) 2 / 7 AT w/AT d - 2(s+ 7) + AT d/ATy]"^ (III.8) The error i n the la t e n t heat f l u x (Q Eft) can be computed: SQE - [(<3QE/3Q* SQ*) 2 + (3Q E/3AQ S SAQ S) 2 + (3Q E/3fl S B ) 2 ] 0 - 5 ( I I I . 9) where the s o l u t i o n of the p a r t i a l s are: 3QE/3Q* = 1/(1+B) (III.10) 3QE/3AQ S - -l/(l+fl) (III.11) 3Q E/3fi - (Q* - AQ S)/(1+B) 2 (III.12) The error i n the sensible heat f l u x (QHfl) can be computed: SQ H = [(3Q H/3Q* SQ*) 2 + (3Q H/3AQ S SAQ S) 2 + (3QH/3B S B ) 2 ] 0 - 5 (III.13) where the s o l u t i o n of the p a r t i a l s are: 3QH/3Q* = fl/(l+B) (III.14) 3Q H/3AQ S = -fl/(l+B) (III.15) 3Q H/3fl = (Q* - AQ S)/(1+B) 2 ( I I I . 16) For Qj-ifl and Q E £ errors, f o r both Q* and AQg an error equal to 5% of Q* was assumed. APPENDIX IV CALCULATION OF STABILITY AND FRICTION VELOCITY Monin Obukhov s t a b i l i t y length (L) and f r i c t i o n v e l o c i t y (u*) were calculated f o r each hour during the study period, using the i t e r a t i v e procedure of van Ulden and Holtslag (1985). It was possible to cal c u l a t e L using two d i f f e r e n t methods. The f i r s t , here termed 'sonic', uses sensible heat f l u x (Q H) data (Randerson, 1984): L - -(u*3 p c p T d ) / ( k g Q H) (IV.1) where u* - f r i c t i o n v e l o c i t y (see below)(m s'^); k - von Karman's constant (0.41); g - acc e l e r a t i o n due to gra v i t y (9.81 m s " 2 ) ; cp - s p e c i f i c heat capacity of a i r at constant pressure (J kg"-'- K"l) p - density (kg m'^); and T d - dry bulb temperature (°C). The second method, termed here 'Bowen', uses the temperature differences measured by the RTDMS (van Ulden and Holtslag, 1985): L - ( T d u* 2)/(k g 0*) (IV.2) where 8* - temperature scale f o r turbulent heat transfer: 6* - (k A 0 ) / [ l n ( ( z 2 - d ) y Z l ) - y,H( (z 2-d)/L) + V>H( (*1 "<*) A ) ] (IV.3) where z 2 , Z]_ - heights of the RTDMS sensors (m) ; d - displacement length (m); (z/L) - corresponding s t a b i l i t y functions (see below); and Ad - potential temperature difference (Mcintosh and Thorn, 1972): A8 = AT (100.0/p) K (IV.4) where K = R/cp; R - gas constant of dry a i r (287.04 J kg" 1 K" 1) (List,1966); and p - pressure (Pa). u* was calculated i t e r a t i v e l y with L using (Van Ulden and Holtslag, 1985): u* = (k u ( z 3 - d ) ) / [ l n ( ( z 3 - d ) / z 0 ) - ^ M ( ( z 3 - d ) / L ) + 0 M ( z o / L ) ] (IV.5) where u ( z 3 ) - wind speed at the height of the anemometer (m s " 1 ) ; z Q - roughness length (m); and i/>M(z/L) - s t a b i l i t y functions (see below). A comparison between measured u* and L and the corresponding modelled values while varying the s t a b i l i t y functions was conducted for unstable conditions. The s t a b i l i t y function used f o r heat when L<0 (unstable) (van Ulden and Holtslag, 1985) i s : ifa - 2 In [(1 + y 2)/2] (IV.6) where y was defined by Dyer (1974) as: y = (1 - 16 z / L ) 0 - 2 5 (IV.7) and a l t e r n a t i v e l y by Dyer and Bradley (1982) as: y = (1 - 14 z / L ) 0 - 2 5 (IV.8) The s t a b i l i t y function f o r momentum when L<0 (unstable) (van Ulden and Holtslag, 1985) i s : V>M = 2 l n [ ( l + X)/2] + l n [ ( l + X 2)/2] - 2 tan" 1(X) + -K/2 (IV.9) where X was defined by Dyer (1974) as: X = (1 - 16 z / L ) 0 - 2 5 (IV.10) and a l t e r n a t i v e l y by Dyer and Bradley (1982) as: X - (1 - 28 z / L ) 0 - 2 5 (IV.11) A comparison was also conducted with values of u* calculated without taking s t a b i l i t y into account. These 'neutral' values are calculated from: u* = k u ( z 3 - d ) / l n ( ( z 3 - d ) / z 0 ) (IV.12) The data used are those c o l l e c t e d by Roth (1988) at the Sunset s i t e i n August-September 1986. 28 hours of turbulence data were a v a i l a b l e . The s t a b i l i t y functions calculated using either Dyer (1974) or Dyer and Bradley (1982) forms are compared with the measured data i n Figures IV.1 and IV.2 and Table IV.1 summarises the s t a t i s t i c a l r e s u l t s . The index of agreement (d) has a range between 0 and 1, where 1 indicates perfect agreement between the observed and predicted values (Wilmott and Wicks, 1980). The highest d value and lowest RMSE (root mean square error) was obtained from the sonic method using the Dyer (1974) s t a b i l i t y function f o r both u* and z/L. It should be noted that the a b i l i t y to predict z/L i s not as good as for u*. The 'neutral' 2 0 1 Figure IV.1 Measured versus modelled u*. (Modelled (+) Bowen (A) Sonic (*) Neutral methods). 0.6\- n = 28 Oyer k Brodley (1982) 0.5 3 T) O s , 0.3 I 0.2 3 0.1 3.0 0.0 0.1 0.2 u* (m 0.3 0 . 4 measured 0.5 0.6 Figure IV.2 2 0 2 Measured versus modelled z/L. (Modelled (+) Bowen (A) Sonic (*) Neutral methods). method i n most cases under-predicts u* r e l a t i v e to the measured values (Fig. I V . 1 ) and i n a l l cases predicts lower u* values than any of the Bowen or sonic methods with the Dyer (1974). No data were av a i l a b l e to test s t a b i l i t y formulations f o r the stable (L>0) case at the Sunset s i t e . Considering the unstable r e s u l t s i t was decided to adopt the Dyer (1974) r e s u l t for heat: V-H - -5 (z-d)/L ( I V . 1 3 ) and f o r momentum that of van Ulden and Holtslag (1985): V>M = -17(1 - exp(-0.29(z-d)/L) ( I V . 1 4 ) Table IV.1 Comparison between measured and modelled values of (a) u* and (b) z/L with d i f f e r e n t s t a b i l i t y functions: Dyer (1974) and Dyer and Bradley (1982) and d i f f e r e n t methods: Bowen and Sonic (see text) (a) u* (m s" 1) Dyer (1974) Dyer and Bradley (1982) Measured Bowen Sonic Bowen Sonic Mean 0.34350 0. .39107 0. , 36232 0. .41411 0. , 38254 S.D. 0.08188 0. .10374 0. .09837 0. ,10946 0. .10308 RMSE - 0, .09089 0. .07140 0. .10768 0. ,08114 d a - 0. .74551 0. .82451 0, ,69240 0. .79592 (b) (z -d)/L Mean -0.80839 .22310 -0, ,70871 -0. ,97800 -0. ,59164 S.D. 0.57445 0. .88792 0, .49203 0. .68211 0. ,39726 RMSE - 1. .04623 0. ,55160 0. .81862 0. ,55595 d - 0. .41471 0. .68398 0, .45604 0. .64476 a d - Index of agreement (Wilmott and Wicks, 1980) 2 0 4 APPENDIX V PROCEDURE FOR ACCESSING DIFFERENT SOURCE AREA GEOMETRIES FROM THE DATABASE To conduct the comparison between d i f f e r e n t boundary l o c a t i o n scenarios d i f f e r e n t geometric shapes had to be accessed from the database. For a l l geometric shapes i f the l o c a t i o n of the boundary included any part of a g r i d square the square was incorporated. V.l Circles and Quadrants Since a c i r c l e i s symmetrical around the y- and x-axes the g r i d squares to be sampled can be determined for one quadrant. For the purposes of t h i s study a quadrant r e f e r s to each of the four 90° sectors around the tower (0-89.9°, 90-179.9°, 180-269.9°, 270-359.9°). If the radius (R) of the c i r c l e i s known then the X and Y co-ordinates can be determined. X i s i n i t i a l l y set to 0.5, the midpoint of the f i r s t g r i d square. X i s incremented by steps of 1.0 a f t e r each Y i s determined, u n t i l X > R. Smaller steps increase both the f i t and the computational time. Y i s determined from: Y = (R 2 - X 2 ) 0 - 5 (V.l) The g r i d squares for the +X, +Y quadrant are the Y values i d e n t i f i e d from equation V . l to Y=l.0 for each X. To determine another quadrant or a c i r c l e the sign(s) of X and Y need to be changed as appropriate. To assign a value to a surface parameter the mean for a l l g r i d squares i d e n t i f i e d i s calculated. V.2 Ellipses The dimensions of the 9 source area e l l i p s e s for each hour were calculated using a modified version of the Schmid (1988) source area model (see section 3.2.2). The a, b+c, and d dimensions (Fig. 3.4) plus mean wind d i r e c t i o n (<p) are used to i d e n t i f y which g r i d squares to use for c a l c u l a t i n g surface para-meters . To calculate the co-ordinates of an e l l i p t i c a l source area i t i s necessary to f i r s t i d e n t i f y the boundaries when i t i s aligned with the x-axis because, by d e f i n i t i o n , an e l l i p s e has to have i t s longest axis p a r a l l e l to eit h e r the x- or y-axis (Draper and Klingman, 1972). The b+c axis i s i n i t i a l l y assumed to be aligned along the x-axis (90°). The unrotated Y values ( Y 9 Q ) are calculated for X values ( X 9 Q ) from minimum (a) to maximum (a+b+c) i n steps of 20 m. The step size can be varied, again the smaller the step the better the f i t but the greater the computational time. If b+c i s the longest axis then the c a l c u l a t i o n i s conducted as follows: Y 9 0 = ( d 2 - ( d 2 ( ( X 9 0 - (a+b)) 2/ b 2 ) ) 0 - 5 (V.2) If the d axis i s the longest then d i s replaced by b and vice-versa i n equation V.2. The located points on the boundaries are then rotated so that the b+c axis i s aligned with <p. As the e l l i p s e i s symmetrical about the x-axis the r o t a t i o n can be calculated using the same equations f i r s t with a +Y 9 Q and second with a -YgQ value. X = (cos(cp-90) X 9 0 + sin(<p-90) Y 9 0)/SQS (V.3) Y = (cos(cp-90) Y 9 0 - sin(cp-90) X 9 0)/SQS (V.4) Only the maximum and minimum Y co-ordinates are stored for each X co-ordinate. Note that the surface parameter value i s determined from the mean of the 9 mean band values i . e . a mean value i s determined between each e l l i p s e and then for composite e l l i p s e . Thus areas closer to the tower have proportionally a greater influence than those further away. V.3 Sectors The area to be i d e n t i f i e d i s determined by cp, the standard deviation of the wind d i r e c t i o n (cfy) and some i n d i c a t i o n of s t a b i l i t y . In th i s study net 2 06 r a d i a t i o n (Q*) was used as a surrogate for s t a b i l i t y . If Q*>0 then the lengths used to define the sector were for unstable conditions otherwise the stable/neutral lengths were used (Table 3.3). Calculations are performed from one concentration l e v e l band (R) to the adjacent band (see F i g . 3.6) i n a step-wise fashion at approximately 30 m i n t e r v a l s ( r ) , and then stepped around at approximately 1° i n t e r v a l s (tp^) from cp-a^ to A+er^: X = (cos(90-(<p + a<p - vi)) (R + r))/SQS (V .9) Y - (sin(90-(<p + 0^ - <pt)) (R + r))/SQS (V.10) As for the e l l i p s e s , only maximum and minimum Y values for each X co-ordinate are stored. The value of a surface parameter, as with the e l l i p s e s , i s the mean of the 9 mean band values. V.4 Discussion For each geometric shape the number of X co-ordinates (or l i n e s of co-ordinate data), and the maximum and minimum value of Y for each X i s stored for each hour. These co-ordinates can then be used to calculate a surface parameter from the database. The co-ordinate f i n d i n g sub-routines can,, obviously, also be linked to the process c a l c u l a t i o n programs. Since the same co-ordinates were used several times they were stored for future use. Publications Grimmond, C.S.B., 1981: An evaluation of the contents of some New Zealand Environmental Impact Reports. U n i v e r s i t y of Otago, Geography Discussion Paper No. 27. F i t z h a r r i s , B.B. and C.S.B. Grimmond, 1982: Assessing snow storage and melt i n a New Zealand mountain environment. Hydrological Aspects of Alpine and High  Mountain Areas. I.A.H.S. Publ. No. 138, 161-168.' Grimmond, C.S.B., 1985: Urban water balance: an in t e g r a t i n g framework. World Meteorological Organization Conference on Urban Climatology and i t s Applications with Regards to T r o p i c a l Areas, Mexico Cit y , Mexico. W.M.O Technical Document No. 7. Grimmond, C.S.B., T.R. Oke and D.G.Steyn, 1986a: Urban water balance I: A model f o r d a i l y t o t a l s . Water Resources Research. 22, 1397-1403. Grimmond, C.S.B. and T.R. Oke, 1986b: Urban water balance I I : Results from a suburb of Vane ouver, B.C. Water Resources Research. 22, 1404-1412. Oke T.R., H.A. Cleugh & S. Grimmond 1988: Evapotranspiration i n urban areas. In Intern. Symp. Hydrological processes and water management i n urban  areas. UNESCO, 24-29 A p r i l , 1988, Duisburg, 107-112. Oke, T.R., H.A. Cleugh, S. Grimmond, HP. Schmid and M. Roth 1988: Evaluation of spatially-averaged fluxes of heat, mass and momentum i n the urban boundary layer. In Proc. Symp. on Topoclimatological i n v e s t i g a t i o n and  mapping. International Geographical Union, Christchurch, August 1988 ( i n press) . 

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