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Development and evaluation of a suburban evaporation model : |b a study of surface and atmospheric controls… Cleugh, Helen Adair 1990

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DEVELOPMENT AND EVALUATION OF A SUBURBAN EVAPORATION MODEL A STUDY OF SURFACE AND ATMOSPHERIC CONTROLS ON THE SUBURBAN EVAPORATION REGIME By HELEN ADAIR CLEUGH B.Sc (Hons.) University of Otago 1982 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Geography) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April 1990 © Helen Adair Cleugh 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 DE-6 (2/88) ABSTRACT This research focusses on observing and modelling the suburban surface energy balance. The i n i t i a l objective i s to use measurements to elucidate the controls on the size and temporal v a r i a b i l i t y of the latent heat flux. This i s achieved by synchronous observations of suburban and rural energy balances. On the basis of this comparison i t i s proposed that the day-to-day v a r i a b i l i t y of the partitioning of the suburban turbulent fluxes i s linked both to larger-scale atmospheric influences and variations i n the energy and moisture a v a i l a b i l i t y within the suburban 'canopy'. This hypothesis i s examined through measurement and modelling. Further observations of the suburban energy balance components reveal that the size of the Bowen r a t i o i s linked to the surface moisture a v a i l a b i l i t y . This i s comprised of s o i l moisture variations i n unirrigated greenspace areas and also the anthropogenic influence of lawn i r r i g a t i o n . However, in addition to t h i s , the day-to-day v a r i a b i l i t y of the Bowen rat i o i s a function of an advective influence upon the saturation d e f i c i t i n the surface and mixed-layers. The mechanisms which determine this relationship are i d e n t i f i e d as meso-scale advective effects resulting from d i f f e r i n g land-uses. This influences the nature of the mixed-layer and hence surface fluxes. In l i g h t of this interaction of scales and atmospheric processes, a model i s developed that couples advectively-dominated mixed-layer dynamics with surface-layer exchanges of heat and mass. The acronym for the model i s SCABLE, Suburban Canopy and Boundary Layer Evaporation model). I t predicts the diurnal evolution of the mixed-layer depth, temperature and humidity. The saturation d e f i c i t of the mixed-layer i s an input to the surface evaporation model. In turn this enables the surface sensible heat flux to be calculated from the surface energy balance (using measurements of the available energy). This modelled surface sensible heat flux drives the growth of t h i s mixed-layer and thus the rate of entrainment from the capping inversion. The temperature and moisture structure of the mixed-layer i s determined by both inputs from the surface-layer, and from the "free" atmosphere. The suburban canopy evaporation sub-model i s based on the 'big leaf' Combination model, with a parameterisation scheme for the surface and aerodynamic resistances based upon the approaches taken by Shuttleworth (1976, 1978). The model performs adequately for simulating the day-to-day v a r i a b i l i t y of the saturation d e f i c i t and surface evaporation. Its performance on an hourly basis indicates that the model weaknesses l i e i n the simulation of the diurnal behaviour of the surface resistance and potential temperature of the mixed-layer. It i s concluded i n the thesis that such an approach i s necessary and v a l i d for predicting and understanding the evaporation regime i n areas the size of suburbia. This i s especially true where there i s l i k e l y to be a combination of factors determining the surface evaporation rate. TABLE OF CONTENTS Easts. ABSTRACT i i TABLE OF CONTENTS i v LIST OF TABLES v i i LIST OF FIGURES v i i i LIST OF SYMBOLS AND ABBREVIATIONS x i i i ACKNOWLEDGEMENTS X vi CHAPTER 1: INTRODUCTION 1.1 Rationale 1 1.2 Theoretical Context 1.2.1 Traditional Approaches to Modelling Evaporation 4 1.2.2 The Urban Surface and Atmosphere 9 1.3 Objectives 20 CHAPTER 2: SITE DESCRIPTION AND OBSERVATIONAL PROGRAMME 2.1 Overview 22 2.2 Site Description 2.2.1 The Rural Site 22 2.2.2 The Suburban Site 24 2.2.3 Climatological Context 27 2.3 Measurement Programmes 2.3.1 Phase I 30 2.3.2 Phase II 32 2.3.3 Data Processing: Hourly Surface Latent Heat Fluxes 42 2.4 Representativeness of a Point Measurement 43 2.4.1 Spatial V a r i a b i l i t y : Net Radiation 44 2.4.2 Spatial V a r i a b i l i t y : Sensible Heat Flux 48 CHAPTER 3: A COMPARISON OF THE ENERGY BALANCE AT A SUBURBAN AND RURAL LOCATION 3.1 summary 52 3.2 Hourly Variation 54 3.3 Day-to-Day Variation 58 3.4 Controls on Suburban Turbulent Flux Partitioning 60 CHAPTER 4: HOURLY AND DAILY VARIATION OF THE SUBURBAN LATENT HEAT FLUX: RESULTS AND DISCUSSION 4.1 Introduction 65 4.2 Average Energy Partitioning 66 iv 4.3 The Diurnal Suburban Energy Balance 4.3.1 Hourly Variation 67 4.3.2 Controls on Diurnal Variation 69 4.4 Day-to-Day Variation of the Suburban Energy Balance 75 4.5 Controls on the Suburban Latent Heat Flux 4.5.1 Energy A v a i l a b i l i t y 78 4.5.2 Water A v a i l a b i l i t y 80 4.5.3 Advection 84 4.6 Concluding Comments 94 CHAPTER 5: DEVELOPMENT AND IMPLEMENTATION OF A SUBURBAN EVAPORATION MODEL, SCABLE I: THE CANOPY EVAPORATION SUB-MODEL 5.1 Theory: Shuttleworth's Multi-Layer Canopy Models 98 5.2. Modification of Shuttleworth (1978) and SW for a Suburban Si t e 5.2.1 Overview 102 5.2.2 Canopy Evaporation Sub-Model Equations 105 5.3 Surface Resistances 5.3.1 Component Areas 109 5.3.2 Unirrigated Substrate 111 5.3.3 Irrigated Substrate 115 5.3.4 Impervious Substrate 117 5.3.5 Pervious Bluff-Body 117 5.4 Aerodynamic Resistances 118 5.4.1 Boundary-Layer 119 5.4.2 Substrate Component and Mean Canopy Flow 120 5.5 Implications and Limitations Arising from Model 125 Assumptions 5.6 S e n s i t i v i t y Analysis: Canopy Evaporation Sub-Model 128 5.6.1 Sen s i t i v i t y to Errors i n Parameterised Terms 129 5.6.2 Model Performance under Varying Conditions 130 CHAPTER 6: DEVELOPMENT OF SCABLE I I : MIXED-LAYER GROWTH SOB-MODEL 6.1 Modelling Convective Boundary-Layers 133 6.2 Model Equations 142 6.3 Model Input Parameters 6.3.1 Data Acquisition: Temperature and Humidity Gradients 148 6.3.2 I n i t i a l i s a t i o n Data 151 6.4 Se n s i t i v i t y Analysis: Mixed-Layer Growth Sub-Model 153 6.5 Integrated SCABLE 157 v CHAPTER 7: PERFORMANCE AND EVALUATION OF SCABLE 7.1 Diurnal Performance of SCABLE 160 7.2 Day-to-Day Performance of SCABLE 7.2.1 Mixed-Layer Depths, Temperature and Humidity 171 7.2.2 Surface Resistances 177 7.2.3 Canopy Evaporation 180 7.3 Evaluation of SCABLE 183 CHAPTER 8: CONCLUSIONS 8.1 Discussion of Objectives 193 8.2 Summary of Conclusions 196 8.3 Suggestions for Future Research 198 REFERENCES 200 APPENDIX 1: URBAN STORAGE HEAT FLUX PARAMETERISATION SCHEME A l . l Introduction 211 A1.2 Theoretical and Empirical Considerations 212 A1.3 Estimating Heat Storage i n the Urban Environement 215 A1.4 Development of an Objective Storage Heat Flux Model 218 A1.5 Preliminary Evaluation 224 A1.6 Discussion 226 APPENDIX 2: CALCULATION OF COMPONENT AREAS 228 APPENDIX 3: INSTRUMENT CALIBRATIONS AND ERROR ANALYSIS A3.1 Relative Humidity and Temperature Sensors 231 A3.2 V e r t i c a l Hind Velocity and Temperature: Spectra and Co-Spectra 233 A3.3 The Reversing D i f f e r e n t i a l Psychrometer System 233 A3.4 Bowen Ratio-Energy Balance and Eddy Correlation Approaches 238 A3.5 Other Measurement Errors 243 APPENDIX 4: PRELIMINARY DATA PROCESSING A4.1 Determination of the Surface Energy Balance 246 v i LIST OF TABLES Table 1.1: Comparison of magnitudes of terms i n Equation 1.3 Table 1.2: Comparison of aerodynamic roughness for various surfaces Table 2.1: Percentages of surfaces i n source area Table 2.2: Climate s t a t i s t i c s for measurement inter v a l : 1983 and 1986 Table 2.3: S t a t i s t i c s for net radiation spatial v a r i a b i l i t y study Table 2.4: S t a t i s t i c s for sensible heat flux density spatial v a r i a b i l i t y study Table 3.1: Average energy par t i t i o n i n g : 1983 Table 4.1: Average energy partitioning: 1983 and 1986 Table 4.2: Additional data to accompany Figure 4.14 Table 5.1: Percentage areal coverage for individual surface types Table 5.2: Fractional s e n s i t i v i t y of modelled Q E to changes i n input parameters Table 6.1: Model equations Table 7.1: Measured and modelled maximum mixed-layer temperatures, humidity and z A Table 7.2: Measured and modelled mean mixed-layer temperature, humidity and saturation d e f i c i t Table 7.3: Summary s t a t i s t i c s for measured and modelled evaporation Table 7.4: Modelled evaporation: Influence of changed surface and atmospheric conditions Table A l . l : Mean dimensions of buildings Table A1.2: Summary of equations used i n parameterisation scheme Table Al.3: Size of objective hysteresis coefficients compared to Oke and Cleugh (1987) LIST OF FIGURES Ease. F i g u r e 1.1: Boundary-layer s t r u c t u r e s over an urban s u r f a c e 10 F i g u r e 1.2: The urban canopy "volume" ( a f t e r Oke, 1987) 12 F i g u r e 2.1: C i t y of Vancouver and surrounding land-use 23 F i g u r e 2.2: L o c a t i o n a l map of study area and o b s e r v a t i o n a l 25 s i t e s F i g u r e 2.3: Calendar showing dates of instrument i n s t a l l a t i o n 33 F i g u r e 2.4: Schematic i l l u s t r a t i o n of measurement tower and 35 l o c a t i o n of instruments F i g u r e 2.5: Schematic i l l u s t r a t i o n of r e v e r s i n g d i f f e r e n t i a l 38 psychrometer system Fi g u r e 2.6: Synchronous obse r v a t i o n s of net r a d i a t i o n 46 F i g u r e 2.7: Comparison between net r a d i a t i o n 46 F i g u r e 2.8: Synchronous o b s e r v a t i o n s of s e n s i b l e heat f l u x 49 F i g u r e 2.9: Comparison between hourly s e n s i b l e heat f l u x 50 d e n s i t i e s : Culloden and Mainwaring F i g u r e 2.10: Comparison between hourly s e n s i b l e heat f l u x 50 d e n s i t i e s : Gordon Pk. and Mainwaring F i g u r e 3.1: D i u r n a l v a r i a t i o n of measured su r f a c e energy 55 balance components: Mainwaring and A i r p o r t / 1983 F i g u r e 3.2: D i u r n a l v a r i a t i o n of QH/Q*, 1983 55 F i g u r e 3.3: D i u r n a l v a r i a t i o n of suburban-rural energy f l u x 57 d i f f e r e n c e s , Vancouver, 1983 F i g u r e 3.4: Day-to-day v a r i a t i o n of mean d a y l i g h t Bowen 59 r a t i o , Vancouver, 1983 F i g u r e 3.5: I n t e r a c t i o n s between atmospheric l a y e r s and 63 t h e i r hypothesised i n f l u e n c e evaporation F i g u r e 4.1: D i u r n a l v a r i a t i o n of s u r f a c e energy budget components, Vancouver, 1986 68 F i g u r e 4.2: D i u r n a l v a r i a t i o n of Bowen r a t i o , Vancouver, 1983 68 F i g u r e 4.3: An example of the d i u r n a l v a r i a t i o n of mixed- 69 l a y e r p o t e n t i a l temperature, MVC s i t e , Vancouver, JD 213, 1986 v i i i F i g u r e 4.4: D i u r n a l v a r i a t i o n of measured s u r f a c e (D 0) and 73 - 74 mixed-layer (D m) s a t u r a t i o n d e f i c i t s F i g u r e 4.5: Day-to-day v a r i a t i o n of the mean d a y l i g h t - h o u r s 76 net r a d i a t i o n and l a t e n t heat f l u x d e n s i t i e s , Vancouver, 1986 F i g u r e 4.6: Day-to-day v a r i a t i o n of the mean d a y l i g h t - h o u r s 77 Bowen r a t i o , Vancouver, 1986 F i g u r e 4.7: Day-to-day v a r i a t i o n of QE/Q* (mean d a y l i g h t - h o u r s ) , 77 Vancouver, 1986 F i g u r e 4.8: Measured l a t e n t heat f l u x (mean d a y l i g h t hours) 79 compared t o the e q u i l i b r i u m l a t e n t heat f l u x F i g u r e 4.9(a): T o t a l d a i l y p r e c i p i t a t i o n measured a t Vancouver 81 I n t e r n a t i o n a l A i r p o r t , 1986 (b): V a r i a t i o n i n % s o i l moisture (0 - 200 mm) 81 i n two u n i r r i g a t e d parks w i t h i n Sunset area F i g u r e 4.10: A comparison between measured d a i l y e x t e r n a l 83 water-use added to p r e c i p i t a t i o n and measured l a t e n t heat f l u x e s , Vancouver, 1986 Fi g u r e 4.11: Measured net r a d i a t i o n and l a t e n t heat f l u x e s f o r J.D. 151 and 152 85 Fig u r e 4.12: As i n F i g u r e 4.11 f o r J.D. 231 and 232 87 Fi g u r e 4.13: As i n F i g u r e 4.11 f o r J.D. 248 - 250 88 F i g u r e 4.14: A suggested c l a s s i f i c a t i o n scheme f o r mean daylight-hourB Bowen r a t i o , based on wind d i r e c t i o n and s a t u r a t i o n d e f i c i t 91 Fi g u r e 5.1: Schematic i l l u s t r a t i o n of SCABLE showing the 97 i n t e r a c t i o n of the two sub-models F i g u r e 5.2: Schematic of SW model (from SW, 1985) 101 F i g u r e 5.3: Schematic of sur f a c e and aerodynamic r e s i s t a n c e 103 scheme i n canopy evaporation sub-model F i g u r e 5.4: R e l a t i o n s h i p between s o i l moisture and 113 u n i r r i g a t e d , s u b s t r a t e r e s i s t a n c e component F i g u r e 5.5: R e l a t i o n s h i p between s u b s t r a t e area i r r i g a t e d 113 and e x t e r n a l water-use a t the Hudson s i t e F i g u r e 5.6: S e n s i t i v i t y of su b s t r a t e s u r f a c e r e s i s t a n c e t o 125 v a r i a t i o n s i n input parameters F i g u r e 5.8: S e n s i t i v i t y of modelled evaporation (percentage 131 change) t o changes i n input parameters ix F i g u r e 6.1: Slab model r e p r e s e n t a t i o n of the PBL 134 F i g u r e 6.2: An example of the d i u r n a l growth of the mixed-layer, Vancouver, JD 213, 1986 134 F i g u r e 6.3: P o t e n t i a l temperature p r o f i l e comparison between Port Hardy and MVC s i t e s : (a) August 26, 1986 149 (b) August 21, 1986 (c) August 22, 1986 150 F i g u r e 6.4: S e n s i t i v i t y of modelled l a t e n t heat f l u x t o gr a d i e n t s (above mixed-layer) i n p o t e n t i a l temperature and humidity 154 F i g u r e 6.5: S e n s i t i v i t y of modelled l a t e n t heat f l u x t o the step change i n p o t e n t i a l temperature 155 F i g u r e 7.1: D i u r n a l v a r i a t i o n , f o r J.D. 201, o f : (a) Energy balance components (b) S a t u r a t i o n d e f i c i t :D0 - s u r f a c e - l a y e r :Dm - mixed-layer 161 F i g u r e 7.2: D i u r n a l v a r i a t i o n , f o r J.D. 203, o f : (a) Energy balance components (b) S a t u r a t i o n d e f i c i t :D0 - s u r f a c e - l a y e r :Dm - mixed-layer 161 F i g u r e 7.3: D i u r n a l v a r i a t i o n , f o r J.D. 212, o f : (a) Energy balance components (b) S a t u r a t i o n d e f i c i t :D0 - s u r f a c e - l a y e r :Dm - mixed-layer 163 F i g u r e 7.4: D i u r n a l v a r i a t i o n , f o r J.D. 213, o f : (a) Energy balance components (b) S a t u r a t i o n d e f i c i t :D0 - s u r f a c e - l a y e r :Dm - mixed-layer 163 F i g u r e 7.5: D i u r n a l v a r i a t i o n , f o r J.D. 214, o f : (a) Energy balance components (b) S a t u r a t i o n d e f i c i t :D0 - s u r f a c e - l a y e r :Dm - mixed-layer 165 F i g u r e 7.6: D i u r n a l v a r i a t i o n , f o r J.D. 215, o f : (a) Energy balance components (b) S a t u r a t i o n d e f i c i t :D0 - s u r f a c e - l a y e r :Dm - mixed-layer 165 F i g u r e 7.7: D i u r n a l v a r i a t i o n , f o r J.D. 224, o f : (a) Energy balance components (b) S a t u r a t i o n d e f i c i t :D0 - s u r f a c e - l a y e r :Dm - mixed-layer 167 x F i g u r e 7.8: D i u r n a l v a r i a t i o n , f o r J.D. 226, o f : (a) Energy balance components (b) S a t u r a t i o n d e f i c i t :D0 - s u r f a c e - l a y e r :Dm - mixed-layer 167 F i g u r e 7.9: Comparison between measured and modelled d a i l y maximum p o t e n t i a l temperature and humidity 170 F i g u r e 7.10: (a) Day-to-day v a r i a t i o n i n a v a i l a b l e energy (b) Day-to-day v a r i a t i o n i n measured s u r f a c e - l a y e r ( D 0 ) , modelled mixed-layer (D m) and measured mixed-layer s a t u r a t i o n d e f i c i t 176 F i g u r e 7.11: Comparison between " e f f e c t i v e " s u r f a c e r e s i s t a n c e from Penman Monteith and modelled s u b s t r a t e r e s i s t a n c e 178 F i g u r e 7.12: Comparison between measured and modelled l a t e n t heat f l u x e s 181 F i g u r e 7.13: Comparison between temporal v a r i a t i o n of measured and modelled l a t e n t heat f l u x e s 181 F i g u r e 7.14: Simulated d i u r n a l v a r i a t i o n of (a) p o t e n t i a l temperature, and (b) depth, of the mixed-layer: with and without a d v e c t i o n 187 F i g u r e 7.15: Map of Vancouver C i t y ( F i g u r e 2.1) 189 F i g u r e A l . l : Comparison between s o i l heat and net r a d i a t i o n f l u x e s 213 F i g u r e A1.2: Schematic of impervious/pervious areas i n 1000 m2 l o t area 220 F i g u r e A l . 3 : Comparison between measured (^Q s s) and modelled (^QSP) hourly storage heat f l u x 225 F i g u r e A1.4: Comparison between measured (AQSS) and modelled (4QS P) mean d a y l i g h t - h o u r s storage heat f l u x 225 F i g u r e A3.1: Comparison of temperature measured u s i n g Campbell S c i e n t i f i c t h e r m i s t o r , and thermocouple from r e v e r s i n g psychrometer 232 F i g u r e A3.2: Comparison of temperature measured using R o t r o n i c s t h e r m i s t o r , and thermocouple from r e v e r s i n g psychrometer 232 F i g u r e A3.3: Comparison of r e l a t i v e humidity measured using R o t r o n i c s sensor, and computed from r e v e r s i n g d i f f e r e n t i a l psychrometer system 234 xi F i g u r e A3.4: Comparison o f s e n s i b l e heat f l u x d e n s i t y computed using a 60 min and 4 x 15 min averaging time (from Roth, 1988) 234 F i g u r e A3.5: D i u r n a l v a r i a t i o n of s e n s i b l e and l a t e n t heat f l u x d e n s i t y f o r J.D. 201, with e r r o r bars F i g u r e A3.6: Comparison of mean da y l i g h t - h o u r s s e n s i b l e heat f l u x determined u s i n g Bowen r a t i o - e n e r g y balance ( Q H B ) and eddy c o r r e l a t i o n approaches ( Q H S ) F i g u r e A3.7: Comparison of mean day l i g h t - h o u r s l a t e n t heat f l u x determined using Bowen ra t i o - e n e r g y balance ( Q E B ) and eddy c o r r e l a t i o n - e n e r g y balance ( Q E R ) approaches F i g u r e A3.8: Comparison of mean day l i g h t - h o u r s l a t e n t heat f l u x determined u s i n g Bowen ratio-energy-balance and eddy c o r r e l a t i o n - e n e r g y balance approaches: s e l e c t e d days F i g u r e A3.9: Comparison of ho u r l y s e n s i b l e heat f l u x determined u s i n g Bowen ra t i o - e n e r g y balance ( Q H B ) and eddy c o r r e l a t i o n ( Q H S ) approaches F i g u r e A4.1: Decison t r e e F i g u r e A4.2: Comparison of l a t e n t heat f l u x determined using the optimum energy balance and eddy c o r r e l a t i o n - energy balance F i g u r e A4.3: Comparison of s e n s i b l e heat f l u x determined using the optimum energy balance and eddy c o r r e l a t i o n approaches 237 240 240 241 242 248 249 249 x i i LIST OF SYMBOLS Symbol Definition Lower Case: a area: a c = bluff-body a s = substrate c proportionality constant for flux of sensible heat at inversion base c q proportionality constant for flux of latent heat at inversion base d zero plane displacement index of agreement e vapour pressure saturation vapour pressure acceleration due to gravity roughness element height von Karman's constant extinction c o e f f i c i e n t for eddy d i f f u s i v i t y e* g h k n q s p e c i f i c humidity general form of aerodynamic resistance: rH r v - water vapour Units m' m kPa kPa m s -2 g k g - 1 s m"1 • st v,V v, ,v l/v2 canopy resistance isothermal or climatological resistance stomatal resistance slope of saturation vapour pressure/temperature curve mean horizontal wind speed and i t s fluctuating component f r i c t i o n velocity l a t e r a l wind velocity and i t s fluctuating component wind signals from G i l l anemometer s m * s m - 1 kPa "C"1 m s" 1 m s - 1 m s _ 1 m s" 1 x i i i w,w' v e r t i c a l wind velocity and i t s m s" 1 fluctuating component x,y horizontal distance from leading edge m z reference or measurement height m Z £ mixed-layer depth m z 0 roughness length m z 0 ' roughness length for substrate m component Upper Case: A available energy W m - 2 Bp - 1 excess resistance parameter B subsidence parameter m s" 1 C a volumetric heat capacity J m"3 D saturation d e f i c i t : kPa D 0, z - in surface-layer D m - i n mixed-layer DB - at surface roughness element spacing m E kinematic latent heat flux g kg" 1 m s" 1 Gr Grashof's number H kinematic sensible heat flux °C m s" 1 I impervious area i n model (proportion) K eddy d i f f u s i v i t y : m2 s~ l K H - heat K E ' v ~ water vapour KM - momentum K h - at canopy-top K short-wave radiation: W n r 2 K* - net K4 - incoming Kt - reflected LAI leaf area index L Monin Obukhov length m L v latent heat of vapourisation J k g - 1 xiv Q* net all-wave radiant flux density W m~2 Q E latent heat flux density W m"2 QH sensible heat flux density W m"2 Q G s o i l heat flux density W m"2 AQS storage heat flux density W m"2 Re Reynolds number Re* roughness Reynold's number T temperature "C W wetted area in model (proportion) Lower Case Greek: a Priestley-Taylor parameter 0 Bowen ratio B' dimensional Bowen r a t i o °C g" 1 kg 1 psychrometric constant kPa ° C _ 1 1 gradient of property ( ) m~1 8 potential temperature K thermal admittance: J m"2 s - 1 / 2 K"1 Ma - a i r Ms - s o i l " kinematic viscosity m2 s" 1 PV vapour density g m - 3 X r a t i o of sensible heat to net radiation Upper Case Greek: AB step change in potential temperature K Aj step change i n s p e c i f i c humidity g kg" 1 APv step change i n vapour density g m"3 il McNaughton and Ja r v i s ' omega factor xv ACKNOWLEDGEMENTS I wish to express my g r a t i t u d e to those who a s s i s t e d throughout the course of t h i s t h e s i s . I am indebted to my s u p e r v i s o r , Dr. Tim Oke, f o r h i s c o n t i n u a l encouragement, support and wise counsel on a l l aspects of t h i s t h e s i s , and c l i m a t o l o g y i n g e n e r a l . I am e s p e c i a l l y a p p r e c i a t i v e of h i s guidance and h e l p over the l a s t 12 months. I'd a l s o l i k e to thank my committee f o r t h e i r combined wisdom and a d v i c e on the t h e s i s - both a t i t s i n c e p t i o n and i n i t s w r i t i n g . In p a r t i c u l a r , s p e c i a l thanks are owed to Dr. Andy Black who not only taught me a great d e a l about micrometeorology, but a l s o loaned equipment and advice f r e e l y . I am g r a t e f u l to Dr. Douw Steyn f o r h i s i n v a l u a b l e h e l p i n the f i e l d and f o r the loan of the tethersonde system. His ready ear and mathematical e x p e r t i s e have been g r e a t l y a p p r e c i a t e d . Thanks are due to my many colleagues who c o n t r i b u t e d t o the t h e s i s through t h e i r h e l p i n the f i e l d : Hu W a l l i s , Matthias Roth, HaPe Schmid, Tim Oke, Douw Steyn, Ian McKendry and K e i t h Ayotte - the "tethersonde s h i f t - w o r k e r s " ; K e i t h Ayotte, HaPe Schmid and Matthias Roth f o r h e l p i n g on the tower, and f o r hours of f r u i t f u l d i s c u s s i o n ; Steve H i l t s , Derek Kay and Mark Cantwell who t o i l e d as research a s s i s t a n t s . The Mainwaring s i t e has been made a v a i l a b l e by B.C. Hydro, and the r e s e a r c h was funded through an NSERC grant to Dr. Tim Oke. I was p e r s o n a l l y funded by a Commonwealth S c h o l a r s h i p . I e s p e c i a l l y want to thank Sue Grimmond and Catherine Souch f o r t h e i r f r i e n d s h i p , a s s i s t a n c e and l i v e l y debate on a l l aspects of l i f e -c l i m a t o l o g i c a l and otherwise. F i n a l l y , thanks John; f o r f i x i n g the Bowen r a t i o motor, c l i m b i n g the tower i n the dark and the r a i n , and t r y i n g to understand c l i m a t o l o g y . But most of a l l , thanks f o r always being there, and keeping me sane and happy. xvi CHAPTER 1: INTRODUCTION 1.1 R a t i o n a l e Urban areas modify boundary-layer c l i m a t e s by a l t e r i n g the exchange of energy, water and momentum between the s u r f a c e and the atmosphere. The water and energy balances are t h e r e f o r e o f t e n used as frameworks f o r p r e d i c t i n g and i n t e r p r e t i n g the i n f l u e n c e of u r b a n i s a t i o n . The f i e l d of urban meteorology can be advanced by developing a b e t t e r understanding of the way i n which urban areas modify these balances. In p a r t i c u l a r , the p a r t i t i o n i n g of a v a i l a b l e energy between the t u r b u l e n t f l u x e s of l a t e n t and s e n s i b l e heat (the Bowen r a t i o ) p l a y s a l a r g e r o l e i n determining the l o c a l c l i m a t e of an urban area. Such knowledge i s a l s o b a s i c t o many a p p l i e d urban problems. For example the s e n s i b l e heat f l u x d r i v e s the growth of the daytime p l a n e t a r y boundary-layer and hence the mixing depth a v a i l a b l e f o r the d i s p e r s i o n of p o l l u t a n t s . S i m i l a r l y , e vaporation i s i n t e g r a l t o s t u d i e s of run - o f f s i m u l a t i o n (Grimmond, 1983), e s t i m a t i o n of urban water requirements and the c o o o l i n g i n f l u e n c e of t r a n s p i r i n g t r e e s and greenspace (Huang et al., 1987). There i s a demand f o r both an understanding of the nature o f , and the a b i l i t y t o p r e d i c t , urban heat and mass f l u x e s . The complexity of the urban atmosphere/surface i n t e r f a c e has somewhat l i m i t e d o b s e r v a t i o n s and modelling of s u r f a c e energy and mass f l u x e s i n the pa s t . Nonetheless a c l e a r e r p i c t u r e of urban s u r f a c e e n e r g e t i c s i s slowly emerging from ongoing o b s e r v a t i o n a l s t u d i e s (Oke, 1988). These i n d i c a t e t h a t w h i l e s e n s i b l e heat i s the dominant heat f l u x i n the suburban environment i n summer, l a t e n t heat may a l s o be an important energy s i n k . -1-T h i s i s even the case during p e r i o d s when p r e c i p i t a t i o n input i s low (Oke and McCaughey, 1983). Kalanda et a./.,(1980) suggest, and Grimmond (1983) subsequently confirms, t h a t lawn i r r i g a t i o n supplements the surface moisture s t o r e to a l e v e l capable of supporting the observed l a t e n t heat f l u x e s . Measurements of the urban energy balance a l s o show c o n s i d e r a b l e day-to-day v a r i a b i l i t y i n the p a r t i t i o n i n g of the s u r f a c e t u r b u l e n t f l u x e s . Such v a r i a b i l i t y has been q u a l i t a t i v e l y l i n k e d t o v a r i a t i o n s i n lawn i r r i g a t i o n (Kalanda et al., 1980) and net r a d i a t i o n (Oke and McCaughey, 1983) - v a r i a b l e s t h a t are u s u a l l y regarded as the dominant c o n t r o l s on s u r f a c e evaporation. However these f a c t o r s alone do not appear to adequately d e s c r i b e the temporal v a r i a b i l i t y of suburban evaporation. Recent o b s e r v a t i o n s over forest canopies suggest t h a t l a r g e r - s c a l e atmospheric processes may a l s o have a r o l e i n determining surface e v a p o r a t i o n . The extent of t h i s 'advective' i n f l u e n c e appears to depend on the nature of the s u r f a c e roughness and the s p a t i a l extent of s i m i l a r s u r f a c e types. McNaughton and J a r v i s (1983) propose t h a t i n aerodynamically rough environments e f f i c i e n t t u r b u l e n t t r a n s f e r enables 'coupling' between the well-mixed outer p o r t i o n (the mixed-layer) of the p l a n e t a r y boundary-layer (the PBL) and the s u r f a c e - l a y e r . The a p p l i c a b i l i t y of such i d e a s t o the urban environment have not been assessed. Thus the c o n t r o l s upon the suburban e v a p o r a t i o n regime have yet to be f u l l y i d e n t i f i e d and understood, d e s p i t e the important r o l e of t h i s f l u x i n the s u r f a c e energy balance and the development of urban boundary-layer c l i m a t e s . There are very few atmospheric models which i n c o r p o r a t e the f e a t u r e s of - 2 -the urban environment, as i l l u s t r a t e d by Loudon (1984). She e m p i r i c a l l y evaluates the a b i l i t y of three numerical models to simulate the urban s u r f a c e energy balance and f i n d s they cannot c o r r e c t l y p a r t i t i o n the a v a i l a b l e energy between the t u r b u l e n t l a t e n t and s e n s i b l e heat f l u x e s . T h i s r e s u l t s , i n p a r t , from the d i f f i c u l t y of s p e c i f y i n g s u r f a c e water a v a i l a b i l i t y . The p a r a m e t e r i s a t i o n of the urban s u r f a c e moisture, thermal and geometric c h a r a c t e r i s t i c s , while fundamental to the p r e d i c t i v e c a p a b i l i t y of these models, has yet to be r e s o l v e d . Thus while numerical models of the PBL e x i s t , they are l i m i t e d i n t h e i r a b i l i t y t o parameterise the heterogeneous urban s u r f a c e . M i c r o - m e t e r o l o g i c a l models, w h i l e m o d e l l i n g canopy processes, do not i n c l u d e any a d v e c t i v e i n f l u e n c e which can r e s u l t from the i n t e r a c t i o n of the s u r f a c e - l a y e r with the remaining PBL. N e i t h e r the s l a b PBL or standard micro-meteorological models are capable of adequately s i m u l a t i n g urban t u r b u l e n t f l u x e s . The aim of the t h e s i s i s t o enhance understanding of the t r a n s f e r of s e n s i b l e and l a t e n t heat i n the urban boundary-layer. In p a r t i c u l a r i t focusses upon an examination of the processes which c o n t r o l the s i z e and v a r i a b i l i t y of the l a t e n t heat f l u x . A p r e d i c t i v e evaporation model which i n c l u d e s these processes i s developed. The next s e c t i o n o u t l i n e s the t h e o r e t i c a l background f o r the t h e s i s and s t a t e s i t s s p e c i f i c o b j e c t i v e s ( S e c t i o n 1.3). -3-1.2 Theoretical Context 1.2.1 Traditional Approaches to Modelling Evaporation (a) The Penman-Monteith Combination Model The Penman-Monteith (PM) model i s a physically-based, one-dimensional Combination model which has been widely and successfully used to estimate evaporation from a variety of vegetated surfaces. Inputs to the model comprise meteorological parameters measured at a reference height above the surface (z) and physiological and aerodynamic resistances to vapour transport between the surface and this reference height. These are: (i) a canopy resistance to vapour transport from within the stomata to the leaf surface. For an individual leaf this i s a stomatal resistance, r e t (Monteith, 1965); and for an entire canopy i t has been shown (Black et al., 1970) that the canopy resistance i s equivalent to the p a r a l l e l sum of the individual stomatal resistances, r c = ( ^ r B t _ 1 ) - 1 . ( i i ) an aerodynamic resistance for the transfer from the surface to the reference height ( r a ) . The PM equation can be expressed: Q E = s(Q* - Q G) + C a D 2/r a s + T ( l + r c / r a ) (1.1) where Q E = latent heat flux density Q* = net radiation flux density Q G = s o i l heat flux density s = slope of saturation vapour pressure curve at a i r temperature 1 = psychrometric constant C a = heat capacity of a i r D2 = vapour pressure d e f i c i t at height z - 4 -Note that the symbols used here are for the general form of the PM equation. They w i l l be changed to symbols more appropriate for the specific model developed in Chapter 5. The Combination model thus includes the dominant evaporation controls: the available energy, saturation d e f i c i t , turbulent transport efficiency and a parameterisation of the surface moisture a v a i l a b i l i t y through r c . It i s one-dimensional i n that the vegetation canopy i s represented as a large leaf. For canopies with a d i s t i n c t v e r t i c a l structure such as forests and crops, multi-level canopy models based on the PM equation have been developed (e.g. Shuttleworth, 1978; Kelliher et al., 1986 - Chapter 5). (b) Equilibrium Evaporation and the Influence of Advection Apart from i t s obvious use for predicting evaporation, the PM model can also be used diagnostically to i l l u s t r a t e the important controls on Q E in different environments. McNaughton and Jarvis (1983), for example, rearrange (1.1) to make e x p l i c i t the differences between the controlling factors i n forest and grassland evaporation, i . e . the role of the available energy, compared to that of the surface resistance and the saturation d e f i c i t : • Over aerodynamically-smooth surfaces that are well-watered r a becomes large and the energy term (Q*-QG) dominates the equation. This i s supported by empirical evidence and explains the re l a t i v e success of simple energy-based evaporation models (such as that of Priestley and Taylor, 1972) in predicting evaporation over grass surfaces (see Clothier et al., 1982). This situation i s termed equilibrium evaporation, defined as: - 5 -Q E E Q - 8 ( Q * - Q G ) ( 1 - 2 ) s+T The vapour pressure d e f i c i t i s i n equilibrium with the surface and AD/AT. = Ae/Az, where e i s the vapour pressure. I t i s as i f the surface-layer were separated from the rest of the PBL by a large resistance such that the grass surfaces are said to be 'decoupled' from the PBL. • For aerodynamically-rough surfaces, r a i s usually small compared to the surface resistance. The second part of ( 1 . 1 ) (the advective term) becomes important and D2 i s s e n s i t i v e to changes i n saturation d e f i c i t throughout the PBL. In these circumstances the surface-layer i s said to be 'coupled' to the PBL. Surface evaporation i s then be linked to changes i n the humidity of the PBL. Rearranging ( 1 . 1 ) r e s u l t s i n : Q E = s (Q*-QG) + C a (D z-D e q) (s+T) <s+f)r a + TTr0 ( 1 . 3 ) I I I where D e q = 'equilibrium' vapour pressure d e f i c i t = s 1 r c ( Q * - Q Q ) ( 1 . 4 ) s+Tf C a and I i s known as the equilibrium term and I I as the saturation d e f i c i t , or advective term. Using t y p i c a l values, the r e l a t i v e sizes of I and I I are i l l u s t r a t e d i n Table 1 . 1 . -6-Table 1.1: Comparison of magnitudes of terms i n Equation 1.3 using (Q* - QG) - 300 w rn"2 Dz = 1.5 kPa T 2 = 15°C r c (s m"1) Term I (W m"2) Term II (W rn"2) r a (s m"1) 10 100 20 187.5 504.2 82.1 100 187.5 67.5 23.3 500 187.5 -126.2 -86.7 It i s evident that the size of the surface resistance plays an important role i n determining the r e l a t i v e sizes of terms I and II. With small values of r a , and low surface resistances, the second term becomes much larger than the f i r s t (II/I = 2.68). As the surface resistance increases, the ratio of term II to term I diminishes to 0.36. In dry conditions both the available energy and the saturation d e f i c i t w i l l influence surface evaporation. In wet conditions the saturation d e f i c i t w i l l be the dominant control. Such a switch in the controls depending upon the moisture status of the surface implies that large variations i n latent heat fluxes can be expected i n environments characterised by a low aerodynamic resistance. McNaughton and Jarvis (1983) define the parameter, O, to express the degree of decoupling between the surface-layer and PBL saturation d e f i c i t s . Thus: Q E = fi (Q*-QG) + (1-rt) C a D m (1.5) s+7 7 r c where D m = saturation d e f i c i t at a reference height in the mixed-layer Similarly, the value of fl can be seen to weight the relative influence of the equilibrium compared to the PBL saturation d e f i c i t s : D 0 = n Deq + (I"*7) Dm (1-6) where D 0 = saturation d e f i c i t at the surface Dm = saturation d e f i c i t of the PBL, defined as: Dm = e*(0) - a(9m - 9Q) - e (1.7) where e*(0) = saturation vapour pressure at the potential temperature and fl = 1 + 1 B+1 r„ -1 (1.8) fl i s a weighting factor which expresses the interaction between the surface and PBL. It i s determined primarily by the r a t i o of the aerodynamic and surface resistances. As r a i s reduced and r c i s increased, the degree of coupling i s enhanced. In forests, fl can be as low as 0.2, compared to a grassland value of 0.8 (McNaughton and Jarvis, 1983). Observations of forest energy balances demonstrate that the v a r i a b i l i t y of evaporation rates i s often related to advective influences. This results from the influence of the mixed-layer saturation d e f i c i t (which may be determined by larger-scale synoptic events) on the surface-layer. Miranda et al. (1984) confirm this mechanism for a heather canopy, as do Verma et al. (1986) who find fl values of 0.35 -0.65 for a deciduous forest. The concept of scale i s central to this discussion of evaporation controls. Jarvis and McNaughton (1986) show that the size of the moisture source determines the s e n s i t i v i t y of the actual evaporation to the saturation d e f i c i t , net radiation and canopy conductance (the inverse of -8-canopy resistance). The moisture sources might be stomata, plants, an extensive canopy or a region. They identify a reference leve l where measurements are not influenced by surface fluxes. It represents an appropriate height of observation and becomes greater with increasing size of the moisture source. For an extensive canopy the reference level must be above the surface-layer but within the PBL. Evaporation from the canopy i s linked to D m and i s also sensitive to changes in the canopy resistance. At the regional-scale the reference level must be above the PBL. Models indicate that for canopy resistances typical of a well-watered agricultural s i t e , this physiological control i s minimal. Therefore available energy and temperature determine the evaporation and thus, for regional-scale evaporation, the Priestley and Taylor (1972) approach may be adequate. Its success depends on the homogeneity of the moisture source - i t must be "similar to the regional norm" (Jarvis and McNaughton, 1986). As further discussed in Chapter 6, de Bruin (1983) and McNaughton and Spriggs (1986) combine a mixed-layer growth model with a surface evaporation model to predict regional evaporation. In t h i s way, feed-backs between the surface evaporation rate and mixed-layer dynamics are incorporated into an interactive model. 1.2.2 The Urban Surface and Atmosphere As with much of boundary-layer theory, the t r a d i t i o n a l evaporation models have been developed for f a i r l y ideal surfaces such as short grass that are uniform with an extensive fetch. There has also been considerable work i n more heterogeneous canopies such as forests and row crops. Urban -9-F i g u r e 1.1: Boundary-layer s t r u c t u r e s over an urban s u r f a c e ( a f t e r Oke, 1984) -10-meteorology uses many of these a g r i c u l t u r a l and f o r e s t micro-meteorological concepts as analogues f o r the urban atmospheric system. For example, Oke (1976) drew such an analogy when he d i f f e r e n t i a t e d between the urban canopy-layer (UCL) and the urban boundary-layer (UBL) (Fi g u r e 1.1). The UCL i s the l a y e r below r o o f - l e v e l . Although t h i s boundary i s o n l y conceptual, i t s presence has been i n d i c a t e d by observations of temperature and humidity p r o f i l e s ( T a e s l e r , 1980; Oke, 1988). The canopy-layer micro-climate i s determined by the roughness element d i s t r i b u t i o n and the sou r c e s / s i n k s f o r energy and mass t r a n s f e r . The UBL i s l o c a t e d above r o o f - l e v e l , and comprises the roughness sub-layer, the s u r f a c e - l a y e r and the remaining PBL. The outer p o r t i o n of the PBL i s r e f e r r e d t o as the mixed-layer. The next s e c t i o n d e s c r i b e s some c h a r a c t e r i s t i c s of the urban surface and atmosphere. I t w i l l be shown t h a t an a p p r o p r i a t e model f o r t u r b u l e n t heat f l u x e s can be e x t r a c t e d from the a g r i c u l t u a l and/or f o r e s t meteorology l i t e r a t u r e . (a) The Urban Surface The d e f i n i t i o n of a 'su r f a c e ' depends upon s c a l e . The focus of t h i s r e s e a r c h i s the f l u x of heat to/from the urban s u r f a c e . These f l u x e s have t h e i r sources w i t h i n the urban volume i l l u s t r a t e d i n Fi g u r e 1.2 and i t i s the a r e a l l y - i n t e g r a t e d f l u x through the top of the volume ( i . e . as measured by instruments l o c a t e d w i t h i n the s u r f a c e - l a y e r ) t h a t i s of i n t e r e s t i n t h i s study. The lower p a r t of the urban volume d e p i c t e d i n Fi g u r e 1.2 i s termed the -11-urban 'canopy' and i s c h a r a c t e r i s e d by i t s convoluted, three-dimensional nature. I t i s made up of a heterogeneous a r r a y of v e r t i c a l , h o r i z o n t a l , s l o p i n g and m u l t i - l e v e l s u r f a c e s . These surfaces are comprised of many d i f f e r e n t m a t e r i a l s - a l l with r a d i a t i v e , moisture-holding and thermal p r o p e r t i e s t h a t vary i n both time and space. Despite the canopy-layer heterogeneity, by analogy t o a f o r e s t canopy we can i d e n t i f y land-use u n i t s which might be regarded as homogeneous. Th i s r e q u i r e s t h a t our o b s e r v a t i o n a l l e v e l i s above the canopy - such a s p a t i a l s c a l e i s r e f e r r e d to as the l o c a l s c a l e . The land-use u n i t of i n t e r e s t here i s suburbia. The aerodynamic roughness of f o r e s t e d and suburban canopies (Table 1.2) are s i m i l a r . There are, however, d i f f e r e n c e s . In suburban areas the dominant b l u f f - b o d y elements are houses and t r e e s whose heights are t y p i c a l l y l e s s than 10 m, compared t o f o r e s t s where the t r e e heights range from 5 - 20 m. Fur t h e r , the b l u f f - b o d y elements are more s p a r s e l y d i s t r i b u t e d i n suburbia. Schmid (1988) and Steyn (1980) found t y p i c a l spacings i n suburban land-use of 20 m. T h i s roughness element spacing i s i n f l u e n c e d by the o r i e n t a t i o n of s t r e e t s and hence shows a st r o n g degree of ani s o t r o p y . T h i s can be compared t o a spacing of 2 m i n the T h e t f o r d F o r e s t (Ford and Deans, 1980; Raupach, 1980) and 3.2 m f o r a e u c a l y p t f o r e s t ( G a r r a t t , 1980). The 'open' suburban canopy s t r u c t u r e p l u s the mix of heterogeneous s u r f a c e s leads t o c o n s i d e r a b l e h o r i z o n t a l i n t e r a c t i o n . The study by Oke (1979) showing the o a s i s e f f e c t i n an i r r i g a t e d suburban lawn i s i l l u s t r a t i v e of the importance of h o r i z o n t a l , m i c r o - s c a l e advection i n the urban environment. -13-Table 1.2: Comparison of aerodynamic roughness for various surfaces Surface Type Canopy Height (m) Roughness Length (m) grass agricultural crops 0.25 - 1.0 0.02 0.02 0.1 0.2 forests -coniferous -deciduous 10 - 28 0.28 1.0 3.9 6.0 suburban terrain -low density -high density 5 - 1 0 10 0.4 0.8 1.2 1.8 Flow within the canopy-layer i s determined by the arrangement of the roughness elements, and the speed and direction of wind flow. Hussain and Lee (1980) simulate atmospheric flow over rectangular blocks (buildings) and find three flow regimes related to a combination of building height and spacing. Based on this and a roughness element analysis, suburban terrain appears to be characterised by their 'wake-interference' flow. This generates the greatest turbulence of the three flow regimes. Suburban land-use can represent a partic u l a r l y rough surface to the atmospheric flow which w i l l affect the transfer of scalars and momentum between the canopy and boundary-layers. The formulation of aerodynamic resistances must account for variations i n the canopy structure. Kondo and Kawanaka (1986) observe that there i s a strong relationship between the geometric structure of the canopy and bulk transfer coefficients. Another characteristic of the suburban canopy i s the separation of the sources and sinks for heat, mass and momentum. Thus while buildings are e f f i c i e n t sinks for momentum, they seldom act as moisture sources. In suburban areas, the moisture sources are predominantly trees, lawns and -14-parks. These are 'patchy' i n terms of t h e i r s p a t i a l d i s t r i b u t i o n and are not always c o i n c i d e n t with surfaces which may generate turbulence ( b u i l d i n g s and dry pavement). M u l t i - l e v e l evaporation models have been developed f o r f o r e s t s and other vegetated canopies which have an obvious v e r t i c a l s t r u c t u r e but t h i s doesn't r e a l l y correspond to the s t r u c t u r e of the suburban canopy. Secondly t h e r e are the s i m p l i f i e d one-dimensional approaches such as t h a t adopted by Shuttleworth and Wallace (1985) to simulate e v a p o r a t i o n from sparse canopies. As d i s c u s s e d , suburban land-use has a low d e n s i t y of b l u f f - b o d i e s which form an open, sparse canopy. Together with the i n t e r v e n i n g h o r i z o n t a l s u r f a c e s , t h i s c r e a t e s a complex a r r a y of s u r f a c e types. The s i m i l a r i t i e s between suburbia and a sparse v e g e t a t i o n canopy suggests t h a t the simple one dimensional approach of Shuttleworth and Wallace (1985) may provide an a p p r o p r i a t e modelling approach. For example, K e l l i h e r et al (1986) show t h a t t h i s approach c o u l d be used to model e v a p o r a t i o n from a two-storey, thinned c o n i f e r o u s f o r e s t , i n c l u d i n g the e v a p o r a t i o n from the s o i l . T h i s d e s c r i p t i o n o f the suburban canopy i s a l s o b a s i c to developing hypotheses about the nature of suburban e v a p o r a t i o n . The aerodynamic roughness of the UCL has been d i s c u s s e d as w e l l as the patchy nature of the moisture sources. Urban areas a l s o experience anthropogenic i n f l u e n c e s which may a f f e c t the l a t e n t heat f l u x . The f i r s t o f these i s the input of moisture and heat through combustion. The second i s the input of water i n t o the urban system through i r r i g a t i o n . The f o l l o w i n g d i s c u s s i o n addresses these aspects under the t o p i c of the urban boundary-layer. -15-fb) The Urban Boundary-Layer Energy Exchanges The energy balance of an urban volume with n e g l i g i b l e advection (see Oke, 1988 f o r a s u b s t a n t i v e review) i s : Q* + Q F = Q E + Q H + 4 2 s (1-9) where Q* = net r a d i a t i o n f l u x d e n s i t y Q F = anthropogenic heat f l u x d e n s i t y Q H = s e n s i b l e heat f l u x d e n s i t y Q E = l a t e n t heat f l u x d e n s i t y AQS = storage heat f l u x d e n s i t y D e s p i t e the range of s u r f a c e and atmospheric e f f e c t s on r a d i a t i v e t r a n s f e r , u r b a n / r u r a l d i f f e r e n c e s of net r a d i a t i o n are found t o be =5% (see Auer, 1981; Oke and McCaughey, 1983; Cleugh and Oke, 1986). The anthropogenic heat f l u x i s a source of energy i n the urban environment not u s u a l l y encountered i n other systems. I t s source i s the energy r e l e a s e d from f u e l combustion ( e s p e c i a l l y domestic heating, t r a n s p o r t a t i o n and i n d u s t r y ) . Estimates of Q F f o r Vancouver have been forwarded by Yap (1973) and Grimmond (1988). They f i n d a peak o f «=15 W m'2 a t midday on a t y p i c a l a n t i c y c l o n i c , summer day. A f i r s t order estimate of =10 W m"2 f o r d a i l y mean Q F i n summer appears a p p r o p r i a t e . T h i s i s r e l a t i v e l y small i n comparison to the other components of the energy balance, but a t nig h t or i n winter t h i s source assumes a l a r g e r r o l e . An adequate understanding of the dynamics of heat storage change {AQS) i n urban areas i s s t i l l e l u s i v e . The r o l e of AQS i s assumed t o i n c r e a s e wit h the degree of urban development, but measurements i n d i c a t e t h a t d i f f e r e n c e s between the thermal i n e r t i a of urban and r u r a l s u r f a c e s are sm a l l (Carlson et al., 1981). Appendix 1, and Oke and Cleugh (1987), d i s c u s s the c h a r a c t e r i s t i c f e a t u r e s of AQS, and the most a p p r o p r i a t e schemes to model the storage component. Observations show the urban l a t e n t heat f l u x to be l e s s than i n r u r a l areas and to be l o o s e l y c o r r e l a t e d with the r e d u c t i o n i n v e g e t a t i o n . However urban evaporation i s f a r from n e g l i g i b l e (except f o r t o t a l l y impervious, dry surfaces) - even d u r i n g drought Q E can s t i l l be an important f l u x (see Coppin, 1979; Kalanda et al.' 1980; Oke and McCaughey, 1983; Cleugh and Oke, 1986). S e n s i b l e heating i s the dominant d i u r n a l energy s i n k i n the urban environment with Q H d i r e c t e d away from the s u r f a c e a f t e r sunset (and sometimes throughout the evening). The storage component i s an energy source i n the l a t e a f ternoon, and through the evening. Considerable day-to-day v a r i a t i o n i n the p a r t i t i o n i n g of the t u r b u l e n t f l u x e s has been observed (Kalanda et al., 1980; McCaughey and Oke, 1983) and i s one of the f o c i i of the present re s e a r c h . Kalanda et al. (1980) note t h a t v a r i a t i o n s i n both lawn i r r i g a t i o n and a v a i l a b l e energy c o n t r i b u t e to the temporal v a r i a b i l i t y . Grimmond and Oke (1986) demonstrate t h a t lawn i r r i g a t i o n can supply s u f f i c i e n t water to s u s t a i n the evaporative f l u x e s r e p o r t e d by Kalanda et al. The day-to-day v a r i a b i l i t y has a l s o been r e l a t e d t o d i f f e r e n c e s i n the s y n o p t i c regime, p r i m a r i l y i n terms of r a d i a t i o n r e c e i p t (Oke and McCaughey, 1983). Temperature and Moisture Budgets The e n t i r e PBL i s i n f l u e n c e d by the u n d e r l y i n g c i t y , hence i t i s o f t e n l a b e l l e d as an urban boundary-layer. The UBL on a t y p i c a l summer day i s d r i e r , deeper, and warmer than i t s r u r a l counterpart. T u r b u l e n t i n t e n s i t i e s are enhanced, wind v e l o c i t i e s are perturbed, as are wind d i r e c t i o n s and momentum budgets. What are the i m p l i c a t i o n s of these changes upon evaporation from the urban s u r f a c e , whose feat u r e s were d e s c r i b e d e a r l i e r ? The v e r t i c a l p r o f i l e s of the temperature and moisture i n the UBL are r e l a t e d i n p a r t to the s u r f a c e energy exchanges. Measurements conducted i n St. Louis during METROMEX f o r summer, daytime c o n d i t i o n s , i n d i c a t e t h a t the v e r t i c a l temperature and humidity p r o f i l e s i n the UBL are warmer and d r i e r than i n the surrounding r u r a l PBL. These d i f f e r e n c e s are found to vary i n v e r s e l y with wind speed (Shea and Auer, 1978), and to extend to heights of 500 - 1000 m (Auer, 1981). Ackerman and Mansell (1978, c i t e d i n Lee, 1984) observe an average midday u r b a n - r u r a l temperature d i f f e r e n c e of ^ l ' c and a r e d u c t i o n i n humidity i n the lower p o r t i o n s of the UBL. Subsequent obse r v a t i o n s (Hildebrand and Ackerman, 1984) show tha t the dry mixed-layer r e s u l t s from a decreased s u r f a c e evaporation and enhanced entrainment of warm a i r from the s t a b l e i n v e r s i o n l a y e r which caps the UBL. The g r e a t e r entrainment r e s u l t s from the i n c r e a s e d mechanical and thermal t u r b u l e n t i n t e n s i t i e s (Bowne and B a l l , 1977; Hogstrom, 1982; Steyn, 1980; Hildebrand and Ackerman, 1984 and Y e r s e l and Goble, 1986). The r e s u l t s from an e x t e n s i v e study of turbulence i n the urban s u r f a c e - l a y e r conducted by C l a r k e et al. (1982) are t y p i c a l . They observe enhanced urban t u r b u l e n t i n t e n s i t i e s , exceeding the r u r a l v a l u e s by 50%, even when normalised by wind speed. T h i s i s due to both the extreme roughness of the u n d e r l y i n g s u r f a c e and the a f f e c t of the urban heat i s l a n d on atmospheric s t a b i l i t y . -18-The e f f e c t of these f e a t u r e s on the l a t e n t heat f l u x e s from the urban s u r f a c e must be c o n s i d e r e d . C o n t r o l s upon evaporation depend upon s c a l e ( J a r v i s and McNaughton, 1986). The degree of h e t e r o g e n e i t y a l s o depends on the s p a t i a l s c a l e being considered (Schmid, 1988). In a c i t y , homogeneous land-use u n i t s such as commercial, i n d u s t r i a l and r e s i d e n t i a l areas can be i d e n t i f i e d . They are considered to be homogeneous a t the local-scale because t h e i r elements are g e n e r a l l y small enough t h a t t h e i r i n d i v i d u a l e f f e c t s are merged w i t h i n the s u r f a c e - l a y e r . Nonetheless these l o c a l - s c a l e u n i t s of land-use c o n t r i b u t e to the urban heterogeneity a t a l a r g e r s c a l e . The lowest p o r t i o n of the atmosphere downwind of a land-use change may be ' f u l l y a d j u s t e d ' to t h a t l o c a l - s c a l e s u r f a c e . The depth of t h i s adjustment depends on the a r e a l extent of the land-use and the s t a b i l i t y of the atmosphere. Measurements of evaporation or any of the energy balance components w i t h i n an adjusted l a y e r should adequately represent the f l u x from t h a t land-use u n i t . The p r o p e r t i e s of the r e s t of the UBL above the s u r f a c e - l a y e r (=«90%) although i n f l u e n c e d to some degree by the immediate u n d e r l y i n g land-use mostly r e f l e c t the e f f e c t s of d i f f e r e n t s u r f a c e s upwind. Thus D m i s not f u l l y a d j u s t e d t o the immediate u n d e r l y i n g s u r f a c e . C e r t a i n l y , the p r o p e r t i e s of the UBL are determined by the a l t e r e d f l u x e s from the l o c a l - s c a l e s u r f a c e s . However h o r i z o n t a l i n t e r a c t i o n s between these leads t o a UBL whose nature i s ' e x t e r n a l l y - s e t ' f o r any f l u x emanating from the canopy-layer. In t h i s way the evaporation from an extended suburban surface (made up of l o c a l - s c a l e s u r f a c e s ) i s analogous to the e v a p o r a t i o n from an e x t e n s i v e canopy d e s c r i b e d by J a r v i s and McNaughton. On the other hand, i f the e n t i r e c i t y s u r f a c e becomes wetted any -19-spatial variation of the moisture a v a i l a b i l i t y may be minimal. As a result the spatial structure of D m may be uniform and the surface resistance low. This i s analogous to the regional evaporation scenario of Jarvis and McNaughton, 1986 (see p.9). The dominant control upon evaporation may then be net radiation. Thus the UBL has two components (Ching et al, 1983; refer also to Figure 1.1): a lower surface-layer (depth ^lOO m) whose nature i s determined by the exchanges with the local-scale land-use units which make up the c i t y and a second layer, the mixed-layer (typically =«1000 m), whose properties are determined by the entire integrated urban area. The atmosphere within the UBL may also be influenced by advection from surfaces upwind of the c i t y . For example a coastal, urban location has a UBL whose dynamics are also affected by the action of land and sea breezes. The increased turbulent intensities and the enhanced entrainment rate at the top of the UBL means that the aerodynamically-rough nature of the urban area should lead to strong linkages between the mixed and surface-layers. 1.3. Obj ectives The s p e c i f i c objectives of this thesis are to: 1. Examine the magnitude and v a r i a b i l i t y of the turbulent heat fluxes i n a suburban environment. This i s achieved f i r s t l y through comparisons with a rural s i t e (Chapter 3). 2. Use observations (Chapters 3 and 4) and modelling (Chapter 7), to determine the v a l i d i t y of the hypothesis that the day-to-day variation i n the pa r t i t i o n i n g of the suburban surface turbulent fluxes results not only -20-from s p a t i a l and temporal v a r i a t i o n s i n surface-based c o n d i t i o n s (e.g. a v a i l a b l e energy or s u r f a c e moisture a v a i l a b i l i t y ) but i s a l s o s i g n i f i c a n t l y a f f e c t e d by the temperature and moisture c h a r a c t e r i s t i c s of the PBL. 3. Incorporate these i n f l u e n c e s i n t o a coupled canopy evaporation and boundary-layer growth model (Chapter 5 and 6) to p r e d i c t suburban e v a p o r a t i o n . 4. Evaluate the performance of such a model i n p r e d i c t i n g evaporation i n a suburban area (Chapter 7 ) . 5. Use the model r e s u l t s and o b s e r v a t i o n s t o assess the c o n t r o l s on ev a p o r a t i o n i n urban areas (Chapters 7 and 8 ) . The t h e s i s t h e r e f o r e seeks t o make c o n t r i b u t i o n s to both urban c l i m a t o l o g y and the study of ev a p o r a t i o n by developing a model which i n c o r p o r a t e s the observed i n f l u e n c e s o f both the canopy- and mixed-layers on s u r f a c e evaporation from a heterogeneous and complex canopy. The suburban s i t e s e l e c t e d f o r both o b s e r v a t i o n s and model t e s t i n g i s a suburb i n Vancouver, B r i t i s h Columbia, Canada. I t i s the l o c a t i o n of many e a r l i e r urban energy balance s t u d i e s . A d e s c r i p t i o n of the s i t e and the measurement programme i s presented i n the f o l l o w i n g chapter. -21-CHAPTER 2: SITE DESCRIPTION AND OBSERVATIONAL PROGRAMME 2.1 Overview The l o c a t i o n of t h i s study i s the c i t y of Vancouver and i t s surrounding a r e a . Vancouver i s l o c a t e d on the west coast of B r i t i s h Columbia and l i e s n o rth of the Fraser R i v e r and i t s d e l t a (Figure 2.1). I t i s a m i d - l a t i t u d e (49°N) c i t y with a p o p u l a t i o n of 1 m i l l i o n i n h a b i t a n t s . The measurement programme c o n s i s t e d of two phases. An i n i t i a l summertime rural-suburban energy balance comparison was conducted i n 1983 (Phase I ) . T h i s was f o l l o w e d i n 1986 by an i n t e n s i v e study t h a t encompassed canopy-, s u r f a c e - and mixed-layer measurements a t a suburban l o c a t i o n (Phase I I ) . During Phase I the r u r a l and suburban energy balances were measured simultaneously f o r 30 days d u r i n g the p e r i o d J u l y 18 - September 22. In Phase II o b s e r v a t i o n s were conducted semi-continuously from A p r i l 5 t o October 5. The f o l l o w i n g chapter documents the nature of the s i t e s , measurement programme, inst r u m e n t a t i o n and procedures used to determine a r e p r e s e n t a t i v e s u r f a c e energy balance f o r each l o c a t i o n . I t a l s o d e s c r i b e s the measurement programme used t o monitor the suburban canopy- and mixed-layer f e a t u r e s . D e t a i l s o f instrument c a l i b r a t i o n s , e r r o r a n a l y s i s and other data p r o c e s s i n g are covered i n Appendix 3. 2.2 Site Description 2.2.1 The Rural S i t e (Phase I) The r u r a l s i t e has a dual r o l e - i t serves as an experimental c o n t r o l - 2 2 -Figure 2.1: City of Vancouver and surrounding land-use a g a i n s t which the suburban r e s u l t s can be compared. Thus i t s f e t c h , f l a t n e s s and homogeneity of surface cover should conform t o the requirements of an ' i d e a l ' s i t e (e.g. Oke, 1987) where standard m i c r o m e t e o r o l o g i c a l theory should apply. Secondly, the s u r f a c e cover i s reasonably t y p i c a l of much of the a g r i c u l t u r a l land-use surrounding Vancouver and thus provides a b a s i s f o r a suburban-rural comparison. The s i t e i s t h e r e f o r e a surrogate f o r the pre-urban/urban comparison recommended by Lowry (1977). A s i t e ( r e f e r r e d t o as ' A i r p o r t ' ) on the grassed f i e l d s adjacent t o the runway a t Vancouver I n t e r n a t i o n a l A i r p o r t (Figure 2.1) was s e l e c t e d . I t i s f l a t w i t h >200 m of s i m i l a r f e t c h i n a l l d i r e c t i o n s . The v e g e t a t i o n cover of grass (0.15 - 0.20 m height) grows i n a s i l t s o i l o v e r l y i n g sand (0.9 m depth) and i s r e g u l a r l y mown. In the winter s u r f a c e ponding occurs but by l a t e summer the water t a b l e drops to a depth of about 1 m. The surface f l o o d i n g produces a mat of dead grass through which regrowth occurs each s p r i n g . T h i s mat l i m i t s the t r a n s f e r of s e n s i b l e heat i n t o the s o i l and a l s o a c t s as a b a r r i e r t o the i n f i l t r a t i o n and evap o r a t i o n of s o i l moisture. The s u r f a c e has an albedo of about 20%. 2.2.2 The Suburban S i t e (Phases I and II) A l l o b s e r v a t i o n s (except water-use, see below) were conducted a t Sunset - a suburb of Vancouver l o c a t e d i n the southern p o r t i o n of the c i t y (Figure 2.1). Over 80% of the area i s s i n g l e f a m i l y , 1 - 2 s t o r e y d w e l l i n g s . Turbulent and r a d i a t i v e f l u x e s were measured from a 30 m high tower s i t e d a t the Mainwaring s u b s t a t i o n a t the i n t e r s e c t i o n o f E. 49th Ave and Inverness S t . (Figure 2.2). A c i r c l e with a 2 km r a d i u s d e f i n e s the -24-33rd 41st Avenue Avenue 39th Ave. co 9) co 35th 37th It:;: [9. CO 49th Ave. 52nd Ave. W (3 Q 7 li! !R i-l! !H 3 i f 51st Ave. Kiffl. 10 53 rd 2km I J tl c cn < 1 Queen Elizabeth Park 2 Langara College 3 Langara Golf Course 4 Sunset Nursery 5 Mountain View Cemetery 6 John Oliver School 7 Memorial Park South 8 Sunset 9 Kensington Park 10 Gordon Park W - Water use monitoring Q - Sites ol spacial variability measurements S » Soil moisture sampling sites Ts - Tethersonde release site A - Site of acoustic sounder R - Ground truth data site for remote sensing F i g u r e 2 . 2 : L o c a t i o n a l map of study area and o b s e r v a t i o n a l s i t e s - 2 5 -predominant source area for turbulent fluxes measured at Mainwaring. Land-use within this area i s 64% (plan view) pervious greenspace and 36% b u i l t (25% buildings and 11% pavement) (Kalanda, 1979). Steyn (1980) computed a roughness length of 0.5 m and zero-plane displacement of 3.5 m based on the geometry and di s t r i b u t i o n of the buildings. Figure 2.1 shows that the measurement tower i s 5 km from the coastline during westerly flow. For a l l wind directions the flow must traverse urban (including industrial and commercial) land-use. For flow from the NW clockwise through to E, the urban fetch i s larger, especially compared to flow from the S and SE. Table 2.1: Percentages of Surfaces i n Source Area Surface Type Plan Area Active Area Pervious 2-D.. ..lawns, f i e l d s and parks 64 40 Impervious 2-D. . ..pavement and roads 16 10 Pervious 3-D.. ..trees n i l 6 Impervious 3-D. . ..roofs and walls 20 44 Note: see Appendix 2 for details of computation At sub-urban spatial scales there are also variations i n land use. Of relevance are a large park (Memorial Pk.) and grassed cemetery (Mountain View) located between 0.75 and 2.0 km NW of the Mainwaring tower (Figure 2.2). An industrial area i s located to the south of the Mainwaring s i t e , on the northern bank of the Fraser River. -26-Using data i n Steyn (1980) and Kalanda (1979) the breakdown of s u r f a c e types i s as presented i n Table 2.1. 2.2.3 C l i m a t o l o g i c a l Context a) General The general c l i m a t o l o g y of Vancouver i s determined by i t s m i d - l a t i t u d e l o c a t i o n on the west coast of the North American c o n t i n e n t . I t thus has a r e l a t i v e l y high annual p r e c i p i t a t i o n (1000 mm) which shows a winter maximum, and r e l a t i v e l y m i l d temperatures (annual mean d a i l y temperature 10°C). The semi-continuous path of f r o n t a l systems t y p i c a l l y ceases i n s p r i n g or e a r l y summer a l l o w i n g f o r the frequent development of a high pressure system. T h i s leads t o warm, dry summertime c o n d i t i o n s o f t e n i n c l u d i n g an extended dry s p e l l e.g. the droughts of 1985 and 1986. During these a n t i c y c l o n i c c o n d i t i o n s the meso-scale sea breeze c i r c u l a t i o n dominates the d i u r n a l flow, r e s u l t i n g i n w e s t e r l y flow by day and weaker e a s t e r l i e s by n i g h t . T h i s regime can be c o n t r a s t e d with the SE cloudy and moist c o n d i t i o n s a s s o c i a t e d w i t h the passage of a f r o n t a l system or the presence of a c o l d low o f f s h o r e . b) Synoptic Background f o r Phase I Although measurements d i d not commence u n t i l mid-July, the s o i l moisture was high a t both s i t e s as a r e s u l t of l a r g e r a i n f a l l s i n J u l y and a damp June. P r e c i p i t a t i o n i n J u l y was the high e s t on re c o r d (twice the average -Table 2.2) as a r e s u l t of i n t e n s e c y c l o n i c a c t i v i t y from 11 - 14 J u l y and 25 -27-Table 2.2: Climate s t a t i s t i c s for measurement i n t e r v a l : 1983 and 1986 Note: boldface: 1983 regular : 1986 (a) Maximum, minimum and mean temperatures (° C): Month Mean Normal Maximum Normal Minimum Normal A p r i l 8 .1 8.8 11.4 12.8 4.7 4.7 May 12 .5 12.2 16.3 16.5 8.6 7.9 June 15 .7 15.3 15.1 19.8 15.1 19.2 11.6 10.9 10.9 July 16 .2 16.6 17.3 20.0 20.5 21.9 12.3 12.6 12.6 August 18 .7 17.9 17.1 23.0 21.8 21.5 14.4 12.6 12.6 Sept. 14 .4 13.5 14.2 18.5 17.5 18.3 10.3 10.1 10.1 October 10 .6 10.0 14.7 13.6 6.8 6.4 (b) Total measured r a i n f a l l Month Monthly Total (mm) Normal (mm) A p r i l 105.8 59.6 May 100.6 51.6 June 39.0 63.2 45.2 July 46.2 79.6 32.0 August trace 24.1 41.1 September 72.2 76.7 67.1 October 49.2 114.0 (c) Total duration of sunshine Month Duration (hours) Normal (hours) A p r i l 119.7 180.5 May 217.3 246.1 June 228.6 179.9 238.4 July 242.2 217.2 307.1 August 314.8 280.3 256.2 September 186.3 199.2 183.1 October 136.2 121.0 Note:- A l l data are from the Atmospheric Environment Service Meteorological Station, Vancouver International Airport. -28-- 28 J u l y . The i n t e r v a l s between, however, were c h a r a c t e r i s e d by high net r a d i a t i o n f l u x e s . Observations at these times are i n d i c a t i v e of energy f l u x e s when s u r f a c e moisture a v a i l a b i l i t y i s v i r t u a l l y u n l i m i t e d . A dry s p e l l began on August 1 and l a s t e d through to August 22. The r a i n f a l l t o t a l f o r August was h a l f and t o t a l sunshine hours twice the average (Table 2.2). c) S y n o p t i c Background f o r Phase II Measurements began on A p r i l 5 during c l e a r and sunny, a n t i c y c l o n i c c o n d i t i o n s . The l a t t e r h a l f of A p r i l and most of May (11 A p r i l - 27 May) was u n s e t t l e d with 88 mm of r a i n f a l l . The s u r f a c e moisture should have been at i t s maximum at t h i s time. T h i s was followed by a r i d g e of high pressure r e s u l t i n g i n a d r y i n g p e r i o d with w e s t e r l y flow from 27 to 31 May, 10 - 12 and 22 - 26 June. The remainder of June and the f i r s t h a l f of J u l y was moist and u n s e t t l e d . A r i d g e developed on J u l y 17 and r e l a t i v e l y s e t t l e d a n t i c y c l o n i c c o n d i t i o n s p r e v a i l e d through u n t i l August 29. T h i s p e r i o d was i n t e r s p e r s e d with some days when marine cloud, drawn i n from Georgia S t r a i t , l e d to o v e r c a s t s k i e s (e.g. 22 - 23 J u l y and 10 - 12 August). In both cases, s k i e s c l e a r e d i n the afternoon to g i v e sunny c o n d i t i o n s with w e s t e r l y flow. A c o l d low moved over the study area on J u l y 26 r e s u l t i n g i n l i g h t r a i n showers a t the Mainwaring s i t e and u n s e t t l e d c o n d i t i o n s through to J u l y 29 whereupon the r i d g e r e - e s t a b l i s h e d . August 23 - 24 and August 28 -September 2 were i n t e r v a l s c h a r a c t e r i s e d by s o u t h - e a s t e r l y c o n d i t i o n s once ag a i n . A r i d g e dominated from September 3 - 7 with heavy dew and ground fog o v e r n i g h t , f o l l o w e d by more u n s e t t l e d c o n d i t i o n s from September 8 onwards. O f f i c i a l l y the drought f i n i s h e d on September 10. -29-A comparison of the c l i m a t e s t a t i s t i c s f o r each month i s presented i n Table 2.2. A p r i l was c o o l e r , wetter and recorded l e s s sunshine than normal. The p r e c i p i t a t i o n recorded i n A p r i l was almost twice the normal amount. T h i s c o o l , moist p a t t e r n continued i n t o May with lower than average sunshine and maximum temperatures, more p r e c i p i t a t i o n (again, almost twice the normal amount), but with warmer mean and minimum temperatures. June was warmer and d r i e r than normal, but with s l i g h t l y l e s s than the normal number of sunshine hours. J u l y saw a r e t u r n to the c o o l , wet, and overcast c o n d i t i o n s experienced i n the s p r i n g . August was warmer (1 - 2°C), d r i e r and sunnier than normal. Only a t r a c e of p r e c i p i t a t i o n was recorded a t the Vancouver A i r p o r t M e t e o r o l o g i c a l S i t e d u r ing August - l e a d i n g to i t being the d r i e s t August on r e c o r d . September was warmer, and sunnier, but a l s o more moist than normal. 2.3 Measurement Programmes 2.3.1. Phase I The energy balance i n s t r u m e n t a t i o n was i d e n t i c a l a t the two s i t e s . The instrument d e t a i l s and l o c a t i o n s are the same f o r the suburban component of Phases I and II and are e x p l a i n e d more f u l l y i n s e c t i o n 2.3.2. Measurements a t both s i t e s began on J u l y 18 and continued through u n t i l August 22, 1983. Net r a d i a t i o n was monitored using a net radiometer (Swissteco Model S-l) mounted so as to view a r e p r e s e n t a t i v e s u r f a c e area ( r u r a l 1 m; suburban 30 m). The s e n s i b l e heat f l u x d e n s i t y was measured at both s i t e s with a s o n i c anemometer-thermometer system, SAT (Campbell S c i e n t i f i c , Model CA 27). The -30-anemometer path length i s 100 mm and the thermometer i s a f i n e - w i r e constantan chromel thermocouple (diameter 12.7 A*m). A sampling frequency of 10 Hz, a sub-averaging i n t e r v a l of 5 min and an averaging time of 60 min. were used. The 60 min averaging time, f o l l o w i n g Wyngaard (1978), reduces e r r o r s by maximising the low frequencies sampled and a v o i d i n g n o n - s t a t i o n a r i t y e f f e c t s . The sub-averaging p e r i o d was d i c t a t e d by the data l o g g i n g system (Campbell S c i e n t i f i c , CR 5). The measurement heights were 1.8 m and 19 m (above zero-plane displacement) at the r u r a l and suburban s i t e s r e s p e c t i v e l y . The r u r a l s o i l heat f l u x was sampled using three s o i l heat f l u x p l a t e s (Middleton Model CN3) connected i n s e r i e s and b u r i e d at 10 mm. The heat storage f l u x a t the suburban s i t e was modelled using the Oke et al (1981) p a r a m e t e r i s a t i o n scheme: AQS = 0.25 (Q*-27) Q'*0 (2.1) AQS = 0.67 Q* Q**0 The l a t e n t heat f l u x e s a t both l o c a t i o n s were evaluated as the r e s i d u a l term i n the energy balance equation assuming n e g l i g i b l e a d v e c t i v e , anthropogenic and p h o t o s y n t h e t i c f l u x e s : Q E ( r u r a l ) = Q* - Q G - Q„ (2.2) Q E (suburb.) = Q* - AQS - Q H Supplementary Observations Incoming s o l a r r a d i a t i o n data were obtained from the nearby Langara and A i r p o r t s i t e s of the UBC S o l a r M o nitoring Network (Hay, 1984). Measurements of the r e f l e c t e d short-wave r a d i a t i o n were made using i n v e r t e d Kipp and Zonen pyranometers mounted a t heights of 1 m and 30 m a t the r u r a l and suburban s i t e s , r e s p e c t i v e l y . Both s i t e s were instrumented t o r e c o r d a i r -31-temperature and humidity (Campbell S c i e n t i f i c Model 101 t h e r m i s t o r and RH s e n s o r ) ; wind speed and d i r e c t i o n (Met One cup anemometer and wind vane) and p r e c i p i t a t i o n . Near-surface (0 - 150 mm) s o i l moisture values were obtained by the g r a v i m e t r i c method from samples gathered twice per week. Three samples were taken at the A i r p o r t and s i x from u n i r r i g a t e d l o c a t i o n s a t Sunset. 2.3.2 Phase II Semi-continuous measurements were obtained from A p r i l 5, 1986 to October 5, 1986. F i g u r e 2.3 i n d i c a t e s the measurement p e r i o d s using both the J u l i a n Day and o r d i n a r y calendars. The p e r i o d of g r e a t e s t i n t e r e s t and most i n t e n s i v e o b s e r v a t i o n s was the d r y i n g c y c l e from J u l y 16 to September 15. Canopy-Layer Observa tions The s p a t i a l v a r i a t i o n of surface temperature, albedo and s u r f a c e moisture s t a t u s can be assessed from the r a d i o m e t r i c data d e r i v e d from a remote sensing f l i g h t undertaken on August 25, 1985 (1500 PDT, and August 26, 0600 PDT). F u l l d e t a i l s of the f l i g h t can be obtained from Schmid (1988) . S o i l moisture samples were taken two to three times per week beginning i n A p r i l (J.D. 100) and c o n t i n u i n g u n t i l October (J.D. 270), 1986. S o i l moisture content was determined g r a v i m e t r i c a l l y t o a depth of 200 mm a t a number of s i t e s s e l e c t e d t o represent u n i r r i g a t e d greenspace. F i g u r e 2.2 shows the l o c a t i o n of these s i t e s ; three were i n parks, one was a t the Mountain View Cemetery (MVC), and two were on grass verges i n r e s i d e n t i a l s t r e e t s . These are the same suburban s i t e s used i n Phase I. -32-J.D. APRIL J.D. MAY J.D. JUNE J.D. JULY J.D. AUGUST J.D. SEPT 1 91 121 152 182 213 TS/SV 244 AS/SV 2 92 122 153 183 214 TS/SV 245 AS/SV 3 93 123 154 184 215 246 AS/SV 4 94 124 155 185 216 247 5 95 Q*/QH/u/T 125 156 186 217 248 6 96 S o i l Moist. 126 157 187 218 G i l l 249 7 97 127 158 188 219 250 AS 8 98 128 159 189 220 251 9 99 129 160 190 221 SV 252 10 100 130 161 191 222 SV 253 11 101 131 162 192 223 SV 254 12 102 132 163 193 224 255 13 103 133 164 194 225 256 14 104 134 RH/QEK 165 195 226 TS 257 15 105 135 166 196 227 258 AS 16 106 136 167 197 228 AS 259 17 107 137 168 198 229 AS 260 18 108 138 169 199 230 SV 261 19 109 139 170 200 231 TS/SV 262 20 110 140 171 201 232 AS/SV 263 21 111 141 172 202 233 TS 264 22 112 142 173 203 234 TS 265 23 113 143 174 204 235 266 24 114 144 175 205 236 AS/SV 267 25 115 145 176 206 237 AS/SV 268 26 116 146 177 QHB/QEB 207 238 TS/SV 269 27 117 147 178 208 239 AS 270 28 118 148 179 209 240 271 29 119 149 180 210 241 272 30 120 150 181 Sounder 211 242 AS 273 31 151 HWU 212 TS/SV 243 AS/SV NOTES: Q* - net radiometer i n s t a l l e d QH - sonic anemometer/fine wire thermocouple i n s t a l l e d u - anemometer and vane i n s t a l l e d T - thermistor probe i n s t a l l e d S o i l moist. - s o i l moisture sampling begins RH - Rotronics r e l a t i v e humidity sensor i n s t a l l e d QEK - Krypton hygrometer i n s t a l l e d QHB,QEB - reversing psychrometer i n s t a l l e d Sounder - acoustic sounder i n s t a l l e d at John Oliver School HWU - meter readings of water-use at Hudson begins SV - spatial v a r i a b i l i t y measurements TS - tethersonde mixed-layer p r o f i l e s AS - airsonde mixed-layer p r o f i l e s G i l l - G i l l propellor anemometer i n s t a l l e d Figure 2.3: Calendar showing dates of instrument i n s t a l l a t i o n - 3 3 -R e s i d e n t i a l water-use was monitored a t the Hudson s i t e (West 52nd Ave-/Oak St. - Figure 2.2). Although t h i s i s not w i t h i n the suburb of Sunset, i t i s one of the few c l o s e d catchments t h a t the C i t y of Vancouver maintains. A Neptune T r i d e n t P r o t e c t u s 6" (Grimmond, 1983) flow meter monitors the piped water i n t a k e . The t o t a l d a i l y water-use was obtained by r e c o r d i n g the meter readings at the same time each day and then t a k i n g d i f f e r e n c e s . The amount of p i p e d - i n water t h a t i s used e x t e r n a l l y i s c a l c u l a t e d by s u b t r a c t i n g the base-load, which i s e q u i v a l e n t to the mean water-use i n the winter-time (162.3 m3 day" 1 a t Hudson, Grimmond, 1983), from the d a i l y t o t a l . The Hudson catchment c o n s i s t s of 31% impervious and 69% pervious surfaces which i s s i m i l a r t o t h a t a t Sunset. D a i l y water-use measurements began on June 29 and continued through to October 5. Surface-Layer Observations As i n 1983 surface energy balance measurements were conducted from the 30 m tower at the Mainwaring s i t e . The e f f e c t i v e measurement height (z-d) a t the top of the tower (Level 5) i s 19 m. The measurement heights f o r a l l instruments are i n d i c a t e d i n F i g u r e 2.4. The s o n i c anemometer/thermocouple system (SAT) was i n s t a l l e d at Level 5 on A p r i l 5 to measure the t u r b u l e n t s e n s i b l e heat f l u x . I t was o r i e n t e d towards the south, on a cross-arm extended a t a d i s t a n c e of 1 m from the tower frame so as to minimise the tower d i s t u r b a n c e during flow from the E (90°) through to the NW (315°). The predominant wind d i r e c t i o n s are SE, SW, and W. Care was taken to l e v e l the s o n i c anemometer to w i t h i n 1° (using a l e v e l l i n g bubble on the instrument i t s e l f ) . In windy c o n d i t i o n s Roth (1988) observes evidence of tower v i b r a t i o n i n the s p e c t r a f o r the v e r t i c a l wind v e l o c i t y and temperature s i g n a l s . I t s c o n t r i b u t i o n t o the f l u x i s -34-c o > O J_J • , . - -C (U O — CO Dl T3 <D (D > n) <j- > co a) i - <u _ i x O UJ _ J (a) (b) ( c ) ( d l 17.6 (j) 10.i» (e) (f) (g) — (h) ( i ) 29.1 27.5 26.9 20.6 19-0 18. li 3 2 2 . i i 13.9 2 20.6 12.1 1 17.^ 8.9 (a) = 2 Propel lor G i l l Anemometer (b) = R.H./T Probe (Rotronics) (c) = Met-101 Wind Vane (d) = Met-101 Cup Anemometer (e) = Net Radiometer (f) = Sonic Anemometer w. Thermocouple. (g) = Krypton Hygrometer (h) l 2 Dimensional Sonic (i) J Anemometer (U.V.) (j) = Bowen Ratio System Fine Wi re F i g u r e 2.4: Schematic i l l u s t r a t i o n of measurement tower and l o c a t i o n o f instruments -35-n e g l i g i b l e . I t i s assumed th a t l e v e l l i n g e r r o r s due to the tower movement are minimal. Temperature and v e r t i c a l wind speed were sampled a t 10 Hz and a sub-averaging i n t e r v a l of 15 min was used. These 15 min valu e s were then averaged to y i e l d a 60 min mean f l u x . A data logger, (Campbell S c i e n t i f i c , Model 21X programmed with covariance software) was used to sample and r e c o r d the s i g n a l s , and perform the computations. A net radiometer (Swissteco, Model S-l) was l o c a t e d a t the same height as, and adjacent t o , the SAT. The polyethylene domes were i n f l a t e d using dry a i r (pumped through s i l i c a g e l ) . The s i g n a l s were sampled a t 1 second i n t e r v a l s using the 21X data logger, and averaged over 30 min. A krypton hygrometer (Campbell S c i e n t i f i c , Model KH20) was l o c a t e d on the eastward ( u s u a l l y downwind) s i d e of the SAT on J.D. 127 (May 7 ) . This i s an a b s o r p t i o n hygrometer. Together with the v e r t i c a l wind speed from the s o n i c anemometer, w'q' covariances are c a l c u l a t e d . The humidity s i g n a l was sampled a t 10 Hz with a 15 min sub-averaging i n t e r v a l . E l e c t r i c a l grounding problems with t h i s instrument meant that a great p o r t i o n of the data had to be d i s c a r d e d (June 24 - August 30). Wind d i r e c t i o n and speeds were monitored from A p r i l 5 using a wind vane and cup anemometer (both Met-One Instrument Co.) mounted a t L e v e l 5. These formed p a r t of a meso-scale wind and temperature monitoring network (Ayotte, 1986). A s h i e l d e d temperature sensor (Campbell S c i e n t i f i c , Model 101 with a Fenwal E l e c t r o n i c s Model UUT51J1 th e r m i s t o r ) was s i t e d a t the same l e v e l . A l l s i g n a l s were recorded on a data logger (Campbell -36-S c i e n t i f i c , Model CR21) a t 10 second i n t e r v a l s , and ho u r l y averages stored. In a d d i t i o n the r e l a t i v e humidity and temperature were measured using a separate humidity sensor, i n s t a l l e d at L e v e l 5 on May 28. The sensor ( R o t r o n i c s , Model MP 100-F) comprises a c a p a c i t i v e hygrometer (Rotronic Hygromer C-80), and a therm i s t o r (Pt 100 RTD) and i s mounted w i t h i n a r a d i a t i o n s h i e l d . S i g n a l s were sampled using the 21X a t 1 second i n t e r v a l s and averaged over 30 min. On J.D. 175 (June 24) the r e v e r s i n g d i f f e r e n t i a l psychrometer (Bowen r a t i o ) system was i n s t a l l e d . I t c o n s i s t e d of two c a r t s , each on i t s own trackway. These two c a r t s were j o i n e d by an aluminium c a b l e , which ran v e r t i c a l l y from the bottom-most c a r t over a wheel a t the top, and down to the upper-most c a r t (Figure 2.5). T h i s cable was then wrapped around a lower wheel, which was d r i v e n by a 12 V D.C. motor. Every 30 min, a timer a c t i v a t e d the motor, t u r n i n g the lower wheel and p u l l i n g the upper c a r t downwards - thereby r e v e r s i n g the c a r t p o s i t i o n s . Each c a r t c a r r i e d a wet-and dry-bulb sensor, an a s p i r a t i o n fan (12 V D.C.) and water r e s e r v o i r s . Thus the wet- and dry-bulb temperature d i f f e r e n c e s (4TW and Ard, r e s p e c t i v e l y ) were obtained between the two c a r t s , separated by the v e r t i c a l d i s t a n c e of 7.2 m. The t r a v e l time f o r the c a r t s t o move the f u l l d i s t a n c e was =» 3 minutes, and a f u r t h e r 7 minutes were allowed f o r e q u i l i b r a t i o n . Thus temperature d i f f e r e n c e s were averaged over 20 minutes i n each h a l f hour i n t e r v a l . Each sensor i s a 10-junction copper-constantan thermopile, with an embedded thermocouple. They were s h i e l d e d , and a s p i r a t e d by fans at a r a t e between 4.3 and 4.6 m s _ 1 . The sensors were mounted approximately 1 m from -37-Tower Idler support arm switch Psychromater cart Support Arm Pivoting sensor control arm Sensor cable support Arm Sensor cable Support arm Limit switches Drive motor assembly Scale 1:25 F i g u r e 2.5: Schematic i l l u s t r a t i o n of r e v e r s i n g d i f f e r e n t i a l psychrometer system - 3 8 -the tower frame, and o r i e n t e d north. These s i g n a l s were logged on the 21X data logger. The thermocouple measurements f o r Tw and Td were referenced to the panel temperature on the 21X. Because of the m u l t i p l e measurements of humidity and a i r temperature, i t i s p o s s i b l e to intercompare: (a) the dry-bulb a i r temperature from the r e v e r s i n g psychrometers, and t h a t measured by the Fenwal and R o t r o n i c s sensors at Level 5, and (b) the humidity from the r e v e r s i n g psychrometer system and that measured by the R o t r o n i c s sensor. These r e s u l t s are provided i n Appendix 3 and show e x c e l l e n t agreement f o r a l l but one sensor. The a i r temperature from the R o t r o n i c s sensor shows a c o n s i s t e n t o f f s e t which was c o r r e c t e d . A m odified G i l l , 2 - p r o p e l l e r anemometer was i n s t a l l e d a t Level 6 on August 7. T h i s anemometer provides f a s t response measurements of the h o r i z o n t a l (u-component) and v e r t i c a l (w-component) wind speeds. Instead of the u sual v e r t i c a l l y - o r i e n t e d p r o p e l l o r , the v e r t i c a l supporting s h a f t i s extended and a second p r o p e l l o r i s added a t an angle of 30° (from the v e r t i c a l a x i s ) . The h o r i z o n t a l s h a f t and p r o p e l l o r r e t a i n t h e i r normal p o s i t i o n , w h i l s t the m o d i f i c a t i o n to the second p r o p e l l o r e l i m i n a t e s the problems of s t a l l and n o n - l i n e a r response a t low wind speeds (< 5 m s " 1 ) , by i n t r o d u c i n g some component of h o r i z o n t a l flow (Pond et al., 1979; Large, 1979). The G i l l anemometer i s mounted with a vane, such t h a t the two p r o p e l l o r s (v1 and v 2 ) are always o r i e n t e d i n t o the flow, and t h i s a l s o p r o v i d e s wind d i r e c t i o n data. Roth (1988) d i s c u s s e s the a n a l y s i s of the s i g n a l s d e r i v e d from t h i s G i l l anemometer, and a l s o the r e l e v a n t response c h a r a c t e r i s t i c s . The v x and v 2 s i g n a l s were sampled a t a frequency of 10 Hz, f o r continuous periods of up to 60 min, using the 21X data logger. These time s e r i e s were t r a n s f e r r e d c o n t i n u o u s l y to a c a s s e t t e recorder, and i n p u t t o the UBC Computing Centre's computer f o r detrending, and -39-p r o c e s s i n g . Approximately 40 hours of data were obtained over s t a b i l i t y c o n d i t i o n s ranging from n e u t r a l t o unstable (Roth, 1988). A l l times were synchronised with LAT, and a l t e r e d every few days to c o i n c i d e with the time of s o l a r noon. Data were t r a n s f e r r e d t o c a s s e t t e tape and input to the UBC computer using a Campbell S c i e n t i f i c C20 i n t e r f a c e f o r f u r t h e r p r o c e s s i n g . For a l l data, the hour used r e f e r s to the average from the preceding hour up to the c i t e d hour, i . e . Q* f o r 1200 LAT i s the average net r a d i a t i o n f o r the hour from 1100 to 1200 LAT. Spatial Variability of Surface Fluxes In order to o b t a i n measurements of the s p a t i a l v a r i a t i o n of the t u r b u l e n t s e n s i b l e heat f l u x (Q H) and the net r a d i a t i o n (Q*) o b s e r v a t i o n s were conducted at v a r y i n g s i t e s from J u l y 31 through to September 3. These s i t e s are r e f e r r e d to as Culloden, Gordon, Ross St., Waverley St., and Memorial Pk. West (Figur e 2.2). The instruments, a SAT and net radiometer (Swissteco, Model S - l ) , were mounted atop a mobile m a s t / t r a i l e r u n i t . The t r a i l e r and mast were moved to the d e s i r e d l o c a t i o n , instruments mounted and the mast then e l e v a t e d t o the r e q u i r e d measurement h e i g h t (30 m). The Q* s i g n a l s were monitored on a data logger (Campbell S c i e n t i f i c , Model CR21) and averaged over 30 min. The s e n s i b l e heat f l u x s i g n a l s were recorded on a Campbell S c i e n t i f i c , Model CR5, data logger and averaged every 15 min ( r e f e r t o Schmid, 1988, f o r f u r t h e r d e t a i l s ) . Simultaneous measurements were made at the f i x e d Mainwaring tower. -40-Mixed-Layer and Upper-Air Observations To complement the s u r f a c e energy balance data, o b s e r v a t i o n s of the temperature and humidity w i t h i n and above the PBL were r e q u i r e d . The mixed-layer depth (z^) was measured using a monostatic a c o u s t i c radar (Aerovironment 300C) mounted on the r o o f - t o p of a nearby school (John O l i v e r Secondary, see F i g u r e 2.2). I t produces a 25 W p u l s e of sound a t 15 Hz every 18 s. The r e t u r n i n g sound echoes are s c a t t e r e d by the thermal s t r u c t u r e of the lower 1000 m of the atmosphere. Output was provided i n the form of a continuous analogue chart which was d i g i t i s e d t o produce estimates of zL f o r the i n i t i a l i s a t i o n and v a l i d a t i o n of the mixed-layer growth model. Tethersonde f l i g h t s were conducted on seven days (see F i g u r e 2.3) and airsonde f l i g h t s on f o u r t e e n days, throughout August and September. The tethersonde system (AIR TS-2 AR) provided v e r t i c a l p r o f i l e s of d r y - and wet-bulb temperatures, wind speed and d i r e c t i o n , and pressure from ground l e v e l t o 800 m. Each ascent and descent took 15 - 20 min to complete and a semi-continuous sequence of v e r t i c a l p r o f i l e s obtained. The r e l e a s e s i t e f o r the tethersonde was the Mountain View Cemetery (MVC), l o c a t e d =*=300 m from the a c o u s t i c sounder and s«2.0 km from Mainwaring (Figu r e 2.2). B a l l o o n ascents began a t s u n r i s e and continued throughout the day u n t i l sunset. The a i r s o n d e system (Model AIR AS-1C-PTH) used the same ground r e c e i v e r as the tethersonde, however the instrument package and b a l l o o n were not t e t h e r e d , and only wet-, dry-bulb temperatures, and pressure were sensed. C a l i b r a t i o n of the sensors a g a i n s t a psychrometer and barometer was performed a t the ground l e v e l , p r i o r to r e l e a s e . Airsondes were r e l e a s e d -41-(one per day) a t approximately 1600 PDT, to c o i n c i d e with the Canadian Atmospheric Environment S e r v i c e radiosonde r e l e a s e a t Port Hardy. 2.3.3 Data Processing: Hourly Surface Latent Heat Fluxes The storage heat f l u x i s an i n t e g r a l , sometimes even dominant, component of the urban s u r f a c e energy balance. I t s measurement i s e s s e n t i a l l y impossible and the f l u x must be modelled. An important aspect of t h i s study i s the development and t e s t i n g of an ' o b j e c t i v e ' storage heat f l u x p a r a m e t e r i s a t i o n scheme. T h i s i s presented i n Appendix 1 and used both i n an a n a l y s i s of the surface energy balance and a l s o i n the evaporation model. The model (see equation 2.13 below) i s based on a n o n - l i n e a r r e l a t i o n s h i p between Q* and 4Q S. With t h i s parameterised storage and the s u r f a c e energy balance measurements summarised above there are a v a r i e t y of approaches a v a i l a b l e t o estimate evaporation. F i r s t , by using the parameterised heat storage, and assuming c l o s u r e of the energy balance: Q E R = Q*-(QHS +A2 SP) (2.3) where Q E R = Q E d e r i v e d as a r e s i d u a l e.g. Q E i n Phase I Q H S = Q H from the SAT ^ Q S P = parameterised storage (see 2.13) Second, u s i n g the d i f f e r e n t i a l psychrometer system (measures 0) and the energy balance: Q E B = ( Q * - 4 2 S P ) < 2- 4> 1+0 where Q E B = Q E d e r i v e d from the Bowen r a t i o - e n e r g y balance approach T h i r d , combining Q H from the SAT with measured 0 y i e l d s : -42-Q - E S = QHS/0 (2.5) where Q E S = Q E d e r i v e d from the d i f f e r e n t i a l psychrometer and the SAT. Given these three methods of determining Q E, we can d e r i v e (at l e a s t ) s i x energy budgets: Q * - ( Q H S + Q E R + / i Q s p ) = 0 (2.6) Q * - ( Q H B + Q E B + A 2 S P ) = ° (2.7) Q * - ( Q H S + Q E S + A 2 S S ) = ° (2.8) Q * - ( Q H s + Q E B + A 3 S p ) = r i (2.9) Q * - ( Q H B + Q E S + A 2 s p ) = r 2 (2.10) Q * - ( Q „ s + Q E S + A 2 s p ) = r 3 (2.11) where Xi'2'3 are r e s i d u a l s A 2 s s = 'measured' r e s i d u a l storage heat f l u x = Q * - ( Q H S + Q E S ) (2.12) Q H B = Q-H f r o m the Bowen r a t i o - e n e r g y balance approach 4 Q S P = 0.33Q* + 0.25 dQ*/dt - 25.9 (2.13) Equation (2.6) i s independent of the d i f f e r e n t i a l psychrometer system, (2.7) i s independent of the SAT and (2.8) i s independent of the parameterised heat storage. An optimum value f o r Q E i s determined from these three budgets (Appendix 4 ) . The advantage of the range of approaches t o estimate Q E, and the energy budget, i s t h a t one method a c t s as a check on the other, e s p e c i a l l y i f they are independently evaluated. 2.4 Representativeness of a Point Measurement A t u r b u l e n t f l u x p o i n t measurement a c t u a l l y r e p r e s e n t s a f l u x which has o r i g i n a t e d from an area whose dimensions and d i r e c t i o n depend upon sensor h e i g h t , wind s p e e d / d i r e c t i o n and atmospheric s t a b i l i t y . T h i s i s termed the source area. In the present context measurements are r e q u i r e d which -43-represent the a r e a l l y - a v e r a g e d f l u x from suburban land-use. Turbulent f l u x e s measured at 30 m are assumed t o o r i g i n a t e from a source area of ca. 10 6 m2 based upon Steyn, 1980. The r e p r e s e n t a t i v e n e s s of a s i n g l e p o i n t measurement i n t h i s source area must be c r i t i c a l l y evaluated. When a component of the energy balance i s determined by the r e s i d u a l approach (e.g. Q E R i n Phases I and II) a number of c r i t e r i a need t o be f u l f i l l e d . F i r s t there should be no l o c a l - s c a l e advection and secondly the source area f o r the r a d i a t i v e f l u x should be r e p r e s e n t a t i v e of the u s u a l l y much l a r g e r t u r b u l e n t f l u x source area. From view f a c t o r theory the source area f o r a r a d i a t i v e f l u x sensor a t 30 m i s ca. 10 3 m2. The que s t i o n t h e r e f o r e i s : "are the dominant s c a l e s of s p a t i a l v a r i a b i l i t y i n suburban Q* encompassed i n t h i s f i e l d of view?" To address these i s s u e s synchronous obse r v a t i o n s of Q H and Q* were conducted w i t h i n the Sunset area - using the Mainwaring s i t e as a base. The f o l l o w i n g d i s c u s s i o n examines the r e s u l t s of these measurements. 2.4.1 S p a t i a l V a r i a b i l i t y : Net R a d i a t i o n Measurements from Cu l l o d e n S t . e x h i b i t the l e a s t v a r i a b i l i t y compared with the Mainwaring o b s e r v a t i o n s ( F i g u r e 2.6 and Table 2.3). Although Q* (Culloden) i s 20 - 30 W m - 2 l e s s than Q* (Mainwaring) from 0600 - 1000 LAT, the agreement from 1400 LAT onwards on a l l days i s e x c e l l e n t . F i g u r e 2.7 i l l u s t r a t e s an example of the intercomparison. The RMSE of 15.3 W m"2 i s w i t h i n the range of instrument and measurement e r r o r . T h i s i s encouraging g i v e n t h a t the Culloden St. s i t e i s more r e s i d e n t i a l i n ch a r a c t e r than Mainwaring s i t e . The mobile mast was l o c a t e d on a s i d e s t r e e t , such t h a t the f i e l d of view from the net radiometer at Culloden encompassed a s t r e e t , -44-Table 2.3: S t a t i s t i c s for net radiation s p a t i a l v a r i a b i l i t y study (a) SITE MOBILE Mean MAINW. Mean RMSE RMSE. RMSE,, MAE Culloden 189.22 191.36 15.25 Gordon Pk 176.71 182.49 21.74 Waverley 232.36 243.29 37.35 Ross St 188.60 190.73 16.09 A l l S i t e s 195.87 201.25 24.41 C a l i b r a t i o n 11.66 2.64 15.02 12.34 17.90 10.95 35.71 2.12 15.95 10.47 W m - 2 15.34 W n r 2 28.50 W n r 2 12.87 w n r 2 6.51 23.52 16.92 W m"2 8.44 W n r 2 (b) SITE Slope I n t e r c e p t C u l l o d e n 0.99 - 0.58 Gordon Pk 0.93 6.36 Waverley 0.99 -10.17 Ross St 1.00 - 2.09 994 987 971 994 0.998 0.995 0.992 0.998 A l l S i t e s 0.98 1.54 0.985 0.996 Table 2.4: S t a t i s t i c s for sensible heat flux density sp a t i a l v a r i a b i l i t y study (a) SITE MOBILE MAINW. Mean Mean RMSE RMSE_ RMSE,. MAE Culloden 143.53 161.81 32.47 21.46 24.36 Gordon Pk. 98.83 150.76 58.73 57.23 13.20 Waverley 149.78 184.84 48.50 35.12 33.45 W. M. Pk. 119.42 148.64 37.91 29.22 24.15 A l l S i t e s 128.25 161.24 45.06 34.08 29.48 C a l i b r a t i o n 60.64 64.96 12.72 24.60 W n r 2 51.93 W i t r 2 39.63 W n r 2 31.77 W r r r 2 36.46 W n r 2 W n r 2 (b) SITE Slope I n t e r c e p t Culloden 0.83 8.3 Gordon Pk 0.64 2.3 Waverley 0.97 -29.7 W. M. Pk 0.99 -29.1 85 91 82 91 0.94 0.78 0.90 0.95 A l l S i t e s 0.88 C a l i b r a t i o n -13.9 0.82 0.97 0.90 - 4 5 --46-footpaths, and s e v e r a l s i n g l e storey houses. The e q u i v a l e n t f i e l d of view f o r the net radiometer at the Mainwaring s i t e was predominantly g r a v e l and u n i r r i g a t e d g r a s s . Cloud cover during the measurement p e r i o d a t Gordon was p a r t i c u l a r l y v a r i a b l e . Under these c o n d i t i o n s s p a t i a l v a r i a b i l i t y i n the r e c e i p t of incoming short-wave r a d i a t i o n could mask any s p a t i a l v a r i a t i o n i n Q* which a r i s e s as a r e s u l t of the surface i n f l u e n c e alone. Taking i n t o account t h i s g r e a t e r sky cover v a r i a b i l i t y , the agreement between the two s i t e s i s f a i r l y good: Q* (Mainwaring) tends to overestimate Q* (Gordon) up to 1000 LAT on J.D. 221 and 222. A f t e r 1600 LAT on J.D. 222 and 223, Q* (Gordon) i s s l i g h t l y g r e a t e r than Q* (Mainwaring). T h i s r e s u l t s i n a 4% d i f f e r e n c e i n the summary s t a t i s t i c s (Table 2.3) with a l a r g e RMSE (21.7 W m" 2). The Ross S t . s i t e comparison shows some systematic d i f f e r e n c e i n the morning hours, where Q* (Ross St.) i s g r e a t e r . T h i s i s rev e r s e d i n the afte r n o o n . The Ross St. s i t e i s on the east s i d e o f , and adjacent t o , Memorial Pk. There are s e v e r a l l a r g e t r e e s c l o s e t o the s i t e which would be on the p e r i p h e r y of the radiometer's f i e l d of view, and the s i t e was not completely l e v e l . The d i f f e r e n c e between the two measurements i s f a i r l y s m a l l , l e s s than 30 W m~2 (the g r e a t e s t percentage d i f f e r e n c e i s 12%). This systematic d i f f e r e n c e leads to a " h y s t e r e s i s loop" i n the s c a t t e r p l o t (Fi g u r e 2.6). The o v e r a l l s t a t i s t i c s demonstrate good agreement. The data from Waverley St. show more s c a t t e r . Again the radiometer i s s i t e d above a more r e s i d e n t i a l area than a t Mainwaring. The increased s c a t t e r e v i d e n t i n Fi g u r e 2.6 r e s u l t s i n a l a r g e r RMSE (37.3 W m~2) f o r the Waverley S t . s i t e (see Table 2.3). Most of t h i s e r r o r i s non-systematic. -47-In summary s p a t i a l d i f f e r e n c e s i n hourly net r a d i a t i o n are r e l a t i v e l y s m a l l . The r a t i o of the RMSE to mean net r a d i a t i o n i s l e s s than 15% f o r a l l s i t e s . The systematic e r r o r i s l e s s than 5% of the mean net r a d i a t i o n . The c o e f f i c i e n t of determination ( r 2 ) and index of agreement (d) s t a t i s t i c are g r e a t e r than 0.95. The o v e r a l l mean average e r r o r (MAE) i s 16.9 W m~2 -l e s s than 10% of the mean net r a d i a t i o n . These f i g u r e s can be compared to the r e s u l t s of an i n t e r - s e n s o r RMSE of 12 W m"2 and MAE of 10 W m"2. The average net r a d i a t i o n a t 30 m i s remarkably s i m i l a r between s i t e s which e x h i b i t very d i f f e r e n t s u r f a c e geometries, types and t e x t u r e s , and t h e r e f o r e probably d i f f e r e n t s u r f a c e temperature and albedo. In co n c l u s i o n , t h i s c o n s e r v a t i v e behavour means tha t a p o i n t o b s e r v a t i o n appears to be r e p r e s e n t a t i v e of the net r a d i a t i o n throughout the source area a t Sunset. 2.4.2 S p a t i a l V a r i a b i l i t y : S e n s i b l e Heat Flux Simultaneous measurements of the t u r b u l e n t s e n s i b l e heat f l u x were obtained a t the f o l l o w i n g s i t e s : Culloden St., Waverley St., Gordon and Memorial Pk. West (with w e s t e r l y f l o w ) . The Gordon s i t e may be l e s s than i d e a l because i t i s l o c a t e d adjacent t o a l a r g e p l a y i n g f i e l d ( s i t e d t o the east of the mast) and c o n s i d e r a b l y c l o s e r to the Fraser R. than Mainwaring. The hourly data f o r the i n d i v i d u a l s i t e s (Figure 2.8) i l l u s t r a t e agreement with Mainwaring f o r the Culloden, Waverley and Memorial Park West s i t e s . F i g u r e 2.9, f o r example, i n d i c a t e s t h a t on a l l three days, the two measurements of Q H (Culloden and Mainwaring) are i n agreement with the ex c e p t i o n of the pe r i o d from 1300 - 1530 on J.D. 213, and the peaks at 1030 and 1630 on J.D. 214. -48-F i g u r e 2.8: Synchronous o b s e r v a t i o n s of s e n s i b l e heat f l u x (hourly) a t the Mainwaring s i t e and 4 s p a t i a l l y - v a r y i n g s i t e s ('Mobile') w i t h i n Sunset area -49-2 5 0 2 0 0 1 5 0 100 5 0 -D 1 : 1 / • JO JD 2 12 Q 213 o So JO 214 A • o o o o a o So o o a / " a a o y O 0 1 i i 1 50 100 150 200 250 QK(Mainwaring>/W m - 2 F i g u r e 2.9: Comparison between h o u r l y s e n s i b l e heat f l u x d e n s i t i e s measured a t the Cull o d e n St. and Mainwaring s i t e s 250 300 100 150 200 QH(Mainwaring)/W m"2 F i g u r e 2.10: Comparison between h o u r l y s e n s i b l e heat f l u x d e n s i t i e s measured a t the Gordon Pk. and Mainwaring s i t e s -50-The r e s u l t s (Figure 2.10) f o r Gordon show that Q H (Gordon) i s c o n s i s t e n t l y l e s s than Q H (Mainwaring), e s p e c i a l l y on J.D. 221. T h i s discrepancy i s smaller f o r the remaining two days. T h i s i s the same as the net r a d i a t i o n r e s u l t s and c o u l d be r e l a t e d t o r e a l d i f f e r e n c e s i n a v a i l a b l e energy. The d i f f e r e n c e s between the two measurements f o r the Memorial Pk. West s i t e on J.D. 243 can be ex p l a i n e d i n terms of the south e a s t e r l y wind. Memorial Park i s then upwind of the mobile sensor. Figure 2.8 i s the composite s c a t t e r p l o t f o r a l l s i t e s . The s t a t i s t i c s , which are summarised i n Table 2.4, show r e l a t i v e l y good agreement. T h i s i s e s p e c i a l l y notable c o n s i d e r i n g these are tu r b u l e n t f l u x measurements. A c a l i b r a t i o n performed a t the Mainwaring s i t e y i e l d e d an RMSE of 12.7 W m~2. I t i s assumed th a t t h i s i s the e r r o r due to instrumentation and data - l o g g i n g d i f f e r e n c e s alone. I t can be compared to 45.1 W m"2 f o r a l l mobile s i t e s . The mean a b s o l u t e e r r o r i s 36 W m"2, and the mean d i f f e r e n c e i s 20% of the mean s e n s i b l e heat f l u x d e n s i t y at Mainwaring). There i s a systematic d i f f e r e n c e between the Mainwaring and the mobile o b s e r v a t i o n s , i n t h a t the former are h i g h e r . T h i s i s r e f l e c t e d i n the equation f o r the l i n e of best f i t with an i n t e r c e p t of -13 W m~2 and slope of 0.88. The r 2 i s 0.83, and the index of agreement i s 0.90. Despite the i n d i v i d u a l s i t e d i f f e r e n c e s the o v e r a l l s t r o n g c o r r e l a t i o n ( r 2 > 0.80) between the two data s e t s and the r e l a t i v e l y small RMSE suggest t h a t the Mainwaring s i t e measurements are a s l i g h t l y b i a s e d sample of the sur f a c e s e n s i b l e heat f l u x d e n s i t y f o r the surrounding suburban land-use. -51-CHAPTER 3: A COMPARISON OF THE ENERGY BALANCE AT A SUBURBAN AND RURAL LOCATION T h i s chapter compares simultaneous energy balance o b s e r v a t i o n s from the A i r p o r t and Mainwaring s i t e s i n 1983. The d i s c u s s i o n addresses the energy balances and t h e i r d i f f e r e n c e s at two t i m e - s c a l e s : hourly and d a i l y 1 . 3.1 Overview Table 3.1 presents a summary of the averaged energy balances f o r each s i t e . These values are d a y l i g h t - h o u r averages f o r the (same) t h i r t y days of measurements conducted from J u l y - September, 1986 (see below). The r a t i o of suburban to r u r a l net r a d i a t i o n shows a 4% surplus fo the former -probably due to the 7% d i f f e r e n c e i n albedo. The suburban albedo of 13% i s c o n s i s t e n t with e a r l i e r o b s e r v a t i o n s at Mainwaring (Steyn and Oke, 1980) and values from other urban areas (Oke, 1988). 1The J u l i a n day calendar i s used f o r the d e s c r i p t i o n of the day-to-day v a r i a t i o n of energy f l u x e s . In t h i s t h e s i s a J u l i a n day (J.D.) i s d e f i n e d as the day number, beginning a t 1 f o r January 1 and ending a t 365 on December 31 i n a non leap-year (Figure 2.3). The J u l i a n day has a s p e c i f i c a stronomical d e f i n i t i o n (The Macquarie D i c t i o n a r y , 1983) however i t i s a common, and accepted, convention i n the m e t e o r o l o g i c a l l i t e r a t u r e t o use J u l i a n day as d e f i n e d above (Henderson-Sellers, pers. comm.). -52-There are l a r g e d i f f e r e n c e s between the storage heat f l u x e s a t the two s i t e s . The r u r a l s o i l heat f l u x i s only 4% of the net r a d i a t i o n as compared Table 3.1.: Average Energy Balance Components: 1983 Land-use Q* Q H Q E AQS a 8 X <p ( a l l i n W m"2) (dimensionless) R u r a l 283 86 187 12 1.09 0.46 0.30 0.66 Suburban 295 129 101 65 0.70 1.28 0.44 0.34 Suburban:rural r a t i o s 1.04 1.51 0.54 note: « = P r i e s t l e y and T a y l o r parameter 0 = Bowen r a t i o X = r a t i o of Q H to Q* <f> = r a t i o of Q E to Q* to the u s u a l 10% f o r short grass, (e.g. de B r u i n and H o l t s l a g , 1982). T h i s small percentage may be due to the long grass and of course the presence of a dead grass "mat" which e f f e c t i v e l y i n s u l a t e s the s o i l from heat flow. The suburban storage f l u x i s not measured but based upon a model. Although l e s s confidence can be p l a c e d upon i t s magnitude i t i s c l e a r t h a t suburban storage i s s i g n i f i c a n t l y l a r g e r than the r u r a l value. Latent heat exchange i s the dominant "sin k " f o r the absorbed r a d i a t i o n a t the r u r a l s i t e . 69% of the a v a i l a b l e energy i s transformed i n t o l a t e n t heat, y i e l d i n g c l o s e t o e q u i l i b r i u m evaporation and a Bowen r a t i o (5) of 0.5. T h i s conforms to a well-watered s i t e with an e x t e n s i v e , low ve g e t a t i o n cover where evaporation proceeds a t the e q u i l i b r i u m r a t e . The suburban l a t e n t heat f l u x uses only 44% of the a v a i l a b l e energy and i s only 54% of the r u r a l . The s e n s i b l e heat f l u x e s dominate the suburban energy budget. The Bowen r a t i o i s 1.28 and 66% of the net r a d i a t i o n i s d i s s i p a t e d as s e n s i b l e heat ( i . e . storage and s e n s i b l e heat f l u x e s ) and only 34% as l a t e n t heat. 3.2 Hourly V a r i a t i o n While Table 3.1 i l l u s t r a t e s the o v e r a l l s i z e s of the energy balance components, i t does not demonstrate t h e i r temporal v a r i a t i o n or how t h i s d i f f e r s between r u r a l and suburban land-use. The next two s e c t i o n s examine t h i s temporal v a r i a t i o n - f i r s t on an hourly or d i u r n a l t i m e - s c a l e and second over the longer day-to-day time s c a l e . The hourly energy f l u x e s were averaged over the 30 measurement days r e s u l t i n g i n the "ensemble average", d i u r n a l budgets presented i n Figure 3.1(a) and (b ) . The r u r a l s o i l heat f l u x i s so small t h a t i t s hourly v a r i a t i o n i s of l i t t l e s i g n i f i c a n c e . The two r u r a l t u r b u l e n t f l u x e s the are i n phase with the net r a d i a t i o n . T h e i r d i u r n a l c y c l e i s t y p i c a l of surfaces whose l a t e n t heat f l u x i s predominantly r a d i a t i v e l y c o n t r o l l e d . These f e a t u r e s c o n f i r m the s e l e c t i o n of t h i s s i t e as a c o n t r o l . The d i u r n a l c y c l e of the f l u x e s i n F i g u r e 3.1(b) r e v e a l s the importance of the storage heat f l u x i n the suburban energy balance. Although i t i s sm a l l e r than the s e n s i b l e and l a t e n t heat f l u x e s , i t i s s t i l l much l a r g e r -54-F i g u r e 3.1: D i u r n a l v a r i a t i o n o f measured s u r f a c e energy balance components a t the (a) Mainwaring and (b) A i r p o r t s i t e s i n Vancouver, 1983. Data represent ensemble averages f o r 30 summer days 0.9 r a x o TIME (LAT) F i g u r e 3.2: Di u r n a l v a r i a t i o n o f QH/Q* a t the Mainwaring s i t e , Vancouver, 1983. Data r e p r e s e n t ensemble averages f o r 30 summer days -55-than the r u r a l s o i l heat f l u x . Two reasons are forwarded to e x p l a i n the s i z e of the l a t e n t heat f l u x i n the morning (0600 - 1000 LAT). F i r s t l y , d e w f a l l i s a common f e a t u r e on many grassed surfaces i n the e a r l y morning i n Sunset. T h i s i n t e r c e p t e d water i s f r e e l y a v a i l a b l e f o r evaporation. Secondly, most r e s i d e n t s i r r i g a t e t h e i r lawns around 1800 LAT and some of t h i s may remain upon impervious s u r f a c e s overnight to c o n t r i b u t e to the a v a i l a b l e moisture supply f o r the next morning. By 1100 LAT t h i s moisture supply has been exhausted and t r a n s p i r a t i o n r a t h e r than evaporation forms the moisture f l u x . T h i s i s c o n t r o l l e d by the stomatal r e s i s t a n c e of the v e g e t a t i o n . The r e s i s t a n c e of the t r e e s t h i s w i l l tend to show an i n c r e a s e throughout the day i n response to the i n c r e a s e i n vapour pressure d e f i c i t . While the l a t e n t heat i s s t i l l important i t i s the t u r b u l e n t s e n s i b l e heat which becomes the dominant f l u x f o r the remainder of the day. The s e n s i b l e heat f l u x becomes i n c r e a s i n g l y important i n r e l a t i v e terms as net r a d i a t i o n decreases and becomes negative i n the l a t e a f t e rnoon. I t can stay p o s i t i v e u n t i l 2100 LAT - three hours a f t e r i t has become negative a t the r u r a l s i t e . T h i s f e a t u r e has been noted p r e v i o u s l y but u s u a l l y at more urbanised l o c a t i o n s (e.g. Vancouver, Yap and Oke, 1974; Uppsala, Oke, 1978; and S t . L o u i s , Ching et al., 1983). A p o s s i b l e reason f o r t h i s was given by Yap and Oke (1974) who suggested t h a t s t o r e d heat i s r e l e a s e d from urban s u r f a c e s as they are plunged i n t o shade. T h i s may happen p r i o r t o the a r e a l l y - a v e r a g e d net r a d i a t i o n becoming negative. A comparison of the d i u r n a l behaviour of QH/Q* (*) i s d i s p l a y e d i n F i g u r e 3.2. These two f l u x e s have been measured d i r e c t l y and t h e i r r a t i o i l l u s t r a t e s a major d i f f e r e n c e i n the p a r t i t i o n i n g of the net r a d i a t i o n at -56-150 i 1 1 1 1 1 1 1 1 1 1 r TIME (LAT) F i g u r e 3.3: D i u r n a l v a r i a t i o n of suburban-rural energy f l u x d i f f e r e n c e s , Vancouver 1983. Data r e p r e s e n t ensemble averages f o r 30 summer days - 5 7 -r u r a l and suburban l o c a t i o n s . The i n c r e a s i n g s i g n i f i c a n c e of s e n s i b l e h e a t i n g i n the l a t e afternoon and e a r l y evening i s l i k e l y t o p l a y a major r o l e i n the genesis of the nocturnal urban heat i s l a n d . F i n a l l y the hourly v a r i a t i o n i n the abs o l u t e d i f f e r e n c e between r u r a l and suburban energy f l u x e s i s i l l u s t r a t e d i n F i g u r e 3.3. I t d e p i c t s the dominance of the s e n s i b l e heat f l u x e s i n the suburban energy balance as compared t o the l a t e n t heat f l u x at a r u r a l s i t e . C l e a r l y u r b a n i s a t i o n r e s u l t s i n a s h i f t towards gr e a t e r s e n s i b l e h e a t i n g . The continued f l u x of s e n s i b l e heat i n t o the lower atmosphere i n the e a r l y evening i s another f e a t u r e i n t r o d u c e d by u r b a n i s a t i o n . 3.3 Day-to-Day V a r i a t i o n The magnitude of the energy balance f l u x e s vary over longer time p e r i o d s as a r e s u l t of v a r i a t i o n s i n sur f a c e and atmospheric c o n t r o l s . F i g u r e 3.4 i l l u s t r a t e s the day-to-day v a r i a t i o n of the daytime (Q*>0) mean Bowen r a t i o (#=Q H/QE) over a d r y i n g p e r i o d . A comparison of the p a r t i t i o n i n g o f the t u r b u l e n t f l u x e s between the r u r a l and suburban s i t e s h i g h l i g h t s the c o n t r o l s , and d i f f e r e n c e s , between the two environments. The day-to-day v a r i a t i o n i n s o i l moisture and r a i n f a l l i s a l s o i n c l u d e d i n Fi g u r e 3.4. The r e s u l t s from the r u r a l s i t e show a 25% i n c r e a s e i n the Bowen r a t i o over the d r y i n g p e r i o d , c o n s i s t e n t with the p a t t e r n of i n c r e a s i n g l y r e s t r i c t e d moisture a v a i l a b i l i t y . The most marked f e a t u r e however i s the l a c k of day-to-day v a r i a t i o n i n 0, e s p e c i a l l y compared t o t h a t measured at the suburban s i t e . The v a r i a t i o n i n suburban 6 i n d i c a t e s t h a t although s e n s i b l e heat may be the dominant t u r b u l e n t f l u x - ev a p o r a t i v e f l u x e s can -58-JULIAN DAY 2.0 1.8 1.6 1.4 Ul IO 1.2 I 1.0 IO II 0.8 IQ. 0.6 0.4 0.2 0.0 24 J£ 22 U J oc 20 => 1ST 18 O 16 _i 14 o 12 Ui 10 202 03 04 05 11 12 16 17 19 20 21 24 25 26 27 28 29 30 31 32 233 —i—i— I r'V-i I A H rVi 1 rVi 1 1—i 1 — i — i — i — i — r 218 231 300 240 . H—I—I HVH H\rl—H\H 1 HAH 1 1—I 1—I—I—I—I—I-* Rainfall Ruralj|j j J Suburban W J 1 . 1 1 i 21 22 23 24 30 31 4 5 7 8 9 12 13 14 15 16 17 18 19 20 21 JULY I AUGUST F i g u r e 3.4: Day-to-day v a r i a t i o n of mean d a y l i g h t Bowen r a t i o at the Mainwaring s i t e , Vancouver, 1983. * represent p r e c i p i t a t i o n events, and v e r t i c a l bars i n d i c t e s o i l moisture v a r i a t i o n s -59-a l s o p l a y a major r o l e i n determining the d a i l y p a r t i t i o n i n g . Such v a r i a b i l i t y has been observed before by other authors. They have r e l a t e d i t to sudden s h i f t s i n s y n o p t i c c o n t r o l (Oke, 1978), or s u r f a c e moisture a v a i l a b i l i t y . Kalanda et al. , 1980, Grimmond and Oke (1986) and Loudon and Oke (1986) demonstrate a c l o s e c o r r e l a t i o n between lawn s p r i n k l i n g and evaporation. Oke and McCaughey (1983) suggest a l i n k a g e between lawn s p r i n k l i n g and p e r i o d s of high r a d i a t i o n loading l e a d i n g to l o c a l - s c a l e advection and enhanced evaporation r a t e s . U n f o r t u n a t e l y no i n f o r m a t i o n regarding e x t e r n a l water-use i s a v a i l a b l e f o r t h i s p e r i o d , but the v a r i a t i o n p i c t u r e d i n Figure 3.4 appears t o be r e l a t e d to f a c t o r s such as the mean d a i l y wind d i r e c t i o n , c l o u d i n e s s and a suppressed vapour pressure d e f i c i t s . T h i s c o r r e l a t i o n i s suggestive not of l o c a l advection caused by s p a t i a l s u r f a c e inhomogeneities ( r e c a l l 2.4) but r a t h e r of a s y n o p t i c - s c a l e c o n t r o l such as the advection of air-masses a l o f t which i n t e r a c t with the boundary- and s u r f a c e - l a y e r s . The v a r i a t i o n a t the r u r a l s i t e suggests t h a t such c o n t r o l i s not a c t i v e there. The f o l l o w i n g s e c t i o n suggests some mechanisms which may determine the suburban l a t e n t heat f l u x e s and e x p l a i n these rural-suburban d i f f e r e n c e s . 3 .4 Controls on Suburban Turbulent Flux Partitioning The p o t e n t i a l r o l e of the PBL on s u r f a c e exchanges of heat, mass and momentum was addressed i n Chapter 1 by r e f e r e n c e to the work of de B r u i n , 1983 and McNaughton and Spriggs (1986). I t was a l s o shown th a t urban areas i n f l u e n c e the e n t i r e PBL (thus i t i s o f t e n c a l l e d an urban boundary-layer) - with i n c r e a s e d turbulence i n t e n s i t i e s and an enhanced entrainment r a t e at the top of the urban, compared t o the r u r a l , boundary-layer. I t was -60-hypothesised t h a t the aerodynamically-rough nature of the urban area would l e a d to strong l i n k a g e s between the mixed and s u r f a c e - l a y e r s . In t u r n the temperature and moisture budgets of the mixed-layer are l i n k e d , v i a entrainment, to the s y n o p t i c a l l y - d r i v e n f r e e atmosphere. By c o n t r a s t the s u r f a c e - l a y e r over grassed s u r f a c e s i s l e s s coupled to the mixed-layer because of g r e a t e r aerodynamic and lower s u r f a c e r e s i s t a n c e s . Therefore v a r i a t i o n s i n the humidity and temperature of the PBL have a smaller i n f l u e n c e on surface f l u x e s because of t h i s poorer c o u p l i n g . Hence such s u r f a c e s , i f well-watered, tend towards an e q u i l i b r i u m s i t u a t i o n where eva p o r a t i o n i s r a d i a t i v e l y - d r i v e n as the r e s u l t s from the r u r a l s i t e demonstrate. Values of McNaughton and J a r v i s ' fl of ^0.44 f o r the suburban s i t e can be d e r i v e d (using aerodynamic r e s i s t a n c e up to instrument height o n l y ) . These approach those v a l u e s quoted f o r f o r e s t s (0.2 f o r f o r e s t s and 0.8 f o r g r a s s l a n d , McNaughton and J a r v i s , 1983). E m p i r i c a l evidence t h e r e f o r e suggests t h a t suburbia may resemble the aerodynamically-rough f o r e s t environment i n terms of the strength of c o u p l i n g between s u r f a c e and mixed-layers. As e x p l a i n e d i n Chapter 1, the mixed-layer heat and moisture budgets are determined not only by the f l u x e s of heat, mass and momentum from the s u r f a c e immediately below i t but a l s o those f l u x e s from upwind s u r f a c e s . I t s s a t u r a t i o n d e f i c i t i s not f u l l y adjusted to the u n d e r l y i n g s u r f a c e and D m can be considered to be ' e x t e r n a l l y - s e t ' f o r a f l u x emanating from w i t h i n the canopy-layer. In t h i s way the extended suburban s u r f a c e (made up Of l o c a l - s c a l e s u r f a c e s ) i s analogous to an extensive canopy as d e s c r i b e d -61-by J a r v i s and McNaughton (1986). Evaporation may d i f f e r between two days, even i f the a v a i l a b l e energy and moisture i s unchanged, simply because of a change i n the imposed s a t u r a t i o n d e f i c i t i n the mixed-layer. A change i n the s u r f a c e r e s i s t a n c e should have a p r o p o r t i o n a l l y l a r g e e f f e c t upon the evaporation - e s p e c i a l l y i f the canopy i s dry. A l t e r n a t i v e l y , i f the e n t i r e c i t y s u r f a c e becomes wetted the s p a t i a l v a r i a t i o n of the moisture a v a i l a b i l i t y may be considered to be homogeneous. The s p a t i a l s t r u c t u r e of D m t h e r e f o r e may be uniform and the s u r f a c e r e s i s t a n c e w i l l be reduced. T h i s i s analogous to the r e g i o n a l evaporation s c e n a r i o ( J a r v i s and McNaughton, 1986). Net r a d i a t i o n could be proposed as the dominant c o n t r o l upon evap o r a t i o n under t h i s s c e n a r i o . By these mechanisms, l a r g e day-to-day v a r i a t i o n i n the p a r t i t i o n i n g of the suburban t u r b u l e n t f l u x e s can be expected. On the b a s i s of these observations and past r e s e a r c h ( d i s c u s s e d i n Chapter 1) a c o n c e p t u a l i s a t i o n of the i n t e r a c t i o n s c o n t r o l l i n g s u r f a c e l a t e n t and s e n s i b l e heat f l u x e s i s given i n F i g u r e 3.5. T h i s forms the framework f o r the c e n t r a l hypothesis of t h i s r e s e a r c h . I t i s proposed t h a t the p a r t i t i o n i n g of the t u r b u l e n t f l u x e s i n suburban areas i s f o r c e d by a combination of f a c t o r s o p e r a t i n g a t a range of s c a l e s . Lawn i r r i g a t i o n and the a v a i l a b l e energy are important canopy-scale i n f l u e n c e s . Meso-scale and s y n o p t i c - s c a l e processes determine the thermal and moisture budgets of the mixed-layer through h o r i z o n t a l a d v e c t i o n and c o n v e c t i v e entrainment. With enhanced t u r b u l e n t mixing these budgets a l s o w i l l i n f l u e n c e the p a r t i t i o n i n g of the s u r f a c e t u r b u l e n t f l u x e s . Furthermore, a feed-back can e x i s t between the s a t u r a t i o n d e f i c i t and the stomatal r e s i s t a n c e of the v e g e t a t i o n (through -62-Atmospheric layer Upper Atmosphere Mixed - Layer Surface and Canopy - Layer Y q A q & • 8 M•^M Z; Z i > °M . Q M QH + Q E DS(Z) 8« q Surface resistance and Aerodynamic resistance Paramelerisalions of Canopy structure and Moisture availability Subscript M : Mixed - Layer 5 : Surface - Layer O : Surface • value 6 : Potential temperature q : Specific humidity D : Saturation deficit Zi : Depth of mixed layer u : Wind speed u : Wind direction T : Gradient A : Step * : Coupling strength, proportional to n Q", Qs, Q H , Q E ,: surface energy balance components i g u r e 3.5: I n t e r a c t i o n s between atmospheric l a y e r s and t h e i r hypothesised i n f l u e n c e on the evaporation from a s u r f a c e -63-feedforward, McNaughton and J a r v i s , 1983). Feedforward has been observed i n many f o r e s t canopies and thus may be an important feedback i n the QE/Dm r e l a t i o n s h i p . U n fortunately there have been few s t u d i e s of t h i s aspect i n urban areas, hence i t has not been i n c o r p o r a t e d i n the model. In t h i s way, the urban boundary-layer i s not on l y i n f l u e n c e d by the un d e r l y i n g canopy, but a l s o by l a r g e r s c a l e f o r c i n g a t the s y n o p t i c - and/or meso- s c a l e s . In order to evaluate the v a l i d i t y of t h i s hypothesis an extensive set of f u r t h e r observations were obtained at the Mainwaring s i t e (Phase I I ) . The v e r t i c a l s t r u c t u r e of the PBL and i t s temperature and humidity are o b v i o u s l y i n t e g r a l to the hypothesis. Hence measurements were made of the mixed-layer and up p e r - a i r temperature and humidity p r o f i l e s . -64 -CHAPTER 4: HOURLY AND DAILY VARIATION OF THE SUBURBAN LATENT HEAT FLUX: RESULTS AND DISCUSSION 4.1 Introduction T h i s chapter presents an a n a l y s i s of the suburban s u r f a c e energy balance based upon the o b s e r v a t i o n s from Phase I I . The p a r t i t i o n i n g of the a v a i l a b l e energy between l a t e n t and s e n s i b l e heat and i t s temporal v a r i a t i o n are the focus. The aim i s to examine e m p i r i c a l l y the v a l i d i t y of the conceptual model from i n Chapter 3. This means tha t two questions must be addressed: a) what i s the nature of the temporal v a r i a t i o n of Q E, and b) what are the c o n t r o l s on t h i s v a r i a t i o n ? A range of c o n t r o l s have a l r e a d y been suggested on the b a s i s of an i n i t i a l set of measurements (Phase I, Chapter 3). They are some of the f i r s t d e t a i l e d suburban energy balance observations and are f o r a l i m i t e d p e r i o d . A f u r t h e r s e t of o b s e r v a t i o n s , obtained over a longer i n t e r v a l c o v e r i n g a g r e a t e r range i n s u r f a c e c o n d i t i o n s and weather, were conducted to v e r i f y the v a r i a b i l i t y and c o n t r o l s suggested i n Chapter 3. Again the v a r i a t i o n of the s u r f a c e energy balance i s considered a t both the d i u r n a l and day-to-day t i m e - s c a l e s . These time-scales are important i n developing an understanding of the processes of energy p a r t i t i o n i n g and t r a n s f e r i n the suburban system. Such knowledge i s a l s o necessary f o r s e l e c t i n g and e v a l u a t i n g a p p r o p r i a t e s i m u l a t i o n models. - 6 5 -4.2 Average Energy P a r t i t i o n i n g Table 4.1 summarises the average f l u x e s and t h e i r p a r t i t i o n i n g as observed at the Mainwaring s i t e during Phase I I . These are averages f o r 100 days during the p e r i o d from A p r i l 5 to October 2, 1986. The r e s u l t s from Phase I are i n c l u d e d f o r comparison. O v e r a l l , the values are s i m i l a r although the extended dry s p e l l (July/August/September) i n 1986 leads to a higher Bowen r a t i o and s e n s i b l e heat f l u x e s . T a b l e 4.1: Average Suburban Energy P a r t i t o n i n g : 1983 and 1986 [ A l l energy f l u x e s i n W m~2] Year Q * Q H Q E Z ! Q S 0 X <p fl Phase I 1983 295 129 101 65 1.28 0.44 0.34 0.44 Phase II 1986 290 145 75 70 2.15 0.50 0.26 0.30 0 = Q H / Q E ? X = Q H / Q * ' ' * = Q E / Q - * The summary t a b l e i n c l u d e s the average McNaughton and J a r v i s fl parameter. T h i s was c a l c u l a t e d by rearranging the Penman-Monteith equation to s o l v e f o r the su r f a c e r e s i s t a n c e . The aerodynamic r e s i s t a n c e i s computed using the l o g a r i t h m i c wind p r o f i l e equation. In 1986 i t ranged from 0.1 -0.4. The f a i r l y low value f o r fl i n d i c a t e s the p o t e n t i a l f o r st r o n g c o u p l i n g between the mixed and s u r f a c e - l a y e r s . Thus the s a t u r a t i o n d e f i c i t a t the surf a c e may be a r e s u l t of meso- or s y n o p t i c - s c a l e c o n t r o l s . T h i s -66-' e x t e r n a l l y - s e t ' d e f i c i t w i l l p lay an important r o l e i n determining the s u r f a c e l a t e n t heat f l u x . Therefore v a r i a t i o n s i n Q E w i l l be r e l a t e d to more than changes i n the a v a i l a b l e energy or moisture a t the s u r f a c e . Given the s i z e of fl and r e c a l l i n g the arguments presented i n Chapter 1 the c o n t r o l s upon the v a r i a t i o n i n Q E should be a combination of the s a t u r a t i o n d e f i c i t , wind speed, s u r f a c e r e s i s t a n c e and a v a i l a b l e energy. T h e r e f o r e a l l of these are analysed i n order to deduce t h e i r r o l e i n determining the p a r t i t i o n i n g of energy between the t u r b u l e n t f l u x e s . 4.3 The D i u r n a l Suburban Energy Balance 4.3.1 Hourly V a r i a t i o n The h o u r l y ensemble averages f o r each of the energy balance components and the r a t i o X are i l l u s t r a t e d i n F i g u r e s 4.1 and 4.2. The dominance of the s e n s i b l e heat f l u x d e n s i t y i n the suburban energy balance, and i t s asymmetric temporal behaviour i s i n d i c a t e d i n F i g u r e 4.1. T h i s i s s i m i l a r t o the r e s u l t s from Phase I. The l a t e n t heat f l u x i s the l a r g e s t energy f l u x i n the e a r l y morning, but i s overtaken by the two s e n s i b l e heat f l u x e s by 0900 LAT u n t i l 1530 LAT whereupon the two t u r b u l e n t f l u x e s dominate. These f e a t u r e s are f u r t h e r emphasised i n F i g u r e 4.2 showing t h a t the p r o p o r t i o n of net r a d i a t i o n d i s s i p a t e d as s e n s i b l e heat i n c r e a s e s almost l i n e a r l y throughout the day. The budget i s s i m i l a r to t h a t presented i n Chapter 3 and can be s a i d to c h a r a c t e r i s e the nature of energy p a r t i t i o n i n g i n the suburban environment. A d i f f e r e n c e between t h i s ensemble budget and t h a t i n Chapter 3 i s the s i z e of Q E v i s a v i s AQS. The budget i n F i g u r e 4.1 i s f o r a much d r i e r and - 6 7 -s I Socio bra) Bioo baoo beoo 600 Goo Coo 5<x> 'BOO 2 0 0 0 2 2 0 0 3*00 T I M E I L A T I F i g u r e 4.1: D i u r n a l v a r i a t i o n of s u r f a c e energy budget components a t the Mainwaring s i t e , Vancouver, 1986. Data represent ensemble averages 0 k ' 1 I 1 1 • 800 1200 1600 T I M E I L A T I F i g u r e 4.2: D i u r n a l v a r i a t i o n of Bowen r a t i o a t the Mainwaring s i t e , Vancouver, 1986. Data represent ensemble averages -68-longer i n t e r v a l than the 30 day budget shown i n Figure 3.1 and thus l e s s energy i s used i n e v a p o r a t i o n . The net r a d i a t i v e f l u x e s are e s s e n t i a l l y i d e n t i c a l f o r 1983 and 1986, t h e r e f o r e i n 1986 more energy must be channelled i n t o the s e n s i b l e heat f l u x e s - both AQS and Q H. The ensemble budgets and p a r t i t i o n i n g presented i n Figures 4.1 and 4.2 cover the Spring to F a l l p e r i o d and t h e r e f o r e span a l a r g e range of incoming s o l a r r a d i a t i o n , s u r f a c e moisture and s y n o p t i c events. The data were s t r a t i f i e d a ccording to time of year and a v a i l a b l e energy to t e s t f o r any d i f f e r e n c e s i n f l u x p a r t i t i o n i n g . Days with low net r a d i a t i o n ( l e s s than 150 W m - 2) channel a g r e a t e r percentage i n t o s e n s i b l e r a t h e r than l a t e n t h e ating. Such days are a s s o c i a t e d with low s a t u r a t i o n d e f i c i t s throughout the PBL which, combined with the small net r a d i a t i o n , leads to a lower l a t e n t heat f l u x . 4.3.2 C o n t r o l s on D i u r n a l V a r i a t i o n As i n Chapter 3, a c h a r a c t e r i s t i c f e a t u r e of the suburban energy balance i s the predominance of the t u r b u l e n t s e n s i b l e heat f l u x i n the afternoon and e a r l y evening. The complex suburban s u r f a c e geometry means th a t some su r f a c e s are shaded a t low s o l a r e l e v a t i o n s even when the a r e a l l y - a v e r a g e d net r a d i a t i o n i s p o s i t i v e . The shading leads to a conductive f l u x from heat s t o r e d i n these surfaces and provides an a d d i t i o n a l source f o r the t u r b u l e n t f l u x of s e n s i b l e heat. In c o n t r a s t t o many vegetated environments, Q H i s p o s i t i v e and the UBL remains warm and unstable past sunset. The l a r g e s e n s i b l e heat f l u x e s i n the afternoon warm both the s u r f a c e and mixed-layers and i n t u r n enhance t h e i r s a t u r a t i o n d e f i c i t . The r o l e of -69-the sea-breeze and mixed-layer depth i n t h i s warming w i l l be d i s c u s s e d subsequently. The enhanced s a t u r a t i o n d e f i c i t does not lead t o a l a r g e r l a t e n t heat f l u x , indeed the s m a l l e r Q E may contribute to a l a r g e r D 0 as a r e s u l t of a reduced vapour f l u x from the s u r f a c e . There are two reasons f o r t h i s : (1) many t r e e s pecies show an i n c r e a s e d stomatal r e s i s t a n c e i n response to an i n c r e a s e i n the s a t u r a t i o n d e f i c i t . Thus the c o n t r i b u t i o n of t r e e s to the l a t e n t heat f l u x i s reduced when the s a t u r a t i o n d e f i c i t i s l a r g e . (2) measurements of the s t a b i l i t y , based on the Monin Obhukov length ( L ) , i n d i c a t e a s h i f t from the u n s t a b l e / n e u t r a l c o n d i t i o n s which occur up to 1200 - 1300 LAT (-z/L ~ 1) to unstable c o n d i t i o n s with a l a r g e r degree of f r e e convection i n the a f t e r n o o n (-z/L ~ 2 - 3). These heat sources are l i k e l y to be l a r g e impervious areas such as roads, parking l o t s e t c . I r r i g a t e d lawns are a major source of moisture i n the suburban environment. These may or may not be l o c a t e d adjacent to the heat sources, but are c e r t a i n l y not c o i n c i d e n t . Although e a r l i e r research i n t o the i r r i g a t i o n h a b i t s of r e s i d e n t s i n the Sunset and Hudson areas (Loudon, 1984; Grimmond, 1984) shows a peak i n i r r i g a t i o n a t around 1800 LAT, t h i s i s not matched by an i n c r e a s e d l a t e n t heat f l u x . T h i s may r e s u l t from the s e p a r a t i o n of sources which d r i v e the moisture f l u x ( i . e . i r r i g a t e d lawns) and turbulence (mostly f r e e c onvection, a r i s i n g from impervious pavement). Any model of suburban l a t e n t heat f l u x e s may be l i m i t e d by t h i s complexity i n the l a t e a fternoon. The t r a d i t i o n a l concepts of m e c h a n i c a l l y - d r i v e n t u r b u l e n t t r a n s f e r and aerodynamic r e s i s t a n c e may not apply. The r o l e of the whole PBL i n the d i u r n a l energy budget must a l s o be -70-c o n s i d e r e d . Vancouver's c o a s t a l l o c a t i o n means t h a t during summer days with high net r a d i a t i o n a sea-breeze c i r c u l a t i o n o f t e n develops (Steyn and Faulkner, 1988). This l e a d s , t y p i c a l l y , t o l i g h t w e sterly flow i n the PBL with e a s t e r l i e s a l o f t . The advection a r i s i n g from the land/sea i n t e r f a c e a l s o r e s u l t s i n a lower mixed-layer depth ( z i ) . Measurements show a maximum heig h t of only 500 - 700 m f o r the c o n v e c t i v e boundary-layer (Steyn and Oke, 1982). The combination, i n the afternoon, of a low mixed-layer depth and l a r g e s u r f a c e s e n s i b l e heat f l u x e s should r e s u l t i n an i n c r e a s i n g l y warmer boundary-layer over the c i t y . However h o r i z o n t a l divergence v i a meso-scale advection diminishes t h i s r a t e of warming. Observations i n d i c a t e t h a t the combination of these f a c t o r s leads to an almost l i n e a r warming of the mixed-layer. Figure 4.3 i l l u s t r a t e s t h i s f o r J.D. 213 (August 1, 1986) at the Mountain View Cemetery (MVC) s i t e i n Sunset. 29 8 o o o 2 9 3 - o E o o o o 2 8 8 -05 0 7 09 1 J 1 3 13 17 19 LAT (x 100 hrs) F i g u r e 4.3: An example of the d i u r n a l v a r i a t i o n of mixed-l a y e r p o t e n t i a l temperature, MVC s i t e , Vancouver, JD 213, 1986 The c l o s e n e s s of the Sunset area to the coast a l s o a f f e c t s the UBL humidity and p o t e n t i a l l y suppresses the s u r f a c e l a t e n t heat f l u x by reducing the v e r t i c a l vapour g r a d i e n t . Evaporation leads to a humid boundary-layer above the ocean s u r f a c e (although the upward mixing of moisture may be l i m i t e d by the s t a b i l i t y of the ocean, e s p e c i a l l y i f the ocean surface i s c o o l ) . The movement of the sea-breeze over the c i t y thus might be expected to advect more humid a i r i n t o the urban mixed-layer. However a n a l y s i s of the h o u r l y v a r i a t i o n of the humidity both at 30 m and at 150 m at the measurement s i t e f a i l e d to i d e n t i f y any i n c r e a s e i n humidity with the a r r i v a l of the sea-breeze. Of course sea-breezes develop under a n t i c y c l o n i c c o n d i t i o n s when a capping subsidence i n v e r s i o n o v e r l i e s the PBL (see Chapter 6). A d d i t i o n a l l y the urban surface i s rough ( r a of ca. 30 s m"1) which leads to strong mixing throughout the PBL (Chapter 1). Hence the entrainment of warmer and d r i e r a i r from a l o f t and the mixing of t h i s throughout the UBL reduces the impact of the humid maritime a i r . Furthermore, the l a t e n t heat f l u x responds to the s a t u r a t i o n d e f i c i t which i s s t r o n g l y l i n k e d t o temperature. The c h a r a c t e r i s t i c warming (evident i n Figure 4.3) leads to an enhanced s a t u r a t i o n d e f i c i t i n the mixed-layer. The combination of l a r g e net r a d i a t i o n , entrainment of dry a i r and mixing t h e r e f o r e leads to p o t e n t i a l l y l a r g e l a t e n t heat f l u x e s i n a n t i c y c l o n i c c o n d i t i o n s . F i g u r e 4.4 shows a comparison between mixed-layer (80 - 800 m) and s u r f a c e - l a y e r (measured at 30 m) s a t u r a t i o n d e f i c i t s . The d i u r n a l p a t t e r n of the two d e f i c i t s i l l u s t r a t e t h a t they are q u i t e c l o s e l y coupled. S u r f a c e - l a y e r s a t u r a t i o n d e f i c i t s are t h e r e f o r e i n f l u e n c e d by both the s u r f a c e f l u x e s and the mixed-layer humidity. T h i s r e s u l t i s important i n two ways. F i r s t l y i t means tha t h o urly and d a i l y v a r i a t i o n s i n s u r f a c e - l a y e r s a t u r a t i o n d e f i c i t can be used as a i n d i c a t o r of those i n the TIME (LAT) F i g u r e 4 . 4 : D i u r n a l v a r i a t i o n o f measured s u r f a c e (D„) and mixed-layer (D m) s a t u r a t i o n d e f i c i t s f o r s e l e c t e d days, Vancouver, 1986 -73-F i g u r e 4.4: continued -74-mixed-layer. T h i s enables i n t e r p r e t a t i o n and a n a l y s i s even on days when there are no mixed-layer measurements. Secondly, i t supports the mechanism u n d e r l y i n g the proposal that suburban evaporation depends upon a c l o s e c o u p l i n g between the mixed and s u r f a c e - l a y e r s . 4.4 Day-to-Day V a r i a t i o n o f the Suburban Energy Balance The mean daytime f l u x e s of net r a d i a t i o n and l a t e n t heat f o r Phase II are presented i n Figure 4.5, and the v a r i a t i o n of Q E/Q*and 8 i n Figures 4.6 and 4.7. The l a t t e r i l l u s t r a t e s a s i m i l a r l y l a r g e degree of day-to-day v a r i a b i l i t y t o that observed i n Phase I, where i t was c o n t r a s t e d to the r e l a t i v e l y constant p a r t i t i o n i n g at a r u r a l s i t e . The f o l l o w i n g comments summarise the major f e a t u r e s . In the Spring and e a r l y Summer l a t e n t heat i s a major sink i n the daytime energy balance, wit h ==35% of Q* used i n evaporation. However, from J.D. 95 - 176 there are p e r i o d s where the s e n s i b l e heat f l u x i s l a r g e e.g. J.D. 141, 142 and 152. From J.D. 176 through to J.D. 195, the p a r t i t i o n i n g becomes more v a r i a b l e with the r a t i o of QE/Q* decreasing t o 0.10 by J.D. 195. The large r a i n f a l l s recorded from J.D. 196 - 198 were immediately followed by an i n t e r v a l of in c r e a s e d l a t e n t heat f l u x e s and mostly a n t i c y c l o n i c c o n d i t i o n s . A drought extended from J.D. 199 to 253. During t h i s p e r i o d were some i n t e r v a l s with r e l a t i v e l y l i t t l e day-to-day v a r i a t i o n i n B and QE/Q*, hut there were others where the p a r t i t i o n i n g i l l u s t r a t e s much g r e a t e r v a r i a t i o n (e.g. J.D. 208 - 212), and pe r i o d s with l a r g e r s e n s i b l e heat f l u x e s (e.g. J.D. 222 - 224 and 226 - 228). The l a t e n t heat f l u x e s from J.D. 226 through to J.D. 228 ( i n c l u s i v e ) are p a r t i c u l a r l y s m a l l . -75-F i g u r e 4.5: Day-to-day v a r i a t i o n of the mean d a y l i g h t - h o u r s net r a d i a t i o n and l a t e n t heat f l u x d e n s i t i e s at the Mainwaring s i t e , Vancouver 1986 -76-o •rH •P rd U C O PQ 6 L 4 h 3 h 134 178 204 216 227 JULIAN DAY 238 _1_ 250 Fi g u r e 4.6: Day-to-day v a r i a t i o n of the mean d a y l i g h t - h o u r B Bowen r a t i o a t the Mainwaring s i t e , Vancouver, 1986 Ot 178 204 216 227 JULIAN DAY 238 250 269 269 F i g u r e 4.7: Day-to-day v a r i a t i o n o f QE/Q* (mean da y l i g h t - h o u r s ) a t the Mainwaring s i t e , Vancouver, 1986 -77-When developing an evaporation model which i n c o r p o r a t e s such features we need f i r s t l y to i d e n t i f y those f a c t o r s t h a t lead to t h i s temporal v a r i a b i l i t y , and secondly to q u a n t i f y t h e i r p h y s i c a l i n f l u e n c e . Therefore i t i s necessary to i n v e s t i g a t e the f a c t o r s which c o n t r o l the temporal v a r i a b i l i t y of the suburban l a t e n t heat f l u x . The next s e c t i o n examines the importance of three i n f l u e n c e s : energy a v a i l a b i l i t y , water a v a i l a b i l i t y and advect i o n . 4.5 C o n t r o l s on the Suburban Latent Heat F l u x 4.5.1 Energy A v a i l a b i l i t y The a v a i l a b l e energy (Q*-A2s) provides an upper energy l i m i t t o the l a t e n t heat f l u x i n the absence of h o r i z o n t a l a d v e c t i o n . I t i s to be expected that v a r i a t i o n s i n Q E w i l l be l i n k e d f i r s t l y to v a r i a t i o n s i n Q*, as i n d i c a t e d g e n e r a l l y i n Figure 4.5. I f Q* were the s o l e cause of v a r i a b i l i t y i n Q E then i t would be expected t h a t the r a t i o of QE/Q* would be f a i r l y c onstant. In f a c t , as Figure 4.7 shows, there are s e v e r a l i n t e r v a l s over the study p e r i o d when t h i s i s so, these i n c l u d e : J.D. 199 -206; J.D. 213 - 214; J.D. 218 - 221; J.D. 237 - 239; and J.D. 246 - 249. However they can be c o n t r a s t e d to other i n t e r v a l s when there i s co n s i d e r a b l e day-to-day v a r i a t i o n i n the r a t i o . To f u r t h e r examine the r e l a t i o n s h i p , Figure 4.8 presents a s c a t t e r p l o t of Q E a g a i n s t the e q u i l i b r i u m e v a p o r a t i o n . Although there i s d e f i n i t e l y a p o s i t i v e c o r r e l a t i o n , there i s a l s o c o n s i d e r a b l e s c a t t e r . I t i s concluded t h a t while the net r a d i a t i o n , and t h e r e f o r e the a v a i l a b l e energy, are indeed important c o n t r o l s upon suburban evaporation, they are not the onl y c o n t r i b u t o r s to the v a r i a b i l i t y presented i n Figure 4.5 and a simple e q u i l i b r i u m model does not f u l l y e x p l a i n the v a r i a t i o n i n measured Q E. -78-0 50 100 150 2 0 0 Q E EQUIL IBRIUM (Wm" 2 ) Figure 4.B: Measured latent heat flux (mean daylight hours) compared to the equilibrium latent heat flux at the Mainwaring s i t e , Vancouver, 1986 -79-4.5.2 Water A v a i l a b i l i t y I t i s e q u a l l y obvious that the a v a i l a b l e moisture w i t h i n the suburban canopy must a l s o determine Q E. The moisture supply i n the pervious component of the suburban canopy i s determined p a r t i a l l y by the input of moisture through p r e c i p i t a t i o n and d e w f a l l . However the suburban context means tha t an a d d i t i o n a l source of moisture from i r r i g a t i o n e x i s t s to supplement the ' n a t u r a l ' moisture supply. T h i s water i s a p p l i e d e x t e r n a l l y to lawns, gardens etc and i s r e f e r r e d to as e x t e r n a l water-use. I t was monitored from J.D. 190 - J.D. 260. F i g u r e 4.9a i l l u s t r a t e s the d i s t r i b u t i o n of r a i n f a l l over the study p e r i o d - measured at the Vancouver I n t e r n a t i o n a l A i r p o r t . I t appears that up to J.D. 198 the suburban s o i l moisture should not be l i m i t e d , even i f t h e r e were no i r r i g a t i o n . The v a r i a t i o n of the percentage s o i l moisture (determined and expressed g r a v i m e t r i c a l l y , over a 0 - 200 mm s o i l depth) at s e v e r a l u n i r r i g a t e d grass s i t e s (Figure 4.9b) confirms t h i s . However the r a i n f a l l input i s n e g l i g i b l e from J.D. 199 - J.D. 258 l e a d i n g to the low s o i l moisture values f o r u n i r r i g a t e d greenspace. Some of the v a r i a t i o n i n Q E i s r e l a t e d to t h i s d r y i n g of the greenspace. For example from J.D. 197 -201, f o l l o w i n g a l a r g e input of r a i n f a l l , s o i l moisture i s l a r g e and Q E i s a l s o l a r g e . However there are a l s o p e r i o d s i n the l a t e Spring (J.D. 141 and 142) when, d e s p i t e an antecedent r a i n f a l l of 200 mm, the evaporative f l u x i s q u i t e low. An even more important f e a t u r e i s the s i z e of QE/Q*, 8 and Q E towards l a t e Summer and e a r l y F a l l ( r e c a l l F i g u r e s 4.7 to 4.9: e.g. J.D. 246 -249). Despite the s o i l moisture values being extremely low as a r e s u l t of more than 50 days with no r a i n , 8 values s i m i l a r to those found i n e a r l y -80-120 160 200 240 280 J U L I A N DAY F i g u r e 4.9(a): T o t a l d a i l y p r e c i p i t a t i o n measured a t Vancouver I n t e r n a t i o n a l A i r p o r t , 1986 (b): V a r i a t i o n i n % B o i l moisture (0 - 200 mm) i n two u n i r r i g a t e d parks w i t h i n Sunset area note: shading h i g h l i g h t s d r y i n g i n t e r v a l Julian Day -81-Summer are observed. I t seems probable t h a t the water s u p p l i e d through i r r i g a t i o n p l a y s a r o l e i n m a i n t a i n i n g these l a t e n t heat f l u x e s . To i l l u s t r a t e t h i s , F i g u r e 4.10 shows the v a r i a t i o n of the t o t a l water i n p u t to the suburban canopy ( i . e . p r e c i p i t a t i o n measured at Vancouver I n t e r n a t i o n a l A i r p o r t added to the measured e x t e r n a l water-use, i n mm/day) together with Q E. For the d u r a t i o n of the drought, the e x t e r n a l water supply provides a v i t a l source of moisture w i t h i n the suburban canopy. S i g n i f i c a n t l y , there i s a l s o c o n s i d e r a b l e 'coupling' of the measured l a t e n t heat f l u x with e x t e r n a l water-use. A simple c o r r e l a t i o n does not bear t h i s out because of the r o l e of other f a c t o r s , however the f o l l o w i n g simple d e s c r i p t i o n i l l u s t r a t e s the p o i n t . R e l a t i v e l y l a r g e e v a p o r a t i v e l o s s e s are measured from J.D. 199 - 202 but these are l i n k e d to high s o i l moisture l e v e l s and not the e x t e r n a l water-use. The o v e r a l l t r e n d i n d i c a t e s a g e n e ral c o r r e l a t i o n d e s p i t e o c c a s i o n a l anomalies, such as the peak water-use (J.D. 221) not c o i n c i d i n g w i t h a peak evaporation. S i m i l a r l y the l a r g e evaporation r a t e on J.D. 225 i s not d i r e c t l y l i n k e d to water-use. The p r e c i p i t a t i o n on J.D. 253 leads to a breakdown i n the c o r r e l a t i o n between eva p o r a t i o n and water-use. J u s t p r i o r t o t h i s , however, the two terms are c l o s e l y r e l a t e d - suggesting that the e x t e r n a l water-use co u l d be a f a c t o r i n determining suburban e v a p o r a t i o n . Note th a t the c o r r e l a t i o n between Q E and water-use may be i n d i r e c t - a r i s i n g from t h e i r i n d i v i d u a l r e l a t i o n s h i p s to the s a t u r a t i o n d e f i c i t . The e x t e r n a l water-use augments the canopy moisture supply. So, although the s o i l moisture i s l i m i t e d by J.D. 220, 8 i s not as l a r g e as -82-9 1 5 • Q E Hudson w a t e r - u s e + p r e c i p i t a t i o n 190 2 0 2 209 215 221 227 2 3 3 2 3 9 246 2 5 2 2 6 0 JUL IAN DAY F i g u r e 4.10: A comparison between measured d a i l y e x t e r n a l water-use added to p r e c i p i t a t i o n and measured l a t e n t heat f l u x e s a t the Mainwaring s i t e , Vancouver, 1986 -83-would perhaps be expected i f s o i l water were the only moisture source. Thus the s o i l moisture content and e x t e r n a l water-use have somewhat complementary r o l e s . They maintain a temporally continuous, but s p a t i a l l y d i s c r e t e , supply of moisture i n the suburban canopy. 4.5.3 Advection In aerodynamically-rough environments i t i s to be expected that the s a t u r a t i o n d e f i c i t w i l l c o n t r i b u t e to the day-to-day v a r i a t i o n i n Q E _ T h i s f o l l o w i n g a n a l y s i s begins by examining the r e l a t i o n s h i p between D 0 and Q E measured w i t h i n the s u r f a c e - l a y e r . As shown p r e v i o u s l y D 0 provides an adequate surrogate f o r the v a r i a t i o n i n mixed-layer s a t u r a t i o n d e f i c i t (Dm)-There i s c o n s i d e r a b l e s c a t t e r i n the r e l a t i o n s h i p between Q E and D c (or D m) because of the m u l t i p l i c i t y of i n f l u e n c e s on Q E. To c l a r i f y the r e l a t i o n s h i p between D Q and hence the a d v e c t i v e i n f l u e n c e on Q E• a sequence of days are s e l e c t e d . These show the e f f e c t s of s h i f t s i n the mean s a t u r a t i o n d e f i c i t when the a v a i l a b l e energy and s u r f a c e moisture are s i m i l a r . Only three case study sequences are s e l e c t e d : J.D. 151 - 152 J.D. 231 - 232 J.D. 248 - 250 J.D. 151 - 152 The comparison between Q* and Q E f o r t h i s p e r i o d i s presented i n Figure 4.11. The l a t e n t heat f l u x e s up to and i n c l u d i n g J.D. 151 were f a i r l y high. Although the net r a d i a t i o n i s very s i m i l a r on the two days i t i s c l e a r that Q E i s lower on J.D. 152. The mean daytime s a t u r a t i o n d e f i c i t on the f i r s t day was 1.93 kPa compared to 1.19 kPa f o r the second. However J.D. 152 -84-TIME (LAT) Measured net r a d i a t i o n and l a t e n t heat f l u x e s f o r J.D. 151 a 152 at the Mainwaring s i t e , Vancouver, 1986 -85-d i f f e r e d from J.D. 151 i n two f u r t h e r ways. F i r s t l y , although the surface wind d i r e c t i o n i s mostly SW to NW on both days, speeds are g r e a t e r i n the afternoon (5 - 6 m s" 1) of J.D. 152. A commonly observed f e a t u r e of the e n t i r e data s e t i s the d e c l i n e i n Q E with high wind v e l o c i t i e s when the s u r f a c e i s dry. Secondly, the f o r e c a s t f o r J.D. 152 p r e d i c t e d the i n t r u s i o n of u p p e r - l e v e l moisture over the study r e g i o n . U n f o r t u n a t e l y there are no measured p r o f i l e s to confirm t h i s but the combination of g r e a t e r t u r b u l e n t mixing and vapour i n p u t from a l o f t are l i k e l y to suppress D m and lower Q E. J .D . 231 - 232 There i s a n o t i c e a b l e s h i f t i n p a r t i t i o n i n g between these two days (August 18 and 19). On J.D. 231 D m i s 0.36 kPa and D 0 i s 0.81 kPa whereas D 0 i n c r e a s e d to to 1.71 kPa the next day. So, d e s p i t e the s i m i l a r net r a d i a t i o n l e v e l s each day, the evaporation r i s e s and 8 i s halved from J.D. 231 to J.D. 232 (Figure 4.12). The l a t t e r was a warm, sea-breeze day and an airsonde ascent i n d i c a t e d that the upper-air was much warmer and d r i e r than the preceding day. The tethersonde p r o f i l e conducted on J.D. 231 revealed i n i t i a l SE - E flow i n the s u r f a c e - and mixed-layers up to 1000 LAT. A f t e r t h i s the wind p r o f i l e s showed a strong d i r e c t i o n a l shear from w e s t e r l y flow w i t h i n the PBL to e a s t e r l y flow above. T h i s i s most unusual as e a s t e r l y flow a l o f t would normally be dry but t h i s i s not the case f o r J.D. 231. The d i r e c t i o n a l shear may i n d i c a t e a lack of c o u p l i n g between the PBL and the u p p e r - a i r which would r e s u l t i n moisture convergence. J.D. 248 - 250 The f i n a l sequence of three days (September 5 to 7) p r e s e n t s an example of 'outflow' c o n d i t i o n s from the c o n t i n e n t a l i n t e r i o r of B r i t i s h Columbia. Again, the net r a d i a t i o n i s s i m i l a r on the three days, however -86-600 TIME (LAT) F i g u r e 4.12: As i n F i g u r e 4.11 f o r J.D. 231 and 232 -87-600 TIME (LAT) F i g u r e 4.13: As i n F i g u r e 4.11 f o r J.D. 248 - 250 -88-the s a t u r a t i o n d e f i c i t s and Q E values (Figure 4.13) d i f f e r . The s u r f a c e wind d i r e c t i o n on J.D. 248 was WNW (D 0 = 1.42 kPa) and SW on J.D. 249 (D 0 = 2.2 kPa) but both days were c h a r a c t e r i s e d by u p p e r - l e v e l e a s t e r l y outflow from the warm and dry i n t e r i o r which lead to the high D 0 v a l u e s . Conversely J.D. 250 i s c h a r a c t e r i s e d by a c o o l southerly flow and a c o r r e s p o n d i n g l y lower D 0 (0.89 kPa) - a s s o c i a t e d with a synoptic low pressure system NW of Vancouver. T h i s a n a l y s i s i n d i c a t e s the important r e l a t i o n s h i p between D 0, D m, and Q E. I t shows that the s a t u r a t i o n d e f i c i t accounts f o r some of the day-to-day v a r i a t i o n i n Q E when the a v a i l a b l e energy and moisture are unchanged. Some f a c t o r s that appear to i n f l u e n c e the s a t u r a t i o n d e f i c i t have been demonstrated, but what are the c o n t r o l s upon D m? There are three s c a l e s of a d v e c t i v e f o r c i n g : l o c a l , meso and s y n o p t i c . The former would a r i s e from the heterogeneity of the s u r f a c e types w i t h i n the t u r b u l e n t f l u x source area - such an e f f e c t could be manifested i n two ways. F i r s t l y , changes i n wind d i r e c t i o n should lead to a change i n f l u x p a r t i t i o n i n g on an hourly b a s i s . Secondly, one would expect to f i n d a s i g n i f i c a n t degree of s p a t i a l v a r i a b i l i t y of the t u r b u l e n t f l u x e s . Although the f l u x p a r t i t i o n i n g does show co n s i d e r a b l e temporal v a r i a t i o n , on an hourly b a s i s there i s no evidence of l o c a l - s c a l e advection s y s t e m a t i c a l l y r e l a t e d to changes i n wind d i r e c t i o n i n t h i s or previous data s e t s (Steyn, 1985; Kalanda et al., 1981; Schmid, 1988). The amount of s p a t i a l v a r i a b i l i t y present i n the t u r b u l e n t f l u x f i e l d at Sunset i s assessed i n Chapter 2 and shown to be s m a l l . In e f f e c t the l o c a l - s c a l e a d v e c t i v e i n f l u e n c e on D 0 i s minimal. The a d v e c t i v e i n f l u e n c e of the meso-scale sea-breeze c i r c u l a t i o n has been addressed i n terms of the d i u r n a l energy balance and mixed-layer depth. I t leads to a more humid, c o o l and shallow mixed-layer than would e x i s t without i t s i n f l u e n c e . However these 'sea-breeze days' are u s u a l l y a s s o c i a t e d with a warm and p o t e n t i a l l y dry mixed-layer i n Vancouver and minimum v a r i a t i o n i n the day-to-day p a r t i t i o n i n g . In c o n t r a s t , SE flow i n the PBL appears to r e s u l t i n a c o o l e r and more humid mixed-layer. T h i s suggests a f u r t h e r p o t e n t i a l advective e f f e c t : the g r e a t e r urban f e t c h f o r westerly compared t o s o u t h - e a s t e r l y flow. Some of the tethersonde data i n d i c a t e d i f f e r e n c e s i n the temperature and humidity of the mixed-layer between these two flows. T h i s i n f l u e n c e i s discus s e d f u r t h e r f o l l o w i n g the modelling s e c t i o n s . Synoptic c o n d i t i o n s o f t e n l i m i t sea-breeze development (e.g. f r o n t a l passage, or the presence of a c o o l low). In such c o n d i t i o n s there i s l i t t l e or no c o n v e c t i v e mixed-layer development and the s y n o p t i c regime dominates the PBL. The presence of s y n o p t i c a l l y - d e t e r m i n e d outflow or an upper trough i s an example of a s y n o p t i c advective c o n t r o l . Two of the c a s e - s t u d i e s presented above i l l u s t r a t e these s i t u a t i o n s . Hence we can conclude that D m i s of t e n i n f l u e n c e d by s y n o p t i c and meso-scale events. Since the surface and mixed-layer s a t u r a t i o n d e f i c i t s are l i n k e d (Figure 4.4), D 0 i s a l s o s e n s i t i v e to these. Combined Advective E f f e c t s : S a t u r a t i o n D e f i c i t . Wind Speed and D i r e c t i o n The complex r e l a t i o n s h i p between the s a t u r a t i o n d e f i c i t , meso-/synoptic- s c a l e a d v e c t i o n and the l a t e n t heat f l u x i s i l l u s t r a t e d by -90-Class 1 2 4 5 6 7 Range of (3 1 0.75<B<1.0 2 1.0< 6(1.5 3 1.5<8ts2.0 4 2.0 < B < 2.5 5 2.5 < B < 3.0 6 3.0 < B < 4.0 7 B > 4.0 1 2 3 4 5 6 7 Class III 25 Class IV tz <D cr CD 1 2 3 4 5 6 7 F i g u r e 4.14: A suggested c l a s s i f i c a t i o n scheme f o r mean day l i g h t - h o u r s Bowen r a t i o , based on wind d i r e c t i o n and s a t u r a t i o n d e f i c i t -91-Table 4.2: Additional data to accompany Figure 4.14 (continues on following page) (a) Class I : Anticyclonic, Westerly Flow-Dominated J.D. Direction r< 0 135 270 51.4 1.97 147 230 49.2 1.36 148 190 85.7 1.64 149 239 96.8 1.11 151 242 137.5 1.05 161 232 106.8 2.03 163 250 107.4 1.90 164 240 161.1 2.31 174 244 56.1 1.76 178 227 105.2 1.33 199 205 48.9 1.48 200 211 63.3 1.56 201 233 65.1 1.40 202 217 57.5 1.48 204 205 48.4 1.87 205 227 62.7 1.59 206 175 59.8 1.57 209 153 56.1 0.82 211 215 75.9 1.90 212 219 88.0 2.03 213 255 95.6 1.52 214 261 94.6 1.59 218* 307 108.9 1.62 219 275 125.6 1.76 220 234 117.2 1.85 221 223 120.3 2.20 225 264 65.3 1.84 229 264 89.5 2.63 230 199 92.1 2.04 232 288 134.2 1.91 233 223 128.1 2.15 238 259 136.8 2.03 239 264 176.3 1.56 246 201 63.8 2.05 247 208 51.6 2.41 248 291 118.5 1.64 255* 291 78.2 1.56 257 177 50.5 2.00 258 201 52.4 1.65 260 240 65.9 1.89 268 248 54.5 1.42 Note: * denote days which f i t into two or more categories. -92-(b) Class I I : North-westerly Flow-Dominated, High QH, D0. J.D. Direction * i 0 150 289 103.8 2.16 152* 296 83.0 3.84 153 304 87.0 2.10 161 270 107.0 2.03 162 270 80.2 3.20 176 264 68.1 2.64 218* 307 108.9 1.62 226 280 61.2 3.84 227 280 70.4 5.75 228 280 69.8 3.04 229 280 89.5 2.63 255* 292 78.3 1.56 (c) Class I I I : Suppressed D 0 > QE, Q*- ^Qs large (thus rL small). Flow Potentially SE/S/SSW. J.D. Direction r i 0 142 180 69.9 5.54 152* 304 83 3.84 160 231 74.4 3.04 175 260 54.1 2.70 177 190 99.8 1.80 189 150 86.4 81.00 190 154 59.9 4.58 195 160 53.5 5.82 203 209 48.4 2.25 208 150 39.5 5.82 210 140 53.2 8.80 215 184 75.1 2.66 216 190 54.9 2.20 217 216 64.2 2.21 222 144 50.6 5.20 223 149 55.2 4.28 224 187 63.1 3.06 231 230 63.6 3.82 234 212 102.5 2.72 235 148 94.5 4.91 236 182 68.1 3.7 (d) Class IV: Unsettled, Cold Low Conditions with lower D0, and Q J.D. Direction 0 240 164.1 164.9 3.17 242 140.8 46.8 3.44 243 155.7 72.6 3.48 244 148.3 63.4 5.38 245 175.9 73.2 3.79 250 161.4 77.6 4.72 251 171.8 60.8 4.71 252 139.8 46.7 4.18 256 80.2 66.3 3.89 259 160.3 51.1 6.38 -93-Figure 4.14. I t shows the frequency of days w i t h i n a p a r t i c u l a r range of 0 (numbered 1 to 7, corresponding to the 6 i n t e r v a l i d e n t i f i e d i n the key). A l s o noted are the predominant surface wind d i r e c t i o n s , speeds and s a t u r a t i o n d e f i c i t s (Table 4.2). The f o l l o w i n g regimes are suggested on the b a s i s of these histograms. C l a s s I i s a s s o c i a t e d with a n t i c y c l o n i c westerly-flow c o n d i t i o n s . Class II i s d i f f e r e n t i a t e d because i t i s c h a r a c t e r i s e d by NW flow, with high wind v e l o c i t i e s . When 0 i s l a r g e r than 7/s an increase i n wind speed reduces the l a t e n t heat f l u x . C l a s s I I I represents those days with low D 0, adequate a v a i l a b l e energy and SE/S/SSW flow. The l a r g e s t 0 values noted i n Chapter 3 f a l l i n t o C l a s s I I I . F i n a l l y , C l a s s IV represents days when a s y n o p t i c c o n t r o l i s dominant; o f t e n due to the presence of a c o l d low and u n s e t t l e d c o n d i t i o n s and a v a i l a b l e energy i s l i m i t e d . Comparing the histograms c l e a r l y i l l u s t r a t e s s i g n i f i c a n t d i f f e r e n c e s i n 0 between Cla s s e s I and I I I . The atmospheric c o n t r o l i s the s a t u r a t i o n d e f i c i t D m ( D 0 ) . The d i f f e r e n c e s i n D m and hence D 0 between C l a s s I and C l a s s I I I shows the r o l e t h a t p a r t i c u l a r s y n o p t i c or meso-scale c o n d i t i o n s p l a y i n determining the humidity of the mixed-layer. The s h i f t i n average wind d i r e c t i o n from C l a s s I to C l a s s I I I i s a l s o an i n d i c a t o r of these c o n d i t i o n s . 4.6 Concluding Comments These r e s u l t s show t h a t the day-to-day p a r t i t i o n i n g of the t u r b u l e n t f l u x e s i s v a r i a b l e . The s i z e of the McNaughton and J a r v i s parameter J7 suggests t h a t the suburban mixed and s u r f a c e - l a y e r s are s t r o n g l y coupled. Thus i t i s not s u p r i s i n g t h a t the l a t e n t heat f l u x i s more than a -94-simple f u n c t i o n of the a v a i l a b l e energy: both the moisture s t a t u s of the suburban canopy and the atmospheric humidity e x e r t a f o r c i n g on Q E. The o b s e r v a t i o n s i l l u s t r a t e the complementary r o l e of the moisture content of u n i r r i g a t e d greenspace and the changing area of the i r r i g a t e d greenspace. Together they provide an urban moisture supply which i s maintained even through a prolonged d r y i n g p e r i o d . Measurements confirm that D 0 and D m are c l o s e l y l i n k e d over a range of c o n d i t i o n s . The a n a l y s i s shows that the s a t u r a t i o n d e f i c i t c o n t r i b u t e s to the day-to-day v a r i a t i o n i n tu r b u l e n t f l u x p a r t i t i o n i n g . A c l a s s i f i c a t i o n of mean d a i l y Bowen r a t i o i l l u s t r a t e s the combination of i n f l u e n c e s . E s s e n t i a l l y i t r e v e a l s t h a t meso-scale processes such as the sea-breeze, and s y n o p t i c - s c a l e s i t u a t i o n s such as outflow c o n t r i b u t e to the s i z e of Dro, D 0 and 0. I t i s concluded that one of the hypotheses of t h i s r e s e a r c h i s supported by the e m p i r i c a l evidence. The next stage i s to develop a model which encompasses these mechanisms and i n f l u e n c e s . I t should combine values f o r the s u r f a c e r e s i s t a n c e , a v a i l a b l e energy and s a t u r a t i o n d e f i c i t . Thus i t should be a Combination model, i n other words a simple model such as P r i e s t l e y - T a y l o r would not be a p p r o p r i a t e . The s u r f a c e r e s i s t a n c e should i n c o r p o r a t e the r o l e of t r e e s , s o i l moisture and i r r i g a t i o n . The a v a i l a b l e energy and s a t u r a t i o n d e f i c i t must be provided through modelling or measurements. - 9 5 -CHAPTER 5: DEVELOPMENT AND IMPLEMENTATION OF A SUBURBAN EVAPORATION MODEL I: THE CANOPY EVAPORATION SUB-MODEL Suburban evaporation i s determined by a combination of the a v a i l a b l e energy and water w i t h i n the canopy and a d v e c t i o n . T h i s i s to be expected (Chapter 1), and has been comfirmed by the o b s e r v a t i o n s (Chapters 3 and 4). Advection c o n t r o l s evaporation v i a the s a t u r a t i o n d e f i c i t (D 0, D r a). I t was shown t h a t the s a t u r a t i o n d e f i c i t i n the s u r f a c e - l a y e r (D 0) i s i n f l u e n c e d not o n l y by the closeness of the a c t i v e s u r f a c e but a l s o by the e x t e r n a l i n f l u e n c e of the mixed-layer s a t u r a t i o n d e f i c i t ( D m ) . In order to develop a p r e d i c t i v e and d i a g n o s t i c evaporation model i t i s t h e r e f o r e necessary to i n c l u d e both the suburban canopy and mixed-layers. S p e c i f i c a l l y , i t means c o u p l i n g a canopy evaporation model with a mixed-layer growth model. The combined model i s c a l l e d SCABLE (Suburban Canopy and Boundary Layer Evaporation model). SCABLE e s s e n t i a l l y comprises three sub-models (Figure 5.1): storage heat f l u x ; canopy evaporation and mixed-layer growth. The storage p a r a m e t e r i s a t i o n scheme i s c e n t r a l to both the measurement and modelling phases and t h e r e f o r e i s d i s c u s s e d i n the appendices (Appendix 1). The next two chapters d i s c u s s the other two sub-components of SCABLE The l i n k s between the sub-models are the p o t e n t i a l s a t u r a t i o n d e f i c i t at a r e f e r e n c e h e i g h t and the surface energy budget. Clo s u r e of the l a t t e r (using modelled evaporation and measured net r a d i a t i o n and storage fluxes) enables the s o l u t i o n of the f u l l s e t of d i f f e r e n t i a l equations which d e s c r i b e mixed-layer growth. This s o l u t i o n p r e d i c t s a new mixed-layer -96-MODEL INITIALISATION n=0 Wind speed Wind direction MTXED-LAYER MODEL CANOPY EVAPORATION MODEL 0o' %• z i 7 7 d: 6m. V z i ( A 5 , A q dt n = n + 1 II! CHECK Q, Q = PREDICTED USING COMBINATION MODEL : * ; SURFACE RESISTANCES AERODYNAMIC RESISTANCES STOP IF<0 Q H = Q* " A Q S - Q E AVAILABLE ENERGY M O J O E T _ . T _ I E D F R O M stcmatal I resistance * area i r r i g * soil moistureII spacing L wind speed roughness element * net radiation Note: arrow head denotes model variable which directly uses parameters at arrow base. = denotes measured variables. F i g u r e 5.1: Schematic i l l u s t r a t i o n of SCABLE showing the i n t e r a c t i o n of the two sub-models -97-s p e c i f i c humidity and temperature, assumed to be constant throughout the e n t i r e mixed-layer depth, and thus a new s a t u r a t i o n d e f i c i t . In t u r n , t h i s i s used to c a l c u l a t e the evaporation r a t e and hence a new s u r f a c e energy budget. Figure 5.1 i s a schematic i l l u s t r a t i o n of the model. 5.1 Theory: Shuttleworth's M u l t i - L a y e r Canopy Models There are few mass t r a n s f e r schemes developed f o r the heterogeneous suburban s u r f a c e ( r e c a l l Chapter 1). Hence urban mete o r o l o g i s t s have borrowed from the e x p e r t i s e of the f o r e s t and a g r i c u l t u r a l modellers, assuming that i n a general way the urban and f o r e s t e d canopies are s i m i l a r . Having e l e c t e d to "borrow" a modelling approach f o r suburbia r a t h e r than develop an e n t i r e l y new scheme, i t i s necessary to i d e n t i f y f o r e s t or crop models which provide an a p p r o p r i a t e analogy. In p a r t i c u l a r i t must be p h y s i c a l l y - b a s e d but a l s o allow f o r a heterogeneous canopy s t r u c t u r e . The work of Shuttleworth i n t h i s arena i s p a r t i c u l a r l y r e l e v a n t . He has developed (1976, 1978) a Combination model which can be a p p l i e d to l a y e r e d and p a r t i a l l y wet canopies. Shuttleworth and Wallace (1985) extended t h i s to model evaporation from sparse canopies. T h i s work i s appealing because the suburban s u r f a c e i s f a r removed from the i d e a l i s e d extended-leaf, isothermal model assumed by Penman. In 1976 Shuttleworth attempts to u n i f y the s i n g l e - s o u r c e approach represented by the PM model with the numerical m u l t i - l a y e r models (e.g. Waggoner and Reifsnyder, 1968). A Combination model i s d e r i v e d t h a t i s s i m i l a r to the s i n g l e - s o u r c e form but i n c o r p o r a t e s d e t a i l about the i n d i v i d u a l canopy elements. The model i s subsequently (Shuttleworth, 1978) s i m p l i f i e d so that i t can be a p p l i e d to a s i n g l e - s o u r c e canopy. The s u r f a c e -98-r e s i s t a n c e f o r the l a t e n t heat f l u x has two a l t e r n a t i v e d e f i n i t i o n s . They are i d e n t i c a l i n e i t h e r t o t a l l y wet or t o t a l l y dry c o n d i t i o n s , but d i f f e r i n p a r t i a l l y wet c o n d i t i o n s . This allows f o r the s i t u a t i o n of a simultaneously wet and dry canopy. By assuming i d e n t i c a l elements (thus removing some of the s h e l t e r f a c t o r s i n the equations) and i g n o r i n g the below canopy f l u x r e s u l t s i n : Q E = s (Q*- A3S) + C a D/R B H (5.1) s + T ( l + r c P M / R a H ) where R a H = r a H + r b R a V = r a V + r b r a H - v = aerodynamic r e s i s t a n c e s from mean canopy-airstream t o r e f e r e n c e height r b = boundary-layer r e s i s t a n c e s R a H ' v = t o t a l aerodynamic r e s i s t a n c e as d e f i n e d by Thorn (1971) Note t h a t the s u r f a c e r e s i s t a n c e (r cPM) i s def i n e d by Shuttleworth i n terms of the wet and dry p r o p o r t i o n s of the canopy, i n con t a s t to the bulk stomatal r e s i s t a n c e ( r c ) i n the o r i g i n a l PM equation (1.1). I t i s : r„PM = 1-W r i + r b * 1 .- (s/-?)r b - r,. where W = E wet a r e a s / t o t a l l e a f area r A = i n t r i n s i c s urface r e s i s t a n c e (Shuttleworth, 1975), e f f e c t i v e l y equal to zero r b * = ( s / T ) r b + r b -99-T h i s d e f i n i t i o n enables the r e p r e s e n t a t i o n of a l a r g e range of intermediate canopy r e s i s t a n c e s as the canopy d r i e s . T h i s i s c o n s i s t e n t with e m p i r i c a l evidence, as argued by Shuttleworth (1977) i n r e p l y t o Monteith (1977). Shuttleworth and Wallace (1985) d e r i v e a form of t h i s equation to p r e d i c t evaporation from a sparse crop. The three-dimensional nature of the crop i s ignored and i t i s assumed that the aerodynamic mixing w i t h i n the crop i s s u f f i c i e n t to enable the development of a mean canopy air - s t r e a m . Energy p a r t i t i o n i n g occurs both at the crop and a t the s u b s t r a t e . Energy f o r the crop and su b s t r a t e as a whole i s conserved. One of the important aspects of t h i s pragmatic approach i s o b v i o u s l y s c a l e - the model i s a p p r o p r i a t e only at a s c a l e where the t o t a l evaporation measured from the crop i s not i n f l u e n c e d by the h o r i z o n t a l inhomogeneity of the crop i t s e l f : " i f a d e s c r i p t i o n of the Monteith type i s t o be used i t i s necessary t h a t the elements of which the model i s composed (e.g. energy f l u x e s , stomatal r e s i s t a n c e , etc.) are d e f i n e d as h o r i z o n t a l averages over area s c a l e s i n which p e r s i s t e n t f e a t u r e s occur i n s u f f i c i e n t numbers to allow such averaging." (Shuttleworth and Wallace, 1985, p. 840). Fi g u r e 5.2 i l l u s t r a t e s the general scheme. Evaporation, and other m e t e o r o l o g i c a l parameters are measured a t a r e f e r e n c e h e i g h t . F i v e r e s i s t a n c e s are d e f i n e d : a surface r e s i s t a n c e to evaporation from the s o i l s u r f a c e i t s e l f ; aerodynamic r e s i s t a n c e s encountered by the l a t e n t and s e n s i b l e heat f l u x e s l e a v i n g the subs t r a t e before they are in c o r p o r a t e d i n t o the mean canopy flow; a boundary-layer r e s i s t a n c e which c o n t r o l s t r a n s f e r from the su r f a c e of the v e g e t a t i o n to the mean canopy flow; a bulk stomatal r e s i s t a n c e f o r the crop; and an aerodynamic r e s i s t a n c e f o r t r a n s f e r between the mean canopy flow and the r e f e r e n c e h e i g h t . -100-T(Z) SCREEN HEIGHT o(Z) aerodynamic resistance Q E MEAN CANOPY FLOW r e r c W v - ^ surface \boundary-resistance\layer res istance CANOPY SOIL SURFACE surface resistance F i g u r e 5.2: Schematic of SW model (from SW, 1985) -101-Unfortunately, t h e i r model i s not t e s t e d against measured data, and a n a l y s i s of the model performance i s r e s t r i c t e d to s e n s i t i v i t y analyses. These i n d i c a t e that the model i s r e l a t i v e l y i n s e n s i t i v e to e r r o r s i n the parameterised aerodynamic r e s i s t a n c e s . T h i s i s important, because the use of g r a d i e n t d i f f u s i o n theory, and the exponential decay f u n c t i o n f o r the momentum d i f f u s i v i t y w i t h i n the canopy i s the major l i m i t a t i o n of the model. SW demonstrate that the model performs r e a l i s t i c a l l y over a range of c o n d i t i o n s i n c l u d i n g those i n the l i m i t - a c l o s e d canopy, and a bare s o i l . Subsequently K e l l i h e r et al (1986) t e s t e d i t f o r a two l a y e r f o r e s t and found i t worked w e l l (see Chapter 2). The canopy evaporation sub-model which i s adopted i n the present r e s e a r c h i s based on the work of Shuttleworth (1978) and SW. The philosophy of the modelling approach i s s i m i l a r to that of SW where the emphasis i s upon s i m p l i c i t y and pragmatism, w h i l s t endeavouring to maintain and i n c l u d e as much p h y s i c a l r e a l i t y as p o s s i b l e . Again, s c a l e i s an important i s s u e . The proposed model i s intended f o r use at the l o c a l s c a l e to estimate the sum t o t a l of evaporation from some heterogenous, extended canopy, at a height where the i n d i v i d u a l sources and si n k s have become averaged. 5.2 M o d i f i c a t i o n o f Shuttleworth (1978) and Shuttleworth and Wallace (1985) f o r a Suburban S i t e 5.2.1 Overview The suburban s u r f a c e - l a y e r i s d i v i d e d i n t o a 'substrate' and a 'canopy'. T h i s d i v i s i o n , although not as obvious as f o r a crop, i s necessary i n order to develop a canopy evaporation sub-model s i m i l a r i n concept t o SW. Figure 5.3 should be con s u l t e d i n conjunction with the f o l l o w i n g d i s c u s s i o n . -102-FREE A T M O S P H E R E B O U N D A R Y L A Y E R (DCF IRCNCC H V f l ) C A N O P Y A R E A : £ a t S I S T A N C I S = « C P M S U B S T R A T E A R E A : £ R C S I S T A N C I = * I R F LEGEND: 2. SAIMP = paved substrate CADRY = trees CAIMP = buildings SAWET = ir r i g a t e d grass SADRY = unirrigated $ra»« boundary: substrate area boundary: bluf f body a r e a Figure 5.3: Schematic of surface and aerodynamic resistance scheme i n canopy evaporation sub-model -103-The 'canopy' i n c l u d e s b u i l d i n g s and t r e e s . T h i s component i s d i f f e r e n t i a t e d from the su b s t r a t e by i t s s i g n i f i c a n c e as a momentum sink and i s r e f e r r e d t o as the blu f f - b o d y component. I t comprises both pervious ( t r a n s p i r i n g ) and impervious s u r f a c e s . The tre e s w i l l be the s o l e moisture source under a n t i c y c l o n i c , dry c o n d i t i o n s . The 'substrate' c o n s i s t s of the remaining ' h o r i z o n t a l ' s u r f a c e s - the grassed and paved areas. The su b s t r a t e area can be sub d i v i d e d f u r t h e r i n t o the f o l l o w i n g elements: i r r i g a t e d greenspace (mainly r e s i d e n t i a l lawns), n o n - i r r i g a t e d greenspace ( t y p i c a l l y r e c r e a t i o n a l parks and vacant l o t s ) and paved areas ( s t r e e t s , pavements, parking l o t s e t c . ) . These d i v i s i o n s are based on the expected r o l e s of these surfaces as moisture sources and the a b i l i t y t o develop para m e t e r i s a t i o n s to de s c r i b e t h e i r moisture a v a i l a b i l i t y s t a t u s . In summary each component (substrate or bluff-body) i s made up of the f o l l o w i n g elements: s u b s t r a t e : i r r i g a t e d greenspace (Ws) dry pavement ( I s ) u n i r r i g a t e d greenspace (1-(W S+I S)) b l u f f - b o d y : dry ( i . e . t r a n s p i r i n g trees) (1-(W C+I C)) wet b u i l d i n g s (Wc) dry b u i l d i n g s ( I c ) The symbols represent the p r o p o r t i o n of the component t h a t each surface -104-type occupies. Each element a c t s as a moisture source and a momentum s i n k . Moisture a v a i l a b i l i t y i s parameterised as an i n d i v i d u a l s u r f a c e r e s i s t a n c e analogous to the stomatal r e s i s t a n c e of a l e a f . These i n d i v i d u a l r e s i s t a n c e s must be summed i n p a r a l l e l to y i e l d a 'bulk' or 'average' surface r e s i s t a n c e f o r each component. A s s i g n i n g of r cPM ( r e c a l l equation 5.1) f o r the bluff-body and the su b s t r a t e i s achieved by adopting the 1978 Shuttleworth scheme. F i g u r e 5.3 d e p i c t s the vapour pathways and the a s s o c i a t e d r e s i s t a n c e s . The boundary-layer r e s i s t a n c e c o n t r o l s the t r a n s f e r between the pervious b l u f f - b o d y components and the mean canopy flow; and the aerodynamic r e s i s t a n c e r e f e r s to the r e s i s t a n c e from the mean canopy flow to the r e f e r e n c e height. The l a t e n t heat f l u x i s computed f o r the s u b s t r a t e and bluff-body components s e p a r a t e l y - as a f u n c t i o n of the a v a i l a b l e energy and the bulk s u r f a c e and aerodynamic r e s i s t a n c e s f o r each component. The combined suburban l a t e n t heat f l u x i s then the sum of the blu f f - b o d y and substrate e v a p o r a t i o n . 5.2.2 Canopy Evaporation Sub-Model Equations These are e s s e n t i a l l y i d e n t i c a l t o those presented by SW, and adopt the same assumptions. D e t a i l i s added to the equations which determine the i n d i v i d u a l s u r f a c e r e s i s t a n c e terms. Core Equations (a) Q E o = Q E t o t a l = ^ E b l u f f - b o d y + ^ E s u b s t r a t e -105-( D ) A t o t a l _ A b l u f f - b o d y + A s u b s t r a t e where A = (Q* - AQS) and thus, A b l u f f - b o d y = Bluff-Body Plan Area x A a b o v e c a n o p y T o t a l Plan Area and, A s u b s t r a t e = Substrate Plan Area x A a b o v e c a n o p y T o t a l Plan Area So the energy a v a i l a b l e t o each component i s simply an areally-weighted average of the above canopy energy (measured at 30 m). (c) Following SW, and t a k i n g the p o t e n t i a l s a t u r a t i o n d e f i c i t a t the s u r f a c e (D s) as: D s = e * ( T s ) - e s (5.2) where e * ( T s ) = s a t u r a t i o n vapour pressure at surface temperature ( T B ) e = vapour pressure ( s u b s c r i p t s or z) and vapour pressure d e f i c i t ( i . e . the s a t u r a t i o n d e f i c i t ) a t the reference height (D z) i s : D z = e * ( T z ) - e 2 (5.3) (d) By combining (5.2) and (5.3) and s o l v i n g f o r D s: D s = D z + (SA - ( s + T ) Q E 0 ] R a H / C a (5.4) T h i s i s e q u i v a l e n t to equation 8 i n SW. (e) Vapour and s e n s i b l e heat are t r a n s f e r r e d with e q u i v a l e n t r e s i s t a n c e s . -106-Bluff-Body Evaporation From equation 5.1 and Shuttleworth (1978) the l a t e n t heat f l u x f o r the bluf f - b o d y component i s the sum of the f l u x e s from the i n d i v i d u a l elements - t r e e s and b u i l d i n g s : ' E b l u f f - b o d y S Ac + < Ca D s / r b c > s + 7 ( 1 + r_PM/r b c) (5.5) p r o v i d i n g t h a t : r cPM = 1-1, + r be s £ + r be ( s / T ) r b c * + r b c * r b c = r b ^ o r b l u f f - b o d y component r s f = 0 (the i n t r i n s i c s u r f a c e r e s i s t a n c e rL f o r a wet impervious component) or 1 0 5 (dry impervious component) r b c * = ( 3 / 7 > r b c + r b c r c c = bulk stomatal r e s i s t a n c e f o r t r e e s , i . e . stomatal r e s i s t a n c e s f o r leaves summed i n p a r a l l e l f o r tre e d area Substrate Evaporation S i m i l a r equations can be developed f o r the su b s t r a t e area, using the three i n d i v i d u a l s u r f a c e types: impervious ( I s ) , i r r i g a t e d greenspace (W s), and n o n - i r r i g a t e d greenspace: Q E s u b s t r a t e = 3 A s + ( c a D s ) / r b £ a + 1(1 + r s P M / r b s ) (5.6) -107-and: r sPM = + 1-(W+I)„ + I, •bs -bs r s f + r b s - 1 (s/Tf)r b 8 + r b E where r b s = r b f o r subs t r a t e r__ = bulk stomatal r e s i s t a n c e f o r u n i r r i g a t e d grass T o t a l Canopy Evaporation Now, adding together the subs t r a t e and bluff-body components, and s u b s t i t u t i n g equation 5.4 f o r D s, r e s u l t s i n : Q E 0 = ^ s u b s t r a t e + [ ( C a / R A s ) (D z + ( s A - < S + 7 ) Q E 0 ) r a m / C a ) ] (s + • 7 ) r b s + Tf r sPM + s A b l u f f body + K c a / R A b ) (°z + ( s A - ( s + T ) Q E 0 ) r a m / C a ) ] (s + f ) r b c + 1 r cPM (5.7) The important m o d i f i c a t i o n i s the i n c l u s i o n of an aerodynamic r e s i s t a n c e which t r a n s p o r t s vapour from the mean canopy a i r s t r e a m to the re f e r e n c e h e i g h t , r a m , considered the same as r a H and r a V i n equation 5.1. T h i s equation can then be solved f o r Q E 0 » and re-arranged t o r e s u l t i n a form s i m i l a r to the Penman-Monteith equations (see SW f o r d e r i v a t i o n s ) : Q E 0 = Cc PMc + Cs PMs (5.8) where PMs = [sA + {C a D 2 - s r a r a A E } / ( r a r a + r b s ) ] s + 7 { l + r s P M / ( r b s + r a m ) } -108-Cs = (1 + [ R s R a / ( R c ( R s + R a ) ) J } " 1 PMc = [SA + {C a D z - s r a m A c } / ( r a m + r b c ) ] 3 + 7 ( 1 + r c P M / ( r b c + r a m ) } Cc = {1 + [ R c R a / ( R s ( R c + R a ) ) l } " 1 where R a = (s+T)r a r a R E = ( s + 7 ) r b s + Tr sPM R c = ( s + ^ ) r b c + Tr cPM The t r a d i t i o n a l Combination model uses the p o t e n t i a l s a t u r a t i o n d e f i c i t (D z above) measured w i t h i n the s u r f a c e - l a y e r ( r e f e r r e d to as D 0 i n Chapter 3). When the model i s implemented f o r use with a mixed-layer growth scheme, which p r e d i c t s a s a t u r a t i o n d e f i c i t i n the mixed-layer ( i . e . at the r e f e r e n c e h e i g h t ) , the value f o r D z w i l l be r e p l a c e d with t h i s p r e d i c t e d value f o r D, Dra. Chapter 6 presents the development of t h i s mixed-layer growth model. 5.3 Surface Resistances T h i s s e c t i o n presents the p a r a m e t e r i s a t i o n s of the surface r e s i s t a n c e s r e q u i r e d to compute 5.8. I t should be noted t h a t these are s p e c i f i c a l l y r e l a t e d to the implementation of 5.8 i n the suburban area s t u d i e d i n t h i s r e s e a r c h . Nonetheless, the general approach i s t r a n s f e r a b l e to other urban, or suburban areas. 5.3.1 Component Areas Table 5.1 i n d i c a t e s the percent s u r f a c e coverage f o r each of the i n d i v i d u a l s urface types o u t l i n e d above, f i r s t l y on a plan area b a s i s , and secondly as a percentage of the e n t i r e 3-D, a c t i v e s u r f a c e area. The t o t a l area r e f e r r e d t o i s t h a t w i t h i n the f e t c h i . e . the area w i t h i n a c i r c l e -109-with a 2.0 km r a d i u s . The centre i s the Mainwaring tower and the c i r c u l a r area i s r e f e r r e d to as Sunset (Chapter 2). The methods used to c a l c u l a t e these areas are d i s c u s s e d i n Appendix 2. Table 5.1: Percentage a r e a l coverage f o r i n d i v i d u a l s u r f a c e types Surface Type % A r e a l Coverage Plan Area Area (m 2) % A c t i v e Surface Area I.SUBSTRATE a) Greenspace 64 8 042 477 .2 40 I r r i g a t e d 56(70) 7 053 677 .2 3 (SAWET) U n i r r i g a t e d 8(10) 988 800 .0 5 (SADRY) b) Pavement 16(20) 2 010 619 .3 10 (SAIMP) Sub-Total 80 10 053 096 . 5 50 II.BLUFF-BODY Plan Active a) Impervious 20 2 513 274.1 8 796 459. 4 43. 8(88 (CAIMP) Roof 20 2 513 274.1 2 513 274. 1} 12. 6 Walls - - 6 283 185. 3} 31. 2 b) Pervious - _ 1 256 637. 0 6. 2(12 (CADRY) Sub-Total 20 2 513 274.1 10 053 096. 5 50 T O T A L 100 12 566 370.6 20 106 193 100 (1) numbers i n brackets r e f e r to values used i n model using 685 trees/250,000 m2 and r = 2 m y i e l d s 100 m3 accumulated l e a f area/1000 m2 plan area. (2) SAWET r e f e r s to the percentage area (plan) which i s lawn, the model assumes th a t 60% i s greenspace which i s p o t e n t i a l l y i r r i g a t e d . -110-The values f o r W and I i n the above equations are d e r i v e d on the b a s i s of the s u r f a c e a n a l y s i s of the c o n t r i b u t i n g area. Thus, the maximum p o t e n t i a l l y i r r i g a t e d area i s 48% of the t o t a l plan area, which corresponds to 60% of the t o t a l s u b s t r a t e plan area. Note th a t the plan and a c t i v e area f o r the s u b s t r a t e are the same. The area of park, which i s u n i r r i g a t e d , i s 10% of the t o t a l s u b s t r a t e plan area, and the area of pavement i s 20%. The remaining 10%, together with that p o r t i o n of p o t e n t i a l l y i r r i g a t e d s u b s t r a t e which i s not being i r r i g a t e d , i s considered to have s i m i l a r moisture s t a t u s to the u n i r r i g a t e d greenspace component. The p r o p o r t i o n of t h i s area i s c a l c u l a t e d by s u b t r a c t i n g the area i r r i g a t e d from 0.70. 5.3.2 U n i r r i g a t e d S u b s t r a t e The u n i r r i g a t e d greenspace s u r f a c e r e s i s t a n c e ( r c s i n 5.6) i s d e r i v e d from an examination of the l i t e r a t u r e p e r t a i n i n g to the r e l a t i o n s h i p between s o i l moisture (expressed e i t h e r i n volumetric or p o t e n t i a l terms) and surface r e s i s t a n c e . S z e i c z and Long (1969), f o r example present a r e l a t i o n s h i p between " e f f e c t i v e " s u r f a c e r e s i s t a n c e s , d e r i v e d from the PM equation, and s o i l moisture p o t e n t i a l f o r a c l o v e r / g r a s s crop i n Denmark. The s u r f a c e r e s i s t a n c e remained constant a t 26 s m"1 from a minimum moisture d e f i c i t through to -0.35 MPa (= 30 mm d e f i c i t ) , a t which stage i t i n c r e a s e d l i n e a r l y to a value of 500 s m"1 at -1.2 MPa. T h i s can be c o n t r a s t e d to Van Bavel (1967) who f i n d s that the measured s u r f a c e r e s i s t a n c e f o r a l f a l f a a t -12 bars i s 1400 s m" 1 . SW note, based on the work of Fuchs and Tanner (1967) th a t a surface r e s i s t a n c e of 2000 s m~1 corresponds to the r e s i s t a n c e f o r a very dry s o i l , and t h a t 500 s m"1 would be expected f o r dry v e g e t a t i o n . I t i s p o s s i b l e t h a t Van Bavel's s u r f a c e r e s i s t a n c e f o r a l f a l f a i s a combined p l a n t and s o i l r e s i s t a n c e . - I l l -I t i s worth noting that Fuchs and Tanner provide an a l t e r n a t i v e approach to r e l a t i n g r e s i s t a n c e to s o i l moisture. They i l l u s t r a t e t h a t a measured s o i l r e s i s t a n c e ( f o r bare s o i l ) i s e q u i v a l e n t to the r e s i s t a n c e to t r a n s f e r from a wet s o i l , l o c a t e d below a depth of dry s o i l , to the s u r f a c e . For a wet sand, l y i n g below a 1.5 cm dry l a y e r , the surface r e s i s t a n c e equals 2490 s m"1 T h i s concept, while c r i t i c i s e d by many i n the l i t e r a t u r e , i s supported by s e v e r a l e m p i r i c a l s t u d i e s (see Novak and Black, 1985; K e l l i h e r et al., 1986). Such an approach was considered f o r the p a r a m e t e r i s a t i o n scheme f o r the u n i r r i g a t e d greenspace component surface r e s i s t a n c e . However the s e l e c t i o n of an a p p r o p r i a t e depth appeared to be even more a r b i t r a r y than using e m p i r i c a l r e l a t i o n s h i p s t o d e r i v e the s u r f a c e r e s i s t a n c e s from measured s o i l moisture v a l u e s . F i g u r e 5.4 shows the scheme s e l e c t e d to compute the s u b s t r a t e surface r e s i s t a n c e . S o i l moisture was determined g r a v i m e t r i c a l l y (over a depth of 0 - 200 mm) a t a number of u n i r r i g a t e d s i t e s throughout the o b s e r v a t i o n p e r i o d . V olumetric moisture contents are c a l c u l a t e d a t the beginning of the model run, based on an assumed bulk d e n s i t y . Because t h i s value can be a l t e r e d f o r each model run, the s e n s i t i v i t y of the model to e r r o r s i n t h i s assumed bulk d e n s i t y can be shown to be minimal. A value of 1.1 x 10 3 kg m"3 was used. Figure 5.4 i s adapted from Oke (1978) which i s m o d i f i e d from Buckman and Brady (1960). The w i l t i n g p o i n t s and f i e l d c a p a c i t i e s shown are simply averages f o r the c l a y , s i l t loam, and loam s o i l s i l l u s t r a t e d t h e r e i n . The range f o r these values was not l a r g e , t h e r e f o r e the use of a mean should be adequate. The a s s o c i a t e d r e s i s t a n c e values are p r i m a r i l y based on the work of S z e i c z and Long (1969) and other values quoted i n the l i t e r a t u r e as noted p r e v i o u s l y . -112-Figure 5 .4: Relationship between s o i l moisture and unirrigated, substrate resistance component 50 400 800 1200 Hudson Water Use (m3 day- 1) 1600 Figure 5.5: Relationship between substrate a r e a i r r i g a t e d and external water-use at the Hudson s i t e There are three stages of d r y i n g . At volumetric moisture contents g r e a t e r than or equal to f i e l d c a p a c i t y , the surface r e s i s t a n c e decreases from 30 s t r r 1 to 0 s m"1 a t some a r b i t r a r y s a t u r a t i o n p o i n t . Beyond w i l t i n g p o i n t , wherein the p l a n t i s no longer t r a n s p i r i n g f r e e l y , i f a t a l l , the r e s i s t a n c e increases from 500 s m"1 ( a f t e r S z e i c z and Long, 1969 -corresponding to a moisture p o t e n t i a l of -1.2 MPa) to 2000 s m"1 at 0% moisture. Between the w i l t i n g p o i n t and the f i e l d c a p a c i t y l i m i t s , r e s i s t a n c e s vary l i n e a r l y fom 30 to 500 s ro.-1. The e x t r a c t a b l e water content which i n d i c a t e s the a v a i l a b i l i t y of moisture to p l a n t s , i s a l s o i l l u s t r a t e d i n Figure 5.4. Measurements of s o i l moisture p o t e n t i a l were obtained i n 1978 (Oke, 1979b) at a s i t e c o i n c i d e n t with one of the 1986 measurement s i t e s (the cemetery s i t e , Appendix 1). When the v i s u a l appearance of the grass was beyond w i l t i n g p o i n t , p o t e n t i a l s of between -2 and -3 MPa were found to depths of 200 mm, i n agreement with F i g u r e 5.4. T h i s scheme i s c l e a r l y very s i m p l i f i e d , and there i s much d i s c u s s i o n i n the l i t e r a t u r e regarding the i n a p p l i c a b i l i t y of the c l a s s i c a l concepts of s o i l - w a t e r a v a i l a b i l i t y , presented above. The arguments ag a i n s t such an approach are based on the f a c t t h a t concepts such as w i l t i n g - p o i n t , and f i e l d c a p a c i t y take a s t a t i c p e r s p e c t i v e of the soil-plant-atmosphere continuum. As H i l l e l (1971) notes, the system i s a dynamic one, and the w i l t i n g p o i n t , and f i e l d c a p a c i t y should be d e f i n e d i n terms of the p o t e n t i a l flow r a t e s , r a t h e r than s o i l moisture l e v e l s . S i m i l a r l y , i t i s u n l i k e l y that the d r y i n g stage i s a l i n e a r one. C l e a r l y t h i s w i l l depend on f a c t o r s such as the s o i l type, s o i l s t r u c t u r e , i t s s p a t i a l l o c a t i o n , antecedent and m e t e o r o l o g i c a l c o n d i t i o n s . Despite these c r i t i c i s m s , the approach i s used p r i m a r i l y because of i t s semi-physical b a s i s , and s i m p l i c i t y . A p p l i c a t i o n of a more r i g o r o u s s o i l - d r y i n g model would n e c e s s i t a t e much g r e a t e r s p a t i a l and temporal sampling of a g r e a t e r number of v a r i a b l e s than was p o s s i b l e i n the study. This i s not to say that g r e a t e r d e t a i l should not be provided i n the f u t u r e . 5.3.3 I r r i g a t e d Substrate Moisture p o t e n t i a l s measured i n an i r r i g a t e d suburban lawn i n 1978 (Oke, 1979) showed the lawn to be at zero moisture p o t e n t i a l . Hence t h i s s u r f a c e r e s i s t a n c e ( r i f i n 5.6) i s set to the i n t r i n s i c s u r f a c e r e s i s t a n c e (Shuttleworth, 1975) f o r the i r r i g a t e d greenspace component. An a l t e r n a t i v e and e q u a l l y v a l i d approach would have been to set t h i s r e s i s t a n c e to some minimum, but non-zero, stomatal r e s i s t a n c e . T h i s would r e f l e c t the f a c t t h a t even when the s o i l s are s a t u r a t e d , there w i l l s t i l l be some r e s i s t a n c e to the t r a n s f e r of water from w i t h i n the s o i l system to the atmosphere. The t o t a l s urface r e s i s t a n c e f o r the i r r i g a t e d substrate v a r i e s with changes i n the t o t a l area which i s being i r r i g a t e d . The computation of t h i s changing area uses a r e l a t i o n s h i p between measured r e s i d e n t i a l e x t e r n a l water-use (monitored on a d a i l y t o t a l b a s i s a t the Hudson s i t e ) and area i r r i g a t e d . The r e s u l t s of an e x t e n s i v e household survey undertaken by Grimmond (1983) showed that an i n c r e a s e i n the volume of e x t e r n a l water-use corresponds to an i n c r e a s e i n the number and hence area of i r r i g a t e d lawns. To q u a n t i f y t h i s i n c r e a s e i n area corresponding to an i n c r e a s e i n water-use, the data d e r i v e d from a remote-sensing f l i g h t undertaken on August 25, 1985 were used to determine the percentage a r e a l coverage of very moist surfaces ( i . e . r e s i d e n t i a l lawns, and other i r r i g a t e d greenspace such as school p l a y i n g grounds e t c . ) . The area sampled c l o s e l y approximated the Sunset area. I t was found t h a t 25% of the t o t a l plan area was i r r i g a t e d . U n f o r t u n a t e l y , water-use i n 1985 was not monitored, and so a d i r e c t r e l a t i o n s h i p between t h i s i r r i g a t e d area and water-use could not be determined. The Greater Vancouver Water D i s t r i c t maintains records f o r the peak ( d a i l y , weekly, and annual) water-use i n v a r i o u s m e t r o p o l i t a n areas, i n c l u d i n g M e t r o p o l i t a n Vancouver. By comparing the s t a t i s t i c s f o r various years, the f o l l o w i n g comments can be made. F i r s t l y , the peak weekly water-use i n 1986 f o r M e t r o p o l i t a n Vancouver c o i n c i d e d with the d a i l y peak water-use at the Hudson s i t e . Secondly, the peak weekly water-use f o r 1985 was s i m i l a r t o that f o r the week- ending August 4, 1987. From these o b s e r v a t i o n s , the peak weekly water-use f o r M e t r o p o l i t a n Vancouver can be seen to be r e l a t e d to peak d a i l y water-use at the Hudson s i t e . F i n a l l y , the base load f o r the Hudson s i t e i s 162 m3 day" 1, i . e . t h i s i s the i n t e r n a l water-use; and the e q u i v a l e n t approximate base-load f o r M e t r o p o l i t a n Vancouver i s 1890 x 10 6 1 day" 1. These f i g u r e s enable us to estimate an e x t e r n a l water-use a t the Hudson s i t e , f o r the day of the remote-sensing f l i g h t as approximately 700 m3 day" 1 (=*= 100 m3 d a y " 1 ) . This e x t e r n a l water-use of 700 m3 day" 1 corresponds to 25% of the c o n t r i b u t i n g f e t c h area being i r r i g a t e d . I t i s assumed that an e x t e r n a l water-use of zero (where e x t e r n a l water-use i s d e f i n e d as the t o t a l water-use monitored a t the Hudson s i t e , minus the base load) i s e q u i v a l e n t t o 0% i r r i g a t e d ( i . e . the z e r o - i n t e r c e p t ) . The percentage area (of the e n t i r e c o n t r i b u t i n g fetch)/Hudson e x t e r n a l water-use r e l a t i o n s h i p can be developed by assuming a l i n e a r r e l a t i o n s h i p between these two p o i n t s , up to a maximum area i r r i g a t e d at a Hudson water-use of 1100 m3 day" 1. T h i s maximum i s based on the observation from Grimmond's study, that at a c e r t a i n peak water-use, the i n c r e a s i n g percentage of households s p r i n k l i n g reaches a p l a t e a u . Figure 5.5 i l l u s t r a t e s the nature of the r e l a t i o n s h i p between: (a) the area of the c o n t r i b u t i n g f e t c h which i s i r r i g a t e d and (b) the water-use measured at the Hudson s i t e . This area i s then converted to an equ i v a l e n t f r a c t i o n of the s u b s t r a t e t o t a l area. 5.3.4 Impervious Substrate For the c o n d i t i o n s being modelled i n t h i s study, t h i s s urface r e s i s t a n c e ( r s f i n 5.5, 5.6) i s set to 10,000 s m"1. 5.3.5 Pervious Bluff-Body ( r c s ) I n i t i a l l y , a l i t e r a t u r e search was conducted to a s c e r t a i n the range and v a r i a b i l i t y of measured stomatal r e s i s t a n c e s f o r the t r e e species present i n the study area. Korner et al. (1979) summarise measured maximum l e a f conductances i n 246 p l a n t species belonging to 13 m o r p h o l o g i c a l l y comparable p l a n t groups. These data are d e r i v e d from the l i t e r a t u r e , are l i m i t e d t o l e a f measurements only, and are assembled with information r e l a t i n g to s i t e and p l a n t c h a r a c t e r i s t i c s . For evergreen c o n i f e r s the range of l e a f stomatal r e s i s t a n c e s c i t e d are 250 - 530, with a mean of 357 s m _ 1. For evergreen woody p l a n t s , the range i s 200 - 500, with a mean of 250 s m - 1. The range f o r deciduous f r u i t t r e e s i s 160 to 290, and the mean i s 230 s m - 1; or 345 s rrr 1 f o r f i e l d grown f r u i t t r e e s . The f i n a l group of i n t e r e s t i s the deciduous woody p l a n t s , the range f o r t h i s group i s 200 -530 s m _ 1, and the mean i s 330 s r r r 1 . I t should be noted t h a t some extremes were observed i n the evergreen c o n i f e r o u s group, e.g. pines had a range from 140 to 1800 s m - 1; and Douglas f i r and Hemlock were c i t e d as having stomatal r e s i s t a n c e s g r e a t e r than 600 and 440 s m _ 1 r e s p e c t i v e l y . The m a j o r i t y of l a r g e t r e e s i n the study area are deciduous ( e s p e c i a l l y maple, b i r c h ) thus the expected stomatal r e s i s t a n c e f o r these t r e e s would be 400 -600 s r r r 1 . The mean d a i l y value was set to 100 s nr 1 f o r days immediately f o l l l p r e c i p i t a t i o n and increased up to 600 s rrr 1 at the end of the drought. The average value of 350 s m"1 agrees with the mean value (365 s m"1 =*= 100 s m"1) obtained by sampling a range of t r e e s i n the Sunset area over s e v e r a l days (Grimmond, 1988). These values quoted are f o r mean d a i l y l e a f stomatal r e s i s t a n c e s . Stomatal r e s i s t a n c e v a r i e s d i u r n a l l y i n response to the atmospheric p o t e n t i a l s a t u r a t i o n d e f i c i t . A survey of the l i t e r a t u r e e l i c i t e d only one study which provided q u a n t i t a t i v e d e t a i l s as to t h i s behaviour f o r deciduous t r e e s . Verma et al. (1986) found that stomatal r e s i s t a n c e s i n a f u l l y - l e a f e d deciduous f o r e s t e x h i b i t e d a d i u r n a l trend which matches the i n c r e a s i n g p o t e n t i a l s a t u r a t i o n d e f i c i t . The d i u r n a l v a r i a t i o n of l e a f stomatal r e s i s t a n c e i s modelled as a f u n c t i o n of the hour of the day thus y i e l d i n g a c h a r a c t e r i s t i c " s" shape. I t i s l e s s than the assumed mean i n the morning, and i n c r e a s e s l i n e a r l y as a f u n c t i o n of time from s o l a r noon. Of course, the term r c s i s a bulk stomatal r e s i s t a n c e , i . e . averaged f o r the t r e e canopy. In order t o i n c l u d e t h i s i n the model i t was necessar to have a measure of the l e a f area index. Estimates f o r t h i s , based on a survey by Grimmond r e v e a l values from 0.7 - 1.0. For t h i s study a LAI of 1 i s used. 5.4 Aerodynamic R e s i s t a n c e s SW i n c o r p o r a t e three aerodynamic r e s i s t a n c e : r a m , r b s , and r b c . r a m i s the aerodynamic r e s i s t a n c e from the mean canopy flow l e v e l up to the re f e r e n c e height. T h i s i s the r e s i s t a n c e d e r i v e d from the l o g a r i t h m i c wind p r o f i l e with s t a b i l i t y c o r r e c t i o n f a c t o r s and a f u n c t i o n to fo r c e an exp o n e n t i a l decrease i n d i f f u s i v i t y w i t h i n the modelled canopy. The second aerodynamic r e s i s t a n c e i s r b s - the aerodynamic r e s i s t a n c e f o r vapour -118-t r a n s f e r from the s u b s t r a t e to be incorporated i n the mean canopy flow. C l e a r l y , t h i s w i l l not only depend on wind speed, but a l s o on s t r u c t u r a l f e a t u r e s of the suburban canopy, such as b u i l d i n g and t r e e spacing. T h i r d i s the boundary-layer r e s i s t a n c e term ( r b c ) . I t i s very d i f f i c u l t to a s s i g n values f o r t h i s boundary-layer r e s i s t a n c e i n any environment, and e s p e c i a l l y so i n the heterogeneous suburban canopy, t h e r e f o r e the f i r s t p a r t of t h i s d i s c u s s i o n w i l l focus on i t s determination. 5.4.1 Boundary-Layer These r e s i s t a n c e s can be c a l c u l a t e d f o r vegetated canopies using e m p i r i c a l equations d e r i v e d f o r a r t i f i c i a l and r e a l leaves. The boundary-layer r e s i s t a n c e i s r e l a t e d to l e a f dimension, wind speed adjacent to the l e a f , and a s h e l t e r f a c t o r to account f o r the e f f e c t s of mutual i n t e r f e r e n c e between leaves (see Landsberg and Powell, 1973; K e l l i h e r et al., 1986). Another approach i s to consider i t as an excess r e s i s t a n c e . Thorn introduced the excess r e s i s t a n c e parameter B p _ 1 i n 1971. When d i v i d e d by the f r i c t i o n v e l o c i t y , i t i s the d i f f e r e n c e between the bulk aerodynamic r e s i s t a n c e f o r t r a n s f e r of vapour and momentum. For any property such as water vapour or s e n s i b l e heat (other than momentum), t r a n s f e r from the canopy as a whole to the atmosphere must be f a c i l i t a t e d through d i f f u s i o n alone, with 'skin f r i c t i o n ' being the only r e s i s t a n c e . Momentum has an a d d i t i o n a l p a r a l l e l r e s i s t o r , that i s the bl u f f - b o d y f o r c e s which r e s u l t from pressure d i f f e r e n c e s created by flow around o b j e c t s . I f i t i s assumed that the two d i f f u s i v e terms are the same f o r vapour and momentum then the excess r e s i s t a n c e i s simply e q u i v a l e n t to the boundary-layer r e s i s t a n c e t o water vapour t r a n s f e r , m u l t i p l i e d by the f r i c t i o n v e l o c i t y . B a l d o c c h i et al., (1987) a l s o use the excess r e s i s t a n c e -119-to d e r i v e the s i z e of the boundary-layer r e s i s t a n c e . Estimates of the magnitude of Bp" 1 are a v a i l a b l e through some of Thorn's c a l c u l a t i o n s , and from other workers i n the f i e l d of f l u i d dynamics. Thus, i t i s p o s s i b l e to a r r i v e at estimates of i t s magnitude i n the urban environment. G a r r a t t and Hicks (1973) present expected values of B p _ 1 , d e r i v e d from s t u d i e s i n the l i t e r a t u r e . In t h e i r paper, excess r e s i s t a n c e i s r e l a t e d to the roughness Reynolds number. Taking approximate values for suburban t e r r a i n y i e l d s an expected B p _ 1 of 10 - 20, and hence an excess r e s i s t a n c e of 30 - 50 s n r 1 . Using equations from Thorn (1972) and approximate values f o r s h e l t e r f a c t o r s r e s u l t s i n estimates of 12 - 30 s n r 1 . Shuttleworth a l s o develops a formula f o r p r e d i c t i n g the boundary-layer r e s i s t a n c e f o r leaves and y i e l d s t y p i c a l values of 5 - 8 s n r 1 . Given t h i s range a constant value of 20 s n r 1 i s adopted. 5.4.2 Substrate Component and Mean Canopy Flow The computation of these two aerodynamic r e s i s t a n c e s i s based on the assumption t h a t a l o g a r i t h m i c wind p r o f i l e can be extended from the r e f e r e n c e h e i g h t , down through the canopy to the e f f e c t i v e source height. As SW note, the s u b j e c t of within-canopy aerodynamic t r a n s f e r and the e f f e c t of d i f f e r i n g v e g e t a t i o n d e n s i t i e s , i s one of the more c o n t r o v e r s i a l i n the f i e l d of micro- meteorology. The model i n t h i s study adopts the same p e r s p e c t i v e as SW, i . e . t h a t the most simple approach i s employed, and the q u a n t i t a t i v e e f f e c t of t h i s i s examined through the use of s e n s i t i v i t y a n a l y s es. I t should be conceded, that such an approach i s not s t r i c t l y v a l i d g iven the l i m i t a t i o n s to gr a d i e n t d i f f u s i o n theory. For a vegetated canopy with complete cover, the e f f e c t i v e source -120-(assumed to be the l o c a t i o n of the mean canopy air-stream) i s at ( z 0 + d). For a bare s u b s t r a t e , ( z 0 + d) i s small, and hence the source i s almost c o i n c i d e n t with the p h y s i c a l s u r f a c e . For a p a r t i a l v e g e t a t i o n cover, SW assume th a t r b s and r a m vary l i n e a r l y between these two l i m i t s , and that z 0 and d are f i x e d f r a c t i o n s of crop height. Within a c l o s e d canopy, the eddy d i f f u s i v i t y (K c) decreases e x p o n e n t i a l l y with height to the base of the canopy: where K n = eddy d i f f u s i v i t y at the canopy top. n = expone n t i a l c o e f f i c i e n t = 2.5 f o r c l o s e d canopy crop. I n t e g r a t i n g over the height ranges 0 to ( z 0 + d) f o r r b s and ( z Q + d) to z f o r r a m y i e l d s the f o l l o w i n g equations (taken d i r e c t l y from SW) f o r a f u l l canopy: r b s = l n f ( z - d > / 2 o ) ) h t e x P n ~ exp[n*]] (5.10) K c = K h exp [ - n ( l - 2 / h ) ] (5.9) u n(h-d) r a m l n [ ( z - d ) / z 0 ) ] ( l n [ ( z - d ) / h - d ) ] + h e x p ( n * ] - l ] 1 u n(h-d) where h = height of canopy top n* = n ( l - ( d + z 0 ) / h ) and f o r the i n t e r v e n i n g s u b s t r a t e : r b s = l n ( z / z 0 ' ) l n [ ( z 0 + d ) / z 0 ' ] / k 2 u (5.12) r a m = In 2 ( z / z 0 ) / k 2 u - r b s (5.13) where z 0 ' = roughness length f o r s u b s t r a t e Assuming a l i n e a r r e l a t i o n s h i p between these l i m i t s , a weighted -121-f u n c t i o n f o r the a c t u a l aerodynamic r e s i s t a n c e s can be d e r i v e d depending on the r e l a t i v e areas of s u b s t r a t e and b l u f f - b o d y component. Now t h i s methodology has to be t r a n s l a t e d to i n c l u d e the suburban flow regime, and the s t r u c t u r a l c h a r a c t e r i s t i c s of the suburban s u r f a c e . F i r s t l y , i t i s assumed that the b l u f f - b o d y area does not change over the m o d e l l i n g p e r i o d , i . e . l e a f area index i s assumed to remain the same, and hence the r e s i s t a n c e p a r a m e t e r i s a t i o n scheme i s f o r one p a r t i c u l a r roughness element arrangement. Let us c o n s i d e r the p o s s i b l e range of flow regimes. I f the flow i s predominantly of the skimming type, there w i l l be l i t t l e i n t e r a c t i o n between above-canopy flow and within-canopy flow, and the e f f e c t i v e source height w i l l be c l o s e to the canopy top, or roof l e v e l , so ( z 0 + d) = h, r b B becomes la r g e and r a m r e v e r t s to the usual aerodynamic r e s i s t a n c e from h to z. In the a l t e r n a t e l i m i t , with i s o l a t e d flow, ( z 0 + d) i s e f f e c t i v e l y l o c a t e d at the p h y s i c a l s u r f a c e , and thus becomes small, r b s tends towards zero, and r a m now r e f e r s to aerodynamic t r a n s f e r from the s u r f a c e to z. C l e a r l y r b s acts as an i n d i c a t o r of the degree of i n t e r a c t i o n between the two components of flow. A l a r g e s u b s t r a t e r e s i s t a n c e term i n d i c a t e s t h a t any property whose source i s p a r t of the i n t e r v e n i n g s u b s t r a t e w i l l be l e s s l i k e l y to be i n c o r p o r a t e d w i t h i n the mean canopy flow, and t h e r e f o r e to be t r a n s f e r r e d above the canopy to the reference h e i g h t . When the s u b s t r a t e r e s i s t a n c e term i s s m a l l , the a c t u a l substrate a c t s as a s i g n i f i c a n t momentum sink , f a c i l i t a t i n g more e f f i c i e n t t r a n s p o r t from these sources to the r e f e r e n c e h e i g h t . The urban canopy s t r u c t u r e i n the Sunset area i s such t h a t wake i n t e r f e r e n c e flow i s l i k e l y to be predominant, and t h i s i m p l i e s the e f f i c i e n t t r a n s f e r of s c a l a r s from sources w i t h i n the canopy. Note that i t -122-i s p o s s i b l e that t h i s w i l l depend on the d i r e c t i o n of the flow, as the nature of the street/house alignment i s l i k e l y to encourage strong a n i s o t r o p y i n the s u r f a c e d i s t r i b u t i o n of the major b l u f f bodies. With wake-interference flow, both the s u b s t r a t e and bluff-body moisture sources are l i k e l y to p a r t i c i p a t e i n the exchange of moisture from t h i s source to the r e f e r e n c e height. C a l c u l a t i o n of the r e s i s t a n c e s can be performed by using the above equations, p r o v i d i n g t h a t an a p p r o p r i a t e ( z 0 + d) i s used. In order to develop an equation with a weighting, s i m i l a r to t h a t of SW, the height:spacing r a t i o i s used as an i n d i c a t i o n of the 'density' of the 'bluff-body components'. Replacing the l e a f area index i n SW equations with HSR (height to spacing r a t i o ) y i e l d s : r a m = HSR. r a m < a ) + (1-HSR). r a m ( 0 ) (5.14) r b s = HSR. r b s < a ) + (1-HSR). r b s ( 0 ) (5.15) where r a m , r b s ( < * ) = c a l c u l a t e d from equations 5.10, 5.12 r a m , r b s ( 0 ) = c a l c u l a t e d from equations 5.11, 5.13 The d e r i v a t i o n of these r e s i s t a n c e s i s f u r t h e r complicated by the e f f e c t s of s t a b i l i t y . In the a n t i c y c l o n i c c o n d i t i o n s p r e v a i l i n g i n the present study, i t can be shown t h a t f r e e convection i s l i k e l y to be as important as forced, e s p e c i a l l y i n some within-canopy areas. Monteith (1973) provides the f o l l o w i n g formulae to compute the r a t i o of f o r c e d to f r e e convection ( r e a l l y the r a t i o of the Reynolds (Re) to Grashof (Gr) numbers): Gr = 158 d 3 ( T E U r f a c e - T a i r ) Re 2 = ( u . d / f ) 2 (5.16) I t i s recognised t h a t t h i s formula, o r i g i n a l l y developed f o r t u r b u l e n t flow over p l a t e s , may not be a p p r o p r i a t e f o r n a t u r a l convection, with l a r g e heat sources. I t i s used to provide an i n d i c a t i o n of the type of convection dominant i n suburban areas. If the mean length s c a l e of the suburban heat sources i s taken as 10 m (Schmid, pers. comm.) and s u r f a c e to a i r temperature d i f f e r e n c e s of at l e a s t 5°C ( d i f f e r e n c e s of g r e a t e r than t h i s were found by Nakamura and Oke (1988) i n an urban canyon i n Kyoto) r e s u l t s i n r a t i o s of 1 - 4. These can be compared to the lower l i m i t of 16, beyond which t r a n s f e r i s by f r e e convection alone. As a r e s u l t , two important comments can be made. F i r s t l y , because free convection i s an important mechanism of t r a n s f e r , the above assumptions r e l a t i n g to excess r e s i s t a n c e and the e x p o n e n t i a l nature of the d i f f u s i v i t i e s are of second-order importance. Secondly, d i a b a t i c i n f l u e n c e f u n c t i o n s may have to be i n c l u d e d i n the aerodynamic r e s i s t a n c e formulations. However a n a l y s i s of f r i c t i o n v e l o c i t y determined using eddy c o r r e l a t i o n and the l o g a r i t h m i c wind p r o f i l e suggests t h a t these f u n c t i o n s are of second order importance f o r the m a j o r i t y of the model s i m u l a t i o n s . S e l e c t i o n of values f o r n i s d i f f i c u l t f o r the suburban environment, i t i s worth n o t i n g t h a t the value used, n=1.4, y i e l d s a r e d u c t i o n of 50% i n the wind speed observed w i t h i n the canyon, compared to t h a t above the urban canyon. Nakamura and Oke (1988) f i n d that wind speeds are reduced by a f a c t o r of 0.7 f o r an urban canyon i n Kyoto. The height:width r a t i o of the canyon was 1 compared to 0.3 f o r the Sunset s i t e . U n f o r t u n a t e l y , no data e x i s t which r e l a t e the r a t i o of wind speed measured above the urban canopy:wind speed w i t h i n the canopy to the d e n s i t y of the canopy. Therefore the v e l o c i t y r e d u c t i o n f o r a canopy with a height:space r a t i o of 0.3 cannot be assessed. The l i k e l y e r r o r invoked by t h i s assumption can be a s c e r t a i n e d by s e n s i t i v i t y a n a l y s i s , which i s discussed below. -124-5 .5 Implications and Limitations Resulting from Model As sumptions (a) Substrate and Bluff-Body Resistance Framework : I t i s acknowledged t h a t t h i s i s an a r t i f i c i a l framework and t h i s o b v i o u s l y imposes l i m i t a t i o n s on the accuracy of the model. In l i g h t of the complex and heterogeneous canopy t h a t suburbia presents, t h i s type of approach i s a necessary f i r s t step i n addressing the problem of q u a n t i f y i n g the moisture s t a t u s . For i n t e r e s t , F i g u r e 5.6 presents the v a r i a t i o n i n s u b s t r a t e surface r e s i s t a n c e c a l c u l a t e d using the e a r l i e r equation (5.7) f o r a range i n input v a r i a b l e s , i t i l l u s t r a t e s reasonable values over t h i s range which supports the type of approach adopted. F i g u r e 5.6: S e n s i t i v i t y of substrate s u r f a c e r e s i s t a n c e parameters to v a r i a t i o n s i n input parameters (b) Non-Jnteractingr Sub-Components : The a v a i l a b l e energy at any -125-e v a p o r a t i n g source i n the model i s assumed to be the net r a d i a t i o n l e s s the storage heat f l u x and energy co n s e r v a t i o n i s preserved f o r each of the s u b s t r a t e and bluff-body components. Therefore, h o r i z o n t a l i n t e r a c t i o n s are n e g l e c t e d , i . e . l o c a l - s c a l e a d v e c t i o n . V e r t i c a l i n t e r a c t i o n s are included, as s e n s i b l e heat t r a n s f e r from the s u b s t r a t e has been shown to augment the e v a p o r a t i o n from the b l u f f - b o d y elements (5.6). ( c ) Energy P a r t i t i o n i n g : ( i ) In c o n t r a s t to SW, both the bluff-body and s u b s t r a t e are assumed to p a r t i t i o n some of the net r a d i a t i o n i n t o storage, thus the a v a i l a b l e energy f o r the s u b s t r a t e and b l u f f - b o d y component i s (Q*-ZJQS). ( i i ) The a v a i l a b l e energy f o r the bluff-body and s u b s t r a t e components i s p a r t i t i o n e d on the b a s i s of the f r a c t i o n a l area of each, i n c o n t r a s t to SW, who use a Beer's Law e x t i n c t i o n model to compute the net r a d i a t i o n reaching the s u b s t r a t e . The f r a c t i o n a l area approach appears to be more ap p r o p r i a t e i n the context of the b u i l t , suburban environment. Plan, r a t h e r than three-dimensional a c t i v e areas are used ( r e f e r to Table 5.1). The f r a c t i o n a l p l a n area approach p o t e n t i a l l y underestimates the energy i n t e r c e p t e d by the b l u f f body component i n the morning and a f t e r n o o n , as the r e c e i p t by w a l l s i s not accounted f o r . S i m i l a r l y , the s u b s t r a t e r e c e i p t i s p o t e n t i a l l y an overestimate, as no account has been made f o r shading. These p o t e n t i a l e r r o r s may be l e s s s e r i o u s than those a r i s i n g from the assumption t h a t the e n t i r e 3-D volume of the t r e e canopy i s p a r t i c i p a t i n g as an a c t i v e s u r f a c e i n the net r a d i a t i o n exchange. The magnitude of the e r r o r s introduced by these assumptions can be -126-assessed through s e n s i t i v i t y analyses. The model could be improved by l i n k i n g a r a d i a t i o n sub-model to the canopy evaporation model. (d) Precipitation Not Included : T h i s i s not an inherent l i m i t a t i o n i n the canopy evaporation model. I t could be used during p r e c i p i t a t i o n , although small time-steps would be r e q u i r e d to account f o r surface drainage. On the other hand, the boundary-layer growth model i s r e s t r i c t e d to s t a t i o n a r y , c l o u d - f r e e c o n d i t i o n s . (e) Gradient Diffusion Approach Within Canopy : The c r i t i c i s m s of t h i s have been w e l l documented elsewhere (Shaw, 1977; Raupach and Thorn, 1981; L i et al. , 1984; Denmead and Bradley, 1985; Raupach et al., 1986). The f o l l o w i n g s e c t i o n on the r e s u l t s of the s e n s i t i v i t y a n a l y s i s i n d i c a t e the magnitude of probable e r r o r s i n c u r r e d by adopting t h i s approach. Many workers have sought to develop a higher order c l o s u r e model f o r the s i m u l a t i o n of t u r b u l e n t t r a n s f e r w i t h i n the canopy, but such models have not been in c o r p o r a t e d i n the present p a r a m e t e r i s a t i o n of aerodyanmic r e s i s t a n c e s . The use of the t r a d i t i o n a l models of grad i e n t d i f f u s i o n i s o b v i o u s l y a l i m i t a t i o n . ffj Equivalence of Resistances for Neat and Water Vapour : Again, t h i s i s not a l i m i t a t i o n i n the general model but r a t h e r i n the way that i t has been implemented f o r use i n the urban context. fg) Neglect of Q$ : The model does not i n c l u d e the anthropogenic heat f l u x as a source of energy. The measured Q*, and AQS, already i n c o r p o r a t e Q F to some extent, as does the modelled Q E, because i t i n c l u d e s measured temperature. -127-5.6 S e n s i t i v i t y A n a l y s i s : Canopy Evaporation Sub-Model The complex nature of the suburban surface n e c e s s i t a t e s many s i m p l i f y i n g assumptions so as to develop a model which i s u s e f u l , but r e t a i n s as much p h y s i c a l b a s i s as p o s s i b l e . The l i m i t a t i o n s t h a t a r i s e from assumptions mentioned i n the previous s e c t i o n can be evaluated the through s e n s i t i v i t y a n a l y s i s . Table 5.2: F r a c t i o n a l s e n s i t i v i t y o f modelled Q E t o changes i n i n p u t parameters Base Q E = 102 W m - 2 Parameter % Change of Base Q E F r a c t i o n a l S e n s i t i v i t y % Impervious Canopy Area (CAIMP) 88/12 - 50/50 24.8 S o i l Moisture % 20% - 5% 42.4 Hudson Water Use 1300 - 100 m3 day" 1 29.0 Tree Stomatal Resistances 800 - 100 s m"1 20.8 Bulk Density 1.1 - 0.8 26.0 x 10 3 kg m - 3 Slope of Fi g u r e 4.5 0.0236 - 0.1436 31.3 n - c o e f f i c i e n t 2.5 - 0.5 6.6 P a r t i t i o n i n g of A v a i l a b l e Energy 37.3 0.7 W m'2/% 2.9 W m"2/% 2.2 W nr 2/100 m3 day" 1 3.0 W m"2/100 s m"1 3.3 W m"2/100 kg n r 3 258 W m 2 / u n i t change 3.3 W m" 2/unit change 1.0 W m"2/% change -128-sub-model. The wind speed, a v a i l a b l e energy and s a t u r a t i o n d e f i c i t are s p e c i f i e d and the percentage change i n the modelled e v a p o r a t i o n i s c a l c u l a t e d over a range of model parameter va l u e s . The range i s s e l e c t e d both on the b a s i s of the expected v a r i a t i o n s i n magnitude and a l s o to examine the behaviour of the model i n i t s l i m i t s . 5.6.1 S e n s i t i v i t y of Modelled Evaporation To E r r o r s i n Parameterised Terms For t h i s purpose, the e x t e r n a l c o n d i t i o n s were set to t y p i c a l summertime c l e a r - d a y values f o r the suburban environment: u = 3.5 m s " 1 ; A = 300 W r r r 2 ; D 0 = 1.5 kPa. Table 5.2 i l l u s t r a t e s the f r a c t i o n a l s e n s i t i v i t y ( i n W r r r 2 / parameter u n i t ) , and a l s o the t o t a l d i f f e r e n c e as a percentage of the base e v a p o r a t i o n . These r e s u l t s i n d i c a t e that the modelled evaporation i s s e n s i t i v e to changes i n a l l of the v a r i a b l e s i n the surface r e s i s t a n c e p a r a m e t e r i s a t i o n : s o i l moisture percentage, Hudson water-use, area i r r i g a t e d , the stomatal r e s i s t a n c e f o r the t r e e component, bulk d e n s i t y , slope of the equation f o r p r e d i c t i n g area i r r i g a t e d and the p a r t i t i o n i n g of the a v a i l a b l e energy. The model i s performing as expected - the surface r e s i s t a n c e and a v a i l a b l e energy are a l l important c o n t r o l s on evaporation, i n the PM evaporation model. Q E i s not s e n s i t i v e to those v a r i a b l e s i n the aerodynamic r e s i s t a n c e equations (n and r b c ) . In order to assess the i n f l u e n c e of e r r o r s i n determining the surface r e s i s t a n c e s , i t i s necessary to examine the f r a c t i o n a l s e n s i t i v i t y data. The most l i k e l y source of e r r o r i s the slope of the l i n e i n F i g u r e 5.5. The other g r e a t e s t source of e r r o r i s l i k e l y to be the p a r t i t i o n i n g of -129-a v a i l a b l e energy (1 W m 2 / % change). V a r i a t i o n s i n the p r o p o r t i o n of b u i l d i n g s and t r e e s (CAIMP) a l s o leads to a 25% d i f f e r e n c e i n Q E. This i s l i k e l y to be a maximum and e r r o r s a r i s i n g from the methods used to c a l c u l a t e the percentage t r e e s and b u i l d i n g s are l i k e l y to introduce e r r o r s of l e s s than 10 W m~2. 5.6.2 Model Performance under Varying C o n d i t i o n s The e i g h t combinations of the e x t e r n a l l y - s e t parameters are: A v a i l a b l e energy (A) = 100 W m"2 and 400 W rn"2. Wind speed (u) = 0.5 m s _ 1 and 4.5 m s " 1 . P o t e n t i a l s a t u r a t i o n d e f i c i t (D 0) = 0.5 kPa and 2.0 kPa. F i g u r e 5.7 presents the r e s u l t s i n terms of the percentage change i n modelled Q E. In summary, i t i s evident t h a t i n low aerodynamic r e s i s t a n c e cases (given the above e x t e r n a l c o n d i t i o n s , t h i s i s when the mean wind speed i s h i g h ) , changes i n any of the sur f a c e r e s i s t a n c e v a r i a b l e s y i e l d s a co r r e s p o n d i n g l y l a r g e change i n Q E, e.g. a 29% i n c r e a s e i n Q E when the HWU (Hudson water-use) i s inc r e a s e d from 100 to 1300 m3 day" 1. Conversely, when r a r a and r b s terms are high (low wind speeds) v a r i a t i o n s i n those f a c t o r s which i n f l u e n c e the evaporation from the tre e s r e s u l t s i n l a r g e changes i n Q E. T h i s i s because the evaporation from the s u b s t r a t e i s l i m i t e d by the l a r g e r aerodynamic r e s i s t a n c e s . Changing the pr o p o r t i o n s of the bl u f f - b o d y component and substrate f o r the r e c e i p t of a v a i l a b l e energy c l e a r l y i n f l u e n c e s the modelled evaporation r a t e f o r a l l r e s i s t a n c e s . The percentage change i n Q E i s greater f o r a -130-1) 100 II III IV -1 Where : I :u = 0.5ms"1 A = 100Wm' 2 II :u = 0.5ms - 1 A = 400WrrT2 III: u = 4.5ms - 1 A « = 1 0 0 W m ' 2 IV:u = 4.5ms'1 A = 400WnV 2 5 : VPD = 0.5kPa | | 20 : VPD = 2.0kPa CAIMP ( .88/ .12->.50/ .50) 2) 100 3) 100 Soil Moisture % (5% -» 20%) Hudson Water Use (100 -» 1300 m 3 day 1) 4) 100 5) 100 (800 -»» 100 A ) 6) 100 j 1 7) 100 Bulk Density (0.8 - » 1.6g cm"3) I ll III IV cu. m . n (2.5->0.5) Available Energy (80/20 50/50) F i g u r e 5 . 7 : S e n s i t i v i t y of modelled evaporation t o changes i n inpu t parameters -131-lower D 0 , than at l a r g e values of D 0 . This can be i n t e r p r e t e d as f o l l o w s . At low values of D 0 , the evaporation from the bluff-body component i s l i m i t e d by the a v a i l a b l e energy, so i f A i s increased, the b l u f f - b o d y component responds with an i n c r e a s e d Q E. When D 0 i s l a r g e , i t i s the p o t e n t i a l s a t u r a t i o n d e f i c i t which i s d r i v i n g the evaporation, thus i n c r e a s i n g the energy supply to the bluff-body area does not y i e l d e q u a l l y as l a r g e evaporation f l u x e s . The r e f e r e n c e height above the s u r f a c e - l a y e r i s a r b i t r a r i l y s e l e c t e d to be 50 m. The observed p r o f i l e s of temperature and humidity i n d i c a t e that i t s r e a l depth w i l l vary from 30 to 100 m during the day. The major e f f e c t of changing the r e f e r e n c e height i s to a l t e r the aerodynamic r e s i s t a n c e . A change i n the r e f e r e n c e height from 50 m to 100m, and from 50 m to 30 m r e s u l t s i n an 8% change i n the modelled evaporation. I n c r e a s i n g the r e f e r e n c e height r e s u l t s , i n some s i t u a t i o n s , i n an i n c r e a s e d Q E, which i s c o u n t e r - i n t u i t i v e . On c l o s e r examination, i t appears t h a t although the s u b s t r a t e evaporation i s reduced, the bluff-body component produces a l a r g e r evaporative f l u x . A p o s s i b l e i n t e r p r e t a t i o n of t h i s i s t h a t s e n s i b l e heat f l u x from the s u b s t r a t e i s enhancing the bluff-body e v a p o r a t i o n . These r e s u l t s enable us to i d e n t i f y the v a r i a b l e s to which Q E i s most s e n s i t i v e . With high aerodynamic r e s i s t a n c e s and a constant a v a i l a b l e energy, the percentage change i n Q E with a change i n D 0 of 1.5 kPa i s 13.4%; while f o r a smaller aerodynamic r e s i s t a n c e , the e q u i v a l e n t percentage change i s 57.7%. S i m i l a r l y , i n an aerodynamically rough environment the s e n s i t i v i t y t o a 300 W rrr 2 i n c r e a s e i n the a v a i l a b l e energy i s 71%, compared to 117% f o r an aerodynamically smooth environment. T h i s i s i n agreement with the conceptual framework d i s c u s s e d i n Chapter 1. CHAPTER 6: DEVELOPMENT OF SCABLE I I : MIXED-LAYER GROWTH SUB-MODEL 6.1 M o d e l l i n g Convective Boundary-Layers Observations of the d i u r n a l behaviour of the PBL have l e d to the model of an inversion-capped, convectively-dominated boundary-layer p i c t u r e d i n Fig u r e 6.1. From t h i s s i m p l i f i c a t i o n a one dimensional " s l a b " model has been d e r i v e d to simulate both the height and the temperature and humidity budgets of the mixed-layer. The convective PBL i s represented as a well-mixed s l a b of a i r capped by an i n v e r s i o n a l o f t and u n d e r l a i n by a r e l a t i v e l y shallow s u r f a c e - l a y e r where steep g r a d i e n t s of temperature and other s c a l a r s can develop (Figure 6.1). P r o f i l e s of temperature and s p e c i f i c humidity w i t h i n the well-mixed l a y e r are assumed to be independent of height as a r e s u l t of e f f i c i e n t t u r b u l e n t mixing. Above the mixed-layer, there i s a p o t e n t i a l temperature i n v e r s i o n while the g r a d i e n t i n s p e c i f i c humidity i s lap s e . The i n t e r f a c e between the mixed-layer and the s t a b l y s t r a t i f i e d f r e e atmosphere i s represented as a temperature step (A8) i n t h i s zero-order model. The mixed-layer depth evolves d i u r n a l l y i n a p a r a b o l i c manner, as the input of s e n s i b l e heat from the surface leads t o encroachment i n t o the noc t u r n a l i n v e r s i o n . "Plume bombardment" at the base of the capping i n v e r s i o n a l s o leads to the entrainment of warm, dry a i r from a l o f t . An example of the d i u r n a l c y c l e of z^ f o r a c o a s t a l s i t e (Vancouver) i s presented i n Fi g u r e 6.2. z^ reaches i t s maximum a t around noon and d e c l i n e s d u r i n g the afternoon. Observations of the d i u r n a l v a r i a t i o n of z± i n d i c a t e t h a t the t r a n s i t i o n from a convectively-dominated to s t a b l e PBL i s di s c o n t i n u o u s . Thus the con v e c t i v e PBL d e c l i n e s and then appears to -133-\ / 70 m Q or q Figure 6.1: Slab model representation of the PBL 600 400 -2 0 0 -05 ° ° 0 c o o ° o o o o o —r~ 07 — I r— 09 1 1 13 15 17 19 LAT (x 100 hrs) Figure 6.2: An example of the diurnal growth of the mixed-layer, MVC s i t e , Vancouver, JD 213, 1986 -134-c o l l a p s e to form a s t a b l e nocturnal PBL. In the urban environment t h i s d e c l i n e i n zL may d i f f e r as the UBL tends to remain n e u t r a l f o r much of the evening. T h i s t r a n s i t i o n has yet to be s u c c e s s f u l l y modelled. Tennekes (1973b) developed the fundamental s e t of equations, assuming h o r i z o n t a l homogeneity and an absence of l a r g e - s c a l e subsidence, r a d i a t i v e and moisture e f f e c t s ( i . e . a dry, c o n v e c t i v e boundary-layer). The time rate of change of mixed-layer depth ( z i ) i s : d Z j / d t = -HL/A8 (6.1) where HL = kinematic s e n s i b l e heat f l u x a t the i n v e r s i o n base = (vi'6')i Secondly, the time r a t e of change of the temperature step a t the base of the capping i n v e r s i o n {AS) i s : dAS/dt = "tg d z i / d t - d# m/dt ( 6 . 2 ) The term 1Q i s the g r a d i e n t of p o t e n t i a l temperature (B) above the mixed-layer. T h i r d l y , he introduces the volume-averaged budget f o r the mean p o t e n t i a l temperature of the mixed-layer, #m: d<?m/dt = HQ-Hi (6.3) where H 0 = surface kinematic s e n s i b l e heat f l u x = ( w ' 0 ' ) o A s o l u t i o n to these b a s i c three equations r e q u i r e s a formulation f o r the heat f l u x a t the top of the boundary-layer (H^). T h i s i s a downward f l u x b r i n g i n g s e n s i b l e heat i n t o the boundary-layer. I n i t i a l observations -135-suggested that H A was p r o p o r t i o n a l to H 0 (see Carson, 1973; S t u l l , 1976; Caughey and Palmer, 1979; Steyn, 1980 and Raynor and Watson, 1989), where the c o e f f i c i e n t of p r o p o r t i o n a l i t y , c, i s = 0.2. Subsequently the entrainment process has been studied (e.g. Deadorff, 1969) and r e l a t e d t o the budget of t u r b u l e n t k i n e t i c energy (TKE) of the PBL. Driedonks (1982) summarises v a r i o u s parameterisations of the TKE budget and concludes that using a simple encroachment model alone e x p l a i n s 80% of mixed-layer growth. Assuming a c of 0.2 p r e d i c t e d z± without b i a s and a standard d e v i a t i o n of * 125 m. I n c l u d i n g a mechanical entrainment c o r r e c t i o n term improved zL estimates to w i t h i n 80 m. He a l s o found t h a t the use of more complex entrainment models d i d not s u b s t a n t i a l l y improve r e s u l t s and t h a t the accurate p r e d i c t i o n of 0m i s not s e n s i t i v e to the form of the entrainment model. However, Manins (1982) i n d i c a t e s t h a t the simple encroachment model, even when modified to i n c l u d e entrainment v i a p r o p o r t i o n a l ' f l u x - c l o s u r e ' , does not perform w e l l when there i s strong wind shear at the m i x e d - l a y e r / i n v e r s i o n i n t e r f a c e . He uses a number of 's l a b ' models to simulate PBL growth and temperature d e r i v e d from the Wangara experiments and f i n d s t h a t the mixed-layer depth i s over-, and temperature under-, estimated when shear i s present at the i n t e r f a c e . The growth of the boundary-layer f o l l o w i n g a step change i n e i t h e r roughness or temperature has a l s o been i n v e s t i g a t e d . Venkatram (1977) uses the s l a b model to study the dynamics of the i n t e r n a l boundary-layer a s s o c i a t e d with changes i n the s u r f a c e temperature. He solves the equations i n a Lagrangian framework, thus a v o i d i n g the numerical, f i n i t e d i f f e r e n c i n g -136-procedure. He notes t h a t another advantage of the 'slab' model i s t h a t eddy d i f f u s i v i t i e s are not used. Steyn (1980) f o l l o w s the approach of Venkatram, and develops a mixed-layer model to p r e d i c t z i and &m i n a c o a s t a l , urban l o c a t i o n . The t y p i c a l f e a t u r e s of mixed-layer growth are a l t e r e d at such a s i t e . T h i s r e s u l t s from two f a c t o r s : the c l o s e proximity to the coast, and the i n f l u e n c e of the urban land-use. The low mixed-layer depths observed by Steyn a t the Vancouver s i t e r e s u l t s from the h o r i z o n t a l divergence of heat a s s o c i a t e d with a growing i n t e r n a l boundary-layer over the l a n d . In order to i n c o r p o r a t e these e f f e c t s i n t o h i s model of mixed-layer growth he transforms Tennekes' set of equations i n t o a Lagrangian framework. The heat budget of an atmospheric l a y e r as i t i s advected by the mean flow downwind from a l e a d i n g edge ( i n t h i s case a c o a s t l i n e ) i s thus simulated (Steyn and Oke, 1982). The model a l s o i n c o r p o r a t e s both advective i n f l u e n c e s and the e f f e c t s of subsidence (meso-scale and s y n o p t i c - s c a l e ) on the mixed-layer. The d e r i v e d s e t of equations represent the time r a t e of change of mixed-layer p r o p e r t i e s a t a f i x e d d i s t a n c e from the coast. Steyn's model (Steyn and Oke, 1982) i s v e r i f i e d a t two c o a s t a l l o c a t i o n s (Vancouver, B.C. and Nanticoke, O n t a r i o ; Canada). While boundary-layer modellers continued t h e i r analyses and modelling of the dynamics of boundary-layer growth, evaporation modellers were becoming aware of the need to l i n k the PBL and s u r f a c e - l a y e r . B r u t s a e r t and h i s c o l l e a g u e s i n 1977 attempted to model r e g i o n a l evaporation a c r o s s the U.S. using radiosonde ascent data and a surface evaporation model l i n k e d to a PBL model. McNaughton (1976) a l s o suggested using mixed-layer modelling to i n v e s t i g a t e a d v e c t i v e enhancement or suppression upon evaporation. These ideas were f u r t h e r i n v e s t i g a t e d by McNaughton and J a r v i s (1983) who derived an e q u i l i b r i u m evaporation assuming a constant mixed-layer depth. However, i t was de B r u i n (1983) who recognised the p o t e n t i a l of l i n k i n g a mixed-layer growth model to a canopy evaporation model. He i n c o r p o r a t e s both moisture and temperature i n a non-advective boundary-layer growth model based on Tennekes' approach. T h i s i n c l u d e s volume budget equations f o r s p e c i f i c humidity and an equation f o r a step change i n the s p e c i f i c humidity at the top of the mixed-layer. He uses the s u r f a c e energy balance to provide a boundary c o n d i t i o n f o r the s u r f a c e - l a y e r , conserving both mass and energy, de B r u i n then examines both atmospheric and surface-based e f f e c t s on the value of the P r i e s t l e y - T a y l o r a. He assumes p r o p o r t i o n a l c l o s u r e f o r the f l u x of l a t e n t heat at the base of the capping i n v e r s i o n ( Q E i ) which i s a d i r e c t analogy to the s e n s i b l e heat f l u x e s . McNaughton and Spriggs (1986) are c r i t i c a l of t h i s aspect of de Bruin's model and argue t h a t i t i s not necessary s i n c e the s u r f a c e energy balance i s used as a boundary c o n d i t i o n . Therefore t h e i r model i s a more g e n e r a l i s e d form of de Bruin's as i t e l i m i n a t e s the assumption t h a t Q E i i s p r o p o r t i o n a l to Q E a t the s u r f a c e . McNaughton and Spriggs note t h a t t h i s approach p r e d i c t s evaporation very w e l l and t h a t i n c l u d i n g the surface energy balance s u b s t a n t i a l l y improves p r e d i c t i o n s of z^. Conversely, they f i n d t h a t the accuracy of the mixed-layer growth model ( i . e . d z A / d t ) i s not c r u c i a l to the s u c c e s s f u l modelling of the s u r f a c e - l a y e r e v aporation. The model adopted i n t h i s study (SCABLE) i s a combination of the Steyn (1980) advectively-dominated mixed-layer growth model and the McNaughton -138-and Spriggs (1986) mixed-layer growth model which i n c o r p o r a t e s humidity. A p o t e n t i a l s a t u r a t i o n d e f i c i t i n the PBL i s p r e d i c t e d from the p o t e n t i a l temperature and s p e c i f i c humidity: Dm = q*<"rn) " lm • (6-4) where 0m = p o t e n t i a l temperature of the mixed-layer q*(0 m) = s a t u r a t i o n s p e c i f i c humidity a t #m q m = s p e c i f i c humidity of mixed-layer McNaughton (1976) was the f i r s t to d e f i n e the s a t u r a t i o n d e f i c i t i n t h i s way, u s i n g the s a t u r a t i o n vapour pressure at p o t e n t i a l temperature, rather than a t the a c t u a l temperature. T h i s approach y i e l d s values of the p o t e n t i a l 'dryness' of the boundary-layer, or f r e e atmosphere, only i n 3terms of the temperature and humidity that a p a r c e l of a i r would achieve i f bought a d i a b a t i c a l l y down to the s u r f a c e - l a y e r . Thus a s a t u r a t i o n d e f i c i t d e f i n e d i n t h i s way does not r e f e r t o i t s a c t u a l dryness a t that e l e v a t i o n . The s a t u r a t i o n d e f i c i t i s i n c o r p o r a t e d i n t o the a d v e c t i v e term i n the PM canopy evaporation model. T h i s determines the s u r f a c e evaporation, which i n t u r n c o n t r o l s the mixed-layer growth, entrainment, and hence mixed-layer p o t e n t i a l temperature and s p e c i f i c humidity. In t h i s way, a r e g i o n a l e v a p o r a t i o n model i s developed t h a t i n c l u d e s the i n f l u e n c e of l a r g e r s c a l e f o r c i n g . More r e c e n t l y Pan and Mahrt (1987) combined a s o i l evaporation model (Mahrt and Pan, 1984) with a numerical atmospheric boundary-layer model (Troen and Mahrt, 1986) to simulate the e f f e c t of v a r i o u s s o i l types on mixed-layer growth and p o t e n t i a l evaporation r a t e s . These models are among the f i r s t to recognise the p o t e n t i a l importance of c o u p l i n g s u r f a c e - l a y e r exchanges with boundary-layer dynamics, thus p r o v i d i n g f o r the i n t e r a c t i o n and feedbacks between the two. -139-More importantly, a coupled model such as that d e s c r i b e d provides an e f f e c t i v e predictive t o o l . Combination models are o f t e n used to p r e d i c t e v a p o r a t i o n but they are l i m i t e d as t r u l y p r e d i c t i v e models by the need to i n p u t the s a t u r a t i o n d e f i c i t . T h i s i s u s u a l l y determined w i t h i n the s u r f a c e - l a y e r and so i s s t r o n g l y i n f l u e n c e d by t h surface l a t e n t and s e n s i b l e heat fluxes yet p r e d i c t i o n s are o f t e n r e q u i r e d f o r land uses that d i f f e r from that over which measurements have been conducted. These p r e d i c t i o n s could be i n e r r o r because the s a t u r a t i o n d e f i c i t used i s not adjusted to the p r e d i c t e d s u r f a c e type. An important feedback between the s u r f a c e and atmosphere i s being overlooked. Such e r r o r s are q u i t e obvious when p o t e n t i a l evaporation r a t e s are p r e d i c t e d using measurements made over an unsaturated surface. A coupled model (e.g. SCABLE) i s r e q u i r e d i n these s i t u a t i o n s , as i t i s the s a t u r a t i o n d e f i c i t at a r e f e r e n c e height above the s u r f a c e - l a y e r that i s modelled and t h i s subsequently determines the surface l a t e n t heat f l u x . These important i n t e r a c t i o n s between the surface and atmosphere have been encompassed by SCABLE. T h i s d i s c u s s i o n has focussed upon the s l a b model approach to modelling c o n v e c t i v e boundary-layers and a Combination model (Chapter 5) f o r determining the p a r t i t i o n i n g of the t u r b u l e n t surface heat f l u x e s . I t must be recognised that there are many other atmospheric boundary-layer models i n e x i s t e n c e - ranging from simple s u r f a c e energy balance models such as Myrup (1969) (subsequently modified by O u t c a l t (1971)), to three dimensional r e g i o n a l - s c a l e models such as Anthes (1978), those reviewed by P i e l k e (1984) and more r e c e n t l y A v i s s a r (1990). A l l of these models simulate the surface energy balance, and the momentum, temperature and humidity budgets of the PBL. The numerical meso-scale models a l s o p r e d i c t -140-a i r f l o w . Thus the modelling approaches, viewed i n terms of the two separate components i n v o l v e d , are not new. However, the s i g n i f i c a n c e of t h i s approach i s i n the i n t e g r a t i o n of two somewhat d i s p a r a t e s c h o o l s : boundary-layer and micro-meteorogical (Combination) modelling. The former adopt a v a r i e t y of schemes to i n c l u d e the surface boundary, and the input of heat and vapour. The most simple use a s i n g l e value to represent the s u r f a c e moisture a v a i l a b i l i t y and the p a r t i t i o n i n g of the t u r b u l e n t f l u x e s . The more complex (e.g. Deardorff, 1978; McCumber and P i e l k e , 1981) adopt modelling schemes f o r the s o i l and v e g e t a t i o n s u b s t r a t e s a l s o . However the l i m i t a t i o n i n these models i s the p r o v i s i o n of i n i t i a l i nput data p l u s they l i m i t e d i n t h e i r a b i l i t y to parameterise surface heterogeneity. Meanwhile, the Combination modellers invoke complex procedures to p a r t i t i o n the a v a i l a b l e energy but thus f a r have ignored the i n f l u e n c e of meso and s y n o p t i c - s c a l e f o r c i n g . Furthermore t h e i r models are not p r o g n o s t i c , as d i s c u s s e d p r e v i o u s l y . The proposed model seeks to r e s o l v e these d i f f e r e n c e s and thus improve our modelling a b i l i t y by combining the two methodologies. The l a c k of ' r e a l i t y ' i n the land s u r f a c e p a r a m e t e r i s a t i o n schemes has been a major c r i t i c i s m of the l a r g e r s c a l e g l o b a l c i r c u l a t i o n models. In recent times, much res e a r c h has been devoted to improving the s u r f a c e p a r a m e t e r i s a t i o n schemes. One of the most comprehensive i s the Simple Biosphere model (SiB, S e l l e r s et al., 1987) which i n c l u d e s a r e s i s t a n c e framework f o r parameterising the exchange of heat, mass and momentum. T h e i r r e s i s t a n c e framework i s s i m i l a r to t h a t developed i n Chapter 5, i n d i c a t i n g t h a t such an approach can be used i n other, even more complex s i t u a t i o n s . -141-6.2 Model Equations R e c a l l i n g equations 6.1 to 6.3, the temperature budget f o r the PBL y i e l d s an equation f o r the time-dependent change i n 9m: Z i d 0 m / d t = H 0 + (0L-0m) d z i / d t = Ho-Hi (6.5) S i m i l a r l y , a c o n s i d e r a t i o n of the s p e c i f i c humidity budget leads t o : z i d < 3 m / d t = E o + (qi-<3m) d Z i / d t = Eo-Ei (6.6) where H 0, E 0 = t u r b u l e n t s u r f a c e - l a y e r kinematic f l u x e s H i ' E i = kinematic f l u x e s at base of capping i n v e r s i o n q m , # m = s p e c i f i c humidity, p o t e n t i a l temperature i n mixed-layer qL, 6^ = s p e c i f i c humidity, p o t e n t i a l temperature above mixed-layer z^ = height of mixed-layer Note th a t f o r s p e c i f i c humidity the kinematic l a t e n t heat f l u x d e n s i t y i s equal to Q E d i v i d e d by (de n s i t y x l a t e n t heat of v a p o r i s a t i o n ( L v ) ) to give the c o r r e c t u n i t s . The time r a t e of change of the temperature step a t the base of the i n v e r s i o n i s parameterised (from 6.2) as: cUW/dt = 1Q d z ^ d t - d 0 m / d t (6.7) and the corresponding humidity step as: d/iq/dt = T q d Z i / d t - d q m/dt (6.8) where T q = g r a d i e n t of s p e c i f i c humidity above the mixed-layer Iq'^Q a r e (measured) time-dependent inputs The mixed-layer growth equation can be d e r i v e d from (6.5) and modified to i n c l u d e mechanical e f f e c t s on entrainment ( a f t e r Driedonks, 1982): -142-A6 d z ^ d t = Ht + b ( u . ) 3 T ( 6 . 9 ) where b = Driedonk's f a c t o r to in c o r p o r a t e mechanical e f f e c t s i n the growth equations u. = f r i c t i o n v e l o c i t y g = g r a v i t a t i o n a l a c c e l e r a t i o n Although a subsidence v e l o c i t y can be in c l u d e d i n the d z ^ d t equations, i t i s p a r t i c u l a r l y d i f f i c u l t to be determined. I t was cons i d e r e d t o be of second order importance i n the modelling of the s u r f a c e evaporation and thus has not been i n c l u d e d . Q E 0 i s determined using the Combination model presented i n Chapter 5 (Equation 5 . 8 ) : Q E 0 = Cc PMc + Cs PMs ( 6 . 1 0 ) where PMs = [sA B + {C a D m - s r a s A s } / ( r a m + r a s ) ] s + Tf{l + r s P M / ( r a e + r a m ) } Cs = [ 1 + ( R s R a / R c ( R E + R a ) ) J " 1 PMc = [sA c + {C a D m - s r b c A c } / ( r a m + r b c ) ] s + Tf{l + r c P M / ( r b c + r a m ) } Cc = [ 1 + ( R c R a / R s ( R c + R a ) ) I " 1 D m = s a t u r a t i o n d e f i c i t at the ref e r e n c e height (converted from s p e c i f i c humidity d e f i c i t p r e d i c t e d by equations 6 . 5 - 6 . 7 ) using the symbols d e f i n e d i n Chapter 5 . The s u r f a c e s e n s i b l e heat f l u x i s c a l c u l a t e d as a r e s i d u a l from the su r f a c e energy balance: Q * - A 2 S = Q E O + Q H O ( 6 . 1 1 ) - 1 4 3 -The assumed r e l a t i o n s h i p between and the kinematic s e n s i b l e heat f l u x the c l o s u r e assumption: Hi = -c H 0 where c = 0.2 su r f a c e kinematic s e n s i b l e heat f l u x a t the base of the i n v e r s i o n i s termed (6.12) To extend the Steyn (1980) model to i n c l u d e humidity, Steyn (1989) d e f i n e s the l a t e n t heat f l u x a t the i n v e r s i o n base ( Q E i ) as: E i = c q E 0 (6.13) T h i s r e l a t i o n s h i p i s v a l i d i n a zero order entrainment model ( i . e . where temperature and humidity t r a n s i t i o n s a t the base of the capping i n v e r s i o n are represented as a step) with a zero humidity g r a d i e n t i n the mixed-layer. Thus, a l i n e a r p r o f i l e i n evap o r a t i o n throughout the mixed-layer i s assumed. Some ob s e r v a t i o n s (e.g. Mahrt, 1976) i n d i c a t e a small g r a d i e n t i n the mixed-layer s p e c i f i c humidity, however p r o f i l e s measured at the Vancouver study area i n d i c a t e a well-mixed water vapour p r o f i l e . Other s t u d i e s have found values of c q of 0.86*0.34 (Kustas and B r u t s a e r t , 1984) and 0.5 to 1.0 (de B r u i n , 1983). Nonetheless, the c r i t i c i s m s by McNaughton and Spriggs (1986) of a s i m i l a r assumption made by de B r u i n means that (6.13) must be used with care. In p a r t i c u l a r , the model r e s u l t s must always be i n t e r p r e t e d with such c r i t i c i s m s i n mind. Equations (6.5) to (6.13) thus are the b a s i c s e t of equations d e f i n i n g the budgets of s p e c i f i c humidity and p o t e n t i a l temperature i n the mixed-layer. Steyn (1980) (see a l s o Steyn and Oke, 1982 and Steyn, 1989) mo d i f i e s these f o r an advectively-dominated mixed-layer by s u b s t i t u t i n g the -144-m a t e r i a l d i f f e r e n t i a l o perator: D/Dt = d/dt + ud/dx (6.14) f o r d/dt terms. Here x i s the upwind d i s t a n c e to the lea d i n g edge, u i s the mean mixed-layer wind speed (measured) and (6.14) expresses the heat budget of a moving a i r ' s l a b ' . Steyn then uses a G a l i l e a n transformation ( i . e . y=t-u/x) such that D/Dt i s : D/Dt = u d/dy (6.15) T h i s then enables the s p a t i a l component of the mixed-layer equations t o be d e r i v e d . The d i s t a n c e , x, to the coast i s determined using the hourly measured wind d i r e c t i o n , and the mixed-layer wind speed i s approximated by s u r f a c e - l a y e r measurements of u. The d e r i v a t i o n i s not d e t a i l e d here, as i t has been f u l l y e xplained elsewhere (Steyn 1980, 1989 and Steyn and Oke, 1982). The a n a l y s i s y i e l d s the f o l l o w i n g set of equations f o r the time r a t e of change of the mixed-layer depth, humidity and temperature (see a l s o Table 6.1). A l l of the equations f o r z i f 6m and q m comprise a s p a t i a l component where the f e t c h , x, determines the r o l e of advection on the tendency f o r each property: dz±/dt = c H 0 -/[u H 0 (l+2c)] (6.16) Ad V 2 1g x d6m/dt = (1+c) H 0 -/ [u 1Q H 0 (1+c) 2] (6.17) zL V 2(l+2c) x dA9/dt = IQ dzL/dt - dSjdt (6.18) dqm/3t = ( l - c q ) E 0 - hu 1 q E„ ( l - c q ) 2 ] (6.19) Z i ^ 2 ( l - 2 c q ) x dAq/dt = T q d Z i / d t - dqm/a t (6.20) Note that v i r t u a l p o t e n t i a l temperature i s used i n pl a c e of p o t e n t i a l temperature, i n c l u d i n g : v i r t u a l s e n s i b l e heat f l u x , v i r t u a l temperature -145-p r o f i l e s i n the i n v e r s i o n and a v i r t u a l temperature jump at the top of the boundary-layer. Steyn (1989) a l s o d e r i v e s a s o l u t i o n f o r c q from the s p a t i a l p a r t of (6.16) and i t s p a r t n e r (6.21) (below) which express the q u a d r a t i c behaviour of the mixed-layer depth: dzL/dt = c H 0 -/[u H 0 (l+2c)] A9 N/ 2 T Q x v -cd E o - / [ u E o d - 2 c q ) (6.20) Aq J 2 Tfq x Thus, i f : H 0/E 0 = 0' then: c q = 0.5 - [0' 1 q n & ] (c+0.5) (6.21) So c q i s c a l c u l a t e d at each time step using the modelled s u r f a c e l a t e n t and s e n s i b l e heat f l u x e s . Although Steyn argues t h a t (6.21) has no p h y s i c a l b a s i s and a r i s e s from the geometry i n the mixed-layer p r o f i l e s , there i s some p h y s i c a l r a t i o n a l e t o (6.21) i n t h a t 0 expresses the r a t i o of surface heating to evaporation. The s u r f a c e heating term d r i v e s the mixed-layer growth and hence entrainment a t the i n t e r f a c e . Thus, i t seems reasonable to i n c l u d e 0 i n an equation which expresses the upwards entrainment of moisture a t the base of the capping i n v e r s i o n . The g r a d i e n t i n s p e c i f i c humidity i s always negative (at l e a s t i n the present s i m u l a t i o n s ) and 0 i s always g r e a t e r than zero ( i . e . Q H o, Q E o > 0 ) . In h i s d e r i v a t i o n , Steyn combines (6.5) and (6.7) and i n t e g r a t e s -146-d(z^A9) with respect to y which leads to a "zeroth approximation" f o r z i and A6 . Tennekes argues that t h i s holds only i f (l+l/c)»l i . e . the dynamics of entrainment q u i c k l y become independent of the i n i t i a l c o n d i t i o n s . The e q u i v a l e n t requirement f o r humidity, and thus c q , i s that ( l - l / c q ) » l which w i l l never occur. T h i s dependence of Aq upon i t s i n i t i a l value may lead to e r r o r s i n the simulated PBL parameters and Q E. Again, as d i s c u s s e d p r e v i o u s l y , care should be taken i n i n t e r p r e t i n g the model r e s u l t s given these l i m i t a t i o n s . In summary - d e s p i t e the concerns regarding c q , the Steyn model has been t e s t e d and v a l i d a t e d independently of t h i s study (Steyn and Oke, 1982 and Steyn, 1989). These s t u d i e s demonstrated t h a t the a d v e c t i v e model performed w e l l i n s i m u l a t i n g mixed-layer growth, humidity and temperature over a c o a s t a l c i t y (Vancouver) and that advection had a strong i n f l u e n c e upon these mixed-layer p r o p e r t i e s . Therefore the Steyn model i s not only an a p p r o p r i a t e one f o r p r e d i c t i n g the mixed-layer s a t u r a t i o n d e f i c i t , but the only one t h a t i n c o r p o r a t e s an advective i n f l u e n c e . Coupling a s t a t e - o f - t h e - a r t mixed-layer model (accounting f o r the i n f l u e n c e of meso-scale advection) with a canopy evaporation model ( f o r c e d by the modelled s a t u r a t i o n d e f i c i t i n the mixed-layer) has o n l y been attempted by two other s t u d i e s (de B r u i n and McNaughton and S p r i g g s ) . N e i t h e r of these i n c l u d e d a d v e c t i v e e f f e c t s , and none have been a p p l i e d t o the urban boundary and s u r f a c e - l a y e r s - thus the a p p l i c a t i o n i s both new and r e l e v a n t . M o d e l l i n g the urban surface energy balance and the growth of the urban mixed-layer n e c e s s i t a t e s such an approach. Furthermore, t h i s i s the only means of developing a t r u l y p r o g n o s t i c evaporation model. -147-6.3 Model Input Parameters 6.3.1 Data A c q u i s i t i o n : Temperature and Humidity Gradients One of the fundamental parameters i n the mixed-layer model i s the g r a d i e n t of p o t e n t i a l temperature and s p e c i f i c humidity above the mixed-layer. I t i s t h i s g r a d i e n t , together with the magnitude of the 'jump' which determines the thermal and moisture content of the a i r entrained i n t o the mixed-layer. From the tethersonde, temperature and vapour pressure p r o f i l e s are a v a i l a b l e a t 20 min i n t e r v a l s up to heights of ^ =800 m (about 200 m above z i ) . A s i n g l e g r a d i e n t i s d e r i v e d by averaging the d a i l y p r o f i l e s above zL. On those days with airsonde r e l e a s e s , only a s i n g l e p r o f i l e i s a v a i l a b l e -which i s assumed to be r e p r e s e n t a t i v e . However, because the airsonde p r o f i l e i s instantaneous and hence l i k e l y t o be i n f l u e n c e d by i n t e r m i t t e n t plumes, a mean p r o f i l e was sought. Anomalies were r e l a t i v e l y easy to i d e n t i f y , but i t i s p o s s i b l e t h a t the g r a d i e n t s on these days are not as accu r a t e as those d e r i v e d from the tethersonde data. A surrogate data base f o r those days with no tethersonde or airsonde coverage i s obtained from the radiosonde ascents conducted by the Canadian Atmospheric Environment S e r v i c e (AES). These are not re l e a s e d from Vancouver, but from Port Hardy at the northern end of Vancouver I s l a n d . Radiosonde ( s i m i l a r to the airsonde system) ascents are conducted twice d a i l y : a t 1200Z (GMT) and 0000Z (GMT). These times correspond to 0400 LAT and 1600 LAT r e s p e c t i v e l y . These AES data were t r a n s f e r r e d to the UBC Computer and used t o determine the temperature and humidity g r a d i e n t s . I t i s c l e a r that the lower p o r t i o n s (at l e a s t the lower 200-300 m) of -148-295 596 297 296 299 3 0 0 301 302 303 304 305 0( K) F i g u r e 6.3: P o t e n t i a l temperature p r o f i l e comparison between Port Hardy and MVC s i t e s : (a) August 26, 1986 (b) AuguBt 21, 1986 (c) August 22, 1986 0 ( K l -149-August 22, 1986 -150-these p r o f i l e s w i l l be marine i n f l u e n c e d . A comparison of the tethersonde and the Port Hardy p r o f i l e s i n d i c a t e that, while the l a t t e r may be c o o l e r , the a c t u a l p r o f i l e s are q u i t e s i m i l a r . Figures 6.3 ( a ) , (b) and (c) g i v e comparisons, of p o t e n t i a l temperature only, f o r both morning and afternoon f l i g h t s . The afternoon f l i g h t s were almost synchronous, while there i s a 1-2 hour d i f f e r e n c e f o r the morning f l i g h t s . On August 26 (a.m.), T0=O.OO75°C m"1 at Port Hardy and 0.0088°C m"1 at Vancouver, over s i m i l a r height ranges (up to ~600m). Above t h i s , the p r o f i l e s are again s i m i l a r (0.0044°C n r 1 and 0.0036°C m" 1). For the afternoon f l i g h t , 16 a t Port Hardy i s s i m i l a r to the morning values, whereas at Vancouver, i t i s e v i d e n t that 10 above 600 m has changed from 0.0036 to 0.0089 °C m - 1. However, f o r the height i n t e r v a l immediately above zL, "'0=0.0025 °C m"1 which i s c l o s e to t h a t a t Port Hardy. The i n f l u e n c e of t h i s degree of u n c e r t a i n t y on the f i n a l modelled evaporation i s addressed l a t e r . The comparison f o r August 21 and 22 i n d i c a t e s general agreement between the p r o f i l e s obtained a t the two s i t e s , although i t i s c l e a r t h a t u n c e r t a i n t y s t i l l e x i s t s . 6.3.2 I n i t i a l i s a t i o n Data There are 5 other i n p u t s r e q u i r e d to i n i t i a l i s e the model. The i n i t i a l mixed-layer depth, z i 0 , can be obtained from the d i g i t i s e d a c o u s t i c sounder t r a c e s . On those days when the c l a r i t y of the t r a c e s was not s u f f i c i e n t to d e f i n e the mixed-layer r i s e ; e i t h e r the tethersonde data or a constant value of 50 m was used. The i n f l u e n c e of t h i s on the modelled evaporation i s 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 s e c t i o n . The i n i t i a l mixed-layer temperature and humidity can be d e r i v e d from the tethersonde data, or from the measurements made at the Mainwaring s u b s t a t i o n s i t e f o r days on which the tethersonde was not r e l e a s e d . A r e g r e s s i o n a n a l y s i s between the temperature measured a t Mainwaring, and the tethersonde y i e l d e d an RMSE of 0.6°C; r 2=0.85; a slope of 0.87, with an i n t e r c e p t of 2°C. For vapour pressure, a r e g r e s s i o n between the two sets of data r e s u l t e d i n an RMSE of 0.072 kPa; mean d i f f e r e n c e = 0.044 kPa; r 2=0.88; a slope of 1.08, and an i n t e r c e p t of -0.079 kPa. When c o n s i d e r i n g whether the Mainwaring data are an adequate s u b s t i t u t e , i t i s necessary to ap p r e c i a t e the e r r o r s i n both approaches. The accuracy of the wet- and dry-bulb sensors on the tethersonde i s probably l e s s than f o r the instruments on the tower. A l s o , the tower-based measurements are an average f o r 30 min, whereas the tethersonde-based measurements are instantaneous. Given the r e s u l t s from the r e g r e s s i o n a n a l y s i s , f o r temperatures i n the range of 10 - 20°C, the d i f f e r e n c e s w i l l be from -3 to +7%. For vapour pressure, over the range of 1.0 to 2.0 kPa, the e r r o r i s 0.1 to 4.1%. The i n f l u e n c e of these e r r o r s upon the modelled ev a p o r a t i o n i s expected to be small, and i s assessed through the s e n s i t i v i t y a n a l y s i s . The f i n a l two inputs are the humidity and temperature steps at the base of the capping i n v e r s i o n . I t i s p o s s i b l e to use the tethersonde data to d e r i v e these provided the precautions o u t l i n e d by Driedonks (1982) are fo l l o w e d . Steyn (1980, 1989) sets the s i z e of the jump as a constant (0.1 K). However the data r e v e a l A6 values l a r g e r than t h i s , between 1 and 2 K. In t h i s model a l a r g e r value (2 K) i s s e l e c t e d f o r the i n i t i a l AO. The numerical s o l u t i o n then provides an e q u i l i b r i u m value as the model i s stepped through time ( u s u a l l y w i t h i n 1 model hour). -152-6.4 S e n s i t i v i t y A n a l y s i s : Mixed-Layer Growth Sub-Model The s e n s i t i v i t y of the modelled evaporation to the f i v e inputs f o r the mixed-layer growth component i s assessed by running the model, f i r s t l y with a base data set (using the input data f o r J.D. 201) then v a r y i n g each parameter, while holding the others constant. The f i v e input values are the i n i t i a l mixed-layer depth, the temperature and humidity steps at the base of the capping i n v e r s i o n , and the s t r e n g t h of the s p e c i f i c humidity g r a d i e n t , and the temperature i n v e r s i o n above the PBL. The s e n s i t i v i t y of the d a i l y mean l a t e n t heat f l u x to the v a r i a t i o n i n the temperature and humidity p r o f i l e s i s demonstrated i n Figure 6.4. I t i s e v i d e n t t h a t changes i n 10 are the most important of the mixed-layer v a r i a b l e s i n determining the modelled e v a p o r a t i o n . T h i s r e f l e c t s the importance of temperature i n the s a t u r a t i o n d e f i c i t term and i t s r o l e i n d r i v i n g the s u r f a c e evaporation. The f r a c t i o n a l s e n s i t i v i t y f o r AO i s 4.13 W m"2/1.0 K (Figure 6.5) a l s o showing the importance of temperature i n m o d e l l i n g evaporation. The s e n s i t i v i t y to T i s s m a l l e r , except f o r very l a r g e p e r t u r b a t i o n s . There i s no s i g n i f i c a n t s e n s i t i v i t y of Q E to Aq, which i s encouraging given the d i s c u s s i o n of the v a l i d i t y of (6.21). I t i s worth comparing these r e s u l t s with those of McNaughton and S p r i g g s . They f i n d t h a t decreasing the s t a b i l i t y i n the capping i n v e r s i o n ( i . e . i n c r e a s i n g 10) enhances the downward t r a n s p o r t of warmer and d r i e r a i r i n t o the mixed-layer. T h i s i n c r e a s e s D m l e a d i n g t o an i n c r e a s e i n Q E p r o v i d i n g t h a t the s u r f a c e r e s i s t a n c e i s not too l a r g e . Hence t h e i r r e s u l t s q u a l i t a t i v e l y agree with the f i n d i n g s here. However, they note a smaller s e n s i t i v i t y of Q E to 10 than found here. T h i s s e n s i t i v i t y i s dependent upon the degree of t u r b u l e n t mixing (Cleugh, 1990), i n p a r t i c u l a r i t depends on -153-Figure 6.4: S e n s i t i v i t y of modelled latent heat flux to gradients (above mixed-layer) in potential temperature and humidity -154--155-ft, i . e . the r a t i o of aerodynamic and surface r e s i s t a n c e s . The p r e s c r i b e d f o r c i n g used low values of both r a and r B (50 s m"1 and 150 s rn"1) r e s p e c t i v e l y . T h i s e x p l a i n s the l a r g e s e n s i t i v i t y of Q E to 19, i n agreement with McNaughton and Spriggs. In terms of the importance of the i n i t i a l i s a t i o n data i n p u t s - i t i s c l e a r t h a t the temperature gr a d i e n t i n the capping i n v e r s i o n and the temperature jump are important i n terms of model performance. M o d e l l i n g e r r o r s c o u l d t h e r e f o r e a r i s e from the s e l e c t i o n of an i n i t i a l temperature p r o f i l e from the Port Hardy s i t e . Many s i t e s ( l i k e Vancouver, B.C.) w i l l not have access to r e g u l a r , twice d a i l y radiosonde ascents, thus a t t e n t i o n should be d i r e c t e d towards examining the nature of the s p a t i a l and temporal s c a l e s of v a r i a b i l i t y a s s o c i a t e d with the g r a d i e n t s of temperature i n the capping i n v e r s i o n , p r e f e r a b l y under a v a r i e t y of c o n d i t i o n s . Given t h a t the p o t e n t i a l temperature p r o f i l e appears to be more important, p o s s i b l y s t a t i o n s which r e l e a s e minisondes (sensing temperature and pressure only) c o u l d be used and the data from other s t a t i o n s used f o r the humidity p r o f i l e . Modelled evaporation i s not s e n s i t i v e to changes i n the i n i t i a l mixed-layer depth from 0 to 100 m. The a c t u a l depth of the boundary-layer has l i t t l e i n f l u e n c e on D 0, and hence evaporation. I t i s dz^/dt t h a t determines entrainment and D m - i n i t i a l depth s e l e c t e d w i l l not a l t e r t h i s entrainment process. -156-6-5 Int e g r a t e d SCABLE Inputs f o r SCABLE are: measured hourly net r a d i a t i o n and parameterised storage heat f l u x e s , measured wind speeds and d i r e c t i o n s ( h o u r l y ) . A d a i l y v a l u e f o r water-use, s o i l moisture and stomatal r e s i s t a n c e i s s p e c i f i e d (see Chapter 5). I n i t i a l &m, q m , 7 q and IB are d e r i v e d from surface-based, radiosonde or tethersonde p r o f i l e s as d e s c r i b e d above. A l l of the input s u r f a c e values are l i n e a r l y i n t e r p o l a t e d t o ten six-minute values f o r each hour. T h i s avoids numerical i n s t a b i l i t y when the set of d i f f e r e n t i a l equations which d e s c r i b e the mixed-layer dynamics are s o l v e d . I n i t i a l l y o nly e a r l y morning values f o r the temperature and humidity p r o f i l e s i n the capping i n v e r s i o n were used. F o l l o w i n g Steyn (1980), the numeric s o l u t i o n t o the mixed-layer equations i s obtained using the L i b r a r y r o u t i n e D.E. provided by the UBC Computing Centre. -157-Table 6.1: Model equations (a) Equations: (1) d Z i / 3 t = c H n - f [ u H n (l+2c)] ' AB I 2 18 x (2) aem/dt = (i+c) H n -/[u ie H n g + c ) 2 ] 2(l+2c) x (3) dA8/dt = IB dZi/dt - d6m/dt (4) 3 q m/dt = ( l - c q ) E 0 -/[u T Q E 0 ( l - c q ) 2 ] Z i J 2 ( l - 2 c q ) x (5) dAq/dt = T q d z . / 3 t - 3 q m / 3 t (6) E 0 = Q E 0/ ( P L v ) Q E 0 = d e f i n e d i n Eqn. 5.8 (7) H 0 = Q/-A2S-QEO (8) c q = 0.5 - 0'1q/1B (c+0.5) (b) I n i t i a l C o n d i t i o n s and Measured F o r c i n g Parameters: z A , < Z m , 8 m , A 8 , A q , 1 6 , 1 ^ : a l l measured inputs provided a t model i n i t i a t i o n Q*, AQB, U, surface and aerodynamic r e s i s t a n c e s : i n t e r p o l a t e d t o 10-minute values which are inp u t a t each model time-step -158-CHAPTER 7: PERFORMANCE AND EVALUATION OF SCABLE The temporal v a r i a t i o n of the suburban surface energy balance components and t h e i r r e l a t i o n s h i p t o mixed-layer temperature and humidity was d i s c u s s e d i n Chapter 4. The f o l l o w i n g chapter addresses the r e s u l t s of modelling these f e a t u r e s using the model (SCABLE) developed i n the preceding two chapters. I t s performance i s assessed by both a s t a t i s t i c a l and d e s c r i p t i v e comparison with measured data. The SCABLE model comprises two major components - a mixed-layer sub-model and a canopy ev a p o r a t i o n sub-model - to p r e d i c t evaporation from the suburban canopy. As suggested by the preceding chapters the two sub-models were developed independently of each other. The s e n s i t i v i t y a n a l y s i s presented i n Chapter 5 i l l u s t r a t e d the behaviour of the canopy evaporation sub-model alone. The boundary-layer growth model has been t e s t e d as a stand-alone model u s i n g measured s e n s i b l e heat f l u x e s as a time-dependent input (Steyn, 1980; Steyn and Oke, 1982) and both s e n s i b l e and l a t e n t heat f l u x e s as i n p u t (Steyn, 1989). The f o l l o w i n g chapter evaluates the performance of the coupled model to p r e d i c t a r e a l e v a poration. Observations from f o r t y days (between J.D. 199 and 246) were s e l e c t e d t o p r o v i d e t e s t data. T h i s i n t e r v a l c o i n c i d e s with both the prolonged d r y i n g p e r i o d d i s c u s s e d i n Chapter 4 and the i n t e n s i v e measurement p e r i o d . The remaining seven days were excluded due to the i n a p p l i c a b i l i t y of the modelling approach under the m e t e o r o l o g i c a l c o n d i t i o n s . The d e f i n i t i o n of day length i s determined by the model because a negative s e n s i b l e heat f l u x r e s u l t s i n numerical e r r o r s - thus the model t y p i c a l l y runs from 0600 to 1800 LAT. The measured data are f o r the same i n t e r v a l - corresponding c l o s e l y to d a y l i g h t hours. 7.1 Diurnal Performance of SCABLE Although i t i s the day-to-day v a r i a b i l i t y of the s u r f a c e evaporation r a t e which i s of most i n t e r e s t i n t h i s r esearch, the hourly performance i s a l s o an i n d i c a t o r of the model's strengths and weaknesses. A s e l e c t i o n of e i g h t case-study days are i n c l u d e d f o r d i s c u s s i o n . They represent a range of r a d i a t i o n , s u r f a c e moisture and s y n o p t i c regimes - and a l s o model performance. The measured a v a i l a b l e energy and modelled s u r f a c e l a t e n t heat f l u x are i l l u s t r a t e d together with p l o t s of the modelled mixed-layer (D m) and measured s u r f a c e - l a y e r s a t u r a t i o n d e f i c i t s ( D 0 ) . These are converted to vapour pressures to be compatible with the measured data. When a v a i l a b l e the measured mixed-layer s a t u r a t i o n d e f i c i t (D m) i s a l s o p l o t t e d . The r e s u l t s are i n t e r p r e t e d and summarised a t the end of t h i s s e c t i o n . J.D. 201 (Figure 7.1): T h i s day represents a n t i c y c l o n i c c o n d i t i o n s with w e s t e r l y flow and low s u r f a c e r e s i s t a n c e s . The agreement between measured and modelled e v a p o r a t i o n i s e x c e l l e n t , even on an hourly b a s i s . The modelled mixed-layer s a t u r a t i o n d e f i c i t does not e x h i b i t the l a t e afternoon peak seen i n the s u r f a c e - l a y e r . The lower Q E would c o n t r i b u t e t o the l a r g e r s u r f a c e s a t u r a t i o n d e f i c i t The modelled humidity i n d i c a t e s continued accumulation of moisture i n the mixed-layer, but the temperature of the mixed-layer and the moisture a v a i l a b i l i t y at the s u r f a c e ensure a r e l a t i v e l y l a r g e f l u x of l a t e n t heat. The s l i g h t asymmetry i n the -160-Note: " values are modelled, others are measured 800 1200 .1600 Time (LAT) 800 1200 1600 Time (LAT) Figure 7.2: Diurnal variation, for J.D. 203, of: (a) Energy balance components (b) Saturation d e f i c i t :D„ - surface-layer :Dm - mixed-layer Note: " values are modelled, others are measured -161-comparison between measured and modelled Q E evident i n Figure 7.1 (measured Q E > modelled Q E i n the morning, and v i c e versa i n the afternoon) i s c h a r a c t e r i s t i c of the model performance under a n t i c y c l o n i c s i t u a t i o n s . J.D. 203 (Figure 7.2): T h i s day i s c h a r a c t e r i s e d by e a r l y morning low c l o u d . The mixed-layer model should not work p a r t i c u l a r l y w e l l i n these s i t u a t i o n s . The o v e r a l l agreement i s adequate, although the presence of cl o u d i n the morning hours ( r e s u l t i n g i n a higher humidity and a low s a t u r a t i o n d e f i c i t ) i s o b v i o u s l y not simulated and leads to a poorer hourly performance. The a v a i l a b l e energy appears t o be the major i n f l u e n c e on both the s a t u r a t i o n d e f i c i t as r e f l e c t e d by both the modelled and measured Q E. J.D. 212 (Figure 7.3): Despite c o n s i d e r a b l e v a r i a t i o n i n measured Q E, the model performs q u i t e w e l l and p r e d i c t s a decrease i n evaporation from the previous day (due to lower a v a i l a b l e energy and mixed-layer s a t u r a t i o n d e f i c i t ) . I n t e r m i t t e n t c l o u d cover i n the morning l e d to v a r i a t i o n s i n measured Q E. E a s t e r l y flow i n the mixed-layer r e s u l t s i n a slow i n c r e a s e (both measured and modelled) i n the s a t u r a t i o n d e f i c i t . The modelled zL i s suppressed, which i s not i n agreement with the tethersonde measurements (see S e c t i o n 7.2 ( a ) ) . The modelled vapour p r e s s u r e (mean d a i l y = 1.36 kPa) i s i n c l o s e agreement with t h a t measured (mean d a i l y = 1.33 kPa) from the tethersonde p r o f i l e s ; as are the mean temperatures (290.9 K compared t o 291.3 K). Although the modelled D m i s l e s s than the measured D m ( p a r t i c u l a r l y i n the a f t e r n o o n ) , the p r e d i c t e d e v a p o r a t i o n a c t u a l l y overestimates t h a t measured. J.D. 213 (Figure 7 . 4 ) : The d a i l y average l a t e n t heat f l u x e s are i n F i g u r e 7 .3: D i u r n a l v a r i a t i o n , f o r J.D. 212, o f : (a) Energy balance components (b) S a t u r a t i o n d e f i c i t :D0 - s u r f a c e - l a y e r :Dm - mixed-layer Note: v a l u e s are modelled, others are measured e >i 500 400 -300 & 200 100 -800 1200 Time (LAT) 1600 800 1200 1600 Time (LAT) F i g u r e 7.4: D i u r n a l v a r i a t i o n , f o r J.D. 213, o f : (a) Energy balance components (b) S a t u r a t i o n d e f i c i t :D0 - s u r f a c e - l a y e r :Dm - mixed-layer Note: " v a l u e s are modelled, others are measured 800 1200 1600 Time (LAT) 800 1200 1600 Time (LAT) - 1 6 3 -e x c e l l e n t agreement. The boundary-layer i s both more moist and warmer than the previous day and the s a t u r a t i o n d e f i c i t i s enhanced. The same p a t t e r n i n the d i u r n a l trend f o r the s a t u r a t i o n d e f i c i t noted f o r J.D. 201 i s e v i d e n t . Both the maximum mixed-layer humidity and temperature are s l i g h t l y underestimated by the model, as compared to the tethersonde-derived measurements. On the other hand the mean humidity and p o t e n t i a l temperature are s l i g h t l y overestimated, l e a d i n g to a higher s a t u r a t i o n d e f i c i t and evaporation r a t e . Again, the c o n t r a d i c t i o n between the within-day v a r i a t i o n of s a t u r a t i o n d e f i c i t and modelled Q E observed f o r J.D. 212 i s e v i d e n t . J.D. 214 (Figure 7.5): The model performs w e l l i n e s t i m a t i n g the d a i l y average evaporation. The humidity (modelled and measured) has i n c r e a s e d y i e l d i n g a s l i g h t l y lower s a t u r a t i o n d e f i c i t , e s p e c i a l l y i n the morning. The modelled zL i s about 60 m lower than the maximum measured z A . The modelled s a t u r a t i o n d e f i c i t appears to simulate the hour-to-hour v a r i a t i o n more s u c c e s s f u l l y than on previous days even though the s y n o p t i c regime was s i m i l a r . J.D. 214 and 213 d i f f e r i n t h e i r r e c e i p t of a v a i l a b l e energy i n the morning, due to c l o u d . In f a c t , J.D. 212 and 214 are s i m i l a r i n t h i s r e s p e c t . The c o o l e r , s l i g h t l y more cloudy, morning slows the i n c r e a s e of the s a t u r a t i o n d e f i c i t and leads to b e t t e r agreement between the observed and p r e d i c t e d v a l u e s . T h i s i s i n c o n t r a s t t o J.D. 199, 201 and 213. J.D. 215 (Figure 7.6): The agreement up to 1000 LAT i s good. However, measured Q E drops o f f f o r the remainder of the day and t h i s t r e n d i s not modelled w e l l . Both the measured s u r f a c e - l a y e r and modelled mixed-layer s a t u r a t i o n d e f i c i t s are suppressed compared to the previous day. In response to the reduced Dro, the maximum l a t e n t heat f l u x i s s m a l l e r than on -164-F i g u r e 7.5: D i u r n a l v a r i a t i o n , f o r J.D. 214, o f : (a) Energy balance components (b) S a t u r a t i o n d e f i c i t :D0 - s u r f a c e - l a y e r :Dm - mixed-layer Note: ' values are modelled, others are measured F i g u r e 7.6: D i u r n a l v a r i a t i o n , f o r J.D. 215, o f : (a) Energy balance components (b) S a t u r a t i o n d e f i c i t :D0 - s u r f a c e - l a y e r :Dm - mixed-layer Note: " values are modelled, others are measured -165-J.D. 214. The average modelled Q E, however, i s g r e a t e r . T h i s leads to a poor s i m u l a t i o n of the evaporation i n terms of both the day-to-day and within-day v a r i a b i l i t y . In t h i s case, the model does not appear to have s u f f i c i e n t s e n s i t i v i t y t o the suppressed s a t u r a t i o n d e f i c i t . J.D. 224 (Figure 7.7): The r e l a t i v e l y low l a t e n t heat f l u x i s modelled w e l l . Although the lowered evaporation must, i n p a r t , be due to the decrease i n a v a i l a b l e energy, i t i s the c o o l e r mixed-layer ( e s p e c i a l l y up to 1400 LAT) that r e s u l t s i n a decrease i n the s a t u r a t i o n d e f i c i t (as evidenced by both the s u r f a c e - l a y e r measured and the mixed-layer modelled values) and thus some of the d r i v i n g f o r c e c o n t r o l l i n g evaporation. As d i s c u s s e d i n Chapter 4 the preceding days were ov e r c a s t (J.D. 222 and 223) because the o f f s h o r e p o s i t i o n of the r i d g e c r e a t e d a pressure gr a d i e n t which drew c o n s i d e r a b l e marine a i r over the Vancouver area. Accompanying these o v e r c a s t days were s o u t h - e a s t e r l y winds a t the s u r f a c e and suppressed l a t e n t heat f l u x e s . The humidity on J.D. 224 t h e r e f o r e i s r e l a t i v e l y low and i t i s the reduced temperature of the mixed-layer that leads to a lower s a t u r a t i o n d e f i c i t . T h i s day i s s i m i l a r t o J.D. 204 and J.D. 203, although the a v a i l a b l e energy i s s l i g h t l y higher. The flow i s from the SE i n the morning, s h i f t i n g through S to SSW i n the afternoon. The f e t c h i n the morning hours would t h e r e f o r e not be over urban, but a mixture of a g r i c u l t u r a l and suburban land-uses. In a d d i t i o n , the d i s t a n c e to the c o a s t l i n e may be g r e a t e r . J.D. 226 (Figure 7.8): The pronounced d e c l i n e i n Q E i n the afternoon hours i s not p r e d i c t e d . The model does p r e d i c t the trend but not the s i z e of a decreased l a t e n t heat f l u x from the previous day. The modelled -166-800 1200 1600 Time (LAT) 800 1200 1600 Time (LAT) Figure 7.7: Diurnal variation, for J.D. 224, of: (a) Energy balance components (b) Saturation d e f i c i t :D0 - surface-layer :Dm - mixed-layer Note: " values are modelled, others are measured e s 800 1200 1600 Time (LAT) Z 1 8 ° 16 O % 12 a I 1 0 2 8 n 4 L c © 2 -o o . Do Dm x x , . x'x 800 1200 1600 Time (LAT) Figure 7.8: Diurnal variation, for J.D. 226, of: (a) Energy balance components (b) Saturation d e f i c i t :D0 - surface-layer :Dm - mixed-layer Note: ~ values are modelled, others are measured -167-mixed-layer s a t u r a t i o n d e f i c i t i s n o t i c e a b l y suppressed, i n agreement with the measurements d e r i v e d from the tethersonde p r o f i l e s . T h i s i s a r e s u l t of continued high humidity and a c o o l e r boundary-layer. The mean modelled and measured mixed-layer temperatures and s a t u r a t i o n d e f i c i t s agree w e l l , although the measured i n c r e a s e i n D m i n the afternoon i s not p r e d i c t e d by the model. T h i s g r e a t e r s a t u r a t i o n d e f i c i t i n the afternoon i s p o s s i b l y due to the development of N/NW flow and thus a smaller but more urban f e t c h . T h i s p a r t i c u l a r s e t of c o n d i t i o n s i s s i m i l a r to t h a t on J.D. 204 and 224, where s i m i l a r l y low evaporation r a t e s were measured and modelled but a v a i l a b l e energy i s g r e a t e r , and the e a s t e r l y flow does not extend to the s u r f a c e - l a y e r on J.D. 226. Summary The within-day performance of the model i s adequate f o r some days but i s poor on o t h e r s . A c o n s i s t e n t f e a t u r e i s the a b i l i t y of the model to p r e d i c t Q E i n the morning but i t s i n a b i l i t y i n the afternoon. Under c l o u d l e s s , a n t i c y c l o n i c c o n d i t i o n s the model appears t o overestimate Q E and underestimate D m i n the afternoon. T h i s i s of i n t e r e s t given the a n a l y s i s of the hourly v a r i a t i o n of the suburban energy balance (Chapter 4) where i t was shown t h a t , on an hourly basis, the enhanced ( s u r f a c e - l a y e r ) s a t u r a t i o n d e f i c i t i n the mid-afternoon was not a s s o c i a t e d with a corresponding i n c r e a s e i n Q E, as might be expected. C l e a r l y there i s a feedback e f f e c t , e s p e c i a l l y between near-surface s a t u r a t i o n d e f i c i t and s u r f a c e Q E. The lower Q E i n the mid to l a t e afternoon c o u l d almost c e r t a i n l y be expected to y i e l d a l a r g e D Q, p a r t i c u l a r l y as the s e n s i b l e heating and a i r temperature i n c r e a s e . T h i s feedback should be reduced f o r D m (Chapters 1 - 3 ) , but c l e a r l y i t s t i l l e x i s t s . -168-Two f u r t h e r reasons f o r d i s c r e p a n c i e s i n the afternoon p e r i o d were proposed: s u r f a c e r e s i s t a n c e s and the separation of sources f o r s e n s i b l e and l a t e n t heat. The afternoon in c r e a s e i n s u r f a c e r e s i s t a n c e i n response to the s a t u r a t i o n d e f i c i t i s i n c l u d e d but i t s s e n s i t i v i t y must be i n c r e a s e d . The second reason r e q u i r e s a great deal more p h y s i c a l i n s i g h t -at present i t would be d i f f i c u l t to p h y s i c a l l y model such an i n f l u e n c e . To e v a l u a t e the a b i l i t y of the model to simulate the hourly v a r i a t i o n of Q E i t i s important to recognise that the c l o s e l y - c o u p l e d nature of Q E and D m ( r e c a l l the s i z e of O) means that each term i s s e n s i t i v e t o e r r o r s i n the o t h e r s . Our understanding of the nature of t u r b u l e n t t r a n s p o r t processes i n the h i g h l y unstable suburban canopy and s u r f a c e l a y e r s (Chapter 4) i s l i m i t e d . Thus, the improved performance i n the morning hours suggests t h a t the model performs adequately under conditions for which it was developed i . e . mixed convective and mechanical turbulence. S i m i l a r l y the mixed-layer sub-model i s not developed f o r cloudy boundary-layers. On cloudy days, such as J.D. 203, the modelled s a t u r a t i o n d e f i c i t and l a t e n t heat f l u x are overestimated. The d i u r n a l c o r r e l a t i o n between measured and modelled D m r e v e a l s a second flaw i n the model: the hourly v a r i a t i o n of mixed-layer p o t e n t i a l temperature. W h i l s t the d a i l y mean D m i s simulated w e l l (see next s e c t i o n ) , the d i u r n a l trend i s not. Rather than p r e d i c t i n g an almost l i n e a r increase i n p o t e n t i a l temperature, the modelled values r i s e q u i c k l y and then slowly i n c r e a s e to a peak at ca. 1400 LAT. -169-Table 7.1: Measured and modelled maximum mixed-layer temperatures, vapour pressures and depths J . D . e m (max) 8(max) (max) Mode (x 10 - 1 kPa) (K) (m ) P 0 P 0 P o 212 13 7 14 .9 292 1 294 7 406 597 TS 213 16 0 15.6 295 6 299 0 510 598 TS 214 17 6 18 .0 296 1 298 3 391 457 TS 226 19 0 17.3 293 8 294 5 477 497 TS 228 13 9 12.2 291 1 296 562 510 A S / J O 229 13 6 14.2 293 8 296 652 520 A S / J O 231 14 6 13.8 288 9 293 7 678 471 TS 232 14 0 10.9 293 0 300 0 617 400 AS 233 15 0 14.5 293 6 296 8 548 517 TS 234 14 8 14.6 294 7 296 4 567 442 TS 238 17 7 16.5 298 7 299 0 445 360 TS 239 15 6 14 .0 297 4 304 0 810 480 AS 243 14 6 14.9 293 9 293 2 614 625 AS 244 13 9 15.0 293 6 295 629 900 AS 245 18 6 16.5 294 9 295 579 650 AS 246 17 1 14 .0 292 4 297 740 500 AS N o t e : P = . . p r e d i c t e d ; O = o b s e r v e d TS = t e t h e r s o n d e ; AS = a i r s o n d e JO = a c o u s t i c s ounder f r om J o h n O l i v e r s i t e Table 7.2: Measured and modelled mean mixed-layer temperature, vapour pressures and saturation d e f i c i t s (x 10 _ 1 kPa) (x 10" 1 kPa) (K) P O P O P o 212 13.56 13.27 6.82 7.43 290 9 291 3 213 15.92 15.11 10.18 9.83 294 9 294 2 214 17 .42 17.64 8.47 7.79 294 8 294 6 226 18.76 16.20 3.84 5.76 292 6 292 2 231 13.73 13.65 3.52 3.60 288 3 288 2 233 14.36 13.35 7.48 10.30 292 6 293 3 234 14.35 13.54 7.67 9.50 292 2 292 9 238 17.60 15.66 13.02 10.83 297 5 295 1 Figure 7.9: Comparison between measured and modelled daily maximum potential temperature and humidity 302 208 204 Maximum Dally - Modelled Maximum Oally - Measured • i i /' i i i ' I I 1 L_ f i l l I L 210 212 2 " 2t» * ! « 220 222 2 2 4 2 2 » 2 3 0 2 3 2 2 3 4 2 3 6 2 3 8 2 4 0 2 4 2 2 4 4 Julian Day -170-7.2 Day-to-Day Performance o f SCABLE 7.2.1 Mixed-Layer Depths, Temperature and Humidity The modelled and measured maximum p o t e n t i a l temperature, humidity and mixed-layer depths are presented i n Table 7.1. For the airsonde ascents, the comparison i s l e s s r i g o r o u s because the airsonde p r o f i l e i s instantaneous. Table 7.2 presents the model-day mean observed and p r e d i c t e d s a t u r a t i o n d e f i c i t , humidity and p o t e n t i a l temperature f o r those days when tethersonde f l i g h t s were conducted. These were the only times when s u f f i c e n t data are a v a i l a b l e f o r computing a mean. (a) Mixed-layer depth {zL) The model's a b i l i t y to simulate the mixed-layer depth i s poor (Table 7.1). There are at l e a s t two reasons f o r t h i s . F i r s t l y only a s i n g l e temperature and humidity p r o f i l e (above the capping i n v e r s i o n ) are provided a t the i n i t i a t i o n of the model and are not v a r i e d throughout the day. When the mixed-layer s t r u c t u r e i s complex, or the e x t e r n a l parameters change throughout the day ( i n t r o d u c i n g n o n - s t a t i o n a r i t i e s ) i t i s necessary t o inpu t time-dependent p r o f i l e s . For example the very l a r g e d i f f e r e n c e s between measured and modelled PBL parameters on JD 232 could r e s u l t from a change i n the gr a d i e n t s of temperature and humidity during the day. There i s , however, no evidence of t h i s from s y n o p t i c c h a r t s and records. Some of the worst days f o r modelled mixed-layer depth are JD 231, 232 and 239. In each case, the simulated zL and humidity i s g r e a t e r than t h a t observed and the modelled p o t e n t i a l temperature i s lower than observed. The v a l i d a t i o n data f o r JD 232 and 239 were obtained from airsonde ascents. The q u a l i t y of these v a l i d a t i o n data i s t h e r e f o r e q u i t e dubious - p a r t i c u l a r l y f o r the mixed-layer depth. In f a c t , the value f o r z^ (modelled) at the time -171-of the airsonde ascent ( r a t h e r than maximum zL) i s w i t h i n 40 m of the observed. While the e r r o r s are s e l f c o n s i s t e n t and t h e o r e t i c a l l y c o r r e c t ( s i m i l a r c o n d i t i o n s were found by Manins, 1982) the s e r i o u s underestimate of 9m on these days demands c l o s e r s c r u t i n y . F o r t u n a t e l y accurate values f o r z i are not necessary f o r p r e d i c t i n g Q E. (b) P o t e n t i a l Temperature and Humidity The r e s u l t s presented i n Table 7.1 and Figure 7.9 i n d i c a t e that the model tends to underestimate the measured maximum mixed-layer temperature, although r e l a t i v e changes are p r e d i c t e d w e l l . The modelled temperatures f o r J.D. 228 and 232 underestimate the measured temperature (from airsonde data) by s e v e r a l degrees. The agreement i s b e t t e r when compared t o the tethersonde d e r i v e d temperatures but there i s s t i l l an o v e r a l l tendency f o r the model to underestimate the maximum temperatures. The maximum humidity i s c o n s i s t e n t l y overestimated by the model. This suggests t h a t (6.21) may be i n e r r o r . I f c q i s too small then there w i l l be an accumulation of moisture i n the PBL l e a d i n g to a higher mixed-layer humidity. The d i s c r e p a n c i e s i n both temperature and humidity are a l s o c o n s i s t e n t with the overestimate of the Q E 0 and concommitant underestimate Q H 0. On the other hand the modelled mean d a i l y mixed-layer p o t e n t i a l temperature and humidity and the measured values from the tethersonde p r o f i l e s agree f a i r l y w e l l (Table 7.2). There are d i f f e r e n c e s , but they appear to be non-systematic i n nature. The d i f f e r e n c e between the performance i n modelling maximum and mean p r o p e r t i e s can be ex p l a i n e d u s i n g the d i u r n a l p a t t e r n s . For example, on J.D. 213 the modelled p o t e n t i a l temperature i n c r e a s e s r a p i d l y f o r the f i r s t two hours a f t e r model i n i t i a t i o n . T h i s r a t e of decrease then d e c l i n e s , l e a d i n g to a gradual r i s e up to the peak at approximately 1400 LAT. Thus, while the maximum temperature may be underestimated by the model, the mean w i l l be s i m i l a r to th a t measured. The reasons f o r the i n a b i l i t y of the model to p r e d i c t the r i s e i n mixed-layer p o t e n t i a l temperature are p o s s i b l y r e l a t e d t o the r o l e of meso-scale advection and i t s i n f l u e n c e upon temperature i n the PBL. In the afternoon, the model tends t o overestimate the h o r i z o n t a l divergence of heat due to a c o a s t a l a d v e c t i v e i n f l u e n c e i n comparison to the convergence of heat which r e s u l t s from a decreasing z A and continued i n p u t of s e n s i b l e heat from the s u r f a c e - l a y e r (see Chapter 4 ) . To simulate t h i s the s i z e of the entrainment parameter, c, was increased, but i t d i d not improve the modelled mixed-layer p o t e n t i a l temperature. The overestimate of s u r f a c e Q E i n the afternoon a l s o l i m i t s the input of s e n s i b l e heat and thus the r i s e i n 0m. Again the p o s s i b i l i t y of e r r o r s i n the v a r i a b l e c q must be examined as a p o t e n t i a l c a u s a l f a c t o r . I t i s d i f f i c u l t , however, t o e x p l a i n the c o o l e r boundary-layer i n terms of e r r o r s i n Q E i -A p o s s i b l e e x p l a n a t i o n f o r these r e s u l t s and p a r t i c u l a r l y the s e r i o u s e r r o r s on J.D. 232 and 239 can be d e r i v e d from the r e s u l t s of Manins (1982). He f i n d s t h a t a simple encroachment (c=0) model simulates the PBL w e l l under f a i r l y calm, sunny c o n d i t i o n s - entrainment at the Wangara f i e l d s i t e does not seem important. However, as the wind speed i n c r e a s e s and shear occurs across the mixed-layer i n t e r f a c e , both the encroachment and f l u x - c l o s u r e models underestimate 0 m and overestimate Z i . He proposes an a l t e r n a t i v e model, based on c r i t i c a l Froude numbers a t the i n t e r f a c e , f o r computing PBL growth and he a t i n g . J.D. 231 i s the only day when 6m i s s e r i o u s l y underestimated and tethersonde f l i g h t s are a v a i l a b l e . These i n d i c a t e wind shear a t the top of the PBL - from w e s t e r l y flow w i t h i n to e a s t e r l y flow above. These s i m i l a r f i n d i n g s may mean t h a t Manins' e x p l a n a t i o n holds f o r t h i s f i e l d s i t e . I t i s unfortunate t h a t tethersonde data are not a v a i l a b l e f o r J.D. 232 and 239. Observations from J.D. 232 do not i n d i c a t e wind shear, however i t i s noted t h a t the airsonde ascent path on J.D. 239 suggests e a s t e r l i e s a l o f t and w e s t e r l i e s a t the s u r f a c e . I n t e r e s t i n g l y , Manins a l s o f i n d s cf^O.2 (based on measurements) up to 1200 AEST and then c decreases to zero by 1430 AEST. A f t e r t h i s time n e i t h e r entrainment nor encroachment occur. Therefore f l u x - c l o s u r e f o r s e n s i b l e heat may not be a s u f f i c i e n t l y robust assumption f o r the mixed-layer dynamics i n Vancouver. T h i s could extend t o l a t e n t heat too. Another common fe a t u r e between J.D. 231, 232 and 239 i s tha t westerly flow dominates w i t h i n the mixed-layer. T h i s leads to a sma l l e r modelled f e t c h and hence a stronger advective i n f l u e n c e . There i s again a problem i n s i m u l a t i n g the r e l a t i v e r o l e s of advective and c o n v e c t i v e f l u x e s i n determining mixed-layer temperature. Although t h e r e are d i s c r e p a n c i e s between modelled and measured humidity, these are not regarded as s e r i o u s f o r the f o l l o w i n g two reasons. F i r s t , an accurate comparison between the two i s l i m i t e d by the e r r o r s i n h e r e n t i n the measurement of humidity by the tethersonde system. Second, the s e n s i t i v i t y a n a l y s i s ( s e c t i o n 6.5) i n d i c a t e s t h a t the humidity i s l e s s important to the s u c c e s s f u l p r e d i c t i o n of the s u r f a c e evaporation. With the exc e p t i o n of J.D. 214, the modelled humidity i s s y s t e m a t i c a l l y g r e a t e r than the measured. The day-to-day changes are p r e d i c t e d except f o r the t r a n s i t i o n from J.D. 231 to 233. (c) S a t u r a t i o n D e f i c i t The r e s u l t s presented i n Table 7.2 demonstrate good agreement f o r J.D. 212 - 214 and J.D. 231. For J.D. 226, 233 and 234, the combination of an over-estimate of the humidity and under-estimate of 6m y i e l d s an under-estimate of the s a t u r a t i o n d e f i c i t . The d i f f e r e n c e s are non-systematic and the trend i s p r e d i c t e d w e l l . The l a t t e r i s shown i n Figure 7.10 (b), p o r t r a y i n g the temporal v a r i a t i o n of measured s u r f a c e - l a y e r s a t u r a t i o n d e f i c i t s and modelled D m. I t i n d i c a t e s t h a t the temporal v a r i a t i o n i n modelled mean d a i l y D m and measured s u r f a c e - l a y e r s a t u r a t i o n d e f i c i t are p o s i t i v e l y c o r r e l a t e d . Secondly, although t h i s v a r i a t i o n i s l i n k e d t o temporal changes i n the a v a i l a b l e energy (Figure 7.10 ( a ) ) , t h i s alone does not account f o r the v a r i a b i l i t y i n e i t h e r of the two s a t u r a t i o n d e f i c i t s or the surface e v a p o r a t i o n . Thus, as d i s c u s s e d i n Chapter 4, the temporal v a r i a t i o n i n both D 0, and D m, must probably be r e l a t e d to another f o r c i n g , a t the s y n o p t i c , or meso-scale. Figure 7.10 (b) a l s o i n c l u d e s measured s a t u r a t i o n d e f i c i t s showing that the agreement between D m (measured) and D m (modelled) i s s i m i l a r t o the comparison between measured and modelled humidity and p o t e n t i a l temperatures. Thus, there i s a tendency f o r the model to underestimate D m. -175-Figure 7.10: (a) Day-to-day variation i n available energy (b) Day-to-day variation i n measured surface-layer (D 0), modelled mixed-layer (Dra) and measured mixed-layer saturation d e f i c i t Note: measured surface-layer ....... modelled mixed-layer x measured mixed-layer -176-In summary, a good mixed-layer model i s not a necessary p r e - r e q u i s i t e f o r a good evaporation model. The v i t a l output from t h i s sub-component i s D m, whose mean i s modelled f a i r l y w e l l . Nonetheless, there c l e a r l y are problems with the mixed-layer sub-model which would need to be r e s o l v e d before being used as a p r e d i c t i v e PBL model. I t i s b e l i e v e d that a p o s s i b l e source of e r r o r may be found i n the assumptions made by Steyn (1989) of p r o p o r t i o n a l f l u x c l o s u r e f o r both the s e n s i b l e and l a t e n t heat terms, but c o n s i d e r a b l y more ob s e r v a t i o n s and modelling are r e q u i r e d before t h i s could be a f f i r m e d . A f i r s t order model f o r dTiS/dt may be r e q u i r e d to adequately model mixed-layer p o t e n t i a l temperature. 7.2.2 Surface R e s i s t a n c e s The s u b s t r a t e and b l u f f - b o d y r e s i s t a n c e s can be compared to the " e f f e c t i v e " s u r f a c e r e s i s t a n c e s ( r c ) , d e r i v e d from r e - a r r a n g i n g the PM equation. Note th a t these are averaged to y i e l d d a i l y means. A problem with e v a l u a t i n g t h i s component of the model i s that the " e f f e c t i v e " s u r f a c e r e s i s t a n c e i s f o r the urban canopy, at a l o c a l s c a l e whereas the model deals with the b l u f f - b o d y and s u b s t r a t e components s e p a r a t e l y . These cannot be combined to be compared d i r e c t l y with the " e f f e c t i v e " s u r f a c e r e s i s t a n c e d e r i v e d from the PM equation, hence an o b j e c t i v e e v a l u a t i o n of the r e s i s t a n c e network cannot be a t t a i n e d d i r e c t l y . In f a c t , the Shuttleworth and Wallace approach aims to avoid the concept of an i n t e g r a t e d s u r f a c e r e s i s t a n c e . As a surrogate f o r such a comparison the v a r i a t i o n i n r sPM (the modelled s u b s t r a t e r e s i s t a n c e ) i s compared to r c . The only t r u e t e s t of the evaporation model can o n l y be i n terms of i t s o v e r a l l performance. -177-F i g u r e 7.11: Comparison between " e f f e c t i v e " s u r f a c e r e s i s t a n c e from Penman Monteith and modelled s u b s t r a t e r e s i s t a n c e (r sPM) Note: J u l i a n days marked r e f e r t o days mentioned i n t e x t -178-The v a r i a t i o n i n r sPM and r c throughout the modelled p e r i o d are p o r t r a y e d i n F i g u r e 7.11. An o v e r a l l i n c r e a s e i n the s u b s t r a t e r e s i s t a n c e i s e v i d e n t . T h i s c o i n c i d e s with the gradual decrease i n s o i l moisture a v a i l a b i l i t y as d r y i n g progresses. Superimposed on t h i s general trend are the day-to-day v a r i a t i o n s a s s o c i a t e d with changes i n water-use (and hence the area i r r i g a t e d , d e f i n e d as SAWET i n Chapter 5), and wind speed. These account f o r the low s u b s t r a t e r e s i s t a n c e s on J.D. 215, and 217 - 221 (note t h a t the e x t e r n a l water-use i s at a seasonal maximum on J.D. 221), 229, 231, 236 and 239. These r e l a t i v e l y lower s u b s t r a t e r e s i s t a n c e s l a t e i n the d r y i n g p e r i o d e x i s t d e s p i t e the dry s t a t e of the u n i r r i g a t e d greenspace. The l a r g e r values f o r r sPM on J.D. 222 - 224 r e f l e c t both the decreased s o i l moisture, and lower water-use on these days. The same o v e r a l l i n c r e a s i n g trend i n r c i s a l s o apparent i n Figure 7.11. The v a r i a t i o n s match those modelled, e s p e c i a l l y up to J.D. 224 but there are s e v e r a l days when the s u r f a c e r e s i s t a n c e d i f f e r s markedly from the modelled r sPM. The model a l s o performed p o o r l y a t these times. - J.D. 203, 215 and 216, 230 and 231. The values f o r these e f f e c t i v e surface r e s i s t a n c e s d i f f e r i n trend e i t h e r from the preceding or f o l l o w i n g day. but the s i z e of d i f f e r e n c e i s not g r e a t . Hence, the agreement between the measured and modelled evaporation on these days remains r e l a t i v e l y good. However, J.D. 227, 235 and J.D. 240 onwards e x h i b i t g r e a t e r d i f f e r e n c e s . - the low r e s i s t a n c e s leads to an overestimate of Q E. On J.D. 242, 243 and 246 the modelled s u r f a c e r e s i s t a n c e i s i n c o r r e c t . Despite t h i s , the r e l a t i v e change i n evaporation i s modelled c o r r e c t l y f o r these days. I t i s p o s s i b l e t h a t the s a t u r a t i o n d e f i c i t and the a v a i l a b l e energy have a compensating e f f e c t on evaporation. -179-The modelling of the s u b s t r a t e r e s i s t a n c e s i s p a r t l y based upon the assumption t h a t a higher e x t e r n a l water-use leads t o a higher evaporation, i f t h e r e i s s u f f i c i e n t a v a i l a b l e energy or the s a t u r a t i o n d e f i c i t i s reasonably l a r g e . The comparison between the e f f e c t i v e s u r f a c e and modelled s u b s t r a t e r e s i s t a n c e s suggests t h a t an important temporal aspect i s being ignored i n t h i s model and t h i s i s the i n f l u e n c e of antecedent c o n d i t i o n s on the s u r f a c e moisture a v a i l a b i l i t y . Some of the modelled s u b s t r a t e r e s i s t a n c e s appear to be 'out of phase' with those measured, e.g. J.D. 215 and 216. In r e t r o s p e c t t h i s aspect i s i n t u i t i v e l y obvious, but to develop such a model which could account f o r the l a g e f f e c t of e x t e r n a l l y a p p l i e d water would r e q u i r e continuous s i m u l a t i o n using, f o r example, a water balance approach to p r e d i c t the moisture s t a t u s a t the end of each model day. 7.2.3 Canopy Evaporation Table 7.3 and Figure 7.12 i l l u s t r a t e the comparison between the mean d a i l y measured and modelled l a t e n t heat f l u x e s , f o r a l l of the 38 days f o l l o w i n g p r e c i p i t a t i o n (two days were d i s c a r d e d on account of numerical i n s t a b i l i t y problems encountered d u r i n g the running of the model). The o v e r a l l agreement i s good, e s p e c i a l l y c o n s i d e r i n g there was no p r i o r c a l i b r a t i o n of the su r f a c e r e s i s t a n c e component, as had been done by McNaughton and Spriggs (1986) and Grimmond (1988) i n s i m i l a r s t u d i e s . The non-systematic root mean square e r r o r (RMSE U) i s s i m i l a r to the systematic (RMSE S), but the index of agreement i s hig h . The c o e f f i c i e n t of determination i s 0.8, however the degree of agreement i s probably best assessed by the MAE (Mean Absolute E r r o r ) and the RMSE. The former i s 14.9 -180-V XI o 60 40 -20 40 60 80 100 Measured Lotent Heot Flux(W Itl" 2 ) 1 70 F i g u r e 7.12: Comparison between measured and modelled l a t e n t heat f l u x e s (mean d a y l i g h t hours) Figure 7.13: Comparison between temporal v a r i a t i o n of measured and modelled l a t e n t heat f l u x e s (mean d a y l i g h t hours) -181-W m"2' and the l a t t e r i s 18.0 W ra"2 r e p r e s e n t i n g 20% and 24% of measured Q r e s p e c t i v e l y . These r a t h e r l a r g e values i n d i c a t e that while the model s u c c e s s f u l l y p r e d i c t s the trend of the measured evaporation, t h e r e i s s c a t t e r which i s both unsystematic and systematic. The slo p e of the r e g r e s s i o n l i n e i n d i c a t e s t h a t the modelled Q E i s l e s s than the measured Q E, however, the l a r g e i n t e r c e p t o f f s e t s t h i s f o r the magnitudes of evaporation measured a t t h i s suburban s i t e . Table 7.3: Summary s t a t i s t i c s for modelled and measured evaporation RMSE RMSEU RMSES MAE d r 2 X Y w m - 2 W n r 2 W n r 2 w i r r 2 w m" (a) 18.0 11.7 13.7 14.9 0.89 0.79 75.0 81.0 (b) 16.2 10.1 12.6 12.9 0.89 0.80 75.6 86.3 (c) 15.1 10.8 10.6 11.7 0.92 0.81 79.2 87.9 (d) 0.75 75.2 95.0 Slope I n t e r c e p t (W m - 2) (a) 0.78 27.2 (b) 0.75 29.8 (c) 0.79 25.1 (d) 0.83 34.1 Key: X,Y: mean measured, modelled (a) : a l l data (b) : without JD:218,227-229, 240 (c) : up to JD 227 (d) : Running canopy evaporation model with measured D 0 and reference height = 30 m On the b a s i s of the d i u r n a l performance of the model, there are a number of days where i t i s known that the model performed p o o r l y . Removal of these values from the data set (J.D. 218, 228, 229, and J.D. 240 onwards) m a r g i n a l l y improves the s t a t i s t i c s as i n d i c a t e d i n Table 6.3. The MAE i s reduced t o 12.9 W m"2, or 17%, and the RMSE to 16.2 W m" 2 , or 21%. -182-The agreement i n tre n d i s supported by Figure 7.13, which i l l u s t r a t e s the temporal v a r i a b i l i t y of the measured and modelled l a t e n t heat f l u x e s . The modelled evaporation c o n s i s t e n t l y exceeds the measured, although the day-to-day v a r i a b i l i t y i s simulated. The o v e r a l l decrease i n evaporation from J.D. 199 through t o J.D. 246 i s evident from both the measured and modelled data. There i s disagreement between the measured and modelled r e s u l t s ( e s p e c i a l l y i n terms of the day-to-day v a r i a b i l i t y ) on J.D. 215, 217, 218, 219 and 227. Reasons f o r t h i s poor agreement are unknown. The peak i n modelled Q E on J.D. 221 i s i n response to a lower s u r f a c e r e s i s t a n c e due to the maximum water-use recorded on t h a t day but the model seems to o v e r - p r e d i c t the boost provided by the g r e a t e r water a v a i l a b i l i t y . The decrease i n evaporation towards the end of the drought i s p r e d i c t e d i n terms of tr e n d , but the magnitude i s overestimated. T h i s appears to be a r e s u l t of an underestimate of the parameterised s u r f a c e r e s i s t a n c e values. 7.3. Evaluation of SCABLE (a) How good i s SCABLE? Intercomparisons of micrometeorological measurements of average daytime l a t e n t heat f l u x i l l u s t r a t e RMSE's of the order of 10-15 W m"2. With t h i s caveat, the model performs adequately i n terms of p r e d i c t i n g the d a i l y mean l a t e n t heat f l u x . The MAE and RMSE (Table 7.3) are l a r g e , as a percentage of the mean f l u x . The r e l a t i v e l y high values f o r the c o r r e l a t i o n c o e f f i c i e n t and the index of agreement i n d i c a t e t h a t the model p r e d i c t s r e l a t i v e changes i n the d a i l y evaporation. The hourly performance i s poorer and reasons f o r t h i s have been d i s c u s s e d . An improvement i n modelling the -183-hourly f l u x e s r e q u i r e s a g r e a t e r p h y s i c a l understanding of the t r a n s f e r of moisture from 'patchy' s u r f a c e s during very unstable c o n d i t i o n s ( i . e . the l a t e a f t e r n o o n ) . The mean d a i l y temperature and humidity of the mixed-layer i s modelled w e l l , l e a d i n g to agreement between the mean measured and modelled d a i l y s a t u r a t i o n d e f i c i t . T h i s appears to be s u f f i c i e n t f o r the p r e d i c t i o n of r e l a t i v e d i f f e r e n c e s i n d a i l y evaporation r a t e s . But again the dynamics of mixed-layer temperature changes over p e r i o d s of a few hours needs to be b e t t e r understood. Although s i m u l a t i o n of z± i s not a p r e r e q u i s i t e f o r m o d e l l i n g Q E, i t s poor p r e d i c t i o n must be noted. I t i s recommended th a t the assumptions of f l u x p r o p o r t i o n a l i t y f o r l a t e n t and s e n s i b l e heat be examined much more c l o s e l y . Improvement of t h i s aspect of the model should l e a d t o an improved modelling of the PBL parameters. I t i s encouraging t h a t the day-to-day v a r i a b i l i t y , so apparent i n the measured f l u x e s , i s p r e d i c t e d . Chapter 4 showed th a t the c o n t r o l s on s u r f a c e evaporation v a r i a b i l i t y are a combination o f : a v a i l a b l e energy, the heat and moisture content of the mixed-layer, and the s u r f a c e r e s i s t a n c e . In t u r n , the mixed-layer does appear to be i n f l u e n c e d by l a r g e r - s c a l e a i r f l o w and s y n o p t i c c o n t r o l s . In terms of model:measured s t a t i s t i c s and the a b i l i t y to f o l l o w the observed v a r i a b i l i t y of d a i l y Q E the SCABLE approach seems u s e f u l . The i s s u e of whether other types of model would be j u s t as a p p r o p r i a t e i s addressed below. Although SCABLE performs adequately, the SW approach alone (Table 7 . 3 ) overestimates the suburban canopy l a t e n t heat f l u x . T h i s i s not a t r u l y f a i r t e s t , as the s a t u r a t i o n d e f i c i t s i n the canopy evaporation model are -184-measured within the s u r f a c e - l a y e r and are thus a response to the surface l a t e n t heat f l u x . These r e s u l t s i n d i c a t e t h a t the model simulates the variability and that the p a r a m e t e r i s a t i o n of surface r e s i s t a n c e s r e q u i r e s improvement. For example d i f f e r e n c e s between means p a r t i a l l y r e s u l t s from d i s c r e p a n c i e s at the end of the d r y i n g i n t e r v a l . A la r g e p r o p o r t i o n of the RMSE i s systematic, i n d i c a t i n g t h a t a change i n the surface r e s i s t a n c e s , which s y s t e m a t i c a l l y reduced a l l d a i l y evaporation t o t a l s , would reduce both the r 2 , d, RMSE and MAE without a l t e r i n g the l i n e a r r e g r e s s i o n equation. Such changes co u l d i n c l u d e i n c r e a s i n g the bluff-body component, or a l t e r n a t i v e l y the sur f a c e r e s i s t a n c e of the tre e d component. For example, i n c r e a s i n g the stomatal r e s i s t a n c e by 100 s m ~ 1 , and i n c r e a s i n g the b l u f f - b o d y component by 5% would y i e l d (approximately) a MAE of 13 W m"2, and d of 0.92 (on the b a s i s of the r e s u l t s of the s e n s i t i v i t y a n a l y s i s ) . C l e a r l y the model performs b e t t e r on a d a i l y b a s i s p a r t l y because the lower value f o r D m o f f s e t s the underestimate i n sur f a c e r e s i s t a n c e . Because D 0 i s c o r r e l a t e d with D m, the SW model alone could be used t o model the canopy evaporation, p r o v i d i n g that the sur f a c e r e s i s t a n c e network i s improved. The modelled s u b s t r a t e r e s i s t a n c e s do i l l u s t r a t e the complementary r o l e s of the s o i l moisture and the area under i r r i g a t i o n . At the beginning of the d r y i n g c y c l e , the s o i l moisture content of the greenspace i s high, y i e l d i n g a r e l a t i v e l y low s u r f a c e r e s i s t a n c e . As the d r y i n g p e r i o d progresses, the n a t u r a l s o i l moisture supply i s depleted but the percentage of i r r i g a t e d greenspace i n c r e a s e s , hence maintaining a lower surface r e s i s t a n c e f o r the e n t i r e greenspace a r e a . -185-b) What are the important c o n t r i b u t i o n s of t h i s modelling approach? SCABLE i s an approach f o r both the prognosis and d i a g n o s i s of suburban l a t e n t heat f l u x e s . I t i n c l u d e s a mixed-layer component which provides a meso-scale f o r c i n g on the suburban evaporation regime. I t a l s o y i e l d s a value f o r the mixed-layer s a t u r a t i o n d e f i c i t which can be input to the canopy evaporation component of the model. An important aspect of t h i s modelling approach i s t h a t i t permits an understanding of the nature and controls upon the evap o r a t i o n regime f o r a p a r t i c u l a r land-use because i t can be used i n a p r e d i c t i v e mode. The mixed-layer temperature and humidity are l i n k e d to both the f l u x e s of moisture and heat from the s u r f a c e and to meso-scale urban i n f l u e n c e s ( r e c a l l Chapter 1 and 2) and a d v e c t i v e e f f e c t s . T h i s i s i l l u s t r a t e d i n Fig u r e 7.14 which shows the change i n zi and 8m when modelled with and without meso-scale a d v e c t i o n . C l e a r l y the d i s t a n c e to a l e a d i n g edge, such as a c o a s t l i n e , has a r o l e i n determining surface evaporation when there i s strong c o u p l i n g between D m and D 0 (as i n d i c a t e d by the s i z e of fi). I f SCABLE i s run f o r a ' r u r a l ' (more a c c u r a t e l y , non-urban) s i t e , l o c a t e d a t the same d i s t a n c e from the c o a s t l i n e , the r e l a t i v e s e n s i t i v i t y of evaporation to meso-scale i n f l u e n c e s can be assessed. In order to simulate a non-urban, moist s i t e , the roughness length i s s e t to 0.01 m and the modelled evaporation m u l t i p l i e d by a f a c t o r of 2 (Cleugh and Oke, 1986). The purpose of the s i m u l a t i o n i s to i l l u s t r a t e the r e l a t i v e -186-298 296 ft • 294 h £ 292 -290 - ; 288 without advection....' " 0m with advection 800 1200 TIME (LAT) 1600 2000 1800 1600 1400 1200 1000 800 600 400 200 0 .•" Zi without advection Zi with advection 800 1200 TIME (LAT) 1600 F i g u r e 7.14: Simulated d i u r n a l v a r i a t i o n of (a) p o t e n t i a l temperature, and (b) depth, of the mixed-layer: w i t h and without advection -187-importance of mixed-layer i n f l u e n c e s - such as a d v e c t i o n - on D m and Q E i n the two regimes t h a t have d i f f e r e n t roughness, and moisture a v a i l a b i l i t y . The s c e n a r i o s presented i n Table 7.4 i n d i c a t e two minor p o i n t s . F i r s t l y the a v a i l a b l e energy i s l e s s important i n determining suburban evaporation. Secondly, even i f the canopy i s wet and D 0 i s suppressed a l a r g e e v a p o r a t i v e f l u x can be achieved. These two aspects are t y p i c a l of aerodynamically -rough environments. More im p o r t a n t l y , the absence of an a d v e c t i o n leads to a 14% i n c r e a s e i n the evaporation r a t e f o r the urban case, compared to a 3% i n c r e a s e f o r the non-urban case. The presence of a d v e c t i o n suppresses the mixed-layer s a t u r a t i o n d e f i c i t and hence Q E i n the urban environment. The d i f f e r i n g s e n s i t i v i t i e s are not s u p r i s i n g i n l i g h t of the l i n k a g e s between D m and D 0, as expressed by the parameter H. Table 7.4: Modelled evaporation: influence of changed surface and atmospheric conditions ( a l l units W m"2) U R B A N N O N - U R B A N Parameter Q E % Change Q E % Change No a d v e c t i o n 130 14 186 3 Q* (+100 W m - 2) 155 31 266 44 Dry s u r f a c e 118 196 Wet s u r f a c e 211 78 236 20 In summary, meso-scale advection has a " f o r c i n g " r o l e upon Q E from the suburban s u r f a c e . Suburban l a t e n t heat f l u x e s may thus be i n f l u e n c e d by the presence of meso-scale v a r i a t i o n s i n land-use. For example at the Mainwaring s i t e the l a t e n t heat f l u x i s a f f e c t e d by i t s closeness to the r u r a l land-use. During westerly and north-westerly winds the flow passes -188-F i g u r e 7.15: Map of Vancouver C i t y ( F i g u r e 2.1) -189-over predominantly urban areas (Fig u r e 7.15). In the case of the w e s t e r l y flow t h i s urban land-use i s mostly suburban w i t h i n which areas of concentrated commercial a c t i v i t y may develop small urban heat i s l a n d s . Hay and Oke (1976) present r e s u l t s of automobile t r a v e r s e s during winter months which i l l u s t r a t e that the K e r r i s d a l e area, f o r example, i s capable of producing i t s own heat i s l a n d . T h i s i s a l s o evident i n the s p a t i a l p a t t e r n of s u r f a c e temperatures observed by Schmid (1988). The t r a j e c t o r y of north-west flow i n c l u d e s s e v e r a l parks and a commercial area. For south or s o u t h - e a s t e r l y flow, the upwind land-use i s a mixture of both r u r a l and urban - i . e . the urban areas of Richmond, the i n d u s t r i a l area on the North F r a s e r and the a g r i c u l t u r a l land t o the east and south of Richmond. Therefore the c o a s t l i n e may not be the only advective i n f l u e n c e upon the s u r f a c e f l u x e s . I t i s c o n c e i v a b l e t h a t D m, D 0 and hence the surface l a t e n t and s e n s i b l e heat f l u x e s w i l l vary with wind d i r e c t i o n , r e f l e c t i n g the upwind land-use. T h i s may e x p l a i n the suppression of Q E with SE flow ( i . e . C l a s s I I I days i n Chapter 4 ) . The flow from that d i r e c t i o n i s p o s s i b l y c o o l e r and more humid due to the c o o l e r , r u r a l boundary-layer to the SE. In a d d i t i o n , an a n a l y s i s of the boundary-layer s t r u c t u r e from the tethersonde measurements i n d i c a t e s t h a t there i s l i t t l e c o u p l i n g between the boundary-layer and u p p e r - l e v e l flow. On days when the flow i s predominantly westerly (Class I ) , the a i r w i t h i n the i n v e r s i o n w i l l be warm and dry (the s t a b i l i t y over the ocean w i l l r e s t r i c t l a r g e f l u x e s of evaporation i n t o the u p p e r - l e v e l atmosphere). In c o n j u n c t i o n with the urban f e t c h t h i s leads to a d r i e r boundary-layer and l a r g e r Dro. Meso-scale advection must a l s o be a f o r c i n g mechanism, i n a d d i t i o n t o the urban i n f l u e n c e , on the energy budget i n suburban Vancouver. T h i s has -190-i m p l i c a t i o n s f o r the t r a n s f e r a b i l i t y of r e s u l t s and models. (c) Are there a l t e r n a t i v e models to Shuttleworth and Wallace (1985)? One of the challenges i n m o d e l l i n g evaporation from such heterogeneous s u r f a c e s as suburbia i s to adequately parameterise the s u r f a c e r e s i s t a n c e s and hence the canopy ev a p o r a t i o n . The SW model, modified as d i s c u s s e d i n Chapter 5, i s one approach and i s found to overestimate evaporation, although the day-to-day v a r i a b i l i t y i s simulated. Provided that the r e l a t i o n s h i p s between s u r f a c e moisture s t a t u s and r e s i s t a n c e s can be improved, such an approach would be v a l i d . Another approach i s proposed as f u t u r e r e s e a r c h . T h i s would adopt a "top-down" method f o l l o w i n g the succcess of a s i m i l a r approach taken by Grimmond (1988). Instead of t r a n s l a t i n g the moisture s t a t u s of each s u r f a c e component i n t o a r e s i s t a n c e and then summing these i n p a r a l l e l ( i . e . i n t e g r a t i n g from the "bottom-up") the a l t e r n a t i v e i s to model the " e f f e c t i v e " s u r f a c e r e s i s t a n c e . Grimmond achieved t h i s by developing a s e m i - e m p i r i c a l model which e s s e n t i a l l y i s a polynomial f i t between the measured " e f f e c t i v e " s u r f a c e r e s i s t a n c e and a number of v a r i a b l e s which c o n t r o l s u r f a c e r e s i s t a n c e s . T h i s i n t e g r a t i o n of a l l s u r f a c e components i n t o one r e s i s t a n c e parameter provides one s o l u t i o n t o the problem of i n t e g r a t i n g s u r f a c e heterogeneity. I t i s , however, i n d i r e c t c o n t r a s t to the philosophy of SW. Future research should examine which method i s more a p p r o p r i a t e . The advantage of the Grimmond model i s t h a t i t y i e l d s an equation with e x c e l l e n t p r e d i c t i v e c a p a b i l i t i e s . A disadvantage l i e s i n i t s empiricism and some l o s s of i n f o r m a t i o n a t s c a l e s s m a l l e r than the l o c a l - s c a l e . -191-In summary, although the model does not perform w e l l on an hourly b a s i s , the day-to-day agreement suggests t h a t the approach i s v i a b l e . Because D 0 i s c o r r e l a t e d w i t h D m, the SW model alone c o u l d be used t o p r e d i c t the canopy e v a p o r a t i o n p r o v i d i n g t h a t the su r f a c e r e s i s t a n c e model i s improved. T h i s demands a f u r t h e r understanding of the changing s t a t u s of the canopy moisture sources, both i n time and space. The preceding d i s c u s s i o n demonstrates t h a t a l t e r n a t i v e approaches t o SW a l s o have l i m i t a t i o n s and f u r t h e r r e s e a r c h i s necessary to determine which i s b e t t e r . -192-CHAPTER 8: CONCLUSIONS 8.1 Discussion of Objectives The f i r s t o b j e c t i v e was to analyse the nature of the suburban energy balance. On an hourly b a s i s the observations i l l u s t r a t e the dominance of s e n s i b l e heat as an energy sink i n the d i u r n a l suburban energy budget and i t s enhancement of the mixed-layer temperature and s a t u r a t i o n d e f i c i t . In the l a t e a fternoon t h i s dry boundary-layer i s not c o r r e l a t e d with an i n c r e a s e i n moisture t r a n s f e r . Two reasons f o r t h i s are proposed: an i n c r e a s e d canopy r e s i s t a n c e i n response to the enhanced s a t u r a t i o n d e f i c i t and the s e p a r a t i o n of moisture and s e n s i b l e heat sources. Furthermore, the s u r f a c e - l a y e r s a t u r a t i o n d e f i c i t i s l i k e l y to r e s u l t from the l i m i t e d s u r f a c e l a t e n t heat f l u x . A second o b j e c t i v e was to assess the v a l i d i t y of the hypothesis that the f l u x e s of heat and water vapour i n the suburban s u r f a c e - l a y e r are determined by a combination of m i c r o - s c a l e (within-canopy) and meso-scale ( w i t h i n mixed-layer) c o n t r o l s . On the b a s i s of t h e o r e t i c a l and e m p i r i c a l evidence, i t i s apparent t h a t the t r a n s f e r of water vapour between the s u r f a c e and the lower atmosphere Is determined by a range of processes o p e r a t i n g a t a number of s p a t i a l and temporal s c a l e s . F i r s t l y , as expected, the a v a i l a b l e energy and moisture w i t h i n the suburban canopy provide a set of m i c r o - s c a l e " c o n t r o l s " on the suburban l a t e n t heat f l u x . Analyses of the r e l a t i o n s h i p s between the temporal v a r i a b i l i t y of Q E and energy a v a i l i b i l i t y , s o i l moisture and e x t e r n a l water-use r e v e a l a number of important f i n d i n g s . While the a v a i l a b l e energy must a f f e c t the v a r i a t i o n and s i z e of the l a t e n t heat f l u x , the o b s e r v a t i o n s suggest t h a t i t s -193-i n f l u e n c e can be over-ridden by the other f a c t o r s . Neither lawn i r r i g a t i o n nor s o i l moisture v a r i a t i o n s (of the u n i r r i g a t e d greensapce) are d i r e c t l y c o r r e l a t e d with Q E. Rather the two e x h i b i t a "complementary" r e l a t i o n s h i p i n m a i n t a i n i n g the within-canopy moisture supply. The day-to-day v a r i a t i o n of Q E i s a l s o determined by the v a r i a t i o n i n t h i s canopy moisture supply. The magnitude of McNaughton and J a r v i s ' fJ i s found to vary from 0.1 -0.4, s i m i l a r t o that observed by Cleugh and Oke (1986). T h i s i n d i c a t e s an environment where the " f r e e " atmosphere, mixed- and s u r f a c e - l a y e r s are s t r o n g l y l i n k e d . The c l o s e c o u p l i n g observed between the surface and mixed-layer s a t u r a t i o n d e f i c i t s i s evidence of t h i s . A number of case s t u d i e s demonstrate t h a t , i n t u r n , the mixed-layer s a t u r a t i o n d e f i c i t i s i n f l u e n c e d by air-mass changes and the meso-scale a d v e c t i o n . A c l a s s i f i c a t i o n scheme i s used to i l l u s t r a t e t h a t a l l three f a c t o r s -a v a i l a b l e energy, canopy moisture and advection (through i t s c o n t r o l on D m) determine the p a r t i t i o n i n g of the t u r b u l e n t l a t e n t and s e n s i b l e heat f l u x e s . T h i s i s i n c o n t r a s t to observations from a r u r a l s i t e which demonstrate t h a t f o r g r a s s l a n d , the dominant c o n t r o l on t h i s p a r t i t i o n i n g , under well-watered c o n d i t i o n s i s the a v a i l a b l e energy i . e . t h a t s i t e e x h i b i t s an e q u i l i b r i u m evaporation regime. These observations thus confirm the i n i t i a l hypothesis e s t a b l i s h e d i n the second o b j e c t i v e and a l s o the conceptual model presented i n Chapter 3. The suburban evaporation regime i s one c h a r a c t e r i s e d by l a r g e temporal v a r i a b i l i t y which, on a day-to-day t i m e - s c a l e , i s d r i v e n by advective e f f e c t s r e s u l t i n g e i t h e r from a i r mass changes or meso-scale advection. The t h i r d and f o u r t h o b j e c t i v e s were to develop and t e s t a p r e d i c t i v e -194-suburban evaporation model. Because of the range of c o n t r o l s on the suburban l a t e n t heat f l u x , t h i s had to i n c o r p o r a t e a sub-model to p r e d i c t the s a t u r a t i o n d e f i c i t (mixed-layer) and the moisture a v a i l a b i l i t y w i t h i n the suburban canopy. These two sub-models are coupled and the model i s termed SCABLE. In a d d i t i o n a storage heat f l u x p a r a m e t e r i s a t i o n was r e q u i r e d f o r both the measurement and modelling of Q H and Q E. The model f o r s i m u l a t i n g AQS i s based on a n o n - l i n e a r r e l a t i o n s h i p between Q* and AQS. T h i s r e l a t i o n s h i p has a " h y s t e r e s i s form". " H y s t e r e s i s " equations f o r each s u r f a c e type were developed and i n t e g r a t e d f o r the suburban canopy. Such an approach i s compatible with t h a t used to d e r i v e r e s i s t a n c e s f o r input i n t o the canopy evaporation sub-model. The theory (Chapter 1) and o b s e r v a t i o n s (Chapter 3 and 4) i n d i c a t e t h a t the mixed-layer sub-model must i n c l u d e the e f f e c t s of meso-scale advection. Hence an advectively-dominated, slab-model was adapted from the work of Steyn (1980, 1989) to model the mixed-layer dynamics. A form of the Combination model developed by Shuttleworth and Wallace (1985) f o r sparse canopies was m o d i f i e d f o r a suburban canopy. The r e s i s t a n c e network i s based on e a r l i e r methods a l s o developed by Shuttleworth (1975, 1978). The approach of the canopy sub-model i s to parameterise the s u r f a c e moisture s t a t u s of each of the b l u f f - b o d y and s u b s t r a t e components as r e s i s t a n c e s . P r e l i m i n a r y t e s t i n g of the urban heat storage p a r a m e t e r i s a t i o n scheme demonstrates t h a t i t works w e l l on an hourly and d a i l y t i m e - s c a l e . The performance of SCABLE i n d i c a t e s a promising approach to modelling l a t e n t -195-heat f l u x at the d a i l y t i m e - s c a l e . The RMSE f o r the d a i l y mean modelled l a t e n t heat f l u x i s of the same order as t h a t r e s u l t i n g from intercomparisons between v a r i o u s methodologies f o r measuring Q E. The p r e d i c t e d temporal v a r i a b i l i t y i n Q E matches the measured v a r i a b i l i t y . The performance of the model on an hourly b a s i s , however, i s weaker. Further improvements to the r e s i s t a n c e network would ameliorate t h i s . A more accurate s i m u l a t i o n of the mixed-layer temperature would enhance the model's a b i l i t y to p r e d i c t h o urly v a r i a t i o n s i n Q E. In p a r t i c u l a r a reassessment of the p r o p o r t i o n a l f l u x c l o s u r e assumption i s r e q u i r e d f o r both the s e n s i b l e and l a t e n t heat f l u x e s a t the base of the capping i n v e r s i o n . A g r e a t e r understanding of t u r b u l e n t t r a n s f e r i n h i g h l y unstable c o n d i t i o n s would a l s o improve the modelling of Q E i n the l a t e a f t e rnoon. 8.2 Summary of C o n c l u s i o n s The f o l l o w i n g are the s p e c i f i c c o n c l u s i o n s drawn from t h i s study. * The nature of the hourly and d a i l y suburban energy balance has been examined through measurements and comparisons with a r u r a l , g r a s s l a n d s i t e . These demonstrate the predominance of s e n s i b l e heat as an energy s i n k i n the suburban environment. However, the l a t e n t heat f l u x i s shown to be an important term, and the p a r t i t i o n i n g between the two t u r b u l e n t f l u x e s shows c o n s i d e r a b l e temporal v a r i a b i l i t y . * The a v a i l a b l e energy and moisture w i t h i n the suburban canopy c o n t r i b u t e to the hourly and d a i l y v a r i a t i o n i n the s i z e of the t u r b u l e n t heat f l u x e s . Observations have demonstrated the linkages between the mixed- and s u r f a c e - l a y e r s a t u r a t i o n d e f i c i t s . The mixed-layer d e f i c i t i s a l s o determined by s y n o p t i c and meso-scale processes such as outflow from the B.C. i n t e r i o r or the d i u r n a l sea-breeze. Together with the c o u p l i n g , t h i s leads to an a d v e c t i v e i n f l u e n c e on the day-to-day -196-v a r i a t i o n i n the suburban evaporation regime. Thus an important c o n t r i b u t i o n of t h i s r esearch i s the i d e n t i f i c a t i o n of both an a d v e c t i v e (and hence l a r g e r - s c a l e ) and m i c r o - s c a l e c o n t r o l on the suburban l a t e n t heat f l u x e s , at l e a s t a t the ho u r l y t i m e - s c a l e . At the hourly t i m e - s c a l e the major c o n t r o l on evap o r a t i o n appears to be the a v a i l a b l e energy. While the s a t u r a t i o n d e f i c i t and a v a i l a b l e moisture e s t a b l i s h the mean l e v e l of evaporation f o r the day, at f i n e r t i m e - s c a l e s the a v a i l a b l e energy dominates. In the l a t e a f ternoon the mixed-layer and s u r f a c e - l a y e r both have l a r g e s a t u r a t i o n d e f i c i t s . E i t h e r because of i n c r e a s e d stomatal r e s i s t a n c e , or the s e p a r a t i o n of moisture and t u r b u l e n t sources - t h i s i s not matched by an i n c r e a s e i n Q E. In order t o measure and model the t u r b u l e n t f l u x e s , a model f o r the urban heat storage has been developed. I t i n c l u d e s a n o n - l i n e a r term to account f o r a ' h y s t e r e s i s ' e f f e c t observed i n net r a d i a t i o n -storage heat f l u x comparisons. T h i s o b j e c t i v e h y s t e r e s i s model i s shown t o y i e l d acceptable estimates of the storage heat f l u x . A canopy evaporation model (based on the SW Combination model) and an advectively-dominated mixed-layer growth model are developed and l i n k e d together t o provide a p r e d i c t i v e and d i a g n o s t i c model (SCABLE) f o r suburban l a t e n t heat f l u x e s . SCABLE i s used t o simulate the l a t e n t heat f l u x on 38 summer days i n a suburb of Vancouver. The performance i s adequate a t the d a i l y t i m e - s c a l e and i t i s concluded that such a model p r o v i d e s a promising approach f o r the s i m u l a t i o n of evaporation i n suburban environments. The poorer performance of SCABLE on an hourly b a s i s i s l i n k e d to two r e l a t e d f a c t o r s : stomatal r e s i s t a n c e i n response t o the s a t u r a t i o n d e f i c i t and modelling p o t e n t i a l temperature and t u r b u l e n t f l u x e s i n the a f t e r n o o n . -197-* The SW model alone over-estimates Q E, i n d i c a t i n g f i r s t l y t h a t the within-day v a r i a t i o n of the s u r f a c e r e s i s t a n c e s should be improved. Nonetheless, the SW i s a v a l i d methodology f o r p r e d i c t i n g evaporation from heterogeneous canopies. I t i s concluded t h a t f u r t h e r research i s r e q u i r e d t o determine whether t h i s approach i s more v a l i d than the "top-down" method of Grimmond (1988). * The mixed-layer model simulates the day-to-day v a r i a b i l i t y of the s a t u r a t i o n d e f i c i t , d e s p i t e e r r o r s on an hourly b a s i s . Conversely, the s i m u l a t i o n of mixed-layer depth i s poor. T h i s does not d e t r a c t from the a b i l i t y to model s u r f a c e evaporation. * S e n s i t i v i t y analyses i n d i c a t e t h a t , , i n terms of modelling evaporation, the i n i t i a l humidity step a t the base of the capping i n v e r s i o n and boundary-layer depth are l e s s important. However, the temperature g r a d i e n t above the mixed-layer, and the i n i t i a l temperature jump are c r u c i a l to the model's performance. 8.3 Suggestions f o r F u r t h e r Research Although the canopy model uses the r a t h e r crude eddy d i f f u s i v i t y approach to parameterise aerodynamic r e s i s t a n c e s w i t h i n the canopy, s e n s i t i v i t y analyses have revealed t h a t the modelled evaporation i s not s e n s i t i v e to the formulation used to parameterise the aerodynamic r e s i s t a n c e f o r the b l u f f body component. A l t e r n a t i v e l y , the stomatal r e s i s t a n c e of the t r e e s i s shown to be an e s s e n t i a l element and thus f u r t h e r study i s r e q u i r e d t o i d e n t i f y the stomatal response of urban t r e e s . The whole s u r f a c e r e s i s t a n c e f o r mulation, i n c l u d i n g the a l l o c a t i o n of values f o r the moisture s t a t u s of the v a r i o u s components of the greenspace, i s c r u c i a l to the accuracy of the canopy evaporation model. Q u a n t i f y i n g and m o d e l l i n g the area being i r r i g a t e d from e x t e r n a l water-use data thus r e q u i r e s f u r t h e r study. In f u t u r e the antecedent moisture c o n d i t i o n s should be i n c l u d e d . T h i s demands tha t a mass balance be i n t e g r a t e d i n t o the -198-present modelling scheme. Improving the s u r f a c e r e s i s t a n c e parameterisation scheme a l s o r e q u i r e s r e - c o n s i d e r a t i o n of the c o n t r i b u t i n g f e t c h / a r e a of i n f l u e n c e concept (see Schmid, 1988; and Grimmond, 1988). F i n a l l y , with regard to the within-canopy processes, the i n c o r p o r a t i o n of an improved r a d i a t i o n sub-model would enable the net r e c e i p t of r a d i a n t energy to be b e t t e r simulated. As with the surface r e s i s t a n c e scheme, t h i s would demand an improved d e s c r i p t i o n of the canopy s t r u c t u r e at the m i c r o - s c a l e . An inherent problem a s s o c i a t e d with i n c r e a s i n g the d e t a i l s of the m i c r o - s c a l e s t r u c t u r e i s t h a t t h i s has to be i n t e g r a t e d to provide a d e s c r i p t i o n of the e n t i r e canopy. I t i s important to recognise t h a t we are attempting to model the averaged f l u x from the e n t i r e suburban canopy. F u r t h e r study of the mixed-layer temperature problem i s needed - a more complex numerical modelling scheme may be r e q u i r e d . 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Clement (1986), Eddy f l u x e s of CO 2 , water vapor, and s e n s i b l e heat f l u x over a deciduous f o r e s t , Boundary-Layer Meteorol., 36, 71 - 91. Waggoner, P.E. and Re i f s n y d e r , W.E. (1968), Simulation of the temperature, humidity and evaproation p r o f i l e s i n a l e a f canopy, J. Appl. Meteorol., 7, 400 - 409. Webb, E.K., G.I. Pearman and R. Leunig (1980), C o r r e c t i o n of f l u x measurments f o r d e n s i t y e f f e c t s due to heat and water vapour t r a n s f e r , Quart. J. B. Met. Soc, 106, 85 - 100. Willmott, C.J. (1982), Some comment on the e v a l u a t i o n of model performance, Bull. Amer. Meteorol. Soc, 63, 1309 - 1313. Wooding, R.A., E.F. Bradley, and J.K. Marshall (1973), Drag due to r e g u l a r a r r a y s of roughness elements of varying geometry, Boundary-Layer Meteorol., 5, 285 - 308. Wyngaard, J.C. (1973), On sur f a c e l a y e r turbulence, i n D.A. Haugen (ed), Workshop on Micrometeorology, A.M.S., Boston, Mass. Yap, D.H. (1973), S e n s i b l e Heat Fluxes i n and Near Vancouver, B.C., Unpub. Ph.D. T h e s i s , Univ. of B r i t i s h Columbia, Vancouver. and T.R. Oke (1974), S e n s i b l e heat f l u x e s over an urban area - Vancouver, B.C., J. Appl. Meteorol., 13, 880 - 890. Y e r s e l , M. and R. Goble (1986), Roughness e f f e c t s on urban turbulence parameters, Boundary-Layer Meteorol., 37, 271 - 284. -210-APPENDIX 1: DEVELOPMENT OF AN OBJECTIVE URBAN HEAT STORAGE PARAMETERISATION SCHEME Al.1 I n t r o d u c t i o n O b t a i n i n g a value f o r the s o i l heat f l u x i s not d i f f i c u l t i n i d e a l i s e d environments, such as a bare s o i l , or s h o r t g r a s s l a n d where a range of e s t i m a t i o n and measurement techniques are a v a i l a b l e . The key f e a t u r e i s the homogeneity and w e l l - d e f i n e d l o c a t i o n of the a c t i v e s u r f a c e (Oke, 1987). In urban environments the a c t i v e s urface i s both m u l t i - f a c e t t e d and extremely complex, so the concept of a s u r f a c e volume i s adopted. Here, the 'storage heat f l u x ' {AQS) i n c l u d e s the conduction of heat i n t o the s u r f a c e media comprising the s u r f a c e volume (e.g. w a l l s , or t r e e s , e t c . ) , and changes i n the heat storage of the a i r volume i t s e l f . The task of d i r e c t measurement then becomes much more d i f f i c u l t , as i t i s necessary to sample a l l of these i n d i v i d u a l components. Recent l i t e r a t u r e documents o b s e r v a t i o n s of the storage heat f l u x i n f o r e s t e d canopies (see Aston, 1985; and Moore and F i s c h , 1985), where r e p l i c a t i o n of temperature sensors i n the canopy components i s f e a s i b l e . In the urban context there have been few attempts t o d i r e c t l y measure the storage heat f l u x f o r the i n t e g r a t e d canopy volume. Those o b s e r v a t i o n a l s t u d i e s t h a t examine the heat flow i n t o m a t e r i a l s such as concrete, or other surrogate urban s u r f a c e s are of i n t e r e s t , but these r e s u l t s cannot represent the e n t i r e urban canopy volume. Hence, r e s e a r c h has turned to m o d e l l i n g as a means of e v a l u a t i n g the s i z e of the urban heat storage component. Oke and Cleugh (1987) provide a summary of the attempts at m o d e l l i n g the urban heat storage f l u x . They conclude t h a t there i s s t i l l a need to c o n s t r u c t p h y s i c a l l y - b a s e d models which acknowledge the t h r e e - d i m e n s i o n a l i t y and complexity of the urban s u r f a c e - and are v a l i d a t e d by o b s e r v a t i o n s . Oke et al. (1981) i n i t i a l l y develop a model based on a l i n e a r r e l a t i o n s h i p between Q* and AQS. Oke and Cleugh (1987) demonstrate t h a t t h i s approach works adequately f o r d a i l y t i m e - s c a l e s . Observations suggest, however, t h a t the d i u r n a l r e l a t i o n s h i p i s n o n - l i n e a r , and c h a r a c t e r i s e d by a 'phase l a g ' i n the r e l a t i v e peaks of Q* and AQS. On the b a s i s of these o b s e r v a t i o n s , a n o n - l i n e a r ' h y s t e r e s i s model' i s forwarded. T h i s appendix develops and evaluates an o b j e c t i v e model f o r p r e d i c t i n g the storage heat f l u x a t an urban l o c a t i o n , w h i l s t m a i n t a i n i n g the form of the h y s t e r e s i s equation proposed by Oke and Cleugh. I t i s a composite model, d e r i v e d from separate h y s t e r e s i s equations f o r each s u r f a c e type comprising the urban volume. A1.2 Theoretical and Empirical Considerations L e t t a u (1951) presents a t h e o r e t i c a l model f o r s u r f a c e temperature, assuming t h a t the r a d i a n t energy at the bare s o i l s u r f a c e can be d e s c r i b e d as a harmonic f u n c t i o n , and using a p r e s c r i b e d , constant evaporation r a t e . He d e r i v e s an a n a l y t i c a l s o l u t i o n showing t h a t the d i u r n a l path of the s u r f a c e s o i l heat f l u x precedes t h a t of the s u r f a c e temperature by e x a c t l y 3 hours. In a s i m i l a r l y i d e a l i s e d environment, a s o l u t i o n f o r the heat conduction equation y i e l d s a s u r f a c e temperature which peaks i n phase with the net r a d i a t i o n ( i . e . the f o r c i n g ) . L e t t a u c i t e s t y p i c a l times f o r the observed peak i n s u r f a c e temperature f o r a v a r i e t y of s u r f a c e types. For c l a y , the time of maximum sur f a c e temperature i s 100 minutes a f t e r the peak i n Q* ( i . e . 1339 h r s ) . T h i s means t h a t the peak i n the s o i l heat f l u x -212-should occur a t 1039 h r s . T h i s n o n - l i n e a r r e l a t i o n s h i p between net r a d i a t i o n and s o i l heat f l u x r e s u l t s i n a ' h y s t e r e s i s ' p a t t e r n when s o i l heat f l u x i s p l o t t e d as a f u n c t i o n of net r a d i a t i o n (Figure A l . l ) . 16 12 08 A Q S ( W m 2 ) Q k 0 -Ok 10 30 50 Q * ( W m 2 ) F i g u r e A l . l : Comparison between s o i l heat and net r a d i a t i o n f l u x e s (from Camuffo and Be r n a r d i , 1982) Many o b s e r v a t i o n a l s t u d i e s note t h a t the s o i l heat f l u x should reach a maximum 3 hrs before the s u r f a c e temperature (see S e l l e r s , 1965; and Monteith, 1973). C l o t h i e r et al. (1986) observe t h a t the s o i l s u r f a c e temperature reaches a peak approximately two hours a f t e r s o l a r noon. They argue, s i m i l a r l y to L e t t a u , t h a t t h i s i m p l i e s a peak i n the s o i l heat f l u x a t about 1130 LAT, or approximately 1 hour out of phase with the net r a d i a t i o n . T h e i r r e s u l t s thus confirm these a n a l y t i c a l arguments f o r -213-c l o u d - f r e e days. I t i s of i n t e r e s t to note that the data are f o r a f u l l cover a l f a l f a crop, d u r i n g both wet and dry s o i l c o n d i t i o n s . Of course, the tim i n g of the s u r f a c e temperature peak i s i t s e l f an i s s u e of debate -mostly because the d e f i n i t i o n of the s u r f a c e i s so d i f f i c u l t i n a l l but the most simple environments. Fuchs and Hadas (1972) a l s o observe a h y s t e r e s i s e f f e c t i n the d i u r n a l p a t t e r n of the r a t i o of the s o i l heat f l u x to net r a d i a t i o n f o r a bare s o i l , as do de Bruin and H o l t s l a g (1982), and Idso et al. (1975). Despite t h i s evidence, p a r a m e t e r i s a t i o n s of the s o i l heat f l u x f o r r u r a l s i t e s have t y p i c a l l y i n v o l v e d a l i n e a r r e l a t i o n s h i p between net r a d i a t i o n and s o i l heat f l u x . A commonly c i t e d ' r u l e ' i s t h a t the magnitude of Q G i s 10% t h a t of Q*. T h i s l i n e a r approach was a l s o adopted by Oke et al. (1981). Although these approaches may y i e l d adequate r e s u l t s f o r mean d a i l y estimates, they l e a d t o i n c o r r e c t d i u r n a l v a r i a t i o n s i n the p a r t i t i o n i n g of a v a i l a b l e energy. An a l t e r n a t i v e approach i s forwarded by Camuffo and Bernardi i n 1982. They suggest t h a t the s o i l heat f l u x can best be parameterised by a n o n - l i n e a r equation: AQS = aQ* + b dQ*/dt + c ( A l . l ) T h i s form i s supported by t h e i r data which demonstrate a h y s t e r e s i s p a t t e r n s i m i l a r t o t h a t mentioned above. Thus, the s o i l heat f l u x d e n s i t y i s found to be a f u n c t i o n not o n l y of net r a d i a t i o n , but a l s o the r a t e and d i r e c t i o n of change of t h i s r a d i a n t f o r c i n g . The a and c c o e f f i c i e n t s are the same c o e f f i c i e n t s as i n the l i n e a r e quation. A p o s i t i v e value of b i m p l i e s a peak i n the s o i l heat f l u x p r i o r t o a peak i n the net r a d i a t i o n . -214-Camuffo and Bernardi f i n d a negative value f o r b, and a t t r i b u t e t h i s to the d r y i n g of the s o i l due to evaporation. As the s o i l moisture content of the s o i l d e c l i n e s , more s e n s i b l e heat i s a v a i l a b l e f o r conduction i n t o the s o i l . Although t h i s e x p l a n a t i o n has appeal i t i s not c o n s i s t e n t with the theory and must be i n c o r r e c t . I t would seem that there i s an anomaly i n t h e i r o b s e r v a t i o n s . A p h y s i c a l e x p l a n a t i o n f o r Lettau's a n a l y t i c s o l u t i o n , and the e m p i r i c a l f i n d i n g s , i s d i f f i c u l t to f i n d i n the l i t e r a t u r e . I t i s l i k e l y to be r e l a t e d t o the r a t i o of the atmospheric to s o i l thermal admittances (M a:M s). Thus i n the morning hours, the atmosphere i s s t i l l r e l a t i v e l y s t a b l e , hence s e n s i b l e heat i s t r a n s f e r r e d more r e a d i l y i n t o the s o i l . In the afternoon when the atmosphere i s unstable, and the c o u p l i n g of the boundary- and s u r f a c e - l a y e r s i s the g r e a t e s t , the t u r b u l e n t t r a n s f e r of heat i n t o the atmosphere i s more e f f i c i e n t than the molecular conduction i n t o the s o i l . Thus i t appears t h a t the equation proposed by Camuffo and Bernardi has g r e a t e r v a l i d i t y than l i n e a r r e g r e s s i o n models i n simple, homogeneous environments. Al-3 E s t i m a t i n g Heat Storage i n the Urban Environment A number of models have been developed t o p r e d i c t the magnitude of the urban heat storage component. These have p r e v i o u s l y been reviewed by Oke and Cleugh (1987). As noted there, the two approaches which attempt t o account f o r the three-dimensional complexity of the urban s u r f a c e (Terjung and o'Rourke, 1980; Siever9 and Zdunkowski, 1986) have not been v a l i d a t e d a g a i n s t o b s e r v a t i o n s . Other s t u d i e s have examined the s i z e of the conductive f l u x i n t o elements of the urban environment, such as as p h a l t ( N a r i t a et al. , 1984), concrete ( D o l l et al., 1986) and r o o f t o p s (Yap, 1973; and T a e s l e r , 1980). While these provide evidence of the thermal r o l e s played by each of these m a t e r i a l s , they are not u s e f u l i n advancing knowledge about the i n t e g r a t e d thermal response of the urban canopy. Hence, the only model which has been compared with measurements i s the l i n e a r model of Oke et al. (1981). T h e i r approach i s t o cons i d e r the s i z e of the conductive heat f l u x f o r many of the i n d i v i d u a l components which comprise the suburban canopy l a y e r . These f l u x e s are then expressed as r a t i o s of the a v a i l a b l e net r a d i a t i o n . A l i n e a r r e g r e s s i o n model i s developed f o r each s u r f a c e type, with the net r a d i a t i o n as the independent v a r i a b l e . These equations are then summed and weighted a c c o r d i n g to t h e i r a r e a l occurrence i n the study area. T h e i r f i n a l equation i s : AQS = 0.25 (Q*-27) Q*>0, (W m"2) (A1.2) AQS = 0.67 Q* Q*<=0,(W rr r 2 ) Although i t i s p o s s i b l e to adapt t h i s to other s i t e s by a d j u s t i n g the weightings, i t has only been developed and t e s t e d under a l i m i t e d set of c o n d i t i o n s . There are a number of p o i n t s t o be noted about t h i s f o r m u l a t i o n . F i r s t l y , i t assumes t h a t the storage f l u x i s l i n e a r l y r e l a t e d t o the net r a d i a t i o n . T h i s i s j u s t i f i e d by the presence of s u r f a c e s which are arranged i n t o 'canyons', thus any phase d i f f e r e n c e s e x h i b i t e d by i n d i v i d u a l surfaces are l i k e l y t o be c a n c e l l e d by those of other s u r f a c e s with d i f f e r e n t aspects and slope angles. -216-Secondly, the data used to represent urban canyons are f o r a p a r t i c u l a r s i t e which may not be r e p r e s e n t a t i v e of the types of canyon s t r u c t u r e s found i n suburban areas. T h i r d l y , the apportionment of the impervious component (comprised of canyons, pavements and rooftops) i s a r b i t r a r y - one t h i r d to each. Thus there i s no f l e x i b i l i t y t o allow the model to be t r a n s f e r r e d t o a l o c a t i o n with a d i f f e r e n t d i s t r i b u t i o n of impervious elements than those present at the developmental s i t e . In p a r t i c u l a r , there i s no i n c l u s i o n of the three dimensional nature of the a c t i v e s u r f a c e , as the land use components are based upon a two-dimensional p l a n view of the urban s u r f a c e . However, as was shown by the authors, the approach y i e l d s r e s u l t s which are reasonable, e s p e c i a l l y when used f o r p e r i o d s g r e a t e r than a day. Oke and Cleugh (1987) demonstrate t h a t the o v e r a l l magnitude of the storage heat f l u x e s p r e d i c t e d by the Oke et al. equation are confirmed by d i r e c t and i n d i r e c t measurements. I n t e r e s t i n g l y , they note t h a t the d i u r n a l trend of the storage f l u x appears to be c h a r a c t e r i s e d by a phase s h i f t , t h a t i s , the storage f l u x appears t o peak one to two hours e a r l i e r than the net r a d i a t i o n . Given t h a t both t h e o r e t i c a l and e m p i r i c a l evidence suggests t h a t t h i s i s t y p i c a l of simple s u r f a c e types, t h i s i s not n e c e s s a r i l y a s u p r i s i n g o b s e r v a t i o n , although i t c o n t r a d i c t s one of the assumptions i n i t i a l l y made by Oke et al. (1981). In Oke and Cleugh (1986), an e m p i r i c a l equation s i m i l a r i n form t o Camuffo and Bernardi i s developed f o r a l i m i t e d number of days when the storage heat f l u x i s measured f o r a suburban s i t e : A2S = ° - 3 5 Q* + ° - 2 8 dQ*/dt - 40 (A1.3) By comparing r e s u l t s from d i f f e r e n t s t u d i e s a t the same l o c a t i o n i n Vancouver i t was concluded t h a t t h i s type of equation f i t t e d the measured storage values w e l l . I t a l s o brought about more complete agreement between s e n s i b l e heat f l u x data which had been measured using d i f f e r e n t methodologies. However t h i s equation was e m p i r i c a l l y d e r i v e d from a very s m a l l s e t of data, under very s p e c i f i c c o n d i t i o n s . F o l l o w i n g on from the c o n c l u s i o n s of Oke and Cleugh (1986), i t i s a p p r o p r i a t e to develop an o b j e c t i v e p a r a m e t e r i s a t i o n scheme, adopting the h y s t e r e s i s model form. A1.4 Development of an Objective Storage Heat Flux Model The s i t e f o r which the model has been s p e c i f i c a l l y developed i s a suburban s i t e l o c a t e d i n Vancouver, B r i t i s h Columbia. The equations thus p e r t a i n t o the p a r t i c u l a r land useage a s s o c i a t e d with t h i s s i t e . I t s t r a n s f e r r a b i l i t y to another l o c a t i o n simply r e q u i r e s a s i m i l a r land-use a n a l y s i s to t h a t used below, t o d e r i v e the weightings which are then a p p l i e d to the b a s i c equations. (a) Land-Use A n a l y s i s S i m i l a r t o Oke et al. (1981), t h i s suburban area can be d i v i d e d i n t o the f o l l o w i n g land-use u n i t s : greenspace - u n i r r i g a t e d - i r r i g a t e d and b u i l t - h o r i z o n t a l , paved areas (concrete, a s p h a l t etc.) - r o o f t o p s - canyon arrangements -218-For the study area, the r e l a t i v e p r o p o r t i o n s of each of these components have been c a l c u l a t e d from land-use surveys. In order to improve upon the scheme devised p r e v i o u s l y , a method of accounting f o r the three-dimensional nature of the suburban environment was developed. From the land-use surveys t h e r e are 23,381 b u i l d i n g s i n a 2 km r a d i u s c i r c l e , c e n t r e d on the o b s e r v a t i o n a l tower at Mainwaring (Steyn, 1980). They are comprised of 34% garages; 64% houses; and 2% l a r g e r b u i l d i n g s . The mean dimensions of each component are summarised i n Table A l . l . Table A l . l : Mean dimensions of buildings Component LxW(m2) Height(m) House 100 8 Garage 40 3.5 Larger 1700 15 Weighted Mean 111.6 6.6 where L i s length and W i s width. Thus each 'average' roughness element has a mean w a l l area of (111.6 1/ 2 X 6.6 X 4 w a l l s ) = 279 m2. With a t o t a l p l a n area surrounding the tower of 12.6 x 10 6 m2 and 23,000 roughness elements, there are approximately 1.8 roughness elements/1000 m2 of p l a n a r e a . Hence, f o r each 1000 m2 l o t , there are 500 m2 ( i . e . 279 m2 x 1.8) of w a l l . The roof area i n the same l o t i s simply 200 m2 (111.6 X 1.8), l e a v i n g 800 m2 remaining to be subdivided between greenspace and impervious land use. Using the previous estimates of the percentage greenspace i n the Sunset area (64%), 640 m2 w i l l be greenspace, and the remaining 160 m2 can be considered to be impervious. -219-The importance of such an approach i s r e a l i s e d when each of the s u r f a c e areas f o r these components i s summed. The t o t a l a c t i v e area f o r each 1000 m2 i s a c t u a l l y 1500 m2. Given t h i s , the percentages f o r each of the components are now: 43% greenspace (640/1500) 13% roof (200/1500) 11% impervious (160/1500) 33% v e r t i c a l w a l l s , or canyons (500/1500) These can be compared to the p r e v i o u s breakdown o f : 64% greenspace 12% roof 12% impervious 12% canyons C l e a r l y the new weighting emphasises the v e r t i c a l w a l l component to a g r e a t e r extent than p r e v i o u s l y , and allows f o r the f a c t t h a t i n any two dimensional p l a n area, the active surface area w i l l be g r e a t e r than the plan-view area (see F i g u r e A1.2). R O O F T O P V IMPERVIOUS = 2 0 0 m 2 V PAVEMENT IMPERVIOUS = 160m* GREENSPACE =640m 2 P L A N V I E W Area = 1000m 2 31.6 m. 31.6m. Figure A1.2: Schematic of impervious/pervious areas i n 1000 m2 l o t area -220-(b) Input Data A range of s o i l heat f l u x / n e t r a d i a t i o n data-sets were i d e n t i f i e d which represented each of these components: (i) Green space A number of d a t a - s e t s were combined to y i e l d an equation f o r the greenspace component. The main c r i t e r i o n f o r s e l e c t i o n was the assurance th a t the s u r f a c e s o i l heat f l u x was measured - with no f l u x divergence between the s o i l heat f l u x sensor and the s u r f a c e . I n i t i a l l y , s t u d i e s r e p r e s e n t a t i v e of both moist and dry c o n d i t i o n s were s e l e c t e d , so t h a t two separate equations c o u l d be developed - f o r i r r i g a t e d and u n i r r i g a t e d greenspace. However th e r e d i d not appear to be any c o n s i s t e n t d i f f e r e n c e s between the two s e t s of equations, and t h e i r d i s t i n c t i o n was abandoned. Another c r i t e r i o n was t h a t the s t u d i e s be conducted over reasonably short g r a s s , as t y p i c a l l y found i n urban environments. These l i m i t a t i o n s e x p l a i n the l a r g e r p r o p o r t i o n of net r a d i a t i o n being channelled i n t o the s o i l heat f l u x (33%) than g e n e r a l l y quoted i n the l i t e r a t u r e . The data s e l e c t e d are considered to represent an a p p r o p r i a t e range of c o n d i t i o n s f o r a suburban s i t e . The D o l l et al. (1986) data are taken from a study of s o i l heat f l u x e s measured i n a s h o r t grass s u r f a c e (part of an unused runway). The short grass appears to be w e l l s u p p l i e d with moisture (10% immediately at the s u r f a c e , t o 45% a t a depth of 0.34 m). The data from the Wangara study, conducted from J u l y - September i n South A u s t r a l i a (see C l a r k e et al., 1971), represent f a i r l y dry s o i l with g r a s s , whereas the s o i l heat f l u x values from Novak (1981) are f o r bare s o i l over a range of moisture c o n d i t i o n s . -221-(ii) Rooftops Rooftop conductive heat f l u x and net r a d i a t i o n data are a v a i l a b l e f o r two urban l o c a t i o n s ; Vancouver (see Yap, 1974) and Uppsala (the Hotel Uplandia s i t e , T a e s l e r , 1980). (iii) Pavement The m a t e r i a l s making up the urban pavement component are not homogeneous, t h e r e f o r e two s e t s of data are used - a s p h a l t and concrete. The a s p h a l t data are from measurements conducted i n a s p h a l t blocks, N a r i t a et al. (1984), and the concrete data are fromthe D o l l et al. (1986) study. The a s p h a l t blocks were i n s u l a t e d t o prevent heat flow through the s i d e s , so o n l y v e r t i c a l heat flows are recorded. (iv) Canyon The canyon data are the same as used by Oke et al. (1981) and represent an i n t e n s i v e s e t of measurements of the s p a t i a l l y - i n t e g r a t e d heat f l u x e s i n t o the e a s t and west f a c i n g w a l l s of a north-south o r i e n t e d canyon, i n Vancouver (see Nunez, 1975). The net r a d i a t i o n f o r the canyon as a whole was a l s o e valuated, and used to develop the equation f o r the canyon component. I t i s of i n t e r e s t t o note t h a t the b - c o e f f i c i e n t f o r the canyon data i s very s m a l l . R e c a l l i n g the j u s t i f i c a t i o n p r o v i d e d by Oke et al, 1981 (see above), t h i s suggests t h a t the arrangement of east/west f a c i n g w a l l s , and the north/south o r i e n t a t i o n of the canyon f l o o r tends to cancel out the h y s t e r e s i s e f f e c t s e vident f o r each of the i n d i v i d u a l canyon components. A study by Ferguson (1987) i n d i c a t e s t h a t the e a s t and west f a c i n g w a l l s d i d show a h y s t e r e s i s e f f e c t , each having a reversed c y c l e , and the f l o o r showing a much more narrow h y s t e r e s i s loop, where the net r a d i a t i o n and s o i l heat f l u x are approximately i n phase. -222-Table A1.2: Summary of equations used i n parameterisation scheme Land-Use Author Weighting Type 1) Greenspace s h o r t grass D o l l et al. Wangara Clarke et al. bare s o i l Novak Regression C o e f f i c i e n t s ( A l . l ) 0.3 0.54 -27.4 0.33 0.026 -11.0 0.38 0.56 -27.3 Weighted Mean Weighting Fa c t o r = 0.43 0.145 0.161 -11.8 2) Rooftops Vancouver Uppsala Yap T a e s l e r 0.167 0.102 -17.0 0.44 0.57 -28.9 Weighted Mean 0.039 0.044 -2.98 Weighting Factor = 0.13 3) Impervious concret e D o l l et al. 0.81 0.48 -79.9 a s p h a l t N a r i t a et al. 0.36 0.23 -19.3 Weighted Mean Weighting F a c t o r = 0.11 0.064 0.039 -5.46 4) Canyon Grandview Nunez 0.32 0.014 -27.7 Weighted Mean Weighting Fa c t o r = 0.33 0.106 0.005 -9.14 TOTAL Note: U n i t s = w m"2 0.35 0.25 -29.4 -223-(c) R e s u l t i n g Model Equations Combining these equations and the a c t i v e area weighting scheme y i e l d s a r e v i s e d form of the suburban heat storage p a r a m e t e r i s a t i o n : AQsp = 0.35 Q* + 0.25 dQ*/dt - 29.4 (W m"2) (A1.4) Table A1.2 summarises the i n d i v i d u a l , and weighted average equations f o r a l l the land-use types. T r a n s f e r r i n g t h i s equation to other l o c a t i o n s simply r e q u i r e s an e v a l u a t i o n of the component areas (greenspace, r o o f s , impervious and canyons). The p r o p o r t i o n s of these provide the weightings to be a p p l i e d to each c o e f f i c i e n t of the component equation. A1.5 Preliminary Evaluation of Urban Heat Storage Model The storage heat f l u x has been estimated using the approaches d i s c u s s e d i n Chapter 2 and. The 'measured' storage heat f l u x can be estimated: A2 S S = Q* - Q H s f l + t f - 1 ) (A1.5) Fi g u r e A1.3 i l l u s t r a t e s the agreement between the hourly storage heat f l u x (parameterised u s i n g equation A1.4), and th a t measured (equation A1.5). C l e a r l y , there i s c o n s i d e r a b l e s c a t t e r , although the e r r o r s can p o t e n t i a l l y become very l a r g e when storage heat f l u x e s are measured as r e s i d u a l s (19 - 32% f o r A Q S S ) - T n e s t a t i s t i c s i n d i c a t e reasonable agreement, i n l i g h t of these magnitudes of e r r o r . The index of agreement, d, i s 0.92, r 2 i s 0.78, mean abs o l u t e e r r o r (MAE) i s 38 W m - 2, and r o o t mean square e r r o r (RMSE) i s 48 W m - 2. The systematic and non-systematic e r r o r s are of the same magnitude. The equation f o r the l i n e of best f i t r e v e a l s that the modelled storage i s a s l i g h t underestimate of the 'measured' . -224-STORAGE HEAT FLUX:MEASURED <W in" 2 ) Figure A1.3: Comparison between measured (^QS S) and modelled (A2 Sp) hourly storage heat flux STORAGE HEAT FLUX:MEASURED (W m - 2 ) Figure A1.4: Comparison between measured (4Q s s) and modelled (^Qsp) mean daylight-hours storage heat flux -225-F i g u r e A1.4 shows the agreement between 'measured' and modelled storage as d a y l i g h t - h o u r means. The equation of best f i t i s s i m i l a r to t h a t f o r the ho u r l y data, as would be expected, with an improvement i n the MAE (15 W m~ 2), and RMSE (20 W m" 2). The unsystematic RMSE i s s l i g h t l y l a r g e r than the systematic RMSE, and the r 2 i s 0.70, and d = 0.90. F i n a l l y , note t h a t the c o e f f i c i e n t s i n the model (Table A1.3) are q u i t e s i m i l a r t o those obtained by Oke and Cleugh (1987). Table A1.3: Size of objective hysteresis co e f f i c i e n t s compared to Oke and Cleugh (1987) a b c Present 0.35 0.25 -29.4 Oke and Cleugh 0.30 0.25 -22.0 T h e i r c o e f f i c i e n t s were d e r i v e d by performing a m u l t i p l e r e g r e s s i o n between measured ^Q s s and Q*, dQ*/dt. These represent a s u r f a c e - l a y e r measurement of the storage heat f l u x . T h e i r e m p i r i c a l model i s thus based on the combined c o n t r i b u t i o n of a l l the i n d i v i d u a l s u r f a c e elements t o AQS. In a sense t h i s approach i s " l o c a l - s c a l e " . I t can be c o n t r a s t e d t o the "micr o - s c a l e " approach t o the development of the c u r r e n t model - where the conductive h e a t i n g f o r each of the sur f a c e elements and i t s r e l a t i o n s h i p to Q*, are i n t e g r a t e d "upwards". The agreement i l l u s t r a t e d i n Table A1.3 o f f e r s a degree of i n d i r e c t support t o the model developed h e r e i n . Al.6. Discussion The value f o r the b c o e f f i c i e n t i s p o s i t i v e , both i n the composite model (equation A1.4), and i n the equations f o r each land-use (Table A1.2). T h i s i n d i r e c t c o n t r a s t with the f i n d i n g s of Camuffo and B e r n a r d i , but i s i n -226-'canyon' component of a suburban area comprises o n l y a t h i r d of the o v e r a l l a c t i v e s u r f a c e , and hence the other c o e f f i c i e n t s a l s o become important -l e a d i n g t o a r e l a t i v e l y l a r g e b. When dQ*/dt becomes zero, the equation reduces t o : A<2S = 0.33 Q* - 29.5 (A1.6) compared t o : AQS = 0.25 Q* - 6.7 (A1.7) from Oke et al. (1981). T h i s means tha t the c u r r e n t model tends to channel more energy i n t o storage and r e s u l t s i n a l a r g e r peak storage value. On a d a i l y b a s i s , these d i f f e r e n c e s w i l l be s m a l l . T h i s i s e s p e c i a l l y so because subsequent measurements of no c t u r n a l AQS r e v e a l i t to be a g r e a t e r p r o p o r t i o n of Q* than the Oke et al. model suggests. -227-APPENDIX 2: CALCULATION OF PERCENTAGE SURFACE TYPES IN SOURCE AREA ( i ) 80% of the p l a n area i n the 2 km source area surrounding the instrument tower i s comprised of h o r i z o n t a l surfaces (Appendix 1), and the remaining 20% of three-dimensional roughness elements or b l u f f - b o d i e s ( t r e e s and b u i l d i n g s ) . T h i s d i v i s i o n of p l a n area i s on the b a s i s of h o r i z o n t a l ( r e f e r r e d to as the s u b s t r a t e ) compared to three-dimensional (bluff-body) surfaces o n l y . ( i i ) Steyn (1980) and Kalanda (1979) c a l c u l a t e d t h a t 64% of the p l a n area i n the source area i s greenspace and 36% i s impervious. Therefore t h i s d i v i s i o n i s on the b a s i s of p e r v i o u s , compared to impervious s u r f a c e s . ( i i i ) I t i s assumed t h a t a l l greenspace i s a l s o h o r i z o n t a l , or s u b s t r a t e , whereas the impervious area i s made up of both b l u f f - b o d y and s u b s t r a t e components. The c a l c u l a t i o n s i n Appendix 1 i l l u s t r a t e that f o r the 36% which i s impervious, 20% i s r o o f t o p ( i . e . a p a r t of the b l u f f - b o d y a r e a ) , and 16% i s pavement ( i . e . a p a r t of the s u b s t r a t e ) . ( i v ) For the 64% of the p l a n area t h a t i s designated as greenspace, a survey of the land-use i n the area i n d i c a t e d t h a t 8% (of the e n t i r e p l a n area) i s u n i r r i g a t e d park. The r e f o r e 56% (of the e n t i r e p l a n area) i s deemed ' p o t e n t i a l l y i r r i g a t e d greenspace' i . e . r e s i d e n t i a l lawns which may be subjected to a r t i f i c i a l i r r i g a t i o n . T h i s d i v i s i o n i s approximate, and based on a Vancouver Parks Board i n f o r m a t i o n sheet, which i n d i c a t e s the area of a l l the parks i n Vancouver. From conversations with the s t a f f of the Park Board, i t appears t h a t most parks are u n i r r i g a t e d , with the -228-exception of those used f o r summer sp o r t . Thus, the area of parks was c a l c u l a t e d , f o r the c o n t r i b u t i n g f e t c h , and t h i s area designated as u n i r r i g a t e d . 50% of the area of Mountain View Cemetery was a l s o considered as u n i r r i g a t e d . These percentages t r a n s l a t e i n t o 10% of the e n t i r e plan s u b s t r a t e area i s u n i r r i g a t e d , and 70% i s p o t e n t i a l l y i r r i g a t e d . The remaining 20% (of the s u b s t r a t e area, or 16% of the e n t i r e plan area) i s pavement. (v) For the 20% of the p l a n area which i s b l u f f - b o d y , the computations presented i n Appendix 1 i n d i c a t e t h a t f o r each 1000 m2 of p l a n area, 500 m2 i s w a l l , and 200 m2 i s r o o f , l e a d i n g to an a d d i t i o n a l 500 m2 of a c t i v e s u r f a c e area and thus 1500 m2 of t o t a l a c t i v e surface area i n any 1000 m2 l o t ( i . e . 800 m2 s u b s t r a t e + 700 m2 b l u f f - b o d y ) . ( v i ) A separate study (Grimmond, pers. comm.) documents approximately 685 t r e e s i n an area of 250,000 m2 surrounding the Mainwaring s i t e . Taking t h i s f r a c t i o n to be r e p r e s e n t a t i v e leads to 2.74 trees/1000 m2 of p l a n area. M o d e l l i n g each t r e e as a sphere (average r a d i u s of 2 m) r e s u l t s i n 91.8 m3 of tree/1000 m2 of p l a n area. T h i s i s rounded up to 100 m2. Thus, with 700 m2 of b u i l d i n g (impervious) a c t i v e s u r f a c e and 100 m2 of t r e e , the t o t a l a c t i v e s u r f a c e area i n the 1000 m2 l o t i s 1600 m2. -229-( v i i ) Combining these data y i e l d s the f o l l o w i n g breakdown: * A c t i v e A c t i v e A c t i v e * A c t i v e A c t i v e A c t i v e s u r f a c e area s u b s t r a t e area greenspace impervious b l u f f - b o d y area impervious t r e e s p l a n a r ea s u b s t r a t e area greenspace impervious b l u f f - b o d y area 1 6 0 0 m 2 (100%) 800 m2/1600 m2 (50%) 640 m2/1600 m2 (40%) 160 m2/1600 m2 (10%) 800 m2/1600 m2 (50%) 700 m2/1600 m2 (43.8%) 100 m2/1600 m2 (6.2%) 1 0 0 0 m 2 (100%) 800 m2/1000 m2 (80%) 640 m2/1000 m2 (64%) 160 m2/1000 m2 (16%) 200 m2/1000 m2 (20%) -230-APPENDIX 3: INSTRUMENT CALIBRATIONS AND ERROR ANALYSES A3.1 Relative Humidity and Temperature Sensors The a r r a y of sensors mounted on the 30 m tower a t Mainwaring provides the a b i l i t y t o intercompare the three temperature and the two r e l a t i v e humidity sensors. The three instruments are r e f e r r e d t o as the Rotronics sensor (measuring r e l a t i v e humidity and temperature), the d i f f e r e n t i a l psychrometer (measures dry- and wet-bulb temperatures), and the Campbell S c i e n t i f i c t h e r m i s t o r (measures dry-bulb a i r temperature o n l y ) . F i g u r e A3.1 i l l u s t r a t e s the c o r r e l a t i o n between the dry-bulb temperature measured by the d i f f e r e n t i a l psychrometer, and the Campbell S c i e n t i f i c t h e r m i s t o r . I t i s c l e a r t h a t the agreement i s e x c e l l e n t . This confirms the p r e c i s i o n of both instruments. The c o r r e l a t i o n between the dry-bulb temperature measured by the d i f f e r e n t i a l psychrometer and the R o t r o n i c s sensor i s presented i n F i g u r e A3.2. There i s s l i g h t l y more s c a t t e r i n t h i s r e l a t i o n s h i p , with a c o n s i s t e n t o f f s e t of 1.5 °C (the reasons f o r t h i s are unknown). However, except f o r the o f f s e t , the agreement i s s t i l l v ery good and thus the R o t r o n i c s a i r temperature can be c o r r e c t e d , by i n c l u d i n g the o f f s e t . F i g u r e A3.3 demonstrates the agreement between the r e l a t i v e humidity d e r i v e d from the d i f f e r e n t i a l psychrometer wet- and dry- bulb measurements, and the r e l a t i v e humidity measured using the R o t r o n i c s sensor. Although there i s some s c a t t e r , the agreement i s a l s o e x c e l l e n t . -231-fcmocr«ture (01ffcrct(•«l flyfironci«.\f °C Figure A3.1: Comparison of temperature measured using Campbell S c i e n t i f i c t h e r m i s t o r , and thermocouple from r e v e r s i n g psychrometer T e m p « r « t w r « (Differential P t T t h r o M l f r ) / °C Figure A3.2: Comparison of temperature measured u s i n g R o t r o n i c s t h e r m i s t o r , and thermocouple from r e v e r s i n g psychrometer -232-A3.2 V e r t i c a l Wind Velocity and Temperature: Spectra and Co-Spectra Roth (1988) measured the time s e r i e s of the temperature and v e r t i c a l wind speed s i g n a l s , from the s o n i c anemometer/thermometer system. From these time s e r i e s (measured a t 10 Hz), the i n d i v i d u a l s p e c t r a , and the c o - s p e c t r a f o r these p r o p e r t i e s can be computed. Roth (1988) shows th a t the s p e c t r a and co-spectra f o r the suburban s i t e agree very c l o s e l y with those of Kaimal (1972). The SATS system i s performing adequately. These are among the f i r s t such spectra t o be computed f o r the suburban environment, and are e s p e c i a l l y encouraging. F i g u r e A3.4 i l l u s t r a t e s the comparison between the s e n s i b l e heat f l u x measured using the 21X data logger, covariance software and an averaging time of 15 min; and those c a l c u l a t e d by Roth using an averaging time of 60 min. The c r i t e r i a f o r minimum e r r o r s suggested by Wyngard (1973) y i e l d s an a p p r o p r i a t e averaging time of about 50 min f o r the Mainwaring s u b s t a t i o n s i t e . I t i s evident from F i g u r e A3.4 t h a t the e r r o r s introduced by using o n l y a 15 min averaging i n t e r v a l are minimal. Note th a t f o r the s e n s i b l e heat f l u x e s d e r i v e d from the 15 min averages, 4 of these 15 min averages are summed to y i e l d an average f l u x f o r the hour, i . e . the i n d i v i d u a l 15 min averages are not used. For f u r t h e r d i s c u s s i o n , and d e t a i l s , r e f e r t o Roth (1988). A3.3 The Reversing D i f f e r e n t i a l Psychrometer System (a) C a l i b r a t i o n Each d i f f e r e n t i a l wet- and dry-bulb sensor c o n s i s t s of a 10- j u n c t i o n thermopile. These were c a l i b r a t e d by the manufacturer a t room temperature (20°C), over a range of ± 5°C. T h i s range covers the maximum temperature -233-10 20 30 <40 SO to 70 So 90 100 R e l a t i v e Humidity ( R o t r o n t c t ) / I F i g u r e A3.3: Comparison of r e l a t i v e humidity measured u s i n g R o t r o n i c s sensor, and computed from r e v e r s i n g d i f f e r e n t i a l psychrometer system F i g u r e A3.4: Comparison of s e n s i b l e heat f l u x d e n s i t y computed usi n g a 60 min and 4 x 15 min averaging time (from Roth, 1988) 300 50 100 150 200 250 Sensible heat flux averaaed over 60' -234-d i f f e r e n c e range l i k e l y to be encountered i n the urban environment. The s t a t i s t i c s i n d i c a t e a small RMSE, and high r 2 (>0.99) hence the accuracy i s high. The equations of best f i t are used t o convert the m i c r o v o l t s i g n a l to temperature d i f f e r e n c e s (°C). (b) E r r o r A n a l y s i s F o l l o w i n g Kalanda (1979), the method of Cook and Rabinowicz (1963) i s used t o compute the absolute and r e l a t i v e e r r o r s f o r 0, and hence the e r r o r s a s s o c i a t e d with the s e n s i b l e and l a t e n t heat f l u x e s d e r i v e d from the Bowen r a t i o - e n e r g y balance (BREB) approach. The expected e r r o r i n any parameter Sp where p = F ( x l f x 2 ) , i s : Sp = [(dp/dxx SXl)2 + (dp/dx2 Sx2)2]i/* (A3.1) Thus, f o r Arw, the equation i s : Aiw = mx + c where x = 4TW ( m i c r o v o l t s ) m = slope c = i n t e r c e p t Sx = e r r o r i n x Thus, ^Tw = 2.48xl0" 3(x) + -0.00326 (A3.2) The e r r o r i n ATw i s , t h e r e f o r e : 5 {ATW) = [ {(5(<ATw)/3c .o"c)2} + {(3(Arw)/3m . Sta)2} + {{d{Alvi)/dx . Sx)2}] !/2 F o l l o w i n g Kalanda (1979), t h i s reduces t o : 6 (ATW) = [{Sc)2 + (x.5m) 2 + (m.o"x) 2 ] 1 / 2 (A3.3) The same procedure can be performed f o r the ^ Td s i g n a l s . -235-For ATw, the e r r o r of the i n t e r c e p t , Sc i s 0.00347805. The e r r o r of the slope (Sm) i s 0.00000290. F i n a l l y , the e r r o r i n the s i g n a l (Sx) must be computed from the s p e c i f i c a t i o n s f o r the 21X data logger. These c i t e an e r r o r of 0.05% of the F u l l Scale Range, f o r the accuracy of the voltage measurement. The FSR used was 5 mV, and t h e r e f o r e the accuracy i s 2 . 5 x l 0 - 3 mV. The e r r o r , then i n Aiw i s approximately 0.007°C. Th i s leads to a 5 -15% e r r o r i n the range of temperature d i f f e r e n c e s measured at the suburban Mainwaring s u b s t a t i o n s i t e . Once S(ATw) and S(Aid) have been determined, an e r r o r f o r the measured Bowen r a t i o , B i s computed: SB = [(8B/d(ATw) . S(ATw))2 + (8B/d(ATd) . S(ATd))2 + (dB/ds . Ss)2]1/2 (A3.4) where s = slope of the s a t u r a t i o n vapour pressure/temperature curve. Kalanda (1979) so l v e s the p a r t i a l d i f f e r e n t i a l equations f o r dB/d(ATw); 8B/d(ATd); and dB/ds, and these are used to c a l c u l a t e 98. S i m i l a r l y , the s e n s i b l e , and l a t e n t heat f l u x d e n s i t i e s are computed a c c o r d i n g to the f o l l o w i n g equations: Q„ = [ ( Q * - 4 2 s ) / ( l + 0 ) ] . 0 Q E = [ ( Q * - A 2 s ) / ( 1 + ' ? ) 1 Thus, the e r r o r i n Q H and i n Q E can f o r the p a r t i a l d i f f e r e n t i a l s presented net r a d i a t i o n , and storage heat f l u x i s (1979). -236-be c a l c u l a t e d using the s o l u t i o n s i n Kalanda, 1979. The e r r o r f o r the s e t to 5% of Q*, f o l l o w i n g Kalanda Figure A3.5: Diurnal variation of sensible and latent heat flux density for J.D. 201, with error bars -237-For measured 8 of 1.5 to 2.0, the r e s u l t a n t e r r o r s are of the order of 10 - 15% f o r the s e n s i b l e heat f l u x , and 15 - 20% f o r the l a t e n t heat f l u x . F i g u r e A3.5 i l l u s t r a t e s a t y p i c a l energy balance with the e r r o r s marked. Note th a t when 8 becomes l a r g e , t h i s i s propogated as l a r g e e r r o r s i n Q H , and e s p e c i a l l y Q E. A3.4 Bowen Ratio-Energy Balance (BREB) and Eddy Correlation Approaches (a) C o r r e c t i o n of La t e n t Heat Fluxes f o r Density V a r i a t i o n s Webb et al. (1980) d i s c u s s c o r r e c t i o n s which are r e q u i r e d when measuring the f l u x of a minor c o n s t i t u e n t of the atmosphere, i n c l u d i n g water vapour and carbon d i o x i d e . These c o r r e c t i o n s a r i s e from the need to account f o r v a r i a t i o n s "of the c o n s t i t u e n t ' s d e n s i t y due to the presence of a f l u x of heat and/or water vapour" (Webb et al., 1980). The crux of t h e i r argument i s as f o l l o w s , a p o s i t i v e heat f l u x during the day i m p l i e s t h a t r i s i n g a i r p a r c e l s w i l l be, on average, warmer and l e s s dense than descending a i r p a r c e l s . Thus, i f we assume a zero mean v e r t i c a l mass f l u x of a i r , there must a l s o be a small upward v e l o c i t y component. The c o n t r i b u t i o n of t h i s v e r t i c a l v e l o c i t y component, and i t s c o r r e l a t i o n with the f l u x of the c o n s t i t u e n t w i l l not be in c l u d e d i n measurements of the c o n s t i t u e n t f l u x . For f l u x - g r a d i e n t measurements, the c o r r e l a t i o n between the f l u c t u a t i o n s f o r t h i s c o n s t i t u e n t and the v e r t i c a l wind speed i s assumed to be r e l a t e d t o the mean gr a d i e n t of the c o n s t i t u e n t , and the t r a n s f e r c o e f f i c i e n t . T h e r e f o r e , a f l u x measured using t h i s approach a l s o r e q u i r e s c o r r e c t i o n . Webb et al. (1980) i l l u s t r a t e t h a t f o r the s e n s i b l e heat f l u x , t h i s c o r r e c t i o n i s very s m a l l , and t h e r e f o r e can be ignored. However they do -238-i n d i c a t e t h a t f o r C0 2, e s p e c i a l l y , and i n some cases water vapour, t h i s c o r r e c t i o n i s important. Therefore, the Q E f l u x e s d e r i v e d from both the Bowen r a t i o and the eddy c o r r e l a t i o n systems must be c o r r e c t e d , u s i n g the f o l l o w i n g formula, from Webb et al.: Q E ( c o r r e c t e d ) = (1+^er)[i+(L„/C a) ( P V / P r ) 0 I a wJ Q E(raw) (A3.5) T h i s c o r r e c t i o n was a p p l i e d to a l l measurements of Q E B (the l a t e n t heat f l u x c a l c u l a t e d using BREB). For a 0 of 2.0, t h i s y i e l d s a d i f f e r e n c e i n QEB of approximately 10%. (b) Comparison of Q H S v Q H B The f i r s t step to a r r i v i n g a t the best estimate f o r Q E i s to compare the performance of the two measurement systems. To achieve t h i s , SATS-based measurements of Q H (Q Hg) are compared with Bowen r a t i o - e n e r g y balance estimates ( Q H B ) . F i g u r e A3.6 shows the daytime mean values of Q „ s and Q H B, and as the s t a t i s t i c s i n d i c a t e , there i s a strong c o r r e l a t i o n between the two, with a tendency f o r Q H B to be g r e a t e r than Q H S. The index of agreement (d) between these two measurements i s 0.94, r 2 = 0.82, and a MAE (Mean Absolute E r r o r ) of 12 W m"2. Although the s c a t t e r of p o i n t s suggests some n o n - l i n e a r i t y i n the r e l a t i o n s h i p , there are i n s u f f i c i e n t data a t the low and high values of Q H f o r t h i s t o be c o n c l u s i v e . A s i m i l a r l y s t r o n g r e l a t i o n s h i p i s observed between Q E B and Q E R (Figure A3.7), with s l i g h t l y more s c a t t e r , d = 0.89, r 2 = 0.73, and MAE = 12 W rn"2. T h i s s c a t t e r can be reduced (MAE = 9.5 W m - 2, d = 0.93, r 2 = 0.8) by removing data p o i n t s f o r seven days, when i t i s known th a t instrument problems may have c o n t r i b u t e d to the l a r g e d i f f e r e n c e s (see Figure A3.8). The hourly values of Q H S and Q H B e x h i b i t more s c a t t e r ( F i g u r e A3.9), but the agreement i s good (MAE = 32 W i r T 2 , r 2 = 0.77, d = 0.93) c o n s i d e r i n g -239-fNj 40 60 80 100 120 140 160 180 200 220 SENSIBLE HEAT FLUX:eddy correlation (W m" 2 ) Figure A3.6: Comparison of mean daylight-hours sensible heat flux determined using Bowen ratio-energy balance (Q H B) and eddy correlation approaches (Q H S) 20 40 60 80 100 120 LATENT HEAT FLUX:eddy correlation (W m- 2 ) Figure A3.7: Comparison of mean daylight-hours latent heat flux determined using Bowen ratio-energy balance (Q B B) and eddy correlation-energy balance (Q E R) approaches -240-—1 1 I I I 20 40 60 80 100 Latent Heat Flux: Bowen Ratio/Energy Balance (W m - 2 ) Fi g u r e A3.8: Comparison of mean d a y l i g h t - h o u r s l a t e n t heat f l u x determined u s i n g Bowen rat i o - e n e r g y - b a l a n c e and eddy c o r r e l a t i o n - e n e r g y balance approaches: s e l e c t e d days -241-F i g u r e A3.9: Comparison of h o u r l y s e n s i b l e heat f l u x determined using Bowen r a t i o - e n e r g y balance ( Q H B ) and eddy c o r r e l a t i o n ( Q H S ) approaches - 242 -these are t u r b u l e n t f l u x e s , measured i n an urban s u r f a c e - l a y e r . These f i g u r e s i n d i c a t e t h a t the e r r o r i s mostly non-systematic, and a l s o confirms the a b i l i t y of the present measurement systems to measure the t u r b u l e n t l a t e n t and s e n s i b l e heat f l u x e s . I t i s c l e a r that any e v a l u a t i o n of the model w i l l be l i m i t e d by the magnitudes of these e r r o r s . These r e s u l t s , together with the c o n f i r m a t i o n of the s o n i c anemometer-thermometer system r e s u l t i n g from the s p e c t r a l a n a l y s i s undertaken by Roth (1988) suggest t h a t both the eddy c o r r e l a t i o n and d i f f e r e n t i a l psychrometer systems performed adequately, and t h a t t u r b u l e n t f l u x e s d e r i v e d from them are r e l i a b l e . A3.5 Other Measurement E r r o r s The magnitude of the between-instrument d i f f e r e n c e s has been p r e v i o u s l y d i s c u s s e d , and i n d i c a t e t h a t they are of the order of 10 - 15 W m - 2. The formal e r r o r a n a l y s i s f o r the d i f f e r e n t i a l psychrometer system has been presented, and the magnitudes of other e r r o r s are now c o n s i d e r e d . F i r s t l y , the e r r o r a s s o c i a t e d with the measurement of net r a d i a t i o n has been r e f e r r e d to p r e v i o u s l y i n the l i t e r a t u r e , and commonly s e t to ± 5% (Cleugh and Oke, 1986). I t i s d i f f i c u l t t o assess the a c t u a l measurement e r r o r a s s o c i a t e d with eddy c o r r e l a t i o n estimates of the s e n s i b l e heat f l u x (QHS). The r e s u l t s from Roth (1988) i n d i c a t e t h a t the s o n i c anemometer-fine wire thermocouple system i s measuring the w'T' C O - s p e c t r a adequately. An intercomparison of two such instruments a t the Mainwaring s u b s t a t i o n s i t e measured h o u r l y RMSE's of 12 W m - 2, i n d i c a t i v e of high p r e c i s i o n . Tanner (pers. comm., -243-1987) suggests that the measurement e r r o r would be l e s s than 10%. The l a r g e s t e r r o r s e x i s t i n the estimates of Q E and Q H, d e r i v e d from the BREB approach. T h i s i s e s p e c i a l l y so when 6 becomes l a r g e , which i s o f t e n the case a t the t r a n s i t i o n time around 0600 LAT and at 1800 LAT. I t should be noted t h a t the BREB approach was used, f i r s t l y , as a 'back-up' system t o the eddy c o r r e l a t i o n / e n e r g y balance approach, and secondly to y i e l d a 8 value to enable the computation of a r e s i d u a l storage (.4QSS). Thus, i t i s f e l t t h a t any e r r o r s a s s o c i a t e d with the BREB approach should have a minimal i n f l u e n c e upon the r e s u l t s of t h i s r e s e a r c h . The measurement e r r o r s f o r Q E S ( l a t e n t heat f l u x determined as the r a t i o of QHS/^) c a n ke c a l c u l a t e d using the method of Cook and Rabinowicz (1963). These are s e n s i t i v e to the e r r o r s i n 8, and over the day w i l l t y p i c a l l y be 25%. The e r r o r i n Q E R ( l a t e n t heat f l u x determined as a r e s i d u a l from the energy balance) i s t o t a l l y dependent upon (a) the e r r o r s a s s o c i a t e d with d e r i v i n g the storage p a r a m e t e r i s a t i o n scheme; (b) the f a c t t h a t a l l the e r r o r s from the other f l u x e s w i l l be accumulated i n Q E R and (c) the i n f l u e n c e of n e g l e c t i n g Q F. Cleugh and Oke (1986) suggest t h a t t y p i c a l e r r o r s are of the order of 12% of Q*. The agreement between the three approaches t o e s t i m a t i n g Q E confirms t h a t e r r o r s o f t h i s s i z e are to be expected. F i n a l l y , the i n f l u e n c e of n e g l e c t i n g Q F should be c o n s i d e r e d . I t should be r e a l i s e d t h a t the e f f e c t of Q F i s al r e a d y i n c o r p o r a t e d t o a c e r t a i n extent i n the measurements of Q*, Q H S, Q H B and Q E B. Thus, although an -244-a d d i t i o n a l source of energy, Q F, i s not i n c l u d e d i n the a v a i l a b l e energy term, i t i s in c l u d e d i n the measurement of these energy s i n k s . T h i s i m p l i e s t h a t the estimates of storage (Appendix 1), are l i k e l y t o be underestimates of the a c t u a l storage f l u x . However, t h i s w i l l depend on the way i n which the anthropogenic heat f l u x i n f l u e n c e s QE and Q*. The d i u r n a l mean Q F has been c a l c u l a t e d to be 8 W m ~ 2 , by Grimmond (1988) f o r a summer day i n the Sunset area of Vancouver. T h i s i s w i t h i n the measurement e r r o r of the remaining f l u x e s . Hence the neg l e c t of Q F i s u n l i k e l y t o i n c u r s e r i o u s e r r o r . -245-APPENDIX 4: PRELIMINARY DATA PROCESSING A4.1 Determination of the Hourly Surface Energy Balance R e c a l l i n g 2.3.3, there are a number of d i f f e r e n t approaches to determining each of the t u r b u l e n t heat f l u x e s . These are repeated i n equations A4.1 to A4.6 below. For each hour, an optimum energy budget must be obtained from a l l of these measurements. There are two o p t i o n s . The f i r s t of these i s to adopt the approach of Steyn (1980), which uses a s e r i e s of c r i t e r i a to d e r i v e the optimum energy budget f o r any hour. T h i s ' d e c i s i o n t r e e ' i s i l l u s t r a t e d i n F i g u r e A4.1. Q*-(QHS +QER + z 3 <2SP>= 0 (A4.1) Q * - ( Q HB + QEB + A2SP)=° (A4.2) Q * - ( Q H S + Q E S + A 2 s s ) = 0 (A4.3) Q*-(Q H S+QEB + i < 3Qsp)= ri (A4.4) Q*-(Q H B +QES + 4Qsp)= r2 (A4.5) Q-*-(Q.Hs +QEs + 4Qsp)= r3 (A4.6) I f e i t h e r of the d i f f e r e n t i a l psychrometer, or eddy c o r r e l a t i o n systems were not o p e r a t i o n a l , then energy budgets (A4.1) or (A4.2) were used. I f both the systems were o p e r a t i o n a l , then the three estimates f o r Q E ( Q E S , Q E R , Q E B ) ; the two estimates f o r Q H (QHB'QHS)' a n c ^ t n e t w o estimates of AQS were compared. The energy budget f o r t h a t hour i s judged to be i n complete agreement i f these f l u x e s agree to w i t h i n 0.0125Q* ± 15 W m~2 ( f o l l o w i n g Steyn, 1980). They are then averaged to y i e l d an average energy budget. The small remaining r e s i d u a l i s d i s t r i b u t e d evenly between the three f l u x e s Q E , Q H , and AQS. I f these f l u x e s are not i n agreement, a number of 'obvious' e r r o r c r i t e r i a are examined (e.g. i f 0^-1.0; or i f Q E ,Q H >Q* i n the morning). In -246-such cases, the a l t e r n a t e budgets were used. F i n a l l y , the remaining group of budgets i n 'incomplete agreement' are c o r r e c t e d by the d i s t r i b u t i o n of r e s i d u a l s technique proposed by Steyn (1980, 1985). With t h i s approach, i t i s assumed t h a t the r e s i d u a l s ( r l f r 2 , r 3 i n equations (A4.4) to (A4.6)) are the r e s u l t of measurement e r r o r s i n the t u r b u l e n t f l u x e s , i . e . Qh+6Qh, and Qe+6Qe. The r a t i o of the measurement e r r o r s i s assumed e q u i v a l e n t to the r a t i o of the r e s i d u a l i n Q E and i n Q H, thus: RQ H/ RQE = 5Q H/ 5QE = ± r (A4.7) S O : RQH = R 1+r" 1  r 0 E = r l±r (A4.8) As t h e r e a r e 3 open budgets, a d e c i s i o n had to be made as to which r e s i d u a l s t o use. Equation (A4.5) i n c l u d e s the Bowen r a t i o twice ( Q H B and Q-ES) s o w a s excluded. The sm a l l e s t r e s i d u a l r e s u l t i n g from the other two budgets was used. These energy budgets are r e f e r r e d t o as the "optimum" energy budgets. A second approach t o d e r i v i n g h ourly estimates f o r Q E i s t o simply use the f i r s t energy budget (A4.1), having v e r i f i e d the v a l i d i t y of both the Q E S and AQSP terms. As Fig u r e s A4.2 and A4.3 i n d i c a t e , on a d a i l y b a s i s t h e r e i s l i t t l e d i f f e r e n c e between the approaches (as would be expected s i n c e both p o p u l a t i o n s c o n s i s t of some Q H S and Q E S v a l u e s ) . On an hourly b a s i s , t h i s second approach leads t o more c o n s i s t e n t trends d u r i n g the day. -247-F i g u r e A4.1: D e c i s i o n Tree Note: See Text f o r Symbols CONDITION ENERGY BUDGET USED (1) Sonic Anemometer/ F i n e Wire Thermocouple Not Operating Q* = Q H B + Q E B + A 2 S p (2) Reversing D i f f e r e n t i a l Psychrometer Not Operating Q* = Q H S + Q E R + 42Sp (3) Both systems o p e r a t i o n a l : Compute { d i f f e r e n c e } : - (QHS-Q-HB) •* <QEB-QES) - ( Q E B - Q E R ) - ( 4 2 S P - A 2 S S > I f { d ifference} < QNCRIT Q* = [Q HS +QHB]/ 2 + IQES+QEB+QER]/ 3 + [AQSP+AQss]/2 (4) Obvious E r r o r : I f Q H B>Q* and LAT<1400 OR I f -1 Q* = QHS + QER + A 2 S P (5) Incomplete Agreement Use D i s t r i b u t e d R e s i d u a l s . -248-F i g u r e A4.2: Comparison of l a t e n t heat f l u x determined u s i n g the optimum energy budget and eddy c o r r e l a t i o n approaches 250 -0 50 100 150 200 250 SENSIBLE HEAT FLUX:eddy correlation (W m" 2 ) F i g u r e A4 .3 : Comparison of s e n s i b l e heat f l u x determined u s i n g the optimum energy budget and eddy c o r r e l a t i o n - e n e r g y budget approaches - 2 4 9 -PTTBT.TfiATTONS : (a) Ptiblished or Accepted f o r P u b l i c a t i o n Oke, T.R., H.A. Cleugh, S. Grimmond, H.P. Schmid and M.Roth (1989), Evaluation of spatially-averaged fluxes of heat, mass and momentum i n the urban boundary-layer, f/eather (submitted and accepted). Oke, T.R., H.A. Cleugh, and C.S.B. Grimmond (1988), Evapotranspiration i n urban areas. In Intern. Symp. Hydro logical Processes and Water Management In Urban Areas, UNESCO, 24 - 29, A p r i l 1988, 107 - 112. Oke, T.R. and H.A. Cleugh (1987), Urban heat storage derived as energy balance r e s i d u a l s , Boundary-Layer Meteorol.,39, 233 - 245 Cleugh, H.A.- and T.R. Oke (1986), Suburban-rural energy balance comparison i n summer f o r Vancouver, B.C., Boundary-Layer Meteorol.,36, 351 - 371. 

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